premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
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stringlengths 684
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⌀ | rule_concentration
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If someone is either not quiet or brave then paul is calm.
Everyone who is either patient or not funny is both not generous and curious.
If john is either brave or funny then paul is not calm.
If susan is both strong and not tall then paul is either not curious or not brave.
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. | Paul is not quiet. | contradiction | ((?[X]:((~quiet(X)<~>brave(X))))=>(calm(paul)))&
(![X]:((patient(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(((brave(john)<~>funny(john)))=>(~calm(paul)))&
(((strong(susan)&~tall(susan)))=>((~curious(paul)<~>~brave(paul))))&
((?[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))) | ~quiet(paul) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1356341846833381083461183
% SZS output start Proof for 1356341846833381083461183
7. ! [X0] : ((~quiet(X0) & ~curious(X0)) <=> (~quiet(X0) | ~creative(X0))) [input p6]
10. ! [X0] : ((~calm(X0) & calm(X0)) <=> ~curious(X0)) [input p9]
21. ~quiet(paul) [input hypothesis]
38. ! [X0] : (((~quiet(X0) & ~curious(X0)) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | (quiet(X0) | curious(X0)))) [nnf transformation 7]
39. ! [X0] : (((~quiet(X0) & ~curious(X0)) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | quiet(X0) | curious(X0))) [flattening 38]
44. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 10]
45. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~calm(X0))) [flattening 44]
78. ~curious(X0) | quiet(X0) [cnf transformation 39]
93. calm(X0) | curious(X0) [cnf transformation 45]
94. ~calm(X0) | curious(X0) [cnf transformation 45]
117. ~quiet(paul) [cnf transformation 21]
156. curious(X0) [subsumption resolution 93,94]
236. quiet(X0) [resolution 78,156]
237. $false [resolution 236,117]
% SZS output end Proof for 1356341846833381083461183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or old is either not happy or generous and vice versa.
If someone is either strong or not calm then fred is not creative.
If paul is calm then mary is both not humble and not rich.
If susan is not creative then someone is both not creative and patient and vice versa.
Everyone who is not curious is not wise or not old.
If someone is either brave or not funny then lucy is rich.
If someone is generous or creative then someone is both not tall and not kind and vice versa.
Everyone who is both not old and old is generous.
Everyone who is generous is not wise and vice versa.
Everyone who is old is not tall or not humble.
If john is both not kind and wise then someone is not rich.
Everyone who is not happy or not brave is not rich.
Everyone who is either humble or not generous is either not generous or not old.
If paul is either old or curious then susan is both quiet and not old.
Everyone who is not tall or not creative is both humble and wise.
Everyone who is tall is humble or wise and vice versa.
John is both patient and wise.
Someone is either not brave or creative.
Paul is both not strong and patient.
Someone is not patient or not generous.
Someone is either patient or humble.
Someone is not patient or not calm.
Paul is either patient or not happy.
John is not humble or not kind. | Paul is humble. | entailment | (![X]:((~curious(X)|old(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>(~creative(fred)))&
((calm(paul))=>((~humble(mary)&~rich(mary))))&
((~creative(susan))<=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:(~curious(X)=>(~wise(X)|~old(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>(rich(lucy)))&
((?[X]:((generous(X)|creative(X))))<=>(?[X]:((~tall(X)&~kind(X)))))&
(![X]:((~old(X)&old(X))=>generous(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(old(X)=>(~tall(X)|~humble(X))))&
(((~kind(john)&wise(john)))=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~brave(X))=>~rich(X)))&
(![X]:((humble(X)<~>~generous(X))=>(~generous(X)<~>~old(X))))&
(((old(paul)<~>curious(paul)))=>((quiet(susan)&~old(susan))))&
(![X]:((~tall(X)|~creative(X))=>(humble(X)&wise(X))))&
(![X]:(tall(X)<=>(humble(X)|wise(X))))&
((patient(john)&wise(john)))&
(?[X]:((~brave(X)<~>creative(X))))&
((~strong(paul)&patient(paul)))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~patient(X)|~calm(X))))&
((patient(paul)<~>~happy(paul)))&
((~humble(john)|~kind(john))) | humble(paul) | [
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2016324971821517205114879
% SZS output start Proof for 2016324971821517205114879
7. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X0] : (~kind(X0) & ~tall(X0)) [input p6]
15. ! [X0] : ((~creative(X0) | ~tall(X0)) => (wise(X0) & humble(X0))) [input p14]
16. ! [X0] : (tall(X0) <=> (wise(X0) | humble(X0))) [input p15]
25. ~humble(paul) [input hypothesis]
26. ? [X0] : (creative(X0) | generous(X0)) <=> ? [X1] : (~kind(X1) & ~tall(X1)) [rectify 7]
42. ! [X0] : ((wise(X0) & humble(X0)) | (creative(X0) & tall(X0))) [ennf transformation 15]
51. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X1] : (~kind(X1) & ~tall(X1)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 26]
52. (? [X0] : (creative(X0) | generous(X0)) | ! [X1] : (kind(X1) | tall(X1))) & (? [X2] : (~kind(X2) & ~tall(X2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [rectify 51]
53. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK1) | generous(sK1)) [choice axiom]
54. ? [X2] : (~kind(X2) & ~tall(X2)) => (~kind(sK2) & ~tall(sK2)) [choice axiom]
55. ((creative(sK1) | generous(sK1)) | ! [X1] : (kind(X1) | tall(X1))) & ((~kind(sK2) & ~tall(sK2)) | ! [X3] : (~creative(X3) & ~generous(X3))) [skolemisation 52,54,53]
61. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ~tall(X0))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~tall(X0))) [flattening 61]
91. ~tall(sK2) | ~creative(X3) [cnf transformation 55]
109. humble(X0) | creative(X0) [cnf transformation 42]
110. wise(X0) | tall(X0) [cnf transformation 42]
114. tall(X0) | ~wise(X0) [cnf transformation 62]
128. ~humble(paul) [cnf transformation 25]
200. 17 <=> ! [X3] : ~creative(X3) [avatar definition]
201. ~creative(X3) <- (17) [avatar component clause 200]
212. 20 <=> tall(sK2) [avatar definition]
214. ~tall(sK2) <- (~20) [avatar component clause 212]
215. 17 | ~20 [avatar split clause 91,212,200]
244. tall(X0) [subsumption resolution 114,110]
291. $false <- (~20) [subsumption resolution 214,244]
292. 20 [avatar contradiction clause 291]
299. creative(paul) [resolution 109,128]
302. $false <- (17) [subsumption resolution 299,201]
303. ~17 [avatar contradiction clause 302]
308. $false [avatar sat refutation 215,292,303]
% SZS output end Proof for 2016324971821517205114879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is tall then someone is not calm or not old and vice versa.
If john is either not tall or rich then lucy is old or patient and vice versa.
Everyone who is patient is both humble and rich.
Everyone who is both quiet and not generous is both not rich and curious.
Everyone who is funny is either not happy or not patient.
Everyone who is both calm and not quiet is either not humble or not wise.
If someone is either generous or curious then someone is humble and vice versa.
Everyone who is either tall or kind is wise.
If someone is not calm then john is either funny or not humble.
Everyone who is both not strong and kind is both not humble and brave and vice versa.
Everyone who is creative is generous or not strong and vice versa.
If john is calm then lucy is tall and vice versa.
Everyone who is not humble is either not humble or creative and vice versa.
Everyone who is either not rich or not quiet is creative and vice versa.
If someone is patient or not creative then someone is either old or generous and vice versa.
Everyone who is not brave is strong or not tall and vice versa.
Lucy is tall.
Paul is either wise or not humble.
Someone is either quiet or not rich.
Mary is both not creative and wise.
Lucy is both strong and not rich.
Someone is not brave or not generous. | Paul is not wise. | neutral | ((tall(lucy))<=>(?[X]:((~calm(X)|~old(X)))))&
(((~tall(john)<~>rich(john)))<=>((old(lucy)|patient(lucy))))&
(![X]:(patient(X)=>(humble(X)&rich(X))))&
(![X]:((quiet(X)&~generous(X))=>(~rich(X)&curious(X))))&
(![X]:(funny(X)=>(~happy(X)<~>~patient(X))))&
(![X]:((calm(X)&~quiet(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>kind(X))=>wise(X)))&
((?[X]:(~calm(X)))=>((funny(john)<~>~humble(john))))&
(![X]:((~strong(X)&kind(X))<=>(~humble(X)&brave(X))))&
(![X]:(creative(X)<=>(generous(X)|~strong(X))))&
((calm(john))<=>(tall(lucy)))&
(![X]:(~humble(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>creative(X)))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(strong(X)|~tall(X))))&
(tall(lucy))&
((wise(paul)<~>~humble(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~creative(mary)&wise(mary)))&
((strong(lucy)&~rich(lucy)))&
(?[X]:((~brave(X)|~generous(X)))) | ~wise(paul) | [] | null | 0 |
Everyone who is both humble and curious is humble and vice versa.
Everyone who is both not tall and humble is not rich or not generous and vice versa.
If mary is both happy and not old then someone is not humble.
If someone is happy then susan is both not curious and not generous.
Everyone who is generous or not brave is either not wise or tall.
If john is not patient then someone is either rich or kind.
Everyone who is either rich or humble is generous.
Everyone who is quiet is either happy or not tall and vice versa.
If someone is both not generous and brave then someone is tall and vice versa.
If susan is brave or not rich then paul is not quiet or generous and vice versa.
Everyone who is either not creative or curious is not kind.
Everyone who is not happy is both not curious and not tall and vice versa.
Everyone who is both not creative and brave is calm or tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
If lucy is old then someone is either not patient or not tall and vice versa.
Everyone who is calm is both wise and not funny.
Paul is either not funny or not rich.
Fred is both not humble and creative.
Someone is both not humble and rich.
Susan is both brave and not happy.
Someone is either creative or not wise.
Paul is either old or funny.
Someone is not wise. | Mary is old. | neutral | (![X]:((humble(X)&curious(X))<=>humble(X)))&
(![X]:((~tall(X)&humble(X))<=>(~rich(X)|~generous(X))))&
(((happy(mary)&~old(mary)))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))=>((~curious(susan)&~generous(susan))))&
(![X]:((generous(X)|~brave(X))=>(~wise(X)<~>tall(X))))&
((~patient(john))=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((rich(X)<~>humble(X))=>generous(X)))&
(![X]:(quiet(X)<=>(happy(X)<~>~tall(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:(tall(X))))&
(((brave(susan)|~rich(susan)))<=>((~quiet(paul)|generous(paul))))&
(![X]:((~creative(X)<~>curious(X))=>~kind(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~tall(X))))&
(![X]:((~creative(X)&brave(X))<=>(calm(X)|tall(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
((old(lucy))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:(calm(X)=>(wise(X)&~funny(X))))&
((~funny(paul)<~>~rich(paul)))&
((~humble(fred)&creative(fred)))&
(?[X]:((~humble(X)&rich(X))))&
((brave(susan)&~happy(susan)))&
(?[X]:((creative(X)<~>~wise(X))))&
((old(paul)<~>funny(paul)))&
(?[X]:(~wise(X))) | old(mary) | [] | null | 0 |
If someone is either creative or tall then someone is both rich and not humble and vice versa. Everyone who is both not old and wise is not generous or not curious and vice versa. If alice is funny or not curious then someone is not happy or not rich. Everyone who is old or not rich is not wise or calm and vice versa. Everyone who is creative is rich. If someone is both not happy and patient then alice is both not calm and wise. Everyone who is either calm or funny is not kind and vice versa. If alice is calm or funny then someone is quiet and vice versa. Everyone who is either funny or generous is both patient and strong and vice versa. Everyone who is either rich or not strong is both calm and humble and vice versa. If susan is either not old or calm then john is either not brave or not creative and vice versa. If paul is not wise then fred is not calm. If mary is both funny and not tall then someone is either not curious or generous and vice versa. Everyone who is not curious is either not funny or not patient and vice versa. If someone is not creative then someone is not old. Everyone who is calm or not strong is both happy and funny. Mary is either not humble or happy. Fred is either tall or not humble. Someone is not generous or happy. Someone is both rich and not quiet. Someone is not quiet or strong. Mary is both not curious and not kind. | Alice is not calm. | neutral | ((?[X]:((creative(X)<~>tall(X))))<=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~old(X)&wise(X))<=>(~generous(X)|~curious(X))))&
(((funny(alice)|~curious(alice)))=>(?[X]:((~happy(X)|~rich(X)))))&
(![X]:((old(X)|~rich(X))<=>(~wise(X)|calm(X))))&
(![X]:(creative(X)=>rich(X)))&
((?[X]:((~happy(X)&patient(X))))=>((~calm(alice)&wise(alice))))&
(![X]:((calm(X)<~>funny(X))<=>~kind(X)))&
(((calm(alice)|funny(alice)))<=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>generous(X))<=>(patient(X)&strong(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(calm(X)&humble(X))))&
(((~old(susan)<~>calm(susan)))<=>((~brave(john)<~>~creative(john))))&
((~wise(paul))=>(~calm(fred)))&
(((funny(mary)&~tall(mary)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:(~curious(X)<=>(~funny(X)<~>~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~old(X))))&
(![X]:((calm(X)|~strong(X))=>(happy(X)&funny(X))))&
((~humble(mary)<~>happy(mary)))&
((tall(fred)<~>~humble(fred)))&
(?[X]:((~generous(X)|happy(X))))&
(?[X]:((rich(X)&~quiet(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~curious(mary)&~kind(mary))) | ~calm(alice) | [] | null | 0 |
If someone is not happy then someone is not quiet or not patient.
If mary is not calm or old then john is not kind or not curious.
If lucy is calm or not brave then someone is creative or strong.
If someone is not kind then someone is curious.
If fred is both not humble and brave then mary is both not old and not humble.
Everyone who is either patient or calm is not tall and vice versa.
Everyone who is both kind and not rich is not tall.
Everyone who is both rich and kind is either not funny or not brave and vice versa.
Everyone who is either not funny or not strong is not curious or humble.
Everyone who is not old or not creative is not strong and vice versa.
Everyone who is either humble or wise is not old.
If susan is not creative then susan is either not curious or humble.
Everyone who is not curious is either strong or not happy and vice versa.
Everyone who is either brave or not brave is both old and rich and vice versa.
If fred is not brave or tall then someone is not calm.
Everyone who is creative or not tall is not quiet or creative and vice versa.
Fred is not kind.
Someone is both wise and tall.
Someone is both kind and not curious.
Fred is not humble.
Mary is curious or tall.
Alice is either not wise or not patient.
Someone is not kind. | Lucy is not brave. | neutral | ((?[X]:(~happy(X)))=>(?[X]:((~quiet(X)|~patient(X)))))&
(((~calm(mary)|old(mary)))=>((~kind(john)|~curious(john))))&
(((calm(lucy)|~brave(lucy)))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:(~kind(X)))=>(?[X]:(curious(X))))&
(((~humble(fred)&brave(fred)))=>((~old(mary)&~humble(mary))))&
(![X]:((patient(X)<~>calm(X))<=>~tall(X)))&
(![X]:((kind(X)&~rich(X))=>~tall(X)))&
(![X]:((rich(X)&kind(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:((~funny(X)<~>~strong(X))=>(~curious(X)|humble(X))))&
(![X]:((~old(X)|~creative(X))<=>~strong(X)))&
(![X]:((humble(X)<~>wise(X))=>~old(X)))&
((~creative(susan))=>((~curious(susan)<~>humble(susan))))&
(![X]:(~curious(X)<=>(strong(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(old(X)&rich(X))))&
(((~brave(fred)|tall(fred)))=>(?[X]:(~calm(X))))&
(![X]:((creative(X)|~tall(X))<=>(~quiet(X)|creative(X))))&
(~kind(fred))&
(?[X]:((wise(X)&tall(X))))&
(?[X]:((kind(X)&~curious(X))))&
(~humble(fred))&
((curious(mary)|tall(mary)))&
((~wise(alice)<~>~patient(alice)))&
(?[X]:(~kind(X))) | ~brave(lucy) | [] | null | 0 |
If paul is brave or not brave then someone is both humble and not creative and vice versa. Everyone who is either not creative or creative is both not tall and rich. If someone is either not calm or calm then mary is both not happy and brave and vice versa. Everyone who is either not strong or not patient is either wise or not tall. Everyone who is generous is not curious and vice versa. If someone is not kind then someone is both patient and not brave. Everyone who is both not old and not calm is either generous or not kind. If someone is not kind then fred is both creative and patient. If alice is either not curious or tall then susan is both funny and not old and vice versa. Everyone who is either kind or not curious is happy or not humble and vice versa. Everyone who is both not humble and not calm is either patient or not creative and vice versa. Everyone who is both not strong and rich is not humble. Everyone who is calm is not patient or not strong. Everyone who is patient or not patient is happy or humble and vice versa. Someone is not creative. Someone is both not curious and generous. Someone is either quiet or not brave. Someone is either tall or curious. Someone is both not curious and kind. Lucy is either happy or rich. Mary is either old or humble. | Lucy is not quiet. | neutral | (((brave(paul)|~brave(paul)))<=>(?[X]:((humble(X)&~creative(X)))))&
(![X]:((~creative(X)<~>creative(X))=>(~tall(X)&rich(X))))&
((?[X]:((~calm(X)<~>calm(X))))<=>((~happy(mary)&brave(mary))))&
(![X]:((~strong(X)<~>~patient(X))=>(wise(X)<~>~tall(X))))&
(![X]:(generous(X)<=>~curious(X)))&
((?[X]:(~kind(X)))=>(?[X]:((patient(X)&~brave(X)))))&
(![X]:((~old(X)&~calm(X))=>(generous(X)<~>~kind(X))))&
((?[X]:(~kind(X)))=>((creative(fred)&patient(fred))))&
(((~curious(alice)<~>tall(alice)))<=>((funny(susan)&~old(susan))))&
(![X]:((kind(X)<~>~curious(X))<=>(happy(X)|~humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)<~>~creative(X))))&
(![X]:((~strong(X)&rich(X))=>~humble(X)))&
(![X]:(calm(X)=>(~patient(X)|~strong(X))))&
(![X]:((patient(X)|~patient(X))<=>(happy(X)|humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)&generous(X))))&
(?[X]:((quiet(X)<~>~brave(X))))&
(?[X]:((tall(X)<~>curious(X))))&
(?[X]:((~curious(X)&kind(X))))&
((happy(lucy)<~>rich(lucy)))&
((old(mary)<~>humble(mary))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is both patient and creative is not curious.
If someone is either calm or quiet then someone is either kind or tall.
Everyone who is strong is not rich and vice versa.
Everyone who is either not rich or creative is both curious and not calm.
If susan is both not curious and not rich then someone is wise or not humble and vice versa.
Everyone who is both wise and curious is either not quiet or not wise and vice versa.
Everyone who is both not quiet and tall is both kind and brave.
If someone is either not quiet or funny then mary is quiet or not tall.
Everyone who is both not tall and strong is tall or not humble.
Everyone who is strong is not patient and vice versa.
If someone is not curious then someone is old or not creative and vice versa.
If someone is either strong or not calm then lucy is both not creative and curious.
If someone is both calm and patient then someone is strong or patient and vice versa.
Everyone who is both not patient and not kind is either calm or happy and vice versa.
If paul is not creative then someone is either not creative or not strong.
If someone is rich then paul is both not brave and wise.
John is either not old or kind.
Someone is either not humble or not generous.
Lucy is brave or not quiet.
Paul is not old or not creative.
John is both humble and kind.
Someone is not wise.
Someone is patient.
Someone is both old and humble. | Paul is not wise. | contradiction | (![X]:((patient(X)&creative(X))=>~curious(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:(strong(X)<=>~rich(X)))&
(![X]:((~rich(X)<~>creative(X))=>(curious(X)&~calm(X))))&
(((~curious(susan)&~rich(susan)))<=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((wise(X)&curious(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:((~quiet(X)&tall(X))=>(kind(X)&brave(X))))&
((?[X]:((~quiet(X)<~>funny(X))))=>((quiet(mary)|~tall(mary))))&
(![X]:((~tall(X)&strong(X))=>(tall(X)|~humble(X))))&
(![X]:(strong(X)<=>~patient(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((old(X)|~creative(X)))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~creative(lucy)&curious(lucy))))&
((?[X]:((calm(X)&patient(X))))<=>(?[X]:((strong(X)|patient(X)))))&
(![X]:((~patient(X)&~kind(X))<=>(calm(X)<~>happy(X))))&
((~creative(paul))=>(?[X]:((~creative(X)<~>~strong(X)))))&
((?[X]:(rich(X)))=>((~brave(paul)&wise(paul))))&
((~old(john)<~>kind(john)))&
(?[X]:((~humble(X)<~>~generous(X))))&
((brave(lucy)|~quiet(lucy)))&
((~old(paul)|~creative(paul)))&
((humble(john)&kind(john)))&
(?[X]:(~wise(X)))&
(?[X]:(patient(X)))&
(?[X]:((old(X)&humble(X)))) | ~wise(paul) | [
"p2",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4504803721469824437324356
% SZS output start Proof for 4504803721469824437324356
3. ! [X0] : (strong(X0) <=> ~rich(X0)) [input p2]
10. ! [X0] : (strong(X0) <=> ~patient(X0)) [input p9]
16. ? [X0] : rich(X0) => (wise(paul) & ~brave(paul)) [input p15]
23. ? [X0] : patient(X0) [input p22]
25. ~wise(paul) [input hypothesis]
41. (wise(paul) & ~brave(paul)) | ! [X0] : ~rich(X0) [ennf transformation 16]
46. ! [X0] : ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0))) [nnf transformation 3]
56. ! [X0] : ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0))) [nnf transformation 10]
79. ? [X0] : patient(X0) => patient(sK9) [choice axiom]
80. patient(sK9) [skolemisation 23,79]
89. rich(X0) | strong(X0) [cnf transformation 46]
110. ~strong(X0) | ~patient(X0) [cnf transformation 56]
133. wise(paul) | ~rich(X0) [cnf transformation 41]
143. patient(sK9) [cnf transformation 80]
146. ~wise(paul) [cnf transformation 25]
255. 25 <=> ! [X1] : ~patient(X1) [avatar definition]
256. ~patient(X1) <- (25) [avatar component clause 255]
287. 32 <=> ! [X0] : ~rich(X0) [avatar definition]
288. ~rich(X0) <- (32) [avatar component clause 287]
290. 33 <=> wise(paul) [avatar definition]
293. 32 | 33 [avatar split clause 133,290,287]
334. ~33 [avatar split clause 146,290]
335. $false <- (25) [resolution 256,143]
336. ~25 [avatar contradiction clause 335]
338. strong(X1) <- (32) [resolution 89,288]
341. ~patient(X0) <- (32) [resolution 338,110]
342. 25 | ~32 [avatar split clause 341,287,255]
343. $false [avatar sat refutation 293,334,336,342]
% SZS output end Proof for 4504803721469824437324356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is tall or not creative and vice versa.
If lucy is patient or not strong then someone is both not kind and not strong.
Everyone who is tall or creative is both calm and not patient.
Everyone who is not brave is both brave and not curious and vice versa.
Everyone who is both not strong and creative is either curious or funny.
If someone is not old or not creative then someone is either not creative or not brave and vice versa.
Everyone who is not rich or not wise is not kind or funny and vice versa.
Everyone who is both not tall and not old is not humble or rich and vice versa.
Everyone who is not humble is patient.
Everyone who is quiet or happy is not curious.
If lucy is both not brave and calm then mary is either not patient or not quiet.
If someone is either curious or not strong then someone is not funny or not brave and vice versa.
If susan is either not old or not calm then someone is not kind or curious.
Everyone who is both not quiet and not old is both generous and wise and vice versa.
Everyone who is not tall is not quiet.
Someone is not funny or generous.
Paul is either humble or not humble.
Someone is either wise or not kind.
Someone is tall or brave. | Susan is humble. | entailment | ((?[X]:(~curious(X)))<=>(?[X]:((tall(X)|~creative(X)))))&
(((patient(lucy)|~strong(lucy)))=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((tall(X)|creative(X))=>(calm(X)&~patient(X))))&
(![X]:(~brave(X)<=>(brave(X)&~curious(X))))&
(![X]:((~strong(X)&creative(X))=>(curious(X)<~>funny(X))))&
((?[X]:((~old(X)|~creative(X))))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(~kind(X)|funny(X))))&
(![X]:((~tall(X)&~old(X))<=>(~humble(X)|rich(X))))&
(![X]:(~humble(X)=>patient(X)))&
(![X]:((quiet(X)|happy(X))=>~curious(X)))&
(((~brave(lucy)&calm(lucy)))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
(((~old(susan)<~>~calm(susan)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&~old(X))<=>(generous(X)&wise(X))))&
(![X]:(~tall(X)=>~quiet(X)))&
(?[X]:((~funny(X)|generous(X))))&
((humble(paul)<~>~humble(paul)))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((tall(X)|brave(X)))) | humble(susan) | [
"p0",
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8717790562756466601105884
% SZS output start Proof for 8717790562756466601105884
1. ? [X0] : ~curious(X0) <=> ? [X0] : (~creative(X0) | tall(X0)) [input p0]
3. ! [X0] : ((creative(X0) | tall(X0)) => (~patient(X0) & calm(X0))) [input p2]
4. ! [X0] : (~brave(X0) <=> (~curious(X0) & brave(X0))) [input p3]
9. ! [X0] : (~humble(X0) => patient(X0)) [input p8]
20. ~humble(susan) [input hypothesis]
21. ? [X0] : ~curious(X0) <=> ? [X1] : (~creative(X1) | tall(X1)) [rectify 1]
26. ! [X0] : ((~patient(X0) & calm(X0)) | (~creative(X0) & ~tall(X0))) [ennf transformation 3]
29. ! [X0] : (patient(X0) | humble(X0)) [ennf transformation 9]
35. (? [X0] : ~curious(X0) | ! [X1] : (creative(X1) & ~tall(X1))) & (? [X1] : (~creative(X1) | tall(X1)) | ! [X0] : curious(X0)) [nnf transformation 21]
36. (? [X0] : ~curious(X0) | ! [X1] : (creative(X1) & ~tall(X1))) & (? [X2] : (~creative(X2) | tall(X2)) | ! [X3] : curious(X3)) [rectify 35]
37. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
38. ? [X2] : (~creative(X2) | tall(X2)) => (~creative(sK1) | tall(sK1)) [choice axiom]
39. (~curious(sK0) | ! [X1] : (creative(X1) & ~tall(X1))) & ((~creative(sK1) | tall(sK1)) | ! [X3] : curious(X3)) [skolemisation 36,38,37]
42. ! [X0] : ((~brave(X0) | (curious(X0) | ~brave(X0))) & ((~curious(X0) & brave(X0)) | brave(X0))) [nnf transformation 4]
43. ! [X0] : ((~brave(X0) | curious(X0) | ~brave(X0)) & ((~curious(X0) & brave(X0)) | brave(X0))) [flattening 42]
75. ~curious(sK0) | creative(X1) [cnf transformation 39]
83. ~patient(X0) | ~creative(X0) [cnf transformation 26]
84. brave(X0) | brave(X0) [cnf transformation 43]
86. ~brave(X0) | curious(X0) | ~brave(X0) [cnf transformation 43]
104. humble(X0) | patient(X0) [cnf transformation 29]
127. ~humble(susan) [cnf transformation 20]
128. brave(X0) [duplicate literal removal 84]
129. ~brave(X0) | curious(X0) [duplicate literal removal 86]
131. 1 <=> ! [X1] : creative(X1) [avatar definition]
132. creative(X1) <- (1) [avatar component clause 131]
134. 2 <=> curious(sK0) [avatar definition]
136. ~curious(sK0) <- (~2) [avatar component clause 134]
137. 1 | ~2 [avatar split clause 75,134,131]
143. 4 <=> ! [X3] : curious(X3) [avatar definition]
144. curious(X3) <- (4) [avatar component clause 143]
259. patient(susan) [resolution 104,127]
260. ~creative(susan) [resolution 259,83]
262. curious(X0) [resolution 129,128]
263. 4 [avatar split clause 262,143]
264. $false <- (~2, 4) [resolution 144,136]
268. 2 | ~4 [avatar contradiction clause 264]
270. $false <- (1) [resolution 132,260]
275. ~1 [avatar contradiction clause 270]
276. $false [avatar sat refutation 137,263,268,275]
% SZS output end Proof for 8717790562756466601105884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both brave and not creative then john is generous and vice versa.
If someone is both not funny and tall then fred is both patient and tall.
Everyone who is happy is either wise or not kind.
Everyone who is either curious or not wise is not humble and vice versa.
Everyone who is either not kind or not funny is either happy or not quiet and vice versa.
Everyone who is not kind or not humble is both curious and not calm and vice versa.
If someone is kind then mary is kind and vice versa.
Everyone who is not happy or not strong is strong.
If mary is not curious or quiet then someone is not strong or not funny.
If john is either not happy or rich then susan is not quiet or kind.
If paul is old or humble then fred is both not generous and kind.
Everyone who is generous or quiet is not kind or not happy.
Everyone who is not curious or quiet is quiet or not strong and vice versa.
Everyone who is patient or not wise is either rich or creative and vice versa.
Everyone who is both creative and not patient is either rich or not calm and vice versa.
If paul is both calm and not calm then someone is kind and vice versa.
Someone is either old or not rich.
Alice is either not rich or rich.
Paul is not tall or kind.
Lucy is both not patient and not old.
Someone is both brave and not patient.
Someone is curious. | Alice is generous. | neutral | (((brave(susan)&~creative(susan)))<=>(generous(john)))&
((?[X]:((~funny(X)&tall(X))))=>((patient(fred)&tall(fred))))&
(![X]:(happy(X)=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)<~>~wise(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>~funny(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~kind(X)|~humble(X))<=>(curious(X)&~calm(X))))&
((?[X]:(kind(X)))<=>(kind(mary)))&
(![X]:((~happy(X)|~strong(X))=>strong(X)))&
(((~curious(mary)|quiet(mary)))=>(?[X]:((~strong(X)|~funny(X)))))&
(((~happy(john)<~>rich(john)))=>((~quiet(susan)|kind(susan))))&
(((old(paul)|humble(paul)))=>((~generous(fred)&kind(fred))))&
(![X]:((generous(X)|quiet(X))=>(~kind(X)|~happy(X))))&
(![X]:((~curious(X)|quiet(X))<=>(quiet(X)|~strong(X))))&
(![X]:((patient(X)|~wise(X))<=>(rich(X)<~>creative(X))))&
(![X]:((creative(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
(((calm(paul)&~calm(paul)))<=>(?[X]:(kind(X))))&
(?[X]:((old(X)<~>~rich(X))))&
((~rich(alice)<~>rich(alice)))&
((~tall(paul)|kind(paul)))&
((~patient(lucy)&~old(lucy)))&
(?[X]:((brave(X)&~patient(X))))&
(?[X]:(curious(X))) | generous(alice) | [] | null | 0 |
If paul is not tall then lucy is not strong and vice versa. If someone is not generous or humble then someone is both happy and not rich and vice versa. Everyone who is not old is either not funny or generous. Everyone who is happy is both not old and not patient and vice versa. Everyone who is both not creative and old is either not patient or not old and vice versa. Everyone who is either tall or not funny is either calm or old. Everyone who is not curious or wise is both generous and not creative. Everyone who is happy is not wise or happy. If mary is both not old and not generous then fred is not strong and vice versa. If someone is generous or humble then john is not patient or calm and vice versa. Everyone who is not rich or creative is not generous and vice versa. Everyone who is both not patient and not curious is not rich. Everyone who is either not curious or generous is curious or brave and vice versa. Everyone who is not creative or not rich is either not rich or not patient. Everyone who is either rich or happy is not calm or brave and vice versa. If someone is both calm and not generous then paul is calm and vice versa. Mary is either not brave or not tall. Someone is either humble or not funny. John is either tall or not creative. Someone is both not wise and kind. Someone is either tall or not patient. Someone is either not wise or happy. Susan is not tall or patient. | Lucy is curious. | entailment | ((~tall(paul))<=>(~strong(lucy)))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:(~old(X)=>(~funny(X)<~>generous(X))))&
(![X]:(happy(X)<=>(~old(X)&~patient(X))))&
(![X]:((~creative(X)&old(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((tall(X)<~>~funny(X))=>(calm(X)<~>old(X))))&
(![X]:((~curious(X)|wise(X))=>(generous(X)&~creative(X))))&
(![X]:(happy(X)=>(~wise(X)|happy(X))))&
(((~old(mary)&~generous(mary)))<=>(~strong(fred)))&
((?[X]:((generous(X)|humble(X))))<=>((~patient(john)|calm(john))))&
(![X]:((~rich(X)|creative(X))<=>~generous(X)))&
(![X]:((~patient(X)&~curious(X))=>~rich(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(curious(X)|brave(X))))&
(![X]:((~creative(X)|~rich(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)<~>happy(X))<=>(~calm(X)|brave(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(calm(paul)))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((humble(X)<~>~funny(X))))&
((tall(john)<~>~creative(john)))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>happy(X))))&
((~tall(susan)|patient(susan))) | curious(lucy) | [
"p4",
"p6",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4102601836831331031489916
% SZS output start Proof for 4102601836831331031489916
5. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & generous(X0))) [input p6]
11. ! [X0] : ((creative(X0) | ~rich(X0)) <=> ~generous(X0)) [input p10]
12. ! [X0] : ((~curious(X0) & ~patient(X0)) => ~rich(X0)) [input p11]
13. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> (brave(X0) | curious(X0))) [input p12]
24. ~curious(lucy) [input hypothesis]
29. ! [X0] : ((~creative(X0) & generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 7]
32. ! [X0] : (~rich(X0) | (curious(X0) | patient(X0))) [ennf transformation 12]
33. ! [X0] : (~rich(X0) | curious(X0) | patient(X0)) [flattening 32]
44. ! [X0] : (((old(X0) & ~creative(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~old(X0) | creative(X0)))) [nnf transformation 5]
45. ! [X0] : (((old(X0) & ~creative(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~old(X0) | creative(X0))) [flattening 44]
54. ! [X0] : (((creative(X0) | ~rich(X0)) | generous(X0)) & (~generous(X0) | (~creative(X0) & rich(X0)))) [nnf transformation 11]
55. ! [X0] : ((creative(X0) | ~rich(X0) | generous(X0)) & (~generous(X0) | (~creative(X0) & rich(X0)))) [flattening 54]
56. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 13]
57. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [flattening 56]
90. ~old(X0) | ~patient(X0) | ~old(X0) | creative(X0) [cnf transformation 45]
95. old(X0) | ~patient(X0) | old(X0) [cnf transformation 45]
100. curious(X0) | generous(X0) [cnf transformation 29]
102. ~creative(X0) | curious(X0) [cnf transformation 29]
112. ~generous(X0) | rich(X0) [cnf transformation 55]
115. ~rich(X0) | curious(X0) | patient(X0) [cnf transformation 33]
118. generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
147. ~curious(lucy) [cnf transformation 24]
150. generous(X0) | ~curious(X0) [duplicate literal removal 118]
151. ~old(X0) | ~patient(X0) | creative(X0) [duplicate literal removal 90]
152. ~patient(X0) | old(X0) [duplicate literal removal 95]
184. 8 <=> ! [X3] : generous(X3) [avatar definition]
185. generous(X3) <- (8) [avatar component clause 184]
193. ~patient(X0) | creative(X0) [subsumption resolution 151,152]
234. generous(X0) [subsumption resolution 150,100]
235. 8 [avatar split clause 234,184]
322. rich(X0) <- (8) [resolution 112,185]
380. curious(X0) | patient(X0) <- (8) [resolution 115,322]
398. patient(lucy) <- (8) [resolution 380,147]
400. creative(lucy) <- (8) [resolution 398,193]
461. curious(lucy) <- (8) [resolution 400,102]
464. $false <- (8) [subsumption resolution 461,147]
465. ~8 [avatar contradiction clause 464]
466. $false [avatar sat refutation 235,465]
% SZS output end Proof for 4102601836831331031489916
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either curious or generous then someone is both not patient and funny. If someone is either rich or not creative then someone is not calm or strong. If someone is both not curious and wise then fred is kind or rich and vice versa. Everyone who is brave or creative is not humble or not quiet. Everyone who is not humble or calm is strong or not wise and vice versa. If someone is both not curious and not funny then someone is rich. If someone is not funny or creative then someone is either not old or not patient and vice versa. Everyone who is either kind or not quiet is rich or humble and vice versa. If someone is both kind and not brave then someone is tall or wise. If someone is both brave and not calm then someone is both not strong and not creative. If someone is either rich or patient then susan is old or calm. If fred is both patient and humble then someone is both not calm and kind and vice versa. Everyone who is not generous is either wise or not wise and vice versa. Everyone who is both not brave and not quiet is not rich. Everyone who is not rich or calm is either funny or not strong. Everyone who is both not humble and happy is both old and not humble. Mary is kind or patient. Someone is both tall and not brave. Someone is creative or wise. Someone is either not strong or curious. Lucy is either not calm or not generous. Susan is wise or not patient. Someone is tall. Someone is either not humble or not rich. | Mary is generous. | contradiction | (((curious(alice)<~>generous(alice)))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~calm(X)|strong(X)))))&
((?[X]:((~curious(X)&wise(X))))<=>((kind(fred)|rich(fred))))&
(![X]:((brave(X)|creative(X))=>(~humble(X)|~quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(strong(X)|~wise(X))))&
((?[X]:((~curious(X)&~funny(X))))=>(?[X]:(rich(X))))&
((?[X]:((~funny(X)|creative(X))))<=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((kind(X)<~>~quiet(X))<=>(rich(X)|humble(X))))&
((?[X]:((kind(X)&~brave(X))))=>(?[X]:((tall(X)|wise(X)))))&
((?[X]:((brave(X)&~calm(X))))=>(?[X]:((~strong(X)&~creative(X)))))&
((?[X]:((rich(X)<~>patient(X))))=>((old(susan)|calm(susan))))&
(((patient(fred)&humble(fred)))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:(~generous(X)<=>(wise(X)<~>~wise(X))))&
(![X]:((~brave(X)&~quiet(X))=>~rich(X)))&
(![X]:((~rich(X)|calm(X))=>(funny(X)<~>~strong(X))))&
(![X]:((~humble(X)&happy(X))=>(old(X)&~humble(X))))&
((kind(mary)|patient(mary)))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
((~calm(lucy)<~>~generous(lucy)))&
((wise(susan)|~patient(susan)))&
(?[X]:(tall(X)))&
(?[X]:((~humble(X)<~>~rich(X)))) | generous(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8332135732620072883108562
% SZS output start Proof for 8332135732620072883108562
13. ! [X0] : (~generous(X0) <=> (wise(X0) <~> ~wise(X0))) [input p12]
25. generous(mary) [input hypothesis]
79. ! [X0] : ((~generous(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | generous(X0))) [nnf transformation 13]
132. ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 79]
133. ~generous(X0) | wise(X0) | wise(X0) [cnf transformation 79]
149. generous(mary) [cnf transformation 25]
150. ~generous(X0) | ~wise(X0) [duplicate literal removal 132]
151. ~generous(X0) | wise(X0) [duplicate literal removal 133]
306. ~generous(X0) [subsumption resolution 150,151]
355. $false [subsumption resolution 149,306]
% SZS output end Proof for 8332135732620072883108562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not wise is kind or not rich and vice versa.
Everyone who is both rich and not curious is not kind.
If john is old then john is both not old and curious and vice versa.
If someone is not patient or not kind then fred is either kind or not wise and vice versa.
Everyone who is either not generous or creative is not brave or not old.
If john is both happy and patient then lucy is both curious and not old.
Everyone who is both not patient and patient is not tall.
If someone is not tall or not strong then someone is either old or humble.
If someone is either not creative or quiet then alice is both not funny and wise and vice versa.
If someone is tall or not happy then someone is old.
If susan is tall then john is both calm and old and vice versa.
If john is brave then susan is either not creative or not wise.
Everyone who is either not creative or calm is not generous or not wise.
If alice is either not kind or quiet then someone is either tall or not strong.
Everyone who is not curious or not creative is both creative and wise.
If mary is both wise and not old then someone is both calm and patient.
Alice is tall or patient.
Someone is not tall.
Someone is not humble.
Lucy is either not funny or happy.
Someone is either not brave or old.
Someone is old or not kind.
Someone is calm. | Fred is kind. | contradiction | (![X]:((~calm(X)&~wise(X))<=>(kind(X)|~rich(X))))&
(![X]:((rich(X)&~curious(X))=>~kind(X)))&
((old(john))<=>((~old(john)&curious(john))))&
((?[X]:((~patient(X)|~kind(X))))<=>((kind(fred)<~>~wise(fred))))&
(![X]:((~generous(X)<~>creative(X))=>(~brave(X)|~old(X))))&
(((happy(john)&patient(john)))=>((curious(lucy)&~old(lucy))))&
(![X]:((~patient(X)&patient(X))=>~tall(X)))&
((?[X]:((~tall(X)|~strong(X))))=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((~funny(alice)&wise(alice))))&
((?[X]:((tall(X)|~happy(X))))=>(?[X]:(old(X))))&
((tall(susan))<=>((calm(john)&old(john))))&
((brave(john))=>((~creative(susan)<~>~wise(susan))))&
(![X]:((~creative(X)<~>calm(X))=>(~generous(X)|~wise(X))))&
(((~kind(alice)<~>quiet(alice)))=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((~curious(X)|~creative(X))=>(creative(X)&wise(X))))&
(((wise(mary)&~old(mary)))=>(?[X]:((calm(X)&patient(X)))))&
((tall(alice)|patient(alice)))&
(?[X]:(~tall(X)))&
(?[X]:(~humble(X)))&
((~funny(lucy)<~>happy(lucy)))&
(?[X]:((~brave(X)<~>old(X))))&
(?[X]:((old(X)|~kind(X))))&
(?[X]:(calm(X))) | kind(fred) | [
"p0",
"p3",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4468208302883759179355933
% SZS output start Proof for 4468208302883759179355933
1. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> (~rich(X0) | kind(X0))) [input p0]
4. ? [X0] : (~kind(X0) | ~patient(X0)) <=> (kind(fred) <~> ~wise(fred)) [input p3]
23. ? [X0] : calm(X0) [input p22]
24. kind(fred) [input hypothesis]
44. ! [X0] : (((~wise(X0) & ~calm(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (wise(X0) | calm(X0)))) [nnf transformation 1]
45. ! [X0] : (((~wise(X0) & ~calm(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | wise(X0) | calm(X0))) [flattening 44]
48. (? [X0] : (~kind(X0) | ~patient(X0)) | ((kind(fred) | wise(fred)) & (~wise(fred) | ~kind(fred)))) & (((wise(fred) | ~kind(fred)) & (~wise(fred) | kind(fred))) | ! [X0] : (kind(X0) & patient(X0))) [nnf transformation 4]
49. (? [X0] : (~kind(X0) | ~patient(X0)) | ((kind(fred) | wise(fred)) & (~wise(fred) | ~kind(fred)))) & (((wise(fred) | ~kind(fred)) & (~wise(fred) | kind(fred))) | ! [X1] : (kind(X1) & patient(X1))) [rectify 48]
50. ? [X0] : (~kind(X0) | ~patient(X0)) => (~kind(sK0) | ~patient(sK0)) [choice axiom]
51. ((~kind(sK0) | ~patient(sK0)) | ((kind(fred) | wise(fred)) & (~wise(fred) | ~kind(fred)))) & (((wise(fred) | ~kind(fred)) & (~wise(fred) | kind(fred))) | ! [X1] : (kind(X1) & patient(X1))) [skolemisation 49,50]
84. ? [X0] : calm(X0) => calm(sK10) [choice axiom]
85. calm(sK10) [skolemisation 23,84]
87. ~kind(X0) | ~calm(X0) [cnf transformation 45]
89. ~wise(X0) | ~kind(X0) [cnf transformation 45]
98. wise(fred) | ~kind(fred) | kind(X1) [cnf transformation 51]
143. calm(sK10) [cnf transformation 85]
144. kind(fred) [cnf transformation 24]
164. 4 <=> kind(fred) [avatar definition]
176. ~kind(fred) | kind(X1) [subsumption resolution 98,89]
178. 7 <=> ! [X1] : kind(X1) [avatar definition]
179. kind(X1) <- (7) [avatar component clause 178]
180. 7 | ~4 [avatar split clause 176,164,178]
367. 4 [avatar split clause 144,164]
372. ~calm(X0) <- (7) [resolution 87,179]
373. $false <- (7) [resolution 372,143]
374. ~7 [avatar contradiction clause 373]
375. $false [avatar sat refutation 180,367,374]
% SZS output end Proof for 4468208302883759179355933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and tall then someone is not generous or rich and vice versa.
If someone is either not tall or not patient then someone is not funny.
If lucy is not kind then john is both funny and not strong and vice versa.
Everyone who is tall is brave or not generous and vice versa.
Everyone who is either curious or rich is not wise or not tall and vice versa.
If john is both not tall and funny then someone is not tall and vice versa.
Everyone who is either not patient or happy is not calm or patient and vice versa.
If someone is generous or old then someone is rich or funny.
If fred is not wise then lucy is either not strong or not curious and vice versa.
If john is both calm and not wise then someone is both wise and not old.
If fred is not rich or happy then someone is both not calm and funny and vice versa.
Everyone who is both kind and not generous is both not quiet and happy.
Everyone who is not brave or calm is both old and wise.
If someone is tall then mary is kind or humble.
Everyone who is old is both not tall and generous and vice versa.
If paul is either not kind or not patient then susan is quiet.
Lucy is either not funny or old.
Fred is not patient or strong.
Lucy is not brave.
Alice is both not curious and tall.
Paul is not curious or not wise.
Paul is both wise and quiet.
Fred is brave. | Lucy is not funny. | contradiction | ((?[X]:((~creative(X)&tall(X))))<=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~tall(X)<~>~patient(X))))=>(?[X]:(~funny(X))))&
((~kind(lucy))<=>((funny(john)&~strong(john))))&
(![X]:(tall(X)<=>(brave(X)|~generous(X))))&
(![X]:((curious(X)<~>rich(X))<=>(~wise(X)|~tall(X))))&
(((~tall(john)&funny(john)))<=>(?[X]:(~tall(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~calm(X)|patient(X))))&
((?[X]:((generous(X)|old(X))))=>(?[X]:((rich(X)|funny(X)))))&
((~wise(fred))<=>((~strong(lucy)<~>~curious(lucy))))&
(((calm(john)&~wise(john)))=>(?[X]:((wise(X)&~old(X)))))&
(((~rich(fred)|happy(fred)))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:((kind(X)&~generous(X))=>(~quiet(X)&happy(X))))&
(![X]:((~brave(X)|calm(X))=>(old(X)&wise(X))))&
((?[X]:(tall(X)))=>((kind(mary)|humble(mary))))&
(![X]:(old(X)<=>(~tall(X)&generous(X))))&
(((~kind(paul)<~>~patient(paul)))=>(quiet(susan)))&
((~funny(lucy)<~>old(lucy)))&
((~patient(fred)|strong(fred)))&
(~brave(lucy))&
((~curious(alice)&tall(alice)))&
((~curious(paul)|~wise(paul)))&
((wise(paul)&quiet(paul)))&
(brave(fred)) | ~funny(lucy) | [
"p12",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1648299156970167846112015
% SZS output start Proof for 1648299156970167846112015
13. ! [X0] : ((calm(X0) | ~brave(X0)) => (wise(X0) & old(X0))) [input p12]
17. ~funny(lucy) <~> old(lucy) [input p16]
19. ~brave(lucy) [input p18]
24. ~funny(lucy) [input hypothesis]
35. ! [X0] : ((wise(X0) & old(X0)) | (~calm(X0) & brave(X0))) [ennf transformation 13]
73. (~old(lucy) | funny(lucy)) & (old(lucy) | ~funny(lucy)) [nnf transformation 17]
117. old(X0) | brave(X0) [cnf transformation 35]
127. ~old(lucy) | funny(lucy) [cnf transformation 73]
129. ~brave(lucy) [cnf transformation 19]
136. ~funny(lucy) [cnf transformation 24]
301. 36 <=> funny(lucy) [avatar definition]
305. 37 <=> old(lucy) [avatar definition]
307. ~old(lucy) <- (~37) [avatar component clause 305]
308. 36 | ~37 [avatar split clause 127,305,301]
329. ~36 [avatar split clause 136,301]
332. brave(lucy) <- (~37) [resolution 117,307]
333. $false <- (~37) [subsumption resolution 332,129]
334. 37 [avatar contradiction clause 333]
335. $false [avatar sat refutation 308,329,334]
% SZS output end Proof for 1648299156970167846112015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not patient and rich then mary is both funny and not humble.
Everyone who is either kind or calm is creative.
Everyone who is not old or wise is both calm and not wise.
If paul is strong then someone is not curious and vice versa.
Everyone who is both not happy and not funny is creative or not brave and vice versa.
Everyone who is creative or not tall is either happy or not curious and vice versa.
Everyone who is funny is wise or not generous.
Everyone who is not brave is humble and vice versa.
If someone is curious then someone is not humble or not calm and vice versa.
Everyone who is calm or not old is kind or brave.
Everyone who is both not strong and brave is either not creative or not patient and vice versa.
If someone is creative or curious then alice is both quiet and not strong and vice versa.
Everyone who is both not calm and happy is old or not patient and vice versa.
Everyone who is either humble or not quiet is patient and vice versa.
If someone is tall then someone is not rich or rich and vice versa.
If mary is either old or curious then someone is kind or not old.
Lucy is either not rich or creative.
Mary is not patient or not humble.
Lucy is funny.
Someone is not quiet or not generous.
Someone is not generous.
Paul is calm.
Someone is creative. | Paul is curious. | contradiction | ((?[X]:((~patient(X)&rich(X))))=>((funny(mary)&~humble(mary))))&
(![X]:((kind(X)<~>calm(X))=>creative(X)))&
(![X]:((~old(X)|wise(X))=>(calm(X)&~wise(X))))&
((strong(paul))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)&~funny(X))<=>(creative(X)|~brave(X))))&
(![X]:((creative(X)|~tall(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(funny(X)=>(wise(X)|~generous(X))))&
(![X]:(~brave(X)<=>humble(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))&
(![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((~rich(lucy)<~>creative(lucy)))&
((~patient(mary)|~humble(mary)))&
(funny(lucy))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:(~generous(X)))&
(calm(paul))&
(?[X]:(creative(X))) | curious(paul) | [
"p3",
"p4",
"p5",
"p10",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3254615687920094313354384
% SZS output start Proof for 3254615687920094313354384
4. strong(paul) <=> ? [X0] : ~curious(X0) [input p3]
5. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> (~brave(X0) | creative(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | creative(X0)) <=> (happy(X0) <~> ~curious(X0))) [input p5]
11. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~creative(X0) <~> ~patient(X0))) [input p10]
13. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (~patient(X0) | old(X0))) [input p12]
22. calm(paul) [input p21]
23. ? [X0] : creative(X0) [input p22]
24. curious(paul) [input hypothesis]
38. (strong(paul) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~strong(paul)) [nnf transformation 4]
39. (strong(paul) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~strong(paul)) [rectify 38]
40. ? [X1] : ~curious(X1) => ~curious(sK0) [choice axiom]
41. (strong(paul) | ! [X0] : curious(X0)) & (~curious(sK0) | ~strong(paul)) [skolemisation 39,40]
42. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (funny(X0) | happy(X0)))) [nnf transformation 5]
43. ! [X0] : (((~funny(X0) & ~happy(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | funny(X0) | happy(X0))) [flattening 42]
44. ! [X0] : (((~tall(X0) | creative(X0)) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0)))) & (((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | (tall(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((~tall(X0) | creative(X0) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0)))) & (((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | (tall(X0) & ~creative(X0)))) [flattening 44]
52. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | (~brave(X0) | strong(X0)))) [nnf transformation 11]
53. ! [X0] : (((brave(X0) & ~strong(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) & (((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ~brave(X0) | strong(X0))) [flattening 52]
59. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 13]
60. ! [X0] : (((happy(X0) & ~calm(X0)) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~happy(X0) | calm(X0))) [flattening 59]
71. ? [X0] : creative(X0) => creative(sK7) [choice axiom]
72. creative(sK7) [skolemisation 23,71]
79. strong(paul) | curious(X0) [cnf transformation 41]
81. ~happy(X0) | ~creative(X0) [cnf transformation 43]
85. ~curious(X0) | happy(X0) | ~creative(X0) [cnf transformation 45]
100. ~strong(X0) | ~patient(X0) | creative(X0) [cnf transformation 53]
111. ~calm(X0) | patient(X0) [cnf transformation 60]
127. calm(paul) [cnf transformation 22]
128. creative(sK7) [cnf transformation 72]
129. curious(paul) [cnf transformation 24]
144. 4 <=> ! [X0] : curious(X0) [avatar definition]
145. curious(X0) <- (4) [avatar component clause 144]
147. 5 <=> strong(paul) [avatar definition]
149. strong(paul) <- (5) [avatar component clause 147]
150. 4 | 5 [avatar split clause 79,147,144]
157. ~curious(X0) | ~creative(X0) [subsumption resolution 85,81]
201. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
202. ~creative(X1) <- (17) [avatar component clause 201]
260. patient(paul) [resolution 111,127]
265. ~creative(paul) [resolution 157,129]
266. ~creative(X0) <- (4) [resolution 157,145]
268. 17 | ~4 [avatar split clause 266,144,201]
269. $false <- (17) [resolution 202,128]
272. ~17 [avatar contradiction clause 269]
310. ~patient(paul) | creative(paul) <- (5) [resolution 100,149]
311. creative(paul) <- (5) [subsumption resolution 310,260]
312. $false <- (5) [subsumption resolution 311,265]
313. ~5 [avatar contradiction clause 312]
314. $false [avatar sat refutation 150,268,272,313]
% SZS output end Proof for 3254615687920094313354384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not humble is either not brave or not rich and vice versa. Everyone who is both not funny and not wise is not rich or not creative and vice versa. If alice is both not rich and old then john is not strong or patient and vice versa. If alice is wise or old then someone is either generous or not creative. Everyone who is wise is either not kind or not funny and vice versa. Everyone who is both generous and happy is rich or not wise and vice versa. Everyone who is patient is either not wise or generous and vice versa. If someone is both humble and old then someone is either curious or not old. Everyone who is not calm is both calm and not calm and vice versa. Everyone who is either not quiet or humble is either not humble or wise. Everyone who is both not funny and not old is wise or old. Everyone who is not kind or not curious is not happy and vice versa. If someone is either not humble or not generous then fred is either tall or calm and vice versa. Everyone who is not calm or not rich is tall or humble and vice versa. John is both not quiet and not humble. Someone is either not curious or funny. Someone is either curious or not patient. Someone is funny or curious. John is strong or not creative. | Alice is not kind. | contradiction | (![X]:((~calm(X)<~>~humble(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~funny(X)&~wise(X))<=>(~rich(X)|~creative(X))))&
(((~rich(alice)&old(alice)))<=>((~strong(john)|patient(john))))&
(((wise(alice)|old(alice)))=>(?[X]:((generous(X)<~>~creative(X)))))&
(![X]:(wise(X)<=>(~kind(X)<~>~funny(X))))&
(![X]:((generous(X)&happy(X))<=>(rich(X)|~wise(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>generous(X))))&
((?[X]:((humble(X)&old(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:(~calm(X)<=>(calm(X)&~calm(X))))&
(![X]:((~quiet(X)<~>humble(X))=>(~humble(X)<~>wise(X))))&
(![X]:((~funny(X)&~old(X))=>(wise(X)|old(X))))&
(![X]:((~kind(X)|~curious(X))<=>~happy(X)))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~calm(X)|~rich(X))<=>(tall(X)|humble(X))))&
((~quiet(john)&~humble(john)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((funny(X)|curious(X))))&
((strong(john)|~creative(john))) | ~kind(alice) | [
"p1",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4830900245124251917630955
% SZS output start Proof for 4830900245124251917630955
2. ! [X0] : ((~wise(X0) & ~funny(X0)) <=> (~creative(X0) | ~rich(X0))) [input p1]
6. ! [X0] : ((happy(X0) & generous(X0)) <=> (~wise(X0) | rich(X0))) [input p5]
12. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> ~happy(X0)) [input p11]
20. ~kind(alice) [input hypothesis]
28. ! [X0] : (((~wise(X0) & ~funny(X0)) | (creative(X0) & rich(X0))) & ((~creative(X0) | ~rich(X0)) | (wise(X0) | funny(X0)))) [nnf transformation 2]
29. ! [X0] : (((~wise(X0) & ~funny(X0)) | (creative(X0) & rich(X0))) & (~creative(X0) | ~rich(X0) | wise(X0) | funny(X0))) [flattening 28]
36. ! [X0] : (((happy(X0) & generous(X0)) | (wise(X0) & ~rich(X0))) & ((~wise(X0) | rich(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 6]
37. ! [X0] : (((happy(X0) & generous(X0)) | (wise(X0) & ~rich(X0))) & (~wise(X0) | rich(X0) | ~happy(X0) | ~generous(X0))) [flattening 36]
46. ! [X0] : (((~curious(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & kind(X0)))) [nnf transformation 12]
47. ! [X0] : ((~curious(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & kind(X0)))) [flattening 46]
73. ~wise(X0) | rich(X0) [cnf transformation 29]
91. ~rich(X0) | happy(X0) [cnf transformation 37]
92. happy(X0) | wise(X0) [cnf transformation 37]
107. ~happy(X0) | kind(X0) [cnf transformation 47]
130. ~kind(alice) [cnf transformation 20]
151. 4 <=> rich(alice) [avatar definition]
152. rich(alice) <- (4) [avatar component clause 151]
167. 7 <=> wise(alice) [avatar definition]
168. wise(alice) <- (7) [avatar component clause 167]
262. kind(X0) | wise(X0) [resolution 107,92]
279. wise(alice) [resolution 262,130]
280. 7 [avatar split clause 279,167]
282. rich(alice) <- (7) [resolution 168,73]
285. 4 | ~7 [avatar split clause 282,167,151]
287. happy(alice) <- (4) [resolution 152,91]
295. kind(alice) <- (4) [resolution 287,107]
296. $false <- (4) [subsumption resolution 295,130]
297. ~4 [avatar contradiction clause 296]
298. $false [avatar sat refutation 280,285,297]
% SZS output end Proof for 4830900245124251917630955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or curious is generous and vice versa.
If john is both not calm and generous then alice is both happy and not strong and vice versa.
Everyone who is not humble is not rich and vice versa.
If someone is old or calm then someone is calm.
Everyone who is both kind and not humble is both not wise and not patient.
If someone is quiet or not strong then someone is both not strong and rich.
If lucy is not humble or tall then someone is both happy and rich and vice versa.
Everyone who is either not quiet or creative is both strong and old and vice versa.
If someone is not brave or not wise then someone is either generous or not happy.
If paul is not generous or brave then someone is funny.
If susan is generous or wise then someone is both funny and creative.
Everyone who is not humble is not wise or funny and vice versa.
Everyone who is kind is either happy or generous and vice versa.
Everyone who is both generous and brave is either not happy or rich.
If paul is both not quiet and not humble then someone is not creative or curious and vice versa.
If lucy is both quiet and not calm then someone is generous or not curious.
Susan is both not quiet and strong.
Someone is both not kind and not patient.
Lucy is either not creative or not patient.
John is calm.
Fred is happy or wise.
Someone is either not old or not generous.
Someone is both not curious and rich.
Fred is either strong or not rich. | Susan is not strong. | contradiction | (![X]:((quiet(X)<~>curious(X))<=>generous(X)))&
(((~calm(john)&generous(john)))<=>((happy(alice)&~strong(alice))))&
(![X]:(~humble(X)<=>~rich(X)))&
((?[X]:((old(X)|calm(X))))=>(?[X]:(calm(X))))&
(![X]:((kind(X)&~humble(X))=>(~wise(X)&~patient(X))))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:((~strong(X)&rich(X)))))&
(((~humble(lucy)|tall(lucy)))<=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((~quiet(X)<~>creative(X))<=>(strong(X)&old(X))))&
((?[X]:((~brave(X)|~wise(X))))=>(?[X]:((generous(X)<~>~happy(X)))))&
(((~generous(paul)|brave(paul)))=>(?[X]:(funny(X))))&
(((generous(susan)|wise(susan)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:(~humble(X)<=>(~wise(X)|funny(X))))&
(![X]:(kind(X)<=>(happy(X)<~>generous(X))))&
(![X]:((generous(X)&brave(X))=>(~happy(X)<~>rich(X))))&
(((~quiet(paul)&~humble(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((quiet(lucy)&~calm(lucy)))=>(?[X]:((generous(X)|~curious(X)))))&
((~quiet(susan)&strong(susan)))&
(?[X]:((~kind(X)&~patient(X))))&
((~creative(lucy)<~>~patient(lucy)))&
(calm(john))&
((happy(fred)|wise(fred)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~curious(X)&rich(X))))&
((strong(fred)<~>~rich(fred))) | ~strong(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 725301266829159552217377
% SZS output start Proof for 725301266829159552217377
17. strong(susan) & ~quiet(susan) [input p16]
25. ~strong(susan) [input hypothesis]
140. strong(susan) [cnf transformation 17]
153. ~strong(susan) [cnf transformation 25]
364. $false [subsumption resolution 153,140]
% SZS output end Proof for 725301266829159552217377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and happy is either not funny or brave and vice versa.
Everyone who is curious or humble is either not brave or patient and vice versa.
If someone is not calm then someone is not generous and vice versa.
If mary is funny or not strong then lucy is not happy and vice versa.
Everyone who is not calm or not happy is not old or not kind and vice versa.
If fred is brave then john is not old or brave.
Everyone who is not kind is either not funny or kind and vice versa.
Everyone who is not funny or old is both happy and brave and vice versa.
If someone is both not rich and not happy then someone is either old or humble and vice versa.
Everyone who is either patient or not kind is wise or rich and vice versa.
Everyone who is either not funny or creative is not curious or not wise.
If someone is generous or humble then someone is not happy.
If someone is calm or tall then alice is not brave.
If john is patient or old then someone is either not quiet or brave.
Everyone who is both funny and wise is not old.
If someone is both not strong and happy then someone is either not tall or generous and vice versa.
Paul is both not quiet and not calm.
Someone is either not humble or rich.
Someone is either not patient or curious.
Mary is either not quiet or happy.
Someone is either not old or creative. | Paul is not tall. | entailment | (![X]:((~patient(X)&happy(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((curious(X)|humble(X))<=>(~brave(X)<~>patient(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~generous(X))))&
(((funny(mary)|~strong(mary)))<=>(~happy(lucy)))&
(![X]:((~calm(X)|~happy(X))<=>(~old(X)|~kind(X))))&
((brave(fred))=>((~old(john)|brave(john))))&
(![X]:(~kind(X)<=>(~funny(X)<~>kind(X))))&
(![X]:((~funny(X)|old(X))<=>(happy(X)&brave(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~kind(X))<=>(wise(X)|rich(X))))&
(![X]:((~funny(X)<~>creative(X))=>(~curious(X)|~wise(X))))&
((?[X]:((generous(X)|humble(X))))=>(?[X]:(~happy(X))))&
((?[X]:((calm(X)|tall(X))))=>(~brave(alice)))&
(((patient(john)|old(john)))=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:((funny(X)&wise(X))=>~old(X)))&
((?[X]:((~strong(X)&happy(X))))<=>(?[X]:((~tall(X)<~>generous(X)))))&
((~quiet(paul)&~calm(paul)))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
((~quiet(mary)<~>happy(mary)))&
(?[X]:((~old(X)<~>creative(X)))) | ~tall(paul) | [
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4941485399745933528382468
% SZS output start Proof for 4941485399745933528382468
7. ! [X0] : (~kind(X0) <=> (~funny(X0) <~> kind(X0))) [input p6]
8. ! [X0] : ((old(X0) | ~funny(X0)) <=> (brave(X0) & happy(X0))) [input p7]
13. ? [X0] : (tall(X0) | calm(X0)) => ~brave(alice) [input p12]
22. tall(paul) [input hypothesis]
32. ~brave(alice) | ! [X0] : (~tall(X0) & ~calm(X0)) [ennf transformation 13]
49. ! [X0] : ((~kind(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) & (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | kind(X0))) [nnf transformation 7]
50. ! [X0] : (((old(X0) | ~funny(X0)) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | (~old(X0) & funny(X0)))) [nnf transformation 8]
51. ! [X0] : ((old(X0) | ~funny(X0) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | (~old(X0) & funny(X0)))) [flattening 50]
103. kind(X0) | ~funny(X0) | kind(X0) [cnf transformation 49]
106. ~kind(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 49]
109. brave(X0) | funny(X0) [cnf transformation 51]
129. ~brave(alice) | ~tall(X0) [cnf transformation 32]
151. tall(paul) [cnf transformation 22]
152. kind(X0) | ~funny(X0) [duplicate literal removal 103]
153. ~kind(X0) | ~funny(X0) [duplicate literal removal 106]
198. ~funny(X0) [subsumption resolution 152,153]
199. brave(X0) [subsumption resolution 109,198]
206. ~tall(X0) [subsumption resolution 129,199]
244. $false [subsumption resolution 151,206]
% SZS output end Proof for 4941485399745933528382468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or humble is not curious or humble and vice versa.
Everyone who is not happy or not humble is either not rich or brave and vice versa.
Everyone who is not strong or not brave is not old and vice versa.
If someone is either old or not generous then lucy is patient or calm.
Everyone who is not funny or quiet is either patient or generous.
Everyone who is brave is curious or not generous.
If mary is not funny or not tall then someone is both not generous and not humble.
Everyone who is happy is not rich or kind and vice versa.
Everyone who is old is humble.
Everyone who is quiet or not patient is strong and vice versa.
If someone is both not generous and funny then someone is not generous or not rich and vice versa.
Everyone who is not quiet is either not tall or rich and vice versa.
Everyone who is quiet is both not curious and not old.
If someone is not kind or not strong then alice is both kind and rich.
Everyone who is calm is both kind and funny and vice versa.
Everyone who is not generous or calm is tall or not brave and vice versa.
Someone is not funny or creative.
John is both creative and not tall.
Alice is either not brave or not funny.
Someone is both not kind and not generous.
Someone is both not calm and curious.
John is kind or not strong.
Susan is both funny and not curious.
Susan is either happy or curious. | John is strong. | neutral | (![X]:((tall(X)|humble(X))<=>(~curious(X)|humble(X))))&
(![X]:((~happy(X)|~humble(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~strong(X)|~brave(X))<=>~old(X)))&
((?[X]:((old(X)<~>~generous(X))))=>((patient(lucy)|calm(lucy))))&
(![X]:((~funny(X)|quiet(X))=>(patient(X)<~>generous(X))))&
(![X]:(brave(X)=>(curious(X)|~generous(X))))&
(((~funny(mary)|~tall(mary)))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(happy(X)<=>(~rich(X)|kind(X))))&
(![X]:(old(X)=>humble(X)))&
(![X]:((quiet(X)|~patient(X))<=>strong(X)))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>rich(X))))&
(![X]:(quiet(X)=>(~curious(X)&~old(X))))&
((?[X]:((~kind(X)|~strong(X))))=>((kind(alice)&rich(alice))))&
(![X]:(calm(X)<=>(kind(X)&funny(X))))&
(![X]:((~generous(X)|calm(X))<=>(tall(X)|~brave(X))))&
(?[X]:((~funny(X)|creative(X))))&
((creative(john)&~tall(john)))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~calm(X)&curious(X))))&
((kind(john)|~strong(john)))&
((funny(susan)&~curious(susan)))&
((happy(susan)<~>curious(susan))) | strong(john) | [] | null | 0 |
Everyone who is rich or not calm is patient or strong. Everyone who is both curious and not old is either not rich or strong and vice versa. Everyone who is brave is both not funny and kind and vice versa. If john is either rich or curious then someone is not humble and vice versa. If someone is funny then susan is old or not humble and vice versa. If lucy is either not quiet or happy then paul is not creative. If alice is either humble or not quiet then someone is both kind and not creative and vice versa. If john is both tall and not happy then someone is both happy and creative. If someone is both funny and not tall then someone is not brave. Everyone who is either strong or not brave is either generous or not rich and vice versa. If fred is either funny or not rich then someone is curious or not kind and vice versa. Everyone who is both brave and not old is both rich and not funny. Everyone who is both curious and not rich is either patient or creative and vice versa. Everyone who is either rich or humble is either not generous or patient and vice versa. Everyone who is both patient and brave is funny or wise. Everyone who is not strong or not funny is not kind. Someone is not old or not generous. Susan is not curious or not funny. Someone is both not humble and not calm. Fred is not humble. Alice is either not calm or curious. Someone is curious. John is both calm and not generous. Someone is both not funny and old. | John is kind. | contradiction | (![X]:((rich(X)|~calm(X))=>(patient(X)|strong(X))))&
(![X]:((curious(X)&~old(X))<=>(~rich(X)<~>strong(X))))&
(![X]:(brave(X)<=>(~funny(X)&kind(X))))&
(((rich(john)<~>curious(john)))<=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))<=>((old(susan)|~humble(susan))))&
(((~quiet(lucy)<~>happy(lucy)))=>(~creative(paul)))&
(((humble(alice)<~>~quiet(alice)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((tall(john)&~happy(john)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(generous(X)<~>~rich(X))))&
(((funny(fred)<~>~rich(fred)))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((brave(X)&~old(X))=>(rich(X)&~funny(X))))&
(![X]:((curious(X)&~rich(X))<=>(patient(X)<~>creative(X))))&
(![X]:((rich(X)<~>humble(X))<=>(~generous(X)<~>patient(X))))&
(![X]:((patient(X)&brave(X))=>(funny(X)|wise(X))))&
(![X]:((~strong(X)|~funny(X))=>~kind(X)))&
(?[X]:((~old(X)|~generous(X))))&
((~curious(susan)|~funny(susan)))&
(?[X]:((~humble(X)&~calm(X))))&
(~humble(fred))&
((~calm(alice)<~>curious(alice)))&
(?[X]:(curious(X)))&
((calm(john)&~generous(john)))&
(?[X]:((~funny(X)&old(X)))) | kind(john) | [
"p1",
"p2",
"p3",
"p9",
"p15",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2985459885631937279718851
% SZS output start Proof for 2985459885631937279718851
2. ! [X0] : ((~old(X0) & curious(X0)) <=> (~rich(X0) <~> strong(X0))) [input p1]
3. ! [X0] : (brave(X0) <=> (kind(X0) & ~funny(X0))) [input p2]
4. (rich(john) <~> curious(john)) <=> ? [X0] : ~humble(X0) [input p3]
10. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (generous(X0) <~> ~rich(X0))) [input p9]
16. ! [X0] : ((~funny(X0) | ~strong(X0)) => ~kind(X0)) [input p15]
20. ~humble(fred) [input p19]
23. ~generous(john) & calm(john) [input p22]
25. kind(john) [input hypothesis]
36. ! [X0] : (~kind(X0) | (funny(X0) & strong(X0))) [ennf transformation 16]
37. ! [X0] : (((~old(X0) & curious(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (old(X0) | ~curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~old(X0) & curious(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | old(X0) | ~curious(X0))) [flattening 37]
39. ! [X0] : ((brave(X0) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | ~brave(X0))) [nnf transformation 3]
40. ! [X0] : ((brave(X0) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | ~brave(X0))) [flattening 39]
41. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (? [X0] : ~humble(X0) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [nnf transformation 4]
42. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (? [X1] : ~humble(X1) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [rectify 41]
43. ? [X1] : ~humble(X1) => ~humble(sK0) [choice axiom]
44. (((~curious(john) | ~rich(john)) & (curious(john) | rich(john))) | ! [X0] : humble(X0)) & (~humble(sK0) | ((rich(john) | ~curious(john)) & (curious(john) | ~rich(john)))) [skolemisation 42,43]
60. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 10]
82. ~strong(X0) | ~rich(X0) | curious(X0) [cnf transformation 38]
85. ~funny(X0) | ~brave(X0) [cnf transformation 40]
91. ~curious(john) | ~rich(john) | humble(X0) [cnf transformation 44]
113. ~strong(X0) | brave(X0) | generous(X0) | rich(X0) [cnf transformation 60]
136. ~kind(X0) | strong(X0) [cnf transformation 36]
137. ~kind(X0) | funny(X0) [cnf transformation 36]
142. ~humble(fred) [cnf transformation 20]
147. ~generous(john) [cnf transformation 23]
150. kind(john) [cnf transformation 25]
152. 1 <=> ! [X0] : humble(X0) [avatar definition]
153. humble(X0) <- (1) [avatar component clause 152]
155. 2 <=> rich(john) [avatar definition]
156. rich(john) <- (2) [avatar component clause 155]
157. ~rich(john) <- (~2) [avatar component clause 155]
159. 3 <=> curious(john) [avatar definition]
162. 1 | ~2 | ~3 [avatar split clause 91,159,155,152]
310. strong(john) [resolution 136,150]
311. funny(john) [resolution 137,150]
312. ~brave(john) [resolution 311,85]
326. ~rich(john) | curious(john) [resolution 82,310]
328. curious(john) <- (2) [subsumption resolution 326,156]
331. 3 | ~2 [avatar split clause 328,155,159]
333. $false <- (1) [resolution 153,142]
338. ~1 [avatar contradiction clause 333]
452. brave(john) | generous(john) | rich(john) [resolution 113,310]
454. generous(john) | rich(john) [subsumption resolution 452,312]
455. rich(john) [subsumption resolution 454,147]
456. $false <- (~2) [subsumption resolution 455,157]
457. 2 [avatar contradiction clause 456]
458. $false [avatar sat refutation 162,331,338,457]
% SZS output end Proof for 2985459885631937279718851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not strong then alice is funny and vice versa.
If fred is not humble then someone is wise or not creative and vice versa.
If mary is both not patient and calm then john is not creative or not rich and vice versa.
If someone is both calm and not patient then someone is either kind or wise.
If john is either not old or not generous then someone is both not creative and happy and vice versa.
If someone is not old then someone is not quiet and vice versa.
If someone is either curious or not funny then alice is both not calm and not strong and vice versa.
Everyone who is either generous or not brave is either tall or not tall and vice versa.
If john is either quiet or brave then john is curious or happy.
Everyone who is not wise is strong or not happy.
Everyone who is brave or tall is not tall and vice versa.
If lucy is both strong and quiet then someone is strong or curious.
If someone is both not humble and brave then someone is curious or not generous.
Everyone who is curious is either curious or funny and vice versa.
Everyone who is either happy or not patient is calm.
Lucy is either not strong or not rich.
Fred is not patient or generous.
Lucy is kind or not funny.
Paul is both not strong and not tall.
Someone is wise or not patient.
Fred is both not funny and strong.
Someone is both rich and happy. | Paul is not generous. | contradiction | ((?[X]:((patient(X)&~strong(X))))<=>(funny(alice)))&
((~humble(fred))<=>(?[X]:((wise(X)|~creative(X)))))&
(((~patient(mary)&calm(mary)))<=>((~creative(john)|~rich(john))))&
((?[X]:((calm(X)&~patient(X))))=>(?[X]:((kind(X)<~>wise(X)))))&
(((~old(john)<~>~generous(john)))<=>(?[X]:((~creative(X)&happy(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(~quiet(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~calm(alice)&~strong(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>(tall(X)<~>~tall(X))))&
(((quiet(john)<~>brave(john)))=>((curious(john)|happy(john))))&
(![X]:(~wise(X)=>(strong(X)|~happy(X))))&
(![X]:((brave(X)|tall(X))<=>~tall(X)))&
(((strong(lucy)&quiet(lucy)))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:(curious(X)<=>(curious(X)<~>funny(X))))&
(![X]:((happy(X)<~>~patient(X))=>calm(X)))&
((~strong(lucy)<~>~rich(lucy)))&
((~patient(fred)|generous(fred)))&
((kind(lucy)|~funny(lucy)))&
((~strong(paul)&~tall(paul)))&
(?[X]:((wise(X)|~patient(X))))&
((~funny(fred)&strong(fred)))&
(?[X]:((rich(X)&happy(X)))) | ~generous(paul) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7308552004136075011395033
% SZS output start Proof for 7308552004136075011395033
8. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p7]
11. ! [X0] : ((tall(X0) | brave(X0)) <=> ~tall(X0)) [input p10]
23. ~generous(paul) [input hypothesis]
64. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 8]
66. ! [X0] : (((tall(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (~tall(X0) & ~brave(X0)))) [nnf transformation 11]
67. ! [X0] : ((tall(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (~tall(X0) & ~brave(X0)))) [flattening 66]
111. ~brave(X0) | generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 64]
112. ~brave(X0) | generous(X0) | tall(X0) | tall(X0) [cnf transformation 64]
119. ~tall(X0) | ~tall(X0) [cnf transformation 67]
120. tall(X0) | brave(X0) | tall(X0) [cnf transformation 67]
140. ~generous(paul) [cnf transformation 23]
143. ~tall(X0) [duplicate literal removal 119]
144. tall(X0) | brave(X0) [duplicate literal removal 120]
145. ~brave(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 111]
146. ~brave(X0) | generous(X0) | tall(X0) [duplicate literal removal 112]
292. ~brave(X0) | generous(X0) [subsumption resolution 145,146]
365. brave(X0) [resolution 144,143]
372. generous(X0) [resolution 292,365]
375. $false [resolution 372,140]
% SZS output end Proof for 7308552004136075011395033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not brave then mary is both kind and not humble and vice versa. Everyone who is not happy or rich is both not calm and not rich and vice versa. If lucy is either kind or not quiet then lucy is either generous or not calm. Everyone who is either strong or not quiet is either not calm or not curious. Everyone who is not humble is not happy or curious and vice versa. If someone is not calm then someone is kind or generous. Everyone who is either not curious or not generous is not patient. Everyone who is not generous is calm or generous and vice versa. Everyone who is not kind is brave or not tall and vice versa. If john is both not strong and not tall then alice is not old. Everyone who is both old and generous is both not quiet and not brave and vice versa. Everyone who is not patient is both kind and not funny and vice versa. Everyone who is not brave or not strong is old. Everyone who is both quiet and not wise is not strong or quiet and vice versa. Everyone who is either old or not generous is either patient or generous and vice versa. Susan is both calm and not strong. Someone is not calm or tall. Fred is either not strong or not curious. Susan is quiet or calm. Someone is either not rich or not curious. Mary is either tall or not wise. | John is quiet. | neutral | ((?[X]:((humble(X)&~brave(X))))<=>((kind(mary)&~humble(mary))))&
(![X]:((~happy(X)|rich(X))<=>(~calm(X)&~rich(X))))&
(((kind(lucy)<~>~quiet(lucy)))=>((generous(lucy)<~>~calm(lucy))))&
(![X]:((strong(X)<~>~quiet(X))=>(~calm(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~happy(X)|curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)|generous(X)))))&
(![X]:((~curious(X)<~>~generous(X))=>~patient(X)))&
(![X]:(~generous(X)<=>(calm(X)|generous(X))))&
(![X]:(~kind(X)<=>(brave(X)|~tall(X))))&
(((~strong(john)&~tall(john)))=>(~old(alice)))&
(![X]:((old(X)&generous(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
(![X]:((~brave(X)|~strong(X))=>old(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~strong(X)|quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>(patient(X)<~>generous(X))))&
((calm(susan)&~strong(susan)))&
(?[X]:((~calm(X)|tall(X))))&
((~strong(fred)<~>~curious(fred)))&
((quiet(susan)|calm(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
((tall(mary)<~>~wise(mary))) | quiet(john) | [] | null | 0 |
Everyone who is not curious or not generous is either not curious or not brave.
Everyone who is not generous or curious is not curious or funny.
If someone is either curious or rich then someone is either not brave or not calm and vice versa.
Everyone who is not quiet or rich is either old or not humble.
Everyone who is funny is not strong.
Everyone who is either strong or not happy is patient or quiet.
Everyone who is tall is either kind or happy.
Everyone who is happy or tall is not brave.
If someone is humble then someone is patient or not wise and vice versa.
If mary is both not happy and creative then someone is tall or not funny.
Everyone who is not happy or creative is both happy and generous and vice versa.
If john is both not brave and not calm then someone is either curious or funny.
Everyone who is not funny or tall is not humble or strong and vice versa.
If paul is either generous or not old then someone is not patient or old and vice versa.
Everyone who is not calm or wise is tall and vice versa.
If mary is patient then someone is either kind or not quiet and vice versa.
Someone is either creative or strong.
Susan is kind or not happy.
Someone is either quiet or not strong.
Paul is both not generous and rich.
Someone is both creative and quiet.
Someone is old or kind. | John is strong. | contradiction | (![X]:((~curious(X)|~generous(X))=>(~curious(X)<~>~brave(X))))&
(![X]:((~generous(X)|curious(X))=>(~curious(X)|funny(X))))&
((?[X]:((curious(X)<~>rich(X))))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|rich(X))=>(old(X)<~>~humble(X))))&
(![X]:(funny(X)=>~strong(X)))&
(![X]:((strong(X)<~>~happy(X))=>(patient(X)|quiet(X))))&
(![X]:(tall(X)=>(kind(X)<~>happy(X))))&
(![X]:((happy(X)|tall(X))=>~brave(X)))&
((?[X]:(humble(X)))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~happy(mary)&creative(mary)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~happy(X)|creative(X))<=>(happy(X)&generous(X))))&
(((~brave(john)&~calm(john)))=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~humble(X)|strong(X))))&
(((generous(paul)<~>~old(paul)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((~calm(X)|wise(X))<=>tall(X)))&
((patient(mary))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(?[X]:((creative(X)<~>strong(X))))&
((kind(susan)|~happy(susan)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((~generous(paul)&rich(paul)))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:((old(X)|kind(X)))) | strong(john) | [
"p0",
"p1",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2880560953462707449390057
% SZS output start Proof for 2880560953462707449390057
1. ! [X0] : ((~generous(X0) | ~curious(X0)) => (~curious(X0) <~> ~brave(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~generous(X0)) => (funny(X0) | ~curious(X0))) [input p1]
5. ! [X0] : (funny(X0) => ~strong(X0)) [input p4]
8. ! [X0] : ((tall(X0) | happy(X0)) => ~brave(X0)) [input p7]
11. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (generous(X0) & happy(X0))) [input p10]
23. strong(john) [input hypothesis]
26. ! [X0] : ((~curious(X0) <~> ~brave(X0)) | (generous(X0) & curious(X0))) [ennf transformation 1]
27. ! [X0] : ((funny(X0) | ~curious(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 2]
28. ! [X0] : (funny(X0) | ~curious(X0) | (~curious(X0) & generous(X0))) [flattening 27]
30. ! [X0] : (~strong(X0) | ~funny(X0)) [ennf transformation 5]
34. ! [X0] : (~brave(X0) | (~tall(X0) & ~happy(X0))) [ennf transformation 8]
39. ! [X0] : (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (generous(X0) & curious(X0))) [nnf transformation 26]
55. ! [X0] : (((creative(X0) | ~happy(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~creative(X0) & happy(X0)))) [nnf transformation 11]
56. ! [X0] : ((creative(X0) | ~happy(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (~creative(X0) & happy(X0)))) [flattening 55]
84. brave(X0) | curious(X0) | curious(X0) [cnf transformation 39]
87. funny(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 28]
100. ~strong(X0) | ~funny(X0) [cnf transformation 30]
105. ~happy(X0) | ~brave(X0) [cnf transformation 34]
111. happy(X0) | happy(X0) [cnf transformation 56]
145. strong(john) [cnf transformation 23]
146. happy(X0) [duplicate literal removal 111]
148. ~curious(X0) | funny(X0) [duplicate literal removal 87]
149. brave(X0) | curious(X0) [duplicate literal removal 84]
328. ~funny(john) [resolution 100,145]
329. ~brave(X0) [resolution 105,146]
341. curious(X0) [resolution 149,329]
342. funny(X0) [resolution 341,148]
344. $false [resolution 342,328]
% SZS output end Proof for 2880560953462707449390057
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not strong is not happy.
Everyone who is old or not creative is either wise or not brave and vice versa.
If someone is both humble and tall then someone is both calm and funny.
If alice is not quiet then mary is either happy or kind and vice versa.
If someone is curious or old then susan is not funny or tall.
Everyone who is either old or not happy is wise.
Everyone who is either not rich or not happy is happy and vice versa.
Everyone who is not strong is funny or not old and vice versa.
If paul is humble then someone is either brave or curious and vice versa.
Everyone who is both not kind and tall is both curious and funny.
If someone is not calm or patient then paul is both tall and not rich.
Everyone who is not generous or not kind is not creative or quiet.
If someone is either quiet or calm then mary is both happy and humble and vice versa.
If lucy is humble or rich then mary is happy or not strong.
If lucy is either curious or not humble then someone is not old or rich.
If mary is not funny then paul is both not kind and not strong.
Someone is both not quiet and not brave.
Someone is either wise or humble.
Paul is kind or calm.
Someone is calm or not calm.
Someone is both not old and patient.
Someone is humble.
Someone is not brave or not curious.
Susan is not creative. | Lucy is not rich. | entailment | (![X]:((~happy(X)|~strong(X))=>~happy(X)))&
(![X]:((old(X)|~creative(X))<=>(wise(X)<~>~brave(X))))&
((?[X]:((humble(X)&tall(X))))=>(?[X]:((calm(X)&funny(X)))))&
((~quiet(alice))<=>((happy(mary)<~>kind(mary))))&
((?[X]:((curious(X)|old(X))))=>((~funny(susan)|tall(susan))))&
(![X]:((old(X)<~>~happy(X))=>wise(X)))&
(![X]:((~rich(X)<~>~happy(X))<=>happy(X)))&
(![X]:(~strong(X)<=>(funny(X)|~old(X))))&
((humble(paul))<=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((~kind(X)&tall(X))=>(curious(X)&funny(X))))&
((?[X]:((~calm(X)|patient(X))))=>((tall(paul)&~rich(paul))))&
(![X]:((~generous(X)|~kind(X))=>(~creative(X)|quiet(X))))&
((?[X]:((quiet(X)<~>calm(X))))<=>((happy(mary)&humble(mary))))&
(((humble(lucy)|rich(lucy)))=>((happy(mary)|~strong(mary))))&
(((curious(lucy)<~>~humble(lucy)))=>(?[X]:((~old(X)|rich(X)))))&
((~funny(mary))=>((~kind(paul)&~strong(paul))))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:((wise(X)<~>humble(X))))&
((kind(paul)|calm(paul)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~old(X)&patient(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)|~curious(X))))&
(~creative(susan)) | ~rich(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5288423063113629028854802
% SZS output start Proof for 5288423063113629028854802
7. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> happy(X0)) [input p6]
25. rich(lucy) [input hypothesis]
49. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | ~happy(X0)) & (happy(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 7]
96. happy(X0) | ~rich(X0) | happy(X0) [cnf transformation 49]
97. ~happy(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 49]
136. rich(lucy) [cnf transformation 25]
137. happy(X0) | ~rich(X0) [duplicate literal removal 96]
138. ~happy(X0) | ~rich(X0) [duplicate literal removal 97]
184. ~rich(X0) [subsumption resolution 137,138]
302. $false [subsumption resolution 136,184]
% SZS output end Proof for 5288423063113629028854802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not brave then mary is both brave and kind and vice versa. If someone is happy or strong then john is both kind and not creative and vice versa. Everyone who is not rich is both funny and strong. Everyone who is both wise and tall is either not humble or not curious and vice versa. Everyone who is brave or creative is kind or creative. If lucy is not patient or not curious then mary is both rich and funny. Everyone who is not strong or not calm is not patient. Everyone who is wise or not happy is not strong or not patient. Everyone who is either not humble or happy is not creative. If someone is not happy or not rich then paul is not happy and vice versa. Everyone who is brave or tall is tall or not patient and vice versa. Everyone who is both not generous and strong is either wise or not calm. Everyone who is both not tall and not wise is both brave and kind and vice versa. Everyone who is calm or strong is kind and vice versa. Everyone who is both strong and not tall is not quiet or not calm and vice versa. If someone is not patient or not tall then someone is both tall and not generous and vice versa. Someone is both not happy and rich. Lucy is either not curious or not humble. Someone is both generous and not happy. Paul is either not old or patient. Someone is either not tall or curious. Someone is not calm. Someone is funny or not funny. Mary is happy or calm. | Paul is old. | contradiction | ((?[X]:((humble(X)&~brave(X))))<=>((brave(mary)&kind(mary))))&
((?[X]:((happy(X)|strong(X))))<=>((kind(john)&~creative(john))))&
(![X]:(~rich(X)=>(funny(X)&strong(X))))&
(![X]:((wise(X)&tall(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((brave(X)|creative(X))=>(kind(X)|creative(X))))&
(((~patient(lucy)|~curious(lucy)))=>((rich(mary)&funny(mary))))&
(![X]:((~strong(X)|~calm(X))=>~patient(X)))&
(![X]:((wise(X)|~happy(X))=>(~strong(X)|~patient(X))))&
(![X]:((~humble(X)<~>happy(X))=>~creative(X)))&
((?[X]:((~happy(X)|~rich(X))))<=>(~happy(paul)))&
(![X]:((brave(X)|tall(X))<=>(tall(X)|~patient(X))))&
(![X]:((~generous(X)&strong(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~tall(X)&~wise(X))<=>(brave(X)&kind(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
(![X]:((strong(X)&~tall(X))<=>(~quiet(X)|~calm(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(?[X]:((~happy(X)&rich(X))))&
((~curious(lucy)<~>~humble(lucy)))&
(?[X]:((generous(X)&~happy(X))))&
((~old(paul)<~>patient(paul)))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:(~calm(X)))&
(?[X]:((funny(X)|~funny(X))))&
((happy(mary)|calm(mary))) | old(paul) | [
"p6",
"p7",
"p9",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1456765624528031392392911
% SZS output start Proof for 1456765624528031392392911
7. ! [X0] : ((~calm(X0) | ~strong(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : ((~happy(X0) | wise(X0)) => (~patient(X0) | ~strong(X0))) [input p7]
10. ? [X0] : (~rich(X0) | ~happy(X0)) <=> ~happy(paul) [input p9]
17. ? [X0] : (rich(X0) & ~happy(X0)) [input p16]
20. ~old(paul) <~> patient(paul) [input p19]
25. old(paul) [input hypothesis]
31. ! [X0] : (~patient(X0) | (calm(X0) & strong(X0))) [ennf transformation 7]
32. ! [X0] : ((~patient(X0) | ~strong(X0)) | (happy(X0) & ~wise(X0))) [ennf transformation 8]
33. ! [X0] : (~patient(X0) | ~strong(X0) | (happy(X0) & ~wise(X0))) [flattening 32]
50. (? [X0] : (~rich(X0) | ~happy(X0)) | happy(paul)) & (~happy(paul) | ! [X0] : (rich(X0) & happy(X0))) [nnf transformation 10]
51. (? [X0] : (~rich(X0) | ~happy(X0)) | happy(paul)) & (~happy(paul) | ! [X1] : (rich(X1) & happy(X1))) [rectify 50]
52. ? [X0] : (~rich(X0) | ~happy(X0)) => (~rich(sK2) | ~happy(sK2)) [choice axiom]
53. ((~rich(sK2) | ~happy(sK2)) | happy(paul)) & (~happy(paul) | ! [X1] : (rich(X1) & happy(X1))) [skolemisation 51,52]
68. ? [X0] : (rich(X0) & ~happy(X0)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
69. rich(sK5) & ~happy(sK5) [skolemisation 17,68]
73. (~patient(paul) | old(paul)) & (patient(paul) | ~old(paul)) [nnf transformation 20]
104. ~patient(X0) | strong(X0) [cnf transformation 31]
107. ~patient(X0) | ~strong(X0) | happy(X0) [cnf transformation 33]
110. ~happy(paul) | happy(X1) [cnf transformation 53]
136. ~happy(sK5) [cnf transformation 69]
142. patient(paul) | ~old(paul) [cnf transformation 73]
149. old(paul) [cnf transformation 25]
220. ~patient(X0) | happy(X0) [subsumption resolution 107,104]
223. 16 <=> happy(paul) [avatar definition]
240. 20 <=> ! [X1] : happy(X1) [avatar definition]
241. happy(X1) <- (20) [avatar component clause 240]
242. 20 | ~16 [avatar split clause 110,223,240]
280. 29 <=> old(paul) [avatar definition]
284. 30 <=> patient(paul) [avatar definition]
285. patient(paul) <- (30) [avatar component clause 284]
288. ~29 | 30 [avatar split clause 142,284,280]
308. 29 [avatar split clause 149,280]
340. happy(paul) <- (30) [resolution 220,285]
345. 16 | ~30 [avatar split clause 340,284,223]
347. $false <- (20) [resolution 241,136]
350. ~20 [avatar contradiction clause 347]
352. $false [avatar sat refutation 242,288,308,345,350]
% SZS output end Proof for 1456765624528031392392911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not creative is tall or patient and vice versa. Everyone who is either humble or old is either not strong or curious. Everyone who is both rich and not patient is both not old and brave and vice versa. Everyone who is rich is either not brave or brave. If someone is both not happy and rich then paul is humble and vice versa. If john is both not patient and not old then someone is both wise and not patient and vice versa. If someone is quiet or not brave then someone is not strong. Everyone who is kind or happy is both strong and quiet. Everyone who is either curious or kind is either humble or not creative and vice versa. If someone is not creative then someone is not calm and vice versa. If fred is either not wise or not humble then susan is brave and vice versa. If someone is both not creative and not rich then paul is either not wise or not calm. If someone is either not patient or not generous then susan is both creative and wise and vice versa. If fred is both funny and not creative then lucy is old and vice versa. Everyone who is both brave and not old is not funny or happy and vice versa. Everyone who is either happy or not wise is both rich and tall. Alice is either old or not generous. Someone is both calm and rich. Someone is kind or not old. Someone is not happy. Someone is either curious or funny. Someone is not generous. Someone is either happy or rich. Someone is not creative. | Alice is strong. | neutral | (![X]:((~old(X)&~creative(X))<=>(tall(X)|patient(X))))&
(![X]:((humble(X)<~>old(X))=>(~strong(X)<~>curious(X))))&
(![X]:((rich(X)&~patient(X))<=>(~old(X)&brave(X))))&
(![X]:(rich(X)=>(~brave(X)<~>brave(X))))&
((?[X]:((~happy(X)&rich(X))))<=>(humble(paul)))&
(((~patient(john)&~old(john)))<=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((quiet(X)|~brave(X))))=>(?[X]:(~strong(X))))&
(![X]:((kind(X)|happy(X))=>(strong(X)&quiet(X))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~calm(X))))&
(((~wise(fred)<~>~humble(fred)))<=>(brave(susan)))&
((?[X]:((~creative(X)&~rich(X))))=>((~wise(paul)<~>~calm(paul))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((creative(susan)&wise(susan))))&
(((funny(fred)&~creative(fred)))<=>(old(lucy)))&
(![X]:((brave(X)&~old(X))<=>(~funny(X)|happy(X))))&
(![X]:((happy(X)<~>~wise(X))=>(rich(X)&tall(X))))&
((old(alice)<~>~generous(alice)))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:(~generous(X)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:(~creative(X))) | strong(alice) | [] | null | 0 |
Everyone who is either not creative or not generous is rich and vice versa.
Everyone who is not brave or not strong is both not old and not wise and vice versa.
If someone is creative or patient then paul is brave and vice versa.
Everyone who is humble is both funny and not quiet.
Everyone who is funny is both happy and not tall and vice versa.
Everyone who is either not calm or not generous is either not wise or not rich and vice versa.
Everyone who is either not brave or curious is happy.
Everyone who is both not creative and quiet is not creative.
Everyone who is funny is not funny or curious and vice versa.
Everyone who is both curious and happy is both brave and kind and vice versa.
Everyone who is either not patient or not rich is either not brave or strong.
If mary is both not brave and calm then someone is either quiet or wise.
If someone is both not brave and humble then alice is both not strong and wise.
If paul is not strong then someone is not generous or rich.
If someone is not wise or patient then someone is either rich or creative and vice versa.
If someone is either rich or old then alice is both not rich and creative.
Someone is not calm or brave.
Alice is patient.
Someone is not patient.
Alice is not creative.
Someone is both not wise and funny. | Alice is not rich. | neutral | (![X]:((~creative(X)<~>~generous(X))<=>rich(X)))&
(![X]:((~brave(X)|~strong(X))<=>(~old(X)&~wise(X))))&
((?[X]:((creative(X)|patient(X))))<=>(brave(paul)))&
(![X]:(humble(X)=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>(happy(X)&~tall(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>curious(X))=>happy(X)))&
(![X]:((~creative(X)&quiet(X))=>~creative(X)))&
(![X]:(funny(X)<=>(~funny(X)|curious(X))))&
(![X]:((curious(X)&happy(X))<=>(brave(X)&kind(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(~brave(X)<~>strong(X))))&
(((~brave(mary)&calm(mary)))=>(?[X]:((quiet(X)<~>wise(X)))))&
((?[X]:((~brave(X)&humble(X))))=>((~strong(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~wise(X)|patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:((rich(X)<~>old(X))))=>((~rich(alice)&creative(alice))))&
(?[X]:((~calm(X)|brave(X))))&
(patient(alice))&
(?[X]:(~patient(X)))&
(~creative(alice))&
(?[X]:((~wise(X)&funny(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is not kind or not creative is both calm and curious and vice versa. If someone is happy then someone is both not curious and old and vice versa. If someone is either generous or funny then lucy is happy. If lucy is brave or not brave then someone is not wise and vice versa. If alice is both patient and strong then alice is creative or not brave and vice versa. Everyone who is both not creative and not quiet is both calm and not rich. If susan is not wise then paul is not kind. Everyone who is both not creative and funny is old or wise and vice versa. Everyone who is either not kind or kind is not generous or not quiet. Everyone who is not calm is both not rich and kind. Everyone who is tall or quiet is not happy and vice versa. If someone is generous then someone is either wise or not creative and vice versa. Everyone who is creative is both happy and calm and vice versa. Everyone who is kind or not patient is not happy. If fred is not calm or wise then susan is both not brave and not curious and vice versa. Someone is either old or not humble. Someone is either not generous or brave. Someone is either not rich or curious. Someone is both not patient and rich. Paul is not strong. Mary is patient or calm. | Susan is wise. | neutral | (![X]:((~kind(X)|~creative(X))<=>(calm(X)&curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)&old(X)))))&
((?[X]:((generous(X)<~>funny(X))))=>(happy(lucy)))&
(((brave(lucy)|~brave(lucy)))<=>(?[X]:(~wise(X))))&
(((patient(alice)&strong(alice)))<=>((creative(alice)|~brave(alice))))&
(![X]:((~creative(X)&~quiet(X))=>(calm(X)&~rich(X))))&
((~wise(susan))=>(~kind(paul)))&
(![X]:((~creative(X)&funny(X))<=>(old(X)|wise(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~generous(X)|~quiet(X))))&
(![X]:(~calm(X)=>(~rich(X)&kind(X))))&
(![X]:((tall(X)|quiet(X))<=>~happy(X)))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(![X]:(creative(X)<=>(happy(X)&calm(X))))&
(![X]:((kind(X)|~patient(X))=>~happy(X)))&
(((~calm(fred)|wise(fred)))<=>((~brave(susan)&~curious(susan))))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:((~patient(X)&rich(X))))&
(~strong(paul))&
((patient(mary)|calm(mary))) | wise(susan) | [] | null | 0 |
Everyone who is kind or not tall is not creative and vice versa. If susan is not brave then someone is either not brave or not humble and vice versa. Everyone who is not strong or creative is both not old and not strong. Everyone who is both humble and funny is either not creative or kind. If someone is both not generous and old then someone is either wise or kind and vice versa. If someone is tall then someone is not patient or not calm. Everyone who is not brave is not calm and vice versa. If someone is happy then lucy is not tall. If someone is not humble or happy then fred is either not strong or rich. Everyone who is both humble and not old is funny or not wise and vice versa. If someone is strong then fred is curious or not patient. If susan is not curious or not wise then someone is patient and vice versa. Everyone who is either not rich or brave is either calm or not tall. Everyone who is either not creative or calm is kind and vice versa. Everyone who is either not generous or not happy is not creative and vice versa. If someone is not happy then someone is both not humble and curious and vice versa. John is patient. Lucy is not generous or not brave. Paul is both not creative and not rich. Someone is not funny or brave. Someone is either not patient or not brave. Someone is both calm and happy. Susan is both not curious and quiet. Paul is either not strong or not old. | Paul is old. | contradiction | (![X]:((kind(X)|~tall(X))<=>~creative(X)))&
((~brave(susan))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:((~strong(X)|creative(X))=>(~old(X)&~strong(X))))&
(![X]:((humble(X)&funny(X))=>(~creative(X)<~>kind(X))))&
((?[X]:((~generous(X)&old(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:(tall(X)))=>(?[X]:((~patient(X)|~calm(X)))))&
(![X]:(~brave(X)<=>~calm(X)))&
((?[X]:(happy(X)))=>(~tall(lucy)))&
((?[X]:((~humble(X)|happy(X))))=>((~strong(fred)<~>rich(fred))))&
(![X]:((humble(X)&~old(X))<=>(funny(X)|~wise(X))))&
((?[X]:(strong(X)))=>((curious(fred)|~patient(fred))))&
(((~curious(susan)|~wise(susan)))<=>(?[X]:(patient(X))))&
(![X]:((~rich(X)<~>brave(X))=>(calm(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
(![X]:((~generous(X)<~>~happy(X))<=>~creative(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((~humble(X)&curious(X)))))&
(patient(john))&
((~generous(lucy)|~brave(lucy)))&
((~creative(paul)&~rich(paul)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~patient(X)<~>~brave(X))))&
(?[X]:((calm(X)&happy(X))))&
((~curious(susan)&quiet(susan)))&
((~strong(paul)<~>~old(paul))) | old(paul) | [
"p2",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7450088987131230686958771
% SZS output start Proof for 7450088987131230686958771
3. ! [X0] : ((creative(X0) | ~strong(X0)) => (~strong(X0) & ~old(X0))) [input p2]
24. ~strong(paul) <~> ~old(paul) [input p23]
25. old(paul) [input hypothesis]
30. ! [X0] : ((~strong(X0) & ~old(X0)) | (~creative(X0) & strong(X0))) [ennf transformation 3]
78. (old(paul) | strong(paul)) & (~old(paul) | ~strong(paul)) [nnf transformation 24]
86. ~old(X0) | strong(X0) [cnf transformation 30]
140. ~old(paul) | ~strong(paul) [cnf transformation 78]
141. old(paul) | strong(paul) [cnf transformation 78]
142. old(paul) [cnf transformation 25]
317. strong(paul) [subsumption resolution 141,86]
318. ~old(paul) [subsumption resolution 140,317]
319. $false [subsumption resolution 142,318]
% SZS output end Proof for 7450088987131230686958771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either strong or happy and vice versa. Everyone who is old is calm or not wise and vice versa. Everyone who is happy or strong is not strong. Everyone who is both quiet and not brave is either tall or not brave and vice versa. If lucy is both old and not generous then paul is either calm or not tall. Everyone who is creative or wise is either calm or strong and vice versa. Everyone who is either not wise or not kind is both not strong and funny. Everyone who is both not patient and not happy is creative. Everyone who is brave or rich is not curious and vice versa. Everyone who is generous or brave is not quiet or wise. If someone is calm or not wise then someone is either happy or not funny. If paul is both not old and not quiet then mary is either calm or creative and vice versa. If someone is both not curious and old then paul is strong and vice versa. If susan is quiet then mary is patient and vice versa. If john is not old or not patient then mary is both strong and old and vice versa. Everyone who is both creative and not old is not kind or calm. Alice is both not generous and happy. Someone is both kind and not generous. Someone is both not tall and not humble. Mary is wise. Someone is old or rich. Paul is not tall. Paul is both not wise and not tall. | John is not rich. | entailment | (![X]:(curious(X)<=>(strong(X)<~>happy(X))))&
(![X]:(old(X)<=>(calm(X)|~wise(X))))&
(![X]:((happy(X)|strong(X))=>~strong(X)))&
(![X]:((quiet(X)&~brave(X))<=>(tall(X)<~>~brave(X))))&
(((old(lucy)&~generous(lucy)))=>((calm(paul)<~>~tall(paul))))&
(![X]:((creative(X)|wise(X))<=>(calm(X)<~>strong(X))))&
(![X]:((~wise(X)<~>~kind(X))=>(~strong(X)&funny(X))))&
(![X]:((~patient(X)&~happy(X))=>creative(X)))&
(![X]:((brave(X)|rich(X))<=>~curious(X)))&
(![X]:((generous(X)|brave(X))=>(~quiet(X)|wise(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((happy(X)<~>~funny(X)))))&
(((~old(paul)&~quiet(paul)))<=>((calm(mary)<~>creative(mary))))&
((?[X]:((~curious(X)&old(X))))<=>(strong(paul)))&
((quiet(susan))<=>(patient(mary)))&
(((~old(john)|~patient(john)))<=>((strong(mary)&old(mary))))&
(![X]:((creative(X)&~old(X))=>(~kind(X)|calm(X))))&
((~generous(alice)&happy(alice)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((~tall(X)&~humble(X))))&
(wise(mary))&
(?[X]:((old(X)|rich(X))))&
(~tall(paul))&
((~wise(paul)&~tall(paul))) | ~rich(john) | [
"p1",
"p2",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2302944526056184557579437
% SZS output start Proof for 2302944526056184557579437
2. ! [X0] : (old(X0) <=> (~wise(X0) | calm(X0))) [input p1]
3. ! [X0] : ((strong(X0) | happy(X0)) => ~strong(X0)) [input p2]
6. ! [X0] : ((wise(X0) | creative(X0)) <=> (calm(X0) <~> strong(X0))) [input p5]
9. ! [X0] : ((rich(X0) | brave(X0)) <=> ~curious(X0)) [input p8]
13. ? [X0] : (old(X0) & ~curious(X0)) <=> strong(paul) [input p12]
24. rich(john) [input hypothesis]
27. ! [X0] : (~strong(X0) | (~strong(X0) & ~happy(X0))) [ennf transformation 3]
39. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & ((~wise(X0) | calm(X0)) | ~old(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | (wise(X0) & ~calm(X0))) & (~wise(X0) | calm(X0) | ~old(X0))) [flattening 39]
44. ! [X0] : (((wise(X0) | creative(X0)) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : ((wise(X0) | creative(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | (~wise(X0) & ~creative(X0)))) [flattening 44]
47. ! [X0] : (((rich(X0) | brave(X0)) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [nnf transformation 9]
48. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & (~curious(X0) | (~rich(X0) & ~brave(X0)))) [flattening 47]
55. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X0] : (~old(X0) | curious(X0))) [nnf transformation 13]
56. (? [X0] : (old(X0) & ~curious(X0)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [rectify 55]
57. ? [X0] : (old(X0) & ~curious(X0)) => (old(sK1) & ~curious(sK1)) [choice axiom]
58. ((old(sK1) & ~curious(sK1)) | ~strong(paul)) & (strong(paul) | ! [X1] : (~old(X1) | curious(X1))) [skolemisation 56,57]
73. ~calm(X0) | old(X0) [cnf transformation 40]
74. wise(X0) | old(X0) [cnf transformation 40]
76. ~strong(X0) | ~strong(X0) [cnf transformation 27]
86. strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 45]
97. ~rich(X0) | ~curious(X0) [cnf transformation 48]
111. strong(paul) | ~old(X1) | curious(X1) [cnf transformation 58]
132. rich(john) [cnf transformation 24]
135. ~strong(X0) [duplicate literal removal 76]
156. ~wise(X0) | calm(X0) [subsumption resolution 86,135]
198. ~old(X1) | curious(X1) [subsumption resolution 111,135]
244. ~curious(john) [resolution 97,132]
246. calm(X0) | old(X0) [resolution 156,74]
249. old(X0) [subsumption resolution 246,73]
253. curious(X0) [resolution 198,249]
257. $false [resolution 253,244]
% SZS output end Proof for 2302944526056184557579437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not curious is either curious or not creative.
If someone is both rich and funny then fred is both kind and generous and vice versa.
If lucy is kind or not creative then lucy is not rich and vice versa.
Everyone who is both not wise and rich is wise or not strong and vice versa.
Everyone who is not curious is not wise or old.
If susan is not generous then fred is either tall or not patient and vice versa.
Everyone who is funny or not patient is rich or not strong.
If someone is both not generous and not rich then fred is not rich and vice versa.
Everyone who is creative is both old and not brave.
If paul is not patient or not generous then alice is not wise or not humble.
Everyone who is both not brave and brave is both brave and not strong.
If someone is either generous or quiet then alice is calm or tall.
Everyone who is both not curious and not strong is both not happy and not humble and vice versa.
If someone is either not creative or calm then john is both humble and creative.
Everyone who is both not tall and creative is either strong or rich.
If someone is not humble then someone is creative.
Someone is both not strong and old.
Someone is both calm and creative.
Fred is funny or happy.
Someone is not old or old.
Lucy is kind.
Someone is either funny or rich.
Lucy is both not calm and creative.
Someone is not brave. | Lucy is funny. | contradiction | (![X]:((happy(X)<~>~curious(X))=>(curious(X)<~>~creative(X))))&
((?[X]:((rich(X)&funny(X))))<=>((kind(fred)&generous(fred))))&
(((kind(lucy)|~creative(lucy)))<=>(~rich(lucy)))&
(![X]:((~wise(X)&rich(X))<=>(wise(X)|~strong(X))))&
(![X]:(~curious(X)=>(~wise(X)|old(X))))&
((~generous(susan))<=>((tall(fred)<~>~patient(fred))))&
(![X]:((funny(X)|~patient(X))=>(rich(X)|~strong(X))))&
((?[X]:((~generous(X)&~rich(X))))<=>(~rich(fred)))&
(![X]:(creative(X)=>(old(X)&~brave(X))))&
(((~patient(paul)|~generous(paul)))=>((~wise(alice)|~humble(alice))))&
(![X]:((~brave(X)&brave(X))=>(brave(X)&~strong(X))))&
((?[X]:((generous(X)<~>quiet(X))))=>((calm(alice)|tall(alice))))&
(![X]:((~curious(X)&~strong(X))<=>(~happy(X)&~humble(X))))&
((?[X]:((~creative(X)<~>calm(X))))=>((humble(john)&creative(john))))&
(![X]:((~tall(X)&creative(X))=>(strong(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:(creative(X))))&
(?[X]:((~strong(X)&old(X))))&
(?[X]:((calm(X)&creative(X))))&
((funny(fred)|happy(fred)))&
(?[X]:((~old(X)|old(X))))&
(kind(lucy))&
(?[X]:((funny(X)<~>rich(X))))&
((~calm(lucy)&creative(lucy)))&
(?[X]:(~brave(X))) | funny(lucy) | [
"p2",
"p3",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6223368099800367986695754
% SZS output start Proof for 6223368099800367986695754
3. (~creative(lucy) | kind(lucy)) <=> ~rich(lucy) [input p2]
4. ! [X0] : ((rich(X0) & ~wise(X0)) <=> (~strong(X0) | wise(X0))) [input p3]
7. ! [X0] : ((~patient(X0) | funny(X0)) => (~strong(X0) | rich(X0))) [input p6]
21. kind(lucy) [input p20]
25. funny(lucy) [input hypothesis]
30. ! [X0] : ((~strong(X0) | rich(X0)) | (patient(X0) & ~funny(X0))) [ennf transformation 7]
31. ! [X0] : (~strong(X0) | rich(X0) | (patient(X0) & ~funny(X0))) [flattening 30]
49. ((~creative(lucy) | kind(lucy)) | rich(lucy)) & (~rich(lucy) | (creative(lucy) & ~kind(lucy))) [nnf transformation 3]
50. (~creative(lucy) | kind(lucy) | rich(lucy)) & (~rich(lucy) | (creative(lucy) & ~kind(lucy))) [flattening 49]
51. ! [X0] : (((rich(X0) & ~wise(X0)) | (strong(X0) & ~wise(X0))) & ((~strong(X0) | wise(X0)) | (~rich(X0) | wise(X0)))) [nnf transformation 4]
52. ! [X0] : (((rich(X0) & ~wise(X0)) | (strong(X0) & ~wise(X0))) & (~strong(X0) | wise(X0) | ~rich(X0) | wise(X0))) [flattening 51]
85. ~rich(lucy) | ~kind(lucy) [cnf transformation 50]
92. strong(X0) | rich(X0) [cnf transformation 52]
98. ~strong(X0) | rich(X0) | ~funny(X0) [cnf transformation 31]
128. kind(lucy) [cnf transformation 21]
134. funny(lucy) [cnf transformation 25]
164. 6 <=> rich(lucy) [avatar definition]
165. ~rich(lucy) <- (~6) [avatar component clause 164]
168. 7 <=> kind(lucy) [avatar definition]
177. ~7 | ~6 [avatar split clause 85,164,168]
196. ~funny(X0) | rich(X0) [subsumption resolution 98,92]
266. 7 [avatar split clause 128,168]
283. rich(lucy) [resolution 196,134]
286. $false <- (~6) [subsumption resolution 283,165]
287. 6 [avatar contradiction clause 286]
288. $false [avatar sat refutation 177,266,287]
% SZS output end Proof for 6223368099800367986695754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not wise then susan is not brave and vice versa. Everyone who is either not quiet or humble is both happy and kind and vice versa. If fred is both not calm and curious then alice is not kind and vice versa. Everyone who is tall is either calm or not humble. Everyone who is either not generous or curious is both not rich and not generous. Everyone who is either not kind or brave is both not patient and not happy and vice versa. Everyone who is not brave is both not kind and patient. Everyone who is curious or humble is not happy or funny and vice versa. If someone is not creative then someone is both not tall and not old. Everyone who is not funny is either not kind or not rich. If someone is not wise then fred is either tall or not quiet and vice versa. Everyone who is not humble is both not calm and not quiet. Everyone who is both happy and curious is not quiet or happy and vice versa. Everyone who is both not wise and not kind is not tall. Everyone who is wise is not old or not happy. John is rich or not tall. Someone is not curious or not strong. Fred is either humble or creative. | Mary is not curious. | contradiction | ((~wise(mary))<=>(~brave(susan)))&
(![X]:((~quiet(X)<~>humble(X))<=>(happy(X)&kind(X))))&
(((~calm(fred)&curious(fred)))<=>(~kind(alice)))&
(![X]:(tall(X)=>(calm(X)<~>~humble(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~rich(X)&~generous(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(~patient(X)&~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)&patient(X))))&
(![X]:((curious(X)|humble(X))<=>(~happy(X)|funny(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:(~funny(X)=>(~kind(X)<~>~rich(X))))&
((?[X]:(~wise(X)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(~humble(X)=>(~calm(X)&~quiet(X))))&
(![X]:((happy(X)&curious(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~wise(X)&~kind(X))=>~tall(X)))&
(![X]:(wise(X)=>(~old(X)|~happy(X))))&
((rich(john)|~tall(john)))&
(?[X]:((~curious(X)|~strong(X))))&
((humble(fred)<~>creative(fred))) | ~curious(mary) | [
"p1",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6824597445331532016574368
% SZS output start Proof for 6824597445331532016574368
2. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (kind(X0) & happy(X0))) [input p1]
12. ! [X0] : (~humble(X0) => (~quiet(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((curious(X0) & happy(X0)) <=> (happy(X0) | ~quiet(X0))) [input p12]
19. ~curious(mary) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~calm(X0)) | humble(X0)) [ennf transformation 12]
33. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 2]
34. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 33]
51. ! [X0] : (((curious(X0) & happy(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 13]
52. ! [X0] : (((curious(X0) & happy(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~curious(X0) | ~happy(X0))) [flattening 51]
57. ~humble(X0) | ~quiet(X0) | happy(X0) [cnf transformation 34]
91. ~quiet(X0) | humble(X0) [cnf transformation 29]
95. curious(X0) | quiet(X0) [cnf transformation 52]
96. ~happy(X0) | curious(X0) [cnf transformation 52]
101. ~curious(mary) [cnf transformation 19]
175. quiet(mary) [resolution 95,101]
181. humble(mary) [resolution 175,91]
184. ~quiet(mary) | happy(mary) [resolution 57,181]
185. happy(mary) [subsumption resolution 184,175]
188. curious(mary) [resolution 185,96]
189. $false [subsumption resolution 188,101]
% SZS output end Proof for 6824597445331532016574368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not humble or not creative then lucy is either not generous or kind and vice versa.
If someone is rich or not happy then someone is not wise and vice versa.
Everyone who is both rich and calm is either curious or strong.
If mary is curious or kind then paul is not patient.
Everyone who is not strong or patient is not generous and vice versa.
If lucy is wise or funny then someone is both happy and old and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Everyone who is not generous is both humble and curious and vice versa.
If someone is not curious or not generous then fred is both creative and old and vice versa.
Someone is either funny or not calm.
Lucy is not wise or calm.
Susan is rich.
Susan is not calm.
Someone is both humble and rich.
Someone is generous or wise.
Paul is not strong or not generous.
Alice is not generous. | Fred is patient. | contradiction | (((~humble(mary)|~creative(mary)))<=>((~generous(lucy)<~>kind(lucy))))&
((?[X]:((rich(X)|~happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((rich(X)&calm(X))=>(curious(X)<~>strong(X))))&
(((curious(mary)|kind(mary)))=>(~patient(paul)))&
(![X]:((~strong(X)|patient(X))<=>~generous(X)))&
(((wise(lucy)|funny(lucy)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X))))&
((~strong(paul)|~generous(paul)))&
(~generous(alice)) | patient(fred) | [
"p4",
"p7",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2212207547425429134355901
% SZS output start Proof for 2212207547425429134355901
5. ! [X0] : ((patient(X0) | ~strong(X0)) <=> ~generous(X0)) [input p4]
8. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p7]
15. ! [X0] : (~generous(X0) <=> (curious(X0) & humble(X0))) [input p14]
16. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p15]
23. ~generous(paul) | ~strong(paul) [input p22]
25. patient(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~curious(X0)) | (~old(X0) & ~generous(X0))) [ennf transformation 8]
42. ! [X0] : (((patient(X0) | ~strong(X0)) | generous(X0)) & (~generous(X0) | (~patient(X0) & strong(X0)))) [nnf transformation 5]
43. ! [X0] : ((patient(X0) | ~strong(X0) | generous(X0)) & (~generous(X0) | (~patient(X0) & strong(X0)))) [flattening 42]
62. ! [X0] : ((~generous(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | generous(X0))) [nnf transformation 15]
63. ! [X0] : ((~generous(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | generous(X0))) [flattening 62]
64. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 16]
65. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 64]
66. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 65]
67. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK4) | ~curious(sK4)) [choice axiom]
68. ((~generous(sK4) | ~curious(sK4)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 66,67]
89. ~generous(X0) | strong(X0) [cnf transformation 43]
90. ~patient(X0) | ~generous(X0) [cnf transformation 43]
100. ~old(X0) | ~curious(X0) [cnf transformation 31]
129. curious(X0) | generous(X0) [cnf transformation 63]
134. old(fred) | generous(X1) [cnf transformation 68]
144. ~generous(paul) | ~strong(paul) [cnf transformation 23]
146. patient(fred) [cnf transformation 25]
271. 27 <=> old(fred) [avatar definition]
272. old(fred) <- (27) [avatar component clause 271]
286. 30 <=> ! [X1] : generous(X1) [avatar definition]
287. generous(X1) <- (30) [avatar component clause 286]
288. 30 | 27 [avatar split clause 134,271,286]
316. ~generous(paul) [subsumption resolution 144,89]
322. ~generous(fred) [resolution 90,146]
324. ~curious(fred) <- (27) [resolution 100,272]
340. generous(fred) <- (27) [resolution 129,324]
341. $false <- (27) [subsumption resolution 340,322]
342. ~27 [avatar contradiction clause 341]
345. $false <- (30) [resolution 287,316]
350. ~30 [avatar contradiction clause 345]
351. $false [avatar sat refutation 288,342,350]
% SZS output end Proof for 2212207547425429134355901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not funny then someone is either not strong or calm. Everyone who is not wise is rich. If someone is rich then john is strong. Everyone who is not quiet or not curious is both generous and not calm and vice versa. Everyone who is either generous or quiet is not kind or not happy and vice versa. If someone is both not humble and creative then someone is not quiet and vice versa. If someone is not calm then susan is generous. Everyone who is either curious or not kind is wise or brave and vice versa. Everyone who is both quiet and not generous is humble and vice versa. Everyone who is both not generous and not brave is both not old and not patient and vice versa. If susan is not wise then someone is not tall. Everyone who is not curious is either not brave or kind and vice versa. If alice is both not wise and wise then fred is both not calm and not creative and vice versa. Everyone who is calm or generous is not generous or happy and vice versa. Everyone who is not old or curious is both strong and not quiet. If someone is both generous and brave then lucy is both not wise and brave. Fred is patient. Paul is calm or not humble. Paul is not rich. Someone is not brave or calm. Lucy is either old or curious. Someone is tall. | Paul is not tall. | neutral | ((?[X]:((~happy(X)&~funny(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:(~wise(X)=>rich(X)))&
((?[X]:(rich(X)))=>(strong(john)))&
(![X]:((~quiet(X)|~curious(X))<=>(generous(X)&~calm(X))))&
(![X]:((generous(X)<~>quiet(X))<=>(~kind(X)|~happy(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(~calm(X)))=>(generous(susan)))&
(![X]:((curious(X)<~>~kind(X))<=>(wise(X)|brave(X))))&
(![X]:((quiet(X)&~generous(X))<=>humble(X)))&
(![X]:((~generous(X)&~brave(X))<=>(~old(X)&~patient(X))))&
((~wise(susan))=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>kind(X))))&
(((~wise(alice)&wise(alice)))<=>((~calm(fred)&~creative(fred))))&
(![X]:((calm(X)|generous(X))<=>(~generous(X)|happy(X))))&
(![X]:((~old(X)|curious(X))=>(strong(X)&~quiet(X))))&
((?[X]:((generous(X)&brave(X))))=>((~wise(lucy)&brave(lucy))))&
(patient(fred))&
((calm(paul)|~humble(paul)))&
(~rich(paul))&
(?[X]:((~brave(X)|calm(X))))&
((old(lucy)<~>curious(lucy)))&
(?[X]:(tall(X))) | ~tall(paul) | [] | null | 0 |
If someone is both not patient and kind then lucy is either funny or humble. Everyone who is not tall is either strong or not calm and vice versa. Everyone who is funny is not tall or not calm and vice versa. Everyone who is not funny or funny is tall or generous. Everyone who is both not happy and strong is rich or kind and vice versa. Everyone who is not old or not rich is both not funny and not happy and vice versa. Everyone who is either wise or strong is not funny or rich. If someone is not quiet then someone is either old or not strong. Everyone who is either not happy or not tall is brave or generous. If someone is quiet or not wise then susan is not patient or funny and vice versa. Everyone who is either not quiet or happy is curious or not quiet and vice versa. Everyone who is both not strong and generous is old. If someone is wise or rich then someone is not humble or not calm. Everyone who is not quiet is both happy and patient. Everyone who is either not tall or not humble is not tall or strong. Everyone who is both generous and not curious is not kind and vice versa. Susan is not tall or generous. Someone is not patient or brave. Fred is either generous or rich. Paul is both not tall and creative. Lucy is happy or not wise. Someone is not strong. Someone is either strong or kind. Susan is either happy or not creative. | Fred is not old. | contradiction | ((?[X]:((~patient(X)&kind(X))))=>((funny(lucy)<~>humble(lucy))))&
(![X]:(~tall(X)<=>(strong(X)<~>~calm(X))))&
(![X]:(funny(X)<=>(~tall(X)|~calm(X))))&
(![X]:((~funny(X)|funny(X))=>(tall(X)|generous(X))))&
(![X]:((~happy(X)&strong(X))<=>(rich(X)|kind(X))))&
(![X]:((~old(X)|~rich(X))<=>(~funny(X)&~happy(X))))&
(![X]:((wise(X)<~>strong(X))=>(~funny(X)|rich(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((~happy(X)<~>~tall(X))=>(brave(X)|generous(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>((~patient(susan)|funny(susan))))&
(![X]:((~quiet(X)<~>happy(X))<=>(curious(X)|~quiet(X))))&
(![X]:((~strong(X)&generous(X))=>old(X)))&
((?[X]:((wise(X)|rich(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:(~quiet(X)=>(happy(X)&patient(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(~tall(X)|strong(X))))&
(![X]:((generous(X)&~curious(X))<=>~kind(X)))&
((~tall(susan)|generous(susan)))&
(?[X]:((~patient(X)|brave(X))))&
((generous(fred)<~>rich(fred)))&
((~tall(paul)&creative(paul)))&
((happy(lucy)|~wise(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((strong(X)<~>kind(X))))&
((happy(susan)<~>~creative(susan))) | ~old(fred) | [
"p1",
"p2",
"p4",
"p5",
"p10",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1059438893368084711185199
% SZS output start Proof for 1059438893368084711185199
2. ! [X0] : (~tall(X0) <=> (strong(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : (funny(X0) <=> (~calm(X0) | ~tall(X0))) [input p2]
5. ! [X0] : ((strong(X0) & ~happy(X0)) <=> (kind(X0) | rich(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | ~old(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5]
11. ! [X0] : ((~quiet(X0) <~> happy(X0)) <=> (~quiet(X0) | curious(X0))) [input p10]
12. ! [X0] : ((generous(X0) & ~strong(X0)) => old(X0)) [input p11]
14. ! [X0] : (~quiet(X0) => (patient(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~curious(X0) & generous(X0)) <=> ~kind(X0)) [input p15]
19. generous(fred) <~> rich(fred) [input p18]
25. ~old(fred) [input hypothesis]
36. ! [X0] : (old(X0) | (~generous(X0) | strong(X0))) [ennf transformation 12]
37. ! [X0] : (old(X0) | ~generous(X0) | strong(X0)) [flattening 36]
39. ! [X0] : ((patient(X0) & happy(X0)) | quiet(X0)) [ennf transformation 14]
43. ! [X0] : ((~tall(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | tall(X0))) [nnf transformation 2]
44. ! [X0] : ((funny(X0) | (calm(X0) & tall(X0))) & ((~calm(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 3]
45. ! [X0] : ((funny(X0) | (calm(X0) & tall(X0))) & (~calm(X0) | ~tall(X0) | ~funny(X0))) [flattening 44]
46. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | (~strong(X0) | happy(X0)))) [nnf transformation 5]
47. ! [X0] : (((strong(X0) & ~happy(X0)) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~strong(X0) | happy(X0))) [flattening 46]
48. ! [X0] : (((~rich(X0) | ~old(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [nnf transformation 6]
49. ! [X0] : ((~rich(X0) | ~old(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (rich(X0) & old(X0)))) [flattening 48]
60. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [nnf transformation 11]
61. ! [X0] : ((((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))))) [flattening 60]
66. ! [X0] : (((~curious(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 16]
67. ! [X0] : (((~curious(X0) & generous(X0)) | kind(X0)) & (~kind(X0) | curious(X0) | ~generous(X0))) [flattening 66]
68. (~rich(fred) | ~generous(fred)) & (rich(fred) | generous(fred)) [nnf transformation 19]
79. ~calm(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 43]
82. tall(X0) | funny(X0) [cnf transformation 45]
83. calm(X0) | funny(X0) [cnf transformation 45]
86. ~strong(X0) | rich(X0) | kind(X0) | happy(X0) [cnf transformation 47]
87. ~rich(X0) | ~happy(X0) [cnf transformation 47]
89. ~rich(X0) | strong(X0) [cnf transformation 47]
90. ~kind(X0) | strong(X0) [cnf transformation 47]
91. ~funny(X0) | old(X0) [cnf transformation 49]
94. ~happy(X0) | rich(X0) [cnf transformation 49]
106. happy(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 61]
110. ~generous(X0) | old(X0) | strong(X0) [cnf transformation 37]
113. happy(X0) | quiet(X0) [cnf transformation 39]
117. ~generous(X0) | curious(X0) | ~kind(X0) [cnf transformation 67]
118. generous(X0) | kind(X0) [cnf transformation 67]
121. rich(fred) | generous(fred) [cnf transformation 68]
131. ~old(fred) [cnf transformation 25]
150. ~happy(X0) [subsumption resolution 94,87]
152. 4 <=> ! [X1] : quiet(X1) [avatar definition]
153. quiet(X1) <- (4) [avatar component clause 152]
190. ~curious(X0) | ~quiet(X0) [subsumption resolution 106,150]
207. quiet(X0) [subsumption resolution 113,150]
208. 4 [avatar split clause 207,152]
211. 17 <=> generous(fred) [avatar definition]
212. generous(fred) <- (17) [avatar component clause 211]
215. 18 <=> rich(fred) [avatar definition]
216. rich(fred) <- (18) [avatar component clause 215]
217. ~rich(fred) <- (~18) [avatar component clause 215]
219. 17 | 18 [avatar split clause 121,215,211]
256. ~tall(X0) | ~strong(X0) | funny(X0) [resolution 79,83]
257. ~strong(X0) | funny(X0) [subsumption resolution 256,82]
271. old(X1) | strong(X1) | kind(X1) [resolution 110,118]
282. old(X1) | strong(X1) [subsumption resolution 271,90]
309. 29 <=> kind(fred) [avatar definition]
313. 30 <=> curious(fred) [avatar definition]
315. curious(fred) <- (30) [avatar component clause 313]
346. strong(fred) <- (18) [resolution 216,89]
355. funny(fred) <- (18) [resolution 346,257]
361. strong(fred) [resolution 282,131]
370. old(fred) <- (18) [resolution 355,91]
371. $false <- (18) [subsumption resolution 370,131]
372. ~18 [avatar contradiction clause 371]
374. 34 <=> strong(fred) [avatar definition]
376. strong(fred) <- (34) [avatar component clause 374]
383. 34 [avatar split clause 361,374]
384. curious(fred) | ~kind(fred) <- (17) [resolution 212,117]
389. rich(fred) | kind(fred) | happy(fred) <- (34) [resolution 376,86]
392. kind(fred) | happy(fred) <- (~18, 34) [subsumption resolution 389,217]
396. kind(fred) <- (~18, 34) [subsumption resolution 392,150]
397. 29 | 18 | ~34 [avatar split clause 396,374,215,309]
398. ~29 | 30 | ~17 [avatar split clause 384,211,313,309]
401. ~quiet(fred) <- (30) [resolution 315,190]
403. $false <- (4, 30) [subsumption resolution 401,153]
404. ~4 | ~30 [avatar contradiction clause 403]
405. $false [avatar sat refutation 208,219,372,383,397,398,404]
% SZS output end Proof for 1059438893368084711185199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not generous then john is not calm and vice versa. Everyone who is both not tall and not brave is either rich or calm and vice versa. Everyone who is curious or brave is generous and vice versa. Everyone who is old is strong or old and vice versa. Everyone who is not calm or not quiet is patient or brave. If someone is both not brave and creative then someone is not creative or not generous. Everyone who is not creative or creative is humble or quiet and vice versa. Everyone who is curious is either not rich or old and vice versa. Everyone who is funny is both strong and not kind. Everyone who is either not rich or calm is not generous. If fred is curious then john is either tall or creative and vice versa. If alice is not brave or not creative then fred is not happy or not funny. Everyone who is both kind and brave is both old and not calm. Everyone who is quiet is happy or humble. If alice is both generous and not rich then john is quiet. If someone is generous or not strong then susan is both not happy and not humble and vice versa. Someone is not humble. Lucy is either not strong or not rich. Someone is either not creative or strong. Someone is old or not brave. Someone is either old or not patient. Someone is either not happy or humble. Someone is funny. | Lucy is old. | entailment | ((?[X]:((brave(X)|~generous(X))))<=>(~calm(john)))&
(![X]:((~tall(X)&~brave(X))<=>(rich(X)<~>calm(X))))&
(![X]:((curious(X)|brave(X))<=>generous(X)))&
(![X]:(old(X)<=>(strong(X)|old(X))))&
(![X]:((~calm(X)|~quiet(X))=>(patient(X)|brave(X))))&
((?[X]:((~brave(X)&creative(X))))=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((~creative(X)|creative(X))<=>(humble(X)|quiet(X))))&
(![X]:(curious(X)<=>(~rich(X)<~>old(X))))&
(![X]:(funny(X)=>(strong(X)&~kind(X))))&
(![X]:((~rich(X)<~>calm(X))=>~generous(X)))&
((curious(fred))<=>((tall(john)<~>creative(john))))&
(((~brave(alice)|~creative(alice)))=>((~happy(fred)|~funny(fred))))&
(![X]:((kind(X)&brave(X))=>(old(X)&~calm(X))))&
(![X]:(quiet(X)=>(happy(X)|humble(X))))&
(((generous(alice)&~rich(alice)))=>(quiet(john)))&
((?[X]:((generous(X)|~strong(X))))<=>((~happy(susan)&~humble(susan))))&
(?[X]:(~humble(X)))&
((~strong(lucy)<~>~rich(lucy)))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((old(X)|~brave(X))))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:((~happy(X)<~>humble(X))))&
(?[X]:(funny(X))) | old(lucy) | [
"p3",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4782652641219906957591144
% SZS output start Proof for 4782652641219906957591144
4. ! [X0] : (old(X0) <=> (old(X0) | strong(X0))) [input p3]
7. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | humble(X0))) [input p6]
14. ! [X0] : (quiet(X0) => (humble(X0) | happy(X0))) [input p13]
16. ? [X0] : (~strong(X0) | generous(X0)) <=> (~humble(susan) & ~happy(susan)) [input p15]
24. ~old(lucy) [input hypothesis]
35. ! [X0] : ((humble(X0) | happy(X0)) | ~quiet(X0)) [ennf transformation 14]
36. ! [X0] : (humble(X0) | happy(X0) | ~quiet(X0)) [flattening 35]
47. ! [X0] : ((old(X0) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | ~old(X0))) [nnf transformation 4]
48. ! [X0] : ((old(X0) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | ~old(X0))) [flattening 47]
52. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 7]
53. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | (~creative(X0) & creative(X0)))) [flattening 52]
57. (? [X0] : (~strong(X0) | generous(X0)) | (humble(susan) | happy(susan))) & ((~humble(susan) & ~happy(susan)) | ! [X0] : (strong(X0) & ~generous(X0))) [nnf transformation 16]
58. (? [X0] : (~strong(X0) | generous(X0)) | humble(susan) | happy(susan)) & ((~humble(susan) & ~happy(susan)) | ! [X0] : (strong(X0) & ~generous(X0))) [flattening 57]
59. (? [X0] : (~strong(X0) | generous(X0)) | humble(susan) | happy(susan)) & ((~humble(susan) & ~happy(susan)) | ! [X1] : (strong(X1) & ~generous(X1))) [rectify 58]
60. ? [X0] : (~strong(X0) | generous(X0)) => (~strong(sK2) | generous(sK2)) [choice axiom]
61. ((~strong(sK2) | generous(sK2)) | humble(susan) | happy(susan)) & ((~humble(susan) & ~happy(susan)) | ! [X1] : (strong(X1) & ~generous(X1))) [skolemisation 59,60]
91. ~strong(X0) | old(X0) [cnf transformation 48]
96. quiet(X0) | humble(X0) | creative(X0) [cnf transformation 53]
97. quiet(X0) | humble(X0) | ~creative(X0) [cnf transformation 53]
113. humble(X0) | happy(X0) | ~quiet(X0) [cnf transformation 36]
116. ~happy(susan) | strong(X1) [cnf transformation 61]
118. ~humble(susan) | strong(X1) [cnf transformation 61]
131. ~old(lucy) [cnf transformation 24]
165. humble(X0) | quiet(X0) [subsumption resolution 96,97]
200. happy(X0) | humble(X0) [subsumption resolution 113,165]
215. 19 <=> ! [X1] : strong(X1) [avatar definition]
216. strong(X1) <- (19) [avatar component clause 215]
218. 20 <=> humble(susan) [avatar definition]
221. 19 | ~20 [avatar split clause 118,218,215]
227. 22 <=> happy(susan) [avatar definition]
229. ~happy(susan) <- (~22) [avatar component clause 227]
230. 19 | ~22 [avatar split clause 116,227,215]
233. 23 <=> strong(lucy) [avatar definition]
234. ~strong(lucy) <- (~23) [avatar component clause 233]
235. strong(lucy) <- (23) [avatar component clause 233]
273. old(lucy) <- (23) [resolution 91,235]
274. $false <- (23) [subsumption resolution 273,131]
275. ~23 [avatar contradiction clause 274]
281. humble(susan) <- (~22) [resolution 200,229]
284. 20 | 22 [avatar split clause 281,227,218]
287. $false <- (19, ~23) [resolution 216,234]
288. ~19 | 23 [avatar contradiction clause 287]
290. $false [avatar sat refutation 221,230,275,284,288]
% SZS output end Proof for 4782652641219906957591144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both kind and rich is both not strong and not old and vice versa.
If mary is either not tall or tall then alice is both rich and wise and vice versa.
If someone is not kind or not old then mary is both funny and not strong and vice versa.
If mary is both not humble and wise then someone is both not generous and old.
Everyone who is wise is not quiet and vice versa.
If someone is either not curious or generous then someone is creative or not calm and vice versa.
If someone is both not rich and not strong then someone is happy or not happy and vice versa.
Everyone who is old is creative.
If someone is wise then someone is both generous and calm and vice versa.
If someone is both kind and not rich then someone is either not brave or not kind.
If someone is generous then someone is tall or not curious.
Everyone who is not funny or old is both brave and not kind.
Everyone who is both not creative and humble is not humble and vice versa.
Everyone who is not rich or rich is not old or not kind and vice versa.
Everyone who is not brave or not old is either old or not generous.
John is both not kind and brave.
Paul is either not generous or calm.
Someone is not rich or not happy.
Mary is brave or not humble.
Someone is calm.
Someone is either calm or not creative.
Alice is not curious.
John is either quiet or strong. | Alice is not humble. | contradiction | (![X]:((kind(X)&rich(X))<=>(~strong(X)&~old(X))))&
(((~tall(mary)<~>tall(mary)))<=>((rich(alice)&wise(alice))))&
((?[X]:((~kind(X)|~old(X))))<=>((funny(mary)&~strong(mary))))&
(((~humble(mary)&wise(mary)))=>(?[X]:((~generous(X)&old(X)))))&
(![X]:(wise(X)<=>~quiet(X)))&
((?[X]:((~curious(X)<~>generous(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:(old(X)=>creative(X)))&
((?[X]:(wise(X)))<=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~funny(X)|old(X))=>(brave(X)&~kind(X))))&
(![X]:((~creative(X)&humble(X))<=>~humble(X)))&
(![X]:((~rich(X)|rich(X))<=>(~old(X)|~kind(X))))&
(![X]:((~brave(X)|~old(X))=>(old(X)<~>~generous(X))))&
((~kind(john)&brave(john)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~rich(X)|~happy(X))))&
((brave(mary)|~humble(mary)))&
(?[X]:(calm(X)))&
(?[X]:((calm(X)<~>~creative(X))))&
(~curious(alice))&
((quiet(john)<~>strong(john))) | ~humble(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5821677736917715101491052
% SZS output start Proof for 5821677736917715101491052
13. ! [X0] : ((humble(X0) & ~creative(X0)) <=> ~humble(X0)) [input p12]
24. ~humble(alice) [input hypothesis]
71. ! [X0] : (((humble(X0) & ~creative(X0)) | humble(X0)) & (~humble(X0) | (~humble(X0) | creative(X0)))) [nnf transformation 13]
72. ! [X0] : (((humble(X0) & ~creative(X0)) | humble(X0)) & (~humble(X0) | ~humble(X0) | creative(X0))) [flattening 71]
128. humble(X0) | humble(X0) [cnf transformation 72]
149. ~humble(alice) [cnf transformation 24]
152. humble(X0) [duplicate literal removal 128]
348. $false [subsumption resolution 149,152]
% SZS output end Proof for 5821677736917715101491052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is either humble or not patient and vice versa.
Everyone who is either wise or happy is both creative and not generous and vice versa.
Everyone who is generous is both not strong and not curious.
If someone is not calm or generous then alice is both wise and not humble.
Everyone who is not strong or not creative is not patient.
If someone is not old or generous then someone is not generous and vice versa.
Everyone who is not quiet or strong is both not rich and not tall.
Everyone who is rich is both rich and not generous and vice versa.
If someone is either not humble or creative then someone is calm and vice versa.
If lucy is not tall then someone is not brave.
If mary is either brave or curious then paul is both not kind and not quiet and vice versa.
Everyone who is both curious and generous is both strong and not old and vice versa.
Everyone who is either wise or creative is both not humble and tall and vice versa.
If someone is quiet then someone is either not rich or not strong.
Everyone who is not funny or brave is not curious.
Everyone who is tall or not happy is both calm and happy and vice versa.
Someone is both happy and not patient.
Someone is both not generous and curious.
Someone is either not rich or not wise.
Someone is not old.
Fred is either not creative or quiet.
Someone is not strong.
Someone is both tall and humble. | John is patient. | contradiction | ((quiet(john))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(creative(X)&~generous(X))))&
(![X]:(generous(X)=>(~strong(X)&~curious(X))))&
((?[X]:((~calm(X)|generous(X))))=>((wise(alice)&~humble(alice))))&
(![X]:((~strong(X)|~creative(X))=>~patient(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|strong(X))=>(~rich(X)&~tall(X))))&
(![X]:(rich(X)<=>(rich(X)&~generous(X))))&
((?[X]:((~humble(X)<~>creative(X))))<=>(?[X]:(calm(X))))&
((~tall(lucy))=>(?[X]:(~brave(X))))&
(((brave(mary)<~>curious(mary)))<=>((~kind(paul)&~quiet(paul))))&
(![X]:((curious(X)&generous(X))<=>(strong(X)&~old(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~humble(X)&tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((~funny(X)|brave(X))=>~curious(X)))&
(![X]:((tall(X)|~happy(X))<=>(calm(X)&happy(X))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(~old(X)))&
((~creative(fred)<~>quiet(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((tall(X)&humble(X)))) | patient(john) | [
"p1",
"p2",
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8284924939005934200845984
% SZS output start Proof for 8284924939005934200845984
2. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~generous(X0) & creative(X0))) [input p1]
3. ! [X0] : (generous(X0) => (~curious(X0) & ~strong(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~strong(X0)) => ~patient(X0)) [input p4]
7. ! [X0] : ((strong(X0) | ~quiet(X0)) => (~tall(X0) & ~rich(X0))) [input p6]
13. ! [X0] : ((wise(X0) <~> creative(X0)) <=> (tall(X0) & ~humble(X0))) [input p12]
16. ! [X0] : ((~happy(X0) | tall(X0)) <=> (happy(X0) & calm(X0))) [input p15]
24. patient(john) [input hypothesis]
29. ! [X0] : ((~curious(X0) & ~strong(X0)) | ~generous(X0)) [ennf transformation 3]
31. ! [X0] : (~patient(X0) | (creative(X0) & strong(X0))) [ennf transformation 5]
32. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~strong(X0) & quiet(X0))) [ennf transformation 7]
40. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (generous(X0) | ~creative(X0))) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | generous(X0) | ~creative(X0)) & ((~generous(X0) & creative(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [flattening 40]
60. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | (~tall(X0) | humble(X0))) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ~tall(X0) | humble(X0)) & ((tall(X0) & ~humble(X0)) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [flattening 60]
66. ! [X0] : (((~happy(X0) | tall(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [nnf transformation 16]
67. ! [X0] : ((~happy(X0) | tall(X0) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | (happy(X0) & ~tall(X0)))) [flattening 66]
91. ~creative(X0) | ~wise(X0) | generous(X0) | ~happy(X0) [cnf transformation 41]
92. ~strong(X0) | ~generous(X0) [cnf transformation 29]
98. ~patient(X0) | strong(X0) [cnf transformation 31]
99. ~patient(X0) | creative(X0) [cnf transformation 31]
106. ~tall(X0) | ~strong(X0) [cnf transformation 32]
128. ~creative(X0) | wise(X0) | tall(X0) [cnf transformation 61]
137. happy(X0) | happy(X0) [cnf transformation 67]
151. patient(john) [cnf transformation 24]
152. happy(X0) [duplicate literal removal 137]
307. strong(john) [resolution 98,151]
308. creative(john) [resolution 99,151]
309. ~generous(john) [resolution 307,92]
337. 35 <=> wise(john) [avatar definition]
345. wise(john) | tall(john) [resolution 128,308]
349. 36 <=> tall(john) [avatar definition]
351. tall(john) <- (36) [avatar component clause 349]
352. 36 | 35 [avatar split clause 345,337,349]
380. ~wise(john) | generous(john) | ~happy(john) [resolution 91,308]
389. ~wise(john) | ~happy(john) [subsumption resolution 380,309]
390. ~wise(john) [subsumption resolution 389,152]
391. ~35 [avatar split clause 390,337]
425. ~strong(john) <- (36) [resolution 351,106]
427. $false <- (36) [subsumption resolution 425,307]
428. ~36 [avatar contradiction clause 427]
429. $false [avatar sat refutation 352,391,428]
% SZS output end Proof for 8284924939005934200845984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not old is both kind and not rich.
If fred is not rich then alice is either curious or funny and vice versa.
Everyone who is not tall or old is old or not funny and vice versa.
If someone is both not curious and patient then paul is funny and vice versa.
If someone is either generous or not quiet then fred is either not patient or not brave.
Everyone who is humble is either old or not quiet and vice versa.
If someone is funny or not quiet then mary is either not kind or not happy.
Everyone who is either not generous or not tall is generous or not funny and vice versa.
Everyone who is either not creative or patient is either humble or quiet and vice versa.
Everyone who is not calm or not curious is both generous and not tall and vice versa.
If someone is both not quiet and not tall then someone is both funny and not rich.
Everyone who is quiet is both humble and not wise and vice versa.
If fred is either creative or tall then paul is both patient and kind and vice versa.
Everyone who is humble is both tall and rich and vice versa.
If mary is both not rich and not happy then someone is strong.
If paul is curious or patient then susan is both quiet and not quiet.
Fred is old.
Fred is not creative.
Mary is both not strong and not quiet.
Someone is not brave or not quiet.
Someone is not creative.
Someone is not humble.
Lucy is either not funny or generous. | Fred is quiet. | contradiction | (![X]:((strong(X)&~old(X))=>(kind(X)&~rich(X))))&
((~rich(fred))<=>((curious(alice)<~>funny(alice))))&
(![X]:((~tall(X)|old(X))<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)&patient(X))))<=>(funny(paul)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((~patient(fred)<~>~brave(fred))))&
(![X]:(humble(X)<=>(old(X)<~>~quiet(X))))&
((?[X]:((funny(X)|~quiet(X))))=>((~kind(mary)<~>~happy(mary))))&
(![X]:((~generous(X)<~>~tall(X))<=>(generous(X)|~funny(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((~calm(X)|~curious(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~quiet(X)&~tall(X))))=>(?[X]:((funny(X)&~rich(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~wise(X))))&
(((creative(fred)<~>tall(fred)))<=>((patient(paul)&kind(paul))))&
(![X]:(humble(X)<=>(tall(X)&rich(X))))&
(((~rich(mary)&~happy(mary)))=>(?[X]:(strong(X))))&
(((curious(paul)|patient(paul)))=>((quiet(susan)&~quiet(susan))))&
(old(fred))&
(~creative(fred))&
((~strong(mary)&~quiet(mary)))&
(?[X]:((~brave(X)|~quiet(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~humble(X)))&
((~funny(lucy)<~>generous(lucy))) | quiet(fred) | [
"p11",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3027982201754751971601573
% SZS output start Proof for 3027982201754751971601573
12. ! [X0] : (quiet(X0) <=> (~wise(X0) & humble(X0))) [input p11]
13. (creative(fred) <~> tall(fred)) <=> (kind(paul) & patient(paul)) [input p12]
14. ! [X0] : (humble(X0) <=> (rich(X0) & tall(X0))) [input p13]
16. (patient(paul) | curious(paul)) => (~quiet(susan) & quiet(susan)) [input p15]
18. ~creative(fred) [input p17]
24. quiet(fred) [input hypothesis]
33. (~quiet(susan) & quiet(susan)) | (~patient(paul) & ~curious(paul)) [ennf transformation 16]
52. ! [X0] : ((quiet(X0) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 12]
53. ! [X0] : ((quiet(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | ~quiet(X0))) [flattening 52]
54. (((~tall(fred) | ~creative(fred)) & (tall(fred) | creative(fred))) | (~kind(paul) | ~patient(paul))) & ((kind(paul) & patient(paul)) | ((creative(fred) | ~tall(fred)) & (tall(fred) | ~creative(fred)))) [nnf transformation 13]
55. (((~tall(fred) | ~creative(fred)) & (tall(fred) | creative(fred))) | ~kind(paul) | ~patient(paul)) & ((kind(paul) & patient(paul)) | ((creative(fred) | ~tall(fred)) & (tall(fred) | ~creative(fred)))) [flattening 54]
56. ! [X0] : ((humble(X0) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | ~humble(X0))) [nnf transformation 14]
57. ! [X0] : ((humble(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | ~humble(X0))) [flattening 56]
113. ~quiet(X0) | humble(X0) [cnf transformation 53]
117. patient(paul) | creative(fred) | ~tall(fred) [cnf transformation 55]
122. ~humble(X0) | tall(X0) [cnf transformation 57]
127. quiet(susan) | ~patient(paul) [cnf transformation 33]
129. ~quiet(susan) | ~patient(paul) [cnf transformation 33]
131. ~creative(fred) [cnf transformation 18]
139. quiet(fred) [cnf transformation 24]
228. 19 <=> patient(paul) [avatar definition]
236. 21 <=> creative(fred) [avatar definition]
240. 22 <=> tall(fred) [avatar definition]
242. ~tall(fred) <- (~22) [avatar component clause 240]
247. ~22 | 21 | 19 [avatar split clause 117,228,236,240]
259. 25 <=> quiet(susan) [avatar definition]
262. ~19 | ~25 [avatar split clause 129,259,228]
268. ~19 | 25 [avatar split clause 127,259,228]
270. ~21 [avatar split clause 131,236]
291. humble(fred) [resolution 113,139]
292. tall(fred) [resolution 122,291]
293. $false <- (~22) [subsumption resolution 292,242]
294. 22 [avatar contradiction clause 293]
295. $false [avatar sat refutation 247,262,268,270,294]
% SZS output end Proof for 3027982201754751971601573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and strong is tall and vice versa. If someone is both curious and wise then someone is not wise. Everyone who is quiet is strong. Everyone who is humble or not humble is creative. Everyone who is either not curious or not funny is both not quiet and old. Everyone who is either tall or creative is both calm and wise. Everyone who is generous or not quiet is not quiet or kind. Everyone who is both not old and calm is both not curious and not funny and vice versa. Everyone who is tall is strong or old and vice versa. Everyone who is both generous and kind is either not creative or not wise and vice versa. Everyone who is either not funny or quiet is either not tall or old. Everyone who is both not funny and humble is both quiet and not curious and vice versa. Everyone who is either brave or happy is not curious or not happy and vice versa. Everyone who is both not tall and not generous is either not generous or not wise and vice versa. Everyone who is both strong and funny is either creative or not rich and vice versa. If someone is both curious and not curious then someone is either not kind or curious and vice versa. Someone is both kind and creative. John is not brave or not quiet. Someone is both creative and not old. Someone is happy. Someone is not creative or patient. Susan is generous or not brave. | Susan is not brave. | entailment | (![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(![X]:((generous(X)&kind(X))<=>(~creative(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>quiet(X))=>(~tall(X)<~>old(X))))&
(![X]:((~funny(X)&humble(X))<=>(quiet(X)&~curious(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~curious(X)|~happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((strong(X)&funny(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((curious(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>curious(X)))))&
(?[X]:((kind(X)&creative(X))))&
((~brave(john)|~quiet(john)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)|patient(X))))&
((generous(susan)|~brave(susan))) | ~brave(susan) | [
"p0",
"p1",
"p3",
"p5",
"p9",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3045122797840854015311260
% SZS output start Proof for 3045122797840854015311260
1. ! [X0] : ((strong(X0) & ~strong(X0)) <=> tall(X0)) [input p0]
2. ? [X0] : (wise(X0) & curious(X0)) => ? [X0] : ~wise(X0) [input p1]
4. ! [X0] : ((~humble(X0) | humble(X0)) => creative(X0)) [input p3]
6. ! [X0] : ((tall(X0) <~> creative(X0)) => (wise(X0) & calm(X0))) [input p5]
10. ! [X0] : ((kind(X0) & generous(X0)) <=> (~creative(X0) <~> ~wise(X0))) [input p9]
16. ? [X0] : (~curious(X0) & curious(X0)) <=> ? [X0] : (~kind(X0) <~> curious(X0)) [input p15]
22. ~brave(susan) | generous(susan) [input p21]
23. brave(susan) [input hypothesis]
24. ? [X0] : (wise(X0) & curious(X0)) => ? [X1] : ~wise(X1) [rectify 2]
25. ? [X0] : (~curious(X0) & curious(X0)) <=> ? [X1] : (~kind(X1) <~> curious(X1)) [rectify 16]
27. ? [X1] : ~wise(X1) | ! [X0] : (~wise(X0) | ~curious(X0)) [ennf transformation 24]
29. ! [X0] : (creative(X0) | (humble(X0) & ~humble(X0))) [ennf transformation 4]
31. ! [X0] : ((wise(X0) & calm(X0)) | (tall(X0) <=> creative(X0))) [ennf transformation 6]
35. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) | strong(X0)))) [nnf transformation 1]
36. ! [X0] : (((strong(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | ~strong(X0) | strong(X0))) [flattening 35]
37. ? [X0] : ~wise(X0) | ! [X1] : (~wise(X1) | ~curious(X1)) [rectify 27]
38. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
39. ~wise(sK0) | ! [X1] : (~wise(X1) | ~curious(X1)) [skolemisation 37,38]
41. ! [X0] : ((wise(X0) & calm(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) [nnf transformation 31]
46. ! [X0] : (((kind(X0) & generous(X0)) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | (~kind(X0) | ~generous(X0)))) [nnf transformation 10]
47. ! [X0] : (((kind(X0) & generous(X0)) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | ~kind(X0) | ~generous(X0))) [flattening 46]
57. (? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : ((~kind(X1) | ~curious(X1)) & (curious(X1) | kind(X1)))) & (? [X1] : ((~curious(X1) | kind(X1)) & (curious(X1) | ~kind(X1))) | ! [X0] : (curious(X0) | ~curious(X0))) [nnf transformation 25]
58. (? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : ((~kind(X1) | ~curious(X1)) & (curious(X1) | kind(X1)))) & (? [X2] : ((~curious(X2) | kind(X2)) & (curious(X2) | ~kind(X2))) | ! [X3] : (curious(X3) | ~curious(X3))) [rectify 57]
59. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK1) & curious(sK1)) [choice axiom]
60. ? [X2] : ((~curious(X2) | kind(X2)) & (curious(X2) | ~kind(X2))) => ((~curious(sK2) | kind(sK2)) & (curious(sK2) | ~kind(sK2))) [choice axiom]
61. ((~curious(sK1) & curious(sK1)) | ! [X1] : ((~kind(X1) | ~curious(X1)) & (curious(X1) | kind(X1)))) & (((~curious(sK2) | kind(sK2)) & (curious(sK2) | ~kind(sK2))) | ! [X3] : (curious(X3) | ~curious(X3))) [skolemisation 58,60,59]
69. ~strong(X0) | ~tall(X0) [cnf transformation 36]
70. ~tall(X0) | strong(X0) [cnf transformation 36]
71. ~wise(sK0) | ~wise(X1) | ~curious(X1) [cnf transformation 39]
73. creative(X0) | ~humble(X0) [cnf transformation 29]
74. creative(X0) | humble(X0) [cnf transformation 29]
82. wise(X0) | tall(X0) | ~creative(X0) [cnf transformation 41]
92. ~wise(X0) | ~creative(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 47]
126. curious(sK1) | curious(X1) | kind(X1) [cnf transformation 61]
128. ~curious(sK1) | curious(X1) | kind(X1) [cnf transformation 61]
136. ~brave(susan) | generous(susan) [cnf transformation 22]
137. brave(susan) [cnf transformation 23]
142. ~tall(X0) [subsumption resolution 69,70]
144. 1 <=> ! [X1] : (~wise(X1) | ~curious(X1)) [avatar definition]
145. ~wise(X1) | ~curious(X1) <- (1) [avatar component clause 144]
147. 2 <=> wise(sK0) [avatar definition]
149. ~wise(sK0) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 71,147,144]
151. creative(X0) [subsumption resolution 73,74]
152. wise(X0) | ~creative(X0) [subsumption resolution 82,142]
153. wise(X0) [subsumption resolution 152,151]
160. ~creative(X0) | ~kind(X0) | ~generous(X0) [subsumption resolution 92,153]
161. ~kind(X0) | ~generous(X0) [subsumption resolution 160,151]
170. 4 <=> curious(sK1) [avatar definition]
175. 5 <=> ! [X1] : (curious(X1) | kind(X1)) [avatar definition]
176. kind(X1) | curious(X1) <- (5) [avatar component clause 175]
177. 5 | ~4 [avatar split clause 128,170,175]
179. 5 | 4 [avatar split clause 126,170,175]
190. 8 <=> generous(susan) [avatar definition]
192. generous(susan) <- (8) [avatar component clause 190]
194. 9 <=> brave(susan) [avatar definition]
197. 8 | ~9 [avatar split clause 136,194,190]
198. 9 [avatar split clause 137,194]
199. $false <- (~2) [subsumption resolution 149,153]
200. 2 [avatar contradiction clause 199]
201. ~curious(X1) <- (1) [subsumption resolution 145,153]
205. curious(X1) | ~generous(X1) <- (5) [resolution 176,161]
206. ~generous(X1) <- (1, 5) [subsumption resolution 205,201]
207. $false <- (1, 5, 8) [resolution 206,192]
208. ~1 | ~5 | ~8 [avatar contradiction clause 207]
209. $false [avatar sat refutation 150,177,179,197,198,200,208]
% SZS output end Proof for 3045122797840854015311260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not patient and not rich.
If fred is either not calm or patient then fred is kind or creative.
Everyone who is either not old or old is not generous or wise.
If someone is not rich or not funny then fred is both tall and strong and vice versa.
Everyone who is kind or humble is both not happy and funny and vice versa.
Everyone who is not generous is either not kind or generous.
Everyone who is calm or generous is both calm and not humble and vice versa.
If paul is strong then someone is either calm or not humble and vice versa.
If someone is calm or brave then alice is both wise and not kind and vice versa.
Everyone who is not old or quiet is both not calm and humble and vice versa.
Everyone who is both not calm and patient is not old or brave and vice versa.
Everyone who is either not calm or rich is both not creative and curious and vice versa.
If mary is both tall and not strong then someone is either not happy or not rich and vice versa.
If susan is calm then fred is not generous or not curious.
Everyone who is curious or not calm is kind and vice versa.
Everyone who is not happy or generous is both kind and not funny and vice versa.
John is strong.
Fred is not brave.
Alice is old or not old.
Paul is either not humble or brave.
Someone is wise. | John is brave. | contradiction | (![X]:(creative(X)=>(~patient(X)&~rich(X))))&
(((~calm(fred)<~>patient(fred)))=>((kind(fred)|creative(fred))))&
(![X]:((~old(X)<~>old(X))=>(~generous(X)|wise(X))))&
((?[X]:((~rich(X)|~funny(X))))<=>((tall(fred)&strong(fred))))&
(![X]:((kind(X)|humble(X))<=>(~happy(X)&funny(X))))&
(![X]:(~generous(X)=>(~kind(X)<~>generous(X))))&
(![X]:((calm(X)|generous(X))<=>(calm(X)&~humble(X))))&
((strong(paul))<=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((calm(X)|brave(X))))<=>((wise(alice)&~kind(alice))))&
(![X]:((~old(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((~calm(X)&patient(X))<=>(~old(X)|brave(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(~creative(X)&curious(X))))&
(((tall(mary)&~strong(mary)))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
((calm(susan))=>((~generous(fred)|~curious(fred))))&
(![X]:((curious(X)|~calm(X))<=>kind(X)))&
(![X]:((~happy(X)|generous(X))<=>(kind(X)&~funny(X))))&
(strong(john))&
(~brave(fred))&
((old(alice)|~old(alice)))&
((~humble(paul)<~>brave(paul)))&
(?[X]:(wise(X))) | brave(john) | [
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4350547349133904380182263
% SZS output start Proof for 4350547349133904380182263
6. ! [X0] : (~generous(X0) => (~kind(X0) <~> generous(X0))) [input p5]
7. ! [X0] : ((generous(X0) | calm(X0)) <=> (~humble(X0) & calm(X0))) [input p6]
11. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (brave(X0) | ~old(X0))) [input p10]
15. ! [X0] : ((~calm(X0) | curious(X0)) <=> kind(X0)) [input p14]
22. brave(john) [input hypothesis]
28. ! [X0] : ((~kind(X0) <~> generous(X0)) | generous(X0)) [ennf transformation 6]
40. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | generous(X0)) [nnf transformation 28]
41. ! [X0] : (((generous(X0) | calm(X0)) | (humble(X0) | ~calm(X0))) & ((~humble(X0) & calm(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 7]
42. ! [X0] : ((generous(X0) | calm(X0) | humble(X0) | ~calm(X0)) & ((~humble(X0) & calm(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 41]
54. ! [X0] : (((patient(X0) & ~calm(X0)) | (~brave(X0) & old(X0))) & ((brave(X0) | ~old(X0)) | (~patient(X0) | calm(X0)))) [nnf transformation 11]
55. ! [X0] : (((patient(X0) & ~calm(X0)) | (~brave(X0) & old(X0))) & (brave(X0) | ~old(X0) | ~patient(X0) | calm(X0))) [flattening 54]
63. ! [X0] : (((~calm(X0) | curious(X0)) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~curious(X0)))) [nnf transformation 15]
64. ! [X0] : ((~calm(X0) | curious(X0) | ~kind(X0)) & (kind(X0) | (calm(X0) & ~curious(X0)))) [flattening 63]
86. generous(X0) | ~kind(X0) | generous(X0) [cnf transformation 40]
89. ~generous(X0) | calm(X0) [cnf transformation 42]
109. ~brave(X0) | ~calm(X0) [cnf transformation 55]
126. kind(X0) | calm(X0) [cnf transformation 64]
139. brave(john) [cnf transformation 22]
140. ~kind(X0) | generous(X0) [duplicate literal removal 86]
297. ~calm(john) [resolution 109,139]
305. generous(X0) | calm(X0) [resolution 140,126]
306. calm(X0) [subsumption resolution 305,89]
308. $false [resolution 306,297]
% SZS output end Proof for 4350547349133904380182263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is brave or generous and vice versa. If fred is either not kind or kind then mary is either not generous or patient. If someone is tall or old then someone is not funny or strong and vice versa. Everyone who is not brave is kind. If susan is not kind or not tall then alice is either not patient or generous and vice versa. Everyone who is brave is generous or calm and vice versa. If alice is not rich then someone is not creative and vice versa. If paul is either not calm or rich then someone is either patient or not creative and vice versa. If susan is either not kind or not old then someone is not calm or not tall. Everyone who is funny is not kind or patient and vice versa. If someone is either brave or funny then someone is both not generous and brave. Everyone who is not generous or wise is either not humble or not quiet. Everyone who is both wise and not wise is both not rich and not tall and vice versa. If someone is not creative or not brave then susan is both not calm and not creative and vice versa. Everyone who is either generous or not humble is brave or not old and vice versa. Everyone who is funny or not generous is both patient and old. Alice is not funny. Someone is both not kind and humble. Someone is not patient or not old. John is rich or creative. Paul is brave or creative. Someone is either curious or humble. Someone is both not strong and quiet. Someone is either not brave or not calm. | Mary is not humble. | contradiction | (![X]:(~happy(X)<=>(brave(X)|generous(X))))&
(((~kind(fred)<~>kind(fred)))=>((~generous(mary)<~>patient(mary))))&
((?[X]:((tall(X)|old(X))))<=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:(~brave(X)=>kind(X)))&
(((~kind(susan)|~tall(susan)))<=>((~patient(alice)<~>generous(alice))))&
(![X]:(brave(X)<=>(generous(X)|calm(X))))&
((~rich(alice))<=>(?[X]:(~creative(X))))&
(((~calm(paul)<~>rich(paul)))<=>(?[X]:((patient(X)<~>~creative(X)))))&
(((~kind(susan)<~>~old(susan)))=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:(funny(X)<=>(~kind(X)|patient(X))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~generous(X)|wise(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((wise(X)&~wise(X))<=>(~rich(X)&~tall(X))))&
((?[X]:((~creative(X)|~brave(X))))<=>((~calm(susan)&~creative(susan))))&
(![X]:((generous(X)<~>~humble(X))<=>(brave(X)|~old(X))))&
(![X]:((funny(X)|~generous(X))=>(patient(X)&old(X))))&
(~funny(alice))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~patient(X)|~old(X))))&
((rich(john)|creative(john)))&
((brave(paul)|creative(paul)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((~strong(X)&quiet(X))))&
(?[X]:((~brave(X)<~>~calm(X)))) | ~humble(mary) | [
"p1",
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4652895107464765138410016
% SZS output start Proof for 4652895107464765138410016
2. (~kind(fred) <~> kind(fred)) => (~generous(mary) <~> patient(mary)) [input p1]
6. ! [X0] : (brave(X0) <=> (calm(X0) | generous(X0))) [input p5]
15. ! [X0] : ((generous(X0) <~> ~humble(X0)) <=> (~old(X0) | brave(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | funny(X0)) => (old(X0) & patient(X0))) [input p15]
25. ~humble(mary) [input hypothesis]
28. (~generous(mary) <~> patient(mary)) | (~kind(fred) <=> kind(fred)) [ennf transformation 2]
33. ! [X0] : ((old(X0) & patient(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 16]
34. ((~patient(mary) | generous(mary)) & (patient(mary) | ~generous(mary))) | ((~kind(fred) | ~kind(fred)) & (kind(fred) | kind(fred))) [nnf transformation 28]
42. ! [X0] : ((brave(X0) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | ~brave(X0))) [nnf transformation 6]
43. ! [X0] : ((brave(X0) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | ~brave(X0))) [flattening 42]
69. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [nnf transformation 15]
70. ! [X0] : ((((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))))) [flattening 69]
85. ~patient(mary) | generous(mary) | kind(fred) | kind(fred) [cnf transformation 34]
86. ~patient(mary) | generous(mary) | ~kind(fred) | ~kind(fred) [cnf transformation 34]
99. ~generous(X0) | brave(X0) [cnf transformation 43]
137. humble(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
140. patient(X0) | generous(X0) [cnf transformation 33]
155. ~humble(mary) [cnf transformation 25]
158. ~patient(mary) | generous(mary) | kind(fred) [duplicate literal removal 85]
159. ~patient(mary) | generous(mary) | ~kind(fred) [duplicate literal removal 86]
161. 1 <=> kind(fred) [avatar definition]
165. 2 <=> generous(mary) [avatar definition]
166. ~generous(mary) <- (~2) [avatar component clause 165]
167. generous(mary) <- (2) [avatar component clause 165]
169. 3 <=> patient(mary) [avatar definition]
171. ~patient(mary) <- (~3) [avatar component clause 169]
172. ~1 | 2 | ~3 [avatar split clause 159,169,165,161]
173. 1 | 2 | ~3 [avatar split clause 158,169,165,161]
330. ~generous(X0) | humble(X0) [subsumption resolution 137,99]
377. generous(mary) <- (~3) [resolution 140,171]
381. $false <- (~2, ~3) [subsumption resolution 377,166]
382. 2 | 3 [avatar contradiction clause 381]
399. humble(mary) <- (2) [resolution 330,167]
403. $false <- (2) [subsumption resolution 399,155]
404. ~2 [avatar contradiction clause 403]
405. $false [avatar sat refutation 172,173,382,404]
% SZS output end Proof for 4652895107464765138410016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or not strong then john is either not patient or not quiet and vice versa. Everyone who is not curious is not brave and vice versa. Everyone who is not funny or creative is not old. Everyone who is not happy is both funny and rich and vice versa. If alice is both not quiet and not rich then someone is either happy or not quiet. Everyone who is not wise or funny is not quiet. Everyone who is either curious or not strong is not creative. If someone is not old then susan is either generous or not happy and vice versa. If someone is wise or kind then fred is either not kind or wise. If paul is generous or old then alice is either not tall or not wise and vice versa. If john is either creative or happy then someone is quiet and vice versa. Everyone who is not patient is humble. If someone is not patient then someone is strong and vice versa. If someone is not calm then mary is not rich. Everyone who is both not rich and not wise is funny and vice versa. If someone is either creative or wise then someone is generous or not funny. Someone is both calm and not strong. Someone is both not rich and not patient. Someone is not brave or creative. Someone is not kind. John is creative. Someone is either funny or not brave. Someone is quiet or not humble. Someone is generous or not curious. | Alice is quiet. | contradiction | ((?[X]:((~humble(X)|~strong(X))))<=>((~patient(john)<~>~quiet(john))))&
(![X]:(~curious(X)<=>~brave(X)))&
(![X]:((~funny(X)|creative(X))=>~old(X)))&
(![X]:(~happy(X)<=>(funny(X)&rich(X))))&
(((~quiet(alice)&~rich(alice)))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(![X]:((~wise(X)|funny(X))=>~quiet(X)))&
(![X]:((curious(X)<~>~strong(X))=>~creative(X)))&
((?[X]:(~old(X)))<=>((generous(susan)<~>~happy(susan))))&
((?[X]:((wise(X)|kind(X))))=>((~kind(fred)<~>wise(fred))))&
(((generous(paul)|old(paul)))<=>((~tall(alice)<~>~wise(alice))))&
(((creative(john)<~>happy(john)))<=>(?[X]:(quiet(X))))&
(![X]:(~patient(X)=>humble(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
((?[X]:(~calm(X)))=>(~rich(mary)))&
(![X]:((~rich(X)&~wise(X))<=>funny(X)))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(?[X]:((calm(X)&~strong(X))))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:(~kind(X)))&
(creative(john))&
(?[X]:((funny(X)<~>~brave(X))))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:((generous(X)|~curious(X)))) | quiet(alice) | [
"p3",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3146003252244703057120970
% SZS output start Proof for 3146003252244703057120970
4. ! [X0] : (~happy(X0) <=> (rich(X0) & funny(X0))) [input p3]
11. (creative(john) <~> happy(john)) <=> ? [X0] : quiet(X0) [input p10]
15. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> funny(X0)) [input p14]
21. creative(john) [input p20]
25. quiet(alice) [input hypothesis]
43. ! [X0] : ((~happy(X0) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | happy(X0))) [nnf transformation 4]
44. ! [X0] : ((~happy(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | happy(X0))) [flattening 43]
56. (((~happy(john) | ~creative(john)) & (happy(john) | creative(john))) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ((creative(john) | ~happy(john)) & (happy(john) | ~creative(john)))) [nnf transformation 11]
57. (((~happy(john) | ~creative(john)) & (happy(john) | creative(john))) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ((creative(john) | ~happy(john)) & (happy(john) | ~creative(john)))) [rectify 56]
58. ? [X1] : quiet(X1) => quiet(sK3) [choice axiom]
59. (((~happy(john) | ~creative(john)) & (happy(john) | creative(john))) | ! [X0] : ~quiet(X0)) & (quiet(sK3) | ((creative(john) | ~happy(john)) & (happy(john) | ~creative(john)))) [skolemisation 57,58]
65. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) | rich(X0)))) [nnf transformation 15]
66. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~funny(X0)) & (funny(X0) | wise(X0) | rich(X0))) [flattening 65]
96. happy(X0) | funny(X0) [cnf transformation 44]
97. rich(X0) | happy(X0) [cnf transformation 44]
122. ~happy(john) | ~creative(john) | ~quiet(X0) [cnf transformation 59]
127. ~rich(X0) | ~funny(X0) [cnf transformation 66]
136. creative(john) [cnf transformation 21]
141. quiet(alice) [cnf transformation 25]
171. 7 <=> quiet(alice) [avatar definition]
173. quiet(alice) <- (7) [avatar component clause 171]
248. 23 <=> ! [X0] : ~quiet(X0) [avatar definition]
249. ~quiet(X0) <- (23) [avatar component clause 248]
251. 24 <=> creative(john) [avatar definition]
255. 25 <=> happy(john) [avatar definition]
257. ~happy(john) <- (~25) [avatar component clause 255]
258. 23 | ~24 | ~25 [avatar split clause 122,255,251,248]
307. 24 [avatar split clause 136,251]
336. 7 [avatar split clause 141,171]
339. $false <- (7, 23) [subsumption resolution 173,249]
340. ~7 | ~23 [avatar contradiction clause 339]
357. ~funny(X0) | happy(X0) [resolution 127,97]
358. happy(X0) [subsumption resolution 357,96]
363. $false <- (~25) [resolution 358,257]
364. 25 [avatar contradiction clause 363]
366. $false [avatar sat refutation 258,307,336,340,364]
% SZS output end Proof for 3146003252244703057120970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient then someone is calm and vice versa.
Everyone who is not happy or not strong is curious.
If mary is both funny and old then susan is strong or not wise.
Everyone who is either calm or wise is both not creative and quiet and vice versa.
If someone is either rich or tall then alice is not brave or kind.
Everyone who is both not generous and not kind is either not generous or old and vice versa.
If lucy is both not curious and kind then paul is both quiet and not quiet and vice versa.
If someone is not happy then someone is both kind and not tall and vice versa.
Everyone who is not brave or not tall is either tall or patient.
If someone is brave then someone is either creative or humble and vice versa.
Everyone who is creative or not patient is both strong and patient and vice versa.
Everyone who is happy is not strong.
If someone is either curious or quiet then mary is not quiet and vice versa.
Everyone who is funny or not strong is either happy or not humble and vice versa.
Everyone who is not tall or old is generous and vice versa.
Everyone who is both old and not humble is either brave or not happy and vice versa.
Someone is either strong or not patient.
Someone is either not old or not rich.
Someone is funny.
Fred is not kind.
Someone is strong or not kind. | Paul is not creative. | neutral | ((?[X]:(~patient(X)))<=>(?[X]:(calm(X))))&
(![X]:((~happy(X)|~strong(X))=>curious(X)))&
(((funny(mary)&old(mary)))=>((strong(susan)|~wise(susan))))&
(![X]:((calm(X)<~>wise(X))<=>(~creative(X)&quiet(X))))&
((?[X]:((rich(X)<~>tall(X))))=>((~brave(alice)|kind(alice))))&
(![X]:((~generous(X)&~kind(X))<=>(~generous(X)<~>old(X))))&
(((~curious(lucy)&kind(lucy)))<=>((quiet(paul)&~quiet(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((kind(X)&~tall(X)))))&
(![X]:((~brave(X)|~tall(X))=>(tall(X)<~>patient(X))))&
((?[X]:(brave(X)))<=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:((creative(X)|~patient(X))<=>(strong(X)&patient(X))))&
(![X]:(happy(X)=>~strong(X)))&
((?[X]:((curious(X)<~>quiet(X))))<=>(~quiet(mary)))&
(![X]:((funny(X)|~strong(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))<=>generous(X)))&
(![X]:((old(X)&~humble(X))<=>(brave(X)<~>~happy(X))))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
(~kind(fred))&
(?[X]:((strong(X)|~kind(X)))) | ~creative(paul) | [] | null | 0 |
If paul is calm or rich then john is either kind or not patient and vice versa. 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 not wise or wise. Someone is not kind. Someone is both quiet and calm. | Fred is funny. | contradiction | (((calm(paul)|rich(paul)))<=>((kind(john)<~>~patient(john))))&
(![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]:((~wise(X)|wise(X))))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)&calm(X)))) | funny(fred) | [
"p6",
"p7",
"p9",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3100266366110616930166983
% SZS output start Proof for 3100266366110616930166983
7. ! [X0] : (funny(X0) <=> (tall(X0) <~> rich(X0))) [input p6]
8. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p7]
10. ? [X0] : tall(X0) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p9]
13. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p12]
14. ! [X0] : ((quiet(X0) <~> ~patient(X0)) <=> (~calm(X0) & ~generous(X0))) [input p13]
15. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p14]
16. ! [X0] : ((~brave(X0) <~> patient(X0)) => (~rich(X0) <~> curious(X0))) [input p15]
20. funny(fred) [input hypothesis]
23. ? [X0] : tall(X0) <=> ? [X1] : (generous(X1) & ~quiet(X1)) [rectify 10]
25. ! [X0] : (funny(X0) => (tall(X0) <~> rich(X0))) [unused predicate definition removal 7]
32. ! [X0] : ((tall(X0) <~> rich(X0)) | ~funny(X0)) [ennf transformation 25]
35. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 15]
36. ! [X0] : ((~rich(X0) <~> curious(X0)) | (~brave(X0) <=> patient(X0))) [ennf transformation 16]
44. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | ~funny(X0)) [nnf transformation 32]
45. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 45]
49. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X1] : (generous(X1) & ~quiet(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 23]
50. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X2] : (generous(X2) & ~quiet(X2)) | ! [X3] : ~tall(X3)) [rectify 49]
51. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
52. ? [X2] : (generous(X2) & ~quiet(X2)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
53. (tall(sK1) | ! [X1] : (~generous(X1) | quiet(X1))) & ((generous(sK2) & ~quiet(sK2)) | ! [X3] : ~tall(X3)) [skolemisation 50,52,51]
60. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 13]
61. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 60]
62. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [nnf transformation 14]
63. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [flattening 62]
64. ! [X0] : (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) [nnf transformation 36]
85. ~funny(X0) | tall(X0) | rich(X0) [cnf transformation 44]
89. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 46]
94. ~quiet(sK2) | ~tall(X3) [cnf transformation 53]
95. generous(sK2) | ~tall(X3) [cnf transformation 53]
104. happy(X0) | curious(X0) [cnf transformation 61]
105. ~curious(X0) | happy(X0) [cnf transformation 61]
106. ~brave(X0) | curious(X0) [cnf transformation 61]
107. ~curious(X0) | ~brave(X0) [cnf transformation 61]
110. ~generous(X0) | quiet(X0) | patient(X0) [cnf transformation 63]
115. ~patient(X0) | ~happy(X0) [cnf transformation 35]
119. curious(X0) | ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 64]
127. funny(fred) [cnf transformation 20]
171. 10 <=> ! [X3] : ~tall(X3) [avatar definition]
172. ~tall(X3) <- (10) [avatar component clause 171]
174. 11 <=> generous(sK2) [avatar definition]
176. generous(sK2) <- (11) [avatar component clause 174]
177. 10 | 11 [avatar split clause 95,174,171]
179. 12 <=> quiet(sK2) [avatar definition]
181. ~quiet(sK2) <- (~12) [avatar component clause 179]
182. 10 | ~12 [avatar split clause 94,179,171]
197. ~brave(X0) [subsumption resolution 106,107]
198. happy(X0) [subsumption resolution 104,105]
200. ~patient(X0) [subsumption resolution 115,198]
201. curious(X0) | ~rich(X0) | brave(X0) [subsumption resolution 119,200]
202. ~rich(X0) | curious(X0) [subsumption resolution 201,197]
210. tall(fred) | rich(fred) [resolution 85,127]
211. rich(fred) <- (10) [subsumption resolution 210,172]
212. curious(fred) <- (10) [resolution 211,202]
216. brave(fred) | patient(fred) <- (10) [resolution 89,212]
217. patient(fred) <- (10) [subsumption resolution 216,197]
218. $false <- (10) [subsumption resolution 217,200]
219. ~10 [avatar contradiction clause 218]
250. quiet(sK2) | patient(sK2) <- (11) [resolution 110,176]
251. patient(sK2) <- (11, ~12) [subsumption resolution 250,181]
252. $false <- (11, ~12) [subsumption resolution 251,200]
253. ~11 | 12 [avatar contradiction clause 252]
254. $false [avatar sat refutation 177,182,219,253]
% SZS output end Proof for 3100266366110616930166983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not old or brave then someone is not happy and vice versa. If someone is not funny then lucy is both rich and not creative. If lucy is not creative or rich then alice is not tall and vice versa. If someone is both not kind and wise then susan is either creative or not kind. Everyone who is both kind and funny is generous and vice versa. If someone is either not tall or not wise then someone is old and vice versa. Everyone who is either calm or funny is either not old or not strong. If john is both kind and not humble then susan is both not quiet and not calm and vice versa. Everyone who is either curious or patient is either curious or not calm and vice versa. Everyone who is both humble and strong is patient or kind and vice versa. If someone is either not kind or patient then fred is patient. If fred is old then fred is either not funny or rich. Everyone who is both not old and quiet is both patient and not humble and vice versa. If alice is not strong then paul is quiet or old. Everyone who is either wise or not kind is curious. If someone is humble or not generous then john is both not funny and not old and vice versa. Someone is both wise and funny. Lucy is not kind. Paul is both rich and not quiet. Someone is not strong. Susan is not curious. Paul is either not quiet or not tall. Mary is curious or brave. | Fred is calm. | contradiction | (((~old(john)<~>brave(john)))<=>(?[X]:(~happy(X))))&
((?[X]:(~funny(X)))=>((rich(lucy)&~creative(lucy))))&
(((~creative(lucy)|rich(lucy)))<=>(~tall(alice)))&
((?[X]:((~kind(X)&wise(X))))=>((creative(susan)<~>~kind(susan))))&
(![X]:((kind(X)&funny(X))<=>generous(X)))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>funny(X))=>(~old(X)<~>~strong(X))))&
(((kind(john)&~humble(john)))<=>((~quiet(susan)&~calm(susan))))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)&strong(X))<=>(patient(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(patient(fred)))&
((old(fred))=>((~funny(fred)<~>rich(fred))))&
(![X]:((~old(X)&quiet(X))<=>(patient(X)&~humble(X))))&
((~strong(alice))=>((quiet(paul)|old(paul))))&
(![X]:((wise(X)<~>~kind(X))=>curious(X)))&
((?[X]:((humble(X)|~generous(X))))<=>((~funny(john)&~old(john))))&
(?[X]:((wise(X)&funny(X))))&
(~kind(lucy))&
((rich(paul)&~quiet(paul)))&
(?[X]:(~strong(X)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((curious(mary)|brave(mary))) | calm(fred) | [
"p8",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3801405018856682968145596
% SZS output start Proof for 3801405018856682968145596
9. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (curious(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((strong(X0) & humble(X0)) <=> (kind(X0) | patient(X0))) [input p9]
11. ? [X0] : (~kind(X0) <~> patient(X0)) => patient(fred) [input p10]
20. ? [X0] : ~strong(X0) [input p19]
24. calm(fred) [input hypothesis]
29. patient(fred) | ! [X0] : (~kind(X0) <=> patient(X0)) [ennf transformation 11]
51. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) & (((calm(X0) | ~curious(X0)) & (~calm(X0) | curious(X0))) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 9]
52. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~strong(X0) | ~humble(X0)))) [nnf transformation 10]
53. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~strong(X0) | ~humble(X0))) [flattening 52]
54. patient(fred) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))) [nnf transformation 29]
66. ? [X0] : ~strong(X0) => ~strong(sK5) [choice axiom]
67. ~strong(sK5) [skolemisation 20,66]
96. ~calm(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 51]
101. ~patient(X0) | ~curious(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 51]
106. ~patient(X0) | strong(X0) [cnf transformation 53]
107. ~kind(X0) | strong(X0) [cnf transformation 53]
108. patient(fred) | patient(X0) | kind(X0) [cnf transformation 54]
129. ~strong(sK5) [cnf transformation 67]
134. calm(fred) [cnf transformation 24]
135. ~calm(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 96]
138. ~patient(X0) | ~curious(X0) | ~calm(X0) [duplicate literal removal 101]
237. ~patient(X0) | ~calm(X0) [subsumption resolution 135,138]
242. 23 <=> patient(fred) [avatar definition]
244. patient(fred) <- (23) [avatar component clause 242]
247. 24 <=> ! [X0] : (patient(X0) | kind(X0)) [avatar definition]
248. patient(X0) | kind(X0) <- (24) [avatar component clause 247]
249. 24 | 23 [avatar split clause 108,242,247]
342. kind(X2) | strong(X2) <- (24) [resolution 248,106]
358. strong(X2) <- (24) [subsumption resolution 342,107]
382. $false <- (24) [resolution 358,129]
383. ~24 [avatar contradiction clause 382]
385. ~calm(fred) <- (23) [resolution 244,237]
388. $false <- (23) [subsumption resolution 385,134]
389. ~23 [avatar contradiction clause 388]
390. $false [avatar sat refutation 249,383,389]
% SZS output end Proof for 3801405018856682968145596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and strong is quiet or not creative and vice versa.
Everyone who is happy is not creative or patient and vice versa.
Everyone who is either old or not brave is not kind and vice versa.
Everyone who is both not happy and not kind is both funny and happy.
Everyone who is happy is both not old and wise.
Everyone who is not quiet is not kind.
Everyone who is either generous or wise is both not happy and calm and vice versa.
If mary is both patient and not humble then someone is either not calm or creative.
Everyone who is both not tall and wise is either not patient or not calm and vice versa.
Everyone who is either not calm or funny is either not old or not wise and vice versa.
If susan is both generous and not wise then someone is old and vice versa.
If alice is curious or not quiet then someone is both not tall and quiet and vice versa.
Everyone who is not tall or generous is either rich or calm and vice versa.
If someone is not rich or tall then someone is both not generous and not funny.
Everyone who is either rich or not kind is either not brave or calm.
Everyone who is quiet is wise and vice versa.
Someone is quiet.
Alice is either funny or rich.
Mary is rich.
Lucy is either not humble or old.
Someone is not kind. | Lucy is calm. | contradiction | (![X]:((rich(X)&strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>~kind(X)))&
(![X]:((~happy(X)&~kind(X))=>(funny(X)&happy(X))))&
(![X]:(happy(X)=>(~old(X)&wise(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((generous(X)<~>wise(X))<=>(~happy(X)&calm(X))))&
(((patient(mary)&~humble(mary)))=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~tall(X)&wise(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~old(X)<~>~wise(X))))&
(((generous(susan)&~wise(susan)))<=>(?[X]:(old(X))))&
(((curious(alice)|~quiet(alice)))<=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:((~tall(X)|generous(X))<=>(rich(X)<~>calm(X))))&
((?[X]:((~rich(X)|tall(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((rich(X)<~>~kind(X))=>(~brave(X)<~>calm(X))))&
(![X]:(quiet(X)<=>wise(X)))&
(?[X]:(quiet(X)))&
((funny(alice)<~>rich(alice)))&
(rich(mary))&
((~humble(lucy)<~>old(lucy)))&
(?[X]:(~kind(X))) | calm(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 318857355889050640218497
% SZS output start Proof for 318857355889050640218497
1. ! [X0] : ((strong(X0) & rich(X0)) <=> (~creative(X0) | quiet(X0))) [input p0]
2. ! [X0] : (happy(X0) <=> (patient(X0) | ~creative(X0))) [input p1]
4. ! [X0] : ((~kind(X0) & ~happy(X0)) => (happy(X0) & funny(X0))) [input p3]
5. ! [X0] : (happy(X0) => (wise(X0) & ~old(X0))) [input p4]
6. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p5]
7. ! [X0] : ((generous(X0) <~> wise(X0)) <=> (calm(X0) & ~happy(X0))) [input p6]
9. ! [X0] : ((wise(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p8]
13. ! [X0] : ((generous(X0) | ~tall(X0)) <=> (rich(X0) <~> calm(X0))) [input p12]
16. ! [X0] : (quiet(X0) <=> wise(X0)) [input p15]
22. calm(lucy) [input hypothesis]
24. ! [X0] : ((happy(X0) & funny(X0)) | (kind(X0) | happy(X0))) [ennf transformation 4]
25. ! [X0] : ((happy(X0) & funny(X0)) | kind(X0) | happy(X0)) [flattening 24]
26. ! [X0] : ((wise(X0) & ~old(X0)) | ~happy(X0)) [ennf transformation 5]
27. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 6]
32. ! [X0] : (((strong(X0) & rich(X0)) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & rich(X0)) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | ~strong(X0) | ~rich(X0))) [flattening 32]
34. ! [X0] : ((happy(X0) | (~patient(X0) & creative(X0))) & ((patient(X0) | ~creative(X0)) | ~happy(X0))) [nnf transformation 2]
35. ! [X0] : ((happy(X0) | (~patient(X0) & creative(X0))) & (patient(X0) | ~creative(X0) | ~happy(X0))) [flattening 34]
37. ! [X0] : ((((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0))))) [nnf transformation 7]
38. ! [X0] : ((((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0))))) [flattening 37]
42. ! [X0] : (((wise(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~wise(X0) | tall(X0)))) [nnf transformation 9]
43. ! [X0] : (((wise(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~wise(X0) | tall(X0))) [flattening 42]
55. ! [X0] : (((generous(X0) | ~tall(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~generous(X0) & tall(X0)))) [nnf transformation 13]
56. ! [X0] : ((generous(X0) | ~tall(X0) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~generous(X0) & tall(X0)))) [flattening 55]
61. ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 16]
69. ~quiet(X0) | rich(X0) [cnf transformation 33]
75. ~patient(X0) | happy(X0) [cnf transformation 35]
81. happy(X0) | kind(X0) | happy(X0) [cnf transformation 25]
83. ~happy(X0) | wise(X0) [cnf transformation 26]
84. ~kind(X0) | quiet(X0) [cnf transformation 27]
86. ~happy(X0) | generous(X0) | ~wise(X0) [cnf transformation 38]
95. ~tall(X0) | ~calm(X0) | patient(X0) [cnf transformation 43]
117. ~calm(X0) | ~rich(X0) | tall(X0) [cnf transformation 56]
118. ~calm(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 56]
129. ~quiet(X0) | wise(X0) [cnf transformation 61]
130. ~wise(X0) | quiet(X0) [cnf transformation 61]
138. calm(lucy) [cnf transformation 22]
139. kind(X0) | happy(X0) [duplicate literal removal 81]
141. ~happy(X0) | generous(X0) [subsumption resolution 86,83]
211. 16 <=> ! [X1] : rich(X1) [avatar definition]
212. rich(X1) <- (16) [avatar component clause 211]
253. happy(X0) | quiet(X0) [resolution 139,84]
285. quiet(X2) | wise(X2) [resolution 253,83]
287. wise(X2) [subsumption resolution 285,129]
333. quiet(X1) [resolution 287,130]
356. ~rich(lucy) | tall(lucy) [resolution 117,138]
359. 32 <=> tall(lucy) [avatar definition]
361. tall(lucy) <- (32) [avatar component clause 359]
363. 33 <=> rich(lucy) [avatar definition]
365. ~rich(lucy) <- (~33) [avatar component clause 363]
366. 32 | ~33 [avatar split clause 356,363,359]
367. ~rich(lucy) | ~generous(lucy) [resolution 118,138]
379. 34 <=> happy(lucy) [avatar definition]
381. happy(lucy) <- (34) [avatar component clause 379]
383. 35 <=> generous(lucy) [avatar definition]
391. 36 <=> patient(lucy) [avatar definition]
392. patient(lucy) <- (36) [avatar component clause 391]
406. rich(X3) [resolution 333,69]
409. 16 [avatar split clause 406,211]
423. $false <- (16, ~33) [resolution 212,365]
424. ~16 | 33 [avatar contradiction clause 423]
426. ~calm(lucy) | patient(lucy) <- (32) [resolution 361,95]
427. patient(lucy) <- (32) [subsumption resolution 426,138]
430. 36 | ~32 [avatar split clause 427,359,391]
433. happy(lucy) <- (36) [resolution 392,75]
434. 34 | ~36 [avatar split clause 433,391,379]
446. generous(lucy) <- (34) [resolution 381,141]
450. 35 | ~34 [avatar split clause 446,379,383]
451. ~generous(lucy) <- (16) [subsumption resolution 367,212]
452. ~35 | ~16 [avatar split clause 451,211,383]
453. $false [avatar sat refutation 366,409,424,430,434,450,452]
% SZS output end Proof for 318857355889050640218497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not old is quiet or not happy.
If susan is both not generous and creative then fred is either not happy or funny and vice versa.
Everyone who is either not strong or calm is both not rich and not brave and vice versa.
If susan is not quiet then paul is both not brave and not rich and vice versa.
Everyone who is either not humble or strong is either curious or funny and vice versa.
If someone is old or funny then someone is not patient or brave and vice versa.
If someone is both humble and generous then fred is both not humble and not kind and vice versa.
Everyone who is either wise or rich is both not wise and not brave.
Everyone who is not humble or not tall is both wise and not curious.
Everyone who is either brave or wise is either not calm or tall.
Everyone who is both not patient and not wise is funny or old and vice versa.
If mary is either not happy or funny then someone is both not creative and not happy and vice versa.
Everyone who is creative is old.
If lucy is not rich or strong then lucy is either not brave or brave and vice versa.
Everyone who is both funny and not quiet is not rich.
If mary is both not tall and quiet then someone is calm or creative and vice versa.
Someone is creative or not funny.
Someone is either not kind or not patient.
Paul is rich or not curious.
Someone is quiet.
Someone is both not quiet and rich.
Lucy is not generous.
Fred is not creative or rich.
Lucy is either quiet or not tall. | Mary is not creative. | entailment | (![X]:((~kind(X)&~old(X))=>(quiet(X)|~happy(X))))&
(((~generous(susan)&creative(susan)))<=>((~happy(fred)<~>funny(fred))))&
(![X]:((~strong(X)<~>calm(X))<=>(~rich(X)&~brave(X))))&
((~quiet(susan))<=>((~brave(paul)&~rich(paul))))&
(![X]:((~humble(X)<~>strong(X))<=>(curious(X)<~>funny(X))))&
((?[X]:((old(X)|funny(X))))<=>(?[X]:((~patient(X)|brave(X)))))&
((?[X]:((humble(X)&generous(X))))<=>((~humble(fred)&~kind(fred))))&
(![X]:((wise(X)<~>rich(X))=>(~wise(X)&~brave(X))))&
(![X]:((~humble(X)|~tall(X))=>(wise(X)&~curious(X))))&
(![X]:((brave(X)<~>wise(X))=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&~wise(X))<=>(funny(X)|old(X))))&
(((~happy(mary)<~>funny(mary)))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:(creative(X)=>old(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~brave(lucy)<~>brave(lucy))))&
(![X]:((funny(X)&~quiet(X))=>~rich(X)))&
(((~tall(mary)&quiet(mary)))<=>(?[X]:((calm(X)|creative(X)))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((~kind(X)<~>~patient(X))))&
((rich(paul)|~curious(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((~quiet(X)&rich(X))))&
(~generous(lucy))&
((~creative(fred)|rich(fred)))&
((quiet(lucy)<~>~tall(lucy))) | ~creative(mary) | [
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 851128375021203092836520
% SZS output start Proof for 851128375021203092836520
9. ! [X0] : ((~tall(X0) | ~humble(X0)) => (~curious(X0) & wise(X0))) [input p8]
11. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> (old(X0) | funny(X0))) [input p10]
13. ! [X0] : (creative(X0) => old(X0)) [input p12]
16. (quiet(mary) & ~tall(mary)) <=> ? [X0] : (creative(X0) | calm(X0)) [input p15]
25. creative(mary) [input hypothesis]
30. ! [X0] : ((~curious(X0) & wise(X0)) | (tall(X0) & humble(X0))) [ennf transformation 9]
32. ! [X0] : (old(X0) | ~creative(X0)) [ennf transformation 13]
54. ! [X0] : (((~wise(X0) & ~patient(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (wise(X0) | patient(X0)))) [nnf transformation 11]
55. ! [X0] : (((~wise(X0) & ~patient(X0)) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | wise(X0) | patient(X0))) [flattening 54]
62. ((quiet(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~calm(X0))) & (? [X0] : (creative(X0) | calm(X0)) | (~quiet(mary) | tall(mary))) [nnf transformation 16]
63. ((quiet(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~calm(X0))) & (? [X0] : (creative(X0) | calm(X0)) | ~quiet(mary) | tall(mary)) [flattening 62]
64. ((quiet(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~calm(X0))) & (? [X1] : (creative(X1) | calm(X1)) | ~quiet(mary) | tall(mary)) [rectify 63]
65. ? [X1] : (creative(X1) | calm(X1)) => (creative(sK4) | calm(sK4)) [choice axiom]
66. ((quiet(mary) & ~tall(mary)) | ! [X0] : (~creative(X0) & ~calm(X0))) & ((creative(sK4) | calm(sK4)) | ~quiet(mary) | tall(mary)) [skolemisation 64,65]
114. tall(X0) | wise(X0) [cnf transformation 30]
125. ~wise(X0) | ~old(X0) [cnf transformation 55]
132. ~creative(X0) | old(X0) [cnf transformation 32]
142. ~tall(mary) | ~creative(X0) [cnf transformation 66]
156. creative(mary) [cnf transformation 25]
294. 29 <=> ! [X0] : ~creative(X0) [avatar definition]
295. ~creative(X0) <- (29) [avatar component clause 294]
306. 32 <=> tall(mary) [avatar definition]
308. ~tall(mary) <- (~32) [avatar component clause 306]
309. 29 | ~32 [avatar split clause 142,306,294]
363. $false <- (29) [resolution 295,156]
364. ~29 [avatar contradiction clause 363]
367. wise(mary) <- (~32) [resolution 114,308]
373. ~old(mary) <- (~32) [resolution 125,367]
375. old(mary) [resolution 132,156]
376. $false <- (~32) [subsumption resolution 375,373]
377. 32 [avatar contradiction clause 376]
378. $false [avatar sat refutation 309,364,377]
% SZS output end Proof for 851128375021203092836520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or not humble then fred is either not humble or not patient and vice versa.
If fred is either humble or not curious then mary is old or calm.
If someone is not brave then lucy is either not rich or brave.
Everyone who is both kind and humble is quiet or humble and vice versa.
Everyone who is either funny or humble is either not funny or patient and vice versa.
Everyone who is both curious and patient is not patient or not quiet and vice versa.
Everyone who is either strong or not creative is tall or not tall.
If someone is not brave then someone is not curious or strong.
Everyone who is either not humble or quiet is old.
If mary is both not happy and curious then someone is either not tall or patient.
If paul is both calm and not humble then someone is both quiet and wise and vice versa.
If lucy is strong then alice is not brave and vice versa.
Everyone who is not humble is either wise or not creative.
If lucy is either not generous or not quiet then someone is not quiet or wise and vice versa.
If susan is either not quiet or wise then lucy is either generous or not rich and vice versa.
Everyone who is old is both not humble and not calm and vice versa.
Lucy is either not patient or brave.
Someone is either happy or not creative.
John is both kind and happy.
Someone is either curious or calm.
Fred is both strong and not generous.
Someone is either not quiet or not patient.
John is kind.
Someone is either funny or tall. | Lucy is brave. | entailment | ((?[X]:((~strong(X)<~>~humble(X))))<=>((~humble(fred)<~>~patient(fred))))&
(((humble(fred)<~>~curious(fred)))=>((old(mary)|calm(mary))))&
((?[X]:(~brave(X)))=>((~rich(lucy)<~>brave(lucy))))&
(![X]:((kind(X)&humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((curious(X)&patient(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((strong(X)<~>~creative(X))=>(tall(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~humble(X)<~>quiet(X))=>old(X)))&
(((~happy(mary)&curious(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((calm(paul)&~humble(paul)))<=>(?[X]:((quiet(X)&wise(X)))))&
((strong(lucy))<=>(~brave(alice)))&
(![X]:(~humble(X)=>(wise(X)<~>~creative(X))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(((~quiet(susan)<~>wise(susan)))<=>((generous(lucy)<~>~rich(lucy))))&
(![X]:(old(X)<=>(~humble(X)&~calm(X))))&
((~patient(lucy)<~>brave(lucy)))&
(?[X]:((happy(X)<~>~creative(X))))&
((kind(john)&happy(john)))&
(?[X]:((curious(X)<~>calm(X))))&
((strong(fred)&~generous(fred)))&
(?[X]:((~quiet(X)<~>~patient(X))))&
(kind(john))&
(?[X]:((funny(X)<~>tall(X)))) | brave(lucy) | [
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6390208723166511903990676
% SZS output start Proof for 6390208723166511903990676
6. ! [X0] : ((patient(X0) & curious(X0)) <=> (~quiet(X0) | ~patient(X0))) [input p5]
17. ~patient(lucy) <~> brave(lucy) [input p16]
25. ~brave(lucy) [input hypothesis]
48. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & ((~quiet(X0) | ~patient(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 6]
49. ! [X0] : (((patient(X0) & curious(X0)) | (quiet(X0) & patient(X0))) & (~quiet(X0) | ~patient(X0) | ~patient(X0) | ~curious(X0))) [flattening 48]
70. (~brave(lucy) | patient(lucy)) & (brave(lucy) | ~patient(lucy)) [nnf transformation 17]
111. patient(X0) | patient(X0) [cnf transformation 49]
144. brave(lucy) | ~patient(lucy) [cnf transformation 70]
159. ~brave(lucy) [cnf transformation 25]
161. patient(X0) [duplicate literal removal 111]
218. 12 <=> brave(lucy) [avatar definition]
328. brave(lucy) [subsumption resolution 144,161]
329. 12 [avatar split clause 328,218]
361. ~12 [avatar split clause 159,218]
362. $false [avatar sat refutation 329,361]
% SZS output end Proof for 6390208723166511903990676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not generous is both not old and not generous.
If lucy is both not creative and quiet then alice is not happy or funny and vice versa.
Everyone who is not curious or curious is either curious or not rich and vice versa.
If alice is not rich or not strong then someone is both not wise and not rich.
Everyone who is not humble or not kind is wise or brave.
Everyone who is either patient or kind is funny or not brave.
Everyone who is not curious is not generous or not happy.
Everyone who is not rich or strong is both strong and creative.
Everyone who is not brave is not wise and vice versa.
Everyone who is both strong and not patient is not quiet.
Everyone who is both humble and not creative is both quiet and brave.
Everyone who is both tall and patient is either old or not old and vice versa.
If paul is calm then someone is either curious or not creative.
Everyone who is calm is strong.
If susan is both not strong and not humble then someone is humble or strong and vice versa.
If someone is old then someone is both quiet and not funny.
Lucy is both not kind and happy.
Mary is either not strong or humble.
Someone is not funny or not quiet.
Lucy is both brave and not old.
Lucy is either not creative or not strong.
Susan is both old and generous.
Someone is tall or quiet.
Alice is either kind or not humble. | Mary is not kind. | neutral | (![X]:((~tall(X)&~generous(X))=>(~old(X)&~generous(X))))&
(((~creative(lucy)&quiet(lucy)))<=>((~happy(alice)|funny(alice))))&
(![X]:((~curious(X)|curious(X))<=>(curious(X)<~>~rich(X))))&
(((~rich(alice)|~strong(alice)))=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:((~humble(X)|~kind(X))=>(wise(X)|brave(X))))&
(![X]:((patient(X)<~>kind(X))=>(funny(X)|~brave(X))))&
(![X]:(~curious(X)=>(~generous(X)|~happy(X))))&
(![X]:((~rich(X)|strong(X))=>(strong(X)&creative(X))))&
(![X]:(~brave(X)<=>~wise(X)))&
(![X]:((strong(X)&~patient(X))=>~quiet(X)))&
(![X]:((humble(X)&~creative(X))=>(quiet(X)&brave(X))))&
(![X]:((tall(X)&patient(X))<=>(old(X)<~>~old(X))))&
((calm(paul))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:(calm(X)=>strong(X)))&
(((~strong(susan)&~humble(susan)))<=>(?[X]:((humble(X)|strong(X)))))&
((?[X]:(old(X)))=>(?[X]:((quiet(X)&~funny(X)))))&
((~kind(lucy)&happy(lucy)))&
((~strong(mary)<~>humble(mary)))&
(?[X]:((~funny(X)|~quiet(X))))&
((brave(lucy)&~old(lucy)))&
((~creative(lucy)<~>~strong(lucy)))&
((old(susan)&generous(susan)))&
(?[X]:((tall(X)|quiet(X))))&
((kind(alice)<~>~humble(alice))) | ~kind(mary) | [] | null | 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and kind then someone is not old or rich.
If someone is both patient and happy then john is rich.
If mary is funny then someone is not wise or not strong.
Everyone who is curious or not old is brave or not wise.
Everyone who is tall is not generous and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
Someone is humble or not brave.
Someone is not kind.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise.
Susan is either not generous or rich.
Someone is either not calm or not quiet. | Fred is not kind. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&kind(X))))=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((patient(X)&happy(X))))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:(~kind(X)))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X)))) | ~kind(fred) | [
"p6",
"p7",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 478914177088514340255403
% SZS output start Proof for 478914177088514340255403
7. ! [X0] : (brave(X0) <=> patient(X0)) [input p6]
8. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p7]
9. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p8]
13. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p12]
14. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p13]
23. kind(fred) [input hypothesis]
41. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 7]
42. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 8]
43. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 44]
53. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [nnf transformation 13]
54. ! [X0] : ((((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))))) [flattening 53]
55. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 14]
56. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 55]
80. ~brave(X0) | patient(X0) [cnf transformation 41]
81. ~patient(X0) | brave(X0) [cnf transformation 41]
85. brave(X0) | patient(X0) | strong(X0) [cnf transformation 43]
87. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 43]
89. ~strong(X0) | ~kind(X0) [cnf transformation 45]
90. ~strong(X0) | calm(X0) [cnf transformation 45]
104. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 54]
108. ~calm(X0) | curious(X0) [cnf transformation 56]
127. kind(fred) [cnf transformation 23]
129. ~brave(X0) | ~curious(X0) [duplicate literal removal 104]
163. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 87,80]
164. strong(X0) | patient(X0) [subsumption resolution 85,80]
234. patient(X0) | calm(X0) [resolution 164,90]
235. ~kind(X1) | patient(X1) [resolution 164,89]
448. brave(X0) | calm(X0) [resolution 234,81]
451. patient(fred) [resolution 235,127]
454. brave(fred) [resolution 451,81]
523. calm(X5) | strong(X5) | calm(X5) [resolution 448,163]
528. calm(X5) | strong(X5) [duplicate literal removal 523]
529. calm(X5) [subsumption resolution 528,90]
591. ~curious(fred) [resolution 454,129]
601. 56 <=> curious(fred) [avatar definition]
603. ~curious(fred) <- (~56) [avatar component clause 601]
605. ~56 [avatar split clause 591,601]
612. curious(X3) [resolution 529,108]
643. $false <- (~56) [resolution 612,603]
644. 56 [avatar contradiction clause 643]
646. $false [avatar sat refutation 605,644]
% SZS output end Proof for 478914177088514340255403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or generous is not generous or not brave and vice versa. If mary is both not calm and happy then lucy is either not strong or funny. Everyone who is not generous or strong is either creative or not strong and vice versa. If someone is brave or old then lucy is not old. If alice is both tall and not funny then someone is not humble and vice versa. If susan is both tall and happy then someone is not brave or humble and vice versa. Everyone who is not rich or generous is humble or brave and vice versa. If john is either not quiet or tall then lucy is both not kind and kind and vice versa. Everyone who is both not creative and not wise is not wise. If lucy is either not wise or old then someone is either not patient or not curious and vice versa. If fred is quiet then someone is funny or generous and vice versa. If fred is either creative or not funny then someone is not wise or tall and vice versa. If lucy is both not wise and not funny then someone is not curious or not strong. Everyone who is either not calm or creative is either wise or not creative. Everyone who is both not humble and happy is creative and vice versa. Everyone who is either creative or not strong is both generous and wise. Someone is not quiet or happy. Mary is both kind and not humble. John is both funny and not tall. Someone is both tall and patient. Fred is not tall. Someone is curious or strong. Mary is generous or not happy. | Mary is not happy. | contradiction | (![X]:((~wise(X)<~>generous(X))<=>(~generous(X)|~brave(X))))&
(((~calm(mary)&happy(mary)))=>((~strong(lucy)<~>funny(lucy))))&
(![X]:((~generous(X)|strong(X))<=>(creative(X)<~>~strong(X))))&
((?[X]:((brave(X)|old(X))))=>(~old(lucy)))&
(((tall(alice)&~funny(alice)))<=>(?[X]:(~humble(X))))&
(((tall(susan)&happy(susan)))<=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)|brave(X))))&
(((~quiet(john)<~>tall(john)))<=>((~kind(lucy)&kind(lucy))))&
(![X]:((~creative(X)&~wise(X))=>~wise(X)))&
(((~wise(lucy)<~>old(lucy)))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
((quiet(fred))<=>(?[X]:((funny(X)|generous(X)))))&
(((creative(fred)<~>~funny(fred)))<=>(?[X]:((~wise(X)|tall(X)))))&
(((~wise(lucy)&~funny(lucy)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~calm(X)<~>creative(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~humble(X)&happy(X))<=>creative(X)))&
(![X]:((creative(X)<~>~strong(X))=>(generous(X)&wise(X))))&
(?[X]:((~quiet(X)|happy(X))))&
((kind(mary)&~humble(mary)))&
((funny(john)&~tall(john)))&
(?[X]:((tall(X)&patient(X))))&
(~tall(fred))&
(?[X]:((curious(X)|strong(X))))&
((generous(mary)|~happy(mary))) | ~happy(mary) | [
"p2",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2362905930695321323137250
% SZS output start Proof for 2362905930695321323137250
3. ! [X0] : ((strong(X0) | ~generous(X0)) <=> (creative(X0) <~> ~strong(X0))) [input p2]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> creative(X0)) [input p14]
16. ! [X0] : ((creative(X0) <~> ~strong(X0)) => (wise(X0) & generous(X0))) [input p15]
24. ~happy(mary) [input hypothesis]
33. ! [X0] : ((wise(X0) & generous(X0)) | (creative(X0) <=> ~strong(X0))) [ennf transformation 16]
37. ! [X0] : (((strong(X0) | ~generous(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~strong(X0) & generous(X0)))) [nnf transformation 3]
38. ! [X0] : ((strong(X0) | ~generous(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) & (((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~strong(X0) & generous(X0)))) [flattening 37]
68. ! [X0] : (((happy(X0) & ~humble(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
69. ! [X0] : (((happy(X0) & ~humble(X0)) | ~creative(X0)) & (creative(X0) | ~happy(X0) | humble(X0))) [flattening 68]
70. ! [X0] : ((wise(X0) & generous(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0)))) [nnf transformation 33]
86. ~strong(X0) | creative(X0) | ~strong(X0) [cnf transformation 38]
90. strong(X0) | ~generous(X0) | creative(X0) | strong(X0) [cnf transformation 38]
136. ~creative(X0) | happy(X0) [cnf transformation 69]
138. generous(X0) | creative(X0) | strong(X0) [cnf transformation 70]
151. ~happy(mary) [cnf transformation 24]
154. ~strong(X0) | creative(X0) [duplicate literal removal 86]
155. strong(X0) | ~generous(X0) | creative(X0) [duplicate literal removal 90]
164. 2 <=> happy(mary) [avatar definition]
166. ~happy(mary) <- (~2) [avatar component clause 164]
336. creative(X0) | strong(X0) [subsumption resolution 138,155]
337. creative(X0) [subsumption resolution 336,154]
363. ~2 [avatar split clause 151,164]
382. happy(X0) [resolution 136,337]
383. $false <- (~2) [resolution 382,166]
384. 2 [avatar contradiction clause 383]
385. $false [avatar sat refutation 363,384]
% SZS output end Proof for 2362905930695321323137250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not funny is either not creative or not old. If someone is not rich or happy then alice is both kind and not patient and vice versa. If someone is either not funny or wise then john is happy or not rich and vice versa. If someone is old then someone is both not rich and not old. Everyone who is generous or not humble is either not kind or patient. If someone is both rich and not happy then mary is not creative or not rich. Everyone who is not rich or generous is both not creative and not generous. Everyone who is curious is not tall or not strong. If someone is both not creative and generous then someone is both not calm and tall and vice versa. Everyone who is quiet or humble is patient. Everyone who is quiet is old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Someone is both not kind and creative. John is either creative or patient. Someone is both tall and funny. Alice is calm. Susan is either not humble or not wise. | Mary is generous. | contradiction | (![X]:((wise(X)&~funny(X))=>(~creative(X)<~>~old(X))))&
((?[X]:((~rich(X)|happy(X))))<=>((kind(alice)&~patient(alice))))&
((?[X]:((~funny(X)<~>wise(X))))<=>((happy(john)|~rich(john))))&
((?[X]:(old(X)))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((generous(X)|~humble(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((rich(X)&~happy(X))))=>((~creative(mary)|~rich(mary))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&~generous(X))))&
(![X]:(curious(X)=>(~tall(X)|~strong(X))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((quiet(X)|humble(X))=>patient(X)))&
(![X]:(quiet(X)=>old(X)))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(?[X]:((~kind(X)&creative(X))))&
((creative(john)<~>patient(john)))&
(?[X]:((tall(X)&funny(X))))&
(calm(alice))&
((~humble(susan)<~>~wise(susan))) | generous(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6252533091072927377830429
% SZS output start Proof for 6252533091072927377830429
7. ! [X0] : ((generous(X0) | ~rich(X0)) => (~generous(X0) & ~creative(X0))) [input p6]
22. generous(mary) [input hypothesis]
32. ! [X0] : ((~generous(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 7]
97. ~generous(X0) | ~generous(X0) [cnf transformation 32]
126. generous(mary) [cnf transformation 22]
127. ~generous(X0) [duplicate literal removal 97]
255. $false [subsumption resolution 126,127]
% SZS output end Proof for 6252533091072927377830429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is strong or not humble. Everyone who is both not kind and kind is not tall or not happy and vice versa. Everyone who is rich is not happy or not curious. If lucy is not old or creative then alice is happy or calm. Everyone who is either tall or old is not strong and vice versa. If alice is not tall then mary is patient. If fred is kind then someone is either brave or quiet and vice versa. Everyone who is either generous or not rich is calm or wise and vice versa. If someone is either not humble or not creative then lucy is creative or kind. If someone is both creative and happy then someone is either not funny or quiet and vice versa. Everyone who is both creative and generous is either not funny or wise and vice versa. If someone is either not strong or patient then someone is not tall or not generous. If someone is both tall and kind then john is both not brave and not strong. If someone is both creative and curious then lucy is not calm or not quiet. Everyone who is not kind or happy is both not creative and not kind and vice versa. If someone is either not generous or generous then lucy is not wise or brave and vice versa. Paul is both wise and happy. Someone is not strong or happy. Paul is both not curious and not calm. Alice is not kind or generous. Paul is not patient or not old. Alice is both not generous and wise. Someone is either tall or patient. | Paul is not rich. | neutral | (![X]:(quiet(X)=>(strong(X)|~humble(X))))&
(![X]:((~kind(X)&kind(X))<=>(~tall(X)|~happy(X))))&
(![X]:(rich(X)=>(~happy(X)|~curious(X))))&
(((~old(lucy)|creative(lucy)))=>((happy(alice)|calm(alice))))&
(![X]:((tall(X)<~>old(X))<=>~strong(X)))&
((~tall(alice))=>(patient(mary)))&
((kind(fred))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((generous(X)<~>~rich(X))<=>(calm(X)|wise(X))))&
((?[X]:((~humble(X)<~>~creative(X))))=>((creative(lucy)|kind(lucy))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
(![X]:((creative(X)&generous(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((~strong(X)<~>patient(X))))=>(?[X]:((~tall(X)|~generous(X)))))&
((?[X]:((tall(X)&kind(X))))=>((~brave(john)&~strong(john))))&
((?[X]:((creative(X)&curious(X))))=>((~calm(lucy)|~quiet(lucy))))&
(![X]:((~kind(X)|happy(X))<=>(~creative(X)&~kind(X))))&
((?[X]:((~generous(X)<~>generous(X))))<=>((~wise(lucy)|brave(lucy))))&
((wise(paul)&happy(paul)))&
(?[X]:((~strong(X)|happy(X))))&
((~curious(paul)&~calm(paul)))&
((~kind(alice)|generous(alice)))&
((~patient(paul)|~old(paul)))&
((~generous(alice)&wise(alice)))&
(?[X]:((tall(X)<~>patient(X)))) | ~rich(paul) | [] | null | 0 |
If alice is strong then someone is happy and vice versa. Everyone who is either not happy or old is not patient. If someone is either patient or happy then lucy is generous or not wise and vice versa. Everyone who is not strong or not quiet is wise or calm. If lucy is not strong then susan is either not rich or not strong. If fred is brave or patient then fred is not rich. If susan is not rich or old then someone is both rich and not patient and vice versa. Everyone who is both patient and not brave is not strong or not patient and vice versa. If someone is both strong and not kind then alice is quiet or patient and vice versa. Everyone who is not creative is curious. If someone is both not patient and generous then someone is not funny and vice versa. Everyone who is either old or generous is not wise and vice versa. If paul is both not rich and not patient then fred is curious or happy and vice versa. Everyone who is either funny or not generous is either not humble or not tall. If someone is wise or curious then lucy is kind or calm. Alice is calm. John is either not quiet or not strong. Alice is not strong or not happy. John is both not tall and not creative. Someone is both not generous and not brave. Someone is both calm and patient. Fred is either not rich or curious. Someone is tall or not happy. | Fred is not happy. | entailment | ((strong(alice))<=>(?[X]:(happy(X))))&
(![X]:((~happy(X)<~>old(X))=>~patient(X)))&
((?[X]:((patient(X)<~>happy(X))))<=>((generous(lucy)|~wise(lucy))))&
(![X]:((~strong(X)|~quiet(X))=>(wise(X)|calm(X))))&
((~strong(lucy))=>((~rich(susan)<~>~strong(susan))))&
(((brave(fred)|patient(fred)))=>(~rich(fred)))&
(((~rich(susan)|old(susan)))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((patient(X)&~brave(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((strong(X)&~kind(X))))<=>((quiet(alice)|patient(alice))))&
(![X]:(~creative(X)=>curious(X)))&
((?[X]:((~patient(X)&generous(X))))<=>(?[X]:(~funny(X))))&
(![X]:((old(X)<~>generous(X))<=>~wise(X)))&
(((~rich(paul)&~patient(paul)))<=>((curious(fred)|happy(fred))))&
(![X]:((funny(X)<~>~generous(X))=>(~humble(X)<~>~tall(X))))&
((?[X]:((wise(X)|curious(X))))=>((kind(lucy)|calm(lucy))))&
(calm(alice))&
((~quiet(john)<~>~strong(john)))&
((~strong(alice)|~happy(alice)))&
((~tall(john)&~creative(john)))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((calm(X)&patient(X))))&
((~rich(fred)<~>curious(fred)))&
(?[X]:((tall(X)|~happy(X)))) | ~happy(fred) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 470449751572966132915724
% SZS output start Proof for 470449751572966132915724
8. ! [X0] : ((~brave(X0) & patient(X0)) <=> (~patient(X0) | ~strong(X0))) [input p7]
13. (~patient(paul) & ~rich(paul)) <=> (happy(fred) | curious(fred)) [input p12]
24. happy(fred) [input hypothesis]
51. ! [X0] : (((~brave(X0) & patient(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (brave(X0) | ~patient(X0)))) [nnf transformation 8]
52. ! [X0] : (((~brave(X0) & patient(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | brave(X0) | ~patient(X0))) [flattening 51]
64. ((~patient(paul) & ~rich(paul)) | (~happy(fred) & ~curious(fred))) & ((happy(fred) | curious(fred)) | (patient(paul) | rich(paul))) [nnf transformation 13]
65. ((~patient(paul) & ~rich(paul)) | (~happy(fred) & ~curious(fred))) & (happy(fred) | curious(fred) | patient(paul) | rich(paul)) [flattening 64]
96. patient(X0) | patient(X0) [cnf transformation 52]
116. ~patient(paul) | ~happy(fred) [cnf transformation 65]
132. happy(fred) [cnf transformation 24]
134. patient(X0) [duplicate literal removal 96]
237. ~happy(fred) [subsumption resolution 116,134]
265. $false [subsumption resolution 132,237]
% SZS output end Proof for 470449751572966132915724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or happy is not tall.
If lucy is not curious then someone is strong.
If someone is not rich or old then alice is happy and vice versa.
If susan is not rich or quiet then someone is strong or not generous.
If someone is both creative and not funny then john is both funny and brave.
If someone is both creative and not kind then someone is happy or not strong.
If someone is either rich or strong then someone is not patient.
If someone is either not quiet or generous then someone is not tall or tall.
Everyone who is both not curious and not happy is not quiet or rich and vice versa.
If lucy is wise then someone is both wise and not patient.
Everyone who is happy or not calm is both not strong and humble and vice versa.
Everyone who is tall or not brave is either rich or not curious and vice versa.
Everyone who is funny or rich is both quiet and not funny and vice versa.
Everyone who is rich or tall is either not curious or happy and vice versa.
Everyone who is either calm or not humble is rich or brave and vice versa.
Someone is both not funny and not generous.
Alice is either strong or patient. | Susan is not wise. | neutral | (![X]:((~old(X)|happy(X))=>~tall(X)))&
((~curious(lucy))=>(?[X]:(strong(X))))&
((?[X]:((~rich(X)|old(X))))<=>(happy(alice)))&
(((~rich(susan)|quiet(susan)))=>(?[X]:((strong(X)|~generous(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((funny(john)&brave(john))))&
((?[X]:((creative(X)&~kind(X))))=>(?[X]:((happy(X)|~strong(X)))))&
((?[X]:((rich(X)<~>strong(X))))=>(?[X]:(~patient(X))))&
((?[X]:((~quiet(X)<~>generous(X))))=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((~curious(X)&~happy(X))<=>(~quiet(X)|rich(X))))&
((wise(lucy))=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((happy(X)|~calm(X))<=>(~strong(X)&humble(X))))&
(![X]:((tall(X)|~brave(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((funny(X)|rich(X))<=>(quiet(X)&~funny(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
(?[X]:((~funny(X)&~generous(X))))&
((strong(alice)<~>patient(alice))) | ~wise(susan) | [] | null | 0 |
Everyone who is both brave and generous is wise and vice versa.
Everyone who is not brave or generous is both not rich and rich.
If john is old or calm then someone is rich or not curious and vice versa.
Everyone who is both humble and not funny is both not happy and not generous and vice versa.
If someone is both strong and not creative then mary is wise or not happy.
Everyone who is either not creative or not rich is either not happy or not generous and vice versa.
Everyone who is not humble is either not humble or happy and vice versa.
Everyone who is not wise is quiet or not wise and vice versa.
If someone is calm or kind then someone is happy and vice versa.
If lucy is either not calm or not old then someone is both not tall and not strong and vice versa.
Everyone who is either not strong or strong is both quiet and not tall.
If fred is either tall or not tall then paul is not rich or not curious and vice versa.
If alice is curious or not wise then lucy is not kind.
If someone is not strong or quiet then someone is either not creative or patient.
If someone is funny then mary is happy.
Everyone who is either brave or tall is not rich and vice versa.
Someone is either not rich or not quiet.
Alice is not wise.
Someone is both not creative and brave. | John is brave. | entailment | (![X]:((brave(X)&generous(X))<=>wise(X)))&
(![X]:((~brave(X)|generous(X))=>(~rich(X)&rich(X))))&
(((old(john)|calm(john)))<=>(?[X]:((rich(X)|~curious(X)))))&
(![X]:((humble(X)&~funny(X))<=>(~happy(X)&~generous(X))))&
((?[X]:((strong(X)&~creative(X))))=>((wise(mary)|~happy(mary))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:(~humble(X)<=>(~humble(X)<~>happy(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~wise(X))))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:(happy(X))))&
(((~calm(lucy)<~>~old(lucy)))<=>(?[X]:((~tall(X)&~strong(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(quiet(X)&~tall(X))))&
(((tall(fred)<~>~tall(fred)))<=>((~rich(paul)|~curious(paul))))&
(((curious(alice)|~wise(alice)))=>(~kind(lucy)))&
((?[X]:((~strong(X)|quiet(X))))=>(?[X]:((~creative(X)<~>patient(X)))))&
((?[X]:(funny(X)))=>(happy(mary)))&
(![X]:((brave(X)<~>tall(X))<=>~rich(X)))&
(?[X]:((~rich(X)<~>~quiet(X))))&
(~wise(alice))&
(?[X]:((~creative(X)&brave(X)))) | brave(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1171375266962184921336429
% SZS output start Proof for 1171375266962184921336429
2. ! [X0] : ((generous(X0) | ~brave(X0)) => (rich(X0) & ~rich(X0))) [input p1]
20. ~brave(john) [input hypothesis]
23. ! [X0] : ((rich(X0) & ~rich(X0)) | (~generous(X0) & brave(X0))) [ennf transformation 2]
68. ~rich(X0) | brave(X0) [cnf transformation 23]
70. rich(X0) | brave(X0) [cnf transformation 23]
131. ~brave(john) [cnf transformation 20]
141. brave(X0) [subsumption resolution 68,70]
288. $false [subsumption resolution 131,141]
% SZS output end Proof for 1171375266962184921336429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both humble and strong then fred is not wise.
Everyone who is happy or not humble is patient or humble.
Everyone who is not brave or tall is both not patient and not humble and vice versa.
Everyone who is both not old and tall is both not calm and not tall and vice versa.
If john is not kind or not strong then fred is either not kind or wise and vice versa.
Everyone who is either not funny or patient is either not humble or not quiet.
Everyone who is either happy or calm is tall.
If someone is not tall or not brave then susan is either rich or funny and vice versa.
If fred is both not patient and not wise then someone is both not rich and not generous and vice versa.
Everyone who is not happy or generous is kind or generous.
Everyone who is not wise is humble and vice versa.
Everyone who is old is both curious and quiet and vice versa.
If fred is both kind and strong then lucy is calm and vice versa.
Everyone who is patient or generous is curious or kind.
If someone is both not quiet and not rich then someone is not humble or not brave and vice versa.
If mary is patient or funny then someone is both not curious and not happy and vice versa.
Lucy is either not happy or not funny.
Fred is rich or not curious.
Someone is strong or kind.
Someone is either generous or rich.
Lucy is either brave or not strong.
Fred is both humble and rich. | Mary is wise. | contradiction | (((humble(susan)&strong(susan)))=>(~wise(fred)))&
(![X]:((happy(X)|~humble(X))=>(patient(X)|humble(X))))&
(![X]:((~brave(X)|tall(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)&~tall(X))))&
(((~kind(john)|~strong(john)))<=>((~kind(fred)<~>wise(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((happy(X)<~>calm(X))=>tall(X)))&
((?[X]:((~tall(X)|~brave(X))))<=>((rich(susan)<~>funny(susan))))&
(((~patient(fred)&~wise(fred)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~happy(X)|generous(X))=>(kind(X)|generous(X))))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:(old(X)<=>(curious(X)&quiet(X))))&
(((kind(fred)&strong(fred)))<=>(calm(lucy)))&
(![X]:((patient(X)|generous(X))=>(curious(X)|kind(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~humble(X)|~brave(X)))))&
(((patient(mary)|funny(mary)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((~happy(lucy)<~>~funny(lucy)))&
((rich(fred)|~curious(fred)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((brave(lucy)<~>~strong(lucy)))&
((humble(fred)&rich(fred))) | wise(mary) | [
"p1",
"p3",
"p6",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3924384480759228608437979
% SZS output start Proof for 3924384480759228608437979
2. ! [X0] : ((~humble(X0) | happy(X0)) => (humble(X0) | patient(X0))) [input p1]
4. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p3]
7. ! [X0] : ((happy(X0) <~> calm(X0)) => tall(X0)) [input p6]
11. ! [X0] : (~wise(X0) <=> humble(X0)) [input p10]
12. ! [X0] : (old(X0) <=> (quiet(X0) & curious(X0))) [input p11]
16. (funny(mary) | patient(mary)) <=> ? [X0] : (~happy(X0) & ~curious(X0)) [input p15]
23. wise(mary) [input hypothesis]
27. ! [X0] : ((humble(X0) | patient(X0)) | (humble(X0) & ~happy(X0))) [ennf transformation 2]
28. ! [X0] : (humble(X0) | patient(X0) | (humble(X0) & ~happy(X0))) [flattening 27]
30. ! [X0] : (tall(X0) | (happy(X0) <=> calm(X0))) [ennf transformation 7]
37. ! [X0] : (((tall(X0) & ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~tall(X0) | old(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & ~old(X0)) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0) | old(X0))) [flattening 37]
42. ! [X0] : (tall(X0) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) [nnf transformation 30]
52. ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 11]
53. ! [X0] : ((old(X0) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | ~old(X0))) [nnf transformation 12]
54. ! [X0] : ((old(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | ~old(X0))) [flattening 53]
62. ((funny(mary) | patient(mary)) | ! [X0] : (happy(X0) | curious(X0))) & (? [X0] : (~happy(X0) & ~curious(X0)) | (~funny(mary) & ~patient(mary))) [nnf transformation 16]
63. (funny(mary) | patient(mary) | ! [X0] : (happy(X0) | curious(X0))) & (? [X0] : (~happy(X0) & ~curious(X0)) | (~funny(mary) & ~patient(mary))) [flattening 62]
64. (funny(mary) | patient(mary) | ! [X0] : (happy(X0) | curious(X0))) & (? [X1] : (~happy(X1) & ~curious(X1)) | (~funny(mary) & ~patient(mary))) [rectify 63]
65. ? [X1] : (~happy(X1) & ~curious(X1)) => (~happy(sK4) & ~curious(sK4)) [choice axiom]
66. (funny(mary) | patient(mary) | ! [X0] : (happy(X0) | curious(X0))) & ((~happy(sK4) & ~curious(sK4)) | (~funny(mary) & ~patient(mary))) [skolemisation 64,65]
76. humble(X0) | patient(X0) | humble(X0) [cnf transformation 28]
83. ~tall(X0) | ~tall(X0) | old(X0) [cnf transformation 38]
85. tall(X0) | tall(X0) | calm(X0) [cnf transformation 38]
97. tall(X0) | happy(X0) | ~calm(X0) [cnf transformation 42]
111. ~wise(X0) | ~humble(X0) [cnf transformation 52]
112. ~old(X0) | curious(X0) [cnf transformation 54]
125. ~curious(sK4) | ~patient(mary) [cnf transformation 66]
127. ~happy(sK4) | ~patient(mary) [cnf transformation 66]
140. wise(mary) [cnf transformation 23]
141. ~tall(X0) | old(X0) [duplicate literal removal 83]
142. calm(X0) | tall(X0) [duplicate literal removal 85]
143. patient(X0) | humble(X0) [duplicate literal removal 76]
177. tall(X0) | happy(X0) [subsumption resolution 97,142]
261. 24 <=> ! [X0] : (happy(X0) | curious(X0)) [avatar definition]
262. curious(X0) | happy(X0) <- (24) [avatar component clause 261]
264. 25 <=> patient(mary) [avatar definition]
265. ~patient(mary) <- (~25) [avatar component clause 264]
273. 27 <=> happy(sK4) [avatar definition]
275. ~happy(sK4) <- (~27) [avatar component clause 273]
277. ~25 | ~27 [avatar split clause 127,273,264]
279. 28 <=> curious(sK4) [avatar definition]
281. ~curious(sK4) <- (~28) [avatar component clause 279]
283. ~25 | ~28 [avatar split clause 125,279,264]
335. ~humble(mary) [resolution 111,140]
339. humble(mary) <- (~25) [resolution 143,265]
341. $false <- (~25) [subsumption resolution 339,335]
342. 25 [avatar contradiction clause 341]
353. old(X0) | happy(X0) [resolution 177,141]
357. happy(sK4) <- (24, ~28) [resolution 262,281]
358. $false <- (24, ~27, ~28) [subsumption resolution 357,275]
359. ~24 | 27 | 28 [avatar contradiction clause 358]
381. happy(X1) | curious(X1) [resolution 353,112]
382. 24 [avatar split clause 381,261]
383. $false [avatar sat refutation 277,283,342,359,382]
% SZS output end Proof for 3924384480759228608437979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both funny and tall then susan is not kind and vice versa.
If someone is both wise and quiet then someone is not old or rich.
Everyone who is not generous or quiet is both calm and not patient and vice versa.
Everyone who is both calm and not calm is not old.
Everyone who is both happy and not kind is both humble and not calm.
Everyone who is quiet is not humble or humble.
If someone is not generous or not patient then someone is happy or curious and vice versa.
If alice is both not kind and not funny then fred is funny or strong and vice versa.
If someone is either kind or not kind then someone is both not patient and generous.
Everyone who is not funny is calm or not calm and vice versa.
Everyone who is either not old or brave is either not happy or not humble.
If fred is both not wise and not patient then someone is quiet.
If john is either creative or not strong then susan is happy or not curious.
Everyone who is either kind or calm is either patient or kind and vice versa.
Everyone who is tall is not funny.
Everyone who is not calm or not patient is either quiet or not rich.
Someone is either quiet or not strong.
Someone is strong or not old.
Susan is not calm.
Someone is both not wise and not quiet.
Paul is both happy and not brave.
John is not quiet or happy.
Alice is not generous or creative.
Paul is old or humble. | Paul is not brave. | entailment | (((funny(fred)&tall(fred)))<=>(~kind(susan)))&
((?[X]:((wise(X)&quiet(X))))=>(?[X]:((~old(X)|rich(X)))))&
(![X]:((~generous(X)|quiet(X))<=>(calm(X)&~patient(X))))&
(![X]:((calm(X)&~calm(X))=>~old(X)))&
(![X]:((happy(X)&~kind(X))=>(humble(X)&~calm(X))))&
(![X]:(quiet(X)=>(~humble(X)|humble(X))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((happy(X)|curious(X)))))&
(((~kind(alice)&~funny(alice)))<=>((funny(fred)|strong(fred))))&
((?[X]:((kind(X)<~>~kind(X))))=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:(~funny(X)<=>(calm(X)|~calm(X))))&
(![X]:((~old(X)<~>brave(X))=>(~happy(X)<~>~humble(X))))&
(((~wise(fred)&~patient(fred)))=>(?[X]:(quiet(X))))&
(((creative(john)<~>~strong(john)))=>((happy(susan)|~curious(susan))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)<~>kind(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((~calm(X)|~patient(X))=>(quiet(X)<~>~rich(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((strong(X)|~old(X))))&
(~calm(susan))&
(?[X]:((~wise(X)&~quiet(X))))&
((happy(paul)&~brave(paul)))&
((~quiet(john)|happy(john)))&
((~generous(alice)|creative(alice)))&
((old(paul)|humble(paul))) | ~brave(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2767838748168176062961453
% SZS output start Proof for 2767838748168176062961453
21. ~brave(paul) & happy(paul) [input p20]
25. brave(paul) [input hypothesis]
133. ~brave(paul) [cnf transformation 21]
137. brave(paul) [cnf transformation 25]
320. $false [subsumption resolution 137,133]
% SZS output end Proof for 2767838748168176062961453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not wise or not tall and vice versa.
Everyone who is either quiet or calm is either happy or not happy and vice versa.
If mary is either brave or old then susan is funny and vice versa.
Everyone who is strong is both creative and not calm.
Everyone who is both old and kind is not old and vice versa.
If alice is either old or not funny then someone is both creative and generous and vice versa.
Everyone who is either not humble or calm is both not brave and not generous.
Everyone who is either brave or not tall is both not patient and tall and vice versa.
If fred is both kind and not old then someone is not wise and vice versa.
Everyone who is either quiet or funny is not brave.
If someone is both patient and not rich then lucy is not patient.
If someone is either not strong or rich then lucy is both quiet and curious.
If alice is happy then lucy is either not humble or patient.
Everyone who is not brave or strong is happy and vice versa.
If alice is not creative or not rich then susan is either not brave or humble.
If someone is brave or humble then someone is either strong or funny.
Someone is both not creative and wise.
Fred is not rich.
Someone is both happy and patient.
Someone is both brave and not patient.
John is not quiet or funny.
Someone is not calm or not quiet. | Alice is creative. | neutral | (![X]:(curious(X)<=>(~wise(X)|~tall(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(happy(X)<~>~happy(X))))&
(((brave(mary)<~>old(mary)))<=>(funny(susan)))&
(![X]:(strong(X)=>(creative(X)&~calm(X))))&
(![X]:((old(X)&kind(X))<=>~old(X)))&
(((old(alice)<~>~funny(alice)))<=>(?[X]:((creative(X)&generous(X)))))&
(![X]:((~humble(X)<~>calm(X))=>(~brave(X)&~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~patient(X)&tall(X))))&
(((kind(fred)&~old(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((quiet(X)<~>funny(X))=>~brave(X)))&
((?[X]:((patient(X)&~rich(X))))=>(~patient(lucy)))&
((?[X]:((~strong(X)<~>rich(X))))=>((quiet(lucy)&curious(lucy))))&
((happy(alice))=>((~humble(lucy)<~>patient(lucy))))&
(![X]:((~brave(X)|strong(X))<=>happy(X)))&
(((~creative(alice)|~rich(alice)))=>((~brave(susan)<~>humble(susan))))&
((?[X]:((brave(X)|humble(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
(?[X]:((~creative(X)&wise(X))))&
(~rich(fred))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~quiet(john)|funny(john)))&
(?[X]:((~calm(X)|~quiet(X)))) | creative(alice) | [] | null | 0 |
Everyone who is both not calm and not old is not tall or not strong and vice versa.
If someone is quiet then mary is either generous or not calm and vice versa.
Everyone who is brave is not patient.
Everyone who is not tall is both calm and not strong.
If mary is either old or brave then alice is both rich and not calm.
If mary is either calm or not calm then someone is not wise.
Everyone who is either brave or not happy is either not tall or not kind and vice versa.
If paul is calm then lucy is either not quiet or quiet.
Everyone who is both rich and not creative is not kind or wise.
Everyone who is funny is both old and happy and vice versa.
If alice is both not wise and kind then lucy is not creative or not strong and vice versa.
Everyone who is either not patient or strong is not happy or calm and vice versa.
If someone is not curious or not rich then someone is either quiet or not quiet.
Everyone who is either not wise or not old is not happy or not old and vice versa.
Everyone who is both not brave and not old is not creative.
Everyone who is either happy or not calm is either not rich or wise.
Someone is generous.
Someone is both rich and tall.
Someone is not old.
Someone is both not kind and not brave.
Alice is both creative and not wise.
Fred is not brave or not happy.
Fred is not quiet. | Alice is brave. | contradiction | (![X]:((~calm(X)&~old(X))<=>(~tall(X)|~strong(X))))&
((?[X]:(quiet(X)))<=>((generous(mary)<~>~calm(mary))))&
(![X]:(brave(X)=>~patient(X)))&
(![X]:(~tall(X)=>(calm(X)&~strong(X))))&
(((old(mary)<~>brave(mary)))=>((rich(alice)&~calm(alice))))&
(((calm(mary)<~>~calm(mary)))=>(?[X]:(~wise(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(~tall(X)<~>~kind(X))))&
((calm(paul))=>((~quiet(lucy)<~>quiet(lucy))))&
(![X]:((rich(X)&~creative(X))=>(~kind(X)|wise(X))))&
(![X]:(funny(X)<=>(old(X)&happy(X))))&
(((~wise(alice)&kind(alice)))<=>((~creative(lucy)|~strong(lucy))))&
(![X]:((~patient(X)<~>strong(X))<=>(~happy(X)|calm(X))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>~old(X))<=>(~happy(X)|~old(X))))&
(![X]:((~brave(X)&~old(X))=>~creative(X)))&
(![X]:((happy(X)<~>~calm(X))=>(~rich(X)<~>wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)&~brave(X))))&
((creative(alice)&~wise(alice)))&
((~brave(fred)|~happy(fred)))&
(~quiet(fred)) | brave(alice) | [
"p0",
"p2",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 604367050569222861482127
% SZS output start Proof for 604367050569222861482127
1. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (~strong(X0) | ~tall(X0))) [input p0]
3. ! [X0] : (brave(X0) => ~patient(X0)) [input p2]
12. ! [X0] : ((~patient(X0) <~> strong(X0)) <=> (calm(X0) | ~happy(X0))) [input p11]
14. ! [X0] : ((~wise(X0) <~> ~old(X0)) <=> (~old(X0) | ~happy(X0))) [input p13]
21. ~wise(alice) & creative(alice) [input p20]
24. brave(alice) [input hypothesis]
27. ! [X0] : (~patient(X0) | ~brave(X0)) [ennf transformation 3]
38. ! [X0] : (((~old(X0) & ~calm(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (old(X0) | calm(X0)))) [nnf transformation 1]
39. ! [X0] : (((~old(X0) & ~calm(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | old(X0) | calm(X0))) [flattening 38]
52. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [nnf transformation 12]
53. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [flattening 52]
58. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (old(X0) & happy(X0))) & ((~old(X0) | ~happy(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [nnf transformation 14]
59. ! [X0] : ((((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (old(X0) & happy(X0))) & (~old(X0) | ~happy(X0) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0))))) [flattening 58]
73. ~old(X0) | strong(X0) [cnf transformation 39]
78. ~patient(X0) | ~brave(X0) [cnf transformation 27]
107. ~strong(X0) | patient(X0) | happy(X0) [cnf transformation 53]
111. ~old(X0) | ~happy(X0) | ~old(X0) | wise(X0) [cnf transformation 59]
116. old(X0) | wise(X0) | old(X0) [cnf transformation 59]
129. ~wise(alice) [cnf transformation 21]
132. brave(alice) [cnf transformation 24]
133. ~old(X0) | ~happy(X0) | wise(X0) [duplicate literal removal 111]
134. wise(X0) | old(X0) [duplicate literal removal 116]
202. 13 <=> wise(alice) [avatar definition]
204. ~wise(alice) <- (~13) [avatar component clause 202]
210. ~happy(X0) | wise(X0) [subsumption resolution 133,134]
213. ~13 [avatar split clause 129,202]
224. old(alice) <- (~13) [resolution 134,204]
227. strong(alice) <- (~13) [resolution 224,73]
232. patient(alice) | happy(alice) <- (~13) [resolution 107,227]
243. 18 <=> happy(alice) [avatar definition]
245. happy(alice) <- (18) [avatar component clause 243]
247. 19 <=> patient(alice) [avatar definition]
249. patient(alice) <- (19) [avatar component clause 247]
250. 18 | 19 | 13 [avatar split clause 232,202,247,243]
268. wise(alice) <- (18) [resolution 245,210]
269. $false <- (~13, 18) [subsumption resolution 268,204]
270. 13 | ~18 [avatar contradiction clause 269]
273. ~brave(alice) <- (19) [resolution 249,78]
274. $false <- (19) [subsumption resolution 273,132]
275. ~19 [avatar contradiction clause 274]
276. $false [avatar sat refutation 213,250,270,275]
% SZS output end Proof for 604367050569222861482127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not funny and not humble is not brave. If susan is either rich or not brave then paul is not generous or patient and vice versa. Everyone who is both happy and wise is curious or funny. If fred is both kind and funny then lucy is not strong or calm and vice versa. Everyone who is not strong or brave is both quiet and old and vice versa. If someone is either not quiet or not tall then someone is both strong and wise and vice versa. Everyone who is kind or wise is strong or not creative. Everyone who is either not curious or not funny is both rich and not rich. If someone is calm or not patient then alice is curious or not old and vice versa. If susan is either not generous or not funny then someone is strong or brave. Everyone who is both not funny and not wise is happy. If alice is not humble then john is not humble. Everyone who is not happy or happy is patient and vice versa. Everyone who is either creative or funny is either not happy or not creative and vice versa. Everyone who is creative is either creative or not quiet. Everyone who is not creative is not funny. Someone is tall or humble. Fred is not happy. Someone is not funny or old. Paul is funny or tall. Fred is either not calm or tall. Someone is both not calm and not quiet. Fred is both humble and creative. | Fred is not funny. | entailment | (![X]:((~funny(X)&~humble(X))=>~brave(X)))&
(((rich(susan)<~>~brave(susan)))<=>((~generous(paul)|patient(paul))))&
(![X]:((happy(X)&wise(X))=>(curious(X)|funny(X))))&
(((kind(fred)&funny(fred)))<=>((~strong(lucy)|calm(lucy))))&
(![X]:((~strong(X)|brave(X))<=>(quiet(X)&old(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((kind(X)|wise(X))=>(strong(X)|~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(rich(X)&~rich(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((curious(alice)|~old(alice))))&
(((~generous(susan)<~>~funny(susan)))=>(?[X]:((strong(X)|brave(X)))))&
(![X]:((~funny(X)&~wise(X))=>happy(X)))&
((~humble(alice))=>(~humble(john)))&
(![X]:((~happy(X)|happy(X))<=>patient(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(creative(X)=>(creative(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>~funny(X)))&
(?[X]:((tall(X)|humble(X))))&
(~happy(fred))&
(?[X]:((~funny(X)|old(X))))&
((funny(paul)|tall(paul)))&
((~calm(fred)<~>tall(fred)))&
(?[X]:((~calm(X)&~quiet(X))))&
((humble(fred)&creative(fred))) | ~funny(fred) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3698053933550710807985945
% SZS output start Proof for 3698053933550710807985945
14. ! [X0] : ((creative(X0) <~> funny(X0)) <=> (~happy(X0) <~> ~creative(X0))) [input p13]
18. ~happy(fred) [input p17]
24. funny(fred) [input hypothesis]
61. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 14]
114. creative(X0) | happy(X0) | creative(X0) | ~funny(X0) [cnf transformation 61]
117. ~funny(X0) | ~creative(X0) | ~creative(X0) | happy(X0) [cnf transformation 61]
123. ~happy(fred) [cnf transformation 18]
132. funny(fred) [cnf transformation 24]
135. creative(X0) | happy(X0) | ~funny(X0) [duplicate literal removal 114]
137. ~funny(X0) | ~creative(X0) | happy(X0) [duplicate literal removal 117]
165. 6 <=> funny(fred) [avatar definition]
167. funny(fred) <- (6) [avatar component clause 165]
269. ~funny(X0) | happy(X0) [subsumption resolution 135,137]
308. 6 [avatar split clause 132,165]
330. happy(fred) <- (6) [resolution 269,167]
332. $false <- (6) [subsumption resolution 330,123]
333. ~6 [avatar contradiction clause 332]
334. $false [avatar sat refutation 308,333]
% SZS output end Proof for 3698053933550710807985945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. If someone is not curious or not generous then fred is both creative and old and vice versa. If someone is funny then alice is not brave or not wise. If someone is either not calm or rich then susan is not calm and vice versa. Everyone who is either not generous or rich is not funny or wise and vice versa. If paul is either rich or not brave then alice is not generous. If mary is either not funny or quiet then someone is both brave and creative and vice versa. Everyone who is both kind and not wise is both not rich and curious. If fred is both calm and not calm then lucy is rich or strong and vice versa. If someone is both not generous and not quiet then alice is both not rich and curious and vice versa. If john is not curious or not brave then someone is brave or humble. John is humble or not patient. Fred is not happy. Mary is tall or not strong. Mary is both not calm and not kind. John is both wise and happy. Fred is rich or not calm. | John is not generous. | contradiction | (((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
((?[X]:(funny(X)))=>((~brave(alice)|~wise(alice))))&
((?[X]:((~calm(X)<~>rich(X))))<=>(~calm(susan)))&
(![X]:((~generous(X)<~>rich(X))<=>(~funny(X)|wise(X))))&
(((rich(paul)<~>~brave(paul)))=>(~generous(alice)))&
(((~funny(mary)<~>quiet(mary)))<=>(?[X]:((brave(X)&creative(X)))))&
(![X]:((kind(X)&~wise(X))=>(~rich(X)&curious(X))))&
(((calm(fred)&~calm(fred)))<=>((rich(lucy)|strong(lucy))))&
((?[X]:((~generous(X)&~quiet(X))))<=>((~rich(alice)&curious(alice))))&
(((~curious(john)|~brave(john)))=>(?[X]:((brave(X)|humble(X)))))&
((humble(john)|~patient(john)))&
(~happy(fred))&
((tall(mary)|~strong(mary)))&
((~calm(mary)&~kind(mary)))&
((wise(john)&happy(john)))&
((rich(fred)|~calm(fred))) | ~generous(john) | [
"p1",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8962724888508729559293065
% SZS output start Proof for 8962724888508729559293065
2. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p1]
6. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p5]
13. (~calm(fred) & calm(fred)) <=> (strong(lucy) | rich(lucy)) [input p12]
22. ~generous(john) [input hypothesis]
32. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 2]
33. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 32]
40. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 6]
41. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 40]
42. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 41]
43. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK0) | ~curious(sK0)) [choice axiom]
44. ((~generous(sK0) | ~curious(sK0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 42,43]
56. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & ((strong(lucy) | rich(lucy)) | (calm(fred) | ~calm(fred))) [nnf transformation 13]
57. ((~calm(fred) & calm(fred)) | (~strong(lucy) & ~rich(lucy))) & (strong(lucy) | rich(lucy) | calm(fred) | ~calm(fred)) [flattening 56]
68. strong(lucy) | ~old(fred) [cnf transformation 33]
84. old(fred) | generous(X1) [cnf transformation 44]
107. calm(fred) | ~strong(lucy) [cnf transformation 57]
109. ~calm(fred) | ~strong(lucy) [cnf transformation 57]
122. ~generous(john) [cnf transformation 22]
142. 5 <=> old(fred) [avatar definition]
151. 7 <=> strong(lucy) [avatar definition]
154. ~5 | 7 [avatar split clause 68,151,142]
170. 11 <=> ! [X1] : generous(X1) [avatar definition]
171. generous(X1) <- (11) [avatar component clause 170]
172. 11 | 5 [avatar split clause 84,142,170]
249. 28 <=> calm(fred) [avatar definition]
252. ~7 | ~28 [avatar split clause 109,249,151]
258. ~7 | 28 [avatar split clause 107,249,151]
315. $false <- (11) [resolution 171,122]
316. ~11 [avatar contradiction clause 315]
317. $false [avatar sat refutation 154,172,252,258,316]
% SZS output end Proof for 8962724888508729559293065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not generous and not happy then someone is either not patient or not old.
If someone is patient then someone is either creative or not wise.
If someone is both not brave and creative then someone is not generous or not brave and vice versa.
Everyone who is both not patient and rich is either not tall or not wise.
If lucy is either strong or not quiet then fred is not kind or not wise.
Everyone who is both not funny and not creative is either not strong or brave.
If someone is humble then susan is either not curious or strong.
Everyone who is either not tall or creative is both not funny and not curious and vice versa.
If someone is kind then someone is either not quiet or not rich and vice versa.
If paul is happy or tall then someone is old.
Everyone who is either strong or not curious is both not wise and curious.
If someone is happy or not strong then john is not quiet.
If someone is strong or not patient then john is either not rich or not humble and vice versa.
Everyone who is quiet or not humble is not strong and vice versa.
If someone is both not curious and not happy then susan is curious.
Everyone who is both brave and not humble is not humble or not wise.
Someone is either not strong or happy.
John is quiet or strong.
John is wise or not wise.
Mary is either wise or not creative.
Someone is not quiet or curious.
Someone is not happy.
Someone is rich or not wise. | Mary is not patient. | neutral | (((~generous(john)&~happy(john)))=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:(patient(X)))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((~generous(X)|~brave(X)))))&
(![X]:((~patient(X)&rich(X))=>(~tall(X)<~>~wise(X))))&
(((strong(lucy)<~>~quiet(lucy)))=>((~kind(fred)|~wise(fred))))&
(![X]:((~funny(X)&~creative(X))=>(~strong(X)<~>brave(X))))&
((?[X]:(humble(X)))=>((~curious(susan)<~>strong(susan))))&
(![X]:((~tall(X)<~>creative(X))<=>(~funny(X)&~curious(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(((happy(paul)|tall(paul)))=>(?[X]:(old(X))))&
(![X]:((strong(X)<~>~curious(X))=>(~wise(X)&curious(X))))&
((?[X]:((happy(X)|~strong(X))))=>(~quiet(john)))&
((?[X]:((strong(X)|~patient(X))))<=>((~rich(john)<~>~humble(john))))&
(![X]:((quiet(X)|~humble(X))<=>~strong(X)))&
((?[X]:((~curious(X)&~happy(X))))=>(curious(susan)))&
(![X]:((brave(X)&~humble(X))=>(~humble(X)|~wise(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
((quiet(john)|strong(john)))&
((wise(john)|~wise(john)))&
((wise(mary)<~>~creative(mary)))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)|~wise(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is brave or not happy is either not rich or not tall and vice versa.
Everyone who is humble or not creative is not brave or not wise.
Everyone who is not kind is curious or not rich.
Everyone who is either not tall or not rich is tall or curious and vice versa.
If someone is not old or not calm then lucy is not generous or quiet and vice versa.
If someone is brave or calm then paul is both not funny and quiet and vice versa.
Everyone who is either brave or rich is either generous or old.
Everyone who is both strong and kind is both not patient and calm and vice versa.
Everyone who is both not rich and not old is not creative and vice versa.
Everyone who is old is strong or not calm.
If someone is both not tall and not strong then someone is funny.
Everyone who is not quiet is not funny and vice versa.
Everyone who is generous is either not brave or not old.
If someone is both not rich and humble then someone is either quiet or not calm and vice versa.
Everyone who is not humble or not generous is either not calm or not tall.
If alice is not creative then fred is either not generous or not tall and vice versa.
Someone is both not calm and not patient.
Someone is quiet or not rich.
Someone is not old or happy.
Paul is not creative or not funny.
Susan is both creative and humble.
Alice is both not curious and not calm.
Someone is calm or tall. | Susan is calm. | contradiction | (![X]:((brave(X)|~happy(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((humble(X)|~creative(X))=>(~brave(X)|~wise(X))))&
(![X]:(~kind(X)=>(curious(X)|~rich(X))))&
(![X]:((~tall(X)<~>~rich(X))<=>(tall(X)|curious(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~generous(lucy)|quiet(lucy))))&
((?[X]:((brave(X)|calm(X))))<=>((~funny(paul)&quiet(paul))))&
(![X]:((brave(X)<~>rich(X))=>(generous(X)<~>old(X))))&
(![X]:((strong(X)&kind(X))<=>(~patient(X)&calm(X))))&
(![X]:((~rich(X)&~old(X))<=>~creative(X)))&
(![X]:(old(X)=>(strong(X)|~calm(X))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:(funny(X))))&
(![X]:(~quiet(X)<=>~funny(X)))&
(![X]:(generous(X)=>(~brave(X)<~>~old(X))))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~generous(X))=>(~calm(X)<~>~tall(X))))&
((~creative(alice))<=>((~generous(fred)<~>~tall(fred))))&
(?[X]:((~calm(X)&~patient(X))))&
(?[X]:((quiet(X)|~rich(X))))&
(?[X]:((~old(X)|happy(X))))&
((~creative(paul)|~funny(paul)))&
((creative(susan)&humble(susan)))&
((~curious(alice)&~calm(alice)))&
(?[X]:((calm(X)|tall(X)))) | calm(susan) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4570538451779235516453218
% SZS output start Proof for 4570538451779235516453218
6. ? [X0] : (calm(X0) | brave(X0)) <=> (quiet(paul) & ~funny(paul)) [input p5]
12. ! [X0] : (~quiet(X0) <=> ~funny(X0)) [input p11]
24. calm(susan) [input hypothesis]
45. (? [X0] : (calm(X0) | brave(X0)) | (~quiet(paul) | funny(paul))) & ((quiet(paul) & ~funny(paul)) | ! [X0] : (~calm(X0) & ~brave(X0))) [nnf transformation 6]
46. (? [X0] : (calm(X0) | brave(X0)) | ~quiet(paul) | funny(paul)) & ((quiet(paul) & ~funny(paul)) | ! [X0] : (~calm(X0) & ~brave(X0))) [flattening 45]
47. (? [X0] : (calm(X0) | brave(X0)) | ~quiet(paul) | funny(paul)) & ((quiet(paul) & ~funny(paul)) | ! [X1] : (~calm(X1) & ~brave(X1))) [rectify 46]
48. ? [X0] : (calm(X0) | brave(X0)) => (calm(sK1) | brave(sK1)) [choice axiom]
49. ((calm(sK1) | brave(sK1)) | ~quiet(paul) | funny(paul)) & ((quiet(paul) & ~funny(paul)) | ! [X1] : (~calm(X1) & ~brave(X1))) [skolemisation 47,48]
58. ! [X0] : ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0))) [nnf transformation 12]
93. ~funny(paul) | ~calm(X1) [cnf transformation 49]
95. quiet(paul) | ~calm(X1) [cnf transformation 49]
111. ~quiet(X0) | funny(X0) [cnf transformation 58]
138. calm(susan) [cnf transformation 24]
169. 7 <=> funny(paul) [avatar definition]
170. ~funny(paul) <- (~7) [avatar component clause 169]
173. 8 <=> quiet(paul) [avatar definition]
174. quiet(paul) <- (8) [avatar component clause 173]
186. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
187. ~calm(X1) <- (11) [avatar component clause 186]
188. 11 | 8 [avatar split clause 95,173,186]
193. 11 | ~7 [avatar split clause 93,169,186]
282. funny(paul) <- (8) [resolution 111,174]
283. $false <- (~7, 8) [subsumption resolution 282,170]
284. 7 | ~8 [avatar contradiction clause 283]
285. $false <- (11) [resolution 187,138]
288. ~11 [avatar contradiction clause 285]
289. $false [avatar sat refutation 188,193,284,288]
% SZS output end Proof for 4570538451779235516453218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either brave or funny then someone is not calm. Everyone who is not kind is either quiet or not brave. Everyone who is both kind and not generous is either quiet or old. If john is both not curious and not generous then someone is either not humble or not kind and vice versa. Everyone who is patient is not strong or not happy. If lucy is either kind or funny then someone is both not patient and not tall. If someone is both not rich and funny then someone is both quiet and creative and vice versa. If alice is both not tall and creative then someone is either not generous or not wise and vice versa. Everyone who is calm or funny is old and vice versa. If someone is not strong or curious then someone is either not strong or funny. Everyone who is strong or not tall is not humble or not quiet and vice versa. Everyone who is not creative is both tall and brave. Everyone who is curious is not creative and vice versa. If someone is both strong and not brave then someone is either not generous or not old. If someone is not kind then someone is either humble or not generous and vice versa. If someone is either generous or patient then john is not tall. Alice is not calm. Someone is not happy or tall. Lucy is generous or old. John is brave. Someone is old or not quiet. Mary is strong. Someone is both not quiet and not happy. Someone is both not kind and wise. | Alice is tall. | neutral | (((brave(alice)<~>funny(alice)))=>(?[X]:(~calm(X))))&
(![X]:(~kind(X)=>(quiet(X)<~>~brave(X))))&
(![X]:((kind(X)&~generous(X))=>(quiet(X)<~>old(X))))&
(((~curious(john)&~generous(john)))<=>(?[X]:((~humble(X)<~>~kind(X)))))&
(![X]:(patient(X)=>(~strong(X)|~happy(X))))&
(((kind(lucy)<~>funny(lucy)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((~rich(X)&funny(X))))<=>(?[X]:((quiet(X)&creative(X)))))&
(((~tall(alice)&creative(alice)))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((calm(X)|funny(X))<=>old(X)))&
((?[X]:((~strong(X)|curious(X))))=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((strong(X)|~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:(~creative(X)=>(tall(X)&brave(X))))&
(![X]:(curious(X)<=>~creative(X)))&
((?[X]:((strong(X)&~brave(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((humble(X)<~>~generous(X)))))&
((?[X]:((generous(X)<~>patient(X))))=>(~tall(john)))&
(~calm(alice))&
(?[X]:((~happy(X)|tall(X))))&
((generous(lucy)|old(lucy)))&
(brave(john))&
(?[X]:((old(X)|~quiet(X))))&
(strong(mary))&
(?[X]:((~quiet(X)&~happy(X))))&
(?[X]:((~kind(X)&wise(X)))) | tall(alice) | [] | null | 0 |
Everyone who is either humble or not tall is either not happy or strong.
If alice is both tall and not strong then lucy is both strong and not funny and vice versa.
If someone is both not strong and not curious then someone is both not old and tall and vice versa.
If someone is patient or creative then someone is both not strong and old.
If paul is creative then paul is either not calm or not humble.
If someone is either not kind or not calm then paul is either not funny or wise.
Everyone who is either patient or wise is either not wise or strong.
Everyone who is rich is not patient or strong and vice versa.
Everyone who is either wise or not curious is tall and vice versa.
If someone is either happy or not kind then lucy is both not wise and strong and vice versa.
If someone is both not curious and generous then someone is either not calm or wise.
If someone is brave or not funny then someone is both not generous and not creative.
If someone is quiet then paul is not kind and vice versa.
If someone is either tall or not tall then someone is both patient and funny and vice versa.
Everyone who is either rich or not happy is strong or rich and vice versa.
Alice is either not creative or rich.
Lucy is both not wise and patient.
Someone is both not humble and not tall.
Someone is both not patient and not creative.
Paul is either generous or patient.
Someone is funny or quiet.
Someone is not generous or not brave. | Alice is kind. | contradiction | (![X]:((humble(X)<~>~tall(X))=>(~happy(X)<~>strong(X))))&
(((tall(alice)&~strong(alice)))<=>((strong(lucy)&~funny(lucy))))&
((?[X]:((~strong(X)&~curious(X))))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:((patient(X)|creative(X))))=>(?[X]:((~strong(X)&old(X)))))&
((creative(paul))=>((~calm(paul)<~>~humble(paul))))&
((?[X]:((~kind(X)<~>~calm(X))))=>((~funny(paul)<~>wise(paul))))&
(![X]:((patient(X)<~>wise(X))=>(~wise(X)<~>strong(X))))&
(![X]:(rich(X)<=>(~patient(X)|strong(X))))&
(![X]:((wise(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((happy(X)<~>~kind(X))))<=>((~wise(lucy)&strong(lucy))))&
((?[X]:((~curious(X)&generous(X))))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:((brave(X)|~funny(X))))=>(?[X]:((~generous(X)&~creative(X)))))&
((?[X]:(quiet(X)))<=>(~kind(paul)))&
((?[X]:((tall(X)<~>~tall(X))))<=>(?[X]:((patient(X)&funny(X)))))&
(![X]:((rich(X)<~>~happy(X))<=>(strong(X)|rich(X))))&
((~creative(alice)<~>rich(alice)))&
((~wise(lucy)&patient(lucy)))&
(?[X]:((~humble(X)&~tall(X))))&
(?[X]:((~patient(X)&~creative(X))))&
((generous(paul)<~>patient(paul)))&
(?[X]:((funny(X)|quiet(X))))&
(?[X]:((~generous(X)|~brave(X)))) | kind(alice) | [
"p6",
"p7",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4969493749501062406314734
% SZS output start Proof for 4969493749501062406314734
7. ! [X0] : ((patient(X0) <~> wise(X0)) => (~wise(X0) <~> strong(X0))) [input p6]
8. ! [X0] : (rich(X0) <=> (strong(X0) | ~patient(X0))) [input p7]
10. ? [X0] : (happy(X0) <~> ~kind(X0)) <=> (strong(lucy) & ~wise(lucy)) [input p9]
15. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> (rich(X0) | strong(X0))) [input p14]
17. patient(lucy) & ~wise(lucy) [input p16]
23. kind(alice) [input hypothesis]
35. ! [X0] : ((~wise(X0) <~> strong(X0)) | (patient(X0) <=> wise(X0))) [ennf transformation 7]
51. ! [X0] : (((~strong(X0) | wise(X0)) & (strong(X0) | ~wise(X0))) | ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0)))) [nnf transformation 35]
52. ! [X0] : ((rich(X0) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 8]
53. ! [X0] : ((rich(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | ~rich(X0))) [flattening 52]
55. (? [X0] : ((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | (~strong(lucy) | wise(lucy))) & ((strong(lucy) & ~wise(lucy)) | ! [X0] : ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) [nnf transformation 10]
56. (? [X0] : ((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ~strong(lucy) | wise(lucy)) & ((strong(lucy) & ~wise(lucy)) | ! [X0] : ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) [flattening 55]
57. (? [X0] : ((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ~strong(lucy) | wise(lucy)) & ((strong(lucy) & ~wise(lucy)) | ! [X1] : ((happy(X1) | kind(X1)) & (~kind(X1) | ~happy(X1)))) [rectify 56]
58. ? [X0] : ((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) => ((kind(sK3) | ~happy(sK3)) & (~kind(sK3) | happy(sK3))) [choice axiom]
59. (((kind(sK3) | ~happy(sK3)) & (~kind(sK3) | happy(sK3))) | ~strong(lucy) | wise(lucy)) & ((strong(lucy) & ~wise(lucy)) | ! [X1] : ((happy(X1) | kind(X1)) & (~kind(X1) | ~happy(X1)))) [skolemisation 57,58]
76. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 15]
77. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [flattening 76]
110. ~strong(X0) | wise(X0) | wise(X0) | ~patient(X0) [cnf transformation 51]
114. ~strong(X0) | rich(X0) [cnf transformation 53]
121. strong(lucy) | ~kind(X1) | ~happy(X1) [cnf transformation 59]
138. rich(X0) | strong(X0) | rich(X0) | happy(X0) [cnf transformation 77]
142. happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 77]
145. ~wise(lucy) [cnf transformation 17]
146. patient(lucy) [cnf transformation 17]
154. kind(alice) [cnf transformation 23]
155. rich(X0) | strong(X0) | happy(X0) [duplicate literal removal 138]
156. ~rich(X0) | happy(X0) [duplicate literal removal 142]
162. ~patient(X0) | wise(X0) | ~strong(X0) [duplicate literal removal 110]
164. 1 <=> strong(lucy) [avatar definition]
165. strong(lucy) <- (1) [avatar component clause 164]
260. 22 <=> wise(lucy) [avatar definition]
261. ~wise(lucy) <- (~22) [avatar component clause 260]
278. 26 <=> ! [X1] : (~kind(X1) | ~happy(X1)) [avatar definition]
279. ~kind(X1) | ~happy(X1) <- (26) [avatar component clause 278]
280. 26 | 1 [avatar split clause 121,164,278]
340. rich(X0) | happy(X0) [subsumption resolution 155,114]
341. happy(X0) [subsumption resolution 340,156]
352. ~22 [avatar split clause 145,260]
374. ~kind(X1) <- (26) [subsumption resolution 279,341]
375. $false <- (26) [resolution 374,154]
376. ~26 [avatar contradiction clause 375]
406. wise(lucy) | ~strong(lucy) [resolution 162,146]
409. ~strong(lucy) <- (~22) [subsumption resolution 406,261]
410. $false <- (1, ~22) [subsumption resolution 409,165]
411. ~1 | 22 [avatar contradiction clause 410]
421. $false [avatar sat refutation 280,352,376,411]
% SZS output end Proof for 4969493749501062406314734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not generous or not happy then fred is not brave or kind and vice versa. If susan is patient or not funny then someone is both tall and brave. If someone is either funny or not creative then lucy is not wise or not strong and vice versa. If john is both not happy and humble then paul is not rich. If john is both tall and not old then someone is both not funny and calm and vice versa. If someone is generous or not happy then someone is both not creative and not humble and vice versa. Everyone who is curious or not rich is either brave or kind and vice versa. Everyone who is either rich or quiet is quiet. Everyone who is both not brave and not humble is not generous or tall and vice versa. If susan is both patient and happy then someone is either creative or not generous and vice versa. If lucy is both generous and patient then susan is not kind or funny and vice versa. If someone is either not old or not generous then someone is not strong. If someone is either not wise or tall then fred is either not strong or wise and vice versa. If alice is either not curious or not creative then susan is either old or not curious. Everyone who is either brave or wise is both not humble and not funny and vice versa. If someone is either curious or creative then someone is not quiet or old. Someone is either brave or wise. Someone is both not kind and not strong. Someone is both not wise and not kind. Mary is either generous or not brave. Someone is not tall or creative. Alice is either not quiet or not happy. Someone is either tall or calm. Someone is not funny or quiet. | John is humble. | neutral | (((~generous(susan)|~happy(susan)))<=>((~brave(fred)|kind(fred))))&
(((patient(susan)|~funny(susan)))=>(?[X]:((tall(X)&brave(X)))))&
((?[X]:((funny(X)<~>~creative(X))))<=>((~wise(lucy)|~strong(lucy))))&
(((~happy(john)&humble(john)))=>(~rich(paul)))&
(((tall(john)&~old(john)))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((generous(X)|~happy(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((generous(mary)<~>~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~funny(X)|quiet(X)))) | humble(john) | [] | null | 0 |
Everyone who is both funny and not rich is either funny or tall.
Everyone who is curious is not tall and vice versa.
If someone is either strong or creative then someone is old and vice versa.
Everyone who is not patient or not funny is not creative or not quiet.
Everyone who is quiet or curious is both wise and not kind.
If someone is rich or creative then mary is creative.
Everyone who is brave is patient.
If someone is either not calm or not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is both patient and not strong is not patient and vice versa.
Everyone who is not strong is patient or not tall.
Susan is both humble and creative.
Lucy is both not quiet and patient.
Someone is either not rich or kind.
Someone is rich or not wise.
Paul is both humble and brave.
Lucy is both generous and not funny. | Lucy is humble. | neutral | (![X]:((funny(X)&~rich(X))=>(funny(X)<~>tall(X))))&
(![X]:(curious(X)<=>~tall(X)))&
((?[X]:((strong(X)<~>creative(X))))<=>(?[X]:(old(X))))&
(![X]:((~patient(X)|~funny(X))=>(~creative(X)|~quiet(X))))&
(![X]:((quiet(X)|curious(X))=>(wise(X)&~kind(X))))&
((?[X]:((rich(X)|creative(X))))=>(creative(mary)))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:((patient(X)&~strong(X))<=>~patient(X)))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
((humble(susan)&creative(susan)))&
((~quiet(lucy)&patient(lucy)))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:((rich(X)|~wise(X))))&
((humble(paul)&brave(paul)))&
((generous(lucy)&~funny(lucy))) | humble(lucy) | [] | null | 0 |
Everyone who is both not old and calm is not strong and vice versa. If alice is both generous and curious then someone is either not tall or not quiet and vice versa. If someone is both not old and not funny then lucy is kind or creative and vice versa. Everyone who is creative or not curious is not creative. If someone is not brave then someone is not brave or old. Everyone who is either tall or creative is both not happy and not patient and vice versa. Everyone who is not kind or tall is either tall or not calm and vice versa. If someone is both funny and not quiet then john is both old and not happy. Everyone who is either not kind or quiet is both not tall and not patient and vice versa. If someone is generous or brave then paul is not patient or rich and vice versa. If fred is either rich or not funny then paul is either curious or not tall. Everyone who is rich or not patient is kind or wise and vice versa. Everyone who is both happy and not calm is happy or not patient and vice versa. If john is patient then someone is kind or patient. Everyone who is quiet is either funny or not brave and vice versa. Everyone who is not kind is both not happy and creative. Paul is both curious and old. Someone is not creative or curious. Someone is patient. Someone is both not tall and humble. John is wise. Alice is either creative or not creative. | John is curious. | neutral | (![X]:((~old(X)&calm(X))<=>~strong(X)))&
(((generous(alice)&curious(alice)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
((?[X]:((~old(X)&~funny(X))))<=>((kind(lucy)|creative(lucy))))&
(![X]:((creative(X)|~curious(X))=>~creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~brave(X)|old(X)))))&
(![X]:((tall(X)<~>creative(X))<=>(~happy(X)&~patient(X))))&
(![X]:((~kind(X)|tall(X))<=>(tall(X)<~>~calm(X))))&
((?[X]:((funny(X)&~quiet(X))))=>((old(john)&~happy(john))))&
(![X]:((~kind(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
((?[X]:((generous(X)|brave(X))))<=>((~patient(paul)|rich(paul))))&
(((rich(fred)<~>~funny(fred)))=>((curious(paul)<~>~tall(paul))))&
(![X]:((rich(X)|~patient(X))<=>(kind(X)|wise(X))))&
(![X]:((happy(X)&~calm(X))<=>(happy(X)|~patient(X))))&
((patient(john))=>(?[X]:((kind(X)|patient(X)))))&
(![X]:(quiet(X)<=>(funny(X)<~>~brave(X))))&
(![X]:(~kind(X)=>(~happy(X)&creative(X))))&
((curious(paul)&old(paul)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:(patient(X)))&
(?[X]:((~tall(X)&humble(X))))&
(wise(john))&
((creative(alice)<~>~creative(alice))) | curious(john) | [] | null | 0 |
Everyone who is either not tall or not humble is either brave or not humble and vice versa.
Everyone who is not wise or not quiet is kind.
Everyone who is both not generous and not funny is either wise or humble and vice versa.
If john is both curious and not strong then lucy is calm or strong and vice versa.
Everyone who is not calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
If fred is not generous then fred is either not tall or patient and vice versa.
Someone is not brave or happy.
Susan is not patient.
Fred is calm.
Alice is both kind and humble.
Someone is both kind and patient. | John is not happy. | contradiction | (![X]:((~tall(X)<~>~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)<~>humble(X))))&
(((curious(john)&~strong(john)))<=>((calm(lucy)|strong(lucy))))&
(![X]:(~calm(X)<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(?[X]:((~brave(X)|happy(X))))&
(~patient(susan))&
(calm(fred))&
((kind(alice)&humble(alice)))&
(?[X]:((kind(X)&patient(X)))) | ~happy(john) | [
"p3",
"p4",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4039743857958074740120178
% SZS output start Proof for 4039743857958074740120178
4. (~strong(john) & curious(john)) <=> (strong(lucy) | calm(lucy)) [input p3]
5. ! [X0] : (~calm(X0) <=> (~wise(X0) & ~happy(X0))) [input p4]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) => (quiet(X0) & calm(X0))) [input p8]
13. ! [X0] : ((wise(X0) & generous(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p12]
21. ~happy(john) [input hypothesis]
29. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & strong(X0))) [ennf transformation 9]
36. ((~strong(john) & curious(john)) | (~strong(lucy) & ~calm(lucy))) & ((strong(lucy) | calm(lucy)) | (strong(john) | ~curious(john))) [nnf transformation 4]
37. ((~strong(john) & curious(john)) | (~strong(lucy) & ~calm(lucy))) & (strong(lucy) | calm(lucy) | strong(john) | ~curious(john)) [flattening 36]
38. ! [X0] : ((~calm(X0) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | calm(X0))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | calm(X0))) [flattening 38]
49. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 13]
50. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | ~wise(X0) | ~generous(X0))) [flattening 49]
79. ~strong(john) | ~calm(lucy) [cnf transformation 37]
83. ~calm(X0) | wise(X0) | happy(X0) [cnf transformation 39]
93. calm(X0) | calm(X0) [cnf transformation 29]
94. strong(X0) | quiet(X0) [cnf transformation 29]
105. ~generous(X0) | ~quiet(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 50]
107. generous(X0) | generous(X0) [cnf transformation 50]
124. ~happy(john) [cnf transformation 21]
125. ~generous(X0) | ~quiet(X0) | ~wise(X0) [duplicate literal removal 105]
126. generous(X0) [duplicate literal removal 107]
127. calm(X0) [duplicate literal removal 93]
139. 2 <=> strong(john) [avatar definition]
141. ~strong(john) <- (~2) [avatar component clause 139]
144. 3 <=> calm(lucy) [avatar definition]
146. ~calm(lucy) <- (~3) [avatar component clause 144]
147. ~3 | ~2 [avatar split clause 79,139,144]
208. ~quiet(X0) | ~wise(X0) [subsumption resolution 125,126]
229. $false <- (~3) [subsumption resolution 146,127]
230. 3 [avatar contradiction clause 229]
232. quiet(john) <- (~2) [resolution 94,141]
238. ~wise(john) <- (~2) [resolution 208,232]
247. happy(X1) | wise(X1) [resolution 83,127]
251. wise(john) [resolution 247,124]
253. $false <- (~2) [subsumption resolution 251,238]
254. 2 [avatar contradiction clause 253]
255. $false [avatar sat refutation 147,230,254]
% SZS output end Proof for 4039743857958074740120178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or humble is not wise.
Everyone who is not funny or brave is generous.
If alice is either rich or not quiet then someone is not tall or curious.
If paul is strong then someone is curious or rich.
If susan is not wise or humble then mary is not generous or kind and vice versa.
If someone is patient or not strong then someone is either rich or not calm.
If paul is both not creative and old then someone is both not generous and not creative and vice versa.
If alice is either not patient or humble then susan is both not patient and wise.
Everyone who is not brave or tall is both brave and not generous.
If someone is not patient or not wise then someone is both not generous and wise.
If alice is either funny or not old then fred is either tall or quiet and vice versa.
Everyone who is either not quiet or old is either generous or not generous.
If fred is creative or humble then mary is both old and not creative and vice versa.
If someone is old or funny then someone is both calm and humble.
Everyone who is both not curious and patient is brave.
Everyone who is not wise is either brave or not kind.
Mary is either not kind or strong.
Someone is either creative or not calm.
Mary is either rich or not old.
Someone is both patient and brave.
Alice is generous.
Someone is not brave or generous. | Alice is funny. | contradiction | (![X]:((~generous(X)<~>humble(X))=>~wise(X)))&
(![X]:((~funny(X)|brave(X))=>generous(X)))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)|curious(X)))))&
((strong(paul))=>(?[X]:((curious(X)|rich(X)))))&
(((~wise(susan)|humble(susan)))<=>((~generous(mary)|kind(mary))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((~creative(paul)&old(paul)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~patient(alice)<~>humble(alice)))=>((~patient(susan)&wise(susan))))&
(![X]:((~brave(X)|tall(X))=>(brave(X)&~generous(X))))&
((?[X]:((~patient(X)|~wise(X))))=>(?[X]:((~generous(X)&wise(X)))))&
(((funny(alice)<~>~old(alice)))<=>((tall(fred)<~>quiet(fred))))&
(![X]:((~quiet(X)<~>old(X))=>(generous(X)<~>~generous(X))))&
(((creative(fred)|humble(fred)))<=>((old(mary)&~creative(mary))))&
((?[X]:((old(X)|funny(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~curious(X)&patient(X))=>brave(X)))&
(![X]:(~wise(X)=>(brave(X)<~>~kind(X))))&
((~kind(mary)<~>strong(mary)))&
(?[X]:((creative(X)<~>~calm(X))))&
((rich(mary)<~>~old(mary)))&
(?[X]:((patient(X)&brave(X))))&
(generous(alice))&
(?[X]:((~brave(X)|generous(X)))) | funny(alice) | [
"p0",
"p1",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6859795373547841700694351
% SZS output start Proof for 6859795373547841700694351
1. ! [X0] : ((~generous(X0) <~> humble(X0)) => ~wise(X0)) [input p0]
2. ! [X0] : ((brave(X0) | ~funny(X0)) => generous(X0)) [input p1]
9. ! [X0] : ((tall(X0) | ~brave(X0)) => (~generous(X0) & brave(X0))) [input p8]
10. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X0] : (wise(X0) & ~generous(X0)) [input p9]
14. ? [X0] : (funny(X0) | old(X0)) => ? [X0] : (humble(X0) & calm(X0)) [input p13]
23. funny(alice) [input hypothesis]
25. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X1] : (wise(X1) & ~generous(X1)) [rectify 10]
26. ? [X0] : (funny(X0) | old(X0)) => ? [X1] : (humble(X1) & calm(X1)) [rectify 14]
30. ! [X0] : (~wise(X0) | (~generous(X0) <=> humble(X0))) [ennf transformation 1]
31. ! [X0] : (generous(X0) | (~brave(X0) & funny(X0))) [ennf transformation 2]
34. ! [X0] : ((~generous(X0) & brave(X0)) | (~tall(X0) & brave(X0))) [ennf transformation 9]
35. ? [X1] : (wise(X1) & ~generous(X1)) | ! [X0] : (wise(X0) & patient(X0)) [ennf transformation 25]
37. ? [X1] : (humble(X1) & calm(X1)) | ! [X0] : (~funny(X0) & ~old(X0)) [ennf transformation 26]
39. ! [X0] : (~wise(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) [nnf transformation 30]
52. ? [X0] : (wise(X0) & ~generous(X0)) | ! [X1] : (wise(X1) & patient(X1)) [rectify 35]
53. ? [X0] : (wise(X0) & ~generous(X0)) => (wise(sK2) & ~generous(sK2)) [choice axiom]
54. (wise(sK2) & ~generous(sK2)) | ! [X1] : (wise(X1) & patient(X1)) [skolemisation 52,53]
59. ? [X0] : (humble(X0) & calm(X0)) | ! [X1] : (~funny(X1) & ~old(X1)) [rectify 37]
60. ? [X0] : (humble(X0) & calm(X0)) => (humble(sK3) & calm(sK3)) [choice axiom]
61. (humble(sK3) & calm(sK3)) | ! [X1] : (~funny(X1) & ~old(X1)) [skolemisation 59,60]
73. ~wise(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 39]
75. ~brave(X0) | generous(X0) [cnf transformation 31]
92. brave(X0) | brave(X0) [cnf transformation 34]
97. ~generous(sK2) | wise(X1) [cnf transformation 54]
120. humble(sK3) | ~funny(X1) [cnf transformation 61]
133. funny(alice) [cnf transformation 23]
134. brave(X0) [duplicate literal removal 92]
213. 17 <=> ! [X1] : wise(X1) [avatar definition]
214. wise(X1) <- (17) [avatar component clause 213]
225. 20 <=> generous(sK2) [avatar definition]
227. ~generous(sK2) <- (~20) [avatar component clause 225]
228. 17 | ~20 [avatar split clause 97,225,213]
239. 23 <=> funny(alice) [avatar definition]
240. funny(alice) <- (23) [avatar component clause 239]
276. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
277. ~funny(X1) <- (29) [avatar component clause 276]
279. 30 <=> humble(sK3) [avatar definition]
281. humble(sK3) <- (30) [avatar component clause 279]
282. 29 | 30 [avatar split clause 120,279,276]
316. 23 [avatar split clause 133,239]
317. $false <- (23, 29) [subsumption resolution 240,277]
318. ~23 | ~29 [avatar contradiction clause 317]
319. generous(X0) [resolution 75,134]
321. $false <- (~20) [resolution 319,227]
322. 20 [avatar contradiction clause 321]
338. ~generous(X0) | ~humble(X0) <- (17) [resolution 73,214]
343. ~humble(X0) <- (17) [subsumption resolution 338,319]
345. $false <- (17, 30) [resolution 343,281]
346. ~17 | ~30 [avatar contradiction clause 345]
347. $false [avatar sat refutation 228,282,316,318,322,346]
% SZS output end Proof for 6859795373547841700694351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and old then mary is either tall or happy.
If lucy is both calm and not calm then mary is both tall and not rich and vice versa.
Everyone who is not quiet or creative is either not tall or not patient.
If someone is both not creative and brave then fred is strong.
Everyone who is not quiet is both patient and humble.
If susan is both patient and humble then someone is not calm and vice versa.
Everyone who is not strong or not quiet is tall and vice versa.
Everyone who is both not funny and brave is either quiet or not creative and vice versa.
If mary is either kind or not strong then someone is creative or brave and vice versa.
Everyone who is quiet or not curious is either creative or not curious.
Everyone who is not calm is either not tall or generous and vice versa.
Everyone who is both old and not rich is not strong or not happy.
If lucy is both not kind and not patient then john is both not quiet and not kind.
If fred is not wise then paul is not strong.
If john is humble or not old then someone is creative.
Everyone who is both not patient and not calm is calm or not calm.
Someone is not kind.
Someone is wise or not quiet.
Someone is not wise.
Paul is wise.
John is both not humble and not curious.
Susan is patient. | Mary is kind. | neutral | ((?[X]:((kind(X)&old(X))))=>((tall(mary)<~>happy(mary))))&
(((calm(lucy)&~calm(lucy)))<=>((tall(mary)&~rich(mary))))&
(![X]:((~quiet(X)|creative(X))=>(~tall(X)<~>~patient(X))))&
((?[X]:((~creative(X)&brave(X))))=>(strong(fred)))&
(![X]:(~quiet(X)=>(patient(X)&humble(X))))&
(((patient(susan)&humble(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)|~quiet(X))<=>tall(X)))&
(![X]:((~funny(X)&brave(X))<=>(quiet(X)<~>~creative(X))))&
(((kind(mary)<~>~strong(mary)))<=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((quiet(X)|~curious(X))=>(creative(X)<~>~curious(X))))&
(![X]:(~calm(X)<=>(~tall(X)<~>generous(X))))&
(![X]:((old(X)&~rich(X))=>(~strong(X)|~happy(X))))&
(((~kind(lucy)&~patient(lucy)))=>((~quiet(john)&~kind(john))))&
((~wise(fred))=>(~strong(paul)))&
(((humble(john)|~old(john)))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:(~wise(X)))&
(wise(paul))&
((~humble(john)&~curious(john)))&
(patient(susan)) | kind(mary) | [] | null | 0 |
Everyone who is calm is old or not creative and vice versa. If alice is either not wise or old then lucy is not humble or old and vice versa. Everyone who is both generous and not funny is not curious and vice versa. Everyone who is either not brave or not generous is wise or tall and vice versa. If someone is either not strong or not creative then someone is either old or not quiet and vice versa. Everyone who is both not rich and kind is not tall or rich and vice versa. Everyone who is not strong is generous or old and vice versa. Everyone who is curious is both not curious and not patient and vice versa. Everyone who is old is not kind or tall and vice versa. If someone is both rich and patient then fred is both not quiet and not brave. Everyone who is calm or brave is both not wise and brave and vice versa. If someone is either funny or not creative then someone is not curious and vice versa. If someone is both not generous and not tall then someone is not humble or not calm. Everyone who is curious or generous is either not happy or calm and vice versa. If someone is both tall and not wise then fred is both not wise and brave and vice versa. Someone is either not generous or not happy. Mary is old or kind. Someone is kind or not humble. Someone is not brave. Fred is not brave. Mary is patient or funny. | Alice is happy. | neutral | (![X]:(calm(X)<=>(old(X)|~creative(X))))&
(((~wise(alice)<~>old(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:((generous(X)&~funny(X))<=>~curious(X)))&
(![X]:((~brave(X)<~>~generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((~strong(X)<~>~creative(X))))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&kind(X))<=>(~tall(X)|rich(X))))&
(![X]:(~strong(X)<=>(generous(X)|old(X))))&
(![X]:(curious(X)<=>(~curious(X)&~patient(X))))&
(![X]:(old(X)<=>(~kind(X)|tall(X))))&
((?[X]:((rich(X)&patient(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((old(mary)|kind(mary)))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(~brave(fred))&
((patient(mary)|funny(mary))) | happy(alice) | [] | null | 0 |
Everyone who is funny or humble is humble and vice versa. Everyone who is not tall or not generous is not tall. If someone is either not quiet or not humble then john is not tall and vice versa. Everyone who is either not strong or not wise is both curious and not kind and vice versa. Everyone who is not generous or generous is both not funny and calm and vice versa. If someone is not humble or not kind then john is not wise. Everyone who is patient is either old or not brave. If mary is either strong or not rich then john is not quiet and vice versa. Everyone who is not generous or not patient is both not curious and strong. If someone is both not patient and patient then someone is both patient and old and vice versa. Everyone who is rich is not funny and vice versa. If someone is humble then someone is not rich or strong and vice versa. If john is rich or not funny then someone is not kind. If someone is either calm or not kind then someone is either not brave or not tall and vice versa. If fred is kind or not quiet then someone is either not humble or strong and vice versa. Everyone who is both not happy and not funny is not rich or not generous and vice versa. Susan is not generous. Someone is either not happy or not strong. Someone is not humble or calm. Paul is not creative. Someone is tall or old. John is either not strong or not calm. Mary is patient. Someone is patient or not humble. | John is not brave. | entailment | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(![X]:((~tall(X)|~generous(X))=>~tall(X)))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(~tall(john)))&
(![X]:((~strong(X)<~>~wise(X))<=>(curious(X)&~kind(X))))&
(![X]:((~generous(X)|generous(X))<=>(~funny(X)&calm(X))))&
((?[X]:((~humble(X)|~kind(X))))=>(~wise(john)))&
(![X]:(patient(X)=>(old(X)<~>~brave(X))))&
(((strong(mary)<~>~rich(mary)))<=>(~quiet(john)))&
(![X]:((~generous(X)|~patient(X))=>(~curious(X)&strong(X))))&
((?[X]:((~patient(X)&patient(X))))<=>(?[X]:((patient(X)&old(X)))))&
(![X]:(rich(X)<=>~funny(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)|strong(X)))))&
(((rich(john)|~funny(john)))=>(?[X]:(~kind(X))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(((kind(fred)|~quiet(fred)))<=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((~happy(X)&~funny(X))<=>(~rich(X)|~generous(X))))&
(~generous(susan))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~humble(X)|calm(X))))&
(~creative(paul))&
(?[X]:((tall(X)|old(X))))&
((~strong(john)<~>~calm(john)))&
(patient(mary))&
(?[X]:((patient(X)|~humble(X)))) | ~brave(john) | [
"p4",
"p6",
"p8",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8834111202180919872896306
% SZS output start Proof for 8834111202180919872896306
5. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (calm(X0) & ~funny(X0))) [input p4]
7. ! [X0] : (patient(X0) => (old(X0) <~> ~brave(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | ~generous(X0)) => (strong(X0) & ~curious(X0))) [input p8]
10. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X0] : (old(X0) & patient(X0)) [input p9]
22. ~strong(john) <~> ~calm(john) [input p21]
25. brave(john) [input hypothesis]
26. ? [X0] : (patient(X0) & ~patient(X0)) <=> ? [X1] : (old(X1) & patient(X1)) [rectify 10]
32. ! [X0] : ((old(X0) <~> ~brave(X0)) | ~patient(X0)) [ennf transformation 7]
33. ! [X0] : ((strong(X0) & ~curious(X0)) | (patient(X0) & generous(X0))) [ennf transformation 9]
43. ! [X0] : (((generous(X0) | ~generous(X0)) | (~calm(X0) | funny(X0))) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((generous(X0) | ~generous(X0) | ~calm(X0) | funny(X0)) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [flattening 43]
45. ! [X0] : (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~patient(X0)) [nnf transformation 32]
47. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~old(X1) | ~patient(X1))) & (? [X1] : (old(X1) & patient(X1)) | ! [X0] : (~patient(X0) | patient(X0))) [nnf transformation 26]
48. (? [X0] : (patient(X0) & ~patient(X0)) | ! [X1] : (~old(X1) | ~patient(X1))) & (? [X2] : (old(X2) & patient(X2)) | ! [X3] : (~patient(X3) | patient(X3))) [rectify 47]
49. ? [X0] : (patient(X0) & ~patient(X0)) => (patient(sK1) & ~patient(sK1)) [choice axiom]
50. ? [X2] : (old(X2) & patient(X2)) => (old(sK2) & patient(sK2)) [choice axiom]
51. ((patient(sK1) & ~patient(sK1)) | ! [X1] : (~old(X1) | ~patient(X1))) & ((old(sK2) & patient(sK2)) | ! [X3] : (~patient(X3) | patient(X3))) [skolemisation 48,50,49]
79. (calm(john) | strong(john)) & (~calm(john) | ~strong(john)) [nnf transformation 22]
99. calm(X0) | generous(X0) [cnf transformation 44]
100. ~generous(X0) | calm(X0) [cnf transformation 44]
104. ~brave(X0) | old(X0) | ~patient(X0) [cnf transformation 45]
113. patient(X0) | strong(X0) [cnf transformation 33]
116. ~patient(sK1) | ~old(X1) | ~patient(X1) [cnf transformation 51]
117. patient(sK1) | ~old(X1) | ~patient(X1) [cnf transformation 51]
149. ~calm(john) | ~strong(john) [cnf transformation 79]
153. brave(john) [cnf transformation 25]
176. calm(X0) [subsumption resolution 99,100]
207. 12 <=> ! [X1] : (~old(X1) | ~patient(X1)) [avatar definition]
208. ~old(X1) | ~patient(X1) <- (12) [avatar component clause 207]
210. 13 <=> patient(sK1) [avatar definition]
213. 12 | 13 [avatar split clause 117,210,207]
214. 12 | ~13 [avatar split clause 116,210,207]
312. ~strong(john) [subsumption resolution 149,176]
385. old(john) | ~patient(john) [resolution 104,153]
388. ~patient(john) <- (12) [subsumption resolution 385,208]
391. strong(john) <- (12) [resolution 388,113]
392. $false <- (12) [subsumption resolution 391,312]
393. ~12 [avatar contradiction clause 392]
394. $false [avatar sat refutation 213,214,393]
% SZS output end Proof for 8834111202180919872896306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not tall or generous then someone is either not tall or not wise.
Everyone who is either quiet or not old is not quiet or strong and vice versa.
If susan is both not patient and calm then lucy is not rich or not old.
Everyone who is not tall is both not patient and not old.
If susan is funny or not happy then fred is either not calm or not generous.
If someone is either generous or not funny then fred is patient or curious.
If someone is both not kind and not quiet then someone is kind or calm and vice versa.
If someone is both happy and not humble then lucy is generous and vice versa.
Everyone who is not tall or creative is both not rich and wise and vice versa.
Everyone who is humble or creative is either not old or not curious and vice versa.
Everyone who is either not tall or not happy is either wise or tall and vice versa.
If someone is both not brave and tall then someone is either not patient or not strong and vice versa.
Everyone who is both not creative and humble is either old or not curious.
If someone is not rich then susan is not patient or humble.
If lucy is strong or old then fred is either not funny or brave.
If someone is not wise or not quiet then someone is either generous or not kind and vice versa.
Lucy is both not wise and brave.
Susan is both rich and strong.
Fred is either old or generous.
Someone is both wise and not old.
Someone is creative or tall.
Someone is kind or old.
Someone is generous or not happy. | Lucy is not rich. | neutral | (((~tall(fred)<~>generous(fred)))=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((quiet(X)<~>~old(X))<=>(~quiet(X)|strong(X))))&
(((~patient(susan)&calm(susan)))=>((~rich(lucy)|~old(lucy))))&
(![X]:(~tall(X)=>(~patient(X)&~old(X))))&
(((funny(susan)|~happy(susan)))=>((~calm(fred)<~>~generous(fred))))&
((?[X]:((generous(X)<~>~funny(X))))=>((patient(fred)|curious(fred))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>(generous(lucy)))&
(![X]:((~tall(X)|creative(X))<=>(~rich(X)&wise(X))))&
(![X]:((humble(X)|creative(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
(![X]:((~creative(X)&humble(X))=>(old(X)<~>~curious(X))))&
((?[X]:(~rich(X)))=>((~patient(susan)|humble(susan))))&
(((strong(lucy)|old(lucy)))=>((~funny(fred)<~>brave(fred))))&
((?[X]:((~wise(X)|~quiet(X))))<=>(?[X]:((generous(X)<~>~kind(X)))))&
((~wise(lucy)&brave(lucy)))&
((rich(susan)&strong(susan)))&
((old(fred)<~>generous(fred)))&
(?[X]:((wise(X)&~old(X))))&
(?[X]:((creative(X)|tall(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((generous(X)|~happy(X)))) | ~rich(lucy) | [] | null | 0 |
If mary is both not tall and not kind then someone is happy or old. If someone is either not rich or not calm then mary is not humble or calm. Everyone who is not generous is both tall and happy. Everyone who is quiet is either not humble or curious and vice versa. Everyone who is curious or not happy is both generous and tall and vice versa. Everyone who is either not humble or generous is old or generous and vice versa. Everyone who is happy is curious and vice versa. Everyone who is rich or happy is either brave or not humble. Everyone who is either not strong or not old is not humble and vice versa. Everyone who is either brave or quiet is curious and vice versa. If alice is quiet or kind then someone is either not quiet or wise and vice versa. If someone is both not patient and wise then susan is both brave and not brave. If paul is not quiet then fred is quiet or not wise and vice versa. If someone is either not quiet or not curious then mary is not creative and vice versa. Everyone who is brave or not humble is not kind or not strong. Everyone who is both not creative and strong is both not funny and funny. Alice is both creative and not wise. Fred is either not old or generous. Someone is both old and not brave. Fred is humble. Someone is curious or not calm. Someone is old. | Alice is not rich. | entailment | (((~tall(mary)&~kind(mary)))=>(?[X]:((happy(X)|old(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~humble(mary)|calm(mary))))&
(![X]:(~generous(X)=>(tall(X)&happy(X))))&
(![X]:(quiet(X)<=>(~humble(X)<~>curious(X))))&
(![X]:((curious(X)|~happy(X))<=>(generous(X)&tall(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(old(X)|generous(X))))&
(![X]:(happy(X)<=>curious(X)))&
(![X]:((rich(X)|happy(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>~old(X))<=>~humble(X)))&
(![X]:((brave(X)<~>quiet(X))<=>curious(X)))&
(((quiet(alice)|kind(alice)))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:((~patient(X)&wise(X))))=>((brave(susan)&~brave(susan))))&
((~quiet(paul))<=>((quiet(fred)|~wise(fred))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(~creative(mary)))&
(![X]:((brave(X)|~humble(X))=>(~kind(X)|~strong(X))))&
(![X]:((~creative(X)&strong(X))=>(~funny(X)&funny(X))))&
((creative(alice)&~wise(alice)))&
((~old(fred)<~>generous(fred)))&
(?[X]:((old(X)&~brave(X))))&
(humble(fred))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:(old(X))) | ~rich(alice) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6126005934145818000498705
% SZS output start Proof for 6126005934145818000498705
3. ! [X0] : (~generous(X0) => (happy(X0) & tall(X0))) [input p2]
4. ! [X0] : (quiet(X0) <=> (~humble(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((~happy(X0) | curious(X0)) <=> (tall(X0) & generous(X0))) [input p4]
6. ! [X0] : ((~humble(X0) <~> generous(X0)) <=> (generous(X0) | old(X0))) [input p5]
7. ! [X0] : (happy(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((happy(X0) | rich(X0)) => (brave(X0) <~> ~humble(X0))) [input p7]
10. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> curious(X0)) [input p9]
14. ? [X0] : (~quiet(X0) <~> ~curious(X0)) <=> ~creative(mary) [input p13]
23. rich(alice) [input hypothesis]
29. ! [X0] : ((happy(X0) & tall(X0)) | generous(X0)) [ennf transformation 3]
30. ! [X0] : ((brave(X0) <~> ~humble(X0)) | (~happy(X0) & ~rich(X0))) [ennf transformation 8]
38. ! [X0] : ((quiet(X0) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0)))) & (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | ~quiet(X0))) [nnf transformation 4]
39. ! [X0] : (((~happy(X0) | curious(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 5]
40. ! [X0] : ((~happy(X0) | curious(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (happy(X0) & ~curious(X0)))) [flattening 39]
41. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [nnf transformation 6]
42. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [flattening 41]
43. ! [X0] : ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))) [nnf transformation 7]
44. ! [X0] : (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~happy(X0) & ~rich(X0))) [nnf transformation 30]
46. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ~curious(X0)) & (curious(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 10]
54. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | creative(mary)) & (~creative(mary) | ! [X0] : ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 14]
55. (? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | creative(mary)) & (~creative(mary) | ! [X1] : ((~quiet(X1) | curious(X1)) & (~curious(X1) | quiet(X1)))) [rectify 54]
56. ? [X0] : ((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) => ((curious(sK2) | quiet(sK2)) & (~curious(sK2) | ~quiet(sK2))) [choice axiom]
57. (((curious(sK2) | quiet(sK2)) & (~curious(sK2) | ~quiet(sK2))) | creative(mary)) & (~creative(mary) | ! [X1] : ((~quiet(X1) | curious(X1)) & (~curious(X1) | quiet(X1)))) [skolemisation 55,56]
69. generous(X0) | happy(X0) [cnf transformation 29]
70. ~quiet(X0) | ~humble(X0) | curious(X0) [cnf transformation 38]
71. ~curious(X0) | humble(X0) | ~quiet(X0) [cnf transformation 38]
73. ~curious(X0) | ~humble(X0) | quiet(X0) [cnf transformation 38]
74. ~curious(X0) | generous(X0) [cnf transformation 40]
84. ~generous(X0) | humble(X0) | ~generous(X0) [cnf transformation 42]
85. ~happy(X0) | curious(X0) [cnf transformation 43]
87. ~humble(X0) | brave(X0) | ~rich(X0) [cnf transformation 44]
95. ~brave(X0) | quiet(X0) | curious(X0) [cnf transformation 46]
98. ~brave(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 46]
108. ~creative(mary) | ~curious(X1) | quiet(X1) [cnf transformation 57]
109. ~creative(mary) | ~quiet(X1) | curious(X1) [cnf transformation 57]
110. ~curious(sK2) | ~quiet(sK2) | creative(mary) [cnf transformation 57]
111. curious(sK2) | quiet(sK2) | creative(mary) [cnf transformation 57]
125. rich(alice) [cnf transformation 23]
127. ~generous(X0) | humble(X0) [duplicate literal removal 84]
168. 10 <=> quiet(alice) [avatar definition]
169. ~quiet(alice) <- (~10) [avatar component clause 168]
170. quiet(alice) <- (10) [avatar component clause 168]
208. 18 <=> creative(mary) [avatar definition]
212. 19 <=> quiet(sK2) [avatar definition]
213. ~quiet(sK2) <- (~19) [avatar component clause 212]
214. quiet(sK2) <- (19) [avatar component clause 212]
216. 20 <=> curious(sK2) [avatar definition]
217. ~curious(sK2) <- (~20) [avatar component clause 216]
218. curious(sK2) <- (20) [avatar component clause 216]
219. 18 | 19 | 20 [avatar split clause 111,216,212,208]
220. 18 | ~19 | ~20 [avatar split clause 110,216,212,208]
222. 21 <=> ! [X1] : (~quiet(X1) | curious(X1)) [avatar definition]
223. ~quiet(X1) | curious(X1) <- (21) [avatar component clause 222]
224. 21 | ~18 [avatar split clause 109,208,222]
226. 22 <=> ! [X1] : (~curious(X1) | quiet(X1)) [avatar definition]
227. ~curious(X1) | quiet(X1) <- (22) [avatar component clause 226]
228. 22 | ~18 [avatar split clause 108,208,226]
254. humble(X0) | happy(X0) [resolution 127,69]
264. ~humble(alice) | curious(alice) <- (10) [resolution 70,170]
265. ~humble(sK2) | curious(sK2) <- (19) [resolution 70,214]
267. 27 <=> curious(alice) [avatar definition]
269. curious(alice) <- (27) [avatar component clause 267]
271. 28 <=> humble(alice) [avatar definition]
272. humble(alice) <- (28) [avatar component clause 271]
273. ~humble(alice) <- (~28) [avatar component clause 271]
274. 27 | ~28 | ~10 [avatar split clause 264,168,271,267]
275. ~humble(sK2) <- (19, ~20) [subsumption resolution 265,217]
276. happy(alice) <- (~28) [resolution 273,254]
278. happy(sK2) <- (19, ~20) [resolution 275,254]
290. curious(alice) <- (~28) [resolution 276,85]
291. 27 | 28 [avatar split clause 290,271,267]
296. humble(alice) | ~quiet(alice) <- (27) [resolution 269,71]
300. ~quiet(alice) <- (27, ~28) [subsumption resolution 296,273]
303. ~10 | ~27 | 28 [avatar split clause 300,271,267,168]
325. curious(sK2) <- (19, ~20) [resolution 278,85]
326. $false <- (19, ~20) [subsumption resolution 325,217]
327. ~19 | 20 [avatar contradiction clause 326]
328. ~humble(sK2) | quiet(sK2) <- (20) [resolution 218,73]
332. generous(sK2) <- (20) [resolution 218,74]
333. ~humble(sK2) <- (~19, 20) [subsumption resolution 328,213]
339. humble(sK2) <- (20) [resolution 332,127]
340. $false <- (~19, 20) [subsumption resolution 339,333]
341. 19 | ~20 [avatar contradiction clause 340]
347. quiet(alice) <- (22, 27) [resolution 227,269]
349. $false <- (~10, 22, 27) [subsumption resolution 347,169]
350. 10 | ~22 | ~27 [avatar contradiction clause 349]
354. brave(alice) | ~rich(alice) <- (28) [resolution 272,87]
370. 35 <=> brave(alice) [avatar definition]
372. brave(alice) <- (35) [avatar component clause 370]
374. brave(alice) <- (28) [subsumption resolution 354,125]
375. 35 | ~28 [avatar split clause 374,271,370]
390. ~quiet(alice) | ~curious(alice) <- (35) [resolution 372,98]
391. quiet(alice) | curious(alice) <- (35) [resolution 372,95]
397. curious(alice) <- (21, 35) [subsumption resolution 391,223]
398. 27 | ~21 | ~35 [avatar split clause 397,370,222,267]
399. ~curious(alice) <- (22, 35) [subsumption resolution 390,227]
400. ~27 | ~22 | ~35 [avatar split clause 399,370,226,267]
401. $false [avatar sat refutation 219,220,224,228,274,291,303,327,341,350,375,398,400]
% SZS output end Proof for 6126005934145818000498705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny then someone is both not funny and not strong and vice versa.
If someone is either wise or generous then someone is either not tall or not humble.
Everyone who is both not curious and not old is not creative or humble and vice versa.
Everyone who is not strong is tall and vice versa.
If susan is generous then susan is wise and vice versa.
If john is both patient and humble then someone is either not strong or funny and vice versa.
Everyone who is not humble or not wise is both humble and not tall.
Everyone who is quiet or not funny is brave and vice versa.
Everyone who is not brave is both not brave and calm and vice versa.
If someone is not rich then someone is not strong and vice versa.
Everyone who is humble or not humble is both not brave and not strong and vice versa.
If alice is not creative or tall then alice is not happy or not tall.
If john is either humble or strong then john is either not creative or creative and vice versa.
Someone is patient or not humble.
Someone is either calm or not generous.
Lucy is not creative or calm.
Someone is patient or not strong.
Fred is funny.
Someone is either kind or brave. | John is not generous. | contradiction | ((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:((wise(X)<~>generous(X))))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~old(X))<=>(~creative(X)|humble(X))))&
(![X]:(~strong(X)<=>tall(X)))&
((generous(susan))<=>(wise(susan)))&
(((patient(john)&humble(john)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)&~tall(X))))&
(![X]:((quiet(X)|~funny(X))<=>brave(X)))&
(![X]:(~brave(X)<=>(~brave(X)&calm(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~humble(X))<=>(~brave(X)&~strong(X))))&
(((~creative(alice)|tall(alice)))=>((~happy(alice)|~tall(alice))))&
(((humble(john)<~>strong(john)))<=>((~creative(john)<~>creative(john))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
((~creative(lucy)|calm(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(funny(fred))&
(?[X]:((kind(X)<~>brave(X)))) | ~generous(john) | [
"p1",
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4057441934671711112874863
% SZS output start Proof for 4057441934671711112874863
2. ? [X0] : (wise(X0) <~> generous(X0)) => ? [X0] : (~tall(X0) <~> ~humble(X0)) [input p1]
4. ! [X0] : (~strong(X0) <=> tall(X0)) [input p3]
7. ! [X0] : ((~wise(X0) | ~humble(X0)) => (~tall(X0) & humble(X0))) [input p6]
11. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~strong(X0) & ~brave(X0))) [input p10]
20. ~generous(john) [input hypothesis]
22. ? [X0] : (wise(X0) <~> generous(X0)) => ? [X1] : (~tall(X1) <~> ~humble(X1)) [rectify 2]
25. ? [X1] : (~tall(X1) <~> ~humble(X1)) | ! [X0] : (wise(X0) <=> generous(X0)) [ennf transformation 22]
26. ! [X0] : ((~tall(X0) & humble(X0)) | (wise(X0) & humble(X0))) [ennf transformation 7]
32. ? [X1] : ((humble(X1) | tall(X1)) & (~humble(X1) | ~tall(X1))) | ! [X0] : ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0))) [nnf transformation 25]
33. ? [X0] : ((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ! [X1] : ((wise(X1) | ~generous(X1)) & (generous(X1) | ~wise(X1))) [rectify 32]
34. ? [X0] : ((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) => ((humble(sK2) | tall(sK2)) & (~humble(sK2) | ~tall(sK2))) [choice axiom]
35. ((humble(sK2) | tall(sK2)) & (~humble(sK2) | ~tall(sK2))) | ! [X1] : ((wise(X1) | ~generous(X1)) & (generous(X1) | ~wise(X1))) [skolemisation 33,34]
38. ! [X0] : ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))) [nnf transformation 4]
54. ! [X0] : (((~humble(X0) | humble(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 11]
55. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (humble(X0) & ~humble(X0)))) [flattening 54]
70. ~humble(sK2) | ~tall(sK2) | generous(X1) | ~wise(X1) [cnf transformation 35]
79. tall(X0) | strong(X0) [cnf transformation 38]
89. humble(X0) | humble(X0) [cnf transformation 26]
92. ~tall(X0) | wise(X0) [cnf transformation 26]
103. ~strong(X0) | ~humble(X0) [cnf transformation 55]
122. ~generous(john) [cnf transformation 20]
127. humble(X0) [duplicate literal removal 89]
153. 7 <=> tall(sK2) [avatar definition]
154. ~tall(sK2) <- (~7) [avatar component clause 153]
157. 8 <=> humble(sK2) [avatar definition]
158. ~humble(sK2) <- (~8) [avatar component clause 157]
162. 9 <=> ! [X1] : (generous(X1) | ~wise(X1)) [avatar definition]
163. ~wise(X1) | generous(X1) <- (9) [avatar component clause 162]
166. 9 | ~7 | ~8 [avatar split clause 70,157,153,162]
218. ~strong(X0) [subsumption resolution 103,127]
241. $false <- (~8) [subsumption resolution 158,127]
242. 8 [avatar contradiction clause 241]
243. strong(sK2) <- (~7) [resolution 79,154]
244. $false <- (~7) [subsumption resolution 243,218]
245. 7 [avatar contradiction clause 244]
250. wise(X0) | strong(X0) [resolution 92,79]
252. wise(X0) [subsumption resolution 250,218]
272. generous(X0) <- (9) [resolution 163,252]
274. $false <- (9) [resolution 272,122]
276. ~9 [avatar contradiction clause 274]
277. $false [avatar sat refutation 166,242,245,276]
% SZS output end Proof for 4057441934671711112874863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not wise and not curious then lucy is either not rich or not humble.
Everyone who is either not strong or kind is either patient or not patient and vice versa.
Everyone who is either kind or not generous is not calm or calm and vice versa.
If paul is not rich then mary is either old or strong and vice versa.
Everyone who is either not quiet or not brave is either not quiet or not kind.
If someone is humble or quiet then someone is either brave or not brave.
If someone is funny or old then someone is not curious or not kind.
If alice is both not rich and old then paul is not quiet.
Everyone who is both creative and strong is not quiet and vice versa.
If someone is either creative or not old then someone is rich and vice versa.
Everyone who is quiet or old is both generous and not funny.
Everyone who is not humble is either not quiet or not kind and vice versa.
If someone is funny then someone is either happy or quiet and vice versa.
If mary is both funny and wise then someone is not patient or not happy.
If someone is both creative and not funny then fred is both not wise and happy and vice versa.
If paul is tall or humble then alice is either happy or not brave.
Someone is both generous and not old.
Paul is both not calm and brave.
John is not tall.
Fred is either not quiet or curious.
Someone is not tall or kind.
Lucy is either happy or not rich.
Fred is kind or rich.
Someone is not brave or not happy. | Alice is kind. | entailment | (((~wise(alice)&~curious(alice)))=>((~rich(lucy)<~>~humble(lucy))))&
(![X]:((~strong(X)<~>kind(X))<=>(patient(X)<~>~patient(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~calm(X)|calm(X))))&
((~rich(paul))<=>((old(mary)<~>strong(mary))))&
(![X]:((~quiet(X)<~>~brave(X))=>(~quiet(X)<~>~kind(X))))&
((?[X]:((humble(X)|quiet(X))))=>(?[X]:((brave(X)<~>~brave(X)))))&
((?[X]:((funny(X)|old(X))))=>(?[X]:((~curious(X)|~kind(X)))))&
(((~rich(alice)&old(alice)))=>(~quiet(paul)))&
(![X]:((creative(X)&strong(X))<=>~quiet(X)))&
((?[X]:((creative(X)<~>~old(X))))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)|old(X))=>(generous(X)&~funny(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>~kind(X))))&
((?[X]:(funny(X)))<=>(?[X]:((happy(X)<~>quiet(X)))))&
(((funny(mary)&wise(mary)))=>(?[X]:((~patient(X)|~happy(X)))))&
((?[X]:((creative(X)&~funny(X))))<=>((~wise(fred)&happy(fred))))&
(((tall(paul)|humble(paul)))=>((happy(alice)<~>~brave(alice))))&
(?[X]:((generous(X)&~old(X))))&
((~calm(paul)&brave(paul)))&
(~tall(john))&
((~quiet(fred)<~>curious(fred)))&
(?[X]:((~tall(X)|kind(X))))&
((happy(lucy)<~>~rich(lucy)))&
((kind(fred)|rich(fred)))&
(?[X]:((~brave(X)|~happy(X)))) | kind(alice) | [
"p1",
"p2",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6220204663772211542220659
% SZS output start Proof for 6220204663772211542220659
2. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (patient(X0) <~> ~patient(X0))) [input p1]
3. ! [X0] : ((kind(X0) <~> ~generous(X0)) <=> (calm(X0) | ~calm(X0))) [input p2]
9. ! [X0] : ((strong(X0) & creative(X0)) <=> ~quiet(X0)) [input p8]
11. ! [X0] : ((old(X0) | quiet(X0)) => (~funny(X0) & generous(X0))) [input p10]
25. ~kind(alice) [input hypothesis]
40. ! [X0] : ((~funny(X0) & generous(X0)) | (~old(X0) & ~quiet(X0))) [ennf transformation 11]
45. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) & (((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 2]
46. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [nnf transformation 3]
47. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [flattening 46]
57. ! [X0] : (((strong(X0) & creative(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) | ~creative(X0)))) [nnf transformation 9]
58. ! [X0] : (((strong(X0) & creative(X0)) | quiet(X0)) & (~quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 57]
90. kind(X0) | ~strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 45]
91. kind(X0) | ~strong(X0) | patient(X0) | patient(X0) [cnf transformation 45]
96. ~generous(X0) | kind(X0) | calm(X0) [cnf transformation 47]
97. ~calm(X0) | kind(X0) | ~generous(X0) [cnf transformation 47]
117. quiet(X0) | strong(X0) [cnf transformation 58]
122. ~quiet(X0) | generous(X0) [cnf transformation 40]
151. ~kind(alice) [cnf transformation 25]
154. kind(X0) | ~strong(X0) | ~patient(X0) [duplicate literal removal 90]
155. ~strong(X0) | kind(X0) | patient(X0) [duplicate literal removal 91]
177. ~strong(X0) | kind(X0) [subsumption resolution 154,155]
179. ~generous(X0) | kind(X0) [subsumption resolution 96,97]
364. generous(X0) | strong(X0) [resolution 122,117]
544. strong(X0) | kind(X0) [resolution 364,179]
545. kind(X0) [subsumption resolution 544,177]
569. $false [resolution 545,151]
% SZS output end Proof for 6220204663772211542220659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not old then paul is both kind and wise.
If john is not curious then fred is not funny.
Everyone who is not calm is either not patient or wise and vice versa.
If someone is wise then mary is either not creative or not happy and vice versa.
Everyone who is not funny is both not strong and funny and vice versa.
If fred is patient then mary is calm and vice versa.
Everyone who is either old or not calm is either not curious or not funny and vice versa.
Everyone who is rich or calm is either tall or not quiet and vice versa.
Everyone who is either not curious or not kind is funny and vice versa.
Everyone who is either rich or not humble is not happy and vice versa.
If someone is creative then someone is both not tall and not funny and vice versa.
Everyone who is either not brave or not kind is not happy or not creative.
Everyone who is both not quiet and not old is not creative and vice versa.
If someone is not rich or funny then alice is either not brave or not funny.
If lucy is not funny or not kind then someone is either not funny or not wise and vice versa.
Everyone who is not wise is not tall or tall.
Alice is not creative or not brave.
Lucy is calm or curious.
Someone is either not rich or not kind.
Someone is both not calm and rich.
Someone is either old or not brave. | Paul is not quiet. | entailment | ((?[X]:((humble(X)<~>~old(X))))=>((kind(paul)&wise(paul))))&
((~curious(john))=>(~funny(fred)))&
(![X]:(~calm(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:(~funny(X)<=>(~strong(X)&funny(X))))&
((patient(fred))<=>(calm(mary)))&
(![X]:((old(X)<~>~calm(X))<=>(~curious(X)<~>~funny(X))))&
(![X]:((rich(X)|calm(X))<=>(tall(X)<~>~quiet(X))))&
(![X]:((~curious(X)<~>~kind(X))<=>funny(X)))&
(![X]:((rich(X)<~>~humble(X))<=>~happy(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~happy(X)|~creative(X))))&
(![X]:((~quiet(X)&~old(X))<=>~creative(X)))&
((?[X]:((~rich(X)|funny(X))))=>((~brave(alice)<~>~funny(alice))))&
(((~funny(lucy)|~kind(lucy)))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:(~wise(X)=>(~tall(X)|tall(X))))&
((~creative(alice)|~brave(alice)))&
((calm(lucy)|curious(lucy)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((old(X)<~>~brave(X)))) | ~quiet(paul) | [
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1306064422887717607244375
% SZS output start Proof for 1306064422887717607244375
5. ! [X0] : (~funny(X0) <=> (funny(X0) & ~strong(X0))) [input p4]
11. ? [X0] : creative(X0) <=> ? [X0] : (~funny(X0) & ~tall(X0)) [input p10]
13. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> ~creative(X0)) [input p12]
22. quiet(paul) [input hypothesis]
23. ? [X0] : creative(X0) <=> ? [X1] : (~funny(X1) & ~tall(X1)) [rectify 11]
37. ! [X0] : ((~funny(X0) | (~funny(X0) | strong(X0))) & ((funny(X0) & ~strong(X0)) | funny(X0))) [nnf transformation 5]
38. ! [X0] : ((~funny(X0) | ~funny(X0) | strong(X0)) & ((funny(X0) & ~strong(X0)) | funny(X0))) [flattening 37]
45. (? [X0] : creative(X0) | ! [X1] : (funny(X1) | tall(X1))) & (? [X1] : (~funny(X1) & ~tall(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 23]
46. (? [X0] : creative(X0) | ! [X1] : (funny(X1) | tall(X1))) & (? [X2] : (~funny(X2) & ~tall(X2)) | ! [X3] : ~creative(X3)) [rectify 45]
47. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
48. ? [X2] : (~funny(X2) & ~tall(X2)) => (~funny(sK2) & ~tall(sK2)) [choice axiom]
49. (creative(sK1) | ! [X1] : (funny(X1) | tall(X1))) & ((~funny(sK2) & ~tall(sK2)) | ! [X3] : ~creative(X3)) [skolemisation 46,48,47]
51. ! [X0] : (((~old(X0) & ~quiet(X0)) | creative(X0)) & (~creative(X0) | (old(X0) | quiet(X0)))) [nnf transformation 13]
52. ! [X0] : (((~old(X0) & ~quiet(X0)) | creative(X0)) & (~creative(X0) | old(X0) | quiet(X0))) [flattening 51]
81. funny(X0) | funny(X0) [cnf transformation 38]
108. ~funny(sK2) | ~creative(X3) [cnf transformation 49]
113. ~quiet(X0) | creative(X0) [cnf transformation 52]
134. quiet(paul) [cnf transformation 22]
135. funny(X0) [duplicate literal removal 81]
199. ~creative(X3) [subsumption resolution 108,135]
201. ~quiet(X0) [subsumption resolution 113,199]
240. $false [subsumption resolution 134,201]
% SZS output end Proof for 1306064422887717607244375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not kind or generous then mary is not wise or wise and vice versa. If someone is both not wise and generous then paul is either not strong or not patient. If someone is patient then someone is quiet or curious and vice versa. Everyone who is humble is wise or not curious and vice versa. Everyone who is either curious or creative is funny. Everyone who is creative or tall is both not kind and quiet and vice versa. Everyone who is not humble or not creative is either not creative or funny and vice versa. Everyone who is not happy is patient or not creative and vice versa. Everyone who is not humble is tall or happy. Everyone who is not humble is both not rich and patient and vice versa. If someone is both patient and not tall then john is both not quiet and not curious. Everyone who is both kind and not old is either not generous or not creative. Everyone who is both not tall and not strong is both generous and brave and vice versa. If lucy is both not humble and not calm then someone is either curious or humble and vice versa. Everyone who is both tall and not old is both not tall and not generous. If paul is either patient or not kind then someone is rich and vice versa. Someone is both not kind and not wise. Someone is both not curious and rich. Someone is rich or wise. John is not creative or generous. Someone is either not happy or strong. Someone is both humble and not brave. Someone is patient. Someone is quiet or creative. | Susan is not kind. | neutral | (((~kind(susan)|generous(susan)))<=>((~wise(mary)|wise(mary))))&
((?[X]:((~wise(X)&generous(X))))=>((~strong(paul)<~>~patient(paul))))&
((?[X]:(patient(X)))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:(humble(X)<=>(wise(X)|~curious(X))))&
(![X]:((curious(X)<~>creative(X))=>funny(X)))&
(![X]:((creative(X)|tall(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~humble(X)|~creative(X))<=>(~creative(X)<~>funny(X))))&
(![X]:(~happy(X)<=>(patient(X)|~creative(X))))&
(![X]:(~humble(X)=>(tall(X)|happy(X))))&
(![X]:(~humble(X)<=>(~rich(X)&patient(X))))&
((?[X]:((patient(X)&~tall(X))))=>((~quiet(john)&~curious(john))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>~creative(X))))&
(![X]:((~tall(X)&~strong(X))<=>(generous(X)&brave(X))))&
(((~humble(lucy)&~calm(lucy)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((tall(X)&~old(X))=>(~tall(X)&~generous(X))))&
(((patient(paul)<~>~kind(paul)))<=>(?[X]:(rich(X))))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:((~curious(X)&rich(X))))&
(?[X]:((rich(X)|wise(X))))&
((~creative(john)|generous(john)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(patient(X)))&
(?[X]:((quiet(X)|creative(X)))) | ~kind(susan) | [] | null | 0 |
Everyone who is not funny or creative is both curious and happy and vice versa. Everyone who is kind or not old is either not wise or not generous. If someone is creative then paul is either not wise or patient. Everyone who is either humble or not quiet is both happy and not rich. If john is both not patient and not calm then someone is both old and kind. If alice is not calm then someone is both happy and not tall. If someone is strong or calm then paul is both quiet and rich. If someone is either calm or not strong then fred is both not curious and not kind. If someone is happy then paul is either humble or not wise and vice versa. If someone is not wise then alice is both not patient and quiet. If someone is not humble then someone is both generous and not brave. Everyone who is both calm and brave is both not patient and not humble and vice versa. Everyone who is not generous or humble is happy or wise and vice versa. Everyone who is both not wise and not happy is either patient or curious and vice versa. Everyone who is not strong is not humble or humble and vice versa. Everyone who is both not happy and not curious is both calm and brave. Alice is not quiet or not rich. Fred is both old and curious. Lucy is both not old and creative. Someone is not strong. John is happy or generous. Fred is not patient. Someone is not patient or not funny. Someone is not rich or rich. | Fred is not creative. | entailment | (![X]:((~funny(X)|creative(X))<=>(curious(X)&happy(X))))&
(![X]:((kind(X)|~old(X))=>(~wise(X)<~>~generous(X))))&
((?[X]:(creative(X)))=>((~wise(paul)<~>patient(paul))))&
(![X]:((humble(X)<~>~quiet(X))=>(happy(X)&~rich(X))))&
(((~patient(john)&~calm(john)))=>(?[X]:((old(X)&kind(X)))))&
((~calm(alice))=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((strong(X)|calm(X))))=>((quiet(paul)&rich(paul))))&
((?[X]:((calm(X)<~>~strong(X))))=>((~curious(fred)&~kind(fred))))&
((?[X]:(happy(X)))<=>((humble(paul)<~>~wise(paul))))&
((?[X]:(~wise(X)))=>((~patient(alice)&quiet(alice))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((calm(X)&brave(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~generous(X)|humble(X))<=>(happy(X)|wise(X))))&
(![X]:((~wise(X)&~happy(X))<=>(patient(X)<~>curious(X))))&
(![X]:(~strong(X)<=>(~humble(X)|humble(X))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)&brave(X))))&
((~quiet(alice)|~rich(alice)))&
((old(fred)&curious(fred)))&
((~old(lucy)&creative(lucy)))&
(?[X]:(~strong(X)))&
((happy(john)|generous(john)))&
(~patient(fred))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((~rich(X)|rich(X)))) | ~creative(fred) | [
"p0",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1896981739439223937458332
% SZS output start Proof for 1896981739439223937458332
1. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (happy(X0) & curious(X0))) [input p0]
14. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> (patient(X0) <~> curious(X0))) [input p13]
18. curious(fred) & old(fred) [input p17]
22. ~patient(fred) [input p21]
25. creative(fred) [input hypothesis]
40. ! [X0] : (((creative(X0) | ~funny(X0)) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | ~funny(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | (~creative(X0) & funny(X0)))) [flattening 40]
61. ! [X0] : (((~happy(X0) & ~wise(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) & (((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | (happy(X0) | wise(X0)))) [nnf transformation 14]
62. ! [X0] : (((~happy(X0) & ~wise(X0)) | ((patient(X0) | ~curious(X0)) & (curious(X0) | ~patient(X0)))) & (((~curious(X0) | ~patient(X0)) & (curious(X0) | patient(X0))) | happy(X0) | wise(X0))) [flattening 61]
74. ~creative(X0) | happy(X0) [cnf transformation 41]
118. ~happy(X0) | patient(X0) | ~curious(X0) [cnf transformation 62]
126. curious(fred) [cnf transformation 18]
131. ~patient(fred) [cnf transformation 22]
134. creative(fred) [cnf transformation 25]
206. 17 <=> curious(fred) [avatar definition]
207. curious(fred) <- (17) [avatar component clause 206]
259. 17 [avatar split clause 126,206]
287. happy(fred) [resolution 74,134]
364. patient(fred) | ~curious(fred) [resolution 118,287]
371. ~curious(fred) [subsumption resolution 364,131]
372. $false <- (17) [subsumption resolution 371,207]
373. ~17 [avatar contradiction clause 372]
389. $false [avatar sat refutation 259,373]
% SZS output end Proof for 1896981739439223937458332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not kind is funny or not rich. If paul is not rich then paul is not strong or patient and vice versa. Everyone who is both strong and not patient is both creative and happy and vice versa. Everyone who is both not rich and tall is both not old and old. If susan is either generous or old then lucy is both strong and not curious. If lucy is not creative then someone is tall. Everyone who is humble is not generous or not happy and vice versa. If susan is either not brave or creative then alice is not curious. Everyone who is kind is both humble and not brave. If lucy is either not wise or brave then john is brave and vice versa. Everyone who is generous or quiet is old or not generous and vice versa. Everyone who is not brave or not happy is both not quiet and generous. Everyone who is either not wise or not humble is happy. Everyone who is calm is quiet or not calm. If alice is quiet or creative then someone is not quiet or funny and vice versa. Everyone who is creative or not rich is both not brave and old. John is either tall or not tall. John is either not rich or not patient. Susan is both not tall and generous. Someone is both funny and calm. Susan is not happy. John is strong. Someone is either not quiet or not curious. | Alice is old. | neutral | (![X]:((funny(X)&~kind(X))=>(funny(X)|~rich(X))))&
((~rich(paul))<=>((~strong(paul)|patient(paul))))&
(![X]:((strong(X)&~patient(X))<=>(creative(X)&happy(X))))&
(![X]:((~rich(X)&tall(X))=>(~old(X)&old(X))))&
(((generous(susan)<~>old(susan)))=>((strong(lucy)&~curious(lucy))))&
((~creative(lucy))=>(?[X]:(tall(X))))&
(![X]:(humble(X)<=>(~generous(X)|~happy(X))))&
(((~brave(susan)<~>creative(susan)))=>(~curious(alice)))&
(![X]:(kind(X)=>(humble(X)&~brave(X))))&
(((~wise(lucy)<~>brave(lucy)))<=>(brave(john)))&
(![X]:((generous(X)|quiet(X))<=>(old(X)|~generous(X))))&
(![X]:((~brave(X)|~happy(X))=>(~quiet(X)&generous(X))))&
(![X]:((~wise(X)<~>~humble(X))=>happy(X)))&
(![X]:(calm(X)=>(quiet(X)|~calm(X))))&
(((quiet(alice)|creative(alice)))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((creative(X)|~rich(X))=>(~brave(X)&old(X))))&
((tall(john)<~>~tall(john)))&
((~rich(john)<~>~patient(john)))&
((~tall(susan)&generous(susan)))&
(?[X]:((funny(X)&calm(X))))&
(~happy(susan))&
(strong(john))&
(?[X]:((~quiet(X)<~>~curious(X)))) | old(alice) | [] | null | 0 |
Everyone who is not wise or tall is both not rich and not humble and vice versa. Everyone who is either not strong or generous is both funny and brave. If john is brave then someone is either brave or not tall and vice versa. If someone is either patient or not humble then someone is humble or brave. If someone is either old or curious then someone is calm. Everyone who is happy is generous and vice versa. Everyone who is either not curious or patient is not old or rich and vice versa. If someone is generous then someone is both old and not strong. If someone is not quiet then lucy is either not old or not brave and vice versa. Everyone who is curious is not strong and vice versa. If mary is both curious and not calm then someone is not tall and vice versa. Everyone who is both rich and not funny is either tall or not brave and vice versa. Everyone who is not old or not tall is both generous and rich and vice versa. Everyone who is curious or not old is either not kind or not patient and vice versa. If someone is not generous or kind then susan is both curious and strong. If someone is both not old and wise then john is not calm or not curious and vice versa. Someone is not quiet or creative. Someone is funny or tall. Someone is either not calm or tall. | Lucy is funny. | neutral | (![X]:((~wise(X)|tall(X))<=>(~rich(X)&~humble(X))))&
(![X]:((~strong(X)<~>generous(X))=>(funny(X)&brave(X))))&
((brave(john))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)|brave(X)))))&
((?[X]:((old(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((~curious(X)<~>patient(X))<=>(~old(X)|rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~quiet(X)))<=>((~old(lucy)<~>~brave(lucy))))&
(![X]:(curious(X)<=>~strong(X)))&
(((curious(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((rich(X)&~funny(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&rich(X))))&
(![X]:((curious(X)|~old(X))<=>(~kind(X)<~>~patient(X))))&
((?[X]:((~generous(X)|kind(X))))=>((curious(susan)&strong(susan))))&
((?[X]:((~old(X)&wise(X))))<=>((~calm(john)|~curious(john))))&
(?[X]:((~quiet(X)|creative(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:((~calm(X)<~>tall(X)))) | funny(lucy) | [] | null | 0 |
Everyone who is tall is both kind and old. Everyone who is humble or not rich is both not brave and not rich and vice versa. If someone is either not old or tall then someone is both not curious and old and vice versa. Everyone who is not patient or creative is strong or curious and vice versa. If someone is both not funny and old then lucy is either not creative or calm. If someone is either rich or creative then someone is funny. Everyone who is both not quiet and quiet is not kind and vice versa. Everyone who is either not quiet or not curious is calm or not creative and vice versa. Everyone who is either not tall or not calm is both not generous and happy and vice versa. If susan is strong then paul is both not brave and not funny. Everyone who is not funny is both not funny and rich and vice versa. If someone is not brave or not tall then someone is both not generous and not kind. Everyone who is not funny or patient is either quiet or not tall. Everyone who is both patient and not brave is brave. If alice is either not kind or not curious then paul is patient. If someone is either old or not kind then fred is either not creative or not generous and vice versa. Alice is both not funny and not creative. John is tall or brave. Someone is not funny. Someone is both not humble and tall. John is calm. Lucy is either not wise or kind. Mary is not curious or creative. Alice is not calm. | Lucy is old. | entailment | (![X]:(tall(X)=>(kind(X)&old(X))))&
(![X]:((humble(X)|~rich(X))<=>(~brave(X)&~rich(X))))&
((?[X]:((~old(X)<~>tall(X))))<=>(?[X]:((~curious(X)&old(X)))))&
(![X]:((~patient(X)|creative(X))<=>(strong(X)|curious(X))))&
((?[X]:((~funny(X)&old(X))))=>((~creative(lucy)<~>calm(lucy))))&
((?[X]:((rich(X)<~>creative(X))))=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)&quiet(X))<=>~kind(X)))&
(![X]:((~quiet(X)<~>~curious(X))<=>(calm(X)|~creative(X))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~generous(X)&happy(X))))&
((strong(susan))=>((~brave(paul)&~funny(paul))))&
(![X]:(~funny(X)<=>(~funny(X)&rich(X))))&
((?[X]:((~brave(X)|~tall(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:((~funny(X)|patient(X))=>(quiet(X)<~>~tall(X))))&
(![X]:((patient(X)&~brave(X))=>brave(X)))&
(((~kind(alice)<~>~curious(alice)))=>(patient(paul)))&
((?[X]:((old(X)<~>~kind(X))))<=>((~creative(fred)<~>~generous(fred))))&
((~funny(alice)&~creative(alice)))&
((tall(john)|brave(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&tall(X))))&
(calm(john))&
((~wise(lucy)<~>kind(lucy)))&
((~curious(mary)|creative(mary)))&
(~calm(alice)) | old(lucy) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8452775406233992710370499
% SZS output start Proof for 8452775406233992710370499
1. ! [X0] : (tall(X0) => (old(X0) & kind(X0))) [input p0]
7. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> ~kind(X0)) [input p6]
12. ? [X0] : (~tall(X0) | ~brave(X0)) => ? [X0] : (~kind(X0) & ~generous(X0)) [input p11]
25. ~old(lucy) [input hypothesis]
28. ? [X0] : (~tall(X0) | ~brave(X0)) => ? [X1] : (~kind(X1) & ~generous(X1)) [rectify 12]
29. ! [X0] : ((old(X0) & kind(X0)) | ~tall(X0)) [ennf transformation 1]
33. ? [X1] : (~kind(X1) & ~generous(X1)) | ! [X0] : (tall(X0) & brave(X0)) [ennf transformation 28]
52. ! [X0] : (((quiet(X0) & ~quiet(X0)) | kind(X0)) & (~kind(X0) | (~quiet(X0) | quiet(X0)))) [nnf transformation 7]
53. ! [X0] : (((quiet(X0) & ~quiet(X0)) | kind(X0)) & (~kind(X0) | ~quiet(X0) | quiet(X0))) [flattening 52]
60. ? [X0] : (~kind(X0) & ~generous(X0)) | ! [X1] : (tall(X1) & brave(X1)) [rectify 33]
61. ? [X0] : (~kind(X0) & ~generous(X0)) => (~kind(sK3) & ~generous(sK3)) [choice axiom]
62. (~kind(sK3) & ~generous(sK3)) | ! [X1] : (tall(X1) & brave(X1)) [skolemisation 60,61]
75. ~tall(X0) | old(X0) [cnf transformation 29]
96. ~quiet(X0) | kind(X0) [cnf transformation 53]
97. quiet(X0) | kind(X0) [cnf transformation 53]
118. ~kind(sK3) | tall(X1) [cnf transformation 62]
145. ~old(lucy) [cnf transformation 25]
170. 6 <=> ! [X3] : old(X3) [avatar definition]
171. old(X3) <- (6) [avatar component clause 170]
206. kind(X0) [subsumption resolution 96,97]
221. tall(X1) [subsumption resolution 118,206]
273. old(X0) [resolution 75,221]
274. 6 [avatar split clause 273,170]
276. $false <- (6) [resolution 171,145]
277. ~6 [avatar contradiction clause 276]
278. $false [avatar sat refutation 274,277]
% SZS output end Proof for 8452775406233992710370499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich or not funny then someone is both not curious and not rich and vice versa.
If someone is either not curious or not old then fred is tall.
Everyone who is either not patient or strong is not funny or not humble and vice versa.
If someone is not happy then someone is calm or rich.
If paul is both tall and not wise then someone is either not kind or not quiet.
If susan is curious then someone is wise.
If lucy is both not old and not calm then fred is both wise and curious.
If lucy is not calm then lucy is strong.
If someone is both wise and rich then fred is not creative or not quiet.
Everyone who is both creative and funny is both strong and not curious.
Everyone who is either not brave or not calm is not quiet or creative.
Everyone who is either not old or kind is strong or not brave.
If someone is both not patient and tall then fred is either brave or not curious.
Everyone who is not funny or old is either old or not creative and vice versa.
Everyone who is both not funny and not rich is not humble.
Everyone who is either not old or happy is either not quiet or not kind and vice versa.
Susan is both happy and not kind.
Someone is not creative or old.
Someone is either not rich or not happy.
Someone is both not old and strong.
Fred is not calm or happy.
Paul is not tall or not strong.
Susan is either not quiet or not happy. | Paul is not quiet. | neutral | (((~rich(lucy)|~funny(lucy)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>(tall(fred)))&
(![X]:((~patient(X)<~>strong(X))<=>(~funny(X)|~humble(X))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)|rich(X)))))&
(((tall(paul)&~wise(paul)))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((curious(susan))=>(?[X]:(wise(X))))&
(((~old(lucy)&~calm(lucy)))=>((wise(fred)&curious(fred))))&
((~calm(lucy))=>(strong(lucy)))&
((?[X]:((wise(X)&rich(X))))=>((~creative(fred)|~quiet(fred))))&
(![X]:((creative(X)&funny(X))=>(strong(X)&~curious(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(~quiet(X)|creative(X))))&
(![X]:((~old(X)<~>kind(X))=>(strong(X)|~brave(X))))&
((?[X]:((~patient(X)&tall(X))))=>((brave(fred)<~>~curious(fred))))&
(![X]:((~funny(X)|old(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~funny(X)&~rich(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>(~quiet(X)<~>~kind(X))))&
((happy(susan)&~kind(susan)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((~old(X)&strong(X))))&
((~calm(fred)|happy(fred)))&
((~tall(paul)|~strong(paul)))&
((~quiet(susan)<~>~happy(susan))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not funny or calm is funny.
Everyone who is not happy or happy is both not tall and creative.
Everyone who is either rich or not wise is calm or rich and vice versa.
Everyone who is both not brave and not wise is both calm and not wise.
If someone is humble then someone is both calm and patient.
If paul is both not patient and not wise then someone is not wise and vice versa.
Everyone who is both calm and patient is either not happy or not creative and vice versa.
Everyone who is either humble or not funny is happy or patient and vice versa.
If fred is either not creative or not patient then alice is either generous or not happy.
If someone is either not creative or quiet then susan is generous or not happy and vice versa.
If fred is either not patient or kind then mary is both generous and old.
If alice is brave then alice is either not strong or generous and vice versa.
Everyone who is both not patient and quiet is either calm or strong and vice versa.
If someone is either not generous or old then someone is old or strong and vice versa.
Paul is happy.
Someone is either not rich or not wise.
Someone is rich or not happy.
Alice is not old.
Fred is not generous or not curious.
Alice is not calm. | Mary is not generous. | neutral | (![X]:((~funny(X)|calm(X))=>funny(X)))&
(![X]:((~happy(X)|happy(X))=>(~tall(X)&creative(X))))&
(![X]:((rich(X)<~>~wise(X))<=>(calm(X)|rich(X))))&
(![X]:((~brave(X)&~wise(X))=>(calm(X)&~wise(X))))&
((?[X]:(humble(X)))=>(?[X]:((calm(X)&patient(X)))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(happy(X)|patient(X))))&
(((~creative(fred)<~>~patient(fred)))=>((generous(alice)<~>~happy(alice))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((generous(susan)|~happy(susan))))&
(((~patient(fred)<~>kind(fred)))=>((generous(mary)&old(mary))))&
((brave(alice))<=>((~strong(alice)<~>generous(alice))))&
(![X]:((~patient(X)&quiet(X))<=>(calm(X)<~>strong(X))))&
((?[X]:((~generous(X)<~>old(X))))<=>(?[X]:((old(X)|strong(X)))))&
(happy(paul))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:((rich(X)|~happy(X))))&
(~old(alice))&
((~generous(fred)|~curious(fred)))&
(~calm(alice)) | ~generous(mary) | [] | null | 0 |
Everyone who is happy or funny is either not calm or rich and vice versa. Everyone who is either not calm or not strong is either not rich or kind and vice versa. Everyone who is either quiet or not humble is either not rich or not patient and vice versa. If someone is either calm or tall then paul is old or not funny and vice versa. Everyone who is wise is either generous or not quiet. If john is not brave then susan is not funny or tall. If lucy is patient or not brave then someone is not funny or not patient. Everyone who is both not wise and not funny is not wise. If someone is either not tall or not kind then someone is either humble or not kind and vice versa. If someone is both not brave and not generous then paul is brave or not strong. Everyone who is strong or creative is either patient or not brave. If paul is either not happy or not rich then paul is either creative or humble and vice versa. Everyone who is either not wise or wise is both not happy and rich and vice versa. If someone is either calm or not funny then john is not humble or not tall and vice versa. Everyone who is not kind or quiet is both strong and patient and vice versa. Everyone who is both funny and calm is tall or not funny. Paul is brave or creative. Lucy is not happy. Fred is patient. Lucy is either not strong or humble. Fred is generous. John is either not patient or not brave. Someone is not rich or patient. John is curious or old. | John is funny. | entailment | (![X]:((happy(X)|funny(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~rich(X)<~>kind(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(~rich(X)<~>~patient(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>((old(paul)|~funny(paul))))&
(![X]:(wise(X)=>(generous(X)<~>~quiet(X))))&
((~brave(john))=>((~funny(susan)|tall(susan))))&
(((patient(lucy)|~brave(lucy)))=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~wise(X)&~funny(X))=>~wise(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((~brave(X)&~generous(X))))=>((brave(paul)|~strong(paul))))&
(![X]:((strong(X)|creative(X))=>(patient(X)<~>~brave(X))))&
(((~happy(paul)<~>~rich(paul)))<=>((creative(paul)<~>humble(paul))))&
(![X]:((~wise(X)<~>wise(X))<=>(~happy(X)&rich(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~humble(john)|~tall(john))))&
(![X]:((~kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((funny(X)&calm(X))=>(tall(X)|~funny(X))))&
((brave(paul)|creative(paul)))&
(~happy(lucy))&
(patient(fred))&
((~strong(lucy)<~>humble(lucy)))&
(generous(fred))&
((~patient(john)<~>~brave(john)))&
(?[X]:((~rich(X)|patient(X))))&
((curious(john)|old(john))) | funny(john) | [
"p0",
"p1",
"p10",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8038026794753197866284075
% SZS output start Proof for 8038026794753197866284075
1. ! [X0] : ((funny(X0) | happy(X0)) <=> (~calm(X0) <~> rich(X0))) [input p0]
2. ! [X0] : ((~calm(X0) <~> ~strong(X0)) <=> (~rich(X0) <~> kind(X0))) [input p1]
11. ! [X0] : ((creative(X0) | strong(X0)) => (patient(X0) <~> ~brave(X0))) [input p10]
13. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) & ~happy(X0))) [input p12]
15. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> (patient(X0) & strong(X0))) [input p14]
22. ~patient(john) <~> ~brave(john) [input p21]
25. ~funny(john) [input hypothesis]
36. ! [X0] : ((patient(X0) <~> ~brave(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 11]
39. ! [X0] : (((funny(X0) | happy(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~funny(X0) & ~happy(X0)))) [nnf transformation 1]
40. ! [X0] : ((funny(X0) | happy(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~funny(X0) & ~happy(X0)))) [flattening 39]
41. ! [X0] : ((((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0)))) & (((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0))))) [nnf transformation 2]
56. ! [X0] : (((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (~creative(X0) & ~strong(X0))) [nnf transformation 36]
58. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 13]
59. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 58]
65. ! [X0] : (((quiet(X0) | ~kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & kind(X0)))) [nnf transformation 15]
66. ! [X0] : ((quiet(X0) | ~kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & kind(X0)))) [flattening 65]
68. (brave(john) | patient(john)) & (~brave(john) | ~patient(john)) [nnf transformation 22]
76. ~rich(X0) | happy(X0) | ~calm(X0) | funny(X0) [cnf transformation 40]
84. ~kind(X0) | calm(X0) | ~rich(X0) | strong(X0) [cnf transformation 41]
114. ~brave(X0) | patient(X0) | ~strong(X0) [cnf transformation 56]
116. ~patient(X0) | brave(X0) | ~strong(X0) [cnf transformation 56]
126. ~happy(X0) | wise(X0) | wise(X0) [cnf transformation 59]
127. ~happy(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 59]
128. rich(X0) | wise(X0) | wise(X0) [cnf transformation 59]
129. rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 59]
138. kind(X0) | strong(X0) [cnf transformation 66]
150. ~brave(john) | ~patient(john) [cnf transformation 68]
151. brave(john) | patient(john) [cnf transformation 68]
153. ~funny(john) [cnf transformation 25]
155. ~happy(X0) | wise(X0) [duplicate literal removal 126]
156. ~wise(X0) | ~happy(X0) [duplicate literal removal 127]
157. rich(X0) | wise(X0) [duplicate literal removal 128]
158. ~wise(X0) | rich(X0) [duplicate literal removal 129]
188. 7 <=> brave(john) [avatar definition]
189. ~brave(john) <- (~7) [avatar component clause 188]
190. brave(john) <- (7) [avatar component clause 188]
290. rich(X0) [subsumption resolution 157,158]
291. ~happy(X0) [subsumption resolution 155,156]
332. 37 <=> patient(john) [avatar definition]
333. ~patient(john) <- (~37) [avatar component clause 332]
334. patient(john) <- (37) [avatar component clause 332]
335. 37 | 7 [avatar split clause 151,188,332]
336. ~37 | ~7 [avatar split clause 150,188,332]
358. patient(john) | ~strong(john) <- (7) [resolution 114,190]
360. ~strong(john) <- (7, ~37) [subsumption resolution 358,333]
395. happy(X1) | ~calm(X1) | funny(X1) [resolution 76,290]
397. ~calm(X1) | funny(X1) [subsumption resolution 395,291]
486. calm(X1) | ~rich(X1) | strong(X1) | strong(X1) [resolution 84,138]
490. calm(X1) | ~rich(X1) | strong(X1) [duplicate literal removal 486]
492. strong(X1) | calm(X1) [subsumption resolution 490,290]
496. calm(john) <- (7, ~37) [resolution 492,360]
687. funny(john) <- (7, ~37) [resolution 496,397]
692. $false <- (7, ~37) [subsumption resolution 687,153]
693. ~7 | 37 [avatar contradiction clause 692]
709. brave(john) | ~strong(john) <- (37) [resolution 334,116]
712. 60 <=> strong(john) [avatar definition]
714. ~strong(john) <- (~60) [avatar component clause 712]
719. ~strong(john) <- (~7, 37) [subsumption resolution 709,189]
720. ~60 | 7 | ~37 [avatar split clause 719,332,188,712]
721. calm(john) <- (~60) [resolution 714,492]
744. funny(john) <- (~60) [resolution 721,397]
750. $false <- (~60) [subsumption resolution 744,153]
751. 60 [avatar contradiction clause 750]
752. $false [avatar sat refutation 335,336,693,720,751]
% SZS output end Proof for 8038026794753197866284075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not funny is either not brave or not calm.
Everyone who is rich or not rich is either creative or happy and vice versa.
If fred is either not quiet or generous then lucy is humble.
If mary is not generous or curious then someone is both not creative and tall and vice versa.
Everyone who is either curious or wise is either not old or brave and vice versa.
Everyone who is happy is both not curious and not tall.
If lucy is either old or not funny then paul is both happy and curious and vice versa.
If paul is either patient or not wise then lucy is not calm.
If someone is kind or not brave then someone is both rich and not generous.
Everyone who is not strong or wise is either quiet or curious and vice versa.
If john is both rich and not brave then mary is not quiet or strong.
Everyone who is wise is either quiet or not curious and vice versa.
If someone is either not rich or calm then someone is not strong and vice versa.
If susan is not brave or not curious then alice is not wise and vice versa.
Everyone who is not brave is not kind or not patient.
If someone is creative then susan is either not kind or quiet.
Alice is either brave or calm.
Someone is not rich.
Susan is not tall.
Susan is either happy or brave.
Mary is quiet.
Susan is either not strong or not calm.
Someone is rich.
Fred is either funny or calm. | Lucy is wise. | contradiction | (![X]:((~creative(X)<~>~funny(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(creative(X)<~>happy(X))))&
(((~quiet(fred)<~>generous(fred)))=>(humble(lucy)))&
(((~generous(mary)|curious(mary)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((curious(X)<~>wise(X))<=>(~old(X)<~>brave(X))))&
(![X]:(happy(X)=>(~curious(X)&~tall(X))))&
(((old(lucy)<~>~funny(lucy)))<=>((happy(paul)&curious(paul))))&
(((patient(paul)<~>~wise(paul)))=>(~calm(lucy)))&
((?[X]:((kind(X)|~brave(X))))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~strong(X)|wise(X))<=>(quiet(X)<~>curious(X))))&
(((rich(john)&~brave(john)))=>((~quiet(mary)|strong(mary))))&
(![X]:(wise(X)<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(~strong(X))))&
(((~brave(susan)|~curious(susan)))<=>(~wise(alice)))&
(![X]:(~brave(X)=>(~kind(X)|~patient(X))))&
((?[X]:(creative(X)))=>((~kind(susan)<~>quiet(susan))))&
((brave(alice)<~>calm(alice)))&
(?[X]:(~rich(X)))&
(~tall(susan))&
((happy(susan)<~>brave(susan)))&
(quiet(mary))&
((~strong(susan)<~>~calm(susan)))&
(?[X]:(rich(X)))&
((funny(fred)<~>calm(fred))) | wise(lucy) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 437989449081933618230743
% SZS output start Proof for 437989449081933618230743
10. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (quiet(X0) <~> curious(X0))) [input p9]
12. ! [X0] : (wise(X0) <=> (quiet(X0) <~> ~curious(X0))) [input p11]
25. wise(lucy) [input hypothesis]
53. ! [X0] : (((wise(X0) | ~strong(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [nnf transformation 10]
54. ! [X0] : ((wise(X0) | ~strong(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [flattening 53]
55. ! [X0] : ((wise(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) & (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ~wise(X0))) [nnf transformation 12]
110. curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 54]
112. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 54]
116. ~curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 55]
117. curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 55]
118. wise(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 55]
142. wise(lucy) [cnf transformation 25]
239. ~curious(X0) | ~quiet(X0) [subsumption resolution 118,112]
240. ~wise(X0) | curious(X0) [subsumption resolution 117,110]
241. ~wise(X0) | quiet(X0) [subsumption resolution 116,110]
350. curious(lucy) [resolution 240,142]
352. quiet(lucy) [resolution 241,142]
354. ~quiet(lucy) [resolution 350,239]
356. $false [subsumption resolution 354,352]
% SZS output end Proof for 437989449081933618230743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not generous and wise.
If someone is not patient or not rich then john is not happy or patient.
If someone is both old and not brave then someone is kind or not creative and vice versa.
If someone is both wise and not rich then alice is not tall and vice versa.
If lucy is either wise or not brave then someone is not quiet.
If someone is either not wise or not funny then someone is both tall and quiet.
If mary is not kind or not patient then someone is humble or not generous.
If someone is either kind or not curious then susan is happy or not generous.
If someone is both not tall and not wise then someone is both creative and quiet and vice versa.
If john is either humble or not patient then someone is not generous or not rich.
If someone is wise or not curious then someone is patient or not wise and vice versa.
If paul is either not strong or quiet then mary is not old.
If john is patient then paul is either not happy or not creative.
If someone is either kind or not brave then someone is not quiet or kind and vice versa.
Everyone who is either not curious or rich is either not funny or creative and vice versa.
If paul is quiet or not wise then lucy is either old or not old.
Someone is both not calm and not humble.
Fred is either not creative or not old.
John is either not creative or strong.
Someone is both not happy and not funny.
Someone is old.
Someone is kind.
Someone is both creative and kind.
Alice is either not rich or strong. | Susan is happy. | neutral | (![X]:(generous(X)=>(~generous(X)&wise(X))))&
((?[X]:((~patient(X)|~rich(X))))=>((~happy(john)|patient(john))))&
((?[X]:((old(X)&~brave(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((wise(X)&~rich(X))))<=>(~tall(alice)))&
(((wise(lucy)<~>~brave(lucy)))=>(?[X]:(~quiet(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>(?[X]:((tall(X)&quiet(X)))))&
(((~kind(mary)|~patient(mary)))=>(?[X]:((humble(X)|~generous(X)))))&
((?[X]:((kind(X)<~>~curious(X))))=>((happy(susan)|~generous(susan))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((creative(X)&quiet(X)))))&
(((humble(john)<~>~patient(john)))=>(?[X]:((~generous(X)|~rich(X)))))&
((?[X]:((wise(X)|~curious(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~strong(paul)<~>quiet(paul)))=>(~old(mary)))&
((patient(john))=>((~happy(paul)<~>~creative(paul))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~funny(X)<~>creative(X))))&
(((quiet(paul)|~wise(paul)))=>((old(lucy)<~>~old(lucy))))&
(?[X]:((~calm(X)&~humble(X))))&
((~creative(fred)<~>~old(fred)))&
((~creative(john)<~>strong(john)))&
(?[X]:((~happy(X)&~funny(X))))&
(?[X]:(old(X)))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)&kind(X))))&
((~rich(alice)<~>strong(alice))) | happy(susan) | [] | null | 0 |
Everyone who is generous is either not generous or humble and vice versa.
Everyone who is tall or humble is either not calm or generous and vice versa.
Everyone who is strong is quiet.
If someone is not generous or not funny then paul is either not strong or not creative.
If mary is rich or not wise then susan is either not rich or not funny and vice versa.
Everyone who is both curious and not old is not quiet and vice versa.
If fred is either not wise or humble then alice is not kind or not happy and vice versa.
If fred is strong then someone is either not kind or wise and vice versa.
Everyone who is both not generous and not curious is humble or wise and vice versa.
Everyone who is both wise and not wise is both old and funny.
Everyone who is both not rich and funny is not wise or happy.
If someone is generous then someone is brave and vice versa.
Everyone who is not old is both not strong and not kind.
If alice is both not tall and not funny then someone is not patient and vice versa.
If someone is rich then lucy is both rich and not wise and vice versa.
If paul is either not kind or happy then paul is either brave or not patient and vice versa.
Paul is both not funny and not calm.
John is not tall.
Someone is funny or not tall.
Someone is both tall and not rich.
Alice is old or not calm.
Someone is wise or quiet.
Someone is both not tall and not calm. | John is generous. | contradiction | (![X]:(generous(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((tall(X)|humble(X))<=>(~calm(X)<~>generous(X))))&
(![X]:(strong(X)=>quiet(X)))&
((?[X]:((~generous(X)|~funny(X))))=>((~strong(paul)<~>~creative(paul))))&
(((rich(mary)|~wise(mary)))<=>((~rich(susan)<~>~funny(susan))))&
(![X]:((curious(X)&~old(X))<=>~quiet(X)))&
(((~wise(fred)<~>humble(fred)))<=>((~kind(alice)|~happy(alice))))&
((strong(fred))<=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:((~generous(X)&~curious(X))<=>(humble(X)|wise(X))))&
(![X]:((wise(X)&~wise(X))=>(old(X)&funny(X))))&
(![X]:((~rich(X)&funny(X))=>(~wise(X)|happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:(brave(X))))&
(![X]:(~old(X)=>(~strong(X)&~kind(X))))&
(((~tall(alice)&~funny(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:(rich(X)))<=>((rich(lucy)&~wise(lucy))))&
(((~kind(paul)<~>happy(paul)))<=>((brave(paul)<~>~patient(paul))))&
((~funny(paul)&~calm(paul)))&
(~tall(john))&
(?[X]:((funny(X)|~tall(X))))&
(?[X]:((tall(X)&~rich(X))))&
((old(alice)|~calm(alice)))&
(?[X]:((wise(X)|quiet(X))))&
(?[X]:((~tall(X)&~calm(X)))) | generous(john) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 170080320862598229066169
% SZS output start Proof for 170080320862598229066169
1. ! [X0] : (generous(X0) <=> (~generous(X0) <~> humble(X0))) [input p0]
9. ! [X0] : ((~curious(X0) & ~generous(X0)) <=> (wise(X0) | humble(X0))) [input p8]
24. generous(john) [input hypothesis]
38. ! [X0] : ((generous(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ~generous(X0))) [nnf transformation 1]
50. ! [X0] : (((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | (curious(X0) | generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | curious(X0) | generous(X0))) [flattening 50]
74. humble(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 38]
76. generous(X0) | humble(X0) | generous(X0) [cnf transformation 38]
105. ~generous(X0) | ~humble(X0) [cnf transformation 51]
135. generous(john) [cnf transformation 24]
136. humble(X0) | ~generous(X0) [duplicate literal removal 74]
137. generous(X0) | humble(X0) [duplicate literal removal 76]
138. humble(X0) [subsumption resolution 136,137]
222. ~generous(X0) [subsumption resolution 105,138]
289. $false [subsumption resolution 135,222]
% SZS output end Proof for 170080320862598229066169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both quiet and old then susan is both humble and not tall and vice versa.
If someone is not patient then susan is both not generous and calm.
If someone is wise then someone is not quiet.
Everyone who is not brave or not happy is either patient or not creative and vice versa.
Everyone who is not patient or patient is either not old or not curious.
If john is both calm and not patient then mary is both rich and brave.
If someone is both not kind and patient then someone is curious and vice versa.
Everyone who is patient is rich or not generous and vice versa.
If paul is both brave and kind then susan is both not kind and humble and vice versa.
Everyone who is either tall or not calm is wise and vice versa.
Everyone who is either not tall or humble is either calm or not kind.
Everyone who is both generous and humble is not rich or happy and vice versa.
Everyone who is both not tall and calm is either not generous or not quiet.
Everyone who is not funny is either not brave or not rich.
If alice is either not wise or curious then someone is both not quiet and humble.
Fred is either brave or not patient.
Someone is both tall and kind.
Mary is both patient and not calm.
Mary is not old or quiet.
Someone is both not old and strong.
Mary is both not calm and wise.
Someone is either not generous or curious.
Susan is funny. | Mary is not rich. | contradiction | (((quiet(john)&old(john)))<=>((humble(susan)&~tall(susan))))&
((?[X]:(~patient(X)))=>((~generous(susan)&calm(susan))))&
((?[X]:(wise(X)))=>(?[X]:(~quiet(X))))&
(![X]:((~brave(X)|~happy(X))<=>(patient(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))=>(~old(X)<~>~curious(X))))&
(((calm(john)&~patient(john)))=>((rich(mary)&brave(mary))))&
((?[X]:((~kind(X)&patient(X))))<=>(?[X]:(curious(X))))&
(![X]:(patient(X)<=>(rich(X)|~generous(X))))&
(((brave(paul)&kind(paul)))<=>((~kind(susan)&humble(susan))))&
(![X]:((tall(X)<~>~calm(X))<=>wise(X)))&
(![X]:((~tall(X)<~>humble(X))=>(calm(X)<~>~kind(X))))&
(![X]:((generous(X)&humble(X))<=>(~rich(X)|happy(X))))&
(![X]:((~tall(X)&calm(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~brave(X)<~>~rich(X))))&
(((~wise(alice)<~>curious(alice)))=>(?[X]:((~quiet(X)&humble(X)))))&
((brave(fred)<~>~patient(fred)))&
(?[X]:((tall(X)&kind(X))))&
((patient(mary)&~calm(mary)))&
((~old(mary)|quiet(mary)))&
(?[X]:((~old(X)&strong(X))))&
((~calm(mary)&wise(mary)))&
(?[X]:((~generous(X)<~>curious(X))))&
(funny(susan)) | ~rich(mary) | [
"p7",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 41416952982566107881169
% SZS output start Proof for 41416952982566107881169
8. ! [X0] : (patient(X0) <=> (~generous(X0) | rich(X0))) [input p7]
12. ! [X0] : ((humble(X0) & generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p11]
18. ~calm(mary) & patient(mary) [input p17]
24. ~rich(mary) [input hypothesis]
52. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & ((~generous(X0) | rich(X0)) | ~patient(X0))) [nnf transformation 8]
53. ! [X0] : ((patient(X0) | (generous(X0) & ~rich(X0))) & (~generous(X0) | rich(X0) | ~patient(X0))) [flattening 52]
58. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 12]
59. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ~humble(X0) | ~generous(X0))) [flattening 58]
94. ~generous(X0) | rich(X0) | ~patient(X0) [cnf transformation 53]
110. rich(X0) | generous(X0) [cnf transformation 59]
124. patient(mary) [cnf transformation 18]
132. ~rich(mary) [cnf transformation 24]
190. 13 <=> rich(mary) [avatar definition]
191. ~rich(mary) <- (~13) [avatar component clause 190]
280. ~13 [avatar split clause 132,190]
287. generous(mary) <- (~13) [resolution 110,191]
394. rich(mary) | ~patient(mary) <- (~13) [resolution 94,287]
396. ~patient(mary) <- (~13) [subsumption resolution 394,191]
397. $false <- (~13) [subsumption resolution 396,124]
398. 13 [avatar contradiction clause 397]
408. $false [avatar sat refutation 280,398]
% SZS output end Proof for 41416952982566107881169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or kind is both not quiet and creative and vice versa.
Everyone who is not quiet or patient is both generous and not calm and vice versa.
If someone is humble then someone is not calm or not old and vice versa.
Everyone who is both not old and strong is either kind or tall.
If someone is brave or quiet then someone is rich or not funny.
If someone is both not calm and strong then someone is either not patient or not calm and vice versa.
Everyone who is either tall or not brave is not funny or curious.
Everyone who is either not strong or creative is old or not old and vice versa.
If someone is either patient or generous then lucy is not curious or not tall and vice versa.
If someone is either not kind or calm then paul is both old and generous.
If fred is either not generous or not tall then fred is humble.
Everyone who is humble or kind is either not generous or not kind and vice versa.
If mary is funny or not curious then someone is both not generous and happy.
If alice is both patient and not patient then someone is tall or not brave.
If fred is both humble and not quiet then john is not wise or kind.
If lucy is not kind or not wise then lucy is either humble or not old.
Someone is patient or not old.
Lucy is either funny or old.
Alice is both happy and brave.
Susan is either not calm or tall.
Someone is either not rich or not tall.
Susan is not creative.
Someone is either not happy or not calm.
Fred is patient. | Paul is not generous. | contradiction | (![X]:((~funny(X)|kind(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~quiet(X)|patient(X))<=>(generous(X)&~calm(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~calm(X)|~old(X)))))&
(![X]:((~old(X)&strong(X))=>(kind(X)<~>tall(X))))&
((?[X]:((brave(X)|quiet(X))))=>(?[X]:((rich(X)|~funny(X)))))&
((?[X]:((~calm(X)&strong(X))))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
(![X]:((tall(X)<~>~brave(X))=>(~funny(X)|curious(X))))&
(![X]:((~strong(X)<~>creative(X))<=>(old(X)|~old(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>((~curious(lucy)|~tall(lucy))))&
((?[X]:((~kind(X)<~>calm(X))))=>((old(paul)&generous(paul))))&
(((~generous(fred)<~>~tall(fred)))=>(humble(fred)))&
(![X]:((humble(X)|kind(X))<=>(~generous(X)<~>~kind(X))))&
(((funny(mary)|~curious(mary)))=>(?[X]:((~generous(X)&happy(X)))))&
(((patient(alice)&~patient(alice)))=>(?[X]:((tall(X)|~brave(X)))))&
(((humble(fred)&~quiet(fred)))=>((~wise(john)|kind(john))))&
(((~kind(lucy)|~wise(lucy)))=>((humble(lucy)<~>~old(lucy))))&
(?[X]:((patient(X)|~old(X))))&
((funny(lucy)<~>old(lucy)))&
((happy(alice)&brave(alice)))&
((~calm(susan)<~>tall(susan)))&
(?[X]:((~rich(X)<~>~tall(X))))&
(~creative(susan))&
(?[X]:((~happy(X)<~>~calm(X))))&
(patient(fred)) | ~generous(paul) | [
"p0",
"p1",
"p9",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6100812325139881886483714
% SZS output start Proof for 6100812325139881886483714
1. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (creative(X0) & ~quiet(X0))) [input p0]
2. ! [X0] : ((patient(X0) | ~quiet(X0)) <=> (~calm(X0) & generous(X0))) [input p1]
10. ? [X0] : (~kind(X0) <~> calm(X0)) => (generous(paul) & old(paul)) [input p9]
12. ! [X0] : ((kind(X0) | humble(X0)) <=> (~generous(X0) <~> ~kind(X0))) [input p11]
24. patient(fred) [input p23]
25. ~generous(paul) [input hypothesis]
34. (generous(paul) & old(paul)) | ! [X0] : (~kind(X0) <=> calm(X0)) [ennf transformation 10]
42. ! [X0] : (((kind(X0) | ~funny(X0)) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | (~kind(X0) & funny(X0)))) [nnf transformation 1]
43. ! [X0] : ((kind(X0) | ~funny(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | (~kind(X0) & funny(X0)))) [flattening 42]
44. ! [X0] : (((patient(X0) | ~quiet(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (~patient(X0) & quiet(X0)))) [nnf transformation 2]
45. ! [X0] : ((patient(X0) | ~quiet(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (~patient(X0) & quiet(X0)))) [flattening 44]
68. (generous(paul) & old(paul)) | ! [X0] : ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))) [nnf transformation 34]
70. ! [X0] : (((kind(X0) | humble(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~kind(X0) & ~humble(X0)))) [nnf transformation 12]
71. ! [X0] : ((kind(X0) | humble(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~kind(X0) & ~humble(X0)))) [flattening 70]
88. ~quiet(X0) | ~kind(X0) [cnf transformation 43]
92. generous(X0) | quiet(X0) [cnf transformation 45]
95. ~calm(X0) | ~patient(X0) [cnf transformation 45]
126. generous(paul) | calm(X0) | kind(X0) [cnf transformation 68]
131. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 71]
158. patient(fred) [cnf transformation 24]
159. ~generous(paul) [cnf transformation 25]
160. ~generous(X0) | ~kind(X0) [duplicate literal removal 131]
204. 11 <=> ! [X1] : ~patient(X1) [avatar definition]
205. ~patient(X1) <- (11) [avatar component clause 204]
270. 24 <=> generous(paul) [avatar definition]
275. 25 <=> ! [X0] : (calm(X0) | kind(X0)) [avatar definition]
276. calm(X0) | kind(X0) <- (25) [avatar component clause 275]
277. 25 | 24 [avatar split clause 126,270,275]
396. ~24 [avatar split clause 159,270]
405. ~kind(X0) | quiet(X0) [resolution 160,92]
407. ~kind(X0) [subsumption resolution 405,88]
411. $false <- (11) [resolution 205,158]
412. ~11 [avatar contradiction clause 411]
420. kind(X2) | ~patient(X2) <- (25) [resolution 276,95]
427. ~patient(X2) <- (25) [subsumption resolution 420,407]
428. 11 | ~25 [avatar split clause 427,275,204]
436. $false [avatar sat refutation 277,396,412,428]
% SZS output end Proof for 6100812325139881886483714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not humble.
Everyone who is curious is not quiet or strong.
Everyone who is old is rich and vice versa.
Everyone who is brave or happy is wise and vice versa.
If alice is both old and not creative then mary is not calm or not strong.
Everyone who is curious is creative and vice versa.
Everyone who is not happy is both not rich and not generous.
If mary is creative then someone is either old or not rich.
Everyone who is curious or quiet is both not patient and not tall.
Everyone who is not rich is either calm or wise.
If someone is both calm and not generous then someone is both not happy and not generous.
If someone is not wise or not quiet then someone is not old.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
If someone is not quiet then someone is strong and vice versa.
If someone is either not brave or curious then someone is both happy and not creative.
Someone is either not funny or generous.
Lucy is creative or not tall.
Mary is either quiet or not wise.
Paul is happy or not kind.
Susan is either not quiet or not funny.
Someone is not happy or not humble.
Someone is kind or not patient. | Lucy is quiet. | entailment | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~humble(X)))&
(![X]:(curious(X)=>(~quiet(X)|strong(X))))&
(![X]:(old(X)<=>rich(X)))&
(![X]:((brave(X)|happy(X))<=>wise(X)))&
(((old(alice)&~creative(alice)))=>((~calm(mary)|~strong(mary))))&
(![X]:(curious(X)<=>creative(X)))&
(![X]:(~happy(X)=>(~rich(X)&~generous(X))))&
((creative(mary))=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((curious(X)|quiet(X))=>(~patient(X)&~tall(X))))&
(![X]:(~rich(X)=>(calm(X)<~>wise(X))))&
((?[X]:((calm(X)&~generous(X))))=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:(~old(X))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(?[X]:((~funny(X)<~>generous(X))))&
((creative(lucy)|~tall(lucy)))&
((quiet(mary)<~>~wise(mary)))&
((happy(paul)|~kind(paul)))&
((~quiet(susan)<~>~funny(susan)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((kind(X)|~patient(X)))) | quiet(lucy) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1085655071036471956842751
% SZS output start Proof for 1085655071036471956842751
1. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~strong(X0)) [input p0]
15. ? [X0] : ~quiet(X0) <=> ? [X0] : strong(X0) [input p14]
24. ~quiet(lucy) [input hypothesis]
27. ? [X0] : ~quiet(X0) <=> ? [X1] : strong(X1) [rectify 15]
43. ! [X0] : (((~humble(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 1]
44. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (humble(X0) & ~humble(X0)))) [flattening 43]
65. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : quiet(X0)) [nnf transformation 27]
66. (? [X0] : ~quiet(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : quiet(X3)) [rectify 65]
67. ? [X0] : ~quiet(X0) => ~quiet(sK4) [choice axiom]
68. ? [X2] : strong(X2) => strong(sK5) [choice axiom]
69. (~quiet(sK4) | ! [X1] : ~strong(X1)) & (strong(sK5) | ! [X3] : quiet(X3)) [skolemisation 66,68,67]
81. ~strong(X0) | ~humble(X0) [cnf transformation 44]
82. ~strong(X0) | humble(X0) [cnf transformation 44]
113. strong(sK5) | quiet(X3) [cnf transformation 69]
128. ~quiet(lucy) [cnf transformation 24]
129. ~strong(X0) [subsumption resolution 81,82]
145. 4 <=> ! [X1] : quiet(X1) [avatar definition]
146. quiet(X1) <- (4) [avatar component clause 145]
180. quiet(X3) [subsumption resolution 113,129]
181. 4 [avatar split clause 180,145]
257. $false <- (4) [resolution 146,128]
258. ~4 [avatar contradiction clause 257]
259. $false [avatar sat refutation 181,258]
% SZS output end Proof for 1085655071036471956842751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or happy then paul is both humble and not kind.
If someone is not kind then someone is both not humble and old and vice versa.
If lucy is not old then someone is both quiet and not quiet and vice versa.
If paul is both wise and not patient then someone is old or calm and vice versa.
If mary is brave or not curious then someone is both not happy and not curious.
If paul is not kind then mary is calm or strong.
Everyone who is either curious or not happy is either rich or wise and vice versa.
Everyone who is both tall and not wise is both patient and quiet.
If someone is both not happy and kind then alice is both brave and not humble.
Everyone who is not strong is kind.
Everyone who is funny or generous is both brave and generous and vice versa.
Everyone who is brave is not happy.
Everyone who is tall is brave.
If someone is generous then john is old.
If alice is either humble or not wise then someone is not kind and vice versa.
Everyone who is either not strong or not kind is not rich or not strong and vice versa.
Someone is both not curious and not strong.
John is both not humble and not tall.
Someone is not strong or not calm.
Someone is not kind.
Someone is not funny.
Alice is both brave and not creative.
Someone is either not kind or strong.
Someone is both wise and humble. | Paul is not wise. | contradiction | (((wise(mary)<~>happy(mary)))=>((humble(paul)&~kind(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((~humble(X)&old(X)))))&
((~old(lucy))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(((wise(paul)&~patient(paul)))<=>(?[X]:((old(X)|calm(X)))))&
(((brave(mary)|~curious(mary)))=>(?[X]:((~happy(X)&~curious(X)))))&
((~kind(paul))=>((calm(mary)|strong(mary))))&
(![X]:((curious(X)<~>~happy(X))<=>(rich(X)<~>wise(X))))&
(![X]:((tall(X)&~wise(X))=>(patient(X)&quiet(X))))&
((?[X]:((~happy(X)&kind(X))))=>((brave(alice)&~humble(alice))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((funny(X)|generous(X))<=>(brave(X)&generous(X))))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(tall(X)=>brave(X)))&
((?[X]:(generous(X)))=>(old(john)))&
(((humble(alice)<~>~wise(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~rich(X)|~strong(X))))&
(?[X]:((~curious(X)&~strong(X))))&
((~humble(john)&~tall(john)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~funny(X)))&
((brave(alice)&~creative(alice)))&
(?[X]:((~kind(X)<~>strong(X))))&
(?[X]:((wise(X)&humble(X)))) | ~wise(paul) | [
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5251028043302654493675834
% SZS output start Proof for 5251028043302654493675834
3. ~old(lucy) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p2]
4. (~patient(paul) & wise(paul)) <=> ? [X0] : (calm(X0) | old(X0)) [input p3]
25. ~wise(paul) [input hypothesis]
45. (~old(lucy) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X0] : (~quiet(X0) & quiet(X0)) | old(lucy)) [nnf transformation 3]
46. (~old(lucy) | ! [X0] : (quiet(X0) | ~quiet(X0))) & (? [X1] : (~quiet(X1) & quiet(X1)) | old(lucy)) [rectify 45]
47. ? [X1] : (~quiet(X1) & quiet(X1)) => (~quiet(sK2) & quiet(sK2)) [choice axiom]
48. (~old(lucy) | ! [X0] : (quiet(X0) | ~quiet(X0))) & ((~quiet(sK2) & quiet(sK2)) | old(lucy)) [skolemisation 46,47]
49. ((~patient(paul) & wise(paul)) | ! [X0] : (~calm(X0) & ~old(X0))) & (? [X0] : (calm(X0) | old(X0)) | (patient(paul) | ~wise(paul))) [nnf transformation 4]
50. ((~patient(paul) & wise(paul)) | ! [X0] : (~calm(X0) & ~old(X0))) & (? [X0] : (calm(X0) | old(X0)) | patient(paul) | ~wise(paul)) [flattening 49]
51. ((~patient(paul) & wise(paul)) | ! [X0] : (~calm(X0) & ~old(X0))) & (? [X1] : (calm(X1) | old(X1)) | patient(paul) | ~wise(paul)) [rectify 50]
52. ? [X1] : (calm(X1) | old(X1)) => (calm(sK3) | old(sK3)) [choice axiom]
53. ((~patient(paul) & wise(paul)) | ! [X0] : (~calm(X0) & ~old(X0))) & ((calm(sK3) | old(sK3)) | patient(paul) | ~wise(paul)) [skolemisation 51,52]
85. quiet(sK2) | old(lucy) [cnf transformation 48]
86. ~quiet(sK2) | old(lucy) [cnf transformation 48]
89. wise(paul) | ~old(X0) [cnf transformation 53]
137. ~wise(paul) [cnf transformation 25]
182. 10 <=> old(lucy) [avatar definition]
184. old(lucy) <- (10) [avatar component clause 182]
186. 11 <=> quiet(sK2) [avatar definition]
189. 10 | ~11 [avatar split clause 86,186,182]
190. 10 | 11 [avatar split clause 85,186,182]
200. 14 <=> ! [X0] : ~old(X0) [avatar definition]
201. ~old(X0) <- (14) [avatar component clause 200]
204. 15 <=> wise(paul) [avatar definition]
208. 14 | 15 [avatar split clause 89,204,200]
293. ~15 [avatar split clause 137,204]
294. $false <- (10, 14) [subsumption resolution 184,201]
295. ~10 | ~14 [avatar contradiction clause 294]
298. $false [avatar sat refutation 189,190,208,293,295]
% SZS output end Proof for 5251028043302654493675834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or strong is both not humble and quiet and vice versa.
Everyone who is happy is creative or quiet and vice versa.
If someone is either not strong or not tall then someone is calm or wise.
If someone is not rich or not kind then someone is both generous and strong and vice versa.
Everyone who is both funny and not curious is either patient or wise and vice versa.
If someone is old or rich then alice is not wise.
If someone is not funny then fred is not curious and vice versa.
If fred is not strong or not quiet then someone is strong and vice versa.
Everyone who is happy or not calm is not brave and vice versa.
Everyone who is either creative or humble is either rich or not rich and vice versa.
If lucy is old or strong then lucy is patient or not funny and vice versa.
If john is generous then lucy is either generous or tall and vice versa.
If someone is curious or not funny then alice is either not curious or not generous and vice versa.
If mary is not funny then someone is wise and vice versa.
Everyone who is patient is either not humble or patient.
Everyone who is either not generous or not funny is both not tall and not calm.
Someone is both not rich and old.
Paul is both wise and not quiet.
Alice is both not kind and not tall.
Someone is brave.
Paul is not kind or not rich.
Lucy is both not strong and not generous. | Paul is generous. | neutral | (![X]:((wise(X)<~>strong(X))<=>(~humble(X)&quiet(X))))&
(![X]:(happy(X)<=>(creative(X)|quiet(X))))&
((?[X]:((~strong(X)<~>~tall(X))))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:((~rich(X)|~kind(X))))<=>(?[X]:((generous(X)&strong(X)))))&
(![X]:((funny(X)&~curious(X))<=>(patient(X)<~>wise(X))))&
((?[X]:((old(X)|rich(X))))=>(~wise(alice)))&
((?[X]:(~funny(X)))<=>(~curious(fred)))&
(((~strong(fred)|~quiet(fred)))<=>(?[X]:(strong(X))))&
(![X]:((happy(X)|~calm(X))<=>~brave(X)))&
(![X]:((creative(X)<~>humble(X))<=>(rich(X)<~>~rich(X))))&
(((old(lucy)|strong(lucy)))<=>((patient(lucy)|~funny(lucy))))&
((generous(john))<=>((generous(lucy)<~>tall(lucy))))&
((?[X]:((curious(X)|~funny(X))))<=>((~curious(alice)<~>~generous(alice))))&
((~funny(mary))<=>(?[X]:(wise(X))))&
(![X]:(patient(X)=>(~humble(X)<~>patient(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(~tall(X)&~calm(X))))&
(?[X]:((~rich(X)&old(X))))&
((wise(paul)&~quiet(paul)))&
((~kind(alice)&~tall(alice)))&
(?[X]:(brave(X)))&
((~kind(paul)|~rich(paul)))&
((~strong(lucy)&~generous(lucy))) | generous(paul) | [] | null | 0 |
Everyone who is both happy and not creative is not quiet or kind and vice versa.
Everyone who is both not tall and not humble is happy or quiet.
If john is either rich or funny then paul is either humble or happy.
If someone is not kind then someone is not rich or not curious and vice versa.
If john is both not strong and not patient then lucy is either not patient or not tall and vice versa.
If someone is wise then paul is rich or not calm.
Everyone who is both kind and not patient is not strong or patient and vice versa.
If someone is not calm then fred is not funny and vice versa.
Everyone who is either humble or calm is not quiet or rich.
If someone is kind or not patient then someone is not patient and vice versa.
If susan is either not wise or not brave then susan is both humble and not tall.
If paul is strong then alice is either tall or not strong and vice versa.
Everyone who is both not happy and kind is both not strong and not funny.
Everyone who is both brave and rich is not curious or not kind and vice versa.
If someone is either patient or not strong then someone is either not curious or not wise.
Everyone who is not creative or not old is not quiet or not brave.
Someone is old.
Someone is happy or not calm.
Mary is both creative and generous.
Someone is both creative and old.
Paul is either not wise or creative. | John is not old. | neutral | (![X]:((happy(X)&~creative(X))<=>(~quiet(X)|kind(X))))&
(![X]:((~tall(X)&~humble(X))=>(happy(X)|quiet(X))))&
(((rich(john)<~>funny(john)))=>((humble(paul)<~>happy(paul))))&
((?[X]:(~kind(X)))<=>(?[X]:((~rich(X)|~curious(X)))))&
(((~strong(john)&~patient(john)))<=>((~patient(lucy)<~>~tall(lucy))))&
((?[X]:(wise(X)))=>((rich(paul)|~calm(paul))))&
(![X]:((kind(X)&~patient(X))<=>(~strong(X)|patient(X))))&
((?[X]:(~calm(X)))<=>(~funny(fred)))&
(![X]:((humble(X)<~>calm(X))=>(~quiet(X)|rich(X))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:(~patient(X))))&
(((~wise(susan)<~>~brave(susan)))=>((humble(susan)&~tall(susan))))&
((strong(paul))<=>((tall(alice)<~>~strong(alice))))&
(![X]:((~happy(X)&kind(X))=>(~strong(X)&~funny(X))))&
(![X]:((brave(X)&rich(X))<=>(~curious(X)|~kind(X))))&
((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~creative(X)|~old(X))=>(~quiet(X)|~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((happy(X)|~calm(X))))&
((creative(mary)&generous(mary)))&
(?[X]:((creative(X)&old(X))))&
((~wise(paul)<~>creative(paul))) | ~old(john) | [] | null | 0 |
Everyone who is brave is not patient or not happy and vice versa.
Everyone who is not rich or old is tall or not happy.
If fred is both not old and funny then someone is not kind or patient and vice versa.
If someone is kind or creative then someone is either not patient or patient and vice versa.
Everyone who is funny or humble is not calm.
Everyone who is either not quiet or wise is not brave or not calm and vice versa.
Everyone who is wise is not kind.
If someone is creative or calm then paul is both not rich and tall and vice versa.
If mary is wise then someone is either not brave or humble and vice versa.
If mary is wise then someone is either happy or not quiet.
If alice is generous or strong then mary is both quiet and not kind.
Everyone who is not calm or not wise is both not funny and not rich and vice versa.
Everyone who is not strong or not creative is not happy or not humble.
If susan is either creative or not curious then alice is not patient and vice versa.
If someone is both not rich and quiet then susan is either not creative or old.
Everyone who is not rich is not wise.
Someone is either not happy or creative.
Someone is both creative and not calm.
John is either not kind or tall.
Someone is both not happy and not strong.
Someone is both not strong and not wise. | Susan is not kind. | contradiction | (![X]:(brave(X)<=>(~patient(X)|~happy(X))))&
(![X]:((~rich(X)|old(X))=>(tall(X)|~happy(X))))&
(((~old(fred)&funny(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
(![X]:((funny(X)|humble(X))=>~calm(X)))&
(![X]:((~quiet(X)<~>wise(X))<=>(~brave(X)|~calm(X))))&
(![X]:(wise(X)=>~kind(X)))&
((?[X]:((creative(X)|calm(X))))<=>((~rich(paul)&tall(paul))))&
((wise(mary))<=>(?[X]:((~brave(X)<~>humble(X)))))&
((wise(mary))=>(?[X]:((happy(X)<~>~quiet(X)))))&
(((generous(alice)|strong(alice)))=>((quiet(mary)&~kind(mary))))&
(![X]:((~calm(X)|~wise(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~strong(X)|~creative(X))=>(~happy(X)|~humble(X))))&
(((creative(susan)<~>~curious(susan)))<=>(~patient(alice)))&
((?[X]:((~rich(X)&quiet(X))))=>((~creative(susan)<~>old(susan))))&
(![X]:(~rich(X)=>~wise(X)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~kind(john)<~>tall(john)))&
(?[X]:((~happy(X)&~strong(X))))&
(?[X]:((~strong(X)&~wise(X)))) | ~kind(susan) | [
"p2",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8774430311283194538146211
% SZS output start Proof for 8774430311283194538146211
3. (funny(fred) & ~old(fred)) <=> ? [X0] : (patient(X0) | ~kind(X0)) [input p2]
5. ! [X0] : ((humble(X0) | funny(X0)) => ~calm(X0)) [input p4]
12. ! [X0] : ((~wise(X0) | ~calm(X0)) <=> (~rich(X0) & ~funny(X0))) [input p11]
22. ~kind(susan) [input hypothesis]
27. ! [X0] : (~calm(X0) | (~humble(X0) & ~funny(X0))) [ennf transformation 5]
37. ((funny(fred) & ~old(fred)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | (~funny(fred) | old(fred))) [nnf transformation 3]
38. ((funny(fred) & ~old(fred)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X0] : (patient(X0) | ~kind(X0)) | ~funny(fred) | old(fred)) [flattening 37]
39. ((funny(fred) & ~old(fred)) | ! [X0] : (~patient(X0) & kind(X0))) & (? [X1] : (patient(X1) | ~kind(X1)) | ~funny(fred) | old(fred)) [rectify 38]
40. ? [X1] : (patient(X1) | ~kind(X1)) => (patient(sK0) | ~kind(sK0)) [choice axiom]
41. ((funny(fred) & ~old(fred)) | ! [X0] : (~patient(X0) & kind(X0))) & ((patient(sK0) | ~kind(sK0)) | ~funny(fred) | old(fred)) [skolemisation 39,40]
61. ! [X0] : (((~wise(X0) | ~calm(X0)) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | (wise(X0) & calm(X0)))) [nnf transformation 12]
62. ! [X0] : ((~wise(X0) | ~calm(X0) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | (wise(X0) & calm(X0)))) [flattening 61]
83. funny(fred) | kind(X0) [cnf transformation 41]
91. ~calm(X0) | ~funny(X0) [cnf transformation 27]
113. ~funny(X0) | calm(X0) [cnf transformation 62]
137. ~kind(susan) [cnf transformation 22]
144. 2 <=> funny(fred) [avatar definition]
146. funny(fred) <- (2) [avatar component clause 144]
149. 3 <=> ! [X0] : kind(X0) [avatar definition]
150. kind(X0) <- (3) [avatar component clause 149]
151. 3 | 2 [avatar split clause 83,144,149]
254. ~funny(X0) [subsumption resolution 113,91]
300. $false <- (2) [subsumption resolution 146,254]
301. ~2 [avatar contradiction clause 300]
302. $false <- (3) [resolution 150,137]
303. ~3 [avatar contradiction clause 302]
304. $false [avatar sat refutation 151,301,303]
% SZS output end Proof for 8774430311283194538146211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or generous is not humble or funny and vice versa.
Everyone who is generous is curious.
If someone is happy or not brave then someone is either not quiet or curious.
If someone is not humble or not wise then mary is both funny and not curious and vice versa.
Everyone who is either not rich or funny is both happy and not brave.
Everyone who is not kind is not humble or not quiet and vice versa.
Everyone who is either rich or tall is happy or not strong and vice versa.
Everyone who is both not kind and not happy is humble or not humble and vice versa.
Everyone who is both humble and not rich is funny and vice versa.
Everyone who is both strong and not generous is not tall.
Everyone who is funny or not humble is not calm or generous and vice versa.
If someone is generous then john is tall and vice versa.
If alice is both not humble and not tall then fred is not rich or not humble.
Everyone who is brave or not brave is not funny or not wise.
Everyone who is wise is not humble.
Everyone who is both strong and not generous is not humble or wise and vice versa.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm.
Someone is either not old or tall.
Someone is not tall or creative. | Alice is patient. | neutral | (![X]:((~curious(X)<~>generous(X))<=>(~humble(X)|funny(X))))&
(![X]:(generous(X)=>curious(X)))&
((?[X]:((happy(X)|~brave(X))))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(happy(X)&~brave(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~quiet(X))))&
(![X]:((rich(X)<~>tall(X))<=>(happy(X)|~strong(X))))&
(![X]:((~kind(X)&~happy(X))<=>(humble(X)|~humble(X))))&
(![X]:((humble(X)&~rich(X))<=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)<~>tall(X))))&
(?[X]:((~tall(X)|creative(X)))) | patient(alice) | [] | null | 0 |
If paul is both not tall and creative then mary is not creative or kind and vice versa. Everyone who is not old or generous is either curious or not calm and vice versa. Everyone who is both brave and patient is tall or curious. If someone is both not curious and strong then someone is not humble. Everyone who is either not rich or funny is either not creative or tall. Everyone who is either wise or patient is calm and vice versa. Everyone who is either creative or not quiet is both not happy and not humble. If someone is both not old and brave then someone is both not quiet and brave. Everyone who is either tall or not quiet is not funny. Everyone who is either not calm or not tall is brave and vice versa. Everyone who is either generous or curious is not curious and vice versa. Everyone who is both not calm and not generous is not rich or wise and vice versa. Everyone who is curious is either old or not calm. Everyone who is generous is not funny and vice versa. If mary is either quiet or happy then mary is not brave or generous and vice versa. If lucy is happy then someone is wise and vice versa. Alice is both not funny and not kind. Someone is rich or not wise. Someone is not kind or not patient. Susan is not tall or calm. Susan is funny or creative. Alice is not quiet or not brave. Paul is brave. John is curious or not kind. | Mary is not creative. | neutral | (((~tall(paul)&creative(paul)))<=>((~creative(mary)|kind(mary))))&
(![X]:((~old(X)|generous(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((brave(X)&patient(X))=>(tall(X)|curious(X))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>funny(X))=>(~creative(X)<~>tall(X))))&
(![X]:((wise(X)<~>patient(X))<=>calm(X)))&
(![X]:((creative(X)<~>~quiet(X))=>(~happy(X)&~humble(X))))&
((?[X]:((~old(X)&brave(X))))=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((tall(X)<~>~quiet(X))=>~funny(X)))&
(![X]:((~calm(X)<~>~tall(X))<=>brave(X)))&
(![X]:((generous(X)<~>curious(X))<=>~curious(X)))&
(![X]:((~calm(X)&~generous(X))<=>(~rich(X)|wise(X))))&
(![X]:(curious(X)=>(old(X)<~>~calm(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(((quiet(mary)<~>happy(mary)))<=>((~brave(mary)|generous(mary))))&
((happy(lucy))<=>(?[X]:(wise(X))))&
((~funny(alice)&~kind(alice)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~kind(X)|~patient(X))))&
((~tall(susan)|calm(susan)))&
((funny(susan)|creative(susan)))&
((~quiet(alice)|~brave(alice)))&
(brave(paul))&
((curious(john)|~kind(john))) | ~creative(mary) | [] | null | 0 |
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