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
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⌀ | rule_concentration
int64 0
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|---|---|---|---|---|---|---|---|
If paul is not strong or quiet then paul is both not strong and not quiet and vice versa.
If lucy is creative or happy then alice is both kind and not tall and vice versa.
If someone is both curious and not happy then mary is not kind and vice versa.
If someone is rich or not tall then lucy is either funny or not rich and vice versa.
If alice is not kind or not happy then paul is wise.
Everyone who is not quiet or not funny is strong and vice versa.
If someone is not calm then someone is both not old and not rich and vice versa.
If someone is not humble or not funny then someone is both patient and not generous and vice versa.
Everyone who is generous or quiet is either not calm or not wise and vice versa.
Everyone who is both old and not funny is both not patient and not wise.
Everyone who is not curious or not kind is brave.
Everyone who is either happy or not funny is both not old and not calm.
Everyone who is not old is funny.
Everyone who is either old or not strong is either curious or strong.
If someone is calm or not quiet then someone is rich.
Everyone who is not humble or kind is both not tall and funny and vice versa.
Fred is creative or not humble.
Someone is not funny.
Someone is both patient and humble.
Alice is both patient and not tall.
Lucy is both brave and curious.
Someone is either generous or not generous.
Someone is not humble.
Someone is kind or old. | Lucy is rich. | entailment | (((~strong(paul)|quiet(paul)))<=>((~strong(paul)&~quiet(paul))))&
(((creative(lucy)|happy(lucy)))<=>((kind(alice)&~tall(alice))))&
((?[X]:((curious(X)&~happy(X))))<=>(~kind(mary)))&
((?[X]:((rich(X)|~tall(X))))<=>((funny(lucy)<~>~rich(lucy))))&
(((~kind(alice)|~happy(alice)))=>(wise(paul)))&
(![X]:((~quiet(X)|~funny(X))<=>strong(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)&~rich(X)))))&
((?[X]:((~humble(X)|~funny(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((generous(X)|quiet(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((old(X)&~funny(X))=>(~patient(X)&~wise(X))))&
(![X]:((~curious(X)|~kind(X))=>brave(X)))&
(![X]:((happy(X)<~>~funny(X))=>(~old(X)&~calm(X))))&
(![X]:(~old(X)=>funny(X)))&
(![X]:((old(X)<~>~strong(X))=>(curious(X)<~>strong(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:(rich(X))))&
(![X]:((~humble(X)|kind(X))<=>(~tall(X)&funny(X))))&
((creative(fred)|~humble(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)&humble(X))))&
((patient(alice)&~tall(alice)))&
((brave(lucy)&curious(lucy)))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)|old(X)))) | rich(lucy) | [
"p3",
"p5",
"p12",
"p13",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 254878046989019482693937
% SZS output start Proof for 254878046989019482693937
4. ? [X0] : (~tall(X0) | rich(X0)) <=> (funny(lucy) <~> ~rich(lucy)) [input p3]
6. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> strong(X0)) [input p5]
13. ! [X0] : (~old(X0) => funny(X0)) [input p12]
14. ! [X0] : ((old(X0) <~> ~strong(X0)) => (curious(X0) <~> strong(X0))) [input p13]
20. ~tall(alice) & patient(alice) [input p19]
21. curious(lucy) & brave(lucy) [input p20]
25. ~rich(lucy) [input hypothesis]
29. curious(lucy) [pure predicate removal 21]
35. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 13]
36. ! [X0] : ((curious(X0) <~> strong(X0)) | (old(X0) <=> ~strong(X0))) [ennf transformation 14]
46. (? [X0] : (~tall(X0) | rich(X0)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X0] : (tall(X0) & ~rich(X0))) [nnf transformation 4]
47. (? [X0] : (~tall(X0) | rich(X0)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X1] : (tall(X1) & ~rich(X1))) [rectify 46]
48. ? [X0] : (~tall(X0) | rich(X0)) => (~tall(sK1) | rich(sK1)) [choice axiom]
49. ((~tall(sK1) | rich(sK1)) | ((funny(lucy) | rich(lucy)) & (~rich(lucy) | ~funny(lucy)))) & (((rich(lucy) | ~funny(lucy)) & (~rich(lucy) | funny(lucy))) | ! [X1] : (tall(X1) & ~rich(X1))) [skolemisation 47,48]
50. ! [X0] : (((~funny(X0) | ~quiet(X0)) | ~strong(X0)) & (strong(X0) | (funny(X0) & quiet(X0)))) [nnf transformation 6]
51. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~strong(X0)) & (strong(X0) | (funny(X0) & quiet(X0)))) [flattening 50]
65. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) [nnf transformation 36]
98. rich(lucy) | ~funny(lucy) | tall(X1) [cnf transformation 49]
104. funny(X0) | strong(X0) [cnf transformation 51]
126. old(X0) | funny(X0) [cnf transformation 35]
129. ~strong(X0) | ~curious(X0) | ~strong(X0) | ~old(X0) [cnf transformation 65]
143. ~tall(alice) [cnf transformation 20]
144. curious(lucy) [cnf transformation 29]
149. ~rich(lucy) [cnf transformation 25]
151. ~old(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 129]
159. 2 <=> tall(alice) [avatar definition]
160. ~tall(alice) <- (~2) [avatar component clause 159]
194. 9 <=> rich(lucy) [avatar definition]
198. 10 <=> funny(lucy) [avatar definition]
199. ~funny(lucy) <- (~10) [avatar component clause 198]
212. 13 <=> ! [X1] : tall(X1) [avatar definition]
213. tall(X1) <- (13) [avatar component clause 212]
214. 13 | ~10 | 9 [avatar split clause 98,194,198,212]
303. ~2 [avatar split clause 143,159]
313. ~9 [avatar split clause 149,194]
320. $false <- (~2, 13) [resolution 213,160]
323. 2 | ~13 [avatar contradiction clause 320]
445. ~curious(X1) | ~strong(X1) | funny(X1) [resolution 151,126]
446. ~curious(X1) | funny(X1) [subsumption resolution 445,104]
480. funny(lucy) [resolution 446,144]
483. $false <- (~10) [subsumption resolution 480,199]
484. 10 [avatar contradiction clause 483]
485. $false [avatar sat refutation 214,303,313,323,484]
% SZS output end Proof for 254878046989019482693937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both not humble and not generous and vice versa. Everyone who is not quiet or not strong is not brave and vice versa. Everyone who is either curious or strong is either not quiet or not brave. If mary is both not calm and not quiet then someone is either happy or not happy and vice versa. If alice is not creative or not strong then someone is either not calm or not humble and vice versa. If susan is not kind or not tall then susan is rich or not quiet and vice versa. If lucy is not generous then someone is either not strong or not calm and vice versa. Everyone who is not humble or rich is not patient and vice versa. If alice is both not strong and funny then someone is creative or not happy and vice versa. If someone is either not curious or not strong then paul is not brave or not patient. If susan is both not quiet and not calm then mary is strong. If mary is either not generous or quiet then someone is either wise or not strong and vice versa. If someone is both not calm and not humble then someone is either patient or rich and vice versa. Everyone who is patient or not patient is not curious. If fred is happy or not rich then paul is not humble or not brave and vice versa. Someone is either creative or humble. Someone is both not rich and not curious. Someone is either not brave or not wise. Mary is both happy and not calm. | Paul is not humble. | entailment | (![X]:(~strong(X)<=>(~humble(X)&~generous(X))))&
(![X]:((~quiet(X)|~strong(X))<=>~brave(X)))&
(![X]:((curious(X)<~>strong(X))=>(~quiet(X)<~>~brave(X))))&
(((~calm(mary)&~quiet(mary)))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(((~creative(alice)|~strong(alice)))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(((~kind(susan)|~tall(susan)))<=>((rich(susan)|~quiet(susan))))&
((~generous(lucy))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~humble(X)|rich(X))<=>~patient(X)))&
(((~strong(alice)&funny(alice)))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~curious(X)<~>~strong(X))))=>((~brave(paul)|~patient(paul))))&
(((~quiet(susan)&~calm(susan)))=>(strong(mary)))&
(((~generous(mary)<~>quiet(mary)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((patient(X)|~patient(X))=>~curious(X)))&
(((happy(fred)|~rich(fred)))<=>((~humble(paul)|~brave(paul))))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
((happy(mary)&~calm(mary))) | ~humble(paul) | [
"p0",
"p1",
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1411942882626828185699428
% SZS output start Proof for 1411942882626828185699428
1. ! [X0] : (~strong(X0) <=> (~generous(X0) & ~humble(X0))) [input p0]
2. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> ~brave(X0)) [input p1]
3. ! [X0] : ((curious(X0) <~> strong(X0)) => (~quiet(X0) <~> ~brave(X0))) [input p2]
14. ! [X0] : ((~patient(X0) | patient(X0)) => ~curious(X0)) [input p13]
20. humble(paul) [input hypothesis]
22. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) | (curious(X0) <=> strong(X0))) [ennf transformation 3]
27. ! [X0] : (~curious(X0) | (patient(X0) & ~patient(X0))) [ennf transformation 14]
28. ! [X0] : ((~strong(X0) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | strong(X0))) [nnf transformation 1]
29. ! [X0] : ((~strong(X0) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | strong(X0))) [flattening 28]
30. ! [X0] : (((~strong(X0) | ~quiet(X0)) | brave(X0)) & (~brave(X0) | (strong(X0) & quiet(X0)))) [nnf transformation 2]
31. ! [X0] : ((~strong(X0) | ~quiet(X0) | brave(X0)) & (~brave(X0) | (strong(X0) & quiet(X0)))) [flattening 30]
32. ! [X0] : (((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) [nnf transformation 22]
76. ~humble(X0) | strong(X0) [cnf transformation 29]
79. ~brave(X0) | quiet(X0) [cnf transformation 31]
81. ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 31]
83. ~brave(X0) | ~quiet(X0) | curious(X0) | ~strong(X0) [cnf transformation 32]
85. brave(X0) | quiet(X0) | curious(X0) | ~strong(X0) [cnf transformation 32]
131. ~curious(X0) | ~patient(X0) [cnf transformation 27]
132. ~curious(X0) | patient(X0) [cnf transformation 27]
145. humble(paul) [cnf transformation 20]
150. ~strong(X0) | curious(X0) | brave(X0) [subsumption resolution 85,81]
152. ~quiet(X0) | curious(X0) | ~strong(X0) [subsumption resolution 83,150]
265. 25 <=> brave(paul) [avatar definition]
266. brave(paul) <- (25) [avatar component clause 265]
346. ~curious(X0) [subsumption resolution 131,132]
357. 44 <=> humble(paul) [avatar definition]
359. humble(paul) <- (44) [avatar component clause 357]
384. 44 [avatar split clause 145,357]
385. strong(paul) <- (44) [resolution 76,359]
472. curious(paul) | brave(paul) <- (44) [resolution 150,385]
474. brave(paul) <- (44) [subsumption resolution 472,346]
477. 25 | ~44 [avatar split clause 474,357,265]
483. quiet(paul) <- (25) [resolution 266,79]
544. curious(paul) | ~strong(paul) <- (25) [resolution 152,483]
545. ~strong(paul) <- (25) [subsumption resolution 544,346]
546. $false <- (25, 44) [subsumption resolution 545,385]
547. ~25 | ~44 [avatar contradiction clause 546]
548. $false [avatar sat refutation 384,477,547]
% SZS output end Proof for 1411942882626828185699428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both happy and not calm then john is kind.
If someone is both not kind and not rich then someone is creative or happy and vice versa.
Everyone who is both humble and not humble is either not generous or calm.
If paul is both not wise and kind then someone is creative or tall and vice versa.
If someone is both not humble and not old then lucy is either not funny or not quiet.
If someone is not generous or calm then susan is both curious and not old.
Everyone who is either generous or calm is either not humble or calm.
If someone is generous or tall then someone is both not funny and not tall and vice versa.
If someone is either not brave or not strong then someone is not curious or generous.
If someone is not strong then fred is either curious or not quiet.
Everyone who is generous is generous or not kind.
If paul is both creative and not wise then alice is not rich or calm.
If john is not humble or not quiet then someone is not quiet or creative.
If alice is either not curious or not funny then mary is wise or quiet and vice versa.
Everyone who is not kind or tall is rich.
Everyone who is both curious and kind is not curious and vice versa.
John is either curious or creative.
Someone is not happy.
Lucy is either not strong or brave.
Someone is happy or not calm.
Fred is not calm or not brave.
Someone is both calm and not happy. | Fred is happy. | contradiction | (((happy(lucy)&~calm(lucy)))=>(kind(john)))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((humble(X)&~humble(X))=>(~generous(X)<~>calm(X))))&
(((~wise(paul)&kind(paul)))<=>(?[X]:((creative(X)|tall(X)))))&
((?[X]:((~humble(X)&~old(X))))=>((~funny(lucy)<~>~quiet(lucy))))&
((?[X]:((~generous(X)|calm(X))))=>((curious(susan)&~old(susan))))&
(![X]:((generous(X)<~>calm(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((generous(X)|tall(X))))<=>(?[X]:((~funny(X)&~tall(X)))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:(~strong(X)))=>((curious(fred)<~>~quiet(fred))))&
(![X]:(generous(X)=>(generous(X)|~kind(X))))&
(((creative(paul)&~wise(paul)))=>((~rich(alice)|calm(alice))))&
(((~humble(john)|~quiet(john)))=>(?[X]:((~quiet(X)|creative(X)))))&
(((~curious(alice)<~>~funny(alice)))<=>((wise(mary)|quiet(mary))))&
(![X]:((~kind(X)|tall(X))=>rich(X)))&
(![X]:((curious(X)&kind(X))<=>~curious(X)))&
((curious(john)<~>creative(john)))&
(?[X]:(~happy(X)))&
((~strong(lucy)<~>brave(lucy)))&
(?[X]:((happy(X)|~calm(X))))&
((~calm(fred)|~brave(fred)))&
(?[X]:((calm(X)&~happy(X)))) | happy(fred) | [
"p1",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2418698298896335158976486
% SZS output start Proof for 2418698298896335158976486
2. ? [X0] : (~rich(X0) & ~kind(X0)) <=> ? [X0] : (happy(X0) | creative(X0)) [input p1]
15. ! [X0] : ((tall(X0) | ~kind(X0)) => rich(X0)) [input p14]
16. ! [X0] : ((kind(X0) & curious(X0)) <=> ~curious(X0)) [input p15]
23. happy(fred) [input hypothesis]
24. ? [X0] : (~rich(X0) & ~kind(X0)) <=> ? [X1] : (happy(X1) | creative(X1)) [rectify 2]
41. ! [X0] : (rich(X0) | (~tall(X0) & kind(X0))) [ennf transformation 15]
42. (? [X0] : (~rich(X0) & ~kind(X0)) | ! [X1] : (~happy(X1) & ~creative(X1))) & (? [X1] : (happy(X1) | creative(X1)) | ! [X0] : (rich(X0) | kind(X0))) [nnf transformation 24]
43. (? [X0] : (~rich(X0) & ~kind(X0)) | ! [X1] : (~happy(X1) & ~creative(X1))) & (? [X2] : (happy(X2) | creative(X2)) | ! [X3] : (rich(X3) | kind(X3))) [rectify 42]
44. ? [X0] : (~rich(X0) & ~kind(X0)) => (~rich(sK0) & ~kind(sK0)) [choice axiom]
45. ? [X2] : (happy(X2) | creative(X2)) => (happy(sK1) | creative(sK1)) [choice axiom]
46. ((~rich(sK0) & ~kind(sK0)) | ! [X1] : (~happy(X1) & ~creative(X1))) & ((happy(sK1) | creative(sK1)) | ! [X3] : (rich(X3) | kind(X3))) [skolemisation 43,45,44]
69. ! [X0] : (((kind(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) | ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : (((kind(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | ~kind(X0) | ~curious(X0))) [flattening 69]
84. ~rich(sK0) | ~happy(X1) [cnf transformation 46]
121. rich(X0) | kind(X0) [cnf transformation 41]
123. ~curious(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 70]
124. curious(X0) | curious(X0) [cnf transformation 70]
135. happy(fred) [cnf transformation 23]
136. ~curious(X0) | ~kind(X0) [duplicate literal removal 123]
137. curious(X0) [duplicate literal removal 124]
154. 4 <=> ! [X1] : ~happy(X1) [avatar definition]
155. ~happy(X1) <- (4) [avatar component clause 154]
157. 5 <=> rich(sK0) [avatar definition]
159. ~rich(sK0) <- (~5) [avatar component clause 157]
160. 4 | ~5 [avatar split clause 84,157,154]
172. 8 <=> ! [X3] : (rich(X3) | kind(X3)) [avatar definition]
173. rich(X3) | kind(X3) <- (8) [avatar component clause 172]
347. 8 [avatar split clause 121,172]
348. ~kind(X0) [subsumption resolution 136,137]
384. rich(X3) <- (8) [subsumption resolution 173,348]
385. $false <- (~5, 8) [subsumption resolution 159,384]
386. 5 | ~8 [avatar contradiction clause 385]
387. $false <- (4) [resolution 155,135]
388. ~4 [avatar contradiction clause 387]
389. $false [avatar sat refutation 160,347,386,388]
% SZS output end Proof for 2418698298896335158976486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not brave is not strong and vice versa.
Everyone who is both generous and not kind is either tall or not creative and vice versa.
Everyone who is not brave or kind is not funny and vice versa.
Everyone who is rich is wise or not tall.
Everyone who is either not curious or not calm is curious and vice versa.
Everyone who is both tall and not generous is either wise or not happy.
Everyone who is not rich is both not calm and calm and vice versa.
If someone is humble or brave then someone is not rich.
Everyone who is either not curious or humble is both not patient and tall.
Everyone who is old is not kind.
If someone is not creative or humble then john is both quiet and not strong and vice versa.
If john is both creative and not happy then paul is not strong.
If mary is brave or not strong then someone is either strong or not patient and vice versa.
Everyone who is either quiet or calm is both not wise and funny and vice versa.
If someone is both humble and curious then someone is either humble or not creative and vice versa.
Fred is either not generous or old.
Alice is either patient or rich.
Lucy is both tall and not curious.
Someone is either not calm or generous.
Susan is either not wise or rich.
Someone is not tall. | John is patient. | neutral | (![X]:((~old(X)&~brave(X))<=>~strong(X)))&
(![X]:((generous(X)&~kind(X))<=>(tall(X)<~>~creative(X))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~tall(X))) | patient(john) | [] | null | 0 |
If someone is both generous and not quiet then someone is not patient.
If someone is kind or patient then someone is not generous or not curious.
Everyone who is not curious is strong or not patient and vice versa.
If john is both brave and not rich then alice is both happy and curious.
Everyone who is not rich is both creative and kind and vice versa.
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.
Everyone who is not funny or strong is either not tall or brave.
Everyone who is not quiet or not tall is not happy or rich and vice versa.
If mary is not brave then paul is not humble.
Lucy is either not brave or calm.
Susan is either patient or not generous.
Susan is both not tall and rich.
Someone is kind or humble. | Paul is not curious. | contradiction | ((?[X]:((generous(X)&~quiet(X))))=>(?[X]:(~patient(X))))&
((?[X]:((kind(X)|patient(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:(~curious(X)<=>(strong(X)|~patient(X))))&
(((brave(john)&~rich(john)))=>((happy(alice)&curious(alice))))&
(![X]:(~rich(X)<=>(creative(X)&kind(X))))&
(![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]:((~funny(X)|strong(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(~happy(X)|rich(X))))&
((~brave(mary))=>(~humble(paul)))&
((~brave(lucy)<~>calm(lucy)))&
((patient(susan)<~>~generous(susan)))&
((~tall(susan)&rich(susan)))&
(?[X]:((kind(X)|humble(X)))) | ~curious(paul) | [
"p5",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 537381466168891821315059
% SZS output start Proof for 537381466168891821315059
6. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p5]
9. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((strong(X0) | curious(X0)) <=> (~kind(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((strong(X0) | ~funny(X0)) => (~tall(X0) <~> brave(X0))) [input p13]
21. ~curious(paul) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 14]
42. ! [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 6]
43. ! [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 42]
45. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 9]
46. ! [X0] : (((strong(X0) | curious(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 10]
47. ! [X0] : ((strong(X0) | curious(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | (~strong(X0) & ~curious(X0)))) [flattening 46]
55. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 55]
57. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~strong(X0) & funny(X0))) [nnf transformation 30]
75. brave(X0) | creative(X0) | creative(X0) [cnf transformation 43]
76. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 43]
89. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
90. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 45]
94. strong(X0) | curious(X0) | kind(X0) [cnf transformation 47]
104. ~tall(X0) | kind(X0) [cnf transformation 56]
109. ~brave(X0) | tall(X0) | ~strong(X0) [cnf transformation 57]
122. ~curious(paul) [cnf transformation 21]
123. ~kind(X0) | ~calm(X0) [duplicate literal removal 89]
124. ~kind(X0) | calm(X0) [duplicate literal removal 90]
125. brave(X0) | creative(X0) [duplicate literal removal 75]
126. ~creative(X0) | brave(X0) [duplicate literal removal 76]
150. 6 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (6) [avatar component clause 150]
172. brave(X0) [subsumption resolution 125,126]
175. ~kind(X0) [subsumption resolution 123,124]
176. 6 [avatar split clause 175,150]
204. ~strong(X0) | tall(X0) [subsumption resolution 109,172]
245. curious(X0) | kind(X0) | tall(X0) [resolution 94,204]
251. tall(X0) | curious(X0) <- (6) [subsumption resolution 245,151]
283. curious(X2) | kind(X2) <- (6) [resolution 251,104]
284. curious(X2) <- (6) [subsumption resolution 283,151]
301. $false <- (6) [resolution 284,122]
305. ~6 [avatar contradiction clause 301]
306. $false [avatar sat refutation 176,305]
% SZS output end Proof for 537381466168891821315059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or old is generous and vice versa. Everyone who is not tall or wise is wise. Everyone who is both not funny and brave is creative. Everyone who is old or quiet is either not quiet or not funny and vice versa. Everyone who is either happy or not quiet is strong. Everyone who is either calm or not strong is either wise or not brave and vice versa. Everyone who is not rich or not strong is both not humble and tall and vice versa. Everyone who is rich is not calm and vice versa. Everyone who is either curious or strong is rich or humble. Everyone who is brave is not humble or not tall. If someone is either funny or tall then alice is either happy or funny. Everyone who is not rich or kind is both not patient and not quiet. If mary is not funny or not kind then someone is not brave and vice versa. Everyone who is both not calm and old is not funny or generous. Everyone who is both not brave and not old is both not curious and not creative and vice versa. Everyone who is both not tall and calm is either not curious or not brave. Someone is humble. Lucy is patient. Someone is brave or tall. Someone is both generous and not patient. Someone is either rich or not quiet. Paul is either happy or funny. Someone is either not humble or strong. Someone is either rich or not funny. | Mary is humble. | neutral | (![X]:((brave(X)|old(X))<=>generous(X)))&
(![X]:((~tall(X)|wise(X))=>wise(X)))&
(![X]:((~funny(X)&brave(X))=>creative(X)))&
(![X]:((old(X)|quiet(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~quiet(X))=>strong(X)))&
(![X]:((calm(X)<~>~strong(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~rich(X)|~strong(X))<=>(~humble(X)&tall(X))))&
(![X]:(rich(X)<=>~calm(X)))&
(![X]:((curious(X)<~>strong(X))=>(rich(X)|humble(X))))&
(![X]:(brave(X)=>(~humble(X)|~tall(X))))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>funny(alice))))&
(![X]:((~rich(X)|kind(X))=>(~patient(X)&~quiet(X))))&
(((~funny(mary)|~kind(mary)))<=>(?[X]:(~brave(X))))&
(![X]:((~calm(X)&old(X))=>(~funny(X)|generous(X))))&
(![X]:((~brave(X)&~old(X))<=>(~curious(X)&~creative(X))))&
(![X]:((~tall(X)&calm(X))=>(~curious(X)<~>~brave(X))))&
(?[X]:(humble(X)))&
(patient(lucy))&
(?[X]:((brave(X)|tall(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
((happy(paul)<~>funny(paul)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:((rich(X)<~>~funny(X)))) | humble(mary) | [] | null | 0 |
Everyone who is either generous or wise is either not humble or not brave.
Everyone who is either not funny or strong is either not patient or rich and vice versa.
Everyone who is either funny or humble is brave or happy and vice versa.
Everyone who is brave is not funny and vice versa.
If someone is both not rich and not creative then someone is both curious and old and vice versa.
Everyone who is either not rich or funny is calm or not curious.
If someone is both not curious and not generous then someone is not generous or old.
If someone is either wise or not old then mary is either not humble or patient and vice versa.
Everyone who is curious is either quiet or not calm and vice versa.
If someone is either not curious or tall then someone is curious.
Everyone who is both happy and calm is humble or tall and vice versa.
Everyone who is rich is both quiet and wise and vice versa.
Everyone who is humble is not generous or not creative and vice versa.
If fred is both humble and not brave then someone is not curious or not patient and vice versa.
Everyone who is not funny is both not generous and not strong and vice versa.
If someone is both brave and creative then someone is patient or not patient.
Someone is not funny or quiet.
Someone is both not kind and wise.
Fred is not strong.
Paul is not quiet.
Someone is not quiet.
Someone is calm.
Someone is not happy or not humble. | Paul is tall. | contradiction | (![X]:((generous(X)<~>wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((funny(X)<~>humble(X))<=>(brave(X)|happy(X))))&
(![X]:(brave(X)<=>~funny(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(calm(X)|~curious(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~generous(X)|old(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>((~humble(mary)<~>patient(mary))))&
(![X]:(curious(X)<=>(quiet(X)<~>~calm(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:(curious(X))))&
(![X]:((happy(X)&calm(X))<=>(humble(X)|tall(X))))&
(![X]:(rich(X)<=>(quiet(X)&wise(X))))&
(![X]:(humble(X)<=>(~generous(X)|~creative(X))))&
(((humble(fred)&~brave(fred)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:(~funny(X)<=>(~generous(X)&~strong(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((patient(X)|~patient(X)))))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((~kind(X)&wise(X))))&
(~strong(fred))&
(~quiet(paul))&
(?[X]:(~quiet(X)))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)|~humble(X)))) | tall(paul) | [
"p2",
"p3",
"p8",
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 88174468865450318156849
% SZS output start Proof for 88174468865450318156849
3. ! [X0] : ((funny(X0) <~> humble(X0)) <=> (happy(X0) | brave(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> ~funny(X0)) [input p3]
9. ! [X0] : (curious(X0) <=> (quiet(X0) <~> ~calm(X0))) [input p8]
11. ! [X0] : ((calm(X0) & happy(X0)) <=> (tall(X0) | humble(X0))) [input p10]
14. (~brave(fred) & humble(fred)) <=> ? [X0] : (~patient(X0) | ~curious(X0)) [input p13]
20. ~quiet(paul) [input p19]
24. tall(paul) [input hypothesis]
38. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~humble(X0) | ~funny(X0)) & (humble(X0) | funny(X0))) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ((funny(X0) | ~humble(X0)) & (humble(X0) | ~funny(X0))))) [flattening 38]
40. ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))) [nnf transformation 4]
54. ! [X0] : ((curious(X0) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~curious(X0))) [nnf transformation 9]
59. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & ((tall(X0) | humble(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 11]
60. ! [X0] : (((calm(X0) & happy(X0)) | (~tall(X0) & ~humble(X0))) & (tall(X0) | humble(X0) | ~calm(X0) | ~happy(X0))) [flattening 59]
65. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | (brave(fred) | ~humble(fred))) [nnf transformation 14]
66. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X0] : (~patient(X0) | ~curious(X0)) | brave(fred) | ~humble(fred)) [flattening 65]
67. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & (? [X1] : (~patient(X1) | ~curious(X1)) | brave(fred) | ~humble(fred)) [rectify 66]
68. ? [X1] : (~patient(X1) | ~curious(X1)) => (~patient(sK5) | ~curious(sK5)) [choice axiom]
69. ((~brave(fred) & humble(fred)) | ! [X0] : (patient(X0) & curious(X0))) & ((~patient(sK5) | ~curious(sK5)) | brave(fred) | ~humble(fred)) [skolemisation 67,68]
102. ~happy(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 39]
104. funny(X0) | brave(X0) [cnf transformation 40]
120. ~calm(X0) | quiet(X0) | ~curious(X0) [cnf transformation 54]
127. ~humble(X0) | happy(X0) [cnf transformation 60]
130. ~tall(X0) | calm(X0) [cnf transformation 60]
138. humble(fred) | curious(X0) [cnf transformation 69]
140. ~brave(fred) | curious(X0) [cnf transformation 69]
149. ~quiet(paul) [cnf transformation 20]
153. tall(paul) [cnf transformation 24]
238. 20 <=> brave(fred) [avatar definition]
240. ~brave(fred) <- (~20) [avatar component clause 238]
243. 21 <=> ! [X0] : curious(X0) [avatar definition]
244. curious(X0) <- (21) [avatar component clause 243]
245. 21 | ~20 [avatar split clause 140,238,243]
247. 22 <=> humble(fred) [avatar definition]
249. humble(fred) <- (22) [avatar component clause 247]
251. 21 | 22 [avatar split clause 138,247,243]
278. happy(fred) <- (22) [resolution 127,249]
282. calm(paul) [resolution 130,153]
316. ~funny(fred) | ~humble(fred) <- (22) [resolution 102,278]
319. ~funny(fred) <- (22) [subsumption resolution 316,249]
325. quiet(paul) | ~curious(paul) [resolution 120,282]
329. ~curious(paul) [subsumption resolution 325,149]
330. $false <- (21) [subsumption resolution 329,244]
331. ~21 [avatar contradiction clause 330]
361. brave(fred) <- (22) [resolution 319,104]
362. $false <- (~20, 22) [subsumption resolution 361,240]
363. 20 | ~22 [avatar contradiction clause 362]
364. $false [avatar sat refutation 245,251,331,363]
% SZS output end Proof for 88174468865450318156849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both calm and kind and vice versa. If someone is strong or not wise then someone is rich or creative and vice versa. Everyone who is both not brave and not curious is either creative or not happy and vice versa. If someone is either generous or not tall then someone is not curious or curious and vice versa. If lucy is humble or funny then someone is both quiet and wise. If john is not old then someone is both not tall and not wise and vice versa. If someone is quiet or not curious then paul is not patient or not tall and vice versa. Everyone who is tall or generous is either funny or not funny and vice versa. If susan is generous or strong then lucy is either patient or old and vice versa. If someone is either happy or not happy then fred is old and vice versa. If someone is old or humble then someone is not wise or quiet. Everyone who is quiet or not happy is not rich or not wise. Everyone who is both rich and funny is either generous or not rich and vice versa. Everyone who is calm or not tall is not humble. Everyone who is not creative or funny is not kind. Everyone who is strong or not creative is either not generous or wise. Paul is happy or not strong. Mary is either funny or not old. Someone is both not quiet and kind. Someone is either rich or curious. Lucy is brave or calm. Someone is generous. Paul is both creative and patient. Someone is funny. | Paul is calm. | neutral | (![X]:(~rich(X)<=>(calm(X)&kind(X))))&
((?[X]:((strong(X)|~wise(X))))<=>(?[X]:((rich(X)|creative(X)))))&
(![X]:((~brave(X)&~curious(X))<=>(creative(X)<~>~happy(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
(((humble(lucy)|funny(lucy)))=>(?[X]:((quiet(X)&wise(X)))))&
((~old(john))<=>(?[X]:((~tall(X)&~wise(X)))))&
((?[X]:((quiet(X)|~curious(X))))<=>((~patient(paul)|~tall(paul))))&
(![X]:((tall(X)|generous(X))<=>(funny(X)<~>~funny(X))))&
(((generous(susan)|strong(susan)))<=>((patient(lucy)<~>old(lucy))))&
((?[X]:((happy(X)<~>~happy(X))))<=>(old(fred)))&
((?[X]:((old(X)|humble(X))))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:((quiet(X)|~happy(X))=>(~rich(X)|~wise(X))))&
(![X]:((rich(X)&funny(X))<=>(generous(X)<~>~rich(X))))&
(![X]:((calm(X)|~tall(X))=>~humble(X)))&
(![X]:((~creative(X)|funny(X))=>~kind(X)))&
(![X]:((strong(X)|~creative(X))=>(~generous(X)<~>wise(X))))&
((happy(paul)|~strong(paul)))&
((funny(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&kind(X))))&
(?[X]:((rich(X)<~>curious(X))))&
((brave(lucy)|calm(lucy)))&
(?[X]:(generous(X)))&
((creative(paul)&patient(paul)))&
(?[X]:(funny(X))) | calm(paul) | [] | null | 0 |
Everyone who is creative or calm is not wise or not old. If someone is curious or brave then someone is not patient. Everyone who is not old is both not curious and not rich. Everyone who is not tall or tall is either not tall or generous. Everyone who is both strong and not wise is both not creative and brave and vice versa. If someone is humble then fred is happy or not kind. If john is curious then someone is patient or not calm and vice versa. If mary is curious then someone is both funny and generous. Everyone who is old is either wise or not patient and vice versa. If fred is strong or not calm then paul is not humble and vice versa. If john is either not kind or not generous then alice is either not quiet or creative. If someone is funny then someone is not quiet and vice versa. Everyone who is either quiet or not creative is not rich and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is not humble or humble is both not patient and not rich. If someone is either not humble or funny then fred is old and vice versa. Paul is calm. Someone is both generous and creative. Someone is both not old and humble. Someone is curious or not generous. Someone is both brave and not old. Fred is either not generous or rich. Someone is wise. Paul is not tall. | Mary is not patient. | entailment | (![X]:((creative(X)|calm(X))=>(~wise(X)|~old(X))))&
((?[X]:((curious(X)|brave(X))))=>(?[X]:(~patient(X))))&
(![X]:(~old(X)=>(~curious(X)&~rich(X))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:((strong(X)&~wise(X))<=>(~creative(X)&brave(X))))&
((?[X]:(humble(X)))=>((happy(fred)|~kind(fred))))&
((curious(john))<=>(?[X]:((patient(X)|~calm(X)))))&
((curious(mary))=>(?[X]:((funny(X)&generous(X)))))&
(![X]:(old(X)<=>(wise(X)<~>~patient(X))))&
(((strong(fred)|~calm(fred)))<=>(~humble(paul)))&
(((~kind(john)<~>~generous(john)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:(funny(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~humble(X)|humble(X))=>(~patient(X)&~rich(X))))&
((?[X]:((~humble(X)<~>funny(X))))<=>(old(fred)))&
(calm(paul))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((~old(X)&humble(X))))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((brave(X)&~old(X))))&
((~generous(fred)<~>rich(fred)))&
(?[X]:(wise(X)))&
(~tall(paul)) | ~patient(mary) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4661774297419332445619333
% SZS output start Proof for 4661774297419332445619333
15. ! [X0] : ((humble(X0) | ~humble(X0)) => (~rich(X0) & ~patient(X0))) [input p14]
25. patient(mary) [input hypothesis]
36. ! [X0] : ((~rich(X0) & ~patient(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 15]
113. ~patient(X0) | humble(X0) [cnf transformation 36]
114. ~patient(X0) | ~humble(X0) [cnf transformation 36]
133. patient(mary) [cnf transformation 25]
157. 6 <=> ! [X0] : ~patient(X0) [avatar definition]
158. ~patient(X0) <- (6) [avatar component clause 157]
235. ~patient(X0) [subsumption resolution 113,114]
236. 6 [avatar split clause 235,157]
269. $false <- (6) [resolution 158,133]
270. ~6 [avatar contradiction clause 269]
271. $false [avatar sat refutation 236,270]
% SZS output end Proof for 4661774297419332445619333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or creative is either not rich or not creative.
Everyone who is either creative or brave is both funny and not strong and vice versa.
Everyone who is brave or not strong is both not rich and not tall.
Everyone who is brave is both not curious and happy.
If someone is either not tall or calm then someone is both not tall and creative and vice versa.
If someone is either not generous or humble then someone is not rich or not generous.
If john is not funny then susan is either not creative or rich.
Everyone who is both not kind and happy is not kind.
If someone is calm then john is not quiet.
Everyone who is both creative and not rich is both old and curious and vice versa.
If someone is not brave or creative then fred is kind and vice versa.
If alice is not curious then paul is both not calm and not old.
If someone is either creative or not patient then someone is both happy and creative.
Everyone who is funny or kind is strong.
If paul is quiet then someone is either tall or not kind.
If someone is quiet or not creative then someone is either patient or not generous.
Alice is humble.
Mary is both not funny and not rich.
Fred is either old or not humble.
John is either not curious or not wise.
Someone is either generous or not generous.
Fred is not generous. | John is patient. | entailment | (![X]:((funny(X)|creative(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((creative(X)<~>brave(X))<=>(funny(X)&~strong(X))))&
(![X]:((brave(X)|~strong(X))=>(~rich(X)&~tall(X))))&
(![X]:(brave(X)=>(~curious(X)&happy(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(?[X]:((~tall(X)&creative(X)))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
((~funny(john))=>((~creative(susan)<~>rich(susan))))&
(![X]:((~kind(X)&happy(X))=>~kind(X)))&
((?[X]:(calm(X)))=>(~quiet(john)))&
(![X]:((creative(X)&~rich(X))<=>(old(X)&curious(X))))&
((?[X]:((~brave(X)|creative(X))))<=>(kind(fred)))&
((~curious(alice))=>((~calm(paul)&~old(paul))))&
((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((happy(X)&creative(X)))))&
(![X]:((funny(X)|kind(X))=>strong(X)))&
((quiet(paul))=>(?[X]:((tall(X)<~>~kind(X)))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((patient(X)<~>~generous(X)))))&
(humble(alice))&
((~funny(mary)&~rich(mary)))&
((old(fred)<~>~humble(fred)))&
((~curious(john)<~>~wise(john)))&
(?[X]:((generous(X)<~>~generous(X))))&
(~generous(fred)) | patient(john) | [
"p0",
"p1",
"p3",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5375541036202241281298182
% SZS output start Proof for 5375541036202241281298182
1. ! [X0] : ((creative(X0) | funny(X0)) => (~rich(X0) <~> ~creative(X0))) [input p0]
2. ! [X0] : ((creative(X0) <~> brave(X0)) <=> (~strong(X0) & funny(X0))) [input p1]
4. ! [X0] : (brave(X0) => (happy(X0) & ~curious(X0))) [input p3]
10. ! [X0] : ((~rich(X0) & creative(X0)) <=> (curious(X0) & old(X0))) [input p9]
13. ? [X0] : (creative(X0) <~> ~patient(X0)) => ? [X0] : (creative(X0) & happy(X0)) [input p12]
14. ! [X0] : ((kind(X0) | funny(X0)) => strong(X0)) [input p13]
23. ~patient(john) [input hypothesis]
26. ? [X0] : (creative(X0) <~> ~patient(X0)) => ? [X1] : (creative(X1) & happy(X1)) [rectify 13]
31. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 1]
33. ! [X0] : ((happy(X0) & ~curious(X0)) | ~brave(X0)) [ennf transformation 4]
39. ? [X1] : (creative(X1) & happy(X1)) | ! [X0] : (creative(X0) <=> ~patient(X0)) [ennf transformation 26]
40. ! [X0] : (strong(X0) | (~kind(X0) & ~funny(X0))) [ennf transformation 14]
42. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (~creative(X0) & ~funny(X0))) [nnf transformation 31]
43. ! [X0] : ((((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))))) [nnf transformation 2]
44. ! [X0] : ((((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))))) [flattening 43]
55. ! [X0] : (((~rich(X0) & creative(X0)) | (~curious(X0) | ~old(X0))) & ((curious(X0) & old(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 10]
56. ! [X0] : (((~rich(X0) & creative(X0)) | ~curious(X0) | ~old(X0)) & ((curious(X0) & old(X0)) | rich(X0) | ~creative(X0))) [flattening 55]
61. ? [X1] : (creative(X1) & happy(X1)) | ! [X0] : ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0))) [nnf transformation 39]
62. ? [X0] : (creative(X0) & happy(X0)) | ! [X1] : ((creative(X1) | patient(X1)) & (~patient(X1) | ~creative(X1))) [rectify 61]
63. ? [X0] : (creative(X0) & happy(X0)) => (creative(sK4) & happy(sK4)) [choice axiom]
64. (creative(sK4) & happy(sK4)) | ! [X1] : ((creative(X1) | patient(X1)) & (~patient(X1) | ~creative(X1))) [skolemisation 62,63]
75. ~creative(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 42]
78. ~creative(X0) | brave(X0) | funny(X0) [cnf transformation 44]
80. ~strong(X0) | brave(X0) | ~creative(X0) [cnf transformation 44]
88. ~curious(X0) | ~brave(X0) [cnf transformation 33]
102. curious(X0) | rich(X0) | ~creative(X0) [cnf transformation 56]
113. creative(sK4) | creative(X1) | patient(X1) [cnf transformation 64]
114. ~funny(X0) | strong(X0) [cnf transformation 40]
128. ~patient(john) [cnf transformation 23]
129. ~rich(X0) | ~creative(X0) [duplicate literal removal 75]
179. 12 <=> funny(john) [avatar definition]
181. funny(john) <- (12) [avatar component clause 179]
193. ~creative(X0) | curious(X0) [subsumption resolution 102,129]
231. 23 <=> ! [X1] : (creative(X1) | patient(X1)) [avatar definition]
232. patient(X1) | creative(X1) <- (23) [avatar component clause 231]
234. 24 <=> creative(sK4) [avatar definition]
236. creative(sK4) <- (24) [avatar component clause 234]
237. 23 | 24 [avatar split clause 113,234,231]
272. 32 <=> curious(john) [avatar definition]
274. curious(john) <- (32) [avatar component clause 272]
281. ~brave(john) <- (32) [resolution 88,274]
286. creative(john) <- (23) [resolution 232,128]
294. brave(john) | funny(john) <- (23) [resolution 78,286]
297. funny(john) <- (23, 32) [subsumption resolution 294,281]
298. 12 | ~23 | ~32 [avatar split clause 297,272,231,179]
308. brave(sK4) | funny(sK4) <- (24) [resolution 236,78]
312. 36 <=> funny(sK4) [avatar definition]
314. funny(sK4) <- (36) [avatar component clause 312]
316. 37 <=> brave(sK4) [avatar definition]
317. ~brave(sK4) <- (~37) [avatar component clause 316]
319. 36 | 37 | ~24 [avatar split clause 308,234,316,312]
325. 38 <=> creative(john) [avatar definition]
327. creative(john) <- (38) [avatar component clause 325]
334. creative(john) <- (23) [resolution 232,128]
336. 38 | ~23 [avatar split clause 334,231,325]
339. curious(sK4) <- (24) [resolution 236,193]
353. strong(sK4) <- (36) [resolution 314,114]
363. ~brave(sK4) <- (24) [resolution 339,88]
364. ~37 | ~24 [avatar split clause 363,234,316]
384. brave(sK4) | ~creative(sK4) <- (36) [resolution 353,80]
385. ~creative(sK4) <- (36, ~37) [subsumption resolution 384,317]
386. $false <- (24, 36, ~37) [subsumption resolution 385,236]
387. ~24 | ~36 | 37 [avatar contradiction clause 386]
391. curious(john) <- (38) [resolution 327,193]
396. 42 <=> brave(john) [avatar definition]
397. ~brave(john) <- (~42) [avatar component clause 396]
400. 32 | ~38 [avatar split clause 391,325,272]
403. strong(john) <- (12) [resolution 181,114]
404. ~brave(john) <- (32) [resolution 274,88]
405. ~42 | ~32 [avatar split clause 404,272,396]
407. brave(john) | ~creative(john) <- (12) [resolution 403,80]
408. ~creative(john) <- (12, ~42) [subsumption resolution 407,397]
409. $false <- (12, 38, ~42) [subsumption resolution 408,327]
410. ~12 | ~38 | 42 [avatar contradiction clause 409]
411. $false [avatar sat refutation 237,298,319,336,364,387,400,405,410]
% SZS output end Proof for 5375541036202241281298182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not humble and creative then mary is either not tall or not old and vice versa. Everyone who is either creative or strong is rich. Everyone who is generous or strong is both not calm and happy. Everyone who is not happy or not brave is strong and vice versa. Everyone who is not generous or funny is both not kind and calm and vice versa. If alice is humble or old then someone is not old or not wise. Everyone who is not strong or humble is either calm or not creative. If fred is brave then someone is brave. If susan is brave then paul is either not calm or happy. Everyone who is both calm and creative is wise or generous and vice versa. If someone is funny or brave then someone is not kind. If someone is both old and not generous then someone is either quiet or not strong. Everyone who is not quiet or kind is both brave and not old. If susan is tall then paul is either brave or patient and vice versa. If alice is both not rich and tall then lucy is either wise or curious. Everyone who is either happy or patient is tall or strong. Lucy is both curious and not patient. Lucy is humble or happy. Susan is tall. Alice is not funny or generous. | Paul is not strong. | entailment | ((?[X]:((~humble(X)&creative(X))))<=>((~tall(mary)<~>~old(mary))))&
(![X]:((creative(X)<~>strong(X))=>rich(X)))&
(![X]:((generous(X)|strong(X))=>(~calm(X)&happy(X))))&
(![X]:((~happy(X)|~brave(X))<=>strong(X)))&
(![X]:((~generous(X)|funny(X))<=>(~kind(X)&calm(X))))&
(((humble(alice)|old(alice)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((~strong(X)|humble(X))=>(calm(X)<~>~creative(X))))&
((brave(fred))=>(?[X]:(brave(X))))&
((brave(susan))=>((~calm(paul)<~>happy(paul))))&
(![X]:((calm(X)&creative(X))<=>(wise(X)|generous(X))))&
((?[X]:((funny(X)|brave(X))))=>(?[X]:(~kind(X))))&
((?[X]:((old(X)&~generous(X))))=>(?[X]:((quiet(X)<~>~strong(X)))))&
(![X]:((~quiet(X)|kind(X))=>(brave(X)&~old(X))))&
((tall(susan))<=>((brave(paul)<~>patient(paul))))&
(((~rich(alice)&tall(alice)))=>((wise(lucy)<~>curious(lucy))))&
(![X]:((happy(X)<~>patient(X))=>(tall(X)|strong(X))))&
((curious(lucy)&~patient(lucy)))&
((humble(lucy)|happy(lucy)))&
(tall(susan))&
((~funny(alice)|generous(alice))) | ~strong(paul) | [
"p2",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7300548431086229828275963
% SZS output start Proof for 7300548431086229828275963
3. ! [X0] : ((strong(X0) | generous(X0)) => (happy(X0) & ~calm(X0))) [input p2]
5. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (calm(X0) & ~kind(X0))) [input p4]
10. ! [X0] : ((creative(X0) & calm(X0)) <=> (generous(X0) | wise(X0))) [input p9]
21. strong(paul) [input hypothesis]
27. ! [X0] : ((happy(X0) & ~calm(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 3]
43. ! [X0] : (((funny(X0) | ~generous(X0)) | (~calm(X0) | kind(X0))) & ((calm(X0) & ~kind(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((funny(X0) | ~generous(X0) | ~calm(X0) | kind(X0)) & ((calm(X0) & ~kind(X0)) | (~funny(X0) & generous(X0)))) [flattening 43]
51. ! [X0] : (((creative(X0) & calm(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (~creative(X0) | ~calm(X0)))) [nnf transformation 10]
52. ! [X0] : (((creative(X0) & calm(X0)) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | ~creative(X0) | ~calm(X0))) [flattening 51]
68. ~calm(X0) | ~generous(X0) [cnf transformation 27]
69. ~calm(X0) | ~strong(X0) [cnf transformation 27]
77. calm(X0) | generous(X0) [cnf transformation 44]
91. calm(X0) | ~generous(X0) [cnf transformation 52]
112. strong(paul) [cnf transformation 21]
178. ~generous(X0) [subsumption resolution 91,68]
233. generous(X0) | ~strong(X0) [resolution 77,69]
235. ~strong(X0) [subsumption resolution 233,178]
236. $false [resolution 235,112]
% SZS output end Proof for 7300548431086229828275963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not wise is not wise and vice versa. Everyone who is not happy or not strong is either not kind or curious. If fred is not rich then fred is not calm and vice versa. Everyone who is either not creative or quiet is both not curious and kind. Everyone who is not happy is both funny and old. Everyone who is strong is not calm or not creative. Everyone who is both not curious and happy is either rich or not rich. Everyone who is either not humble or humble is both quiet and not kind. Everyone who is both strong and not funny is both creative and not calm and vice versa. If paul is either not kind or humble then someone is both brave and old and vice versa. Everyone who is not kind is wise or not wise and vice versa. Everyone who is curious is either not kind or strong and vice versa. If paul is either quiet or old then paul is not strong and vice versa. Everyone who is creative or not generous is not tall or creative and vice versa. Paul is not kind or not strong. Fred is either not brave or not tall. Paul is not brave or not funny. Someone is rich. Paul is either not old or not rich. Alice is calm or not kind. Someone is either not curious or not tall. Fred is not rich or patient. | Alice is strong. | entailment | (![X]:((brave(X)<~>~wise(X))<=>~wise(X)))&
(![X]:((~happy(X)|~strong(X))=>(~kind(X)<~>curious(X))))&
((~rich(fred))<=>(~calm(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(~curious(X)&kind(X))))&
(![X]:(~happy(X)=>(funny(X)&old(X))))&
(![X]:(strong(X)=>(~calm(X)|~creative(X))))&
(![X]:((~curious(X)&happy(X))=>(rich(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>humble(X))=>(quiet(X)&~kind(X))))&
(![X]:((strong(X)&~funny(X))<=>(creative(X)&~calm(X))))&
(((~kind(paul)<~>humble(paul)))<=>(?[X]:((brave(X)&old(X)))))&
(![X]:(~kind(X)<=>(wise(X)|~wise(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>strong(X))))&
(((quiet(paul)<~>old(paul)))<=>(~strong(paul)))&
(![X]:((creative(X)|~generous(X))<=>(~tall(X)|creative(X))))&
((~kind(paul)|~strong(paul)))&
((~brave(fred)<~>~tall(fred)))&
((~brave(paul)|~funny(paul)))&
(?[X]:(rich(X)))&
((~old(paul)<~>~rich(paul)))&
((calm(alice)|~kind(alice)))&
(?[X]:((~curious(X)<~>~tall(X))))&
((~rich(fred)|patient(fred))) | strong(alice) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1890789449292987789162517
% SZS output start Proof for 1890789449292987789162517
2. ! [X0] : ((~strong(X0) | ~happy(X0)) => (~kind(X0) <~> curious(X0))) [input p1]
8. ! [X0] : ((~humble(X0) <~> humble(X0)) => (~kind(X0) & quiet(X0))) [input p7]
12. ! [X0] : (curious(X0) <=> (~kind(X0) <~> strong(X0))) [input p11]
23. ~strong(alice) [input hypothesis]
25. ! [X0] : ((~kind(X0) <~> curious(X0)) | (strong(X0) & happy(X0))) [ennf transformation 2]
32. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 8]
34. ! [X0] : (((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | (strong(X0) & happy(X0))) [nnf transformation 25]
38. ! [X0] : ((~kind(X0) & quiet(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 32]
47. ! [X0] : ((curious(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ~curious(X0))) [nnf transformation 12]
65. ~curious(X0) | kind(X0) | strong(X0) [cnf transformation 34]
79. ~kind(X0) | humble(X0) | humble(X0) [cnf transformation 38]
80. ~kind(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 38]
96. curious(X0) | strong(X0) | kind(X0) [cnf transformation 47]
116. ~strong(alice) [cnf transformation 23]
119. ~kind(X0) | humble(X0) [duplicate literal removal 79]
120. ~humble(X0) | ~kind(X0) [duplicate literal removal 80]
134. ~kind(X0) [subsumption resolution 119,120]
149. curious(X0) | strong(X0) [subsumption resolution 96,134]
189. kind(X0) | strong(X0) | strong(X0) [resolution 65,149]
190. kind(X0) | strong(X0) [duplicate literal removal 189]
194. strong(X0) [subsumption resolution 190,134]
196. $false [resolution 194,116]
% SZS output end Proof for 1890789449292987789162517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not wise and not calm then susan is tall or not creative.
If paul is old or generous then someone is not generous and vice versa.
Everyone who is creative or not wise is happy or not old and vice versa.
Everyone who is both strong and patient is old and vice versa.
Everyone who is both happy and not calm is brave or humble and vice versa.
Everyone who is both rich and calm is not wise or not happy.
Everyone who is both not humble and not rich is both not patient and not curious.
Everyone who is strong is not wise or generous.
Everyone who is tall is both not generous and not calm and vice versa.
If someone is either humble or kind then susan is creative.
Everyone who is both tall and strong is not curious.
Everyone who is both brave and not generous is either not kind or tall and vice versa.
If someone is quiet or not patient then paul is not quiet or not creative.
Everyone who is both not tall and strong is not rich.
Everyone who is not happy is not strong or not wise and vice versa.
Everyone who is both rich and not strong is not humble.
Lucy is not curious.
Susan is either humble or old.
Someone is either not quiet or not calm.
Susan is patient or brave.
Mary is not humble.
Susan is either not old or tall.
Susan is both not tall and funny.
Someone is either kind or not calm. | Paul is not generous. | contradiction | (((~wise(john)&~calm(john)))=>((tall(susan)|~creative(susan))))&
(((old(paul)|generous(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~wise(X))<=>(happy(X)|~old(X))))&
(![X]:((strong(X)&patient(X))<=>old(X)))&
(![X]:((happy(X)&~calm(X))<=>(brave(X)|humble(X))))&
(![X]:((rich(X)&calm(X))=>(~wise(X)|~happy(X))))&
(![X]:((~humble(X)&~rich(X))=>(~patient(X)&~curious(X))))&
(![X]:(strong(X)=>(~wise(X)|generous(X))))&
(![X]:(tall(X)<=>(~generous(X)&~calm(X))))&
((?[X]:((humble(X)<~>kind(X))))=>(creative(susan)))&
(![X]:((tall(X)&strong(X))=>~curious(X)))&
(![X]:((brave(X)&~generous(X))<=>(~kind(X)<~>tall(X))))&
((?[X]:((quiet(X)|~patient(X))))=>((~quiet(paul)|~creative(paul))))&
(![X]:((~tall(X)&strong(X))=>~rich(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&~strong(X))=>~humble(X)))&
(~curious(lucy))&
((humble(susan)<~>old(susan)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((patient(susan)|brave(susan)))&
(~humble(mary))&
((~old(susan)<~>tall(susan)))&
((~tall(susan)&funny(susan)))&
(?[X]:((kind(X)<~>~calm(X)))) | ~generous(paul) | [
"p1",
"p2",
"p3",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3502758201339773760399382
% SZS output start Proof for 3502758201339773760399382
2. (generous(paul) | old(paul)) <=> ? [X0] : ~generous(X0) [input p1]
3. ! [X0] : ((~wise(X0) | creative(X0)) <=> (~old(X0) | happy(X0))) [input p2]
4. ! [X0] : ((patient(X0) & strong(X0)) <=> old(X0)) [input p3]
8. ! [X0] : (strong(X0) => (generous(X0) | ~wise(X0))) [input p7]
15. ! [X0] : (~happy(X0) <=> (~wise(X0) | ~strong(X0))) [input p14]
25. ~generous(paul) [input hypothesis]
36. ! [X0] : ((generous(X0) | ~wise(X0)) | ~strong(X0)) [ennf transformation 8]
37. ! [X0] : (generous(X0) | ~wise(X0) | ~strong(X0)) [flattening 36]
45. ((generous(paul) | old(paul)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (~generous(paul) & ~old(paul))) [nnf transformation 2]
46. (generous(paul) | old(paul) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (~generous(paul) & ~old(paul))) [flattening 45]
47. (generous(paul) | old(paul) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | (~generous(paul) & ~old(paul))) [rectify 46]
48. ? [X1] : ~generous(X1) => ~generous(sK0) [choice axiom]
49. (generous(paul) | old(paul) | ! [X0] : generous(X0)) & (~generous(sK0) | (~generous(paul) & ~old(paul))) [skolemisation 47,48]
50. ! [X0] : (((~wise(X0) | creative(X0)) | (old(X0) & ~happy(X0))) & ((~old(X0) | happy(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 3]
51. ! [X0] : ((~wise(X0) | creative(X0) | (old(X0) & ~happy(X0))) & (~old(X0) | happy(X0) | (wise(X0) & ~creative(X0)))) [flattening 50]
52. ! [X0] : (((patient(X0) & strong(X0)) | ~old(X0)) & (old(X0) | (~patient(X0) | ~strong(X0)))) [nnf transformation 4]
53. ! [X0] : (((patient(X0) & strong(X0)) | ~old(X0)) & (old(X0) | ~patient(X0) | ~strong(X0))) [flattening 52]
61. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 15]
62. ! [X0] : ((~happy(X0) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | happy(X0))) [flattening 61]
74. generous(paul) | old(paul) | generous(X0) [cnf transformation 49]
76. ~old(X0) | happy(X0) | wise(X0) [cnf transformation 51]
80. ~old(X0) | strong(X0) [cnf transformation 53]
89. ~strong(X0) | ~wise(X0) | generous(X0) [cnf transformation 37]
106. ~happy(X0) | wise(X0) [cnf transformation 62]
119. ~generous(paul) [cnf transformation 25]
138. 5 <=> ! [X0] : generous(X0) [avatar definition]
139. generous(X0) <- (5) [avatar component clause 138]
141. 6 <=> old(paul) [avatar definition]
143. old(paul) <- (6) [avatar component clause 141]
145. 7 <=> generous(paul) [avatar definition]
146. ~generous(paul) <- (~7) [avatar component clause 145]
148. 5 | 6 | 7 [avatar split clause 74,145,141,138]
223. ~7 [avatar split clause 119,145]
224. $false <- (5, ~7) [resolution 146,139]
225. ~5 | 7 [avatar contradiction clause 224]
226. strong(paul) <- (6) [resolution 80,143]
238. happy(paul) | wise(paul) <- (6) [resolution 76,143]
239. wise(paul) <- (6) [subsumption resolution 238,106]
263. ~wise(paul) | generous(paul) <- (6) [resolution 89,226]
265. generous(paul) <- (6) [subsumption resolution 263,239]
266. $false <- (6, ~7) [subsumption resolution 265,146]
267. ~6 | 7 [avatar contradiction clause 266]
269. $false [avatar sat refutation 148,223,225,267]
% SZS output end Proof for 3502758201339773760399382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then john is either brave or calm and vice versa.
Everyone who is not humble is humble.
If lucy is both curious and tall then someone is strong or not patient and vice versa.
Everyone who is happy is both rich and not kind and vice versa.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | John is brave. | neutral | ((?[X]:((kind(X)<~>old(X))))<=>((brave(john)<~>calm(john))))&
(![X]:(~humble(X)=>humble(X)))&
(((curious(lucy)&tall(lucy)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:(happy(X)<=>(rich(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | brave(john) | [] | null | 0 |
Everyone who is either not rich or not happy is not curious.
If lucy is not patient or not humble then alice is both not brave and not strong and vice versa.
Everyone who is not strong or not funny is either creative or not wise.
If mary is both patient and humble then lucy is kind or not strong.
Everyone who is both patient and old is not generous or humble.
Everyone who is funny or not generous is not wise or old.
If someone is funny then lucy is wise or not kind.
If paul is both not creative and creative then susan is either not generous or not curious and vice versa.
If someone is either quiet or wise then someone is not quiet or not tall and vice versa.
If lucy is creative then someone is either not patient or not old.
If someone is both wise and curious then fred is either not funny or not happy.
Everyone who is tall or not curious is brave or not generous.
If susan is not generous or not curious then someone is calm.
If mary is wise then someone is both not wise and not tall.
Everyone who is either funny or not brave is either humble or not tall and vice versa.
If fred is either quiet or not funny then someone is not kind or not brave and vice versa.
Someone is not generous or generous.
Lucy is not wise or not happy.
Someone is not funny.
Mary is either curious or tall.
Paul is either brave or quiet.
Alice is both old and not patient.
Fred is not happy.
Someone is either funny or not happy. | Fred is happy. | contradiction | (![X]:((~rich(X)<~>~happy(X))=>~curious(X)))&
(((~patient(lucy)|~humble(lucy)))<=>((~brave(alice)&~strong(alice))))&
(![X]:((~strong(X)|~funny(X))=>(creative(X)<~>~wise(X))))&
(((patient(mary)&humble(mary)))=>((kind(lucy)|~strong(lucy))))&
(![X]:((patient(X)&old(X))=>(~generous(X)|humble(X))))&
(![X]:((funny(X)|~generous(X))=>(~wise(X)|old(X))))&
((?[X]:(funny(X)))=>((wise(lucy)|~kind(lucy))))&
(((~creative(paul)&creative(paul)))<=>((~generous(susan)<~>~curious(susan))))&
((?[X]:((quiet(X)<~>wise(X))))<=>(?[X]:((~quiet(X)|~tall(X)))))&
((creative(lucy))=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:((wise(X)&curious(X))))=>((~funny(fred)<~>~happy(fred))))&
(![X]:((tall(X)|~curious(X))=>(brave(X)|~generous(X))))&
(((~generous(susan)|~curious(susan)))=>(?[X]:(calm(X))))&
((wise(mary))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((funny(X)<~>~brave(X))<=>(humble(X)<~>~tall(X))))&
(((quiet(fred)<~>~funny(fred)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(?[X]:((~generous(X)|generous(X))))&
((~wise(lucy)|~happy(lucy)))&
(?[X]:(~funny(X)))&
((curious(mary)<~>tall(mary)))&
((brave(paul)<~>quiet(paul)))&
((old(alice)&~patient(alice)))&
(~happy(fred))&
(?[X]:((funny(X)<~>~happy(X)))) | happy(fred) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 85941870347459631288639
% SZS output start Proof for 85941870347459631288639
23. ~happy(fred) [input p22]
25. happy(fred) [input hypothesis]
133. ~happy(fred) [cnf transformation 23]
136. happy(fred) [cnf transformation 25]
255. 27 <=> happy(fred) [avatar definition]
323. ~27 [avatar split clause 133,255]
334. 27 [avatar split clause 136,255]
335. $false [avatar sat refutation 323,334]
% SZS output end Proof for 85941870347459631288639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is calm.
Everyone who is not funny is either generous or not curious and vice versa.
If someone is creative or not creative then someone is both generous and not kind.
Everyone who is not strong or strong is both curious and not funny.
Everyone who is both not patient and humble is either generous or funny and vice versa.
Everyone who is either not rich or creative is both not funny and calm.
Everyone who is either not funny or brave is strong or not quiet and vice versa.
If someone is brave or tall then john is both funny and wise and vice versa.
Everyone who is both not creative and curious is wise or not brave.
If lucy is both not tall and not creative then mary is funny or not quiet and vice versa.
Everyone who is both quiet and not strong is both not humble and not generous and vice versa.
If someone is either funny or not wise then someone is both old and quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Someone is not wise or creative.
Someone is calm or not old.
Lucy is patient or not tall.
John is either not happy or not calm.
Someone is strong. | John is not tall. | entailment | (![X]:(generous(X)=>calm(X)))&
(![X]:(~funny(X)<=>(generous(X)<~>~curious(X))))&
((?[X]:((creative(X)|~creative(X))))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((~strong(X)|strong(X))=>(curious(X)&~funny(X))))&
(![X]:((~patient(X)&humble(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~rich(X)<~>creative(X))=>(~funny(X)&calm(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((brave(X)|tall(X))))<=>((funny(john)&wise(john))))&
(![X]:((~creative(X)&curious(X))=>(wise(X)|~brave(X))))&
(((~tall(lucy)&~creative(lucy)))<=>((funny(mary)|~quiet(mary))))&
(![X]:((quiet(X)&~strong(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((funny(X)<~>~wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(?[X]:((~wise(X)|creative(X))))&
(?[X]:((calm(X)|~old(X))))&
((patient(lucy)|~tall(lucy)))&
((~happy(john)<~>~calm(john)))&
(?[X]:(strong(X))) | ~tall(john) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7592754620764189155848778
% SZS output start Proof for 7592754620764189155848778
4. ! [X0] : ((strong(X0) | ~strong(X0)) => (~funny(X0) & curious(X0))) [input p3]
8. ? [X0] : (tall(X0) | brave(X0)) <=> (wise(john) & funny(john)) [input p7]
21. tall(john) [input hypothesis]
26. ! [X0] : ((~funny(X0) & curious(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 4]
40. (? [X0] : (tall(X0) | brave(X0)) | (~wise(john) | ~funny(john))) & ((wise(john) & funny(john)) | ! [X0] : (~tall(X0) & ~brave(X0))) [nnf transformation 8]
41. (? [X0] : (tall(X0) | brave(X0)) | ~wise(john) | ~funny(john)) & ((wise(john) & funny(john)) | ! [X0] : (~tall(X0) & ~brave(X0))) [flattening 40]
42. (? [X0] : (tall(X0) | brave(X0)) | ~wise(john) | ~funny(john)) & ((wise(john) & funny(john)) | ! [X1] : (~tall(X1) & ~brave(X1))) [rectify 41]
43. ? [X0] : (tall(X0) | brave(X0)) => (tall(sK1) | brave(sK1)) [choice axiom]
44. ((tall(sK1) | brave(sK1)) | ~wise(john) | ~funny(john)) & ((wise(john) & funny(john)) | ! [X1] : (~tall(X1) & ~brave(X1))) [skolemisation 42,43]
79. ~funny(X0) | strong(X0) [cnf transformation 26]
80. ~funny(X0) | ~strong(X0) [cnf transformation 26]
98. funny(john) | ~tall(X1) [cnf transformation 44]
136. tall(john) [cnf transformation 21]
155. ~funny(X0) [subsumption resolution 79,80]
164. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
165. ~tall(X1) <- (5) [avatar component clause 164]
175. ~tall(X1) [subsumption resolution 98,155]
176. 5 [avatar split clause 175,164]
277. $false <- (5) [resolution 165,136]
278. ~5 [avatar contradiction clause 277]
279. $false [avatar sat refutation 176,278]
% SZS output end Proof for 7592754620764189155848778
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not calm or funny then someone is both not creative and not generous and vice versa.
Everyone who is both kind and wise is either kind or not funny.
Everyone who is calm or not happy is not kind or happy and vice versa.
If someone is not patient then john is both curious and strong and vice versa.
If someone is either not kind or curious then someone is curious.
If someone is not generous then lucy is not curious.
Everyone who is either rich or not generous is not generous.
Everyone who is not humble or not tall is either curious or old and vice versa.
If john is patient then someone is not happy.
Everyone who is not wise is either not humble or calm and vice versa.
Everyone who is not kind or old is not old and vice versa.
Everyone who is patient is both brave and quiet and vice versa.
Everyone who is quiet is funny or rich and vice versa.
Everyone who is both not kind and old is either patient or not brave and vice versa.
If someone is both not brave and not patient then lucy is both patient and kind and vice versa.
Everyone who is not wise or not kind is not patient and vice versa.
Alice is humble or rich.
Someone is either not funny or calm.
Mary is not quiet.
Susan is either happy or calm.
Someone is calm or not patient. | Mary is patient. | contradiction | (((~calm(alice)|funny(alice)))<=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)<~>~funny(X))))&
(![X]:((calm(X)|~happy(X))<=>(~kind(X)|happy(X))))&
((?[X]:(~patient(X)))<=>((curious(john)&strong(john))))&
((?[X]:((~kind(X)<~>curious(X))))=>(?[X]:(curious(X))))&
((?[X]:(~generous(X)))=>(~curious(lucy)))&
(![X]:((rich(X)<~>~generous(X))=>~generous(X)))&
(![X]:((~humble(X)|~tall(X))<=>(curious(X)<~>old(X))))&
((patient(john))=>(?[X]:(~happy(X))))&
(![X]:(~wise(X)<=>(~humble(X)<~>calm(X))))&
(![X]:((~kind(X)|old(X))<=>~old(X)))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
((?[X]:((~brave(X)&~patient(X))))<=>((patient(lucy)&kind(lucy))))&
(![X]:((~wise(X)|~kind(X))<=>~patient(X)))&
((humble(alice)|rich(alice)))&
(?[X]:((~funny(X)<~>calm(X))))&
(~quiet(mary))&
((happy(susan)<~>calm(susan)))&
(?[X]:((calm(X)|~patient(X)))) | patient(mary) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2664011895520545969667914
% SZS output start Proof for 2664011895520545969667914
11. ! [X0] : ((old(X0) | ~kind(X0)) <=> ~old(X0)) [input p10]
12. ! [X0] : (patient(X0) <=> (quiet(X0) & brave(X0))) [input p11]
14. ! [X0] : ((old(X0) & ~kind(X0)) <=> (patient(X0) <~> ~brave(X0))) [input p13]
22. patient(mary) [input hypothesis]
53. ! [X0] : (((old(X0) | ~kind(X0)) | old(X0)) & (~old(X0) | (~old(X0) & kind(X0)))) [nnf transformation 11]
54. ! [X0] : ((old(X0) | ~kind(X0) | old(X0)) & (~old(X0) | (~old(X0) & kind(X0)))) [flattening 53]
55. ! [X0] : ((patient(X0) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | ~patient(X0))) [nnf transformation 12]
56. ! [X0] : ((patient(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | ~patient(X0))) [flattening 55]
59. ! [X0] : (((old(X0) & ~kind(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (~old(X0) | kind(X0)))) [nnf transformation 14]
60. ! [X0] : (((old(X0) & ~kind(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0)))) & (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~old(X0) | kind(X0))) [flattening 59]
105. ~old(X0) | ~old(X0) [cnf transformation 54]
107. brave(X0) | ~patient(X0) [cnf transformation 56]
117. old(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 60]
118. old(X0) | patient(X0) | brave(X0) [cnf transformation 60]
133. patient(mary) [cnf transformation 22]
134. ~old(X0) [duplicate literal removal 105]
211. patient(X0) | brave(X0) [subsumption resolution 118,134]
212. brave(X0) [subsumption resolution 211,107]
213. ~brave(X0) | ~patient(X0) [subsumption resolution 117,134]
214. ~patient(X0) [subsumption resolution 213,212]
237. $false [subsumption resolution 133,214]
% SZS output end Proof for 2664011895520545969667914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is funny or not creative and vice versa.
If mary is not tall then john is not brave or patient and vice versa.
If john is either curious or not tall then someone is either not strong or generous.
Everyone who is either quiet or not rich is creative and vice versa.
Everyone who is both humble and rich is not patient or humble and vice versa.
Everyone who is either kind or happy is both funny and brave and vice versa.
Everyone who is both not brave and not creative is either calm or not old.
Everyone who is both brave and not funny is either not quiet or not rich.
If someone is happy then someone is not curious or not happy and vice versa.
Everyone who is old or not brave is either not funny or not kind.
If alice is both not humble and not funny then someone is both not patient and wise.
Everyone who is not humble is either not happy or not humble and vice versa.
If alice is either not funny or patient then mary is not patient.
Everyone who is either humble or not old is either strong or not old and vice versa.
If paul is not rich or creative then someone is either kind or not creative and vice versa.
Everyone who is not patient is not generous or not creative and vice versa.
Susan is either patient or quiet.
Paul is wise.
Someone is either calm or not kind.
Someone is either not old or generous.
Someone is both quiet and curious.
Lucy is both not funny and happy.
Someone is both calm and not old. | Mary is not strong. | neutral | (![X]:(curious(X)<=>(funny(X)|~creative(X))))&
((~tall(mary))<=>((~brave(john)|patient(john))))&
(((curious(john)<~>~tall(john)))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>creative(X)))&
(![X]:((humble(X)&rich(X))<=>(~patient(X)|humble(X))))&
(![X]:((kind(X)<~>happy(X))<=>(funny(X)&brave(X))))&
(![X]:((~brave(X)&~creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((brave(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(![X]:((old(X)|~brave(X))=>(~funny(X)<~>~kind(X))))&
(((~humble(alice)&~funny(alice)))=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(~humble(X)<=>(~happy(X)<~>~humble(X))))&
(((~funny(alice)<~>patient(alice)))=>(~patient(mary)))&
(![X]:((humble(X)<~>~old(X))<=>(strong(X)<~>~old(X))))&
(((~rich(paul)|creative(paul)))<=>(?[X]:((kind(X)<~>~creative(X)))))&
(![X]:(~patient(X)<=>(~generous(X)|~creative(X))))&
((patient(susan)<~>quiet(susan)))&
(wise(paul))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:((quiet(X)&curious(X))))&
((~funny(lucy)&happy(lucy)))&
(?[X]:((calm(X)&~old(X)))) | ~strong(mary) | [] | null | 0 |
Everyone who is funny or not creative is not generous or rich and vice versa. Everyone who is both curious and not kind is funny or generous and vice versa. Everyone who is not calm is either funny or quiet. Everyone who is either old or not tall is funny or old and vice versa. If lucy is both not humble and not creative then mary is not rich or patient. If paul is both not creative and funny then someone is humble or calm. Everyone who is not calm is rich and vice versa. Everyone who is either quiet or not generous is both not curious and not wise. If fred is both quiet and happy then john is either generous or not wise. Everyone who is tall is not kind or patient. Everyone who is not tall or calm is calm. Everyone who is not kind is both not calm and calm and vice versa. If paul is not calm then someone is either creative or not calm. Everyone who is either quiet or not rich is both rich and generous and vice versa. Everyone who is generous or not rich is either tall or not patient and vice versa. If someone is humble or tall then someone is not humble or not strong. Someone is either not happy or not humble. Someone is patient or not humble. Someone is humble. Fred is curious or not creative. Alice is either not brave or not wise. Lucy is both not wise and curious. Lucy is either funny or calm. | Mary is patient. | entailment | (![X]:((funny(X)|~creative(X))<=>(~generous(X)|rich(X))))&
(![X]:((curious(X)&~kind(X))<=>(funny(X)|generous(X))))&
(![X]:(~calm(X)=>(funny(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|old(X))))&
(((~humble(lucy)&~creative(lucy)))=>((~rich(mary)|patient(mary))))&
(((~creative(paul)&funny(paul)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:(~calm(X)<=>rich(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~curious(X)&~wise(X))))&
(((quiet(fred)&happy(fred)))=>((generous(john)<~>~wise(john))))&
(![X]:(tall(X)=>(~kind(X)|patient(X))))&
(![X]:((~tall(X)|calm(X))=>calm(X)))&
(![X]:(~kind(X)<=>(~calm(X)&calm(X))))&
((~calm(paul))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:(humble(X)))&
((curious(fred)|~creative(fred)))&
((~brave(alice)<~>~wise(alice)))&
((~wise(lucy)&curious(lucy)))&
((funny(lucy)<~>calm(lucy))) | patient(mary) | [
"p1",
"p3",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3161793777393875485324832
% SZS output start Proof for 3161793777393875485324832
2. ! [X0] : ((~kind(X0) & curious(X0)) <=> (generous(X0) | funny(X0))) [input p1]
4. ! [X0] : ((old(X0) <~> ~tall(X0)) <=> (old(X0) | funny(X0))) [input p3]
10. ! [X0] : (tall(X0) => (patient(X0) | ~kind(X0))) [input p9]
12. ! [X0] : (~kind(X0) <=> (calm(X0) & ~calm(X0))) [input p11]
24. ~patient(mary) [input hypothesis]
35. ! [X0] : ((patient(X0) | ~kind(X0)) | ~tall(X0)) [ennf transformation 10]
36. ! [X0] : (patient(X0) | ~kind(X0) | ~tall(X0)) [flattening 35]
41. ! [X0] : (((~kind(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 2]
42. ! [X0] : (((~kind(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | kind(X0) | ~curious(X0))) [flattening 41]
44. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [nnf transformation 4]
45. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [flattening 44]
51. ! [X0] : ((~kind(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | kind(X0))) [nnf transformation 12]
52. ! [X0] : ((~kind(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | kind(X0))) [flattening 51]
76. ~kind(X0) | ~funny(X0) [cnf transformation 42]
81. old(X0) | funny(X0) | old(X0) | tall(X0) [cnf transformation 45]
85. tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 45]
96. ~tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 36]
99. ~calm(X0) | kind(X0) [cnf transformation 52]
100. calm(X0) | kind(X0) [cnf transformation 52]
127. ~patient(mary) [cnf transformation 24]
130. old(X0) | funny(X0) | tall(X0) [duplicate literal removal 81]
131. ~old(X0) | tall(X0) [duplicate literal removal 85]
132. tall(X0) | funny(X0) [subsumption resolution 130,131]
146. 4 <=> patient(mary) [avatar definition]
147. ~patient(mary) <- (~4) [avatar component clause 146]
186. kind(X0) [subsumption resolution 99,100]
253. ~4 [avatar split clause 127,146]
255. ~funny(X0) [resolution 76,186]
286. ~kind(X0) | patient(X0) | funny(X0) [resolution 96,132]
288. patient(X0) | funny(X0) [subsumption resolution 286,186]
289. patient(X0) [subsumption resolution 288,255]
290. $false <- (~4) [resolution 289,147]
291. 4 [avatar contradiction clause 290]
292. $false [avatar sat refutation 253,291]
% SZS output end Proof for 3161793777393875485324832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or calm is not quiet and vice versa. If someone is either not old or creative then mary is curious or calm and vice versa. Everyone who is not generous or not calm is not tall or not creative and vice versa. If john is not strong or not happy then someone is not humble or not strong. If susan is either old or kind then someone is either not humble or patient. Everyone who is humble or kind is brave or calm. If alice is not creative or not brave then someone is either not quiet or old. If someone is not tall then someone is tall or not humble. Everyone who is not curious or not brave is either not curious or not kind. Everyone who is not quiet or old is either wise or not brave. Everyone who is both brave and not generous is either not rich or wise and vice versa. Everyone who is either kind or quiet is calm or not old and vice versa. Everyone who is not funny or not kind is either wise or curious and vice versa. Everyone who is calm is either happy or not wise. If john is both generous and curious then someone is both not tall and not curious and vice versa. If mary is both not generous and not curious then susan is either not strong or not wise and vice versa. Someone is brave. Lucy is not calm. Someone is not calm. Paul is calm or not happy. Someone is curious. Someone is either not brave or funny. John is both not happy and not wise. Alice is kind or creative. | John is not happy. | entailment | (![X]:((old(X)|calm(X))<=>~quiet(X)))&
((?[X]:((~old(X)<~>creative(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((~generous(X)|~calm(X))<=>(~tall(X)|~creative(X))))&
(((~strong(john)|~happy(john)))=>(?[X]:((~humble(X)|~strong(X)))))&
(((old(susan)<~>kind(susan)))=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((humble(X)|kind(X))=>(brave(X)|calm(X))))&
(((~creative(alice)|~brave(alice)))=>(?[X]:((~quiet(X)<~>old(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~curious(X)|~brave(X))=>(~curious(X)<~>~kind(X))))&
(![X]:((~quiet(X)|old(X))=>(wise(X)<~>~brave(X))))&
(![X]:((brave(X)&~generous(X))<=>(~rich(X)<~>wise(X))))&
(![X]:((kind(X)<~>quiet(X))<=>(calm(X)|~old(X))))&
(![X]:((~funny(X)|~kind(X))<=>(wise(X)<~>curious(X))))&
(![X]:(calm(X)=>(happy(X)<~>~wise(X))))&
(((generous(john)&curious(john)))<=>(?[X]:((~tall(X)&~curious(X)))))&
(((~generous(mary)&~curious(mary)))<=>((~strong(susan)<~>~wise(susan))))&
(?[X]:(brave(X)))&
(~calm(lucy))&
(?[X]:(~calm(X)))&
((calm(paul)|~happy(paul)))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)<~>funny(X))))&
((~happy(john)&~wise(john)))&
((kind(alice)|creative(alice))) | ~happy(john) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1129458993472726186117793
% SZS output start Proof for 1129458993472726186117793
23. ~wise(john) & ~happy(john) [input p22]
25. happy(john) [input hypothesis]
152. ~happy(john) [cnf transformation 23]
155. happy(john) [cnf transformation 25]
186. 7 <=> happy(john) [avatar definition]
324. ~7 [avatar split clause 152,186]
330. 7 [avatar split clause 155,186]
331. $false [avatar sat refutation 324,330]
% SZS output end Proof for 1129458993472726186117793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is both brave and kind and vice versa. Everyone who is happy or not patient is not patient. Everyone who is both not quiet and not brave is not patient or funny. Everyone who is both not calm and creative is not humble or not creative and vice versa. Everyone who is either wise or not quiet is not patient. Everyone who is either not creative or not kind is rich or not patient and vice versa. If someone is not funny then someone is both wise and not humble. If someone is strong then alice is not rich. If someone is tall or not patient then someone is both not patient and creative and vice versa. Everyone who is not creative is both not funny and not quiet. If someone is not creative then someone is not tall or old. If alice is both strong and not old then someone is either not tall or tall and vice versa. Everyone who is quiet or not tall is calm. Everyone who is both wise and happy is both not happy and not old. Someone is either not rich or not strong. Paul is wise or strong. Mary is either old or creative. Someone is either old or not kind. | Alice is not wise. | neutral | (![X]:((~old(X)<~>old(X))<=>(brave(X)&kind(X))))&
(![X]:((happy(X)|~patient(X))=>~patient(X)))&
(![X]:((~quiet(X)&~brave(X))=>(~patient(X)|funny(X))))&
(![X]:((~calm(X)&creative(X))<=>(~humble(X)|~creative(X))))&
(![X]:((wise(X)<~>~quiet(X))=>~patient(X)))&
(![X]:((~creative(X)<~>~kind(X))<=>(rich(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
((?[X]:((tall(X)|~patient(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:(~creative(X)=>(~funny(X)&~quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)|old(X)))))&
(((strong(alice)&~old(alice)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((quiet(X)|~tall(X))=>calm(X)))&
(![X]:((wise(X)&happy(X))=>(~happy(X)&~old(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((wise(paul)|strong(paul)))&
((old(mary)<~>creative(mary)))&
(?[X]:((old(X)<~>~kind(X)))) | ~wise(alice) | [] | null | 0 |
Everyone who is not tall is creative or not funny and vice versa. If someone is not calm or not funny then mary is both funny and curious. Everyone who is not funny or not wise is calm and vice versa. Everyone who is not tall or not wise is both not wise and creative. Everyone who is strong is either calm or wise and vice versa. Everyone who is creative is not funny. Everyone who is both curious and not humble is both calm and curious and vice versa. Everyone who is either not patient or not wise is either old or not calm and vice versa. Everyone who is humble is either quiet or old. Everyone who is not wise is both not kind and not patient and vice versa. Everyone who is both not old and curious is both tall and calm and vice versa. If someone is humble or not creative then someone is not old or kind. Everyone who is either not creative or not wise is either not brave or not wise and vice versa. If someone is kind or not funny then someone is not patient or not humble. Everyone who is either old or not calm is both quiet and not generous and vice versa. Everyone who is not tall is happy. Paul is creative or patient. Lucy is quiet or patient. Someone is happy or not creative. Someone is both not generous and not tall. Lucy is happy. Someone is both not humble and not happy. Someone is either humble or not funny. Someone is either not rich or strong. | Lucy is not patient. | neutral | (![X]:(~tall(X)<=>(creative(X)|~funny(X))))&
((?[X]:((~calm(X)|~funny(X))))=>((funny(mary)&curious(mary))))&
(![X]:((~funny(X)|~wise(X))<=>calm(X)))&
(![X]:((~tall(X)|~wise(X))=>(~wise(X)&creative(X))))&
(![X]:(strong(X)<=>(calm(X)<~>wise(X))))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((curious(X)&~humble(X))<=>(calm(X)&curious(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(old(X)<~>~calm(X))))&
(![X]:(humble(X)=>(quiet(X)<~>old(X))))&
(![X]:(~wise(X)<=>(~kind(X)&~patient(X))))&
(![X]:((~old(X)&curious(X))<=>(tall(X)&calm(X))))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:((~old(X)|kind(X)))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~brave(X)<~>~wise(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((old(X)<~>~calm(X))<=>(quiet(X)&~generous(X))))&
(![X]:(~tall(X)=>happy(X)))&
((creative(paul)|patient(paul)))&
((quiet(lucy)|patient(lucy)))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(happy(lucy))&
(?[X]:((~humble(X)&~happy(X))))&
(?[X]:((humble(X)<~>~funny(X))))&
(?[X]:((~rich(X)<~>strong(X)))) | ~patient(lucy) | [] | null | 0 |
If paul is either not funny or not rich then someone is not curious.
If mary is wise then john is not wise or not tall.
Everyone who is either not curious or patient is old or not kind.
Everyone who is not happy is both not strong and not patient.
Everyone who is both brave and happy is not creative and vice versa.
If john is both not strong and kind then someone is either calm or rich and vice versa.
Everyone who is both not happy and creative is both not calm and not generous and vice versa.
Everyone who is either kind or not tall is not old or not tall and vice versa.
Everyone who is both funny and wise is not calm and vice versa.
Everyone who is both funny and not wise is calm or old and vice versa.
Everyone who is not patient is not humble and vice versa.
Everyone who is happy or generous is not curious or not old and vice versa.
Everyone who is not quiet or patient is patient and vice versa.
If someone is both not brave and kind then paul is not kind or not quiet and vice versa.
Everyone who is kind or not calm is curious or not wise.
If alice is not patient or wise then fred is either not happy or not generous and vice versa.
Lucy is either patient or not quiet.
Lucy is not calm.
Alice is funny or kind.
Someone is not brave or tall.
Someone is not calm or not funny.
Lucy is not rich or not happy.
Alice is old or humble.
Susan is not creative. | Susan is generous. | neutral | (((~funny(paul)<~>~rich(paul)))=>(?[X]:(~curious(X))))&
((wise(mary))=>((~wise(john)|~tall(john))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~kind(X))))&
(![X]:(~happy(X)=>(~strong(X)&~patient(X))))&
(![X]:((brave(X)&happy(X))<=>~creative(X)))&
(((~strong(john)&kind(john)))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~calm(X)&~generous(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~old(X)|~tall(X))))&
(![X]:((funny(X)&wise(X))<=>~calm(X)))&
(![X]:((funny(X)&~wise(X))<=>(calm(X)|old(X))))&
(![X]:(~patient(X)<=>~humble(X)))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)|~old(X))))&
(![X]:((~quiet(X)|patient(X))<=>patient(X)))&
((?[X]:((~brave(X)&kind(X))))<=>((~kind(paul)|~quiet(paul))))&
(![X]:((kind(X)|~calm(X))=>(curious(X)|~wise(X))))&
(((~patient(alice)|wise(alice)))<=>((~happy(fred)<~>~generous(fred))))&
((patient(lucy)<~>~quiet(lucy)))&
(~calm(lucy))&
((funny(alice)|kind(alice)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~calm(X)|~funny(X))))&
((~rich(lucy)|~happy(lucy)))&
((old(alice)|humble(alice)))&
(~creative(susan)) | generous(susan) | [] | null | 0 |
Everyone who is either rich or not quiet is rich and vice versa. Everyone who is wise or not happy is kind and vice versa. If john is not strong then someone is either not calm or old and vice versa. If alice is not humble then john is both wise and not old. If alice is both not happy and not curious then someone is both curious and creative and vice versa. Everyone who is both not humble and rich is either old or humble. Everyone who is both not strong and not curious is either not funny or old and vice versa. Everyone who is either funny or creative is tall. If john is both not happy and brave then john is not rich or not patient and vice versa. Everyone who is both not generous and not strong is curious. If mary is not wise then someone is either not happy or happy and vice versa. If lucy is not curious then someone is both not calm and not generous and vice versa. If lucy is either generous or calm then someone is both wise and strong. Everyone who is kind or wise is not creative. If lucy is either humble or quiet then someone is not funny or not kind and vice versa. Everyone who is both funny and happy is either tall or patient and vice versa. Fred is both not humble and not strong. Someone is creative or funny. Someone is both not rich and old. Someone is either not tall or not calm. Paul is not old or not curious. Someone is either happy or not curious. Paul is either not humble or generous. | Lucy is not quiet. | contradiction | (![X]:((rich(X)<~>~quiet(X))<=>rich(X)))&
(![X]:((wise(X)|~happy(X))<=>kind(X)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>old(X)))))&
((~humble(alice))=>((wise(john)&~old(john))))&
(((~happy(alice)&~curious(alice)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((~humble(X)&rich(X))=>(old(X)<~>humble(X))))&
(![X]:((~strong(X)&~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((funny(X)<~>creative(X))=>tall(X)))&
(((~happy(john)&brave(john)))<=>((~rich(john)|~patient(john))))&
(![X]:((~generous(X)&~strong(X))=>curious(X)))&
((~wise(mary))<=>(?[X]:((~happy(X)<~>happy(X)))))&
((~curious(lucy))<=>(?[X]:((~calm(X)&~generous(X)))))&
(((generous(lucy)<~>calm(lucy)))=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((kind(X)|wise(X))=>~creative(X)))&
(((humble(lucy)<~>quiet(lucy)))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:((funny(X)&happy(X))<=>(tall(X)<~>patient(X))))&
((~humble(fred)&~strong(fred)))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:((~tall(X)<~>~calm(X))))&
((~old(paul)|~curious(paul)))&
(?[X]:((happy(X)<~>~curious(X))))&
((~humble(paul)<~>generous(paul))) | ~quiet(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 77492228880314566941626
% SZS output start Proof for 77492228880314566941626
1. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> rich(X0)) [input p0]
24. ~quiet(lucy) [input hypothesis]
33. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ~rich(X0)) & (rich(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 1]
80. rich(X0) | rich(X0) | quiet(X0) [cnf transformation 33]
82. quiet(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 33]
149. ~quiet(lucy) [cnf transformation 24]
153. rich(X0) | quiet(X0) [duplicate literal removal 80]
154. quiet(X0) | ~rich(X0) [duplicate literal removal 82]
155. quiet(X0) [subsumption resolution 153,154]
358. $false [subsumption resolution 149,155]
% SZS output end Proof for 77492228880314566941626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not creative and not brave and vice versa.
Everyone who is not calm or not funny is tall or not humble and vice versa.
If someone is curious or tall then someone is both tall and brave.
If lucy is both curious and not funny then susan is either not humble or brave.
Everyone who is both patient and not tall is either not tall or not humble and vice versa.
Everyone who is strong or calm is kind.
Everyone who is quiet or not rich is both not happy and kind.
If someone is not quiet then someone is either patient or not brave.
If mary is either old or not patient then john is both patient and not rich and vice versa.
Everyone who is not wise is either not old or not humble and vice versa.
Everyone who is either humble or not humble is not happy or not wise and vice versa.
If someone is generous then susan is either quiet or not kind and vice versa.
If mary is creative or old then someone is either not patient or kind and vice versa.
Everyone who is either strong or not creative is kind or not wise and vice versa.
Everyone who is not old is not funny or not humble.
Everyone who is either not old or not calm is either strong or brave and vice versa.
Someone is either funny or creative.
Fred is either not calm or happy.
Paul is both not old and wise.
Someone is both not brave and funny.
Someone is either calm or not old.
Someone is both humble and not brave.
Someone is happy. | Mary is not quiet. | neutral | (![X]:((~calm(X)|calm(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~calm(X)|~funny(X))<=>(tall(X)|~humble(X))))&
((?[X]:((curious(X)|tall(X))))=>(?[X]:((tall(X)&brave(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~humble(susan)<~>brave(susan))))&
(![X]:((patient(X)&~tall(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((strong(X)|calm(X))=>kind(X)))&
(![X]:((quiet(X)|~rich(X))=>(~happy(X)&kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(((old(mary)<~>~patient(mary)))<=>((patient(john)&~rich(john))))&
(![X]:(~wise(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(~happy(X)|~wise(X))))&
((?[X]:(generous(X)))<=>((quiet(susan)<~>~kind(susan))))&
(((creative(mary)|old(mary)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(kind(X)|~wise(X))))&
(![X]:(~old(X)=>(~funny(X)|~humble(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(strong(X)<~>brave(X))))&
(?[X]:((funny(X)<~>creative(X))))&
((~calm(fred)<~>happy(fred)))&
((~old(paul)&wise(paul)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(happy(X))) | ~quiet(mary) | [] | null | 0 |
If fred is both not generous and not kind then fred is not wise or generous. If susan is either not strong or rich then alice is both not generous and not creative and vice versa. Everyone who is either not tall or not rich is both not generous and not patient and vice versa. If fred is either not funny or humble then someone is both not patient and quiet and vice versa. If mary is not patient then paul is both not old and old. Everyone who is both quiet and not humble is both not generous and old. Everyone who is both creative and not brave is humble or not wise. If someone is patient then someone is not brave or calm and vice versa. Everyone who is strong or old is either strong or not curious and vice versa. If john is not brave or creative then paul is old. Everyone who is wise or patient is quiet or curious and vice versa. If mary is either generous or calm then susan is quiet or calm and vice versa. Everyone who is either tall or old is both kind and wise. If someone is either quiet or funny then lucy is not strong and vice versa. Everyone who is quiet is curious or rich and vice versa. Everyone who is either tall or rich is both not strong and not generous and vice versa. Someone is not calm or quiet. Someone is either curious or humble. John is either not humble or old. Fred is either happy or not kind. Someone is not generous. Someone is both not funny and not calm. Someone is both calm and not curious. Fred is not quiet. | Fred is not curious. | entailment | (((~generous(fred)&~kind(fred)))=>((~wise(fred)|generous(fred))))&
(((~strong(susan)<~>rich(susan)))<=>((~generous(alice)&~creative(alice))))&
(![X]:((~tall(X)<~>~rich(X))<=>(~generous(X)&~patient(X))))&
(((~funny(fred)<~>humble(fred)))<=>(?[X]:((~patient(X)&quiet(X)))))&
((~patient(mary))=>((~old(paul)&old(paul))))&
(![X]:((quiet(X)&~humble(X))=>(~generous(X)&old(X))))&
(![X]:((creative(X)&~brave(X))=>(humble(X)|~wise(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|calm(X)))))&
(![X]:((strong(X)|old(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(john)|creative(john)))=>(old(paul)))&
(![X]:((wise(X)|patient(X))<=>(quiet(X)|curious(X))))&
(((generous(mary)<~>calm(mary)))<=>((quiet(susan)|calm(susan))))&
(![X]:((tall(X)<~>old(X))=>(kind(X)&wise(X))))&
((?[X]:((quiet(X)<~>funny(X))))<=>(~strong(lucy)))&
(![X]:(quiet(X)<=>(curious(X)|rich(X))))&
(![X]:((tall(X)<~>rich(X))<=>(~strong(X)&~generous(X))))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((~humble(john)<~>old(john)))&
((happy(fred)<~>~kind(fred)))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((calm(X)&~curious(X))))&
(~quiet(fred)) | ~curious(fred) | [
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 824019921149352637196804
% SZS output start Proof for 824019921149352637196804
15. ! [X0] : (quiet(X0) <=> (rich(X0) | curious(X0))) [input p14]
24. ~quiet(fred) [input p23]
25. curious(fred) [input hypothesis]
60. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 15]
61. ! [X0] : ((quiet(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~quiet(X0))) [flattening 60]
131. ~curious(X0) | quiet(X0) [cnf transformation 61]
151. ~quiet(fred) [cnf transformation 24]
152. curious(fred) [cnf transformation 25]
339. quiet(fred) [resolution 131,152]
341. $false [subsumption resolution 339,151]
% SZS output end Proof for 824019921149352637196804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or quiet is not old and vice versa.
If someone is both not humble and creative then fred is both not calm and not rich.
If paul is either generous or patient then alice is strong.
Everyone who is either not creative or not generous is not quiet.
Everyone who is both not old and old is not quiet.
If someone is both calm and not brave then someone is either not quiet or happy.
If someone is both curious and not generous then someone is quiet and vice versa.
Everyone who is either funny or brave is funny or not brave and vice versa.
Everyone who is both not generous and curious is both not creative and not generous and vice versa.
Everyone who is both not quiet and tall is either curious or generous.
If paul is both not happy and not rich then paul is quiet.
If susan is rich then lucy is either not quiet or kind and vice versa.
Everyone who is creative is calm and vice versa.
If someone is happy or not curious then mary is either patient or kind and vice versa.
Everyone who is not funny is either rich or old.
Alice is both not rich and not tall.
John is either not tall or happy.
John is not kind.
Someone is not curious.
Paul is happy or not wise. | Lucy is generous. | neutral | (![X]:((~kind(X)|quiet(X))<=>~old(X)))&
((?[X]:((~humble(X)&creative(X))))=>((~calm(fred)&~rich(fred))))&
(((generous(paul)<~>patient(paul)))=>(strong(alice)))&
(![X]:((~creative(X)<~>~generous(X))=>~quiet(X)))&
(![X]:((~old(X)&old(X))=>~quiet(X)))&
((?[X]:((calm(X)&~brave(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>brave(X))<=>(funny(X)|~brave(X))))&
(![X]:((~generous(X)&curious(X))<=>(~creative(X)&~generous(X))))&
(![X]:((~quiet(X)&tall(X))=>(curious(X)<~>generous(X))))&
(((~happy(paul)&~rich(paul)))=>(quiet(paul)))&
((rich(susan))<=>((~quiet(lucy)<~>kind(lucy))))&
(![X]:(creative(X)<=>calm(X)))&
((?[X]:((happy(X)|~curious(X))))<=>((patient(mary)<~>kind(mary))))&
(![X]:(~funny(X)=>(rich(X)<~>old(X))))&
((~rich(alice)&~tall(alice)))&
((~tall(john)<~>happy(john)))&
(~kind(john))&
(?[X]:(~curious(X)))&
((happy(paul)|~wise(paul))) | generous(lucy) | [] | null | 0 |
If someone is not tall or quiet then someone is either not funny or not happy and vice versa.
Everyone who is either generous or not humble is not creative and vice versa.
If someone is wise then paul is not quiet or not creative and vice versa.
Everyone who is both curious and not strong is either not brave or calm and vice versa.
If someone is both strong and creative then someone is not patient and vice versa.
Everyone who is not creative or not strong is old.
Everyone who is either not patient or not strong is strong and vice versa.
Everyone who is humble or not calm is old and vice versa.
If someone is either humble or quiet then someone is not humble.
If alice is either not patient or quiet then someone is tall.
Everyone who is either humble or generous is both funny and kind and vice versa.
Everyone who is either wise or not kind is both strong and not brave and vice versa.
Everyone who is tall is rich or quiet and vice versa.
If someone is kind or not rich then someone is strong or creative and vice versa.
If susan is curious then someone is both not generous and not tall.
Everyone who is both humble and not quiet is either not wise or not tall.
Mary is either kind or not wise.
Someone is both not calm and not rich.
Mary is either not creative or generous.
Someone is both brave and not happy.
Susan is both brave and not tall.
Someone is kind or not generous.
Someone is either not kind or not creative.
Someone is not kind. | Mary is humble. | contradiction | ((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((generous(X)<~>~humble(X))<=>~creative(X)))&
((?[X]:(wise(X)))<=>((~quiet(paul)|~creative(paul))))&
(![X]:((curious(X)&~strong(X))<=>(~brave(X)<~>calm(X))))&
((?[X]:((strong(X)&creative(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~creative(X)|~strong(X))=>old(X)))&
(![X]:((~patient(X)<~>~strong(X))<=>strong(X)))&
(![X]:((humble(X)|~calm(X))<=>old(X)))&
((?[X]:((humble(X)<~>quiet(X))))=>(?[X]:(~humble(X))))&
(((~patient(alice)<~>quiet(alice)))=>(?[X]:(tall(X))))&
(![X]:((humble(X)<~>generous(X))<=>(funny(X)&kind(X))))&
(![X]:((wise(X)<~>~kind(X))<=>(strong(X)&~brave(X))))&
(![X]:(tall(X)<=>(rich(X)|quiet(X))))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:((strong(X)|creative(X)))))&
((curious(susan))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((humble(X)&~quiet(X))=>(~wise(X)<~>~tall(X))))&
((kind(mary)<~>~wise(mary)))&
(?[X]:((~calm(X)&~rich(X))))&
((~creative(mary)<~>generous(mary)))&
(?[X]:((brave(X)&~happy(X))))&
((brave(susan)&~tall(susan)))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(?[X]:(~kind(X))) | humble(mary) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6992386176494304067390794
% SZS output start Proof for 6992386176494304067390794
2. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> ~creative(X0)) [input p1]
19. ~creative(mary) <~> generous(mary) [input p18]
25. humble(mary) [input hypothesis]
44. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | creative(X0)) & (~creative(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 2]
82. (~generous(mary) | creative(mary)) & (generous(mary) | ~creative(mary)) [nnf transformation 19]
98. ~creative(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 44]
100. ~humble(X0) | generous(X0) | creative(X0) [cnf transformation 44]
152. generous(mary) | ~creative(mary) [cnf transformation 82]
153. ~generous(mary) | creative(mary) [cnf transformation 82]
162. humble(mary) [cnf transformation 25]
319. 36 <=> creative(mary) [avatar definition]
321. creative(mary) <- (36) [avatar component clause 319]
323. 37 <=> generous(mary) [avatar definition]
324. generous(mary) <- (37) [avatar component clause 323]
326. 36 | ~37 [avatar split clause 153,323,319]
327. ~36 | 37 [avatar split clause 152,323,319]
364. generous(mary) | creative(mary) [resolution 100,162]
368. 36 | 37 [avatar split clause 364,323,319]
370. ~humble(mary) | ~generous(mary) <- (36) [resolution 321,98]
371. ~generous(mary) <- (36) [subsumption resolution 370,162]
372. $false <- (36, 37) [subsumption resolution 371,324]
373. ~36 | ~37 [avatar contradiction clause 372]
374. $false [avatar sat refutation 326,327,368,373]
% SZS output end Proof for 6992386176494304067390794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then susan is not rich.
If lucy is both not calm and patient then susan is not brave or patient.
Everyone who is both not brave and not rich is not curious or not creative and vice versa.
Everyone who is not quiet is not funny or old and vice versa.
Everyone who is both not wise and kind is tall.
Everyone who is both not patient and old is either funny or strong and vice versa.
If john is either not humble or not quiet then alice is either tall or not brave and vice versa.
Everyone who is either kind or not patient is both funny and not wise and vice versa.
If someone is either not tall or not rich then alice is both not tall and not wise and vice versa.
Everyone who is either humble or not kind is either humble or strong.
Everyone who is curious or old is either not rich or not patient and vice versa.
Everyone who is tall is not generous or funny and vice versa.
If fred is curious then someone is creative.
Everyone who is either not quiet or calm is either quiet or not humble.
If someone is brave or not calm then lucy is both not curious and not funny.
Everyone who is both curious and patient is strong or not creative and vice versa.
Someone is either not brave or creative.
Someone is not tall.
Lucy is not rich.
Someone is either brave or not quiet.
Someone is old.
Someone is happy.
Someone is patient or not tall.
Someone is either generous or not brave. | Lucy is patient. | neutral | ((?[X]:(strong(X)))=>(~rich(susan)))&
(((~calm(lucy)&patient(lucy)))=>((~brave(susan)|patient(susan))))&
(![X]:((~brave(X)&~rich(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&kind(X))=>tall(X)))&
(![X]:((~patient(X)&old(X))<=>(funny(X)<~>strong(X))))&
(((~humble(john)<~>~quiet(john)))<=>((tall(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~patient(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~tall(X)<~>~rich(X))))<=>((~tall(alice)&~wise(alice))))&
(![X]:((humble(X)<~>~kind(X))=>(humble(X)<~>strong(X))))&
(![X]:((curious(X)|old(X))<=>(~rich(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(~generous(X)|funny(X))))&
((curious(fred))=>(?[X]:(creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|~creative(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
(?[X]:(~tall(X)))&
(~rich(lucy))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:(old(X)))&
(?[X]:(happy(X)))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((generous(X)<~>~brave(X)))) | patient(lucy) | [] | null | 0 |
Everyone who is both humble and not old is humble or generous and vice versa.
Everyone who is both not strong and not calm is not brave.
Everyone who is both patient and not generous is both tall and not humble and vice versa.
Everyone who is either rich or kind is both not tall and brave and vice versa.
Everyone who is not patient or not kind is brave and vice versa.
If john is both funny and not kind then fred is generous.
Everyone who is both wise and brave is either wise or not calm.
Everyone who is not generous is both tall and not strong.
Everyone who is humble is both not old and happy.
Everyone who is not generous or not tall is either patient or not generous.
If lucy is not quiet then someone is brave and vice versa.
If alice is both curious and strong then susan is kind or funny and vice versa.
Everyone who is not calm is both patient and not patient.
If mary is creative then fred is both not brave and not humble and vice versa.
Everyone who is both not patient and calm is either not strong or not rich and vice versa.
Paul is calm or not funny.
Lucy is either funny or creative. | Alice is wise. | neutral | (![X]:((humble(X)&~old(X))<=>(humble(X)|generous(X))))&
(![X]:((~strong(X)&~calm(X))=>~brave(X)))&
(![X]:((patient(X)&~generous(X))<=>(tall(X)&~humble(X))))&
(![X]:((rich(X)<~>kind(X))<=>(~tall(X)&brave(X))))&
(![X]:((~patient(X)|~kind(X))<=>brave(X)))&
(((funny(john)&~kind(john)))=>(generous(fred)))&
(![X]:((wise(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:(~generous(X)=>(tall(X)&~strong(X))))&
(![X]:(humble(X)=>(~old(X)&happy(X))))&
(![X]:((~generous(X)|~tall(X))=>(patient(X)<~>~generous(X))))&
((~quiet(lucy))<=>(?[X]:(brave(X))))&
(((curious(alice)&strong(alice)))<=>((kind(susan)|funny(susan))))&
(![X]:(~calm(X)=>(patient(X)&~patient(X))))&
((creative(mary))<=>((~brave(fred)&~humble(fred))))&
(![X]:((~patient(X)&calm(X))<=>(~strong(X)<~>~rich(X))))&
((calm(paul)|~funny(paul)))&
((funny(lucy)<~>creative(lucy))) | wise(alice) | [] | null | 0 |
If alice is creative or strong then alice is not generous or kind and vice versa.
Everyone who is both not creative and curious is kind and vice versa.
Everyone who is not happy or wise is both old and not patient and vice versa.
If john is not calm then someone is both not wise and not tall.
If susan is either not happy or not patient then susan is not humble and vice versa.
Everyone who is tall or rich is both rich and not strong and vice versa.
Everyone who is not strong is not curious or not brave and vice versa.
Everyone who is either not funny or old is both tall and patient.
Everyone who is generous is not funny and vice versa.
If someone is not patient then someone is old and vice versa.
Everyone who is both not brave and not kind is either creative or kind and vice versa.
If someone is patient then someone is either not quiet or quiet.
Everyone who is either kind or brave is both brave and curious.
Everyone who is either brave or not old is either not funny or not rich.
Everyone who is both humble and not funny is both not curious and brave and vice versa.
John is humble.
Someone is either not curious or not calm.
Someone is either kind or not wise.
Someone is quiet.
Lucy is both not calm and quiet.
Paul is not humble or not wise.
Someone is old or curious. | John is not generous. | entailment | (((creative(alice)|strong(alice)))<=>((~generous(alice)|kind(alice))))&
(![X]:((~creative(X)&curious(X))<=>kind(X)))&
(![X]:((~happy(X)|wise(X))<=>(old(X)&~patient(X))))&
((~calm(john))=>(?[X]:((~wise(X)&~tall(X)))))&
(((~happy(susan)<~>~patient(susan)))<=>(~humble(susan)))&
(![X]:((tall(X)|rich(X))<=>(rich(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(![X]:(generous(X)<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&curious(X))))&
(![X]:((brave(X)<~>~old(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))<=>(~curious(X)&brave(X))))&
(humble(john))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(quiet(X)))&
((~calm(lucy)&quiet(lucy)))&
((~humble(paul)|~wise(paul)))&
(?[X]:((old(X)|curious(X)))) | ~generous(john) | [
"p1",
"p8",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8425435155977013943288370
% SZS output start Proof for 8425435155977013943288370
2. ! [X0] : ((curious(X0) & ~creative(X0)) <=> kind(X0)) [input p1]
9. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p8]
11. ! [X0] : ((~kind(X0) & ~brave(X0)) <=> (creative(X0) <~> kind(X0))) [input p10]
13. ! [X0] : ((kind(X0) <~> brave(X0)) => (curious(X0) & brave(X0))) [input p12]
15. ! [X0] : ((~funny(X0) & humble(X0)) <=> (brave(X0) & ~curious(X0))) [input p14]
16. humble(john) [input p15]
23. generous(john) [input hypothesis]
29. ! [X0] : ((curious(X0) & brave(X0)) | (kind(X0) <=> brave(X0))) [ennf transformation 13]
33. ! [X0] : (((curious(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | (~curious(X0) | creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((curious(X0) & ~creative(X0)) | ~kind(X0)) & (kind(X0) | ~curious(X0) | creative(X0))) [flattening 33]
45. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 9]
51. ! [X0] : (((~kind(X0) & ~brave(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (kind(X0) | brave(X0)))) [nnf transformation 11]
52. ! [X0] : (((~kind(X0) & ~brave(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | kind(X0) | brave(X0))) [flattening 51]
57. ! [X0] : ((curious(X0) & brave(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 29]
59. ! [X0] : (((~funny(X0) & humble(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 15]
60. ! [X0] : (((~funny(X0) & humble(X0)) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | funny(X0) | ~humble(X0))) [flattening 59]
75. ~curious(X0) | kind(X0) | creative(X0) [cnf transformation 34]
76. ~kind(X0) | ~creative(X0) [cnf transformation 34]
101. ~funny(X0) | ~generous(X0) [cnf transformation 45]
105. kind(X0) | creative(X0) | kind(X0) | brave(X0) [cnf transformation 52]
107. ~brave(X0) | kind(X0) | ~creative(X0) [cnf transformation 52]
110. ~kind(X0) | creative(X0) | ~kind(X0) [cnf transformation 52]
116. curious(X0) | kind(X0) | ~brave(X0) [cnf transformation 57]
122. ~humble(X0) | funny(X0) | brave(X0) [cnf transformation 60]
125. humble(john) [cnf transformation 16]
135. generous(john) [cnf transformation 23]
137. kind(X0) | creative(X0) | brave(X0) [duplicate literal removal 105]
138. ~kind(X0) | creative(X0) [duplicate literal removal 110]
206. ~kind(X0) [subsumption resolution 138,76]
207. ~brave(X0) | ~creative(X0) [subsumption resolution 107,206]
208. brave(X0) | creative(X0) [subsumption resolution 137,206]
209. ~brave(X0) | curious(X0) [subsumption resolution 116,206]
245. curious(X0) | creative(X0) [resolution 209,208]
250. creative(X0) | kind(X0) | creative(X0) [resolution 245,75]
251. creative(X0) | kind(X0) [duplicate literal removal 250]
252. creative(X0) [subsumption resolution 251,206]
272. 22 <=> funny(john) [avatar definition]
274. funny(john) <- (22) [avatar component clause 272]
286. funny(john) | brave(john) [resolution 122,125]
289. 25 <=> brave(john) [avatar definition]
291. brave(john) <- (25) [avatar component clause 289]
292. 25 | 22 [avatar split clause 286,272,289]
300. ~generous(john) <- (22) [resolution 274,101]
315. $false <- (22) [subsumption resolution 300,135]
316. ~22 [avatar contradiction clause 315]
385. ~creative(john) <- (25) [resolution 291,207]
390. $false <- (25) [subsumption resolution 385,252]
391. ~25 [avatar contradiction clause 390]
392. $false [avatar sat refutation 292,316,391]
% SZS output end Proof for 8425435155977013943288370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is not funny or not generous.
Everyone who is either calm or funny is both funny and not quiet and vice versa.
Everyone who is both not generous and not rich is either not generous or humble and vice versa.
Everyone who is both funny and strong is both happy and not curious.
If lucy is both happy and generous then lucy is kind or not wise and vice versa.
If susan is both wise and not old then someone is not tall or generous.
Everyone who is either not rich or creative is quiet or strong and vice versa.
If alice is brave then someone is not generous.
If john is either not generous or not brave then someone is not quiet and vice versa.
Everyone who is kind or not creative is not creative.
If someone is both calm and rich then alice is humble.
If susan is not calm or not creative then someone is not kind or not funny.
If someone is not wise then someone is brave.
Everyone who is calm or generous is both brave and calm and vice versa.
If john is either not quiet or not happy then lucy is either creative or funny and vice versa.
If someone is not funny then john is both not wise and not strong and vice versa.
Someone is either calm or quiet.
Someone is either happy or curious.
Someone is both brave and not old.
Lucy is either strong or not humble.
Someone is both not generous and brave.
Mary is not strong or not kind.
Someone is not brave. | Lucy is wise. | neutral | (![X]:(wise(X)=>(~funny(X)|~generous(X))))&
(![X]:((calm(X)<~>funny(X))<=>(funny(X)&~quiet(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((funny(X)&strong(X))=>(happy(X)&~curious(X))))&
(((happy(lucy)&generous(lucy)))<=>((kind(lucy)|~wise(lucy))))&
(((wise(susan)&~old(susan)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(quiet(X)|strong(X))))&
((brave(alice))=>(?[X]:(~generous(X))))&
(((~generous(john)<~>~brave(john)))<=>(?[X]:(~quiet(X))))&
(![X]:((kind(X)|~creative(X))=>~creative(X)))&
((?[X]:((calm(X)&rich(X))))=>(humble(alice)))&
(((~calm(susan)|~creative(susan)))=>(?[X]:((~kind(X)|~funny(X)))))&
((?[X]:(~wise(X)))=>(?[X]:(brave(X))))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&calm(X))))&
(((~quiet(john)<~>~happy(john)))<=>((creative(lucy)<~>funny(lucy))))&
((?[X]:(~funny(X)))<=>((~wise(john)&~strong(john))))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((brave(X)&~old(X))))&
((strong(lucy)<~>~humble(lucy)))&
(?[X]:((~generous(X)&brave(X))))&
((~strong(mary)|~kind(mary)))&
(?[X]:(~brave(X))) | wise(lucy) | [] | null | 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. | Paul is old. | 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))) | old(paul) | [] | null | 0 |
If someone is creative then someone is not tall or not generous and vice versa. Everyone who is generous is both funny and rich. Everyone who is either humble or old is both generous and funny. Everyone who is humble is calm and vice versa. Everyone who is humble is generous and vice versa. If someone is either happy or not humble then someone is either patient or not creative. Everyone who is both not strong and not creative is not brave or tall and vice versa. Everyone who is calm or not quiet is generous or patient and vice versa. Everyone who is not strong is either not kind or funny and vice versa. Everyone who is not happy or brave is either not brave or not creative and vice versa. If alice is old then paul is both not happy and generous. Everyone who is either humble or strong is both curious and not creative. Everyone who is both not strong and not creative is either brave or not calm and vice versa. Everyone who is both not old and tall is patient. Everyone who is old or tall is both not strong and happy. Susan is either not creative or not old. Someone is quiet or not brave. Fred is not wise or not old. Someone is not calm or old. Someone is either patient or rich. Susan is rich or not generous. | Alice is strong. | contradiction | ((?[X]:(creative(X)))<=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:(generous(X)=>(funny(X)&rich(X))))&
(![X]:((humble(X)<~>old(X))=>(generous(X)&funny(X))))&
(![X]:(humble(X)<=>calm(X)))&
(![X]:(humble(X)<=>generous(X)))&
((?[X]:((happy(X)<~>~humble(X))))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~brave(X)|tall(X))))&
(![X]:((calm(X)|~quiet(X))<=>(generous(X)|patient(X))))&
(![X]:(~strong(X)<=>(~kind(X)<~>funny(X))))&
(![X]:((~happy(X)|brave(X))<=>(~brave(X)<~>~creative(X))))&
((old(alice))=>((~happy(paul)&generous(paul))))&
(![X]:((humble(X)<~>strong(X))=>(curious(X)&~creative(X))))&
(![X]:((~strong(X)&~creative(X))<=>(brave(X)<~>~calm(X))))&
(![X]:((~old(X)&tall(X))=>patient(X)))&
(![X]:((old(X)|tall(X))=>(~strong(X)&happy(X))))&
((~creative(susan)<~>~old(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
((~wise(fred)|~old(fred)))&
(?[X]:((~calm(X)|old(X))))&
(?[X]:((patient(X)<~>rich(X))))&
((rich(susan)|~generous(susan))) | strong(alice) | [
"p0",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1265267439543868361334189
% SZS output start Proof for 1265267439543868361334189
1. ? [X0] : creative(X0) <=> ? [X0] : (~generous(X0) | ~tall(X0)) [input p0]
7. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (tall(X0) | ~brave(X0))) [input p6]
10. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p9]
22. strong(alice) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : (~generous(X1) | ~tall(X1)) [rectify 1]
35. (? [X0] : creative(X0) | ! [X1] : (generous(X1) & tall(X1))) & (? [X1] : (~generous(X1) | ~tall(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 23]
36. (? [X0] : creative(X0) | ! [X1] : (generous(X1) & tall(X1))) & (? [X2] : (~generous(X2) | ~tall(X2)) | ! [X3] : ~creative(X3)) [rectify 35]
37. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
38. ? [X2] : (~generous(X2) | ~tall(X2)) => (~generous(sK1) | ~tall(sK1)) [choice axiom]
39. (creative(sK0) | ! [X1] : (generous(X1) & tall(X1))) & ((~generous(sK1) | ~tall(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 36,38,37]
47. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | creative(X0) | strong(X0))) [flattening 47]
52. ! [X0] : (((brave(X0) | ~happy(X0)) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((brave(X0) | ~happy(X0) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~brave(X0) & happy(X0)))) [flattening 52]
66. creative(sK0) | tall(X1) [cnf transformation 39]
84. ~strong(X0) | ~tall(X0) [cnf transformation 48]
85. ~creative(X0) | brave(X0) [cnf transformation 48]
96. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 53]
123. strong(alice) [cnf transformation 22]
124. ~creative(X0) | ~brave(X0) [duplicate literal removal 96]
130. 2 <=> creative(sK0) [avatar definition]
132. creative(sK0) <- (2) [avatar component clause 130]
135. 3 <=> ! [X1] : tall(X1) [avatar definition]
136. tall(X1) <- (3) [avatar component clause 135]
137. 3 | 2 [avatar split clause 66,130,135]
139. 4 <=> ! [X3] : ~creative(X3) [avatar definition]
140. ~creative(X3) <- (4) [avatar component clause 139]
169. ~creative(X0) [subsumption resolution 124,85]
170. 4 [avatar split clause 169,139]
228. $false <- (2, 4) [subsumption resolution 132,140]
229. ~2 | ~4 [avatar contradiction clause 228]
240. ~tall(alice) [resolution 84,123]
241. $false <- (3) [subsumption resolution 240,136]
242. ~3 [avatar contradiction clause 241]
243. $false [avatar sat refutation 137,170,229,242]
% SZS output end Proof for 1265267439543868361334189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not kind then someone is both humble and tall.
Everyone who is both not brave and not humble is not wise or not humble and vice versa.
Everyone who is not rich or not brave is humble and vice versa.
If someone is old or tall then alice is generous or not rich.
If alice is not brave or not quiet then someone is either not brave or quiet and vice versa.
Everyone who is both happy and not tall is either not patient or not funny and vice versa.
If someone is either old or quiet then mary is either generous or not generous.
Everyone who is both not generous and calm is either not tall or calm and vice versa.
Everyone who is either brave or old is happy.
Everyone who is either creative or not quiet is not brave or brave.
Everyone who is both calm and not creative is strong and vice versa.
Everyone who is not wise is not old or funny.
Everyone who is both not humble and generous is either not brave or rich.
Everyone who is both strong and old is either not quiet or not old and vice versa.
If mary is either brave or not brave then someone is kind.
If alice is not old or brave then mary is either not rich or not brave.
Someone is not rich or not wise.
Someone is not brave or funny.
Paul is either not happy or happy.
John is not funny or old.
Susan is either not creative or not kind.
Mary is both not brave and creative.
John is not old.
Someone is not old or old. | Paul is not wise. | contradiction | ((?[X]:((strong(X)&~kind(X))))=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((~brave(X)&~humble(X))<=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|~brave(X))<=>humble(X)))&
((?[X]:((old(X)|tall(X))))=>((generous(alice)|~rich(alice))))&
(((~brave(alice)|~quiet(alice)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:((happy(X)&~tall(X))<=>(~patient(X)<~>~funny(X))))&
((?[X]:((old(X)<~>quiet(X))))=>((generous(mary)<~>~generous(mary))))&
(![X]:((~generous(X)&calm(X))<=>(~tall(X)<~>calm(X))))&
(![X]:((brave(X)<~>old(X))=>happy(X)))&
(![X]:((creative(X)<~>~quiet(X))=>(~brave(X)|brave(X))))&
(![X]:((calm(X)&~creative(X))<=>strong(X)))&
(![X]:(~wise(X)=>(~old(X)|funny(X))))&
(![X]:((~humble(X)&generous(X))=>(~brave(X)<~>rich(X))))&
(![X]:((strong(X)&old(X))<=>(~quiet(X)<~>~old(X))))&
(((brave(mary)<~>~brave(mary)))=>(?[X]:(kind(X))))&
(((~old(alice)|brave(alice)))=>((~rich(mary)<~>~brave(mary))))&
(?[X]:((~rich(X)|~wise(X))))&
(?[X]:((~brave(X)|funny(X))))&
((~happy(paul)<~>happy(paul)))&
((~funny(john)|old(john)))&
((~creative(susan)<~>~kind(susan)))&
((~brave(mary)&creative(mary)))&
(~old(john))&
(?[X]:((~old(X)|old(X)))) | ~wise(paul) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6050306027561765910717463
% SZS output start Proof for 6050306027561765910717463
2. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (~humble(X0) | ~wise(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> humble(X0)) [input p2]
25. ~wise(paul) [input hypothesis]
43. ! [X0] : (((~humble(X0) & ~brave(X0)) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 2]
44. ! [X0] : (((~humble(X0) & ~brave(X0)) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | humble(X0) | brave(X0))) [flattening 43]
45. ! [X0] : (((~brave(X0) | ~rich(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) & rich(X0)))) [nnf transformation 3]
46. ! [X0] : ((~brave(X0) | ~rich(X0) | ~humble(X0)) & (humble(X0) | (brave(X0) & rich(X0)))) [flattening 45]
80. ~brave(X0) | humble(X0) [cnf transformation 44]
81. ~humble(X0) | wise(X0) [cnf transformation 44]
84. humble(X0) | brave(X0) [cnf transformation 46]
143. ~wise(paul) [cnf transformation 25]
164. humble(X0) [subsumption resolution 84,80]
270. wise(X0) [resolution 81,164]
271. $false [resolution 270,143]
% SZS output end Proof for 6050306027561765910717463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not funny is kind.
If someone is calm then paul is both not brave and brave and vice versa.
If mary is both not old and brave then someone is either patient or not rich and vice versa.
Everyone who is not brave or not quiet is brave and vice versa.
Everyone who is either happy or strong is not tall and vice versa.
Everyone who is both calm and generous is both happy and not wise and vice versa.
Everyone who is not humble is curious or rich and vice versa.
If someone is either humble or not calm then paul is either generous or not kind and vice versa.
If alice is either not quiet or not patient then someone is both not strong and old and vice versa.
Everyone who is not kind or not calm is both creative and wise and vice versa.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
Someone is either quiet or not happy.
John is humble or rich.
Susan is both not rich and creative.
Someone is both not quiet and humble.
Alice is rich. | Mary is rich. | neutral | (![X]:((~strong(X)&~funny(X))=>kind(X)))&
((?[X]:(calm(X)))<=>((~brave(paul)&brave(paul))))&
(((~old(mary)&brave(mary)))<=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~brave(X)|~quiet(X))<=>brave(X)))&
(![X]:((happy(X)<~>strong(X))<=>~tall(X)))&
(![X]:((calm(X)&generous(X))<=>(happy(X)&~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)|rich(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~quiet(alice)<~>~patient(alice)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
((humble(john)|rich(john)))&
((~rich(susan)&creative(susan)))&
(?[X]:((~quiet(X)&humble(X))))&
(rich(alice)) | rich(mary) | [] | null | 0 |
Everyone who is either not patient or not wise is not creative and vice versa. Everyone who is either patient or not patient is either not tall or not brave. If someone is tall then fred is either not tall or brave. Everyone who is both not strong and funny is either not kind or not wise and vice versa. If mary is not funny or brave then paul is not curious and vice versa. Everyone who is kind is not patient. Everyone who is brave or not generous is both not humble and kind. If lucy is creative then someone is both not creative and not quiet and vice versa. If someone is both not kind and tall then paul is both not patient and not happy. If lucy is brave then someone is not generous and vice versa. Everyone who is not happy or generous is not strong. If lucy is not patient or quiet then alice is rich or humble and vice versa. Everyone who is not happy or curious is patient and vice versa. Everyone who is not curious is happy and vice versa. If john is happy then someone is both not calm and not quiet and vice versa. Fred is quiet or not quiet. Someone is either not happy or kind. Someone is kind. Susan is both brave and not tall. Someone is not quiet. Fred is not humble or strong. Someone is rich or not tall. | John is not curious. | entailment | (![X]:((~patient(X)<~>~wise(X))<=>~creative(X)))&
(![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~brave(X))))&
((?[X]:(tall(X)))=>((~tall(fred)<~>brave(fred))))&
(![X]:((~strong(X)&funny(X))<=>(~kind(X)<~>~wise(X))))&
(((~funny(mary)|brave(mary)))<=>(~curious(paul)))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((brave(X)|~generous(X))=>(~humble(X)&kind(X))))&
((creative(lucy))<=>(?[X]:((~creative(X)&~quiet(X)))))&
((?[X]:((~kind(X)&tall(X))))=>((~patient(paul)&~happy(paul))))&
((brave(lucy))<=>(?[X]:(~generous(X))))&
(![X]:((~happy(X)|generous(X))=>~strong(X)))&
(((~patient(lucy)|quiet(lucy)))<=>((rich(alice)|humble(alice))))&
(![X]:((~happy(X)|curious(X))<=>patient(X)))&
(![X]:(~curious(X)<=>happy(X)))&
((happy(john))<=>(?[X]:((~calm(X)&~quiet(X)))))&
((quiet(fred)|~quiet(fred)))&
(?[X]:((~happy(X)<~>kind(X))))&
(?[X]:(kind(X)))&
((brave(susan)&~tall(susan)))&
(?[X]:(~quiet(X)))&
((~humble(fred)|strong(fred)))&
(?[X]:((rich(X)|~tall(X)))) | ~curious(john) | [
"p1",
"p2",
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7852446116710661896153707
% SZS output start Proof for 7852446116710661896153707
2. ! [X0] : ((patient(X0) <~> ~patient(X0)) => (~tall(X0) <~> ~brave(X0))) [input p1]
3. ? [X0] : tall(X0) => (~tall(fred) <~> brave(fred)) [input p2]
6. ! [X0] : (kind(X0) => ~patient(X0)) [input p5]
7. ! [X0] : ((~generous(X0) | brave(X0)) => (kind(X0) & ~humble(X0))) [input p6]
13. ! [X0] : ((curious(X0) | ~happy(X0)) <=> patient(X0)) [input p12]
23. curious(john) [input hypothesis]
24. ! [X0] : ((~tall(X0) <~> ~brave(X0)) | (patient(X0) <=> ~patient(X0))) [ennf transformation 2]
25. (~tall(fred) <~> brave(fred)) | ! [X0] : ~tall(X0) [ennf transformation 3]
26. ! [X0] : (~patient(X0) | ~kind(X0)) [ennf transformation 6]
27. ! [X0] : ((kind(X0) & ~humble(X0)) | (generous(X0) & ~brave(X0))) [ennf transformation 7]
31. ! [X0] : (((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 24]
32. ((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : ~tall(X0) [nnf transformation 25]
47. ! [X0] : (((curious(X0) | ~happy(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) & happy(X0)))) [nnf transformation 13]
48. ! [X0] : ((curious(X0) | ~happy(X0) | ~patient(X0)) & (patient(X0) | (~curious(X0) & happy(X0)))) [flattening 47]
67. ~brave(X0) | ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 31]
68. ~brave(X0) | ~tall(X0) | patient(X0) | patient(X0) [cnf transformation 31]
69. brave(X0) | tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 31]
70. brave(X0) | tall(X0) | patient(X0) | patient(X0) [cnf transformation 31]
71. brave(fred) | ~tall(fred) | ~tall(X0) [cnf transformation 32]
72. ~brave(fred) | tall(fred) | ~tall(X0) [cnf transformation 32]
82. ~kind(X0) | ~patient(X0) [cnf transformation 26]
85. ~brave(X0) | kind(X0) [cnf transformation 27]
101. ~curious(X0) | patient(X0) [cnf transformation 48]
117. curious(john) [cnf transformation 23]
118. ~brave(X0) | ~tall(X0) | ~patient(X0) [duplicate literal removal 67]
119. ~brave(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 68]
120. brave(X0) | tall(X0) | ~patient(X0) [duplicate literal removal 69]
121. brave(X0) | tall(X0) | patient(X0) [duplicate literal removal 70]
122. brave(X0) | tall(X0) [subsumption resolution 120,121]
123. ~brave(X0) | ~tall(X0) [subsumption resolution 118,119]
124. ~brave(fred) | ~tall(X0) [subsumption resolution 72,123]
126. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
127. ~tall(X0) <- (1) [avatar component clause 126]
129. 2 <=> brave(fred) [avatar definition]
132. 1 | ~2 [avatar split clause 124,129,126]
133. brave(fred) | ~tall(X0) [subsumption resolution 71,122]
134. 1 | 2 [avatar split clause 133,129,126]
277. patient(john) [resolution 101,117]
288. tall(X0) | kind(X0) [resolution 122,85]
292. kind(X0) <- (1) [subsumption resolution 288,127]
320. ~patient(X0) <- (1) [resolution 292,82]
330. $false <- (1) [subsumption resolution 277,320]
331. ~1 [avatar contradiction clause 330]
332. $false [avatar sat refutation 132,134,331]
% SZS output end Proof for 7852446116710661896153707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is not humble and vice versa.
If someone is strong then someone is both not old and not wise.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is either tall or not strong is not humble and vice versa.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If someone is not brave then someone is both happy and rich.
Everyone who is kind is not strong or rich.
Someone is both not quiet and not creative.
Someone is both not kind and not brave.
Fred is both old and strong.
Mary is rich or old.
Susan is not tall or not calm. | Fred is not tall. | contradiction | (![X]:((~quiet(X)|humble(X))<=>~humble(X)))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((tall(X)<~>~strong(X))<=>~humble(X)))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:((~kind(X)&~brave(X))))&
((old(fred)&strong(fred)))&
((rich(mary)|old(mary)))&
((~tall(susan)|~calm(susan))) | ~tall(fred) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 279149056607242771718015
% SZS output start Proof for 279149056607242771718015
9. ? [X0] : ~tall(X0) => ~rich(alice) [input p8]
11. ! [X0] : ((~rich(X0) | ~brave(X0)) => (rich(X0) & ~curious(X0))) [input p10]
19. ~tall(fred) [input hypothesis]
29. ~rich(alice) | ! [X0] : tall(X0) [ennf transformation 9]
30. ! [X0] : ((rich(X0) & ~curious(X0)) | (rich(X0) & brave(X0))) [ennf transformation 11]
89. ~rich(alice) | tall(X0) [cnf transformation 29]
98. rich(X0) | rich(X0) [cnf transformation 30]
108. ~tall(fred) [cnf transformation 19]
109. rich(X0) [duplicate literal removal 98]
179. 15 <=> ! [X0] : tall(X0) [avatar definition]
180. tall(X0) <- (15) [avatar component clause 179]
182. 16 <=> rich(alice) [avatar definition]
184. ~rich(alice) <- (~16) [avatar component clause 182]
185. 15 | ~16 [avatar split clause 89,182,179]
216. $false <- (~16) [subsumption resolution 184,109]
217. 16 [avatar contradiction clause 216]
218. $false <- (15) [resolution 180,108]
219. ~15 [avatar contradiction clause 218]
220. $false [avatar sat refutation 185,217,219]
% SZS output end Proof for 279149056607242771718015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or strong is both not brave and not rich and vice versa.
If paul is not generous then lucy is either quiet or not calm and vice versa.
Everyone who is funny is either not calm or not rich and vice versa.
Everyone who is generous or patient is both not calm and not generous.
If someone is not calm or not humble then someone is tall and vice versa.
Everyone who is both not tall and not brave is brave or not rich.
If john is both strong and not kind then someone is both not funny and not patient and vice versa.
Everyone who is not creative or not funny is not brave or rich.
Everyone who is calm is not funny.
Everyone who is not tall is creative or funny and vice versa.
Everyone who is both not curious and funny is generous or not calm and vice versa.
If someone is not wise then paul is not generous.
Everyone who is both curious and humble is both brave and not patient.
Everyone who is either not humble or not brave is either not kind or strong and vice versa.
Everyone who is not funny or happy is not brave or quiet and vice versa.
If paul is not patient then someone is either creative or curious and vice versa.
Someone is both not brave and not wise.
Someone is both quiet and not funny.
Someone is either not happy or not quiet.
Someone is both old and not creative.
John is either curious or not happy. | John is curious. | neutral | (![X]:((~brave(X)<~>strong(X))<=>(~brave(X)&~rich(X))))&
((~generous(paul))<=>((quiet(lucy)<~>~calm(lucy))))&
(![X]:(funny(X)<=>(~calm(X)<~>~rich(X))))&
(![X]:((generous(X)|patient(X))=>(~calm(X)&~generous(X))))&
((?[X]:((~calm(X)|~humble(X))))<=>(?[X]:(tall(X))))&
(![X]:((~tall(X)&~brave(X))=>(brave(X)|~rich(X))))&
(((strong(john)&~kind(john)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((~creative(X)|~funny(X))=>(~brave(X)|rich(X))))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:(~tall(X)<=>(creative(X)|funny(X))))&
(![X]:((~curious(X)&funny(X))<=>(generous(X)|~calm(X))))&
((?[X]:(~wise(X)))=>(~generous(paul)))&
(![X]:((curious(X)&humble(X))=>(brave(X)&~patient(X))))&
(![X]:((~humble(X)<~>~brave(X))<=>(~kind(X)<~>strong(X))))&
(![X]:((~funny(X)|happy(X))<=>(~brave(X)|quiet(X))))&
((~patient(paul))<=>(?[X]:((creative(X)<~>curious(X)))))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:((quiet(X)&~funny(X))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:((old(X)&~creative(X))))&
((curious(john)<~>~happy(john))) | curious(john) | [] | null | 0 |
Everyone who is happy or funny is either not calm or rich and vice versa. Everyone who is either not calm or not strong is either not rich or kind and vice versa. Everyone who is either quiet or not humble is either not rich or not patient and vice versa. If someone is either calm or tall then paul is old or not funny and vice versa. Everyone who is wise is either generous or not quiet. If john is not brave then susan is not funny or tall. If lucy is patient or not brave then someone is not funny or not patient. Everyone who is both not wise and not funny is not wise. If someone is either not tall or not kind then someone is either humble or not kind and vice versa. If someone is both not brave and not generous then paul is brave or not strong. Everyone who is strong or creative is either patient or not brave. If paul is either not happy or not rich then paul is either creative or humble and vice versa. Everyone who is either not wise or wise is both not happy and rich and vice versa. If someone is either calm or not funny then john is not humble or not tall and vice versa. Everyone who is not kind or quiet is both strong and patient and vice versa. Everyone who is both funny and calm is tall or not funny. Paul is brave or creative. Lucy is not happy. Fred is patient. Lucy is either not strong or humble. Fred is generous. John is either not patient or not brave. Someone is not rich or patient. John is curious or old. | Fred is rich. | entailment | (![X]:((happy(X)|funny(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~rich(X)<~>kind(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~rich(X)<~>~patient(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>((old(paul)|~funny(paul))))&
(![X]:(wise(X)=>(generous(X)<~>~quiet(X))))&
((~brave(john))=>((~funny(susan)|tall(susan))))&
(((patient(lucy)|~brave(lucy)))=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~wise(X)&~funny(X))=>~wise(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((~brave(X)&~generous(X))))=>((brave(paul)|~strong(paul))))&
(![X]:((strong(X)|creative(X))=>(patient(X)<~>~brave(X))))&
(((~happy(paul)<~>~rich(paul)))<=>((creative(paul)<~>humble(paul))))&
(![X]:((~wise(X)<~>wise(X))<=>(~happy(X)&rich(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~humble(john)|~tall(john))))&
(![X]:((~kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((funny(X)&calm(X))=>(tall(X)|~funny(X))))&
((brave(paul)|creative(paul)))&
(~happy(lucy))&
(patient(fred))&
((~strong(lucy)<~>humble(lucy)))&
(generous(fred))&
((~patient(john)<~>~brave(john)))&
(?[X]:((~rich(X)|patient(X))))&
((curious(john)|old(john))) | rich(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6572296214137838294767170
% SZS output start Proof for 6572296214137838294767170
13. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) & ~happy(X0))) [input p12]
25. ~rich(fred) [input hypothesis]
58. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 58]
128. rich(X0) | wise(X0) | wise(X0) [cnf transformation 59]
129. rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 59]
153. ~rich(fred) [cnf transformation 25]
157. rich(X0) | wise(X0) [duplicate literal removal 128]
158. rich(X0) | ~wise(X0) [duplicate literal removal 129]
290. rich(X0) [subsumption resolution 157,158]
338. $false [subsumption resolution 153,290]
% SZS output end Proof for 6572296214137838294767170
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or wise is either not tall or not wise and vice versa.
Everyone who is creative or funny is brave or kind and vice versa.
Everyone who is both tall and wise is either wise or creative.
Everyone who is both generous and not tall is both kind and happy.
If alice is kind or calm then someone is rich or not strong and vice versa.
If someone is either old or wise then susan is either quiet or old and vice versa.
Everyone who is not kind is not strong and vice versa.
If someone is not generous then lucy is happy or not quiet and vice versa.
If susan is both not old and creative then john is humble or not old and vice versa.
Everyone who is either curious or wise is wise or not patient.
Everyone who is not creative or not humble is both humble and not patient.
If mary is both generous and funny then mary is humble or calm.
Everyone who is tall is either not calm or quiet and vice versa.
If fred is happy or not curious then someone is not old or tall and vice versa.
Everyone who is wise or not brave is both wise and not quiet and vice versa.
Everyone who is either patient or tall is curious or not curious.
Someone is generous.
Alice is either patient or creative.
Someone is either tall or strong.
Fred is generous or not rich.
Lucy is not wise or not happy.
Alice is not brave or humble.
Someone is both funny and not curious. | Alice is not humble. | contradiction | (![X]:((~wise(X)|wise(X))<=>(~tall(X)<~>~wise(X))))&
(![X]:((creative(X)|funny(X))<=>(brave(X)|kind(X))))&
(![X]:((tall(X)&wise(X))=>(wise(X)<~>creative(X))))&
(![X]:((generous(X)&~tall(X))=>(kind(X)&happy(X))))&
(((kind(alice)|calm(alice)))<=>(?[X]:((rich(X)|~strong(X)))))&
((?[X]:((old(X)<~>wise(X))))<=>((quiet(susan)<~>old(susan))))&
(![X]:(~kind(X)<=>~strong(X)))&
((?[X]:(~generous(X)))<=>((happy(lucy)|~quiet(lucy))))&
(((~old(susan)&creative(susan)))<=>((humble(john)|~old(john))))&
(![X]:((curious(X)<~>wise(X))=>(wise(X)|~patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(humble(X)&~patient(X))))&
(((generous(mary)&funny(mary)))=>((humble(mary)|calm(mary))))&
(![X]:(tall(X)<=>(~calm(X)<~>quiet(X))))&
(((happy(fred)|~curious(fred)))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((wise(X)|~brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((patient(X)<~>tall(X))=>(curious(X)|~curious(X))))&
(?[X]:(generous(X)))&
((patient(alice)<~>creative(alice)))&
(?[X]:((tall(X)<~>strong(X))))&
((generous(fred)|~rich(fred)))&
((~wise(lucy)|~happy(lucy)))&
((~brave(alice)|humble(alice)))&
(?[X]:((funny(X)&~curious(X)))) | ~humble(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 828751027521401146654262
% SZS output start Proof for 828751027521401146654262
11. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~patient(X0) & humble(X0))) [input p10]
24. ~humble(alice) [input hypothesis]
31. ! [X0] : ((~patient(X0) & humble(X0)) | (humble(X0) & creative(X0))) [ennf transformation 11]
115. humble(X0) | humble(X0) [cnf transformation 31]
144. ~humble(alice) [cnf transformation 24]
145. humble(X0) [duplicate literal removal 115]
295. $false [subsumption resolution 144,145]
% SZS output end Proof for 828751027521401146654262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is quiet or not old then someone is either not wise or humble and vice versa.
Everyone who is strong is generous or not brave.
Everyone who is funny or brave is not strong.
Everyone who is not wise is not strong or happy.
If someone is either not kind or brave then someone is not strong or not old and vice versa.
Everyone who is both rich and tall is old or strong.
Everyone who is rich or happy is both quiet and not strong.
Everyone who is not quiet is both not tall and not strong and vice versa.
Everyone who is not creative or not quiet is either old or not rich and vice versa.
Everyone who is either humble or not tall is both wise and not patient and vice versa.
If mary is quiet then lucy is not old or not quiet and vice versa.
If john is either tall or rich then someone is strong.
If someone is rich then lucy is both not quiet and not humble and vice versa.
Everyone who is wise is not wise or not patient and vice versa.
Everyone who is not creative is patient or wise and vice versa.
Everyone who is both calm and funny is not curious and vice versa.
Someone is not kind.
Fred is rich or not brave.
Alice is either rich or curious.
Lucy is both wise and not brave.
Susan is either not patient or not brave.
John is not curious or calm.
Someone is not generous. | Alice is patient. | contradiction | (((quiet(susan)|~old(susan)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(strong(X)=>(generous(X)|~brave(X))))&
(![X]:((funny(X)|brave(X))=>~strong(X)))&
(![X]:(~wise(X)=>(~strong(X)|happy(X))))&
((?[X]:((~kind(X)<~>brave(X))))<=>(?[X]:((~strong(X)|~old(X)))))&
(![X]:((rich(X)&tall(X))=>(old(X)|strong(X))))&
(![X]:((rich(X)|happy(X))=>(quiet(X)&~strong(X))))&
(![X]:(~quiet(X)<=>(~tall(X)&~strong(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(old(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(wise(X)&~patient(X))))&
((quiet(mary))<=>((~old(lucy)|~quiet(lucy))))&
(((tall(john)<~>rich(john)))=>(?[X]:(strong(X))))&
((?[X]:(rich(X)))<=>((~quiet(lucy)&~humble(lucy))))&
(![X]:(wise(X)<=>(~wise(X)|~patient(X))))&
(![X]:(~creative(X)<=>(patient(X)|wise(X))))&
(![X]:((calm(X)&funny(X))<=>~curious(X)))&
(?[X]:(~kind(X)))&
((rich(fred)|~brave(fred)))&
((rich(alice)<~>curious(alice)))&
((wise(lucy)&~brave(lucy)))&
((~patient(susan)<~>~brave(susan)))&
((~curious(john)|calm(john)))&
(?[X]:(~generous(X))) | patient(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5503421223100969801420962
% SZS output start Proof for 5503421223100969801420962
14. ! [X0] : (wise(X0) <=> (~patient(X0) | ~wise(X0))) [input p13]
24. patient(alice) [input hypothesis]
61. ! [X0] : ((wise(X0) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | ~wise(X0))) [flattening 61]
117. ~patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 62]
118. wise(X0) | wise(X0) [cnf transformation 62]
136. patient(alice) [cnf transformation 24]
137. ~patient(X0) | ~wise(X0) [duplicate literal removal 117]
138. wise(X0) [duplicate literal removal 118]
247. ~patient(X0) [subsumption resolution 137,138]
270. $false [subsumption resolution 136,247]
% SZS output end Proof for 5503421223100969801420962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not rich then lucy is not generous or happy.
Everyone who is both funny and creative is either brave or happy.
If john is not old or not calm then lucy is either not creative or kind.
Everyone who is not kind or not strong is either not brave or funny and vice versa.
Everyone who is either quiet or not strong is curious and vice versa.
Everyone who is quiet is either not quiet or calm and vice versa.
Everyone who is both rich and not humble is both not funny and not strong and vice versa.
Everyone who is either not brave or not patient is strong or not brave.
Everyone who is not rich or calm is not patient.
Everyone who is humble is funny or not old.
If someone is calm then someone is either not creative or curious and vice versa.
Everyone who is either not tall or not rich is not kind.
If someone is not kind or not creative then someone is not quiet.
If someone is both tall and not generous then susan is both wise and not generous.
Everyone who is creative is both not humble and calm.
Everyone who is happy or not strong is both creative and not rich and vice versa.
Someone is either not brave or strong.
Someone is curious or not generous.
Someone is either not brave or funny.
Someone is either not brave or not wise.
Alice is both old and wise.
John is either creative or wise. | John is not strong. | contradiction | ((?[X]:((~kind(X)|~rich(X))))=>((~generous(lucy)|happy(lucy))))&
(![X]:((funny(X)&creative(X))=>(brave(X)<~>happy(X))))&
(((~old(john)|~calm(john)))=>((~creative(lucy)<~>kind(lucy))))&
(![X]:((~kind(X)|~strong(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~strong(X))<=>curious(X)))&
(![X]:(quiet(X)<=>(~quiet(X)<~>calm(X))))&
(![X]:((rich(X)&~humble(X))<=>(~funny(X)&~strong(X))))&
(![X]:((~brave(X)<~>~patient(X))=>(strong(X)|~brave(X))))&
(![X]:((~rich(X)|calm(X))=>~patient(X)))&
(![X]:(humble(X)=>(funny(X)|~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((~tall(X)<~>~rich(X))=>~kind(X)))&
((?[X]:((~kind(X)|~creative(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((tall(X)&~generous(X))))=>((wise(susan)&~generous(susan))))&
(![X]:(creative(X)=>(~humble(X)&calm(X))))&
(![X]:((happy(X)|~strong(X))<=>(creative(X)&~rich(X))))&
(?[X]:((~brave(X)<~>strong(X))))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
((old(alice)&wise(alice)))&
((creative(john)<~>wise(john))) | ~strong(john) | [
"p3",
"p5",
"p6",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8311180217198286697134601
% SZS output start Proof for 8311180217198286697134601
4. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (~brave(X0) <~> funny(X0))) [input p3]
6. ! [X0] : (quiet(X0) <=> (~quiet(X0) <~> calm(X0))) [input p5]
7. ! [X0] : ((~humble(X0) & rich(X0)) <=> (~strong(X0) & ~funny(X0))) [input p6]
8. ! [X0] : ((~brave(X0) <~> ~patient(X0)) => (~brave(X0) | strong(X0))) [input p7]
9. ! [X0] : ((calm(X0) | ~rich(X0)) => ~patient(X0)) [input p8]
16. ! [X0] : ((~strong(X0) | happy(X0)) <=> (~rich(X0) & creative(X0))) [input p15]
23. ~strong(john) [input hypothesis]
31. ! [X0] : ((~brave(X0) | strong(X0)) | (~brave(X0) <=> ~patient(X0))) [ennf transformation 8]
32. ! [X0] : (~brave(X0) | strong(X0) | (~brave(X0) <=> ~patient(X0))) [flattening 31]
33. ! [X0] : (~patient(X0) | (~calm(X0) & rich(X0))) [ennf transformation 9]
42. ! [X0] : (((~strong(X0) | ~kind(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (strong(X0) & kind(X0)))) [nnf transformation 4]
43. ! [X0] : ((~strong(X0) | ~kind(X0) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (strong(X0) & kind(X0)))) [flattening 42]
45. ! [X0] : ((quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | ~quiet(X0))) [nnf transformation 6]
46. ! [X0] : (((~humble(X0) & rich(X0)) | (strong(X0) | funny(X0))) & ((~strong(X0) & ~funny(X0)) | (humble(X0) | ~rich(X0)))) [nnf transformation 7]
47. ! [X0] : (((~humble(X0) & rich(X0)) | strong(X0) | funny(X0)) & ((~strong(X0) & ~funny(X0)) | humble(X0) | ~rich(X0))) [flattening 46]
48. ! [X0] : (~brave(X0) | strong(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) [nnf transformation 32]
58. ! [X0] : (((~strong(X0) | happy(X0)) | (rich(X0) | ~creative(X0))) & ((~rich(X0) & creative(X0)) | (strong(X0) & ~happy(X0)))) [nnf transformation 16]
59. ! [X0] : ((~strong(X0) | happy(X0) | rich(X0) | ~creative(X0)) & ((~rich(X0) & creative(X0)) | (strong(X0) & ~happy(X0)))) [flattening 58]
83. ~funny(X0) | brave(X0) | strong(X0) [cnf transformation 43]
90. calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 45]
92. quiet(X0) | calm(X0) | quiet(X0) [cnf transformation 45]
96. strong(X0) | rich(X0) | funny(X0) [cnf transformation 47]
99. ~brave(X0) | strong(X0) | ~brave(X0) | patient(X0) [cnf transformation 48]
101. ~patient(X0) | ~calm(X0) [cnf transformation 33]
118. ~rich(X0) | strong(X0) [cnf transformation 59]
131. ~strong(john) [cnf transformation 23]
132. ~brave(X0) | strong(X0) | patient(X0) [duplicate literal removal 99]
133. calm(X0) | ~quiet(X0) [duplicate literal removal 90]
134. quiet(X0) | calm(X0) [duplicate literal removal 92]
171. calm(X0) [subsumption resolution 133,134]
172. ~patient(X0) [subsumption resolution 101,171]
293. rich(john) | funny(john) [resolution 96,131]
297. 30 <=> funny(john) [avatar definition]
299. funny(john) <- (30) [avatar component clause 297]
301. 31 <=> rich(john) [avatar definition]
303. rich(john) <- (31) [avatar component clause 301]
304. 30 | 31 [avatar split clause 293,301,297]
340. brave(john) | strong(john) <- (30) [resolution 299,83]
347. brave(john) <- (30) [subsumption resolution 340,131]
396. strong(john) | patient(john) <- (30) [resolution 347,132]
401. patient(john) <- (30) [subsumption resolution 396,131]
402. $false <- (30) [subsumption resolution 401,172]
403. ~30 [avatar contradiction clause 402]
429. strong(john) <- (31) [resolution 303,118]
439. $false <- (31) [subsumption resolution 429,131]
440. ~31 [avatar contradiction clause 439]
441. $false [avatar sat refutation 304,403,440]
% SZS output end Proof for 8311180217198286697134601
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is brave or wise.
Everyone who is both curious and happy is funny.
Everyone who is either creative or not funny is either not generous or not calm.
Everyone who is not creative is humble and vice versa.
Everyone who is not creative is rich or funny and vice versa.
Everyone who is not humble or not funny is both tall and not funny and vice versa.
Everyone who is either not generous or humble is both not kind and not tall and vice versa.
If someone is kind or not creative then fred is both humble and not rich.
Everyone who is wise is generous or not calm and vice versa.
If someone is not kind or strong then susan is not rich.
If lucy is both not calm and patient then susan is not brave or patient.
Everyone who is both not brave and not rich is not curious or not creative and vice versa.
Everyone who is not quiet is not funny or old and vice versa.
Everyone who is both not wise and kind is tall.
Everyone who is both not patient and old is either funny or strong and vice versa.
If john is either not humble or not quiet then alice is either tall or not brave and vice versa.
Someone is quiet.
Mary is either creative or not kind.
Someone is calm.
Someone is not strong or not rich.
John is not generous.
Someone is kind or not calm.
Lucy is either funny or not strong. | Fred is not brave. | entailment | (![X]:(~quiet(X)=>(brave(X)|wise(X))))&
(![X]:((curious(X)&happy(X))=>funny(X)))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:(~creative(X)<=>(rich(X)|funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(tall(X)&~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((kind(X)|~creative(X))))=>((humble(fred)&~rich(fred))))&
(![X]:(wise(X)<=>(generous(X)|~calm(X))))&
((?[X]:((~kind(X)|strong(X))))=>(~rich(susan)))&
(((~calm(lucy)&patient(lucy)))=>((~brave(susan)|patient(susan))))&
(![X]:((~brave(X)&~rich(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&kind(X))=>tall(X)))&
(![X]:((~patient(X)&old(X))<=>(funny(X)<~>strong(X))))&
(((~humble(john)<~>~quiet(john)))<=>((tall(alice)<~>~brave(alice))))&
(?[X]:(quiet(X)))&
((creative(mary)<~>~kind(mary)))&
(?[X]:(calm(X)))&
(?[X]:((~strong(X)|~rich(X))))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X))))&
((funny(lucy)<~>~strong(lucy))) | ~brave(fred) | [
"p3",
"p7",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6621077521484564037421798
% SZS output start Proof for 6621077521484564037421798
4. ! [X0] : (~creative(X0) <=> humble(X0)) [input p3]
8. ? [X0] : (~creative(X0) | kind(X0)) => (~rich(fred) & humble(fred)) [input p7]
12. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> (~creative(X0) | ~curious(X0))) [input p11]
18. creative(mary) <~> ~kind(mary) [input p17]
24. brave(fred) [input hypothesis]
30. (~rich(fred) & humble(fred)) | ! [X0] : (creative(X0) & ~kind(X0)) [ennf transformation 8]
39. ! [X0] : ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))) [nnf transformation 4]
46. ! [X0] : (((~rich(X0) & ~brave(X0)) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | (rich(X0) | brave(X0)))) [nnf transformation 12]
47. ! [X0] : (((~rich(X0) & ~brave(X0)) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | rich(X0) | brave(X0))) [flattening 46]
55. (kind(mary) | ~creative(mary)) & (~kind(mary) | creative(mary)) [nnf transformation 18]
69. ~humble(X0) | ~creative(X0) [cnf transformation 39]
84. humble(fred) | ~kind(X0) [cnf transformation 30]
85. humble(fred) | creative(X0) [cnf transformation 30]
94. ~brave(X0) | creative(X0) [cnf transformation 47]
117. kind(mary) | ~creative(mary) [cnf transformation 55]
124. brave(fred) [cnf transformation 24]
128. 1 <=> ! [X0] : creative(X0) [avatar definition]
129. creative(X0) <- (1) [avatar component clause 128]
136. 3 <=> ! [X0] : ~kind(X0) [avatar definition]
137. ~kind(X0) <- (3) [avatar component clause 136]
140. 4 <=> humble(fred) [avatar definition]
142. humble(fred) <- (4) [avatar component clause 140]
143. 1 | 4 [avatar split clause 85,140,128]
144. 3 | 4 [avatar split clause 84,140,136]
201. 16 <=> creative(mary) [avatar definition]
203. ~creative(mary) <- (~16) [avatar component clause 201]
205. 17 <=> kind(mary) [avatar definition]
207. kind(mary) <- (17) [avatar component clause 205]
208. ~16 | 17 [avatar split clause 117,205,201]
230. ~creative(fred) <- (4) [resolution 69,142]
239. creative(fred) [resolution 94,124]
241. $false <- (4) [subsumption resolution 239,230]
242. ~4 [avatar contradiction clause 241]
246. $false <- (1, ~16) [resolution 129,203]
247. ~1 | 16 [avatar contradiction clause 246]
248. $false <- (3, 17) [subsumption resolution 207,137]
249. ~3 | ~17 [avatar contradiction clause 248]
250. $false [avatar sat refutation 143,144,208,242,247,249]
% SZS output end Proof for 6621077521484564037421798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and not funny then fred is happy and vice versa.
Everyone who is either not patient or quiet is both not brave and not tall and vice versa.
Everyone who is either not curious or humble is both not calm and not funny and vice versa.
If someone is either not creative or kind then john is patient or funny.
Everyone who is not humble is patient.
If someone is old then someone is either not happy or rich and vice versa.
Everyone who is not tall is not creative or tall.
If someone is both not curious and not funny then someone is kind or not curious and vice versa.
If alice is not tall or not strong then susan is both not generous and strong and vice versa.
Everyone who is either not patient or brave is humble or not strong and vice versa.
If someone is funny then someone is both not patient and not humble.
If alice is either rich or not calm then susan is either tall or old and vice versa.
If john is wise then alice is not kind or creative.
Everyone who is patient is curious and vice versa.
Everyone who is either not tall or kind is not tall or quiet and vice versa.
If someone is not old then alice is not brave or funny.
Someone is not humble or not funny.
Lucy is either not old or creative.
Susan is both tall and not strong.
Susan is either rich or old.
Susan is either not calm or not curious.
Susan is not wise.
Susan is both not curious and old.
Paul is both quiet and rich. | Susan is not rich. | entailment | (((~wise(mary)&~funny(mary)))<=>(happy(fred)))&
(![X]:((~patient(X)<~>quiet(X))<=>(~brave(X)&~tall(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(~calm(X)&~funny(X))))&
((?[X]:((~creative(X)<~>kind(X))))=>((patient(john)|funny(john))))&
(![X]:(~humble(X)=>patient(X)))&
((?[X]:(old(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~tall(X)=>(~creative(X)|tall(X))))&
((?[X]:((~curious(X)&~funny(X))))<=>(?[X]:((kind(X)|~curious(X)))))&
(((~tall(alice)|~strong(alice)))<=>((~generous(susan)&strong(susan))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)|~strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
(((rich(alice)<~>~calm(alice)))<=>((tall(susan)<~>old(susan))))&
((wise(john))=>((~kind(alice)|creative(alice))))&
(![X]:(patient(X)<=>curious(X)))&
(![X]:((~tall(X)<~>kind(X))<=>(~tall(X)|quiet(X))))&
((?[X]:(~old(X)))=>((~brave(alice)|funny(alice))))&
(?[X]:((~humble(X)|~funny(X))))&
((~old(lucy)<~>creative(lucy)))&
((tall(susan)&~strong(susan)))&
((rich(susan)<~>old(susan)))&
((~calm(susan)<~>~curious(susan)))&
(~wise(susan))&
((~curious(susan)&old(susan)))&
((quiet(paul)&rich(paul))) | ~rich(susan) | [
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9025554371416545634752467
% SZS output start Proof for 9025554371416545634752467
20. rich(susan) <~> old(susan) [input p19]
23. old(susan) & ~curious(susan) [input p22]
25. rich(susan) [input hypothesis]
70. (~old(susan) | ~rich(susan)) & (old(susan) | rich(susan)) [nnf transformation 20]
137. ~old(susan) | ~rich(susan) [cnf transformation 70]
142. old(susan) [cnf transformation 23]
145. rich(susan) [cnf transformation 25]
272. 28 <=> old(susan) [avatar definition]
343. 42 <=> rich(susan) [avatar definition]
346. ~42 | ~28 [avatar split clause 137,272,343]
358. 28 [avatar split clause 142,272]
360. 42 [avatar split clause 145,343]
361. $false [avatar sat refutation 346,358,360]
% SZS output end Proof for 9025554371416545634752467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not calm and vice versa.
Everyone who is not rich is both humble and patient.
If paul is both generous and not generous then someone is not rich or kind and vice versa.
Everyone who is either not strong or not calm is patient.
Everyone who is either strong or brave is either not creative or humble.
If mary is rich then alice is not patient or not happy and vice versa.
Everyone who is both creative and not kind is not creative.
If paul is funny or not wise then paul is both not funny and not kind and vice versa.
Everyone who is both old and curious is not humble or kind and vice versa.
If someone is not calm or not rich then john is both not calm and not quiet.
If mary is strong or not happy then fred is either not generous or not wise.
If someone is either curious or not rich then someone is either not funny or not patient and vice versa.
If someone is not patient or not generous then someone is either not kind or not brave and vice versa.
If alice is not funny then someone is either not kind or not happy.
If someone is not patient or not happy then john is tall or not strong and vice versa.
Everyone who is both not quiet and not curious is either calm or brave and vice versa.
Someone is either strong or quiet.
Fred is both not patient and not curious.
Someone is both not funny and not calm.
Someone is either not generous or wise.
Someone is not old or old.
John is happy or old.
Someone is strong or not curious. | Fred is wise. | neutral | (![X]:(~brave(X)<=>~calm(X)))&
(![X]:(~rich(X)=>(humble(X)&patient(X))))&
(((generous(paul)&~generous(paul)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))=>patient(X)))&
(![X]:((strong(X)<~>brave(X))=>(~creative(X)<~>humble(X))))&
((rich(mary))<=>((~patient(alice)|~happy(alice))))&
(![X]:((creative(X)&~kind(X))=>~creative(X)))&
(((funny(paul)|~wise(paul)))<=>((~funny(paul)&~kind(paul))))&
(![X]:((old(X)&curious(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((~calm(john)&~quiet(john))))&
(((strong(mary)|~happy(mary)))=>((~generous(fred)<~>~wise(fred))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
((~funny(alice))=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((~patient(X)|~happy(X))))<=>((tall(john)|~strong(john))))&
(![X]:((~quiet(X)&~curious(X))<=>(calm(X)<~>brave(X))))&
(?[X]:((strong(X)<~>quiet(X))))&
((~patient(fred)&~curious(fred)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((~old(X)|old(X))))&
((happy(john)|old(john)))&
(?[X]:((strong(X)|~curious(X)))) | wise(fred) | [] | null | 0 |
If someone is kind then someone is tall or kind and vice versa. Everyone who is both curious and not happy is both happy and curious and vice versa. Everyone who is calm is either calm or creative. If fred is rich then someone is both not funny and not brave. Everyone who is both tall and not brave is not creative or not kind. If alice is both strong and happy then someone is tall and vice versa. If someone is creative then someone is both not funny and patient and vice versa. Everyone who is not rich is not kind and vice versa. Everyone who is either generous or funny is not calm or not kind. Everyone who is both not rich and quiet is either not funny or not strong. If alice is either brave or not patient then someone is both brave and not calm and vice versa. Everyone who is both strong and not patient is either not quiet or not humble. If lucy is creative or old then paul is rich and vice versa. If someone is either not kind or calm then someone is either not tall or not patient. If someone is both not calm and happy then fred is both not tall and brave and vice versa. If someone is not wise then someone is wise. Lucy is both not quiet and not kind. Fred is either funny or not brave. Someone is both rich and humble. Paul is both patient and kind. Lucy is either strong or happy. Lucy is patient or not old. Lucy is generous or kind. Lucy is not brave. | Lucy is strong. | neutral | ((?[X]:(kind(X)))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:((curious(X)&~happy(X))<=>(happy(X)&curious(X))))&
(![X]:(calm(X)=>(calm(X)<~>creative(X))))&
((rich(fred))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((tall(X)&~brave(X))=>(~creative(X)|~kind(X))))&
(((strong(alice)&happy(alice)))<=>(?[X]:(tall(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:(~rich(X)<=>~kind(X)))&
(![X]:((generous(X)<~>funny(X))=>(~calm(X)|~kind(X))))&
(![X]:((~rich(X)&quiet(X))=>(~funny(X)<~>~strong(X))))&
(((brave(alice)<~>~patient(alice)))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((strong(X)&~patient(X))=>(~quiet(X)<~>~humble(X))))&
(((creative(lucy)|old(lucy)))<=>(rich(paul)))&
((?[X]:((~kind(X)<~>calm(X))))=>(?[X]:((~tall(X)<~>~patient(X)))))&
((?[X]:((~calm(X)&happy(X))))<=>((~tall(fred)&brave(fred))))&
((?[X]:(~wise(X)))=>(?[X]:(wise(X))))&
((~quiet(lucy)&~kind(lucy)))&
((funny(fred)<~>~brave(fred)))&
(?[X]:((rich(X)&humble(X))))&
((patient(paul)&kind(paul)))&
((strong(lucy)<~>happy(lucy)))&
((patient(lucy)|~old(lucy)))&
((generous(lucy)|kind(lucy)))&
(~brave(lucy)) | strong(lucy) | [] | null | 0 |
If fred is old or not patient then someone is not generous or tall.
If susan is either not creative or funny then someone is either not brave or tall.
If someone is wise or patient then someone is both funny and rich.
Everyone who is both strong and creative is brave or not happy and vice versa.
Everyone who is both not funny and funny is not tall and vice versa.
Everyone who is not tall is quiet or not humble.
If mary is not tall then someone is not rich or not brave and vice versa.
If john is either calm or not strong then someone is not wise or quiet.
If someone is not curious or not wise then someone is curious or not creative.
Everyone who is quiet is either creative or quiet.
Everyone who is either rich or not humble is not patient and vice versa.
Everyone who is either strong or not brave is creative and vice versa.
Everyone who is either strong or humble is either generous or calm and vice versa.
Everyone who is either not happy or not curious is either brave or strong.
If someone is curious then paul is not happy or generous.
Everyone who is either creative or not kind is humble and vice versa.
Someone is not tall or rich.
Someone is both humble and not patient.
John is not curious or not strong.
Someone is patient.
Alice is either humble or quiet.
Someone is either not happy or generous.
Lucy is not quiet or creative. | Mary is not creative. | contradiction | (((old(fred)|~patient(fred)))=>(?[X]:((~generous(X)|tall(X)))))&
(((~creative(susan)<~>funny(susan)))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)|~happy(X))))&
(![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(?[X]:((~tall(X)|rich(X))))&
(?[X]:((humble(X)&~patient(X))))&
((~curious(john)|~strong(john)))&
(?[X]:(patient(X)))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy))) | ~creative(mary) | [
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 50622614722150473513492
% SZS output start Proof for 50622614722150473513492
4. ! [X0] : ((creative(X0) & strong(X0)) <=> (~happy(X0) | brave(X0))) [input p3]
5. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p4]
7. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p6]
24. ~creative(mary) [input hypothesis]
47. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (~creative(X0) | ~strong(X0)))) [nnf transformation 4]
48. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ~creative(X0) | ~strong(X0))) [flattening 47]
49. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 5]
50. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 49]
51. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 7]
52. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 51]
53. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK3) | ~rich(sK3)) [choice axiom]
54. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK3) | ~rich(sK3)) | tall(mary)) [skolemisation 52,53]
89. ~brave(X0) | creative(X0) [cnf transformation 48]
92. ~funny(X0) | tall(X0) [cnf transformation 50]
93. funny(X0) | tall(X0) [cnf transformation 50]
97. ~tall(mary) | brave(X0) [cnf transformation 54]
139. ~creative(mary) [cnf transformation 24]
192. tall(X0) [subsumption resolution 92,93]
193. brave(X0) [subsumption resolution 97,192]
283. creative(X0) [resolution 89,193]
284. $false [resolution 283,139]
% SZS output end Proof for 50622614722150473513492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is strong then alice is either not calm or generous and vice versa.
If susan is generous then susan is not old or patient.
If lucy is both calm and rich then someone is old or quiet and vice versa.
If paul is kind or rich then lucy is both not strong and happy and vice versa.
Everyone who is patient is both not brave and not curious.
Everyone who is both calm and tall is either not wise or wise.
If lucy is both not strong and strong then paul is funny or not rich and vice versa.
If someone is brave then alice is either old or not quiet.
If susan is wise then susan is funny or not curious and vice versa.
Everyone who is either rich or humble is not brave and vice versa.
If someone is either wise or not brave then susan is not funny.
Everyone who is not calm or wise is not quiet or not old.
If mary is either not funny or humble then paul is tall and vice versa.
If fred is both funny and not calm then someone is both not kind and not happy.
Everyone who is calm is both kind and patient.
Everyone who is calm or not happy is rich or patient and vice versa.
John is not calm.
Someone is either not strong or calm.
John is either kind or creative.
Lucy is not curious or wise.
Susan is both not calm and not quiet.
Someone is either not happy or not rich. | Fred is not old. | neutral | ((strong(alice))<=>((~calm(alice)<~>generous(alice))))&
((generous(susan))=>((~old(susan)|patient(susan))))&
(((calm(lucy)&rich(lucy)))<=>(?[X]:((old(X)|quiet(X)))))&
(((kind(paul)|rich(paul)))<=>((~strong(lucy)&happy(lucy))))&
(![X]:(patient(X)=>(~brave(X)&~curious(X))))&
(![X]:((calm(X)&tall(X))=>(~wise(X)<~>wise(X))))&
(((~strong(lucy)&strong(lucy)))<=>((funny(paul)|~rich(paul))))&
((?[X]:(brave(X)))=>((old(alice)<~>~quiet(alice))))&
((wise(susan))<=>((funny(susan)|~curious(susan))))&
(![X]:((rich(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((wise(X)<~>~brave(X))))=>(~funny(susan)))&
(![X]:((~calm(X)|wise(X))=>(~quiet(X)|~old(X))))&
(((~funny(mary)<~>humble(mary)))<=>(tall(paul)))&
(((funny(fred)&~calm(fred)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((calm(X)|~happy(X))<=>(rich(X)|patient(X))))&
(~calm(john))&
(?[X]:((~strong(X)<~>calm(X))))&
((kind(john)<~>creative(john)))&
((~curious(lucy)|wise(lucy)))&
((~calm(susan)&~quiet(susan)))&
(?[X]:((~happy(X)<~>~rich(X)))) | ~old(fred) | [] | null | 0 |
If mary is creative or not funny then someone is either patient or not brave and vice versa. Everyone who is humble or not wise is quiet. Everyone who is either strong or not funny is not generous or not old and vice versa. Everyone who is both calm and not patient is rich. Everyone who is not old is either calm or not generous and vice versa. Everyone who is not happy is creative. If someone is calm then someone is not rich or kind. Everyone who is both not patient and creative is both not old and creative and vice versa. If someone is both humble and quiet then someone is not funny or tall and vice versa. Everyone who is either not strong or happy is not funny or not rich. Everyone who is quiet or creative is both tall and not humble. If john is both not quiet and not happy then mary is both old and quiet. Everyone who is both not happy and not strong is both strong and not rich. Everyone who is either not happy or kind is both brave and rich. Everyone who is both not tall and calm is both humble and not brave. Everyone who is either old or rich is not wise or not quiet. Lucy is not old. Fred is either not happy or kind. Paul is both not kind and not calm. Someone is not tall or not patient. Paul is both not brave and happy. Someone is either patient or not calm. | Paul is not tall. | entailment | (((creative(mary)|~funny(mary)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((strong(X)<~>~funny(X))<=>(~generous(X)|~old(X))))&
(![X]:((calm(X)&~patient(X))=>rich(X)))&
(![X]:(~old(X)<=>(calm(X)<~>~generous(X))))&
(![X]:(~happy(X)=>creative(X)))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((quiet(X)|creative(X))=>(tall(X)&~humble(X))))&
(((~quiet(john)&~happy(john)))=>((old(mary)&quiet(mary))))&
(![X]:((~happy(X)&~strong(X))=>(strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
(![X]:((~tall(X)&calm(X))=>(humble(X)&~brave(X))))&
(![X]:((old(X)<~>rich(X))=>(~wise(X)|~quiet(X))))&
(~old(lucy))&
((~happy(fred)<~>kind(fred)))&
((~kind(paul)&~calm(paul)))&
(?[X]:((~tall(X)|~patient(X))))&
((~brave(paul)&happy(paul)))&
(?[X]:((patient(X)<~>~calm(X)))) | ~tall(paul) | [
"p1",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8984281202546141330502114
% SZS output start Proof for 8984281202546141330502114
2. ! [X0] : ((~wise(X0) | humble(X0)) => quiet(X0)) [input p1]
9. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X0] : (tall(X0) | ~funny(X0)) [input p8]
11. ! [X0] : ((creative(X0) | quiet(X0)) => (~humble(X0) & tall(X0))) [input p10]
23. tall(paul) [input hypothesis]
25. ? [X0] : (quiet(X0) & humble(X0)) <=> ? [X1] : (tall(X1) | ~funny(X1)) [rectify 9]
26. ! [X0] : (quiet(X0) | (wise(X0) & ~humble(X0))) [ennf transformation 2]
33. ! [X0] : ((~humble(X0) & tall(X0)) | (~creative(X0) & ~quiet(X0))) [ennf transformation 11]
56. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X1] : (tall(X1) | ~funny(X1)) | ! [X0] : (~quiet(X0) | ~humble(X0))) [nnf transformation 25]
57. (? [X0] : (quiet(X0) & humble(X0)) | ! [X1] : (~tall(X1) & funny(X1))) & (? [X2] : (tall(X2) | ~funny(X2)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [rectify 56]
58. ? [X0] : (quiet(X0) & humble(X0)) => (quiet(sK2) & humble(sK2)) [choice axiom]
59. ? [X2] : (tall(X2) | ~funny(X2)) => (tall(sK3) | ~funny(sK3)) [choice axiom]
60. ((quiet(sK2) & humble(sK2)) | ! [X1] : (~tall(X1) & funny(X1))) & ((tall(sK3) | ~funny(sK3)) | ! [X3] : (~quiet(X3) | ~humble(X3))) [skolemisation 57,59,58]
76. quiet(X0) | ~humble(X0) [cnf transformation 26]
97. humble(sK2) | ~tall(X1) [cnf transformation 60]
104. ~humble(X0) | ~quiet(X0) [cnf transformation 33]
128. tall(paul) [cnf transformation 23]
171. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
172. ~tall(X1) <- (10) [avatar component clause 171]
183. 13 <=> humble(sK2) [avatar definition]
185. humble(sK2) <- (13) [avatar component clause 183]
186. 10 | 13 [avatar split clause 97,183,171]
190. 14 <=> ! [X3] : ~humble(X3) [avatar definition]
191. ~humble(X3) <- (14) [avatar component clause 190]
201. ~humble(X0) [subsumption resolution 104,76]
202. 14 [avatar split clause 201,190]
252. $false <- (13, 14) [subsumption resolution 185,191]
253. ~13 | ~14 [avatar contradiction clause 252]
254. $false <- (10) [resolution 172,128]
255. ~10 [avatar contradiction clause 254]
256. $false [avatar sat refutation 186,202,253,255]
% SZS output end Proof for 8984281202546141330502114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not funny then someone is either not rich or brave.
Everyone who is either not kind or not quiet is either quiet or kind.
If someone is not calm or calm then john is either not wise or funny.
Everyone who is both brave and happy is both not quiet and not curious and vice versa.
Everyone who is funny is both not kind and not old and vice versa.
If lucy is both strong and not old then someone is both funny and not funny and vice versa.
If mary is rich or not tall then fred is brave and vice versa.
Everyone who is brave or not humble is curious.
Everyone who is either not kind or patient is tall or brave and vice versa.
If someone is not funny or patient then fred is both not calm and strong.
Everyone who is generous or not funny is either quiet or not kind.
If someone is either not happy or not strong then someone is not generous.
Everyone who is either not tall or patient is patient and vice versa.
If someone is both not funny and not calm then alice is not humble and vice versa.
Everyone who is either generous or happy is not wise or happy and vice versa.
Everyone who is creative or tall is both patient and old.
Someone is either not strong or kind.
Someone is both kind and happy.
Someone is happy or wise.
Mary is not wise or funny. | Lucy is kind. | entailment | ((?[X]:((calm(X)|~funny(X))))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>~quiet(X))=>(quiet(X)<~>kind(X))))&
((?[X]:((~calm(X)|calm(X))))=>((~wise(john)<~>funny(john))))&
(![X]:((brave(X)&happy(X))<=>(~quiet(X)&~curious(X))))&
(![X]:(funny(X)<=>(~kind(X)&~old(X))))&
(((strong(lucy)&~old(lucy)))<=>(?[X]:((funny(X)&~funny(X)))))&
(((rich(mary)|~tall(mary)))<=>(brave(fred)))&
(![X]:((brave(X)|~humble(X))=>curious(X)))&
(![X]:((~kind(X)<~>patient(X))<=>(tall(X)|brave(X))))&
((?[X]:((~funny(X)|patient(X))))=>((~calm(fred)&strong(fred))))&
(![X]:((generous(X)|~funny(X))=>(quiet(X)<~>~kind(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~funny(X)&~calm(X))))<=>(~humble(alice)))&
(![X]:((generous(X)<~>happy(X))<=>(~wise(X)|happy(X))))&
(![X]:((creative(X)|tall(X))=>(patient(X)&old(X))))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:((happy(X)|wise(X))))&
((~wise(mary)|funny(mary))) | kind(lucy) | [
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 428267103894049321196874
% SZS output start Proof for 428267103894049321196874
9. ! [X0] : ((~kind(X0) <~> patient(X0)) <=> (brave(X0) | tall(X0))) [input p8]
13. ! [X0] : ((~tall(X0) <~> patient(X0)) <=> patient(X0)) [input p12]
16. ! [X0] : ((tall(X0) | creative(X0)) => (old(X0) & patient(X0))) [input p15]
21. ~kind(lucy) [input hypothesis]
24. ! [X0] : (tall(X0) => (old(X0) & patient(X0))) [pure predicate removal 16]
32. ! [X0] : ((old(X0) & patient(X0)) | ~tall(X0)) [ennf transformation 24]
50. ! [X0] : ((((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))))) [nnf transformation 9]
51. ! [X0] : ((((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))))) [flattening 50]
57. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ~patient(X0)) & (patient(X0) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [nnf transformation 13]
103. ~patient(X0) | kind(X0) | ~tall(X0) [cnf transformation 51]
115. patient(X0) | patient(X0) | tall(X0) [cnf transformation 57]
118. ~patient(X0) | tall(X0) | ~patient(X0) [cnf transformation 57]
128. patient(X0) | ~tall(X0) [cnf transformation 32]
136. ~kind(lucy) [cnf transformation 21]
139. patient(X0) | tall(X0) [duplicate literal removal 115]
140. ~patient(X0) | tall(X0) [duplicate literal removal 118]
235. tall(X0) [subsumption resolution 139,140]
256. patient(X0) [subsumption resolution 128,235]
322. kind(X0) | ~tall(X0) [resolution 103,256]
323. kind(X0) [subsumption resolution 322,235]
324. $false [resolution 323,136]
% SZS output end Proof for 428267103894049321196874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not generous then john is either calm or not calm and vice versa.
If mary is either not strong or not old then alice is either tall or patient and vice versa.
Everyone who is either not curious or not kind is both not brave and not funny and vice versa.
Everyone who is not wise or not curious is not old and vice versa.
Everyone who is funny or not patient is funny or curious and vice versa.
If someone is either not creative or tall then susan is not brave and vice versa.
Everyone who is both not humble and strong is calm or not generous and vice versa.
Everyone who is old is calm or not old and vice versa.
Everyone who is both not creative and not wise is not generous or tall.
If someone is both kind and wise then lucy is either not creative or not old.
Everyone who is either curious or brave is both not quiet and not kind and vice versa.
If fred is both calm and not happy then someone is not rich and vice versa.
If alice is tall then someone is brave or humble.
Everyone who is either not funny or not calm is either tall or not humble.
Everyone who is either not quiet or not generous is not rich.
Everyone who is both not calm and not funny is both not wise and generous and vice versa.
Someone is rich or not creative.
Fred is either old or not patient.
Fred is either not calm or calm.
Someone is not creative.
Someone is either not funny or not creative.
Someone is both curious and not patient.
Susan is not humble or not old. | Alice is creative. | neutral | ((?[X]:((wise(X)<~>~generous(X))))<=>((calm(john)<~>~calm(john))))&
(((~strong(mary)<~>~old(mary)))<=>((tall(alice)<~>patient(alice))))&
(![X]:((~curious(X)<~>~kind(X))<=>(~brave(X)&~funny(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((funny(X)|~patient(X))<=>(funny(X)|curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(~brave(susan)))&
(![X]:((~humble(X)&strong(X))<=>(calm(X)|~generous(X))))&
(![X]:(old(X)<=>(calm(X)|~old(X))))&
(![X]:((~creative(X)&~wise(X))=>(~generous(X)|tall(X))))&
((?[X]:((kind(X)&wise(X))))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((curious(X)<~>brave(X))<=>(~quiet(X)&~kind(X))))&
(((calm(fred)&~happy(fred)))<=>(?[X]:(~rich(X))))&
((tall(alice))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~funny(X)<~>~calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>~rich(X)))&
(![X]:((~calm(X)&~funny(X))<=>(~wise(X)&generous(X))))&
(?[X]:((rich(X)|~creative(X))))&
((old(fred)<~>~patient(fred)))&
((~calm(fred)<~>calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(?[X]:((curious(X)&~patient(X))))&
((~humble(susan)|~old(susan))) | creative(alice) | [] | null | 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is creative is generous or not calm and vice versa.
If susan is both not calm and happy then someone is both rich and not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich.
Someone is happy or strong. | Mary is old. | neutral | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(creative(X)<=>(generous(X)|~calm(X))))&
(((~calm(susan)&happy(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan)))&
(?[X]:((happy(X)|strong(X)))) | old(mary) | [] | null | 0 |
If paul is not happy then someone is both not curious and quiet and vice versa.
If john is not generous or not creative then mary is not old or tall and vice versa.
If susan is either brave or funny then someone is not humble.
If someone is both not kind and not tall then paul is generous or not humble.
Everyone who is either not quiet or humble is humble or not happy.
Everyone who is both not quiet and quiet is calm or not rich and vice versa.
If someone is either wise or generous then someone is either not strong or old and vice versa.
If lucy is calm then someone is both not funny and curious and vice versa.
If john is either brave or funny then lucy is not generous or not quiet and vice versa.
Everyone who is creative or not generous is both funny and creative.
Everyone who is not humble is either not old or generous.
Everyone who is either not tall or not creative is both not tall and generous and vice versa.
Everyone who is strong is not strong or not kind.
If someone is either calm or not calm then someone is humble or strong and vice versa.
If susan is both not old and not quiet then paul is either not creative or old and vice versa.
Lucy is either not rich or not kind.
John is either not curious or not old.
Someone is not kind or humble.
Someone is either brave or kind.
Someone is patient.
Someone is both generous and creative.
Someone is both not happy and not humble.
Fred is either happy or funny. | Mary is creative. | entailment | ((~happy(paul))<=>(?[X]:((~curious(X)&quiet(X)))))&
(((~generous(john)|~creative(john)))<=>((~old(mary)|tall(mary))))&
(((brave(susan)<~>funny(susan)))=>(?[X]:(~humble(X))))&
((?[X]:((~kind(X)&~tall(X))))=>((generous(paul)|~humble(paul))))&
(![X]:((~quiet(X)<~>humble(X))=>(humble(X)|~happy(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(calm(X)|~rich(X))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~strong(X)<~>old(X)))))&
((calm(lucy))<=>(?[X]:((~funny(X)&curious(X)))))&
(((brave(john)<~>funny(john)))<=>((~generous(lucy)|~quiet(lucy))))&
(![X]:((creative(X)|~generous(X))=>(funny(X)&creative(X))))&
(![X]:(~humble(X)=>(~old(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~creative(X))<=>(~tall(X)&generous(X))))&
(![X]:(strong(X)=>(~strong(X)|~kind(X))))&
((?[X]:((calm(X)<~>~calm(X))))<=>(?[X]:((humble(X)|strong(X)))))&
(((~old(susan)&~quiet(susan)))<=>((~creative(paul)<~>old(paul))))&
((~rich(lucy)<~>~kind(lucy)))&
((~curious(john)<~>~old(john)))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:(patient(X)))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((~happy(X)&~humble(X))))&
((happy(fred)<~>funny(fred))) | creative(mary) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4515653510336127772935002
% SZS output start Proof for 4515653510336127772935002
10. ! [X0] : ((~generous(X0) | creative(X0)) => (creative(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~tall(X0) <~> ~creative(X0)) <=> (generous(X0) & ~tall(X0))) [input p11]
24. ~creative(mary) [input hypothesis]
33. ! [X0] : ((creative(X0) & funny(X0)) | (generous(X0) & ~creative(X0))) [ennf transformation 10]
61. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [nnf transformation 12]
62. ! [X0] : ((((creative(X0) | tall(X0)) & (~creative(X0) | ~tall(X0))) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))))) [flattening 61]
119. creative(X0) | generous(X0) [cnf transformation 33]
123. ~tall(X0) | ~tall(X0) | creative(X0) [cnf transformation 62]
127. creative(X0) | tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 62]
154. ~creative(mary) [cnf transformation 24]
158. ~tall(X0) | creative(X0) [duplicate literal removal 123]
159. creative(X0) | tall(X0) | ~generous(X0) [duplicate literal removal 127]
286. creative(X0) | tall(X0) [subsumption resolution 159,119]
288. creative(X0) [subsumption resolution 158,286]
357. $false [subsumption resolution 154,288]
% SZS output end Proof for 4515653510336127772935002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both wise and not funny and vice versa.
Everyone who is either not strong or calm is both not calm and not old.
Everyone who is both not kind and not wise is not generous or not happy and vice versa.
Everyone who is kind is humble or brave.
If susan is both not strong and not old then paul is either not creative or not brave.
Everyone who is both generous and humble is both not happy and not patient.
Everyone who is both kind and generous is not patient and vice versa.
Everyone who is not patient is both creative and not calm and vice versa.
Everyone who is not happy is strong.
If someone is both not wise and kind then someone is not rich.
Everyone who is both generous and not strong is either not happy or not funny and vice versa.
If someone is either not old or funny then someone is not creative or not strong and vice versa.
If someone is both not calm and strong then someone is not curious or not funny and vice versa.
Everyone who is either not quiet or rich is both not quiet and brave and vice versa.
If someone is both generous and not funny then someone is brave or not rich and vice versa.
Everyone who is tall or not curious is not creative or not humble.
John is either not brave or not generous.
Alice is both kind and not curious.
Someone is wise or strong.
Someone is both not calm and funny.
Paul is either not happy or not curious. | Paul is calm. | contradiction | (![X]:(~generous(X)<=>(wise(X)&~funny(X))))&
(![X]:((~strong(X)<~>calm(X))=>(~calm(X)&~old(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~generous(X)|~happy(X))))&
(![X]:(kind(X)=>(humble(X)|brave(X))))&
(((~strong(susan)&~old(susan)))=>((~creative(paul)<~>~brave(paul))))&
(![X]:((generous(X)&humble(X))=>(~happy(X)&~patient(X))))&
(![X]:((kind(X)&generous(X))<=>~patient(X)))&
(![X]:(~patient(X)<=>(creative(X)&~calm(X))))&
(![X]:(~happy(X)=>strong(X)))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:(~rich(X))))&
(![X]:((generous(X)&~strong(X))<=>(~happy(X)<~>~funny(X))))&
((?[X]:((~old(X)<~>funny(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((~calm(X)&strong(X))))<=>(?[X]:((~curious(X)|~funny(X)))))&
(![X]:((~quiet(X)<~>rich(X))<=>(~quiet(X)&brave(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:((brave(X)|~rich(X)))))&
(![X]:((tall(X)|~curious(X))=>(~creative(X)|~humble(X))))&
((~brave(john)<~>~generous(john)))&
((kind(alice)&~curious(alice)))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((~calm(X)&funny(X))))&
((~happy(paul)<~>~curious(paul))) | calm(paul) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7635531012324253335822443
% SZS output start Proof for 7635531012324253335822443
1. ! [X0] : (~generous(X0) <=> (~funny(X0) & wise(X0))) [input p0]
2. ! [X0] : ((~strong(X0) <~> calm(X0)) => (~old(X0) & ~calm(X0))) [input p1]
3. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~happy(X0) | ~generous(X0))) [input p2]
7. ! [X0] : ((generous(X0) & kind(X0)) <=> ~patient(X0)) [input p6]
8. ! [X0] : (~patient(X0) <=> (~calm(X0) & creative(X0))) [input p7]
9. ! [X0] : (~happy(X0) => strong(X0)) [input p8]
11. ! [X0] : ((~strong(X0) & generous(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p10]
22. calm(paul) [input hypothesis]
28. ! [X0] : ((~old(X0) & ~calm(X0)) | (~strong(X0) <=> calm(X0))) [ennf transformation 2]
35. ! [X0] : (strong(X0) | happy(X0)) [ennf transformation 9]
39. ! [X0] : ((~generous(X0) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | generous(X0))) [nnf transformation 1]
40. ! [X0] : ((~generous(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | generous(X0))) [flattening 39]
41. ! [X0] : ((~old(X0) & ~calm(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) [nnf transformation 28]
42. ! [X0] : (((~wise(X0) & ~kind(X0)) | (happy(X0) & generous(X0))) & ((~happy(X0) | ~generous(X0)) | (wise(X0) | kind(X0)))) [nnf transformation 3]
43. ! [X0] : (((~wise(X0) & ~kind(X0)) | (happy(X0) & generous(X0))) & (~happy(X0) | ~generous(X0) | wise(X0) | kind(X0))) [flattening 42]
45. ! [X0] : (((generous(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | (~generous(X0) | ~kind(X0)))) [nnf transformation 7]
46. ! [X0] : (((generous(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | ~generous(X0) | ~kind(X0))) [flattening 45]
47. ! [X0] : ((~patient(X0) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | patient(X0))) [nnf transformation 8]
48. ! [X0] : ((~patient(X0) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | patient(X0))) [flattening 47]
52. ! [X0] : (((~strong(X0) & generous(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (strong(X0) | ~generous(X0)))) [nnf transformation 11]
53. ! [X0] : (((~strong(X0) & generous(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | strong(X0) | ~generous(X0))) [flattening 52]
77. wise(X0) | generous(X0) [cnf transformation 40]
79. ~wise(X0) | funny(X0) | ~generous(X0) [cnf transformation 40]
81. ~calm(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 41]
84. ~happy(X0) | ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 43]
87. ~wise(X0) | generous(X0) [cnf transformation 43]
94. ~patient(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 46]
98. ~calm(X0) | patient(X0) [cnf transformation 48]
100. happy(X0) | strong(X0) [cnf transformation 35]
102. ~funny(X0) | ~happy(X0) | strong(X0) | ~generous(X0) [cnf transformation 53]
106. ~strong(X0) | ~funny(X0) | happy(X0) [cnf transformation 53]
140. calm(paul) [cnf transformation 22]
143. ~calm(X0) | ~strong(X0) [duplicate literal removal 81]
144. generous(X0) [subsumption resolution 87,77]
145. ~happy(X0) | wise(X0) | kind(X0) [subsumption resolution 84,144]
166. ~patient(X0) | ~kind(X0) [subsumption resolution 94,144]
175. ~funny(X0) | happy(X0) [subsumption resolution 106,100]
176. ~funny(X0) | ~happy(X0) | strong(X0) [subsumption resolution 102,144]
177. ~funny(X0) | strong(X0) [subsumption resolution 176,175]
276. 29 <=> happy(paul) [avatar definition]
277. ~happy(paul) <- (~29) [avatar component clause 276]
278. happy(paul) <- (29) [avatar component clause 276]
289. patient(paul) [resolution 98,140]
290. ~strong(paul) [resolution 143,140]
296. ~kind(paul) [resolution 166,289]
347. wise(paul) | kind(paul) <- (29) [resolution 145,278]
351. wise(paul) <- (29) [subsumption resolution 347,296]
361. funny(paul) | ~generous(paul) <- (29) [resolution 351,79]
363. funny(paul) <- (29) [subsumption resolution 361,144]
371. strong(paul) <- (29) [resolution 363,177]
374. $false <- (29) [subsumption resolution 371,290]
375. ~29 [avatar contradiction clause 374]
377. strong(paul) <- (~29) [resolution 277,100]
378. $false <- (~29) [subsumption resolution 377,290]
379. 29 [avatar contradiction clause 378]
380. $false [avatar sat refutation 375,379]
% SZS output end Proof for 7635531012324253335822443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is funny then someone is either curious or not humble and vice versa.
Everyone who is not humble or quiet is both tall and curious and vice versa.
Everyone who is both not curious and strong is both happy and not tall.
Everyone who is either funny or humble is either funny or not calm and vice versa.
If someone is kind then someone is either funny or strong.
Everyone who is not brave is generous and vice versa.
Everyone who is both not funny and not calm is both not tall and not wise and vice versa.
Everyone who is either generous or calm is both tall and wise and vice versa.
If paul is either not funny or strong then paul is not happy or calm.
If john is either generous or calm then fred is curious.
Everyone who is not kind is not calm or funny.
Everyone who is strong or quiet is not humble.
If someone is humble then mary is not humble or strong.
Everyone who is either calm or rich is not humble or funny.
Everyone who is not generous is not patient.
Everyone who is either not tall or quiet is either happy or brave.
John is not rich or funny.
Fred is not calm or not happy.
Someone is both not generous and not strong.
Someone is either not creative or not curious.
Someone is calm or not kind.
Someone is not old.
John is both not rich and not kind.
Someone is both wise and not happy. | Paul is calm. | neutral | ((funny(john))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(![X]:((~humble(X)|quiet(X))<=>(tall(X)&curious(X))))&
(![X]:((~curious(X)&strong(X))=>(happy(X)&~tall(X))))&
(![X]:((funny(X)<~>humble(X))<=>(funny(X)<~>~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:(~brave(X)<=>generous(X)))&
(![X]:((~funny(X)&~calm(X))<=>(~tall(X)&~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(tall(X)&wise(X))))&
(((~funny(paul)<~>strong(paul)))=>((~happy(paul)|calm(paul))))&
(((generous(john)<~>calm(john)))=>(curious(fred)))&
(![X]:(~kind(X)=>(~calm(X)|funny(X))))&
(![X]:((strong(X)|quiet(X))=>~humble(X)))&
((?[X]:(humble(X)))=>((~humble(mary)|strong(mary))))&
(![X]:((calm(X)<~>rich(X))=>(~humble(X)|funny(X))))&
(![X]:(~generous(X)=>~patient(X)))&
(![X]:((~tall(X)<~>quiet(X))=>(happy(X)<~>brave(X))))&
((~rich(john)|funny(john)))&
((~calm(fred)|~happy(fred)))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:(~old(X)))&
((~rich(john)&~kind(john)))&
(?[X]:((wise(X)&~happy(X)))) | calm(paul) | [] | null | 0 |
If fred is either quiet or not tall then mary is either not funny or quiet. Everyone who is not old or not strong is both curious and calm and vice versa. If someone is either not wise or generous then someone is either kind or not old and vice versa. If someone is humble then susan is old or not tall and vice versa. Everyone who is both tall and patient is tall or not rich. Everyone who is not happy or not curious is curious or not humble. If someone is not funny then paul is old. Everyone who is either rich or not quiet is calm or not generous. If someone is either not tall or not strong then someone is rich and vice versa. Everyone who is kind is either quiet or not calm and vice versa. Everyone who is either tall or quiet is not curious. Everyone who is either happy or strong is tall. Everyone who is curious is both not calm and not tall. Everyone who is both patient and not funny is not funny and vice versa. If someone is not creative then someone is either not creative or generous. Everyone who is brave is quiet and vice versa. Mary is both calm and generous. Someone is kind. Lucy is either not brave or not humble. Paul is not happy. Someone is quiet. John is both not funny and not brave. | Susan is not curious. | neutral | (((quiet(fred)<~>~tall(fred)))=>((~funny(mary)<~>quiet(mary))))&
(![X]:((~old(X)|~strong(X))<=>(curious(X)&calm(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:(humble(X)))<=>((old(susan)|~tall(susan))))&
(![X]:((tall(X)&patient(X))=>(tall(X)|~rich(X))))&
(![X]:((~happy(X)|~curious(X))=>(curious(X)|~humble(X))))&
((?[X]:(~funny(X)))=>(old(paul)))&
(![X]:((rich(X)<~>~quiet(X))=>(calm(X)|~generous(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:(rich(X))))&
(![X]:(kind(X)<=>(quiet(X)<~>~calm(X))))&
(![X]:((tall(X)<~>quiet(X))=>~curious(X)))&
(![X]:((happy(X)<~>strong(X))=>tall(X)))&
(![X]:(curious(X)=>(~calm(X)&~tall(X))))&
(![X]:((patient(X)&~funny(X))<=>~funny(X)))&
((?[X]:(~creative(X)))=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:(brave(X)<=>quiet(X)))&
((calm(mary)&generous(mary)))&
(?[X]:(kind(X)))&
((~brave(lucy)<~>~humble(lucy)))&
(~happy(paul))&
(?[X]:(quiet(X)))&
((~funny(john)&~brave(john))) | ~curious(susan) | [] | null | 0 |
Everyone who is rich is either not patient or not rich.
Everyone who is not brave is both humble and strong and vice versa.
Everyone who is both not humble and not tall is either not strong or not wise and vice versa.
Everyone who is quiet or not quiet is both not quiet and creative and vice versa.
Everyone who is both not quiet and not kind is both funny and not kind.
Everyone who is not creative is rich.
Everyone who is both brave and strong is not creative and vice versa.
If paul is not curious then fred is humble or not generous and vice versa.
If susan is creative then fred is not happy and vice versa.
Everyone who is either not patient or not wise is creative or not brave.
Everyone who is not old or rich is either not calm or kind and vice versa.
If someone is humble or not creative then paul is calm and vice versa.
If fred is strong then someone is either happy or not patient and vice versa.
Everyone who is both humble and rich is both tall and creative and vice versa.
If fred is both not tall and funny then someone is either happy or not wise.
Paul is not rich or strong.
Lucy is curious.
Fred is wise or not curious.
Fred is both not calm and not brave.
Alice is strong.
Someone is both happy and humble.
Someone is not humble.
Someone is both creative and curious. | Alice is wise. | entailment | (![X]:(rich(X)=>(~patient(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>(humble(X)&strong(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~quiet(X)&~kind(X))=>(funny(X)&~kind(X))))&
(![X]:(~creative(X)=>rich(X)))&
(![X]:((brave(X)&strong(X))<=>~creative(X)))&
((~curious(paul))<=>((humble(fred)|~generous(fred))))&
((creative(susan))<=>(~happy(fred)))&
(![X]:((~patient(X)<~>~wise(X))=>(creative(X)|~brave(X))))&
(![X]:((~old(X)|rich(X))<=>(~calm(X)<~>kind(X))))&
((?[X]:((humble(X)|~creative(X))))<=>(calm(paul)))&
((strong(fred))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((humble(X)&rich(X))<=>(tall(X)&creative(X))))&
(((~tall(fred)&funny(fred)))=>(?[X]:((happy(X)<~>~wise(X)))))&
((~rich(paul)|strong(paul)))&
(curious(lucy))&
((wise(fred)|~curious(fred)))&
((~calm(fred)&~brave(fred)))&
(strong(alice))&
(?[X]:((happy(X)&humble(X))))&
(?[X]:(~humble(X)))&
(?[X]:((creative(X)&curious(X)))) | wise(alice) | [
"p1",
"p2",
"p3",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4188754996344338445425459
% SZS output start Proof for 4188754996344338445425459
2. ! [X0] : (~brave(X0) <=> (strong(X0) & humble(X0))) [input p1]
3. ! [X0] : ((~tall(X0) & ~humble(X0)) <=> (~strong(X0) <~> ~wise(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (creative(X0) & ~quiet(X0))) [input p3]
7. ! [X0] : ((strong(X0) & brave(X0)) <=> ~creative(X0)) [input p6]
20. strong(alice) [input p19]
24. ~wise(alice) [input hypothesis]
34. ! [X0] : ((~brave(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | brave(X0))) [nnf transformation 2]
35. ! [X0] : ((~brave(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | brave(X0))) [flattening 34]
36. ! [X0] : (((~tall(X0) & ~humble(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | (tall(X0) | humble(X0)))) [nnf transformation 3]
37. ! [X0] : (((~tall(X0) & ~humble(X0)) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | tall(X0) | humble(X0))) [flattening 36]
38. ! [X0] : (((~quiet(X0) | quiet(X0)) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 4]
39. ! [X0] : ((~quiet(X0) | quiet(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 38]
40. ! [X0] : (((strong(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | ~brave(X0)))) [nnf transformation 7]
41. ! [X0] : (((strong(X0) & brave(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | ~brave(X0))) [flattening 40]
69. humble(X0) | brave(X0) [cnf transformation 35]
75. ~strong(X0) | ~humble(X0) | wise(X0) [cnf transformation 37]
80. creative(X0) | ~quiet(X0) [cnf transformation 39]
81. creative(X0) | quiet(X0) [cnf transformation 39]
86. ~creative(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 41]
120. strong(alice) [cnf transformation 20]
126. ~wise(alice) [cnf transformation 24]
130. creative(X0) [subsumption resolution 80,81]
132. ~strong(X0) | ~brave(X0) [subsumption resolution 86,130]
225. ~brave(alice) [resolution 132,120]
231. ~humble(alice) | wise(alice) [resolution 75,120]
234. ~humble(alice) [subsumption resolution 231,126]
251. brave(alice) [resolution 234,69]
252. $false [subsumption resolution 251,225]
% SZS output end Proof for 4188754996344338445425459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative or not calm then someone is either not calm or not rich.
Everyone who is both generous and not calm is both not humble and quiet.
If someone is both curious and not patient then john is brave.
If someone is both kind and not strong then mary is either humble or funny.
If someone is not old or calm then someone is patient.
Everyone who is either not patient or kind is either not tall or not curious and vice versa.
Everyone who is both not happy and not tall is strong.
If lucy is tall then fred is strong and vice versa.
Everyone who is both not generous and not happy is either not curious or not tall.
If someone is creative then alice is not old or curious.
Everyone who is not tall is both not old and brave.
Everyone who is patient or not patient is not happy or old and vice versa.
If john is both not rich and patient then someone is both not calm and not tall and vice versa.
Everyone who is old or not happy is not creative or not humble.
Everyone who is creative is tall.
If someone is kind or not brave then john is not quiet and vice versa.
Someone is both patient and generous.
Lucy is not kind or brave.
Alice is not funny or not tall.
Lucy is either not patient or strong.
John is quiet or not quiet.
Someone is both quiet and not funny.
Susan is either not calm or calm.
Someone is not generous or kind. | Alice is not funny. | neutral | (((~creative(alice)|~calm(alice)))=>(?[X]:((~calm(X)<~>~rich(X)))))&
(![X]:((generous(X)&~calm(X))=>(~humble(X)&quiet(X))))&
((?[X]:((curious(X)&~patient(X))))=>(brave(john)))&
((?[X]:((kind(X)&~strong(X))))=>((humble(mary)<~>funny(mary))))&
((?[X]:((~old(X)|calm(X))))=>(?[X]:(patient(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((~happy(X)&~tall(X))=>strong(X)))&
((tall(lucy))<=>(strong(fred)))&
(![X]:((~generous(X)&~happy(X))=>(~curious(X)<~>~tall(X))))&
((?[X]:(creative(X)))=>((~old(alice)|curious(alice))))&
(![X]:(~tall(X)=>(~old(X)&brave(X))))&
(![X]:((patient(X)|~patient(X))<=>(~happy(X)|old(X))))&
(((~rich(john)&patient(john)))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((old(X)|~happy(X))=>(~creative(X)|~humble(X))))&
(![X]:(creative(X)=>tall(X)))&
((?[X]:((kind(X)|~brave(X))))<=>(~quiet(john)))&
(?[X]:((patient(X)&generous(X))))&
((~kind(lucy)|brave(lucy)))&
((~funny(alice)|~tall(alice)))&
((~patient(lucy)<~>strong(lucy)))&
((quiet(john)|~quiet(john)))&
(?[X]:((quiet(X)&~funny(X))))&
((~calm(susan)<~>calm(susan)))&
(?[X]:((~generous(X)|kind(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is wise or not generous is quiet and vice versa.
If fred is both creative and not old then someone is not quiet or kind and vice versa.
Everyone who is both not tall and creative is either creative or not happy and vice versa.
Everyone who is not generous is both not patient and not brave.
Everyone who is either not kind or not patient is not calm or tall and vice versa.
Everyone who is creative is both not rich and not patient.
Everyone who is happy is funny or not funny and vice versa.
If susan is either creative or not happy then fred is not quiet and vice versa.
Everyone who is both calm and not quiet is not funny.
If alice is either funny or not happy then alice is both not brave and generous and vice versa.
If someone is not patient or wise then susan is both not funny and rich and vice versa.
Everyone who is either not kind or calm is either patient or funny and vice versa.
If fred is both humble and kind then someone is not creative or humble.
If someone is both rich and not tall then someone is curious or not patient.
Someone is either not rich or not strong.
John is not curious or not wise.
Alice is humble or not tall.
Lucy is either not generous or old.
Someone is both not quiet and not old.
John is both not patient and not creative.
Someone is not kind. | Fred is rich. | contradiction | (![X]:((wise(X)|~generous(X))<=>quiet(X)))&
(((creative(fred)&~old(fred)))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)<~>~happy(X))))&
(![X]:(~generous(X)=>(~patient(X)&~brave(X))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~calm(X)|tall(X))))&
(![X]:(creative(X)=>(~rich(X)&~patient(X))))&
(![X]:(happy(X)<=>(funny(X)|~funny(X))))&
(((creative(susan)<~>~happy(susan)))<=>(~quiet(fred)))&
(![X]:((calm(X)&~quiet(X))=>~funny(X)))&
(((funny(alice)<~>~happy(alice)))<=>((~brave(alice)&generous(alice))))&
((?[X]:((~patient(X)|wise(X))))<=>((~funny(susan)&rich(susan))))&
(![X]:((~kind(X)<~>calm(X))<=>(patient(X)<~>funny(X))))&
(((humble(fred)&kind(fred)))=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:((rich(X)&~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((~curious(john)|~wise(john)))&
((humble(alice)|~tall(alice)))&
((~generous(lucy)<~>old(lucy)))&
(?[X]:((~quiet(X)&~old(X))))&
((~patient(john)&~creative(john)))&
(?[X]:(~kind(X))) | rich(fred) | [
"p1",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8487500742540003188215886
% SZS output start Proof for 8487500742540003188215886
2. (~old(fred) & creative(fred)) <=> ? [X0] : (kind(X0) | ~quiet(X0)) [input p1]
6. ! [X0] : (creative(X0) => (~patient(X0) & ~rich(X0))) [input p5]
19. ? [X0] : (~old(X0) & ~quiet(X0)) [input p18]
22. rich(fred) [input hypothesis]
25. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~creative(X0)) [ennf transformation 6]
33. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X0] : (kind(X0) | ~quiet(X0)) | (old(fred) | ~creative(fred))) [nnf transformation 2]
34. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X0] : (kind(X0) | ~quiet(X0)) | old(fred) | ~creative(fred)) [flattening 33]
35. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X1] : (kind(X1) | ~quiet(X1)) | old(fred) | ~creative(fred)) [rectify 34]
36. ? [X1] : (kind(X1) | ~quiet(X1)) => (kind(sK0) | ~quiet(sK0)) [choice axiom]
37. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & ((kind(sK0) | ~quiet(sK0)) | old(fred) | ~creative(fred)) [skolemisation 35,36]
62. ? [X0] : (~old(X0) & ~quiet(X0)) => (~old(sK5) & ~quiet(sK5)) [choice axiom]
63. ~old(sK5) & ~quiet(sK5) [skolemisation 19,62]
70. creative(fred) | quiet(X0) [cnf transformation 37]
88. ~rich(X0) | ~creative(X0) [cnf transformation 25]
125. ~quiet(sK5) [cnf transformation 63]
130. rich(fred) [cnf transformation 22]
142. 3 <=> ! [X0] : quiet(X0) [avatar definition]
143. quiet(X0) <- (3) [avatar component clause 142]
146. 4 <=> creative(fred) [avatar definition]
150. 3 | 4 [avatar split clause 70,146,142]
292. ~creative(fred) [resolution 88,130]
297. ~4 [avatar split clause 292,146]
298. $false <- (3) [resolution 143,125]
301. ~3 [avatar contradiction clause 298]
302. $false [avatar sat refutation 150,297,301]
% SZS output end Proof for 8487500742540003188215886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not happy is both generous and not strong and vice versa.
If fred is both quiet and generous then paul is quiet or tall and vice versa.
Everyone who is either not kind or not strong is both happy and not old and vice versa.
Everyone who is not old or brave is funny and vice versa.
If someone is not brave or not curious then john is either not wise or not patient and vice versa.
Everyone who is wise is both not wise and not quiet and vice versa.
Everyone who is tall or not kind is both patient and not humble.
Everyone who is curious is not brave.
Everyone who is curious or strong is both not patient and rich.
If fred is not patient or generous then someone is brave.
If someone is wise or happy then someone is either kind or not old and vice versa.
If someone is not wise or brave then someone is not strong and vice versa.
Everyone who is both not curious and not funny is either patient or happy and vice versa.
If alice is both old and not kind then someone is curious.
If someone is wise then susan is either quiet or not strong.
If someone is both not old and strong then someone is both not humble and calm.
Lucy is funny or not wise.
Lucy is not humble or not curious.
Someone is either not humble or not curious.
Someone is both generous and humble.
John is not generous.
Someone is either not happy or not rich.
Someone is both not brave and not curious.
Someone is not happy or wise. | Lucy is not funny. | neutral | (![X]:((funny(X)&~happy(X))<=>(generous(X)&~strong(X))))&
(((quiet(fred)&generous(fred)))<=>((quiet(paul)|tall(paul))))&
(![X]:((~kind(X)<~>~strong(X))<=>(happy(X)&~old(X))))&
(![X]:((~old(X)|brave(X))<=>funny(X)))&
((?[X]:((~brave(X)|~curious(X))))<=>((~wise(john)<~>~patient(john))))&
(![X]:(wise(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((tall(X)|~kind(X))=>(patient(X)&~humble(X))))&
(![X]:(curious(X)=>~brave(X)))&
(![X]:((curious(X)|strong(X))=>(~patient(X)&rich(X))))&
(((~patient(fred)|generous(fred)))=>(?[X]:(brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&~funny(X))<=>(patient(X)<~>happy(X))))&
(((old(alice)&~kind(alice)))=>(?[X]:(curious(X))))&
((?[X]:(wise(X)))=>((quiet(susan)<~>~strong(susan))))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~humble(X)&calm(X)))))&
((funny(lucy)|~wise(lucy)))&
((~humble(lucy)|~curious(lucy)))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((generous(X)&humble(X))))&
(~generous(john))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~brave(X)&~curious(X))))&
(?[X]:((~happy(X)|wise(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is both brave and patient is quiet and vice versa. Everyone who is not curious or old is brave. If mary is both not generous and not strong then john is not brave and vice versa. If paul is happy then john is not rich and vice versa. If fred is quiet or not creative then someone is both not quiet and not brave and vice versa. Everyone who is not strong or not rich is both generous and not generous. Everyone who is kind or tall is not quiet and vice versa. If someone is either not funny or not happy then someone is not patient or quiet and vice versa. If susan is not curious then someone is either generous or brave and vice versa. If someone is both generous and creative then someone is not brave or quiet and vice versa. Everyone who is both funny and not strong is both not tall and not rich. If john is both not old and curious then alice is not funny. Everyone who is both not humble and strong is not generous or calm. Everyone who is either not tall or not old is either not humble or not funny. If susan is not quiet then susan is either not patient or tall. Everyone who is both not curious and old is both wise and humble and vice versa. Lucy is both not creative and tall. John is not tall. Alice is not wise. Mary is not creative. Someone is both not tall and not brave. Someone is both patient and wise. Someone is either not generous or not kind. Paul is not brave. | Mary is not strong. | contradiction | (![X]:((brave(X)&patient(X))<=>quiet(X)))&
(![X]:((~curious(X)|old(X))=>brave(X)))&
(((~generous(mary)&~strong(mary)))<=>(~brave(john)))&
((happy(paul))<=>(~rich(john)))&
(((quiet(fred)|~creative(fred)))<=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:((~strong(X)|~rich(X))=>(generous(X)&~generous(X))))&
(![X]:((kind(X)|tall(X))<=>~quiet(X)))&
((?[X]:((~funny(X)<~>~happy(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
((~curious(susan))<=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((generous(X)&creative(X))))<=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:((funny(X)&~strong(X))=>(~tall(X)&~rich(X))))&
(((~old(john)&curious(john)))=>(~funny(alice)))&
(![X]:((~humble(X)&strong(X))=>(~generous(X)|calm(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~humble(X)<~>~funny(X))))&
((~quiet(susan))=>((~patient(susan)<~>tall(susan))))&
(![X]:((~curious(X)&old(X))<=>(wise(X)&humble(X))))&
((~creative(lucy)&tall(lucy)))&
(~tall(john))&
(~wise(alice))&
(~creative(mary))&
(?[X]:((~tall(X)&~brave(X))))&
(?[X]:((patient(X)&wise(X))))&
(?[X]:((~generous(X)<~>~kind(X))))&
(~brave(paul)) | ~strong(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3518916930722256801956687
% SZS output start Proof for 3518916930722256801956687
6. ! [X0] : ((~rich(X0) | ~strong(X0)) => (~generous(X0) & generous(X0))) [input p5]
25. ~strong(mary) [input hypothesis]
30. ! [X0] : ((~generous(X0) & generous(X0)) | (rich(X0) & strong(X0))) [ennf transformation 6]
89. generous(X0) | strong(X0) [cnf transformation 30]
91. ~generous(X0) | strong(X0) [cnf transformation 30]
136. ~strong(mary) [cnf transformation 25]
188. strong(X0) [subsumption resolution 89,91]
307. $false [subsumption resolution 136,188]
% SZS output end Proof for 3518916930722256801956687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not strong then someone is both not quiet and rich and vice versa.
Everyone who is not brave is both old and funny and vice versa.
If lucy is not curious then mary is kind.
If someone is both curious and wise then someone is either not old or not generous and vice versa.
Everyone who is wise or creative is generous or not strong.
If alice is strong then someone is not patient.
Everyone who is both not curious and not happy is either not calm or not funny and vice versa.
If susan is kind or calm then john is either not calm or old and vice versa.
Everyone who is both not rich and not calm is either humble or not tall.
Everyone who is tall or not happy is not creative and vice versa.
Everyone who is tall is not creative and vice versa.
If mary is not calm or happy then someone is creative or not quiet.
If someone is both not generous and strong then someone is curious or generous and vice versa.
Everyone who is both quiet and not wise is generous or not brave and vice versa.
Everyone who is both not quiet and calm is either humble or brave.
If paul is both not generous and not rich then someone is curious.
Fred is not tall or creative.
Alice is rich.
Someone is either not generous or not patient.
Fred is not curious.
Someone is not curious or not patient.
Paul is not tall or not curious.
Lucy is happy.
Fred is either not happy or funny. | Susan is not tall. | neutral | ((?[X]:((happy(X)<~>~strong(X))))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:(~brave(X)<=>(old(X)&funny(X))))&
((~curious(lucy))=>(kind(mary)))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((wise(X)|creative(X))=>(generous(X)|~strong(X))))&
((strong(alice))=>(?[X]:(~patient(X))))&
(![X]:((~curious(X)&~happy(X))<=>(~calm(X)<~>~funny(X))))&
(((kind(susan)|calm(susan)))<=>((~calm(john)<~>old(john))))&
(![X]:((~rich(X)&~calm(X))=>(humble(X)<~>~tall(X))))&
(![X]:((tall(X)|~happy(X))<=>~creative(X)))&
(![X]:(tall(X)<=>~creative(X)))&
(((~calm(mary)|happy(mary)))=>(?[X]:((creative(X)|~quiet(X)))))&
((?[X]:((~generous(X)&strong(X))))<=>(?[X]:((curious(X)|generous(X)))))&
(![X]:((quiet(X)&~wise(X))<=>(generous(X)|~brave(X))))&
(![X]:((~quiet(X)&calm(X))=>(humble(X)<~>brave(X))))&
(((~generous(paul)&~rich(paul)))=>(?[X]:(curious(X))))&
((~tall(fred)|creative(fred)))&
(rich(alice))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~curious(fred))&
(?[X]:((~curious(X)|~patient(X))))&
((~tall(paul)|~curious(paul)))&
(happy(lucy))&
((~happy(fred)<~>funny(fred))) | ~tall(susan) | [] | null | 0 |
Everyone who is both calm and not happy is calm and vice versa.
Everyone who is calm or generous is both brave and not tall and vice versa.
If someone is either not tall or not strong then someone is both happy and not quiet and vice versa.
Everyone who is not strong or old is both creative and patient.
If mary is either quiet or patient then fred is either not patient or not calm.
If john is both not quiet and not patient then fred is both patient and not strong and vice versa.
Everyone who is rich or patient is either not kind or not happy and vice versa.
If alice is both curious and not kind then alice is not humble or tall and vice versa.
If someone is both not calm and not happy then john is either not old or strong.
If mary is either not funny or not creative then mary is not humble and vice versa.
Everyone who is not old is both not humble and funny and vice versa.
If susan is either not creative or not humble then paul is curious and vice versa.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
If someone is either not quiet or patient then someone is either not quiet or not generous and vice versa.
Someone is either not old or old.
Someone is quiet.
John is both quiet and kind.
Someone is not calm.
Someone is both generous and rich.
Someone is both brave and curious.
Paul is either rich or patient. | Alice is calm. | contradiction | (![X]:((calm(X)&~happy(X))<=>calm(X)))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(?[X]:((~old(X)<~>old(X))))&
(?[X]:(quiet(X)))&
((quiet(john)&kind(john)))&
(?[X]:(~calm(X)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((brave(X)&curious(X))))&
((rich(paul)<~>patient(paul))) | calm(alice) | [
"p0",
"p1",
"p2",
"p3",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6776275992494508260641514
% SZS output start Proof for 6776275992494508260641514
1. ! [X0] : ((~happy(X0) & calm(X0)) <=> calm(X0)) [input p0]
2. ! [X0] : ((generous(X0) | calm(X0)) <=> (~tall(X0) & brave(X0))) [input p1]
3. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X0] : (~quiet(X0) & happy(X0)) [input p2]
4. ! [X0] : ((old(X0) | ~strong(X0)) => (patient(X0) & creative(X0))) [input p3]
13. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p12]
14. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> ~calm(X0)) [input p13]
15. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (wise(X0) & creative(X0))) [input p14]
24. calm(alice) [input hypothesis]
25. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X1] : (~quiet(X1) & happy(X1)) [rectify 3]
27. ! [X0] : ((patient(X0) & creative(X0)) | (~old(X0) & strong(X0))) [ennf transformation 4]
30. ! [X0] : (((~happy(X0) & calm(X0)) | ~calm(X0)) & (calm(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 1]
31. ! [X0] : (((~happy(X0) & calm(X0)) | ~calm(X0)) & (calm(X0) | happy(X0) | ~calm(X0))) [flattening 30]
32. ! [X0] : (((generous(X0) | calm(X0)) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 2]
33. ! [X0] : ((generous(X0) | calm(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 32]
34. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X1] : (~quiet(X1) & happy(X1)) | ! [X0] : ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 25]
35. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X2] : (~quiet(X2) & happy(X2)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [rectify 34]
36. ? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) => ((strong(sK0) | tall(sK0)) & (~strong(sK0) | ~tall(sK0))) [choice axiom]
37. ? [X2] : (~quiet(X2) & happy(X2)) => (~quiet(sK1) & happy(sK1)) [choice axiom]
38. (((strong(sK0) | tall(sK0)) & (~strong(sK0) | ~tall(sK0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & ((~quiet(sK1) & happy(sK1)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [skolemisation 35,37,36]
51. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 13]
52. ! [X0] : (((~funny(X0) | ~wise(X0)) | calm(X0)) & (~calm(X0) | (funny(X0) & wise(X0)))) [nnf transformation 14]
53. ! [X0] : ((~funny(X0) | ~wise(X0) | calm(X0)) & (~calm(X0) | (funny(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 15]
55. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 54]
75. ~happy(X0) | ~calm(X0) [cnf transformation 31]
78. ~tall(X0) | ~calm(X0) [cnf transformation 33]
83. ~quiet(sK1) | ~strong(X3) | tall(X3) [cnf transformation 38]
87. creative(X0) | strong(X0) [cnf transformation 27]
123. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 51]
126. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 51]
127. ~calm(X0) | wise(X0) [cnf transformation 53]
135. ~wise(X0) | happy(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 55]
156. calm(alice) [cnf transformation 24]
158. ~wise(X0) | happy(X0) | ~creative(X0) [duplicate literal removal 135]
159. wise(X0) | quiet(X0) [duplicate literal removal 123]
160. ~wise(X0) | quiet(X0) [duplicate literal removal 126]
178. 5 <=> quiet(sK1) [avatar definition]
180. ~quiet(sK1) <- (~5) [avatar component clause 178]
183. 6 <=> ! [X3] : (~strong(X3) | tall(X3)) [avatar definition]
184. ~strong(X3) | tall(X3) <- (6) [avatar component clause 183]
185. 6 | ~5 [avatar split clause 83,178,183]
231. 15 <=> tall(alice) [avatar definition]
232. tall(alice) <- (15) [avatar component clause 231]
296. quiet(X0) [subsumption resolution 159,160]
329. $false <- (~5) [subsumption resolution 180,296]
330. 5 [avatar contradiction clause 329]
353. wise(alice) [resolution 127,156]
419. 42 <=> happy(alice) [avatar definition]
420. ~happy(alice) <- (~42) [avatar component clause 419]
421. happy(alice) <- (42) [avatar component clause 419]
465. 47 <=> creative(alice) [avatar definition]
466. ~creative(alice) <- (~47) [avatar component clause 465]
470. happy(alice) | ~creative(alice) [resolution 158,353]
473. ~creative(alice) <- (~42) [subsumption resolution 470,420]
474. ~47 | 42 [avatar split clause 473,419,465]
524. strong(alice) <- (~47) [resolution 466,87]
557. tall(alice) <- (6, ~47) [resolution 524,184]
560. 15 | ~6 | 47 [avatar split clause 557,465,183,231]
563. ~calm(alice) <- (15) [resolution 232,78]
564. $false <- (15) [subsumption resolution 563,156]
565. ~15 [avatar contradiction clause 564]
568. ~calm(alice) <- (42) [resolution 421,75]
579. $false <- (42) [subsumption resolution 568,156]
580. ~42 [avatar contradiction clause 579]
581. $false [avatar sat refutation 185,330,474,560,565,580]
% SZS output end Proof for 6776275992494508260641514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or patient is either humble or not wise and vice versa.
If mary is both not rich and wise then someone is either not calm or strong and vice versa.
If someone is either quiet or not calm then someone is both generous and not strong and vice versa.
If someone is not generous then someone is tall or curious and vice versa.
If john is not tall then someone is not humble.
Everyone who is not generous or not tall is both not tall and not strong.
If someone is not quiet then someone is both not patient and not humble.
If someone is either tall or brave then lucy is not kind.
If someone is not rich or not old then susan is not brave or not generous and vice versa.
Everyone who is both creative and not funny is both not funny and not curious and vice versa.
Everyone who is wise or brave is both not strong and kind and vice versa.
If mary is both brave and not funny then fred is brave or old and vice versa.
If alice is either not wise or not calm then john is not wise or kind and vice versa.
Everyone who is either not strong or not rich is old and vice versa.
If someone is either not curious or not old then someone is both not happy and not curious and vice versa.
If john is tall then someone is both kind and tall and vice versa.
John is not funny or old.
Someone is both happy and not patient.
Lucy is not curious.
Lucy is both patient and not humble.
Someone is both not happy and not strong.
Someone is not funny or wise.
Lucy is either humble or not tall.
Someone is either not strong or rich. | Lucy is patient. | entailment | (![X]:((wise(X)|patient(X))<=>(humble(X)<~>~wise(X))))&
(((~rich(mary)&wise(mary)))<=>(?[X]:((~calm(X)<~>strong(X)))))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((tall(X)|curious(X)))))&
((~tall(john))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|~tall(X))=>(~tall(X)&~strong(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
((?[X]:((tall(X)<~>brave(X))))=>(~kind(lucy)))&
((?[X]:((~rich(X)|~old(X))))<=>((~brave(susan)|~generous(susan))))&
(![X]:((creative(X)&~funny(X))<=>(~funny(X)&~curious(X))))&
(![X]:((wise(X)|brave(X))<=>(~strong(X)&kind(X))))&
(((brave(mary)&~funny(mary)))<=>((brave(fred)|old(fred))))&
(((~wise(alice)<~>~calm(alice)))<=>((~wise(john)|kind(john))))&
(![X]:((~strong(X)<~>~rich(X))<=>old(X)))&
((?[X]:((~curious(X)<~>~old(X))))<=>(?[X]:((~happy(X)&~curious(X)))))&
((tall(john))<=>(?[X]:((kind(X)&tall(X)))))&
((~funny(john)|old(john)))&
(?[X]:((happy(X)&~patient(X))))&
(~curious(lucy))&
((patient(lucy)&~humble(lucy)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~funny(X)|wise(X))))&
((humble(lucy)<~>~tall(lucy)))&
(?[X]:((~strong(X)<~>rich(X)))) | patient(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5536434681098442239121783
% SZS output start Proof for 5536434681098442239121783
20. ~humble(lucy) & patient(lucy) [input p19]
25. ~patient(lucy) [input hypothesis]
161. patient(lucy) [cnf transformation 20]
170. ~patient(lucy) [cnf transformation 25]
431. $false [subsumption resolution 170,161]
% SZS output end Proof for 5536434681098442239121783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not tall or old then alice is curious or not rich.
Everyone who is both not brave and rich is not patient and vice versa.
Everyone who is quiet or funny is both not brave and rich and vice versa.
Everyone who is rich or not humble is either not rich or strong and vice versa.
Everyone who is both brave and not funny is either not wise or not humble.
If someone is not quiet or brave then someone is either not calm or funny.
If someone is either calm or old then someone is not happy or quiet and vice versa.
If someone is humble then someone is both not rich and kind and vice versa.
Everyone who is either not strong or not funny is patient and vice versa.
If susan is quiet then john is not brave or patient.
Everyone who is either not curious or not happy is either humble or quiet and vice versa.
If alice is not curious or not old then someone is not quiet or strong.
Everyone who is both not happy and not calm is curious and vice versa.
If someone is not happy or not calm then alice is both not tall and not rich.
If susan is not rich or not kind then someone is brave.
Everyone who is not funny is either not happy or calm.
Mary is both tall and kind.
Alice is not patient.
Susan is kind or not quiet.
Alice is not tall.
Lucy is either rich or calm.
Someone is either funny or quiet.
Susan is strong. | Alice is old. | neutral | (((~tall(fred)<~>old(fred)))=>((curious(alice)|~rich(alice))))&
(![X]:((~brave(X)&rich(X))<=>~patient(X)))&
(![X]:((quiet(X)|funny(X))<=>(~brave(X)&rich(X))))&
(![X]:((rich(X)|~humble(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((brave(X)&~funny(X))=>(~wise(X)<~>~humble(X))))&
((?[X]:((~quiet(X)|brave(X))))=>(?[X]:((~calm(X)<~>funny(X)))))&
((?[X]:((calm(X)<~>old(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>patient(X)))&
((quiet(susan))=>((~brave(john)|patient(john))))&
(![X]:((~curious(X)<~>~happy(X))<=>(humble(X)<~>quiet(X))))&
(((~curious(alice)|~old(alice)))=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~calm(X))<=>curious(X)))&
((?[X]:((~happy(X)|~calm(X))))=>((~tall(alice)&~rich(alice))))&
(((~rich(susan)|~kind(susan)))=>(?[X]:(brave(X))))&
(![X]:(~funny(X)=>(~happy(X)<~>calm(X))))&
((tall(mary)&kind(mary)))&
(~patient(alice))&
((kind(susan)|~quiet(susan)))&
(~tall(alice))&
((rich(lucy)<~>calm(lucy)))&
(?[X]:((funny(X)<~>quiet(X))))&
(strong(susan)) | old(alice) | [] | null | 0 |
Everyone who is brave is not patient or not quiet. Everyone who is both not brave and rich is curious and vice versa. Everyone who is either curious or brave is quiet. If someone is both not kind and rich then someone is not curious or wise. If someone is either tall or generous then someone is rich and vice versa. Everyone who is either creative or brave is not tall or not kind. Everyone who is not wise or calm is both brave and not creative and vice versa. If fred is old or not funny then someone is both not happy and not brave. Everyone who is both funny and rich is either calm or kind. Everyone who is either generous or not happy is both generous and not patient and vice versa. Everyone who is either old or curious is not patient or humble and vice versa. If paul is curious or strong then someone is both not rich and creative. If paul is either not kind or not patient then john is quiet or not strong. If susan is calm or not funny then mary is not old. If someone is not happy or not old then fred is brave and vice versa. Someone is either not funny or rich. Someone is either creative or not tall. Someone is funny or not wise. Someone is both not old and not funny. Someone is both kind and not happy. Someone is calm or not wise. Someone is either not brave or not calm. Someone is both not quiet and generous. | Fred is patient. | contradiction | (![X]:(brave(X)=>(~patient(X)|~quiet(X))))&
(![X]:((~brave(X)&rich(X))<=>curious(X)))&
(![X]:((curious(X)<~>brave(X))=>quiet(X)))&
((?[X]:((~kind(X)&rich(X))))=>(?[X]:((~curious(X)|wise(X)))))&
((?[X]:((tall(X)<~>generous(X))))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)<~>brave(X))=>(~tall(X)|~kind(X))))&
(![X]:((~wise(X)|calm(X))<=>(brave(X)&~creative(X))))&
(((old(fred)|~funny(fred)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((funny(X)&rich(X))=>(calm(X)<~>kind(X))))&
(![X]:((generous(X)<~>~happy(X))<=>(generous(X)&~patient(X))))&
(![X]:((old(X)<~>curious(X))<=>(~patient(X)|humble(X))))&
(((curious(paul)|strong(paul)))=>(?[X]:((~rich(X)&creative(X)))))&
(((~kind(paul)<~>~patient(paul)))=>((quiet(john)|~strong(john))))&
(((calm(susan)|~funny(susan)))=>(~old(mary)))&
((?[X]:((~happy(X)|~old(X))))<=>(brave(fred)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((funny(X)|~wise(X))))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((kind(X)&~happy(X))))&
(?[X]:((calm(X)|~wise(X))))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((~quiet(X)&generous(X)))) | patient(fred) | [
"p0",
"p1",
"p2",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4742208948625196704570758
% SZS output start Proof for 4742208948625196704570758
1. ! [X0] : (brave(X0) => (~quiet(X0) | ~patient(X0))) [input p0]
2. ! [X0] : ((rich(X0) & ~brave(X0)) <=> curious(X0)) [input p1]
3. ! [X0] : ((curious(X0) <~> brave(X0)) => quiet(X0)) [input p2]
15. ? [X0] : (~old(X0) | ~happy(X0)) <=> brave(fred) [input p14]
19. ? [X0] : (~funny(X0) & ~old(X0)) [input p18]
24. patient(fred) [input hypothesis]
29. ! [X0] : ((~quiet(X0) | ~patient(X0)) | ~brave(X0)) [ennf transformation 1]
30. ! [X0] : (~quiet(X0) | ~patient(X0) | ~brave(X0)) [flattening 29]
31. ! [X0] : (quiet(X0) | (curious(X0) <=> brave(X0))) [ennf transformation 3]
40. ! [X0] : (((rich(X0) & ~brave(X0)) | ~curious(X0)) & (curious(X0) | (~rich(X0) | brave(X0)))) [nnf transformation 2]
41. ! [X0] : (((rich(X0) & ~brave(X0)) | ~curious(X0)) & (curious(X0) | ~rich(X0) | brave(X0))) [flattening 40]
42. ! [X0] : (quiet(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) [nnf transformation 31]
63. (? [X0] : (~old(X0) | ~happy(X0)) | ~brave(fred)) & (brave(fred) | ! [X0] : (old(X0) & happy(X0))) [nnf transformation 15]
64. (? [X0] : (~old(X0) | ~happy(X0)) | ~brave(fred)) & (brave(fred) | ! [X1] : (old(X1) & happy(X1))) [rectify 63]
65. ? [X0] : (~old(X0) | ~happy(X0)) => (~old(sK5) | ~happy(sK5)) [choice axiom]
66. ((~old(sK5) | ~happy(sK5)) | ~brave(fred)) & (brave(fred) | ! [X1] : (old(X1) & happy(X1))) [skolemisation 64,65]
75. ? [X0] : (~funny(X0) & ~old(X0)) => (~funny(sK9) & ~old(sK9)) [choice axiom]
76. ~funny(sK9) & ~old(sK9) [skolemisation 19,75]
86. ~quiet(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 30]
88. ~curious(X0) | ~brave(X0) [cnf transformation 41]
91. quiet(X0) | curious(X0) | ~brave(X0) [cnf transformation 42]
127. brave(fred) | old(X1) [cnf transformation 66]
134. ~old(sK9) [cnf transformation 76]
143. patient(fred) [cnf transformation 24]
146. ~brave(X0) | quiet(X0) [subsumption resolution 91,88]
234. 20 <=> brave(fred) [avatar definition]
235. brave(fred) <- (20) [avatar component clause 234]
247. 23 <=> ! [X1] : old(X1) [avatar definition]
248. old(X1) <- (23) [avatar component clause 247]
249. 23 | 20 [avatar split clause 127,234,247]
300. quiet(fred) <- (20) [resolution 146,235]
304. ~patient(fred) | ~brave(fred) <- (20) [resolution 300,86]
305. ~brave(fred) <- (20) [subsumption resolution 304,143]
306. $false <- (20) [subsumption resolution 305,235]
307. ~20 [avatar contradiction clause 306]
308. $false <- (23) [resolution 248,134]
313. ~23 [avatar contradiction clause 308]
314. $false [avatar sat refutation 249,307,313]
% SZS output end Proof for 4742208948625196704570758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or curious is happy.
Everyone who is both patient and not patient is not old or wise and vice versa.
Everyone who is either not happy or patient is old.
Everyone who is kind is both funny and not funny.
If fred is not patient then someone is either generous or creative and vice versa.
If alice is not brave then paul is either not creative or wise and vice versa.
Everyone who is not creative or not rich is both funny and not curious and vice versa.
If john is both rich and creative then paul is old or strong and vice versa.
If someone is not patient then susan is calm and vice versa.
Everyone who is not curious or tall is tall or calm and vice versa.
Everyone who is both not humble and patient is both calm and patient.
If someone is not kind then someone is both not creative and not brave.
Everyone who is both rich and not happy is not funny.
If someone is either tall or not tall then susan is either patient or not old.
If someone is either old or not strong then fred is both brave and rich.
Everyone who is not old is both quiet and not generous and vice versa.
Someone is not tall or rich.
Paul is not humble or kind.
Someone is both not calm and not tall.
Someone is either wise or not brave.
Someone is both not wise and not happy.
Susan is both not quiet and not wise.
John is both not generous and not quiet. | John is not kind. | entailment | (![X]:((~humble(X)|curious(X))=>happy(X)))&
(![X]:((patient(X)&~patient(X))<=>(~old(X)|wise(X))))&
(![X]:((~happy(X)<~>patient(X))=>old(X)))&
(![X]:(kind(X)=>(funny(X)&~funny(X))))&
((~patient(fred))<=>(?[X]:((generous(X)<~>creative(X)))))&
((~brave(alice))<=>((~creative(paul)<~>wise(paul))))&
(![X]:((~creative(X)|~rich(X))<=>(funny(X)&~curious(X))))&
(((rich(john)&creative(john)))<=>((old(paul)|strong(paul))))&
((?[X]:(~patient(X)))<=>(calm(susan)))&
(![X]:((~curious(X)|tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~humble(X)&patient(X))=>(calm(X)&patient(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((rich(X)&~happy(X))=>~funny(X)))&
((?[X]:((tall(X)<~>~tall(X))))=>((patient(susan)<~>~old(susan))))&
((?[X]:((old(X)<~>~strong(X))))=>((brave(fred)&rich(fred))))&
(![X]:(~old(X)<=>(quiet(X)&~generous(X))))&
(?[X]:((~tall(X)|rich(X))))&
((~humble(paul)|kind(paul)))&
(?[X]:((~calm(X)&~tall(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~wise(X)&~happy(X))))&
((~quiet(susan)&~wise(susan)))&
((~generous(john)&~quiet(john))) | ~kind(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7553182343526390432200978
% SZS output start Proof for 7553182343526390432200978
4. ! [X0] : (kind(X0) => (~funny(X0) & funny(X0))) [input p3]
24. kind(john) [input hypothesis]
28. ! [X0] : ((~funny(X0) & funny(X0)) | ~kind(X0)) [ennf transformation 4]
79. funny(X0) | ~kind(X0) [cnf transformation 28]
80. ~funny(X0) | ~kind(X0) [cnf transformation 28]
133. kind(john) [cnf transformation 24]
140. ~kind(X0) [subsumption resolution 79,80]
249. $false [subsumption resolution 133,140]
% SZS output end Proof for 7553182343526390432200978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not funny or curious and vice versa.
Everyone who is both not patient and happy is quiet or not kind and vice versa.
If someone is both not creative and tall then john is old or not generous and vice versa.
Everyone who is either not creative or old is not rich or not tall.
Everyone who is not patient is funny.
If someone is both kind and strong then alice is happy or patient.
If someone is either not kind or not generous then lucy is calm and vice versa.
Everyone who is both happy and not quiet is both not tall and wise.
If lucy is both not patient and not happy then someone is both not generous and not funny and vice versa.
If fred is generous or not calm then lucy is both not kind and not curious and vice versa.
Everyone who is not happy is either not calm or brave and vice versa.
If susan is patient or not tall then lucy is not happy or not tall and vice versa.
If someone is either not happy or generous then someone is not brave or funny.
If someone is either not patient or funny then someone is either not kind or not calm.
Everyone who is rich is either not humble or humble and vice versa.
If someone is either old or curious then lucy is either rich or not quiet and vice versa.
Fred is both not humble and not calm.
Someone is not tall or patient.
Someone is brave or not rich.
Someone is both not calm and not creative.
Mary is not rich or funny.
Paul is not wise or not humble.
Alice is both strong and not happy.
Alice is strong. | Mary is not curious. | entailment | (![X]:(~funny(X)<=>(~funny(X)<~>curious(X))))&
(![X]:((~patient(X)&happy(X))<=>(quiet(X)|~kind(X))))&
((?[X]:((~creative(X)&tall(X))))<=>((old(john)|~generous(john))))&
(![X]:((~creative(X)<~>old(X))=>(~rich(X)|~tall(X))))&
(![X]:(~patient(X)=>funny(X)))&
((?[X]:((kind(X)&strong(X))))=>((happy(alice)|patient(alice))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(calm(lucy)))&
(![X]:((happy(X)&~quiet(X))=>(~tall(X)&wise(X))))&
(((~patient(lucy)&~happy(lucy)))<=>(?[X]:((~generous(X)&~funny(X)))))&
(((generous(fred)|~calm(fred)))<=>((~kind(lucy)&~curious(lucy))))&
(![X]:(~happy(X)<=>(~calm(X)<~>brave(X))))&
(((patient(susan)|~tall(susan)))<=>((~happy(lucy)|~tall(lucy))))&
((?[X]:((~happy(X)<~>generous(X))))=>(?[X]:((~brave(X)|funny(X)))))&
((?[X]:((~patient(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(rich(X)<=>(~humble(X)<~>humble(X))))&
((?[X]:((old(X)<~>curious(X))))<=>((rich(lucy)<~>~quiet(lucy))))&
((~humble(fred)&~calm(fred)))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~calm(X)&~creative(X))))&
((~rich(mary)|funny(mary)))&
((~wise(paul)|~humble(paul)))&
((strong(alice)&~happy(alice)))&
(strong(alice)) | ~curious(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8374323740616622136556998
% SZS output start Proof for 8374323740616622136556998
1. ! [X0] : (~funny(X0) <=> (~funny(X0) <~> curious(X0))) [input p0]
25. curious(mary) [input hypothesis]
37. ! [X0] : ((~funny(X0) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) & (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | funny(X0))) [nnf transformation 1]
80. ~curious(X0) | funny(X0) | funny(X0) [cnf transformation 37]
82. ~funny(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 37]
149. curious(mary) [cnf transformation 25]
152. ~curious(X0) | funny(X0) [duplicate literal removal 80]
153. ~funny(X0) | ~curious(X0) [duplicate literal removal 82]
154. ~curious(X0) [subsumption resolution 152,153]
337. $false [subsumption resolution 149,154]
% SZS output end Proof for 8374323740616622136556998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or quiet is both not wise and not quiet. If fred is both tall and strong then someone is happy or not kind and vice versa. Everyone who is both generous and not curious is curious. If someone is either not brave or not wise then alice is calm. Everyone who is tall or not strong is not calm or not brave and vice versa. Everyone who is not wise is either calm or curious and vice versa. If lucy is both wise and calm then someone is either not brave or not quiet. If paul is both quiet and not brave then lucy is either strong or not generous. Everyone who is not funny or not tall is not humble or curious and vice versa. If someone is either not generous or quiet then susan is both wise and generous and vice versa. If someone is old or not calm then john is quiet. Everyone who is rich is both funny and not wise and vice versa. If someone is either creative or generous then someone is brave or not kind and vice versa. Everyone who is both humble and kind is either old or brave and vice versa. Everyone who is both kind and generous is either quiet or funny and vice versa. Someone is strong or not rich. Someone is wise or not patient. Someone is both happy and not generous. Alice is wise. Someone is both happy and not curious. Fred is both kind and not humble. Someone is strong or old. Someone is happy or not patient. | Alice is brave. | contradiction | (![X]:((humble(X)|quiet(X))=>(~wise(X)&~quiet(X))))&
(((tall(fred)&strong(fred)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((generous(X)&~curious(X))=>curious(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>(calm(alice)))&
(![X]:((tall(X)|~strong(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>curious(X))))&
(((wise(lucy)&calm(lucy)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((quiet(paul)&~brave(paul)))=>((strong(lucy)<~>~generous(lucy))))&
(![X]:((~funny(X)|~tall(X))<=>(~humble(X)|curious(X))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((wise(susan)&generous(susan))))&
((?[X]:((old(X)|~calm(X))))=>(quiet(john)))&
(![X]:(rich(X)<=>(funny(X)&~wise(X))))&
((?[X]:((creative(X)<~>generous(X))))<=>(?[X]:((brave(X)|~kind(X)))))&
(![X]:((humble(X)&kind(X))<=>(old(X)<~>brave(X))))&
(![X]:((kind(X)&generous(X))<=>(quiet(X)<~>funny(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:((happy(X)&~generous(X))))&
(wise(alice))&
(?[X]:((happy(X)&~curious(X))))&
((kind(fred)&~humble(fred)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((happy(X)|~patient(X)))) | brave(alice) | [
"p0",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6542361698150921705960781
% SZS output start Proof for 6542361698150921705960781
1. ! [X0] : ((quiet(X0) | humble(X0)) => (~quiet(X0) & ~wise(X0))) [input p0]
11. ? [X0] : (~calm(X0) | old(X0)) => quiet(john) [input p10]
14. ! [X0] : ((kind(X0) & humble(X0)) <=> (old(X0) <~> brave(X0))) [input p13]
19. wise(alice) [input p18]
24. brave(alice) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 1]
37. quiet(john) | ! [X0] : (calm(X0) & ~old(X0)) [ennf transformation 11]
65. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~kind(X0) | ~humble(X0)))) [nnf transformation 14]
66. ! [X0] : (((kind(X0) & humble(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | ~kind(X0) | ~humble(X0))) [flattening 65]
77. ~wise(X0) | ~humble(X0) [cnf transformation 29]
80. ~quiet(X0) | ~quiet(X0) [cnf transformation 29]
111. quiet(john) | ~old(X0) [cnf transformation 37]
123. humble(X0) | old(X0) | ~brave(X0) [cnf transformation 66]
135. wise(alice) [cnf transformation 19]
141. brave(alice) [cnf transformation 24]
143. ~quiet(X0) [duplicate literal removal 80]
219. ~old(X0) [subsumption resolution 111,143]
252. ~brave(X0) | humble(X0) [subsumption resolution 123,219]
269. ~humble(alice) [resolution 77,135]
273. humble(alice) [resolution 252,141]
274. $false [subsumption resolution 273,269]
% SZS output end Proof for 6542361698150921705960781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and old is both generous and not humble. Everyone who is old or curious is humble or generous and vice versa. Everyone who is both creative and not quiet is either not rich or not kind and vice versa. Everyone who is not strong is quiet or rich. Everyone who is either kind or not rich is both brave and not old. If mary is either strong or not rich then someone is funny. If lucy is quiet or funny then someone is not old. If fred is either kind or not brave then someone is not calm or brave and vice versa. If someone is either not rich or not quiet then someone is either not generous or not rich. If john is both kind and curious then someone is either not creative or rich and vice versa. Everyone who is both not funny and not curious is both not wise and not tall. Everyone who is both not curious and not quiet is either happy or funny. If john is funny then someone is not quiet or not funny and vice versa. Everyone who is both not kind and patient is either creative or not rich and vice versa. Everyone who is either not happy or funny is funny. If someone is either old or brave then someone is both not brave and not curious and vice versa. Fred is not strong. Someone is creative. Alice is quiet. Someone is happy or not generous. Someone is both not curious and not wise. Susan is calm. Paul is not calm. Someone is either not tall or not patient. | Fred is not rich. | contradiction | (![X]:((creative(X)&old(X))=>(generous(X)&~humble(X))))&
(![X]:((old(X)|curious(X))<=>(humble(X)|generous(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~rich(X)<~>~kind(X))))&
(![X]:(~strong(X)=>(quiet(X)|rich(X))))&
(![X]:((kind(X)<~>~rich(X))=>(brave(X)&~old(X))))&
(((strong(mary)<~>~rich(mary)))=>(?[X]:(funny(X))))&
(((quiet(lucy)|funny(lucy)))=>(?[X]:(~old(X))))&
(((kind(fred)<~>~brave(fred)))<=>(?[X]:((~calm(X)|brave(X)))))&
((?[X]:((~rich(X)<~>~quiet(X))))=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((kind(john)&curious(john)))<=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:((~funny(X)&~curious(X))=>(~wise(X)&~tall(X))))&
(![X]:((~curious(X)&~quiet(X))=>(happy(X)<~>funny(X))))&
((funny(john))<=>(?[X]:((~quiet(X)|~funny(X)))))&
(![X]:((~kind(X)&patient(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((~happy(X)<~>funny(X))=>funny(X)))&
((?[X]:((old(X)<~>brave(X))))<=>(?[X]:((~brave(X)&~curious(X)))))&
(~strong(fred))&
(?[X]:(creative(X)))&
(quiet(alice))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~curious(X)&~wise(X))))&
(calm(susan))&
(~calm(paul))&
(?[X]:((~tall(X)<~>~patient(X)))) | ~rich(fred) | [
"p2",
"p3",
"p4",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 181073841475010567835682
% SZS output start Proof for 181073841475010567835682
3. ! [X0] : ((~quiet(X0) & creative(X0)) <=> (~rich(X0) <~> ~kind(X0))) [input p2]
4. ! [X0] : (~strong(X0) => (rich(X0) | quiet(X0))) [input p3]
5. ! [X0] : ((kind(X0) <~> ~rich(X0)) => (~old(X0) & brave(X0))) [input p4]
8. (kind(fred) <~> ~brave(fred)) <=> ? [X0] : (brave(X0) | ~calm(X0)) [input p7]
17. ~strong(fred) [input p16]
25. ~rich(fred) [input hypothesis]
32. ! [X0] : ((rich(X0) | quiet(X0)) | strong(X0)) [ennf transformation 4]
33. ! [X0] : (rich(X0) | quiet(X0) | strong(X0)) [flattening 32]
34. ! [X0] : ((~old(X0) & brave(X0)) | (kind(X0) <=> ~rich(X0))) [ennf transformation 5]
45. ! [X0] : (((~quiet(X0) & creative(X0)) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | (quiet(X0) | ~creative(X0)))) [nnf transformation 3]
46. ! [X0] : (((~quiet(X0) & creative(X0)) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) & (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | quiet(X0) | ~creative(X0))) [flattening 45]
47. ! [X0] : ((~old(X0) & brave(X0)) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) [nnf transformation 34]
53. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : (~brave(X0) & calm(X0))) & (? [X0] : (brave(X0) | ~calm(X0)) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [nnf transformation 8]
54. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : (~brave(X0) & calm(X0))) & (? [X1] : (brave(X1) | ~calm(X1)) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [rectify 53]
55. ? [X1] : (brave(X1) | ~calm(X1)) => (brave(sK2) | ~calm(sK2)) [choice axiom]
56. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : (~brave(X0) & calm(X0))) & ((brave(sK2) | ~calm(sK2)) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [skolemisation 54,55]
98. ~kind(X0) | ~quiet(X0) | rich(X0) [cnf transformation 46]
100. strong(X0) | quiet(X0) | rich(X0) [cnf transformation 33]
102. brave(X0) | kind(X0) | rich(X0) [cnf transformation 47]
112. ~brave(fred) | kind(fred) | ~brave(X0) [cnf transformation 56]
145. ~strong(fred) [cnf transformation 17]
154. ~rich(fred) [cnf transformation 25]
185. 7 <=> ! [X0] : ~brave(X0) [avatar definition]
186. ~brave(X0) <- (7) [avatar component clause 185]
188. 8 <=> kind(fred) [avatar definition]
189. kind(fred) <- (8) [avatar component clause 188]
190. ~kind(fred) <- (~8) [avatar component clause 188]
192. 9 <=> brave(fred) [avatar definition]
193. ~brave(fred) <- (~9) [avatar component clause 192]
194. brave(fred) <- (9) [avatar component clause 192]
200. 7 | 8 | ~9 [avatar split clause 112,192,188,185]
382. quiet(fred) | rich(fred) [resolution 100,145]
383. quiet(fred) [subsumption resolution 382,154]
386. kind(fred) | rich(fred) <- (~9) [resolution 102,193]
388. rich(fred) <- (~8, ~9) [subsumption resolution 386,190]
389. $false <- (~8, ~9) [subsumption resolution 388,154]
390. 8 | 9 [avatar contradiction clause 389]
401. ~quiet(fred) | rich(fred) <- (8) [resolution 189,98]
403. rich(fred) <- (8) [subsumption resolution 401,383]
404. $false <- (8) [subsumption resolution 403,154]
405. ~8 [avatar contradiction clause 404]
411. $false <- (7, 9) [resolution 194,186]
412. ~7 | ~9 [avatar contradiction clause 411]
413. $false [avatar sat refutation 200,390,405,412]
% SZS output end Proof for 181073841475010567835682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not calm is either quiet or not happy.
Everyone who is both funny and not strong is generous or happy and vice versa.
Everyone who is both not curious and calm is both creative and not quiet.
Everyone who is not tall or funny is wise or not rich and vice versa.
If fred is not generous or not patient then someone is wise or calm.
Everyone who is not rich is generous and vice versa.
Everyone who is brave or happy is both curious and creative.
Everyone who is wise or not humble is not creative.
If someone is calm then someone is happy or kind and vice versa.
If john is not wise then paul is funny.
Everyone who is both not quiet and creative is humble.
Everyone who is either not happy or curious is not funny and vice versa.
Everyone who is not calm is both not old and not quiet and vice versa.
If paul is either humble or brave then someone is either not tall or patient.
If lucy is not kind then susan is both humble and strong.
If alice is brave or rich then someone is not old or generous.
Alice is either not generous or not funny.
Mary is not generous or humble.
Someone is either wise or quiet.
Paul is both not brave and not strong.
John is not creative.
Someone is generous or not generous.
Someone is tall. | Fred is rich. | neutral | (![X]:((creative(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~strong(X))<=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&calm(X))=>(creative(X)&~quiet(X))))&
(![X]:((~tall(X)|funny(X))<=>(wise(X)|~rich(X))))&
(((~generous(fred)|~patient(fred)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((brave(X)|happy(X))=>(curious(X)&creative(X))))&
(![X]:((wise(X)|~humble(X))=>~creative(X)))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|kind(X)))))&
((~wise(john))=>(funny(paul)))&
(![X]:((~quiet(X)&creative(X))=>humble(X)))&
(![X]:((~happy(X)<~>curious(X))<=>~funny(X)))&
(![X]:(~calm(X)<=>(~old(X)&~quiet(X))))&
(((humble(paul)<~>brave(paul)))=>(?[X]:((~tall(X)<~>patient(X)))))&
((~kind(lucy))=>((humble(susan)&strong(susan))))&
(((brave(alice)|rich(alice)))=>(?[X]:((~old(X)|generous(X)))))&
((~generous(alice)<~>~funny(alice)))&
((~generous(mary)|humble(mary)))&
(?[X]:((wise(X)<~>quiet(X))))&
((~brave(paul)&~strong(paul)))&
(~creative(john))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:(tall(X))) | rich(fred) | [] | null | 0 |
If susan is either generous or not funny then someone is generous and vice versa. Everyone who is not brave or generous is calm or brave. If someone is both not wise and not kind then someone is either not happy or generous and vice versa. Everyone who is not rich or tall is both not rich and not generous. Everyone who is not brave is strong and vice versa. Everyone who is both not brave and not calm is not generous and vice versa. If fred is both not tall and wise then susan is not wise. If someone is both funny and brave then someone is patient or kind. If lucy is either not tall or not happy then susan is tall. If someone is wise then someone is both funny and not humble and vice versa. Everyone who is curious is either strong or generous. If someone is either wise or old then someone is humble or not calm. Everyone who is creative is rich. If lucy is both happy and not generous then alice is either brave or not generous and vice versa. If someone is either kind or not rich then susan is either rich or not old. Mary is not curious or happy. Someone is either wise or not curious. Someone is not humble. Someone is not old or not curious. Susan is either not curious or not rich. Someone is patient or not funny. Someone is wise. | Susan is not generous. | contradiction | (((generous(susan)<~>~funny(susan)))<=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|generous(X))=>(calm(X)|brave(X))))&
((?[X]:((~wise(X)&~kind(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~rich(X)|tall(X))=>(~rich(X)&~generous(X))))&
(![X]:(~brave(X)<=>strong(X)))&
(![X]:((~brave(X)&~calm(X))<=>~generous(X)))&
(((~tall(fred)&wise(fred)))=>(~wise(susan)))&
((?[X]:((funny(X)&brave(X))))=>(?[X]:((patient(X)|kind(X)))))&
(((~tall(lucy)<~>~happy(lucy)))=>(tall(susan)))&
((?[X]:(wise(X)))<=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:(curious(X)=>(strong(X)<~>generous(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(creative(X)=>rich(X)))&
(((happy(lucy)&~generous(lucy)))<=>((brave(alice)<~>~generous(alice))))&
((?[X]:((kind(X)<~>~rich(X))))=>((rich(susan)<~>~old(susan))))&
((~curious(mary)|happy(mary)))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~old(X)|~curious(X))))&
((~curious(susan)<~>~rich(susan)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:(wise(X))) | ~generous(susan) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 183278676714287394840258
% SZS output start Proof for 183278676714287394840258
2. ! [X0] : ((generous(X0) | ~brave(X0)) => (brave(X0) | calm(X0))) [input p1]
6. ! [X0] : ((~calm(X0) & ~brave(X0)) <=> ~generous(X0)) [input p5]
23. ~generous(susan) [input hypothesis]
31. ! [X0] : ((brave(X0) | calm(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 2]
32. ! [X0] : (brave(X0) | calm(X0) | (~generous(X0) & brave(X0))) [flattening 31]
50. ! [X0] : (((~calm(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | (calm(X0) | brave(X0)))) [nnf transformation 6]
51. ! [X0] : (((~calm(X0) & ~brave(X0)) | generous(X0)) & (~generous(X0) | calm(X0) | brave(X0))) [flattening 50]
80. brave(X0) | calm(X0) | brave(X0) [cnf transformation 32]
95. ~brave(X0) | generous(X0) [cnf transformation 51]
96. ~calm(X0) | generous(X0) [cnf transformation 51]
125. ~generous(susan) [cnf transformation 23]
126. calm(X0) | brave(X0) [duplicate literal removal 80]
131. 2 <=> generous(susan) [avatar definition]
133. ~generous(susan) <- (~2) [avatar component clause 131]
314. ~2 [avatar split clause 125,131]
322. brave(X0) | generous(X0) [resolution 126,96]
323. generous(X0) [subsumption resolution 322,95]
331. $false <- (~2) [resolution 323,133]
338. 2 [avatar contradiction clause 331]
339. $false [avatar sat refutation 314,338]
% SZS output end Proof for 183278676714287394840258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not brave and not quiet then john is either curious or not old and vice versa. If someone is humble then susan is both calm and strong and vice versa. If paul is quiet or not old then mary is old and vice versa. If someone is either not brave or calm then mary is either not happy or brave and vice versa. Everyone who is not brave is kind and vice versa. If john is humble or not patient then someone is either not generous or not curious and vice versa. If lucy is not funny or wise then lucy is either not wise or tall. If someone is happy then someone is not strong. Everyone who is rich or not tall is both curious and not creative and vice versa. Everyone who is not humble or not strong is strong and vice versa. If someone is happy or kind then someone is either not curious or funny and vice versa. Everyone who is generous is either happy or not tall and vice versa. Everyone who is not old or curious is brave and vice versa. Everyone who is both not wise and creative is not tall or not funny and vice versa. Everyone who is either not curious or wise is not wise and vice versa. Someone is creative. Susan is either tall or calm. Lucy is both not brave and kind. Paul is either brave or not tall. Fred is old or calm. Susan is not kind or strong. Susan is old or not curious. | John is tall. | entailment | (((~brave(paul)&~quiet(paul)))<=>((curious(john)<~>~old(john))))&
((?[X]:(humble(X)))<=>((calm(susan)&strong(susan))))&
(((quiet(paul)|~old(paul)))<=>(old(mary)))&
((?[X]:((~brave(X)<~>calm(X))))<=>((~happy(mary)<~>brave(mary))))&
(![X]:(~brave(X)<=>kind(X)))&
(((humble(john)|~patient(john)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~funny(lucy)|wise(lucy)))=>((~wise(lucy)<~>tall(lucy))))&
((?[X]:(happy(X)))=>(?[X]:(~strong(X))))&
(![X]:((rich(X)|~tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~humble(X)|~strong(X))<=>strong(X)))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
(![X]:((~old(X)|curious(X))<=>brave(X)))&
(![X]:((~wise(X)&creative(X))<=>(~tall(X)|~funny(X))))&
(![X]:((~curious(X)<~>wise(X))<=>~wise(X)))&
(?[X]:(creative(X)))&
((tall(susan)<~>calm(susan)))&
((~brave(lucy)&kind(lucy)))&
((brave(paul)<~>~tall(paul)))&
((old(fred)|calm(fred)))&
((~kind(susan)|strong(susan)))&
((old(susan)|~curious(susan))) | tall(john) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2720384011971330612281111
% SZS output start Proof for 2720384011971330612281111
9. ! [X0] : ((~tall(X0) | rich(X0)) <=> (~creative(X0) & curious(X0))) [input p8]
14. ! [X0] : ((creative(X0) & ~wise(X0)) <=> (~funny(X0) | ~tall(X0))) [input p13]
23. ~tall(john) [input hypothesis]
51. ! [X0] : (((~tall(X0) | rich(X0)) | (creative(X0) | ~curious(X0))) & ((~creative(X0) & curious(X0)) | (tall(X0) & ~rich(X0)))) [nnf transformation 9]
52. ! [X0] : ((~tall(X0) | rich(X0) | creative(X0) | ~curious(X0)) & ((~creative(X0) & curious(X0)) | (tall(X0) & ~rich(X0)))) [flattening 51]
63. ! [X0] : (((creative(X0) & ~wise(X0)) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | (~creative(X0) | wise(X0)))) [nnf transformation 14]
64. ! [X0] : (((creative(X0) & ~wise(X0)) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | ~creative(X0) | wise(X0))) [flattening 63]
106. ~creative(X0) | tall(X0) [cnf transformation 52]
127. creative(X0) | tall(X0) [cnf transformation 64]
143. ~tall(john) [cnf transformation 23]
312. tall(X0) [subsumption resolution 127,106]
328. $false [subsumption resolution 143,312]
% SZS output end Proof for 2720384011971330612281111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not humble is funny or humble and vice versa. If someone is not quiet or generous then fred is both not strong and quiet and vice versa. If fred is both kind and not rich then alice is either humble or strong and vice versa. If alice is both strong and tall then someone is not calm or quiet. Everyone who is either funny or not humble is quiet or not curious and vice versa. Everyone who is either not rich or not kind is rich or not patient. If someone is both rich and not strong then alice is either not patient or strong. If alice is not brave or not calm then fred is both not wise and brave. Everyone who is not generous is not rich and vice versa. Everyone who is humble or not strong is calm or not kind. Everyone who is not rich is strong or not kind. If john is either tall or strong then someone is tall or strong. Everyone who is not tall or patient is humble or not creative and vice versa. If someone is either strong or humble then lucy is both not creative and not brave. If fred is calm then someone is both not humble and not calm. Fred is both not old and not creative. Someone is both not brave and old. Someone is both not tall and not patient. Alice is both not brave and rich. Paul is either calm or generous. Someone is not tall. Someone is both patient and not creative. Someone is either not creative or creative. | Alice is strong. | contradiction | (![X]:((~quiet(X)&~humble(X))<=>(funny(X)|humble(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>((~strong(fred)&quiet(fred))))&
(((kind(fred)&~rich(fred)))<=>((humble(alice)<~>strong(alice))))&
(((strong(alice)&tall(alice)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(rich(X)|~patient(X))))&
((?[X]:((rich(X)&~strong(X))))=>((~patient(alice)<~>strong(alice))))&
(((~brave(alice)|~calm(alice)))=>((~wise(fred)&brave(fred))))&
(![X]:(~generous(X)<=>~rich(X)))&
(![X]:((humble(X)|~strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~rich(X)=>(strong(X)|~kind(X))))&
(((tall(john)<~>strong(john)))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:((~tall(X)|patient(X))<=>(humble(X)|~creative(X))))&
((?[X]:((strong(X)<~>humble(X))))=>((~creative(lucy)&~brave(lucy))))&
((calm(fred))=>(?[X]:((~humble(X)&~calm(X)))))&
((~old(fred)&~creative(fred)))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((~tall(X)&~patient(X))))&
((~brave(alice)&rich(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((~creative(X)<~>creative(X)))) | strong(alice) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7417076372349330988929451
% SZS output start Proof for 7417076372349330988929451
1. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (humble(X0) | funny(X0))) [input p0]
2. ? [X0] : (generous(X0) | ~quiet(X0)) <=> (quiet(fred) & ~strong(fred)) [input p1]
3. (~rich(fred) & kind(fred)) <=> (humble(alice) <~> strong(alice)) [input p2]
9. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p8]
11. ! [X0] : (~rich(X0) => (~kind(X0) | strong(X0))) [input p10]
19. rich(alice) & ~brave(alice) [input p18]
24. strong(alice) [input hypothesis]
34. ! [X0] : ((~kind(X0) | strong(X0)) | rich(X0)) [ennf transformation 11]
35. ! [X0] : (~kind(X0) | strong(X0) | rich(X0)) [flattening 34]
39. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & ((humble(X0) | funny(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 1]
40. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & (humble(X0) | funny(X0) | humble(X0) | quiet(X0))) [flattening 39]
41. (? [X0] : (generous(X0) | ~quiet(X0)) | (~quiet(fred) | strong(fred))) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [nnf transformation 2]
42. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [flattening 41]
43. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [rectify 42]
44. ? [X0] : (generous(X0) | ~quiet(X0)) => (generous(sK0) | ~quiet(sK0)) [choice axiom]
45. ((generous(sK0) | ~quiet(sK0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [skolemisation 43,44]
46. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | (rich(fred) | ~kind(fred))) [nnf transformation 3]
47. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | rich(fred) | ~kind(fred)) [flattening 46]
54. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 9]
79. ~humble(X0) | ~humble(X0) [cnf transformation 40]
81. ~strong(fred) | ~generous(X1) [cnf transformation 45]
88. kind(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
90. ~rich(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
104. ~rich(X0) | generous(X0) [cnf transformation 54]
108. ~kind(X0) | strong(X0) | rich(X0) [cnf transformation 35]
128. rich(alice) [cnf transformation 19]
136. strong(alice) [cnf transformation 24]
139. ~humble(X0) [duplicate literal removal 79]
142. 1 <=> strong(fred) [avatar definition]
159. 5 <=> ! [X1] : ~generous(X1) [avatar definition]
160. ~generous(X1) <- (5) [avatar component clause 159]
166. 5 | ~1 [avatar split clause 81,142,159]
168. ~rich(fred) | ~strong(alice) [subsumption resolution 90,139]
170. 7 <=> strong(alice) [avatar definition]
174. 8 <=> rich(fred) [avatar definition]
176. ~rich(fred) <- (~8) [avatar component clause 174]
177. ~7 | ~8 [avatar split clause 168,174,170]
178. kind(fred) | ~strong(alice) [subsumption resolution 88,139]
180. 9 <=> kind(fred) [avatar definition]
182. kind(fred) <- (9) [avatar component clause 180]
183. ~7 | 9 [avatar split clause 178,180,170]
278. 7 [avatar split clause 136,170]
279. generous(alice) [resolution 104,128]
287. strong(fred) | rich(fred) <- (9) [resolution 108,182]
291. strong(fred) <- (~8, 9) [subsumption resolution 287,176]
292. 1 | 8 | ~9 [avatar split clause 291,180,174,142]
293. $false <- (5) [resolution 160,279]
294. ~5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 166,177,183,278,292,294]
% SZS output end Proof for 7417076372349330988929451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and not brave then john is creative or curious.
Everyone who is either patient or curious is both strong and rich and vice versa.
Everyone who is either not wise or not patient is either not generous or patient.
If someone is either not funny or calm then alice is either rich or not curious.
Everyone who is not patient or not humble is both funny and not funny and vice versa.
If lucy is either not happy or not funny then lucy is both wise and not funny and vice versa.
Everyone who is wise or not happy is not rich.
Everyone who is not humble or not patient is either curious or rich.
If someone is kind or not brave then someone is not strong and vice versa.
If paul is happy then lucy is creative or not humble and vice versa.
Everyone who is either creative or quiet is both not old and rich and vice versa.
Everyone who is not curious is both not curious and tall.
Everyone who is both not brave and not old is either not patient or humble and vice versa.
If fred is either not humble or not wise then someone is both curious and brave and vice versa.
If paul is both not funny and tall then susan is both not patient and not funny and vice versa.
If someone is both curious and calm then someone is not creative or not curious and vice versa.
Someone is both quiet and not calm.
Someone is curious or not creative.
Paul is both kind and not wise.
Someone is both not creative and not curious.
John is both wise and quiet.
Someone is not kind or not tall.
Someone is both not strong and not tall. | John is not rich. | entailment | ((?[X]:((tall(X)&~brave(X))))=>((creative(john)|curious(john))))&
(![X]:((patient(X)<~>curious(X))<=>(strong(X)&rich(X))))&
(![X]:((~wise(X)<~>~patient(X))=>(~generous(X)<~>patient(X))))&
((?[X]:((~funny(X)<~>calm(X))))=>((rich(alice)<~>~curious(alice))))&
(![X]:((~patient(X)|~humble(X))<=>(funny(X)&~funny(X))))&
(((~happy(lucy)<~>~funny(lucy)))<=>((wise(lucy)&~funny(lucy))))&
(![X]:((wise(X)|~happy(X))=>~rich(X)))&
(![X]:((~humble(X)|~patient(X))=>(curious(X)<~>rich(X))))&
((?[X]:((kind(X)|~brave(X))))<=>(?[X]:(~strong(X))))&
((happy(paul))<=>((creative(lucy)|~humble(lucy))))&
(![X]:((creative(X)<~>quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~curious(X)&tall(X))))&
(![X]:((~brave(X)&~old(X))<=>(~patient(X)<~>humble(X))))&
(((~humble(fred)<~>~wise(fred)))<=>(?[X]:((curious(X)&brave(X)))))&
(((~funny(paul)&tall(paul)))<=>((~patient(susan)&~funny(susan))))&
((?[X]:((curious(X)&calm(X))))<=>(?[X]:((~creative(X)|~curious(X)))))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((curious(X)|~creative(X))))&
((kind(paul)&~wise(paul)))&
(?[X]:((~creative(X)&~curious(X))))&
((wise(john)&quiet(john)))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((~strong(X)&~tall(X)))) | ~rich(john) | [
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3305177488940700612165467
% SZS output start Proof for 3305177488940700612165467
7. ! [X0] : ((~happy(X0) | wise(X0)) => ~rich(X0)) [input p6]
21. quiet(john) & wise(john) [input p20]
24. rich(john) [input hypothesis]
31. ! [X0] : (~rich(X0) | (happy(X0) & ~wise(X0))) [ennf transformation 7]
101. ~wise(X0) | ~rich(X0) [cnf transformation 31]
149. wise(john) [cnf transformation 21]
154. rich(john) [cnf transformation 24]
319. ~rich(john) [resolution 101,149]
321. $false [subsumption resolution 319,154]
% SZS output end Proof for 3305177488940700612165467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and wise is either not curious or not calm and vice versa.
If someone is not generous or not quiet then mary is both creative and brave.
If someone is happy then paul is kind or not patient.
If someone is either kind or generous then someone is not humble.
Everyone who is both not wise and rich is funny or humble and vice versa.
Everyone who is either quiet or humble is both not tall and not old and vice versa.
If someone is not tall or not calm then susan is old.
If someone is not humble then alice is both kind and brave and vice versa.
If lucy is not funny or not brave then lucy is either funny or not curious and vice versa.
Everyone who is both curious and brave is both not patient and old and vice versa.
If someone is either curious or funny then mary is both not funny and not old.
Everyone who is not funny or not brave is not wise.
Everyone who is both not happy and brave is either not calm or strong and vice versa.
Everyone who is both not generous and not wise is either not kind or not generous.
Everyone who is both not tall and generous is brave or not brave and vice versa.
If paul is not wise or not calm then fred is either not wise or not brave and vice versa.
Someone is not old or happy.
Someone is both happy and quiet.
Fred is not quiet or not funny.
Fred is not patient or not old.
Someone is either quiet or wise.
Someone is both brave and curious.
Lucy is brave. | Mary is not funny. | neutral | (![X]:((~generous(X)&wise(X))<=>(~curious(X)<~>~calm(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>((creative(mary)&brave(mary))))&
((?[X]:(happy(X)))=>((kind(paul)|~patient(paul))))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~humble(X))))&
(![X]:((~wise(X)&rich(X))<=>(funny(X)|humble(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~tall(X)&~old(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(old(susan)))&
((?[X]:(~humble(X)))<=>((kind(alice)&brave(alice))))&
(((~funny(lucy)|~brave(lucy)))<=>((funny(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&brave(X))<=>(~patient(X)&old(X))))&
((?[X]:((curious(X)<~>funny(X))))=>((~funny(mary)&~old(mary))))&
(![X]:((~funny(X)|~brave(X))=>~wise(X)))&
(![X]:((~happy(X)&brave(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(brave(X)|~brave(X))))&
(((~wise(paul)|~calm(paul)))<=>((~wise(fred)<~>~brave(fred))))&
(?[X]:((~old(X)|happy(X))))&
(?[X]:((happy(X)&quiet(X))))&
((~quiet(fred)|~funny(fred)))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((brave(X)&curious(X))))&
(brave(lucy)) | ~funny(mary) | [] | null | 0 |
Everyone who is both not brave and not creative is either not old or not humble.
If paul is both wise and not brave then mary is calm and vice versa.
If paul is not happy then someone is not wise or not patient.
Everyone who is both not humble and not old is both not patient and not quiet and vice versa.
If paul is either old or not wise then someone is not patient.
Everyone who is both not calm and not curious is not rich and vice versa.
Everyone who is creative or not wise is either patient or strong and vice versa.
If someone is either rich or happy then someone is generous or not patient.
Everyone who is either not old or not curious is either generous or patient and vice versa.
Everyone who is not rich is not calm and vice versa.
Everyone who is not wise is not funny and vice versa.
If fred is brave or not humble then someone is not curious or not rich and vice versa.
Everyone who is not brave is humble.
Everyone who is either not humble or old is quiet.
If someone is either old or not kind then someone is humble or old and vice versa.
Everyone who is strong or not humble is not brave or wise and vice versa.
Someone is either not kind or not creative.
Susan is both not strong and not old.
Someone is both creative and tall.
Someone is either humble or tall.
Someone is either calm or brave.
Paul is both happy and not old.
Someone is either not humble or rich.
Susan is not funny. | Mary is not tall. | neutral | (![X]:((~brave(X)&~creative(X))=>(~old(X)<~>~humble(X))))&
(((wise(paul)&~brave(paul)))<=>(calm(mary)))&
((~happy(paul))=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((~humble(X)&~old(X))<=>(~patient(X)&~quiet(X))))&
(((old(paul)<~>~wise(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)&~curious(X))<=>~rich(X)))&
(![X]:((creative(X)|~wise(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((rich(X)<~>happy(X))))=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((~old(X)<~>~curious(X))<=>(generous(X)<~>patient(X))))&
(![X]:(~rich(X)<=>~calm(X)))&
(![X]:(~wise(X)<=>~funny(X)))&
(((brave(fred)|~humble(fred)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(![X]:(~brave(X)=>humble(X)))&
(![X]:((~humble(X)<~>old(X))=>quiet(X)))&
((?[X]:((old(X)<~>~kind(X))))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((strong(X)|~humble(X))<=>(~brave(X)|wise(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~strong(susan)&~old(susan)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((calm(X)<~>brave(X))))&
((happy(paul)&~old(paul)))&
(?[X]:((~humble(X)<~>rich(X))))&
(~funny(susan)) | ~tall(mary) | [] | null | 0 |
Everyone who is generous is brave and vice versa.
Everyone who is either calm or creative is brave or not brave.
Everyone who is both not funny and not humble is generous or curious and vice versa.
Everyone who is wise is not brave or not humble.
Everyone who is strong is either humble or not funny and vice versa.
Everyone who is wise or not rich is quiet.
If someone is not humble or not curious then someone is both rich and not brave and vice versa.
Everyone who is both not quiet and not creative is creative or brave and vice versa.
If someone is either not wise or funny then someone is both not old and not wise and vice versa.
Everyone who is either not curious or happy is not wise or not humble and vice versa.
Everyone who is both humble and not generous is either humble or generous and vice versa.
If john is brave then lucy is both calm and wise.
Everyone who is both funny and creative is both creative and quiet.
Everyone who is either not strong or not brave is either not humble or not patient and vice versa.
Everyone who is both creative and generous is not happy or funny and vice versa.
If alice is not brave then someone is not happy or wise and vice versa.
Lucy is not wise or not funny.
Someone is curious or kind.
Someone is both calm and not rich.
Someone is either brave or wise.
Mary is either not happy or not kind.
Someone is either not quiet or calm.
Someone is rich. | Mary is quiet. | entailment | (![X]:(generous(X)<=>brave(X)))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|~brave(X))))&
(![X]:((~funny(X)&~humble(X))<=>(generous(X)|curious(X))))&
(![X]:(wise(X)=>(~brave(X)|~humble(X))))&
(![X]:(strong(X)<=>(humble(X)<~>~funny(X))))&
(![X]:((wise(X)|~rich(X))=>quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>(creative(X)|brave(X))))&
((?[X]:((~wise(X)<~>funny(X))))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~curious(X)<~>happy(X))<=>(~wise(X)|~humble(X))))&
(![X]:((humble(X)&~generous(X))<=>(humble(X)<~>generous(X))))&
((brave(john))=>((calm(lucy)&wise(lucy))))&
(![X]:((funny(X)&creative(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~humble(X)<~>~patient(X))))&
(![X]:((creative(X)&generous(X))<=>(~happy(X)|funny(X))))&
((~brave(alice))<=>(?[X]:((~happy(X)|wise(X)))))&
((~wise(lucy)|~funny(lucy)))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:((calm(X)&~rich(X))))&
(?[X]:((brave(X)<~>wise(X))))&
((~happy(mary)<~>~kind(mary)))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:(rich(X))) | quiet(mary) | [
"p0",
"p2",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 320778699900557717346383
% SZS output start Proof for 320778699900557717346383
1. ! [X0] : (generous(X0) <=> brave(X0)) [input p0]
3. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (curious(X0) | generous(X0))) [input p2]
8. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (brave(X0) | creative(X0))) [input p7]
11. ! [X0] : ((~generous(X0) & humble(X0)) <=> (humble(X0) <~> generous(X0))) [input p10]
24. ~quiet(mary) [input hypothesis]
35. ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0))) [nnf transformation 1]
37. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 3]
38. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | humble(X0) | funny(X0))) [flattening 37]
45. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 8]
46. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | creative(X0) | quiet(X0))) [flattening 45]
54. ! [X0] : (((~generous(X0) & humble(X0)) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) & (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | (generous(X0) | ~humble(X0)))) [nnf transformation 11]
55. ! [X0] : (((~generous(X0) & humble(X0)) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) & (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | generous(X0) | ~humble(X0))) [flattening 54]
77. ~brave(X0) | generous(X0) [cnf transformation 35]
83. ~humble(X0) | ~generous(X0) [cnf transformation 38]
97. brave(X0) | creative(X0) | creative(X0) | quiet(X0) [cnf transformation 46]
100. ~creative(X0) | ~creative(X0) [cnf transformation 46]
119. ~generous(X0) | humble(X0) | ~generous(X0) [cnf transformation 55]
151. ~quiet(mary) [cnf transformation 24]
155. ~generous(X0) | humble(X0) [duplicate literal removal 119]
156. brave(X0) | creative(X0) | quiet(X0) [duplicate literal removal 97]
157. ~creative(X0) [duplicate literal removal 100]
176. quiet(X0) | brave(X0) [subsumption resolution 156,157]
210. ~generous(X0) [subsumption resolution 155,83]
290. brave(mary) [resolution 176,151]
293. generous(mary) [resolution 290,77]
294. $false [subsumption resolution 293,210]
% SZS output end Proof for 320778699900557717346383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not old is not wise or tall.
Everyone who is not quiet is not strong.
If someone is not funny or not brave then susan is both creative and curious.
Everyone who is not generous or happy is either funny or not funny and vice versa.
Everyone who is either not strong or not curious is either kind or not generous.
If alice is humble or creative then someone is tall and vice versa.
If susan is generous then susan is wise and vice versa.
If john is both patient and humble then someone is either not strong or funny and vice versa.
Everyone who is not humble or not wise is both humble and not tall.
Everyone who is quiet or not funny is brave and vice versa.
Everyone who is not brave is both not brave and calm and vice versa.
If someone is not rich then someone is not strong and vice versa.
Everyone who is humble or not humble is both not brave and not strong and vice versa.
If alice is not creative or tall then alice is not happy or not tall.
Everyone who is humble is curious and vice versa.
Someone is both not brave and not quiet.
Someone is tall or humble.
Someone is both tall and not brave.
Someone is patient or brave.
Someone is both not quiet and patient.
Fred is both calm and not happy.
Someone is old. | John is not humble. | contradiction | (![X]:((brave(X)|~old(X))=>(~wise(X)|tall(X))))&
(![X]:(~quiet(X)=>~strong(X)))&
((?[X]:((~funny(X)|~brave(X))))=>((creative(susan)&curious(susan))))&
(![X]:((~generous(X)|happy(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>~curious(X))=>(kind(X)<~>~generous(X))))&
(((humble(alice)|creative(alice)))<=>(?[X]:(tall(X))))&
((generous(susan))<=>(wise(susan)))&
(((patient(john)&humble(john)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)&~tall(X))))&
(![X]:((quiet(X)|~funny(X))<=>brave(X)))&
(![X]:(~brave(X)<=>(~brave(X)&calm(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~humble(X))<=>(~brave(X)&~strong(X))))&
(((~creative(alice)|tall(alice)))=>((~happy(alice)|~tall(alice))))&
(![X]:(humble(X)<=>curious(X)))&
(?[X]:((~brave(X)&~quiet(X))))&
(?[X]:((tall(X)|humble(X))))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:((patient(X)|brave(X))))&
(?[X]:((~quiet(X)&patient(X))))&
((calm(fred)&~happy(fred)))&
(?[X]:(old(X))) | ~humble(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3512842874565107822183959
% SZS output start Proof for 3512842874565107822183959
9. ! [X0] : ((~wise(X0) | ~humble(X0)) => (~tall(X0) & humble(X0))) [input p8]
23. ~humble(john) [input hypothesis]
32. ! [X0] : ((~tall(X0) & humble(X0)) | (wise(X0) & humble(X0))) [ennf transformation 9]
98. humble(X0) | humble(X0) [cnf transformation 32]
129. ~humble(john) [cnf transformation 23]
131. humble(X0) [duplicate literal removal 98]
239. $false [subsumption resolution 129,131]
% SZS output end Proof for 3512842874565107822183959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not strong or not generous then john is curious or calm. Everyone who is not humble or strong is both not happy and not patient. If susan is not patient then lucy is both not brave and quiet and vice versa. If someone is either not old or not calm then susan is not generous or not tall and vice versa. If mary is both tall and not strong then someone is calm and vice versa. If someone is not brave then lucy is happy. Everyone who is rich or generous is both strong and calm. If someone is not wise or curious then someone is not curious and vice versa. Everyone who is not kind or patient is both not kind and wise. If someone is both calm and not quiet then someone is calm and vice versa. If mary is curious or strong then lucy is both happy and not strong and vice versa. Everyone who is not wise is not tall or wise. If someone is brave or funny then fred is not happy and vice versa. If someone is not calm or funny then someone is creative. Everyone who is not curious is not patient or not rich. Everyone who is either not funny or not old is not humble or rich. Susan is either brave or generous. Fred is not calm or not curious. Lucy is both not generous and not humble. Someone is patient. Someone is either creative or not quiet. Someone is generous or quiet. Someone is kind. Someone is both happy and not wise. | Susan is strong. | contradiction | (((~strong(paul)<~>~generous(paul)))=>((curious(john)|calm(john))))&
(![X]:((~humble(X)|strong(X))=>(~happy(X)&~patient(X))))&
((~patient(susan))<=>((~brave(lucy)&quiet(lucy))))&
((?[X]:((~old(X)<~>~calm(X))))<=>((~generous(susan)|~tall(susan))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:(calm(X))))&
((?[X]:(~brave(X)))=>(happy(lucy)))&
(![X]:((rich(X)|generous(X))=>(strong(X)&calm(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)|patient(X))=>(~kind(X)&wise(X))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:(calm(X))))&
(((curious(mary)|strong(mary)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:(~wise(X)=>(~tall(X)|wise(X))))&
((?[X]:((brave(X)|funny(X))))<=>(~happy(fred)))&
((?[X]:((~calm(X)|funny(X))))=>(?[X]:(creative(X))))&
(![X]:(~curious(X)=>(~patient(X)|~rich(X))))&
(![X]:((~funny(X)<~>~old(X))=>(~humble(X)|rich(X))))&
((brave(susan)<~>generous(susan)))&
((~calm(fred)|~curious(fred)))&
((~generous(lucy)&~humble(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((happy(X)&~wise(X)))) | strong(susan) | [
"p1",
"p2",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6157577567992462652226399
% SZS output start Proof for 6157577567992462652226399
2. ! [X0] : ((strong(X0) | ~humble(X0)) => (~patient(X0) & ~happy(X0))) [input p1]
3. ~patient(susan) <=> (quiet(lucy) & ~brave(lucy)) [input p2]
6. ? [X0] : ~brave(X0) => happy(lucy) [input p5]
19. ~humble(lucy) & ~generous(lucy) [input p18]
25. strong(susan) [input hypothesis]
31. ! [X0] : ((~patient(X0) & ~happy(X0)) | (~strong(X0) & humble(X0))) [ennf transformation 2]
32. happy(lucy) | ! [X0] : brave(X0) [ennf transformation 6]
43. (~patient(susan) | (~quiet(lucy) | brave(lucy))) & ((quiet(lucy) & ~brave(lucy)) | patient(susan)) [nnf transformation 3]
44. (~patient(susan) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | patient(susan)) [flattening 43]
89. ~happy(X0) | humble(X0) [cnf transformation 31]
92. ~patient(X0) | ~strong(X0) [cnf transformation 31]
93. ~brave(lucy) | patient(susan) [cnf transformation 44]
105. happy(lucy) | brave(X0) [cnf transformation 32]
138. ~humble(lucy) [cnf transformation 19]
146. strong(susan) [cnf transformation 25]
167. 5 <=> brave(lucy) [avatar definition]
168. ~brave(lucy) <- (~5) [avatar component clause 167]
175. 7 <=> patient(susan) [avatar definition]
176. patient(susan) <- (7) [avatar component clause 175]
180. 7 | ~5 [avatar split clause 93,167,175]
228. 18 <=> ! [X0] : brave(X0) [avatar definition]
229. brave(X0) <- (18) [avatar component clause 228]
231. 19 <=> happy(lucy) [avatar definition]
233. happy(lucy) <- (19) [avatar component clause 231]
234. 18 | 19 [avatar split clause 105,231,228]
355. $false <- (~5, 18) [subsumption resolution 168,229]
356. 5 | ~18 [avatar contradiction clause 355]
360. humble(lucy) <- (19) [resolution 89,233]
361. $false <- (19) [subsumption resolution 360,138]
362. ~19 [avatar contradiction clause 361]
367. ~strong(susan) <- (7) [resolution 92,176]
368. $false <- (7) [subsumption resolution 367,146]
369. ~7 [avatar contradiction clause 368]
370. $false [avatar sat refutation 180,234,356,362,369]
% SZS output end Proof for 6157577567992462652226399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and not strong is humble or not tall and vice versa.
If someone is both wise and quiet then someone is both humble and quiet and vice versa.
Everyone who is either quiet or not generous is both not wise and not happy and vice versa.
Everyone who is either not humble or not strong is tall or not old.
If someone is funny or not wise then someone is calm.
If paul is happy then lucy is kind or calm.
Everyone who is brave is either wise or creative and vice versa.
Everyone who is wise or happy is both curious and old and vice versa.
If someone is either not strong or curious then john is curious.
Everyone who is not happy is either not tall or not rich.
Everyone who is creative or kind is both not kind and rich and vice versa.
If someone is both calm and not strong then alice is both not curious and kind.
If someone is not tall then paul is both wise and rich.
If someone is either not quiet or old then someone is creative or quiet and vice versa.
Everyone who is either not brave or not curious is both curious and creative and vice versa.
If someone is both happy and quiet then someone is either quiet or not kind and vice versa.
Someone is either brave or not old.
Someone is both calm and old.
Someone is not rich or kind. | Alice is not funny. | neutral | (![X]:((~humble(X)&~strong(X))<=>(humble(X)|~tall(X))))&
((?[X]:((wise(X)&quiet(X))))<=>(?[X]:((humble(X)&quiet(X)))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~wise(X)&~happy(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(tall(X)|~old(X))))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:(calm(X))))&
((happy(paul))=>((kind(lucy)|calm(lucy))))&
(![X]:(brave(X)<=>(wise(X)<~>creative(X))))&
(![X]:((wise(X)|happy(X))<=>(curious(X)&old(X))))&
((?[X]:((~strong(X)<~>curious(X))))=>(curious(john)))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:((calm(X)&old(X))))&
(?[X]:((~rich(X)|kind(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is both strong and calm is not generous or not strong and vice versa.
Everyone who is happy is both not tall and old and vice versa.
If someone is both not humble and tall then alice is either tall or not happy.
Everyone who is both not wise and not rich is not calm.
If fred is either not kind or old then someone is both not quiet and creative and vice versa.
Everyone who is tall or old is not patient or brave.
Everyone who is either funny or not happy is either not tall or patient and vice versa.
Everyone who is not curious is either tall or happy.
If alice is both not happy and old then john is both rich and brave and vice versa.
If someone is either not strong or not patient then someone is not strong and vice versa.
If john is either not tall or not creative then john is humble or not calm and vice versa.
Everyone who is not wise or calm is funny.
Everyone who is either quiet or not strong is not patient or not old and vice versa.
Everyone who is both not generous and strong is not humble or not calm and vice versa.
Everyone who is both not brave and calm is either wise or tall.
Lucy is not creative.
Someone is either not quiet or not kind.
Someone is either brave or curious.
Susan is kind.
Someone is either not kind or generous. | Lucy is curious. | entailment | (![X]:((strong(X)&calm(X))<=>(~generous(X)|~strong(X))))&
(![X]:(happy(X)<=>(~tall(X)&old(X))))&
((?[X]:((~humble(X)&tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&~rich(X))=>~calm(X)))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
(![X]:((~generous(X)&strong(X))<=>(~humble(X)|~calm(X))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)<~>tall(X))))&
(~creative(lucy))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(kind(susan))&
(?[X]:((~kind(X)<~>generous(X)))) | curious(lucy) | [
"p0",
"p1",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3224711396776418739467878
% SZS output start Proof for 3224711396776418739467878
1. ! [X0] : ((calm(X0) & strong(X0)) <=> (~strong(X0) | ~generous(X0))) [input p0]
2. ! [X0] : (happy(X0) <=> (old(X0) & ~tall(X0))) [input p1]
7. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~tall(X0) <~> patient(X0))) [input p6]
8. ! [X0] : (~curious(X0) => (tall(X0) <~> happy(X0))) [input p7]
10. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X0] : ~strong(X0) [input p9]
12. ! [X0] : ((calm(X0) | ~wise(X0)) => funny(X0)) [input p11]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~calm(X0) | ~humble(X0))) [input p13]
21. ~curious(lucy) [input hypothesis]
22. ? [X0] : (~strong(X0) <~> ~patient(X0)) <=> ? [X1] : ~strong(X1) [rectify 10]
28. ! [X0] : ((tall(X0) <~> happy(X0)) | curious(X0)) [ennf transformation 8]
29. ! [X0] : (funny(X0) | (~calm(X0) & wise(X0))) [ennf transformation 12]
32. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 1]
33. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | ~calm(X0) | ~strong(X0))) [flattening 32]
34. ! [X0] : ((happy(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~happy(X0))) [nnf transformation 2]
35. ! [X0] : ((happy(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~happy(X0))) [flattening 34]
41. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0)))) & (((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 7]
42. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | curious(X0)) [nnf transformation 28]
45. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 22]
46. (? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [rectify 45]
47. ? [X0] : ((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) => ((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) [choice axiom]
48. ? [X2] : ~strong(X2) => ~strong(sK2) [choice axiom]
49. (((patient(sK1) | strong(sK1)) & (~patient(sK1) | ~strong(sK1))) | ! [X1] : strong(X1)) & (~strong(sK2) | ! [X3] : ((~strong(X3) | patient(X3)) & (~patient(X3) | strong(X3)))) [skolemisation 46,48,47]
54. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
55. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~strong(X0) | generous(X0))) [flattening 54]
68. strong(X0) | strong(X0) [cnf transformation 33]
69. generous(X0) | calm(X0) [cnf transformation 33]
71. ~tall(X0) | ~happy(X0) [cnf transformation 35]
87. ~patient(X0) | tall(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 41]
92. happy(X0) | ~funny(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 41]
93. curious(X0) | tall(X0) | happy(X0) [cnf transformation 42]
100. ~strong(sK2) | ~strong(X3) | patient(X3) [cnf transformation 49]
110. ~calm(X0) | funny(X0) [cnf transformation 29]
119. ~generous(X0) | calm(X0) [cnf transformation 55]
132. ~curious(lucy) [cnf transformation 21]
134. strong(X0) [duplicate literal removal 68]
176. ~funny(X0) | ~tall(X0) | ~patient(X0) [subsumption resolution 92,71]
178. ~funny(X0) | ~happy(X0) | ~patient(X0) [subsumption resolution 87,176]
196. ~strong(X3) | patient(X3) [subsumption resolution 100,134]
197. patient(X3) [subsumption resolution 196,134]
223. calm(X0) [subsumption resolution 119,69]
260. funny(X1) [resolution 110,223]
269. tall(lucy) | happy(lucy) [resolution 93,132]
272. 22 <=> happy(lucy) [avatar definition]
274. happy(lucy) <- (22) [avatar component clause 272]
276. 23 <=> tall(lucy) [avatar definition]
278. tall(lucy) <- (23) [avatar component clause 276]
279. 22 | 23 [avatar split clause 269,276,272]
290. ~tall(X0) | ~patient(X0) [resolution 176,260]
292. ~tall(X0) [subsumption resolution 290,197]
295. ~happy(X0) | ~patient(X0) [resolution 178,260]
297. ~happy(X0) [subsumption resolution 295,197]
298. $false <- (22) [resolution 297,274]
299. ~22 [avatar contradiction clause 298]
300. $false <- (23) [subsumption resolution 278,292]
301. ~23 [avatar contradiction clause 300]
302. $false [avatar sat refutation 279,299,301]
% SZS output end Proof for 3224711396776418739467878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and curious then paul is not curious and vice versa. Everyone who is both quiet and old is both not wise and calm. If john is wise or not kind then fred is not humble and vice versa. Everyone who is both tall and generous is humble or wise. Everyone who is both not brave and creative is both wise and not brave and vice versa. Everyone who is not creative is either not creative or not rich and vice versa. Everyone who is either tall or not kind is not quiet and vice versa. Everyone who is not funny or quiet is strong and vice versa. Everyone who is happy is both not old and generous. Everyone who is both not happy and not strong is either not brave or not creative. Everyone who is both rich and not wise is not funny or creative. If alice is both patient and rich then someone is both not brave and generous. Everyone who is not creative or not humble is either not old or not brave and vice versa. Everyone who is not generous is brave. If mary is either not kind or not happy then someone is both creative and brave. If someone is happy then fred is either humble or not kind and vice versa. Someone is kind. Paul is humble or kind. Alice is creative. Someone is both not funny and humble. Mary is both not funny and rich. John is not kind or not strong. Someone is quiet. Alice is not generous or generous. | Alice is curious. | neutral | ((?[X]:((happy(X)&curious(X))))<=>(~curious(paul)))&
(![X]:((quiet(X)&old(X))=>(~wise(X)&calm(X))))&
(((wise(john)|~kind(john)))<=>(~humble(fred)))&
(![X]:((tall(X)&generous(X))=>(humble(X)|wise(X))))&
(![X]:((~brave(X)&creative(X))<=>(wise(X)&~brave(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>~rich(X))))&
(![X]:((tall(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((~funny(X)|quiet(X))<=>strong(X)))&
(![X]:(happy(X)=>(~old(X)&generous(X))))&
(![X]:((~happy(X)&~strong(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((rich(X)&~wise(X))=>(~funny(X)|creative(X))))&
(((patient(alice)&rich(alice)))=>(?[X]:((~brave(X)&generous(X)))))&
(![X]:((~creative(X)|~humble(X))<=>(~old(X)<~>~brave(X))))&
(![X]:(~generous(X)=>brave(X)))&
(((~kind(mary)<~>~happy(mary)))=>(?[X]:((creative(X)&brave(X)))))&
((?[X]:(happy(X)))<=>((humble(fred)<~>~kind(fred))))&
(?[X]:(kind(X)))&
((humble(paul)|kind(paul)))&
(creative(alice))&
(?[X]:((~funny(X)&humble(X))))&
((~funny(mary)&rich(mary)))&
((~kind(john)|~strong(john)))&
(?[X]:(quiet(X)))&
((~generous(alice)|generous(alice))) | curious(alice) | [] | null | 0 |
If fred is not old then alice is not creative and vice versa. Everyone who is either generous or old is either humble or quiet. Everyone who is either brave or generous is either not humble or not rich. Everyone who is either quiet or old is tall or curious and vice versa. Everyone who is funny is not quiet or humble and vice versa. Everyone who is not quiet is both brave and not old. Everyone who is generous or humble is both not strong and not creative. Everyone who is both not humble and old is brave and vice versa. Everyone who is not creative is either not wise or not creative. If fred is either not brave or funny then someone is either quiet or happy. If someone is not wise or happy then someone is both creative and quiet and vice versa. Everyone who is both not patient and curious is not quiet and vice versa. If someone is both kind and not funny then someone is quiet or not wise. Everyone who is not kind or wise is either not wise or not old and vice versa. Everyone who is old is either not strong or not happy and vice versa. Everyone who is both funny and not funny is not old and vice versa. Someone is not curious. Someone is either brave or patient. Alice is either not humble or not rich. Fred is either not creative or strong. Someone is generous or not wise. | Fred is not humble. | entailment | ((~old(fred))<=>(~creative(alice)))&
(![X]:((generous(X)<~>old(X))=>(humble(X)<~>quiet(X))))&
(![X]:((brave(X)<~>generous(X))=>(~humble(X)<~>~rich(X))))&
(![X]:((quiet(X)<~>old(X))<=>(tall(X)|curious(X))))&
(![X]:(funny(X)<=>(~quiet(X)|humble(X))))&
(![X]:(~quiet(X)=>(brave(X)&~old(X))))&
(![X]:((generous(X)|humble(X))=>(~strong(X)&~creative(X))))&
(![X]:((~humble(X)&old(X))<=>brave(X)))&
(![X]:(~creative(X)=>(~wise(X)<~>~creative(X))))&
(((~brave(fred)<~>funny(fred)))=>(?[X]:((quiet(X)<~>happy(X)))))&
((?[X]:((~wise(X)|happy(X))))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~patient(X)&curious(X))<=>~quiet(X)))&
((?[X]:((kind(X)&~funny(X))))=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((~kind(X)|wise(X))<=>(~wise(X)<~>~old(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~happy(X))))&
(![X]:((funny(X)&~funny(X))<=>~old(X)))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((~humble(alice)<~>~rich(alice)))&
((~creative(fred)<~>strong(fred)))&
(?[X]:((generous(X)|~wise(X)))) | ~humble(fred) | [
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8804107895631798943254088
% SZS output start Proof for 8804107895631798943254088
7. ! [X0] : ((humble(X0) | generous(X0)) => (~creative(X0) & ~strong(X0))) [input p6]
9. ! [X0] : (~creative(X0) => (~wise(X0) <~> ~creative(X0))) [input p8]
14. ! [X0] : ((wise(X0) | ~kind(X0)) <=> (~wise(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((~funny(X0) & funny(X0)) <=> ~old(X0)) [input p15]
22. humble(fred) [input hypothesis]
28. ! [X0] : ((~creative(X0) & ~strong(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 7]
29. ! [X0] : ((~wise(X0) <~> ~creative(X0)) | creative(X0)) [ennf transformation 9]
41. ! [X0] : (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | creative(X0)) [nnf transformation 29]
55. ! [X0] : (((wise(X0) | ~kind(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~wise(X0) & kind(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~kind(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~wise(X0) & kind(X0)))) [flattening 55]
58. ! [X0] : (((~funny(X0) & funny(X0)) | old(X0)) & (~old(X0) | (funny(X0) | ~funny(X0)))) [nnf transformation 16]
59. ! [X0] : (((~funny(X0) & funny(X0)) | old(X0)) & (~old(X0) | funny(X0) | ~funny(X0))) [flattening 58]
93. ~humble(X0) | ~creative(X0) [cnf transformation 28]
98. creative(X0) | wise(X0) | creative(X0) [cnf transformation 41]
113. ~old(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 56]
123. funny(X0) | old(X0) [cnf transformation 59]
124. ~funny(X0) | old(X0) [cnf transformation 59]
133. humble(fred) [cnf transformation 22]
134. ~wise(X0) | ~old(X0) [duplicate literal removal 113]
136. wise(X0) | creative(X0) [duplicate literal removal 98]
209. old(X0) [subsumption resolution 123,124]
259. ~creative(fred) [resolution 93,133]
273. creative(X0) | ~old(X0) [resolution 136,134]
277. creative(X0) [subsumption resolution 273,209]
287. $false [subsumption resolution 259,277]
% SZS output end Proof for 8804107895631798943254088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is wise or quiet then mary is rich and vice versa.
Everyone who is either curious or not curious is both not old and not brave and vice versa.
Everyone who is both wise and brave is not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Everyone who is both not curious and not kind is calm.
Someone is either calm or not wise.
Someone is either not happy or not old.
Someone is not curious.
Someone is rich.
Someone is not quiet or not generous.
Someone is not curious or funny. | Fred is not wise. | entailment | (((wise(alice)|quiet(alice)))<=>(rich(mary)))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((wise(X)&brave(X))<=>~kind(X)))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~curious(X)&~kind(X))=>calm(X)))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~curious(X)|funny(X)))) | ~wise(fred) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 640412111047902252297055
% SZS output start Proof for 640412111047902252297055
2. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~brave(X0) & ~old(X0))) [input p1]
4. ! [X0] : ((creative(X0) | wise(X0)) <=> (brave(X0) & ~quiet(X0))) [input p3]
22. wise(fred) [input hypothesis]
31. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (brave(X0) | old(X0))) & ((~brave(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 2]
32. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | brave(X0) | old(X0)) & ((~brave(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 31]
35. ! [X0] : (((creative(X0) | wise(X0)) | (~brave(X0) | quiet(X0))) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 4]
36. ! [X0] : ((creative(X0) | wise(X0) | ~brave(X0) | quiet(X0)) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 35]
90. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 32]
91. ~brave(X0) | curious(X0) | curious(X0) [cnf transformation 32]
99. brave(X0) | ~wise(X0) [cnf transformation 36]
153. wise(fred) [cnf transformation 22]
156. ~brave(X0) | ~curious(X0) [duplicate literal removal 90]
157. ~brave(X0) | curious(X0) [duplicate literal removal 91]
173. ~brave(X0) [subsumption resolution 156,157]
177. ~wise(X0) [subsumption resolution 99,173]
273. $false [subsumption resolution 153,177]
% SZS output end Proof for 640412111047902252297055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and happy then someone is both happy and strong.
If someone is both not generous and generous then susan is kind or not generous and vice versa.
Everyone who is not patient is both creative and not funny.
If someone is patient then lucy is both funny and humble and vice versa.
Everyone who is generous is not happy or not tall.
Everyone who is both not kind and not calm is humble or not creative and vice versa.
Everyone who is brave or not patient is both not generous and not wise and vice versa.
If john is either patient or brave then mary is not brave.
Everyone who is either not wise or not old is either not tall or brave and vice versa.
If someone is either not calm or brave then someone is either humble or not strong and vice versa.
Everyone who is strong or calm is both old and rich.
If john is both kind and not patient then someone is not quiet.
Everyone who is not calm is either brave or old.
Everyone who is brave or not happy is either humble or not curious.
Everyone who is not calm is patient and vice versa.
Everyone who is both humble and curious is both tall and humble and vice versa.
Paul is either not wise or not generous.
Someone is calm.
Lucy is not creative.
Lucy is either creative or generous.
Paul is wise or patient.
Someone is not strong.
Alice is either not old or brave.
Lucy is tall. | Paul is not brave. | entailment | ((?[X]:((~strong(X)&happy(X))))=>(?[X]:((happy(X)&strong(X)))))&
((?[X]:((~generous(X)&generous(X))))<=>((kind(susan)|~generous(susan))))&
(![X]:(~patient(X)=>(creative(X)&~funny(X))))&
((?[X]:(patient(X)))<=>((funny(lucy)&humble(lucy))))&
(![X]:(generous(X)=>(~happy(X)|~tall(X))))&
(![X]:((~kind(X)&~calm(X))<=>(humble(X)|~creative(X))))&
(![X]:((brave(X)|~patient(X))<=>(~generous(X)&~wise(X))))&
(((patient(john)<~>brave(john)))=>(~brave(mary)))&
(![X]:((~wise(X)<~>~old(X))<=>(~tall(X)<~>brave(X))))&
((?[X]:((~calm(X)<~>brave(X))))<=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((strong(X)|calm(X))=>(old(X)&rich(X))))&
(((kind(john)&~patient(john)))=>(?[X]:(~quiet(X))))&
(![X]:(~calm(X)=>(brave(X)<~>old(X))))&
(![X]:((brave(X)|~happy(X))=>(humble(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>patient(X)))&
(![X]:((humble(X)&curious(X))<=>(tall(X)&humble(X))))&
((~wise(paul)<~>~generous(paul)))&
(?[X]:(calm(X)))&
(~creative(lucy))&
((creative(lucy)<~>generous(lucy)))&
((wise(paul)|patient(paul)))&
(?[X]:(~strong(X)))&
((~old(alice)<~>brave(alice)))&
(tall(lucy)) | ~brave(paul) | [
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7031324417367098246477699
% SZS output start Proof for 7031324417367098246477699
7. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~wise(X0) & ~generous(X0))) [input p6]
17. ~wise(paul) <~> ~generous(paul) [input p16]
25. brave(paul) [input hypothesis]
53. ! [X0] : (((~patient(X0) | brave(X0)) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 7]
54. ! [X0] : ((~patient(X0) | brave(X0) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | (patient(X0) & ~brave(X0)))) [flattening 53]
67. (generous(paul) | wise(paul)) & (~generous(paul) | ~wise(paul)) [nnf transformation 17]
92. ~brave(X0) | ~generous(X0) [cnf transformation 54]
94. ~wise(X0) | ~brave(X0) [cnf transformation 54]
130. generous(paul) | wise(paul) [cnf transformation 67]
140. brave(paul) [cnf transformation 25]
244. 22 <=> wise(paul) [avatar definition]
246. wise(paul) <- (22) [avatar component clause 244]
248. 23 <=> generous(paul) [avatar definition]
251. 22 | 23 [avatar split clause 130,248,244]
262. ~generous(paul) [resolution 92,140]
266. ~brave(paul) <- (22) [resolution 94,246]
267. $false <- (22) [subsumption resolution 266,140]
268. ~22 [avatar contradiction clause 267]
269. ~23 [avatar split clause 262,248]
270. $false [avatar sat refutation 251,268,269]
% SZS output end Proof for 7031324417367098246477699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and old is either not quiet or not creative and vice versa. Everyone who is creative or not generous is both not curious and not creative and vice versa. If lucy is either kind or tall then lucy is either quiet or old. Everyone who is either not strong or happy is not funny or not rich and vice versa. Everyone who is generous or not creative is not wise and vice versa. If someone is not calm or wise then someone is curious or not humble and vice versa. If someone is creative or not strong then mary is either not wise or not generous and vice versa. Everyone who is both patient and brave is not strong or calm. Everyone who is not strong or rich is creative. Everyone who is old or not happy is brave or not calm and vice versa. If someone is happy or not calm then mary is tall or strong and vice versa. If someone is funny or not kind then someone is either wise or rich. If someone is both not funny and funny then someone is either not old or not creative. Everyone who is tall is both not wise and not patient. If lucy is not generous or not funny then someone is either humble or brave and vice versa. Everyone who is not tall is curious or not old. Someone is brave or not creative. Fred is either patient or not creative. Someone is old or not humble. Lucy is either not rich or humble. Someone is both not creative and calm. | Fred is happy. | entailment | (![X]:((~brave(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((creative(X)|~generous(X))<=>(~curious(X)&~creative(X))))&
(((kind(lucy)<~>tall(lucy)))=>((quiet(lucy)<~>old(lucy))))&
(![X]:((~strong(X)<~>happy(X))<=>(~funny(X)|~rich(X))))&
(![X]:((generous(X)|~creative(X))<=>~wise(X)))&
((?[X]:((~calm(X)|wise(X))))<=>(?[X]:((curious(X)|~humble(X)))))&
((?[X]:((creative(X)|~strong(X))))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((patient(X)&brave(X))=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
(![X]:((old(X)|~happy(X))<=>(brave(X)|~calm(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((tall(mary)|strong(mary))))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(tall(X)=>(~wise(X)&~patient(X))))&
(((~generous(lucy)|~funny(lucy)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(?[X]:((brave(X)|~creative(X))))&
((patient(fred)<~>~creative(fred)))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X)))) | happy(fred) | [
"p1",
"p3",
"p4",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7781510816091602254214447
% SZS output start Proof for 7781510816091602254214447
2. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~creative(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~rich(X0) | ~funny(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | generous(X0)) <=> ~wise(X0)) [input p4]
9. ! [X0] : ((rich(X0) | ~strong(X0)) => creative(X0)) [input p8]
12. ? [X0] : (~kind(X0) | funny(X0)) => ? [X0] : (wise(X0) <~> rich(X0)) [input p11]
22. ~happy(fred) [input hypothesis]
24. ? [X0] : (~kind(X0) | funny(X0)) => ? [X1] : (wise(X1) <~> rich(X1)) [rectify 12]
29. ! [X0] : (creative(X0) | (~rich(X0) & strong(X0))) [ennf transformation 9]
30. ? [X1] : (wise(X1) <~> rich(X1)) | ! [X0] : (kind(X0) & ~funny(X0)) [ennf transformation 24]
37. ! [X0] : (((~generous(X0) | creative(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 2]
38. ! [X0] : ((~generous(X0) | creative(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [flattening 37]
40. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 40]
42. ! [X0] : (((~creative(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) & ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : ((~creative(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (creative(X0) & ~generous(X0)))) [flattening 42]
60. ? [X1] : ((~rich(X1) | ~wise(X1)) & (rich(X1) | wise(X1))) | ! [X0] : (kind(X0) & ~funny(X0)) [nnf transformation 30]
61. ? [X0] : ((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ! [X1] : (kind(X1) & ~funny(X1)) [rectify 60]
62. ? [X0] : ((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) => ((~rich(sK4) | ~wise(sK4)) & (rich(sK4) | wise(sK4))) [choice axiom]
63. ((~rich(sK4) | ~wise(sK4)) & (rich(sK4) | wise(sK4))) | ! [X1] : (kind(X1) & ~funny(X1)) [skolemisation 61,62]
89. ~creative(X0) | ~creative(X0) [cnf transformation 38]
98. ~strong(X0) | happy(X0) | funny(X0) [cnf transformation 41]
103. ~wise(X0) | creative(X0) [cnf transformation 43]
116. creative(X0) | strong(X0) [cnf transformation 29]
117. creative(X0) | ~rich(X0) [cnf transformation 29]
126. rich(sK4) | wise(sK4) | ~funny(X1) [cnf transformation 63]
149. ~happy(fred) [cnf transformation 22]
150. ~creative(X0) [duplicate literal removal 89]
172. ~wise(X0) [subsumption resolution 103,150]
212. 13 <=> ! [X1] : strong(X1) [avatar definition]
213. strong(X1) <- (13) [avatar component clause 212]
215. ~rich(X0) [subsumption resolution 117,150]
216. strong(X0) [subsumption resolution 116,150]
217. 13 [avatar split clause 216,212]
243. wise(sK4) | ~funny(X1) [subsumption resolution 126,215]
244. ~funny(X1) [subsumption resolution 243,172]
286. happy(X0) | funny(X0) <- (13) [resolution 98,213]
288. happy(X0) <- (13) [subsumption resolution 286,244]
289. $false <- (13) [resolution 288,149]
290. ~13 [avatar contradiction clause 289]
291. $false [avatar sat refutation 217,290]
% SZS output end Proof for 7781510816091602254214447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or not humble is quiet or curious.
Everyone who is either curious or not brave is generous and vice versa.
Everyone who is either happy or not curious is either not generous or wise and vice versa.
Everyone who is not old or generous is either tall or wise and vice versa.
Everyone who is not generous or generous is not old and vice versa.
Everyone who is either patient or not kind is either quiet or not wise and vice versa.
Everyone who is either generous or calm is either not kind or quiet and vice versa.
If paul is either not rich or happy then someone is both not quiet and quiet.
Everyone who is either not patient or patient is both not old and not quiet.
Everyone who is not patient is either not creative or funny and vice versa.
If susan is either not happy or kind then susan is either not tall or not old and vice versa.
Everyone who is either old or not generous is calm or happy.
If someone is not happy or tall then someone is either patient or not kind.
If fred is not happy then fred is either brave or not quiet and vice versa.
Everyone who is strong is both strong and not quiet and vice versa.
Paul is both not calm and rich.
Someone is either patient or not happy.
Mary is either curious or not brave.
Someone is not tall or not humble.
Paul is not kind.
Lucy is calm.
Mary is not creative. | Susan is funny. | neutral | (![X]:((generous(X)|~humble(X))=>(quiet(X)|curious(X))))&
(![X]:((curious(X)<~>~brave(X))<=>generous(X)))&
(![X]:((happy(X)<~>~curious(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
(![X]:((old(X)<~>~generous(X))=>(calm(X)|happy(X))))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((~happy(fred))<=>((brave(fred)<~>~quiet(fred))))&
(![X]:(strong(X)<=>(strong(X)&~quiet(X))))&
((~calm(paul)&rich(paul)))&
(?[X]:((patient(X)<~>~happy(X))))&
((curious(mary)<~>~brave(mary)))&
(?[X]:((~tall(X)|~humble(X))))&
(~kind(paul))&
(calm(lucy))&
(~creative(mary)) | funny(susan) | [] | null | 0 |
Everyone who is either patient or not brave is strong.
Everyone who is old or not curious is not happy or not brave and vice versa.
Everyone who is both not generous and humble is not patient and vice versa.
Everyone who is not creative is either calm or kind.
Everyone who is both not strong and not kind is both not generous and not kind and vice versa.
If someone is generous then someone is calm or not funny.
If john is either not patient or not curious then someone is brave or old and vice versa.
Everyone who is calm or not rich is not calm and vice versa.
Everyone who is not funny is not patient.
Everyone who is both brave and old is tall or generous.
Everyone who is not happy or kind is either not humble or patient.
If alice is calm then lucy is wise and vice versa.
Everyone who is humble or calm is not brave or happy and vice versa.
Everyone who is quiet is not creative and vice versa.
Everyone who is both not rich and not brave is either not curious or not strong.
If someone is either patient or not patient then john is both not old and not creative and vice versa.
John is not calm.
Mary is not quiet or generous.
Paul is either not old or patient.
Lucy is not happy or not creative.
Someone is either creative or not kind.
Lucy is not rich or funny.
Someone is both old and creative. | Alice is not calm. | entailment | (![X]:((patient(X)<~>~brave(X))=>strong(X)))&
(![X]:((old(X)|~curious(X))<=>(~happy(X)|~brave(X))))&
(![X]:((~generous(X)&humble(X))<=>~patient(X)))&
(![X]:(~creative(X)=>(calm(X)<~>kind(X))))&
(![X]:((~strong(X)&~kind(X))<=>(~generous(X)&~kind(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)|~funny(X)))))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:((brave(X)|old(X)))))&
(![X]:((calm(X)|~rich(X))<=>~calm(X)))&
(![X]:(~funny(X)=>~patient(X)))&
(![X]:((brave(X)&old(X))=>(tall(X)|generous(X))))&
(![X]:((~happy(X)|kind(X))=>(~humble(X)<~>patient(X))))&
((calm(alice))<=>(wise(lucy)))&
(![X]:((humble(X)|calm(X))<=>(~brave(X)|happy(X))))&
(![X]:(quiet(X)<=>~creative(X)))&
(![X]:((~rich(X)&~brave(X))=>(~curious(X)<~>~strong(X))))&
((?[X]:((patient(X)<~>~patient(X))))<=>((~old(john)&~creative(john))))&
(~calm(john))&
((~quiet(mary)|generous(mary)))&
((~old(paul)<~>patient(paul)))&
((~happy(lucy)|~creative(lucy)))&
(?[X]:((creative(X)<~>~kind(X))))&
((~rich(lucy)|funny(lucy)))&
(?[X]:((old(X)&creative(X)))) | ~calm(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 543199257754364475533043
% SZS output start Proof for 543199257754364475533043
8. ! [X0] : ((~rich(X0) | calm(X0)) <=> ~calm(X0)) [input p7]
24. calm(alice) [input hypothesis]
51. ! [X0] : (((~rich(X0) | calm(X0)) | calm(X0)) & (~calm(X0) | (rich(X0) & ~calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((~rich(X0) | calm(X0) | calm(X0)) & (~calm(X0) | (rich(X0) & ~calm(X0)))) [flattening 51]
91. ~calm(X0) | ~calm(X0) [cnf transformation 52]
124. calm(alice) [cnf transformation 24]
129. ~calm(X0) [duplicate literal removal 91]
244. $false [subsumption resolution 124,129]
% SZS output end Proof for 543199257754364475533043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is rich then someone is old and vice versa.
Everyone who is either not quiet or happy is not tall and vice versa.
If someone is not curious or not calm then susan is both humble and not humble and vice versa.
Everyone who is happy or not happy is either not kind or not creative and vice versa.
Everyone who is either not funny or generous is not patient or wise.
If someone is wise or not humble then someone is both not calm and happy and vice versa.
If someone is not strong then someone is either old or not quiet.
If someone is generous then paul is either wise or kind and vice versa.
Everyone who is not brave is both not creative and funny and vice versa.
Everyone who is either not strong or generous is both kind and brave.
If mary is both not calm and kind then someone is either curious or tall and vice versa.
If someone is both not funny and not curious then someone is either kind or not old and vice versa.
Everyone who is wise is both rich and patient.
If someone is not old or not tall then susan is both not brave and not funny and vice versa.
Everyone who is both calm and not funny is old or not generous and vice versa.
Everyone who is strong is humble or not brave.
Someone is either patient or calm. | Susan is patient. | contradiction | ((rich(alice))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>happy(X))<=>~tall(X)))&
((?[X]:((~curious(X)|~calm(X))))<=>((humble(susan)&~humble(susan))))&
(![X]:((happy(X)|~happy(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((~funny(X)<~>generous(X))=>(~patient(X)|wise(X))))&
((?[X]:((wise(X)|~humble(X))))<=>(?[X]:((~calm(X)&happy(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((old(X)<~>~quiet(X)))))&
((?[X]:(generous(X)))<=>((wise(paul)<~>kind(paul))))&
(![X]:(~brave(X)<=>(~creative(X)&funny(X))))&
(![X]:((~strong(X)<~>generous(X))=>(kind(X)&brave(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:((curious(X)<~>tall(X)))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:(wise(X)=>(rich(X)&patient(X))))&
((?[X]:((~old(X)|~tall(X))))<=>((~brave(susan)&~funny(susan))))&
(![X]:((calm(X)&~funny(X))<=>(old(X)|~generous(X))))&
(![X]:(strong(X)=>(humble(X)|~brave(X))))&
(?[X]:((patient(X)<~>calm(X)))) | patient(susan) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8151092845168377911109088
% SZS output start Proof for 8151092845168377911109088
3. ? [X0] : (~calm(X0) | ~curious(X0)) <=> (~humble(susan) & humble(susan)) [input p2]
5. ! [X0] : ((~funny(X0) <~> generous(X0)) => (wise(X0) | ~patient(X0))) [input p4]
6. ? [X0] : (~humble(X0) | wise(X0)) <=> ? [X0] : (happy(X0) & ~calm(X0)) [input p5]
8. ? [X0] : generous(X0) <=> (wise(paul) <~> kind(paul)) [input p7]
9. ! [X0] : (~brave(X0) <=> (funny(X0) & ~creative(X0))) [input p8]
12. ? [X0] : (~curious(X0) & ~funny(X0)) <=> ? [X0] : (kind(X0) <~> ~old(X0)) [input p11]
14. ? [X0] : (~tall(X0) | ~old(X0)) <=> (~funny(susan) & ~brave(susan)) [input p13]
15. ! [X0] : ((~funny(X0) & calm(X0)) <=> (~generous(X0) | old(X0))) [input p14]
18. patient(susan) [input hypothesis]
19. ? [X0] : (~humble(X0) | wise(X0)) <=> ? [X1] : (happy(X1) & ~calm(X1)) [rectify 6]
21. ? [X0] : (~curious(X0) & ~funny(X0)) <=> ? [X1] : (kind(X1) <~> ~old(X1)) [rectify 12]
22. ! [X0] : ((wise(X0) | ~patient(X0)) | (~funny(X0) <=> generous(X0))) [ennf transformation 5]
23. ! [X0] : (wise(X0) | ~patient(X0) | (~funny(X0) <=> generous(X0))) [flattening 22]
34. (? [X0] : (~calm(X0) | ~curious(X0)) | (humble(susan) | ~humble(susan))) & ((~humble(susan) & humble(susan)) | ! [X0] : (calm(X0) & curious(X0))) [nnf transformation 3]
35. (? [X0] : (~calm(X0) | ~curious(X0)) | humble(susan) | ~humble(susan)) & ((~humble(susan) & humble(susan)) | ! [X0] : (calm(X0) & curious(X0))) [flattening 34]
36. (? [X0] : (~calm(X0) | ~curious(X0)) | humble(susan) | ~humble(susan)) & ((~humble(susan) & humble(susan)) | ! [X1] : (calm(X1) & curious(X1))) [rectify 35]
37. ? [X0] : (~calm(X0) | ~curious(X0)) => (~calm(sK1) | ~curious(sK1)) [choice axiom]
38. ((~calm(sK1) | ~curious(sK1)) | humble(susan) | ~humble(susan)) & ((~humble(susan) & humble(susan)) | ! [X1] : (calm(X1) & curious(X1))) [skolemisation 36,37]
41. ! [X0] : (wise(X0) | ~patient(X0) | ((~funny(X0) | ~generous(X0)) & (generous(X0) | funny(X0)))) [nnf transformation 23]
42. (? [X0] : (~humble(X0) | wise(X0)) | ! [X1] : (~happy(X1) | calm(X1))) & (? [X1] : (happy(X1) & ~calm(X1)) | ! [X0] : (humble(X0) & ~wise(X0))) [nnf transformation 19]
43. (? [X0] : (~humble(X0) | wise(X0)) | ! [X1] : (~happy(X1) | calm(X1))) & (? [X2] : (happy(X2) & ~calm(X2)) | ! [X3] : (humble(X3) & ~wise(X3))) [rectify 42]
44. ? [X0] : (~humble(X0) | wise(X0)) => (~humble(sK2) | wise(sK2)) [choice axiom]
45. ? [X2] : (happy(X2) & ~calm(X2)) => (happy(sK3) & ~calm(sK3)) [choice axiom]
46. ((~humble(sK2) | wise(sK2)) | ! [X1] : (~happy(X1) | calm(X1))) & ((happy(sK3) & ~calm(sK3)) | ! [X3] : (humble(X3) & ~wise(X3))) [skolemisation 43,45,44]
51. (? [X0] : generous(X0) | ((wise(paul) | ~kind(paul)) & (kind(paul) | ~wise(paul)))) & (((~kind(paul) | ~wise(paul)) & (kind(paul) | wise(paul))) | ! [X0] : ~generous(X0)) [nnf transformation 8]
52. (? [X0] : generous(X0) | ((wise(paul) | ~kind(paul)) & (kind(paul) | ~wise(paul)))) & (((~kind(paul) | ~wise(paul)) & (kind(paul) | wise(paul))) | ! [X1] : ~generous(X1)) [rectify 51]
53. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
54. (generous(sK5) | ((wise(paul) | ~kind(paul)) & (kind(paul) | ~wise(paul)))) & (((~kind(paul) | ~wise(paul)) & (kind(paul) | wise(paul))) | ! [X1] : ~generous(X1)) [skolemisation 52,53]
55. ! [X0] : ((~brave(X0) | (~funny(X0) | creative(X0))) & ((funny(X0) & ~creative(X0)) | brave(X0))) [nnf transformation 9]
56. ! [X0] : ((~brave(X0) | ~funny(X0) | creative(X0)) & ((funny(X0) & ~creative(X0)) | brave(X0))) [flattening 55]
63. (? [X0] : (~curious(X0) & ~funny(X0)) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X1] : ((old(X1) | ~kind(X1)) & (~old(X1) | kind(X1))) | ! [X0] : (curious(X0) | funny(X0))) [nnf transformation 21]
64. (? [X0] : (~curious(X0) & ~funny(X0)) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) | ! [X3] : (curious(X3) | funny(X3))) [rectify 63]
65. ? [X0] : (~curious(X0) & ~funny(X0)) => (~curious(sK7) & ~funny(sK7)) [choice axiom]
66. ? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) => ((old(sK8) | ~kind(sK8)) & (~old(sK8) | kind(sK8))) [choice axiom]
67. ((~curious(sK7) & ~funny(sK7)) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (((old(sK8) | ~kind(sK8)) & (~old(sK8) | kind(sK8))) | ! [X3] : (curious(X3) | funny(X3))) [skolemisation 64,66,65]
68. (? [X0] : (~tall(X0) | ~old(X0)) | (funny(susan) | brave(susan))) & ((~funny(susan) & ~brave(susan)) | ! [X0] : (tall(X0) & old(X0))) [nnf transformation 14]
69. (? [X0] : (~tall(X0) | ~old(X0)) | funny(susan) | brave(susan)) & ((~funny(susan) & ~brave(susan)) | ! [X0] : (tall(X0) & old(X0))) [flattening 68]
70. (? [X0] : (~tall(X0) | ~old(X0)) | funny(susan) | brave(susan)) & ((~funny(susan) & ~brave(susan)) | ! [X1] : (tall(X1) & old(X1))) [rectify 69]
71. ? [X0] : (~tall(X0) | ~old(X0)) => (~tall(sK9) | ~old(sK9)) [choice axiom]
72. ((~tall(sK9) | ~old(sK9)) | funny(susan) | brave(susan)) & ((~funny(susan) & ~brave(susan)) | ! [X1] : (tall(X1) & old(X1))) [skolemisation 70,71]
73. ! [X0] : (((~funny(X0) & calm(X0)) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | (funny(X0) | ~calm(X0)))) [nnf transformation 15]
74. ! [X0] : (((~funny(X0) & calm(X0)) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | funny(X0) | ~calm(X0))) [flattening 73]
84. humble(susan) | curious(X1) [cnf transformation 38]
85. humble(susan) | calm(X1) [cnf transformation 38]
86. ~humble(susan) | curious(X1) [cnf transformation 38]
87. ~humble(susan) | calm(X1) [cnf transformation 38]
95. ~patient(X0) | wise(X0) | generous(X0) | funny(X0) [cnf transformation 41]
97. ~calm(sK3) | ~wise(X3) [cnf transformation 46]
104. kind(paul) | wise(paul) | ~generous(X1) [cnf transformation 54]
109. brave(X0) | funny(X0) [cnf transformation 56]
125. ~curious(sK7) | ~old(X1) | ~kind(X1) [cnf transformation 67]
129. ~brave(susan) | old(X1) [cnf transformation 72]
131. ~funny(susan) | old(X1) [cnf transformation 72]
137. ~funny(X0) | ~old(X0) [cnf transformation 74]
142. patient(susan) [cnf transformation 18]
157. 4 <=> ! [X1] : calm(X1) [avatar definition]
158. calm(X1) <- (4) [avatar component clause 157]
160. 5 <=> humble(susan) [avatar definition]
163. 4 | ~5 [avatar split clause 87,160,157]
165. 6 <=> ! [X1] : curious(X1) [avatar definition]
166. curious(X1) <- (6) [avatar component clause 165]
167. 6 | ~5 [avatar split clause 86,160,165]
168. 4 | 5 [avatar split clause 85,160,157]
169. 6 | 5 [avatar split clause 84,160,165]
193. 12 <=> ! [X3] : ~wise(X3) [avatar definition]
194. ~wise(X3) <- (12) [avatar component clause 193]
197. 13 <=> calm(sK3) [avatar definition]
199. ~calm(sK3) <- (~13) [avatar component clause 197]
201. 12 | ~13 [avatar split clause 97,197,193]
216. 17 <=> kind(paul) [avatar definition]
217. kind(paul) <- (17) [avatar component clause 216]
220. 18 <=> wise(paul) [avatar definition]
222. wise(paul) <- (18) [avatar component clause 220]
230. 20 <=> ! [X1] : ~generous(X1) [avatar definition]
231. ~generous(X1) <- (20) [avatar component clause 230]
233. 20 | 18 | 17 [avatar split clause 104,216,220,230]
266. 28 <=> curious(sK7) [avatar definition]
268. ~curious(sK7) <- (~28) [avatar component clause 266]
271. 29 <=> ! [X1] : (~old(X1) | ~kind(X1)) [avatar definition]
272. ~kind(X1) | ~old(X1) <- (29) [avatar component clause 271]
273. 29 | ~28 [avatar split clause 125,266,271]
297. 35 <=> funny(susan) [avatar definition]
298. funny(susan) <- (35) [avatar component clause 297]
299. ~funny(susan) <- (~35) [avatar component clause 297]
302. 36 <=> ! [X1] : old(X1) [avatar definition]
303. old(X1) <- (36) [avatar component clause 302]
304. 36 | ~35 [avatar split clause 131,297,302]
306. 37 <=> brave(susan) [avatar definition]
308. ~brave(susan) <- (~37) [avatar component clause 306]
310. 36 | ~37 [avatar split clause 129,306,302]
321. $false <- (4, ~13) [resolution 199,158]
322. ~4 | 13 [avatar contradiction clause 321]
327. $false <- (6, ~28) [resolution 268,166]
328. ~6 | 28 [avatar contradiction clause 327]
331. funny(susan) <- (~37) [resolution 109,308]
332. $false <- (~35, ~37) [subsumption resolution 331,299]
333. 35 | 37 [avatar contradiction clause 332]
346. ~old(paul) <- (17, 29) [resolution 272,217]
348. $false <- (17, 29, 36) [subsumption resolution 346,303]
349. ~17 | ~29 | ~36 [avatar contradiction clause 348]
355. ~old(susan) <- (35) [resolution 298,137]
358. $false <- (35, 36) [subsumption resolution 355,303]
359. ~35 | ~36 [avatar contradiction clause 358]
385. wise(susan) | generous(susan) | funny(susan) [resolution 95,142]
386. generous(susan) | funny(susan) <- (12) [subsumption resolution 385,194]
387. funny(susan) <- (12, 20) [subsumption resolution 386,231]
388. $false <- (12, 20, ~35) [subsumption resolution 387,299]
389. ~12 | ~20 | 35 [avatar contradiction clause 388]
391. $false <- (12, 18) [subsumption resolution 222,194]
392. ~12 | ~18 [avatar contradiction clause 391]
393. $false [avatar sat refutation 163,167,168,169,201,233,273,304,310,322,328,333,349,359,389,392]
% SZS output end Proof for 8151092845168377911109088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or tall is both humble and brave and vice versa.
Everyone who is not wise is both old and kind and vice versa.
If someone is humble then fred is either not tall or not strong.
If someone is both patient and not calm then alice is brave and vice versa.
If lucy is calm or not happy then someone is both not humble and not tall and vice versa.
Everyone who is both not wise and happy is either happy or kind and vice versa.
If someone is both old and not curious then alice is not humble.
If fred is both not tall and not quiet then someone is either tall or patient and vice versa.
If lucy is quiet or not curious then someone is happy and vice versa.
If someone is curious or creative then alice is both not happy and not creative and vice versa.
Everyone who is either not creative or generous is either not humble or brave and vice versa.
Everyone who is brave is humble or funny.
Everyone who is both not wise and not brave is not quiet or brave and vice versa.
If susan is not creative or curious then someone is creative.
Everyone who is both funny and old is either quiet or funny.
Everyone who is not patient or rich is either not brave or old.
Lucy is either not tall or curious.
John is tall or not tall.
Someone is not curious or not rich.
Someone is either not creative or not tall.
Lucy is either rich or generous.
Someone is either not wise or not brave. | Lucy is curious. | contradiction | (![X]:((humble(X)|tall(X))<=>(humble(X)&brave(X))))&
(![X]:(~wise(X)<=>(old(X)&kind(X))))&
((?[X]:(humble(X)))=>((~tall(fred)<~>~strong(fred))))&
((?[X]:((patient(X)&~calm(X))))<=>(brave(alice)))&
(((calm(lucy)|~happy(lucy)))<=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((~wise(X)&happy(X))<=>(happy(X)<~>kind(X))))&
((?[X]:((old(X)&~curious(X))))=>(~humble(alice)))&
(((~tall(fred)&~quiet(fred)))<=>(?[X]:((tall(X)<~>patient(X)))))&
(((quiet(lucy)|~curious(lucy)))<=>(?[X]:(happy(X))))&
((?[X]:((curious(X)|creative(X))))<=>((~happy(alice)&~creative(alice))))&
(![X]:((~creative(X)<~>generous(X))<=>(~humble(X)<~>brave(X))))&
(![X]:(brave(X)=>(humble(X)|funny(X))))&
(![X]:((~wise(X)&~brave(X))<=>(~quiet(X)|brave(X))))&
(((~creative(susan)|curious(susan)))=>(?[X]:(creative(X))))&
(![X]:((funny(X)&old(X))=>(quiet(X)<~>funny(X))))&
(![X]:((~patient(X)|rich(X))=>(~brave(X)<~>old(X))))&
((~tall(lucy)<~>curious(lucy)))&
((tall(john)|~tall(john)))&
(?[X]:((~curious(X)|~rich(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
((rich(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)<~>~brave(X)))) | curious(lucy) | [
"p0",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6244967927105825972480728
% SZS output start Proof for 6244967927105825972480728
1. ! [X0] : ((tall(X0) | humble(X0)) <=> (brave(X0) & humble(X0))) [input p0]
13. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> (brave(X0) | ~quiet(X0))) [input p12]
17. ~tall(lucy) <~> curious(lucy) [input p16]
23. curious(lucy) [input hypothesis]
32. ! [X0] : (((tall(X0) | humble(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (~tall(X0) & ~humble(X0)))) [nnf transformation 1]
33. ! [X0] : ((tall(X0) | humble(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (~tall(X0) & ~humble(X0)))) [flattening 32]
64. ! [X0] : (((~brave(X0) & ~wise(X0)) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | (brave(X0) | wise(X0)))) [nnf transformation 13]
65. ! [X0] : (((~brave(X0) & ~wise(X0)) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | brave(X0) | wise(X0))) [flattening 64]
70. (~curious(lucy) | tall(lucy)) & (curious(lucy) | ~tall(lucy)) [nnf transformation 17]
81. ~tall(X0) | humble(X0) [cnf transformation 33]
82. ~humble(X0) | brave(X0) [cnf transformation 33]
132. ~brave(X0) | ~brave(X0) [cnf transformation 65]
142. ~curious(lucy) | tall(lucy) [cnf transformation 70]
151. curious(lucy) [cnf transformation 23]
154. ~brave(X0) [duplicate literal removal 132]
255. 22 <=> curious(lucy) [avatar definition]
314. 33 <=> tall(lucy) [avatar definition]
316. tall(lucy) <- (33) [avatar component clause 314]
317. 33 | ~22 [avatar split clause 142,255,314]
349. 22 [avatar split clause 151,255]
350. humble(lucy) <- (33) [resolution 81,316]
351. brave(lucy) <- (33) [resolution 82,350]
352. $false <- (33) [subsumption resolution 351,154]
353. ~33 [avatar contradiction clause 352]
354. $false [avatar sat refutation 317,349,353]
% SZS output end Proof for 6244967927105825972480728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not humble or curious.
If someone is both not creative and not strong then paul is wise and vice versa.
If someone is either not tall or old then someone is either not happy or old and vice versa.
Everyone who is either brave or calm is rich or generous and vice versa.
If alice is either generous or not generous then alice is both brave and not kind.
Everyone who is not tall or wise is both not rich and quiet and vice versa.
Everyone who is both not tall and not patient is either calm or quiet.
Everyone who is not quiet or not humble is humble or old.
If alice is not brave or not happy then someone is patient or not happy.
Everyone who is patient or happy is either not happy or old and vice versa.
If someone is both not patient and not quiet then someone is either not tall or rich and vice versa.
If someone is not strong or humble then someone is not rich and vice versa.
If mary is both not generous and not curious then alice is both not curious and strong.
Everyone who is both not wise and not quiet is not rich and vice versa.
Everyone who is old or not funny is not strong and vice versa.
John is either not brave or happy.
John is both not happy and not humble.
Lucy is either old or not quiet.
Alice is not strong.
Someone is creative or calm.
Alice is not quiet or kind.
Someone is quiet or kind.
Someone is either not quiet or not calm. | John is not strong. | entailment | (![X]:(happy(X)=>(~humble(X)|curious(X))))&
((?[X]:((~creative(X)&~strong(X))))<=>(wise(paul)))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(rich(X)|generous(X))))&
(((generous(alice)<~>~generous(alice)))=>((brave(alice)&~kind(alice))))&
(![X]:((~tall(X)|wise(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~tall(X)&~patient(X))=>(calm(X)<~>quiet(X))))&
(![X]:((~quiet(X)|~humble(X))=>(humble(X)|old(X))))&
(((~brave(alice)|~happy(alice)))=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((patient(X)|happy(X))<=>(~happy(X)<~>old(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~tall(X)<~>rich(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:(~rich(X))))&
(((~generous(mary)&~curious(mary)))=>((~curious(alice)&strong(alice))))&
(![X]:((~wise(X)&~quiet(X))<=>~rich(X)))&
(![X]:((old(X)|~funny(X))<=>~strong(X)))&
((~brave(john)<~>happy(john)))&
((~happy(john)&~humble(john)))&
((old(lucy)<~>~quiet(lucy)))&
(~strong(alice))&
(?[X]:((creative(X)|calm(X))))&
((~quiet(alice)|kind(alice)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((~quiet(X)<~>~calm(X)))) | ~strong(john) | [
"p7",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4822227374976340828879698
% SZS output start Proof for 4822227374976340828879698
8. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (old(X0) | humble(X0))) [input p7]
15. ! [X0] : ((~funny(X0) | old(X0)) <=> ~strong(X0)) [input p14]
17. ~humble(john) & ~happy(john) [input p16]
24. strong(john) [input hypothesis]
33. ! [X0] : ((old(X0) | humble(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 8]
34. ! [X0] : (old(X0) | humble(X0) | (humble(X0) & quiet(X0))) [flattening 33]
69. ! [X0] : (((~funny(X0) | old(X0)) | strong(X0)) & (~strong(X0) | (funny(X0) & ~old(X0)))) [nnf transformation 15]
70. ! [X0] : ((~funny(X0) | old(X0) | strong(X0)) & (~strong(X0) | (funny(X0) & ~old(X0)))) [flattening 69]
110. old(X0) | humble(X0) | humble(X0) [cnf transformation 34]
133. ~old(X0) | ~strong(X0) [cnf transformation 70]
139. ~humble(john) [cnf transformation 17]
148. strong(john) [cnf transformation 24]
151. old(X0) | humble(X0) [duplicate literal removal 110]
403. ~strong(X0) | humble(X0) [resolution 151,133]
436. humble(john) [resolution 403,148]
438. $false [subsumption resolution 436,139]
% SZS output end Proof for 4822227374976340828879698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either humble or not tall then someone is not kind or not wise. Everyone who is either tall or quiet is strong and vice versa. Everyone who is brave is both rich and not curious. Everyone who is both not calm and not quiet is not brave and vice versa. Everyone who is funny or creative is happy and vice versa. If susan is both brave and not wise then someone is not kind and vice versa. If someone is old then susan is rich or not quiet. If mary is both tall and not kind then someone is old. Everyone who is both not wise and not patient is not brave and vice versa. Everyone who is both creative and funny is either quiet or humble. Everyone who is quiet or generous is not old or not happy. If lucy is both kind and not tall then someone is curious. If someone is rich then someone is either not tall or not wise. If someone is either not humble or wise then susan is old or kind. Everyone who is not calm or not curious is brave and vice versa. If someone is not patient or not tall then someone is not patient and vice versa. John is not old. Someone is both wise and not kind. Someone is both not patient and brave. Susan is not curious. Someone is both not tall and not strong. Paul is not kind or humble. Someone is happy. | Lucy is not tall. | neutral | (((humble(fred)<~>~tall(fred)))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((tall(X)<~>quiet(X))<=>strong(X)))&
(![X]:(brave(X)=>(rich(X)&~curious(X))))&
(![X]:((~calm(X)&~quiet(X))<=>~brave(X)))&
(![X]:((funny(X)|creative(X))<=>happy(X)))&
(((brave(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(old(X)))=>((rich(susan)|~quiet(susan))))&
(((tall(mary)&~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~patient(X))<=>~brave(X)))&
(![X]:((creative(X)&funny(X))=>(quiet(X)<~>humble(X))))&
(![X]:((quiet(X)|generous(X))=>(~old(X)|~happy(X))))&
(((kind(lucy)&~tall(lucy)))=>(?[X]:(curious(X))))&
((?[X]:(rich(X)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~humble(X)<~>wise(X))))=>((old(susan)|kind(susan))))&
(![X]:((~calm(X)|~curious(X))<=>brave(X)))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~patient(X))))&
(~old(john))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((~patient(X)&brave(X))))&
(~curious(susan))&
(?[X]:((~tall(X)&~strong(X))))&
((~kind(paul)|humble(paul)))&
(?[X]:(happy(X))) | ~tall(lucy) | [] | null | 0 |
Everyone who is both brave and not patient is patient or not creative and vice versa. If lucy is not calm or happy then someone is both not wise and not generous and vice versa. Everyone who is humble or not generous is both not calm and not rich and vice versa. Everyone who is both generous and not quiet is both old and creative and vice versa. If fred is curious then someone is not brave. If someone is both not creative and rich then someone is both patient and quiet and vice versa. If someone is both happy and quiet then alice is not brave and vice versa. If susan is either not curious or kind then fred is both humble and curious and vice versa. Everyone who is either not rich or not generous is either not generous or happy. Everyone who is either kind or not humble is both not wise and not curious and vice versa. If someone is both patient and not patient then paul is either happy or kind and vice versa. Everyone who is either quiet or calm is either rich or not generous. If someone is not tall then john is brave. If someone is wise then someone is funny. Everyone who is both curious and not tall is rich and vice versa. If someone is not old or generous then someone is either patient or old and vice versa. John is either not wise or wise. Someone is curious. Paul is creative or strong. John is not generous or rich. Someone is both not quiet and not kind. Someone is both rich and not brave. | John is generous. | contradiction | (![X]:((brave(X)&~patient(X))<=>(patient(X)|~creative(X))))&
(((~calm(lucy)|happy(lucy)))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((humble(X)|~generous(X))<=>(~calm(X)&~rich(X))))&
(![X]:((generous(X)&~quiet(X))<=>(old(X)&creative(X))))&
((curious(fred))=>(?[X]:(~brave(X))))&
((?[X]:((~creative(X)&rich(X))))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((happy(X)&quiet(X))))<=>(~brave(alice)))&
(((~curious(susan)<~>kind(susan)))<=>((humble(fred)&curious(fred))))&
(![X]:((~rich(X)<~>~generous(X))=>(~generous(X)<~>happy(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(~wise(X)&~curious(X))))&
((?[X]:((patient(X)&~patient(X))))<=>((happy(paul)<~>kind(paul))))&
(![X]:((quiet(X)<~>calm(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(~tall(X)))=>(brave(john)))&
((?[X]:(wise(X)))=>(?[X]:(funny(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
((~wise(john)<~>wise(john)))&
(?[X]:(curious(X)))&
((creative(paul)|strong(paul)))&
((~generous(john)|rich(john)))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((rich(X)&~brave(X)))) | generous(john) | [
"p0",
"p5",
"p12",
"p14",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1885473079647979939855946
% SZS output start Proof for 1885473079647979939855946
1. ! [X0] : ((~patient(X0) & brave(X0)) <=> (~creative(X0) | patient(X0))) [input p0]
6. ? [X0] : (rich(X0) & ~creative(X0)) <=> ? [X0] : (quiet(X0) & patient(X0)) [input p5]
13. ? [X0] : ~tall(X0) => brave(john) [input p12]
15. ! [X0] : ((~tall(X0) & curious(X0)) <=> rich(X0)) [input p14]
20. rich(john) | ~generous(john) [input p19]
22. ? [X0] : (~brave(X0) & rich(X0)) [input p21]
23. generous(john) [input hypothesis]
24. ? [X0] : (rich(X0) & ~creative(X0)) <=> ? [X1] : (quiet(X1) & patient(X1)) [rectify 6]
32. brave(john) | ! [X0] : tall(X0) [ennf transformation 13]
33. ! [X0] : (((~patient(X0) & brave(X0)) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | (patient(X0) | ~brave(X0)))) [nnf transformation 1]
34. ! [X0] : (((~patient(X0) & brave(X0)) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | patient(X0) | ~brave(X0))) [flattening 33]
46. (? [X0] : (rich(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) | ~patient(X1))) & (? [X1] : (quiet(X1) & patient(X1)) | ! [X0] : (~rich(X0) | creative(X0))) [nnf transformation 24]
47. (? [X0] : (rich(X0) & ~creative(X0)) | ! [X1] : (~quiet(X1) | ~patient(X1))) & (? [X2] : (quiet(X2) & patient(X2)) | ! [X3] : (~rich(X3) | creative(X3))) [rectify 46]
48. ? [X0] : (rich(X0) & ~creative(X0)) => (rich(sK2) & ~creative(sK2)) [choice axiom]
49. ? [X2] : (quiet(X2) & patient(X2)) => (quiet(sK3) & patient(sK3)) [choice axiom]
50. ((rich(sK2) & ~creative(sK2)) | ! [X1] : (~quiet(X1) | ~patient(X1))) & ((quiet(sK3) & patient(sK3)) | ! [X3] : (~rich(X3) | creative(X3))) [skolemisation 47,49,48]
65. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | (tall(X0) | ~curious(X0)))) [nnf transformation 15]
66. ! [X0] : (((~tall(X0) & curious(X0)) | ~rich(X0)) & (rich(X0) | tall(X0) | ~curious(X0))) [flattening 65]
77. ? [X0] : (~brave(X0) & rich(X0)) => (~brave(sK10) & rich(sK10)) [choice axiom]
78. ~brave(sK10) & rich(sK10) [skolemisation 22,77]
79. ~creative(X0) | patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 34]
82. ~patient(X0) | ~patient(X0) [cnf transformation 34]
99. patient(sK3) | ~rich(X3) | creative(X3) [cnf transformation 50]
132. brave(john) | tall(X0) [cnf transformation 32]
135. ~tall(X0) | ~rich(X0) [cnf transformation 66]
145. rich(john) | ~generous(john) [cnf transformation 20]
148. rich(sK10) [cnf transformation 78]
150. generous(john) [cnf transformation 23]
153. ~creative(X0) | patient(X0) | ~brave(X0) [duplicate literal removal 79]
154. ~patient(X0) [duplicate literal removal 82]
155. ~creative(X0) | ~brave(X0) [subsumption resolution 153,154]
190. 8 <=> ! [X3] : (~rich(X3) | creative(X3)) [avatar definition]
191. ~rich(X3) | creative(X3) <- (8) [avatar component clause 190]
197. ~rich(X3) | creative(X3) [subsumption resolution 99,154]
198. 8 [avatar split clause 197,190]
249. 19 <=> ! [X0] : tall(X0) [avatar definition]
250. tall(X0) <- (19) [avatar component clause 249]
252. 20 <=> brave(john) [avatar definition]
254. brave(john) <- (20) [avatar component clause 252]
255. 19 | 20 [avatar split clause 132,252,249]
284. 27 <=> generous(john) [avatar definition]
288. 28 <=> rich(john) [avatar definition]
290. rich(john) <- (28) [avatar component clause 288]
291. ~27 | 28 [avatar split clause 145,288,284]
292. 27 [avatar split clause 150,284]
300. ~rich(X0) <- (19) [resolution 135,250]
303. creative(john) <- (8, 28) [resolution 191,290]
304. $false <- (19) [resolution 300,148]
307. ~19 [avatar contradiction clause 304]
329. ~brave(john) <- (8, 28) [resolution 303,155]
330. $false <- (8, 20, 28) [subsumption resolution 329,254]
331. ~8 | ~20 | ~28 [avatar contradiction clause 330]
332. $false [avatar sat refutation 198,255,291,292,307,331]
% SZS output end Proof for 1885473079647979939855946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or kind is tall.
If john is kind then alice is either not brave or not patient.
Everyone who is wise or not wise is rich.
Everyone who is both rich and not kind is both funny and strong and vice versa.
If someone is either tall or generous then someone is both not old and not wise.
Everyone who is not old or not calm is not tall or creative.
Everyone who is either not kind or not rich is either not creative or curious and vice versa.
Everyone who is both patient and not kind is both not curious and not happy.
Everyone who is not patient is not funny or kind and vice versa.
If someone is both not quiet and rich then mary is either not happy or not brave.
Everyone who is both not humble and strong is both kind and not quiet and vice versa.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
If someone is not humble or happy then paul is both not tall and not generous and vice versa.
Everyone who is calm or generous is either rich or patient and vice versa.
Mary is both not humble and not brave.
Someone is both tall and brave.
Someone is both not funny and not wise.
Someone is either tall or happy.
Someone is generous or not curious.
John is patient.
Someone is not rich or not wise. | Mary is not patient. | entailment | (![X]:((~funny(X)|kind(X))=>tall(X)))&
((kind(john))=>((~brave(alice)<~>~patient(alice))))&
(![X]:((wise(X)|~wise(X))=>rich(X)))&
(![X]:((rich(X)&~kind(X))<=>(funny(X)&strong(X))))&
((?[X]:((tall(X)<~>generous(X))))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~old(X)|~calm(X))=>(~tall(X)|creative(X))))&
(![X]:((~kind(X)<~>~rich(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((patient(X)&~kind(X))=>(~curious(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~funny(X)|kind(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((~happy(mary)<~>~brave(mary))))&
(![X]:((~humble(X)&strong(X))<=>(kind(X)&~quiet(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
((?[X]:((~humble(X)|happy(X))))<=>((~tall(paul)&~generous(paul))))&
(![X]:((calm(X)|generous(X))<=>(rich(X)<~>patient(X))))&
((~humble(mary)&~brave(mary)))&
(?[X]:((tall(X)&brave(X))))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((tall(X)<~>happy(X))))&
(?[X]:((generous(X)|~curious(X))))&
(patient(john))&
(?[X]:((~rich(X)|~wise(X)))) | ~patient(mary) | [
"p2",
"p3",
"p8",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5776884799142317866144514
% SZS output start Proof for 5776884799142317866144514
3. ! [X0] : ((~wise(X0) | wise(X0)) => rich(X0)) [input p2]
4. ! [X0] : ((~kind(X0) & rich(X0)) <=> (strong(X0) & funny(X0))) [input p3]
9. ! [X0] : (~patient(X0) <=> (kind(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((strong(X0) & ~humble(X0)) <=> (~quiet(X0) & kind(X0))) [input p10]
17. ~brave(mary) & ~humble(mary) [input p16]
24. patient(mary) [input hypothesis]
28. ! [X0] : (rich(X0) | (wise(X0) & ~wise(X0))) [ennf transformation 3]
38. ! [X0] : (((~kind(X0) & rich(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 4]
39. ! [X0] : (((~kind(X0) & rich(X0)) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | kind(X0) | ~rich(X0))) [flattening 38]
45. ! [X0] : ((~patient(X0) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | patient(X0))) [nnf transformation 9]
46. ! [X0] : ((~patient(X0) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | patient(X0))) [flattening 45]
48. ! [X0] : (((strong(X0) & ~humble(X0)) | (quiet(X0) | ~kind(X0))) & ((~quiet(X0) & kind(X0)) | (~strong(X0) | humble(X0)))) [nnf transformation 11]
49. ! [X0] : (((strong(X0) & ~humble(X0)) | quiet(X0) | ~kind(X0)) & ((~quiet(X0) & kind(X0)) | ~strong(X0) | humble(X0))) [flattening 48]
76. rich(X0) | ~wise(X0) [cnf transformation 28]
77. rich(X0) | wise(X0) [cnf transformation 28]
79. strong(X0) | kind(X0) | ~rich(X0) [cnf transformation 39]
100. ~patient(X0) | ~kind(X0) [cnf transformation 46]
103. kind(X0) | ~strong(X0) | humble(X0) [cnf transformation 49]
127. ~humble(mary) [cnf transformation 17]
138. patient(mary) [cnf transformation 24]
153. rich(X0) [subsumption resolution 76,77]
154. strong(X0) | kind(X0) [subsumption resolution 79,153]
195. humble(X0) | kind(X0) [subsumption resolution 103,154]
273. ~kind(mary) [resolution 100,138]
280. kind(mary) [resolution 195,127]
282. $false [subsumption resolution 280,273]
% SZS output end Proof for 5776884799142317866144514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or generous is not calm.
If fred is either generous or rich then susan is both old and kind.
Everyone who is humble is either not brave or not rich and vice versa.
Everyone who is generous or not funny is not old and vice versa.
If someone is rich or kind then alice is both curious and humble.
Everyone who is strong is both rich and not old and vice versa.
If susan is not curious or brave then someone is both wise and not quiet.
Everyone who is either not humble or rich is patient or wise.
If someone is both quiet and not tall then someone is kind and vice versa.
If paul is creative or not quiet then someone is wise or calm and vice versa.
If someone is both not brave and not patient then john is both generous and not generous.
Everyone who is not funny is generous or not funny.
Everyone who is not patient or kind is both not strong and not humble and vice versa.
Everyone who is strong is funny or wise.
Everyone who is funny or not strong is happy or quiet.
Everyone who is old or kind is funny.
Someone is brave or not kind.
Someone is old or brave.
Alice is rich or not rich.
Susan is both creative and happy.
Paul is both not rich and funny.
Someone is either kind or creative.
Lucy is not wise.
Paul is generous or not old. | Alice is patient. | entailment | (![X]:((~tall(X)|generous(X))=>~calm(X)))&
(((generous(fred)<~>rich(fred)))=>((old(susan)&kind(susan))))&
(![X]:(humble(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((generous(X)|~funny(X))<=>~old(X)))&
((?[X]:((rich(X)|kind(X))))=>((curious(alice)&humble(alice))))&
(![X]:(strong(X)<=>(rich(X)&~old(X))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(patient(X)|wise(X))))&
((?[X]:((quiet(X)&~tall(X))))<=>(?[X]:(kind(X))))&
(((creative(paul)|~quiet(paul)))<=>(?[X]:((wise(X)|calm(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((generous(john)&~generous(john))))&
(![X]:(~funny(X)=>(generous(X)|~funny(X))))&
(![X]:((~patient(X)|kind(X))<=>(~strong(X)&~humble(X))))&
(![X]:(strong(X)=>(funny(X)|wise(X))))&
(![X]:((funny(X)|~strong(X))=>(happy(X)|quiet(X))))&
(![X]:((old(X)|kind(X))=>funny(X)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((old(X)|brave(X))))&
((rich(alice)|~rich(alice)))&
((creative(susan)&happy(susan)))&
((~rich(paul)&funny(paul)))&
(?[X]:((kind(X)<~>creative(X))))&
(~wise(lucy))&
((generous(paul)|~old(paul))) | patient(alice) | [
"p2",
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1778080455864779805154772
% SZS output start Proof for 1778080455864779805154772
3. ! [X0] : (humble(X0) <=> (~brave(X0) <~> ~rich(X0))) [input p2]
5. ? [X0] : (kind(X0) | rich(X0)) => (humble(alice) & curious(alice)) [input p4]
11. ? [X0] : (~patient(X0) & ~brave(X0)) => (~generous(john) & generous(john)) [input p10]
13. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (~humble(X0) & ~strong(X0))) [input p12]
25. ~patient(alice) [input hypothesis]
30. ? [X0] : (kind(X0) | rich(X0)) => humble(alice) [pure predicate removal 5]
33. humble(alice) | ! [X0] : (~kind(X0) & ~rich(X0)) [ennf transformation 30]
37. (~generous(john) & generous(john)) | ! [X0] : (patient(X0) | brave(X0)) [ennf transformation 11]
44. ! [X0] : ((humble(X0) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) & (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | ~humble(X0))) [nnf transformation 3]
62. ! [X0] : (((kind(X0) | ~patient(X0)) | (humble(X0) | strong(X0))) & ((~humble(X0) & ~strong(X0)) | (~kind(X0) & patient(X0)))) [nnf transformation 13]
63. ! [X0] : ((kind(X0) | ~patient(X0) | humble(X0) | strong(X0)) & ((~humble(X0) & ~strong(X0)) | (~kind(X0) & patient(X0)))) [flattening 62]
80. ~brave(X0) | humble(X0) | rich(X0) [cnf transformation 44]
84. humble(alice) | ~rich(X0) [cnf transformation 33]
100. generous(john) | patient(X0) | brave(X0) [cnf transformation 37]
101. ~generous(john) | patient(X0) | brave(X0) [cnf transformation 37]
105. ~humble(X0) | patient(X0) [cnf transformation 63]
121. ~patient(alice) [cnf transformation 25]
146. 6 <=> humble(alice) [avatar definition]
147. ~humble(alice) <- (~6) [avatar component clause 146]
148. humble(alice) <- (6) [avatar component clause 146]
151. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
152. ~rich(X0) <- (7) [avatar component clause 151]
153. 7 | 6 [avatar split clause 84,146,151]
213. 21 <=> ! [X0] : (patient(X0) | brave(X0)) [avatar definition]
214. patient(X0) | brave(X0) <- (21) [avatar component clause 213]
216. 22 <=> generous(john) [avatar definition]
219. 21 | ~22 [avatar split clause 101,216,213]
220. 21 | 22 [avatar split clause 100,216,213]
254. patient(alice) <- (6) [resolution 105,148]
255. $false <- (6) [subsumption resolution 254,121]
256. ~6 [avatar contradiction clause 255]
262. brave(alice) <- (21) [resolution 214,121]
264. humble(alice) | rich(alice) <- (21) [resolution 80,262]
265. rich(alice) <- (~6, 21) [subsumption resolution 264,147]
266. $false <- (~6, 7, 21) [subsumption resolution 265,152]
267. 6 | ~7 | ~21 [avatar contradiction clause 266]
268. $false [avatar sat refutation 153,219,220,256,267]
% SZS output end Proof for 1778080455864779805154772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not strong.
Everyone who is either brave or not strong is either not funny or not tall and vice versa.
Everyone who is not calm or wise is both happy and not patient and vice versa.
Everyone who is both not brave and not tall is both quiet and strong.
Everyone who is patient is either brave or not wise and vice versa.
If john is happy or calm then someone is either quiet or not tall and vice versa.
If someone is not patient then someone is both not strong and happy and vice versa.
If alice is not calm or wise then mary is both not curious and not generous and vice versa.
Everyone who is quiet or not wise is not kind or kind.
If someone is both old and calm then someone is both not happy and old and vice versa.
If paul is not curious then someone is patient or not brave and vice versa.
If someone is either not brave or funny then someone is calm and vice versa.
Everyone who is either not strong or kind is either not patient or not funny.
Everyone who is both not old and not funny is wise or funny and vice versa.
Everyone who is wise or not strong is tall or not creative and vice versa.
Everyone who is both rich and not kind is tall or not curious and vice versa.
Alice is wise.
Mary is both calm and rich.
Lucy is not happy or not strong.
Someone is both rich and generous.
Someone is not brave or kind. | Paul is patient. | neutral | (![X]:(brave(X)=>~strong(X)))&
(![X]:((brave(X)<~>~strong(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~patient(X))))&
(![X]:((~brave(X)&~tall(X))=>(quiet(X)&strong(X))))&
(![X]:(patient(X)<=>(brave(X)<~>~wise(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((~strong(X)&happy(X)))))&
(((~calm(alice)|wise(alice)))<=>((~curious(mary)&~generous(mary))))&
(![X]:((quiet(X)|~wise(X))=>(~kind(X)|kind(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((~happy(X)&old(X)))))&
((~curious(paul))<=>(?[X]:((patient(X)|~brave(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)|funny(X))))&
(![X]:((wise(X)|~strong(X))<=>(tall(X)|~creative(X))))&
(![X]:((rich(X)&~kind(X))<=>(tall(X)|~curious(X))))&
(wise(alice))&
((calm(mary)&rich(mary)))&
((~happy(lucy)|~strong(lucy)))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((~brave(X)|kind(X)))) | patient(paul) | [] | null | 0 |
If someone is quiet then mary is not rich and vice versa.
Everyone who is either calm or rich is both funny and old.
If mary is both creative and wise then someone is either happy or rich.
If susan is kind or creative then susan is both brave and creative and vice versa.
Everyone who is both patient and calm is not old.
Everyone who is either not strong or not wise is patient.
If mary is brave or not brave then mary is both old and not kind and vice versa.
Everyone who is quiet is old.
Everyone who is both not humble and not brave is either creative or not patient.
If susan is either not happy or brave then someone is both rich and not strong and vice versa.
Everyone who is both not kind and not happy is both not old and not wise and vice versa.
If someone is not tall or patient then susan is both not tall and not happy.
If john is not old then someone is either brave or tall.
Everyone who is either not generous or not humble is either strong or not generous and vice versa.
Everyone who is both kind and rich is either humble or not tall and vice versa.
Everyone who is either not old or calm is rich.
Someone is either patient or not calm.
Someone is both not old and not strong.
Someone is humble.
Someone is not brave.
Someone is either not old or not calm.
Alice is either creative or strong.
Someone is kind or quiet.
Someone is either generous or not quiet. | Susan is calm. | entailment | ((?[X]:(quiet(X)))<=>(~rich(mary)))&
(![X]:((calm(X)<~>rich(X))=>(funny(X)&old(X))))&
(((creative(mary)&wise(mary)))=>(?[X]:((happy(X)<~>rich(X)))))&
(((kind(susan)|creative(susan)))<=>((brave(susan)&creative(susan))))&
(![X]:((patient(X)&calm(X))=>~old(X)))&
(![X]:((~strong(X)<~>~wise(X))=>patient(X)))&
(((brave(mary)|~brave(mary)))<=>((old(mary)&~kind(mary))))&
(![X]:(quiet(X)=>old(X)))&
(![X]:((~humble(X)&~brave(X))=>(creative(X)<~>~patient(X))))&
(((~happy(susan)<~>brave(susan)))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((~kind(X)&~happy(X))<=>(~old(X)&~wise(X))))&
((?[X]:((~tall(X)|patient(X))))=>((~tall(susan)&~happy(susan))))&
((~old(john))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(strong(X)<~>~generous(X))))&
(![X]:((kind(X)&rich(X))<=>(humble(X)<~>~tall(X))))&
(![X]:((~old(X)<~>calm(X))=>rich(X)))&
(?[X]:((patient(X)<~>~calm(X))))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:(humble(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~old(X)<~>~calm(X))))&
((creative(alice)<~>strong(alice)))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((generous(X)<~>~quiet(X)))) | calm(susan) | [
"p1",
"p3",
"p5",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5376719794793796018918041
% SZS output start Proof for 5376719794793796018918041
2. ! [X0] : ((calm(X0) <~> rich(X0)) => (old(X0) & funny(X0))) [input p1]
4. (creative(susan) | kind(susan)) <=> (creative(susan) & brave(susan)) [input p3]
6. ! [X0] : ((~strong(X0) <~> ~wise(X0)) => patient(X0)) [input p5]
10. (~happy(susan) <~> brave(susan)) <=> ? [X0] : (~strong(X0) & rich(X0)) [input p9]
11. ! [X0] : ((~happy(X0) & ~kind(X0)) <=> (~wise(X0) & ~old(X0))) [input p10]
12. ? [X0] : (patient(X0) | ~tall(X0)) => (~happy(susan) & ~tall(susan)) [input p11]
14. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (strong(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : ((rich(X0) & kind(X0)) <=> (humble(X0) <~> ~tall(X0))) [input p14]
16. ! [X0] : ((~old(X0) <~> calm(X0)) => rich(X0)) [input p15]
18. ? [X0] : (~strong(X0) & ~old(X0)) [input p17]
25. ~calm(susan) [input hypothesis]
26. ! [X0] : ((calm(X0) <~> rich(X0)) => old(X0)) [pure predicate removal 2]
27. ! [X0] : (old(X0) | (calm(X0) <=> rich(X0))) [ennf transformation 26]
32. ! [X0] : (patient(X0) | (~strong(X0) <=> ~wise(X0))) [ennf transformation 6]
36. (~happy(susan) & ~tall(susan)) | ! [X0] : (~patient(X0) & tall(X0)) [ennf transformation 12]
38. ! [X0] : (rich(X0) | (~old(X0) <=> calm(X0))) [ennf transformation 16]
43. ! [X0] : (old(X0) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) [nnf transformation 27]
47. ((creative(susan) | kind(susan)) | (~creative(susan) | ~brave(susan))) & ((creative(susan) & brave(susan)) | (~creative(susan) & ~kind(susan))) [nnf transformation 4]
48. (creative(susan) | kind(susan) | ~creative(susan) | ~brave(susan)) & ((creative(susan) & brave(susan)) | (~creative(susan) & ~kind(susan))) [flattening 47]
49. ! [X0] : (patient(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) [nnf transformation 32]
53. (((~brave(susan) | happy(susan)) & (brave(susan) | ~happy(susan))) | ! [X0] : (strong(X0) | ~rich(X0))) & (? [X0] : (~strong(X0) & rich(X0)) | ((~happy(susan) | ~brave(susan)) & (brave(susan) | happy(susan)))) [nnf transformation 10]
54. (((~brave(susan) | happy(susan)) & (brave(susan) | ~happy(susan))) | ! [X0] : (strong(X0) | ~rich(X0))) & (? [X1] : (~strong(X1) & rich(X1)) | ((~happy(susan) | ~brave(susan)) & (brave(susan) | happy(susan)))) [rectify 53]
55. ? [X1] : (~strong(X1) & rich(X1)) => (~strong(sK2) & rich(sK2)) [choice axiom]
56. (((~brave(susan) | happy(susan)) & (brave(susan) | ~happy(susan))) | ! [X0] : (strong(X0) | ~rich(X0))) & ((~strong(sK2) & rich(sK2)) | ((~happy(susan) | ~brave(susan)) & (brave(susan) | happy(susan)))) [skolemisation 54,55]
57. ! [X0] : (((~happy(X0) & ~kind(X0)) | (wise(X0) | old(X0))) & ((~wise(X0) & ~old(X0)) | (happy(X0) | kind(X0)))) [nnf transformation 11]
58. ! [X0] : (((~happy(X0) & ~kind(X0)) | wise(X0) | old(X0)) & ((~wise(X0) & ~old(X0)) | happy(X0) | kind(X0))) [flattening 57]
62. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) & (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 14]
63. ! [X0] : (((rich(X0) & kind(X0)) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) & (((tall(X0) | ~humble(X0)) & (~tall(X0) | humble(X0))) | (~rich(X0) | ~kind(X0)))) [nnf transformation 15]
64. ! [X0] : (((rich(X0) & kind(X0)) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) & (((tall(X0) | ~humble(X0)) & (~tall(X0) | humble(X0))) | ~rich(X0) | ~kind(X0))) [flattening 63]
65. ! [X0] : (rich(X0) | ((~old(X0) | ~calm(X0)) & (calm(X0) | old(X0)))) [nnf transformation 38]
69. ? [X0] : (~strong(X0) & ~old(X0)) => (~strong(sK5) & ~old(sK5)) [choice axiom]
70. ~strong(sK5) & ~old(sK5) [skolemisation 18,69]
86. ~calm(X0) | rich(X0) | old(X0) [cnf transformation 43]
87. ~rich(X0) | calm(X0) | old(X0) [cnf transformation 43]
90. brave(susan) | ~kind(susan) [cnf transformation 48]
96. ~wise(X0) | patient(X0) | strong(X0) [cnf transformation 49]
111. ~brave(susan) | happy(susan) | strong(X0) | ~rich(X0) [cnf transformation 56]
112. ~old(X0) | happy(X0) | kind(X0) [cnf transformation 58]
114. ~kind(X0) | wise(X0) | old(X0) [cnf transformation 58]
118. ~happy(susan) | tall(X0) [cnf transformation 36]
119. ~happy(susan) | ~patient(X0) [cnf transformation 36]
123. ~generous(X0) | strong(X0) | ~generous(X0) | humble(X0) [cnf transformation 62]
129. humble(X0) | generous(X0) | strong(X0) | generous(X0) [cnf transformation 62]
132. ~tall(X0) | kind(X0) | ~humble(X0) [cnf transformation 64]
136. rich(X0) | calm(X0) | old(X0) [cnf transformation 65]
140. ~old(sK5) [cnf transformation 70]
141. ~strong(sK5) [cnf transformation 70]
151. ~calm(susan) [cnf transformation 25]
152. ~generous(X0) | strong(X0) | humble(X0) [duplicate literal removal 123]
155. generous(X0) | humble(X0) | strong(X0) [duplicate literal removal 129]
188. 8 <=> kind(susan) [avatar definition]
190. ~kind(susan) <- (~8) [avatar component clause 188]
197. 10 <=> brave(susan) [avatar definition]
201. ~8 | 10 [avatar split clause 90,197,188]
219. 14 <=> ! [X0] : (strong(X0) | ~rich(X0)) [avatar definition]
220. ~rich(X0) | strong(X0) <- (14) [avatar component clause 219]
222. 15 <=> happy(susan) [avatar definition]
223. ~happy(susan) <- (~15) [avatar component clause 222]
225. 14 | 15 | ~10 [avatar split clause 111,197,222,219]
240. 18 <=> ! [X0] : ~patient(X0) [avatar definition]
241. ~patient(X0) <- (18) [avatar component clause 240]
242. 18 | ~15 [avatar split clause 119,222,240]
244. 19 <=> ! [X0] : tall(X0) [avatar definition]
245. tall(X0) <- (19) [avatar component clause 244]
246. 19 | ~15 [avatar split clause 118,222,244]
268. humble(X0) | strong(X0) [subsumption resolution 152,155]
270. old(X0) | calm(X0) [subsumption resolution 136,87]
322. calm(sK5) [resolution 270,140]
325. rich(sK5) | old(sK5) [resolution 322,86]
327. rich(sK5) [subsumption resolution 325,140]
329. strong(sK5) <- (14) [resolution 327,220]
330. $false <- (14) [subsumption resolution 329,141]
331. ~14 [avatar contradiction clause 330]
333. kind(X0) | happy(X0) | calm(X0) [resolution 112,270]
488. happy(susan) | calm(susan) <- (~8) [resolution 333,190]
490. calm(susan) <- (~8, ~15) [subsumption resolution 488,223]
491. $false <- (~8, ~15) [subsumption resolution 490,151]
492. 8 | 15 [avatar contradiction clause 491]
528. ~humble(X2) | kind(X2) <- (19) [resolution 245,132]
562. strong(X0) | kind(X0) <- (19) [resolution 528,268]
646. kind(sK5) <- (19) [resolution 562,141]
670. wise(sK5) | old(sK5) <- (19) [resolution 646,114]
672. wise(sK5) <- (19) [subsumption resolution 670,140]
700. patient(sK5) | strong(sK5) <- (19) [resolution 672,96]
701. strong(sK5) <- (18, 19) [subsumption resolution 700,241]
702. $false <- (18, 19) [subsumption resolution 701,141]
703. ~18 | ~19 [avatar contradiction clause 702]
704. $false [avatar sat refutation 201,225,242,246,331,492,703]
% SZS output end Proof for 5376719794793796018918041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or strong is both happy and rich. Everyone who is funny is not old or not humble and vice versa. If mary is old or not creative then alice is strong or calm. If someone is humble or not calm then someone is humble and vice versa. If someone is either calm or wise then lucy is wise or humble and vice versa. If john is not kind then someone is both happy and not tall and vice versa. Everyone who is either not strong or not funny is patient and vice versa. If susan is quiet then john is not brave or patient. Everyone who is either not curious or not happy is either humble or quiet and vice versa. If alice is not curious or not old then someone is not quiet or strong. Everyone who is both not happy and not calm is curious and vice versa. If someone is not happy or not calm then alice is both not tall and not rich. If susan is not rich or not kind then someone is brave. Everyone who is not funny is either not happy or calm. If mary is both not old and not calm then someone is not patient and vice versa. Everyone who is either old or not funny is both not funny and old. Alice is both not funny and not brave. Someone is both quiet and wise. Someone is either calm or not patient. Someone is strong or not generous. Susan is either not creative or not funny. Someone is creative. Someone is patient. | John is calm. | entailment | (![X]:((~quiet(X)|strong(X))=>(happy(X)&rich(X))))&
(![X]:(funny(X)<=>(~old(X)|~humble(X))))&
(((old(mary)|~creative(mary)))=>((strong(alice)|calm(alice))))&
((?[X]:((humble(X)|~calm(X))))<=>(?[X]:(humble(X))))&
((?[X]:((calm(X)<~>wise(X))))<=>((wise(lucy)|humble(lucy))))&
((~kind(john))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>patient(X)))&
((quiet(susan))=>((~brave(john)|patient(john))))&
(![X]:((~curious(X)<~>~happy(X))<=>(humble(X)<~>quiet(X))))&
(((~curious(alice)|~old(alice)))=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~calm(X))<=>curious(X)))&
((?[X]:((~happy(X)|~calm(X))))=>((~tall(alice)&~rich(alice))))&
(((~rich(susan)|~kind(susan)))=>(?[X]:(brave(X))))&
(![X]:(~funny(X)=>(~happy(X)<~>calm(X))))&
(((~old(mary)&~calm(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((old(X)<~>~funny(X))=>(~funny(X)&old(X))))&
((~funny(alice)&~brave(alice)))&
(?[X]:((quiet(X)&wise(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~creative(susan)<~>~funny(susan)))&
(?[X]:(creative(X)))&
(?[X]:(patient(X))) | calm(john) | [
"p0",
"p1",
"p8",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8876689609983893853625892
% SZS output start Proof for 8876689609983893853625892
1. ! [X0] : ((strong(X0) | ~quiet(X0)) => (rich(X0) & happy(X0))) [input p0]
2. ! [X0] : (funny(X0) <=> (~humble(X0) | ~old(X0))) [input p1]
9. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> (humble(X0) <~> quiet(X0))) [input p8]
11. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> curious(X0)) [input p10]
12. ? [X0] : (~calm(X0) | ~happy(X0)) => (~rich(alice) & ~tall(alice)) [input p11]
14. ! [X0] : (~funny(X0) => (~happy(X0) <~> calm(X0))) [input p13]
17. ~brave(alice) & ~funny(alice) [input p16]
24. ~calm(john) [input hypothesis]
27. ! [X0] : ((rich(X0) & happy(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 1]
33. (~rich(alice) & ~tall(alice)) | ! [X0] : (calm(X0) & happy(X0)) [ennf transformation 12]
35. ! [X0] : ((~happy(X0) <~> calm(X0)) | funny(X0)) [ennf transformation 14]
37. ! [X0] : ((funny(X0) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | ~funny(X0))) [nnf transformation 2]
38. ! [X0] : ((funny(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | ~funny(X0))) [flattening 37]
54. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 9]
57. ! [X0] : (((~calm(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (calm(X0) | happy(X0)))) [nnf transformation 11]
58. ! [X0] : (((~calm(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | calm(X0) | happy(X0))) [flattening 57]
61. ! [X0] : (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | funny(X0)) [nnf transformation 35]
78. happy(X0) | quiet(X0) [cnf transformation 27]
80. rich(X0) | quiet(X0) [cnf transformation 27]
84. humble(X0) | funny(X0) [cnf transformation 38]
106. ~humble(X0) | ~quiet(X0) | ~happy(X0) | curious(X0) [cnf transformation 54]
107. ~quiet(X0) | ~humble(X0) | ~curious(X0) | happy(X0) [cnf transformation 54]
114. curious(X0) | calm(X0) | happy(X0) [cnf transformation 58]
115. ~curious(X0) | ~happy(X0) [cnf transformation 58]
120. ~rich(alice) | calm(X0) [cnf transformation 33]
123. ~happy(X0) | calm(X0) | funny(X0) [cnf transformation 61]
124. ~calm(X0) | happy(X0) | funny(X0) [cnf transformation 61]
132. ~funny(alice) [cnf transformation 17]
142. ~calm(john) [cnf transformation 24]
176. 8 <=> ! [X3] : calm(X3) [avatar definition]
177. calm(X3) <- (8) [avatar component clause 176]
245. ~curious(X0) | ~humble(X0) | happy(X0) [subsumption resolution 107,78]
266. 27 <=> rich(alice) [avatar definition]
268. ~rich(alice) <- (~27) [avatar component clause 266]
269. 8 | ~27 [avatar split clause 120,266,176]
328. $false <- (8) [resolution 177,142]
329. ~8 [avatar contradiction clause 328]
333. quiet(alice) <- (~27) [resolution 80,268]
427. ~humble(X1) | happy(X1) | calm(X1) | happy(X1) [resolution 245,114]
428. ~humble(X1) | happy(X1) | calm(X1) [duplicate literal removal 427]
440. ~quiet(X0) | ~happy(X0) | curious(X0) | funny(X0) [resolution 106,84]
461. ~happy(X0) | ~quiet(X0) | funny(X0) [subsumption resolution 440,115]
545. happy(X1) | calm(X1) | funny(X1) [resolution 428,84]
549. calm(X1) | funny(X1) [subsumption resolution 545,123]
614. funny(X2) | happy(X2) | funny(X2) [resolution 549,124]
620. funny(X2) | happy(X2) [duplicate literal removal 614]
628. 70 <=> happy(alice) [avatar definition]
629. ~happy(alice) <- (~70) [avatar component clause 628]
630. happy(alice) <- (70) [avatar component clause 628]
666. ~quiet(alice) | funny(alice) <- (70) [resolution 630,461]
668. funny(alice) <- (~27, 70) [subsumption resolution 666,333]
669. $false <- (~27, 70) [subsumption resolution 668,132]
670. 27 | ~70 [avatar contradiction clause 669]
685. happy(alice) [resolution 620,132]
689. $false <- (~70) [subsumption resolution 685,629]
690. 70 [avatar contradiction clause 689]
691. $false [avatar sat refutation 269,329,670,690]
% SZS output end Proof for 8876689609983893853625892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
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