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1.64k
| hypothesis
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stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
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|---|---|---|---|---|---|---|---|
Everyone who is either not kind or not calm is not kind or brave. Everyone who is quiet is not brave or not kind. Everyone who is not rich is tall. If mary is curious or kind then fred is both not curious and rich and vice versa. If someone is both calm and not strong then someone is either generous or funny and vice versa. Everyone who is both not patient and happy is not brave or brave and vice versa. Everyone who is not strong or rich is both generous and funny and vice versa. If susan is both creative and not wise then john is not tall and vice versa. If fred is funny then someone is both creative and not patient and vice versa. If mary is generous then fred is either quiet or humble and vice versa. Everyone who is not strong or not generous is either not rich or curious. If paul is either quiet or not brave then someone is both not generous and not brave and vice versa. If paul is not creative or not humble then mary is both happy and funny and vice versa. Everyone who is either not generous or kind is both not happy and not quiet. Everyone who is humble or not wise is both brave and rich and vice versa. If someone is both not curious and rich then someone is either not old or rich. Someone is either strong or not tall. John is either not brave or curious. Susan is not funny or not brave. Someone is both not curious and not patient. Alice is either tall or wise. Fred is not kind. Someone is either not humble or wise. Someone is curious or tall. | Alice is not funny. | contradiction | (![X]:((~kind(X)<~>~calm(X))=>(~kind(X)|brave(X))))&
(![X]:(quiet(X)=>(~brave(X)|~kind(X))))&
(![X]:(~rich(X)=>tall(X)))&
(((curious(mary)|kind(mary)))<=>((~curious(fred)&rich(fred))))&
((?[X]:((calm(X)&~strong(X))))<=>(?[X]:((generous(X)<~>funny(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~brave(X)|brave(X))))&
(![X]:((~strong(X)|rich(X))<=>(generous(X)&funny(X))))&
(((creative(susan)&~wise(susan)))<=>(~tall(john)))&
((funny(fred))<=>(?[X]:((creative(X)&~patient(X)))))&
((generous(mary))<=>((quiet(fred)<~>humble(fred))))&
(![X]:((~strong(X)|~generous(X))=>(~rich(X)<~>curious(X))))&
(((quiet(paul)<~>~brave(paul)))<=>(?[X]:((~generous(X)&~brave(X)))))&
(((~creative(paul)|~humble(paul)))<=>((happy(mary)&funny(mary))))&
(![X]:((~generous(X)<~>kind(X))=>(~happy(X)&~quiet(X))))&
(![X]:((humble(X)|~wise(X))<=>(brave(X)&rich(X))))&
((?[X]:((~curious(X)&rich(X))))=>(?[X]:((~old(X)<~>rich(X)))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~brave(john)<~>curious(john)))&
((~funny(susan)|~brave(susan)))&
(?[X]:((~curious(X)&~patient(X))))&
((tall(alice)<~>wise(alice)))&
(~kind(fred))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((curious(X)|tall(X)))) | ~funny(alice) | [
"p2",
"p6",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2544188710187498900350872
% SZS output start Proof for 2544188710187498900350872
3. ! [X0] : (~rich(X0) => tall(X0)) [input p2]
7. ! [X0] : ((rich(X0) | ~strong(X0)) <=> (funny(X0) & generous(X0))) [input p6]
15. ! [X0] : ((~wise(X0) | humble(X0)) <=> (rich(X0) & brave(X0))) [input p14]
21. tall(alice) <~> wise(alice) [input p20]
25. ~funny(alice) [input hypothesis]
32. ! [X0] : (tall(X0) | rich(X0)) [ennf transformation 3]
46. ! [X0] : (((rich(X0) | ~strong(X0)) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | (~rich(X0) & strong(X0)))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | ~strong(X0) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | (~rich(X0) & strong(X0)))) [flattening 46]
63. ! [X0] : (((~wise(X0) | humble(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (wise(X0) & ~humble(X0)))) [nnf transformation 15]
64. ! [X0] : ((~wise(X0) | humble(X0) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | (wise(X0) & ~humble(X0)))) [flattening 63]
75. (~wise(alice) | ~tall(alice)) & (wise(alice) | tall(alice)) [nnf transformation 21]
84. tall(X0) | rich(X0) [cnf transformation 32]
104. ~rich(X0) | funny(X0) [cnf transformation 47]
138. wise(X0) | rich(X0) [cnf transformation 64]
150. ~wise(alice) | ~tall(alice) [cnf transformation 75]
155. ~funny(alice) [cnf transformation 25]
343. 38 <=> tall(alice) [avatar definition]
345. ~tall(alice) <- (~38) [avatar component clause 343]
347. 39 <=> wise(alice) [avatar definition]
349. ~wise(alice) <- (~39) [avatar component clause 347]
350. ~38 | ~39 [avatar split clause 150,347,343]
382. rich(alice) <- (~39) [resolution 138,349]
384. funny(alice) <- (~39) [resolution 382,104]
386. $false <- (~39) [subsumption resolution 384,155]
387. 39 [avatar contradiction clause 386]
388. rich(alice) <- (~38) [resolution 345,84]
396. funny(alice) <- (~38) [resolution 388,104]
398. $false <- (~38) [subsumption resolution 396,155]
399. 38 [avatar contradiction clause 398]
400. $false [avatar sat refutation 350,387,399]
% SZS output end Proof for 2544188710187498900350872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both quiet and not old then fred is both not strong and rich and vice versa. Everyone who is not old is either not humble or kind. If someone is old or not patient then mary is creative or not wise and vice versa. If paul is either not brave or happy then lucy is not wise or not creative. Everyone who is strong is not calm. If someone is either curious or old then susan is generous or not wise. Everyone who is both kind and patient is strong or not generous and vice versa. If someone is funny then someone is either strong or brave. If paul is both not old and not happy then susan is either wise or not humble. Everyone who is calm or quiet is both not patient and not funny and vice versa. Everyone who is not happy is generous and vice versa. Everyone who is calm is not rich. Everyone who is either not quiet or strong is strong and vice versa. If someone is either not humble or not brave then susan is happy and vice versa. If someone is not generous then someone is creative and vice versa. If someone is both tall and not funny then alice is curious or not brave. Someone is humble or not rich. Lucy is not funny. Someone is both not old and quiet. Mary is either creative or quiet. Someone is either kind or calm. Paul is either not humble or calm. Fred is old or not brave. | Alice is creative. | contradiction | (((quiet(mary)&~old(mary)))<=>((~strong(fred)&rich(fred))))&
(![X]:(~old(X)=>(~humble(X)<~>kind(X))))&
((?[X]:((old(X)|~patient(X))))<=>((creative(mary)|~wise(mary))))&
(((~brave(paul)<~>happy(paul)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:(strong(X)=>~calm(X)))&
((?[X]:((curious(X)<~>old(X))))=>((generous(susan)|~wise(susan))))&
(![X]:((kind(X)&patient(X))<=>(strong(X)|~generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~old(paul)&~happy(paul)))=>((wise(susan)<~>~humble(susan))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:(calm(X)=>~rich(X)))&
(![X]:((~quiet(X)<~>strong(X))<=>strong(X)))&
((?[X]:((~humble(X)<~>~brave(X))))<=>(happy(susan)))&
((?[X]:(~generous(X)))<=>(?[X]:(creative(X))))&
((?[X]:((tall(X)&~funny(X))))=>((curious(alice)|~brave(alice))))&
(?[X]:((humble(X)|~rich(X))))&
(~funny(lucy))&
(?[X]:((~old(X)&quiet(X))))&
((creative(mary)<~>quiet(mary)))&
(?[X]:((kind(X)<~>calm(X))))&
((~humble(paul)<~>calm(paul)))&
((old(fred)|~brave(fred))) | creative(alice) | [
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7429519579690028744672961
% SZS output start Proof for 7429519579690028744672961
7. ! [X0] : ((patient(X0) & kind(X0)) <=> (~generous(X0) | strong(X0))) [input p6]
10. ! [X0] : ((quiet(X0) | calm(X0)) <=> (~funny(X0) & ~patient(X0))) [input p9]
13. ! [X0] : ((~quiet(X0) <~> strong(X0)) <=> strong(X0)) [input p12]
15. ? [X0] : ~generous(X0) <=> ? [X0] : creative(X0) [input p14]
24. creative(alice) [input hypothesis]
26. ? [X0] : ~generous(X0) <=> ? [X1] : creative(X1) [rectify 15]
48. ! [X0] : (((patient(X0) & kind(X0)) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | (~patient(X0) | ~kind(X0)))) [nnf transformation 7]
49. ! [X0] : (((patient(X0) & kind(X0)) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | ~patient(X0) | ~kind(X0))) [flattening 48]
55. ! [X0] : (((quiet(X0) | calm(X0)) | (funny(X0) | patient(X0))) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 10]
56. ! [X0] : ((quiet(X0) | calm(X0) | funny(X0) | patient(X0)) & ((~funny(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 55]
58. ! [X0] : ((((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~strong(X0)) & (strong(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0))))) [nnf transformation 13]
63. (? [X0] : ~generous(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : generous(X0)) [nnf transformation 26]
64. (? [X0] : ~generous(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : generous(X3)) [rectify 63]
65. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
66. ? [X2] : creative(X2) => creative(sK4) [choice axiom]
67. (~generous(sK3) | ! [X1] : ~creative(X1)) & (creative(sK4) | ! [X3] : generous(X3)) [skolemisation 64,66,65]
96. generous(X0) | patient(X0) [cnf transformation 49]
102. ~patient(X0) | ~quiet(X0) [cnf transformation 56]
109. strong(X0) | strong(X0) | quiet(X0) [cnf transformation 58]
112. ~strong(X0) | quiet(X0) | ~strong(X0) [cnf transformation 58]
118. ~generous(sK3) | ~creative(X1) [cnf transformation 67]
130. creative(alice) [cnf transformation 24]
131. strong(X0) | quiet(X0) [duplicate literal removal 109]
132. ~strong(X0) | quiet(X0) [duplicate literal removal 112]
236. quiet(X0) [subsumption resolution 131,132]
260. 29 <=> ! [X1] : ~creative(X1) [avatar definition]
261. ~creative(X1) <- (29) [avatar component clause 260]
263. 30 <=> generous(sK3) [avatar definition]
265. ~generous(sK3) <- (~30) [avatar component clause 263]
266. 29 | ~30 [avatar split clause 118,263,260]
319. $false <- (29) [resolution 261,130]
320. ~29 [avatar contradiction clause 319]
322. patient(sK3) <- (~30) [resolution 96,265]
323. ~quiet(sK3) <- (~30) [resolution 102,322]
324. $false <- (~30) [subsumption resolution 323,236]
325. 30 [avatar contradiction clause 324]
326. $false [avatar sat refutation 266,320,325]
% SZS output end Proof for 7429519579690028744672961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and kind is both not kind and funny. Everyone who is both not quiet and not kind is both rich and kind. Everyone who is not strong is both humble and not patient and vice versa. If susan is either not rich or not humble then someone is quiet and vice versa. If paul is not generous or patient then someone is either kind or old. Everyone who is wise is brave or not kind. Everyone who is either old or humble is tall. Everyone who is old or not curious is tall and vice versa. Everyone who is not funny or not brave is patient. If mary is not generous then susan is both generous and not curious and vice versa. Everyone who is both not funny and not generous is not curious. Everyone who is both not curious and old is not funny or kind and vice versa. Everyone who is humble or quiet is either tall or not strong. If someone is not brave then fred is not calm or not wise. Everyone who is patient or tall is rich. If susan is old then alice is tall or not humble and vice versa. Fred is either not curious or not happy. Alice is not happy. Someone is not curious. Fred is either generous or not tall. Someone is both kind and strong. Someone is not brave or generous. Someone is both not funny and not quiet. | Susan is not happy. | neutral | (![X]:((~wise(X)&kind(X))=>(~kind(X)&funny(X))))&
(![X]:((~quiet(X)&~kind(X))=>(rich(X)&kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~patient(X))))&
(((~rich(susan)<~>~humble(susan)))<=>(?[X]:(quiet(X))))&
(((~generous(paul)|patient(paul)))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:(wise(X)=>(brave(X)|~kind(X))))&
(![X]:((old(X)<~>humble(X))=>tall(X)))&
(![X]:((old(X)|~curious(X))<=>tall(X)))&
(![X]:((~funny(X)|~brave(X))=>patient(X)))&
((~generous(mary))<=>((generous(susan)&~curious(susan))))&
(![X]:((~funny(X)&~generous(X))=>~curious(X)))&
(![X]:((~curious(X)&old(X))<=>(~funny(X)|kind(X))))&
(![X]:((humble(X)|quiet(X))=>(tall(X)<~>~strong(X))))&
((?[X]:(~brave(X)))=>((~calm(fred)|~wise(fred))))&
(![X]:((patient(X)|tall(X))=>rich(X)))&
((old(susan))<=>((tall(alice)|~humble(alice))))&
((~curious(fred)<~>~happy(fred)))&
(~happy(alice))&
(?[X]:(~curious(X)))&
((generous(fred)<~>~tall(fred)))&
(?[X]:((kind(X)&strong(X))))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:((~funny(X)&~quiet(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is happy is either funny or not generous and vice versa. If someone is brave then someone is both generous and not funny. Everyone who is strong or old is curious or humble. If someone is both wise and not quiet then someone is not funny or not generous and vice versa. Everyone who is not kind or not humble is curious and vice versa. Everyone who is not wise or not calm is both wise and not rich. Everyone who is either strong or generous is wise or not curious and vice versa. Everyone who is both wise and not strong is either not patient or quiet and vice versa. Everyone who is tall is not patient or not brave. If someone is not strong then lucy is funny. Everyone who is tall or not rich is not kind. If fred is both creative and not curious then someone is not happy or strong. Everyone who is both not brave and kind is either patient or not brave. Everyone who is both not rich and patient is both wise and not brave. Everyone who is both funny and calm is both curious and not brave. If fred is quiet then someone is tall. Someone is both not calm and creative. Someone is both generous and curious. Paul is either not humble or tall. Someone is strong or not rich. Someone is both not strong and not kind. Susan is either calm or not generous. Someone is both funny and calm. | Paul is rich. | neutral | (![X]:(happy(X)<=>(funny(X)<~>~generous(X))))&
((?[X]:(brave(X)))=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((strong(X)|old(X))=>(curious(X)|humble(X))))&
((?[X]:((wise(X)&~quiet(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:((~kind(X)|~humble(X))<=>curious(X)))&
(![X]:((~wise(X)|~calm(X))=>(wise(X)&~rich(X))))&
(![X]:((strong(X)<~>generous(X))<=>(wise(X)|~curious(X))))&
(![X]:((wise(X)&~strong(X))<=>(~patient(X)<~>quiet(X))))&
(![X]:(tall(X)=>(~patient(X)|~brave(X))))&
((?[X]:(~strong(X)))=>(funny(lucy)))&
(![X]:((tall(X)|~rich(X))=>~kind(X)))&
(((creative(fred)&~curious(fred)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~brave(X)&kind(X))=>(patient(X)<~>~brave(X))))&
(![X]:((~rich(X)&patient(X))=>(wise(X)&~brave(X))))&
(![X]:((funny(X)&calm(X))=>(curious(X)&~brave(X))))&
((quiet(fred))=>(?[X]:(tall(X))))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((generous(X)&curious(X))))&
((~humble(paul)<~>tall(paul)))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((~strong(X)&~kind(X))))&
((calm(susan)<~>~generous(susan)))&
(?[X]:((funny(X)&calm(X)))) | rich(paul) | [] | null | 0 |
Everyone who is either humble or not curious is both generous and not strong and vice versa. If someone is not tall or patient then fred is either funny or happy. Everyone who is kind or not humble is happy or not humble. Everyone who is not wise is creative or not brave. Everyone who is strong is calm or old. Everyone who is not funny is both not brave and not patient. Everyone who is not strong or rich is both not calm and not happy. If someone is not old then someone is not creative and vice versa. If fred is quiet then someone is creative. If someone is tall or not wise then fred is both not quiet and not brave. Everyone who is both not patient and not happy is either funny or patient. If someone is not rich then someone is both not funny and not patient and vice versa. Everyone who is kind or not humble is not wise or not happy and vice versa. If someone is strong then someone is not humble or not generous and vice versa. If someone is either old or funny then someone is either old or brave and vice versa. Everyone who is rich or tall is both old and patient and vice versa. Someone is not kind or generous. Alice is humble. Fred is not rich. Someone is both creative and not old. Someone is not kind or not curious. Lucy is not happy. Someone is either tall or old. | Fred is not old. | neutral | (![X]:((humble(X)<~>~curious(X))<=>(generous(X)&~strong(X))))&
((?[X]:((~tall(X)|patient(X))))=>((funny(fred)<~>happy(fred))))&
(![X]:((kind(X)|~humble(X))=>(happy(X)|~humble(X))))&
(![X]:(~wise(X)=>(creative(X)|~brave(X))))&
(![X]:(strong(X)=>(calm(X)|old(X))))&
(![X]:(~funny(X)=>(~brave(X)&~patient(X))))&
(![X]:((~strong(X)|rich(X))=>(~calm(X)&~happy(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~creative(X))))&
((quiet(fred))=>(?[X]:(creative(X))))&
((?[X]:((tall(X)|~wise(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)<~>patient(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~funny(X)&~patient(X)))))&
(![X]:((kind(X)|~humble(X))<=>(~wise(X)|~happy(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~humble(X)|~generous(X)))))&
((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((rich(X)|tall(X))<=>(old(X)&patient(X))))&
(?[X]:((~kind(X)|generous(X))))&
(humble(alice))&
(~rich(fred))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(~happy(lucy))&
(?[X]:((tall(X)<~>old(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is not calm is either strong or humble.
If mary is either rich or creative then susan is both patient and creative.
Everyone who is generous is both not brave and patient and vice versa.
If someone is either creative or not wise then someone is both kind and tall and vice versa.
If someone is both creative and not old then someone is both not happy and not creative.
Everyone who is creative or humble is either calm or brave.
Everyone who is quiet or not patient is either not rich or quiet.
Everyone who is either not wise or not generous is not quiet or not humble and vice versa.
If mary is not patient or not old then someone is both not humble and not happy.
If someone is either not kind or old then fred is not brave or not kind.
Everyone who is either not happy or creative is not old.
If mary is not strong or happy then john is not old and vice versa.
If john is curious then someone is both wise and not rich.
Everyone who is not patient or humble is funny or not wise.
If someone is both not patient and not quiet then alice is kind or generous.
Everyone who is either not tall or happy is funny.
Fred is both not kind and not brave.
Fred is both not rich and not generous.
Someone is either not tall or old.
Mary is either not wise or not old.
Someone is not wise or funny.
Someone is humble or old.
Someone is not happy or curious.
Mary is not old. | Fred is funny. | entailment | (![X]:(~calm(X)=>(strong(X)<~>humble(X))))&
(((rich(mary)<~>creative(mary)))=>((patient(susan)&creative(susan))))&
(![X]:(generous(X)<=>(~brave(X)&patient(X))))&
((?[X]:((creative(X)<~>~wise(X))))<=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:((creative(X)&~old(X))))=>(?[X]:((~happy(X)&~creative(X)))))&
(![X]:((creative(X)|humble(X))=>(calm(X)<~>brave(X))))&
(![X]:((quiet(X)|~patient(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~quiet(X)|~humble(X))))&
(((~patient(mary)|~old(mary)))=>(?[X]:((~humble(X)&~happy(X)))))&
((?[X]:((~kind(X)<~>old(X))))=>((~brave(fred)|~kind(fred))))&
(![X]:((~happy(X)<~>creative(X))=>~old(X)))&
(((~strong(mary)|happy(mary)))<=>(~old(john)))&
((curious(john))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~patient(X)|humble(X))=>(funny(X)|~wise(X))))&
((?[X]:((~patient(X)&~quiet(X))))=>((kind(alice)|generous(alice))))&
(![X]:((~tall(X)<~>happy(X))=>funny(X)))&
((~kind(fred)&~brave(fred)))&
((~rich(fred)&~generous(fred)))&
(?[X]:((~tall(X)<~>old(X))))&
((~wise(mary)<~>~old(mary)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((humble(X)|old(X))))&
(?[X]:((~happy(X)|curious(X))))&
(~old(mary)) | funny(fred) | [
"p2",
"p6",
"p7",
"p13",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 97858880525750735530700
% SZS output start Proof for 97858880525750735530700
3. ! [X0] : (generous(X0) <=> (patient(X0) & ~brave(X0))) [input p2]
7. ! [X0] : ((~patient(X0) | quiet(X0)) => (~rich(X0) <~> quiet(X0))) [input p6]
8. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((humble(X0) | ~patient(X0)) => (~wise(X0) | funny(X0))) [input p13]
17. ~brave(fred) & ~kind(fred) [input p16]
18. ~generous(fred) & ~rich(fred) [input p17]
25. ~funny(fred) [input hypothesis]
32. ! [X0] : ((~rich(X0) <~> quiet(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 7]
38. ! [X0] : ((~wise(X0) | funny(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 14]
39. ! [X0] : (~wise(X0) | funny(X0) | (~humble(X0) & patient(X0))) [flattening 38]
45. ! [X0] : ((generous(X0) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | ~generous(X0))) [nnf transformation 3]
46. ! [X0] : ((generous(X0) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | ~generous(X0))) [flattening 45]
56. ! [X0] : (((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (patient(X0) & ~quiet(X0))) [nnf transformation 32]
57. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 8]
58. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [flattening 57]
85. ~generous(X0) | patient(X0) [cnf transformation 46]
86. ~patient(X0) | generous(X0) | brave(X0) [cnf transformation 46]
101. ~quiet(X0) | rich(X0) | ~quiet(X0) [cnf transformation 56]
107. quiet(X0) | wise(X0) | generous(X0) [cnf transformation 58]
122. ~wise(X0) | funny(X0) | patient(X0) [cnf transformation 39]
128. ~brave(fred) [cnf transformation 17]
129. ~rich(fred) [cnf transformation 18]
130. ~generous(fred) [cnf transformation 18]
139. ~funny(fred) [cnf transformation 25]
140. ~quiet(X0) | rich(X0) [duplicate literal removal 101]
229. 20 <=> brave(fred) [avatar definition]
231. ~brave(fred) <- (~20) [avatar component clause 229]
282. ~20 [avatar split clause 128,229]
407. wise(X1) | generous(X1) | rich(X1) [resolution 107,140]
496. generous(X1) | rich(X1) | funny(X1) | patient(X1) [resolution 407,122]
514. 66 <=> patient(fred) [avatar definition]
516. patient(fred) <- (66) [avatar component clause 514]
551. funny(X1) | rich(X1) | patient(X1) [subsumption resolution 496,85]
561. rich(fred) | patient(fred) [resolution 551,139]
562. patient(fred) [subsumption resolution 561,129]
563. 66 [avatar split clause 562,514]
564. generous(fred) | brave(fred) <- (66) [resolution 516,86]
565. brave(fred) <- (66) [subsumption resolution 564,130]
566. $false <- (~20, 66) [subsumption resolution 565,231]
567. 20 | ~66 [avatar contradiction clause 566]
568. $false [avatar sat refutation 282,563,567]
% SZS output end Proof for 97858880525750735530700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not patient then someone is calm or not old.
Everyone who is either wise or not patient is either not curious or patient and vice versa.
Everyone who is either not kind or not creative is old or calm.
If mary is both not brave and quiet then someone is either old or not happy.
Everyone who is not brave is not kind or strong.
If someone is either generous or not tall then someone is curious or not patient.
Everyone who is funny or not calm is both not brave and curious and vice versa.
If susan is rich then someone is old or kind.
If fred is both not old and rich then someone is both not kind and wise and vice versa.
If someone is not curious then someone is creative or rich and vice versa.
Everyone who is not rich or not curious is tall.
If susan is either wise or generous then lucy is either not funny or tall and vice versa.
Everyone who is not patient or not humble is either creative or tall and vice versa.
Everyone who is both humble and strong is both humble and not patient and vice versa.
Everyone who is either humble or quiet is both not funny and not kind.
Everyone who is tall or rich is both not patient and not happy.
Lucy is both brave and not curious.
John is either kind or not kind.
Someone is not funny.
Someone is both not kind and not curious.
Someone is either funny or happy.
Paul is either not happy or not generous.
Someone is both not creative and not patient. | John is not patient. | entailment | ((?[X]:((creative(X)<~>~patient(X))))=>(?[X]:((calm(X)|~old(X)))))&
(![X]:((wise(X)<~>~patient(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(old(X)|calm(X))))&
(((~brave(mary)&quiet(mary)))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:(~brave(X)=>(~kind(X)|strong(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~brave(X)&curious(X))))&
((rich(susan))=>(?[X]:((old(X)|kind(X)))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)&strong(X))<=>(humble(X)&~patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)|rich(X))=>(~patient(X)&~happy(X))))&
((brave(lucy)&~curious(lucy)))&
((kind(john)<~>~kind(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:((funny(X)<~>happy(X))))&
((~happy(paul)<~>~generous(paul)))&
(?[X]:((~creative(X)&~patient(X)))) | ~patient(john) | [
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 511395963068354663526007
% SZS output start Proof for 511395963068354663526007
11. ! [X0] : ((~curious(X0) | ~rich(X0)) => tall(X0)) [input p10]
16. ! [X0] : ((rich(X0) | tall(X0)) => (~happy(X0) & ~patient(X0))) [input p15]
24. patient(john) [input hypothesis]
37. ! [X0] : (tall(X0) | (curious(X0) & rich(X0))) [ennf transformation 11]
39. ! [X0] : ((~happy(X0) & ~patient(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 16]
114. rich(X0) | tall(X0) [cnf transformation 37]
138. ~tall(X0) | ~patient(X0) [cnf transformation 39]
139. ~rich(X0) | ~patient(X0) [cnf transformation 39]
155. patient(john) [cnf transformation 24]
336. ~patient(X0) | tall(X0) [resolution 139,114]
352. ~patient(X0) [subsumption resolution 336,138]
365. $false [resolution 352,155]
% SZS output end Proof for 511395963068354663526007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or quiet is not creative.
Everyone who is both kind and generous is rich.
If fred is either curious or not funny then someone is either old or patient and vice versa.
Everyone who is not tall or not happy is not old or tall.
If fred is not generous then someone is not calm and vice versa.
If fred is both not creative and not humble then someone is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
Alice is either brave or happy.
Someone is calm or generous.
John is old or not rich.
Someone is funny or creative.
Someone is generous or not curious.
Alice is not patient or happy.
Lucy is strong or not quiet.
Someone is happy. | Alice is not quiet. | entailment | (![X]:((happy(X)|quiet(X))=>~creative(X)))&
(![X]:((kind(X)&generous(X))=>rich(X)))&
(((curious(fred)<~>~funny(fred)))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:((~tall(X)|~happy(X))=>(~old(X)|tall(X))))&
((~generous(fred))<=>(?[X]:(~calm(X))))&
(((~creative(fred)&~humble(fred)))=>(?[X]:((~old(X)&~tall(X)))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((brave(alice)<~>happy(alice)))&
(?[X]:((calm(X)|generous(X))))&
((old(john)|~rich(john)))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((generous(X)|~curious(X))))&
((~patient(alice)|happy(alice)))&
((strong(lucy)|~quiet(lucy)))&
(?[X]:(happy(X))) | ~quiet(alice) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3287775028091741019133137
% SZS output start Proof for 3287775028091741019133137
11. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p10]
13. ! [X0] : (funny(X0) <=> (~quiet(X0) & happy(X0))) [input p12]
25. quiet(alice) [input hypothesis]
50. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 11]
51. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 50]
54. ! [X0] : ((funny(X0) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 13]
55. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [flattening 54]
104. funny(X0) | funny(X0) [cnf transformation 51]
110. ~quiet(X0) | ~funny(X0) [cnf transformation 55]
133. quiet(alice) [cnf transformation 25]
135. funny(X0) [duplicate literal removal 104]
242. ~quiet(X0) [subsumption resolution 110,135]
269. $false [subsumption resolution 133,242]
% SZS output end Proof for 3287775028091741019133137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then mary is not curious or funny and vice versa. Everyone who is not happy is either kind or generous. Everyone who is not rich or not patient is either not brave or generous. Everyone who is both not curious and rich is not rich or not funny. Everyone who is both not rich and quiet is both happy and old and vice versa. Everyone who is not creative or creative is not old or quiet and vice versa. Everyone who is quiet is curious or not brave and vice versa. Everyone who is creative or not kind is not wise or not curious. If lucy is wise or not brave then someone is not happy or not funny and vice versa. Everyone who is not creative or strong is both not tall and patient. If someone is old or not funny then mary is old. If alice is both generous and old then susan is humble and vice versa. Everyone who is wise or not old is either rich or not humble. Everyone who is both not strong and brave is strong or old. If someone is either patient or not rich then john is both not quiet and not patient. If alice is either rich or creative then mary is either not generous or humble. Fred is both not old and funny. Paul is not kind or happy. Fred is quiet or generous. John is not creative. Alice is not strong or patient. Someone is both not generous and kind. Alice is patient or rich. | Susan is not generous. | neutral | ((?[X]:(curious(X)))<=>((~curious(mary)|funny(mary))))&
(![X]:(~happy(X)=>(kind(X)<~>generous(X))))&
(![X]:((~rich(X)|~patient(X))=>(~brave(X)<~>generous(X))))&
(![X]:((~curious(X)&rich(X))=>(~rich(X)|~funny(X))))&
(![X]:((~rich(X)&quiet(X))<=>(happy(X)&old(X))))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~creative(X)|strong(X))=>(~tall(X)&patient(X))))&
((?[X]:((old(X)|~funny(X))))=>(old(mary)))&
(((generous(alice)&old(alice)))<=>(humble(susan)))&
(![X]:((wise(X)|~old(X))=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)&brave(X))=>(strong(X)|old(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>((~quiet(john)&~patient(john))))&
(((rich(alice)<~>creative(alice)))=>((~generous(mary)<~>humble(mary))))&
((~old(fred)&funny(fred)))&
((~kind(paul)|happy(paul)))&
((quiet(fred)|generous(fred)))&
(~creative(john))&
((~strong(alice)|patient(alice)))&
(?[X]:((~generous(X)&kind(X))))&
((patient(alice)|rich(alice))) | ~generous(susan) | [] | null | 0 |
If john is either not tall or not strong then lucy is both not quiet and not kind.
Everyone who is both not happy and not brave is not calm or not old.
If john is both not quiet and calm then susan is not happy or happy and vice versa.
Everyone who is not brave or not funny is either not quiet or happy.
Everyone who is humble or quiet is both not generous and funny and vice versa.
Everyone who is either quiet or creative is both strong and not wise and vice versa.
Everyone who is either old or not old is either not tall or humble and vice versa.
If lucy is either not calm or not kind then someone is either not kind or strong and vice versa.
Everyone who is not happy is either not creative or curious and vice versa.
Everyone who is both generous and not happy is both patient and not generous.
If someone is tall or not old then paul is both not happy and not patient.
Everyone who is both funny and curious is either not happy or creative and vice versa.
Everyone who is both kind and not happy is either rich or not creative and vice versa.
If someone is not happy or not creative then alice is not old or creative.
Everyone who is either generous or not brave is not humble and vice versa.
If someone is either not creative or kind then fred is both not happy and strong.
John is both not kind and creative.
Someone is either kind or not funny.
Someone is either not generous or not old.
Mary is not funny. | Mary is brave. | contradiction | (((~tall(john)<~>~strong(john)))=>((~quiet(lucy)&~kind(lucy))))&
(![X]:((~happy(X)&~brave(X))=>(~calm(X)|~old(X))))&
(((~quiet(john)&calm(john)))<=>((~happy(susan)|happy(susan))))&
(![X]:((~brave(X)|~funny(X))=>(~quiet(X)<~>happy(X))))&
(![X]:((humble(X)|quiet(X))<=>(~generous(X)&funny(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(strong(X)&~wise(X))))&
(![X]:((old(X)<~>~old(X))<=>(~tall(X)<~>humble(X))))&
(((~calm(lucy)<~>~kind(lucy)))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:(~happy(X)<=>(~creative(X)<~>curious(X))))&
(![X]:((generous(X)&~happy(X))=>(patient(X)&~generous(X))))&
((?[X]:((tall(X)|~old(X))))=>((~happy(paul)&~patient(paul))))&
(![X]:((funny(X)&curious(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((kind(X)&~happy(X))<=>(rich(X)<~>~creative(X))))&
((?[X]:((~happy(X)|~creative(X))))=>((~old(alice)|creative(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>~humble(X)))&
((?[X]:((~creative(X)<~>kind(X))))=>((~happy(fred)&strong(fred))))&
((~kind(john)&creative(john)))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~funny(mary)) | brave(mary) | [
"p3",
"p4",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2845497833731712101360849
% SZS output start Proof for 2845497833731712101360849
4. ! [X0] : ((~funny(X0) | ~brave(X0)) => (~quiet(X0) <~> happy(X0))) [input p3]
5. ! [X0] : ((quiet(X0) | humble(X0)) <=> (funny(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((~happy(X0) & generous(X0)) => (~generous(X0) & patient(X0))) [input p9]
15. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> ~humble(X0)) [input p14]
20. ~funny(mary) [input p19]
21. brave(mary) [input hypothesis]
25. ! [X0] : ((~quiet(X0) <~> happy(X0)) | (funny(X0) & brave(X0))) [ennf transformation 4]
26. ! [X0] : ((~generous(X0) & patient(X0)) | (happy(X0) | ~generous(X0))) [ennf transformation 10]
27. ! [X0] : ((~generous(X0) & patient(X0)) | happy(X0) | ~generous(X0)) [flattening 26]
35. ! [X0] : (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (funny(X0) & brave(X0))) [nnf transformation 25]
36. ! [X0] : (((quiet(X0) | humble(X0)) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | (~quiet(X0) & ~humble(X0)))) [nnf transformation 5]
37. ! [X0] : ((quiet(X0) | humble(X0) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | (~quiet(X0) & ~humble(X0)))) [flattening 36]
50. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | humble(X0)) & (~humble(X0) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 15]
71. ~happy(X0) | quiet(X0) | funny(X0) [cnf transformation 35]
73. ~generous(X0) | ~quiet(X0) [cnf transformation 37]
74. ~humble(X0) | funny(X0) [cnf transformation 37]
104. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 27]
125. ~brave(X0) | generous(X0) | humble(X0) [cnf transformation 50]
137. ~funny(mary) [cnf transformation 20]
138. brave(mary) [cnf transformation 21]
139. ~generous(X0) | happy(X0) [duplicate literal removal 104]
334. generous(mary) | humble(mary) [resolution 125,138]
337. 29 <=> humble(mary) [avatar definition]
339. humble(mary) <- (29) [avatar component clause 337]
341. 30 <=> generous(mary) [avatar definition]
343. generous(mary) <- (30) [avatar component clause 341]
344. 29 | 30 [avatar split clause 334,341,337]
347. funny(mary) <- (29) [resolution 339,74]
348. $false <- (29) [subsumption resolution 347,137]
349. ~29 [avatar contradiction clause 348]
353. happy(mary) <- (30) [resolution 343,139]
354. ~quiet(mary) <- (30) [resolution 343,73]
361. quiet(mary) | funny(mary) <- (30) [resolution 353,71]
373. funny(mary) <- (30) [subsumption resolution 361,354]
374. $false <- (30) [subsumption resolution 373,137]
375. ~30 [avatar contradiction clause 374]
376. $false [avatar sat refutation 344,349,375]
% SZS output end Proof for 2845497833731712101360849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both strong and wise and vice versa. Everyone who is quiet is both strong and not humble and vice versa. Everyone who is not tall or rich is tall or not brave and vice versa. Everyone who is patient is both not curious and not rich and vice versa. Everyone who is either not curious or curious is either old or not rich and vice versa. If someone is calm or not brave then someone is not rich or patient. Everyone who is old is not patient and vice versa. Everyone who is not humble or not curious is either not brave or wise. Everyone who is not patient is either not kind or funny and vice versa. If lucy is not quiet or curious then susan is creative. If john is both tall and old then someone is not curious and vice versa. Everyone who is either not kind or not calm is both not patient and rich. Everyone who is not wise or calm is both old and patient. If mary is either not curious or kind then lucy is old. If fred is either not funny or funny then susan is not curious or not rich and vice versa. Everyone who is both wise and calm is both not creative and tall. Someone is not happy. Someone is either not calm or not happy. Someone is not curious or rich. | Lucy is happy. | neutral | (![X]:(~patient(X)<=>(strong(X)&wise(X))))&
(![X]:(quiet(X)<=>(strong(X)&~humble(X))))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|~brave(X))))&
(![X]:(patient(X)<=>(~curious(X)&~rich(X))))&
(![X]:((~curious(X)<~>curious(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((~humble(X)|~curious(X))=>(~brave(X)<~>wise(X))))&
(![X]:(~patient(X)<=>(~kind(X)<~>funny(X))))&
(((~quiet(lucy)|curious(lucy)))=>(creative(susan)))&
(((tall(john)&old(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)<~>~calm(X))=>(~patient(X)&rich(X))))&
(![X]:((~wise(X)|calm(X))=>(old(X)&patient(X))))&
(((~curious(mary)<~>kind(mary)))=>(old(lucy)))&
(((~funny(fred)<~>funny(fred)))<=>((~curious(susan)|~rich(susan))))&
(![X]:((wise(X)&calm(X))=>(~creative(X)&tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:((~curious(X)|rich(X)))) | happy(lucy) | [] | null | 0 |
Everyone who is tall is not patient.
If someone is not strong or not generous then someone is either not funny or not old and vice versa.
Everyone who is not wise or happy is not rich and vice versa.
Everyone who is both humble and brave is not tall.
Everyone who is not curious is both generous and not kind and vice versa.
Everyone who is not brave is both quiet and humble.
Everyone who is both not quiet and quiet is not humble or kind and vice versa.
If someone is not quiet or funny then someone is not creative or old and vice versa.
If susan is both humble and calm then someone is not curious or not strong.
Everyone who is either creative or quiet is both not patient and not generous.
Everyone who is either rich or not humble is old and vice versa.
Everyone who is either not happy or patient is both funny and not creative and vice versa.
Everyone who is either old or creative is either not calm or not tall.
Everyone who is rich is tall or old and vice versa.
If someone is tall or not rich then someone is either quiet or creative and vice versa.
Everyone who is kind or not generous is either strong or not quiet and vice versa.
Lucy is not patient.
John is not generous or generous.
Mary is tall or not strong.
Lucy is not calm or not humble.
Someone is generous or patient.
Alice is both generous and not rich.
Susan is not curious.
Lucy is humble or quiet. | Mary is humble. | entailment | (![X]:(tall(X)=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~wise(X)|happy(X))<=>~rich(X)))&
(![X]:((humble(X)&brave(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
(~patient(lucy))&
((~generous(john)|generous(john)))&
((tall(mary)|~strong(mary)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy))) | humble(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4466521179502848952724297
% SZS output start Proof for 4466521179502848952724297
7. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (kind(X0) | ~humble(X0))) [input p6]
25. ~humble(mary) [input hypothesis]
46. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 7]
47. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~quiet(X0) | quiet(X0))) [flattening 46]
87. ~quiet(X0) | humble(X0) [cnf transformation 47]
89. quiet(X0) | humble(X0) [cnf transformation 47]
138. ~humble(mary) [cnf transformation 25]
174. humble(X0) [subsumption resolution 87,89]
278. $false [subsumption resolution 138,174]
% SZS output end Proof for 4466521179502848952724297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either calm or not strong.
Everyone who is not calm is either not strong or not brave.
Everyone who is both happy and funny is generous or creative and vice versa.
Everyone who is both happy and not strong is old or not calm and vice versa.
Everyone who is generous is not rich or not happy and vice versa.
Everyone who is both curious and old is both humble and wise.
Everyone who is not quiet or strong is both generous and not generous.
If someone is funny or not kind then lucy is not brave or quiet.
If someone is either funny or brave then alice is kind or rich.
If someone is wise or not curious then alice is kind or generous.
If someone is rich or not calm then susan is either not creative or patient.
Everyone who is not curious is tall or kind.
If paul is not brave then someone is patient or wise and vice versa.
If john is both old and not happy then someone is old and vice versa.
Everyone who is not rich or calm is generous or not humble and vice versa.
Everyone who is both not funny and happy is both not generous and humble and vice versa.
Someone is not calm.
Fred is kind.
Lucy is rich.
Someone is not old or not curious.
Someone is not patient. | Paul is not old. | entailment | (![X]:(patient(X)=>(calm(X)<~>~strong(X))))&
(![X]:(~calm(X)=>(~strong(X)<~>~brave(X))))&
(![X]:((happy(X)&funny(X))<=>(generous(X)|creative(X))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)|~calm(X))))&
(![X]:(generous(X)<=>(~rich(X)|~happy(X))))&
(![X]:((curious(X)&old(X))=>(humble(X)&wise(X))))&
(![X]:((~quiet(X)|strong(X))=>(generous(X)&~generous(X))))&
((?[X]:((funny(X)|~kind(X))))=>((~brave(lucy)|quiet(lucy))))&
((?[X]:((funny(X)<~>brave(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((wise(X)|~curious(X))))=>((kind(alice)|generous(alice))))&
((?[X]:((rich(X)|~calm(X))))=>((~creative(susan)<~>patient(susan))))&
(![X]:(~curious(X)=>(tall(X)|kind(X))))&
((~brave(paul))<=>(?[X]:((patient(X)|wise(X)))))&
(((old(john)&~happy(john)))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)|calm(X))<=>(generous(X)|~humble(X))))&
(![X]:((~funny(X)&happy(X))<=>(~generous(X)&humble(X))))&
(?[X]:(~calm(X)))&
(kind(fred))&
(rich(lucy))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:(~patient(X))) | ~old(paul) | [
"p2",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3789344736177267961633387
% SZS output start Proof for 3789344736177267961633387
3. ! [X0] : ((funny(X0) & happy(X0)) <=> (creative(X0) | generous(X0))) [input p2]
5. ! [X0] : (generous(X0) <=> (~happy(X0) | ~rich(X0))) [input p4]
14. (~happy(john) & old(john)) <=> ? [X0] : old(X0) [input p13]
22. old(paul) [input hypothesis]
38. ! [X0] : (((funny(X0) & happy(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((funny(X0) & happy(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ~funny(X0) | ~happy(X0))) [flattening 38]
42. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | ~generous(X0))) [nnf transformation 5]
43. ! [X0] : ((generous(X0) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ~generous(X0))) [flattening 42]
49. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (happy(john) | ~old(john))) [nnf transformation 14]
50. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | happy(john) | ~old(john)) [flattening 49]
51. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | happy(john) | ~old(john)) [rectify 50]
52. ? [X1] : old(X1) => old(sK1) [choice axiom]
53. ((~happy(john) & old(john)) | ! [X0] : ~old(X0)) & (old(sK1) | happy(john) | ~old(john)) [skolemisation 51,52]
67. happy(X0) | ~generous(X0) [cnf transformation 39]
78. generous(X0) | happy(X0) [cnf transformation 43]
90. ~happy(john) | ~old(X0) [cnf transformation 53]
102. old(paul) [cnf transformation 22]
103. happy(X0) [subsumption resolution 78,67]
145. ~old(X0) [subsumption resolution 90,103]
147. $false [subsumption resolution 102,145]
% SZS output end Proof for 3789344736177267961633387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or tall is either rich or wise. If john is either curious or strong then lucy is tall. If paul is both quiet and not humble then fred is generous. If someone is wise or old then someone is not rich or not kind. Everyone who is either not quiet or not humble is creative. If fred is either not happy or not generous then someone is either not curious or not brave. Everyone who is creative or not rich is both strong and brave. Everyone who is both old and wise is either curious or patient and vice versa. Everyone who is not patient is not kind or not old and vice versa. Everyone who is curious or quiet is either not old or not strong. Everyone who is old or funny is either quiet or not calm. If someone is both not old and kind then someone is both not tall and not patient. Everyone who is either rich or not patient is not quiet or not tall. Everyone who is either wise or strong is old. If someone is either strong or not quiet then someone is both strong and rich. Everyone who is either not creative or kind is not patient or curious. Lucy is either generous or not creative. John is both not calm and not strong. Mary is tall. Someone is not old. Fred is brave or patient. Someone is quiet. | Paul is not humble. | neutral | (![X]:((brave(X)|tall(X))=>(rich(X)<~>wise(X))))&
(((curious(john)<~>strong(john)))=>(tall(lucy)))&
(((quiet(paul)&~humble(paul)))=>(generous(fred)))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((~quiet(X)<~>~humble(X))=>creative(X)))&
(((~happy(fred)<~>~generous(fred)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)|~rich(X))=>(strong(X)&brave(X))))&
(![X]:((old(X)&wise(X))<=>(curious(X)<~>patient(X))))&
(![X]:(~patient(X)<=>(~kind(X)|~old(X))))&
(![X]:((curious(X)|quiet(X))=>(~old(X)<~>~strong(X))))&
(![X]:((old(X)|funny(X))=>(quiet(X)<~>~calm(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:((rich(X)<~>~patient(X))=>(~quiet(X)|~tall(X))))&
(![X]:((wise(X)<~>strong(X))=>old(X)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((~creative(X)<~>kind(X))=>(~patient(X)|curious(X))))&
((generous(lucy)<~>~creative(lucy)))&
((~calm(john)&~strong(john)))&
(tall(mary))&
(?[X]:(~old(X)))&
((brave(fred)|patient(fred)))&
(?[X]:(quiet(X))) | ~humble(paul) | [] | null | 0 |
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
If paul is both not curious and old then lucy is not kind and vice versa.
If someone is both not humble and not patient then someone is not generous.
If someone is not generous or patient then someone is either strong or happy.
Someone is both quiet and not happy.
Someone is either curious or humble.
Paul is both creative and calm.
Alice is not patient.
Someone is either not curious or not wise.
Someone is curious.
Fred is not old. | Susan is wise. | neutral | (((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
(((~curious(paul)&old(paul)))<=>(~kind(lucy)))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~generous(X)|patient(X))))=>(?[X]:((strong(X)<~>happy(X)))))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X))))&
((creative(paul)&calm(paul)))&
(~patient(alice))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:(curious(X)))&
(~old(fred)) | wise(susan) | [] | null | 0 |
Everyone who is curious or not strong is either not patient or not old. Everyone who is both wise and not quiet is both not calm and old. If susan is both not funny and not kind then fred is not rich and vice versa. Everyone who is either creative or humble is both not generous and brave and vice versa. Everyone who is either not brave or not strong is brave or quiet and vice versa. If someone is either kind or not quiet then someone is not funny. If someone is either not humble or funny then alice is wise or not kind and vice versa. If someone is either not tall or not humble then someone is not happy or humble. Everyone who is either curious or calm is either creative or not brave and vice versa. If lucy is not funny or not wise then lucy is curious or strong. Everyone who is both not calm and not creative is both patient and brave. If john is funny then susan is both not old and not tall and vice versa. Everyone who is both creative and curious is either brave or not quiet and vice versa. Everyone who is both not calm and not old is both not brave and generous and vice versa. If mary is both humble and patient then someone is both old and brave and vice versa. Everyone who is either not calm or not quiet is curious. Lucy is brave. Someone is not strong. Alice is either quiet or not wise. Someone is not funny. Alice is not kind or not quiet. Someone is not patient or not calm. Someone is either not brave or not wise. | Fred is not strong. | neutral | (![X]:((curious(X)|~strong(X))=>(~patient(X)<~>~old(X))))&
(![X]:((wise(X)&~quiet(X))=>(~calm(X)&old(X))))&
(((~funny(susan)&~kind(susan)))<=>(~rich(fred)))&
(![X]:((creative(X)<~>humble(X))<=>(~generous(X)&brave(X))))&
(![X]:((~brave(X)<~>~strong(X))<=>(brave(X)|quiet(X))))&
((?[X]:((kind(X)<~>~quiet(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((wise(alice)|~kind(alice))))&
((?[X]:((~tall(X)<~>~humble(X))))=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((curious(X)<~>calm(X))<=>(creative(X)<~>~brave(X))))&
(((~funny(lucy)|~wise(lucy)))=>((curious(lucy)|strong(lucy))))&
(![X]:((~calm(X)&~creative(X))=>(patient(X)&brave(X))))&
((funny(john))<=>((~old(susan)&~tall(susan))))&
(![X]:((creative(X)&curious(X))<=>(brave(X)<~>~quiet(X))))&
(![X]:((~calm(X)&~old(X))<=>(~brave(X)&generous(X))))&
(((humble(mary)&patient(mary)))<=>(?[X]:((old(X)&brave(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>curious(X)))&
(brave(lucy))&
(?[X]:(~strong(X)))&
((quiet(alice)<~>~wise(alice)))&
(?[X]:(~funny(X)))&
((~kind(alice)|~quiet(alice)))&
(?[X]:((~patient(X)|~calm(X))))&
(?[X]:((~brave(X)<~>~wise(X)))) | ~strong(fred) | [] | null | 0 |
If someone is wise or kind then someone is brave or strong.
Everyone who is not funny is both not funny and tall and vice versa.
If someone is tall or kind then someone is both humble and not kind and vice versa.
Everyone who is not humble is both old and not curious.
Everyone who is generous is both not curious and not kind.
Everyone who is tall or strong is both generous and not patient.
If john is either not creative or not tall then someone is not brave or patient and vice versa.
If someone is not brave then someone is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not calm or not brave and vice versa.
Everyone who is not calm is not old or not happy and vice versa.
Everyone who is both strong and humble is old or not brave and vice versa.
If someone is both not quiet and not curious then someone is not curious.
If mary is tall or calm then fred is either tall or not quiet and vice versa.
If someone is kind then someone is both not humble and not brave and vice versa.
Paul is either creative or not patient.
John is both creative and not curious.
Paul is both calm and old.
Someone is kind or not curious.
Someone is funny or not patient. | Susan is not calm. | contradiction | ((?[X]:((wise(X)|kind(X))))=>(?[X]:((brave(X)|strong(X)))))&
(![X]:(~funny(X)<=>(~funny(X)&tall(X))))&
((?[X]:((tall(X)|kind(X))))<=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:(~humble(X)=>(old(X)&~curious(X))))&
(![X]:(generous(X)=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|strong(X))=>(generous(X)&~patient(X))))&
(((~creative(john)<~>~tall(john)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~brave(X)))))&
((creative(paul)<~>~patient(paul)))&
((creative(john)&~curious(john)))&
((calm(paul)&old(paul)))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((funny(X)|~patient(X)))) | ~calm(susan) | [
"p3",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7927601226111826798165743
% SZS output start Proof for 7927601226111826798165743
4. ! [X0] : (~humble(X0) => (~curious(X0) & old(X0))) [input p3]
9. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~kind(X0) | ~happy(X0))) [input p8]
13. ! [X0] : ((humble(X0) & strong(X0)) <=> (~brave(X0) | old(X0))) [input p12]
16. ? [X0] : kind(X0) <=> ? [X0] : (~brave(X0) & ~humble(X0)) [input p15]
22. ~calm(susan) [input hypothesis]
27. ? [X0] : kind(X0) <=> ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 16]
31. ! [X0] : ((~curious(X0) & old(X0)) | humble(X0)) [ennf transformation 4]
53. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 9]
54. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 53]
59. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 13]
60. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~humble(X0) | ~strong(X0))) [flattening 59]
66. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 27]
67. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X2] : (~brave(X2) & ~humble(X2)) | ! [X3] : ~kind(X3)) [rectify 66]
68. ? [X0] : kind(X0) => kind(sK6) [choice axiom]
69. ? [X2] : (~brave(X2) & ~humble(X2)) => (~brave(sK7) & ~humble(sK7)) [choice axiom]
70. (kind(sK6) | ! [X1] : (brave(X1) | humble(X1))) & ((~brave(sK7) & ~humble(sK7)) | ! [X3] : ~kind(X3)) [skolemisation 67,69,68]
85. old(X0) | humble(X0) [cnf transformation 31]
103. ~humble(X0) | calm(X0) | kind(X0) [cnf transformation 54]
116. humble(X0) | ~old(X0) [cnf transformation 60]
125. ~humble(sK7) | ~kind(X3) [cnf transformation 70]
136. ~calm(susan) [cnf transformation 22]
138. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
139. ~kind(X1) <- (1) [avatar component clause 138]
213. humble(X0) [subsumption resolution 116,85]
250. ~kind(X3) [subsumption resolution 125,213]
251. 1 [avatar split clause 250,138]
309. calm(X1) | kind(X1) [resolution 103,213]
311. calm(X1) <- (1) [subsumption resolution 309,139]
312. $false <- (1) [resolution 311,136]
317. ~1 [avatar contradiction clause 312]
318. $false [avatar sat refutation 251,317]
% SZS output end Proof for 7927601226111826798165743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and funny is both kind and brave.
Everyone who is tall is creative or kind.
Everyone who is both not happy and brave is either brave or curious and vice versa.
If john is either rich or not tall then mary is either generous or creative.
If paul is rich then someone is both not tall and wise and vice versa.
Everyone who is either not curious or generous is either funny or not curious.
Everyone who is either old or not generous is old or kind and vice versa.
Everyone who is old is not funny.
Everyone who is either tall or not brave is funny and vice versa.
If someone is both creative and not generous then someone is both patient and curious.
Everyone who is not happy or not generous is not happy.
If lucy is both not old and generous then john is not wise or quiet.
If someone is strong then someone is both not strong and not curious.
Everyone who is either patient or not rich is either not funny or not calm.
If paul is either wise or rich then john is not patient.
Everyone who is not creative is either not brave or not strong.
Someone is not rich or curious.
Paul is creative or kind.
Someone is either tall or not generous.
Someone is not wise.
Lucy is both patient and not funny.
Susan is either not happy or not humble.
Someone is creative.
Someone is both not calm and patient. | Lucy is not curious. | entailment | (![X]:((strong(X)&funny(X))=>(kind(X)&brave(X))))&
(![X]:(tall(X)=>(creative(X)|kind(X))))&
(![X]:((~happy(X)&brave(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
(![X]:(old(X)=>~funny(X)))&
(![X]:((tall(X)<~>~brave(X))<=>funny(X)))&
((?[X]:((creative(X)&~generous(X))))=>(?[X]:((patient(X)&curious(X)))))&
(![X]:((~happy(X)|~generous(X))=>~happy(X)))&
(((~old(lucy)&generous(lucy)))=>((~wise(john)|quiet(john))))&
((?[X]:(strong(X)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((patient(X)<~>~rich(X))=>(~funny(X)<~>~calm(X))))&
(((wise(paul)<~>rich(paul)))=>(~patient(john)))&
(![X]:(~creative(X)=>(~brave(X)<~>~strong(X))))&
(?[X]:((~rich(X)|curious(X))))&
((creative(paul)|kind(paul)))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:(~wise(X)))&
((patient(lucy)&~funny(lucy)))&
((~happy(susan)<~>~humble(susan)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)&patient(X)))) | ~curious(lucy) | [
"p2",
"p5",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5191260458672238548194179
% SZS output start Proof for 5191260458672238548194179
3. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (brave(X0) <~> curious(X0))) [input p2]
6. ! [X0] : ((~curious(X0) <~> generous(X0)) => (funny(X0) <~> ~curious(X0))) [input p5]
11. ! [X0] : ((~generous(X0) | ~happy(X0)) => ~happy(X0)) [input p10]
21. ~funny(lucy) & patient(lucy) [input p20]
25. curious(lucy) [input hypothesis]
34. ! [X0] : ((funny(X0) <~> ~curious(X0)) | (~curious(X0) <=> generous(X0))) [ennf transformation 6]
37. ! [X0] : (~happy(X0) | (generous(X0) & happy(X0))) [ennf transformation 11]
42. ! [X0] : (((brave(X0) & ~happy(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 3]
43. ! [X0] : (((brave(X0) & ~happy(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ~brave(X0) | happy(X0))) [flattening 42]
49. ! [X0] : (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 34]
78. ~curious(X0) | ~brave(X0) | ~brave(X0) | happy(X0) [cnf transformation 43]
82. brave(X0) | brave(X0) | ~curious(X0) [cnf transformation 43]
91. ~curious(X0) | funny(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 49]
108. ~happy(X0) | generous(X0) [cnf transformation 37]
125. ~funny(lucy) [cnf transformation 21]
131. curious(lucy) [cnf transformation 25]
134. ~generous(X0) | funny(X0) | ~curious(X0) [duplicate literal removal 91]
136. ~curious(X0) | ~brave(X0) | happy(X0) [duplicate literal removal 78]
137. ~curious(X0) | brave(X0) [duplicate literal removal 82]
138. ~curious(X0) | happy(X0) [subsumption resolution 136,137]
254. happy(lucy) [resolution 138,131]
255. generous(lucy) [resolution 254,108]
390. funny(lucy) | ~curious(lucy) [resolution 134,255]
403. ~curious(lucy) [subsumption resolution 390,125]
404. $false [subsumption resolution 403,131]
% SZS output end Proof for 5191260458672238548194179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is patient or creative then someone is not tall or old.
Everyone who is both wise and brave is either not rich or patient and vice versa.
Everyone who is both not patient and kind is not wise and vice versa.
Everyone who is not funny is curious.
If paul is curious then lucy is not tall.
Everyone who is both not tall and funny is wise and vice versa.
Everyone who is both not tall and happy is either not quiet or humble.
Everyone who is not patient or strong is patient and vice versa.
Everyone who is humble is not quiet and vice versa.
Everyone who is not rich or brave is either not quiet or calm and vice versa.
If someone is not calm or not humble then someone is not quiet or wise.
If someone is rich or happy then someone is kind and vice versa.
Everyone who is rich is quiet and vice versa.
Everyone who is both creative and patient is either not strong or not curious and vice versa.
Everyone who is either kind or calm is rich and vice versa.
Fred is either not rich or happy.
Someone is not creative.
Someone is either generous or not kind.
Someone is not generous.
Someone is not calm.
Alice is not old or wise. | Paul is generous. | neutral | (((patient(paul)|creative(paul)))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((wise(X)&brave(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((~patient(X)&kind(X))<=>~wise(X)))&
(![X]:(~funny(X)=>curious(X)))&
((curious(paul))=>(~tall(lucy)))&
(![X]:((~tall(X)&funny(X))<=>wise(X)))&
(![X]:((~tall(X)&happy(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~patient(X)|strong(X))<=>patient(X)))&
(![X]:(humble(X)<=>~quiet(X)))&
(![X]:((~rich(X)|brave(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~calm(X)|~humble(X))))=>(?[X]:((~quiet(X)|wise(X)))))&
((?[X]:((rich(X)|happy(X))))<=>(?[X]:(kind(X))))&
(![X]:(rich(X)<=>quiet(X)))&
(![X]:((creative(X)&patient(X))<=>(~strong(X)<~>~curious(X))))&
(![X]:((kind(X)<~>calm(X))<=>rich(X)))&
((~rich(fred)<~>happy(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((generous(X)<~>~kind(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~calm(X)))&
((~old(alice)|wise(alice))) | generous(paul) | [] | null | 0 |
Everyone who is wise is either not curious or not old and vice versa.
If someone is happy then lucy is either not happy or humble and vice versa.
Everyone who is both not quiet and not patient is either old or not patient and vice versa.
Everyone who is both old and not brave is both not humble and not old.
Everyone who is both tall and happy is either brave or not patient and vice versa.
If alice is both happy and curious then someone is not wise.
Everyone who is not creative or not rich is both not happy and brave.
Everyone who is either not humble or rich is either kind or not wise and vice versa.
If lucy is not happy or not quiet then lucy is tall.
Everyone who is both strong and tall is not brave or strong.
Everyone who is calm is not humble.
If mary is not strong then mary is either not curious or tall.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
If fred is both not old and calm then susan is either not happy or not humble and vice versa.
If someone is either strong or funny then someone is either patient or rich and vice versa.
Someone is not rich or not creative.
Someone is either wise or funny.
Lucy is both not kind and not rich.
Alice is both not patient and tall.
Mary is not calm or not humble.
John is not patient or not generous.
Mary is not quiet or happy. | Mary is generous. | neutral | (![X]:(wise(X)<=>(~curious(X)<~>~old(X))))&
((?[X]:(happy(X)))<=>((~happy(lucy)<~>humble(lucy))))&
(![X]:((~quiet(X)&~patient(X))<=>(old(X)<~>~patient(X))))&
(![X]:((old(X)&~brave(X))=>(~humble(X)&~old(X))))&
(![X]:((tall(X)&happy(X))<=>(brave(X)<~>~patient(X))))&
(((happy(alice)&curious(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~creative(X)|~rich(X))=>(~happy(X)&brave(X))))&
(![X]:((~humble(X)<~>rich(X))<=>(kind(X)<~>~wise(X))))&
(((~happy(lucy)|~quiet(lucy)))=>(tall(lucy)))&
(![X]:((strong(X)&tall(X))=>(~brave(X)|strong(X))))&
(![X]:(calm(X)=>~humble(X)))&
((~strong(mary))=>((~curious(mary)<~>tall(mary))))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
(((~old(fred)&calm(fred)))<=>((~happy(susan)<~>~humble(susan))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~kind(lucy)&~rich(lucy)))&
((~patient(alice)&tall(alice)))&
((~calm(mary)|~humble(mary)))&
((~patient(john)|~generous(john)))&
((~quiet(mary)|happy(mary))) | generous(mary) | [] | null | 0 |
Everyone who is not strong or not tall is both not happy and not patient and vice versa.
Everyone who is either not creative or generous is either not funny or not humble and vice versa.
If mary is either not generous or not brave then mary is happy and vice versa.
Everyone who is strong is not calm or not humble.
Everyone who is not creative is either not calm or brave and vice versa.
Everyone who is patient is either kind or generous and vice versa.
If alice is not creative or generous then someone is not happy.
Everyone who is either not brave or not old is either not tall or humble and vice versa.
Everyone who is either not patient or generous is both not humble and patient and vice versa.
Everyone who is both patient and not happy is both not creative and creative.
If susan is not generous then mary is not generous or strong and vice versa.
If someone is both happy and strong then john is strong and vice versa.
If someone is either creative or not strong then mary is both happy and not creative.
If fred is not generous then someone is not curious or old and vice versa.
Everyone who is kind is humble and vice versa.
If someone is both not patient and curious then fred is either not funny or not tall and vice versa.
Someone is both not happy and old.
Alice is either not creative or not curious.
Lucy is both happy and kind.
Someone is not rich or generous.
Someone is both tall and not quiet.
Someone is strong or generous.
Someone is either curious or not tall.
John is either not curious or not kind. | Fred is strong. | entailment | (![X]:((~strong(X)|~tall(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~funny(X)<~>~humble(X))))&
(((~generous(mary)<~>~brave(mary)))<=>(happy(mary)))&
(![X]:(strong(X)=>(~calm(X)|~humble(X))))&
(![X]:(~creative(X)<=>(~calm(X)<~>brave(X))))&
(![X]:(patient(X)<=>(kind(X)<~>generous(X))))&
(((~creative(alice)|generous(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~humble(X)&patient(X))))&
(![X]:((patient(X)&~happy(X))=>(~creative(X)&creative(X))))&
((~generous(susan))<=>((~generous(mary)|strong(mary))))&
((?[X]:((happy(X)&strong(X))))<=>(strong(john)))&
((?[X]:((creative(X)<~>~strong(X))))=>((happy(mary)&~creative(mary))))&
((~generous(fred))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:(kind(X)<=>humble(X)))&
((?[X]:((~patient(X)&curious(X))))<=>((~funny(fred)<~>~tall(fred))))&
(?[X]:((~happy(X)&old(X))))&
((~creative(alice)<~>~curious(alice)))&
((happy(lucy)&kind(lucy)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(?[X]:((strong(X)|generous(X))))&
(?[X]:((curious(X)<~>~tall(X))))&
((~curious(john)<~>~kind(john))) | strong(fred) | [
"p0",
"p8",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2188202325038192161897226
% SZS output start Proof for 2188202325038192161897226
1. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (~patient(X0) & ~happy(X0))) [input p0]
9. ! [X0] : ((~patient(X0) <~> generous(X0)) <=> (patient(X0) & ~humble(X0))) [input p8]
14. ~generous(fred) <=> ? [X0] : (old(X0) | ~curious(X0)) [input p13]
17. ? [X0] : (old(X0) & ~happy(X0)) [input p16]
25. ~strong(fred) [input hypothesis]
34. ! [X0] : (((~tall(X0) | ~strong(X0)) | (patient(X0) | happy(X0))) & ((~patient(X0) & ~happy(X0)) | (tall(X0) & strong(X0)))) [nnf transformation 1]
35. ! [X0] : ((~tall(X0) | ~strong(X0) | patient(X0) | happy(X0)) & ((~patient(X0) & ~happy(X0)) | (tall(X0) & strong(X0)))) [flattening 34]
43. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (~patient(X0) | humble(X0))) & ((patient(X0) & ~humble(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [nnf transformation 9]
44. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ~patient(X0) | humble(X0)) & ((patient(X0) & ~humble(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [flattening 43]
52. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & (? [X0] : (old(X0) | ~curious(X0)) | generous(fred)) [nnf transformation 14]
53. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & (? [X1] : (old(X1) | ~curious(X1)) | generous(fred)) [rectify 52]
54. ? [X1] : (old(X1) | ~curious(X1)) => (old(sK2) | ~curious(sK2)) [choice axiom]
55. (~generous(fred) | ! [X0] : (~old(X0) & curious(X0))) & ((old(sK2) | ~curious(sK2)) | generous(fred)) [skolemisation 53,54]
61. ? [X0] : (old(X0) & ~happy(X0)) => (old(sK4) & ~happy(sK4)) [choice axiom]
62. old(sK4) & ~happy(sK4) [skolemisation 17,61]
74. ~patient(X0) | strong(X0) [cnf transformation 35]
110. patient(X0) | generous(X0) | patient(X0) [cnf transformation 44]
128. ~generous(fred) | ~old(X0) [cnf transformation 55]
138. old(sK4) [cnf transformation 62]
149. ~strong(fred) [cnf transformation 25]
150. generous(X0) | patient(X0) [duplicate literal removal 110]
228. 16 <=> ! [X0] : ~old(X0) [avatar definition]
229. ~old(X0) <- (16) [avatar component clause 228]
231. 17 <=> generous(fred) [avatar definition]
233. ~generous(fred) <- (~17) [avatar component clause 231]
234. 16 | ~17 [avatar split clause 128,231,228]
318. patient(fred) <- (~17) [resolution 150,233]
333. strong(fred) <- (~17) [resolution 318,74]
334. $false <- (~17) [subsumption resolution 333,149]
335. 17 [avatar contradiction clause 334]
336. $false <- (16) [resolution 229,138]
337. ~16 [avatar contradiction clause 336]
338. $false [avatar sat refutation 234,335,337]
% SZS output end Proof for 2188202325038192161897226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is either not strong or not old and vice versa. If someone is patient then someone is both not humble and not patient. If someone is either strong or curious then someone is either happy or not wise and vice versa. Everyone who is either not patient or not funny is either not curious or not tall and vice versa. Everyone who is either curious or wise is calm and vice versa. Everyone who is both not curious and not rich is generous or not patient and vice versa. Everyone who is either not creative or not old is either humble or not strong. If someone is humble then someone is either creative or not brave. If fred is either not creative or not curious then someone is either not strong or creative and vice versa. If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Everyone who is not old or calm is not humble or not wise. Someone is either creative or not quiet. Someone is either creative or wise. John is both calm and quiet. Fred is rich. Someone is either not creative or old. Alice is either not calm or creative. Someone is either not funny or humble. | John is not creative. | entailment | (![X]:(~rich(X)<=>(~strong(X)<~>~old(X))))&
((?[X]:(patient(X)))=>(?[X]:((~humble(X)&~patient(X)))))&
((?[X]:((strong(X)<~>curious(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:((curious(X)<~>wise(X))<=>calm(X)))&
(![X]:((~curious(X)&~rich(X))<=>(generous(X)|~patient(X))))&
(![X]:((~creative(X)<~>~old(X))=>(humble(X)<~>~strong(X))))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>~brave(X)))))&
(((~creative(fred)<~>~curious(fred)))<=>(?[X]:((~strong(X)<~>creative(X)))))&
((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
(![X]:((~old(X)|calm(X))=>(~humble(X)|~wise(X))))&
(?[X]:((creative(X)<~>~quiet(X))))&
(?[X]:((creative(X)<~>wise(X))))&
((calm(john)&quiet(john)))&
(rich(fred))&
(?[X]:((~creative(X)<~>old(X))))&
((~calm(alice)<~>creative(alice)))&
(?[X]:((~funny(X)<~>humble(X)))) | ~creative(john) | [
"p4",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8734189196499765965507369
% SZS output start Proof for 8734189196499765965507369
5. ! [X0] : ((curious(X0) <~> wise(X0)) <=> calm(X0)) [input p4]
13. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (~strong(X0) | ~wise(X0))) [input p12]
15. ! [X0] : ((creative(X0) | happy(X0)) => (~creative(X0) | curious(X0))) [input p14]
19. quiet(john) & calm(john) [input p18]
24. creative(john) [input hypothesis]
33. ! [X0] : ((~creative(X0) | curious(X0)) | (~creative(X0) & ~happy(X0))) [ennf transformation 15]
34. ! [X0] : (~creative(X0) | curious(X0) | (~creative(X0) & ~happy(X0))) [flattening 33]
47. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | ~calm(X0)) & (calm(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 5]
70. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 13]
71. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 70]
112. ~calm(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 47]
147. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 71]
154. ~creative(X0) | curious(X0) | ~creative(X0) [cnf transformation 34]
161. calm(john) [cnf transformation 19]
170. creative(john) [cnf transformation 24]
171. ~creative(X0) | curious(X0) [duplicate literal removal 154]
175. ~curious(X0) | wise(X0) [duplicate literal removal 147]
388. curious(john) [resolution 171,170]
400. wise(john) [resolution 175,388]
456. ~curious(john) | ~wise(john) [resolution 112,161]
458. ~wise(john) [subsumption resolution 456,388]
459. $false [subsumption resolution 458,400]
% SZS output end Proof for 8734189196499765965507369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and brave then mary is not quiet or not creative.
If someone is not tall then john is not tall.
Everyone who is old or not kind is both not funny and curious and vice versa.
Everyone who is happy or humble is not generous or kind and vice versa.
If someone is both tall and not wise then someone is calm or curious and vice versa.
If susan is both old and not kind then john is both not brave and wise.
Everyone who is both not curious and strong is both tall and old and vice versa.
If mary is either quiet or tall then someone is both calm and curious.
If someone is calm or not tall then someone is both not wise and not humble and vice versa.
If someone is humble or not humble then someone is either not brave or wise.
If susan is either calm or not brave then lucy is either tall or not humble and vice versa.
Everyone who is both not kind and strong is patient or not creative.
Everyone who is either not humble or generous is both curious and not happy.
Everyone who is both creative and wise is both not wise and not kind and vice versa.
If someone is kind then someone is either old or not humble.
If alice is happy or patient then someone is not rich or happy and vice versa.
Someone is not quiet or happy.
Alice is both generous and curious.
Someone is both not creative and funny.
Someone is wise.
Lucy is not tall or strong.
Someone is not strong or not humble.
Alice is both creative and old.
Someone is either funny or tall. | John is not tall. | entailment | ((?[X]:((~happy(X)&brave(X))))=>((~quiet(mary)|~creative(mary))))&
((?[X]:(~tall(X)))=>(~tall(john)))&
(![X]:((old(X)|~kind(X))<=>(~funny(X)&curious(X))))&
(![X]:((happy(X)|humble(X))<=>(~generous(X)|kind(X))))&
((?[X]:((tall(X)&~wise(X))))<=>(?[X]:((calm(X)|curious(X)))))&
(((old(susan)&~kind(susan)))=>((~brave(john)&wise(john))))&
(![X]:((~curious(X)&strong(X))<=>(tall(X)&old(X))))&
(((quiet(mary)<~>tall(mary)))=>(?[X]:((calm(X)&curious(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((humble(X)|~humble(X))))=>(?[X]:((~brave(X)<~>wise(X)))))&
(((calm(susan)<~>~brave(susan)))<=>((tall(lucy)<~>~humble(lucy))))&
(![X]:((~kind(X)&strong(X))=>(patient(X)|~creative(X))))&
(![X]:((~humble(X)<~>generous(X))=>(curious(X)&~happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~wise(X)&~kind(X))))&
((?[X]:(kind(X)))=>(?[X]:((old(X)<~>~humble(X)))))&
(((happy(alice)|patient(alice)))<=>(?[X]:((~rich(X)|happy(X)))))&
(?[X]:((~quiet(X)|happy(X))))&
((generous(alice)&curious(alice)))&
(?[X]:((~creative(X)&funny(X))))&
(?[X]:(wise(X)))&
((~tall(lucy)|strong(lucy)))&
(?[X]:((~strong(X)|~humble(X))))&
((creative(alice)&old(alice)))&
(?[X]:((funny(X)<~>tall(X)))) | ~tall(john) | [
"p1",
"p2",
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2658932596312364497850124
% SZS output start Proof for 2658932596312364497850124
2. ? [X0] : ~tall(X0) => ~tall(john) [input p1]
3. ! [X0] : ((~kind(X0) | old(X0)) <=> (curious(X0) & ~funny(X0))) [input p2]
7. ! [X0] : ((strong(X0) & ~curious(X0)) <=> (old(X0) & tall(X0))) [input p6]
23. old(alice) & creative(alice) [input p22]
25. tall(john) [input hypothesis]
32. ~tall(john) | ! [X0] : tall(X0) [ennf transformation 2]
41. ! [X0] : (((~kind(X0) | old(X0)) | (~curious(X0) | funny(X0))) & ((curious(X0) & ~funny(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 3]
42. ! [X0] : ((~kind(X0) | old(X0) | ~curious(X0) | funny(X0)) & ((curious(X0) & ~funny(X0)) | (kind(X0) & ~old(X0)))) [flattening 41]
50. ! [X0] : (((strong(X0) & ~curious(X0)) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | (~strong(X0) | curious(X0)))) [nnf transformation 7]
51. ! [X0] : (((strong(X0) & ~curious(X0)) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ~strong(X0) | curious(X0))) [flattening 50]
89. ~tall(john) | tall(X0) [cnf transformation 32]
92. ~old(X0) | curious(X0) [cnf transformation 42]
108. ~curious(X0) | ~old(X0) | ~tall(X0) [cnf transformation 51]
155. old(alice) [cnf transformation 23]
158. tall(john) [cnf transformation 25]
174. 4 <=> ! [X0] : tall(X0) [avatar definition]
175. tall(X0) <- (4) [avatar component clause 174]
177. 5 <=> tall(john) [avatar definition]
180. 4 | ~5 [avatar split clause 89,177,174]
229. ~old(X0) | ~tall(X0) [subsumption resolution 108,92]
386. 5 [avatar split clause 158,177]
406. ~tall(alice) [resolution 229,155]
407. $false <- (4) [subsumption resolution 406,175]
408. ~4 [avatar contradiction clause 407]
409. $false [avatar sat refutation 180,386,408]
% SZS output end Proof for 2658932596312364497850124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not old is both not curious and strong.
Everyone who is kind or not creative is generous or not calm.
Everyone who is not calm or curious is not strong and vice versa.
If someone is either tall or quiet then susan is not rich or happy.
If someone is not funny or creative then alice is both curious and creative and vice versa.
Everyone who is either wise or quiet is either not creative or not humble.
Everyone who is not tall is not patient or rich.
Everyone who is generous is either not curious or not tall and vice versa.
Everyone who is strong is patient and vice versa.
If mary is both not old and not quiet then someone is wise or not creative.
Everyone who is not old or tall is rich or kind.
Everyone who is not kind is both happy and curious.
If someone is either kind or wise then lucy is either not strong or calm.
Everyone who is not humble or not happy is funny and vice versa.
Everyone who is both calm and funny is not brave or not creative.
Everyone who is either not generous or strong is tall or kind and vice versa.
Someone is not happy.
Alice is generous or old.
Someone is not tall or not strong.
Susan is quiet or not happy.
Someone is not quiet.
Someone is either patient or funny.
Someone is old.
Someone is both generous and not patient. | Mary is creative. | neutral | (![X]:((humble(X)|~old(X))=>(~curious(X)&strong(X))))&
(![X]:((kind(X)|~creative(X))=>(generous(X)|~calm(X))))&
(![X]:((~calm(X)|curious(X))<=>~strong(X)))&
((?[X]:((tall(X)<~>quiet(X))))=>((~rich(susan)|happy(susan))))&
((?[X]:((~funny(X)|creative(X))))<=>((curious(alice)&creative(alice))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(~patient(X)|rich(X))))&
(![X]:(generous(X)<=>(~curious(X)<~>~tall(X))))&
(![X]:(strong(X)<=>patient(X)))&
(((~old(mary)&~quiet(mary)))=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~old(X)|tall(X))=>(rich(X)|kind(X))))&
(![X]:(~kind(X)=>(happy(X)&curious(X))))&
((?[X]:((kind(X)<~>wise(X))))=>((~strong(lucy)<~>calm(lucy))))&
(![X]:((~humble(X)|~happy(X))<=>funny(X)))&
(![X]:((calm(X)&funny(X))=>(~brave(X)|~creative(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(tall(X)|kind(X))))&
(?[X]:(~happy(X)))&
((generous(alice)|old(alice)))&
(?[X]:((~tall(X)|~strong(X))))&
((quiet(susan)|~happy(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((patient(X)<~>funny(X))))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~patient(X)))) | creative(mary) | [] | null | 0 |
Everyone who is either brave or patient is either old or happy.
If lucy is not kind then someone is either curious or generous.
Everyone who is brave is both not rich and tall and vice versa.
Everyone who is either calm or not rich is rich or not calm and vice versa.
Everyone who is funny is curious and vice versa.
Everyone who is not curious or not rich is either humble or not humble and vice versa.
Everyone who is both old and wise is both old and rich and vice versa.
Everyone who is tall is not calm or not tall and vice versa.
If lucy is either wise or calm then someone is not rich or calm and vice versa.
If someone is either not happy or not wise then someone is both creative and not creative and vice versa.
Everyone who is not funny or creative is either brave or not patient.
Everyone who is not old or not humble is either strong or patient and vice versa.
If fred is not calm or tall then susan is patient or not strong.
If someone is either not generous or old then fred is either not tall or not patient.
Everyone who is both not rich and patient is curious.
If someone is both brave and creative then someone is both wise and tall.
Someone is curious or not brave.
John is not strong or wise.
Someone is both not quiet and creative.
John is either strong or funny.
Someone is either brave or not kind.
Fred is creative.
Someone is both not wise and generous.
Alice is not generous or not humble. | Lucy is wise. | entailment | (![X]:((brave(X)<~>patient(X))=>(old(X)<~>happy(X))))&
((~kind(lucy))=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:(brave(X)<=>(~rich(X)&tall(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(rich(X)|~calm(X))))&
(![X]:(funny(X)<=>curious(X)))&
(![X]:((~curious(X)|~rich(X))<=>(humble(X)<~>~humble(X))))&
(![X]:((old(X)&wise(X))<=>(old(X)&rich(X))))&
(![X]:(tall(X)<=>(~calm(X)|~tall(X))))&
(((wise(lucy)<~>calm(lucy)))<=>(?[X]:((~rich(X)|calm(X)))))&
((?[X]:((~happy(X)<~>~wise(X))))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((~funny(X)|creative(X))=>(brave(X)<~>~patient(X))))&
(![X]:((~old(X)|~humble(X))<=>(strong(X)<~>patient(X))))&
(((~calm(fred)|tall(fred)))=>((patient(susan)|~strong(susan))))&
((?[X]:((~generous(X)<~>old(X))))=>((~tall(fred)<~>~patient(fred))))&
(![X]:((~rich(X)&patient(X))=>curious(X)))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((wise(X)&tall(X)))))&
(?[X]:((curious(X)|~brave(X))))&
((~strong(john)|wise(john)))&
(?[X]:((~quiet(X)&creative(X))))&
((strong(john)<~>funny(john)))&
(?[X]:((brave(X)<~>~kind(X))))&
(creative(fred))&
(?[X]:((~wise(X)&generous(X))))&
((~generous(alice)|~humble(alice))) | wise(lucy) | [
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3615021081979328090505645
% SZS output start Proof for 3615021081979328090505645
4. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (~calm(X0) | rich(X0))) [input p3]
8. ! [X0] : (tall(X0) <=> (~tall(X0) | ~calm(X0))) [input p7]
9. (wise(lucy) <~> calm(lucy)) <=> ? [X0] : (calm(X0) | ~rich(X0)) [input p8]
25. ~wise(lucy) [input hypothesis]
44. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (calm(X0) & ~rich(X0))) & ((~calm(X0) | rich(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 4]
45. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (calm(X0) & ~rich(X0))) & (~calm(X0) | rich(X0) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [flattening 44]
51. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & ((~tall(X0) | ~calm(X0)) | ~tall(X0))) [nnf transformation 8]
52. ! [X0] : ((tall(X0) | (tall(X0) & calm(X0))) & (~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 51]
53. (((~calm(lucy) | ~wise(lucy)) & (calm(lucy) | wise(lucy))) | ! [X0] : (~calm(X0) & rich(X0))) & (? [X0] : (calm(X0) | ~rich(X0)) | ((wise(lucy) | ~calm(lucy)) & (calm(lucy) | ~wise(lucy)))) [nnf transformation 9]
54. (((~calm(lucy) | ~wise(lucy)) & (calm(lucy) | wise(lucy))) | ! [X0] : (~calm(X0) & rich(X0))) & (? [X1] : (calm(X1) | ~rich(X1)) | ((wise(lucy) | ~calm(lucy)) & (calm(lucy) | ~wise(lucy)))) [rectify 53]
55. ? [X1] : (calm(X1) | ~rich(X1)) => (calm(sK1) | ~rich(sK1)) [choice axiom]
56. (((~calm(lucy) | ~wise(lucy)) & (calm(lucy) | wise(lucy))) | ! [X0] : (~calm(X0) & rich(X0))) & ((calm(sK1) | ~rich(sK1)) | ((wise(lucy) | ~calm(lucy)) & (calm(lucy) | ~wise(lucy)))) [skolemisation 54,55]
91. ~rich(X0) | calm(X0) | calm(X0) [cnf transformation 45]
106. ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 52]
108. tall(X0) | tall(X0) [cnf transformation 52]
111. calm(lucy) | wise(lucy) | rich(X0) [cnf transformation 56]
151. ~wise(lucy) [cnf transformation 25]
152. ~tall(X0) | ~calm(X0) [duplicate literal removal 106]
153. tall(X0) [duplicate literal removal 108]
159. ~rich(X0) | calm(X0) [duplicate literal removal 91]
175. ~calm(X0) [subsumption resolution 152,153]
176. wise(lucy) | rich(X0) [subsumption resolution 111,175]
178. 4 <=> ! [X0] : rich(X0) [avatar definition]
179. rich(X0) <- (4) [avatar component clause 178]
181. 5 <=> wise(lucy) [avatar definition]
184. 4 | 5 [avatar split clause 176,181,178]
276. ~5 [avatar split clause 151,181]
278. calm(X0) <- (4) [resolution 159,179]
279. $false <- (4) [subsumption resolution 278,175]
280. ~4 [avatar contradiction clause 279]
281. $false [avatar sat refutation 184,276,280]
% SZS output end Proof for 3615021081979328090505645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old is either brave or not happy and vice versa.
Everyone who is either quiet or tall is not happy or not humble and vice versa.
Everyone who is not generous or not kind is both generous and creative and vice versa.
Everyone who is both old and not strong is both humble and old and vice versa.
Everyone who is not kind is either not rich or humble.
Everyone who is not patient is funny.
Everyone who is funny is either old or not happy and vice versa.
If john is funny then fred is either wise or creative.
Everyone who is either quiet or happy is both not old and not tall and vice versa.
If lucy is either patient or not calm then alice is both wise and not tall and vice versa.
If paul is both not calm and tall then someone is both curious and kind.
If someone is both not curious and kind then susan is both not wise and not curious.
Everyone who is both rich and not calm is either not brave or not rich and vice versa.
Everyone who is both not happy and not rich is both generous and not old.
If someone is not calm then someone is both not wise and not quiet and vice versa.
Everyone who is not happy or not brave is not quiet.
Lucy is either quiet or not generous.
Someone is both curious and not old.
Paul is calm.
Someone is not kind or tall.
Mary is not curious or not old.
Susan is not kind or not old.
Someone is either rich or not brave.
Someone is happy or not creative. | John is not happy. | neutral | (![X]:((~happy(X)<~>~old(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)|~humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>(generous(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(humble(X)&old(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>humble(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(funny(X)<=>(old(X)<~>~happy(X))))&
((funny(john))=>((wise(fred)<~>creative(fred))))&
(![X]:((quiet(X)<~>happy(X))<=>(~old(X)&~tall(X))))&
(((patient(lucy)<~>~calm(lucy)))<=>((wise(alice)&~tall(alice))))&
(((~calm(paul)&tall(paul)))=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:((~curious(X)&kind(X))))=>((~wise(susan)&~curious(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~happy(X)&~rich(X))=>(generous(X)&~old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((quiet(lucy)<~>~generous(lucy)))&
(?[X]:((curious(X)&~old(X))))&
(calm(paul))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)|~old(mary)))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:((happy(X)|~creative(X)))) | ~happy(john) | [] | null | 0 |
If someone is not funny then someone is both not patient and wise and vice versa. Everyone who is generous is calm or tall and vice versa. Everyone who is kind is either not old or wise. Everyone who is creative is not wise and vice versa. Everyone who is not curious or curious is not creative or not old. If susan is either not humble or funny then paul is not quiet or not strong and vice versa. Everyone who is not wise is both not tall and tall. Everyone who is both strong and not generous is funny or not calm and vice versa. Everyone who is not creative is not old. Everyone who is either tall or not generous is both not generous and not quiet and vice versa. If someone is not brave or brave then someone is not rich. Everyone who is both old and not creative is both funny and patient and vice versa. Everyone who is both creative and old is both not kind and wise. Everyone who is either not tall or humble is both not strong and not curious. If john is either not rich or not old then lucy is both not old and not tall and vice versa. Everyone who is not rich or strong is either not strong or creative. Someone is either not patient or brave. Alice is not quiet or wise. Someone is funny or wise. | John is old. | contradiction | ((?[X]:(~funny(X)))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|tall(X))))&
(![X]:(kind(X)=>(~old(X)<~>wise(X))))&
(![X]:(creative(X)<=>~wise(X)))&
(![X]:((~curious(X)|curious(X))=>(~creative(X)|~old(X))))&
(((~humble(susan)<~>funny(susan)))<=>((~quiet(paul)|~strong(paul))))&
(![X]:(~wise(X)=>(~tall(X)&tall(X))))&
(![X]:((strong(X)&~generous(X))<=>(funny(X)|~calm(X))))&
(![X]:(~creative(X)=>~old(X)))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)&~creative(X))<=>(funny(X)&patient(X))))&
(![X]:((creative(X)&old(X))=>(~kind(X)&wise(X))))&
(![X]:((~tall(X)<~>humble(X))=>(~strong(X)&~curious(X))))&
(((~rich(john)<~>~old(john)))<=>((~old(lucy)&~tall(lucy))))&
(![X]:((~rich(X)|strong(X))=>(~strong(X)<~>creative(X))))&
(?[X]:((~patient(X)<~>brave(X))))&
((~quiet(alice)|wise(alice)))&
(?[X]:((funny(X)|wise(X)))) | old(john) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5234096529043759993416183
% SZS output start Proof for 5234096529043759993416183
5. ! [X0] : ((curious(X0) | ~curious(X0)) => (~old(X0) | ~creative(X0))) [input p4]
9. ! [X0] : (~creative(X0) => ~old(X0)) [input p8]
20. old(john) [input hypothesis]
25. ! [X0] : ((~old(X0) | ~creative(X0)) | (~curious(X0) & curious(X0))) [ennf transformation 5]
26. ! [X0] : (~old(X0) | ~creative(X0) | (~curious(X0) & curious(X0))) [flattening 25]
28. ! [X0] : (~old(X0) | creative(X0)) [ennf transformation 9]
70. ~old(X0) | ~creative(X0) | curious(X0) [cnf transformation 26]
71. ~old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 26]
85. ~old(X0) | creative(X0) [cnf transformation 28]
117. old(john) [cnf transformation 20]
142. ~old(X0) | ~creative(X0) [subsumption resolution 70,71]
166. ~old(X0) [subsumption resolution 85,142]
198. $false [subsumption resolution 117,166]
% SZS output end Proof for 5234096529043759993416183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is either not quiet or calm and vice versa. Everyone who is either wise or not humble is either not generous or wise and vice versa. Everyone who is not old or generous is either tall or wise and vice versa. Everyone who is not generous or generous is not old and vice versa. Everyone who is either patient or not kind is either quiet or not wise and vice versa. Everyone who is either generous or calm is either not kind or quiet and vice versa. If paul is either not rich or happy then someone is both not quiet and quiet. Everyone who is either not patient or patient is both not old and not quiet. Everyone who is not patient is either not creative or funny and vice versa. If susan is either not happy or kind then susan is either not tall or not old and vice versa. 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. If susan is old or patient then alice is both not curious and curious. Someone is both curious and not brave. Someone is not tall or not humble. Paul is not kind. Mary is not creative. Susan is either brave or not happy. | Susan is not humble. | contradiction | (![X]:((~quiet(X)|humble(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
(![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))))&
(((old(susan)|patient(susan)))=>((~curious(alice)&curious(alice))))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~tall(X)|~humble(X))))&
(~kind(paul))&
(~creative(mary))&
((brave(susan)<~>~happy(susan))) | ~humble(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7413320090231871968930124
% SZS output start Proof for 7413320090231871968930124
1. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> (~quiet(X0) <~> calm(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> (~generous(X0) <~> wise(X0))) [input p1]
3. ! [X0] : ((generous(X0) | ~old(X0)) <=> (tall(X0) <~> wise(X0))) [input p2]
4. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~old(X0)) [input p3]
5. ! [X0] : ((patient(X0) <~> ~kind(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p4]
6. ! [X0] : ((generous(X0) <~> calm(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p5]
8. ! [X0] : ((~patient(X0) <~> patient(X0)) => (~quiet(X0) & ~old(X0))) [input p7]
10. (~happy(susan) <~> kind(susan)) <=> (~tall(susan) <~> ~old(susan)) [input p9]
11. ! [X0] : ((old(X0) <~> ~generous(X0)) => (happy(X0) | calm(X0))) [input p10]
15. (patient(susan) | old(susan)) => (curious(alice) & ~curious(alice)) [input p14]
21. ~humble(susan) [input hypothesis]
24. ! [X0] : ((~quiet(X0) & ~old(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 8]
25. ! [X0] : ((happy(X0) | calm(X0)) | (old(X0) <=> ~generous(X0))) [ennf transformation 11]
26. ! [X0] : (happy(X0) | calm(X0) | (old(X0) <=> ~generous(X0))) [flattening 25]
28. (curious(alice) & ~curious(alice)) | (~patient(susan) & ~old(susan)) [ennf transformation 15]
29. ! [X0] : (((humble(X0) | ~quiet(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~humble(X0) & quiet(X0)))) [nnf transformation 1]
30. ! [X0] : ((humble(X0) | ~quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~humble(X0) & quiet(X0)))) [flattening 29]
31. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 2]
32. ! [X0] : (((generous(X0) | ~old(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [nnf transformation 3]
33. ! [X0] : ((generous(X0) | ~old(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [flattening 32]
34. ! [X0] : (((generous(X0) | ~generous(X0)) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 4]
35. ! [X0] : ((generous(X0) | ~generous(X0) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [flattening 34]
36. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 6]
41. ! [X0] : ((~quiet(X0) & ~old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 24]
43. (((~kind(susan) | happy(susan)) & (kind(susan) | ~happy(susan))) | ((~tall(susan) | old(susan)) & (~old(susan) | tall(susan)))) & (((old(susan) | tall(susan)) & (~old(susan) | ~tall(susan))) | ((~happy(susan) | ~kind(susan)) & (kind(susan) | happy(susan)))) [nnf transformation 10]
44. ! [X0] : (happy(X0) | calm(X0) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0)))) [nnf transformation 26]
59. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 30]
64. wise(X0) | ~generous(X0) | wise(X0) | humble(X0) [cnf transformation 31]
70. humble(X0) | ~wise(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 31]
73. ~tall(X0) | ~wise(X0) | old(X0) [cnf transformation 33]
77. ~old(X0) | generous(X0) [cnf transformation 35]
78. ~old(X0) | ~generous(X0) [cnf transformation 35]
85. ~kind(X0) | patient(X0) | quiet(X0) | wise(X0) [cnf transformation 36]
88. quiet(X0) | ~kind(X0) | calm(X0) | ~generous(X0) [cnf transformation 37]
92. calm(X0) | generous(X0) | quiet(X0) | kind(X0) [cnf transformation 37]
95. ~calm(X0) | ~generous(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 37]
102. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 41]
103. ~quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 41]
111. old(susan) | tall(susan) | ~happy(susan) | ~kind(susan) [cnf transformation 43]
117. happy(X0) | calm(X0) | old(X0) | generous(X0) [cnf transformation 44]
130. ~curious(alice) | ~patient(susan) [cnf transformation 28]
132. curious(alice) | ~patient(susan) [cnf transformation 28]
140. ~humble(susan) [cnf transformation 21]
143. ~quiet(X0) | patient(X0) [duplicate literal removal 102]
144. ~patient(X0) | ~quiet(X0) [duplicate literal removal 103]
145. wise(X0) | ~generous(X0) | humble(X0) [duplicate literal removal 64]
148. ~generous(X0) | ~wise(X0) | humble(X0) [duplicate literal removal 70]
149. ~calm(X0) | quiet(X0) [duplicate literal removal 59]
152. ~generous(X0) | humble(X0) [subsumption resolution 145,148]
153. ~old(X0) [subsumption resolution 77,78]
154. ~kind(X0) | ~generous(X0) | ~calm(X0) [subsumption resolution 95,149]
155. kind(X0) | quiet(X0) | generous(X0) [subsumption resolution 92,149]
157. ~kind(X0) | quiet(X0) | ~generous(X0) [subsumption resolution 88,154]
174. ~quiet(X0) [subsumption resolution 143,144]
177. 4 <=> tall(susan) [avatar definition]
178. tall(susan) <- (4) [avatar component clause 177]
181. 5 <=> happy(susan) [avatar definition]
182. ~happy(susan) <- (~5) [avatar component clause 181]
185. 6 <=> kind(susan) [avatar definition]
186. kind(susan) <- (6) [avatar component clause 185]
187. ~kind(susan) <- (~6) [avatar component clause 185]
191. tall(susan) | ~happy(susan) | ~kind(susan) [subsumption resolution 111,153]
192. ~6 | ~5 | 4 [avatar split clause 191,177,181,185]
195. happy(X0) | calm(X0) | generous(X0) [subsumption resolution 117,153]
227. 13 <=> patient(susan) [avatar definition]
229. ~patient(susan) <- (~13) [avatar component clause 227]
231. 14 <=> curious(alice) [avatar definition]
234. ~13 | 14 [avatar split clause 132,231,227]
235. ~13 | ~14 [avatar split clause 130,231,227]
261. quiet(susan) | generous(susan) <- (~6) [resolution 155,187]
264. generous(susan) <- (~6) [subsumption resolution 261,174]
288. humble(susan) <- (~6) [resolution 264,152]
289. $false <- (~6) [subsumption resolution 288,140]
290. 6 [avatar contradiction clause 289]
293. quiet(susan) | ~generous(susan) <- (6) [resolution 186,157]
295. ~generous(susan) <- (6) [subsumption resolution 293,174]
297. calm(susan) | generous(susan) <- (~5) [resolution 195,182]
299. calm(susan) <- (~5, 6) [subsumption resolution 297,295]
359. quiet(susan) <- (~5, 6) [resolution 299,149]
360. $false <- (~5, 6) [subsumption resolution 359,174]
361. 5 | ~6 [avatar contradiction clause 360]
366. ~wise(susan) | old(susan) <- (4) [resolution 178,73]
367. ~wise(susan) <- (4) [subsumption resolution 366,153]
407. patient(susan) | quiet(susan) | wise(susan) <- (6) [resolution 85,186]
410. quiet(susan) | wise(susan) <- (6, ~13) [subsumption resolution 407,229]
411. wise(susan) <- (6, ~13) [subsumption resolution 410,174]
412. $false <- (4, 6, ~13) [subsumption resolution 411,367]
413. ~4 | ~6 | 13 [avatar contradiction clause 412]
414. $false [avatar sat refutation 192,234,235,290,361,413]
% SZS output end Proof for 7413320090231871968930124
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not rich then someone is both quiet and not kind. Everyone who is both old and not tall is not quiet or patient and vice versa. Everyone who is not wise is not calm. Everyone who is either brave or not rich is both wise and rich. Everyone who is wise or not funny is humble. Everyone who is wise is not curious and vice versa. If someone is either curious or not brave then someone is both creative and not humble. Everyone who is both quiet and wise is both not calm and not quiet. Everyone who is either rich or old is not tall or old. Everyone who is not happy is strong and vice versa. Everyone who is not brave or not calm is both not kind and not patient and vice versa. Everyone who is strong or happy is not strong and vice versa. If paul is old or kind then someone is funny or kind. Everyone who is not patient is either quiet or curious and vice versa. Everyone who is brave is not kind or strong and vice versa. If alice is not generous or not tall then paul is not kind or not brave. Fred is either funny or not rich. Someone is either not old or not kind. Susan is not quiet. Someone is strong or not creative. | Alice is not strong. | entailment | ((?[X]:((kind(X)|~rich(X))))=>(?[X]:((quiet(X)&~kind(X)))))&
(![X]:((old(X)&~tall(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~wise(X)=>~calm(X)))&
(![X]:((brave(X)<~>~rich(X))=>(wise(X)&rich(X))))&
(![X]:((wise(X)|~funny(X))=>humble(X)))&
(![X]:(wise(X)<=>~curious(X)))&
((?[X]:((curious(X)<~>~brave(X))))=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((quiet(X)&wise(X))=>(~calm(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))=>(~tall(X)|old(X))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((~brave(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
(![X]:((strong(X)|happy(X))<=>~strong(X)))&
(((old(paul)|kind(paul)))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:(~patient(X)<=>(quiet(X)<~>curious(X))))&
(![X]:(brave(X)<=>(~kind(X)|strong(X))))&
(((~generous(alice)|~tall(alice)))=>((~kind(paul)|~brave(paul))))&
((funny(fred)<~>~rich(fred)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~quiet(susan))&
(?[X]:((strong(X)|~creative(X)))) | ~strong(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4696432294396339443150270
% SZS output start Proof for 4696432294396339443150270
12. ! [X0] : ((happy(X0) | strong(X0)) <=> ~strong(X0)) [input p11]
21. strong(alice) [input hypothesis]
52. ! [X0] : (((happy(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~happy(X0) & ~strong(X0)))) [nnf transformation 12]
53. ! [X0] : ((happy(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~happy(X0) & ~strong(X0)))) [flattening 52]
98. ~strong(X0) | ~strong(X0) [cnf transformation 53]
117. strong(alice) [cnf transformation 21]
118. ~strong(X0) [duplicate literal removal 98]
208. $false [subsumption resolution 117,118]
% SZS output end Proof for 4696432294396339443150270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either tall or not kind then someone is old.
Everyone who is strong or generous is old and vice versa.
Everyone who is both not old and wise is both humble and funny and vice versa.
Everyone who is both generous and not quiet is not happy or not quiet.
If alice is either tall or not humble then alice is either not funny or funny and vice versa.
Everyone who is creative or tall is both generous and not funny and vice versa.
Everyone who is both not kind and not wise is either not funny or not tall and vice versa.
If someone is curious then lucy is not funny.
Everyone who is either happy or not quiet is both quiet and not rich.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Everyone who is curious or not patient is both not humble and quiet.
Someone is strong or brave.
Someone is brave.
Someone is either old or humble. | Paul is tall. | entailment | (((tall(mary)<~>~kind(mary)))=>(?[X]:(old(X))))&
(![X]:((strong(X)|generous(X))<=>old(X)))&
(![X]:((~old(X)&wise(X))<=>(humble(X)&funny(X))))&
(![X]:((generous(X)&~quiet(X))=>(~happy(X)|~quiet(X))))&
(((tall(alice)<~>~humble(alice)))<=>((~funny(alice)<~>funny(alice))))&
(![X]:((creative(X)|tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((~kind(X)&~wise(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(curious(X)))=>(~funny(lucy)))&
(![X]:((happy(X)<~>~quiet(X))=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|~patient(X))=>(~humble(X)&quiet(X))))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:(brave(X)))&
(?[X]:((old(X)<~>humble(X)))) | tall(paul) | [
"p5",
"p6",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7865273243082612809452303
% SZS output start Proof for 7865273243082612809452303
6. ! [X0] : ((tall(X0) | creative(X0)) <=> (~funny(X0) & generous(X0))) [input p5]
7. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p6]
10. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p9]
11. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X0] : (~tall(X0) & wise(X0)) [input p10]
12. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~happy(X0) | wise(X0))) [input p11]
19. ~tall(paul) [input hypothesis]
20. ? [X0] : (generous(X0) & kind(X0)) <=> ? [X1] : (~tall(X1) & wise(X1)) [rectify 11]
31. ! [X0] : ((~happy(X0) | wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 12]
32. ! [X0] : (~happy(X0) | wise(X0) | (rich(X0) & creative(X0))) [flattening 31]
42. ! [X0] : (((tall(X0) | creative(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 6]
43. ! [X0] : ((tall(X0) | creative(X0) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 42]
44. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | wise(X0) | kind(X0))) [flattening 44]
47. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 10]
48. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 47]
49. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X1] : (~tall(X1) & wise(X1)) | ! [X0] : (~generous(X0) | ~kind(X0))) [nnf transformation 20]
50. (? [X0] : (generous(X0) & kind(X0)) | ! [X1] : (tall(X1) | ~wise(X1))) & (? [X2] : (~tall(X2) & wise(X2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [rectify 49]
51. ? [X0] : (generous(X0) & kind(X0)) => (generous(sK1) & kind(sK1)) [choice axiom]
52. ? [X2] : (~tall(X2) & wise(X2)) => (~tall(sK2) & wise(sK2)) [choice axiom]
53. ((generous(sK1) & kind(sK1)) | ! [X1] : (tall(X1) | ~wise(X1))) & ((~tall(sK2) & wise(sK2)) | ! [X3] : (~generous(X3) | ~kind(X3))) [skolemisation 50,52,51]
80. ~creative(X0) | ~funny(X0) [cnf transformation 43]
81. ~funny(X0) | ~tall(X0) [cnf transformation 43]
84. funny(X0) | tall(X0) | wise(X0) | kind(X0) [cnf transformation 45]
87. ~wise(X0) | ~tall(X0) | funny(X0) [cnf transformation 45]
93. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 48]
94. happy(X0) | happy(X0) [cnf transformation 48]
98. kind(sK1) | tall(X1) | ~wise(X1) [cnf transformation 53]
100. ~happy(X0) | wise(X0) | creative(X0) [cnf transformation 32]
108. ~tall(paul) [cnf transformation 19]
109. ~kind(X0) | ~happy(X0) [duplicate literal removal 93]
110. happy(X0) [duplicate literal removal 94]
147. ~wise(X0) | ~tall(X0) [subsumption resolution 87,81]
150. ~kind(X0) [subsumption resolution 109,110]
153. 7 <=> ! [X1] : ~wise(X1) [avatar definition]
154. ~wise(X1) <- (7) [avatar component clause 153]
160. tall(X1) | ~wise(X1) [subsumption resolution 98,150]
161. ~wise(X1) [subsumption resolution 160,147]
162. 7 [avatar split clause 161,153]
164. creative(X0) | wise(X0) [subsumption resolution 100,110]
171. 10 <=> tall(paul) [avatar definition]
173. ~tall(paul) <- (~10) [avatar component clause 171]
191. ~10 [avatar split clause 108,171]
194. wise(X0) | ~funny(X0) [resolution 164,80]
196. ~funny(X0) <- (7) [subsumption resolution 194,154]
213. tall(X2) | wise(X2) | kind(X2) <- (7) [resolution 84,196]
220. tall(X2) | kind(X2) <- (7) [subsumption resolution 213,154]
221. tall(X2) <- (7) [subsumption resolution 220,150]
223. $false <- (7, ~10) [resolution 221,173]
225. ~7 | 10 [avatar contradiction clause 223]
227. $false [avatar sat refutation 162,191,225]
% SZS output end Proof for 7865273243082612809452303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and rich is both not patient and not old.
Everyone who is either old or quiet is either not patient or not funny and vice versa.
If mary is not wise then alice is generous.
Everyone who is rich or calm is not rich and vice versa.
Everyone who is either kind or old is either rich or patient and vice versa.
If alice is either not happy or patient then someone is either not curious or tall and vice versa.
Everyone who is not kind or not curious is either not happy or funny and vice versa.
Everyone who is not tall or not brave is both not patient and tall and vice versa.
Everyone who is brave or not tall is both not brave and not quiet and vice versa.
If someone is both not old and not humble then paul is not funny or not quiet.
If lucy is either not kind or calm then susan is both funny and not kind and vice versa.
If someone is either not creative or not brave then someone is not quiet.
Everyone who is either funny or not rich is both not wise and not rich.
Everyone who is not rich is not wise and vice versa.
Everyone who is strong is not wise.
Susan is kind or happy.
Susan is curious or not brave.
Someone is either kind or tall.
John is humble or generous. | Paul is humble. | neutral | (![X]:((~quiet(X)&rich(X))=>(~patient(X)&~old(X))))&
(![X]:((old(X)<~>quiet(X))<=>(~patient(X)<~>~funny(X))))&
((~wise(mary))=>(generous(alice)))&
(![X]:((rich(X)|calm(X))<=>~rich(X)))&
(![X]:((kind(X)<~>old(X))<=>(rich(X)<~>patient(X))))&
(((~happy(alice)<~>patient(alice)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)&tall(X))))&
(![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~old(X)&~humble(X))))=>((~funny(paul)|~quiet(paul))))&
(((~kind(lucy)<~>calm(lucy)))<=>((funny(susan)&~kind(susan))))&
((?[X]:((~creative(X)<~>~brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>~wise(X)))&
(![X]:(strong(X)=>~wise(X)))&
((kind(susan)|happy(susan)))&
((curious(susan)|~brave(susan)))&
(?[X]:((kind(X)<~>tall(X))))&
((humble(john)|generous(john))) | humble(paul) | [] | null | 0 |
Everyone who is both wise and not calm is quiet. Everyone who is not patient or not generous is happy or humble. If someone is brave or humble then mary is not generous. Everyone who is funny is not quiet and vice versa. If lucy is generous then someone is either not old or tall and vice versa. If paul is kind or strong then lucy is either not creative or funny and vice versa. If john is either not funny or strong then someone is either wise or happy and vice versa. Everyone who is both not funny and patient is both quiet and not strong. Everyone who is not quiet or not curious is both not strong and tall. Everyone who is not funny is both not strong and wise and vice versa. If paul is both wise and not humble then someone is either not tall or curious and vice versa. Everyone who is either brave or tall is not funny. If someone is curious then mary is not happy. Everyone who is quiet is either not funny or not creative and vice versa. If someone is both old and kind then someone is humble and vice versa. Everyone who is calm is both not old and not funny and vice versa. Mary is both not curious and kind. Fred is both not quiet and not kind. Someone is not patient or strong. Someone is generous or not happy. Someone is either humble or not patient. Mary is not happy or not wise. Susan is either not humble or not kind. | Mary is generous. | contradiction | (![X]:((wise(X)&~calm(X))=>quiet(X)))&
(![X]:((~patient(X)|~generous(X))=>(happy(X)|humble(X))))&
((?[X]:((brave(X)|humble(X))))=>(~generous(mary)))&
(![X]:(funny(X)<=>~quiet(X)))&
((generous(lucy))<=>(?[X]:((~old(X)<~>tall(X)))))&
(((kind(paul)|strong(paul)))<=>((~creative(lucy)<~>funny(lucy))))&
(((~funny(john)<~>strong(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&~strong(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~strong(X)&tall(X))))&
(![X]:(~funny(X)<=>(~strong(X)&wise(X))))&
(((wise(paul)&~humble(paul)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((brave(X)<~>tall(X))=>~funny(X)))&
((?[X]:(curious(X)))=>(~happy(mary)))&
(![X]:(quiet(X)<=>(~funny(X)<~>~creative(X))))&
((?[X]:((old(X)&kind(X))))<=>(?[X]:(humble(X))))&
(![X]:(calm(X)<=>(~old(X)&~funny(X))))&
((~curious(mary)&kind(mary)))&
((~quiet(fred)&~kind(fred)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~happy(mary)|~wise(mary)))&
((~humble(susan)<~>~kind(susan))) | generous(mary) | [
"p2",
"p3",
"p8",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8345299666477597627501103
% SZS output start Proof for 8345299666477597627501103
3. ? [X0] : (humble(X0) | brave(X0)) => ~generous(mary) [input p2]
4. ! [X0] : (funny(X0) <=> ~quiet(X0)) [input p3]
9. ! [X0] : ((~curious(X0) | ~quiet(X0)) => (tall(X0) & ~strong(X0))) [input p8]
12. ! [X0] : ((brave(X0) <~> tall(X0)) => ~funny(X0)) [input p11]
18. ~kind(fred) & ~quiet(fred) [input p17]
24. generous(mary) [input hypothesis]
31. ~generous(mary) | ! [X0] : (~humble(X0) & ~brave(X0)) [ennf transformation 3]
34. ! [X0] : ((tall(X0) & ~strong(X0)) | (curious(X0) & quiet(X0))) [ennf transformation 9]
35. ! [X0] : (~funny(X0) | (brave(X0) <=> tall(X0))) [ennf transformation 12]
38. ! [X0] : ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))) [nnf transformation 4]
56. ! [X0] : (~funny(X0) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) [nnf transformation 35]
74. ~generous(mary) | ~brave(X0) [cnf transformation 31]
76. ~funny(X0) | ~quiet(X0) [cnf transformation 38]
77. funny(X0) | quiet(X0) [cnf transformation 38]
100. tall(X0) | quiet(X0) [cnf transformation 34]
112. ~tall(X0) | brave(X0) | ~funny(X0) [cnf transformation 56]
125. ~quiet(fred) [cnf transformation 18]
134. generous(mary) [cnf transformation 24]
139. 2 <=> generous(mary) [avatar definition]
144. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
145. ~brave(X0) <- (3) [avatar component clause 144]
146. 3 | ~2 [avatar split clause 74,139,144]
318. 2 [avatar split clause 134,139]
373. brave(X0) | ~funny(X0) | quiet(X0) [resolution 112,100]
375. ~funny(X0) | quiet(X0) <- (3) [subsumption resolution 373,145]
376. ~funny(X0) <- (3) [subsumption resolution 375,76]
378. quiet(X1) <- (3) [resolution 376,77]
405. $false <- (3) [resolution 378,125]
406. ~3 [avatar contradiction clause 405]
407. $false [avatar sat refutation 146,318,406]
% SZS output end Proof for 8345299666477597627501103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is brave or humble then someone is not creative or not quiet.
Everyone who is curious is both not rich and not brave and vice versa.
If someone is strong or not rich then susan is both not generous and patient.
Everyone who is both not brave and kind is not curious and vice versa.
If someone is not generous then alice is not happy and vice versa.
If someone is calm or not curious then someone is either kind or rich and vice versa.
Everyone who is both old and not calm is either old or wise.
If someone is either wise or tall then lucy is either quiet or old and vice versa.
Everyone who is either not funny or happy is not quiet or quiet.
If mary is either not wise or tall then someone is not humble and vice versa.
If someone is both creative and not funny then susan is both not wise and not happy and vice versa.
Everyone who is kind or curious is either not humble or not quiet.
Everyone who is not patient is either tall or not humble.
If susan is both not creative and humble then alice is humble and vice versa.
Alice is either rich or not old.
Lucy is both not quiet and generous.
Susan is not tall.
Someone is patient.
Someone is both not quiet and not funny.
Susan is not creative. | Susan is happy. | neutral | ((?[X]:((brave(X)|humble(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:(curious(X)<=>(~rich(X)&~brave(X))))&
((?[X]:((strong(X)|~rich(X))))=>((~generous(susan)&patient(susan))))&
(![X]:((~brave(X)&kind(X))<=>~curious(X)))&
((?[X]:(~generous(X)))<=>(~happy(alice)))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((old(X)&~calm(X))=>(old(X)<~>wise(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>((quiet(lucy)<~>old(lucy))))&
(![X]:((~funny(X)<~>happy(X))=>(~quiet(X)|quiet(X))))&
(((~wise(mary)<~>tall(mary)))<=>(?[X]:(~humble(X))))&
((?[X]:((creative(X)&~funny(X))))<=>((~wise(susan)&~happy(susan))))&
(![X]:((kind(X)|curious(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>(tall(X)<~>~humble(X))))&
(((~creative(susan)&humble(susan)))<=>(humble(alice)))&
((rich(alice)<~>~old(alice)))&
((~quiet(lucy)&generous(lucy)))&
(~tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)&~funny(X))))&
(~creative(susan)) | happy(susan) | [] | null | 0 |
Everyone who is kind or not humble is both old and not tall. Everyone who is strong or old is both not wise and rich and vice versa. If lucy is either not tall or generous then john is either generous or happy. Everyone who is brave is not kind. Everyone who is either not patient or patient is either not old or old and vice versa. Everyone who is both old and funny is both not calm and old. Everyone who is not wise is not tall. Everyone who is not brave or strong is generous or not curious and vice versa. Everyone who is either wise or not funny is both not humble and not patient and vice versa. Everyone who is both not creative and creative is both not funny and wise and vice versa. If someone is tall or not curious then fred is wise and vice versa. If john is not patient then someone is both wise and happy. If someone is either not humble or not old then someone is both not tall and not creative. Everyone who is strong or patient is not calm. Everyone who is not creative is not happy or kind and vice versa. Someone is either tall or not brave. Susan is either calm or old. Someone is not quiet. Someone is both kind and not brave. Lucy is not rich or patient. Someone is rich. Fred is funny or not patient. Someone is strong or not brave. | Susan is tall. | contradiction | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:((strong(X)|patient(X))=>~calm(X)))&
(![X]:(~creative(X)<=>(~happy(X)|kind(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((calm(susan)<~>old(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)&~brave(X))))&
((~rich(lucy)|patient(lucy)))&
(?[X]:(rich(X)))&
((funny(fred)|~patient(fred)))&
(?[X]:((strong(X)|~brave(X)))) | tall(susan) | [
"p0",
"p1",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7560565715197997706400313
% SZS output start Proof for 7560565715197997706400313
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
2. ! [X0] : ((old(X0) | strong(X0)) <=> (rich(X0) & ~wise(X0))) [input p1]
9. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p9]
11. ? [X0] : (~curious(X0) | tall(X0)) <=> wise(fred) [input p10]
24. tall(susan) [input hypothesis]
27. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
36. ! [X0] : (((old(X0) | strong(X0)) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 2]
37. ! [X0] : ((old(X0) | strong(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [flattening 36]
42. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 9]
43. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 42]
44. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 10]
45. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 44]
46. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 11]
47. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [rectify 46]
48. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK0) | tall(sK0)) [choice axiom]
49. ((~curious(sK0) | tall(sK0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [skolemisation 47,48]
69. old(X0) | humble(X0) [cnf transformation 27]
73. ~wise(X0) | ~old(X0) [cnf transformation 37]
97. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
105. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
106. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
107. wise(fred) | ~tall(X1) [cnf transformation 49]
131. tall(susan) [cnf transformation 24]
160. ~wise(X0) | funny(X0) [subsumption resolution 105,106]
162. 5 <=> wise(fred) [avatar definition]
163. wise(fred) <- (5) [avatar component clause 162]
179. 9 <=> ! [X1] : ~tall(X1) [avatar definition]
180. ~tall(X1) <- (9) [avatar component clause 179]
181. 9 | 5 [avatar split clause 107,162,179]
248. 23 <=> funny(fred) [avatar definition]
250. funny(fred) <- (23) [avatar component clause 248]
284. funny(fred) <- (5) [resolution 160,163]
287. 23 | ~5 [avatar split clause 284,162,248]
290. $false <- (9) [resolution 180,131]
293. ~9 [avatar contradiction clause 290]
295. ~old(fred) <- (5) [resolution 163,73]
300. humble(fred) <- (5) [resolution 295,69]
308. ~humble(fred) | ~wise(fred) <- (23) [resolution 97,250]
309. ~wise(fred) <- (5, 23) [subsumption resolution 308,300]
310. $false <- (5, 23) [subsumption resolution 309,163]
311. ~5 | ~23 [avatar contradiction clause 310]
312. $false [avatar sat refutation 181,287,293,311]
% SZS output end Proof for 7560565715197997706400313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not curious is both not generous and not happy and vice versa. If someone is either tall or happy then someone is either not strong or not creative. Everyone who is either creative or not brave is humble or not creative and vice versa. Everyone who is either not humble or curious is either generous or not curious and vice versa. Everyone who is funny or not calm is wise and vice versa. If fred is either not quiet or kind then someone is not rich or not curious and vice versa. If someone is not humble or not creative then someone is old and vice versa. If mary is either not calm or quiet then someone is tall or not funny and vice versa. Everyone who is both patient and not brave is either not creative or calm and vice versa. Everyone who is either not humble or generous is both not curious and funny and vice versa. Everyone who is both old and not calm is curious. If someone is rich or creative then mary is both patient and curious and vice versa. Everyone who is not tall is not wise or funny and vice versa. Everyone who is not creative is not brave and vice versa. Everyone who is curious is not humble. If lucy is tall or not strong then lucy is not tall. Alice is not calm. Mary is either generous or not rich. Someone is not curious. Someone is either calm or not old. Someone is either not humble or brave. Someone is both not curious and happy. | Fred is wise. | entailment | (![X]:((happy(X)<~>~curious(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((tall(X)<~>happy(X))))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>(humble(X)|~creative(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)<~>~curious(X))))&
(![X]:((funny(X)|~calm(X))<=>wise(X)))&
(((~quiet(fred)<~>kind(fred)))<=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:(old(X))))&
(((~calm(mary)<~>quiet(mary)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>calm(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(~curious(X)&funny(X))))&
(![X]:((old(X)&~calm(X))=>curious(X)))&
((?[X]:((rich(X)|creative(X))))<=>((patient(mary)&curious(mary))))&
(![X]:(~tall(X)<=>(~wise(X)|funny(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:(curious(X)=>~humble(X)))&
(((tall(lucy)|~strong(lucy)))=>(~tall(lucy)))&
(~calm(alice))&
((generous(mary)<~>~rich(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((~curious(X)&happy(X)))) | wise(fred) | [
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2675931470289989757553751
% SZS output start Proof for 2675931470289989757553751
4. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (generous(X0) <~> ~curious(X0))) [input p3]
5. ! [X0] : ((~calm(X0) | funny(X0)) <=> wise(X0)) [input p4]
10. ! [X0] : ((~humble(X0) <~> generous(X0)) <=> (funny(X0) & ~curious(X0))) [input p9]
23. ~wise(fred) [input hypothesis]
39. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0)))) & (((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 4]
40. ! [X0] : (((~calm(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (calm(X0) & ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : ((~calm(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (calm(X0) & ~funny(X0)))) [flattening 40]
57. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [nnf transformation 10]
58. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [flattening 57]
95. ~curious(X0) | generous(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 39]
96. curious(X0) | ~generous(X0) | curious(X0) | humble(X0) [cnf transformation 39]
99. curious(X0) | ~humble(X0) | generous(X0) | curious(X0) [cnf transformation 39]
100. ~curious(X0) | humble(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 39]
102. ~funny(X0) | wise(X0) [cnf transformation 41]
128. funny(X0) | generous(X0) | humble(X0) [cnf transformation 58]
129. funny(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 58]
156. ~wise(fred) [cnf transformation 23]
158. ~curious(X0) | generous(X0) | ~humble(X0) [duplicate literal removal 95]
159. curious(X0) | ~generous(X0) | humble(X0) [duplicate literal removal 96]
160. curious(X0) | ~humble(X0) | generous(X0) [duplicate literal removal 99]
161. ~curious(X0) | humble(X0) | ~generous(X0) [duplicate literal removal 100]
185. ~generous(X0) | humble(X0) [subsumption resolution 159,161]
186. generous(X0) | ~humble(X0) [subsumption resolution 158,160]
240. 17 <=> ! [X0] : funny(X0) [avatar definition]
241. funny(X0) <- (17) [avatar component clause 240]
269. funny(X0) | ~humble(X0) [subsumption resolution 129,186]
270. funny(X0) | humble(X0) [subsumption resolution 128,185]
271. funny(X0) [subsumption resolution 270,269]
272. 17 [avatar split clause 271,240]
310. wise(X0) <- (17) [resolution 102,241]
312. $false <- (17) [resolution 310,156]
313. ~17 [avatar contradiction clause 312]
314. $false [avatar sat refutation 272,313]
% SZS output end Proof for 2675931470289989757553751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not humble and vice versa. Everyone who is both not creative and not happy is not generous or generous. If susan is either not quiet or happy then paul is not quiet. Everyone who is either not happy or quiet is either wise or not brave and vice versa. Everyone who is curious or funny is both old and wise and vice versa. If john is both kind and not calm then someone is not humble. Everyone who is humble is not happy or not curious and vice versa. If fred is generous or wise then someone is humble or curious and vice versa. If alice is either calm or not curious then mary is either not old or creative and vice versa. Everyone who is both patient and creative is both not kind and not creative and vice versa. If someone is both not brave and not happy then someone is calm or wise. If lucy is quiet or happy then someone is both brave and not tall. If someone is not strong or not patient then someone is both funny and happy. If susan is both generous and rich then alice is brave. Everyone who is calm is both calm and not old. If someone is not happy then john is wise or not calm. Someone is not quiet. Alice is both not brave and not rich. Fred is rich or curious. Someone is happy or calm. Someone is not curious or not creative. Alice is not wise. John is not wise. | Mary is creative. | neutral | (![X]:(funny(X)<=>~humble(X)))&
(![X]:((~creative(X)&~happy(X))=>(~generous(X)|generous(X))))&
(((~quiet(susan)<~>happy(susan)))=>(~quiet(paul)))&
(![X]:((~happy(X)<~>quiet(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((curious(X)|funny(X))<=>(old(X)&wise(X))))&
(((kind(john)&~calm(john)))=>(?[X]:(~humble(X))))&
(![X]:(humble(X)<=>(~happy(X)|~curious(X))))&
(((generous(fred)|wise(fred)))<=>(?[X]:((humble(X)|curious(X)))))&
(((calm(alice)<~>~curious(alice)))<=>((~old(mary)<~>creative(mary))))&
(![X]:((patient(X)&creative(X))<=>(~kind(X)&~creative(X))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:((calm(X)|wise(X)))))&
(((quiet(lucy)|happy(lucy)))=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((~strong(X)|~patient(X))))=>(?[X]:((funny(X)&happy(X)))))&
(((generous(susan)&rich(susan)))=>(brave(alice)))&
(![X]:(calm(X)=>(calm(X)&~old(X))))&
((?[X]:(~happy(X)))=>((wise(john)|~calm(john))))&
(?[X]:(~quiet(X)))&
((~brave(alice)&~rich(alice)))&
((rich(fred)|curious(fred)))&
(?[X]:((happy(X)|calm(X))))&
(?[X]:((~curious(X)|~creative(X))))&
(~wise(alice))&
(~wise(john)) | creative(mary) | [] | null | 0 |
If alice is either not curious or not funny then susan is both not quiet and rich and vice versa. Everyone who is both funny and tall is either kind or not happy. Everyone who is both tall and not quiet is not strong. Everyone who is both rich and not old is tall or not quiet and vice versa. Everyone who is both funny and not generous is not brave. Everyone who is either not humble or not funny is either kind or not generous. If someone is both not rich and not wise then someone is either calm or curious. Everyone who is calm or not creative is humble or not humble. Everyone who is not rich or quiet is not patient and vice versa. Everyone who is both not generous and not old is not funny and vice versa. Everyone who is either happy or not kind is not wise or strong. If someone is either not calm or not rich then someone is kind or not kind and vice versa. Everyone who is either curious or not old is both creative and humble and vice versa. Everyone who is both not brave and generous is not rich and vice versa. If someone is either not quiet or creative then someone is patient and vice versa. Everyone who is not funny or strong is strong or not generous and vice versa. Lucy is either not quiet or not funny. Susan is both not rich and happy. Someone is not brave or not curious. John is not creative or generous. Fred is both not generous and brave. Susan is not strong or creative. Fred is both happy and not curious. | Susan is not generous. | contradiction | (((~curious(alice)<~>~funny(alice)))<=>((~quiet(susan)&rich(susan))))&
(![X]:((funny(X)&tall(X))=>(kind(X)<~>~happy(X))))&
(![X]:((tall(X)&~quiet(X))=>~strong(X)))&
(![X]:((rich(X)&~old(X))<=>(tall(X)|~quiet(X))))&
(![X]:((funny(X)&~generous(X))=>~brave(X)))&
(![X]:((~humble(X)<~>~funny(X))=>(kind(X)<~>~generous(X))))&
((?[X]:((~rich(X)&~wise(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((calm(X)|~creative(X))=>(humble(X)|~humble(X))))&
(![X]:((~rich(X)|quiet(X))<=>~patient(X)))&
(![X]:((~generous(X)&~old(X))<=>~funny(X)))&
(![X]:((happy(X)<~>~kind(X))=>(~wise(X)|strong(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((curious(X)<~>~old(X))<=>(creative(X)&humble(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((~quiet(lucy)<~>~funny(lucy)))&
((~rich(susan)&happy(susan)))&
(?[X]:((~brave(X)|~curious(X))))&
((~creative(john)|generous(john)))&
((~generous(fred)&brave(fred)))&
((~strong(susan)|creative(susan)))&
((happy(fred)&~curious(fred))) | ~generous(susan) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2223532351249258510937910
% SZS output start Proof for 2223532351249258510937910
14. ! [X0] : ((generous(X0) & ~brave(X0)) <=> ~rich(X0)) [input p13]
18. happy(susan) & ~rich(susan) [input p17]
24. ~generous(susan) [input hypothesis]
62. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | (~generous(X0) | brave(X0)))) [nnf transformation 14]
63. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | ~generous(X0) | brave(X0))) [flattening 62]
119. generous(X0) | rich(X0) [cnf transformation 63]
130. ~rich(susan) [cnf transformation 18]
139. ~generous(susan) [cnf transformation 24]
145. 2 <=> rich(susan) [avatar definition]
147. ~rich(susan) <- (~2) [avatar component clause 145]
229. ~2 [avatar split clause 130,145]
266. rich(susan) [resolution 119,139]
268. $false <- (~2) [subsumption resolution 266,147]
269. 2 [avatar contradiction clause 268]
270. $false [avatar sat refutation 229,269]
% SZS output end Proof for 2223532351249258510937910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Everyone who is either not brave or patient is either not rich or curious.
Someone is both calm and wise.
Lucy is rich or not tall.
Mary is wise or happy.
Someone is curious or old. | Lucy is not funny. | entailment | (![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((rich(lucy)|~tall(lucy)))&
((wise(mary)|happy(mary)))&
(?[X]:((curious(X)|old(X)))) | ~funny(lucy) | [
"p5",
"p6",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6373777414139461478827855
% SZS output start Proof for 6373777414139461478827855
6. ! [X0] : (funny(X0) <=> (tall(X0) <~> rich(X0))) [input p5]
7. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p6]
12. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p11]
14. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~brave(X0) <~> patient(X0)) => (~rich(X0) <~> curious(X0))) [input p14]
17. ~tall(lucy) | rich(lucy) [input p16]
20. funny(lucy) [input hypothesis]
25. ! [X0] : (funny(X0) => (tall(X0) <~> rich(X0))) [unused predicate definition removal 6]
31. ! [X0] : ((tall(X0) <~> rich(X0)) | ~funny(X0)) [ennf transformation 25]
34. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 14]
35. ! [X0] : ((~rich(X0) <~> curious(X0)) | (~brave(X0) <=> patient(X0))) [ennf transformation 15]
41. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | ~funny(X0)) [nnf transformation 31]
42. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 7]
43. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 42]
57. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 12]
58. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 57]
61. ! [X0] : (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) [nnf transformation 35]
73. ~funny(X0) | tall(X0) | rich(X0) [cnf transformation 41]
77. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 43]
92. happy(X0) | curious(X0) [cnf transformation 58]
93. ~curious(X0) | happy(X0) [cnf transformation 58]
94. ~brave(X0) | curious(X0) [cnf transformation 58]
95. ~curious(X0) | ~brave(X0) [cnf transformation 58]
103. ~patient(X0) | ~happy(X0) [cnf transformation 34]
107. curious(X0) | ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 61]
113. ~tall(lucy) | rich(lucy) [cnf transformation 17]
116. funny(lucy) [cnf transformation 20]
152. ~brave(X0) [subsumption resolution 94,95]
153. happy(X0) [subsumption resolution 92,93]
155. ~patient(X0) [subsumption resolution 103,153]
156. curious(X0) | ~rich(X0) | brave(X0) [subsumption resolution 107,155]
157. ~rich(X0) | curious(X0) [subsumption resolution 156,152]
159. 9 <=> rich(lucy) [avatar definition]
161. rich(lucy) <- (9) [avatar component clause 159]
163. 10 <=> tall(lucy) [avatar definition]
165. ~tall(lucy) <- (~10) [avatar component clause 163]
166. 9 | ~10 [avatar split clause 113,163,159]
169. tall(lucy) | rich(lucy) [resolution 73,116]
170. rich(lucy) <- (~10) [subsumption resolution 169,165]
171. 9 | 10 [avatar split clause 170,163,159]
172. curious(lucy) <- (9) [resolution 161,157]
176. brave(lucy) | patient(lucy) <- (9) [resolution 77,172]
177. patient(lucy) <- (9) [subsumption resolution 176,152]
178. $false <- (9) [subsumption resolution 177,155]
179. ~9 [avatar contradiction clause 178]
180. $false [avatar sat refutation 166,171,179]
% SZS output end Proof for 6373777414139461478827855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or happy then john is either tall or happy and vice versa. If someone is either tall or not quiet then alice is both strong and not strong. If someone is either tall or not humble then someone is not calm and vice versa. Everyone who is both not strong and funny is both not old and not funny and vice versa. Everyone who is both generous and not strong is both not wise and not old. If fred is either not creative or not wise then someone is both rich and old. Everyone who is either not brave or not curious is not brave and vice versa. Everyone who is not generous or patient is either happy or generous and vice versa. Everyone who is both not humble and not generous is not kind or not creative and vice versa. If susan is both generous and not quiet then someone is either not calm or strong and vice versa. Everyone who is both kind and not happy is patient or not kind. Everyone who is either curious or not humble is either quiet or happy and vice versa. If someone is wise then john is not calm or not creative. Everyone who is either not patient or curious is both happy and generous. Everyone who is patient is either not strong or not calm and vice versa. Everyone who is wise is patient and vice versa. Someone is brave. Lucy is brave or not wise. Fred is either not wise or not brave. Alice is not strong. Mary is either humble or not generous. Someone is rich. Mary is both not brave and humble. Paul is humble. | Susan is not brave. | neutral | (((~happy(paul)<~>happy(paul)))<=>((tall(john)<~>happy(john))))&
((?[X]:((tall(X)<~>~quiet(X))))=>((strong(alice)&~strong(alice))))&
((?[X]:((tall(X)<~>~humble(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&~funny(X))))&
(![X]:((generous(X)&~strong(X))=>(~wise(X)&~old(X))))&
(((~creative(fred)<~>~wise(fred)))=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((~generous(X)|patient(X))<=>(happy(X)<~>generous(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)|~creative(X))))&
(((generous(susan)&~quiet(susan)))<=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((kind(X)&~happy(X))=>(patient(X)|~kind(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(quiet(X)<~>happy(X))))&
((?[X]:(wise(X)))=>((~calm(john)|~creative(john))))&
(![X]:((~patient(X)<~>curious(X))=>(happy(X)&generous(X))))&
(![X]:(patient(X)<=>(~strong(X)<~>~calm(X))))&
(![X]:(wise(X)<=>patient(X)))&
(?[X]:(brave(X)))&
((brave(lucy)|~wise(lucy)))&
((~wise(fred)<~>~brave(fred)))&
(~strong(alice))&
((humble(mary)<~>~generous(mary)))&
(?[X]:(rich(X)))&
((~brave(mary)&humble(mary)))&
(humble(paul)) | ~brave(susan) | [] | null | 0 |
If someone is either not creative or generous then susan is both tall and happy.
Everyone who is creative is either quiet or not tall.
If alice is both not strong and not old then someone is calm or tall and vice versa.
Everyone who is rich is either funny or strong.
If alice is both quiet and not calm then someone is rich or calm and vice versa.
Everyone who is both patient and not tall is both creative and not strong and vice versa.
If lucy is either kind or brave then john is strong or funny and vice versa.
If someone is both generous and not humble then fred is quiet or not humble.
Everyone who is not calm is not quiet and vice versa.
Everyone who is old or tall is not patient or humble and vice versa.
Everyone who is either funny or not strong is humble and vice versa.
Everyone who is not humble is curious or not calm.
If paul is either curious or strong then paul is not old or happy and vice versa.
Everyone who is not quiet or strong is not kind and vice versa.
If lucy is brave then someone is either tall or not creative.
If fred is generous or funny then john is both kind and not humble and vice versa.
Someone is either not wise or not curious.
Susan is not quiet or not generous.
Mary is both not quiet and tall.
Someone is not quiet or patient.
Mary is kind or not brave.
Susan is strong or not funny.
Susan is both not funny and strong. | John is not rich. | entailment | ((?[X]:((~creative(X)<~>generous(X))))=>((tall(susan)&happy(susan))))&
(![X]:(creative(X)=>(quiet(X)<~>~tall(X))))&
(((~strong(alice)&~old(alice)))<=>(?[X]:((calm(X)|tall(X)))))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((quiet(alice)&~calm(alice)))<=>(?[X]:((rich(X)|calm(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~strong(X))))&
(((kind(lucy)<~>brave(lucy)))<=>((strong(john)|funny(john))))&
((?[X]:((generous(X)&~humble(X))))=>((quiet(fred)|~humble(fred))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(![X]:((old(X)|tall(X))<=>(~patient(X)|humble(X))))&
(![X]:((funny(X)<~>~strong(X))<=>humble(X)))&
(![X]:(~humble(X)=>(curious(X)|~calm(X))))&
(((curious(paul)<~>strong(paul)))<=>((~old(paul)|happy(paul))))&
(![X]:((~quiet(X)|strong(X))<=>~kind(X)))&
((brave(lucy))=>(?[X]:((tall(X)<~>~creative(X)))))&
(((generous(fred)|funny(fred)))<=>((kind(john)&~humble(john))))&
(?[X]:((~wise(X)<~>~curious(X))))&
((~quiet(susan)|~generous(susan)))&
((~quiet(mary)&tall(mary)))&
(?[X]:((~quiet(X)|patient(X))))&
((kind(mary)|~brave(mary)))&
((strong(susan)|~funny(susan)))&
((~funny(susan)&strong(susan))) | ~rich(john) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8490692622215919265738433
% SZS output start Proof for 8490692622215919265738433
5. (~calm(alice) & quiet(alice)) <=> ? [X0] : (calm(X0) | rich(X0)) [input p4]
9. ! [X0] : (~calm(X0) <=> ~quiet(X0)) [input p8]
24. rich(john) [input hypothesis]
41. ((~calm(alice) & quiet(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) & (? [X0] : (calm(X0) | rich(X0)) | (calm(alice) | ~quiet(alice))) [nnf transformation 5]
42. ((~calm(alice) & quiet(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) & (? [X0] : (calm(X0) | rich(X0)) | calm(alice) | ~quiet(alice)) [flattening 41]
43. ((~calm(alice) & quiet(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) & (? [X1] : (calm(X1) | rich(X1)) | calm(alice) | ~quiet(alice)) [rectify 42]
44. ? [X1] : (calm(X1) | rich(X1)) => (calm(sK1) | rich(sK1)) [choice axiom]
45. ((~calm(alice) & quiet(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) & ((calm(sK1) | rich(sK1)) | calm(alice) | ~quiet(alice)) [skolemisation 43,44]
50. ! [X0] : ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))) [nnf transformation 9]
82. quiet(alice) | ~rich(X0) [cnf transformation 45]
84. ~calm(alice) | ~rich(X0) [cnf transformation 45]
97. ~quiet(X0) | calm(X0) [cnf transformation 50]
134. rich(john) [cnf transformation 24]
181. 11 <=> calm(alice) [avatar definition]
183. ~calm(alice) <- (~11) [avatar component clause 181]
186. 12 <=> ! [X0] : ~rich(X0) [avatar definition]
187. ~rich(X0) <- (12) [avatar component clause 186]
188. 12 | ~11 [avatar split clause 84,181,186]
190. 13 <=> quiet(alice) [avatar definition]
192. quiet(alice) <- (13) [avatar component clause 190]
194. 12 | 13 [avatar split clause 82,190,186]
345. calm(alice) <- (13) [resolution 97,192]
346. $false <- (~11, 13) [subsumption resolution 345,183]
347. 11 | ~13 [avatar contradiction clause 346]
348. $false <- (12) [resolution 187,134]
349. ~12 [avatar contradiction clause 348]
350. $false [avatar sat refutation 188,194,347,349]
% SZS output end Proof for 8490692622215919265738433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is quiet or not old and vice versa.
Everyone who is old is both wise and rich and vice versa.
If someone is either patient or humble then john is calm.
If someone is rich then alice is not calm and vice versa.
If someone is not wise then susan is either not calm or not generous.
If someone is not curious or old then someone is strong.
If someone is either not strong or not calm then someone is not generous or kind and vice versa.
If john is either not funny or curious then someone is both not tall and old.
Everyone who is either old or not curious is not funny and vice versa.
Everyone who is curious is not kind or not brave.
If lucy is either not quiet or creative then paul is wise or not quiet.
If susan is not kind or not quiet then paul is curious or not creative.
Everyone who is curious or humble is either creative or not generous.
Everyone who is both not wise and not generous is either strong or not curious and vice versa.
If paul is either not brave or curious then susan is strong or not funny and vice versa.
Someone is not rich.
Someone is not curious or patient.
Someone is not brave or funny.
Someone is either generous or not rich. | John is not calm. | neutral | (![X]:(wise(X)<=>(quiet(X)|~old(X))))&
(![X]:(old(X)<=>(wise(X)&rich(X))))&
((?[X]:((patient(X)<~>humble(X))))=>(calm(john)))&
((?[X]:(rich(X)))<=>(~calm(alice)))&
((?[X]:(~wise(X)))=>((~calm(susan)<~>~generous(susan))))&
((?[X]:((~curious(X)|old(X))))=>(?[X]:(strong(X))))&
((?[X]:((~strong(X)<~>~calm(X))))<=>(?[X]:((~generous(X)|kind(X)))))&
(((~funny(john)<~>curious(john)))=>(?[X]:((~tall(X)&old(X)))))&
(![X]:((old(X)<~>~curious(X))<=>~funny(X)))&
(![X]:(curious(X)=>(~kind(X)|~brave(X))))&
(((~quiet(lucy)<~>creative(lucy)))=>((wise(paul)|~quiet(paul))))&
(((~kind(susan)|~quiet(susan)))=>((curious(paul)|~creative(paul))))&
(![X]:((curious(X)|humble(X))=>(creative(X)<~>~generous(X))))&
(![X]:((~wise(X)&~generous(X))<=>(strong(X)<~>~curious(X))))&
(((~brave(paul)<~>curious(paul)))<=>((strong(susan)|~funny(susan))))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((generous(X)<~>~rich(X)))) | ~calm(john) | [] | null | 0 |
Everyone who is both not patient and rich is either not brave or happy and vice versa. If someone is both humble and funny then someone is both not old and rich. If someone is not funny or not calm then someone is either not old or not creative. If alice is both brave and not wise then someone is either funny or calm. Everyone who is either old or not humble is both not creative and not funny and vice versa. Everyone who is not happy or not old is either not curious or not patient and vice versa. Everyone who is either not strong or happy is either not wise or not creative. If lucy is calm or not old then mary is strong. Everyone who is both calm and brave is not tall or wise. If someone is strong then susan is not quiet and vice versa. Everyone who is both not quiet and rich is either funny or strong and vice versa. Everyone who is not strong or not funny is brave. Everyone who is either generous or not kind is not patient or not happy and vice versa. If mary is not quiet then john is both not old and not wise. If lucy is happy then someone is not calm. If mary is not strong or wise then susan is humble and vice versa. Susan is not creative or not old. Someone is not rich or not brave. Someone is wise or strong. John is not wise or brave. Susan is not humble. Lucy is either not curious or not humble. Alice is either curious or funny. Paul is both not quiet and not happy. | Susan is not quiet. | entailment | (![X]:((~patient(X)&rich(X))<=>(~brave(X)<~>happy(X))))&
((?[X]:((humble(X)&funny(X))))=>(?[X]:((~old(X)&rich(X)))))&
((?[X]:((~funny(X)|~calm(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(((brave(alice)&~wise(alice)))=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>happy(X))=>(~wise(X)<~>~creative(X))))&
(((calm(lucy)|~old(lucy)))=>(strong(mary)))&
(![X]:((calm(X)&brave(X))=>(~tall(X)|wise(X))))&
((?[X]:(strong(X)))<=>(~quiet(susan)))&
(![X]:((~quiet(X)&rich(X))<=>(funny(X)<~>strong(X))))&
(![X]:((~strong(X)|~funny(X))=>brave(X)))&
(![X]:((generous(X)<~>~kind(X))<=>(~patient(X)|~happy(X))))&
((~quiet(mary))=>((~old(john)&~wise(john))))&
((happy(lucy))=>(?[X]:(~calm(X))))&
(((~strong(mary)|wise(mary)))<=>(humble(susan)))&
((~creative(susan)|~old(susan)))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:((wise(X)|strong(X))))&
((~wise(john)|brave(john)))&
(~humble(susan))&
((~curious(lucy)<~>~humble(lucy)))&
((curious(alice)<~>funny(alice)))&
((~quiet(paul)&~happy(paul))) | ~quiet(susan) | [
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1241644128305798942143182
% SZS output start Proof for 1241644128305798942143182
10. ? [X0] : strong(X0) <=> ~quiet(susan) [input p9]
16. (wise(mary) | ~strong(mary)) <=> humble(susan) [input p15]
21. ~humble(susan) [input p20]
25. quiet(susan) [input hypothesis]
55. (? [X0] : strong(X0) | quiet(susan)) & (~quiet(susan) | ! [X0] : ~strong(X0)) [nnf transformation 10]
56. (? [X0] : strong(X0) | quiet(susan)) & (~quiet(susan) | ! [X1] : ~strong(X1)) [rectify 55]
57. ? [X0] : strong(X0) => strong(sK3) [choice axiom]
58. (strong(sK3) | quiet(susan)) & (~quiet(susan) | ! [X1] : ~strong(X1)) [skolemisation 56,57]
65. ((wise(mary) | ~strong(mary)) | ~humble(susan)) & (humble(susan) | (~wise(mary) & strong(mary))) [nnf transformation 16]
66. (wise(mary) | ~strong(mary) | ~humble(susan)) & (humble(susan) | (~wise(mary) & strong(mary))) [flattening 65]
105. ~quiet(susan) | ~strong(X1) [cnf transformation 58]
124. humble(susan) | strong(mary) [cnf transformation 66]
131. ~humble(susan) [cnf transformation 21]
138. quiet(susan) [cnf transformation 25]
193. 13 <=> strong(mary) [avatar definition]
195. strong(mary) <- (13) [avatar component clause 193]
203. 15 <=> quiet(susan) [avatar definition]
212. 17 <=> ! [X1] : ~strong(X1) [avatar definition]
213. ~strong(X1) <- (17) [avatar component clause 212]
214. 17 | ~15 [avatar split clause 105,203,212]
239. 23 <=> humble(susan) [avatar definition]
248. 13 | 23 [avatar split clause 124,239,193]
281. ~23 [avatar split clause 131,239]
302. 15 [avatar split clause 138,203]
303. $false <- (13, 17) [subsumption resolution 195,213]
304. ~13 | ~17 [avatar contradiction clause 303]
305. $false [avatar sat refutation 214,248,281,302,304]
% SZS output end Proof for 1241644128305798942143182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not kind is humble or rich and vice versa.
If fred is both not wise and 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. | John is not creative. | neutral | (![X]:((~calm(X)&~kind(X))<=>(humble(X)|rich(X))))&
(((~wise(fred)&rich(fred)))<=>((~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)) | ~creative(john) | [] | null | 0 |
Everyone who is either brave or curious is both old and not calm and vice versa. If someone is either wise or not strong then alice is either not kind or quiet and vice versa. Everyone who is curious is tall or strong and vice versa. Everyone who is not funny or not generous is not strong and vice versa. Everyone who is not quiet is either not humble or curious. Everyone who is both humble and happy is either not tall or funny and vice versa. If someone is not funny then fred is either not tall or not old. If john is curious then john is not curious or calm. If someone is either quiet or kind then lucy is both not generous and not wise. Everyone who is humble is not happy or old. Everyone who is tall or old is not tall or strong and vice versa. If someone is quiet or not old then someone is both not wise and wise. If someone is both patient and not quiet then fred is calm. Everyone who is either not tall or not calm is both creative and not wise and vice versa. If someone is not creative or not generous then someone is both wise and not kind. If fred is both happy and old then john is funny and vice versa. Someone is both creative and not calm. Someone is not generous. Mary is both not curious and patient. Alice is happy or funny. Mary is not creative. Someone is not calm or strong. Alice is not old or funny. Alice is both not quiet and creative. | John is not funny. | contradiction | (![X]:((brave(X)<~>curious(X))<=>(old(X)&~calm(X))))&
((?[X]:((wise(X)<~>~strong(X))))<=>((~kind(alice)<~>quiet(alice))))&
(![X]:(curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>~strong(X)))&
(![X]:(~quiet(X)=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~generous(X)))&
((~curious(mary)&patient(mary)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice))) | ~funny(john) | [
"p2",
"p3",
"p4",
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6057491839340119396204518
% SZS output start Proof for 6057491839340119396204518
3. ! [X0] : (curious(X0) <=> (strong(X0) | tall(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~funny(X0)) <=> ~strong(X0)) [input p3]
5. ! [X0] : (~quiet(X0) => (~humble(X0) <~> curious(X0))) [input p4]
6. ! [X0] : ((happy(X0) & humble(X0)) <=> (~tall(X0) <~> funny(X0))) [input p5]
11. ! [X0] : ((old(X0) | tall(X0)) <=> (strong(X0) | ~tall(X0))) [input p10]
12. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p11]
25. ~funny(john) [input hypothesis]
26. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 12]
28. ! [X0] : ((~humble(X0) <~> curious(X0)) | quiet(X0)) [ennf transformation 5]
35. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 26]
44. ! [X0] : ((curious(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | ~curious(X0))) [nnf transformation 3]
45. ! [X0] : ((curious(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | ~curious(X0))) [flattening 44]
46. ! [X0] : (((~generous(X0) | ~funny(X0)) | strong(X0)) & (~strong(X0) | (generous(X0) & funny(X0)))) [nnf transformation 4]
47. ! [X0] : ((~generous(X0) | ~funny(X0) | strong(X0)) & (~strong(X0) | (generous(X0) & funny(X0)))) [flattening 46]
48. ! [X0] : (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 28]
49. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (~happy(X0) | ~humble(X0)))) [nnf transformation 6]
50. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0) | ~humble(X0))) [flattening 49]
53. ! [X0] : (((old(X0) | tall(X0)) | (~strong(X0) & tall(X0))) & ((strong(X0) | ~tall(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 11]
54. ! [X0] : ((old(X0) | tall(X0) | (~strong(X0) & tall(X0))) & (strong(X0) | ~tall(X0) | (~old(X0) & ~tall(X0)))) [flattening 53]
55. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 35]
56. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
57. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 55,56]
85. ~curious(X0) | tall(X0) | strong(X0) [cnf transformation 45]
86. ~tall(X0) | curious(X0) [cnf transformation 45]
88. ~strong(X0) | funny(X0) [cnf transformation 47]
91. ~humble(X0) | curious(X0) | quiet(X0) [cnf transformation 48]
95. humble(X0) | funny(X0) | tall(X0) [cnf transformation 50]
107. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
111. ~wise(sK1) | ~quiet(X1) [cnf transformation 57]
113. wise(sK1) | ~quiet(X1) [cnf transformation 57]
140. ~funny(john) [cnf transformation 25]
141. ~tall(X0) | strong(X0) [duplicate literal removal 107]
188. 10 <=> curious(john) [avatar definition]
189. curious(john) <- (10) [avatar component clause 188]
218. 17 <=> wise(sK1) [avatar definition]
223. 18 <=> ! [X1] : ~quiet(X1) [avatar definition]
224. ~quiet(X1) <- (18) [avatar component clause 223]
225. 18 | 17 [avatar split clause 113,218,223]
227. 18 | ~17 [avatar split clause 111,218,223]
255. 25 <=> funny(john) [avatar definition]
257. ~funny(john) <- (~25) [avatar component clause 255]
289. ~25 [avatar split clause 140,255]
332. funny(X0) | tall(X0) | curious(X0) | quiet(X0) [resolution 95,91]
333. funny(X0) | tall(X0) | curious(X0) <- (18) [subsumption resolution 332,224]
334. funny(X0) | curious(X0) <- (18) [subsumption resolution 333,86]
351. curious(john) <- (18, ~25) [resolution 334,257]
357. 10 | ~18 | 25 [avatar split clause 351,255,223,188]
359. tall(john) | strong(john) <- (10) [resolution 189,85]
362. strong(john) <- (10) [subsumption resolution 359,141]
371. funny(john) <- (10) [resolution 362,88]
373. $false <- (10, ~25) [subsumption resolution 371,257]
374. ~10 | 25 [avatar contradiction clause 373]
375. $false [avatar sat refutation 225,227,289,357,374]
% SZS output end Proof for 6057491839340119396204518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or tall is wise.
Everyone who is not old is not strong or not creative.
Everyone who is happy or not happy is not brave.
Everyone who is either generous or rich is tall or not tall and vice versa.
If someone is both not wise and rich then lucy is not calm or not kind and vice versa.
Everyone who is both humble and creative is not happy and vice versa.
If someone is strong or not kind then someone is not generous or strong.
Everyone who is patient is not brave or curious and vice versa.
Everyone who is not brave or generous is either funny or strong.
If susan is either not strong or quiet then someone is not quiet or not creative and vice versa.
Everyone who is not rich is either not rich or not funny.
If john is not patient then paul is not old or creative.
Everyone who is both not creative and not tall is not kind or not humble.
If someone is both wise and funny then someone is both tall and not strong.
Everyone who is not wise is not tall or wise.
Everyone who is either humble or creative is either not humble or not patient.
Paul is both calm and not tall.
Someone is either not brave or wise.
Someone is humble or not tall.
Someone is tall.
Susan is both old and not curious.
Someone is both wise and tall.
Someone is not generous.
Paul is not old. | Susan is quiet. | neutral | (![X]:((~rich(X)<~>tall(X))=>wise(X)))&
(![X]:(~old(X)=>(~strong(X)|~creative(X))))&
(![X]:((happy(X)|~happy(X))=>~brave(X)))&
(![X]:((generous(X)<~>rich(X))<=>(tall(X)|~tall(X))))&
((?[X]:((~wise(X)&rich(X))))<=>((~calm(lucy)|~kind(lucy))))&
(![X]:((humble(X)&creative(X))<=>~happy(X)))&
((?[X]:((strong(X)|~kind(X))))=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:(patient(X)<=>(~brave(X)|curious(X))))&
(![X]:((~brave(X)|generous(X))=>(funny(X)<~>strong(X))))&
(((~strong(susan)<~>quiet(susan)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:(~rich(X)=>(~rich(X)<~>~funny(X))))&
((~patient(john))=>((~old(paul)|creative(paul))))&
(![X]:((~creative(X)&~tall(X))=>(~kind(X)|~humble(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)|wise(X))))&
(![X]:((humble(X)<~>creative(X))=>(~humble(X)<~>~patient(X))))&
((calm(paul)&~tall(paul)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(tall(X)))&
((old(susan)&~curious(susan)))&
(?[X]:((wise(X)&tall(X))))&
(?[X]:(~generous(X)))&
(~old(paul)) | quiet(susan) | [] | null | 0 |
Everyone who is both not brave and wise is not generous.
Everyone who is rich is both not curious and not rich and vice versa.
Everyone who is not quiet is brave and vice versa.
If someone is both old and not wise then someone is either calm or not calm and vice versa.
Everyone who is both not old and humble is tall.
Everyone who is either not kind or not patient is either happy or calm and vice versa.
Everyone who is quiet or not funny is both not creative and not quiet and vice versa.
If alice is either not wise or not brave then paul is both wise and not quiet and vice versa.
Everyone who is not patient or not humble is both not quiet and quiet.
Everyone who is either not old or not quiet is both curious and strong.
Everyone who is not kind is either not curious or not humble.
If someone is not calm then someone is both not generous and wise and vice versa.
Everyone who is either old or not generous is not happy or not humble and vice versa.
Everyone who is either strong or kind is either not humble or not kind.
Everyone who is either tall or not happy is not old or not strong and vice versa.
Someone is not strong or strong.
John is not creative.
Someone is curious or kind.
Someone is old or not brave.
Susan is either not quiet or funny. | John is not calm. | neutral | (![X]:((~brave(X)&wise(X))=>~generous(X)))&
(![X]:(rich(X)<=>(~curious(X)&~rich(X))))&
(![X]:(~quiet(X)<=>brave(X)))&
((?[X]:((old(X)&~wise(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~old(X)&humble(X))=>tall(X)))&
(![X]:((~kind(X)<~>~patient(X))<=>(happy(X)<~>calm(X))))&
(![X]:((quiet(X)|~funny(X))<=>(~creative(X)&~quiet(X))))&
(((~wise(alice)<~>~brave(alice)))<=>((wise(paul)&~quiet(paul))))&
(![X]:((~patient(X)|~humble(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(curious(X)&strong(X))))&
(![X]:(~kind(X)=>(~curious(X)<~>~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((old(X)<~>~generous(X))<=>(~happy(X)|~humble(X))))&
(![X]:((strong(X)<~>kind(X))=>(~humble(X)<~>~kind(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(~old(X)|~strong(X))))&
(?[X]:((~strong(X)|strong(X))))&
(~creative(john))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:((old(X)|~brave(X))))&
((~quiet(susan)<~>funny(susan))) | ~calm(john) | [] | null | 0 |
Everyone who is either kind or quiet is either not curious or not tall and vice versa. Everyone who is not humble is humble or brave and vice versa. Everyone who is strong is brave or not strong and vice versa. Everyone who is either tall or funny is either happy or not kind and vice versa. Everyone who is both strong and rich is both not strong and not happy and vice versa. Everyone who is not funny is not generous. Everyone who is curious is humble. Everyone who is both not wise and quiet is both patient and not generous and vice versa. If susan is not tall or not funny then lucy is happy and vice versa. Everyone who is either not humble or not funny is either not brave or not old. If someone is either funny or patient then mary is either curious or creative and vice versa. If alice is either happy or wise then someone is funny or kind. If someone is not creative or tall then mary is either not tall or not wise. If susan is not funny or old then someone is either not wise or not calm. If lucy is either not funny or not humble then paul is happy and vice versa. Everyone who is not brave or not kind is patient and vice versa. Someone is both strong and not calm. Someone is strong or not brave. Fred is not funny or not generous. Someone is not rich. Someone is old. Someone is either not funny or rich. Someone is not calm. | Susan is not generous. | neutral | (![X]:((kind(X)<~>quiet(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:(~humble(X)<=>(humble(X)|brave(X))))&
(![X]:(strong(X)<=>(brave(X)|~strong(X))))&
(![X]:((tall(X)<~>funny(X))<=>(happy(X)<~>~kind(X))))&
(![X]:((strong(X)&rich(X))<=>(~strong(X)&~happy(X))))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:(curious(X)=>humble(X)))&
(![X]:((~wise(X)&quiet(X))<=>(patient(X)&~generous(X))))&
(((~tall(susan)|~funny(susan)))<=>(happy(lucy)))&
(![X]:((~humble(X)<~>~funny(X))=>(~brave(X)<~>~old(X))))&
((?[X]:((funny(X)<~>patient(X))))<=>((curious(mary)<~>creative(mary))))&
(((happy(alice)<~>wise(alice)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((~creative(X)|tall(X))))=>((~tall(mary)<~>~wise(mary))))&
(((~funny(susan)|old(susan)))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(happy(paul)))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:((strong(X)|~brave(X))))&
((~funny(fred)|~generous(fred)))&
(?[X]:(~rich(X)))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:(~calm(X))) | ~generous(susan) | [] | null | 0 |
Everyone who is not strong or not tall is either not curious or kind and vice versa. If someone is either humble or tall then someone is kind. If someone is brave then someone is either brave or not funny and vice versa. Everyone who is brave or old is not wise or not brave and vice versa. If mary is not creative or not kind then john is humble or funny and vice versa. If someone is both humble and not humble then susan is both not patient and not curious and vice versa. Everyone who is not quiet is both not curious and not generous. Everyone who is not wise is either generous or wise. Everyone who is either not old or old is not generous. If john is not brave or not tall then john is not kind or not rich. If someone is not humble then someone is either creative or generous and vice versa. If paul is not generous then someone is both calm and not brave and vice versa. If someone is both strong and not strong then paul is kind. Everyone who is patient is either quiet or creative and vice versa. If john is both calm and not quiet then someone is either quiet or strong. Someone is either not curious or not old. Someone is either humble or funny. Lucy is not creative. John is tall. Mary is both not humble and creative. Paul is brave or not generous. John is either creative or not tall. | Paul is not wise. | contradiction | (![X]:((~strong(X)|~tall(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((brave(X)|old(X))<=>(~wise(X)|~brave(X))))&
(((~creative(mary)|~kind(mary)))<=>((humble(john)|funny(john))))&
((?[X]:((humble(X)&~humble(X))))<=>((~patient(susan)&~curious(susan))))&
(![X]:(~quiet(X)=>(~curious(X)&~generous(X))))&
(![X]:(~wise(X)=>(generous(X)<~>wise(X))))&
(![X]:((~old(X)<~>old(X))=>~generous(X)))&
(((~brave(john)|~tall(john)))=>((~kind(john)|~rich(john))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~generous(paul))<=>(?[X]:((calm(X)&~brave(X)))))&
((?[X]:((strong(X)&~strong(X))))=>(kind(paul)))&
(![X]:(patient(X)<=>(quiet(X)<~>creative(X))))&
(((calm(john)&~quiet(john)))=>(?[X]:((quiet(X)<~>strong(X)))))&
(?[X]:((~curious(X)<~>~old(X))))&
(?[X]:((humble(X)<~>funny(X))))&
(~creative(lucy))&
(tall(john))&
((~humble(mary)&creative(mary)))&
((brave(paul)|~generous(paul)))&
((creative(john)<~>~tall(john))) | ~wise(paul) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2580147072748786376575873
% SZS output start Proof for 2580147072748786376575873
8. ! [X0] : (~wise(X0) => (generous(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((~old(X0) <~> old(X0)) => ~generous(X0)) [input p8]
23. ~wise(paul) [input hypothesis]
30. ! [X0] : ((generous(X0) <~> wise(X0)) | wise(X0)) [ennf transformation 8]
31. ! [X0] : (~generous(X0) | (~old(X0) <=> old(X0))) [ennf transformation 9]
55. ! [X0] : (((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | wise(X0)) [nnf transformation 30]
56. ! [X0] : (~generous(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 31]
103. wise(X0) | generous(X0) | wise(X0) [cnf transformation 55]
105. ~generous(X0) | old(X0) | old(X0) [cnf transformation 56]
106. ~generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 56]
132. ~wise(paul) [cnf transformation 23]
133. ~generous(X0) | old(X0) [duplicate literal removal 105]
134. ~generous(X0) | ~old(X0) [duplicate literal removal 106]
135. generous(X0) | wise(X0) [duplicate literal removal 103]
209. ~generous(X0) [subsumption resolution 133,134]
277. wise(X2) [resolution 135,209]
278. $false [resolution 277,132]
% SZS output end Proof for 2580147072748786376575873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not kind is either kind or not patient and vice versa.
If someone is not kind or quiet then lucy is either old or not generous.
Everyone who is both not creative and not generous is creative and vice versa.
If someone is not rich then someone is either curious or not calm.
Everyone who is patient is not quiet and vice versa.
If someone is either not kind or not tall then john is either not funny or not quiet and vice versa.
Everyone who is either patient or curious is both kind and humble and vice versa.
Everyone who is either not tall or curious is creative or brave.
If someone is either not humble or not calm then fred is strong and vice versa.
If lucy is tall or not creative then someone is both not calm and generous.
If someone is either funny or not happy then someone is both tall and happy.
Everyone who is either brave or not strong is wise and vice versa.
Everyone who is not wise is old and vice versa.
Everyone who is not funny or brave is both generous and tall and vice versa.
Someone is both generous and strong.
Susan is either old or not creative.
Someone is not strong or not creative.
Someone is not humble or not happy.
Lucy is humble.
Paul is either not wise or quiet. | Paul is not humble. | neutral | (![X]:((~patient(X)|~kind(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((old(lucy)<~>~generous(lucy))))&
(![X]:((~creative(X)&~generous(X))<=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(patient(X)<=>~quiet(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((~funny(john)<~>~quiet(john))))&
(![X]:((patient(X)<~>curious(X))<=>(kind(X)&humble(X))))&
(![X]:((~tall(X)<~>curious(X))=>(creative(X)|brave(X))))&
((?[X]:((~humble(X)<~>~calm(X))))<=>(strong(fred)))&
(((tall(lucy)|~creative(lucy)))=>(?[X]:((~calm(X)&generous(X)))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((tall(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>wise(X)))&
(![X]:(~wise(X)<=>old(X)))&
(![X]:((~funny(X)|brave(X))<=>(generous(X)&tall(X))))&
(?[X]:((generous(X)&strong(X))))&
((old(susan)<~>~creative(susan)))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~humble(X)|~happy(X))))&
(humble(lucy))&
((~wise(paul)<~>quiet(paul))) | ~humble(paul) | [] | null | 0 |
If someone is not old or not generous then someone is not creative or kind and vice versa.
Everyone who is either funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
Lucy is not curious or rich.
Susan is both not old and calm.
Someone is both not funny and not brave.
John is either happy or not humble.
Paul is not tall or kind.
Someone is either calm or happy. | Mary is tall. | entailment | ((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((~curious(lucy)|rich(lucy)))&
((~old(susan)&calm(susan)))&
(?[X]:((~funny(X)&~brave(X))))&
((happy(john)<~>~humble(john)))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>happy(X)))) | tall(mary) | [
"p2",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4271667104266774035362739
% SZS output start Proof for 4271667104266774035362739
3. ! [X0] : ((kind(X0) | humble(X0)) <=> (tall(X0) & calm(X0))) [input p2]
10. ! [X0] : ((~calm(X0) | old(X0)) => (humble(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((~curious(X0) & old(X0)) <=> (~rich(X0) | happy(X0))) [input p10]
13. ! [X0] : ((~old(X0) <~> rich(X0)) <=> (~rich(X0) | ~kind(X0))) [input p12]
23. ~tall(mary) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~calm(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 10]
41. ! [X0] : (((kind(X0) | humble(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((kind(X0) | humble(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [flattening 41]
55. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | (curious(X0) | ~old(X0)))) [nnf transformation 11]
56. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | curious(X0) | ~old(X0))) [flattening 55]
59. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0))))) [flattening 59]
79. ~humble(X0) | calm(X0) [cnf transformation 42]
82. ~kind(X0) | tall(X0) [cnf transformation 42]
110. ~calm(X0) | ~old(X0) [cnf transformation 28]
113. humble(X0) | calm(X0) [cnf transformation 28]
116. old(X0) | rich(X0) [cnf transformation 56]
125. ~rich(X0) | old(X0) | kind(X0) [cnf transformation 60]
144. ~tall(mary) [cnf transformation 23]
213. 15 <=> tall(mary) [avatar definition]
215. ~tall(mary) <- (~15) [avatar component clause 213]
251. calm(X0) [subsumption resolution 113,79]
252. ~old(X0) [subsumption resolution 110,251]
254. rich(X0) [subsumption resolution 116,252]
256. old(X0) | kind(X0) [subsumption resolution 125,254]
257. kind(X0) [subsumption resolution 256,252]
271. ~15 [avatar split clause 144,213]
276. tall(X0) [resolution 82,257]
277. $false <- (~15) [resolution 276,215]
278. 15 [avatar contradiction clause 277]
279. $false [avatar sat refutation 271,278]
% SZS output end Proof for 4271667104266774035362739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then lucy is kind and vice versa.
Everyone who is both tall and patient is either curious or not happy.
If someone is strong or happy then alice is both curious and tall and vice versa.
Everyone who is not funny or creative is either wise or happy.
If someone is either not brave or not funny then someone is either generous or not tall.
If someone is not calm or not tall then someone is either humble or not humble.
Everyone who is not rich or not curious is both not tall and not kind and vice versa.
Everyone who is either wise or funny is calm and vice versa.
If john is not humble or brave then someone is not quiet.
If someone is either quiet or funny then alice is not quiet.
Everyone who is not tall or not humble is not tall.
If someone is curious then john is either humble or not funny and vice versa.
Everyone who is tall or not quiet is both not strong and quiet and vice versa.
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Someone is not tall or not happy.
Alice is creative or not patient.
Someone is not brave.
Paul is both patient and generous.
Someone is either calm or not strong. | Alice is wise. | neutral | ((?[X]:((~curious(X)<~>~old(X))))<=>(kind(lucy)))&
(![X]:((tall(X)&patient(X))=>(curious(X)<~>~happy(X))))&
((?[X]:((strong(X)|happy(X))))<=>((curious(alice)&tall(alice))))&
(![X]:((~funny(X)|creative(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>calm(X)))&
(((~humble(john)|brave(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>funny(X))))=>(~quiet(alice)))&
(![X]:((~tall(X)|~humble(X))=>~tall(X)))&
((?[X]:(curious(X)))<=>((humble(john)<~>~funny(john))))&
(![X]:((tall(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(?[X]:((~tall(X)|~happy(X))))&
((creative(alice)|~patient(alice)))&
(?[X]:(~brave(X)))&
((patient(paul)&generous(paul)))&
(?[X]:((calm(X)<~>~strong(X)))) | wise(alice) | [] | null | 0 |
Everyone who is funny or not creative is either funny or generous.
Everyone who is not creative or creative is kind or not humble.
Everyone who is not strong is both not kind and calm and vice versa.
Everyone who is both wise and old is both calm and quiet and vice versa.
Everyone who is both old and not tall is not strong or not curious and vice versa.
If lucy is not brave or not wise then lucy is both wise and not rich.
If someone is not generous then alice is generous or calm.
Everyone who is not strong or not rich is both curious and humble.
Everyone who is either not curious or brave is calm.
Everyone who is either tall or kind is both not creative and kind.
Everyone who is both happy and rich is either not strong or strong and vice versa.
Everyone who is either not tall or patient is strong and vice versa.
Everyone who is either tall or not brave is not old.
Everyone who is both not generous and strong is either not generous or generous and vice versa.
If susan is not tall then someone is both rich and calm.
If someone is calm or not tall then someone is both patient and quiet and vice versa.
Alice is not wise.
Fred is either not generous or kind.
Someone is both not quiet and rich.
Mary is either generous or not generous.
Alice is either strong or curious.
Someone is happy.
Someone is patient. | Lucy is not kind. | contradiction | (![X]:((funny(X)|~creative(X))=>(funny(X)<~>generous(X))))&
(![X]:((~creative(X)|creative(X))=>(kind(X)|~humble(X))))&
(![X]:(~strong(X)<=>(~kind(X)&calm(X))))&
(![X]:((wise(X)&old(X))<=>(calm(X)&quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~strong(X)|~curious(X))))&
(((~brave(lucy)|~wise(lucy)))=>((wise(lucy)&~rich(lucy))))&
((?[X]:(~generous(X)))=>((generous(alice)|calm(alice))))&
(![X]:((~strong(X)|~rich(X))=>(curious(X)&humble(X))))&
(![X]:((~curious(X)<~>brave(X))=>calm(X)))&
(![X]:((tall(X)<~>kind(X))=>(~creative(X)&kind(X))))&
(![X]:((happy(X)&rich(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~tall(X)<~>patient(X))<=>strong(X)))&
(![X]:((tall(X)<~>~brave(X))=>~old(X)))&
(![X]:((~generous(X)&strong(X))<=>(~generous(X)<~>generous(X))))&
((~tall(susan))=>(?[X]:((rich(X)&calm(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>(?[X]:((patient(X)&quiet(X)))))&
(~wise(alice))&
((~generous(fred)<~>kind(fred)))&
(?[X]:((~quiet(X)&rich(X))))&
((generous(mary)<~>~generous(mary)))&
((strong(alice)<~>curious(alice)))&
(?[X]:(happy(X)))&
(?[X]:(patient(X))) | ~kind(lucy) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8304885696138764926764461
% SZS output start Proof for 8304885696138764926764461
3. ! [X0] : (~strong(X0) <=> (calm(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((old(X0) & wise(X0)) <=> (quiet(X0) & calm(X0))) [input p3]
5. ! [X0] : ((~tall(X0) & old(X0)) <=> (~curious(X0) | ~strong(X0))) [input p4]
6. (~wise(lucy) | ~brave(lucy)) => (~rich(lucy) & wise(lucy)) [input p5]
9. ! [X0] : ((~curious(X0) <~> brave(X0)) => calm(X0)) [input p8]
11. ! [X0] : ((rich(X0) & happy(X0)) <=> (~strong(X0) <~> strong(X0))) [input p10]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~generous(X0) <~> generous(X0))) [input p13]
24. ~kind(lucy) [input hypothesis]
29. (~rich(lucy) & wise(lucy)) | (wise(lucy) & brave(lucy)) [ennf transformation 6]
33. ! [X0] : (calm(X0) | (~curious(X0) <=> brave(X0))) [ennf transformation 9]
38. ! [X0] : ((~strong(X0) | (~calm(X0) | kind(X0))) & ((calm(X0) & ~kind(X0)) | strong(X0))) [nnf transformation 3]
39. ! [X0] : ((~strong(X0) | ~calm(X0) | kind(X0)) & ((calm(X0) & ~kind(X0)) | strong(X0))) [flattening 38]
40. ! [X0] : (((old(X0) & wise(X0)) | (~quiet(X0) | ~calm(X0))) & ((quiet(X0) & calm(X0)) | (~old(X0) | ~wise(X0)))) [nnf transformation 4]
41. ! [X0] : (((old(X0) & wise(X0)) | ~quiet(X0) | ~calm(X0)) & ((quiet(X0) & calm(X0)) | ~old(X0) | ~wise(X0))) [flattening 40]
42. ! [X0] : (((~tall(X0) & old(X0)) | (curious(X0) & strong(X0))) & ((~curious(X0) | ~strong(X0)) | (tall(X0) | ~old(X0)))) [nnf transformation 5]
43. ! [X0] : (((~tall(X0) & old(X0)) | (curious(X0) & strong(X0))) & (~curious(X0) | ~strong(X0) | tall(X0) | ~old(X0))) [flattening 42]
44. ! [X0] : (calm(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) [nnf transformation 33]
46. ! [X0] : (((rich(X0) & happy(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~rich(X0) | ~happy(X0)))) [nnf transformation 11]
47. ! [X0] : (((rich(X0) & happy(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~rich(X0) | ~happy(X0))) [flattening 46]
50. ! [X0] : (((strong(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
51. ! [X0] : (((strong(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | ~strong(X0) | generous(X0))) [flattening 50]
76. ~calm(X0) | ~strong(X0) | kind(X0) [cnf transformation 39]
77. ~old(X0) | calm(X0) | ~wise(X0) [cnf transformation 41]
83. curious(X0) | old(X0) [cnf transformation 43]
87. wise(lucy) | wise(lucy) [cnf transformation 29]
88. ~rich(lucy) | brave(lucy) [cnf transformation 29]
96. ~brave(X0) | ~curious(X0) | calm(X0) [cnf transformation 44]
105. rich(X0) | strong(X0) | strong(X0) [cnf transformation 47]
106. rich(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 47]
117. strong(X0) | generous(X0) | generous(X0) [cnf transformation 51]
118. strong(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 51]
137. ~kind(lucy) [cnf transformation 24]
142. strong(X0) | generous(X0) [duplicate literal removal 117]
143. ~generous(X0) | strong(X0) [duplicate literal removal 118]
146. rich(X0) | strong(X0) [duplicate literal removal 105]
147. ~strong(X0) | rich(X0) [duplicate literal removal 106]
149. wise(lucy) [duplicate literal removal 87]
153. 1 <=> wise(lucy) [avatar definition]
155. wise(lucy) <- (1) [avatar component clause 153]
157. 2 <=> rich(lucy) [avatar definition]
159. ~rich(lucy) <- (~2) [avatar component clause 157]
162. 3 <=> brave(lucy) [avatar definition]
164. brave(lucy) <- (3) [avatar component clause 162]
165. 3 | ~2 [avatar split clause 88,157,162]
166. 1 [avatar split clause 149,153]
180. rich(X0) [subsumption resolution 146,147]
184. strong(X0) [subsumption resolution 142,143]
230. $false <- (~2) [subsumption resolution 159,180]
231. 2 [avatar contradiction clause 230]
288. ~curious(lucy) | calm(lucy) <- (3) [resolution 96,164]
292. 18 <=> calm(lucy) [avatar definition]
294. calm(lucy) <- (18) [avatar component clause 292]
296. 19 <=> curious(lucy) [avatar definition]
298. ~curious(lucy) <- (~19) [avatar component clause 296]
299. 18 | ~19 | ~3 [avatar split clause 288,162,296,292]
313. old(lucy) <- (~19) [resolution 298,83]
352. calm(lucy) | ~wise(lucy) <- (~19) [resolution 313,77]
354. calm(lucy) <- (1, ~19) [subsumption resolution 352,155]
355. 18 | ~1 | 19 [avatar split clause 354,296,153,292]
356. ~strong(lucy) | kind(lucy) <- (18) [resolution 294,76]
357. kind(lucy) <- (18) [subsumption resolution 356,184]
358. $false <- (18) [subsumption resolution 357,137]
359. ~18 [avatar contradiction clause 358]
360. $false [avatar sat refutation 165,166,231,299,355,359]
% SZS output end Proof for 8304885696138764926764461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or wise is either funny or brave.
Everyone who is either not quiet or patient is either rich or not tall and vice versa.
If someone is either not quiet or not tall then someone is either not funny or brave and vice versa.
Everyone who is calm or not funny is not happy.
Everyone who is humble is both old and kind and vice versa.
Everyone who is either old or not curious is tall.
If someone is either not generous or patient then someone is kind or not creative.
Everyone who is wise or not old is not funny.
Everyone who is either kind or tall is brave.
If fred is both not generous and humble then susan is not happy and vice versa.
If someone is generous or not strong then someone is not old.
Everyone who is quiet or patient is wise.
Everyone who is brave or tall is both rich and happy and vice versa.
If someone is strong then alice is not kind or not wise.
Everyone who is not happy is not rich or curious.
Susan is creative or tall.
Alice is either not wise or wise.
Someone is tall or patient.
Susan is either not calm or patient.
Someone is not quiet or quiet. | Susan is quiet. | contradiction | (![X]:((curious(X)|wise(X))=>(funny(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((calm(X)|~funny(X))=>~happy(X)))&
(![X]:(humble(X)<=>(old(X)&kind(X))))&
(![X]:((old(X)<~>~curious(X))=>tall(X)))&
((?[X]:((~generous(X)<~>patient(X))))=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((wise(X)|~old(X))=>~funny(X)))&
(![X]:((kind(X)<~>tall(X))=>brave(X)))&
(((~generous(fred)&humble(fred)))<=>(~happy(susan)))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|patient(X))=>wise(X)))&
(![X]:((brave(X)|tall(X))<=>(rich(X)&happy(X))))&
((?[X]:(strong(X)))=>((~kind(alice)|~wise(alice))))&
(![X]:(~happy(X)=>(~rich(X)|curious(X))))&
((creative(susan)|tall(susan)))&
((~wise(alice)<~>wise(alice)))&
(?[X]:((tall(X)|patient(X))))&
((~calm(susan)<~>patient(susan)))&
(?[X]:((~quiet(X)|quiet(X)))) | quiet(susan) | [
"p0",
"p3",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6284815591523702672510381
% SZS output start Proof for 6284815591523702672510381
1. ! [X0] : ((wise(X0) | curious(X0)) => (funny(X0) <~> brave(X0))) [input p0]
4. ! [X0] : ((~funny(X0) | calm(X0)) => ~happy(X0)) [input p3]
8. ! [X0] : ((~old(X0) | wise(X0)) => ~funny(X0)) [input p7]
12. ! [X0] : ((patient(X0) | quiet(X0)) => wise(X0)) [input p11]
13. ! [X0] : ((tall(X0) | brave(X0)) <=> (happy(X0) & rich(X0))) [input p12]
21. quiet(susan) [input hypothesis]
25. ! [X0] : ((funny(X0) <~> brave(X0)) | (~wise(X0) & ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (~happy(X0) | (funny(X0) & ~calm(X0))) [ennf transformation 4]
29. ! [X0] : (~funny(X0) | (old(X0) & ~wise(X0))) [ennf transformation 8]
32. ! [X0] : (wise(X0) | (~patient(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : (((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (~wise(X0) & ~curious(X0))) [nnf transformation 25]
57. ! [X0] : (((tall(X0) | brave(X0)) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 13]
58. ! [X0] : ((tall(X0) | brave(X0) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 57]
66. ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 37]
86. ~happy(X0) | funny(X0) [cnf transformation 26]
94. ~funny(X0) | ~wise(X0) [cnf transformation 29]
103. ~quiet(X0) | wise(X0) [cnf transformation 32]
107. ~brave(X0) | happy(X0) [cnf transformation 58]
119. quiet(susan) [cnf transformation 21]
173. 13 <=> happy(susan) [avatar definition]
174. ~happy(susan) <- (~13) [avatar component clause 173]
175. happy(susan) <- (13) [avatar component clause 173]
240. funny(susan) <- (13) [resolution 86,175]
241. ~wise(susan) <- (13) [resolution 94,240]
243. wise(susan) [resolution 103,119]
245. $false <- (13) [subsumption resolution 243,241]
246. ~13 [avatar contradiction clause 245]
253. funny(susan) | brave(susan) [resolution 66,243]
256. 28 <=> brave(susan) [avatar definition]
258. brave(susan) <- (28) [avatar component clause 256]
260. 29 <=> funny(susan) [avatar definition]
262. funny(susan) <- (29) [avatar component clause 260]
263. 28 | 29 [avatar split clause 253,260,256]
295. happy(susan) <- (28) [resolution 258,107]
302. $false <- (~13, 28) [subsumption resolution 295,174]
303. 13 | ~28 [avatar contradiction clause 302]
363. ~wise(susan) <- (29) [resolution 262,94]
364. $false <- (29) [subsumption resolution 363,243]
365. ~29 [avatar contradiction clause 364]
366. $false [avatar sat refutation 246,263,303,365]
% SZS output end Proof for 6284815591523702672510381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not curious or tall and vice versa. Everyone who is either not brave or wise is either funny or brave. Everyone who is both not generous and rich is not calm. Everyone who is not curious is old or not quiet. If someone is not old or not quiet then paul is both not happy and not generous and vice versa. If someone is not rich then someone is funny or rich. Everyone who is both patient and generous is either generous or humble. If someone is generous then someone is either not old or not rich and vice versa. If someone is strong then someone is rich and vice versa. If susan is humble then susan is both quiet and tall and vice versa. If someone is not rich or not creative then alice is not patient or funny. Everyone who is not strong or not calm is not wise. Everyone who is either not kind or quiet is either not quiet or funny and vice versa. If john is not wise then mary is happy. Everyone who is either not strong or not generous is both brave and wise. If mary is both not happy and rich then someone is creative and vice versa. Paul is either funny or old. Someone is not kind or not wise. Someone is patient or not wise. John is patient. Someone is either quiet or not old. Someone is both calm and not quiet. Alice is not old. Someone is either not quiet or not brave. | Alice is not patient. | neutral | (![X]:(~calm(X)<=>(~curious(X)|tall(X))))&
(![X]:((~brave(X)<~>wise(X))=>(funny(X)<~>brave(X))))&
(![X]:((~generous(X)&rich(X))=>~calm(X)))&
(![X]:(~curious(X)=>(old(X)|~quiet(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~happy(paul)&~generous(paul))))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((patient(X)&generous(X))=>(generous(X)<~>humble(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
((?[X]:(strong(X)))<=>(?[X]:(rich(X))))&
((humble(susan))<=>((quiet(susan)&tall(susan))))&
((?[X]:((~rich(X)|~creative(X))))=>((~patient(alice)|funny(alice))))&
(![X]:((~strong(X)|~calm(X))=>~wise(X)))&
(![X]:((~kind(X)<~>quiet(X))<=>(~quiet(X)<~>funny(X))))&
((~wise(john))=>(happy(mary)))&
(![X]:((~strong(X)<~>~generous(X))=>(brave(X)&wise(X))))&
(((~happy(mary)&rich(mary)))<=>(?[X]:(creative(X))))&
((funny(paul)<~>old(paul)))&
(?[X]:((~kind(X)|~wise(X))))&
(?[X]:((patient(X)|~wise(X))))&
(patient(john))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((calm(X)&~quiet(X))))&
(~old(alice))&
(?[X]:((~quiet(X)<~>~brave(X)))) | ~patient(alice) | [] | null | 0 |
If someone is either not quiet or happy then someone is both funny and not humble. If fred is funny then paul is not quiet or old. If someone is both not generous and wise then john is either not happy or happy and vice versa. Everyone who is not curious or not tall is either not rich or funny. If someone is either not strong or generous then paul is happy or curious. Everyone who is happy or not wise is both not rich and not curious. Everyone who is both not curious and not quiet is not creative or not quiet and vice versa. Everyone who is both happy and humble is not wise or strong and vice versa. Everyone who is not happy or humble is either kind or not brave and vice versa. Everyone who is both calm and not calm is not curious and vice versa. If susan is old or not wise then fred is not wise or rich. Everyone who is calm or curious is either not creative or not rich and vice versa. Everyone who is not humble is not curious and vice versa. If alice is not calm or brave then someone is either funny or creative and vice versa. If someone is not curious then lucy is not strong or not creative. Someone is not wise or not brave. Someone is not patient or quiet. Lucy is generous or kind. Someone is both not generous and not happy. Someone is not patient. | Lucy is happy. | contradiction | ((?[X]:((~quiet(X)<~>happy(X))))=>(?[X]:((funny(X)&~humble(X)))))&
((funny(fred))=>((~quiet(paul)|old(paul))))&
((?[X]:((~generous(X)&wise(X))))<=>((~happy(john)<~>happy(john))))&
(![X]:((~curious(X)|~tall(X))=>(~rich(X)<~>funny(X))))&
((?[X]:((~strong(X)<~>generous(X))))=>((happy(paul)|curious(paul))))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&~curious(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~creative(X)|~quiet(X))))&
(![X]:((happy(X)&humble(X))<=>(~wise(X)|strong(X))))&
(![X]:((~happy(X)|humble(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((calm(X)&~calm(X))<=>~curious(X)))&
(((old(susan)|~wise(susan)))=>((~wise(fred)|rich(fred))))&
(![X]:((calm(X)|curious(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:(~humble(X)<=>~curious(X)))&
(((~calm(alice)|brave(alice)))<=>(?[X]:((funny(X)<~>creative(X)))))&
((?[X]:(~curious(X)))=>((~strong(lucy)|~creative(lucy))))&
(?[X]:((~wise(X)|~brave(X))))&
(?[X]:((~patient(X)|quiet(X))))&
((generous(lucy)|kind(lucy)))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:(~patient(X))) | happy(lucy) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 179504027705349544073469
% SZS output start Proof for 179504027705349544073469
6. ! [X0] : ((~wise(X0) | happy(X0)) => (~curious(X0) & ~rich(X0))) [input p5]
10. ! [X0] : ((~calm(X0) & calm(X0)) <=> ~curious(X0)) [input p9]
21. happy(lucy) [input hypothesis]
32. ! [X0] : ((~curious(X0) & ~rich(X0)) | (wise(X0) & ~happy(X0))) [ennf transformation 6]
53. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~calm(X0))) [flattening 53]
84. ~curious(X0) | ~happy(X0) [cnf transformation 32]
103. calm(X0) | curious(X0) [cnf transformation 54]
104. ~calm(X0) | curious(X0) [cnf transformation 54]
126. happy(lucy) [cnf transformation 21]
194. curious(X0) [subsumption resolution 103,104]
263. ~happy(X0) [resolution 84,194]
264. $false [resolution 263,126]
% SZS output end Proof for 179504027705349544073469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and patient is both not creative and not happy.
Everyone who is tall or not generous is curious and vice versa.
Everyone who is not strong or not wise is old.
If paul is both curious and not patient then fred is strong.
Everyone who is either funny or quiet is old or not tall and vice versa.
Everyone who is both tall and not happy is both not humble and not happy and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is not calm or kind is strong and vice versa.
Everyone who is not funny is both humble and not wise and vice versa.
Everyone who is not kind or generous is old or not old.
Everyone who is patient or tall is not strong and vice versa.
If fred is both not creative and not quiet then susan is either not kind or wise and vice versa.
If someone is either not humble or not tall then someone is either not creative or funny.
Everyone who is humble is not wise and vice versa.
Everyone who is patient or generous is rich or not creative.
Everyone who is quiet or funny is either quiet or not quiet.
Someone is both not kind and funny.
Alice is not patient.
John is curious or wise.
Mary is either not brave or not happy.
Someone is either not kind or not patient.
Fred is both brave and not calm.
Mary is tall. | Fred is creative. | neutral | (![X]:((curious(X)&patient(X))=>(~creative(X)&~happy(X))))&
(![X]:((tall(X)|~generous(X))<=>curious(X)))&
(![X]:((~strong(X)|~wise(X))=>old(X)))&
(((curious(paul)&~patient(paul)))=>(strong(fred)))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)|~tall(X))))&
(![X]:((tall(X)&~happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:((~calm(X)|kind(X))<=>strong(X)))&
(![X]:(~funny(X)<=>(humble(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(old(X)|~old(X))))&
(![X]:((patient(X)|tall(X))<=>~strong(X)))&
(((~creative(fred)&~quiet(fred)))<=>((~kind(susan)<~>wise(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((patient(X)|generous(X))=>(rich(X)|~creative(X))))&
(![X]:((quiet(X)|funny(X))=>(quiet(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&funny(X))))&
(~patient(alice))&
((curious(john)|wise(john)))&
((~brave(mary)<~>~happy(mary)))&
(?[X]:((~kind(X)<~>~patient(X))))&
((brave(fred)&~calm(fred)))&
(tall(mary)) | creative(fred) | [] | null | 0 |
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.
If john is both not generous and not creative then someone is both quiet and not funny and vice versa.
If someone is not calm then alice is quiet or wise and vice versa.
Everyone who is both not humble and not tall is humble and vice versa.
Everyone who is both not brave and old is both wise and happy.
If someone is wise then someone is both calm and rich and vice versa.
Everyone who is not happy or not patient is not wise and vice versa.
Everyone who is kind or not tall is generous and vice versa.
Everyone who is both curious and kind is generous or not quiet.
Everyone who is calm is not quiet or not patient and vice versa.
If someone is either not creative or not quiet then alice is patient and vice versa.
If someone is both humble and calm then someone is either humble or not tall.
If lucy is both kind and tall then someone is not creative or creative and vice versa.
John is either patient or not tall.
Someone is both not old and curious.
Someone is either not wise or creative.
Someone is not brave.
Someone is patient.
Alice is not quiet or not wise.
Someone is both quiet and not kind.
Someone is both not kind and not patient. | John is rich. | neutral | (![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)))))&
(((~generous(john)&~creative(john)))<=>(?[X]:((quiet(X)&~funny(X)))))&
((?[X]:(~calm(X)))<=>((quiet(alice)|wise(alice))))&
(![X]:((~humble(X)&~tall(X))<=>humble(X)))&
(![X]:((~brave(X)&old(X))=>(wise(X)&happy(X))))&
((?[X]:(wise(X)))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:((~happy(X)|~patient(X))<=>~wise(X)))&
(![X]:((kind(X)|~tall(X))<=>generous(X)))&
(![X]:((curious(X)&kind(X))=>(generous(X)|~quiet(X))))&
(![X]:(calm(X)<=>(~quiet(X)|~patient(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))<=>(patient(alice)))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:((humble(X)<~>~tall(X)))))&
(((kind(lucy)&tall(lucy)))<=>(?[X]:((~creative(X)|creative(X)))))&
((patient(john)<~>~tall(john)))&
(?[X]:((~old(X)&curious(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:(patient(X)))&
((~quiet(alice)|~wise(alice)))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~kind(X)&~patient(X)))) | rich(john) | [] | null | 0 |
If someone is tall or not funny then lucy is quiet or creative and vice versa.
Everyone who is either kind or strong is not tall.
If someone is not patient or not generous then fred is kind.
Everyone who is humble is calm or not kind and vice versa.
If susan is not creative then alice is not funny or not kind and vice versa.
Everyone who is both generous and not calm is not patient or not happy.
Everyone who is either not old or not calm is either funny or calm.
If alice is either not happy or patient then lucy is not happy or not quiet.
Everyone who is both wise and not wise is generous and vice versa.
If someone is both not tall and not wise then mary is curious and vice versa.
If someone is curious then john is not happy or brave and vice versa.
Everyone who is both not calm and curious is either not wise or not funny and vice versa.
Everyone who is not brave is quiet or not calm.
Everyone who is funny or humble is not old.
Everyone who is either wise or creative is not strong.
If susan is either not calm or not happy then someone is funny or not calm and vice versa.
Someone is patient or not funny.
Someone is both not rich and not curious.
Alice is both not wise and creative.
Someone is not quiet or rich.
Susan is both calm and not rich.
John is either calm or not tall.
Susan is not creative or not humble. | Alice is old. | contradiction | ((?[X]:((tall(X)|~funny(X))))<=>((quiet(lucy)|creative(lucy))))&
(![X]:((kind(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~patient(X)|~generous(X))))=>(kind(fred)))&
(![X]:(humble(X)<=>(calm(X)|~kind(X))))&
((~creative(susan))<=>((~funny(alice)|~kind(alice))))&
(![X]:((generous(X)&~calm(X))=>(~patient(X)|~happy(X))))&
(![X]:((~old(X)<~>~calm(X))=>(funny(X)<~>calm(X))))&
(((~happy(alice)<~>patient(alice)))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&~wise(X))<=>generous(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>(curious(mary)))&
((?[X]:(curious(X)))<=>((~happy(john)|brave(john))))&
(![X]:((~calm(X)&curious(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:(~brave(X)=>(quiet(X)|~calm(X))))&
(![X]:((funny(X)|humble(X))=>~old(X)))&
(![X]:((wise(X)<~>creative(X))=>~strong(X)))&
(((~calm(susan)<~>~happy(susan)))<=>(?[X]:((funny(X)|~calm(X)))))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((~rich(X)&~curious(X))))&
((~wise(alice)&creative(alice)))&
(?[X]:((~quiet(X)|rich(X))))&
((calm(susan)&~rich(susan)))&
((calm(john)<~>~tall(john)))&
((~creative(susan)|~humble(susan))) | old(alice) | [
"p3",
"p4",
"p6",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2644563476130826041900266
% SZS output start Proof for 2644563476130826041900266
4. ! [X0] : (humble(X0) <=> (~kind(X0) | calm(X0))) [input p3]
5. ~creative(susan) <=> (~kind(alice) | ~funny(alice)) [input p4]
7. ! [X0] : ((~old(X0) <~> ~calm(X0)) => (funny(X0) <~> calm(X0))) [input p6]
14. ! [X0] : ((humble(X0) | funny(X0)) => ~old(X0)) [input p13]
21. ~rich(susan) & calm(susan) [input p20]
23. ~humble(susan) | ~creative(susan) [input p22]
24. old(alice) [input hypothesis]
25. ! [X0] : ((~kind(X0) | calm(X0)) => humble(X0)) [unused predicate definition removal 4]
28. ! [X0] : (humble(X0) | (kind(X0) & ~calm(X0))) [ennf transformation 25]
31. ! [X0] : ((funny(X0) <~> calm(X0)) | (~old(X0) <=> ~calm(X0))) [ennf transformation 7]
36. ! [X0] : (~old(X0) | (~humble(X0) & ~funny(X0))) [ennf transformation 14]
44. (~creative(susan) | (kind(alice) & funny(alice))) & ((~kind(alice) | ~funny(alice)) | creative(susan)) [nnf transformation 5]
45. (~creative(susan) | (kind(alice) & funny(alice))) & (~kind(alice) | ~funny(alice) | creative(susan)) [flattening 44]
46. ! [X0] : (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) [nnf transformation 31]
81. ~calm(X0) | humble(X0) [cnf transformation 28]
82. humble(X0) | kind(X0) [cnf transformation 28]
83. ~kind(alice) | ~funny(alice) | creative(susan) [cnf transformation 45]
88. calm(X0) | funny(X0) | ~old(X0) | calm(X0) [cnf transformation 46]
110. ~old(X0) | ~humble(X0) [cnf transformation 36]
125. calm(susan) [cnf transformation 21]
129. ~humble(susan) | ~creative(susan) [cnf transformation 23]
130. old(alice) [cnf transformation 24]
131. ~old(X0) | funny(X0) | calm(X0) [duplicate literal removal 88]
172. 10 <=> kind(alice) [avatar definition]
176. 11 <=> creative(susan) [avatar definition]
181. 12 <=> funny(alice) [avatar definition]
182. ~funny(alice) <- (~12) [avatar component clause 181]
185. 11 | ~12 | ~10 [avatar split clause 83,172,181,176]
241. 25 <=> calm(susan) [avatar definition]
243. calm(susan) <- (25) [avatar component clause 241]
283. 25 [avatar split clause 125,241]
295. 36 <=> humble(susan) [avatar definition]
298. ~11 | ~36 [avatar split clause 129,295,176]
299. humble(susan) <- (25) [resolution 81,243]
300. 36 | ~25 [avatar split clause 299,241,295]
302. ~humble(alice) [resolution 110,130]
313. kind(alice) [resolution 302,82]
314. 10 [avatar split clause 313,172]
345. funny(alice) | calm(alice) [resolution 131,130]
346. calm(alice) <- (~12) [subsumption resolution 345,182]
351. humble(alice) <- (~12) [resolution 346,81]
361. $false <- (~12) [subsumption resolution 351,302]
362. 12 [avatar contradiction clause 361]
363. $false [avatar sat refutation 185,283,298,300,314,362]
% SZS output end Proof for 2644563476130826041900266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not happy is not curious or kind and vice versa. Everyone who is either not strong or not rich is curious. Everyone who is not generous is not tall and vice versa. If lucy is not funny then someone is both not old and not tall. If someone is either patient or creative then someone is both tall and not kind and vice versa. If susan is both not tall and humble then mary is old and vice versa. Everyone who is not calm or not patient is either old or curious. If paul is either patient or not funny then someone is both happy and calm. Everyone who is kind or humble is either not wise or not calm and vice versa. Everyone who is happy is both patient and not creative and vice versa. Everyone who is not brave is either rich or happy. If someone is not curious or not kind then mary is both not tall and kind and vice versa. If someone is either not creative or creative then susan is both curious and not strong and vice versa. Everyone who is either quiet or tall is both not kind and not funny and vice versa. If paul is both not creative and not funny then someone is both tall and kind. If someone is either not quiet or strong then alice is not brave. John is either not happy or creative. Someone is not calm. Someone is brave. Someone is both not patient and brave. Someone is both generous and quiet. John is both not tall and not generous. Someone is not tall or old. Someone is either not wise or not patient. | Mary is kind. | entailment | (![X]:((~tall(X)<~>~happy(X))<=>(~curious(X)|kind(X))))&
(![X]:((~strong(X)<~>~rich(X))=>curious(X)))&
(![X]:(~generous(X)<=>~tall(X)))&
((~funny(lucy))=>(?[X]:((~old(X)&~tall(X)))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((tall(X)&~kind(X)))))&
(((~tall(susan)&humble(susan)))<=>(old(mary)))&
(![X]:((~calm(X)|~patient(X))=>(old(X)<~>curious(X))))&
(((patient(paul)<~>~funny(paul)))=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((kind(X)|humble(X))<=>(~wise(X)<~>~calm(X))))&
(![X]:(happy(X)<=>(patient(X)&~creative(X))))&
(![X]:(~brave(X)=>(rich(X)<~>happy(X))))&
((?[X]:((~curious(X)|~kind(X))))<=>((~tall(mary)&kind(mary))))&
((?[X]:((~creative(X)<~>creative(X))))<=>((curious(susan)&~strong(susan))))&
(![X]:((quiet(X)<~>tall(X))<=>(~kind(X)&~funny(X))))&
(((~creative(paul)&~funny(paul)))=>(?[X]:((tall(X)&kind(X)))))&
((?[X]:((~quiet(X)<~>strong(X))))=>(~brave(alice)))&
((~happy(john)<~>creative(john)))&
(?[X]:(~calm(X)))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:((generous(X)&quiet(X))))&
((~tall(john)&~generous(john)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((~wise(X)<~>~patient(X)))) | kind(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4312105686397984249300926
% SZS output start Proof for 4312105686397984249300926
12. ? [X0] : (~kind(X0) | ~curious(X0)) <=> (kind(mary) & ~tall(mary)) [input p11]
25. ~kind(mary) [input hypothesis]
57. (? [X0] : (~kind(X0) | ~curious(X0)) | (~kind(mary) | tall(mary))) & ((kind(mary) & ~tall(mary)) | ! [X0] : (kind(X0) & curious(X0))) [nnf transformation 12]
58. (? [X0] : (~kind(X0) | ~curious(X0)) | ~kind(mary) | tall(mary)) & ((kind(mary) & ~tall(mary)) | ! [X0] : (kind(X0) & curious(X0))) [flattening 57]
59. (? [X0] : (~kind(X0) | ~curious(X0)) | ~kind(mary) | tall(mary)) & ((kind(mary) & ~tall(mary)) | ! [X1] : (kind(X1) & curious(X1))) [rectify 58]
60. ? [X0] : (~kind(X0) | ~curious(X0)) => (~kind(sK4) | ~curious(sK4)) [choice axiom]
61. ((~kind(sK4) | ~curious(sK4)) | ~kind(mary) | tall(mary)) & ((kind(mary) & ~tall(mary)) | ! [X1] : (kind(X1) & curious(X1))) [skolemisation 59,60]
129. kind(mary) | kind(X1) [cnf transformation 61]
160. ~kind(mary) [cnf transformation 25]
250. 19 <=> kind(mary) [avatar definition]
252. ~kind(mary) <- (~19) [avatar component clause 250]
263. 22 <=> ! [X1] : kind(X1) [avatar definition]
264. kind(X1) <- (22) [avatar component clause 263]
265. 22 | 19 [avatar split clause 129,250,263]
337. ~19 [avatar split clause 160,250]
340. $false <- (~19, 22) [subsumption resolution 252,264]
341. 19 | ~22 [avatar contradiction clause 340]
343. $false [avatar sat refutation 265,337,341]
% SZS output end Proof for 4312105686397984249300926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not generous is both calm and quiet.
If lucy is not creative or patient then paul is quiet or kind.
If someone is either not humble or not creative then someone is not strong and vice versa.
If someone is either not strong or quiet then someone is old and vice versa.
Everyone who is both not rich and not happy is not rich or brave.
If someone is either generous or calm then someone is not tall and vice versa.
Everyone who is humble or brave is both happy and not generous and vice versa.
Everyone who is funny is wise or not funny and vice versa.
Everyone who is both not patient and not kind is not wise.
Everyone who is wise is both curious and generous and vice versa.
If fred is either not kind or not happy then someone is kind or not strong and vice versa.
If paul is tall then susan is both not old and strong.
If someone is funny or happy then susan is not funny or not calm and vice versa.
Everyone who is both not quiet and patient is either not patient or not old and vice versa.
If susan is either not quiet or calm then fred is both patient and not funny and vice versa.
Everyone who is happy is either not strong or curious.
Someone is both not calm and happy.
Someone is both not rich and not old.
Someone is wise.
Someone is both creative and not rich.
Someone is not quiet or not tall.
Someone is both happy and strong. | Fred is wise. | entailment | (![X]:((~tall(X)&~generous(X))=>(calm(X)&quiet(X))))&
(((~creative(lucy)|patient(lucy)))=>((quiet(paul)|kind(paul))))&
((?[X]:((~humble(X)<~>~creative(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~strong(X)<~>quiet(X))))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&~happy(X))=>(~rich(X)|brave(X))))&
((?[X]:((generous(X)<~>calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((humble(X)|brave(X))<=>(happy(X)&~generous(X))))&
(![X]:(funny(X)<=>(wise(X)|~funny(X))))&
(![X]:((~patient(X)&~kind(X))=>~wise(X)))&
(![X]:(wise(X)<=>(curious(X)&generous(X))))&
(((~kind(fred)<~>~happy(fred)))<=>(?[X]:((kind(X)|~strong(X)))))&
((tall(paul))=>((~old(susan)&strong(susan))))&
((?[X]:((funny(X)|happy(X))))<=>((~funny(susan)|~calm(susan))))&
(![X]:((~quiet(X)&patient(X))<=>(~patient(X)<~>~old(X))))&
(((~quiet(susan)<~>calm(susan)))<=>((patient(fred)&~funny(fred))))&
(![X]:(happy(X)=>(~strong(X)<~>curious(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:((happy(X)&strong(X)))) | wise(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5635156050672879537388352
% SZS output start Proof for 5635156050672879537388352
8. ! [X0] : (funny(X0) <=> (~funny(X0) | wise(X0))) [input p7]
23. ~wise(fred) [input hypothesis]
54. ! [X0] : ((funny(X0) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | ~funny(X0))) [nnf transformation 8]
55. ! [X0] : ((funny(X0) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | ~funny(X0))) [flattening 54]
106. ~funny(X0) | wise(X0) | ~funny(X0) [cnf transformation 55]
108. funny(X0) | funny(X0) [cnf transformation 55]
149. ~wise(fred) [cnf transformation 23]
152. ~funny(X0) | wise(X0) [duplicate literal removal 106]
153. funny(X0) [duplicate literal removal 108]
247. wise(X0) [subsumption resolution 152,153]
327. $false [subsumption resolution 149,247]
% SZS output end Proof for 5635156050672879537388352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and brave is both not strong and quiet and vice versa. If someone is either not creative or creative then lucy is not calm. If someone is not wise then someone is not rich. Everyone who is not curious is creative or not patient and vice versa. Everyone who is old or not quiet is either not creative or not curious and vice versa. If someone is both not generous and not funny then someone is not quiet. Everyone who is quiet or not curious is both not funny and generous and vice versa. If fred is both humble and not creative then someone is brave or not curious and vice versa. If fred is generous then john is funny and vice versa. Everyone who is not strong is creative or not generous and vice versa. If someone is either kind or not old then mary is both tall and not calm. Everyone who is both strong and not old is not happy or not generous and vice versa. Everyone who is calm is not quiet. Everyone who is both happy and not creative is not quiet or generous and vice versa. Everyone who is not calm is not funny or old and vice versa. Everyone who is both generous and not happy is not wise or not generous and vice versa. Susan is quiet or creative. Paul is either not happy or funny. Lucy is both not funny and wise. Lucy is not humble or not kind. Someone is not rich or not old. Someone is either not calm or not quiet. | Paul is not funny. | contradiction | (![X]:((quiet(X)&brave(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(~calm(lucy)))&
((?[X]:(~wise(X)))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~funny(X)&generous(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((brave(X)|~curious(X)))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
(![X]:((generous(X)&~happy(X))<=>(~wise(X)|~generous(X))))&
((quiet(susan)|creative(susan)))&
((~happy(paul)<~>funny(paul)))&
((~funny(lucy)&wise(lucy)))&
((~humble(lucy)|~kind(lucy)))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((~calm(X)<~>~quiet(X)))) | ~funny(paul) | [
"p9",
"p11",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 427963282935603770620401
% SZS output start Proof for 427963282935603770620401
10. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p9]
12. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p11]
14. ! [X0] : ((~creative(X0) & happy(X0)) <=> (generous(X0) | ~quiet(X0))) [input p13]
18. ~happy(paul) <~> funny(paul) [input p17]
23. ~funny(paul) [input hypothesis]
51. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 10]
52. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 51]
54. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 12]
55. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 54]
56. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 14]
57. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | creative(X0) | ~happy(X0))) [flattening 56]
62. (~funny(paul) | happy(paul)) & (funny(paul) | ~happy(paul)) [nnf transformation 18]
96. ~strong(X0) | generous(X0) [cnf transformation 52]
101. strong(X0) | generous(X0) [cnf transformation 55]
107. happy(X0) | ~generous(X0) [cnf transformation 57]
119. funny(paul) | ~happy(paul) [cnf transformation 62]
126. ~funny(paul) [cnf transformation 23]
202. generous(X0) [subsumption resolution 101,96]
206. happy(X0) [subsumption resolution 107,202]
209. funny(paul) [subsumption resolution 119,206]
228. $false [subsumption resolution 126,209]
% SZS output end Proof for 427963282935603770620401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not creative and old then john is old. If mary is both not old and not strong then someone is funny and vice versa. If paul is not creative then someone is old or calm and vice versa. Everyone who is both not rich and not quiet is not patient. If john is either humble or kind then mary is both humble and patient and vice versa. If someone is not quiet then alice is wise or not calm and vice versa. Everyone who is not funny or not old is strong or not kind. Everyone who is wise or brave is not rich or not curious and vice versa. If someone is brave then someone is either not kind or brave. If someone is strong or not brave then someone is either happy or calm and vice versa. If alice is either humble or not happy then fred is not strong. Everyone who is calm is both humble and not brave and vice versa. Everyone who is both funny and happy is both creative and tall and vice versa. Everyone who is curious is both not creative and wise. Everyone who is happy is not curious or not tall and vice versa. Everyone who is creative or not patient is curious or not wise. John is either not curious or not old. John is either not tall or not quiet. Fred is both not curious and funny. Someone is either wise or tall. Susan is patient. John is both tall and wise. Lucy is not old. Someone is either not quiet or not creative. | John is creative. | contradiction | (((~creative(john)&old(john)))=>(old(john)))&
(((~old(mary)&~strong(mary)))<=>(?[X]:(funny(X))))&
((~creative(paul))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~rich(X)&~quiet(X))=>~patient(X)))&
(((humble(john)<~>kind(john)))<=>((humble(mary)&patient(mary))))&
((?[X]:(~quiet(X)))<=>((wise(alice)|~calm(alice))))&
(![X]:((~funny(X)|~old(X))=>(strong(X)|~kind(X))))&
(![X]:((wise(X)|brave(X))<=>(~rich(X)|~curious(X))))&
((?[X]:(brave(X)))=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:((strong(X)|~brave(X))))<=>(?[X]:((happy(X)<~>calm(X)))))&
(((humble(alice)<~>~happy(alice)))=>(~strong(fred)))&
(![X]:(calm(X)<=>(humble(X)&~brave(X))))&
(![X]:((funny(X)&happy(X))<=>(creative(X)&tall(X))))&
(![X]:(curious(X)=>(~creative(X)&wise(X))))&
(![X]:(happy(X)<=>(~curious(X)|~tall(X))))&
(![X]:((creative(X)|~patient(X))=>(curious(X)|~wise(X))))&
((~curious(john)<~>~old(john)))&
((~tall(john)<~>~quiet(john)))&
((~curious(fred)&funny(fred)))&
(?[X]:((wise(X)<~>tall(X))))&
(patient(susan))&
((tall(john)&wise(john)))&
(~old(lucy))&
(?[X]:((~quiet(X)<~>~creative(X)))) | creative(john) | [
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5650409172376964170365060
% SZS output start Proof for 5650409172376964170365060
14. ! [X0] : (curious(X0) => (wise(X0) & ~creative(X0))) [input p13]
16. ! [X0] : ((~patient(X0) | creative(X0)) => (~wise(X0) | curious(X0))) [input p15]
22. wise(john) & tall(john) [input p21]
25. creative(john) [input hypothesis]
36. ! [X0] : ((wise(X0) & ~creative(X0)) | ~curious(X0)) [ennf transformation 14]
37. ! [X0] : ((~wise(X0) | curious(X0)) | (patient(X0) & ~creative(X0))) [ennf transformation 16]
38. ! [X0] : (~wise(X0) | curious(X0) | (patient(X0) & ~creative(X0))) [flattening 37]
121. ~curious(X0) | ~creative(X0) [cnf transformation 36]
126. ~wise(X0) | curious(X0) | ~creative(X0) [cnf transformation 38]
138. wise(john) [cnf transformation 22]
142. creative(john) [cnf transformation 25]
283. ~wise(X0) | ~creative(X0) [subsumption resolution 126,121]
331. ~creative(john) [resolution 283,138]
333. $false [subsumption resolution 331,142]
% SZS output end Proof for 5650409172376964170365060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not tall or not brave then mary is kind and vice versa.
Everyone who is not happy is strong and vice versa.
If someone is not brave or old then someone is either generous or strong and vice versa.
Everyone who is humble is both happy and not wise and vice versa.
Everyone who is either not kind or brave is both not calm and old and vice versa.
If someone is both generous and not wise then john is not strong.
Everyone who is not strong is not quiet and vice versa.
Everyone who is generous is either not kind or old and vice versa.
If susan is curious or humble then someone is tall or kind and vice versa.
Everyone who is quiet is either not kind or creative and vice versa.
If someone is either not curious or humble then someone is both wise and patient and vice versa.
If someone is either rich or calm then someone is not creative or quiet.
Everyone who is both generous and not strong is both calm and brave.
Everyone who is either old or not kind is tall and vice versa.
If someone is either old or curious then someone is not happy and vice versa.
Everyone who is both not strong and funny is not humble and vice versa.
Someone is either brave or not humble.
Paul is not old or wise.
Someone is both not brave and funny.
Susan is not tall or curious.
Someone is rich or quiet.
Fred is either wise or not calm.
Someone is not quiet or not generous. | Mary is not generous. | neutral | (((~tall(paul)<~>~brave(paul)))<=>(kind(mary)))&
(![X]:(~happy(X)<=>strong(X)))&
((?[X]:((~brave(X)|old(X))))<=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:(humble(X)<=>(happy(X)&~wise(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~calm(X)&old(X))))&
((?[X]:((generous(X)&~wise(X))))=>(~strong(john)))&
(![X]:(~strong(X)<=>~quiet(X)))&
(![X]:(generous(X)<=>(~kind(X)<~>old(X))))&
(((curious(susan)|humble(susan)))<=>(?[X]:((tall(X)|kind(X)))))&
(![X]:(quiet(X)<=>(~kind(X)<~>creative(X))))&
((?[X]:((~curious(X)<~>humble(X))))<=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((rich(X)<~>calm(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:((generous(X)&~strong(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)<~>~kind(X))<=>tall(X)))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)&funny(X))<=>~humble(X)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~old(paul)|wise(paul)))&
(?[X]:((~brave(X)&funny(X))))&
((~tall(susan)|curious(susan)))&
(?[X]:((rich(X)|quiet(X))))&
((wise(fred)<~>~calm(fred)))&
(?[X]:((~quiet(X)|~generous(X)))) | ~generous(mary) | [] | null | 0 |
Everyone who is both not strong and humble is either not kind or calm and vice versa.
If john is not generous then lucy is both kind and curious and vice versa.
Everyone who is either not curious or not humble is both not creative and not humble and vice versa.
If someone is either not tall or not strong then susan is both old and not generous and vice versa.
Everyone who is both rich and brave is both not rich and brave.
Everyone who is both brave and strong is creative or not patient and vice versa.
Everyone who is calm is both not humble and kind.
Everyone who is not funny or tall is tall and vice versa.
If fred is generous then john is either patient or calm and vice versa.
Everyone who is either rich or not curious is either not kind or not strong.
If lucy is both not rich and rich then john is brave and vice versa.
If someone is not quiet or rich then someone is either not wise or kind.
If someone is both not wise and not quiet then someone is not wise or old.
Everyone who is either kind or old is not brave.
If someone is either rich or generous then susan is tall.
If someone is either strong or generous then someone is not wise or strong and vice versa.
Lucy is wise.
Someone is both not tall and happy.
Someone is either not humble or not kind.
Someone is not wise or old.
Lucy is either strong or old.
Someone is either not rich or not curious.
Someone is curious. | John is brave. | contradiction | (![X]:((~strong(X)&humble(X))<=>(~kind(X)<~>calm(X))))&
((~generous(john))<=>((kind(lucy)&curious(lucy))))&
(![X]:((~curious(X)<~>~humble(X))<=>(~creative(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((old(susan)&~generous(susan))))&
(![X]:((rich(X)&brave(X))=>(~rich(X)&brave(X))))&
(![X]:((brave(X)&strong(X))<=>(creative(X)|~patient(X))))&
(![X]:(calm(X)=>(~humble(X)&kind(X))))&
(![X]:((~funny(X)|tall(X))<=>tall(X)))&
((generous(fred))<=>((patient(john)<~>calm(john))))&
(![X]:((rich(X)<~>~curious(X))=>(~kind(X)<~>~strong(X))))&
(((~rich(lucy)&rich(lucy)))<=>(brave(john)))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:((~wise(X)<~>kind(X)))))&
((?[X]:((~wise(X)&~quiet(X))))=>(?[X]:((~wise(X)|old(X)))))&
(![X]:((kind(X)<~>old(X))=>~brave(X)))&
((?[X]:((rich(X)<~>generous(X))))=>(tall(susan)))&
((?[X]:((strong(X)<~>generous(X))))<=>(?[X]:((~wise(X)|strong(X)))))&
(wise(lucy))&
(?[X]:((~tall(X)&happy(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((~wise(X)|old(X))))&
((strong(lucy)<~>old(lucy)))&
(?[X]:((~rich(X)<~>~curious(X))))&
(?[X]:(curious(X))) | brave(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6681503539322480064543351
% SZS output start Proof for 6681503539322480064543351
11. (rich(lucy) & ~rich(lucy)) <=> brave(john) [input p10]
24. brave(john) [input hypothesis]
55. ((rich(lucy) & ~rich(lucy)) | ~brave(john)) & (brave(john) | (~rich(lucy) | rich(lucy))) [nnf transformation 11]
56. ((rich(lucy) & ~rich(lucy)) | ~brave(john)) & (brave(john) | ~rich(lucy) | rich(lucy)) [flattening 55]
123. ~rich(lucy) | ~brave(john) [cnf transformation 56]
124. rich(lucy) | ~brave(john) [cnf transformation 56]
147. brave(john) [cnf transformation 24]
211. 13 <=> brave(john) [avatar definition]
215. 14 <=> rich(lucy) [avatar definition]
218. ~13 | 14 [avatar split clause 124,215,211]
219. ~13 | ~14 [avatar split clause 123,215,211]
318. 13 [avatar split clause 147,211]
319. $false [avatar sat refutation 218,219,318]
% SZS output end Proof for 6681503539322480064543351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either calm or not curious.
If susan is not strong then someone is either not generous or old and vice versa.
If lucy is either not strong or not curious then someone is funny and vice versa.
Everyone who is not rich is kind and vice versa.
If paul is both not calm and happy then mary is either not calm or humble and vice versa.
If someone is either not patient or strong then someone is not brave.
If fred is either brave or kind then someone is either funny or patient.
If someone is both quiet and not patient then someone is either not calm or not old and vice versa.
If someone is patient or curious then someone is not curious and vice versa.
If someone is either kind or not rich then someone is either tall or humble.
If someone is not generous or not strong then fred is either patient or curious.
If someone is not happy or kind then someone is either not strong or humble and vice versa.
Everyone who is both not generous and tall is kind or not brave and vice versa.
If john is either not patient or curious then lucy is either not curious or not creative.
Everyone who is rich or not brave is both happy and generous.
If fred is not funny or not kind then mary is either not strong or not rich and vice versa.
Mary is both not rich and humble.
Someone is not happy or happy.
Lucy is old.
Alice is both not happy and quiet.
Fred is either not funny or not calm.
Someone is not tall or not creative. | Susan is generous. | neutral | (![X]:(~kind(X)=>(calm(X)<~>~curious(X))))&
((~strong(susan))<=>(?[X]:((~generous(X)<~>old(X)))))&
(((~strong(lucy)<~>~curious(lucy)))<=>(?[X]:(funny(X))))&
(![X]:(~rich(X)<=>kind(X)))&
(((~calm(paul)&happy(paul)))<=>((~calm(mary)<~>humble(mary))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~brave(X))))&
(((brave(fred)<~>kind(fred)))=>(?[X]:((funny(X)<~>patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))<=>(?[X]:((~calm(X)<~>~old(X)))))&
((?[X]:((patient(X)|curious(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((kind(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>humble(X)))))&
((?[X]:((~generous(X)|~strong(X))))=>((patient(fred)<~>curious(fred))))&
((?[X]:((~happy(X)|kind(X))))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:((~generous(X)&tall(X))<=>(kind(X)|~brave(X))))&
(((~patient(john)<~>curious(john)))=>((~curious(lucy)<~>~creative(lucy))))&
(![X]:((rich(X)|~brave(X))=>(happy(X)&generous(X))))&
(((~funny(fred)|~kind(fred)))<=>((~strong(mary)<~>~rich(mary))))&
((~rich(mary)&humble(mary)))&
(?[X]:((~happy(X)|happy(X))))&
(old(lucy))&
((~happy(alice)&quiet(alice)))&
((~funny(fred)<~>~calm(fred)))&
(?[X]:((~tall(X)|~creative(X)))) | generous(susan) | [] | null | 0 |
If lucy is not tall then lucy is either not humble or calm and vice versa.
Everyone who is patient is not creative or not patient and vice versa.
Everyone who is either not happy or kind is kind and vice versa.
If someone is either happy or not old then someone is either not old or not brave and vice versa.
Everyone who is both not rich and tall is both kind and not quiet.
Everyone who is both wise and not happy is either curious or creative.
Everyone who is either rich or not happy is either not old or brave.
If someone is not wise then lucy is either kind or curious and vice versa.
If someone is both not funny and not happy then someone is not curious or quiet and vice versa.
Everyone who is not happy or not calm is not quiet and vice versa.
Everyone who is either funny or not old is both not tall and not quiet and vice versa.
If someone is either old or wise then alice is both wise and creative.
Everyone who is both strong and not brave is not strong and vice versa.
Everyone who is either not generous or calm is not generous and vice versa.
If someone is both rich and generous then lucy is not rich.
Everyone who is both not rich and not old is wise or humble.
Someone is not strong or not creative.
John is not rich.
Lucy is not generous.
Susan is both curious and not humble.
Someone is either humble or kind. | Alice is not calm. | entailment | ((~tall(lucy))<=>((~humble(lucy)<~>calm(lucy))))&
(![X]:(patient(X)<=>(~creative(X)|~patient(X))))&
(![X]:((~happy(X)<~>kind(X))<=>kind(X)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:((~rich(X)&tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((wise(X)&~happy(X))=>(curious(X)<~>creative(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~old(X)<~>brave(X))))&
((?[X]:(~wise(X)))<=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~old(X))<=>(~tall(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>((wise(alice)&creative(alice))))&
(![X]:((strong(X)&~brave(X))<=>~strong(X)))&
(![X]:((~generous(X)<~>calm(X))<=>~generous(X)))&
((?[X]:((rich(X)&generous(X))))=>(~rich(lucy)))&
(![X]:((~rich(X)&~old(X))=>(wise(X)|humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
(~rich(john))&
(~generous(lucy))&
((curious(susan)&~humble(susan)))&
(?[X]:((humble(X)<~>kind(X)))) | ~calm(alice) | [
"p2",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7159774928757829586256603
% SZS output start Proof for 7159774928757829586256603
3. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> kind(X0)) [input p2]
9. ? [X0] : (~happy(X0) & ~funny(X0)) <=> ? [X0] : (quiet(X0) | ~curious(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | ~happy(X0)) <=> ~quiet(X0)) [input p9]
22. calm(alice) [input hypothesis]
24. ? [X0] : (~happy(X0) & ~funny(X0)) <=> ? [X1] : (quiet(X1) | ~curious(X1)) [rectify 9]
37. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~kind(X0)) & (kind(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 3]
49. (? [X0] : (~happy(X0) & ~funny(X0)) | ! [X1] : (~quiet(X1) & curious(X1))) & (? [X1] : (quiet(X1) | ~curious(X1)) | ! [X0] : (happy(X0) | funny(X0))) [nnf transformation 24]
50. (? [X0] : (~happy(X0) & ~funny(X0)) | ! [X1] : (~quiet(X1) & curious(X1))) & (? [X2] : (quiet(X2) | ~curious(X2)) | ! [X3] : (happy(X3) | funny(X3))) [rectify 49]
51. ? [X0] : (~happy(X0) & ~funny(X0)) => (~happy(sK3) & ~funny(sK3)) [choice axiom]
52. ? [X2] : (quiet(X2) | ~curious(X2)) => (quiet(sK4) | ~curious(sK4)) [choice axiom]
53. ((~happy(sK3) & ~funny(sK3)) | ! [X1] : (~quiet(X1) & curious(X1))) & ((quiet(sK4) | ~curious(sK4)) | ! [X3] : (happy(X3) | funny(X3))) [skolemisation 50,52,51]
54. ! [X0] : (((~calm(X0) | ~happy(X0)) | quiet(X0)) & (~quiet(X0) | (calm(X0) & happy(X0)))) [nnf transformation 10]
55. ! [X0] : ((~calm(X0) | ~happy(X0) | quiet(X0)) & (~quiet(X0) | (calm(X0) & happy(X0)))) [flattening 54]
74. kind(X0) | kind(X0) | happy(X0) [cnf transformation 37]
77. ~kind(X0) | happy(X0) | ~kind(X0) [cnf transformation 37]
102. ~happy(sK3) | ~quiet(X1) [cnf transformation 53]
105. ~calm(X0) | ~happy(X0) | quiet(X0) [cnf transformation 55]
132. calm(alice) [cnf transformation 22]
137. kind(X0) | happy(X0) [duplicate literal removal 74]
138. ~kind(X0) | happy(X0) [duplicate literal removal 77]
158. happy(X0) [subsumption resolution 137,138]
209. ~quiet(X1) [subsumption resolution 102,158]
211. ~calm(X0) | quiet(X0) [subsumption resolution 105,158]
212. ~calm(X0) [subsumption resolution 211,209]
237. $false [subsumption resolution 132,212]
% SZS output end Proof for 7159774928757829586256603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not kind is quiet and vice versa. If someone is not generous then mary is both calm and old and vice versa. If someone is not calm then paul is not old. Everyone who is both patient and tall is both humble and creative. Everyone who is not kind is either brave or not humble. Everyone who is happy or creative is humble. If fred is kind then someone is humble or curious. Everyone who is not rich is not funny or funny. If john is both not quiet and calm then someone is both not patient and calm. Everyone who is either not patient or not kind is not tall or not kind and vice versa. If paul is creative or not old then mary is either not rich or humble. Everyone who is not patient is calm or not old and vice versa. If someone is not humble or not funny then susan is not old and vice versa. Everyone who is either happy or wise is both generous and calm and vice versa. Everyone who is both not rich and strong is either calm or strong and vice versa. Lucy is not wise or not curious. Susan is strong. Fred is both funny and not kind. Mary is not humble. Someone is not rich or not tall. Susan is not tall or humble. Someone is rich or not funny. | Mary is happy. | contradiction | (![X]:((humble(X)&~kind(X))<=>quiet(X)))&
((?[X]:(~generous(X)))<=>((calm(mary)&old(mary))))&
((?[X]:(~calm(X)))=>(~old(paul)))&
(![X]:((patient(X)&tall(X))=>(humble(X)&creative(X))))&
(![X]:(~kind(X)=>(brave(X)<~>~humble(X))))&
(![X]:((happy(X)|creative(X))=>humble(X)))&
((kind(fred))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:(~rich(X)=>(~funny(X)|funny(X))))&
(((~quiet(john)&calm(john)))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>(~tall(X)|~kind(X))))&
(((creative(paul)|~old(paul)))=>((~rich(mary)<~>humble(mary))))&
(![X]:(~patient(X)<=>(calm(X)|~old(X))))&
((?[X]:((~humble(X)|~funny(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>wise(X))<=>(generous(X)&calm(X))))&
(![X]:((~rich(X)&strong(X))<=>(calm(X)<~>strong(X))))&
((~wise(lucy)|~curious(lucy)))&
(strong(susan))&
((funny(fred)&~kind(fred)))&
(~humble(mary))&
(?[X]:((~rich(X)|~tall(X))))&
((~tall(susan)|humble(susan)))&
(?[X]:((rich(X)|~funny(X)))) | happy(mary) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4374289216052396033846241
% SZS output start Proof for 4374289216052396033846241
6. ! [X0] : ((creative(X0) | happy(X0)) => humble(X0)) [input p5]
19. ~humble(mary) [input p18]
23. happy(mary) [input hypothesis]
30. ! [X0] : (humble(X0) | (~creative(X0) & ~happy(X0))) [ennf transformation 6]
74. ~happy(X0) | humble(X0) [cnf transformation 30]
112. ~humble(mary) [cnf transformation 19]
116. happy(mary) [cnf transformation 23]
184. 15 <=> humble(mary) [avatar definition]
186. ~humble(mary) <- (~15) [avatar component clause 184]
227. ~15 [avatar split clause 112,184]
255. humble(mary) [resolution 74,116]
256. $false <- (~15) [subsumption resolution 255,186]
257. 15 [avatar contradiction clause 256]
258. $false [avatar sat refutation 227,257]
% SZS output end Proof for 4374289216052396033846241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not strong is either not creative or not old and vice versa.
If someone is either calm or not patient then susan is both not strong and not patient and vice versa.
Everyone who is not funny is either not curious or not rich and vice versa.
Everyone who is either not old or curious is either wise or not kind and vice versa.
If mary is tall then john is either funny or not quiet.
If someone is either not quiet or funny then fred is either old or not patient.
Everyone who is funny or kind is humble or not rich and vice versa.
Everyone who is either patient or not creative is not wise and vice versa.
Everyone who is either happy or patient is either not brave or not calm.
If someone is not curious then lucy is both not strong and strong and vice versa.
Everyone who is tall is not kind or not brave and vice versa.
If someone is brave or not brave then mary is either not rich or tall.
Everyone who is either not humble or not rich is both not calm and quiet.
Everyone who is both tall and not kind is wise or brave.
If alice is both wise and rich then john is wise and vice versa.
Everyone who is both not calm and calm is either old or patient.
Someone is strong.
Someone is not tall or old.
John is both not calm and not tall.
John is generous.
Someone is either not kind or not old.
Lucy is either patient or not funny.
Susan is either not rich or not generous.
Lucy is generous or happy. | John is not kind. | contradiction | (![X]:((generous(X)<~>~strong(X))<=>(~creative(X)<~>~old(X))))&
((?[X]:((calm(X)<~>~patient(X))))<=>((~strong(susan)&~patient(susan))))&
(![X]:(~funny(X)<=>(~curious(X)<~>~rich(X))))&
(![X]:((~old(X)<~>curious(X))<=>(wise(X)<~>~kind(X))))&
((tall(mary))=>((funny(john)<~>~quiet(john))))&
((?[X]:((~quiet(X)<~>funny(X))))=>((old(fred)<~>~patient(fred))))&
(![X]:((funny(X)|kind(X))<=>(humble(X)|~rich(X))))&
(![X]:((patient(X)<~>~creative(X))<=>~wise(X)))&
(![X]:((happy(X)<~>patient(X))=>(~brave(X)<~>~calm(X))))&
((?[X]:(~curious(X)))<=>((~strong(lucy)&strong(lucy))))&
(![X]:(tall(X)<=>(~kind(X)|~brave(X))))&
((?[X]:((brave(X)|~brave(X))))=>((~rich(mary)<~>tall(mary))))&
(![X]:((~humble(X)<~>~rich(X))=>(~calm(X)&quiet(X))))&
(![X]:((tall(X)&~kind(X))=>(wise(X)|brave(X))))&
(((wise(alice)&rich(alice)))<=>(wise(john)))&
(![X]:((~calm(X)&calm(X))=>(old(X)<~>patient(X))))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)|old(X))))&
((~calm(john)&~tall(john)))&
(generous(john))&
(?[X]:((~kind(X)<~>~old(X))))&
((patient(lucy)<~>~funny(lucy)))&
((~rich(susan)<~>~generous(susan)))&
((generous(lucy)|happy(lucy))) | ~kind(john) | [
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5826873934816748887829452
% SZS output start Proof for 5826873934816748887829452
11. ! [X0] : (tall(X0) <=> (~brave(X0) | ~kind(X0))) [input p10]
19. ~tall(john) & ~calm(john) [input p18]
25. ~kind(john) [input hypothesis]
54. ! [X0] : ((tall(X0) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | ~tall(X0))) [nnf transformation 11]
55. ! [X0] : ((tall(X0) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~tall(X0))) [flattening 54]
118. tall(X0) | kind(X0) [cnf transformation 55]
137. ~tall(john) [cnf transformation 19]
146. ~kind(john) [cnf transformation 25]
294. kind(john) [resolution 118,137]
297. $false [subsumption resolution 294,146]
% SZS output end Proof for 5826873934816748887829452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or not tall then someone is either rich or wise.
Everyone who is creative or not rich is happy or strong and vice versa.
Everyone who is both not humble and strong is either strong or patient and vice versa.
If someone is either generous or curious then john is both quiet and generous.
If someone is not rich or not wise then susan is either curious or tall.
If lucy is not quiet or old then john is both strong and not curious and vice versa.
If susan is both not strong and strong then susan is both funny and tall.
Everyone who is not generous or curious is humble.
If someone is both not strong and not brave then susan is either happy or not patient and vice versa.
If alice is either not curious or not kind then someone is both humble and not calm.
Everyone who is either old or not brave is patient or creative.
If someone is not wise or not old then mary is both not tall and not wise.
Everyone who is either old or brave is tall or funny.
Everyone who is both wise and not brave is generous or tall and vice versa.
If someone is happy or not rich then someone is either not kind or strong and vice versa.
Everyone who is both generous and not creative is generous and vice versa.
Mary is either creative or not wise.
Susan is both not generous and not calm.
Susan is both not generous and not wise.
Mary is either not happy or humble.
Someone is both not patient and rich.
Someone is not kind.
John is not strong.
Paul is both not brave and old. | Susan is not tall. | entailment | ((?[X]:((~wise(X)<~>~tall(X))))=>(?[X]:((rich(X)<~>wise(X)))))&
(![X]:((creative(X)|~rich(X))<=>(happy(X)|strong(X))))&
(![X]:((~humble(X)&strong(X))<=>(strong(X)<~>patient(X))))&
((?[X]:((generous(X)<~>curious(X))))=>((quiet(john)&generous(john))))&
((?[X]:((~rich(X)|~wise(X))))=>((curious(susan)<~>tall(susan))))&
(((~quiet(lucy)|old(lucy)))<=>((strong(john)&~curious(john))))&
(((~strong(susan)&strong(susan)))=>((funny(susan)&tall(susan))))&
(![X]:((~generous(X)|curious(X))=>humble(X)))&
((?[X]:((~strong(X)&~brave(X))))<=>((happy(susan)<~>~patient(susan))))&
(((~curious(alice)<~>~kind(alice)))=>(?[X]:((humble(X)&~calm(X)))))&
(![X]:((old(X)<~>~brave(X))=>(patient(X)|creative(X))))&
((?[X]:((~wise(X)|~old(X))))=>((~tall(mary)&~wise(mary))))&
(![X]:((old(X)<~>brave(X))=>(tall(X)|funny(X))))&
(![X]:((wise(X)&~brave(X))<=>(generous(X)|tall(X))))&
((?[X]:((happy(X)|~rich(X))))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:((generous(X)&~creative(X))<=>generous(X)))&
((creative(mary)<~>~wise(mary)))&
((~generous(susan)&~calm(susan)))&
((~generous(susan)&~wise(susan)))&
((~happy(mary)<~>humble(mary)))&
(?[X]:((~patient(X)&rich(X))))&
(?[X]:(~kind(X)))&
(~strong(john))&
((~brave(paul)&old(paul))) | ~tall(susan) | [
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5742040801743863546256078
% SZS output start Proof for 5742040801743863546256078
14. ! [X0] : ((~brave(X0) & wise(X0)) <=> (tall(X0) | generous(X0))) [input p13]
19. ~wise(susan) & ~generous(susan) [input p18]
25. tall(susan) [input hypothesis]
62. ! [X0] : (((~brave(X0) & wise(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (brave(X0) | ~wise(X0)))) [nnf transformation 14]
63. ! [X0] : (((~brave(X0) & wise(X0)) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | brave(X0) | ~wise(X0))) [flattening 62]
123. wise(X0) | ~tall(X0) [cnf transformation 63]
139. ~wise(susan) [cnf transformation 19]
148. tall(susan) [cnf transformation 25]
164. 4 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
165. ~tall(X1) | wise(X1) <- (4) [avatar component clause 164]
196. 11 <=> tall(susan) [avatar definition]
197. tall(susan) <- (11) [avatar component clause 196]
281. 4 [avatar split clause 123,164]
330. 11 [avatar split clause 148,196]
334. wise(susan) <- (4, 11) [resolution 165,197]
335. $false <- (4, 11) [subsumption resolution 334,139]
336. ~4 | ~11 [avatar contradiction clause 335]
337. $false [avatar sat refutation 281,330,336]
% SZS output end Proof for 5742040801743863546256078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is both not kind and wise and vice versa. If someone is happy then paul is both happy and not patient. If someone is both not patient and not curious then lucy is both not brave and quiet and vice versa. Everyone who is either wise or brave is not humble or brave and vice versa. Everyone who is both curious and humble is both not happy and brave. Everyone who is both not humble and not happy is not brave and vice versa. Everyone who is calm or not old is calm or not rich and vice versa. Everyone who is either funny or wise is either not strong or not calm and vice versa. Everyone who is not old is not happy or funny. If someone is either not old or not patient then someone is not wise. Everyone who is curious is not kind and vice versa. Everyone who is wise is both not rich and patient. Everyone who is rich or not happy is both not quiet and not curious. If someone is not kind then john is not old and vice versa. Everyone who is humble or calm is not funny or happy and vice versa. Everyone who is brave or kind is rich and vice versa. Paul is not quiet or brave. Fred is both not curious and generous. Someone is wise or not strong. Mary is either not old or not happy. Someone is humble. | Paul is not humble. | contradiction | (![X]:((~rich(X)&~generous(X))<=>(~kind(X)&wise(X))))&
((?[X]:(happy(X)))=>((happy(paul)&~patient(paul))))&
((?[X]:((~patient(X)&~curious(X))))<=>((~brave(lucy)&quiet(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)|brave(X))))&
(![X]:((curious(X)&humble(X))=>(~happy(X)&brave(X))))&
(![X]:((~humble(X)&~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|~old(X))<=>(calm(X)|~rich(X))))&
(![X]:((funny(X)<~>wise(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:(~old(X)=>(~happy(X)|funny(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:(~wise(X))))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:(wise(X)=>(~rich(X)&patient(X))))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(~old(john)))&
(![X]:((humble(X)|calm(X))<=>(~funny(X)|happy(X))))&
(![X]:((brave(X)|kind(X))<=>rich(X)))&
((~quiet(paul)|brave(paul)))&
((~curious(fred)&generous(fred)))&
(?[X]:((wise(X)|~strong(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:(humble(X))) | ~humble(paul) | [
"p1",
"p2",
"p3",
"p5",
"p10",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5763435867005996874223734
% SZS output start Proof for 5763435867005996874223734
2. ? [X0] : happy(X0) => (~patient(paul) & happy(paul)) [input p1]
3. ? [X0] : (~curious(X0) & ~patient(X0)) <=> (quiet(lucy) & ~brave(lucy)) [input p2]
4. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (brave(X0) | ~humble(X0))) [input p3]
6. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> ~brave(X0)) [input p5]
11. ! [X0] : (curious(X0) <=> ~kind(X0)) [input p10]
12. ! [X0] : (wise(X0) => (patient(X0) & ~rich(X0))) [input p11]
13. ! [X0] : ((~happy(X0) | rich(X0)) => (~curious(X0) & ~quiet(X0))) [input p12]
16. ! [X0] : ((kind(X0) | brave(X0)) <=> rich(X0)) [input p15]
22. ~humble(paul) [input hypothesis]
24. (~patient(paul) & happy(paul)) | ! [X0] : ~happy(X0) [ennf transformation 2]
30. ! [X0] : ((patient(X0) & ~rich(X0)) | ~wise(X0)) [ennf transformation 12]
31. ! [X0] : ((~curious(X0) & ~quiet(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 13]
34. (? [X0] : (~curious(X0) & ~patient(X0)) | (~quiet(lucy) | brave(lucy))) & ((quiet(lucy) & ~brave(lucy)) | ! [X0] : (curious(X0) | patient(X0))) [nnf transformation 3]
35. (? [X0] : (~curious(X0) & ~patient(X0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X0] : (curious(X0) | patient(X0))) [flattening 34]
36. (? [X0] : (~curious(X0) & ~patient(X0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X1] : (curious(X1) | patient(X1))) [rectify 35]
37. ? [X0] : (~curious(X0) & ~patient(X0)) => (~curious(sK0) & ~patient(sK0)) [choice axiom]
38. ((~curious(sK0) & ~patient(sK0)) | ~quiet(lucy) | brave(lucy)) & ((quiet(lucy) & ~brave(lucy)) | ! [X1] : (curious(X1) | patient(X1))) [skolemisation 36,37]
39. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | (~brave(X0) & humble(X0))) & ((brave(X0) | ~humble(X0)) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [nnf transformation 4]
40. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | (~brave(X0) & humble(X0))) & (brave(X0) | ~humble(X0) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [flattening 39]
41. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (happy(X0) | humble(X0)))) [nnf transformation 6]
42. ! [X0] : (((~happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | happy(X0) | humble(X0))) [flattening 41]
50. ! [X0] : ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0))) [nnf transformation 11]
57. ! [X0] : (((kind(X0) | brave(X0)) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [nnf transformation 16]
58. ! [X0] : ((kind(X0) | brave(X0) | ~rich(X0)) & (rich(X0) | (~kind(X0) & ~brave(X0)))) [flattening 57]
68. happy(paul) | ~happy(X0) [cnf transformation 24]
69. ~patient(paul) | ~happy(X0) [cnf transformation 24]
70. ~brave(lucy) | curious(X1) | patient(X1) [cnf transformation 38]
71. quiet(lucy) | curious(X1) | patient(X1) [cnf transformation 38]
76. humble(X0) | wise(X0) | brave(X0) [cnf transformation 40]
82. ~brave(X0) | happy(X0) | humble(X0) [cnf transformation 42]
83. ~humble(X0) | brave(X0) [cnf transformation 42]
84. ~happy(X0) | brave(X0) [cnf transformation 42]
101. curious(X0) | kind(X0) [cnf transformation 50]
102. ~wise(X0) | ~rich(X0) [cnf transformation 30]
105. ~quiet(X0) | happy(X0) [cnf transformation 31]
106. ~curious(X0) | ~rich(X0) [cnf transformation 31]
107. ~curious(X0) | happy(X0) [cnf transformation 31]
114. ~brave(X0) | rich(X0) [cnf transformation 58]
115. ~kind(X0) | rich(X0) [cnf transformation 58]
124. ~humble(paul) [cnf transformation 22]
128. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
129. ~happy(X0) <- (1) [avatar component clause 128]
131. 2 <=> patient(paul) [avatar definition]
134. 1 | ~2 [avatar split clause 69,131,128]
136. 3 <=> happy(paul) [avatar definition]
138. happy(paul) <- (3) [avatar component clause 136]
139. 1 | 3 [avatar split clause 68,136,128]
141. 4 <=> brave(lucy) [avatar definition]
142. ~brave(lucy) <- (~4) [avatar component clause 141]
145. 5 <=> quiet(lucy) [avatar definition]
146. quiet(lucy) <- (5) [avatar component clause 145]
159. 8 <=> ! [X1] : (curious(X1) | patient(X1)) [avatar definition]
160. curious(X1) | patient(X1) <- (8) [avatar component clause 159]
161. 8 | 5 [avatar split clause 71,145,159]
162. 8 | ~4 [avatar split clause 70,141,159]
186. 14 <=> ! [X1] : kind(X1) [avatar definition]
187. kind(X1) <- (14) [avatar component clause 186]
194. 16 <=> brave(paul) [avatar definition]
195. ~brave(paul) <- (~16) [avatar component clause 194]
196. brave(paul) <- (16) [avatar component clause 194]
218. brave(paul) <- (3) [resolution 84,138]
219. 16 | ~3 [avatar split clause 218,136,194]
224. happy(lucy) <- (5) [resolution 105,146]
225. brave(lucy) <- (5) [resolution 224,84]
226. $false <- (~4, 5) [subsumption resolution 225,142]
227. 4 | ~5 [avatar contradiction clause 226]
229. happy(X0) | kind(X0) [resolution 107,101]
239. ~rich(X1) | patient(X1) <- (8) [resolution 160,106]
267. wise(X1) | brave(X1) | brave(X1) [resolution 76,83]
268. brave(X1) | wise(X1) [duplicate literal removal 267]
341. happy(paul) | humble(paul) <- (16) [resolution 196,82]
343. rich(paul) <- (16) [resolution 196,114]
475. patient(paul) <- (8, 16) [resolution 239,343]
481. 2 | ~8 | ~16 [avatar split clause 475,194,159,131]
483. kind(X0) <- (1) [resolution 129,229]
485. 14 | ~1 [avatar split clause 483,128,186]
486. humble(paul) <- (1, 16) [subsumption resolution 341,129]
487. $false <- (1, 16) [subsumption resolution 486,124]
488. ~1 | ~16 [avatar contradiction clause 487]
491. rich(X1) <- (14) [resolution 187,115]
523. wise(paul) <- (~16) [resolution 268,195]
558. ~rich(paul) <- (~16) [resolution 523,102]
559. $false <- (14, ~16) [subsumption resolution 558,491]
560. ~14 | 16 [avatar contradiction clause 559]
561. $false [avatar sat refutation 134,139,161,162,219,227,481,485,488,560]
% SZS output end Proof for 5763435867005996874223734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both quiet and patient then someone is not humble and vice versa.
If fred is not tall then someone is not kind or not generous.
Everyone who is not kind is either not patient or old.
Everyone who is strong or funny is both strong and kind.
If someone is either not calm or not rich then someone is not generous.
If someone is both not calm and creative then mary is both humble and not patient.
If someone is both not old and tall then someone is both calm and not creative.
Everyone who is not rich or old is not old and vice versa.
If someone is not creative then someone is both not old and not wise and vice versa.
Everyone who is both quiet and not curious is not kind and vice versa.
Everyone who is both old and not generous is both calm and humble.
Everyone who is not patient is both not quiet and quiet.
Everyone who is both happy and calm is humble and vice versa.
Everyone who is either not generous or not rich is both not funny and not creative and vice versa.
Everyone who is both not humble and old is either wise or brave and vice versa.
If someone is both brave and not wise then john is funny and vice versa.
John is not creative or not patient.
Someone is kind.
Someone is not humble.
Lucy is either not old or quiet.
Mary is either old or strong.
Alice is happy or not patient.
Fred is both not calm and quiet. | Alice is kind. | entailment | (((quiet(susan)&patient(susan)))<=>(?[X]:(~humble(X))))&
((~tall(fred))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>old(X))))&
(![X]:((strong(X)|funny(X))=>(strong(X)&kind(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~calm(X)&creative(X))))=>((humble(mary)&~patient(mary))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((~rich(X)|old(X))<=>~old(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((quiet(X)&~curious(X))<=>~kind(X)))&
(![X]:((old(X)&~generous(X))=>(calm(X)&humble(X))))&
(![X]:(~patient(X)=>(~quiet(X)&quiet(X))))&
(![X]:((happy(X)&calm(X))<=>humble(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~funny(X)&~creative(X))))&
(![X]:((~humble(X)&old(X))<=>(wise(X)<~>brave(X))))&
((?[X]:((brave(X)&~wise(X))))<=>(funny(john)))&
((~creative(john)|~patient(john)))&
(?[X]:(kind(X)))&
(?[X]:(~humble(X)))&
((~old(lucy)<~>quiet(lucy)))&
((old(mary)<~>strong(mary)))&
((happy(alice)|~patient(alice)))&
((~calm(fred)&quiet(fred))) | kind(alice) | [
"p2",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6189408597432579677737012
% SZS output start Proof for 6189408597432579677737012
3. ! [X0] : (~kind(X0) => (~patient(X0) <~> old(X0))) [input p2]
8. ! [X0] : ((old(X0) | ~rich(X0)) <=> ~old(X0)) [input p7]
12. ! [X0] : (~patient(X0) => (quiet(X0) & ~quiet(X0))) [input p11]
24. ~kind(alice) [input hypothesis]
29. ! [X0] : ((~patient(X0) <~> old(X0)) | kind(X0)) [ennf transformation 3]
36. ! [X0] : ((quiet(X0) & ~quiet(X0)) | patient(X0)) [ennf transformation 12]
44. ! [X0] : (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | kind(X0)) [nnf transformation 29]
52. ! [X0] : (((old(X0) | ~rich(X0)) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [nnf transformation 8]
53. ! [X0] : ((old(X0) | ~rich(X0) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [flattening 52]
81. ~patient(X0) | old(X0) | kind(X0) [cnf transformation 44]
94. ~old(X0) | ~old(X0) [cnf transformation 53]
104. ~quiet(X0) | patient(X0) [cnf transformation 36]
105. patient(X0) | quiet(X0) [cnf transformation 36]
134. ~kind(alice) [cnf transformation 24]
135. ~old(X0) [duplicate literal removal 94]
223. patient(X0) [subsumption resolution 104,105]
249. old(X1) | kind(X1) [resolution 81,223]
250. kind(X1) [subsumption resolution 249,135]
251. $false [resolution 250,134]
% SZS output end Proof for 6189408597432579677737012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not creative is either generous or not wise.
If someone is both strong and rich then someone is both not quiet and not generous.
If someone is both curious and not kind then someone is humble and vice versa.
If lucy is either not generous or not old then fred is wise or patient.
Everyone who is not happy or generous is both generous and not strong and vice versa.
Everyone who is quiet or not generous is both not creative and wise and vice versa.
Everyone who is not kind is either not old or old and vice versa.
If fred is wise then mary is either creative or calm.
If lucy is happy then susan is both wise and not kind and vice versa.
If someone is either brave or happy then someone is either not calm or rich.
If john is not kind then someone is both not rich and humble and vice versa.
Everyone who is both not brave and not calm is not brave or happy.
Everyone who is either brave or wise is not strong or not kind and vice versa.
Everyone who is both funny and happy is both not calm and rich.
If someone is not humble or humble then someone is both not curious and not old and vice versa.
Everyone who is both old and kind is both not kind and quiet and vice versa.
Someone is both creative and not strong.
Someone is strong or funny.
Someone is generous.
John is kind or not brave.
Someone is not curious.
Someone is both calm and not wise. | Fred is creative. | entailment | (![X]:((~tall(X)|~creative(X))=>(generous(X)<~>~wise(X))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((~quiet(X)&~generous(X)))))&
((?[X]:((curious(X)&~kind(X))))<=>(?[X]:(humble(X))))&
(((~generous(lucy)<~>~old(lucy)))=>((wise(fred)|patient(fred))))&
(![X]:((~happy(X)|generous(X))<=>(generous(X)&~strong(X))))&
(![X]:((quiet(X)|~generous(X))<=>(~creative(X)&wise(X))))&
(![X]:(~kind(X)<=>(~old(X)<~>old(X))))&
((wise(fred))=>((creative(mary)<~>calm(mary))))&
((happy(lucy))<=>((wise(susan)&~kind(susan))))&
((?[X]:((brave(X)<~>happy(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
((~kind(john))<=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~brave(X)&~calm(X))=>(~brave(X)|happy(X))))&
(![X]:((brave(X)<~>wise(X))<=>(~strong(X)|~kind(X))))&
(![X]:((funny(X)&happy(X))=>(~calm(X)&rich(X))))&
((?[X]:((~humble(X)|humble(X))))<=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((old(X)&kind(X))<=>(~kind(X)&quiet(X))))&
(?[X]:((creative(X)&~strong(X))))&
(?[X]:((strong(X)|funny(X))))&
(?[X]:(generous(X)))&
((kind(john)|~brave(john)))&
(?[X]:(~curious(X)))&
(?[X]:((calm(X)&~wise(X)))) | creative(fred) | [
"p0",
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 101794098034956434210768
% SZS output start Proof for 101794098034956434210768
1. ! [X0] : ((~creative(X0) | ~tall(X0)) => (generous(X0) <~> ~wise(X0))) [input p0]
6. ! [X0] : ((~generous(X0) | quiet(X0)) <=> (wise(X0) & ~creative(X0))) [input p5]
7. ! [X0] : (~kind(X0) <=> (~old(X0) <~> old(X0))) [input p6]
16. ! [X0] : ((kind(X0) & old(X0)) <=> (quiet(X0) & ~kind(X0))) [input p15]
23. ~creative(fred) [input hypothesis]
29. ! [X0] : (~creative(X0) => (generous(X0) <~> ~wise(X0))) [pure predicate removal 1]
30. ! [X0] : ((generous(X0) <~> ~wise(X0)) | creative(X0)) [ennf transformation 29]
38. ! [X0] : (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | creative(X0)) [nnf transformation 30]
49. ! [X0] : (((~generous(X0) | quiet(X0)) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | (generous(X0) & ~quiet(X0)))) [nnf transformation 6]
50. ! [X0] : ((~generous(X0) | quiet(X0) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | (generous(X0) & ~quiet(X0)))) [flattening 49]
51. ! [X0] : ((~kind(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | kind(X0))) [nnf transformation 7]
70. ! [X0] : (((kind(X0) & old(X0)) | (~quiet(X0) | kind(X0))) & ((quiet(X0) & ~kind(X0)) | (~kind(X0) | ~old(X0)))) [nnf transformation 16]
71. ! [X0] : (((kind(X0) & old(X0)) | ~quiet(X0) | kind(X0)) & ((quiet(X0) & ~kind(X0)) | ~kind(X0) | ~old(X0))) [flattening 70]
82. ~wise(X0) | generous(X0) | creative(X0) [cnf transformation 38]
83. ~generous(X0) | wise(X0) | creative(X0) [cnf transformation 38]
97. wise(X0) | generous(X0) [cnf transformation 50]
98. ~generous(X0) | quiet(X0) | ~wise(X0) | creative(X0) [cnf transformation 50]
101. ~kind(X0) | old(X0) | old(X0) [cnf transformation 51]
102. ~kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 51]
132. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 71]
141. ~creative(fred) [cnf transformation 23]
143. kind(X0) | ~quiet(X0) [duplicate literal removal 132]
144. ~kind(X0) | old(X0) [duplicate literal removal 101]
145. ~old(X0) | ~kind(X0) [duplicate literal removal 102]
180. ~wise(X0) | quiet(X0) | creative(X0) [subsumption resolution 98,82]
181. ~kind(X0) [subsumption resolution 144,145]
183. 9 <=> wise(fred) [avatar definition]
184. wise(fred) <- (9) [avatar component clause 183]
185. ~wise(fred) <- (~9) [avatar component clause 183]
244. ~quiet(X0) [subsumption resolution 143,181]
265. generous(fred) <- (~9) [resolution 97,185]
274. wise(fred) | creative(fred) <- (~9) [resolution 83,265]
288. creative(fred) <- (~9) [subsumption resolution 274,185]
289. $false <- (~9) [subsumption resolution 288,141]
290. 9 [avatar contradiction clause 289]
328. quiet(fred) | creative(fred) <- (9) [resolution 180,184]
331. creative(fred) <- (9) [subsumption resolution 328,244]
332. $false <- (9) [subsumption resolution 331,141]
333. ~9 [avatar contradiction clause 332]
336. $false [avatar sat refutation 290,333]
% SZS output end Proof for 101794098034956434210768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is not old and vice versa. If john is both not rich and not quiet then fred is rich or not quiet and vice versa. Everyone who is quiet is wise and vice versa. Everyone who is quiet is either not tall or curious and vice versa. If alice is either curious or kind then someone is both not funny and not quiet. If mary is both wise and patient then someone is not brave or not calm and vice versa. Everyone who is not wise or creative is both tall and happy. If someone is either not kind or not funny then someone is both brave and not old and vice versa. Everyone who is both patient and tall is quiet or not patient and vice versa. Everyone who is either funny or rich is not calm and vice versa. If fred is either not wise or not happy then mary is happy or not funny. Everyone who is not patient or not funny is not creative or old and vice versa. If someone is not old then someone is not old or not rich. If paul is either old or not old then paul is creative. Everyone who is either not humble or wise is patient or funny. If someone is patient or strong then mary is either not wise or calm. Fred is both funny and not humble. Someone is either rich or not wise. Someone is kind. Paul is either kind or not brave. Someone is wise. | Mary is tall. | entailment | ((?[X]:(~strong(X)))<=>(?[X]:(~old(X))))&
(((~rich(john)&~quiet(john)))<=>((rich(fred)|~quiet(fred))))&
(![X]:(quiet(X)<=>wise(X)))&
(![X]:(quiet(X)<=>(~tall(X)<~>curious(X))))&
(((curious(alice)<~>kind(alice)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((wise(mary)&patient(mary)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(tall(X)&happy(X))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((patient(X)&tall(X))<=>(quiet(X)|~patient(X))))&
(![X]:((funny(X)<~>rich(X))<=>~calm(X)))&
(((~wise(fred)<~>~happy(fred)))=>((happy(mary)|~funny(mary))))&
(![X]:((~patient(X)|~funny(X))<=>(~creative(X)|old(X))))&
((?[X]:(~old(X)))=>(?[X]:((~old(X)|~rich(X)))))&
(((old(paul)<~>~old(paul)))=>(creative(paul)))&
(![X]:((~humble(X)<~>wise(X))=>(patient(X)|funny(X))))&
((?[X]:((patient(X)|strong(X))))=>((~wise(mary)<~>calm(mary))))&
((funny(fred)&~humble(fred)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:(kind(X)))&
((kind(paul)<~>~brave(paul)))&
(?[X]:(wise(X))) | tall(mary) | [
"p2",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8864308645574734795596674
% SZS output start Proof for 8864308645574734795596674
3. ! [X0] : (quiet(X0) <=> wise(X0)) [input p2]
6. (patient(mary) & wise(mary)) <=> ? [X0] : (~calm(X0) | ~brave(X0)) [input p5]
9. ! [X0] : ((tall(X0) & patient(X0)) <=> (~patient(X0) | quiet(X0))) [input p8]
16. ? [X0] : (strong(X0) | patient(X0)) => (~wise(mary) <~> calm(mary)) [input p15]
22. ~tall(mary) [input hypothesis]
34. (~wise(mary) <~> calm(mary)) | ! [X0] : (~strong(X0) & ~patient(X0)) [ennf transformation 16]
42. ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 3]
47. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X0] : (~calm(X0) | ~brave(X0)) | (~patient(mary) | ~wise(mary))) [nnf transformation 6]
48. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X0] : (~calm(X0) | ~brave(X0)) | ~patient(mary) | ~wise(mary)) [flattening 47]
49. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & (? [X1] : (~calm(X1) | ~brave(X1)) | ~patient(mary) | ~wise(mary)) [rectify 48]
50. ? [X1] : (~calm(X1) | ~brave(X1)) => (~calm(sK3) | ~brave(sK3)) [choice axiom]
51. ((patient(mary) & wise(mary)) | ! [X0] : (calm(X0) & brave(X0))) & ((~calm(sK3) | ~brave(sK3)) | ~patient(mary) | ~wise(mary)) [skolemisation 49,50]
57. ! [X0] : (((tall(X0) & patient(X0)) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | (~tall(X0) | ~patient(X0)))) [nnf transformation 9]
58. ! [X0] : (((tall(X0) & patient(X0)) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ~tall(X0) | ~patient(X0))) [flattening 57]
68. ((~calm(mary) | wise(mary)) & (calm(mary) | ~wise(mary))) | ! [X0] : (~strong(X0) & ~patient(X0)) [nnf transformation 34]
85. ~wise(X0) | quiet(X0) [cnf transformation 42]
96. wise(mary) | calm(X0) [cnf transformation 51]
111. patient(X0) | patient(X0) [cnf transformation 58]
112. ~quiet(X0) | tall(X0) [cnf transformation 58]
131. ~calm(mary) | wise(mary) | ~patient(X0) [cnf transformation 68]
141. ~tall(mary) [cnf transformation 22]
145. patient(X0) [duplicate literal removal 111]
204. 13 <=> ! [X0] : calm(X0) [avatar definition]
205. calm(X0) <- (13) [avatar component clause 204]
216. 16 <=> wise(mary) [avatar definition]
218. wise(mary) <- (16) [avatar component clause 216]
219. 13 | 16 [avatar split clause 96,216,204]
307. 35 <=> calm(mary) [avatar definition]
309. ~calm(mary) <- (~35) [avatar component clause 307]
311. ~calm(mary) | wise(mary) [subsumption resolution 131,145]
312. 16 | ~35 [avatar split clause 311,307,216]
336. $false <- (13, ~35) [resolution 309,205]
337. ~13 | 35 [avatar contradiction clause 336]
341. quiet(mary) <- (16) [resolution 85,218]
348. tall(mary) <- (16) [resolution 112,341]
349. $false <- (16) [subsumption resolution 348,141]
350. ~16 [avatar contradiction clause 349]
351. $false [avatar sat refutation 219,312,337,350]
% SZS output end Proof for 8864308645574734795596674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not quiet then someone is not creative or quiet. If someone is kind then john is not old. Everyone who is both humble and not tall is both not curious and not rich and vice versa. Everyone who is either strong or kind is either happy or wise. Everyone who is both kind and strong is either not strong or strong and vice versa. Everyone who is either generous or funny is both curious and quiet and vice versa. Everyone who is strong or quiet is not old. Everyone who is not rich is not patient and vice versa. Everyone who is both wise and rich is either not calm or not old and vice versa. If susan is quiet or not calm then paul is both not patient and funny and vice versa. Everyone who is not patient is not wise or brave. If someone is either patient or humble then someone is not strong and vice versa. Everyone who is both not calm and calm is either not tall or brave. Everyone who is either kind or not funny is humble. If mary is either funny or creative then susan is humble and vice versa. Everyone who is not curious is curious or creative and vice versa. Alice is strong or not creative. Lucy is not happy or strong. Someone is tall or not curious. Susan is not generous or not creative. Alice is both creative and not generous. Susan is not happy. Fred is rich or patient. | Mary is tall. | entailment | ((?[X]:((~happy(X)<~>~quiet(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:(kind(X)))=>(~old(john)))&
(![X]:((humble(X)&~tall(X))<=>(~curious(X)&~rich(X))))&
(![X]:((strong(X)<~>kind(X))=>(happy(X)<~>wise(X))))&
(![X]:((kind(X)&strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((generous(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((strong(X)|quiet(X))=>~old(X)))&
(![X]:(~rich(X)<=>~patient(X)))&
(![X]:((wise(X)&rich(X))<=>(~calm(X)<~>~old(X))))&
(((quiet(susan)|~calm(susan)))<=>((~patient(paul)&funny(paul))))&
(![X]:(~patient(X)=>(~wise(X)|brave(X))))&
((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&calm(X))=>(~tall(X)<~>brave(X))))&
(![X]:((kind(X)<~>~funny(X))=>humble(X)))&
(((funny(mary)<~>creative(mary)))<=>(humble(susan)))&
(![X]:(~curious(X)<=>(curious(X)|creative(X))))&
((strong(alice)|~creative(alice)))&
((~happy(lucy)|strong(lucy)))&
(?[X]:((tall(X)|~curious(X))))&
((~generous(susan)|~creative(susan)))&
((creative(alice)&~generous(alice)))&
(~happy(susan))&
((rich(fred)|patient(fred))) | tall(mary) | [
"p2",
"p4",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1005248323180099929929193
% SZS output start Proof for 1005248323180099929929193
3. ! [X0] : ((~tall(X0) & humble(X0)) <=> (~rich(X0) & ~curious(X0))) [input p2]
5. ! [X0] : ((strong(X0) & kind(X0)) <=> (~strong(X0) <~> strong(X0))) [input p4]
8. ! [X0] : (~rich(X0) <=> ~patient(X0)) [input p7]
12. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X0] : ~strong(X0) [input p11]
16. ! [X0] : (~curious(X0) <=> (creative(X0) | curious(X0))) [input p15]
24. ~tall(mary) [input hypothesis]
26. ? [X0] : (patient(X0) <~> humble(X0)) <=> ? [X1] : ~strong(X1) [rectify 12]
40. ! [X0] : (((~tall(X0) & humble(X0)) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | (tall(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((~tall(X0) & humble(X0)) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | tall(X0) | ~humble(X0))) [flattening 40]
43. ! [X0] : (((strong(X0) & kind(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~strong(X0) | ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & kind(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~strong(X0) | ~kind(X0))) [flattening 43]
47. ! [X0] : ((~rich(X0) | patient(X0)) & (~patient(X0) | rich(X0))) [nnf transformation 8]
52. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) [nnf transformation 26]
53. (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [rectify 52]
54. ? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) => ((~humble(sK1) | ~patient(sK1)) & (humble(sK1) | patient(sK1))) [choice axiom]
55. ? [X2] : ~strong(X2) => ~strong(sK2) [choice axiom]
56. (((~humble(sK1) | ~patient(sK1)) & (humble(sK1) | patient(sK1))) | ! [X1] : strong(X1)) & (~strong(sK2) | ! [X3] : ((patient(X3) | ~humble(X3)) & (humble(X3) | ~patient(X3)))) [skolemisation 53,55,54]
60. ! [X0] : ((~curious(X0) | (~creative(X0) & ~curious(X0))) & ((creative(X0) | curious(X0)) | curious(X0))) [nnf transformation 16]
61. ! [X0] : ((~curious(X0) | (~creative(X0) & ~curious(X0))) & (creative(X0) | curious(X0) | curious(X0))) [flattening 60]
68. ~rich(X0) | tall(X0) | ~humble(X0) [cnf transformation 41]
69. rich(X0) | humble(X0) | curious(X0) [cnf transformation 41]
79. strong(X0) | strong(X0) | strong(X0) [cnf transformation 44]
89. ~patient(X0) | rich(X0) [cnf transformation 47]
90. ~rich(X0) | patient(X0) [cnf transformation 47]
103. ~strong(sK2) | humble(X3) | ~patient(X3) [cnf transformation 56]
104. ~strong(sK2) | patient(X3) | ~humble(X3) [cnf transformation 56]
116. ~curious(X0) | ~curious(X0) [cnf transformation 61]
126. ~tall(mary) [cnf transformation 24]
128. ~curious(X0) [duplicate literal removal 116]
133. strong(X0) [duplicate literal removal 79]
185. ~humble(X3) | patient(X3) [subsumption resolution 104,133]
186. ~patient(X3) | humble(X3) [subsumption resolution 103,133]
230. humble(X1) | curious(X1) | patient(X1) [resolution 69,90]
231. humble(X1) | patient(X1) [subsumption resolution 230,128]
232. patient(X1) [subsumption resolution 231,185]
234. humble(X0) [resolution 232,186]
235. rich(X1) [resolution 232,89]
239. tall(X0) | ~humble(X0) [resolution 235,68]
241. tall(X0) [subsumption resolution 239,234]
243. $false [resolution 241,126]
% SZS output end Proof for 1005248323180099929929193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not wise then someone is either not brave or curious and vice versa. Everyone who is not humble or tall is happy and vice versa. Everyone who is both not quiet and not brave is either brave or not wise and vice versa. Everyone who is not brave is not old and vice versa. Everyone who is both patient and not curious is both not quiet and curious. If someone is both calm and not creative then susan is either brave or funny and vice versa. If someone is both not patient and not curious then someone is both not creative and generous. Everyone who is not rich or happy is either curious or quiet. Everyone who is either generous or humble is both kind and happy. Everyone who is brave or not calm is not wise and vice versa. Everyone who is not kind is either not kind or not humble and vice versa. Everyone who is either calm or not calm is curious or generous. Everyone who is patient or not funny is patient or not brave. If someone is either wise or creative then someone is either generous or old and vice versa. Everyone who is not curious or not wise is both old and not rich and vice versa. If mary is both generous and not tall then someone is both not calm and funny. John is either kind or humble. Paul is not kind. Someone is either not generous or not tall. John is happy. Someone is not tall or funny. Mary is not generous or not humble. Paul is tall or not rich. | Paul is not quiet. | neutral | ((?[X]:((quiet(X)&~wise(X))))<=>(?[X]:((~brave(X)<~>curious(X)))))&
(![X]:((~humble(X)|tall(X))<=>happy(X)))&
(![X]:((~quiet(X)&~brave(X))<=>(brave(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>~old(X)))&
(![X]:((patient(X)&~curious(X))=>(~quiet(X)&curious(X))))&
((?[X]:((calm(X)&~creative(X))))<=>((brave(susan)<~>funny(susan))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((~rich(X)|happy(X))=>(curious(X)<~>quiet(X))))&
(![X]:((generous(X)<~>humble(X))=>(kind(X)&happy(X))))&
(![X]:((brave(X)|~calm(X))<=>~wise(X)))&
(![X]:(~kind(X)<=>(~kind(X)<~>~humble(X))))&
(![X]:((calm(X)<~>~calm(X))=>(curious(X)|generous(X))))&
(![X]:((patient(X)|~funny(X))=>(patient(X)|~brave(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~curious(X)|~wise(X))<=>(old(X)&~rich(X))))&
(((generous(mary)&~tall(mary)))=>(?[X]:((~calm(X)&funny(X)))))&
((kind(john)<~>humble(john)))&
(~kind(paul))&
(?[X]:((~generous(X)<~>~tall(X))))&
(happy(john))&
(?[X]:((~tall(X)|funny(X))))&
((~generous(mary)|~humble(mary)))&
((tall(paul)|~rich(paul))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not calm is not old or not creative.
If someone is not curious or rich then someone is not funny and vice versa.
Everyone who is either not quiet or not rich is either old or humble and vice versa.
Everyone who is creative or generous is either not brave or funny.
If someone is rich then mary is not wise and vice versa.
If someone is both not patient and creative then susan is quiet and vice versa.
Everyone who is both generous and not generous is kind or not generous and vice versa.
Everyone who is not generous or calm is strong or old.
If someone is not quiet or not brave then john is not brave or quiet and vice versa.
If paul is quiet or wise then someone is not brave or happy and vice versa.
Everyone who is creative is both calm and creative.
Everyone who is wise is either not kind or not generous and vice versa.
Everyone who is either not patient or not old is not strong or not kind and vice versa.
If someone is patient then someone is curious or creative and vice versa.
Everyone who is brave is both rich and not creative.
Everyone who is both rich and not generous is both not old and not generous.
John is not brave.
Someone is tall or old.
Paul is either kind or not rich.
Someone is either funny or not kind.
Someone is both humble and curious. | Susan is curious. | neutral | (![X]:(~calm(X)=>(~old(X)|~creative(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~quiet(X)<~>~rich(X))<=>(old(X)<~>humble(X))))&
(![X]:((creative(X)|generous(X))=>(~brave(X)<~>funny(X))))&
((?[X]:(rich(X)))<=>(~wise(mary)))&
((?[X]:((~patient(X)&creative(X))))<=>(quiet(susan)))&
(![X]:((generous(X)&~generous(X))<=>(kind(X)|~generous(X))))&
(![X]:((~generous(X)|calm(X))=>(strong(X)|old(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((~brave(john)|quiet(john))))&
(((quiet(paul)|wise(paul)))<=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:(creative(X)=>(calm(X)&creative(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~old(X))<=>(~strong(X)|~kind(X))))&
((?[X]:(patient(X)))<=>(?[X]:((curious(X)|creative(X)))))&
(![X]:(brave(X)=>(rich(X)&~creative(X))))&
(![X]:((rich(X)&~generous(X))=>(~old(X)&~generous(X))))&
(~brave(john))&
(?[X]:((tall(X)|old(X))))&
((kind(paul)<~>~rich(paul)))&
(?[X]:((funny(X)<~>~kind(X))))&
(?[X]:((humble(X)&curious(X)))) | curious(susan) | [] | null | 0 |
If someone is both quiet and calm then paul is creative and vice versa.
If paul is both not funny and not brave then someone is either not funny or not patient.
Everyone who is both generous and not humble is either brave or not funny and vice versa.
If alice is not calm or kind then john is either happy or not happy and vice versa.
Everyone who is strong or creative is not old and vice versa.
Everyone who is both wise and creative is both curious and generous and vice versa.
Everyone who is funny or not creative is both not strong and not wise.
If someone is not rich then john is either brave or funny.
If lucy is both curious and rich then someone is not rich.
Everyone who is both not quiet and strong is not creative and vice versa.
If someone is either not tall or not strong then someone is both strong and not curious.
Everyone who is creative or not rich is quiet.
If paul is either patient or not strong then someone is both brave and not calm and vice versa.
Everyone who is both not creative and strong is not wise and vice versa.
If susan is quiet then mary is quiet or not creative and vice versa.
If alice is not tall or not funny then paul is both rich and kind.
Someone is not rich or old.
Lucy is not humble or not calm.
Someone is either tall or patient.
Someone is not rich.
Someone is not kind.
Someone is either not old or not patient. | Susan is not kind. | neutral | ((?[X]:((quiet(X)&calm(X))))<=>(creative(paul)))&
(((~funny(paul)&~brave(paul)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
(![X]:((generous(X)&~humble(X))<=>(brave(X)<~>~funny(X))))&
(((~calm(alice)|kind(alice)))<=>((happy(john)<~>~happy(john))))&
(![X]:((strong(X)|creative(X))<=>~old(X)))&
(![X]:((wise(X)&creative(X))<=>(curious(X)&generous(X))))&
(![X]:((funny(X)|~creative(X))=>(~strong(X)&~wise(X))))&
((?[X]:(~rich(X)))=>((brave(john)<~>funny(john))))&
(((curious(lucy)&rich(lucy)))=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)&strong(X))<=>~creative(X)))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:((creative(X)|~rich(X))=>quiet(X)))&
(((patient(paul)<~>~strong(paul)))<=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((~creative(X)&strong(X))<=>~wise(X)))&
((quiet(susan))<=>((quiet(mary)|~creative(mary))))&
(((~tall(alice)|~funny(alice)))=>((rich(paul)&kind(paul))))&
(?[X]:((~rich(X)|old(X))))&
((~humble(lucy)|~calm(lucy)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~old(X)<~>~patient(X)))) | ~kind(susan) | [] | null | 0 |
If alice is either not creative or tall then susan is either not creative or not generous and vice versa.
Everyone who is generous or not happy is both not curious and not funny.
If someone is rich or not humble then someone is humble or calm.
If john is either not old or wise then susan is not rich or not calm.
Everyone who is either not strong or not patient is either creative or generous.
Everyone who is creative or brave is either not curious or not old and vice versa.
Everyone who is either not tall or not funny is wise and vice versa.
Everyone who is both quiet and not old is quiet and vice versa.
Everyone who is old or not kind is not funny or tall and vice versa.
Everyone who is both old and quiet is both not calm and not strong.
Everyone who is not humble or rich is either not rich or not creative and vice versa.
Everyone who is patient is not kind and vice versa.
Everyone who is not patient is either old or not wise and vice versa.
Everyone who is rich or not rich is not wise or quiet and vice versa.
If someone is not happy or not kind then john is either not curious or not brave and vice versa.
Everyone who is both not humble and not curious is both not funny and curious and vice versa.
Paul is either not curious or not old.
Someone is not brave.
Someone is not rich or wise.
Someone is quiet or curious.
Paul is either not strong or not kind.
Someone is wise.
Someone is curious or humble.
Someone is either calm or not funny. | Paul is not strong. | contradiction | (((~creative(alice)<~>tall(alice)))<=>((~creative(susan)<~>~generous(susan))))&
(![X]:((generous(X)|~happy(X))=>(~curious(X)&~funny(X))))&
((?[X]:((rich(X)|~humble(X))))=>(?[X]:((humble(X)|calm(X)))))&
(((~old(john)<~>wise(john)))=>((~rich(susan)|~calm(susan))))&
(![X]:((~strong(X)<~>~patient(X))=>(creative(X)<~>generous(X))))&
(![X]:((creative(X)|brave(X))<=>(~curious(X)<~>~old(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>wise(X)))&
(![X]:((quiet(X)&~old(X))<=>quiet(X)))&
(![X]:((old(X)|~kind(X))<=>(~funny(X)|tall(X))))&
(![X]:((old(X)&quiet(X))=>(~calm(X)&~strong(X))))&
(![X]:((~humble(X)|rich(X))<=>(~rich(X)<~>~creative(X))))&
(![X]:(patient(X)<=>~kind(X)))&
(![X]:(~patient(X)<=>(old(X)<~>~wise(X))))&
(![X]:((rich(X)|~rich(X))<=>(~wise(X)|quiet(X))))&
((?[X]:((~happy(X)|~kind(X))))<=>((~curious(john)<~>~brave(john))))&
(![X]:((~humble(X)&~curious(X))<=>(~funny(X)&curious(X))))&
((~curious(paul)<~>~old(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((quiet(X)|curious(X))))&
((~strong(paul)<~>~kind(paul)))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((calm(X)<~>~funny(X)))) | ~strong(paul) | [
"p6",
"p7",
"p8",
"p11",
"p12",
"p13",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 916080919255735954310282
% SZS output start Proof for 916080919255735954310282
7. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> wise(X0)) [input p6]
8. ! [X0] : ((~old(X0) & quiet(X0)) <=> quiet(X0)) [input p7]
9. ! [X0] : ((~kind(X0) | old(X0)) <=> (tall(X0) | ~funny(X0))) [input p8]
12. ! [X0] : (patient(X0) <=> ~kind(X0)) [input p11]
13. ! [X0] : (~patient(X0) <=> (old(X0) <~> ~wise(X0))) [input p12]
14. ! [X0] : ((~rich(X0) | rich(X0)) <=> (quiet(X0) | ~wise(X0))) [input p13]
16. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (curious(X0) & ~funny(X0))) [input p15]
17. ~curious(paul) <~> ~old(paul) [input p16]
21. ~strong(paul) <~> ~kind(paul) [input p20]
25. ~strong(paul) [input hypothesis]
42. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | ~wise(X0)) & (wise(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 7]
43. ! [X0] : (((~old(X0) & quiet(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) | ~quiet(X0)))) [nnf transformation 8]
44. ! [X0] : (((~old(X0) & quiet(X0)) | ~quiet(X0)) & (quiet(X0) | old(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) | old(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (kind(X0) & ~old(X0)))) [nnf transformation 9]
46. ! [X0] : ((~kind(X0) | old(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | (kind(X0) & ~old(X0)))) [flattening 45]
49. ! [X0] : ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))) [nnf transformation 12]
50. ! [X0] : ((~patient(X0) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | patient(X0))) [nnf transformation 13]
51. ! [X0] : (((~rich(X0) | rich(X0)) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | (rich(X0) & ~rich(X0)))) [nnf transformation 14]
52. ! [X0] : ((~rich(X0) | rich(X0) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | (rich(X0) & ~rich(X0)))) [flattening 51]
57. ! [X0] : (((~curious(X0) & ~humble(X0)) | (~curious(X0) | funny(X0))) & ((curious(X0) & ~funny(X0)) | (curious(X0) | humble(X0)))) [nnf transformation 16]
58. ! [X0] : (((~curious(X0) & ~humble(X0)) | ~curious(X0) | funny(X0)) & ((curious(X0) & ~funny(X0)) | curious(X0) | humble(X0))) [flattening 57]
59. (old(paul) | curious(paul)) & (~old(paul) | ~curious(paul)) [nnf transformation 17]
66. (kind(paul) | strong(paul)) & (~kind(paul) | ~strong(paul)) [nnf transformation 21]
100. ~funny(X0) | wise(X0) | tall(X0) [cnf transformation 42]
106. ~quiet(X0) | ~old(X0) [cnf transformation 44]
110. ~kind(X0) | old(X0) | ~tall(X0) [cnf transformation 46]
119. ~kind(X0) | ~patient(X0) [cnf transformation 49]
121. ~wise(X0) | old(X0) | patient(X0) [cnf transformation 50]
122. ~old(X0) | wise(X0) | patient(X0) [cnf transformation 50]
125. quiet(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 52]
126. ~wise(X0) | quiet(X0) | rich(X0) [cnf transformation 52]
138. ~curious(X0) | ~curious(X0) | funny(X0) [cnf transformation 58]
140. old(paul) | curious(paul) [cnf transformation 59]
145. kind(paul) | strong(paul) [cnf transformation 66]
150. ~strong(paul) [cnf transformation 25]
152. ~curious(X0) | funny(X0) [duplicate literal removal 138]
213. ~wise(X0) | quiet(X0) [subsumption resolution 125,126]
243. 19 <=> curious(paul) [avatar definition]
245. curious(paul) <- (19) [avatar component clause 243]
247. 20 <=> old(paul) [avatar definition]
249. old(paul) <- (20) [avatar component clause 247]
250. 19 | 20 [avatar split clause 140,247,243]
271. 25 <=> strong(paul) [avatar definition]
275. 26 <=> kind(paul) [avatar definition]
277. kind(paul) <- (26) [avatar component clause 275]
278. 25 | 26 [avatar split clause 145,275,271]
290. ~25 [avatar split clause 150,271]
294. ~patient(paul) <- (26) [resolution 119,277]
297. funny(paul) <- (19) [resolution 152,245]
317. wise(paul) | tall(paul) <- (19) [resolution 100,297]
319. 31 <=> tall(paul) [avatar definition]
323. 32 <=> wise(paul) [avatar definition]
325. wise(paul) <- (32) [avatar component clause 323]
326. 31 | 32 | ~19 [avatar split clause 317,243,323,319]
378. old(paul) | ~tall(paul) <- (26) [resolution 110,277]
383. wise(paul) | patient(paul) <- (20) [resolution 122,249]
390. wise(paul) <- (20, 26) [subsumption resolution 383,294]
391. 32 | ~20 | ~26 [avatar split clause 390,275,247,323]
401. ~31 | 20 | ~26 [avatar split clause 378,275,247,319]
514. old(paul) | patient(paul) <- (32) [resolution 325,121]
517. quiet(paul) <- (32) [resolution 325,213]
523. 56 <=> quiet(paul) [avatar definition]
525. quiet(paul) <- (56) [avatar component clause 523]
527. 56 | ~32 [avatar split clause 517,323,523]
686. ~old(paul) <- (56) [resolution 525,106]
690. ~20 | ~56 [avatar split clause 686,523,247]
692. old(paul) <- (26, 32) [subsumption resolution 514,294]
693. 20 | ~26 | ~32 [avatar split clause 692,323,275,247]
698. $false [avatar sat refutation 250,278,290,326,391,401,527,690,693]
% SZS output end Proof for 916080919255735954310282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is brave then alice is generous or kind and vice versa. Everyone who is both not curious and rich is either happy or creative. Everyone who is strong or kind is both not strong and calm and vice versa. Everyone who is strong is either not wise or generous. If alice is old then someone is both rich and patient and vice versa. Everyone who is either brave or not rich is both tall and not quiet and vice versa. If lucy is either humble or not curious then someone is either not brave or not wise and vice versa. If someone is not strong or not funny then someone is not kind and vice versa. Everyone who is curious is kind or not strong and vice versa. If someone is either brave or kind then susan is both not brave and wise and vice versa. Everyone who is brave is not calm and vice versa. Everyone who is kind is not tall or curious. Everyone who is either kind or not patient is strong. If someone is either humble or not humble then alice is both happy and old and vice versa. Mary is either not funny or old. Susan is not kind or not happy. Someone is both not old and not creative. Lucy is not humble or not strong. Lucy is either wise or quiet. Someone is either not rich or not curious. | Alice is not quiet. | neutral | ((?[X]:(brave(X)))<=>((generous(alice)|kind(alice))))&
(![X]:((~curious(X)&rich(X))=>(happy(X)<~>creative(X))))&
(![X]:((strong(X)|kind(X))<=>(~strong(X)&calm(X))))&
(![X]:(strong(X)=>(~wise(X)<~>generous(X))))&
((old(alice))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>(tall(X)&~quiet(X))))&
(((humble(lucy)<~>~curious(lucy)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((~strong(X)|~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:(curious(X)<=>(kind(X)|~strong(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>((~brave(susan)&wise(susan))))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:(kind(X)=>(~tall(X)|curious(X))))&
(![X]:((kind(X)<~>~patient(X))=>strong(X)))&
((?[X]:((humble(X)<~>~humble(X))))<=>((happy(alice)&old(alice))))&
((~funny(mary)<~>old(mary)))&
((~kind(susan)|~happy(susan)))&
(?[X]:((~old(X)&~creative(X))))&
((~humble(lucy)|~strong(lucy)))&
((wise(lucy)<~>quiet(lucy)))&
(?[X]:((~rich(X)<~>~curious(X)))) | ~quiet(alice) | [] | null | 0 |
If someone is strong or calm then paul is not tall or tall and vice versa.
If someone is kind or patient then someone is both rich and happy and vice versa.
If someone is not rich or kind then john is not strong.
If someone is rich then someone is strong or not wise and vice versa.
If mary is curious or not rich then john is both tall and brave and vice versa.
Everyone who is both kind and not old is patient or not tall.
Everyone who is kind or rich is not rich.
Everyone who is either quiet or tall is tall.
Everyone who is humble is both not funny and tall.
If someone is both happy and rich then someone is not generous or humble.
Everyone who is both not wise and not brave is happy.
If john is brave or not quiet then someone is wise or not rich.
Everyone who is both not tall and not old is generous.
If someone is not brave or quiet then someone is both kind and not generous and vice versa.
If john is both humble and tall then someone is both not rich and not generous and vice versa.
Lucy is both humble and not old.
Someone is not strong or funny.
Susan is both not patient and not calm.
Susan is not creative or not happy.
Someone is calm.
Someone is not creative or brave. | Susan is wise. | entailment | ((?[X]:((strong(X)|calm(X))))<=>((~tall(paul)|tall(paul))))&
((?[X]:((kind(X)|patient(X))))<=>(?[X]:((rich(X)&happy(X)))))&
((?[X]:((~rich(X)|kind(X))))=>(~strong(john)))&
((?[X]:(rich(X)))<=>(?[X]:((strong(X)|~wise(X)))))&
(((curious(mary)|~rich(mary)))<=>((tall(john)&brave(john))))&
(![X]:((kind(X)&~old(X))=>(patient(X)|~tall(X))))&
(![X]:((kind(X)|rich(X))=>~rich(X)))&
(![X]:((quiet(X)<~>tall(X))=>tall(X)))&
(![X]:(humble(X)=>(~funny(X)&tall(X))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~wise(X)&~brave(X))=>happy(X)))&
(((brave(john)|~quiet(john)))=>(?[X]:((wise(X)|~rich(X)))))&
(![X]:((~tall(X)&~old(X))=>generous(X)))&
((?[X]:((~brave(X)|quiet(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
(((humble(john)&tall(john)))<=>(?[X]:((~rich(X)&~generous(X)))))&
((humble(lucy)&~old(lucy)))&
(?[X]:((~strong(X)|funny(X))))&
((~patient(susan)&~calm(susan)))&
((~creative(susan)|~happy(susan)))&
(?[X]:(calm(X)))&
(?[X]:((~creative(X)|brave(X)))) | wise(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1394444771335774618336662
% SZS output start Proof for 1394444771335774618336662
4. ? [X0] : rich(X0) <=> ? [X0] : (~wise(X0) | strong(X0)) [input p3]
7. ! [X0] : ((rich(X0) | kind(X0)) => ~rich(X0)) [input p6]
22. ~wise(susan) [input hypothesis]
24. ? [X0] : rich(X0) <=> ? [X1] : (~wise(X1) | strong(X1)) [rectify 4]
32. ! [X0] : (~rich(X0) | (~rich(X0) & ~kind(X0))) [ennf transformation 7]
51. (? [X0] : rich(X0) | ! [X1] : (wise(X1) & ~strong(X1))) & (? [X1] : (~wise(X1) | strong(X1)) | ! [X0] : ~rich(X0)) [nnf transformation 24]
52. (? [X0] : rich(X0) | ! [X1] : (wise(X1) & ~strong(X1))) & (? [X2] : (~wise(X2) | strong(X2)) | ! [X3] : ~rich(X3)) [rectify 51]
53. ? [X0] : rich(X0) => rich(sK3) [choice axiom]
54. ? [X2] : (~wise(X2) | strong(X2)) => (~wise(sK4) | strong(sK4)) [choice axiom]
55. (rich(sK3) | ! [X1] : (wise(X1) & ~strong(X1))) & ((~wise(sK4) | strong(sK4)) | ! [X3] : ~rich(X3)) [skolemisation 52,54,53]
91. rich(sK3) | wise(X1) [cnf transformation 55]
99. ~rich(X0) | ~rich(X0) [cnf transformation 32]
124. ~wise(susan) [cnf transformation 22]
126. ~rich(X0) [duplicate literal removal 99]
181. 13 <=> ! [X1] : wise(X1) [avatar definition]
182. wise(X1) <- (13) [avatar component clause 181]
184. 14 <=> rich(sK3) [avatar definition]
186. rich(sK3) <- (14) [avatar component clause 184]
187. 13 | 14 [avatar split clause 91,184,181]
193. 16 <=> ! [X3] : ~rich(X3) [avatar definition]
194. ~rich(X3) <- (16) [avatar component clause 193]
225. 16 [avatar split clause 126,193]
311. $false <- (14, 16) [subsumption resolution 186,194]
312. ~14 | ~16 [avatar contradiction clause 311]
313. $false <- (13) [resolution 182,124]
314. ~13 [avatar contradiction clause 313]
315. $false [avatar sat refutation 187,225,312,314]
% SZS output end Proof for 1394444771335774618336662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not kind then paul is either not brave or patient and vice versa.
If someone is both not quiet and strong then someone is not wise or humble.
Everyone who is either not tall or not calm is either not brave or not creative and vice versa.
If someone is not brave or kind then someone is not funny or brave and vice versa.
Everyone who is both not funny and brave is creative or not brave and vice versa.
Everyone who is either not old or happy is both not happy and creative.
If lucy is both patient and not happy then someone is funny.
Everyone who is either humble or happy is both strong and not curious and vice versa.
Everyone who is both kind and not rich is either brave or wise and vice versa.
If fred is either wise or creative then paul is humble or patient.
Everyone who is both old and quiet is both not humble and rich and vice versa.
Everyone who is not wise or not patient is humble or generous.
Everyone who is both patient and funny is not wise or old and vice versa.
Everyone who is not old or creative is both not tall and calm.
Someone is humble or not strong.
Someone is either not funny or patient.
Susan is both strong and not kind.
Someone is not creative or not rich.
Alice is either calm or funny.
Someone is patient.
Someone is not tall or not patient. | Paul is not funny. | contradiction | ((~kind(john))<=>((~brave(paul)<~>patient(paul))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((~brave(X)|kind(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~funny(X)&brave(X))<=>(creative(X)|~brave(X))))&
(![X]:((~old(X)<~>happy(X))=>(~happy(X)&creative(X))))&
(((patient(lucy)&~happy(lucy)))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>happy(X))<=>(strong(X)&~curious(X))))&
(![X]:((kind(X)&~rich(X))<=>(brave(X)<~>wise(X))))&
(((wise(fred)<~>creative(fred)))=>((humble(paul)|patient(paul))))&
(![X]:((old(X)&quiet(X))<=>(~humble(X)&rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)|generous(X))))&
(![X]:((patient(X)&funny(X))<=>(~wise(X)|old(X))))&
(![X]:((~old(X)|creative(X))=>(~tall(X)&calm(X))))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:((~funny(X)<~>patient(X))))&
((strong(susan)&~kind(susan)))&
(?[X]:((~creative(X)|~rich(X))))&
((calm(alice)<~>funny(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~tall(X)|~patient(X)))) | ~funny(paul) | [
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4678674474288483637173344
% SZS output start Proof for 4678674474288483637173344
3. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~funny(X0)) <=> (~brave(X0) | creative(X0))) [input p4]
13. ! [X0] : ((funny(X0) & patient(X0)) <=> (old(X0) | ~wise(X0))) [input p12]
14. ! [X0] : ((creative(X0) | ~old(X0)) => (calm(X0) & ~tall(X0))) [input p13]
22. ~funny(paul) [input hypothesis]
32. ! [X0] : ((calm(X0) & ~tall(X0)) | (~creative(X0) & old(X0))) [ennf transformation 14]
37. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [nnf transformation 3]
43. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (~brave(X0) | funny(X0)))) [nnf transformation 5]
44. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | ~brave(X0) | funny(X0))) [flattening 43]
55. ! [X0] : (((funny(X0) & patient(X0)) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 13]
56. ! [X0] : (((funny(X0) & patient(X0)) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | ~funny(X0) | ~patient(X0))) [flattening 55]
74. ~creative(X0) | ~brave(X0) | ~calm(X0) | tall(X0) [cnf transformation 37]
86. ~brave(X0) | creative(X0) | ~brave(X0) | funny(X0) [cnf transformation 44]
90. brave(X0) | brave(X0) [cnf transformation 44]
118. ~old(X0) | funny(X0) [cnf transformation 56]
120. ~creative(X0) | ~tall(X0) [cnf transformation 32]
121. old(X0) | calm(X0) [cnf transformation 32]
133. ~funny(paul) [cnf transformation 22]
135. ~brave(X0) | creative(X0) | funny(X0) [duplicate literal removal 86]
136. brave(X0) [duplicate literal removal 90]
194. 14 <=> ! [X3] : brave(X3) [avatar definition]
195. brave(X3) <- (14) [avatar component clause 194]
197. 14 [avatar split clause 136,194]
284. funny(X0) | calm(X0) [resolution 121,118]
289. calm(paul) [resolution 284,133]
308. funny(X0) | creative(X0) <- (14) [resolution 135,195]
311. creative(paul) <- (14) [resolution 308,133]
315. ~brave(paul) | ~calm(paul) | tall(paul) <- (14) [resolution 311,74]
318. ~tall(paul) <- (14) [resolution 311,120]
320. ~calm(paul) | tall(paul) <- (14) [subsumption resolution 315,195]
321. tall(paul) <- (14) [subsumption resolution 320,289]
322. $false <- (14) [subsumption resolution 318,321]
323. ~14 [avatar contradiction clause 322]
324. $false [avatar sat refutation 197,323]
% SZS output end Proof for 4678674474288483637173344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and strong is not old or not generous.
If alice is generous then mary is either not kind or brave and vice versa.
If mary is funny or not humble then fred is both not wise and calm and vice versa.
Everyone who is not strong or wise is both not tall and humble.
Everyone who is either not humble or not generous is either not happy or rich and vice versa.
Everyone who is either humble or rich is old.
Everyone who is either humble or not calm is both curious and not quiet and vice versa.
Everyone who is curious or creative is patient or tall and vice versa.
Everyone who is not strong or not old is strong or not old.
Everyone who is both quiet and tall is either happy or not rich and vice versa.
Everyone who is not tall or funny is either not happy or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
Paul is either not quiet or patient.
Someone is not wise.
Fred is not happy or kind.
Someone is both funny and not rich.
John is either creative or not happy.
Someone is either not quiet or not brave.
Someone is both rich and not brave.
Mary is both not humble and not kind. | Paul is not tall. | entailment | (![X]:((~curious(X)&strong(X))=>(~old(X)|~generous(X))))&
((generous(alice))<=>((~kind(mary)<~>brave(mary))))&
(((funny(mary)|~humble(mary)))<=>((~wise(fred)&calm(fred))))&
(![X]:((~strong(X)|wise(X))=>(~tall(X)&humble(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((humble(X)<~>rich(X))=>old(X)))&
(![X]:((humble(X)<~>~calm(X))<=>(curious(X)&~quiet(X))))&
(![X]:((curious(X)|creative(X))<=>(patient(X)|tall(X))))&
(![X]:((~strong(X)|~old(X))=>(strong(X)|~old(X))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)<~>~rich(X))))&
(![X]:((~tall(X)|funny(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((~quiet(paul)<~>patient(paul)))&
(?[X]:(~wise(X)))&
((~happy(fred)|kind(fred)))&
(?[X]:((funny(X)&~rich(X))))&
((creative(john)<~>~happy(john)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:((rich(X)&~brave(X))))&
((~humble(mary)&~kind(mary))) | ~tall(paul) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3225843307498894000324399
% SZS output start Proof for 3225843307498894000324399
4. ! [X0] : ((wise(X0) | ~strong(X0)) => (humble(X0) & ~tall(X0))) [input p3]
15. (~curious(paul) & ~strong(paul)) <=> (rich(john) | ~rich(john)) [input p14]
25. tall(paul) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~tall(X0)) | (~wise(X0) & strong(X0))) [ennf transformation 4]
57. ((~curious(paul) & ~strong(paul)) | (~rich(john) & rich(john))) & ((rich(john) | ~rich(john)) | (curious(paul) | strong(paul))) [nnf transformation 15]
58. ((~curious(paul) & ~strong(paul)) | (~rich(john) & rich(john))) & (rich(john) | ~rich(john) | curious(paul) | strong(paul)) [flattening 57]
81. ~tall(X0) | strong(X0) [cnf transformation 30]
123. ~strong(paul) | rich(john) [cnf transformation 58]
124. ~strong(paul) | ~rich(john) [cnf transformation 58]
149. tall(paul) [cnf transformation 25]
215. 13 <=> rich(john) [avatar definition]
225. 15 <=> strong(paul) [avatar definition]
227. ~strong(paul) <- (~15) [avatar component clause 225]
228. ~13 | ~15 [avatar split clause 124,225,215]
229. 13 | ~15 [avatar split clause 123,225,215]
273. strong(paul) [resolution 81,149]
274. $false <- (~15) [subsumption resolution 273,227]
275. 15 [avatar contradiction clause 274]
276. $false [avatar sat refutation 228,229,275]
% SZS output end Proof for 3225843307498894000324399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and tall is either not kind or not curious and vice versa.
Everyone who is both not calm and calm is either patient or strong.
If mary is tall or rich then someone is not old or old.
Everyone who is patient is not humble or tall and vice versa.
If someone is calm or quiet then someone is either not generous or not kind.
Everyone who is not humble is not brave or not kind and vice versa.
If someone is not quiet or not strong then susan is both happy and patient and vice versa.
If someone is either not calm or generous then susan is both not funny and not tall and vice versa.
If someone is not tall or generous then alice is not patient or quiet.
Everyone who is both wise and kind is either not humble or not old.
Everyone who is tall or kind is both not calm and not patient.
Everyone who is humble is funny and vice versa.
If paul is either happy or not rich then someone is old and vice versa.
If someone is not happy or not rich then susan is both strong and happy.
Everyone who is both calm and not calm is kind and vice versa.
If mary is either patient or not creative then someone is either funny or calm and vice versa.
Someone is happy.
Paul is strong.
John is calm.
Lucy is not quiet.
Someone is not happy or not quiet.
Someone is either not patient or creative.
Alice is either strong or happy. | Lucy is curious. | contradiction | (![X]:((~curious(X)&tall(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&calm(X))=>(patient(X)<~>strong(X))))&
(((tall(mary)|rich(mary)))=>(?[X]:((~old(X)|old(X)))))&
(![X]:(patient(X)<=>(~humble(X)|tall(X))))&
((?[X]:((calm(X)|quiet(X))))=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:(~humble(X)<=>(~brave(X)|~kind(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((happy(susan)&patient(susan))))&
((?[X]:((~calm(X)<~>generous(X))))<=>((~funny(susan)&~tall(susan))))&
((?[X]:((~tall(X)|generous(X))))=>((~patient(alice)|quiet(alice))))&
(![X]:((wise(X)&kind(X))=>(~humble(X)<~>~old(X))))&
(![X]:((tall(X)|kind(X))=>(~calm(X)&~patient(X))))&
(![X]:(humble(X)<=>funny(X)))&
(((happy(paul)<~>~rich(paul)))<=>(?[X]:(old(X))))&
((?[X]:((~happy(X)|~rich(X))))=>((strong(susan)&happy(susan))))&
(![X]:((calm(X)&~calm(X))<=>kind(X)))&
(((patient(mary)<~>~creative(mary)))<=>(?[X]:((funny(X)<~>calm(X)))))&
(?[X]:(happy(X)))&
(strong(paul))&
(calm(john))&
(~quiet(lucy))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
((strong(alice)<~>happy(alice))) | curious(lucy) | [
"p0",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5309424881586556913816954
% SZS output start Proof for 5309424881586556913816954
1. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p0]
11. ! [X0] : ((kind(X0) | tall(X0)) => (~patient(X0) & ~calm(X0))) [input p10]
15. ! [X0] : ((~calm(X0) & calm(X0)) <=> kind(X0)) [input p14]
24. curious(lucy) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~calm(X0)) | (~kind(X0) & ~tall(X0))) [ennf transformation 11]
35. ! [X0] : (((tall(X0) & ~curious(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (~tall(X0) | curious(X0)))) [nnf transformation 1]
36. ! [X0] : (((tall(X0) & ~curious(X0)) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~tall(X0) | curious(X0))) [flattening 35]
63. ! [X0] : (((~calm(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~calm(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | calm(X0) | ~calm(X0))) [flattening 63]
79. ~curious(X0) | ~curious(X0) | kind(X0) [cnf transformation 36]
111. ~calm(X0) | ~kind(X0) [cnf transformation 33]
125. calm(X0) | ~kind(X0) [cnf transformation 64]
144. curious(lucy) [cnf transformation 24]
146. ~curious(X0) | kind(X0) [duplicate literal removal 79]
271. ~kind(X0) [subsumption resolution 125,111]
351. kind(lucy) [resolution 146,144]
352. $false [subsumption resolution 351,271]
% SZS output end Proof for 5309424881586556913816954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either curious or not old then paul is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
If fred is either patient or old then paul is not funny and vice versa.
If someone is both not quiet and not humble then john is both not generous and not funny.
Everyone who is not patient is both patient and not patient and vice versa.
Everyone who is not strong or not curious is both humble and not humble and vice versa.
Everyone who is not funny is either happy or curious and vice versa.
Everyone who is both funny and calm is not calm.
If someone is not curious or not patient then john is either not brave or creative.
If someone is both happy and not old then someone is not curious or creative and vice versa.
Everyone who is not quiet or not patient is both brave and not generous and vice versa.
Everyone who is old is either old or not happy and vice versa.
If someone is not humble or old then mary is both curious and brave and vice versa.
If susan is either not rich or not wise then someone is not rich and vice versa.
Someone is both tall and funny.
Someone is not quiet.
Someone is not brave or not kind.
Fred is happy or not funny.
Lucy is either kind or generous. | Fred is generous. | contradiction | (((curious(fred)<~>~old(fred)))<=>((quiet(paul)<~>rich(paul))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(((patient(fred)<~>old(fred)))<=>(~funny(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~generous(john)&~funny(john))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(![X]:((~strong(X)|~curious(X))<=>(humble(X)&~humble(X))))&
(![X]:(~funny(X)<=>(happy(X)<~>curious(X))))&
(![X]:((funny(X)&calm(X))=>~calm(X)))&
((?[X]:((~curious(X)|~patient(X))))=>((~brave(john)<~>creative(john))))&
((?[X]:((happy(X)&~old(X))))<=>(?[X]:((~curious(X)|creative(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(brave(X)&~generous(X))))&
(![X]:(old(X)<=>(old(X)<~>~happy(X))))&
((?[X]:((~humble(X)|old(X))))<=>((curious(mary)&brave(mary))))&
(((~rich(susan)<~>~wise(susan)))<=>(?[X]:(~rich(X))))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)|~kind(X))))&
((happy(fred)|~funny(fred)))&
((kind(lucy)<~>generous(lucy))) | generous(fred) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6525147353994052946757147
% SZS output start Proof for 6525147353994052946757147
2. ? [X0] : (~funny(X0) | generous(X0)) => ~strong(john) [input p1]
8. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~humble(X0) & humble(X0))) [input p7]
22. generous(fred) [input hypothesis]
25. ~strong(john) | ! [X0] : (funny(X0) & ~generous(X0)) [ennf transformation 2]
37. ! [X0] : (((~curious(X0) | ~strong(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 8]
38. ! [X0] : ((~curious(X0) | ~strong(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [flattening 37]
73. ~strong(john) | ~generous(X0) [cnf transformation 25]
90. humble(X0) | strong(X0) [cnf transformation 38]
92. ~humble(X0) | strong(X0) [cnf transformation 38]
133. generous(fred) [cnf transformation 22]
167. 6 <=> strong(john) [avatar definition]
169. ~strong(john) <- (~6) [avatar component clause 167]
172. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
173. ~generous(X0) <- (7) [avatar component clause 172]
174. 7 | ~6 [avatar split clause 73,167,172]
201. strong(X0) [subsumption resolution 90,92]
291. $false <- (~6) [subsumption resolution 169,201]
292. 6 [avatar contradiction clause 291]
301. $false <- (7) [resolution 173,133]
302. ~7 [avatar contradiction clause 301]
303. $false [avatar sat refutation 174,292,302]
% SZS output end Proof for 6525147353994052946757147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not happy is not wise or quiet and vice versa.
Everyone who is not tall or not patient is creative or not kind.
If someone is both not quiet and patient then paul is not quiet or not brave and vice versa.
Everyone who is wise is both not funny and curious.
Everyone who is either not wise or not happy is either not brave or not creative.
Everyone who is not kind or creative is both funny and wise.
Everyone who is both tall and not funny is not wise.
Everyone who is both kind and curious is not curious or not wise.
Everyone who is either funny or happy is either not curious or not generous.
Everyone who is either calm or quiet is both creative and old and vice versa.
If someone is both kind and not patient then someone is tall.
If susan is either patient or wise then alice is not rich and vice versa.
If susan is patient or generous then fred is funny.
If someone is either curious or not old then someone is either not strong or strong and vice versa.
If susan is brave or not tall then susan is not generous.
Everyone who is not funny or curious is funny.
Someone is both humble and not quiet.
Someone is old or kind.
John is funny or not tall.
Fred is either not kind or not curious.
Someone is not strong.
Someone is not brave. | Fred is patient. | entailment | (![X]:((generous(X)&~happy(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~tall(X)|~patient(X))=>(creative(X)|~kind(X))))&
((?[X]:((~quiet(X)&patient(X))))<=>((~quiet(paul)|~brave(paul))))&
(![X]:(wise(X)=>(~funny(X)&curious(X))))&
(![X]:((~wise(X)<~>~happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~kind(X)|creative(X))=>(funny(X)&wise(X))))&
(![X]:((tall(X)&~funny(X))=>~wise(X)))&
(![X]:((kind(X)&curious(X))=>(~curious(X)|~wise(X))))&
(![X]:((funny(X)<~>happy(X))=>(~curious(X)<~>~generous(X))))&
(![X]:((calm(X)<~>quiet(X))<=>(creative(X)&old(X))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:(tall(X))))&
(((patient(susan)<~>wise(susan)))<=>(~rich(alice)))&
(((patient(susan)|generous(susan)))=>(funny(fred)))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~strong(X)<~>strong(X)))))&
(((brave(susan)|~tall(susan)))=>(~generous(susan)))&
(![X]:((~funny(X)|curious(X))=>funny(X)))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((old(X)|kind(X))))&
((funny(john)|~tall(john)))&
((~kind(fred)<~>~curious(fred)))&
(?[X]:(~strong(X)))&
(?[X]:(~brave(X))) | patient(fred) | [
"p1",
"p3",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6433359791383067396267361
% SZS output start Proof for 6433359791383067396267361
2. ! [X0] : ((~patient(X0) | ~tall(X0)) => (~kind(X0) | creative(X0))) [input p1]
4. ! [X0] : (wise(X0) => (curious(X0) & ~funny(X0))) [input p3]
6. ! [X0] : ((creative(X0) | ~kind(X0)) => (wise(X0) & funny(X0))) [input p5]
16. ! [X0] : ((curious(X0) | ~funny(X0)) => funny(X0)) [input p15]
23. ~patient(fred) [input hypothesis]
27. ! [X0] : ((~kind(X0) | creative(X0)) | (patient(X0) & tall(X0))) [ennf transformation 2]
28. ! [X0] : (~kind(X0) | creative(X0) | (patient(X0) & tall(X0))) [flattening 27]
29. ! [X0] : ((curious(X0) & ~funny(X0)) | ~wise(X0)) [ennf transformation 4]
31. ! [X0] : ((wise(X0) & funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 6]
40. ! [X0] : (funny(X0) | (~curious(X0) & funny(X0))) [ennf transformation 16]
76. ~kind(X0) | creative(X0) | patient(X0) [cnf transformation 28]
82. ~funny(X0) | ~wise(X0) [cnf transformation 29]
90. kind(X0) | wise(X0) [cnf transformation 31]
91. ~creative(X0) | wise(X0) [cnf transformation 31]
121. funny(X0) | funny(X0) [cnf transformation 40]
130. ~patient(fred) [cnf transformation 23]
131. funny(X0) [duplicate literal removal 121]
247. ~wise(X0) [resolution 82,131]
279. creative(X0) | patient(X0) | wise(X0) [resolution 76,90]
281. creative(X0) | patient(X0) [subsumption resolution 279,247]
287. patient(X0) | wise(X0) [resolution 281,91]
289. patient(X0) [subsumption resolution 287,247]
290. $false [resolution 289,130]
% SZS output end Proof for 6433359791383067396267361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both wise and not humble then lucy is both calm and not old.
Everyone who is both funny and not happy is not old or not kind and vice versa.
If someone is not wise or not calm then someone is wise or not brave.
Everyone who is wise is calm or creative and vice versa.
If someone is not tall or not calm then alice is both not humble and not patient.
If someone is either patient or creative then someone is either not curious or not calm and vice versa.
Everyone who is both generous and calm is generous or rich.
Everyone who is kind is both tall and not wise and vice versa.
If paul is either not rich or patient then someone is either not quiet or old and vice versa.
Everyone who is both not kind and not happy is not funny.
If someone is not calm then alice is both quiet and not curious.
Everyone who is either wise or brave is tall or not rich.
Everyone who is not quiet or not wise is either patient or kind and vice versa.
If someone is wise then someone is happy or rich.
Everyone who is either tall or not funny is patient and vice versa.
If mary is humble or tall then paul is funny or kind and vice versa.
Fred is either not quiet or brave.
Someone is either not wise or not kind. | Fred is funny. | contradiction | (((wise(paul)&~humble(paul)))=>((calm(lucy)&~old(lucy))))&
(![X]:((funny(X)&~happy(X))<=>(~old(X)|~kind(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(wise(X)<=>(calm(X)|creative(X))))&
((?[X]:((~tall(X)|~calm(X))))=>((~humble(alice)&~patient(alice))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((generous(X)&calm(X))=>(generous(X)|rich(X))))&
(![X]:(kind(X)<=>(tall(X)&~wise(X))))&
(((~rich(paul)<~>patient(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((~kind(X)&~happy(X))=>~funny(X)))&
((?[X]:(~calm(X)))=>((quiet(alice)&~curious(alice))))&
(![X]:((wise(X)<~>brave(X))=>(tall(X)|~rich(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)|rich(X)))))&
(![X]:((tall(X)<~>~funny(X))<=>patient(X)))&
(((humble(mary)|tall(mary)))<=>((funny(paul)|kind(paul))))&
((~quiet(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~kind(X)))) | funny(fred) | [
"p1",
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6132372080273741146164260
% SZS output start Proof for 6132372080273741146164260
2. ! [X0] : ((~happy(X0) & funny(X0)) <=> (~kind(X0) | ~old(X0))) [input p1]
8. ! [X0] : (kind(X0) <=> (~wise(X0) & tall(X0))) [input p7]
10. ! [X0] : ((~happy(X0) & ~kind(X0)) => ~funny(X0)) [input p9]
13. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> (patient(X0) <~> kind(X0))) [input p12]
15. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> patient(X0)) [input p14]
19. funny(fred) [input hypothesis]
29. ! [X0] : (~funny(X0) | (happy(X0) | kind(X0))) [ennf transformation 10]
30. ! [X0] : (~funny(X0) | happy(X0) | kind(X0)) [flattening 29]
35. ! [X0] : (((~happy(X0) & funny(X0)) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : (((~happy(X0) & funny(X0)) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | happy(X0) | ~funny(X0))) [flattening 35]
47. ! [X0] : ((kind(X0) | (wise(X0) | ~tall(X0))) & ((~wise(X0) & tall(X0)) | ~kind(X0))) [nnf transformation 8]
48. ! [X0] : ((kind(X0) | wise(X0) | ~tall(X0)) & ((~wise(X0) & tall(X0)) | ~kind(X0))) [flattening 47]
54. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (wise(X0) & quiet(X0)))) [nnf transformation 13]
55. ! [X0] : ((~wise(X0) | ~quiet(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (wise(X0) & quiet(X0)))) [flattening 54]
59. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~patient(X0)) & (patient(X0) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 15]
70. kind(X0) | funny(X0) [cnf transformation 36]
72. ~happy(X0) | kind(X0) [cnf transformation 36]
91. ~kind(X0) | tall(X0) [cnf transformation 48]
92. ~kind(X0) | ~wise(X0) [cnf transformation 48]
102. ~funny(X0) | happy(X0) | kind(X0) [cnf transformation 30]
110. ~kind(X0) | ~patient(X0) | wise(X0) [cnf transformation 55]
114. ~tall(X0) | ~funny(X0) | patient(X0) [cnf transformation 59]
126. funny(fred) [cnf transformation 19]
167. 10 <=> ! [X0] : tall(X0) [avatar definition]
168. tall(X0) <- (10) [avatar component clause 167]
242. ~funny(X0) | kind(X0) [subsumption resolution 102,72]
243. kind(X0) [subsumption resolution 242,70]
254. ~patient(X0) | wise(X0) [subsumption resolution 110,243]
257. 28 <=> ! [X1] : ~wise(X1) [avatar definition]
258. ~wise(X1) <- (28) [avatar component clause 257]
302. tall(X1) [resolution 91,243]
303. 10 [avatar split clause 302,167]
305. ~wise(X1) [resolution 92,243]
318. ~funny(X1) | patient(X1) <- (10) [resolution 114,168]
325. patient(fred) <- (10) [resolution 318,126]
332. wise(fred) <- (10) [resolution 325,254]
335. $false <- (10, 28) [subsumption resolution 332,258]
336. ~10 | ~28 [avatar contradiction clause 335]
337. 28 [avatar split clause 305,257]
339. $false [avatar sat refutation 303,336,337]
% SZS output end Proof for 6132372080273741146164260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is kind or creative and vice versa.
If lucy is not old or funny then someone is both not humble and humble.
If someone is both not old and not rich then someone is not curious or strong.
Everyone who is patient is quiet and vice versa.
Everyone who is either brave or not tall is not strong.
If susan is either not humble or not creative then paul is either not wise or not patient and vice versa.
Everyone who is not happy is rich and vice versa.
If someone is not funny or not tall then someone is not patient or not happy.
If someone is funny or happy then someone is not strong or not calm and vice versa.
If someone is either creative or rich then mary is either not calm or quiet and vice versa.
Everyone who is both not rich and creative is either calm or not rich.
Everyone who is not old is curious and vice versa.
If someone is wise or quiet then paul is happy or not tall.
If fred is both not brave and wise then lucy is creative or funny and vice versa.
If someone is not quiet then john is both humble and strong and vice versa.
If alice is either not patient or kind then alice is either not humble or calm.
Someone is both humble and not creative.
John is not quiet or not rich.
Someone is not generous.
Susan is both not wise and not calm.
Someone is both kind and not brave.
Alice is both old and not strong.
Alice is generous or curious. | Lucy is not funny. | entailment | (![X]:(~old(X)<=>(kind(X)|creative(X))))&
(((~old(lucy)|funny(lucy)))=>(?[X]:((~humble(X)&humble(X)))))&
((?[X]:((~old(X)&~rich(X))))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:(patient(X)<=>quiet(X)))&
(![X]:((brave(X)<~>~tall(X))=>~strong(X)))&
(((~humble(susan)<~>~creative(susan)))<=>((~wise(paul)<~>~patient(paul))))&
(![X]:(~happy(X)<=>rich(X)))&
((?[X]:((~funny(X)|~tall(X))))=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~strong(X)|~calm(X)))))&
((?[X]:((creative(X)<~>rich(X))))<=>((~calm(mary)<~>quiet(mary))))&
(![X]:((~rich(X)&creative(X))=>(calm(X)<~>~rich(X))))&
(![X]:(~old(X)<=>curious(X)))&
((?[X]:((wise(X)|quiet(X))))=>((happy(paul)|~tall(paul))))&
(((~brave(fred)&wise(fred)))<=>((creative(lucy)|funny(lucy))))&
((?[X]:(~quiet(X)))<=>((humble(john)&strong(john))))&
(((~patient(alice)<~>kind(alice)))=>((~humble(alice)<~>calm(alice))))&
(?[X]:((humble(X)&~creative(X))))&
((~quiet(john)|~rich(john)))&
(?[X]:(~generous(X)))&
((~wise(susan)&~calm(susan)))&
(?[X]:((kind(X)&~brave(X))))&
((old(alice)&~strong(alice)))&
((generous(alice)|curious(alice))) | ~funny(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5811330733887140174709943
% SZS output start Proof for 5811330733887140174709943
2. (funny(lucy) | ~old(lucy)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p1]
24. funny(lucy) [input hypothesis]
28. ? [X0] : (humble(X0) & ~humble(X0)) | (~funny(lucy) & old(lucy)) [ennf transformation 2]
39. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK0) & ~humble(sK0)) [choice axiom]
40. (humble(sK0) & ~humble(sK0)) | (~funny(lucy) & old(lucy)) [skolemisation 28,39]
80. ~humble(sK0) | ~funny(lucy) [cnf transformation 40]
82. humble(sK0) | ~funny(lucy) [cnf transformation 40]
141. funny(lucy) [cnf transformation 24]
144. 1 <=> funny(lucy) [avatar definition]
148. 2 <=> humble(sK0) [avatar definition]
151. ~1 | 2 [avatar split clause 82,148,144]
157. ~1 | ~2 [avatar split clause 80,148,144]
362. 1 [avatar split clause 141,144]
363. $false [avatar sat refutation 151,157,362]
% SZS output end Proof for 5811330733887140174709943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not brave is not quiet and vice versa. If someone is both not kind and not creative then someone is happy or not happy. If lucy is not curious or not kind then fred is both kind and not patient and vice versa. If someone is not calm or rich then paul is either strong or generous and vice versa. If lucy is either not patient or strong then someone is kind and vice versa. If john is not quiet or kind then someone is humble and vice versa. Everyone who is calm is funny and vice versa. Everyone who is not curious or not rich is both funny and not rich. If lucy is patient then paul is both strong and not humble. Everyone who is either kind or not quiet is patient and vice versa. Everyone who is either tall or happy is either patient or wise. If alice is both not rich and funny then lucy is not tall and vice versa. Everyone who is both not generous and not rich is not patient and vice versa. Everyone who is not curious is either not brave or not quiet. Everyone who is either not quiet or not funny is not wise or humble. Everyone who is tall is either patient or not kind. Someone is both patient and not tall. Someone is both not rich and not curious. Alice is curious or not brave. Someone is both creative and old. Someone is either not patient or not wise. Susan is both generous and not strong. | Alice is not brave. | neutral | (![X]:((brave(X)|~brave(X))<=>~quiet(X)))&
((?[X]:((~kind(X)&~creative(X))))=>(?[X]:((happy(X)|~happy(X)))))&
(((~curious(lucy)|~kind(lucy)))<=>((kind(fred)&~patient(fred))))&
((?[X]:((~calm(X)|rich(X))))<=>((strong(paul)<~>generous(paul))))&
(((~patient(lucy)<~>strong(lucy)))<=>(?[X]:(kind(X))))&
(((~quiet(john)|kind(john)))<=>(?[X]:(humble(X))))&
(![X]:(calm(X)<=>funny(X)))&
(![X]:((~curious(X)|~rich(X))=>(funny(X)&~rich(X))))&
((patient(lucy))=>((strong(paul)&~humble(paul))))&
(![X]:((kind(X)<~>~quiet(X))<=>patient(X)))&
(![X]:((tall(X)<~>happy(X))=>(patient(X)<~>wise(X))))&
(((~rich(alice)&funny(alice)))<=>(~tall(lucy)))&
(![X]:((~generous(X)&~rich(X))<=>~patient(X)))&
(![X]:(~curious(X)=>(~brave(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~wise(X)|humble(X))))&
(![X]:(tall(X)=>(patient(X)<~>~kind(X))))&
(?[X]:((patient(X)&~tall(X))))&
(?[X]:((~rich(X)&~curious(X))))&
((curious(alice)|~brave(alice)))&
(?[X]:((creative(X)&old(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
((generous(susan)&~strong(susan))) | ~brave(alice) | [] | null | 0 |
Everyone who is both quiet and not funny is either curious or not generous and vice versa. Everyone who is both tall and not generous is creative or wise and vice versa. If someone is not generous or not funny then lucy is either not generous or not wise and vice versa. Everyone who is creative is curious or generous and vice versa. Everyone who is not funny or rich is both not patient and not calm. Everyone who is either creative or not brave is either generous or tall and vice versa. Everyone who is both quiet and not strong is tall and vice versa. Everyone who is strong is happy. Everyone who is both not calm and old is both not patient and generous. Everyone who is both not curious and not generous is both not humble and not quiet and vice versa. Everyone who is not strong is both not strong and humble. If someone is tall or curious then someone is humble and vice versa. Everyone who is not tall is not wise or not patient and vice versa. Everyone who is either not funny or kind is either not old or happy and vice versa. If john is rich or creative then someone is not tall or humble. Everyone who is not happy is either wise or old. Alice is both not happy and funny. Paul is wise or tall. Alice is both not old and not rich. Someone is either not funny or not strong. John is both humble and not generous. | Lucy is not humble. | contradiction | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|wise(X))))&
((?[X]:((~generous(X)|~funny(X))))<=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:(creative(X)<=>(curious(X)|generous(X))))&
(![X]:((~funny(X)|rich(X))=>(~patient(X)&~calm(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(generous(X)<~>tall(X))))&
(![X]:((quiet(X)&~strong(X))<=>tall(X)))&
(![X]:(strong(X)=>happy(X)))&
(![X]:((~calm(X)&old(X))=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(~strong(X)=>(~strong(X)&humble(X))))&
((?[X]:((tall(X)|curious(X))))<=>(?[X]:(humble(X))))&
(![X]:(~tall(X)<=>(~wise(X)|~patient(X))))&
(![X]:((~funny(X)<~>kind(X))<=>(~old(X)<~>happy(X))))&
(((rich(john)|creative(john)))=>(?[X]:((~tall(X)|humble(X)))))&
(![X]:(~happy(X)=>(wise(X)<~>old(X))))&
((~happy(alice)&funny(alice)))&
((wise(paul)|tall(paul)))&
((~old(alice)&~rich(alice)))&
(?[X]:((~funny(X)<~>~strong(X))))&
((humble(john)&~generous(john))) | ~humble(lucy) | [
"p1",
"p2",
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 193486614030200002605270
% SZS output start Proof for 193486614030200002605270
2. ! [X0] : ((~generous(X0) & tall(X0)) <=> (wise(X0) | creative(X0))) [input p1]
3. ? [X0] : (~funny(X0) | ~generous(X0)) <=> (~generous(lucy) <~> ~wise(lucy)) [input p2]
4. ! [X0] : (creative(X0) <=> (generous(X0) | curious(X0))) [input p3]
7. ! [X0] : ((~strong(X0) & quiet(X0)) <=> tall(X0)) [input p6]
11. ! [X0] : (~strong(X0) => (humble(X0) & ~strong(X0))) [input p10]
22. ~humble(lucy) [input hypothesis]
31. ! [X0] : ((humble(X0) & ~strong(X0)) | strong(X0)) [ennf transformation 11]
36. ! [X0] : (((~generous(X0) & tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((~generous(X0) & tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | generous(X0) | ~tall(X0))) [flattening 36]
38. (? [X0] : (~funny(X0) | ~generous(X0)) | ((~generous(lucy) | wise(lucy)) & (~wise(lucy) | generous(lucy)))) & (((wise(lucy) | generous(lucy)) & (~wise(lucy) | ~generous(lucy))) | ! [X0] : (funny(X0) & generous(X0))) [nnf transformation 3]
39. (? [X0] : (~funny(X0) | ~generous(X0)) | ((~generous(lucy) | wise(lucy)) & (~wise(lucy) | generous(lucy)))) & (((wise(lucy) | generous(lucy)) & (~wise(lucy) | ~generous(lucy))) | ! [X1] : (funny(X1) & generous(X1))) [rectify 38]
40. ? [X0] : (~funny(X0) | ~generous(X0)) => (~funny(sK0) | ~generous(sK0)) [choice axiom]
41. ((~funny(sK0) | ~generous(sK0)) | ((~generous(lucy) | wise(lucy)) & (~wise(lucy) | generous(lucy)))) & (((wise(lucy) | generous(lucy)) & (~wise(lucy) | ~generous(lucy))) | ! [X1] : (funny(X1) & generous(X1))) [skolemisation 39,40]
42. ! [X0] : ((creative(X0) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ~creative(X0))) [nnf transformation 4]
43. ! [X0] : ((creative(X0) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ~creative(X0))) [flattening 42]
45. ! [X0] : (((~strong(X0) & quiet(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) | ~quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((~strong(X0) & quiet(X0)) | ~tall(X0)) & (tall(X0) | strong(X0) | ~quiet(X0))) [flattening 45]
71. ~wise(X0) | tall(X0) [cnf transformation 37]
72. ~creative(X0) | ~generous(X0) [cnf transformation 37]
76. wise(lucy) | generous(lucy) | generous(X1) [cnf transformation 41]
82. creative(X0) | ~generous(X0) [cnf transformation 43]
95. ~strong(X0) | ~tall(X0) [cnf transformation 46]
104. humble(X0) | strong(X0) [cnf transformation 31]
130. ~humble(lucy) [cnf transformation 22]
133. 1 <=> generous(lucy) [avatar definition]
134. generous(lucy) <- (1) [avatar component clause 133]
147. 4 <=> wise(lucy) [avatar definition]
148. wise(lucy) <- (4) [avatar component clause 147]
156. 6 <=> ! [X1] : generous(X1) [avatar definition]
157. generous(X1) <- (6) [avatar component clause 156]
158. 6 | 1 | 4 [avatar split clause 76,147,133,156]
159. ~generous(X0) [subsumption resolution 82,72]
219. tall(lucy) <- (4) [resolution 71,148]
226. strong(lucy) [resolution 104,130]
228. ~tall(lucy) [resolution 226,95]
229. $false <- (4) [subsumption resolution 228,219]
230. ~4 [avatar contradiction clause 229]
231. $false <- (6) [subsumption resolution 157,159]
232. ~6 [avatar contradiction clause 231]
233. $false <- (1) [subsumption resolution 134,159]
234. ~1 [avatar contradiction clause 233]
235. $false [avatar sat refutation 158,230,232,234]
% SZS output end Proof for 193486614030200002605270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is either not patient or not generous and vice versa.
If mary is either strong or not funny then mary is either humble or kind.
If lucy is not old or not funny then lucy is either calm or not funny.
If fred is both funny and not humble then paul is both not rich and quiet and vice versa.
If alice is both humble and funny then mary is generous or creative.
Everyone who is either generous or not generous is either creative or not rich.
If paul is both rich and generous then someone is either not humble or not tall and vice versa.
Everyone who is not kind is either not tall or not happy.
If lucy is either funny or not brave then susan is either wise or not curious and vice versa.
Everyone who is either wise or not wise is not strong or not tall.
Everyone who is tall is not humble and vice versa.
If lucy is not funny then someone is calm and vice versa.
If susan is either creative or calm then fred is both curious and not calm.
Everyone who is both wise and patient is both tall and rich and vice versa.
If someone is both not curious and not wise then paul is not wise or not brave.
If someone is either not generous or not funny then someone is either not curious or not generous and vice versa.
John is either tall or generous.
Someone is old or not old.
Someone is both not tall and not quiet.
Susan is both not humble and not happy.
Susan is both not rich and old.
Susan is either not tall or kind.
Someone is either rich or patient. | Susan is not strong. | entailment | (![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(((strong(mary)<~>~funny(mary)))=>((humble(mary)<~>kind(mary))))&
(((~old(lucy)|~funny(lucy)))=>((calm(lucy)<~>~funny(lucy))))&
(((funny(fred)&~humble(fred)))<=>((~rich(paul)&quiet(paul))))&
(((humble(alice)&funny(alice)))=>((generous(mary)|creative(mary))))&
(![X]:((generous(X)<~>~generous(X))=>(creative(X)<~>~rich(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
(![X]:(tall(X)<=>~humble(X)))&
((~funny(lucy))<=>(?[X]:(calm(X))))&
(((creative(susan)<~>calm(susan)))=>((curious(fred)&~calm(fred))))&
(![X]:((wise(X)&patient(X))<=>(tall(X)&rich(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((~wise(paul)|~brave(paul))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((tall(john)<~>generous(john)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
((~humble(susan)&~happy(susan)))&
((~rich(susan)&old(susan)))&
((~tall(susan)<~>kind(susan)))&
(?[X]:((rich(X)<~>patient(X)))) | ~strong(susan) | [
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1163381427521201325234838
% SZS output start Proof for 1163381427521201325234838
10. ! [X0] : ((wise(X0) <~> ~wise(X0)) => (~tall(X0) | ~strong(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p10]
20. ~happy(susan) & ~humble(susan) [input p19]
24. strong(susan) [input hypothesis]
32. ! [X0] : ((~tall(X0) | ~strong(X0)) | (wise(X0) <=> ~wise(X0))) [ennf transformation 10]
33. ! [X0] : (~tall(X0) | ~strong(X0) | (wise(X0) <=> ~wise(X0))) [flattening 32]
51. ! [X0] : (~tall(X0) | ~strong(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 33]
52. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 11]
113. ~tall(X0) | ~strong(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 51]
114. ~tall(X0) | ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 51]
116. tall(X0) | humble(X0) [cnf transformation 52]
141. ~humble(susan) [cnf transformation 20]
149. strong(susan) [cnf transformation 24]
150. ~tall(X0) | ~strong(X0) | ~wise(X0) [duplicate literal removal 113]
151. ~tall(X0) | ~strong(X0) | wise(X0) [duplicate literal removal 114]
278. ~tall(X0) | ~strong(X0) [subsumption resolution 150,151]
367. 43 <=> tall(susan) [avatar definition]
368. ~tall(susan) <- (~43) [avatar component clause 367]
369. tall(susan) <- (43) [avatar component clause 367]
395. humble(susan) <- (~43) [resolution 116,368]
400. $false <- (~43) [subsumption resolution 395,141]
401. 43 [avatar contradiction clause 400]
424. ~strong(susan) <- (43) [resolution 278,369]
425. $false <- (43) [subsumption resolution 424,149]
426. ~43 [avatar contradiction clause 425]
427. $false [avatar sat refutation 401,426]
% SZS output end Proof for 1163381427521201325234838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and not calm then susan is either funny or kind and vice versa.
Everyone who is either not generous or not old is tall and vice versa.
Everyone who is not rich is either strong or wise and vice versa.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
If fred is wise or not happy then lucy is humble or funny.
If lucy is both not creative and not happy then lucy is not brave and vice versa.
If someone is not strong then lucy is not tall.
Everyone who is either not patient or calm is both humble and not old and vice versa.
Everyone who is calm is strong.
Everyone who is not happy or not curious is both wise and kind and vice versa.
If fred is generous or quiet then someone is happy or patient.
Someone is not creative or not calm.
Someone is creative or curious.
Someone is not humble or not calm.
Someone is either strong or not creative.
Fred is generous or strong.
Someone is either not quiet or not old.
Fred is both not strong and not funny.
John is not wise or calm. | Lucy is not wise. | contradiction | ((?[X]:((~patient(X)&~calm(X))))<=>((funny(susan)<~>kind(susan))))&
(![X]:((~generous(X)<~>~old(X))<=>tall(X)))&
(![X]:(~rich(X)<=>(strong(X)<~>wise(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(((wise(fred)|~happy(fred)))=>((humble(lucy)|funny(lucy))))&
(((~creative(lucy)&~happy(lucy)))<=>(~brave(lucy)))&
((?[X]:(~strong(X)))=>(~tall(lucy)))&
(![X]:((~patient(X)<~>calm(X))<=>(humble(X)&~old(X))))&
(![X]:(calm(X)=>strong(X)))&
(![X]:((~happy(X)|~curious(X))<=>(wise(X)&kind(X))))&
(((generous(fred)|quiet(fred)))=>(?[X]:((happy(X)|patient(X)))))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((generous(fred)|strong(fred)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~strong(fred)&~funny(fred)))&
((~wise(john)|calm(john))) | ~wise(lucy) | [
"p5",
"p8",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 203489394035779453613205
% SZS output start Proof for 203489394035779453613205
6. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~tall(X0)) [input p5]
9. ! [X0] : (~curious(X0) <=> (generous(X0) | quiet(X0))) [input p8]
12. ? [X0] : ~strong(X0) => ~tall(lucy) [input p11]
15. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (kind(X0) & wise(X0))) [input p14]
23. ~funny(fred) & ~strong(fred) [input p22]
25. ~wise(lucy) [input hypothesis]
31. ~tall(lucy) | ! [X0] : strong(X0) [ennf transformation 12]
45. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 6]
46. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | creative(X0))) [flattening 45]
49. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | curious(X0))) [nnf transformation 9]
50. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | curious(X0))) [flattening 49]
55. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 15]
56. ! [X0] : ((~curious(X0) | ~happy(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [flattening 55]
93. quiet(X0) | tall(X0) [cnf transformation 46]
100. ~quiet(X0) | ~curious(X0) [cnf transformation 50]
107. ~tall(lucy) | strong(X0) [cnf transformation 31]
116. curious(X0) | wise(X0) [cnf transformation 56]
130. ~strong(fred) [cnf transformation 23]
133. ~wise(lucy) [cnf transformation 25]
225. 20 <=> ! [X0] : strong(X0) [avatar definition]
226. strong(X0) <- (20) [avatar component clause 225]
228. 21 <=> tall(lucy) [avatar definition]
231. 20 | ~21 [avatar split clause 107,228,225]
288. 34 <=> strong(fred) [avatar definition]
289. ~strong(fred) <- (~34) [avatar component clause 288]
302. ~34 [avatar split clause 130,288]
316. ~curious(X0) | tall(X0) [resolution 100,93]
325. wise(X1) | tall(X1) [resolution 316,116]
530. tall(lucy) [resolution 325,133]
534. 21 [avatar split clause 530,228]
536. $false <- (20, ~34) [resolution 226,289]
537. ~20 | 34 [avatar contradiction clause 536]
539. $false [avatar sat refutation 231,302,534,537]
% SZS output end Proof for 203489394035779453613205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not funny is not creative and vice versa. Everyone who is both not patient and humble is not patient or wise and vice versa. Everyone who is both not brave and tall is patient. If someone is generous then fred is either not quiet or generous. If lucy is wise or tall then someone is not creative or not brave. If mary is quiet or not old then someone is curious. Everyone who is not wise or not rich is both not quiet and not old and vice versa. Everyone who is not quiet or not patient is both wise and not tall and vice versa. Everyone who is either not funny or not kind is kind or not calm. Everyone who is tall or funny is both not funny and not quiet. If john is generous or not curious then fred is either wise or creative. If paul is curious then someone is either curious or quiet. If someone is both not patient and old then paul is not strong. Everyone who is both wise and not kind is either patient or strong and vice versa. If lucy is not humble then someone is either generous or wise and vice versa. Mary is not old or funny. John is either old or generous. Paul is either humble or curious. Paul is not kind or old. Mary is both not calm and strong. Paul is either rich or not happy. Someone is curious. | Mary is not kind. | entailment | (![X]:((~happy(X)&~funny(X))<=>~creative(X)))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)|wise(X))))&
(![X]:((~brave(X)&tall(X))=>patient(X)))&
((?[X]:(generous(X)))=>((~quiet(fred)<~>generous(fred))))&
(((wise(lucy)|tall(lucy)))=>(?[X]:((~creative(X)|~brave(X)))))&
(((quiet(mary)|~old(mary)))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&~old(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(wise(X)&~tall(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(kind(X)|~calm(X))))&
(![X]:((tall(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((generous(john)|~curious(john)))=>((wise(fred)<~>creative(fred))))&
((curious(paul))=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:((~patient(X)&old(X))))=>(~strong(paul)))&
(![X]:((wise(X)&~kind(X))<=>(patient(X)<~>strong(X))))&
((~humble(lucy))<=>(?[X]:((generous(X)<~>wise(X)))))&
((~old(mary)|funny(mary)))&
((old(john)<~>generous(john)))&
((humble(paul)<~>curious(paul)))&
((~kind(paul)|old(paul)))&
((~calm(mary)&strong(mary)))&
((rich(paul)<~>~happy(paul)))&
(?[X]:(curious(X))) | ~kind(mary) | [
"p1",
"p6",
"p7",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1610342487380760401368512
% SZS output start Proof for 1610342487380760401368512
2. ! [X0] : ((humble(X0) & ~patient(X0)) <=> (wise(X0) | ~patient(X0))) [input p1]
7. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (~old(X0) & ~quiet(X0))) [input p6]
8. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~tall(X0) & wise(X0))) [input p7]
14. ! [X0] : ((~kind(X0) & wise(X0)) <=> (patient(X0) <~> strong(X0))) [input p13]
20. strong(mary) & ~calm(mary) [input p19]
23. kind(mary) [input hypothesis]
25. strong(mary) [pure predicate removal 20]
37. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (~humble(X0) | patient(X0)))) [nnf transformation 2]
38. ! [X0] : (((humble(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | ~humble(X0) | patient(X0))) [flattening 37]
44. ! [X0] : (((~rich(X0) | ~wise(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 7]
45. ! [X0] : ((~rich(X0) | ~wise(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [flattening 44]
46. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 8]
47. ! [X0] : ((~patient(X0) | ~quiet(X0) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | (patient(X0) & quiet(X0)))) [flattening 46]
52. ! [X0] : (((~kind(X0) & wise(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (kind(X0) | ~wise(X0)))) [nnf transformation 14]
53. ! [X0] : (((~kind(X0) & wise(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | kind(X0) | ~wise(X0))) [flattening 52]
68. ~wise(X0) | ~patient(X0) [cnf transformation 38]
78. ~quiet(X0) | wise(X0) [cnf transformation 45]
83. wise(X0) | quiet(X0) [cnf transformation 47]
104. ~strong(X0) | patient(X0) | ~kind(X0) [cnf transformation 53]
115. strong(mary) [cnf transformation 25]
119. kind(mary) [cnf transformation 23]
166. wise(X0) [subsumption resolution 83,78]
255. ~patient(X0) [resolution 68,166]
273. patient(mary) | ~kind(mary) [resolution 104,115]
274. ~kind(mary) [subsumption resolution 273,255]
275. $false [subsumption resolution 274,119]
% SZS output end Proof for 1610342487380760401368512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then lucy is not kind or not tall and vice versa. Everyone who is both brave and wise is either rich or not curious. Everyone who is either rich or strong is either not rich or quiet and vice versa. If someone is both creative and not rich then alice is either not funny or strong and vice versa. Everyone who is both tall and happy is both funny and tall and vice versa. If someone is either not old or not quiet then susan is both generous and not humble and vice versa. If someone is old or funny then john is both old and not rich and vice versa. If someone is creative or strong then someone is not curious and vice versa. If someone is kind or funny then someone is not curious. Everyone who is not patient is both not tall and curious and vice versa. Everyone who is not wise is old. If someone is curious then mary is generous and vice versa. If someone is either not tall or not kind then mary is not old and vice versa. Everyone who is not quiet or not patient is either curious or creative and vice versa. If mary is funny then someone is either not kind or curious. Everyone who is either generous or not curious is humble or not wise. Alice is either quiet or not curious. Paul is not rich. Alice is not rich or strong. Someone is either humble or brave. Someone is not funny. Someone is happy or not funny. Someone is either kind or not tall. Alice is not curious or patient. | Alice is creative. | entailment | ((?[X]:(brave(X)))<=>((~kind(lucy)|~tall(lucy))))&
(![X]:((brave(X)&wise(X))=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)<~>strong(X))<=>(~rich(X)<~>quiet(X))))&
((?[X]:((creative(X)&~rich(X))))<=>((~funny(alice)<~>strong(alice))))&
(![X]:((tall(X)&happy(X))<=>(funny(X)&tall(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>((generous(susan)&~humble(susan))))&
((?[X]:((old(X)|funny(X))))<=>((old(john)&~rich(john))))&
((?[X]:((creative(X)|strong(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((kind(X)|funny(X))))=>(?[X]:(~curious(X))))&
(![X]:(~patient(X)<=>(~tall(X)&curious(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:(curious(X)))<=>(generous(mary)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(~old(mary)))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>creative(X))))&
((funny(mary))=>(?[X]:((~kind(X)<~>curious(X)))))&
(![X]:((generous(X)<~>~curious(X))=>(humble(X)|~wise(X))))&
((quiet(alice)<~>~curious(alice)))&
(~rich(paul))&
((~rich(alice)|strong(alice)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
((~curious(alice)|patient(alice))) | creative(alice) | [
"p9",
"p13",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 822252894975422021762990
% SZS output start Proof for 822252894975422021762990
10. ! [X0] : (~patient(X0) <=> (curious(X0) & ~tall(X0))) [input p9]
14. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (curious(X0) <~> creative(X0))) [input p13]
17. quiet(alice) <~> ~curious(alice) [input p16]
24. patient(alice) | ~curious(alice) [input p23]
25. ~creative(alice) [input hypothesis]
66. ! [X0] : ((~patient(X0) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | patient(X0))) [nnf transformation 10]
67. ! [X0] : ((~patient(X0) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | patient(X0))) [flattening 66]
76. ! [X0] : (((~patient(X0) | ~quiet(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (patient(X0) & quiet(X0)))) [nnf transformation 14]
77. ! [X0] : ((~patient(X0) | ~quiet(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (patient(X0) & quiet(X0)))) [flattening 76]
82. (curious(alice) | ~quiet(alice)) & (~curious(alice) | quiet(alice)) [nnf transformation 17]
133. patient(X0) | curious(X0) [cnf transformation 67]
142. creative(X0) | curious(X0) | quiet(X0) [cnf transformation 77]
146. ~patient(X0) | ~quiet(X0) | creative(X0) | ~curious(X0) [cnf transformation 77]
152. ~curious(alice) | quiet(alice) [cnf transformation 82]
153. curious(alice) | ~quiet(alice) [cnf transformation 82]
162. patient(alice) | ~curious(alice) [cnf transformation 24]
163. ~creative(alice) [cnf transformation 25]
353. 41 <=> quiet(alice) [avatar definition]
357. 42 <=> curious(alice) [avatar definition]
360. ~41 | 42 [avatar split clause 153,357,353]
361. 41 | ~42 [avatar split clause 152,357,353]
396. patient(alice) [subsumption resolution 162,133]
433. curious(alice) | quiet(alice) [resolution 142,163]
494. ~quiet(alice) | creative(alice) | ~curious(alice) [resolution 146,396]
515. ~quiet(alice) | ~curious(alice) [subsumption resolution 494,163]
516. ~42 | ~41 [avatar split clause 515,353,357]
517. 41 | 42 [avatar split clause 433,357,353]
523. $false [avatar sat refutation 360,361,516,517]
% SZS output end Proof for 822252894975422021762990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and tall is both not generous and not creative.
Everyone who is happy or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Someone is both patient and not quiet.
John is not rich or not creative.
Paul is either not brave or happy.
Susan is either happy or not generous.
Someone is both tall and kind.
Susan is not creative. | John is not happy. | neutral | (![X]:((humble(X)&tall(X))=>(~generous(X)&~creative(X))))&
(![X]:((happy(X)|~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X))))&
(~creative(susan)) | ~happy(john) | [] | null | 0 |
If someone is both not curious and creative then someone is either not calm or creative. If someone is not humble then someone is either not funny or not humble. If john is either curious or not creative then someone is either not generous or brave and vice versa. If someone is either brave or not quiet then fred is either not funny or not humble and vice versa. Everyone who is both not wise and generous is either rich or not curious. If someone is calm or not calm then lucy is both creative and not generous and vice versa. If someone is not generous or not curious then fred is not wise and vice versa. Everyone who is either not calm or not happy is not calm and vice versa. If someone is not curious then someone is kind or not happy. Everyone who is either not kind or not rich is tall and vice versa. Everyone who is not generous or not rich is curious. If john is either humble or kind then john is either not kind or not brave. Everyone who is not patient is old or calm. Everyone who is not generous or not brave is both old and kind. Everyone who is not brave is not curious and vice versa. If lucy is not creative or happy then someone is not calm. Someone is wise. Lucy is not quiet or calm. Someone is not humble. Susan is either not strong or kind. Someone is rich. Mary is not humble or not wise. Fred is generous or wise. Someone is either patient or not wise. | Fred is not rich. | contradiction | ((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((curious(john)<~>~creative(john)))<=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~wise(X)&generous(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
(?[X]:(wise(X)))&
((~quiet(lucy)|calm(lucy)))&
(?[X]:(~humble(X)))&
((~strong(susan)<~>kind(susan)))&
(?[X]:(rich(X)))&
((~humble(mary)|~wise(mary)))&
((generous(fred)|wise(fred)))&
(?[X]:((patient(X)<~>~wise(X)))) | ~rich(fred) | [
"p4",
"p5",
"p6",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2778550964599838467584138
% SZS output start Proof for 2778550964599838467584138
5. ! [X0] : ((generous(X0) & ~wise(X0)) => (rich(X0) <~> ~curious(X0))) [input p4]
6. ? [X0] : (~calm(X0) | calm(X0)) <=> (~generous(lucy) & creative(lucy)) [input p5]
7. ? [X0] : (~curious(X0) | ~generous(X0)) <=> ~wise(fred) [input p6]
11. ! [X0] : ((~rich(X0) | ~generous(X0)) => curious(X0)) [input p10]
23. wise(fred) | generous(fred) [input p22]
25. ~rich(fred) [input hypothesis]
33. ! [X0] : ((rich(X0) <~> ~curious(X0)) | (~generous(X0) | wise(X0))) [ennf transformation 5]
34. ! [X0] : ((rich(X0) <~> ~curious(X0)) | ~generous(X0) | wise(X0)) [flattening 33]
36. ! [X0] : (curious(X0) | (rich(X0) & generous(X0))) [ennf transformation 11]
56. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~generous(X0) | wise(X0)) [nnf transformation 34]
57. (? [X0] : (~calm(X0) | calm(X0)) | (generous(lucy) | ~creative(lucy))) & ((~generous(lucy) & creative(lucy)) | ! [X0] : (calm(X0) & ~calm(X0))) [nnf transformation 6]
58. (? [X0] : (~calm(X0) | calm(X0)) | generous(lucy) | ~creative(lucy)) & ((~generous(lucy) & creative(lucy)) | ! [X0] : (calm(X0) & ~calm(X0))) [flattening 57]
59. (? [X0] : (~calm(X0) | calm(X0)) | generous(lucy) | ~creative(lucy)) & ((~generous(lucy) & creative(lucy)) | ! [X1] : (calm(X1) & ~calm(X1))) [rectify 58]
60. ? [X0] : (~calm(X0) | calm(X0)) => (~calm(sK4) | calm(sK4)) [choice axiom]
61. ((~calm(sK4) | calm(sK4)) | generous(lucy) | ~creative(lucy)) & ((~generous(lucy) & creative(lucy)) | ! [X1] : (calm(X1) & ~calm(X1))) [skolemisation 59,60]
62. (? [X0] : (~curious(X0) | ~generous(X0)) | wise(fred)) & (~wise(fred) | ! [X0] : (curious(X0) & generous(X0))) [nnf transformation 7]
63. (? [X0] : (~curious(X0) | ~generous(X0)) | wise(fred)) & (~wise(fred) | ! [X1] : (curious(X1) & generous(X1))) [rectify 62]
64. ? [X0] : (~curious(X0) | ~generous(X0)) => (~curious(sK5) | ~generous(sK5)) [choice axiom]
65. ((~curious(sK5) | ~generous(sK5)) | wise(fred)) & (~wise(fred) | ! [X1] : (curious(X1) & generous(X1))) [skolemisation 63,64]
104. ~generous(X0) | rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 56]
108. ~generous(lucy) | ~calm(X1) [cnf transformation 61]
109. ~generous(lucy) | calm(X1) [cnf transformation 61]
111. ~wise(fred) | generous(X1) [cnf transformation 65]
120. rich(X0) | curious(X0) [cnf transformation 36]
138. wise(fred) | generous(fred) [cnf transformation 23]
141. ~rich(fred) [cnf transformation 25]
233. 19 <=> ! [X1] : calm(X1) [avatar definition]
234. calm(X1) <- (19) [avatar component clause 233]
236. 20 <=> generous(lucy) [avatar definition]
238. ~generous(lucy) <- (~20) [avatar component clause 236]
239. 19 | ~20 [avatar split clause 109,236,233]
241. 21 <=> ! [X1] : ~calm(X1) [avatar definition]
242. ~calm(X1) <- (21) [avatar component clause 241]
243. 21 | ~20 [avatar split clause 108,236,241]
251. 23 <=> wise(fred) [avatar definition]
252. ~wise(fred) <- (~23) [avatar component clause 251]
268. 27 <=> ! [X1] : generous(X1) [avatar definition]
269. generous(X1) <- (27) [avatar component clause 268]
270. 27 | ~23 [avatar split clause 111,251,268]
322. 38 <=> generous(fred) [avatar definition]
324. generous(fred) <- (38) [avatar component clause 322]
325. 38 | 23 [avatar split clause 138,251,322]
336. $false <- (19, 21) [subsumption resolution 234,242]
337. ~19 | ~21 [avatar contradiction clause 336]
342. $false <- (~20, 27) [subsumption resolution 238,269]
343. 20 | ~27 [avatar contradiction clause 342]
350. curious(fred) [resolution 120,141]
372. rich(fred) | ~curious(fred) | wise(fred) <- (38) [resolution 104,324]
375. ~curious(fred) | wise(fred) <- (38) [subsumption resolution 372,141]
376. wise(fred) <- (38) [subsumption resolution 375,350]
377. $false <- (~23, 38) [subsumption resolution 376,252]
378. 23 | ~38 [avatar contradiction clause 377]
399. $false [avatar sat refutation 239,243,270,325,337,343,378]
% SZS output end Proof for 2778550964599838467584138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not humble and not happy and vice versa.
If someone is rich or not humble then someone is not brave or tall.
Everyone who is not strong is patient and vice versa.
If someone is either patient or kind then someone is not happy or quiet and vice versa.
If fred is not generous or not happy then someone is tall or not rich.
Everyone who is creative is wise or generous.
Everyone who is not generous or funny is not funny or not generous and vice versa.
Everyone who is not humble is rich or happy.
Everyone who is both not humble and creative is either not patient or old.
Everyone who is either old or not happy is not kind.
If lucy is both happy and not tall then john is both calm and not old.
If someone is both not generous and not old then someone is not calm and vice versa.
Everyone who is not curious or rich is either quiet or not quiet and vice versa.
Everyone who is either wise or patient is patient and vice versa.
Everyone who is either not humble or generous is humble or not kind.
Everyone who is not kind is strong or rich.
Lucy is either patient or not rich.
Someone is both not curious and patient.
Susan is either tall or not strong.
Someone is both quiet and not happy.
John is both tall and rich. | Susan is not rich. | contradiction | (![X]:(~wise(X)<=>(~humble(X)&~happy(X))))&
((?[X]:((rich(X)|~humble(X))))=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:(~strong(X)<=>patient(X)))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
(((~generous(fred)|~happy(fred)))=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:(creative(X)=>(wise(X)|generous(X))))&
(![X]:((~generous(X)|funny(X))<=>(~funny(X)|~generous(X))))&
(![X]:(~humble(X)=>(rich(X)|happy(X))))&
(![X]:((~humble(X)&creative(X))=>(~patient(X)<~>old(X))))&
(![X]:((old(X)<~>~happy(X))=>~kind(X)))&
(((happy(lucy)&~tall(lucy)))=>((calm(john)&~old(john))))&
((?[X]:((~generous(X)&~old(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)|rich(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((~humble(X)<~>generous(X))=>(humble(X)|~kind(X))))&
(![X]:(~kind(X)=>(strong(X)|rich(X))))&
((patient(lucy)<~>~rich(lucy)))&
(?[X]:((~curious(X)&patient(X))))&
((tall(susan)<~>~strong(susan)))&
(?[X]:((quiet(X)&~happy(X))))&
((tall(john)&rich(john))) | ~rich(susan) | [
"p0",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5269099356383451090536964
% SZS output start Proof for 5269099356383451090536964
1. ! [X0] : (~wise(X0) <=> (~happy(X0) & ~humble(X0))) [input p0]
8. ! [X0] : (~humble(X0) => (happy(X0) | rich(X0))) [input p7]
14. ! [X0] : ((wise(X0) <~> patient(X0)) <=> patient(X0)) [input p13]
22. ~rich(susan) [input hypothesis]
30. ! [X0] : ((happy(X0) | rich(X0)) | humble(X0)) [ennf transformation 8]
31. ! [X0] : (happy(X0) | rich(X0) | humble(X0)) [flattening 30]
39. ! [X0] : ((~wise(X0) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | wise(X0))) [nnf transformation 1]
40. ! [X0] : ((~wise(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | wise(X0))) [flattening 39]
59. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ~patient(X0)) & (patient(X0) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 14]
67. ~humble(X0) | wise(X0) [cnf transformation 40]
68. ~happy(X0) | wise(X0) [cnf transformation 40]
84. rich(X0) | happy(X0) | humble(X0) [cnf transformation 31]
98. patient(X0) | patient(X0) | ~wise(X0) [cnf transformation 59]
101. ~patient(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 59]
115. ~rich(susan) [cnf transformation 22]
117. patient(X0) | ~wise(X0) [duplicate literal removal 98]
118. ~patient(X0) | ~wise(X0) [duplicate literal removal 101]
212. ~wise(X0) [subsumption resolution 117,118]
241. happy(susan) | humble(susan) [resolution 84,115]
245. 25 <=> humble(susan) [avatar definition]
247. humble(susan) <- (25) [avatar component clause 245]
249. 26 <=> happy(susan) [avatar definition]
251. happy(susan) <- (26) [avatar component clause 249]
252. 25 | 26 [avatar split clause 241,249,245]
263. wise(susan) <- (25) [resolution 247,67]
264. $false <- (25) [subsumption resolution 263,212]
265. ~25 [avatar contradiction clause 264]
270. wise(susan) <- (26) [resolution 251,68]
271. $false <- (26) [subsumption resolution 270,212]
272. ~26 [avatar contradiction clause 271]
273. $false [avatar sat refutation 252,265,272]
% SZS output end Proof for 5269099356383451090536964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not old and not calm then susan is either not quiet or generous.
Everyone who is not quiet or not curious is not wise and vice versa.
Everyone who is curious or old is not creative or wise and vice versa.
If susan is either calm or not brave then someone is patient or not tall.
If someone is both old and not kind then mary is not generous.
Everyone who is both not brave and kind is creative or not happy and vice versa.
Everyone who is not patient is both not wise and not humble and vice versa.
Everyone who is both not kind and not wise is funny and vice versa.
Everyone who is old or quiet is funny or kind and vice versa.
Everyone who is not creative or humble is both brave and not patient and vice versa.
If someone is not calm then someone is not funny.
If someone is creative then john is creative and vice versa.
Everyone who is both not calm and kind is either not patient or quiet.
If someone is either old or wise then someone is both brave and not happy.
If paul is humble then lucy is both patient and quiet.
Alice is either not patient or not rich.
Someone is either not patient or not kind.
Someone is kind.
Mary is quiet or curious. | Mary is not calm. | neutral | (((~old(john)&~calm(john)))=>((~quiet(susan)<~>generous(susan))))&
(![X]:((~quiet(X)|~curious(X))<=>~wise(X)))&
(![X]:((curious(X)|old(X))<=>(~creative(X)|wise(X))))&
(((calm(susan)<~>~brave(susan)))=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((old(X)&~kind(X))))=>(~generous(mary)))&
(![X]:((~brave(X)&kind(X))<=>(creative(X)|~happy(X))))&
(![X]:(~patient(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~kind(X)&~wise(X))<=>funny(X)))&
(![X]:((old(X)|quiet(X))<=>(funny(X)|kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(brave(X)&~patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~funny(X))))&
((?[X]:(creative(X)))<=>(creative(john)))&
(![X]:((~calm(X)&kind(X))=>(~patient(X)<~>quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((humble(paul))=>((patient(lucy)&quiet(lucy))))&
((~patient(alice)<~>~rich(alice)))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:(kind(X)))&
((quiet(mary)|curious(mary))) | ~calm(mary) | [] | null | 0 |
Everyone who is not kind or not tall is patient or old. If paul is either not calm or calm then someone is not funny and vice versa. If susan is not curious then alice is not funny or not quiet and vice versa. If paul is not strong then someone is either not creative or not strong and vice versa. Everyone who is not creative or not funny is brave and vice versa. If fred is brave then someone is funny and vice versa. Everyone who is both not calm and patient is either not curious or not calm and vice versa. Everyone who is both old and not curious is rich. If susan is both rich and not quiet then alice is either not patient or not happy and vice versa. If fred is not funny then someone is creative or not old and vice versa. Everyone who is both tall and not humble is either brave or curious and vice versa. If john is either rich or not tall then mary is either generous or creative. If paul is rich then someone is both not tall and wise and vice versa. Everyone who is either not curious or generous is either funny or not curious. Everyone who is either old or not generous is old or kind and vice versa. Everyone who is old is not funny. Someone is not tall. Fred is both not strong and not creative. John is either not old or curious. Fred is generous. Someone is strong. Someone is not strong. Someone is both not old and humble. | Alice is not quiet. | neutral | (![X]:((~kind(X)|~tall(X))=>(patient(X)|old(X))))&
(((~calm(paul)<~>calm(paul)))<=>(?[X]:(~funny(X))))&
((~curious(susan))<=>((~funny(alice)|~quiet(alice))))&
((~strong(paul))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:((~creative(X)|~funny(X))<=>brave(X)))&
((brave(fred))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)&patient(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~curious(X))=>rich(X)))&
(((rich(susan)&~quiet(susan)))<=>((~patient(alice)<~>~happy(alice))))&
((~funny(fred))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((tall(X)&~humble(X))<=>(brave(X)<~>curious(X))))&
(((rich(john)<~>~tall(john)))=>((generous(mary)<~>creative(mary))))&
((rich(paul))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~curious(X)<~>generous(X))=>(funny(X)<~>~curious(X))))&
(![X]:((old(X)<~>~generous(X))<=>(old(X)|kind(X))))&
(![X]:(old(X)=>~funny(X)))&
(?[X]:(~tall(X)))&
((~strong(fred)&~creative(fred)))&
((~old(john)<~>curious(john)))&
(generous(fred))&
(?[X]:(strong(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)&humble(X)))) | ~quiet(alice) | [] | null | 0 |
Everyone who is either strong or rich is not quiet and vice versa.
Everyone who is both creative and tall is both calm and rich and vice versa.
If someone is either funny or not curious then lucy is both not funny and old and vice versa.
If susan is both rich and curious then paul is either calm or not generous and vice versa.
Everyone who is either curious or not generous is rich or not brave and vice versa.
Everyone who is both humble and kind is either not rich or not funny.
If lucy is not old then lucy is creative or calm.
If someone is not strong then susan is funny or calm.
Everyone who is both not rich and quiet is both calm and not tall.
If someone is either not quiet or old then fred is either not quiet or happy.
Everyone who is either not brave or not generous is not wise.
If someone is not brave then susan is kind or not wise and vice versa.
If someone is either not funny or creative then susan is both funny and not kind.
Everyone who is not quiet or kind is both creative and quiet.
Everyone who is either not curious or humble is not quiet or not curious.
Everyone who is both not happy and strong is funny.
Lucy is not old or creative.
Lucy is funny.
Paul is both not happy and tall.
Lucy is rich.
John is either not funny or patient.
Someone is generous or not calm.
Susan is either not creative or not wise. | Lucy is not curious. | entailment | (![X]:((strong(X)<~>rich(X))<=>~quiet(X)))&
(![X]:((creative(X)&tall(X))<=>(calm(X)&rich(X))))&
((?[X]:((funny(X)<~>~curious(X))))<=>((~funny(lucy)&old(lucy))))&
(((rich(susan)&curious(susan)))<=>((calm(paul)<~>~generous(paul))))&
(![X]:((curious(X)<~>~generous(X))<=>(rich(X)|~brave(X))))&
(![X]:((humble(X)&kind(X))=>(~rich(X)<~>~funny(X))))&
((~old(lucy))=>((creative(lucy)|calm(lucy))))&
((?[X]:(~strong(X)))=>((funny(susan)|calm(susan))))&
(![X]:((~rich(X)&quiet(X))=>(calm(X)&~tall(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~quiet(fred)<~>happy(fred))))&
(![X]:((~brave(X)<~>~generous(X))=>~wise(X)))&
((?[X]:(~brave(X)))<=>((kind(susan)|~wise(susan))))&
((?[X]:((~funny(X)<~>creative(X))))=>((funny(susan)&~kind(susan))))&
(![X]:((~quiet(X)|kind(X))=>(creative(X)&quiet(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~quiet(X)|~curious(X))))&
(![X]:((~happy(X)&strong(X))=>funny(X)))&
((~old(lucy)|creative(lucy)))&
(funny(lucy))&
((~happy(paul)&tall(paul)))&
(rich(lucy))&
((~funny(john)<~>patient(john)))&
(?[X]:((generous(X)|~calm(X))))&
((~creative(susan)<~>~wise(susan))) | ~curious(lucy) | [
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6769318164324355137869232
% SZS output start Proof for 6769318164324355137869232
3. ? [X0] : (funny(X0) <~> ~curious(X0)) <=> (old(lucy) & ~funny(lucy)) [input p2]
18. funny(lucy) [input p17]
24. curious(lucy) [input hypothesis]
44. (? [X0] : ((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | (~old(lucy) | funny(lucy))) & ((old(lucy) & ~funny(lucy)) | ! [X0] : ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) [nnf transformation 3]
45. (? [X0] : ((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ~old(lucy) | funny(lucy)) & ((old(lucy) & ~funny(lucy)) | ! [X0] : ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) [flattening 44]
46. (? [X0] : ((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | ~old(lucy) | funny(lucy)) & ((old(lucy) & ~funny(lucy)) | ! [X1] : ((funny(X1) | curious(X1)) & (~curious(X1) | ~funny(X1)))) [rectify 45]
47. ? [X0] : ((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) => ((curious(sK0) | ~funny(sK0)) & (~curious(sK0) | funny(sK0))) [choice axiom]
48. (((curious(sK0) | ~funny(sK0)) & (~curious(sK0) | funny(sK0))) | ~old(lucy) | funny(lucy)) & ((old(lucy) & ~funny(lucy)) | ! [X1] : ((funny(X1) | curious(X1)) & (~curious(X1) | ~funny(X1)))) [skolemisation 46,47]
75. ~funny(lucy) | ~curious(X1) | ~funny(X1) [cnf transformation 48]
120. funny(lucy) [cnf transformation 18]
129. curious(lucy) [cnf transformation 24]
133. 1 <=> funny(lucy) [avatar definition]
135. funny(lucy) <- (1) [avatar component clause 133]
155. 6 <=> ! [X1] : (~curious(X1) | ~funny(X1)) [avatar definition]
156. ~curious(X1) | ~funny(X1) <- (6) [avatar component clause 155]
159. 6 | ~1 [avatar split clause 75,133,155]
251. 1 [avatar split clause 120,133]
279. ~funny(lucy) <- (6) [resolution 156,129]
281. $false <- (1, 6) [subsumption resolution 279,135]
282. ~1 | ~6 [avatar contradiction clause 281]
283. $false [avatar sat refutation 159,251,282]
% SZS output end Proof for 6769318164324355137869232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both old and not wise then lucy is both not happy and not creative and vice versa.
Everyone who is either happy or quiet is quiet and vice versa.
Everyone who is both patient and not creative is not happy.
If mary is not wise or not patient then someone is both not tall and old.
Everyone who is happy or not strong is both old and strong.
Everyone who is old or creative is not generous.
Everyone who is generous is both creative and not curious.
If someone is either not creative or curious then someone is not creative or not rich.
Everyone who is rich is both not humble and not old and vice versa.
If someone is both kind and not wise then paul is generous or not rich.
If fred is patient or not kind then paul is both happy and tall and vice versa.
If fred is patient or wise then someone is both tall and not calm and vice versa.
If susan is not rich or curious then paul is both creative and generous.
If fred is both not generous and not tall then someone is both kind and not curious and vice versa.
Everyone who is not patient or not funny is either not funny or not happy.
If someone is both wise and not kind then fred is not calm.
Someone is either not quiet or happy.
Someone is curious or not rich.
Someone is both not kind and not rich.
Someone is either not humble or not curious.
Someone is humble.
Alice is both not tall and not humble. | Paul is generous. | contradiction | (((old(fred)&~wise(fred)))<=>((~happy(lucy)&~creative(lucy))))&
(![X]:((happy(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((patient(X)&~creative(X))=>~happy(X)))&
(((~wise(mary)|~patient(mary)))=>(?[X]:((~tall(X)&old(X)))))&
(![X]:((happy(X)|~strong(X))=>(old(X)&strong(X))))&
(![X]:((old(X)|creative(X))=>~generous(X)))&
(![X]:(generous(X)=>(creative(X)&~curious(X))))&
((?[X]:((~creative(X)<~>curious(X))))=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:(rich(X)<=>(~humble(X)&~old(X))))&
((?[X]:((kind(X)&~wise(X))))=>((generous(paul)|~rich(paul))))&
(((patient(fred)|~kind(fred)))<=>((happy(paul)&tall(paul))))&
(((patient(fred)|wise(fred)))<=>(?[X]:((tall(X)&~calm(X)))))&
(((~rich(susan)|curious(susan)))=>((creative(paul)&generous(paul))))&
(((~generous(fred)&~tall(fred)))<=>(?[X]:((kind(X)&~curious(X)))))&
(![X]:((~patient(X)|~funny(X))=>(~funny(X)<~>~happy(X))))&
((?[X]:((wise(X)&~kind(X))))=>(~calm(fred)))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:(humble(X)))&
((~tall(alice)&~humble(alice))) | generous(paul) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7930018148440533847420204
% SZS output start Proof for 7930018148440533847420204
6. ! [X0] : ((creative(X0) | old(X0)) => ~generous(X0)) [input p5]
7. ! [X0] : (generous(X0) => (~curious(X0) & creative(X0))) [input p6]
23. generous(paul) [input hypothesis]
30. ! [X0] : (~generous(X0) | (~creative(X0) & ~old(X0))) [ennf transformation 6]
31. ! [X0] : ((~curious(X0) & creative(X0)) | ~generous(X0)) [ennf transformation 7]
89. ~generous(X0) | ~creative(X0) [cnf transformation 30]
90. creative(X0) | ~generous(X0) [cnf transformation 31]
131. generous(paul) [cnf transformation 23]
176. ~generous(X0) [subsumption resolution 90,89]
287. $false [subsumption resolution 131,176]
% SZS output end Proof for 7930018148440533847420204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
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