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stringlengths 940
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If fred is either not curious or patient then lucy is not tall. Everyone who is both not rich and not old is not old. Everyone who is not humble or not patient is funny or brave. Everyone who is not funny or not old is either not curious or not rich. Everyone who is not rich is not humble. Everyone who is both not funny and rich is tall. If fred is funny or not wise then someone is either calm or brave. Everyone who is either curious or calm is not patient and vice versa. If lucy is either rich or old then someone is funny and vice versa. Everyone who is not calm or funny is not creative or not humble. If someone is calm or not funny then mary is both not quiet and quiet and vice versa. Everyone who is kind or not rich is brave or not wise. Everyone who is quiet or not happy is both kind and not tall. Everyone who is brave or not wise is rich or brave. Everyone who is both not quiet and curious is either curious or funny. Everyone who is either quiet or not patient is kind. John is both not rich and not creative. Someone is both humble and curious. Someone is both humble and not calm. Someone is both funny and not generous. Someone is either creative or old. John is either funny or not patient. Someone is either patient or not old. Alice is wise. | John is brave. | entailment | (((~curious(fred)<~>patient(fred)))=>(~tall(lucy)))&
(![X]:((~rich(X)&~old(X))=>~old(X)))&
(![X]:((~humble(X)|~patient(X))=>(funny(X)|brave(X))))&
(![X]:((~funny(X)|~old(X))=>(~curious(X)<~>~rich(X))))&
(![X]:(~rich(X)=>~humble(X)))&
(![X]:((~funny(X)&rich(X))=>tall(X)))&
(((funny(fred)|~wise(fred)))=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((curious(X)<~>calm(X))<=>~patient(X)))&
(((rich(lucy)<~>old(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|funny(X))=>(~creative(X)|~humble(X))))&
((?[X]:((calm(X)|~funny(X))))<=>((~quiet(mary)&quiet(mary))))&
(![X]:((kind(X)|~rich(X))=>(brave(X)|~wise(X))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)&~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)|brave(X))))&
(![X]:((~quiet(X)&curious(X))=>(curious(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~patient(X))=>kind(X)))&
((~rich(john)&~creative(john)))&
(?[X]:((humble(X)&curious(X))))&
(?[X]:((humble(X)&~calm(X))))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((creative(X)<~>old(X))))&
((funny(john)<~>~patient(john)))&
(?[X]:((patient(X)<~>~old(X))))&
(wise(alice)) | brave(john) | [
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 475551141223024031369291
% SZS output start Proof for 475551141223024031369291
12. ! [X0] : ((~rich(X0) | kind(X0)) => (~wise(X0) | brave(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | brave(X0)) => (brave(X0) | rich(X0))) [input p13]
17. ~creative(john) & ~rich(john) [input p16]
25. ~brave(john) [input hypothesis]
40. ! [X0] : ((~wise(X0) | brave(X0)) | (rich(X0) & ~kind(X0))) [ennf transformation 12]
41. ! [X0] : (~wise(X0) | brave(X0) | (rich(X0) & ~kind(X0))) [flattening 40]
43. ! [X0] : ((brave(X0) | rich(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 14]
44. ! [X0] : (brave(X0) | rich(X0) | (wise(X0) & ~brave(X0))) [flattening 43]
109. ~wise(X0) | brave(X0) | rich(X0) [cnf transformation 41]
113. brave(X0) | rich(X0) | wise(X0) [cnf transformation 44]
118. ~rich(john) [cnf transformation 17]
132. ~brave(john) [cnf transformation 25]
201. brave(X0) | rich(X0) [subsumption resolution 113,109]
243. rich(john) [resolution 201,132]
244. $false [subsumption resolution 243,118]
% SZS output end Proof for 475551141223024031369291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or not tall then alice is not wise or strong and vice versa.
If mary is not generous or creative then someone is not old.
If fred is curious or kind then someone is either not generous or not creative.
Everyone who is both kind and not wise is tall.
Everyone who is either calm or happy is both not wise and not curious and vice versa.
Everyone who is both tall and not old is either not kind or funny and vice versa.
If someone is either not patient or not funny then fred is both wise and strong.
Everyone who is wise or not humble is not happy and vice versa.
Everyone who is funny or not old is either generous or not patient and vice versa.
If someone is funny then paul is wise and vice versa.
If alice is both rich and tall then paul is either not calm or brave and vice versa.
Everyone who is brave or not calm is both funny and not funny.
If fred is both wise and not curious then someone is humble or not strong.
Everyone who is either patient or not happy is not creative or generous and vice versa.
If someone is not quiet then john is curious and vice versa.
Everyone who is humble or patient is calm or not patient.
Someone is not rich.
Someone is generous.
Someone is both happy and not kind. | Alice is kind. | neutral | (((kind(john)<~>~tall(john)))<=>((~wise(alice)|strong(alice))))&
(((~generous(mary)|creative(mary)))=>(?[X]:(~old(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((kind(X)&~wise(X))=>tall(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~wise(X)&~curious(X))))&
(![X]:((tall(X)&~old(X))<=>(~kind(X)<~>funny(X))))&
((?[X]:((~patient(X)<~>~funny(X))))=>((wise(fred)&strong(fred))))&
(![X]:((wise(X)|~humble(X))<=>~happy(X)))&
(![X]:((funny(X)|~old(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:(funny(X)))<=>(wise(paul)))&
(((rich(alice)&tall(alice)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((brave(X)|~calm(X))=>(funny(X)&~funny(X))))&
(((wise(fred)&~curious(fred)))=>(?[X]:((humble(X)|~strong(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>(~creative(X)|generous(X))))&
((?[X]:(~quiet(X)))<=>(curious(john)))&
(![X]:((humble(X)|patient(X))=>(calm(X)|~patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((happy(X)&~kind(X)))) | kind(alice) | [] | null | 0 |
Everyone who is either brave or not funny is either old or not funny.
Everyone who is both not rich and not quiet is both wise and creative and vice versa.
If someone is either not wise or brave then someone is either humble or happy and vice versa.
Everyone who is tall or strong is not funny and vice versa.
If someone is wise or not rich then someone is not funny or rich.
If someone is not happy or patient then lucy is both quiet and not old and vice versa.
Everyone who is either wise or not creative is either quiet or humble and vice versa.
Everyone who is not strong is not happy and vice versa.
If someone is either strong or not kind then someone is either not wise or quiet and vice versa.
Everyone who is either not kind or wise is wise.
If someone is not wise then someone is both not wise and not creative.
Everyone who is both not kind and not tall is both not patient and not curious.
If lucy is either not rich or curious then someone is both not funny and happy and vice versa.
If john is either not wise or creative then fred is not curious and vice versa.
If someone is not patient then someone is not generous or not calm.
Everyone who is not happy or not curious is either brave or not curious.
Fred is either patient or curious.
Alice is brave.
Someone is not creative.
Someone is patient or not kind.
Alice is creative or not creative.
Someone is both creative and patient.
Alice is quiet.
Fred is either patient or not humble. | Lucy is not rich. | neutral | (![X]:((brave(X)<~>~funny(X))=>(old(X)<~>~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(wise(X)&creative(X))))&
((?[X]:((~wise(X)<~>brave(X))))<=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:((tall(X)|strong(X))<=>~funny(X)))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~funny(X)|rich(X)))))&
((?[X]:((~happy(X)|patient(X))))<=>((quiet(lucy)&~old(lucy))))&
(![X]:((wise(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(~strong(X)<=>~happy(X)))&
((?[X]:((strong(X)<~>~kind(X))))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((~kind(X)<~>wise(X))=>wise(X)))&
((?[X]:(~wise(X)))=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:((~kind(X)&~tall(X))=>(~patient(X)&~curious(X))))&
(((~rich(lucy)<~>curious(lucy)))<=>(?[X]:((~funny(X)&happy(X)))))&
(((~wise(john)<~>creative(john)))<=>(~curious(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((~generous(X)|~calm(X)))))&
(![X]:((~happy(X)|~curious(X))=>(brave(X)<~>~curious(X))))&
((patient(fred)<~>curious(fred)))&
(brave(alice))&
(?[X]:(~creative(X)))&
(?[X]:((patient(X)|~kind(X))))&
((creative(alice)|~creative(alice)))&
(?[X]:((creative(X)&patient(X))))&
(quiet(alice))&
((patient(fred)<~>~humble(fred))) | ~rich(lucy) | [] | null | 0 |
Everyone who is creative or tall is both funny and not funny. Everyone who is not strong or not generous is rich. Everyone who is not humble is both brave and not tall and vice versa. Everyone who is either happy or not quiet is not brave or calm and vice versa. Everyone who is not calm is both not curious and patient and vice versa. Everyone who is both curious and not generous is both not wise and not kind and vice versa. If someone is both not calm and wise then someone is not brave. Everyone who is not quiet is kind and vice versa. If susan is both not kind and calm then john is both tall and funny. If alice is strong then alice is both not old and not curious and vice versa. If alice is not curious then alice is either curious or not quiet and vice versa. If alice is either not happy or humble then mary is either rich or not strong. If someone is calm then someone is creative. Everyone who is both not brave and not rich is both not creative and not old and vice versa. Everyone who is both creative and not calm is not old or not happy and vice versa. Someone is generous. Someone is generous or not happy. Someone is either not curious or wise. Someone is quiet or not rich. Susan is not brave or not rich. | Alice is patient. | entailment | (![X]:((creative(X)|tall(X))=>(funny(X)&~funny(X))))&
(![X]:((~strong(X)|~generous(X))=>rich(X)))&
(![X]:(~humble(X)<=>(brave(X)&~tall(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~brave(X)|calm(X))))&
(![X]:(~calm(X)<=>(~curious(X)&patient(X))))&
(![X]:((curious(X)&~generous(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~calm(X)&wise(X))))=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(((~kind(susan)&calm(susan)))=>((tall(john)&funny(john))))&
((strong(alice))<=>((~old(alice)&~curious(alice))))&
((~curious(alice))<=>((curious(alice)<~>~quiet(alice))))&
(((~happy(alice)<~>humble(alice)))=>((rich(mary)<~>~strong(mary))))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>(~creative(X)&~old(X))))&
(![X]:((creative(X)&~calm(X))<=>(~old(X)|~happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((quiet(X)|~rich(X))))&
((~brave(susan)|~rich(susan))) | patient(alice) | [
"p0",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7473027473208306314529203
% SZS output start Proof for 7473027473208306314529203
1. ! [X0] : ((tall(X0) | creative(X0)) => (~funny(X0) & funny(X0))) [input p0]
5. ! [X0] : (~calm(X0) <=> (patient(X0) & ~curious(X0))) [input p4]
13. ? [X0] : calm(X0) => ? [X0] : creative(X0) [input p12]
21. ~patient(alice) [input hypothesis]
23. ? [X0] : calm(X0) => ? [X1] : creative(X1) [rectify 13]
24. ! [X0] : ((~funny(X0) & funny(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 1]
30. ? [X1] : creative(X1) | ! [X0] : ~calm(X0) [ennf transformation 23]
35. ! [X0] : ((~calm(X0) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | calm(X0))) [nnf transformation 5]
36. ! [X0] : ((~calm(X0) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | calm(X0))) [flattening 35]
47. ? [X0] : creative(X0) | ! [X1] : ~calm(X1) [rectify 30]
48. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
49. creative(sK1) | ! [X1] : ~calm(X1) [skolemisation 47,48]
63. funny(X0) | ~creative(X0) [cnf transformation 24]
65. ~funny(X0) | ~creative(X0) [cnf transformation 24]
79. patient(X0) | calm(X0) [cnf transformation 36]
101. creative(sK1) | ~calm(X1) [cnf transformation 49]
117. ~patient(alice) [cnf transformation 21]
121. ~creative(X0) [subsumption resolution 63,65]
191. ~calm(X1) [subsumption resolution 101,121]
231. calm(alice) [resolution 79,117]
232. $false [subsumption resolution 231,191]
% SZS output end Proof for 7473027473208306314529203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not calm is either not old or not rich and vice versa. If someone is not calm then someone is happy or not rich and vice versa. Everyone who is either not old or tall is not generous or not calm. Everyone who is both strong and not tall is both generous and not funny and vice versa. Everyone who is old or happy is either not calm or not curious and vice versa. Everyone who is either patient or brave is quiet. Everyone who is both not curious and not old is not tall. Everyone who is both not wise and curious is either not strong or not kind. Everyone who is not funny is patient or calm and vice versa. Everyone who is calm or not happy is not old and vice versa. If someone is both not kind and generous then someone is both not rich and old. Everyone who is either not quiet or patient is both not brave and old and vice versa. If lucy is calm then lucy is either not funny or tall and vice versa. Everyone who is both patient and not generous is wise and vice versa. If susan is both kind and happy then someone is not old. If someone is either not funny or not rich then someone is patient and vice versa. Someone is old or kind. Someone is either brave or funny. Someone is curious. Someone is not wise or not happy. Someone is either kind or not generous. Fred is both curious and not calm. John is not brave. Lucy is calm. | Lucy is calm. | entailment | (![X]:((~happy(X)|~calm(X))<=>(~old(X)<~>~rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~old(X)<~>tall(X))=>(~generous(X)|~calm(X))))&
(![X]:((strong(X)&~tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((old(X)|happy(X))<=>(~calm(X)<~>~curious(X))))&
(![X]:((patient(X)<~>brave(X))=>quiet(X)))&
(![X]:((~curious(X)&~old(X))=>~tall(X)))&
(![X]:((~wise(X)&curious(X))=>(~strong(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(patient(X)|calm(X))))&
(![X]:((calm(X)|~happy(X))<=>~old(X)))&
((?[X]:((~kind(X)&generous(X))))=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~brave(X)&old(X))))&
((calm(lucy))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((patient(X)&~generous(X))<=>wise(X)))&
(((kind(susan)&happy(susan)))=>(?[X]:(~old(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:(patient(X))))&
(?[X]:((old(X)|kind(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((~wise(X)|~happy(X))))&
(?[X]:((kind(X)<~>~generous(X))))&
((curious(fred)&~calm(fred)))&
(~brave(john))&
(calm(lucy)) | calm(lucy) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6230822056698153587129748
% SZS output start Proof for 6230822056698153587129748
24. calm(lucy) [input p23]
25. ~calm(lucy) [input hypothesis]
146. calm(lucy) [cnf transformation 24]
147. ~calm(lucy) [cnf transformation 25]
196. 12 <=> calm(lucy) [avatar definition]
278. 12 [avatar split clause 146,196]
279. ~12 [avatar split clause 147,196]
280. $false [avatar sat refutation 278,279]
% SZS output end Proof for 6230822056698153587129748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not creative is not strong or rich and vice versa.
If someone is either brave or humble then mary is either not rich or not patient.
If fred is not strong or tall then susan is curious or kind.
Everyone who is either not calm or not humble is creative or not humble and vice versa.
Everyone who is both not wise and generous is both not happy and happy and vice versa.
If lucy is either not strong or not wise then someone is either not funny or not brave.
If mary is both not happy and not calm then someone is both calm and tall.
Everyone who is either not strong or not calm is both not generous and not kind and vice versa.
Everyone who is kind is not kind or old and vice versa.
If susan is either creative or not happy then fred is both not brave and tall.
Everyone who is not wise or not patient is funny.
Everyone who is not calm is both funny and not patient and vice versa.
Everyone who is either generous or creative is old or not curious and vice versa.
If someone is either not creative or not strong then someone is not brave or not old.
If someone is not strong then someone is not creative or not kind.
If someone is either not wise or kind then fred is funny or not brave and vice versa.
Someone is old or not rich.
John is brave or not calm.
Paul is either rich or not tall.
Someone is both kind and rich.
Susan is not tall or not generous.
Someone is both not humble and creative.
Mary is funny or not funny. | Mary is humble. | neutral | (![X]:((calm(X)&~creative(X))<=>(~strong(X)|rich(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((~rich(mary)<~>~patient(mary))))&
(((~strong(fred)|tall(fred)))=>((curious(susan)|kind(susan))))&
(![X]:((~calm(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
(![X]:((~wise(X)&generous(X))<=>(~happy(X)&happy(X))))&
(((~strong(lucy)<~>~wise(lucy)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(((~happy(mary)&~calm(mary)))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~generous(X)&~kind(X))))&
(![X]:(kind(X)<=>(~kind(X)|old(X))))&
(((creative(susan)<~>~happy(susan)))=>((~brave(fred)&tall(fred))))&
(![X]:((~wise(X)|~patient(X))=>funny(X)))&
(![X]:(~calm(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)<~>creative(X))<=>(old(X)|~curious(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~creative(X)|~kind(X)))))&
((?[X]:((~wise(X)<~>kind(X))))<=>((funny(fred)|~brave(fred))))&
(?[X]:((old(X)|~rich(X))))&
((brave(john)|~calm(john)))&
((rich(paul)<~>~tall(paul)))&
(?[X]:((kind(X)&rich(X))))&
((~tall(susan)|~generous(susan)))&
(?[X]:((~humble(X)&creative(X))))&
((funny(mary)|~funny(mary))) | humble(mary) | [] | null | 0 |
If john is both brave and curious then someone is both curious and tall and vice versa.
If susan is both happy and not funny then someone is either generous or rich.
Everyone who is both not strong and tall is tall and vice versa.
Everyone who is either calm or not happy is either humble or not generous and vice versa.
Everyone who is both quiet and happy is either not generous or rich and vice versa.
If someone is not strong or not creative then susan is either not generous or not wise.
Everyone who is either calm or kind is not generous.
If someone is kind or creative then someone is either not creative or wise and vice versa.
If john is both strong and patient then fred is either calm or old and vice versa.
Everyone who is creative or not wise is not brave or not quiet.
If someone is not wise or not humble then susan is funny or wise and vice versa.
If someone is generous or not brave then susan is patient and vice versa.
Everyone who is both not patient and not generous is both generous and not generous.
Everyone who is not funny is not happy and vice versa.
If susan is not rich then mary is generous or not patient and vice versa.
Everyone who is not quiet is either quiet or not funny and vice versa.
Someone is not old.
Paul is both not brave and not rich.
Lucy is not calm or not happy.
Susan is brave.
Someone is not old or creative.
Alice is either not kind or not strong. | Paul is not creative. | neutral | (((brave(john)&curious(john)))<=>(?[X]:((curious(X)&tall(X)))))&
(((happy(susan)&~funny(susan)))=>(?[X]:((generous(X)<~>rich(X)))))&
(![X]:((~strong(X)&tall(X))<=>tall(X)))&
(![X]:((calm(X)<~>~happy(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((quiet(X)&happy(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((~strong(X)|~creative(X))))=>((~generous(susan)<~>~wise(susan))))&
(![X]:((calm(X)<~>kind(X))=>~generous(X)))&
((?[X]:((kind(X)|creative(X))))<=>(?[X]:((~creative(X)<~>wise(X)))))&
(((strong(john)&patient(john)))<=>((calm(fred)<~>old(fred))))&
(![X]:((creative(X)|~wise(X))=>(~brave(X)|~quiet(X))))&
((?[X]:((~wise(X)|~humble(X))))<=>((funny(susan)|wise(susan))))&
((?[X]:((generous(X)|~brave(X))))<=>(patient(susan)))&
(![X]:((~patient(X)&~generous(X))=>(generous(X)&~generous(X))))&
(![X]:(~funny(X)<=>~happy(X)))&
((~rich(susan))<=>((generous(mary)|~patient(mary))))&
(![X]:(~quiet(X)<=>(quiet(X)<~>~funny(X))))&
(?[X]:(~old(X)))&
((~brave(paul)&~rich(paul)))&
((~calm(lucy)|~happy(lucy)))&
(brave(susan))&
(?[X]:((~old(X)|creative(X))))&
((~kind(alice)<~>~strong(alice))) | ~creative(paul) | [] | null | 0 |
If someone is not funny or old then someone is either generous or not curious.
Everyone who is curious or not quiet is not calm or not happy and vice versa.
If someone is either not generous or kind then someone is either old or calm.
Everyone who is not generous is old.
Everyone who is not kind or kind is not happy and vice versa.
If paul is humble or happy then john is old or not patient and vice versa.
Everyone who is either not kind or not old is both not kind and tall and vice versa.
Everyone who is not happy is both not humble and quiet.
Everyone who is both not strong and rich is not rich.
If paul is either tall or not generous then alice is generous or not funny.
If someone is creative or tall then john is both not wise and not happy and vice versa.
If someone is both curious and quiet then fred is not old or not kind.
If someone is kind or not strong then someone is not brave.
If someone is not old then john is either not wise or not strong.
If someone is both patient and quiet then someone is either not creative or calm and vice versa.
Everyone who is not old is rich.
Fred is not tall.
Someone is old.
Someone is rich.
Paul is not generous.
Fred is strong or not strong.
Someone is not generous or not tall.
Paul is both wise and not tall. | John is not old. | entailment | ((?[X]:((~funny(X)|old(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:((old(X)<~>calm(X)))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((~kind(X)|kind(X))<=>~happy(X)))&
(((humble(paul)|happy(paul)))<=>((old(john)|~patient(john))))&
(![X]:((~kind(X)<~>~old(X))<=>(~kind(X)&tall(X))))&
(![X]:(~happy(X)=>(~humble(X)&quiet(X))))&
(![X]:((~strong(X)&rich(X))=>~rich(X)))&
(((tall(paul)<~>~generous(paul)))=>((generous(alice)|~funny(alice))))&
((?[X]:((creative(X)|tall(X))))<=>((~wise(john)&~happy(john))))&
((?[X]:((curious(X)&quiet(X))))=>((~old(fred)|~kind(fred))))&
((?[X]:((kind(X)|~strong(X))))=>(?[X]:(~brave(X))))&
((?[X]:(~old(X)))=>((~wise(john)<~>~strong(john))))&
((?[X]:((patient(X)&quiet(X))))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(![X]:(~old(X)=>rich(X)))&
(~tall(fred))&
(?[X]:(old(X)))&
(?[X]:(rich(X)))&
(~generous(paul))&
((strong(fred)|~strong(fred)))&
(?[X]:((~generous(X)|~tall(X))))&
((wise(paul)&~tall(paul))) | ~old(john) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3057805875219791834837931
% SZS output start Proof for 3057805875219791834837931
5. ! [X0] : ((kind(X0) | ~kind(X0)) <=> ~happy(X0)) [input p4]
6. (happy(paul) | humble(paul)) <=> (~patient(john) | old(john)) [input p5]
8. ! [X0] : (~happy(X0) => (quiet(X0) & ~humble(X0))) [input p7]
24. old(john) [input hypothesis]
33. ! [X0] : ((quiet(X0) & ~humble(X0)) | happy(X0)) [ennf transformation 8]
52. ! [X0] : (((kind(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (~kind(X0) & kind(X0)))) [nnf transformation 5]
53. ! [X0] : ((kind(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (~kind(X0) & kind(X0)))) [flattening 52]
54. ((happy(paul) | humble(paul)) | (patient(john) & ~old(john))) & ((~patient(john) | old(john)) | (~happy(paul) & ~humble(paul))) [nnf transformation 6]
55. (happy(paul) | humble(paul) | (patient(john) & ~old(john))) & (~patient(john) | old(john) | (~happy(paul) & ~humble(paul))) [flattening 54]
89. ~happy(X0) | kind(X0) [cnf transformation 53]
90. ~happy(X0) | ~kind(X0) [cnf transformation 53]
94. happy(paul) | humble(paul) | ~old(john) [cnf transformation 55]
102. ~humble(X0) | happy(X0) [cnf transformation 33]
130. old(john) [cnf transformation 24]
170. ~happy(X0) [subsumption resolution 89,90]
177. 10 <=> humble(paul) [avatar definition]
179. humble(paul) <- (10) [avatar component clause 177]
181. humble(paul) | ~old(john) [subsumption resolution 94,170]
183. 11 <=> old(john) [avatar definition]
186. ~11 | 10 [avatar split clause 181,177,183]
189. ~humble(X0) [subsumption resolution 102,170]
287. 11 [avatar split clause 130,183]
288. $false <- (10) [subsumption resolution 179,189]
289. ~10 [avatar contradiction clause 288]
290. $false [avatar sat refutation 186,287,289]
% SZS output end Proof for 3057805875219791834837931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not tall is both brave and wise and vice versa.
Everyone who is not rich or strong is both not generous and not brave.
If someone is strong then someone is both not strong and not tall and vice versa.
Everyone who is both not tall and not generous is kind or strong and vice versa.
Everyone who is both creative and wise is both not tall and tall.
If someone is not brave or kind then someone is both not rich and generous.
If someone is both creative and not old then susan is both brave and not tall and vice versa.
If paul is kind then john is not rich or not wise.
If lucy is not quiet or not brave then alice is not calm or generous and vice versa.
Everyone who is not funny or not old is either not curious or tall.
If someone is both quiet and tall then paul is both rich and humble.
Everyone who is not patient is not kind and vice versa.
Everyone who is either patient or kind is either not old or happy and vice versa.
Everyone who is both not happy and generous is either wise or calm.
Everyone who is both not generous and tall is not humble and vice versa.
Everyone who is not curious or not calm is both old and not patient and vice versa.
Someone is creative or not humble.
Susan is not calm or quiet.
John is both not patient and quiet.
John is either not curious or not humble.
Alice is not humble.
Mary is not strong or funny. | Alice is wise. | contradiction | (![X]:((~creative(X)&~tall(X))<=>(brave(X)&wise(X))))&
(![X]:((~rich(X)|strong(X))=>(~generous(X)&~brave(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&~tall(X)))))&
(![X]:((~tall(X)&~generous(X))<=>(kind(X)|strong(X))))&
(![X]:((creative(X)&wise(X))=>(~tall(X)&tall(X))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~rich(X)&generous(X)))))&
((?[X]:((creative(X)&~old(X))))<=>((brave(susan)&~tall(susan))))&
((kind(paul))=>((~rich(john)|~wise(john))))&
(((~quiet(lucy)|~brave(lucy)))<=>((~calm(alice)|generous(alice))))&
(![X]:((~funny(X)|~old(X))=>(~curious(X)<~>tall(X))))&
((?[X]:((quiet(X)&tall(X))))=>((rich(paul)&humble(paul))))&
(![X]:(~patient(X)<=>~kind(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~old(X)<~>happy(X))))&
(![X]:((~happy(X)&generous(X))=>(wise(X)<~>calm(X))))&
(![X]:((~generous(X)&tall(X))<=>~humble(X)))&
(![X]:((~curious(X)|~calm(X))<=>(old(X)&~patient(X))))&
(?[X]:((creative(X)|~humble(X))))&
((~calm(susan)|quiet(susan)))&
((~patient(john)&quiet(john)))&
((~curious(john)<~>~humble(john)))&
(~humble(alice))&
((~strong(mary)|funny(mary))) | wise(alice) | [
"p0",
"p1",
"p5",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3521149428896916941175928
% SZS output start Proof for 3521149428896916941175928
1. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> (wise(X0) & brave(X0))) [input p0]
2. ! [X0] : ((strong(X0) | ~rich(X0)) => (~brave(X0) & ~generous(X0))) [input p1]
6. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X0] : (generous(X0) & ~rich(X0)) [input p5]
15. ! [X0] : ((tall(X0) & ~generous(X0)) <=> ~humble(X0)) [input p14]
21. ~humble(alice) [input p20]
23. wise(alice) [input hypothesis]
25. ? [X0] : (kind(X0) | ~brave(X0)) => ? [X1] : (generous(X1) & ~rich(X1)) [rectify 6]
28. ! [X0] : ((~brave(X0) & ~generous(X0)) | (~strong(X0) & rich(X0))) [ennf transformation 2]
31. ? [X1] : (generous(X1) & ~rich(X1)) | ! [X0] : (~kind(X0) & brave(X0)) [ennf transformation 25]
38. ! [X0] : (((~tall(X0) & ~creative(X0)) | (~wise(X0) | ~brave(X0))) & ((wise(X0) & brave(X0)) | (tall(X0) | creative(X0)))) [nnf transformation 1]
39. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~wise(X0) | ~brave(X0)) & ((wise(X0) & brave(X0)) | tall(X0) | creative(X0))) [flattening 38]
47. ? [X0] : (generous(X0) & ~rich(X0)) | ! [X1] : (~kind(X1) & brave(X1)) [rectify 31]
48. ? [X0] : (generous(X0) & ~rich(X0)) => (generous(sK2) & ~rich(sK2)) [choice axiom]
49. (generous(sK2) & ~rich(sK2)) | ! [X1] : (~kind(X1) & brave(X1)) [skolemisation 47,48]
61. ! [X0] : (((tall(X0) & ~generous(X0)) | humble(X0)) & (~humble(X0) | (~tall(X0) | generous(X0)))) [nnf transformation 15]
62. ! [X0] : (((tall(X0) & ~generous(X0)) | humble(X0)) & (~humble(X0) | ~tall(X0) | generous(X0))) [flattening 61]
71. ~wise(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 39]
72. ~generous(X0) | rich(X0) [cnf transformation 28]
86. ~rich(sK2) | brave(X1) [cnf transformation 49]
88. generous(sK2) | brave(X1) [cnf transformation 49]
117. humble(X0) | tall(X0) [cnf transformation 62]
129. ~humble(alice) [cnf transformation 21]
130. wise(alice) [cnf transformation 23]
157. 7 <=> generous(sK2) [avatar definition]
159. generous(sK2) <- (7) [avatar component clause 157]
162. 8 <=> ! [X1] : brave(X1) [avatar definition]
163. brave(X1) <- (8) [avatar component clause 162]
164. 8 | 7 [avatar split clause 88,157,162]
166. 9 <=> rich(sK2) [avatar definition]
168. ~rich(sK2) <- (~9) [avatar component clause 166]
170. 8 | ~9 [avatar split clause 86,166,162]
272. rich(sK2) <- (7) [resolution 72,159]
273. $false <- (7, ~9) [subsumption resolution 272,168]
274. ~7 | 9 [avatar contradiction clause 273]
282. tall(alice) [resolution 117,129]
309. ~tall(alice) | ~brave(alice) [resolution 71,130]
311. ~brave(alice) [subsumption resolution 309,282]
312. $false <- (8) [subsumption resolution 311,163]
313. ~8 [avatar contradiction clause 312]
314. $false [avatar sat refutation 164,170,274,313]
% SZS output end Proof for 3521149428896916941175928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either not generous or not rich and vice versa.
Everyone who is humble is both not wise and generous.
If susan is tall or creative then someone is both generous and patient.
If someone is both curious and not generous then someone is both not funny and creative.
Everyone who is both not creative and not calm is either not humble or generous.
Everyone who is both not patient and rich is old and vice versa.
Everyone who is either brave or not strong is both wise and not funny.
Everyone who is either funny or not strong is not wise or strong and vice versa.
Everyone who is not strong or not calm is not brave and vice versa.
If someone is both rich and not brave then fred is either calm or funny.
Everyone who is both not brave and tall is both not happy and tall and vice versa.
If paul is either not rich or not funny then someone is either patient or calm and vice versa.
If someone is both not funny and not curious then susan is happy.
If fred is not patient or quiet then john is not calm and vice versa.
Lucy is both humble and not creative.
Susan is generous or patient.
Mary is both not humble and quiet.
John is both kind and not rich.
Fred is not creative.
Paul is strong or patient. | Paul is not brave. | entailment | (![X]:(curious(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(humble(X)=>(~wise(X)&generous(X))))&
(((tall(susan)|creative(susan)))=>(?[X]:((generous(X)&patient(X)))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~creative(X)&~calm(X))=>(~humble(X)<~>generous(X))))&
(![X]:((~patient(X)&rich(X))<=>old(X)))&
(![X]:((brave(X)<~>~strong(X))=>(wise(X)&~funny(X))))&
(![X]:((funny(X)<~>~strong(X))<=>(~wise(X)|strong(X))))&
(![X]:((~strong(X)|~calm(X))<=>~brave(X)))&
((?[X]:((rich(X)&~brave(X))))=>((calm(fred)<~>funny(fred))))&
(![X]:((~brave(X)&tall(X))<=>(~happy(X)&tall(X))))&
(((~rich(paul)<~>~funny(paul)))<=>(?[X]:((patient(X)<~>calm(X)))))&
((?[X]:((~funny(X)&~curious(X))))=>(happy(susan)))&
(((~patient(fred)|quiet(fred)))<=>(~calm(john)))&
((humble(lucy)&~creative(lucy)))&
((generous(susan)|patient(susan)))&
((~humble(mary)&quiet(mary)))&
((kind(john)&~rich(john)))&
(~creative(fred))&
((strong(paul)|patient(paul))) | ~brave(paul) | [
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8950720951373667102512933
% SZS output start Proof for 8950720951373667102512933
7. ! [X0] : ((brave(X0) <~> ~strong(X0)) => (~funny(X0) & wise(X0))) [input p6]
8. ! [X0] : ((funny(X0) <~> ~strong(X0)) <=> (strong(X0) | ~wise(X0))) [input p7]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> ~brave(X0)) [input p8]
21. brave(paul) [input hypothesis]
29. ! [X0] : ((~funny(X0) & wise(X0)) | (brave(X0) <=> ~strong(X0))) [ennf transformation 7]
39. ! [X0] : ((~funny(X0) & wise(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0)))) [nnf transformation 29]
40. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [nnf transformation 8]
41. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [flattening 40]
42. ! [X0] : (((~calm(X0) | ~strong(X0)) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [nnf transformation 9]
43. ! [X0] : ((~calm(X0) | ~strong(X0) | brave(X0)) & (~brave(X0) | (calm(X0) & strong(X0)))) [flattening 42]
69. ~strong(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 39]
74. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 41]
77. ~brave(X0) | strong(X0) [cnf transformation 43]
106. brave(paul) [cnf transformation 21]
108. ~strong(X0) | funny(X0) [duplicate literal removal 74]
164. 13 <=> funny(paul) [avatar definition]
165. ~funny(paul) <- (~13) [avatar component clause 164]
166. funny(paul) <- (13) [avatar component clause 164]
219. 24 <=> strong(paul) [avatar definition]
221. strong(paul) <- (24) [avatar component clause 219]
228. strong(paul) [resolution 77,106]
230. funny(paul) <- (24) [resolution 108,221]
231. $false <- (~13, 24) [subsumption resolution 230,165]
232. 13 | ~24 [avatar contradiction clause 231]
233. 24 [avatar split clause 228,219]
293. ~funny(paul) | ~brave(paul) <- (24) [resolution 69,221]
295. ~brave(paul) <- (13, 24) [subsumption resolution 293,166]
296. $false <- (13, 24) [subsumption resolution 295,106]
297. ~13 | ~24 [avatar contradiction clause 296]
298. $false [avatar sat refutation 232,233,297]
% SZS output end Proof for 8950720951373667102512933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is generous.
Everyone who is both not tall and brave is rich.
If mary is both not kind and patient then someone is either not generous or not wise.
If someone is both not wise and not brave then mary is calm or creative.
Everyone who is either tall or not funny is either not rich or quiet.
If someone is happy then susan is both not generous and brave and vice versa.
Everyone who is either not old or patient is both wise and not brave.
Everyone who is not generous or kind is either calm or not quiet and vice versa.
Everyone who is both tall and curious is generous or not wise.
If someone is old or not humble then someone is both not wise and not humble and vice versa.
Everyone who is not kind or strong is either not quiet or rich.
If someone is kind or not rich then someone is patient.
Everyone who is not happy is both not kind and tall.
Everyone who is not creative is either wise or not kind.
Everyone who is curious or old is not old and vice versa.
If someone is wise or not happy then someone is rich and vice versa.
Fred is either not calm or not rich.
Someone is strong or not calm.
John is either happy or brave.
Fred is not calm or tall.
Paul is not patient or not brave.
Someone is not creative. | Mary is not kind. | entailment | (![X]:(patient(X)=>generous(X)))&
(![X]:((~tall(X)&brave(X))=>rich(X)))&
(((~kind(mary)&patient(mary)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((~wise(X)&~brave(X))))=>((calm(mary)|creative(mary))))&
(![X]:((tall(X)<~>~funny(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:(happy(X)))<=>((~generous(susan)&brave(susan))))&
(![X]:((~old(X)<~>patient(X))=>(wise(X)&~brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:((tall(X)&curious(X))=>(generous(X)|~wise(X))))&
((?[X]:((old(X)|~humble(X))))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~kind(X)|strong(X))=>(~quiet(X)<~>rich(X))))&
((?[X]:((kind(X)|~rich(X))))=>(?[X]:(patient(X))))&
(![X]:(~happy(X)=>(~kind(X)&tall(X))))&
(![X]:(~creative(X)=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)|old(X))<=>~old(X)))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:(rich(X))))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:((strong(X)|~calm(X))))&
((happy(john)<~>brave(john)))&
((~calm(fred)|tall(fred)))&
((~patient(paul)|~brave(paul)))&
(?[X]:(~creative(X))) | ~kind(mary) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9105232002249397970753005
% SZS output start Proof for 9105232002249397970753005
1. ! [X0] : (patient(X0) => generous(X0)) [input p0]
6. ? [X0] : happy(X0) <=> (brave(susan) & ~generous(susan)) [input p5]
7. ! [X0] : ((~old(X0) <~> patient(X0)) => (~brave(X0) & wise(X0))) [input p6]
13. ! [X0] : (~happy(X0) => (tall(X0) & ~kind(X0))) [input p12]
15. ! [X0] : ((old(X0) | curious(X0)) <=> ~old(X0)) [input p14]
23. kind(mary) [input hypothesis]
27. ! [X0] : (generous(X0) | ~patient(X0)) [ennf transformation 1]
35. ! [X0] : ((~brave(X0) & wise(X0)) | (~old(X0) <=> patient(X0))) [ennf transformation 7]
40. ! [X0] : ((tall(X0) & ~kind(X0)) | happy(X0)) [ennf transformation 13]
46. (? [X0] : happy(X0) | (~brave(susan) | generous(susan))) & ((brave(susan) & ~generous(susan)) | ! [X0] : ~happy(X0)) [nnf transformation 6]
47. (? [X0] : happy(X0) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X0] : ~happy(X0)) [flattening 46]
48. (? [X0] : happy(X0) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X1] : ~happy(X1)) [rectify 47]
49. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
50. (happy(sK1) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X1] : ~happy(X1)) [skolemisation 48,49]
51. ! [X0] : ((~brave(X0) & wise(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) [nnf transformation 35]
64. ! [X0] : (((old(X0) | curious(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~curious(X0)))) [nnf transformation 15]
65. ! [X0] : ((old(X0) | curious(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~curious(X0)))) [flattening 64]
77. ~patient(X0) | generous(X0) [cnf transformation 27]
86. ~generous(susan) | ~happy(X1) [cnf transformation 50]
87. brave(susan) | ~happy(X1) [cnf transformation 50]
91. ~brave(X0) | patient(X0) | old(X0) [cnf transformation 51]
111. ~kind(X0) | happy(X0) [cnf transformation 40]
116. ~old(X0) | ~old(X0) [cnf transformation 65]
129. kind(mary) [cnf transformation 23]
130. ~old(X0) [duplicate literal removal 116]
133. 1 <=> kind(mary) [avatar definition]
135. kind(mary) <- (1) [avatar component clause 133]
163. 8 <=> generous(susan) [avatar definition]
164. ~generous(susan) <- (~8) [avatar component clause 163]
167. 9 <=> brave(susan) [avatar definition]
168. brave(susan) <- (9) [avatar component clause 167]
176. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
177. ~happy(X1) <- (11) [avatar component clause 176]
178. 11 | 9 [avatar split clause 87,167,176]
179. 11 | ~8 [avatar split clause 86,163,176]
201. 17 <=> ! [X3] : ~old(X3) [avatar definition]
202. ~old(X3) <- (17) [avatar component clause 201]
222. 17 [avatar split clause 130,201]
290. 1 [avatar split clause 129,133]
292. happy(mary) <- (1) [resolution 111,135]
307. $false <- (1, 11) [resolution 177,292]
312. ~1 | ~11 [avatar contradiction clause 307]
328. patient(susan) | old(susan) <- (9) [resolution 91,168]
329. patient(susan) <- (9, 17) [subsumption resolution 328,202]
330. generous(susan) <- (9, 17) [resolution 329,77]
331. $false <- (~8, 9, 17) [subsumption resolution 330,164]
332. 8 | ~9 | ~17 [avatar contradiction clause 331]
333. $false [avatar sat refutation 178,179,222,290,312,332]
% SZS output end Proof for 9105232002249397970753005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not calm is not happy. If someone is both not wise and not happy then fred is not old and vice versa. If fred is not generous or not kind then someone is either brave or not creative and vice versa. If mary is creative then someone is either not creative or brave. If alice is both patient and calm then someone is tall or calm and vice versa. If someone is not old then someone is happy or not curious. Everyone who is either not patient or calm is not kind or calm. Everyone who is calm or not old is either not calm or humble. Everyone who is both strong and wise is not creative or quiet and vice versa. Everyone who is both tall and not strong is either funny or patient and vice versa. Everyone who is not curious is either patient or curious. If someone is either creative or wise then someone is either tall or creative. Everyone who is calm or not brave is either not quiet or old and vice versa. Everyone who is not curious or not kind is not humble or not calm. Everyone who is strong or curious is not strong and vice versa. Everyone who is not wise is both brave and not patient. Fred is either funny or tall. Someone is both not funny and curious. John is not tall. Someone is both not kind and not generous. | Fred is curious. | entailment | (![X]:((strong(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>(~old(fred)))&
(((~generous(fred)|~kind(fred)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
((creative(mary))=>(?[X]:((~creative(X)<~>brave(X)))))&
(((patient(alice)&calm(alice)))<=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(~kind(X)|calm(X))))&
(![X]:((calm(X)|~old(X))=>(~calm(X)<~>humble(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)|quiet(X))))&
(![X]:((tall(X)&~strong(X))<=>(funny(X)<~>patient(X))))&
(![X]:(~curious(X)=>(patient(X)<~>curious(X))))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((calm(X)|~brave(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((~curious(X)|~kind(X))=>(~humble(X)|~calm(X))))&
(![X]:((strong(X)|curious(X))<=>~strong(X)))&
(![X]:(~wise(X)=>(brave(X)&~patient(X))))&
((funny(fred)<~>tall(fred)))&
(?[X]:((~funny(X)&curious(X))))&
(~tall(john))&
(?[X]:((~kind(X)&~generous(X)))) | curious(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7727914594403504605124024
% SZS output start Proof for 7727914594403504605124024
15. ! [X0] : ((curious(X0) | strong(X0)) <=> ~strong(X0)) [input p14]
21. ~curious(fred) [input hypothesis]
69. ! [X0] : (((curious(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [nnf transformation 15]
70. ! [X0] : ((curious(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (~curious(X0) & ~strong(X0)))) [flattening 69]
126. ~strong(X0) | ~strong(X0) [cnf transformation 70]
128. curious(X0) | strong(X0) | strong(X0) [cnf transformation 70]
138. ~curious(fred) [cnf transformation 21]
139. ~strong(X0) [duplicate literal removal 126]
140. curious(X0) | strong(X0) [duplicate literal removal 128]
296. strong(fred) [resolution 140,138]
299. $false [subsumption resolution 296,139]
% SZS output end Proof for 7727914594403504605124024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not wise and strong and vice versa.
Everyone who is both patient and rich is curious and vice versa.
Everyone who is not rich is generous and vice versa.
Everyone who is quiet or kind is both curious and not humble.
Everyone who is tall is either patient or happy.
Everyone who is both not brave and not kind is wise and vice versa.
Everyone who is either not old or not funny is both kind and quiet.
If someone is either calm or not humble then someone is not patient.
If someone is not funny then alice is either not generous or not tall.
Everyone who is both not rich and not kind is funny.
If someone is both calm and not humble then someone is not strong or funny and vice versa.
Everyone who is both old and not strong is both not generous and not creative and vice versa.
Everyone who is calm is rich.
Everyone who is strong or rich is both not brave and creative.
If lucy is both tall and not strong then alice is both kind and curious and vice versa.
Everyone who is not patient or not brave is not humble or patient.
Someone is both not tall and wise.
Someone is patient.
Someone is wise.
Someone is curious.
Someone is old or not curious.
Susan is both not wise and rich.
Fred is either not brave or calm. | Fred is not calm. | entailment | (![X]:(kind(X)<=>(~wise(X)&strong(X))))&
(![X]:((patient(X)&rich(X))<=>curious(X)))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((quiet(X)|kind(X))=>(curious(X)&~humble(X))))&
(![X]:(tall(X)=>(patient(X)<~>happy(X))))&
(![X]:((~brave(X)&~kind(X))<=>wise(X)))&
(![X]:((~old(X)<~>~funny(X))=>(kind(X)&quiet(X))))&
((?[X]:((calm(X)<~>~humble(X))))=>(?[X]:(~patient(X))))&
((?[X]:(~funny(X)))=>((~generous(alice)<~>~tall(alice))))&
(![X]:((~rich(X)&~kind(X))=>funny(X)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((old(X)&~strong(X))<=>(~generous(X)&~creative(X))))&
(![X]:(calm(X)=>rich(X)))&
(![X]:((strong(X)|rich(X))=>(~brave(X)&creative(X))))&
(((tall(lucy)&~strong(lucy)))<=>((kind(alice)&curious(alice))))&
(![X]:((~patient(X)|~brave(X))=>(~humble(X)|patient(X))))&
(?[X]:((~tall(X)&wise(X))))&
(?[X]:(patient(X)))&
(?[X]:(wise(X)))&
(?[X]:(curious(X)))&
(?[X]:((old(X)|~curious(X))))&
((~wise(susan)&rich(susan)))&
((~brave(fred)<~>calm(fred))) | ~calm(fred) | [
"p12",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1464077875566887917966554
% SZS output start Proof for 1464077875566887917966554
13. ! [X0] : (calm(X0) => rich(X0)) [input p12]
14. ! [X0] : ((rich(X0) | strong(X0)) => (creative(X0) & ~brave(X0))) [input p13]
23. ~brave(fred) <~> calm(fred) [input p22]
24. calm(fred) [input hypothesis]
34. ! [X0] : (rich(X0) | ~calm(X0)) [ennf transformation 13]
35. ! [X0] : ((creative(X0) & ~brave(X0)) | (~rich(X0) & ~strong(X0))) [ennf transformation 14]
71. (~calm(fred) | brave(fred)) & (calm(fred) | ~brave(fred)) [nnf transformation 23]
107. ~calm(X0) | rich(X0) [cnf transformation 34]
109. ~brave(X0) | ~rich(X0) [cnf transformation 35]
127. ~calm(fred) | brave(fred) [cnf transformation 71]
128. calm(fred) [cnf transformation 24]
217. 20 <=> brave(fred) [avatar definition]
219. brave(fred) <- (20) [avatar component clause 217]
221. 21 <=> calm(fred) [avatar definition]
222. calm(fred) <- (21) [avatar component clause 221]
224. 20 | ~21 [avatar split clause 127,221,217]
226. 21 [avatar split clause 128,221]
239. rich(fred) <- (21) [resolution 107,222]
241. ~rich(fred) <- (20) [resolution 109,219]
242. $false <- (20, 21) [subsumption resolution 241,239]
243. ~20 | ~21 [avatar contradiction clause 242]
244. $false [avatar sat refutation 224,226,243]
% SZS output end Proof for 1464077875566887917966554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not rich then john is tall.
Everyone who is not creative is both not patient and not humble and vice versa.
If someone is either wise or not creative then lucy is not old.
If someone is both old and calm then john is brave or not funny and vice versa.
Everyone who is either not wise or not humble is either not creative or humble and vice versa.
Everyone who is calm or quiet is both not tall and tall.
Everyone who is kind 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.
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.
Paul is either not humble or rich.
Mary is funny.
Someone is not patient.
Someone is curious or not curious.
Someone is either not tall or not curious.
Paul is both not calm and not brave.
Someone is either kind or not funny.
John is brave or not quiet. | Susan is creative. | entailment | ((~rich(fred))=>(tall(john)))&
(![X]:(~creative(X)<=>(~patient(X)&~humble(X))))&
((?[X]:((wise(X)<~>~creative(X))))=>(~old(lucy)))&
((?[X]:((old(X)&calm(X))))<=>((brave(john)|~funny(john))))&
(![X]:((~wise(X)<~>~humble(X))<=>(~creative(X)<~>humble(X))))&
(![X]:((calm(X)|quiet(X))=>(~tall(X)&tall(X))))&
(![X]:(kind(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))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
((~humble(paul)<~>rich(paul)))&
(funny(mary))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~tall(X)<~>~curious(X))))&
((~calm(paul)&~brave(paul)))&
(?[X]:((kind(X)<~>~funny(X))))&
((brave(john)|~quiet(john))) | creative(susan) | [
"p1",
"p4",
"p5",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1074510848696188291628408
% SZS output start Proof for 1074510848696188291628408
2. ! [X0] : (~creative(X0) <=> (~humble(X0) & ~patient(X0))) [input p1]
5. ! [X0] : ((~wise(X0) <~> ~humble(X0)) <=> (~creative(X0) <~> humble(X0))) [input p4]
6. ! [X0] : ((quiet(X0) | calm(X0)) => (tall(X0) & ~tall(X0))) [input p5]
10. ! [X0] : ((~old(X0) | curious(X0)) => (~wise(X0) | brave(X0))) [input p9]
12. ! [X0] : (brave(X0) <=> patient(X0)) [input p11]
14. (~tall(susan) | old(susan)) => ? [X0] : quiet(X0) [input p13]
24. ~creative(susan) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~tall(X0)) | (~quiet(X0) & ~calm(X0))) [ennf transformation 6]
32. ! [X0] : ((~wise(X0) | brave(X0)) | (old(X0) & ~curious(X0))) [ennf transformation 10]
33. ! [X0] : (~wise(X0) | brave(X0) | (old(X0) & ~curious(X0))) [flattening 32]
34. ? [X0] : quiet(X0) | (tall(susan) & ~old(susan)) [ennf transformation 14]
35. ! [X0] : ((~creative(X0) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | creative(X0))) [nnf transformation 2]
36. ! [X0] : ((~creative(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | creative(X0))) [flattening 35]
43. ! [X0] : ((((humble(X0) | wise(X0)) & (~humble(X0) | ~wise(X0))) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0)))) & (((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))))) [nnf transformation 5]
47. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 12]
50. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
51. quiet(sK2) | (tall(susan) & ~old(susan)) [skolemisation 34,50]
69. ~patient(X0) | creative(X0) [cnf transformation 36]
70. ~humble(X0) | creative(X0) [cnf transformation 36]
85. humble(X0) | wise(X0) | humble(X0) | creative(X0) [cnf transformation 43]
88. ~tall(X0) | ~quiet(X0) [cnf transformation 27]
90. ~quiet(X0) | tall(X0) [cnf transformation 27]
95. ~wise(X0) | brave(X0) | old(X0) [cnf transformation 33]
98. ~brave(X0) | patient(X0) [cnf transformation 47]
106. quiet(sK2) | ~old(susan) [cnf transformation 51]
125. ~creative(susan) [cnf transformation 24]
129. humble(X0) | wise(X0) | creative(X0) [duplicate literal removal 85]
140. 3 <=> ! [X0] : (wise(X0) | creative(X0)) [avatar definition]
141. wise(X0) | creative(X0) <- (3) [avatar component clause 140]
175. wise(X0) | creative(X0) [subsumption resolution 129,70]
176. 3 [avatar split clause 175,140]
180. ~quiet(X0) [subsumption resolution 88,90]
208. ~old(susan) [subsumption resolution 106,180]
281. brave(X0) | old(X0) | creative(X0) <- (3) [resolution 95,141]
285. old(X1) | creative(X1) | patient(X1) <- (3) [resolution 281,98]
304. old(X1) | creative(X1) <- (3) [subsumption resolution 285,69]
327. creative(susan) <- (3) [resolution 304,208]
328. $false <- (3) [subsumption resolution 327,125]
329. ~3 [avatar contradiction clause 328]
330. $false [avatar sat refutation 176,329]
% SZS output end Proof for 1074510848696188291628408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not quiet is either generous or not creative and vice versa.
If someone is both brave and not old then lucy is either not calm or calm and vice versa.
If mary is not patient then alice is not calm.
If lucy is both not tall and calm then someone is quiet and vice versa.
If someone is not happy then someone is not wise or patient.
Everyone who is both not brave and not wise is either happy or not wise and vice versa.
If someone is not creative or quiet then someone is either not patient or not creative.
Everyone who is old is both not old and tall.
If someone is not happy then someone is not wise.
If someone is either calm or not generous then someone is not wise and vice versa.
Everyone who is funny or not patient is either tall or wise.
Everyone who is both old and not creative is curious or calm and vice versa.
If susan is either calm or old then mary is either not funny or not patient.
Everyone who is not brave or not patient is both calm and not patient.
If someone is both not tall and not strong then alice is either kind or not generous and vice versa.
Everyone who is both not patient and not quiet is either not funny or not strong.
Fred is both not humble and not funny.
John is not generous or not curious.
Susan is not creative.
Someone is either not strong or not quiet.
Lucy is both wise and humble. | Alice is funny. | neutral | (![X]:((creative(X)|~quiet(X))<=>(generous(X)<~>~creative(X))))&
((?[X]:((brave(X)&~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
((~patient(mary))=>(~calm(alice)))&
(((~tall(lucy)&calm(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|~patient(X))=>(calm(X)&~patient(X))))&
((?[X]:((~tall(X)&~strong(X))))<=>((kind(alice)<~>~generous(alice))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~strong(X))))&
((~humble(fred)&~funny(fred)))&
((~generous(john)|~curious(john)))&
(~creative(susan))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((wise(lucy)&humble(lucy))) | funny(alice) | [] | null | 0 |
If alice is not calm or not creative then someone is either old or wise.
Everyone who is both not happy and not patient is either old or not happy and vice versa.
If mary is either not brave or brave then lucy is not funny.
If someone is either generous or old then someone is either creative or wise and vice versa.
Everyone who is not kind or not curious is either not generous or not happy.
Everyone who is not old or funny is not calm and vice versa.
If someone is both rich and not curious then someone is either not kind or brave and vice versa.
If someone is humble then someone is funny.
If alice is kind then alice is either creative or kind and vice versa.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
If paul is patient or funny then alice is not happy or not patient and vice versa.
Someone is both curious and humble.
Lucy is not creative.
Lucy is either not generous or humble.
Fred is either creative or not wise.
Someone is either not quiet or patient.
Mary is both not curious and quiet.
Someone is both patient and not quiet. | Alice is creative. | contradiction | (((~calm(alice)|~creative(alice)))=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~brave(mary)<~>brave(mary)))=>(~funny(lucy)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|funny(X))<=>~calm(X)))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((kind(alice))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
(((patient(paul)|funny(paul)))<=>((~happy(alice)|~patient(alice))))&
(?[X]:((curious(X)&humble(X))))&
(~creative(lucy))&
((~generous(lucy)<~>humble(lucy)))&
((creative(fred)<~>~wise(fred)))&
(?[X]:((~quiet(X)<~>patient(X))))&
((~curious(mary)&quiet(mary)))&
(?[X]:((patient(X)&~quiet(X)))) | creative(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4004127512784437641965629
% SZS output start Proof for 4004127512784437641965629
9. kind(alice) <=> (creative(alice) <~> kind(alice)) [input p8]
24. creative(alice) [input hypothesis]
57. (kind(alice) | ((creative(alice) | ~kind(alice)) & (kind(alice) | ~creative(alice)))) & (((~kind(alice) | ~creative(alice)) & (kind(alice) | creative(alice))) | ~kind(alice)) [nnf transformation 9]
117. ~kind(alice) | ~creative(alice) | ~kind(alice) [cnf transformation 57]
118. kind(alice) | kind(alice) | ~creative(alice) [cnf transformation 57]
158. creative(alice) [cnf transformation 24]
159. ~kind(alice) | ~creative(alice) [duplicate literal removal 117]
160. kind(alice) | ~creative(alice) [duplicate literal removal 118]
166. 1 <=> creative(alice) [avatar definition]
272. 24 <=> kind(alice) [avatar definition]
275. ~1 | 24 [avatar split clause 160,272,166]
276. ~1 | ~24 [avatar split clause 159,272,166]
372. 1 [avatar split clause 158,166]
373. $false [avatar sat refutation 275,276,372]
% SZS output end Proof for 4004127512784437641965629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not curious and not funny then lucy is either generous or not funny.
If someone is both not brave and not calm then someone is wise or creative and vice versa.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.
Everyone who is both old and not old is both rich and funny and vice versa.
If someone is either not wise or not funny then mary is both not humble and not happy.
If someone is kind or tall then susan is either not patient or not happy and vice versa.
Everyone who is brave is both kind and not kind and vice versa.
Everyone who is both generous and not creative is quiet or not happy and vice versa.
If susan is not creative then mary is both not strong and patient and vice versa.
If mary is not strong or kind then paul is not tall and vice versa.
Everyone who is either not generous or patient is not brave and vice versa.
Everyone who is both not rich and not patient is either calm or not old and vice versa.
Everyone who is not happy or rich is not patient or rich and vice versa.
Everyone who is happy or not strong is either not curious or not patient.
If someone is both happy and brave then someone is not brave.
Someone is both not happy and old.
Mary is creative or brave.
Alice is either not creative or not curious.
John is either not kind or not patient.
Susan is either not brave or not strong.
John is either old or not humble.
Alice is not humble.
Alice is happy or not old. | Susan is not funny. | entailment | (((~curious(alice)&~funny(alice)))=>((generous(lucy)<~>~funny(lucy))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((wise(X)|creative(X)))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~humble(mary)&~happy(mary))))&
((?[X]:((kind(X)|tall(X))))<=>((~patient(susan)<~>~happy(susan))))&
(![X]:(brave(X)<=>(kind(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(quiet(X)|~happy(X))))&
((~creative(susan))<=>((~strong(mary)&patient(mary))))&
(((~strong(mary)|kind(mary)))<=>(~tall(paul)))&
(![X]:((~generous(X)<~>patient(X))<=>~brave(X)))&
(![X]:((~rich(X)&~patient(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((?[X]:((happy(X)&brave(X))))=>(?[X]:(~brave(X))))&
(?[X]:((~happy(X)&old(X))))&
((creative(mary)|brave(mary)))&
((~creative(alice)<~>~curious(alice)))&
((~kind(john)<~>~patient(john)))&
((~brave(susan)<~>~strong(susan)))&
((old(john)<~>~humble(john)))&
(~humble(alice))&
((happy(alice)|~old(alice))) | ~funny(susan) | [
"p2",
"p4",
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8954062569025376043730684
% SZS output start Proof for 8954062569025376043730684
3. ? [X0] : (~patient(X0) <~> ~kind(X0)) => tall(fred) [input p2]
5. ! [X0] : ((~old(X0) & old(X0)) <=> (funny(X0) & rich(X0))) [input p4]
7. ? [X0] : (tall(X0) | kind(X0)) <=> (~patient(susan) <~> ~happy(susan)) [input p6]
14. ! [X0] : ((rich(X0) | ~happy(X0)) <=> (rich(X0) | ~patient(X0))) [input p13]
20. ~kind(john) <~> ~patient(john) [input p19]
25. funny(susan) [input hypothesis]
30. tall(fred) | ! [X0] : (~patient(X0) <=> ~kind(X0)) [ennf transformation 3]
40. tall(fred) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))) [nnf transformation 30]
43. ! [X0] : (((~old(X0) & old(X0)) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | (old(X0) | ~old(X0)))) [nnf transformation 5]
44. ! [X0] : (((~old(X0) & old(X0)) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | old(X0) | ~old(X0))) [flattening 43]
46. (? [X0] : (tall(X0) | kind(X0)) | ((~patient(susan) | happy(susan)) & (~happy(susan) | patient(susan)))) & (((happy(susan) | patient(susan)) & (~happy(susan) | ~patient(susan))) | ! [X0] : (~tall(X0) & ~kind(X0))) [nnf transformation 7]
47. (? [X0] : (tall(X0) | kind(X0)) | ((~patient(susan) | happy(susan)) & (~happy(susan) | patient(susan)))) & (((happy(susan) | patient(susan)) & (~happy(susan) | ~patient(susan))) | ! [X1] : (~tall(X1) & ~kind(X1))) [rectify 46]
48. ? [X0] : (tall(X0) | kind(X0)) => (tall(sK2) | kind(sK2)) [choice axiom]
49. ((tall(sK2) | kind(sK2)) | ((~patient(susan) | happy(susan)) & (~happy(susan) | patient(susan)))) & (((happy(susan) | patient(susan)) & (~happy(susan) | ~patient(susan))) | ! [X1] : (~tall(X1) & ~kind(X1))) [skolemisation 47,48]
61. ! [X0] : (((rich(X0) | ~happy(X0)) | (~rich(X0) & patient(X0))) & ((rich(X0) | ~patient(X0)) | (~rich(X0) & happy(X0)))) [nnf transformation 14]
62. ! [X0] : ((rich(X0) | ~happy(X0) | (~rich(X0) & patient(X0))) & (rich(X0) | ~patient(X0) | (~rich(X0) & happy(X0)))) [flattening 61]
70. (patient(john) | kind(john)) & (~patient(john) | ~kind(john)) [nnf transformation 20]
81. tall(fred) | ~patient(X0) | kind(X0) [cnf transformation 40]
88. old(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 44]
89. ~rich(X0) | ~funny(X0) | ~old(X0) [cnf transformation 44]
94. ~happy(susan) | ~patient(susan) | ~kind(X1) [cnf transformation 49]
95. ~happy(susan) | ~patient(susan) | ~tall(X1) [cnf transformation 49]
96. happy(susan) | patient(susan) | ~kind(X1) [cnf transformation 49]
97. happy(susan) | patient(susan) | ~tall(X1) [cnf transformation 49]
124. ~patient(X0) | rich(X0) | happy(X0) [cnf transformation 62]
126. ~happy(X0) | rich(X0) | patient(X0) [cnf transformation 62]
139. patient(john) | kind(john) [cnf transformation 70]
146. funny(susan) [cnf transformation 25]
196. 12 <=> ! [X0] : (~patient(X0) | kind(X0)) [avatar definition]
197. ~patient(X0) | kind(X0) <- (12) [avatar component clause 196]
199. 13 <=> tall(fred) [avatar definition]
201. tall(fred) <- (13) [avatar component clause 199]
202. 12 | 13 [avatar split clause 81,199,196]
207. ~rich(X0) | ~funny(X0) [subsumption resolution 88,89]
227. 19 <=> happy(susan) [avatar definition]
229. happy(susan) <- (19) [avatar component clause 227]
231. 20 <=> patient(susan) [avatar definition]
232. patient(susan) <- (20) [avatar component clause 231]
245. 23 <=> ! [X1] : ~tall(X1) [avatar definition]
246. ~tall(X1) <- (23) [avatar component clause 245]
247. 23 | 20 | 19 [avatar split clause 97,227,231,245]
249. 24 <=> ! [X1] : ~kind(X1) [avatar definition]
250. ~kind(X1) <- (24) [avatar component clause 249]
251. 24 | 20 | 19 [avatar split clause 96,227,231,249]
252. 23 | ~20 | ~19 [avatar split clause 95,227,231,245]
253. 24 | ~20 | ~19 [avatar split clause 94,227,231,249]
291. 31 <=> kind(john) [avatar definition]
292. ~kind(john) <- (~31) [avatar component clause 291]
293. kind(john) <- (31) [avatar component clause 291]
295. 32 <=> patient(john) [avatar definition]
297. patient(john) <- (32) [avatar component clause 295]
298. 31 | 32 [avatar split clause 139,295,291]
373. rich(susan) | patient(susan) <- (19) [resolution 126,229]
397. 43 <=> rich(susan) [avatar definition]
399. rich(susan) <- (43) [avatar component clause 397]
400. 20 | 43 | ~19 [avatar split clause 373,227,397,231]
401. rich(susan) | happy(susan) <- (20) [resolution 232,124]
405. $false <- (13, 23) [resolution 246,201]
406. ~13 | ~23 [avatar contradiction clause 405]
409. $false <- (24, 31) [resolution 250,293]
410. ~24 | ~31 [avatar contradiction clause 409]
412. 19 | 43 | ~20 [avatar split clause 401,231,397,227]
436. kind(john) <- (12, 32) [resolution 297,197]
440. $false <- (12, ~31, 32) [subsumption resolution 436,292]
441. ~12 | 31 | ~32 [avatar contradiction clause 440]
460. ~funny(susan) <- (43) [resolution 399,207]
466. $false <- (43) [subsumption resolution 460,146]
467. ~43 [avatar contradiction clause 466]
468. $false [avatar sat refutation 202,247,251,252,253,298,400,406,410,412,441,467]
% SZS output end Proof for 8954062569025376043730684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either strong or curious then alice is both not quiet and not old and vice versa.
Everyone who is strong is kind or not strong and vice versa.
Everyone who is patient or not humble is not creative or not tall and vice versa.
If lucy is both not patient and not happy then someone is either patient or not calm.
Everyone who is not humble or not rich is either not wise or happy and vice versa.
If john is calm or quiet then mary is both not calm and kind.
If someone is either not old or not creative then someone is tall or not humble.
If paul is either not generous or not calm then paul is creative or not tall.
If someone is not old then someone is patient or not brave and vice versa.
Everyone who is both not old and kind is both not calm and not strong and vice versa.
Everyone who is both not patient and not generous is either strong or not tall.
If fred is not calm or not tall then someone is wise and vice versa.
If someone is both creative and not calm then someone is not rich or funny.
Everyone who is either not generous or not creative is either not humble or patient.
If someone is kind then mary is either tall or not patient and vice versa.
Everyone who is both not generous and old is not curious and vice versa.
Someone is not quiet.
Someone is rich or generous.
Someone is either not patient or not calm.
Someone is either not funny or not generous.
Someone is not brave or funny.
John is strong.
Someone is either not funny or not brave. | Alice is brave. | entailment | (((strong(fred)<~>curious(fred)))<=>((~quiet(alice)&~old(alice))))&
(![X]:(strong(X)<=>(kind(X)|~strong(X))))&
(![X]:((patient(X)|~humble(X))<=>(~creative(X)|~tall(X))))&
(((~patient(lucy)&~happy(lucy)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(~wise(X)<~>happy(X))))&
(((calm(john)|quiet(john)))=>((~calm(mary)&kind(mary))))&
((?[X]:((~old(X)<~>~creative(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(((~generous(paul)<~>~calm(paul)))=>((creative(paul)|~tall(paul))))&
((?[X]:(~old(X)))<=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~old(X)&kind(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&~generous(X))=>(strong(X)<~>~tall(X))))&
(((~calm(fred)|~tall(fred)))<=>(?[X]:(wise(X))))&
((?[X]:((creative(X)&~calm(X))))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))=>(~humble(X)<~>patient(X))))&
((?[X]:(kind(X)))<=>((tall(mary)<~>~patient(mary))))&
(![X]:((~generous(X)&old(X))<=>~curious(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((~brave(X)|funny(X))))&
(strong(john))&
(?[X]:((~funny(X)<~>~brave(X)))) | brave(alice) | [
"p1",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4578446273626256915199422
% SZS output start Proof for 4578446273626256915199422
2. ! [X0] : (strong(X0) <=> (~strong(X0) | kind(X0))) [input p1]
9. ? [X0] : ~old(X0) <=> ? [X0] : (~brave(X0) | patient(X0)) [input p8]
10. ! [X0] : ((kind(X0) & ~old(X0)) <=> (~strong(X0) & ~calm(X0))) [input p9]
24. ~brave(alice) [input hypothesis]
26. ? [X0] : ~old(X0) <=> ? [X1] : (~brave(X1) | patient(X1)) [rectify 9]
40. ! [X0] : ((strong(X0) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | ~strong(X0))) [nnf transformation 2]
41. ! [X0] : ((strong(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | ~strong(X0))) [flattening 40]
54. (? [X0] : ~old(X0) | ! [X1] : (brave(X1) & ~patient(X1))) & (? [X1] : (~brave(X1) | patient(X1)) | ! [X0] : old(X0)) [nnf transformation 26]
55. (? [X0] : ~old(X0) | ! [X1] : (brave(X1) & ~patient(X1))) & (? [X2] : (~brave(X2) | patient(X2)) | ! [X3] : old(X3)) [rectify 54]
56. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
57. ? [X2] : (~brave(X2) | patient(X2)) => (~brave(sK3) | patient(sK3)) [choice axiom]
58. (~old(sK2) | ! [X1] : (brave(X1) & ~patient(X1))) & ((~brave(sK3) | patient(sK3)) | ! [X3] : old(X3)) [skolemisation 55,57,56]
59. ! [X0] : (((kind(X0) & ~old(X0)) | (strong(X0) | calm(X0))) & ((~strong(X0) & ~calm(X0)) | (~kind(X0) | old(X0)))) [nnf transformation 10]
60. ! [X0] : (((kind(X0) & ~old(X0)) | strong(X0) | calm(X0)) & ((~strong(X0) & ~calm(X0)) | ~kind(X0) | old(X0))) [flattening 59]
98. ~strong(X0) | kind(X0) | ~strong(X0) [cnf transformation 41]
100. strong(X0) | strong(X0) [cnf transformation 41]
123. ~old(sK2) | brave(X1) [cnf transformation 58]
125. ~strong(X0) | ~kind(X0) | old(X0) [cnf transformation 60]
155. ~brave(alice) [cnf transformation 24]
156. ~strong(X0) | kind(X0) [duplicate literal removal 98]
157. strong(X0) [duplicate literal removal 100]
180. kind(X0) [subsumption resolution 156,157]
248. 20 <=> ! [X1] : brave(X1) [avatar definition]
249. brave(X1) <- (20) [avatar component clause 248]
251. 21 <=> old(sK2) [avatar definition]
253. ~old(sK2) <- (~21) [avatar component clause 251]
254. 20 | ~21 [avatar split clause 123,251,248]
260. 23 <=> ! [X3] : old(X3) [avatar definition]
261. old(X3) <- (23) [avatar component clause 260]
271. ~kind(X0) | old(X0) [subsumption resolution 125,157]
272. old(X0) [subsumption resolution 271,180]
273. 23 [avatar split clause 272,260]
367. $false <- (~21, 23) [subsumption resolution 253,261]
368. 21 | ~23 [avatar contradiction clause 367]
371. $false <- (20) [resolution 249,155]
372. ~20 [avatar contradiction clause 371]
373. $false [avatar sat refutation 254,273,368,372]
% SZS output end Proof for 4578446273626256915199422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not quiet or kind then fred is both creative and not wise and vice versa. If paul is calm or not old then susan is both generous and humble and vice versa. If john is humble then lucy is both curious and not patient. If alice is either wise or rich then susan is not rich or not calm. If fred is happy or patient then someone is both not generous and calm and vice versa. Everyone who is either creative or brave is old and vice versa. If alice is not curious or not old then fred is either not kind or not patient. If someone is kind then someone is both not kind and not patient and vice versa. Everyone who is tall or calm is either patient or not tall and vice versa. If someone is either not calm or happy then paul is generous. Everyone who is wise or rich is both strong and calm and vice versa. Everyone who is either not curious or not strong is either patient or calm and vice versa. If alice is not funny then lucy is kind and vice versa. Everyone who is either humble or not happy is both not brave and not creative and vice versa. If mary is either funny or wise then fred is kind. Everyone who is either brave or not strong is both rich and old and vice versa. Paul is either not kind or curious. Someone is both curious and not brave. John is calm. Lucy is kind or not creative. John is not quiet. John is either brave or funny. Someone is not kind or old. Alice is not old. | John is not curious. | neutral | (((~quiet(paul)<~>kind(paul)))<=>((creative(fred)&~wise(fred))))&
(((calm(paul)|~old(paul)))<=>((generous(susan)&humble(susan))))&
((humble(john))=>((curious(lucy)&~patient(lucy))))&
(((wise(alice)<~>rich(alice)))=>((~rich(susan)|~calm(susan))))&
(((happy(fred)|patient(fred)))<=>(?[X]:((~generous(X)&calm(X)))))&
(![X]:((creative(X)<~>brave(X))<=>old(X)))&
(((~curious(alice)|~old(alice)))=>((~kind(fred)<~>~patient(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((tall(X)|calm(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((~calm(X)<~>happy(X))))=>(generous(paul)))&
(![X]:((wise(X)|rich(X))<=>(strong(X)&calm(X))))&
(![X]:((~curious(X)<~>~strong(X))<=>(patient(X)<~>calm(X))))&
((~funny(alice))<=>(kind(lucy)))&
(![X]:((humble(X)<~>~happy(X))<=>(~brave(X)&~creative(X))))&
(((funny(mary)<~>wise(mary)))=>(kind(fred)))&
(![X]:((brave(X)<~>~strong(X))<=>(rich(X)&old(X))))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((curious(X)&~brave(X))))&
(calm(john))&
((kind(lucy)|~creative(lucy)))&
(~quiet(john))&
((brave(john)<~>funny(john)))&
(?[X]:((~kind(X)|old(X))))&
(~old(alice)) | ~curious(john) | [] | null | 0 |
Everyone who is funny is both not strong and not happy.
Everyone who is both wise and not kind is either old or not creative and vice versa.
If someone is not strong or not wise then john is kind or not calm and vice versa.
Everyone who is not tall or quiet is not quiet.
If someone is either not strong or kind then someone is both funny and brave and vice versa.
Everyone who is either not wise or not strong is either not happy or quiet and vice versa.
If fred is generous or happy then susan is not rich or calm and vice versa.
If someone is not patient or curious then someone is happy or creative.
If alice is not wise then susan is either quiet or not brave.
If someone is either wise or not curious then alice is both not happy and strong and vice versa.
If someone is both not creative and kind then susan is not rich.
Everyone who is both not funny and not calm is both wise and not happy and vice versa.
If susan is not calm then lucy is not patient.
Everyone who is both curious and not creative is calm and vice versa.
Everyone who is not funny or not humble is either quiet or calm.
Someone is both old and patient.
Someone is both brave and not funny.
Someone is both curious and generous.
Someone is strong or quiet.
Alice is rich.
Susan is not rich or not tall.
Someone is either not rich or not calm. | John is kind. | entailment | (![X]:(funny(X)=>(~strong(X)&~happy(X))))&
(![X]:((wise(X)&~kind(X))<=>(old(X)<~>~creative(X))))&
((?[X]:((~strong(X)|~wise(X))))<=>((kind(john)|~calm(john))))&
(![X]:((~tall(X)|quiet(X))=>~quiet(X)))&
((?[X]:((~strong(X)<~>kind(X))))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)<~>quiet(X))))&
(((generous(fred)|happy(fred)))<=>((~rich(susan)|calm(susan))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:((happy(X)|creative(X)))))&
((~wise(alice))=>((quiet(susan)<~>~brave(susan))))&
((?[X]:((wise(X)<~>~curious(X))))<=>((~happy(alice)&strong(alice))))&
((?[X]:((~creative(X)&kind(X))))=>(~rich(susan)))&
(![X]:((~funny(X)&~calm(X))<=>(wise(X)&~happy(X))))&
((~calm(susan))=>(~patient(lucy)))&
(![X]:((curious(X)&~creative(X))<=>calm(X)))&
(![X]:((~funny(X)|~humble(X))=>(quiet(X)<~>calm(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:((strong(X)|quiet(X))))&
(rich(alice))&
((~rich(susan)|~tall(susan)))&
(?[X]:((~rich(X)<~>~calm(X)))) | kind(john) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7959504968933427595692481
% SZS output start Proof for 7959504968933427595692481
1. ! [X0] : (funny(X0) => (~happy(X0) & ~strong(X0))) [input p0]
3. ? [X0] : (~wise(X0) | ~strong(X0)) <=> (~calm(john) | kind(john)) [input p2]
4. ! [X0] : ((quiet(X0) | ~tall(X0)) => ~quiet(X0)) [input p3]
6. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~happy(X0) <~> quiet(X0))) [input p5]
10. ? [X0] : (wise(X0) <~> ~curious(X0)) <=> (strong(alice) & ~happy(alice)) [input p9]
12. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (~happy(X0) & wise(X0))) [input p11]
14. ! [X0] : ((~creative(X0) & curious(X0)) <=> calm(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | ~funny(X0)) => (quiet(X0) <~> calm(X0))) [input p14]
23. ~kind(john) [input hypothesis]
26. ! [X0] : (~funny(X0) => (quiet(X0) <~> calm(X0))) [pure predicate removal 15]
27. ! [X0] : ((~happy(X0) & ~strong(X0)) | ~funny(X0)) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (~quiet(X0) & tall(X0))) [ennf transformation 4]
33. ! [X0] : ((quiet(X0) <~> calm(X0)) | funny(X0)) [ennf transformation 26]
36. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & ((~calm(john) | kind(john)) | ! [X0] : (wise(X0) & strong(X0))) [nnf transformation 3]
37. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X0] : (wise(X0) & strong(X0))) [flattening 36]
38. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X1] : (wise(X1) & strong(X1))) [rectify 37]
39. ? [X0] : (~wise(X0) | ~strong(X0)) => (~wise(sK0) | ~strong(sK0)) [choice axiom]
40. ((~wise(sK0) | ~strong(sK0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X1] : (wise(X1) & strong(X1))) [skolemisation 38,39]
46. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 6]
53. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | (~strong(alice) | happy(alice))) & ((strong(alice) & ~happy(alice)) | ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [nnf transformation 10]
54. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [flattening 53]
55. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X1] : ((wise(X1) | curious(X1)) & (~curious(X1) | ~wise(X1)))) [rectify 54]
56. ? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) => ((curious(sK4) | ~wise(sK4)) & (~curious(sK4) | wise(sK4))) [choice axiom]
57. (((curious(sK4) | ~wise(sK4)) & (~curious(sK4) | wise(sK4))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X1] : ((wise(X1) | curious(X1)) & (~curious(X1) | ~wise(X1)))) [skolemisation 55,56]
58. ! [X0] : (((~calm(X0) & ~funny(X0)) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | (calm(X0) | funny(X0)))) [nnf transformation 12]
59. ! [X0] : (((~calm(X0) & ~funny(X0)) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | calm(X0) | funny(X0))) [flattening 58]
60. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) | ~curious(X0)))) [nnf transformation 14]
61. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | creative(X0) | ~curious(X0))) [flattening 60]
62. ! [X0] : (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | funny(X0)) [nnf transformation 33]
74. ~strong(X0) | ~funny(X0) [cnf transformation 27]
75. ~happy(X0) | ~funny(X0) [cnf transformation 27]
83. ~calm(john) | kind(john) | wise(X1) [cnf transformation 40]
87. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
100. strong(X0) | wise(X0) | quiet(X0) | happy(X0) [cnf transformation 46]
110. ~happy(alice) | ~curious(X1) | ~wise(X1) [cnf transformation 57]
119. ~funny(X0) | happy(X0) | ~wise(X0) [cnf transformation 59]
120. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 59]
123. ~calm(X0) | curious(X0) [cnf transformation 61]
125. calm(X0) | quiet(X0) | funny(X0) [cnf transformation 62]
138. ~kind(john) [cnf transformation 23]
139. ~quiet(X0) [duplicate literal removal 87]
141. 1 <=> calm(john) [avatar definition]
142. ~calm(john) <- (~1) [avatar component clause 141]
143. calm(john) <- (1) [avatar component clause 141]
154. 4 <=> kind(john) [avatar definition]
159. 5 <=> ! [X1] : wise(X1) [avatar definition]
160. wise(X1) <- (5) [avatar component clause 159]
161. 5 | 4 | ~1 [avatar split clause 83,141,154,159]
197. wise(X0) | strong(X0) | happy(X0) [subsumption resolution 100,139]
222. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
223. ~curious(X1) <- (18) [avatar component clause 222]
248. 24 <=> happy(alice) [avatar definition]
249. ~happy(alice) <- (~24) [avatar component clause 248]
270. 29 <=> ! [X1] : (~curious(X1) | ~wise(X1)) [avatar definition]
271. ~curious(X1) | ~wise(X1) <- (29) [avatar component clause 270]
274. 29 | ~24 [avatar split clause 110,248,270]
279. ~wise(X0) | ~funny(X0) [subsumption resolution 119,75]
286. calm(X0) | funny(X0) [subsumption resolution 125,139]
303. ~4 [avatar split clause 138,154]
330. curious(john) <- (1) [resolution 143,123]
332. ~funny(X0) <- (5) [resolution 160,279]
356. happy(X1) | ~wise(X1) | funny(X1) [resolution 120,286]
360. happy(X1) | funny(X1) <- (5) [subsumption resolution 356,160]
361. happy(X1) <- (5) [subsumption resolution 360,332]
362. $false <- (5, ~24) [resolution 361,249]
365. ~5 | 24 [avatar contradiction clause 362]
366. ~curious(X1) <- (5, 29) [subsumption resolution 271,160]
367. 18 | ~5 | ~29 [avatar split clause 366,270,159,222]
368. $false <- (1, 18) [resolution 223,330]
375. ~1 | ~18 [avatar contradiction clause 368]
405. funny(john) <- (~1) [resolution 142,286]
407. 40 <=> funny(john) [avatar definition]
409. funny(john) <- (40) [avatar component clause 407]
415. 40 | 1 [avatar split clause 405,141,407]
450. strong(X0) | happy(X0) | ~funny(X0) [resolution 197,279]
453. strong(X0) | ~funny(X0) [subsumption resolution 450,75]
454. ~funny(X0) [subsumption resolution 453,74]
485. $false <- (40) [resolution 454,409]
488. ~40 [avatar contradiction clause 485]
490. $false [avatar sat refutation 161,274,303,365,367,375,415,488]
% SZS output end Proof for 7959504968933427595692481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then john is both rich and not tall and vice versa. Everyone who is both rich and humble is kind and vice versa. Everyone who is both not wise and not tall is curious or tall and vice versa. Everyone who is either not happy or happy is both brave and strong and vice versa. If susan is not patient or tall then someone is tall and vice versa. Everyone who is not creative is not old or wise. If fred is both not strong and not brave then paul is happy or rich and vice versa. Everyone who is both not quiet and not curious is either happy or not calm. Everyone who is either happy or creative is either happy or not brave. If someone is kind then john is strong or generous. Everyone who is both not patient and rich is not quiet or curious and vice versa. Everyone who is both not generous and wise is not generous. Everyone who is brave is not tall or not funny and vice versa. Everyone who is either old or generous is both kind and not funny. If mary is happy then someone is not curious or not humble. If someone is both not quiet and happy then someone is not calm or generous. Mary is either wise or not wise. Fred is either wise or quiet. Someone is quiet or calm. Someone is both not happy and not funny. Fred is calm or happy. Fred is either creative or not generous. | Fred is not patient. | entailment | ((?[X]:(patient(X)))<=>((rich(john)&~tall(john))))&
(![X]:((rich(X)&humble(X))<=>kind(X)))&
(![X]:((~wise(X)&~tall(X))<=>(curious(X)|tall(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(brave(X)&strong(X))))&
(((~patient(susan)|tall(susan)))<=>(?[X]:(tall(X))))&
(![X]:(~creative(X)=>(~old(X)|wise(X))))&
(((~strong(fred)&~brave(fred)))<=>((happy(paul)|rich(paul))))&
(![X]:((~quiet(X)&~curious(X))=>(happy(X)<~>~calm(X))))&
(![X]:((happy(X)<~>creative(X))=>(happy(X)<~>~brave(X))))&
((?[X]:(kind(X)))=>((strong(john)|generous(john))))&
(![X]:((~patient(X)&rich(X))<=>(~quiet(X)|curious(X))))&
(![X]:((~generous(X)&wise(X))=>~generous(X)))&
(![X]:(brave(X)<=>(~tall(X)|~funny(X))))&
(![X]:((old(X)<~>generous(X))=>(kind(X)&~funny(X))))&
((happy(mary))=>(?[X]:((~curious(X)|~humble(X)))))&
((?[X]:((~quiet(X)&happy(X))))=>(?[X]:((~calm(X)|generous(X)))))&
((wise(mary)<~>~wise(mary)))&
((wise(fred)<~>quiet(fred)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((~happy(X)&~funny(X))))&
((calm(fred)|happy(fred)))&
((creative(fred)<~>~generous(fred))) | ~patient(fred) | [
"p2",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3251783540114630508340285
% SZS output start Proof for 3251783540114630508340285
3. ! [X0] : ((~tall(X0) & ~wise(X0)) <=> (tall(X0) | curious(X0))) [input p2]
11. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (curious(X0) | ~quiet(X0))) [input p10]
18. wise(fred) <~> quiet(fred) [input p17]
23. patient(fred) [input hypothesis]
44. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (tall(X0) | wise(X0)))) [nnf transformation 3]
45. ! [X0] : (((~tall(X0) & ~wise(X0)) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | tall(X0) | wise(X0))) [flattening 44]
57. ! [X0] : (((rich(X0) & ~patient(X0)) | (~curious(X0) & quiet(X0))) & ((curious(X0) | ~quiet(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 11]
58. ! [X0] : (((rich(X0) & ~patient(X0)) | (~curious(X0) & quiet(X0))) & (curious(X0) | ~quiet(X0) | ~rich(X0) | patient(X0))) [flattening 57]
68. (~quiet(fred) | ~wise(fred)) & (quiet(fred) | wise(fred)) [nnf transformation 18]
80. tall(X0) | curious(X0) | tall(X0) | wise(X0) [cnf transformation 45]
84. ~tall(X0) | ~tall(X0) [cnf transformation 45]
108. ~patient(X0) | quiet(X0) [cnf transformation 58]
109. ~curious(X0) | ~patient(X0) [cnf transformation 58]
125. ~quiet(fred) | ~wise(fred) [cnf transformation 68]
132. patient(fred) [cnf transformation 23]
139. tall(X0) | curious(X0) | wise(X0) [duplicate literal removal 80]
140. ~tall(X0) [duplicate literal removal 84]
159. curious(X0) | wise(X0) [subsumption resolution 139,140]
192. 11 <=> wise(fred) [avatar definition]
194. ~wise(fred) <- (~11) [avatar component clause 192]
196. 12 <=> quiet(fred) [avatar definition]
199. ~11 | ~12 [avatar split clause 125,196,192]
231. quiet(fred) [resolution 108,132]
236. 12 [avatar split clause 231,196]
238. ~patient(X1) | wise(X1) [resolution 159,109]
241. wise(fred) [resolution 238,132]
244. $false <- (~11) [subsumption resolution 241,194]
245. 11 [avatar contradiction clause 244]
246. $false [avatar sat refutation 199,236,245]
% SZS output end Proof for 3251783540114630508340285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or creative is both not generous and not happy and vice versa.
Everyone who is either not calm or calm is either not patient or not funny.
Everyone who is not curious or kind is either not creative or strong.
If someone is rich or not humble then someone is both not wise and patient and vice versa.
If someone is either happy or funny then paul is not calm.
If fred is either not humble or not tall then mary is not humble or old and vice versa.
Everyone who is either creative or humble is patient or quiet and vice versa.
Everyone who is funny is either wise or not kind.
Everyone who is happy or curious is curious.
If someone is either not generous or old then someone is not kind.
If someone is not quiet then someone is rich or not wise.
Everyone who is either not funny or not quiet is not quiet or humble and vice versa.
If paul is not quiet then someone is either patient or not calm and vice versa.
If someone is both not calm and not kind then alice is either not old or not curious.
Everyone who is both old and not rich is both not kind and not curious and vice versa.
If someone is either not tall or generous then fred is curious.
Someone is tall or generous.
John is not rich or old.
Paul is old.
Fred is humble.
Someone is not creative or wise.
Alice is not tall or not strong.
Mary is tall or rich.
Alice is both not calm and not wise. | Fred is humble. | entailment | (![X]:((~generous(X)|creative(X))<=>(~generous(X)&~happy(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((~curious(X)|kind(X))=>(~creative(X)<~>strong(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(?[X]:((~wise(X)&patient(X)))))&
((?[X]:((happy(X)<~>funny(X))))=>(~calm(paul)))&
(((~humble(fred)<~>~tall(fred)))<=>((~humble(mary)|old(mary))))&
(![X]:((creative(X)<~>humble(X))<=>(patient(X)|quiet(X))))&
(![X]:(funny(X)=>(wise(X)<~>~kind(X))))&
(![X]:((happy(X)|curious(X))=>curious(X)))&
((?[X]:((~generous(X)<~>old(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(~quiet(X)|humble(X))))&
((~quiet(paul))<=>(?[X]:((patient(X)<~>~calm(X)))))&
((?[X]:((~calm(X)&~kind(X))))=>((~old(alice)<~>~curious(alice))))&
(![X]:((old(X)&~rich(X))<=>(~kind(X)&~curious(X))))&
((?[X]:((~tall(X)<~>generous(X))))=>(curious(fred)))&
(?[X]:((tall(X)|generous(X))))&
((~rich(john)|old(john)))&
(old(paul))&
(humble(fred))&
(?[X]:((~creative(X)|wise(X))))&
((~tall(alice)|~strong(alice)))&
((tall(mary)|rich(mary)))&
((~calm(alice)&~wise(alice))) | humble(fred) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8346725261906962061658328
% SZS output start Proof for 8346725261906962061658328
20. humble(fred) [input p19]
25. ~humble(fred) [input hypothesis]
134. humble(fred) [cnf transformation 20]
140. ~humble(fred) [cnf transformation 25]
196. 12 <=> humble(fred) [avatar definition]
303. 12 [avatar split clause 134,196]
331. ~12 [avatar split clause 140,196]
332. $false [avatar sat refutation 303,331]
% SZS output end Proof for 8346725261906962061658328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is either kind or not curious.
Everyone who is both not calm and not patient is either brave or calm.
Everyone who is both calm and curious is wise.
If someone is either rich or not kind then susan is either old or not humble and vice versa.
Everyone who is either funny or not humble is generous or not happy.
If susan is not happy then someone is either not strong or not humble and vice versa.
If susan is generous then someone is both not creative and kind and vice versa.
If someone is strong or not wise then paul is not creative or old and vice versa.
Everyone who is both generous and not kind is not generous.
If alice is both kind and not old then john is either not generous or not brave.
If someone is rich then paul is both calm and not happy and vice versa.
Everyone who is either kind or not curious is wise or not happy and vice versa.
If paul is not happy then someone is rich.
If someone is both wise and not funny then someone is either not brave or creative and vice versa.
If lucy is both curious and not wise then someone is tall and vice versa.
Someone is not creative.
Someone is generous.
Someone is not quiet or generous.
Fred is either quiet or strong.
Someone is humble.
Fred is generous or quiet. | Alice is brave. | neutral | (![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&~patient(X))=>(brave(X)<~>calm(X))))&
(![X]:((calm(X)&curious(X))=>wise(X)))&
((?[X]:((rich(X)<~>~kind(X))))<=>((old(susan)<~>~humble(susan))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(X)|~happy(X))))&
((~happy(susan))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
((generous(susan))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((strong(X)|~wise(X))))<=>((~creative(paul)|old(paul))))&
(![X]:((generous(X)&~kind(X))=>~generous(X)))&
(((kind(alice)&~old(alice)))=>((~generous(john)<~>~brave(john))))&
((?[X]:(rich(X)))<=>((calm(paul)&~happy(paul))))&
(![X]:((kind(X)<~>~curious(X))<=>(wise(X)|~happy(X))))&
((~happy(paul))=>(?[X]:(rich(X))))&
((?[X]:((wise(X)&~funny(X))))<=>(?[X]:((~brave(X)<~>creative(X)))))&
(((curious(lucy)&~wise(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
(?[X]:((~quiet(X)|generous(X))))&
((quiet(fred)<~>strong(fred)))&
(?[X]:(humble(X)))&
((generous(fred)|quiet(fred))) | brave(alice) | [] | null | 0 |
If paul is either not curious or quiet then someone is both not humble and calm and vice versa.
Everyone who is strong or not curious is both not strong and wise.
Everyone who is rich or not generous is not brave.
If john is wise or not generous then paul is happy or not generous and vice versa.
If someone is patient then someone is both not rich and rich.
If someone is either not brave or not patient then someone is both humble and not humble.
Everyone who is either not old or generous is either generous or not curious.
Everyone who is both funny and strong is not rich or humble and vice versa.
If someone is old or strong then someone is not funny or humble.
Everyone who is not kind is not tall or curious and vice versa.
Everyone who is calm is either not kind or rich and vice versa.
If john is not patient then someone is either generous or strong.
Everyone who is not tall or brave is either funny or not happy and vice versa.
If alice is either kind or not quiet then mary is both generous and not tall and vice versa.
Everyone who is not curious or brave is kind or humble and vice versa.
If someone is either generous or curious then susan is creative and vice versa.
Mary is old or funny.
Someone is either funny or not generous.
Fred is not funny or not humble.
Someone is kind or not strong.
Susan is either wise or brave.
Someone is either quiet or not rich.
Lucy is not happy or not creative. | Mary is not old. | neutral | (((~curious(paul)<~>quiet(paul)))<=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((strong(X)|~curious(X))=>(~strong(X)&wise(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
(((wise(john)|~generous(john)))<=>((happy(paul)|~generous(paul))))&
((?[X]:(patient(X)))=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:((~old(X)<~>generous(X))=>(generous(X)<~>~curious(X))))&
(![X]:((funny(X)&strong(X))<=>(~rich(X)|humble(X))))&
((?[X]:((old(X)|strong(X))))=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:(~kind(X)<=>(~tall(X)|curious(X))))&
(![X]:(calm(X)<=>(~kind(X)<~>rich(X))))&
((~patient(john))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((~tall(X)|brave(X))<=>(funny(X)<~>~happy(X))))&
(((kind(alice)<~>~quiet(alice)))<=>((generous(mary)&~tall(mary))))&
(![X]:((~curious(X)|brave(X))<=>(kind(X)|humble(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(creative(susan)))&
((old(mary)|funny(mary)))&
(?[X]:((funny(X)<~>~generous(X))))&
((~funny(fred)|~humble(fred)))&
(?[X]:((kind(X)|~strong(X))))&
((wise(susan)<~>brave(susan)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~happy(lucy)|~creative(lucy))) | ~old(mary) | [] | null | 0 |
If someone is not kind then someone is either not humble or tall.
If john is kind then someone is either happy or calm and vice versa.
Everyone who is not creative or brave is calm.
If john is old or quiet then mary is not wise or creative.
Everyone who is tall or generous is either not humble or not funny and vice versa.
Everyone who is not brave or generous is not brave.
Everyone who is both not creative and not tall is both not happy and strong and vice versa.
Everyone who is patient is not patient or not funny and vice versa.
Everyone who is not calm is either not kind or not patient.
If someone is not tall then fred is not patient.
Everyone who is either not calm or rich is both kind and rich and vice versa.
If fred is not strong then mary is creative.
Everyone who is either not happy or not humble is either not happy or not patient and vice versa.
If someone is patient or not creative then someone is both not rich and not creative.
Everyone who is patient or happy is both calm and not happy.
If someone is both not tall and not calm then john is both not creative and calm and vice versa.
Someone is not creative or kind.
Susan is either humble or rich.
Mary is either wise or humble.
Someone is rich.
Someone is not curious or funny.
Someone is not creative. | Fred is funny. | contradiction | ((?[X]:(~kind(X)))=>(?[X]:((~humble(X)<~>tall(X)))))&
((kind(john))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((~creative(X)|brave(X))=>calm(X)))&
(((old(john)|quiet(john)))=>((~wise(mary)|creative(mary))))&
(![X]:((tall(X)|generous(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~brave(X)|generous(X))=>~brave(X)))&
(![X]:((~creative(X)&~tall(X))<=>(~happy(X)&strong(X))))&
(![X]:(patient(X)<=>(~patient(X)|~funny(X))))&
(![X]:(~calm(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>(~patient(fred)))&
(![X]:((~calm(X)<~>rich(X))<=>(kind(X)&rich(X))))&
((~strong(fred))=>(creative(mary)))&
(![X]:((~happy(X)<~>~humble(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((patient(X)|~creative(X))))=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((patient(X)|happy(X))=>(calm(X)&~happy(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>((~creative(john)&calm(john))))&
(?[X]:((~creative(X)|kind(X))))&
((humble(susan)<~>rich(susan)))&
((wise(mary)<~>humble(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)|funny(X))))&
(?[X]:(~creative(X))) | funny(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6417450967585571094739749
% SZS output start Proof for 6417450967585571094739749
8. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p7]
23. funny(fred) [input hypothesis]
49. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
50. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 49]
91. ~funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 50]
92. patient(X0) | patient(X0) [cnf transformation 50]
131. funny(fred) [cnf transformation 23]
139. ~funny(X0) | ~patient(X0) [duplicate literal removal 91]
140. patient(X0) [duplicate literal removal 92]
176. ~funny(X0) [subsumption resolution 139,140]
222. $false [subsumption resolution 131,176]
% SZS output end Proof for 6417450967585571094739749
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or not generous then fred is rich or not generous and vice versa.
Everyone who is generous is either not old or not humble and vice versa.
If susan is either humble or strong then someone is both not kind and not old.
Everyone who is not tall or old is both wise and kind.
Everyone who is both not funny and not brave is either not old or old.
If someone is funny then paul is both not rich and not generous and vice versa.
Everyone who is tall is either not tall or not rich.
Everyone who is both generous and wise is both not tall and not patient.
Everyone who is creative is curious or not generous and vice versa.
If susan is both not rich and not curious then alice is not happy or not funny and vice versa.
Everyone who is wise or not happy is not tall or rich and vice versa.
If someone is not humble then someone is either not tall or not rich and vice versa.
Everyone who is curious or not funny is both generous and rich and vice versa.
Everyone who is humble or strong is not creative.
If john is both not wise and not rich then john is quiet or curious.
If someone is both rich and happy then fred is curious or not funny and vice versa.
Alice is not rich or not humble.
Susan is both quiet and brave.
Someone is either not humble or rich.
Someone is not rich or patient.
Paul is kind or not strong.
Mary is either rich or not curious.
Someone is generous.
Alice is both funny and not old. | Fred is not funny. | neutral | ((?[X]:((wise(X)<~>~generous(X))))<=>((rich(fred)|~generous(fred))))&
(![X]:(generous(X)<=>(~old(X)<~>~humble(X))))&
(((humble(susan)<~>strong(susan)))=>(?[X]:((~kind(X)&~old(X)))))&
(![X]:((~tall(X)|old(X))=>(wise(X)&kind(X))))&
(![X]:((~funny(X)&~brave(X))=>(~old(X)<~>old(X))))&
((?[X]:(funny(X)))<=>((~rich(paul)&~generous(paul))))&
(![X]:(tall(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((generous(X)&wise(X))=>(~tall(X)&~patient(X))))&
(![X]:(creative(X)<=>(curious(X)|~generous(X))))&
(((~rich(susan)&~curious(susan)))<=>((~happy(alice)|~funny(alice))))&
(![X]:((wise(X)|~happy(X))<=>(~tall(X)|rich(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((curious(X)|~funny(X))<=>(generous(X)&rich(X))))&
(![X]:((humble(X)|strong(X))=>~creative(X)))&
(((~wise(john)&~rich(john)))=>((quiet(john)|curious(john))))&
((?[X]:((rich(X)&happy(X))))<=>((curious(fred)|~funny(fred))))&
((~rich(alice)|~humble(alice)))&
((quiet(susan)&brave(susan)))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~rich(X)|patient(X))))&
((kind(paul)|~strong(paul)))&
((rich(mary)<~>~curious(mary)))&
(?[X]:(generous(X)))&
((funny(alice)&~old(alice))) | ~funny(fred) | [] | null | 0 |
Everyone who is either not old or not funny is patient and vice versa.
Everyone who is either not curious or not rich is either not calm or not tall.
If alice is not brave or quiet then john is either happy or not humble and vice versa.
If someone is not patient or quiet then alice is curious or creative and vice versa.
If alice is both strong and not kind then someone is either quiet or not curious.
Everyone who is both not humble and not curious is either not happy or not patient and vice versa.
If someone is both not rich and not tall then fred is happy or not happy and vice versa.
If someone is humble or old then alice is not quiet.
Everyone who is both not wise and not humble is either not happy or rich and vice versa.
Everyone who is calm is both patient and kind.
Everyone who is both not creative and not brave is kind and vice versa.
Everyone who is humble is not happy and vice versa.
If someone is happy or creative then alice is not wise or humble and vice versa.
Everyone who is either not tall or calm is either not brave or not quiet.
Everyone who is either kind or patient is either not brave or humble.
Everyone who is either not old or not tall is both not curious and old.
Someone is rich.
Fred is both funny and rich.
Someone is funny.
Someone is strong or not rich.
Someone is not kind.
Someone is generous or not humble.
Someone is either not strong or not happy.
Paul is not humble. | Paul is funny. | neutral | (![X]:((~old(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~curious(X)<~>~rich(X))=>(~calm(X)<~>~tall(X))))&
(((~brave(alice)|quiet(alice)))<=>((happy(john)<~>~humble(john))))&
((?[X]:((~patient(X)|quiet(X))))<=>((curious(alice)|creative(alice))))&
(((strong(alice)&~kind(alice)))=>(?[X]:((quiet(X)<~>~curious(X)))))&
(![X]:((~humble(X)&~curious(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((~rich(X)&~tall(X))))<=>((happy(fred)|~happy(fred))))&
((?[X]:((humble(X)|old(X))))=>(~quiet(alice)))&
(![X]:((~wise(X)&~humble(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(calm(X)=>(patient(X)&kind(X))))&
(![X]:((~creative(X)&~brave(X))<=>kind(X)))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:((happy(X)|creative(X))))<=>((~wise(alice)|humble(alice))))&
(![X]:((~tall(X)<~>calm(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>patient(X))=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)<~>~tall(X))=>(~curious(X)&old(X))))&
(?[X]:(rich(X)))&
((funny(fred)&rich(fred)))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:((~strong(X)<~>~happy(X))))&
(~humble(paul)) | funny(paul) | [] | null | 0 |
Everyone who is strong or not curious is either happy or not curious and vice versa.
If alice is not generous then lucy is not wise or curious.
Everyone who is both old and not strong is either not funny or not happy and vice versa.
Everyone who is not curious is creative or tall and vice versa.
If someone is not wise or not creative then john is both not humble and curious and vice versa.
If someone is either funny or creative then paul is brave or happy.
If susan is not quiet then john is funny and vice versa.
Everyone who is either tall or wise is either rich or not kind.
If paul is curious or patient then someone is either not old or not curious and vice versa.
Everyone who is patient or wise is creative or humble and vice versa.
If alice is creative or not funny then paul is calm or kind and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not old is both calm and not calm.
If someone is either humble or quiet then someone is not humble or not strong and vice versa.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Someone is both old and kind.
Someone is humble or not wise.
Paul is brave or not strong.
Susan is either rich or not brave.
John is calm or not strong.
Someone is generous. | Mary is not curious. | entailment | (![X]:((strong(X)|~curious(X))<=>(happy(X)<~>~curious(X))))&
((~generous(alice))=>((~wise(lucy)|curious(lucy))))&
(![X]:((old(X)&~strong(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(creative(X)|tall(X))))&
((?[X]:((~wise(X)|~creative(X))))<=>((~humble(john)&curious(john))))&
((?[X]:((funny(X)<~>creative(X))))=>((brave(paul)|happy(paul))))&
((~quiet(susan))<=>(funny(john)))&
(![X]:((tall(X)<~>wise(X))=>(rich(X)<~>~kind(X))))&
(((curious(paul)|patient(paul)))<=>(?[X]:((~old(X)<~>~curious(X)))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|humble(X))))&
(((creative(alice)|~funny(alice)))<=>((calm(paul)|kind(paul))))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)=>(calm(X)&~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((~humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(?[X]:((old(X)&kind(X))))&
(?[X]:((humble(X)|~wise(X))))&
((brave(paul)|~strong(paul)))&
((rich(susan)<~>~brave(susan)))&
((calm(john)|~strong(john)))&
(?[X]:(generous(X))) | ~curious(mary) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9184584933404005170244292
% SZS output start Proof for 9184584933404005170244292
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> (happy(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : ((~strong(X0) & old(X0)) <=> (~funny(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : (~curious(X0) <=> (tall(X0) | creative(X0))) [input p3]
5. ? [X0] : (~creative(X0) | ~wise(X0)) <=> (curious(john) & ~humble(john)) [input p4]
7. ~quiet(susan) <=> funny(john) [input p6]
13. ! [X0] : (~old(X0) => (~calm(X0) & calm(X0))) [input p12]
16. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p15]
23. curious(mary) [input hypothesis]
30. ! [X0] : ((~calm(X0) & calm(X0)) | old(X0)) [ennf transformation 13]
32. ! [X0] : (((~curious(X0) | strong(X0)) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0)))) & (((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | (curious(X0) & ~strong(X0)))) [nnf transformation 1]
33. ! [X0] : ((~curious(X0) | strong(X0) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0)))) & (((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | (curious(X0) & ~strong(X0)))) [flattening 32]
34. ! [X0] : (((~strong(X0) & old(X0)) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) & (((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (strong(X0) | ~old(X0)))) [nnf transformation 3]
35. ! [X0] : (((~strong(X0) & old(X0)) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) & (((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | strong(X0) | ~old(X0))) [flattening 34]
36. ! [X0] : ((~curious(X0) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | curious(X0))) [nnf transformation 4]
37. ! [X0] : ((~curious(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | curious(X0))) [flattening 36]
38. (? [X0] : (~creative(X0) | ~wise(X0)) | (~curious(john) | humble(john))) & ((curious(john) & ~humble(john)) | ! [X0] : (creative(X0) & wise(X0))) [nnf transformation 5]
39. (? [X0] : (~creative(X0) | ~wise(X0)) | ~curious(john) | humble(john)) & ((curious(john) & ~humble(john)) | ! [X0] : (creative(X0) & wise(X0))) [flattening 38]
40. (? [X0] : (~creative(X0) | ~wise(X0)) | ~curious(john) | humble(john)) & ((curious(john) & ~humble(john)) | ! [X1] : (creative(X1) & wise(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~wise(X0)) => (~creative(sK0) | ~wise(sK0)) [choice axiom]
42. ((~creative(sK0) | ~wise(sK0)) | ~curious(john) | humble(john)) & ((curious(john) & ~humble(john)) | ! [X1] : (creative(X1) & wise(X1))) [skolemisation 40,41]
44. (~quiet(susan) | ~funny(john)) & (funny(john) | quiet(susan)) [nnf transformation 7]
62. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 16]
63. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 62]
69. ~curious(X0) | happy(X0) | ~strong(X0) [cnf transformation 33]
73. ~curious(X0) | strong(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 33]
76. ~old(X0) | funny(X0) | strong(X0) | happy(X0) [cnf transformation 35]
79. ~happy(X0) | ~strong(X0) | funny(X0) [cnf transformation 35]
82. ~creative(X0) | ~curious(X0) [cnf transformation 37]
87. curious(john) | creative(X1) [cnf transformation 42]
92. ~quiet(susan) | ~funny(john) [cnf transformation 44]
115. calm(X0) | old(X0) [cnf transformation 30]
116. ~calm(X0) | old(X0) [cnf transformation 30]
129. ~old(X0) | quiet(X0) [cnf transformation 63]
137. curious(mary) [cnf transformation 23]
139. ~happy(X0) | strong(X0) | ~curious(X0) [duplicate literal removal 73]
145. 2 <=> curious(john) [avatar definition]
146. curious(john) <- (2) [avatar component clause 145]
158. 5 <=> ! [X1] : creative(X1) [avatar definition]
159. creative(X1) <- (5) [avatar component clause 158]
160. 5 | 2 [avatar split clause 87,145,158]
184. 11 <=> funny(john) [avatar definition]
186. ~funny(john) <- (~11) [avatar component clause 184]
188. 12 <=> quiet(susan) [avatar definition]
190. ~quiet(susan) <- (~12) [avatar component clause 188]
191. ~11 | ~12 [avatar split clause 92,188,184]
241. old(X0) [subsumption resolution 115,116]
294. quiet(X0) [subsumption resolution 129,241]
324. 41 <=> strong(john) [avatar definition]
325. strong(john) <- (41) [avatar component clause 324]
326. ~strong(john) <- (~41) [avatar component clause 324]
333. $false <- (~12) [subsumption resolution 190,294]
334. 12 [avatar contradiction clause 333]
342. happy(john) | ~strong(john) <- (2) [resolution 69,146]
374. funny(X0) | strong(X0) | happy(X0) [resolution 76,241]
417. strong(john) | happy(john) <- (~11) [resolution 374,186]
425. happy(john) <- (~11, ~41) [subsumption resolution 417,326]
452. strong(john) | ~curious(john) <- (~11, ~41) [resolution 425,139]
456. ~curious(john) <- (~11, ~41) [subsumption resolution 452,326]
457. $false <- (2, ~11, ~41) [subsumption resolution 456,146]
458. ~2 | 11 | 41 [avatar contradiction clause 457]
460. 56 <=> happy(john) [avatar definition]
462. happy(john) <- (56) [avatar component clause 460]
464. ~41 | 56 | ~2 [avatar split clause 342,145,460,324]
472. ~strong(john) | funny(john) <- (56) [resolution 462,79]
475. funny(john) <- (41, 56) [subsumption resolution 472,325]
476. $false <- (~11, 41, 56) [subsumption resolution 475,186]
477. 11 | ~41 | ~56 [avatar contradiction clause 476]
480. ~curious(X1) <- (5) [resolution 159,82]
517. $false <- (5) [resolution 480,137]
520. ~5 [avatar contradiction clause 517]
521. $false [avatar sat refutation 160,191,334,458,464,477,520]
% SZS output end Proof for 9184584933404005170244292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then paul is not curious or not humble and vice versa.
If alice is not brave or curious then someone is not strong and vice versa.
Everyone who is not tall is both not kind and brave.
Everyone who is either strong or patient is not tall or not kind and vice versa.
If someone is not curious or funny then fred is old or quiet and vice versa.
Everyone who is creative is curious or not tall and vice versa.
If someone is either humble or patient then john is either calm or old and vice versa.
Everyone who is both not quiet and brave is either not quiet or not kind and vice versa.
Everyone who is both quiet and tall is happy.
Everyone who is either old or creative is both not happy and old.
If mary is both tall and not wise then alice is humble.
Everyone who is funny or curious is creative or not wise.
Everyone who is not generous or humble is not brave and vice versa.
Everyone who is both not funny and not rich is rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
Someone is both old and not rich.
John is not kind or calm.
John is both not humble and not happy.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Fred is either not calm or funny. | John is generous. | contradiction | ((?[X]:((~curious(X)<~>~old(X))))<=>((~curious(paul)|~humble(paul))))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~tall(X)=>(~kind(X)&brave(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~tall(X)|~kind(X))))&
((?[X]:((~curious(X)|funny(X))))<=>((old(fred)|quiet(fred))))&
(![X]:(creative(X)<=>(curious(X)|~tall(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>((calm(john)<~>old(john))))&
(![X]:((~quiet(X)&brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((quiet(X)&tall(X))=>happy(X)))&
(![X]:((old(X)<~>creative(X))=>(~happy(X)&old(X))))&
(((tall(mary)&~wise(mary)))=>(humble(alice)))&
(![X]:((funny(X)|curious(X))=>(creative(X)|~wise(X))))&
(![X]:((~generous(X)|humble(X))<=>~brave(X)))&
(![X]:((~funny(X)&~rich(X))<=>rich(X)))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
(?[X]:((old(X)&~rich(X))))&
((~kind(john)|calm(john)))&
((~humble(john)&~happy(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
((~calm(fred)<~>funny(fred))) | generous(john) | [
"p2",
"p7",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5676562654766781979382619
% SZS output start Proof for 5676562654766781979382619
3. ! [X0] : (~tall(X0) => (brave(X0) & ~kind(X0))) [input p2]
8. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~quiet(X0) <~> ~kind(X0))) [input p7]
13. ! [X0] : ((humble(X0) | ~generous(X0)) <=> ~brave(X0)) [input p12]
16. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> kind(X0)) [input p15]
19. ~happy(john) & ~humble(john) [input p18]
24. generous(john) [input hypothesis]
25. ! [X0] : ((brave(X0) & ~kind(X0)) | tall(X0)) [ennf transformation 3]
56. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (~brave(X0) | quiet(X0)))) [nnf transformation 8]
57. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) & (((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ~brave(X0) | quiet(X0))) [flattening 56]
59. ! [X0] : (((humble(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) & generous(X0)))) [nnf transformation 13]
60. ! [X0] : ((humble(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~humble(X0) & generous(X0)))) [flattening 59]
67. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) | tall(X0)))) [nnf transformation 16]
68. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | ~quiet(X0) | tall(X0))) [flattening 67]
85. ~kind(X0) | tall(X0) [cnf transformation 25]
109. kind(X0) | quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 57]
111. ~quiet(X0) | ~quiet(X0) | kind(X0) [cnf transformation 57]
124. ~generous(X0) | humble(X0) | brave(X0) [cnf transformation 60]
132. ~tall(X0) | ~kind(X0) [cnf transformation 68]
137. ~humble(john) [cnf transformation 19]
145. generous(john) [cnf transformation 24]
149. kind(X0) | quiet(X0) | ~brave(X0) [duplicate literal removal 109]
150. ~quiet(X0) | kind(X0) [duplicate literal removal 111]
255. ~brave(X0) | kind(X0) [subsumption resolution 149,150]
280. ~kind(X0) [subsumption resolution 132,85]
351. humble(john) | brave(john) [resolution 124,145]
352. brave(john) [subsumption resolution 351,137]
358. kind(john) [resolution 352,255]
361. $false [subsumption resolution 358,280]
% SZS output end Proof for 5676562654766781979382619
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not quiet is curious and vice versa.
If alice is either not happy or not rich then susan is both not quiet and not humble.
Everyone who is wise is either not patient or wise and vice versa.
If someone is not wise then someone is not strong or not quiet.
Everyone who is both brave and rich is either curious or generous and vice versa.
Everyone who is either strong or wise is wise or creative and vice versa.
If alice is generous or not funny then mary is not tall.
If someone is not tall then someone is both quiet and not humble.
Everyone who is calm or curious is both brave and old and vice versa.
If alice is either not quiet or generous then someone is old or generous.
Everyone who is either funny or not happy is kind or not curious and vice versa.
If someone is both not old and generous then susan is both not curious and curious.
Everyone who is not creative or old is either not wise or not humble and vice versa.
Everyone who is both funny and not patient is either brave or not brave.
If lucy is both not quiet and patient then someone is either not old or not brave and vice versa.
If someone is creative or not funny then mary is tall.
Someone is not kind or not tall.
Someone is not brave or not creative.
John is not calm or rich.
Someone is both not calm and rich.
Someone is both not strong and generous.
Paul is either strong or happy.
Lucy is not curious or wise. | John is not patient. | contradiction | (![X]:((humble(X)<~>~quiet(X))<=>curious(X)))&
(((~happy(alice)<~>~rich(alice)))=>((~quiet(susan)&~humble(susan))))&
(![X]:(wise(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((brave(X)&rich(X))<=>(curious(X)<~>generous(X))))&
(![X]:((strong(X)<~>wise(X))<=>(wise(X)|creative(X))))&
(((generous(alice)|~funny(alice)))=>(~tall(mary)))&
((?[X]:(~tall(X)))=>(?[X]:((quiet(X)&~humble(X)))))&
(![X]:((calm(X)|curious(X))<=>(brave(X)&old(X))))&
(((~quiet(alice)<~>generous(alice)))=>(?[X]:((old(X)|generous(X)))))&
(![X]:((funny(X)<~>~happy(X))<=>(kind(X)|~curious(X))))&
((?[X]:((~old(X)&generous(X))))=>((~curious(susan)&curious(susan))))&
(![X]:((~creative(X)|old(X))<=>(~wise(X)<~>~humble(X))))&
(![X]:((funny(X)&~patient(X))=>(brave(X)<~>~brave(X))))&
(((~quiet(lucy)&patient(lucy)))<=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((creative(X)|~funny(X))))=>(tall(mary)))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((~brave(X)|~creative(X))))&
((~calm(john)|rich(john)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~strong(X)&generous(X))))&
((strong(paul)<~>happy(paul)))&
((~curious(lucy)|wise(lucy))) | ~patient(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5156217559952621913633038
% SZS output start Proof for 5156217559952621913633038
3. ! [X0] : (wise(X0) <=> (~patient(X0) <~> wise(X0))) [input p2]
24. ~patient(john) [input hypothesis]
38. ! [X0] : ((wise(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~wise(X0))) [nnf transformation 3]
82. ~wise(X0) | patient(X0) | ~wise(X0) [cnf transformation 38]
83. wise(X0) | wise(X0) | patient(X0) [cnf transformation 38]
143. ~patient(john) [cnf transformation 24]
146. ~wise(X0) | patient(X0) [duplicate literal removal 82]
147. wise(X0) | patient(X0) [duplicate literal removal 83]
168. patient(X0) [subsumption resolution 146,147]
310. $false [subsumption resolution 143,168]
% SZS output end Proof for 5156217559952621913633038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not calm is not patient or calm and vice versa.
If paul is either strong or funny then lucy is funny and vice versa.
Everyone who is either calm or not wise is not wise and vice versa.
Everyone who is tall is either rich or tall.
Everyone who is both funny and not tall is either funny or not creative and vice versa.
Everyone who is both not curious and creative is both strong and not patient.
If someone is not funny then john is both not funny and not rich.
Everyone who is either brave or curious is both kind and not patient and vice versa.
If alice is strong then lucy is calm or strong and vice versa.
Everyone who is either not happy or not strong is both not humble and not quiet and vice versa.
Everyone who is not humble is both humble and not quiet.
If mary is quiet then susan is not generous or old and vice versa.
Everyone who is happy is either funny or not tall and vice versa.
If someone is not strong then fred is strong or rich and vice versa.
Everyone who is both not old and not wise is either not happy or curious.
If someone is either tall or curious then paul is old or brave.
Alice is patient.
Someone is generous or calm.
Fred is wise or not tall.
Lucy is either brave or not funny.
Someone is both patient and not calm.
Fred is not funny.
Alice is funny or old. | Alice is brave. | entailment | (![X]:((~tall(X)<~>~calm(X))<=>(~patient(X)|calm(X))))&
(((strong(paul)<~>funny(paul)))<=>(funny(lucy)))&
(![X]:((calm(X)<~>~wise(X))<=>~wise(X)))&
(![X]:(tall(X)=>(rich(X)<~>tall(X))))&
(![X]:((funny(X)&~tall(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((~curious(X)&creative(X))=>(strong(X)&~patient(X))))&
((?[X]:(~funny(X)))=>((~funny(john)&~rich(john))))&
(![X]:((brave(X)<~>curious(X))<=>(kind(X)&~patient(X))))&
((strong(alice))<=>((calm(lucy)|strong(lucy))))&
(![X]:((~happy(X)<~>~strong(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(~humble(X)=>(humble(X)&~quiet(X))))&
((quiet(mary))<=>((~generous(susan)|old(susan))))&
(![X]:(happy(X)<=>(funny(X)<~>~tall(X))))&
((?[X]:(~strong(X)))<=>((strong(fred)|rich(fred))))&
(![X]:((~old(X)&~wise(X))=>(~happy(X)<~>curious(X))))&
((?[X]:((tall(X)<~>curious(X))))=>((old(paul)|brave(paul))))&
(patient(alice))&
(?[X]:((generous(X)|calm(X))))&
((wise(fred)|~tall(fred)))&
((brave(lucy)<~>~funny(lucy)))&
(?[X]:((patient(X)&~calm(X))))&
(~funny(fred))&
((funny(alice)|old(alice))) | brave(alice) | [
"p0",
"p4",
"p5",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5681134190965142605886701
% SZS output start Proof for 5681134190965142605886701
1. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (calm(X0) | ~patient(X0))) [input p0]
5. ! [X0] : ((~tall(X0) & funny(X0)) <=> (funny(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((creative(X0) & ~curious(X0)) => (~patient(X0) & strong(X0))) [input p5]
8. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (~patient(X0) & kind(X0))) [input p7]
17. patient(alice) [input p16]
24. ~brave(alice) [input hypothesis]
26. ! [X0] : ((~patient(X0) & strong(X0)) | (~creative(X0) | curious(X0))) [ennf transformation 6]
27. ! [X0] : ((~patient(X0) & strong(X0)) | ~creative(X0) | curious(X0)) [flattening 26]
34. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | (~calm(X0) & patient(X0))) & ((calm(X0) | ~patient(X0)) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [nnf transformation 1]
35. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | (~calm(X0) & patient(X0))) & (calm(X0) | ~patient(X0) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [flattening 34]
39. ! [X0] : (((~tall(X0) & funny(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (tall(X0) | ~funny(X0)))) [nnf transformation 5]
40. ! [X0] : (((~tall(X0) & funny(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) & (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | tall(X0) | ~funny(X0))) [flattening 39]
41. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 8]
42. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [flattening 41]
63. calm(X0) | ~patient(X0) | ~tall(X0) | calm(X0) [cnf transformation 35]
65. ~calm(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 35]
79. creative(X0) | ~funny(X0) | tall(X0) | ~funny(X0) [cnf transformation 40]
81. funny(X0) | funny(X0) | creative(X0) [cnf transformation 40]
85. ~creative(X0) | ~patient(X0) | curious(X0) [cnf transformation 27]
91. ~curious(X0) | brave(X0) | ~patient(X0) [cnf transformation 42]
119. patient(alice) [cnf transformation 17]
128. ~brave(alice) [cnf transformation 24]
130. creative(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 79]
131. creative(X0) | funny(X0) [duplicate literal removal 81]
135. calm(X0) | ~patient(X0) | ~tall(X0) [duplicate literal removal 63]
136. ~calm(X0) | ~tall(X0) [duplicate literal removal 65]
137. ~patient(X0) | ~tall(X0) [subsumption resolution 135,136]
155. creative(X0) | tall(X0) [subsumption resolution 130,131]
263. ~patient(X0) | curious(X0) | tall(X0) [resolution 85,155]
265. ~patient(X0) | curious(X0) [subsumption resolution 263,137]
266. curious(alice) [resolution 265,119]
282. brave(alice) | ~patient(alice) [resolution 91,266]
284. ~patient(alice) [subsumption resolution 282,128]
285. $false [subsumption resolution 284,119]
% SZS output end Proof for 5681134190965142605886701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or brave is wise and vice versa. If alice is not rich or not generous then mary is rich and vice versa. Everyone who is curious or patient is both not kind and wise and vice versa. If someone is not wise then susan is not wise. If someone is both generous and not kind then john is not quiet or not happy. If susan is not brave or funny then alice is either not curious or funny. If alice is both calm and not quiet then someone is wise or not old. If mary is either quiet or not rich then someone is either tall or curious. Everyone who is both curious and strong is both old and tall. Everyone who is either quiet or wise is creative or calm. If someone is not humble then someone is both happy and not funny. If susan is not strong then someone is not humble. Everyone who is not tall is both not creative and tall. If someone is not old or humble then someone is not tall and vice versa. Everyone who is either happy or generous is happy or quiet and vice versa. Everyone who is funny is not tall. John is both not rich and not happy. Alice is not humble. Someone is not curious or strong. Lucy is either quiet or not kind. Susan is happy or wise. Someone is patient. Someone is rich or not old. Someone is calm. | Susan is not tall. | contradiction | (![X]:((happy(X)<~>brave(X))<=>wise(X)))&
(((~rich(alice)|~generous(alice)))<=>(rich(mary)))&
(![X]:((curious(X)|patient(X))<=>(~kind(X)&wise(X))))&
((?[X]:(~wise(X)))=>(~wise(susan)))&
((?[X]:((generous(X)&~kind(X))))=>((~quiet(john)|~happy(john))))&
(((~brave(susan)|funny(susan)))=>((~curious(alice)<~>funny(alice))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:((wise(X)|~old(X)))))&
(((quiet(mary)<~>~rich(mary)))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((curious(X)&strong(X))=>(old(X)&tall(X))))&
(![X]:((quiet(X)<~>wise(X))=>(creative(X)|calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((happy(X)&~funny(X)))))&
((~strong(susan))=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)=>(~creative(X)&tall(X))))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:(~tall(X))))&
(![X]:((happy(X)<~>generous(X))<=>(happy(X)|quiet(X))))&
(![X]:(funny(X)=>~tall(X)))&
((~rich(john)&~happy(john)))&
(~humble(alice))&
(?[X]:((~curious(X)|strong(X))))&
((quiet(lucy)<~>~kind(lucy)))&
((happy(susan)|wise(susan)))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:(calm(X))) | ~tall(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 462473365818183849373455
% SZS output start Proof for 462473365818183849373455
13. ! [X0] : (~tall(X0) => (tall(X0) & ~creative(X0))) [input p12]
25. ~tall(susan) [input hypothesis]
41. ! [X0] : ((tall(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 13]
107. tall(X0) | tall(X0) [cnf transformation 41]
128. ~tall(susan) [cnf transformation 25]
131. tall(X0) [duplicate literal removal 107]
272. $false [subsumption resolution 128,131]
% SZS output end Proof for 462473365818183849373455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or funny is both not generous and not kind and vice versa. If lucy is not humble then mary is not old or funny. If someone is happy or not patient then someone is either not brave or rich and vice versa. If someone is both not strong and not quiet then someone is brave or not humble. Everyone who is both quiet and curious is either not generous or not quiet and vice versa. Everyone who is happy or not brave is not kind. Everyone who is not funny or kind is not happy and vice versa. If fred is either curious or not calm then lucy is both not strong and not quiet. If alice is either happy or calm then susan is both not quiet and quiet. If john is either humble or not humble then someone is not generous and vice versa. Everyone who is not old is both funny and not patient. Everyone who is not kind or not generous is both tall and kind and vice versa. If someone is either tall or calm then mary is creative or not strong and vice versa. Everyone who is quiet is not generous or not kind and vice versa. If someone is either brave or not humble then mary is creative and vice versa. Everyone who is either old or curious is either calm or curious and vice versa. Someone is both rich and old. Alice is not happy or old. Someone is either generous or brave. Someone is curious or quiet. John is both humble and not patient. Someone is not generous. | John is not brave. | contradiction | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
((~humble(lucy))=>((~old(mary)|funny(mary))))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((~brave(X)<~>rich(X)))))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(?[X]:((rich(X)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(?[X]:(~generous(X))) | ~brave(john) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2081675011056225989813319
% SZS output start Proof for 2081675011056225989813319
6. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p5]
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
23. ~brave(john) [input hypothesis]
29. ! [X0] : (~kind(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 6]
53. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 12]
54. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 53]
97. ~kind(X0) | brave(X0) [cnf transformation 29]
117. kind(X0) | kind(X0) [cnf transformation 54]
150. ~brave(john) [cnf transformation 23]
155. kind(X0) [duplicate literal removal 117]
327. brave(X0) [resolution 97,155]
328. $false [resolution 327,150]
% SZS output end Proof for 2081675011056225989813319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not quiet then john is both not kind and happy and vice versa.
Everyone who is either brave or curious is either calm or curious and vice versa.
Everyone who is not humble or creative is both not quiet and rich and vice versa.
If paul is both tall and not humble then alice is strong or not kind.
If paul is either not tall or not generous then mary is both not creative and old and vice versa.
Everyone who is both not tall and brave is patient or not calm and vice versa.
Everyone who is strong is not wise and vice versa.
If paul is both not curious and not old then fred is either not kind or not quiet and vice versa.
Everyone who is both not old and not funny is not brave or rich.
If mary is both humble and strong then susan is not old and vice versa.
If alice is not old then someone is both happy and not wise.
Everyone who is not strong or brave is old.
Everyone who is creative or kind is either not creative or brave and vice versa.
If someone is calm or not calm then someone is both not wise and not tall and vice versa.
If someone is either not generous or not strong then someone is both rich and not creative.
Everyone who is kind is rich and vice versa.
Mary is humble or calm.
Someone is not patient.
Susan is happy.
Someone is creative.
Paul is generous or not happy.
Susan is both old and not rich.
Someone is either funny or not tall. | John is not brave. | contradiction | ((?[X]:((happy(X)<~>~quiet(X))))<=>((~kind(john)&happy(john))))&
(![X]:((brave(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:((~humble(X)|creative(X))<=>(~quiet(X)&rich(X))))&
(((tall(paul)&~humble(paul)))=>((strong(alice)|~kind(alice))))&
(((~tall(paul)<~>~generous(paul)))<=>((~creative(mary)&old(mary))))&
(![X]:((~tall(X)&brave(X))<=>(patient(X)|~calm(X))))&
(![X]:(strong(X)<=>~wise(X)))&
(((~curious(paul)&~old(paul)))<=>((~kind(fred)<~>~quiet(fred))))&
(![X]:((~old(X)&~funny(X))=>(~brave(X)|rich(X))))&
(((humble(mary)&strong(mary)))<=>(~old(susan)))&
((~old(alice))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~strong(X)|brave(X))=>old(X)))&
(![X]:((creative(X)|kind(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:((calm(X)|~calm(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:((~generous(X)<~>~strong(X))))=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:(kind(X)<=>rich(X)))&
((humble(mary)|calm(mary)))&
(?[X]:(~patient(X)))&
(happy(susan))&
(?[X]:(creative(X)))&
((generous(paul)|~happy(paul)))&
((old(susan)&~rich(susan)))&
(?[X]:((funny(X)<~>~tall(X)))) | ~brave(john) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 249028556472613092638804
% SZS output start Proof for 249028556472613092638804
2. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p1]
6. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~calm(X0) | patient(X0))) [input p5]
24. ~brave(john) [input hypothesis]
39. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 2]
44. ! [X0] : (((brave(X0) & ~tall(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~brave(X0) | tall(X0)))) [nnf transformation 6]
45. ! [X0] : (((brave(X0) & ~tall(X0)) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ~brave(X0) | tall(X0))) [flattening 44]
78. curious(X0) | calm(X0) | curious(X0) | ~brave(X0) [cnf transformation 39]
81. ~curious(X0) | ~calm(X0) | brave(X0) | ~curious(X0) [cnf transformation 39]
82. curious(X0) | brave(X0) | curious(X0) | ~calm(X0) [cnf transformation 39]
85. ~curious(X0) | ~brave(X0) | calm(X0) | ~curious(X0) [cnf transformation 39]
102. brave(X0) | calm(X0) [cnf transformation 45]
145. ~brave(john) [cnf transformation 24]
148. curious(X0) | calm(X0) | ~brave(X0) [duplicate literal removal 78]
149. ~curious(X0) | ~calm(X0) | brave(X0) [duplicate literal removal 81]
150. curious(X0) | brave(X0) | ~calm(X0) [duplicate literal removal 82]
151. ~curious(X0) | ~brave(X0) | calm(X0) [duplicate literal removal 85]
180. ~calm(X0) | brave(X0) [subsumption resolution 149,150]
181. ~brave(X0) | calm(X0) [subsumption resolution 148,151]
217. calm(X0) [subsumption resolution 102,181]
323. brave(X0) [resolution 180,217]
327. $false [resolution 323,145]
% SZS output end Proof for 249028556472613092638804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not tall and not patient then someone is not kind.
If someone is curious then someone is both generous and not funny and vice versa.
If someone is both curious and creative then someone is both generous and tall.
Everyone who is either not curious or quiet is either not tall or humble.
If someone is either patient or not brave then john is both not calm and not humble and vice versa.
Everyone who is either not strong or not tall is calm and vice versa.
If someone is not curious then alice is either curious or not creative.
Everyone who is either tall or not humble is either not strong or wise.
If lucy is not rich then fred is either strong or happy.
Everyone who is both not tall and not calm is both curious and rich and vice versa.
Everyone who is either not funny or happy is old and vice versa.
Everyone who is not quiet is not humble and vice versa.
If alice is tall then mary is both creative and old and vice versa.
Everyone who is not kind or happy is either not calm or kind.
Everyone who is kind is not strong.
Everyone who is brave or calm is either not brave or not strong and vice versa.
Someone is not patient.
Mary is tall.
Mary is both calm and wise.
Someone is brave.
Someone is either old or generous.
Susan is humble or not kind.
Alice is not curious. | Mary is quiet. | contradiction | (((~tall(alice)&~patient(alice)))=>(?[X]:(~kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((curious(X)&creative(X))))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((~curious(X)<~>quiet(X))=>(~tall(X)<~>humble(X))))&
((?[X]:((patient(X)<~>~brave(X))))<=>((~calm(john)&~humble(john))))&
(![X]:((~strong(X)<~>~tall(X))<=>calm(X)))&
((?[X]:(~curious(X)))=>((curious(alice)<~>~creative(alice))))&
(![X]:((tall(X)<~>~humble(X))=>(~strong(X)<~>wise(X))))&
((~rich(lucy))=>((strong(fred)<~>happy(fred))))&
(![X]:((~tall(X)&~calm(X))<=>(curious(X)&rich(X))))&
(![X]:((~funny(X)<~>happy(X))<=>old(X)))&
(![X]:(~quiet(X)<=>~humble(X)))&
((tall(alice))<=>((creative(mary)&old(mary))))&
(![X]:((~kind(X)|happy(X))=>(~calm(X)<~>kind(X))))&
(![X]:(kind(X)=>~strong(X)))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)<~>~strong(X))))&
(?[X]:(~patient(X)))&
(tall(mary))&
((calm(mary)&wise(mary)))&
(?[X]:(brave(X)))&
(?[X]:((old(X)<~>generous(X))))&
((humble(susan)|~kind(susan)))&
(~curious(alice)) | quiet(mary) | [
"p7",
"p11",
"p13",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4321747213949338533693752
% SZS output start Proof for 4321747213949338533693752
8. ! [X0] : ((tall(X0) <~> ~humble(X0)) => (~strong(X0) <~> wise(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> ~humble(X0)) [input p11]
14. ! [X0] : ((happy(X0) | ~kind(X0)) => (~calm(X0) <~> kind(X0))) [input p13]
15. ! [X0] : (kind(X0) => ~strong(X0)) [input p14]
18. tall(mary) [input p17]
19. wise(mary) & calm(mary) [input p18]
24. quiet(mary) [input hypothesis]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | (tall(X0) <=> ~humble(X0))) [ennf transformation 8]
34. ! [X0] : ((~calm(X0) <~> kind(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 14]
35. ! [X0] : (~strong(X0) | ~kind(X0)) [ennf transformation 15]
54. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) [nnf transformation 32]
59. ! [X0] : ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))) [nnf transformation 12]
62. ! [X0] : (((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (~happy(X0) & kind(X0))) [nnf transformation 34]
96. ~wise(X0) | strong(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 54]
109. ~quiet(X0) | humble(X0) [cnf transformation 59]
113. kind(X0) | ~calm(X0) | kind(X0) [cnf transformation 62]
117. ~strong(X0) | ~kind(X0) [cnf transformation 35]
125. tall(mary) [cnf transformation 18]
126. calm(mary) [cnf transformation 19]
127. wise(mary) [cnf transformation 19]
133. quiet(mary) [cnf transformation 24]
136. ~calm(X0) | kind(X0) [duplicate literal removal 113]
270. humble(mary) [resolution 109,133]
272. kind(mary) [resolution 136,126]
397. 42 <=> strong(mary) [avatar definition]
398. ~strong(mary) <- (~42) [avatar component clause 397]
399. strong(mary) <- (42) [avatar component clause 397]
433. ~kind(mary) <- (42) [resolution 399,117]
440. $false <- (42) [subsumption resolution 433,272]
441. ~42 [avatar contradiction clause 440]
443. strong(mary) | ~humble(mary) | ~tall(mary) [resolution 96,127]
444. ~humble(mary) | ~tall(mary) <- (~42) [subsumption resolution 443,398]
445. ~tall(mary) <- (~42) [subsumption resolution 444,270]
446. $false <- (~42) [subsumption resolution 445,125]
447. 42 [avatar contradiction clause 446]
448. $false [avatar sat refutation 441,447]
% SZS output end Proof for 4321747213949338533693752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is kind.
If someone is quiet or not wise then someone is both not calm and creative and vice versa.
If lucy is not kind then susan is either patient or not creative.
If john is either not patient or not creative then alice is both not rich and rich.
If someone is either creative or not creative then lucy is patient and vice versa.
Everyone who is not patient or not tall is both not tall and not creative.
If someone is patient then someone is either not calm or wise.
If someone is not quiet then fred is either wise or tall.
Everyone who is patient or not wise is not old and vice versa.
Everyone who is generous or calm is both wise and not funny and vice versa.
Everyone who is either not tall or not kind is both not generous and wise and vice versa.
Everyone who is either not wise or not old is funny or not brave.
Everyone who is strong or not patient is calm or quiet.
If paul is not brave then someone is happy and vice versa.
Everyone who is not quiet or not patient is both not generous and funny and vice versa.
If lucy is either patient or not calm then lucy is both not happy and not funny and vice versa.
Susan is either not rich or creative.
John is calm.
Mary is either curious or not quiet.
Someone is either not brave or not creative.
Someone is brave or not generous.
Mary is not quiet.
Mary is creative.
Someone is either tall or not patient. | John is not old. | entailment | (![X]:(~curious(X)=>kind(X)))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~calm(X)&creative(X)))))&
((~kind(lucy))=>((patient(susan)<~>~creative(susan))))&
(((~patient(john)<~>~creative(john)))=>((~rich(alice)&rich(alice))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(patient(lucy)))&
(![X]:((~patient(X)|~tall(X))=>(~tall(X)&~creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((~calm(X)<~>wise(X)))))&
((?[X]:(~quiet(X)))=>((wise(fred)<~>tall(fred))))&
(![X]:((patient(X)|~wise(X))<=>~old(X)))&
(![X]:((generous(X)|calm(X))<=>(wise(X)&~funny(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~generous(X)&wise(X))))&
(![X]:((~wise(X)<~>~old(X))=>(funny(X)|~brave(X))))&
(![X]:((strong(X)|~patient(X))=>(calm(X)|quiet(X))))&
((~brave(paul))<=>(?[X]:(happy(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(~generous(X)&funny(X))))&
(((patient(lucy)<~>~calm(lucy)))<=>((~happy(lucy)&~funny(lucy))))&
((~rich(susan)<~>creative(susan)))&
(calm(john))&
((curious(mary)<~>~quiet(mary)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((brave(X)|~generous(X))))&
(~quiet(mary))&
(creative(mary))&
(?[X]:((tall(X)<~>~patient(X)))) | ~old(john) | [
"p8",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 537887533330165482921941
% SZS output start Proof for 537887533330165482921941
9. ! [X0] : ((~wise(X0) | patient(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((calm(X0) | generous(X0)) <=> (~funny(X0) & wise(X0))) [input p9]
15. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (funny(X0) & ~generous(X0))) [input p14]
18. calm(john) [input p17]
25. old(john) [input hypothesis]
55. ! [X0] : (((~wise(X0) | patient(X0)) | old(X0)) & (~old(X0) | (wise(X0) & ~patient(X0)))) [nnf transformation 9]
56. ! [X0] : ((~wise(X0) | patient(X0) | old(X0)) & (~old(X0) | (wise(X0) & ~patient(X0)))) [flattening 55]
57. ! [X0] : (((calm(X0) | generous(X0)) | (funny(X0) | ~wise(X0))) & ((~funny(X0) & wise(X0)) | (~calm(X0) & ~generous(X0)))) [nnf transformation 10]
58. ! [X0] : ((calm(X0) | generous(X0) | funny(X0) | ~wise(X0)) & ((~funny(X0) & wise(X0)) | (~calm(X0) & ~generous(X0)))) [flattening 57]
66. ! [X0] : (((~patient(X0) | ~quiet(X0)) | (~funny(X0) | generous(X0))) & ((funny(X0) & ~generous(X0)) | (patient(X0) & quiet(X0)))) [nnf transformation 15]
67. ! [X0] : ((~patient(X0) | ~quiet(X0) | ~funny(X0) | generous(X0)) & ((funny(X0) & ~generous(X0)) | (patient(X0) & quiet(X0)))) [flattening 66]
104. ~old(X0) | ~patient(X0) [cnf transformation 56]
110. ~funny(X0) | ~calm(X0) [cnf transformation 58]
126. funny(X0) | patient(X0) [cnf transformation 67]
136. calm(john) [cnf transformation 18]
146. old(john) [cnf transformation 25]
198. 12 <=> patient(john) [avatar definition]
333. ~patient(john) [resolution 104,146]
340. ~calm(X0) | patient(X0) [resolution 126,110]
483. patient(john) [resolution 340,136]
486. 12 [avatar split clause 483,198]
487. ~12 [avatar split clause 333,198]
488. $false [avatar sat refutation 486,487]
% SZS output end Proof for 537887533330165482921941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and happy then susan is kind or not humble.
Everyone who is both creative and not generous is generous.
Everyone who is both tall and wise is both not creative and generous.
Everyone who is funny or not generous is both calm and creative.
If someone is generous then lucy is either patient or creative.
Everyone who is humble is both brave and not curious.
Everyone who is either not creative or quiet is tall and vice versa.
Everyone who is not strong or not tall is brave or not tall.
If lucy is not tall or brave then fred is either wise or generous and vice versa.
If paul is both not creative and creative then someone is not strong or not patient and vice versa.
If someone is both not tall and generous then fred is both not happy and old and vice versa.
If someone is not kind then someone is creative or happy and vice versa.
If paul is either not rich or not tall then someone is both not wise and tall.
If someone is both not old and old then someone is brave and vice versa.
Everyone who is patient or tall is both tall and strong and vice versa.
If someone is both funny and calm then someone is not strong or quiet.
Someone is old.
Fred is either patient or not rich.
Someone is not quiet or funny.
Someone is humble or not creative.
Someone is wise or not wise.
Someone is old or wise.
Someone is curious. | Paul is not generous. | contradiction | ((?[X]:((brave(X)&happy(X))))=>((kind(susan)|~humble(susan))))&
(![X]:((creative(X)&~generous(X))=>generous(X)))&
(![X]:((tall(X)&wise(X))=>(~creative(X)&generous(X))))&
(![X]:((funny(X)|~generous(X))=>(calm(X)&creative(X))))&
((?[X]:(generous(X)))=>((patient(lucy)<~>creative(lucy))))&
(![X]:(humble(X)=>(brave(X)&~curious(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>tall(X)))&
(![X]:((~strong(X)|~tall(X))=>(brave(X)|~tall(X))))&
(((~tall(lucy)|brave(lucy)))<=>((wise(fred)<~>generous(fred))))&
(((~creative(paul)&creative(paul)))<=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~tall(X)&generous(X))))<=>((~happy(fred)&old(fred))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)|happy(X)))))&
(((~rich(paul)<~>~tall(paul)))=>(?[X]:((~wise(X)&tall(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)|tall(X))<=>(tall(X)&strong(X))))&
((?[X]:((funny(X)&calm(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(?[X]:(old(X)))&
((patient(fred)<~>~rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((humble(X)|~creative(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((old(X)|wise(X))))&
(?[X]:(curious(X))) | ~generous(paul) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7007927625113521912230534
% SZS output start Proof for 7007927625113521912230534
2. ! [X0] : ((~generous(X0) & creative(X0)) => generous(X0)) [input p1]
4. ! [X0] : ((~generous(X0) | funny(X0)) => (creative(X0) & calm(X0))) [input p3]
24. ~generous(paul) [input hypothesis]
30. ! [X0] : (generous(X0) | (generous(X0) | ~creative(X0))) [ennf transformation 2]
31. ! [X0] : (generous(X0) | generous(X0) | ~creative(X0)) [flattening 30]
34. ! [X0] : ((creative(X0) & calm(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 4]
87. generous(X0) | generous(X0) | ~creative(X0) [cnf transformation 31]
93. creative(X0) | generous(X0) [cnf transformation 34]
143. ~generous(paul) [cnf transformation 24]
144. generous(X0) | ~creative(X0) [duplicate literal removal 87]
157. generous(X0) [subsumption resolution 93,144]
325. $false [subsumption resolution 143,157]
% SZS output end Proof for 7007927625113521912230534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not rich is generous or not kind.
If someone is calm or not creative then paul is either not happy or not strong and vice versa.
If lucy is both not generous and not strong then fred is kind or calm and vice versa.
Everyone who is brave or not rich is not calm or not rich.
If alice is tall then john is both rich and not patient and vice versa.
If alice is both happy and not kind then someone is either strong or not funny.
If someone is not wise or happy then fred is not funny or not rich.
If fred is not quiet or kind then someone is creative.
Everyone who is either not old or quiet is happy.
If paul is either not tall or not rich then someone is either not funny or quiet and vice versa.
If someone is not quiet or happy then someone is either funny or brave.
Everyone who is happy is both not old and rich.
Everyone who is not tall is not funny or quiet and vice versa.
If fred is both generous and kind then someone is both generous and not tall.
Everyone who is old or not creative is not rich.
Everyone who is not creative is not brave and vice versa.
Mary is either tall or not quiet.
Someone is not brave.
Mary is creative or brave.
Alice is happy or tall.
Someone is patient or not brave.
Alice is not old.
Someone is brave or patient. | Mary is old. | neutral | (![X]:((happy(X)&~rich(X))=>(generous(X)|~kind(X))))&
((?[X]:((calm(X)|~creative(X))))<=>((~happy(paul)<~>~strong(paul))))&
(((~generous(lucy)&~strong(lucy)))<=>((kind(fred)|calm(fred))))&
(![X]:((brave(X)|~rich(X))=>(~calm(X)|~rich(X))))&
((tall(alice))<=>((rich(john)&~patient(john))))&
(((happy(alice)&~kind(alice)))=>(?[X]:((strong(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|happy(X))))=>((~funny(fred)|~rich(fred))))&
(((~quiet(fred)|kind(fred)))=>(?[X]:(creative(X))))&
(![X]:((~old(X)<~>quiet(X))=>happy(X)))&
(((~tall(paul)<~>~rich(paul)))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(happy(X)=>(~old(X)&rich(X))))&
(![X]:(~tall(X)<=>(~funny(X)|quiet(X))))&
(((generous(fred)&kind(fred)))=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((old(X)|~creative(X))=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
((tall(mary)<~>~quiet(mary)))&
(?[X]:(~brave(X)))&
((creative(mary)|brave(mary)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(~old(alice))&
(?[X]:((brave(X)|patient(X)))) | old(mary) | [] | null | 0 |
Everyone who is not tall or not old is both not funny and wise. Everyone who is humble or not wise is both not brave and not curious and vice versa. If someone is either kind or rich then fred is wise or not strong. Everyone who is both not happy and calm is both not tall and old and vice versa. Everyone who is curious is patient. Everyone who is patient or not humble is either strong or not curious and vice versa. If someone is not kind then john is generous or creative. Everyone who is creative or not calm is either generous or curious and vice versa. If someone is not old then alice is wise and vice versa. Everyone who is strong is not quiet or not creative and vice versa. If mary is both not curious and rich then someone is old and vice versa. Everyone who is wise is both strong and not old and vice versa. If someone is not curious or rich then alice is not wise or not funny and vice versa. Everyone who is not funny is either humble or rich. Everyone who is wise or creative is both not patient and not wise and vice versa. Everyone who is happy or not quiet is either not creative or not funny. Lucy is either rich or quiet. Mary is either not kind or old. Mary is not strong. Lucy is tall or patient. | Fred is not humble. | neutral | (![X]:((~tall(X)|~old(X))=>(~funny(X)&wise(X))))&
(![X]:((humble(X)|~wise(X))<=>(~brave(X)&~curious(X))))&
((?[X]:((kind(X)<~>rich(X))))=>((wise(fred)|~strong(fred))))&
(![X]:((~happy(X)&calm(X))<=>(~tall(X)&old(X))))&
(![X]:(curious(X)=>patient(X)))&
(![X]:((patient(X)|~humble(X))<=>(strong(X)<~>~curious(X))))&
((?[X]:(~kind(X)))=>((generous(john)|creative(john))))&
(![X]:((creative(X)|~calm(X))<=>(generous(X)<~>curious(X))))&
((?[X]:(~old(X)))<=>(wise(alice)))&
(![X]:(strong(X)<=>(~quiet(X)|~creative(X))))&
(((~curious(mary)&rich(mary)))<=>(?[X]:(old(X))))&
(![X]:(wise(X)<=>(strong(X)&~old(X))))&
((?[X]:((~curious(X)|rich(X))))<=>((~wise(alice)|~funny(alice))))&
(![X]:(~funny(X)=>(humble(X)<~>rich(X))))&
(![X]:((wise(X)|creative(X))<=>(~patient(X)&~wise(X))))&
(![X]:((happy(X)|~quiet(X))=>(~creative(X)<~>~funny(X))))&
((rich(lucy)<~>quiet(lucy)))&
((~kind(mary)<~>old(mary)))&
(~strong(mary))&
((tall(lucy)|patient(lucy))) | ~humble(fred) | [] | null | 0 |
If lucy is both quiet and curious then fred is patient and vice versa.
Everyone who is not tall is both not humble and creative.
If john is both quiet and not patient then someone is either not quiet or not patient and vice versa.
If someone is both quiet and kind then someone is kind or not happy and vice versa.
If paul is either not old or creative then john is kind or quiet.
Everyone who is not tall or old is not patient or humble and vice versa.
If john is kind or humble then someone is not brave or quiet.
If lucy is not rich or creative then lucy is tall or funny and vice versa.
If mary is either not patient or not generous then mary is not happy or kind.
If fred is not humble or brave then someone is not brave.
Everyone who is either not tall or curious is not tall or quiet and vice versa.
Everyone who is either strong or not quiet is not patient and vice versa.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Everyone who is both not old and not strong is strong or not strong and vice versa.
If someone is calm then alice is strong or humble and vice versa.
Susan is happy or not brave.
John is both not funny and not old.
Someone is either not brave or funny.
Fred is both not quiet and not generous.
Mary is not patient.
Someone is not humble.
Someone is either not strong or wise. | Paul is strong. | contradiction | (((quiet(lucy)&curious(lucy)))<=>(patient(fred)))&
(![X]:(~tall(X)=>(~humble(X)&creative(X))))&
(((quiet(john)&~patient(john)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&kind(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
(((~old(paul)<~>creative(paul)))=>((kind(john)|quiet(john))))&
(![X]:((~tall(X)|old(X))<=>(~patient(X)|humble(X))))&
(((kind(john)|humble(john)))=>(?[X]:((~brave(X)|quiet(X)))))&
(((~rich(lucy)|creative(lucy)))<=>((tall(lucy)|funny(lucy))))&
(((~patient(mary)<~>~generous(mary)))=>((~happy(mary)|kind(mary))))&
(((~humble(fred)|brave(fred)))=>(?[X]:(~brave(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(~tall(X)|quiet(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:((~old(X)&~strong(X))<=>(strong(X)|~strong(X))))&
((?[X]:(calm(X)))<=>((strong(alice)|humble(alice))))&
((happy(susan)|~brave(susan)))&
((~funny(john)&~old(john)))&
(?[X]:((~brave(X)<~>funny(X))))&
((~quiet(fred)&~generous(fred)))&
(~patient(mary))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)<~>wise(X)))) | strong(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7241529210636501126536534
% SZS output start Proof for 7241529210636501126536534
15. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~strong(X0) | strong(X0))) [input p14]
24. strong(paul) [input hypothesis]
67. ! [X0] : (((~strong(X0) & ~old(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (strong(X0) | old(X0)))) [nnf transformation 15]
68. ! [X0] : (((~strong(X0) & ~old(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | strong(X0) | old(X0))) [flattening 67]
132. ~strong(X0) | ~strong(X0) [cnf transformation 68]
148. strong(paul) [cnf transformation 24]
150. ~strong(X0) [duplicate literal removal 132]
375. $false [subsumption resolution 148,150]
% SZS output end Proof for 7241529210636501126536534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and rich is either strong or not generous and vice versa. If someone is both rich and not calm then lucy is either strong or curious. If mary is not wise then someone is not tall or kind. Everyone who is not humble is tall or not happy. If someone is both strong and quiet then susan is happy and vice versa. Everyone who is quiet is not wise or not rich. Everyone who is both not rich and tall is not generous. 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. Paul is both not humble and not generous. Someone is either not funny or not wise. Someone is either not brave or not funny. Alice is both calm and not tall. Susan is not funny or funny. Someone is both not tall and not wise. | Alice is kind. | contradiction | (![X]:((~curious(X)&rich(X))<=>(strong(X)<~>~generous(X))))&
((?[X]:((rich(X)&~calm(X))))=>((strong(lucy)<~>curious(lucy))))&
((~wise(mary))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:(~humble(X)=>(tall(X)|~happy(X))))&
((?[X]:((strong(X)&quiet(X))))<=>(happy(susan)))&
(![X]:(quiet(X)=>(~wise(X)|~rich(X))))&
(![X]:((~rich(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))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | kind(alice) | [
"p7",
"p8",
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6725360586608013504436690
% SZS output start Proof for 6725360586608013504436690
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
14. ! [X0] : ((~curious(X0) <~> ~brave(X0)) <=> (funny(X0) | curious(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
20. ~tall(alice) & calm(alice) [input p19]
23. kind(alice) [input hypothesis]
44. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
45. ! [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 9]
46. ! [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 45]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 47]
56. ! [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 14]
57. ! [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 56]
58. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
59. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 58]
85. ~brave(X0) | patient(X0) [cnf transformation 44]
86. ~patient(X0) | brave(X0) [cnf transformation 44]
90. brave(X0) | patient(X0) | strong(X0) [cnf transformation 46]
94. ~kind(X0) | ~strong(X0) [cnf transformation 48]
108. ~brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 57]
112. ~calm(X0) | curious(X0) [cnf transformation 59]
127. calm(alice) [cnf transformation 20]
132. kind(alice) [cnf transformation 23]
134. ~brave(X0) | ~curious(X0) [duplicate literal removal 108]
180. patient(X0) | strong(X0) [subsumption resolution 90,85]
228. ~strong(alice) [resolution 94,132]
235. curious(alice) [resolution 112,127]
242. brave(X0) | strong(X0) [resolution 180,86]
442. ~curious(X2) | strong(X2) [resolution 242,134]
497. strong(alice) [resolution 442,235]
503. $false [subsumption resolution 497,228]
% SZS output end Proof for 6725360586608013504436690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If paul is brave then someone is both not calm and brave and vice versa. Everyone who is quiet or not happy is quiet or old and vice versa. If mary is not wise or creative then someone is either not rich or not quiet and vice versa. Everyone who is kind is either not kind or not curious and vice versa. If someone is creative or not kind then someone is strong and vice versa. If paul is quiet or creative then someone is creative or kind. If susan is both not old and not funny then lucy is both not quiet and brave and vice versa. If someone is either happy or not creative then someone is both not quiet and not wise and vice versa. If fred is curious or brave then someone is either tall or not strong and vice versa. If someone is strong then lucy is not rich or old. Everyone who is creative is either tall or not creative and vice versa. Everyone who is either rich or strong is not generous or wise. If alice is humble then someone is not generous or old. Everyone who is not old or brave is both not calm and not generous. If fred is curious then someone is generous and vice versa. Everyone who is not humble is either creative or calm and vice versa. Alice is not wise. Mary is either tall or rich. Someone is funny. Alice is either brave or not tall. Someone is brave. John is not curious. Mary is not curious or rich. | Alice is not calm. | entailment | ((brave(paul))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((quiet(X)|~happy(X))<=>(quiet(X)|old(X))))&
(((~wise(mary)|creative(mary)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:(kind(X)<=>(~kind(X)<~>~curious(X))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:(strong(X))))&
(((quiet(paul)|creative(paul)))=>(?[X]:((creative(X)|kind(X)))))&
(((~old(susan)&~funny(susan)))<=>((~quiet(lucy)&brave(lucy))))&
((?[X]:((happy(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)&~wise(X)))))&
(((curious(fred)|brave(fred)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
((?[X]:(strong(X)))=>((~rich(lucy)|old(lucy))))&
(![X]:(creative(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((rich(X)<~>strong(X))=>(~generous(X)|wise(X))))&
((humble(alice))=>(?[X]:((~generous(X)|old(X)))))&
(![X]:((~old(X)|brave(X))=>(~calm(X)&~generous(X))))&
((curious(fred))<=>(?[X]:(generous(X))))&
(![X]:(~humble(X)<=>(creative(X)<~>calm(X))))&
(~wise(alice))&
((tall(mary)<~>rich(mary)))&
(?[X]:(funny(X)))&
((brave(alice)<~>~tall(alice)))&
(?[X]:(brave(X)))&
(~curious(john))&
((~curious(mary)|rich(mary))) | ~calm(alice) | [
"p10",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 844755367508486820075393
% SZS output start Proof for 844755367508486820075393
11. ! [X0] : (creative(X0) <=> (tall(X0) <~> ~creative(X0))) [input p10]
14. ! [X0] : ((brave(X0) | ~old(X0)) => (~generous(X0) & ~calm(X0))) [input p13]
20. brave(alice) <~> ~tall(alice) [input p19]
24. calm(alice) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~calm(X0)) | (~brave(X0) & old(X0))) [ennf transformation 14]
67. ! [X0] : ((creative(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0)))) & (((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | ~creative(X0))) [nnf transformation 11]
79. (tall(alice) | ~brave(alice)) & (~tall(alice) | brave(alice)) [nnf transformation 20]
121. ~creative(X0) | tall(X0) | ~creative(X0) [cnf transformation 67]
124. creative(X0) | tall(X0) | creative(X0) [cnf transformation 67]
129. ~calm(X0) | ~brave(X0) [cnf transformation 34]
140. ~tall(alice) | brave(alice) [cnf transformation 79]
145. calm(alice) [cnf transformation 24]
146. ~creative(X0) | tall(X0) [duplicate literal removal 121]
147. creative(X0) | tall(X0) [duplicate literal removal 124]
323. tall(X0) [subsumption resolution 146,147]
339. brave(alice) [subsumption resolution 140,323]
349. ~brave(alice) [resolution 129,145]
350. $false [subsumption resolution 349,339]
% SZS output end Proof for 844755367508486820075393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and curious then susan is not humble or curious and vice versa. Everyone who is generous is generous or not kind and vice versa. If someone is both kind and quiet then someone is strong or not old. Everyone who is both old and not calm is not rich or not funny and vice versa. Everyone who is both rich and not wise is both curious and quiet. If john is both curious and old then susan is rich and vice versa. Everyone who is either patient or happy is funny or not curious and vice versa. If someone is rich or calm then alice is rich or not old and vice versa. Everyone who is either tall or not funny is both strong and funny and vice versa. If john is both not patient and calm then someone is either not happy or not funny and vice versa. Everyone who is either not rich or not tall is either funny or happy and vice versa. Everyone who is both calm and not humble is not brave or not generous. If someone is not humble or humble then someone is tall. If mary is wise then lucy is either not calm or not happy and vice versa. If someone is not strong or not humble then alice is both patient and quiet and vice versa. If someone is calm then mary is curious and vice versa. Susan is either kind or not calm. Lucy is not quiet. Someone is not generous. Someone is both old and not rich. Someone is both not kind and tall. Someone is not happy or quiet. Mary is both not humble and not creative. Someone is humble or not wise. | Mary is not kind. | neutral | ((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(![X]:((tall(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
(((~patient(john)&calm(john)))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
(![X]:((~rich(X)<~>~tall(X))<=>(funny(X)<~>happy(X))))&
(![X]:((calm(X)&~humble(X))=>(~brave(X)|~generous(X))))&
((?[X]:((~humble(X)|humble(X))))=>(?[X]:(tall(X))))&
((wise(mary))<=>((~calm(lucy)<~>~happy(lucy))))&
((?[X]:((~strong(X)|~humble(X))))<=>((patient(alice)&quiet(alice))))&
((?[X]:(calm(X)))<=>(curious(mary)))&
((kind(susan)<~>~calm(susan)))&
(~quiet(lucy))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)&~rich(X))))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((~happy(X)|quiet(X))))&
((~humble(mary)&~creative(mary)))&
(?[X]:((humble(X)|~wise(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is calm is either not creative or not calm and vice versa.
If someone is quiet or humble then alice is both old and not brave and vice versa.
Everyone who is patient is both kind and not kind and vice versa.
If someone is either not kind or calm then alice is either kind or not generous.
If someone is not funny then someone is both not funny and not quiet.
Everyone who is not rich is either generous or happy.
Everyone who is humble is not humble.
If alice is brave or kind then paul is both not brave and not rich.
If john is not funny then john is either patient or not calm and vice versa.
Everyone who is kind or strong is curious and vice versa.
If someone is patient then someone is not generous.
If john is both happy and not quiet then fred is not quiet and vice versa.
Everyone who is either not strong or generous is funny.
If someone is either funny or kind then someone is both kind and not quiet.
Everyone who is humble is both humble and not kind.
Everyone who is not quiet or not patient is either curious or happy and vice versa.
Someone is either not wise or creative.
Someone is wise.
Paul is both not creative and not patient.
Mary is rich.
Susan is not rich or quiet.
Someone is either generous or tall.
Someone is either not rich or brave.
Someone is not kind. | Alice is not humble. | entailment | (![X]:(calm(X)<=>(~creative(X)<~>~calm(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((old(alice)&~brave(alice))))&
(![X]:(patient(X)<=>(kind(X)&~kind(X))))&
((?[X]:((~kind(X)<~>calm(X))))=>((kind(alice)<~>~generous(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(generous(X)<~>happy(X))))&
(![X]:(humble(X)=>~humble(X)))&
(((brave(alice)|kind(alice)))=>((~brave(paul)&~rich(paul))))&
((~funny(john))<=>((patient(john)<~>~calm(john))))&
(![X]:((kind(X)|strong(X))<=>curious(X)))&
((?[X]:(patient(X)))=>(?[X]:(~generous(X))))&
(((happy(john)&~quiet(john)))<=>(~quiet(fred)))&
(![X]:((~strong(X)<~>generous(X))=>funny(X)))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:((kind(X)&~quiet(X)))))&
(![X]:(humble(X)=>(humble(X)&~kind(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>happy(X))))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:(wise(X)))&
((~creative(paul)&~patient(paul)))&
(rich(mary))&
((~rich(susan)|quiet(susan)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:(~kind(X))) | ~humble(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8258181528718086292768179
% SZS output start Proof for 8258181528718086292768179
7. ! [X0] : (humble(X0) => ~humble(X0)) [input p6]
25. humble(alice) [input hypothesis]
32. ! [X0] : (~humble(X0) | ~humble(X0)) [ennf transformation 7]
99. ~humble(X0) | ~humble(X0) [cnf transformation 32]
141. humble(alice) [cnf transformation 25]
142. ~humble(X0) [duplicate literal removal 99]
164. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
165. ~humble(X1) <- (5) [avatar component clause 164]
205. 5 [avatar split clause 142,164]
295. $false <- (5) [resolution 165,141]
296. ~5 [avatar contradiction clause 295]
297. $false [avatar sat refutation 205,296]
% SZS output end Proof for 8258181528718086292768179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or old is both calm and not brave and vice versa. Everyone who is both humble and calm is both wise and rich. Everyone who is not rich or not patient is creative. Everyone who is humble or not humble is both not strong and not tall. Everyone who is brave or not old is tall. If someone is either not funny or not creative then paul is strong or old. If someone is not wise then someone is either calm or not curious and vice versa. If someone is either not patient or not curious then fred is not patient. If lucy is both kind and not generous then fred is either old or patient and vice versa. Everyone who is both funny and happy is not patient or funny. If alice is both tall and not rich then someone is brave or happy and vice versa. If someone is either not strong or not curious then fred is not generous or strong and vice versa. If someone is both rich and kind then someone is either not strong or happy. If someone is either humble or not kind then someone is either not brave or not strong and vice versa. Everyone who is tall is tall or not curious. Paul is either strong or quiet. John is curious. Paul is not tall. Someone is not tall. Someone is both creative and not wise. Someone is either wise or brave. Paul is not happy or not strong. Paul is both creative and quiet. | Alice is old. | entailment | (![X]:((happy(X)<~>old(X))<=>(calm(X)&~brave(X))))&
(![X]:((humble(X)&calm(X))=>(wise(X)&rich(X))))&
(![X]:((~rich(X)|~patient(X))=>creative(X)))&
(![X]:((humble(X)|~humble(X))=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)|~old(X))=>tall(X)))&
((?[X]:((~funny(X)<~>~creative(X))))=>((strong(paul)|old(paul))))&
((?[X]:(~wise(X)))<=>(?[X]:((calm(X)<~>~curious(X)))))&
((?[X]:((~patient(X)<~>~curious(X))))=>(~patient(fred)))&
(((kind(lucy)&~generous(lucy)))<=>((old(fred)<~>patient(fred))))&
(![X]:((funny(X)&happy(X))=>(~patient(X)|funny(X))))&
(((tall(alice)&~rich(alice)))<=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:((~strong(X)<~>~curious(X))))<=>((~generous(fred)|strong(fred))))&
((?[X]:((rich(X)&kind(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
(![X]:(tall(X)=>(tall(X)|~curious(X))))&
((strong(paul)<~>quiet(paul)))&
(curious(john))&
(~tall(paul))&
(?[X]:(~tall(X)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((wise(X)<~>brave(X))))&
((~happy(paul)|~strong(paul)))&
((creative(paul)&quiet(paul))) | old(alice) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7626434595904860489175236
% SZS output start Proof for 7626434595904860489175236
4. ! [X0] : ((~humble(X0) | humble(X0)) => (~tall(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((~old(X0) | brave(X0)) => tall(X0)) [input p4]
24. ~old(alice) [input hypothesis]
31. ! [X0] : ((~tall(X0) & ~strong(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 4]
32. ! [X0] : (tall(X0) | (old(X0) & ~brave(X0))) [ennf transformation 5]
91. ~tall(X0) | ~humble(X0) [cnf transformation 31]
92. ~tall(X0) | humble(X0) [cnf transformation 31]
94. tall(X0) | old(X0) [cnf transformation 32]
144. ~old(alice) [cnf transformation 24]
145. ~tall(X0) [subsumption resolution 91,92]
147. old(X0) [subsumption resolution 94,145]
241. $false [subsumption resolution 144,147]
% SZS output end Proof for 7626434595904860489175236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not tall is not brave or not wise and vice versa. Everyone who is happy or not creative is not kind. If someone is either not happy or kind then someone is either kind or patient and vice versa. If paul is both happy and strong then fred is not quiet or old and vice versa. If alice is either not old or curious then lucy is not old. If someone is either happy or not old then someone is either rich or calm and vice versa. Everyone who is either not creative or not old is both brave and not happy. Everyone who is not funny or brave is either not calm or humble. Everyone who is both creative and not humble is both not rich and not creative. If mary is both creative and quiet then someone is generous or humble and vice versa. If lucy is tall or not rich then fred is patient or strong and vice versa. Everyone who is not strong is strong. If someone is patient or old then someone is brave or curious and vice versa. Everyone who is either rich or not creative is creative or not generous and vice versa. Everyone who is both not tall and curious is not strong. If lucy is either not quiet or happy then fred is either creative or calm. Someone is both not quiet and rich. John is not strong or kind. Lucy is humble. Alice is generous or not rich. Fred is either not strong or strong. Someone is both not humble and strong. Someone is old or funny. | John is not rich. | contradiction | (![X]:((quiet(X)<~>~tall(X))<=>(~brave(X)|~wise(X))))&
(![X]:((happy(X)|~creative(X))=>~kind(X)))&
((?[X]:((~happy(X)<~>kind(X))))<=>(?[X]:((kind(X)<~>patient(X)))))&
(((happy(paul)&strong(paul)))<=>((~quiet(fred)|old(fred))))&
(((~old(alice)<~>curious(alice)))=>(~old(lucy)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((rich(X)<~>calm(X)))))&
(![X]:((~creative(X)<~>~old(X))=>(brave(X)&~happy(X))))&
(![X]:((~funny(X)|brave(X))=>(~calm(X)<~>humble(X))))&
(![X]:((creative(X)&~humble(X))=>(~rich(X)&~creative(X))))&
(((creative(mary)&quiet(mary)))<=>(?[X]:((generous(X)|humble(X)))))&
(((tall(lucy)|~rich(lucy)))<=>((patient(fred)|strong(fred))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((rich(X)<~>~creative(X))<=>(creative(X)|~generous(X))))&
(![X]:((~tall(X)&curious(X))=>~strong(X)))&
(((~quiet(lucy)<~>happy(lucy)))=>((creative(fred)<~>calm(fred))))&
(?[X]:((~quiet(X)&rich(X))))&
((~strong(john)|kind(john)))&
(humble(lucy))&
((generous(alice)|~rich(alice)))&
((~strong(fred)<~>strong(fred)))&
(?[X]:((~humble(X)&strong(X))))&
(?[X]:((old(X)|funny(X)))) | ~rich(john) | [
"p1",
"p11",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 802728255048696726122099
% SZS output start Proof for 802728255048696726122099
2. ! [X0] : ((~creative(X0) | happy(X0)) => ~kind(X0)) [input p1]
12. ! [X0] : (~strong(X0) => strong(X0)) [input p11]
14. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> (~generous(X0) | creative(X0))) [input p13]
18. kind(john) | ~strong(john) [input p17]
24. ~rich(john) [input hypothesis]
30. ! [X0] : (~kind(X0) | (creative(X0) & ~happy(X0))) [ennf transformation 2]
36. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 12]
69. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 14]
70. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [flattening 69]
84. ~kind(X0) | creative(X0) [cnf transformation 30]
125. strong(X0) | strong(X0) [cnf transformation 36]
132. ~creative(X0) | rich(X0) | ~creative(X0) [cnf transformation 70]
143. kind(john) | ~strong(john) [cnf transformation 18]
150. ~rich(john) [cnf transformation 24]
152. ~creative(X0) | rich(X0) [duplicate literal removal 132]
153. strong(X0) [duplicate literal removal 125]
362. kind(john) [subsumption resolution 143,153]
379. creative(john) [resolution 84,362]
381. rich(john) [resolution 379,152]
382. $false [subsumption resolution 381,150]
% SZS output end Proof for 802728255048696726122099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or funny then lucy is both strong and wise and vice versa.
Everyone who is either not strong or not patient is either kind or calm and vice versa.
If susan is either old or not patient then fred is either quiet or not funny and vice versa.
Everyone who is either old or not humble is not quiet or quiet.
Everyone who is humble is both calm and tall and vice versa.
If someone is quiet then susan is not strong or not happy and vice versa.
If alice is strong then mary is either not patient or not quiet.
Everyone who is funny is not old or not kind and vice versa.
If someone is not wise or wise then someone is both brave and curious and vice versa.
If susan is generous then someone is not patient or kind.
If someone is both tall and happy then someone is kind and vice versa.
Everyone who is either humble or curious is either rich or happy and vice versa.
Everyone who is either not kind or not brave is either not tall or old and vice versa.
If lucy is tall or not strong then lucy is either brave or not curious.
If someone is not rich or not curious then someone is both not brave and not humble.
Everyone who is funny is not rich or wise and vice versa.
Paul is brave.
Someone is patient or happy.
Someone is both not humble and not rich.
Someone is both funny and strong.
Someone is curious.
Someone is not kind.
John is both not brave and patient.
Someone is quiet or calm. | Lucy is not funny. | contradiction | ((?[X]:((kind(X)|funny(X))))<=>((strong(lucy)&wise(lucy))))&
(![X]:((~strong(X)<~>~patient(X))<=>(kind(X)<~>calm(X))))&
(((old(susan)<~>~patient(susan)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|quiet(X))))&
(![X]:(humble(X)<=>(calm(X)&tall(X))))&
((?[X]:(quiet(X)))<=>((~strong(susan)|~happy(susan))))&
((strong(alice))=>((~patient(mary)<~>~quiet(mary))))&
(![X]:(funny(X)<=>(~old(X)|~kind(X))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:((brave(X)&curious(X)))))&
((generous(susan))=>(?[X]:((~patient(X)|kind(X)))))&
((?[X]:((tall(X)&happy(X))))<=>(?[X]:(kind(X))))&
(![X]:((humble(X)<~>curious(X))<=>(rich(X)<~>happy(X))))&
(![X]:((~kind(X)<~>~brave(X))<=>(~tall(X)<~>old(X))))&
(((tall(lucy)|~strong(lucy)))=>((brave(lucy)<~>~curious(lucy))))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:(funny(X)<=>(~rich(X)|wise(X))))&
(brave(paul))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((~humble(X)&~rich(X))))&
(?[X]:((funny(X)&strong(X))))&
(?[X]:(curious(X)))&
(?[X]:(~kind(X)))&
((~brave(john)&patient(john)))&
(?[X]:((quiet(X)|calm(X)))) | ~funny(lucy) | [
"p0",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 864407004952093701190800
% SZS output start Proof for 864407004952093701190800
1. ? [X0] : (funny(X0) | kind(X0)) <=> (wise(lucy) & strong(lucy)) [input p0]
8. ! [X0] : (funny(X0) <=> (~kind(X0) | ~old(X0))) [input p7]
16. ! [X0] : (funny(X0) <=> (wise(X0) | ~rich(X0))) [input p15]
25. ~funny(lucy) [input hypothesis]
35. (? [X0] : (funny(X0) | kind(X0)) | (~wise(lucy) | ~strong(lucy))) & ((wise(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & ~kind(X0))) [nnf transformation 1]
36. (? [X0] : (funny(X0) | kind(X0)) | ~wise(lucy) | ~strong(lucy)) & ((wise(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & ~kind(X0))) [flattening 35]
37. (? [X0] : (funny(X0) | kind(X0)) | ~wise(lucy) | ~strong(lucy)) & ((wise(lucy) & strong(lucy)) | ! [X1] : (~funny(X1) & ~kind(X1))) [rectify 36]
38. ? [X0] : (funny(X0) | kind(X0)) => (funny(sK0) | kind(sK0)) [choice axiom]
39. ((funny(sK0) | kind(sK0)) | ~wise(lucy) | ~strong(lucy)) & ((wise(lucy) & strong(lucy)) | ! [X1] : (~funny(X1) & ~kind(X1))) [skolemisation 37,38]
51. ! [X0] : ((funny(X0) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | ~funny(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | ~funny(X0))) [flattening 51]
69. ! [X0] : ((funny(X0) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ~funny(X0))) [nnf transformation 16]
70. ! [X0] : ((funny(X0) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ~funny(X0))) [flattening 69]
85. wise(lucy) | ~kind(X1) [cnf transformation 39]
116. funny(X0) | kind(X0) [cnf transformation 52]
151. ~wise(X0) | funny(X0) [cnf transformation 70]
163. ~funny(lucy) [cnf transformation 25]
169. 2 <=> wise(lucy) [avatar definition]
170. wise(lucy) <- (2) [avatar component clause 169]
186. 6 <=> ! [X1] : ~kind(X1) [avatar definition]
187. ~kind(X1) <- (6) [avatar component clause 186]
188. 6 | 2 [avatar split clause 85,169,186]
342. kind(lucy) [resolution 116,163]
344. $false <- (6) [subsumption resolution 342,187]
345. ~6 [avatar contradiction clause 344]
368. funny(lucy) <- (2) [resolution 170,151]
369. $false <- (2) [subsumption resolution 368,163]
370. ~2 [avatar contradiction clause 369]
371. $false [avatar sat refutation 188,345,370]
% SZS output end Proof for 864407004952093701190800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both old and kind and vice versa.
If someone is funny or not kind then john is both not creative and brave and vice versa.
If someone is not curious or rich then fred is both patient and not patient and vice versa.
Everyone who is not happy is both not quiet and not strong and vice versa.
Everyone who is either kind or not brave is both not patient and kind and vice versa.
Everyone who is not funny is either not patient or brave and vice versa.
Everyone who is either patient or not humble is not funny.
If john is wise then someone is tall and vice versa.
Everyone who is either curious or not generous is both brave and strong.
Everyone who is creative is both creative and curious and vice versa.
If someone is both not funny and strong then someone is either not kind or not calm and vice versa.
If someone is not funny then someone is both wise and generous and vice versa.
Everyone who is either wise or rich is not creative.
Everyone who is creative is not happy and vice versa.
Everyone who is happy is strong and vice versa.
Alice is either wise or not curious.
Lucy is both tall and happy.
Someone is generous or creative.
Someone is not creative. | John is not quiet. | neutral | (![X]:(~brave(X)<=>(old(X)&kind(X))))&
((?[X]:((funny(X)|~kind(X))))<=>((~creative(john)&brave(john))))&
((?[X]:((~curious(X)|rich(X))))<=>((patient(fred)&~patient(fred))))&
(![X]:(~happy(X)<=>(~quiet(X)&~strong(X))))&
(![X]:((kind(X)<~>~brave(X))<=>(~patient(X)&kind(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((patient(X)<~>~humble(X))=>~funny(X)))&
((wise(john))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)<~>~generous(X))=>(brave(X)&strong(X))))&
(![X]:(creative(X)<=>(creative(X)&curious(X))))&
((?[X]:((~funny(X)&strong(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((wise(X)<~>rich(X))=>~creative(X)))&
(![X]:(creative(X)<=>~happy(X)))&
(![X]:(happy(X)<=>strong(X)))&
((wise(alice)<~>~curious(alice)))&
((tall(lucy)&happy(lucy)))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:(~creative(X))) | ~quiet(john) | [] | null | 0 |
Everyone who is both happy and not calm is not wise and vice versa. Everyone who is either generous or old is either curious or rich. Everyone who is not calm or not strong is both not funny and not tall. If lucy is either not tall or creative then john is both not curious and not funny and vice versa. If susan is not brave then someone is not humble. If someone is both creative and not patient then lucy is not humble or generous and vice versa. If john is brave or creative then lucy is not old or not humble and vice versa. Everyone who is both not rich and not old is old and vice versa. If fred is both not quiet and not creative then someone is either not brave or not patient and vice versa. If someone is wise then lucy is happy or generous. Everyone who is either quiet or not creative is either humble or rich and vice versa. Everyone who is both calm and not brave is not strong and vice versa. Everyone who is generous or not old is strong. Everyone who is not brave or not rich is both not funny and tall. If someone is either tall or not rich then alice is patient or wise and vice versa. Everyone who is either funny or not creative is calm and vice versa. Someone is not calm or not tall. Paul is not happy or calm. Paul is both not creative and curious. Someone is either not generous or not humble. | Paul is not old. | entailment | (![X]:((happy(X)&~calm(X))<=>~wise(X)))&
(![X]:((generous(X)<~>old(X))=>(curious(X)<~>rich(X))))&
(![X]:((~calm(X)|~strong(X))=>(~funny(X)&~tall(X))))&
(((~tall(lucy)<~>creative(lucy)))<=>((~curious(john)&~funny(john))))&
((~brave(susan))=>(?[X]:(~humble(X))))&
((?[X]:((creative(X)&~patient(X))))<=>((~humble(lucy)|generous(lucy))))&
(((brave(john)|creative(john)))<=>((~old(lucy)|~humble(lucy))))&
(![X]:((~rich(X)&~old(X))<=>old(X)))&
(((~quiet(fred)&~creative(fred)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
((?[X]:(wise(X)))=>((happy(lucy)|generous(lucy))))&
(![X]:((quiet(X)<~>~creative(X))<=>(humble(X)<~>rich(X))))&
(![X]:((calm(X)&~brave(X))<=>~strong(X)))&
(![X]:((generous(X)|~old(X))=>strong(X)))&
(![X]:((~brave(X)|~rich(X))=>(~funny(X)&tall(X))))&
((?[X]:((tall(X)<~>~rich(X))))<=>((patient(alice)|wise(alice))))&
(![X]:((funny(X)<~>~creative(X))<=>calm(X)))&
(?[X]:((~calm(X)|~tall(X))))&
((~happy(paul)|calm(paul)))&
((~creative(paul)&curious(paul)))&
(?[X]:((~generous(X)<~>~humble(X)))) | ~old(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 913806776685812599110078
% SZS output start Proof for 913806776685812599110078
8. ! [X0] : ((~old(X0) & ~rich(X0)) <=> old(X0)) [input p7]
21. old(paul) [input hypothesis]
46. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (old(X0) | rich(X0)))) [nnf transformation 8]
47. ! [X0] : (((~old(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | old(X0) | rich(X0))) [flattening 46]
94. ~old(X0) | ~old(X0) [cnf transformation 47]
133. old(paul) [cnf transformation 21]
135. ~old(X0) [duplicate literal removal 94]
292. $false [subsumption resolution 133,135]
% SZS output end Proof for 913806776685812599110078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is old or not happy and vice versa.
Everyone who is quiet is either quiet or brave.
If someone is both kind and quiet then someone is both curious and creative and vice versa.
If susan is kind then someone is patient or rich and vice versa.
Everyone who is happy is both not humble and brave and vice versa.
Everyone who is not strong or tall is both strong and humble and vice versa.
If john is old or tall then lucy is either happy or wise.
If someone is brave or tall then someone is both patient and kind.
Everyone who is kind is either not rich or funny.
If alice is either not humble or kind then someone is both not quiet and humble.
If paul is happy or not funny then someone is not funny.
Everyone who is calm is not calm or not tall.
If someone is not calm then someone is both not tall and not old and vice versa.
Everyone who is quiet is either not rich or rich.
Everyone who is both generous and not kind is not curious.
Everyone who is calm is either funny or strong.
Mary is either not brave or not old.
Lucy is wise or not quiet.
Someone is either patient or kind.
Paul is not funny.
Paul is not kind or calm.
Alice is both not tall and funny.
Alice is both not patient and happy. | Susan is humble. | contradiction | (![X]:((~tall(X)<~>~humble(X))<=>(old(X)|~happy(X))))&
(![X]:(quiet(X)=>(quiet(X)<~>brave(X))))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
((kind(susan))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:(happy(X)<=>(~humble(X)&brave(X))))&
(![X]:((~strong(X)|tall(X))<=>(strong(X)&humble(X))))&
(((old(john)|tall(john)))=>((happy(lucy)<~>wise(lucy))))&
((?[X]:((brave(X)|tall(X))))=>(?[X]:((patient(X)&kind(X)))))&
(![X]:(kind(X)=>(~rich(X)<~>funny(X))))&
(((~humble(alice)<~>kind(alice)))=>(?[X]:((~quiet(X)&humble(X)))))&
(((happy(paul)|~funny(paul)))=>(?[X]:(~funny(X))))&
(![X]:(calm(X)=>(~calm(X)|~tall(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:(quiet(X)=>(~rich(X)<~>rich(X))))&
(![X]:((generous(X)&~kind(X))=>~curious(X)))&
(![X]:(calm(X)=>(funny(X)<~>strong(X))))&
((~brave(mary)<~>~old(mary)))&
((wise(lucy)|~quiet(lucy)))&
(?[X]:((patient(X)<~>kind(X))))&
(~funny(paul))&
((~kind(paul)|calm(paul)))&
((~tall(alice)&funny(alice)))&
((~patient(alice)&happy(alice))) | humble(susan) | [
"p0",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1915794616524615321960648
% SZS output start Proof for 1915794616524615321960648
1. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~happy(X0) | old(X0))) [input p0]
5. ! [X0] : (happy(X0) <=> (brave(X0) & ~humble(X0))) [input p4]
6. ! [X0] : ((tall(X0) | ~strong(X0)) <=> (humble(X0) & strong(X0))) [input p5]
24. humble(susan) [input hypothesis]
39. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 1]
40. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [flattening 39]
51. ! [X0] : ((happy(X0) | (~brave(X0) | humble(X0))) & ((brave(X0) & ~humble(X0)) | ~happy(X0))) [nnf transformation 5]
52. ! [X0] : ((happy(X0) | ~brave(X0) | humble(X0)) & ((brave(X0) & ~humble(X0)) | ~happy(X0))) [flattening 51]
53. ! [X0] : (((tall(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | (~tall(X0) & strong(X0)))) [nnf transformation 6]
54. ! [X0] : ((tall(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | (~tall(X0) & strong(X0)))) [flattening 53]
79. ~humble(X0) | ~tall(X0) | happy(X0) [cnf transformation 40]
91. ~happy(X0) | ~humble(X0) [cnf transformation 52]
94. strong(X0) | strong(X0) [cnf transformation 54]
98. tall(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 54]
134. humble(susan) [cnf transformation 24]
136. strong(X0) [duplicate literal removal 94]
137. ~strong(X0) | tall(X0) | ~humble(X0) [duplicate literal removal 98]
330. ~tall(susan) | happy(susan) [resolution 79,134]
359. ~humble(X1) | tall(X1) [resolution 137,136]
375. 42 <=> happy(susan) [avatar definition]
377. happy(susan) <- (42) [avatar component clause 375]
379. 43 <=> tall(susan) [avatar definition]
382. 42 | ~43 [avatar split clause 330,379,375]
391. tall(susan) [resolution 359,134]
400. 43 [avatar split clause 391,379]
412. ~humble(susan) <- (42) [resolution 377,91]
413. $false <- (42) [subsumption resolution 412,134]
414. ~42 [avatar contradiction clause 413]
415. $false [avatar sat refutation 382,400,414]
% SZS output end Proof for 1915794616524615321960648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is not old and vice versa.
Everyone who is not old or generous is not curious and vice versa.
Everyone who is calm or funny is calm and vice versa.
Everyone who is not tall is either funny or strong and vice versa.
If john is not creative then someone is patient and vice versa.
Everyone who is not calm is both not rich and tall and vice versa.
Everyone who is not generous or not funny is not brave or not strong and vice versa.
If someone is old or creative then fred is not patient.
If someone is tall or strong then susan is either wise or not tall.
If lucy is either not rich or not old then someone is both not strong and wise and vice versa.
If mary is old then fred is rich or kind and vice versa.
If someone is patient or old then someone is wise and vice versa.
If someone is not old or not wise then someone is either not old or not brave.
If someone is patient or creative then mary is not curious or quiet.
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Someone is tall.
Paul is not wise or tall.
Mary is both funny and not brave.
Someone is old or humble.
Someone is curious.
Paul is not tall.
Susan is not wise or wise.
Someone is not quiet. | Lucy is old. | entailment | ((patient(fred))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)|generous(X))<=>~curious(X)))&
(![X]:((calm(X)|funny(X))<=>calm(X)))&
(![X]:(~tall(X)<=>(funny(X)<~>strong(X))))&
((~creative(john))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~rich(X)&tall(X))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((old(X)|creative(X))))=>(~patient(fred)))&
((?[X]:((tall(X)|strong(X))))=>((wise(susan)<~>~tall(susan))))&
(((~rich(lucy)<~>~old(lucy)))<=>(?[X]:((~strong(X)&wise(X)))))&
((old(mary))<=>((rich(fred)|kind(fred))))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((patient(X)|creative(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(?[X]:(tall(X)))&
((~wise(paul)|tall(paul)))&
((funny(mary)&~brave(mary)))&
(?[X]:((old(X)|humble(X))))&
(?[X]:(curious(X)))&
(~tall(paul))&
((~wise(susan)|wise(susan)))&
(?[X]:(~quiet(X))) | old(lucy) | [
"p0",
"p1",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8866438770465535996973984
% SZS output start Proof for 8866438770465535996973984
1. patient(fred) <=> ? [X0] : ~old(X0) [input p0]
2. ! [X0] : ((generous(X0) | ~old(X0)) <=> ~curious(X0)) [input p1]
8. ? [X0] : (creative(X0) | old(X0)) => ~patient(fred) [input p7]
21. ? [X0] : curious(X0) [input p20]
25. ~old(lucy) [input hypothesis]
29. ~patient(fred) | ! [X0] : (~creative(X0) & ~old(X0)) [ennf transformation 8]
34. (patient(fred) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~patient(fred)) [nnf transformation 1]
35. (patient(fred) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~patient(fred)) [rectify 34]
36. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
37. (patient(fred) | ! [X0] : old(X0)) & (~old(sK0) | ~patient(fred)) [skolemisation 35,36]
38. ! [X0] : (((generous(X0) | ~old(X0)) | curious(X0)) & (~curious(X0) | (~generous(X0) & old(X0)))) [nnf transformation 2]
39. ! [X0] : ((generous(X0) | ~old(X0) | curious(X0)) & (~curious(X0) | (~generous(X0) & old(X0)))) [flattening 38]
74. ? [X0] : curious(X0) => curious(sK8) [choice axiom]
75. curious(sK8) [skolemisation 21,74]
79. patient(fred) | old(X0) [cnf transformation 37]
80. ~curious(X0) | old(X0) [cnf transformation 39]
99. ~patient(fred) | ~old(X0) [cnf transformation 29]
135. curious(sK8) [cnf transformation 75]
139. ~old(lucy) [cnf transformation 25]
141. 1 <=> ! [X0] : old(X0) [avatar definition]
142. old(X0) <- (1) [avatar component clause 141]
144. 2 <=> patient(fred) [avatar definition]
147. 1 | 2 [avatar split clause 79,144,141]
171. 8 <=> ! [X0] : ~old(X0) [avatar definition]
172. ~old(X0) <- (8) [avatar component clause 171]
173. 8 | ~2 [avatar split clause 99,144,171]
200. 15 <=> old(lucy) [avatar definition]
201. ~old(lucy) <- (~15) [avatar component clause 200]
306. ~15 [avatar split clause 139,200]
319. $false <- (1, ~15) [resolution 201,142]
320. ~1 | 15 [avatar contradiction clause 319]
325. old(sK8) [resolution 80,135]
326. $false <- (8) [subsumption resolution 325,172]
327. ~8 [avatar contradiction clause 326]
328. $false [avatar sat refutation 147,173,306,320,327]
% SZS output end Proof for 8866438770465535996973984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or rich is both not wise and not brave and vice versa.
Everyone who is both old and generous is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not calm or not brave and vice versa.
Everyone who is not calm is not old or not happy and vice versa.
Everyone who is both strong and humble is old or not brave and vice versa.
If someone is both not quiet and not curious then someone is not curious.
If mary is tall or calm then fred is either tall or not quiet and vice versa.
If someone is kind then someone is both not humble and not brave and vice versa.
Everyone who is not generous is either strong or not kind.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
If mary is not brave or not quiet then lucy is wise or curious and vice versa.
Alice is not funny or not generous.
Mary is either funny or calm.
Paul is either old or not funny.
Someone is either creative or not wise. | Alice is old. | entailment | (![X]:((brave(X)|rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:((old(X)&generous(X))=>(~tall(X)|calm(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>~kind(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul)))&
(?[X]:((creative(X)<~>~wise(X)))) | old(alice) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 293862244198528194023462
% SZS output start Proof for 293862244198528194023462
1. ! [X0] : ((rich(X0) | brave(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
3. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
6. ! [X0] : (~calm(X0) <=> (~happy(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((humble(X0) & strong(X0)) <=> (~brave(X0) | old(X0))) [input p6]
10. ? [X0] : kind(X0) <=> ? [X0] : (~brave(X0) & ~humble(X0)) [input p9]
19. ~old(alice) [input hypothesis]
21. ? [X0] : kind(X0) <=> ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 10]
27. ! [X0] : (((rich(X0) | brave(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~rich(X0) & ~brave(X0)))) [nnf transformation 1]
28. ! [X0] : ((rich(X0) | brave(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~rich(X0) & ~brave(X0)))) [flattening 27]
29. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 3]
30. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 29]
33. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | calm(X0))) [nnf transformation 6]
34. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | calm(X0))) [flattening 33]
35. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 7]
36. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~humble(X0) | ~strong(X0))) [flattening 35]
42. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 21]
43. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X2] : (~brave(X2) & ~humble(X2)) | ! [X3] : ~kind(X3)) [rectify 42]
44. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
45. ? [X2] : (~brave(X2) & ~humble(X2)) => (~brave(sK2) & ~humble(sK2)) [choice axiom]
46. (kind(sK1) | ! [X1] : (brave(X1) | humble(X1))) & ((~brave(sK2) & ~humble(sK2)) | ! [X3] : ~kind(X3)) [skolemisation 43,45,44]
59. ~brave(X0) | ~brave(X0) [cnf transformation 28]
66. ~humble(X0) | calm(X0) | kind(X0) [cnf transformation 30]
76. ~calm(X0) | old(X0) [cnf transformation 34]
82. humble(X0) | brave(X0) [cnf transformation 36]
90. ~humble(sK2) | ~kind(X3) [cnf transformation 46]
110. ~old(alice) [cnf transformation 19]
111. ~brave(X0) [duplicate literal removal 59]
127. humble(X0) [subsumption resolution 82,111]
159. ~kind(X3) [subsumption resolution 90,127]
232. calm(X0) | kind(X0) [resolution 66,127]
233. calm(X0) [subsumption resolution 232,159]
237. old(X2) [resolution 233,76]
240. $false [resolution 237,110]
% SZS output end Proof for 293862244198528194023462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not curious or not happy then susan is either not old or tall and vice versa.
Everyone who is either calm or not creative is not curious or strong.
Everyone who is not tall is curious or brave and vice versa.
Everyone who is not curious or not generous is curious.
If lucy is both not wise and not quiet then john is both not curious and quiet.
Everyone who is both funny and not old is both not strong and creative.
Everyone who is both not brave and not patient is both brave and tall.
Everyone who is either creative or tall is not old or wise and vice versa.
Everyone who is either not rich or not strong is not wise.
If paul is both kind and tall then someone is not brave and vice versa.
Everyone who is either curious or old is not rich or rich.
Everyone who is not brave is either not strong or not wise and vice versa.
Everyone who is not humble is both humble and strong and vice versa.
If mary is not strong or old then someone is funny or brave.
Everyone who is both humble and not rich is either funny or kind.
Everyone who is rich or quiet is curious or strong.
Someone is either generous or humble.
Someone is both not tall and not kind.
Someone is not wise or not humble.
Paul is calm.
Someone is old or generous.
Alice is either generous or not happy. | Lucy is not quiet. | contradiction | (((~curious(susan)|~happy(susan)))<=>((~old(susan)<~>tall(susan))))&
(![X]:((calm(X)<~>~creative(X))=>(~curious(X)|strong(X))))&
(![X]:(~tall(X)<=>(curious(X)|brave(X))))&
(![X]:((~curious(X)|~generous(X))=>curious(X)))&
(((~wise(lucy)&~quiet(lucy)))=>((~curious(john)&quiet(john))))&
(![X]:((funny(X)&~old(X))=>(~strong(X)&creative(X))))&
(![X]:((~brave(X)&~patient(X))=>(brave(X)&tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~old(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>~wise(X)))&
(((kind(paul)&tall(paul)))<=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>old(X))=>(~rich(X)|rich(X))))&
(![X]:(~brave(X)<=>(~strong(X)<~>~wise(X))))&
(![X]:(~humble(X)<=>(humble(X)&strong(X))))&
(((~strong(mary)|old(mary)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((humble(X)&~rich(X))=>(funny(X)<~>kind(X))))&
(![X]:((rich(X)|quiet(X))=>(curious(X)|strong(X))))&
(?[X]:((generous(X)<~>humble(X))))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(calm(paul))&
(?[X]:((old(X)|generous(X))))&
((generous(alice)<~>~happy(alice))) | ~quiet(lucy) | [
"p2",
"p3",
"p4",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 656042956184790215844045
% SZS output start Proof for 656042956184790215844045
3. ! [X0] : (~tall(X0) <=> (brave(X0) | curious(X0))) [input p2]
4. ! [X0] : ((~generous(X0) | ~curious(X0)) => curious(X0)) [input p3]
5. (~quiet(lucy) & ~wise(lucy)) => (quiet(john) & ~curious(john)) [input p4]
10. (tall(paul) & kind(paul)) <=> ? [X0] : ~brave(X0) [input p9]
12. ! [X0] : (~brave(X0) <=> (~strong(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : (~humble(X0) <=> (strong(X0) & humble(X0))) [input p12]
23. ~quiet(lucy) [input hypothesis]
27. ! [X0] : (curious(X0) | (generous(X0) & curious(X0))) [ennf transformation 4]
28. (quiet(john) & ~curious(john)) | (quiet(lucy) | wise(lucy)) [ennf transformation 5]
29. (quiet(john) & ~curious(john)) | quiet(lucy) | wise(lucy) [flattening 28]
43. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | tall(X0))) [nnf transformation 3]
44. ! [X0] : ((~tall(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | tall(X0))) [flattening 43]
48. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~tall(paul) | ~kind(paul))) [nnf transformation 10]
49. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~tall(paul) | ~kind(paul)) [flattening 48]
50. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~tall(paul) | ~kind(paul)) [rectify 49]
51. ? [X1] : ~brave(X1) => ~brave(sK0) [choice axiom]
52. ((tall(paul) & kind(paul)) | ! [X0] : brave(X0)) & (~brave(sK0) | ~tall(paul) | ~kind(paul)) [skolemisation 50,51]
54. ! [X0] : ((~brave(X0) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0)))) & (((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | brave(X0))) [nnf transformation 12]
55. ! [X0] : ((~humble(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | humble(X0))) [nnf transformation 13]
56. ! [X0] : ((~humble(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | humble(X0))) [flattening 55]
79. ~tall(X0) | ~curious(X0) [cnf transformation 44]
81. curious(X0) | curious(X0) [cnf transformation 27]
83. ~curious(john) | quiet(lucy) | wise(lucy) [cnf transformation 29]
97. tall(paul) | brave(X0) [cnf transformation 52]
102. ~wise(X0) | ~brave(X0) | strong(X0) [cnf transformation 54]
104. humble(X0) | humble(X0) [cnf transformation 56]
106. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 56]
122. ~quiet(lucy) [cnf transformation 23]
123. humble(X0) [duplicate literal removal 104]
124. ~humble(X0) | ~strong(X0) [duplicate literal removal 106]
125. curious(X0) [duplicate literal removal 81]
149. 5 <=> wise(lucy) [avatar definition]
151. wise(lucy) <- (5) [avatar component clause 149]
153. 6 <=> quiet(lucy) [avatar definition]
161. quiet(lucy) | wise(lucy) [subsumption resolution 83,125]
162. 5 | 6 [avatar split clause 161,153,149]
164. 8 <=> ! [X0] : brave(X0) [avatar definition]
165. brave(X0) <- (8) [avatar component clause 164]
167. 9 <=> tall(paul) [avatar definition]
169. tall(paul) <- (9) [avatar component clause 167]
170. 8 | 9 [avatar split clause 97,167,164]
222. ~6 [avatar split clause 122,153]
227. ~strong(X1) [resolution 124,123]
254. ~brave(lucy) | strong(lucy) <- (5) [resolution 102,151]
257. strong(lucy) <- (5, 8) [subsumption resolution 254,165]
258. $false <- (5, 8) [subsumption resolution 257,227]
259. ~5 | ~8 [avatar contradiction clause 258]
274. ~curious(paul) <- (9) [resolution 169,79]
275. $false <- (9) [subsumption resolution 274,125]
276. ~9 [avatar contradiction clause 275]
277. $false [avatar sat refutation 162,170,222,259,276]
% SZS output end Proof for 656042956184790215844045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not patient then someone is either funny or not funny and vice versa.
Everyone who is both quiet and not humble is not happy or not humble.
If someone is both not generous and rich then someone is not rich.
If someone is not kind or kind then someone is not kind and vice versa.
Everyone who is calm is either strong or not strong and vice versa.
Everyone who is not generous or not happy is either brave or not creative and vice versa.
If someone is not wise or not patient then mary is funny or not tall.
Everyone who is strong or not quiet is kind and vice versa.
If someone is not happy then someone is either not old or patient.
If susan is strong then someone is both not quiet and not brave and vice versa.
If someone is both brave and not strong then john is not happy and vice versa.
If fred is old then someone is strong or tall.
If fred is both not creative and not quiet then john is both generous and wise.
Everyone who is either quiet or not brave is not brave or wise.
If someone is not wise then someone is not creative.
Everyone who is either not humble or calm is both not humble and not wise and vice versa.
Someone is patient or not creative.
Paul is either generous or tall.
Susan is both not rich and generous.
Mary is rich or tall.
Paul is not happy or curious.
Mary is not kind or not tall.
Someone is not curious. | Susan is not wise. | contradiction | ((?[X]:((kind(X)&~patient(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((quiet(X)&~humble(X))=>(~happy(X)|~humble(X))))&
((?[X]:((~generous(X)&rich(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:(~kind(X))))&
(![X]:(calm(X)<=>(strong(X)<~>~strong(X))))&
(![X]:((~generous(X)|~happy(X))<=>(brave(X)<~>~creative(X))))&
((?[X]:((~wise(X)|~patient(X))))=>((funny(mary)|~tall(mary))))&
(![X]:((strong(X)|~quiet(X))<=>kind(X)))&
((?[X]:(~happy(X)))=>(?[X]:((~old(X)<~>patient(X)))))&
((strong(susan))<=>(?[X]:((~quiet(X)&~brave(X)))))&
((?[X]:((brave(X)&~strong(X))))<=>(~happy(john)))&
((old(fred))=>(?[X]:((strong(X)|tall(X)))))&
(((~creative(fred)&~quiet(fred)))=>((generous(john)&wise(john))))&
(![X]:((quiet(X)<~>~brave(X))=>(~brave(X)|wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:(~creative(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~humble(X)&~wise(X))))&
(?[X]:((patient(X)|~creative(X))))&
((generous(paul)<~>tall(paul)))&
((~rich(susan)&generous(susan)))&
((rich(mary)|tall(mary)))&
((~happy(paul)|curious(paul)))&
((~kind(mary)|~tall(mary)))&
(?[X]:(~curious(X))) | ~wise(susan) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4205659890423123790915862
% SZS output start Proof for 4205659890423123790915862
5. ! [X0] : (calm(X0) <=> (strong(X0) <~> ~strong(X0))) [input p4]
16. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~wise(X0) & ~humble(X0))) [input p15]
24. ~wise(susan) [input hypothesis]
55. ! [X0] : ((calm(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~calm(X0))) [nnf transformation 5]
78. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (wise(X0) | humble(X0))) & ((~wise(X0) & ~humble(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 16]
79. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | wise(X0) | humble(X0)) & ((~wise(X0) & ~humble(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 78]
98. calm(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 55]
99. calm(X0) | strong(X0) | strong(X0) [cnf transformation 55]
126. ~humble(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 79]
130. ~calm(X0) | humble(X0) | wise(X0) | humble(X0) [cnf transformation 79]
140. ~wise(susan) [cnf transformation 24]
141. ~humble(X0) | ~calm(X0) [duplicate literal removal 126]
142. ~calm(X0) | humble(X0) | wise(X0) [duplicate literal removal 130]
144. calm(X0) | ~strong(X0) [duplicate literal removal 98]
145. strong(X0) | calm(X0) [duplicate literal removal 99]
188. calm(X0) [subsumption resolution 144,145]
290. wise(X0) | humble(X0) [subsumption resolution 142,188]
292. ~humble(X0) [subsumption resolution 141,188]
334. humble(susan) [resolution 290,140]
335. $false [subsumption resolution 334,292]
% SZS output end Proof for 4205659890423123790915862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not wise is either not old or not humble. If fred is both calm and not kind then susan is not tall. Everyone who is not generous is brave and vice versa. Everyone who is both patient and creative is not curious. If someone is both not happy and funny then someone is both not wise and rich and vice versa. If someone is funny then mary is wise. If paul is brave or not strong then someone is rich or not wise. Everyone who is either not tall or wise is both happy and quiet and vice versa. If someone is both not tall and quiet then john is not creative and vice versa. Everyone who is either calm or rich is rich or not generous. Everyone who is either creative or strong is both generous and not kind. If someone is quiet then fred is both calm and not old and vice versa. Everyone who is both not generous and not patient is curious and vice versa. If paul is both not kind and not funny then mary is not curious or not funny. Everyone who is both not creative and happy is not kind. Everyone who is not tall is either not generous or not strong and vice versa. Mary is either tall or kind. Lucy is both calm and rich. Someone is either old or not generous. Someone is kind. Someone is brave. Someone is humble. Mary is happy. Susan is either wise or calm. | Lucy is curious. | neutral | (![X]:((funny(X)&~wise(X))=>(~old(X)<~>~humble(X))))&
(((calm(fred)&~kind(fred)))=>(~tall(susan)))&
(![X]:(~generous(X)<=>brave(X)))&
(![X]:((patient(X)&creative(X))=>~curious(X)))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((~wise(X)&rich(X)))))&
((?[X]:(funny(X)))=>(wise(mary)))&
(((brave(paul)|~strong(paul)))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((~tall(X)<~>wise(X))<=>(happy(X)&quiet(X))))&
((?[X]:((~tall(X)&quiet(X))))<=>(~creative(john)))&
(![X]:((calm(X)<~>rich(X))=>(rich(X)|~generous(X))))&
(![X]:((creative(X)<~>strong(X))=>(generous(X)&~kind(X))))&
((?[X]:(quiet(X)))<=>((calm(fred)&~old(fred))))&
(![X]:((~generous(X)&~patient(X))<=>curious(X)))&
(((~kind(paul)&~funny(paul)))=>((~curious(mary)|~funny(mary))))&
(![X]:((~creative(X)&happy(X))=>~kind(X)))&
(![X]:(~tall(X)<=>(~generous(X)<~>~strong(X))))&
((tall(mary)<~>kind(mary)))&
((calm(lucy)&rich(lucy)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
(?[X]:(humble(X)))&
(happy(mary))&
((wise(susan)<~>calm(susan))) | curious(lucy) | [] | null | 0 |
If someone is patient or not calm then fred is either not creative or not patient.
Everyone who is both not kind and calm is both not tall and not humble and vice versa.
If someone is not kind then fred is not humble and vice versa.
Everyone who is both humble and tall is not patient or wise.
Everyone who is tall is patient or funny and vice versa.
Everyone who is both funny and creative is not calm and vice versa.
Everyone who is not humble or kind is not humble or creative.
Everyone who is either tall or old is both generous and not strong.
Everyone who is either not rich or funny is both strong and funny.
If someone is both old and not brave then someone is both not quiet and not old.
Everyone who is either quiet or old is both creative and not calm and vice versa.
If john is wise or funny then someone is either curious or rich.
Everyone who is not kind is not kind or kind and vice versa.
Everyone who is either quiet or not calm is either not patient or not generous and vice versa.
If someone is either not tall or not funny then someone is either curious or not brave and vice versa.
Everyone who is both not brave and not old is both not wise and humble.
Paul is not wise or not strong.
Someone is not happy.
Fred is not old.
Someone is either not strong or happy.
John is either not strong or funny.
Someone is either not rich or not funny.
Someone is either strong or brave. | Paul is not strong. | neutral | ((?[X]:((patient(X)|~calm(X))))=>((~creative(fred)<~>~patient(fred))))&
(![X]:((~kind(X)&calm(X))<=>(~tall(X)&~humble(X))))&
((?[X]:(~kind(X)))<=>(~humble(fred)))&
(![X]:((humble(X)&tall(X))=>(~patient(X)|wise(X))))&
(![X]:(tall(X)<=>(patient(X)|funny(X))))&
(![X]:((funny(X)&creative(X))<=>~calm(X)))&
(![X]:((~humble(X)|kind(X))=>(~humble(X)|creative(X))))&
(![X]:((tall(X)<~>old(X))=>(generous(X)&~strong(X))))&
(![X]:((~rich(X)<~>funny(X))=>(strong(X)&funny(X))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(![X]:((quiet(X)<~>old(X))<=>(creative(X)&~calm(X))))&
(((wise(john)|funny(john)))=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(~kind(X)|kind(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(~patient(X)<~>~generous(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~brave(X)&~old(X))=>(~wise(X)&humble(X))))&
((~wise(paul)|~strong(paul)))&
(?[X]:(~happy(X)))&
(~old(fred))&
(?[X]:((~strong(X)<~>happy(X))))&
((~strong(john)<~>funny(john)))&
(?[X]:((~rich(X)<~>~funny(X))))&
(?[X]:((strong(X)<~>brave(X)))) | ~strong(paul) | [] | null | 0 |
If alice is not rich then someone is not wise and vice versa. If someone is either funny or tall then someone is either not calm or generous. If lucy is kind then susan is either brave or tall and vice versa. If susan is both old and not happy then someone is humble and vice versa. If someone is strong then alice is not humble or not kind. If someone is brave then alice is not humble or quiet. Everyone who is both not kind and not funny is both not brave and not creative. Everyone who is quiet is either not old or wise. If fred is either not wise or not generous then someone is brave. If paul is both kind and not wise then someone is both not old and not happy. If alice is not rich then someone is both not curious and not calm and vice versa. If mary is either not wise or funny then susan is not old or brave. Everyone who is not calm is both not funny and not quiet and vice versa. Everyone who is either not creative or wise is both calm and not creative. Everyone who is not rich is both not happy and not curious and vice versa. Everyone who is both old and kind is tall and vice versa. Susan is not brave or wise. Susan is not creative. Susan is both calm and not old. Someone is not curious or brave. Someone is both calm and not strong. Someone is either not happy or tall. John is both funny and generous. Paul is either creative or rich. | John is humble. | contradiction | ((~rich(alice))<=>(?[X]:(~wise(X))))&
((?[X]:((funny(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>generous(X)))))&
((kind(lucy))<=>((brave(susan)<~>tall(susan))))&
(((old(susan)&~happy(susan)))<=>(?[X]:(humble(X))))&
((?[X]:(strong(X)))=>((~humble(alice)|~kind(alice))))&
((?[X]:(brave(X)))=>((~humble(alice)|quiet(alice))))&
(![X]:((~kind(X)&~funny(X))=>(~brave(X)&~creative(X))))&
(![X]:(quiet(X)=>(~old(X)<~>wise(X))))&
(((~wise(fred)<~>~generous(fred)))=>(?[X]:(brave(X))))&
(((kind(paul)&~wise(paul)))=>(?[X]:((~old(X)&~happy(X)))))&
((~rich(alice))<=>(?[X]:((~curious(X)&~calm(X)))))&
(((~wise(mary)<~>funny(mary)))=>((~old(susan)|brave(susan))))&
(![X]:(~calm(X)<=>(~funny(X)&~quiet(X))))&
(![X]:((~creative(X)<~>wise(X))=>(calm(X)&~creative(X))))&
(![X]:(~rich(X)<=>(~happy(X)&~curious(X))))&
(![X]:((old(X)&kind(X))<=>tall(X)))&
((~brave(susan)|wise(susan)))&
(~creative(susan))&
((calm(susan)&~old(susan)))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:((calm(X)&~strong(X))))&
(?[X]:((~happy(X)<~>tall(X))))&
((funny(john)&generous(john)))&
((creative(paul)<~>rich(paul))) | humble(john) | [
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3898352636276524634648055
% SZS output start Proof for 3898352636276524634648055
4. (~happy(susan) & old(susan)) <=> ? [X0] : humble(X0) [input p3]
19. ~old(susan) & calm(susan) [input p18]
25. humble(john) [input hypothesis]
50. ((~happy(susan) & old(susan)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (happy(susan) | ~old(susan))) [nnf transformation 4]
51. ((~happy(susan) & old(susan)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | happy(susan) | ~old(susan)) [flattening 50]
52. ((~happy(susan) & old(susan)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | happy(susan) | ~old(susan)) [rectify 51]
53. ? [X1] : humble(X1) => humble(sK2) [choice axiom]
54. ((~happy(susan) & old(susan)) | ! [X0] : ~humble(X0)) & (humble(sK2) | happy(susan) | ~old(susan)) [skolemisation 52,53]
92. old(susan) | ~humble(X0) [cnf transformation 54]
124. ~old(susan) [cnf transformation 19]
133. humble(john) [cnf transformation 25]
183. 11 <=> ! [X0] : ~humble(X0) [avatar definition]
184. ~humble(X0) <- (11) [avatar component clause 183]
191. 13 <=> old(susan) [avatar definition]
194. 11 | 13 [avatar split clause 92,191,183]
273. ~13 [avatar split clause 124,191]
303. $false <- (11) [resolution 184,133]
304. ~11 [avatar contradiction clause 303]
305. $false [avatar sat refutation 194,273,304]
% SZS output end Proof for 3898352636276524634648055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny or quiet then someone is not generous or old. If fred is both not old and not happy then john is not brave or not curious and vice versa. If someone is not brave or wise then fred is not strong or happy. If lucy is not humble or not curious then someone is calm and vice versa. Everyone who is either strong or not wise is happy or not brave. Everyone who is not quiet or not funny is either not strong or creative. Everyone who is not calm or old is not old and vice versa. If fred is both happy and not happy then someone is not quiet or rich. Everyone who is both brave and not brave is either not patient or not happy and vice versa. Everyone who is either not brave or tall is funny. Everyone who is either not happy or strong is not curious or tall. Everyone who is both not quiet and tall is either old or not happy and vice versa. If someone is not kind or not brave then john is not funny and vice versa. Everyone who is not tall is funny or brave and vice versa. Everyone who is not rich or not brave is creative. Everyone who is both not patient and wise is quiet or brave. Lucy is either not creative or not tall. Alice is not humble. Someone is not kind or not creative. Lucy is both not strong and not kind. Someone is kind. Someone is both strong and not old. | Fred is funny. | neutral | (((~funny(mary)|quiet(mary)))=>(?[X]:((~generous(X)|old(X)))))&
(((~old(fred)&~happy(fred)))<=>((~brave(john)|~curious(john))))&
((?[X]:((~brave(X)|wise(X))))=>((~strong(fred)|happy(fred))))&
(((~humble(lucy)|~curious(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((strong(X)<~>~wise(X))=>(happy(X)|~brave(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~strong(X)<~>creative(X))))&
(![X]:((~calm(X)|old(X))<=>~old(X)))&
(((happy(fred)&~happy(fred)))=>(?[X]:((~quiet(X)|rich(X)))))&
(![X]:((brave(X)&~brave(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((~brave(X)<~>tall(X))=>funny(X)))&
(![X]:((~happy(X)<~>strong(X))=>(~curious(X)|tall(X))))&
(![X]:((~quiet(X)&tall(X))<=>(old(X)<~>~happy(X))))&
((?[X]:((~kind(X)|~brave(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>(funny(X)|brave(X))))&
(![X]:((~rich(X)|~brave(X))=>creative(X)))&
(![X]:((~patient(X)&wise(X))=>(quiet(X)|brave(X))))&
((~creative(lucy)<~>~tall(lucy)))&
(~humble(alice))&
(?[X]:((~kind(X)|~creative(X))))&
((~strong(lucy)&~kind(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)&~old(X)))) | funny(fred) | [] | null | 0 |
If someone is either humble or not kind then someone is both tall and not creative.
If mary is not curious then someone is not wise or generous and vice versa.
Everyone who is either wise or patient is both not old and happy and vice versa.
Everyone who is not kind is not creative or not quiet and vice versa.
If someone is calm then someone is both not creative and quiet.
Everyone who is calm or not happy is both humble and not quiet.
If john is not kind then mary is not tall or curious and vice versa.
Everyone who is either wise or brave is brave or tall and vice versa.
Everyone who is funny or not strong is wise or not funny and vice versa.
Everyone who is either patient or humble is either brave or not old.
Everyone who is both wise and not generous is tall and vice versa.
If fred is both not generous and funny then someone is both not curious and not generous.
Everyone who is both not generous and not quiet is both not patient and strong.
Everyone who is either not creative or not patient is not happy.
Everyone who is either creative or patient is both happy and creative.
Everyone who is brave is either not tall or patient.
Someone is both calm and not creative.
Paul is either not strong or generous.
Susan is either not calm or strong.
John is both not brave and not old.
Someone is tall.
John is both not tall and not creative.
John is either not brave or not humble. | Paul is generous. | contradiction | ((?[X]:((humble(X)<~>~kind(X))))=>(?[X]:((tall(X)&~creative(X)))))&
((~curious(mary))<=>(?[X]:((~wise(X)|generous(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(~old(X)&happy(X))))&
(![X]:(~kind(X)<=>(~creative(X)|~quiet(X))))&
((?[X]:(calm(X)))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)&~quiet(X))))&
((~kind(john))<=>((~tall(mary)|curious(mary))))&
(![X]:((wise(X)<~>brave(X))<=>(brave(X)|tall(X))))&
(![X]:((funny(X)|~strong(X))<=>(wise(X)|~funny(X))))&
(![X]:((patient(X)<~>humble(X))=>(brave(X)<~>~old(X))))&
(![X]:((wise(X)&~generous(X))<=>tall(X)))&
(((~generous(fred)&funny(fred)))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:((~generous(X)&~quiet(X))=>(~patient(X)&strong(X))))&
(![X]:((~creative(X)<~>~patient(X))=>~happy(X)))&
(![X]:((creative(X)<~>patient(X))=>(happy(X)&creative(X))))&
(![X]:(brave(X)=>(~tall(X)<~>patient(X))))&
(?[X]:((calm(X)&~creative(X))))&
((~strong(paul)<~>generous(paul)))&
((~calm(susan)<~>strong(susan)))&
((~brave(john)&~old(john)))&
(?[X]:(tall(X)))&
((~tall(john)&~creative(john)))&
((~brave(john)<~>~humble(john))) | generous(paul) | [
"p7",
"p8",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 263055639467125087265451
% SZS output start Proof for 263055639467125087265451
8. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (tall(X0) | brave(X0))) [input p7]
9. ! [X0] : ((~strong(X0) | funny(X0)) <=> (~funny(X0) | wise(X0))) [input p8]
11. ! [X0] : ((~generous(X0) & wise(X0)) <=> tall(X0)) [input p10]
18. ~strong(paul) <~> generous(paul) [input p17]
24. generous(paul) [input hypothesis]
55. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | (~tall(X0) & ~brave(X0))) & ((tall(X0) | brave(X0)) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [nnf transformation 8]
56. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | (~tall(X0) & ~brave(X0))) & (tall(X0) | brave(X0) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [flattening 55]
57. ! [X0] : (((~strong(X0) | funny(X0)) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | (strong(X0) & ~funny(X0)))) [nnf transformation 9]
58. ! [X0] : ((~strong(X0) | funny(X0) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | (strong(X0) & ~funny(X0)))) [flattening 57]
60. ! [X0] : (((~generous(X0) & wise(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) | ~wise(X0)))) [nnf transformation 11]
61. ! [X0] : (((~generous(X0) & wise(X0)) | ~tall(X0)) & (tall(X0) | generous(X0) | ~wise(X0))) [flattening 60]
69. (~generous(paul) | strong(paul)) & (generous(paul) | ~strong(paul)) [nnf transformation 18]
99. tall(X0) | brave(X0) | brave(X0) | ~wise(X0) [cnf transformation 56]
103. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 56]
105. ~funny(X0) | wise(X0) | ~funny(X0) [cnf transformation 58]
108. ~strong(X0) | funny(X0) | funny(X0) [cnf transformation 58]
115. ~generous(X0) | ~tall(X0) [cnf transformation 61]
131. ~generous(paul) | strong(paul) [cnf transformation 69]
141. generous(paul) [cnf transformation 24]
143. ~funny(X0) | wise(X0) [duplicate literal removal 105]
144. ~strong(X0) | funny(X0) [duplicate literal removal 108]
145. tall(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 99]
146. ~brave(X0) | ~wise(X0) [duplicate literal removal 103]
210. ~wise(X0) | tall(X0) [subsumption resolution 145,146]
231. 19 <=> strong(paul) [avatar definition]
233. strong(paul) <- (19) [avatar component clause 231]
235. 20 <=> generous(paul) [avatar definition]
236. generous(paul) <- (20) [avatar component clause 235]
238. 19 | ~20 [avatar split clause 131,235,231]
251. 20 [avatar split clause 141,235]
259. ~tall(paul) <- (20) [resolution 115,236]
260. funny(paul) <- (19) [resolution 144,233]
261. wise(paul) <- (19) [resolution 260,143]
264. tall(paul) <- (19) [resolution 261,210]
265. $false <- (19, 20) [subsumption resolution 264,259]
266. ~19 | ~20 [avatar contradiction clause 265]
267. $false [avatar sat refutation 238,251,266]
% SZS output end Proof for 263055639467125087265451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or brave then someone is not strong or not funny.
If mary is both brave and patient then alice is both not generous and not quiet.
Everyone who is either generous or not curious is both not humble and creative and vice versa.
If susan is both not humble and calm then susan is funny or calm and vice versa.
Everyone who is not patient is not happy and vice versa.
If fred is not quiet then someone is both not humble and not happy and vice versa.
If someone is not patient or not quiet then mary is both not rich and curious and vice versa.
If someone is either not calm or brave then alice is not wise or not kind.
If someone is either not patient or not quiet then someone is both strong and old.
Everyone who is either not wise or rich is both happy and funny and vice versa.
Everyone who is kind is calm and vice versa.
If someone is either kind or generous then fred is not patient or creative and vice versa.
If alice is kind or not quiet then mary is either not creative or not quiet and vice versa.
Everyone who is either calm or funny is both strong and tall.
If susan is both not tall and generous then someone is either rich or not tall.
Everyone who is old is not rich.
Someone is either not wise or tall.
Fred is both rich and patient.
Fred is not calm.
Lucy is old.
Someone is not humble or happy.
Someone is both humble and not quiet.
Someone is funny.
Someone is both funny and strong. | Susan is kind. | neutral | ((?[X]:((kind(X)|brave(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(((brave(mary)&patient(mary)))=>((~generous(alice)&~quiet(alice))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)&creative(X))))&
(((~humble(susan)&calm(susan)))<=>((funny(susan)|calm(susan))))&
(![X]:(~patient(X)<=>~happy(X)))&
((~quiet(fred))<=>(?[X]:((~humble(X)&~happy(X)))))&
((?[X]:((~patient(X)|~quiet(X))))<=>((~rich(mary)&curious(mary))))&
((?[X]:((~calm(X)<~>brave(X))))=>((~wise(alice)|~kind(alice))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((strong(X)&old(X)))))&
(![X]:((~wise(X)<~>rich(X))<=>(happy(X)&funny(X))))&
(![X]:(kind(X)<=>calm(X)))&
((?[X]:((kind(X)<~>generous(X))))<=>((~patient(fred)|creative(fred))))&
(((kind(alice)|~quiet(alice)))<=>((~creative(mary)<~>~quiet(mary))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&tall(X))))&
(((~tall(susan)&generous(susan)))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(old(X)=>~rich(X)))&
(?[X]:((~wise(X)<~>tall(X))))&
((rich(fred)&patient(fred)))&
(~calm(fred))&
(old(lucy))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&strong(X)))) | kind(susan) | [] | null | 0 |
Everyone who is not happy is either not humble or old.
If someone is either happy or tall then someone is both not wise and not calm and vice versa.
If alice is either not old or humble then someone is not patient or not quiet.
Everyone who is either happy or not creative is either not calm or not brave and vice versa.
Everyone who is not quiet or not happy is either rich or not generous.
If someone is generous then john is either not generous or wise.
If fred is tall then alice is either brave or happy.
If someone is not old then fred is not kind.
If someone is not wise then lucy is both not rich and tall and vice versa.
If someone is strong or kind then john is not strong.
Everyone who is both not calm and brave is not rich.
If lucy is not funny then susan is patient or curious.
Everyone who is wise or kind is humble or calm and vice versa.
If susan is either not humble or wise then someone is brave.
If someone is both not creative and curious then lucy is both patient and not calm and vice versa.
If someone is either not curious or brave then someone is both not funny and calm.
Susan is both generous and wise.
Someone is either not curious or funny.
Someone is generous or not calm.
Someone is either not calm or not kind.
Someone is not curious or not happy.
Alice is both not wise and not rich.
Susan is either strong or quiet.
Someone is not brave or tall. | Lucy is rich. | contradiction | (![X]:(~happy(X)=>(~humble(X)<~>old(X))))&
((?[X]:((happy(X)<~>tall(X))))<=>(?[X]:((~wise(X)&~calm(X)))))&
(((~old(alice)<~>humble(alice)))=>(?[X]:((~patient(X)|~quiet(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((~quiet(X)|~happy(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(generous(X)))=>((~generous(john)<~>wise(john))))&
((tall(fred))=>((brave(alice)<~>happy(alice))))&
((?[X]:(~old(X)))=>(~kind(fred)))&
((?[X]:(~wise(X)))<=>((~rich(lucy)&tall(lucy))))&
((?[X]:((strong(X)|kind(X))))=>(~strong(john)))&
(![X]:((~calm(X)&brave(X))=>~rich(X)))&
((~funny(lucy))=>((patient(susan)|curious(susan))))&
(![X]:((wise(X)|kind(X))<=>(humble(X)|calm(X))))&
(((~humble(susan)<~>wise(susan)))=>(?[X]:(brave(X))))&
((?[X]:((~creative(X)&curious(X))))<=>((patient(lucy)&~calm(lucy))))&
((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((~funny(X)&calm(X)))))&
((generous(susan)&wise(susan)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((generous(X)|~calm(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((~curious(X)|~happy(X))))&
((~wise(alice)&~rich(alice)))&
((strong(susan)<~>quiet(susan)))&
(?[X]:((~brave(X)|tall(X)))) | rich(lucy) | [
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 780844184361360850991876
% SZS output start Proof for 780844184361360850991876
9. ? [X0] : ~wise(X0) <=> (tall(lucy) & ~rich(lucy)) [input p8]
22. ~rich(alice) & ~wise(alice) [input p21]
25. rich(lucy) [input hypothesis]
54. (? [X0] : ~wise(X0) | (~tall(lucy) | rich(lucy))) & ((tall(lucy) & ~rich(lucy)) | ! [X0] : wise(X0)) [nnf transformation 9]
55. (? [X0] : ~wise(X0) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X0] : wise(X0)) [flattening 54]
56. (? [X0] : ~wise(X0) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X1] : wise(X1)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. (~wise(sK3) | ~tall(lucy) | rich(lucy)) & ((tall(lucy) & ~rich(lucy)) | ! [X1] : wise(X1)) [skolemisation 56,57]
113. ~rich(lucy) | wise(X1) [cnf transformation 58]
142. ~wise(alice) [cnf transformation 22]
147. rich(lucy) [cnf transformation 25]
233. 20 <=> rich(lucy) [avatar definition]
246. 23 <=> ! [X1] : wise(X1) [avatar definition]
247. wise(X1) <- (23) [avatar component clause 246]
249. 23 | ~20 [avatar split clause 113,233,246]
388. 20 [avatar split clause 147,233]
395. $false <- (23) [resolution 247,142]
396. ~23 [avatar contradiction clause 395]
397. $false [avatar sat refutation 249,388,396]
% SZS output end Proof for 780844184361360850991876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not rich then lucy is either creative or calm and vice versa. Everyone who is both not curious and not humble is not strong or not patient and vice versa. If someone is both not happy and old then john is humble or happy. If mary is kind or creative then someone is not calm or not curious. If someone is either not kind or not curious then someone is not tall and vice versa. Everyone who is not humble is not quiet or not kind and vice versa. Everyone who is strong or curious is either patient or not rich. Everyone who is either happy or strong is both calm and not funny. Everyone who is either not patient or not humble is either not happy or generous and vice versa. Everyone who is wise is both not humble and humble. If someone is strong or not calm then someone is either not funny or not wise and vice versa. Everyone who is either curious or not generous is humble or brave and vice versa. Everyone who is both not happy and kind is brave or not tall and vice versa. Everyone who is not humble is both kind and calm. Everyone who is either kind or not tall is not patient and vice versa. Everyone who is not humble is either not funny or not brave. Someone is old or not creative. Mary is both calm and not old. John is not wise. John is either kind or happy. | Paul is not quiet. | entailment | ((~rich(paul))<=>((creative(lucy)<~>calm(lucy))))&
(![X]:((~curious(X)&~humble(X))<=>(~strong(X)|~patient(X))))&
((?[X]:((~happy(X)&old(X))))=>((humble(john)|happy(john))))&
(((kind(mary)|creative(mary)))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~kind(X))))&
(![X]:((strong(X)|curious(X))=>(patient(X)<~>~rich(X))))&
(![X]:((happy(X)<~>strong(X))=>(calm(X)&~funny(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(~happy(X)<~>generous(X))))&
(![X]:(wise(X)=>(~humble(X)&humble(X))))&
((?[X]:((strong(X)|~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:((curious(X)<~>~generous(X))<=>(humble(X)|brave(X))))&
(![X]:((~happy(X)&kind(X))<=>(brave(X)|~tall(X))))&
(![X]:(~humble(X)=>(kind(X)&calm(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:(~humble(X)=>(~funny(X)<~>~brave(X))))&
(?[X]:((old(X)|~creative(X))))&
((calm(mary)&~old(mary)))&
(~wise(john))&
((kind(john)<~>happy(john))) | ~quiet(paul) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1773508444932026950527608
% SZS output start Proof for 1773508444932026950527608
2. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~patient(X0) | ~strong(X0))) [input p1]
6. ! [X0] : (~humble(X0) <=> (~kind(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> strong(X0)) => (~funny(X0) & calm(X0))) [input p7]
9. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> (~happy(X0) <~> generous(X0))) [input p8]
10. ! [X0] : (wise(X0) => (humble(X0) & ~humble(X0))) [input p9]
11. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X0] : (~funny(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : ((curious(X0) <~> ~generous(X0)) <=> (brave(X0) | humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~tall(X0) | brave(X0))) [input p12]
14. ! [X0] : (~humble(X0) => (calm(X0) & kind(X0))) [input p13]
15. ! [X0] : ((kind(X0) <~> ~tall(X0)) <=> ~patient(X0)) [input p14]
16. ! [X0] : (~humble(X0) => (~funny(X0) <~> ~brave(X0))) [input p15]
21. quiet(paul) [input hypothesis]
23. ? [X0] : (~calm(X0) | strong(X0)) <=> ? [X1] : (~funny(X1) <~> ~wise(X1)) [rectify 11]
28. ! [X0] : ((~funny(X0) & calm(X0)) | (happy(X0) <=> strong(X0))) [ennf transformation 8]
29. ! [X0] : ((humble(X0) & ~humble(X0)) | ~wise(X0)) [ennf transformation 10]
30. ! [X0] : ((calm(X0) & kind(X0)) | humble(X0)) [ennf transformation 14]
31. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | humble(X0)) [ennf transformation 16]
33. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & ((~patient(X0) | ~strong(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 2]
34. ! [X0] : (((~humble(X0) & ~curious(X0)) | (patient(X0) & strong(X0))) & (~patient(X0) | ~strong(X0) | humble(X0) | curious(X0))) [flattening 33]
42. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | humble(X0))) [nnf transformation 6]
43. ! [X0] : ((~humble(X0) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | humble(X0))) [flattening 42]
45. ! [X0] : ((~funny(X0) & calm(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 28]
46. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 9]
47. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X1] : ((wise(X1) | funny(X1)) & (~wise(X1) | ~funny(X1))) | ! [X0] : (calm(X0) & ~strong(X0))) [nnf transformation 23]
48. (? [X0] : (~calm(X0) | strong(X0)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) | ! [X3] : (calm(X3) & ~strong(X3))) [rectify 47]
49. ? [X0] : (~calm(X0) | strong(X0)) => (~calm(sK3) | strong(sK3)) [choice axiom]
50. ? [X2] : ((wise(X2) | funny(X2)) & (~wise(X2) | ~funny(X2))) => ((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) [choice axiom]
51. ((~calm(sK3) | strong(sK3)) | ! [X1] : ((~funny(X1) | wise(X1)) & (~wise(X1) | funny(X1)))) & (((wise(sK4) | funny(sK4)) & (~wise(sK4) | ~funny(sK4))) | ! [X3] : (calm(X3) & ~strong(X3))) [skolemisation 48,50,49]
52. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [nnf transformation 12]
53. ! [X0] : ((((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))))) [flattening 52]
54. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 13]
55. ! [X0] : (((kind(X0) & ~happy(X0)) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | ~kind(X0) | happy(X0))) [flattening 54]
56. ! [X0] : ((((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | patient(X0)) & (~patient(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0))))) [nnf transformation 15]
57. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | humble(X0)) [nnf transformation 31]
66. ~curious(X0) | strong(X0) [cnf transformation 34]
67. ~curious(X0) | patient(X0) [cnf transformation 34]
68. ~humble(X0) | strong(X0) [cnf transformation 34]
69. ~humble(X0) | patient(X0) [cnf transformation 34]
77. ~quiet(X0) | ~kind(X0) | humble(X0) [cnf transformation 43]
79. ~humble(X0) | kind(X0) [cnf transformation 43]
87. ~funny(X0) | happy(X0) | ~strong(X0) [cnf transformation 45]
89. ~happy(X0) | generous(X0) | ~patient(X0) | humble(X0) [cnf transformation 46]
91. ~generous(X0) | happy(X0) | ~patient(X0) | humble(X0) [cnf transformation 46]
92. ~humble(X0) | ~patient(X0) | generous(X0) | happy(X0) [cnf transformation 46]
94. humble(X0) | patient(X0) | generous(X0) | happy(X0) [cnf transformation 46]
95. humble(X0) | patient(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 46]
96. ~humble(X0) | ~wise(X0) [cnf transformation 29]
97. ~wise(X0) | humble(X0) [cnf transformation 29]
100. wise(sK4) | funny(sK4) | ~strong(X3) [cnf transformation 51]
105. brave(X0) | humble(X0) | curious(X0) | generous(X0) [cnf transformation 53]
106. ~generous(X0) | curious(X0) | ~humble(X0) [cnf transformation 53]
107. ~brave(X0) | curious(X0) | ~generous(X0) [cnf transformation 53]
108. ~humble(X0) | ~curious(X0) | generous(X0) [cnf transformation 53]
110. ~tall(X0) | brave(X0) | ~kind(X0) | happy(X0) [cnf transformation 55]
112. ~happy(X0) | tall(X0) [cnf transformation 55]
115. kind(X0) | humble(X0) [cnf transformation 30]
117. ~patient(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 56]
120. tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 56]
121. ~brave(X0) | ~funny(X0) | humble(X0) [cnf transformation 57]
122. brave(X0) | funny(X0) | humble(X0) [cnf transformation 57]
129. quiet(paul) [cnf transformation 21]
202. ~generous(X0) | ~happy(X0) | patient(X0) [subsumption resolution 95,69]
203. generous(X0) | patient(X0) | happy(X0) [subsumption resolution 94,69]
205. ~humble(X0) | generous(X0) | happy(X0) [subsumption resolution 92,203]
206. ~wise(X0) [subsumption resolution 96,97]
225. 21 <=> funny(sK4) [avatar definition]
227. funny(sK4) <- (21) [avatar component clause 225]
229. funny(sK4) | ~strong(X3) [subsumption resolution 100,206]
231. 22 <=> ! [X3] : ~strong(X3) [avatar definition]
232. ~strong(X3) <- (22) [avatar component clause 231]
233. 22 | 21 [avatar split clause 229,225,231]
234. kind(X0) [subsumption resolution 115,79]
235. tall(X0) | patient(X0) [subsumption resolution 120,234]
236. ~tall(X0) | ~patient(X0) [subsumption resolution 117,234]
258. ~kind(paul) | humble(paul) [resolution 77,129]
259. humble(paul) [subsumption resolution 258,234]
263. strong(paul) [resolution 259,68]
293. 29 <=> happy(sK4) [avatar definition]
294. happy(sK4) <- (29) [avatar component clause 293]
297. 30 <=> strong(sK4) [avatar definition]
325. funny(X2) | humble(X2) | curious(X2) | ~generous(X2) [resolution 122,107]
330. ~generous(X2) | curious(X2) | funny(X2) [subsumption resolution 325,106]
366. humble(X0) | curious(X0) | generous(X0) | ~funny(X0) | humble(X0) [resolution 105,121]
373. ~funny(X0) | curious(X0) | generous(X0) | humble(X0) [duplicate literal removal 366]
374. brave(X0) | ~kind(X0) | happy(X0) | patient(X0) [resolution 110,235]
376. brave(X0) | happy(X0) | patient(X0) [subsumption resolution 374,234]
411. curious(X0) | funny(X0) | patient(X0) | happy(X0) [resolution 330,203]
413. funny(X0) | patient(X0) | happy(X0) [subsumption resolution 411,67]
414. happy(X0) | patient(X0) | ~funny(X0) | humble(X0) [resolution 376,121]
419. happy(X0) | patient(X0) | ~funny(X0) [subsumption resolution 414,69]
420. happy(X0) | patient(X0) [subsumption resolution 419,413]
451. 38 <=> humble(sK4) [avatar definition]
452. ~humble(sK4) <- (~38) [avatar component clause 451]
453. humble(sK4) <- (38) [avatar component clause 451]
455. 39 <=> generous(sK4) [avatar definition]
456. ~generous(sK4) <- (~39) [avatar component clause 455]
457. generous(sK4) <- (39) [avatar component clause 455]
459. 40 <=> curious(sK4) [avatar definition]
461. curious(sK4) <- (40) [avatar component clause 459]
463. $false <- (22) [resolution 232,263]
467. ~22 [avatar contradiction clause 463]
468. curious(sK4) | generous(sK4) | humble(sK4) <- (21) [resolution 227,373]
469. happy(sK4) | ~strong(sK4) <- (21) [resolution 227,87]
471. generous(sK4) | happy(sK4) <- (38) [resolution 453,205]
472. ~curious(sK4) | generous(sK4) <- (38) [resolution 453,108]
475. patient(sK4) <- (38) [resolution 453,69]
476. strong(sK4) <- (38) [resolution 453,68]
479. 39 | ~40 | ~38 [avatar split clause 472,451,459,455]
482. 29 | 39 | ~38 [avatar split clause 471,451,455,293]
484. 30 | ~38 [avatar split clause 476,451,297]
485. ~30 | 29 | ~21 [avatar split clause 469,225,293,297]
490. tall(sK4) <- (29) [resolution 294,112]
494. ~patient(sK4) <- (29) [resolution 490,236]
495. $false <- (29, 38) [subsumption resolution 494,475]
496. ~29 | ~38 [avatar contradiction clause 495]
505. happy(sK4) | ~patient(sK4) | humble(sK4) <- (39) [resolution 457,91]
507. ~happy(sK4) | patient(sK4) <- (39) [resolution 457,202]
509. patient(sK4) <- (29, 39) [subsumption resolution 507,294]
510. $false <- (29, 39) [subsumption resolution 509,494]
511. ~29 | ~39 [avatar contradiction clause 510]
512. patient(sK4) <- (39) [subsumption resolution 507,420]
513. happy(sK4) | humble(sK4) <- (39) [subsumption resolution 505,512]
514. happy(sK4) <- (~38, 39) [subsumption resolution 513,452]
515. 29 | 38 | ~39 [avatar split clause 514,455,451,293]
516. curious(sK4) | generous(sK4) <- (21, ~38) [subsumption resolution 468,452]
517. 39 | 40 | ~21 | 38 [avatar split clause 516,451,225,459,455]
525. patient(sK4) <- (40) [resolution 461,67]
526. strong(sK4) <- (40) [resolution 461,66]
529. 30 | ~40 [avatar split clause 526,459,297]
532. generous(sK4) | ~patient(sK4) | humble(sK4) <- (29) [resolution 294,89]
535. ~patient(sK4) | humble(sK4) <- (29, ~39) [subsumption resolution 532,456]
536. humble(sK4) <- (29, ~39, 40) [subsumption resolution 535,525]
537. $false <- (29, ~38, ~39, 40) [subsumption resolution 536,452]
538. ~29 | 38 | 39 | ~40 [avatar contradiction clause 537]
539. $false [avatar sat refutation 233,467,479,482,484,485,496,511,515,517,529,538]
% SZS output end Proof for 1773508444932026950527608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or brave then alice is not kind and vice versa.
Everyone who is not generous or wise is both not calm and not old and vice versa.
If paul is not kind then someone is both not happy and not calm and vice versa.
Everyone who is funny or not humble is kind or old and vice versa.
Everyone who is both humble and patient is not calm and vice versa.
If someone is either not happy or not rich then someone is generous or funny and vice versa.
If paul is either wise or not tall then lucy is quiet.
If someone is not funny or not kind then someone is not tall or not quiet.
Everyone who is funny is not kind.
If someone is not brave then someone is brave and vice versa.
If someone is either not patient or not quiet then fred is happy or not curious and vice versa.
If someone is either old or kind then someone is not generous and vice versa.
Everyone who is brave or not rich is not wise or not curious.
If alice is rich or not generous then someone is rich or not curious and vice versa.
If someone is brave then someone is both creative and not wise.
Paul is either not curious or not tall.
Someone is rich or quiet.
Someone is old.
Fred is both rich and not happy.
Lucy is not patient or calm.
Someone is not happy or not old.
John is strong or not wise. | Fred is not happy. | entailment | (((curious(alice)|brave(alice)))<=>(~kind(alice)))&
(![X]:((~generous(X)|wise(X))<=>(~calm(X)&~old(X))))&
((~kind(paul))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((funny(X)|~humble(X))<=>(kind(X)|old(X))))&
(![X]:((humble(X)&patient(X))<=>~calm(X)))&
((?[X]:((~happy(X)<~>~rich(X))))<=>(?[X]:((generous(X)|funny(X)))))&
(((wise(paul)<~>~tall(paul)))=>(quiet(lucy)))&
((?[X]:((~funny(X)|~kind(X))))=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:(funny(X)=>~kind(X)))&
((?[X]:(~brave(X)))<=>(?[X]:(brave(X))))&
((?[X]:((~patient(X)<~>~quiet(X))))<=>((happy(fred)|~curious(fred))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:((brave(X)|~rich(X))=>(~wise(X)|~curious(X))))&
(((rich(alice)|~generous(alice)))<=>(?[X]:((rich(X)|~curious(X)))))&
((?[X]:(brave(X)))=>(?[X]:((creative(X)&~wise(X)))))&
((~curious(paul)<~>~tall(paul)))&
(?[X]:((rich(X)|quiet(X))))&
(?[X]:(old(X)))&
((rich(fred)&~happy(fred)))&
((~patient(lucy)|calm(lucy)))&
(?[X]:((~happy(X)|~old(X))))&
((strong(john)|~wise(john))) | ~happy(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 835456482692307866436499
% SZS output start Proof for 835456482692307866436499
19. ~happy(fred) & rich(fred) [input p18]
23. happy(fred) [input hypothesis]
141. ~happy(fred) [cnf transformation 19]
144. happy(fred) [cnf transformation 23]
272. 30 <=> happy(fred) [avatar definition]
357. ~30 [avatar split clause 141,272]
368. 30 [avatar split clause 144,272]
369. $false [avatar sat refutation 357,368]
% SZS output end Proof for 835456482692307866436499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not wise then someone is both not strong and not quiet and vice versa.
Everyone who is kind is not creative.
If mary is not happy then someone is not curious.
Everyone who is brave or not generous is not old and vice versa.
If someone is rich or not patient then someone is not funny or not wise.
Everyone who is not curious or patient is both not generous and kind.
If someone is either patient or generous then someone is both funny and kind and vice versa.
Everyone who is humble or not funny is both old and wise.
If alice is not curious or tall then someone is both wise and not humble and vice versa.
If someone is not strong or happy then someone is either calm or not funny.
If someone is generous then someone is old.
If someone is either calm or not wise then someone is both old and not happy.
Everyone who is not generous is humble.
If paul is curious then fred is kind or generous.
Everyone who is either not quiet or happy is not calm or funny and vice versa.
If john is not wise or not tall then someone is generous.
Paul is not patient or strong.
John is wise or not funny.
Someone is rich or calm.
Susan is either rich or happy.
Fred is not curious or brave.
Mary is either not quiet or not humble.
Someone is either curious or not curious. | John is curious. | entailment | (((~kind(mary)&~wise(mary)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:(kind(X)=>~creative(X)))&
((~happy(mary))=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~generous(X))<=>~old(X)))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((~curious(X)|patient(X))=>(~generous(X)&kind(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((humble(X)|~funny(X))=>(old(X)&wise(X))))&
(((~curious(alice)|tall(alice)))<=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((calm(X)<~>~funny(X)))))&
((?[X]:(generous(X)))=>(?[X]:(old(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:((old(X)&~happy(X)))))&
(![X]:(~generous(X)=>humble(X)))&
((curious(paul))=>((kind(fred)|generous(fred))))&
(![X]:((~quiet(X)<~>happy(X))<=>(~calm(X)|funny(X))))&
(((~wise(john)|~tall(john)))=>(?[X]:(generous(X))))&
((~patient(paul)|strong(paul)))&
((wise(john)|~funny(john)))&
(?[X]:((rich(X)|calm(X))))&
((rich(susan)<~>happy(susan)))&
((~curious(fred)|brave(fred)))&
((~quiet(mary)<~>~humble(mary)))&
(?[X]:((curious(X)<~>~curious(X)))) | curious(john) | [
"p3",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 42023042688609770260303
% SZS output start Proof for 42023042688609770260303
4. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~old(X0)) [input p3]
6. ! [X0] : ((patient(X0) | ~curious(X0)) => (kind(X0) & ~generous(X0))) [input p5]
8. ! [X0] : ((~funny(X0) | humble(X0)) => (wise(X0) & old(X0))) [input p7]
13. ! [X0] : (~generous(X0) => humble(X0)) [input p12]
24. ~curious(john) [input hypothesis]
30. ! [X0] : ((~generous(X0) | brave(X0)) => ~old(X0)) [unused predicate definition removal 4]
33. ! [X0] : (~old(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 30]
35. ! [X0] : ((kind(X0) & ~generous(X0)) | (~patient(X0) & curious(X0))) [ennf transformation 6]
36. ! [X0] : ((wise(X0) & old(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 8]
40. ! [X0] : (humble(X0) | generous(X0)) [ennf transformation 13]
92. ~old(X0) | generous(X0) [cnf transformation 33]
95. ~generous(X0) | curious(X0) [cnf transformation 35]
105. ~humble(X0) | old(X0) [cnf transformation 36]
123. humble(X0) | generous(X0) [cnf transformation 40]
143. ~curious(john) [cnf transformation 24]
385. generous(X1) | old(X1) [resolution 123,105]
390. generous(X1) [subsumption resolution 385,92]
411. curious(X0) [resolution 390,95]
489. $false [resolution 411,143]
% SZS output end Proof for 42023042688609770260303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not kind is either not rich or calm. If someone is both not kind and not calm then alice is not brave or not rich. If someone is either not rich or not happy then someone is humble or calm. If lucy is both not quiet and not brave then someone is either not old or calm and vice versa. Everyone who is not humble or tall is not rich. If someone is either not quiet or kind then paul is wise or not quiet and vice versa. Everyone who is both humble and not wise is kind and vice versa. Everyone who is calm or tall is both not strong and not tall. If someone is either funny or not brave then alice is either not old or not rich and vice versa. Everyone who is both humble and curious is both not happy and not old. If paul is both not funny and not happy then lucy is either curious or funny and vice versa. Everyone who is either funny or brave is not brave or curious and vice versa. If someone is both not wise and humble then someone is not humble and vice versa. If mary is not creative then someone is not generous and vice versa. If someone is rich or not humble then lucy is not quiet or not funny and vice versa. Everyone who is both not patient and not strong is not tall and vice versa. Alice is both not patient and funny. Someone is funny. John is either rich or generous. Someone is rich. Fred is calm or not funny. Paul is both not creative and quiet. Someone is either curious or strong. Lucy is not patient. | Alice is tall. | contradiction | (![X]:((tall(X)<~>~kind(X))=>(~rich(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((~brave(alice)|~rich(alice))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((humble(X)|calm(X)))))&
(((~quiet(lucy)&~brave(lucy)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~humble(X)|tall(X))=>~rich(X)))&
((?[X]:((~quiet(X)<~>kind(X))))<=>((wise(paul)|~quiet(paul))))&
(![X]:((humble(X)&~wise(X))<=>kind(X)))&
(![X]:((calm(X)|tall(X))=>(~strong(X)&~tall(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>((~old(alice)<~>~rich(alice))))&
(![X]:((humble(X)&curious(X))=>(~happy(X)&~old(X))))&
(((~funny(paul)&~happy(paul)))<=>((curious(lucy)<~>funny(lucy))))&
(![X]:((funny(X)<~>brave(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~wise(X)&humble(X))))<=>(?[X]:(~humble(X))))&
((~creative(mary))<=>(?[X]:(~generous(X))))&
((?[X]:((rich(X)|~humble(X))))<=>((~quiet(lucy)|~funny(lucy))))&
(![X]:((~patient(X)&~strong(X))<=>~tall(X)))&
((~patient(alice)&funny(alice)))&
(?[X]:(funny(X)))&
((rich(john)<~>generous(john)))&
(?[X]:(rich(X)))&
((calm(fred)|~funny(fred)))&
((~creative(paul)&quiet(paul)))&
(?[X]:((curious(X)<~>strong(X))))&
(~patient(lucy)) | tall(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6454046368181375759712845
% SZS output start Proof for 6454046368181375759712845
8. ! [X0] : ((tall(X0) | calm(X0)) => (~tall(X0) & ~strong(X0))) [input p7]
25. tall(alice) [input hypothesis]
33. ! [X0] : ((~tall(X0) & ~strong(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 8]
112. ~tall(X0) | ~tall(X0) [cnf transformation 33]
159. tall(alice) [cnf transformation 25]
162. ~tall(X0) [duplicate literal removal 112]
368. $false [subsumption resolution 159,162]
% SZS output end Proof for 6454046368181375759712845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or brave is rich.
If mary is patient or strong then paul is both brave and strong.
If fred is either not strong or funny then susan is either happy or kind.
Everyone who is not strong is either not creative or not patient.
If mary is either creative or not strong then someone is either funny or kind.
Everyone who is not old or kind is either curious or happy and vice versa.
Everyone who is both patient and brave is not humble and vice versa.
Everyone who is either quiet or not patient is strong and vice versa.
If someone is quiet then someone is kind.
Everyone who is both not creative and quiet is not humble or not strong and vice versa.
If paul is both happy and rich then someone is both not calm and curious and vice versa.
If lucy is both patient and not strong then susan is not quiet and vice versa.
Everyone who is either quiet or not tall is not quiet and vice versa.
If someone is either humble or not brave then mary is not quiet or quiet and vice versa.
Everyone who is happy or not humble is either not tall or quiet.
Everyone who is creative is either not happy or funny.
Fred is generous or not generous.
John is either wise or not funny.
Alice is humble or rich.
Someone is humble.
Susan is both curious and humble. | Mary is rich. | entailment | (![X]:((~brave(X)<~>brave(X))=>rich(X)))&
(((patient(mary)|strong(mary)))=>((brave(paul)&strong(paul))))&
(((~strong(fred)<~>funny(fred)))=>((happy(susan)<~>kind(susan))))&
(![X]:(~strong(X)=>(~creative(X)<~>~patient(X))))&
(((creative(mary)<~>~strong(mary)))=>(?[X]:((funny(X)<~>kind(X)))))&
(![X]:((~old(X)|kind(X))<=>(curious(X)<~>happy(X))))&
(![X]:((patient(X)&brave(X))<=>~humble(X)))&
(![X]:((quiet(X)<~>~patient(X))<=>strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:(kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~humble(X)|~strong(X))))&
(((happy(paul)&rich(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((patient(lucy)&~strong(lucy)))<=>(~quiet(susan)))&
(![X]:((quiet(X)<~>~tall(X))<=>~quiet(X)))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~quiet(mary)|quiet(mary))))&
(![X]:((happy(X)|~humble(X))=>(~tall(X)<~>quiet(X))))&
(![X]:(creative(X)=>(~happy(X)<~>funny(X))))&
((generous(fred)|~generous(fred)))&
((wise(john)<~>~funny(john)))&
((humble(alice)|rich(alice)))&
(?[X]:(humble(X)))&
((curious(susan)&humble(susan))) | rich(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7440146600292801366620083
% SZS output start Proof for 7440146600292801366620083
1. ! [X0] : ((~brave(X0) <~> brave(X0)) => rich(X0)) [input p0]
22. ~rich(mary) [input hypothesis]
24. ! [X0] : (rich(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 1]
32. ! [X0] : (rich(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 24]
66. rich(X0) | brave(X0) | brave(X0) [cnf transformation 32]
67. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 32]
131. ~rich(mary) [cnf transformation 22]
134. rich(X0) | brave(X0) [duplicate literal removal 66]
135. rich(X0) | ~brave(X0) [duplicate literal removal 67]
136. rich(X0) [subsumption resolution 134,135]
270. $false [subsumption resolution 131,136]
% SZS output end Proof for 7440146600292801366620083
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or curious is wise.
If paul is either brave or not brave then someone is not wise or old.
If someone is not curious or quiet then alice is either humble or not kind and vice versa.
If someone is not happy then someone is humble.
If someone is not tall or not brave then someone is both not tall and wise and vice versa.
Everyone who is creative or wise is quiet.
If someone is both happy and quiet then alice is either not strong or not creative and vice versa.
Everyone who is not humble or not tall is both not patient and not brave and vice versa.
Everyone who is either curious or not generous is not funny or not curious and vice versa.
If someone is either not rich or rich then paul is either quiet or not rich.
Everyone who is not funny is not happy or quiet and vice versa.
Everyone who is either creative or not humble is generous.
Everyone who is wise is not kind.
Everyone who is either not brave or not quiet is kind and vice versa.
Everyone who is either curious or patient is not tall.
If someone is not old or generous then someone is not brave and vice versa.
Susan is old.
Paul is either quiet or not old.
Someone is wise or not kind.
Mary is either not funny or not creative.
Mary is both not strong and not rich.
Alice is tall. | Mary is humble. | entailment | (![X]:((generous(X)<~>curious(X))=>wise(X)))&
(((brave(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)|old(X)))))&
((?[X]:((~curious(X)|quiet(X))))<=>((humble(alice)<~>~kind(alice))))&
((?[X]:(~happy(X)))=>(?[X]:(humble(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((creative(X)|wise(X))=>quiet(X)))&
((?[X]:((happy(X)&quiet(X))))<=>((~strong(alice)<~>~creative(alice))))&
(![X]:((~humble(X)|~tall(X))<=>(~patient(X)&~brave(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>((quiet(paul)<~>~rich(paul))))&
(![X]:(~funny(X)<=>(~happy(X)|quiet(X))))&
(![X]:((creative(X)<~>~humble(X))=>generous(X)))&
(![X]:(wise(X)=>~kind(X)))&
(![X]:((~brave(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((curious(X)<~>patient(X))=>~tall(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~brave(X))))&
(old(susan))&
((quiet(paul)<~>~old(paul)))&
(?[X]:((wise(X)|~kind(X))))&
((~funny(mary)<~>~creative(mary)))&
((~strong(mary)&~rich(mary)))&
(tall(alice)) | humble(mary) | [
"p4",
"p5",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3202648980898636728450634
% SZS output start Proof for 3202648980898636728450634
5. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X0] : (wise(X0) & ~tall(X0)) [input p4]
6. ! [X0] : ((wise(X0) | creative(X0)) => quiet(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~brave(X0) & ~patient(X0))) [input p7]
13. ! [X0] : (wise(X0) => ~kind(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p13]
23. ~humble(mary) [input hypothesis]
25. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X1] : (wise(X1) & ~tall(X1)) [rectify 5]
30. ! [X0] : (quiet(X0) | (~wise(X0) & ~creative(X0))) [ennf transformation 6]
33. ! [X0] : (~kind(X0) | ~wise(X0)) [ennf transformation 13]
46. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X1] : (wise(X1) & ~tall(X1)) | ! [X0] : (brave(X0) & tall(X0))) [nnf transformation 25]
47. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X2] : (wise(X2) & ~tall(X2)) | ! [X3] : (brave(X3) & tall(X3))) [rectify 46]
48. ? [X0] : (~brave(X0) | ~tall(X0)) => (~brave(sK3) | ~tall(sK3)) [choice axiom]
49. ? [X2] : (wise(X2) & ~tall(X2)) => (wise(sK4) & ~tall(sK4)) [choice axiom]
50. ((~brave(sK3) | ~tall(sK3)) | ! [X1] : (~wise(X1) | tall(X1))) & ((wise(sK4) & ~tall(sK4)) | ! [X3] : (brave(X3) & tall(X3))) [skolemisation 47,49,48]
55. ! [X0] : (((~tall(X0) | ~humble(X0)) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 8]
56. ! [X0] : ((~tall(X0) | ~humble(X0) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [flattening 55]
63. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~kind(X0)) & (kind(X0) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [nnf transformation 14]
86. ~tall(sK4) | brave(X3) [cnf transformation 50]
87. wise(sK4) | tall(X3) [cnf transformation 50]
91. ~wise(X0) | quiet(X0) [cnf transformation 30]
100. ~brave(X0) | humble(X0) [cnf transformation 56]
101. ~brave(X0) | tall(X0) [cnf transformation 56]
118. ~kind(X0) | ~wise(X0) [cnf transformation 33]
119. ~quiet(X0) | kind(X0) | brave(X0) [cnf transformation 63]
137. ~humble(mary) [cnf transformation 23]
209. 15 <=> ! [X3] : brave(X3) [avatar definition]
210. brave(X3) <- (15) [avatar component clause 209]
212. 16 <=> wise(sK4) [avatar definition]
214. wise(sK4) <- (16) [avatar component clause 212]
217. 17 <=> ! [X3] : tall(X3) [avatar definition]
218. tall(X3) <- (17) [avatar component clause 217]
219. 17 | 16 [avatar split clause 87,212,217]
221. 18 <=> tall(sK4) [avatar definition]
223. ~tall(sK4) <- (~18) [avatar component clause 221]
224. 15 | ~18 [avatar split clause 86,221,209]
310. quiet(sK4) <- (16) [resolution 91,214]
333. kind(sK4) | brave(sK4) <- (16) [resolution 119,310]
346. 38 <=> brave(sK4) [avatar definition]
348. brave(sK4) <- (38) [avatar component clause 346]
350. 39 <=> kind(sK4) [avatar definition]
352. kind(sK4) <- (39) [avatar component clause 350]
353. 38 | 39 | ~16 [avatar split clause 333,212,350,346]
430. ~wise(sK4) <- (39) [resolution 352,118]
435. ~16 | ~39 [avatar split clause 430,350,212]
456. $false <- (17, ~18) [resolution 218,223]
459. ~17 | 18 [avatar contradiction clause 456]
470. tall(sK4) <- (38) [resolution 348,101]
474. 18 | ~38 [avatar split clause 470,346,221]
488. humble(X2) <- (15) [resolution 210,100]
499. $false <- (15) [resolution 488,137]
500. ~15 [avatar contradiction clause 499]
501. $false [avatar sat refutation 219,224,353,435,459,474,500]
% SZS output end Proof for 3202648980898636728450634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or funny is either not generous or not happy and vice versa.
If someone is funny then paul is humble or not brave.
Everyone who is both not tall and happy is not humble and vice versa.
Everyone who is not patient is rich.
Everyone who is calm or not calm is both not humble and curious and vice versa.
Everyone who is generous is not quiet and vice versa.
If someone is calm or not rich then someone is both wise and not calm and vice versa.
Everyone who is both not curious and not brave is both creative and not creative and vice versa.
If paul is both calm and funny then john is either not tall or not generous.
Everyone who is both not quiet and humble is either not kind or wise.
If paul is not wise or creative then john is both generous and not kind.
Everyone who is either not old or not patient is both quiet and kind and vice versa.
If john is not creative or patient then lucy is both not brave and quiet.
Everyone who is not creative is calm or not old and vice versa.
If someone is not generous then someone is funny or not wise and vice versa.
If someone is not brave then someone is both kind and calm.
Someone is both curious and old.
Someone is both not patient and not wise.
Someone is not old.
Fred is both curious and not funny.
Someone is not patient.
Someone is both kind and not tall.
Susan is tall or kind. | Fred is not happy. | contradiction | (![X]:((~patient(X)<~>funny(X))<=>(~generous(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>((humble(paul)|~brave(paul))))&
(![X]:((~tall(X)&happy(X))<=>~humble(X)))&
(![X]:(~patient(X)=>rich(X)))&
(![X]:((calm(X)|~calm(X))<=>(~humble(X)&curious(X))))&
(![X]:(generous(X)<=>~quiet(X)))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((~curious(X)&~brave(X))<=>(creative(X)&~creative(X))))&
(((calm(paul)&funny(paul)))=>((~tall(john)<~>~generous(john))))&
(![X]:((~quiet(X)&humble(X))=>(~kind(X)<~>wise(X))))&
(((~wise(paul)|creative(paul)))=>((generous(john)&~kind(john))))&
(![X]:((~old(X)<~>~patient(X))<=>(quiet(X)&kind(X))))&
(((~creative(john)|patient(john)))=>((~brave(lucy)&quiet(lucy))))&
(![X]:(~creative(X)<=>(calm(X)|~old(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((funny(X)|~wise(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((kind(X)&calm(X)))))&
(?[X]:((curious(X)&old(X))))&
(?[X]:((~patient(X)&~wise(X))))&
(?[X]:(~old(X)))&
((curious(fred)&~funny(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((kind(X)&~tall(X))))&
((tall(susan)|kind(susan))) | ~happy(fred) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1098697620821103179766792
% SZS output start Proof for 1098697620821103179766792
3. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~humble(X0)) [input p2]
5. ! [X0] : ((~calm(X0) | calm(X0)) <=> (curious(X0) & ~humble(X0))) [input p4]
24. ~happy(fred) [input hypothesis]
39. ! [X0] : (((happy(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 3]
40. ! [X0] : (((happy(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | ~happy(X0) | tall(X0))) [flattening 39]
41. ! [X0] : (((~calm(X0) | calm(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & ~calm(X0)))) [nnf transformation 5]
42. ! [X0] : ((~calm(X0) | calm(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & ~calm(X0)))) [flattening 41]
86. humble(X0) | happy(X0) [cnf transformation 40]
88. ~humble(X0) | ~calm(X0) [cnf transformation 42]
89. ~humble(X0) | calm(X0) [cnf transformation 42]
141. ~happy(fred) [cnf transformation 24]
155. ~humble(X0) [subsumption resolution 88,89]
295. happy(X0) [resolution 86,155]
296. $false [resolution 295,141]
% SZS output end Proof for 1098697620821103179766792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or strong is not tall or not creative.
Everyone who is strong is generous or not creative and vice versa.
Everyone who is either not strong or patient is both humble and brave and vice versa.
If susan is not kind or patient then someone is both not old and funny and vice versa.
Everyone who is both humble and creative is either not quiet or not old.
Everyone who is not patient or not creative is both rich and not humble.
Everyone who is both rich and kind is quiet.
Everyone who is both kind and tall is patient and vice versa.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
If someone is either not patient or not creative then john is not funny.
If fred is creative then john is not tall or strong.
Everyone who is either not generous or not kind is humble or not old.
Everyone who is strong is either old or creative and vice versa.
Everyone who is wise or not brave is wise or not old.
Everyone who is either not brave or not happy is funny.
Someone is not old.
Alice is both patient and calm.
Susan is quiet or strong.
Someone is both funny and not patient.
Someone is not quiet.
Someone is not wise.
Mary is either curious or kind.
Someone is both rich and not calm. | Alice is not brave. | entailment | (![X]:((rich(X)|strong(X))=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(generous(X)|~creative(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)&brave(X))))&
(((~kind(susan)|patient(susan)))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:((rich(X)&kind(X))=>quiet(X)))&
(![X]:((kind(X)&tall(X))<=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~patient(X)<~>~creative(X))))=>(~funny(john)))&
((creative(fred))=>((~tall(john)|strong(john))))&
(![X]:((~generous(X)<~>~kind(X))=>(humble(X)|~old(X))))&
(![X]:(strong(X)<=>(old(X)<~>creative(X))))&
(![X]:((wise(X)|~brave(X))=>(wise(X)|~old(X))))&
(![X]:((~brave(X)<~>~happy(X))=>funny(X)))&
(?[X]:(~old(X)))&
((patient(alice)&calm(alice)))&
((quiet(susan)|strong(susan)))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(~wise(X)))&
((curious(mary)<~>kind(mary)))&
(?[X]:((rich(X)&~calm(X)))) | ~brave(alice) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5786043772695689442375289
% SZS output start Proof for 5786043772695689442375289
1. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) | ~tall(X0))) [input p0]
2. ! [X0] : (strong(X0) <=> (~creative(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (brave(X0) & humble(X0))) [input p2]
6. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~humble(X0) & rich(X0))) [input p5]
8. ! [X0] : ((tall(X0) & kind(X0)) <=> patient(X0)) [input p7]
13. ! [X0] : ((~generous(X0) <~> ~kind(X0)) => (~old(X0) | humble(X0))) [input p12]
14. ! [X0] : (strong(X0) <=> (old(X0) <~> creative(X0))) [input p13]
18. calm(alice) & patient(alice) [input p17]
25. brave(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 1]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (~strong(X0) & ~rich(X0))) [flattening 27]
31. ! [X0] : ((~humble(X0) & rich(X0)) | (creative(X0) & patient(X0))) [ennf transformation 6]
39. ! [X0] : ((~old(X0) | humble(X0)) | (~generous(X0) <=> ~kind(X0))) [ennf transformation 13]
40. ! [X0] : (~old(X0) | humble(X0) | (~generous(X0) <=> ~kind(X0))) [flattening 39]
44. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 2]
45. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | ~strong(X0))) [flattening 44]
46. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [nnf transformation 3]
47. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [flattening 46]
54. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) | ~kind(X0)))) [nnf transformation 8]
55. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~tall(X0) | ~kind(X0))) [flattening 54]
62. ! [X0] : (~old(X0) | humble(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) [nnf transformation 40]
63. ! [X0] : ((strong(X0) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) & (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | ~strong(X0))) [nnf transformation 14]
77. ~creative(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 28]
79. ~generous(X0) | strong(X0) [cnf transformation 45]
80. creative(X0) | strong(X0) [cnf transformation 45]
82. ~patient(X0) | ~strong(X0) | humble(X0) [cnf transformation 47]
86. ~brave(X0) | strong(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 47]
97. ~humble(X0) | creative(X0) [cnf transformation 31]
100. ~patient(X0) | kind(X0) [cnf transformation 55]
101. ~patient(X0) | tall(X0) [cnf transformation 55]
109. ~old(X0) | humble(X0) | ~kind(X0) | generous(X0) [cnf transformation 62]
114. strong(X0) | old(X0) | ~creative(X0) [cnf transformation 63]
120. patient(alice) [cnf transformation 18]
131. brave(alice) [cnf transformation 25]
205. old(X0) | strong(X0) [subsumption resolution 114,80]
227. kind(alice) [resolution 100,120]
230. tall(alice) [resolution 101,120]
257. ~strong(alice) | humble(alice) [resolution 82,120]
261. 22 <=> humble(alice) [avatar definition]
263. humble(alice) <- (22) [avatar component clause 261]
265. 23 <=> strong(alice) [avatar definition]
266. strong(alice) <- (23) [avatar component clause 265]
268. 22 | ~23 [avatar split clause 257,265,261]
351. strong(alice) | ~patient(alice) | ~humble(alice) [resolution 86,131]
372. humble(X1) | ~kind(X1) | generous(X1) | strong(X1) [resolution 109,205]
375. ~kind(X1) | humble(X1) | strong(X1) [subsumption resolution 372,79]
475. 50 <=> creative(alice) [avatar definition]
477. creative(alice) <- (50) [avatar component clause 475]
518. humble(alice) | strong(alice) [resolution 375,227]
524. 23 | 22 [avatar split clause 518,261,265]
525. strong(alice) | ~humble(alice) [subsumption resolution 351,120]
526. ~22 | 23 [avatar split clause 525,265,261]
528. creative(alice) <- (22) [resolution 263,97]
669. ~tall(alice) | ~strong(alice) <- (50) [resolution 477,77]
673. ~strong(alice) <- (50) [subsumption resolution 669,230]
674. $false <- (23, 50) [subsumption resolution 673,266]
675. ~23 | ~50 [avatar contradiction clause 674]
679. 50 | ~22 [avatar split clause 528,261,475]
680. $false [avatar sat refutation 268,524,526,675,679]
% SZS output end Proof for 5786043772695689442375289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and curious is not kind or not happy and vice versa.
If paul is either strong or calm then someone is both brave and generous.
If someone is both not humble and quiet then susan is kind and vice versa.
Everyone who is not calm or not kind is not brave.
Everyone who is both tall and not rich is either humble or not old and vice versa.
If alice is not humble then someone is not curious and vice versa.
Everyone who is either humble or rich is either wise or not kind and vice versa.
Everyone who is not wise or not quiet is both tall and generous.
If paul is both quiet and tall then someone is either not rich or not kind and vice versa.
If lucy is both not curious and not brave then someone is funny and vice versa.
Everyone who is both funny and not happy is both calm and strong and vice versa.
Everyone who is funny is both wise and not creative and vice versa.
Everyone who is wise is either generous or not old.
Everyone who is not quiet is not rich or curious.
Everyone who is both not creative and not tall is funny and vice versa.
Everyone who is strong is both not curious and not rich and vice versa.
Susan is either curious or tall.
Susan is not generous.
Someone is either not tall or quiet.
John is both not quiet and not kind.
Fred is either wise or happy.
Someone is rich or not wise.
Paul is brave.
Paul is either not curious or old. | Susan is not strong. | entailment | (![X]:((old(X)&curious(X))<=>(~kind(X)|~happy(X))))&
(((strong(paul)<~>calm(paul)))=>(?[X]:((brave(X)&generous(X)))))&
((?[X]:((~humble(X)&quiet(X))))<=>(kind(susan)))&
(![X]:((~calm(X)|~kind(X))=>~brave(X)))&
(![X]:((tall(X)&~rich(X))<=>(humble(X)<~>~old(X))))&
((~humble(alice))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)<~>rich(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(tall(X)&generous(X))))&
(((quiet(paul)&tall(paul)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(((~curious(lucy)&~brave(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)&~happy(X))<=>(calm(X)&strong(X))))&
(![X]:(funny(X)<=>(wise(X)&~creative(X))))&
(![X]:(wise(X)=>(generous(X)<~>~old(X))))&
(![X]:(~quiet(X)=>(~rich(X)|curious(X))))&
(![X]:((~creative(X)&~tall(X))<=>funny(X)))&
(![X]:(strong(X)<=>(~curious(X)&~rich(X))))&
((curious(susan)<~>tall(susan)))&
(~generous(susan))&
(?[X]:((~tall(X)<~>quiet(X))))&
((~quiet(john)&~kind(john)))&
((wise(fred)<~>happy(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(brave(paul))&
((~curious(paul)<~>old(paul))) | ~strong(susan) | [
"p0",
"p4",
"p6",
"p7",
"p12",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2723795831688446368370378
% SZS output start Proof for 2723795831688446368370378
1. ! [X0] : ((curious(X0) & old(X0)) <=> (~happy(X0) | ~kind(X0))) [input p0]
5. ! [X0] : ((~rich(X0) & tall(X0)) <=> (humble(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((humble(X0) <~> rich(X0)) <=> (wise(X0) <~> ~kind(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) | ~wise(X0)) => (generous(X0) & tall(X0))) [input p7]
13. ! [X0] : (wise(X0) => (generous(X0) <~> ~old(X0))) [input p12]
16. ! [X0] : (strong(X0) <=> (~rich(X0) & ~curious(X0))) [input p15]
17. curious(susan) <~> tall(susan) [input p16]
18. ~generous(susan) [input p17]
25. strong(susan) [input hypothesis]
28. ! [X0] : ((generous(X0) & tall(X0)) | (quiet(X0) & wise(X0))) [ennf transformation 8]
29. ! [X0] : ((generous(X0) <~> ~old(X0)) | ~wise(X0)) [ennf transformation 13]
32. ! [X0] : (((curious(X0) & old(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 1]
33. ! [X0] : (((curious(X0) & old(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~curious(X0) | ~old(X0))) [flattening 32]
41. ! [X0] : (((~rich(X0) & tall(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (rich(X0) | ~tall(X0)))) [nnf transformation 5]
42. ! [X0] : (((~rich(X0) & tall(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | rich(X0) | ~tall(X0))) [flattening 41]
47. ! [X0] : ((((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0)))) & (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0))))) [nnf transformation 7]
62. ! [X0] : (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ~wise(X0)) [nnf transformation 29]
65. ! [X0] : ((strong(X0) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | ~strong(X0))) [nnf transformation 16]
66. ! [X0] : ((strong(X0) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | ~strong(X0))) [flattening 65]
67. (~tall(susan) | ~curious(susan)) & (tall(susan) | curious(susan)) [nnf transformation 17]
76. kind(X0) | old(X0) [cnf transformation 33]
90. ~tall(X0) | ~humble(X0) | rich(X0) | old(X0) [cnf transformation 42]
94. ~rich(X0) | humble(X0) | old(X0) [cnf transformation 42]
101. ~wise(X0) | humble(X0) | ~kind(X0) | rich(X0) [cnf transformation 47]
107. wise(X0) | generous(X0) [cnf transformation 28]
125. ~old(X0) | generous(X0) | ~wise(X0) [cnf transformation 62]
131. ~strong(X0) | ~curious(X0) [cnf transformation 66]
132. ~rich(X0) | ~strong(X0) [cnf transformation 66]
134. tall(susan) | curious(susan) [cnf transformation 67]
136. ~generous(susan) [cnf transformation 18]
147. strong(susan) [cnf transformation 25]
245. ~old(X0) | generous(X0) [subsumption resolution 125,107]
247. 22 <=> curious(susan) [avatar definition]
251. 23 <=> tall(susan) [avatar definition]
252. tall(susan) <- (23) [avatar component clause 251]
255. 22 | 23 [avatar split clause 134,251,247]
305. ~curious(susan) [resolution 131,147]
309. ~22 [avatar split clause 305,247]
460. 43 <=> old(susan) [avatar definition]
461. old(susan) <- (43) [avatar component clause 460]
464. 44 <=> rich(susan) [avatar definition]
466. rich(susan) <- (44) [avatar component clause 464]
468. 45 <=> humble(susan) [avatar definition]
469. ~humble(susan) <- (~45) [avatar component clause 468]
497. ~humble(susan) | rich(susan) | old(susan) <- (23) [resolution 90,252]
542. ~kind(X0) | humble(X0) | rich(X0) | generous(X0) [resolution 101,107]
767. humble(X1) | rich(X1) | generous(X1) | old(X1) [resolution 542,76]
772. humble(X1) | generous(X1) | old(X1) [subsumption resolution 767,94]
773. humble(X1) | generous(X1) [subsumption resolution 772,245]
940. generous(susan) <- (~45) [resolution 773,469]
949. $false <- (~45) [subsumption resolution 940,136]
950. 45 [avatar contradiction clause 949]
951. 43 | 44 | ~45 | ~23 [avatar split clause 497,251,468,464,460]
953. generous(susan) <- (43) [resolution 461,245]
954. $false <- (43) [subsumption resolution 953,136]
955. ~43 [avatar contradiction clause 954]
961. ~strong(susan) <- (44) [resolution 466,132]
967. $false <- (44) [subsumption resolution 961,147]
968. ~44 [avatar contradiction clause 967]
973. $false [avatar sat refutation 255,309,950,951,955,968]
% SZS output end Proof for 2723795831688446368370378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not kind or not calm then someone is not patient or not kind and vice versa.
If someone is either not patient or not wise then someone is not kind or not wise.
Everyone who is either old or brave is both happy and not brave and vice versa.
Everyone who is either kind or calm is both not tall and not humble and vice versa.
Everyone who is not humble is either not kind or kind.
If mary is either rich or tall then someone is either not old or not calm and vice versa.
Everyone who is both not humble and not creative is either not curious or not patient.
Everyone who is old or rich is not rich or strong and vice versa.
If alice is both old and not generous then someone is both old and not creative.
Everyone who is not quiet or patient is not patient.
Everyone who is funny is wise.
If someone is either not patient or wise then someone is both not quiet and not old.
If mary is both not curious and tall then someone is old or wise and vice versa.
Everyone who is not curious is funny and vice versa.
If someone is both not tall and wise then lucy is either patient or not curious and vice versa.
If someone is both wise and not curious then someone is both not humble and patient.
Someone is either not calm or not curious.
Someone is strong or humble.
Mary is strong or not calm.
Someone is both generous and not wise.
Mary is both not patient and not creative.
Someone is calm. | Lucy is not rich. | contradiction | (((~kind(paul)|~calm(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((old(X)<~>brave(X))<=>(happy(X)&~brave(X))))&
(![X]:((kind(X)<~>calm(X))<=>(~tall(X)&~humble(X))))&
(![X]:(~humble(X)=>(~kind(X)<~>kind(X))))&
(((rich(mary)<~>tall(mary)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~humble(X)&~creative(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((old(X)|rich(X))<=>(~rich(X)|strong(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~quiet(X)|patient(X))=>~patient(X)))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~old(X)))))&
(((~curious(mary)&tall(mary)))<=>(?[X]:((old(X)|wise(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
((?[X]:((~tall(X)&wise(X))))<=>((patient(lucy)<~>~curious(lucy))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~humble(X)&patient(X)))))&
(?[X]:((~calm(X)<~>~curious(X))))&
(?[X]:((strong(X)|humble(X))))&
((strong(mary)|~calm(mary)))&
(?[X]:((generous(X)&~wise(X))))&
((~patient(mary)&~creative(mary)))&
(?[X]:(calm(X))) | ~rich(lucy) | [
"p7",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5583895839964411210281834
% SZS output start Proof for 5583895839964411210281834
8. ! [X0] : ((rich(X0) | old(X0)) <=> (strong(X0) | ~rich(X0))) [input p7]
10. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~patient(X0)) [input p9]
11. ! [X0] : (funny(X0) => wise(X0)) [input p10]
13. (tall(mary) & ~curious(mary)) <=> ? [X0] : (wise(X0) | old(X0)) [input p12]
14. ! [X0] : (~curious(X0) <=> funny(X0)) [input p13]
16. ? [X0] : (~curious(X0) & wise(X0)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p15]
23. ~rich(lucy) [input hypothesis]
26. ? [X0] : (~curious(X0) & wise(X0)) => ? [X1] : (patient(X1) & ~humble(X1)) [rectify 16]
33. ! [X0] : (~patient(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 10]
34. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 11]
36. ? [X1] : (patient(X1) & ~humble(X1)) | ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 26]
56. ! [X0] : (((rich(X0) | old(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (~rich(X0) & ~old(X0)))) [nnf transformation 8]
57. ! [X0] : ((rich(X0) | old(X0) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | (~rich(X0) & ~old(X0)))) [flattening 56]
62. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | (~tall(mary) | curious(mary))) [nnf transformation 13]
63. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X0] : (wise(X0) | old(X0)) | ~tall(mary) | curious(mary)) [flattening 62]
64. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & (? [X1] : (wise(X1) | old(X1)) | ~tall(mary) | curious(mary)) [rectify 63]
65. ? [X1] : (wise(X1) | old(X1)) => (wise(sK4) | old(sK4)) [choice axiom]
66. ((tall(mary) & ~curious(mary)) | ! [X0] : (~wise(X0) & ~old(X0))) & ((wise(sK4) | old(sK4)) | ~tall(mary) | curious(mary)) [skolemisation 64,65]
67. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 14]
72. ? [X0] : (patient(X0) & ~humble(X0)) | ! [X1] : (curious(X1) | ~wise(X1)) [rectify 36]
73. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK6) & ~humble(sK6)) [choice axiom]
74. (patient(sK6) & ~humble(sK6)) | ! [X1] : (curious(X1) | ~wise(X1)) [skolemisation 72,73]
116. rich(X0) | old(X0) | rich(X0) [cnf transformation 57]
119. ~patient(X0) | ~patient(X0) [cnf transformation 33]
120. ~funny(X0) | wise(X0) [cnf transformation 34]
126. ~curious(mary) | ~old(X0) [cnf transformation 66]
130. funny(X0) | curious(X0) [cnf transformation 67]
139. patient(sK6) | curious(X1) | ~wise(X1) [cnf transformation 74]
148. ~rich(lucy) [cnf transformation 23]
149. ~patient(X0) [duplicate literal removal 119]
151. rich(X0) | old(X0) [duplicate literal removal 116]
246. 21 <=> ! [X0] : ~old(X0) [avatar definition]
247. ~old(X0) <- (21) [avatar component clause 246]
250. 22 <=> curious(mary) [avatar definition]
252. ~curious(mary) <- (~22) [avatar component clause 250]
254. 21 | ~22 [avatar split clause 126,250,246]
285. curious(X1) | ~wise(X1) [subsumption resolution 139,149]
319. curious(X0) | wise(X0) [resolution 130,120]
320. curious(X0) [subsumption resolution 319,285]
323. $false <- (~22) [resolution 320,252]
326. 22 [avatar contradiction clause 323]
330. old(lucy) [resolution 151,148]
333. $false <- (21) [subsumption resolution 330,247]
334. ~21 [avatar contradiction clause 333]
338. $false [avatar sat refutation 254,326,334]
% SZS output end Proof for 5583895839964411210281834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or brave then someone is happy or patient. If john is either happy or calm then fred is not happy or not old and vice versa. Everyone who is either not brave or not generous is either not patient or not creative and vice versa. If fred is either not happy or not tall then fred is either strong or not generous and vice versa. If someone is brave or generous then someone is either not generous or not funny. If someone is both not kind and not rich then paul is not patient or not quiet. If mary is both not wise and old then fred is either rich or creative. Everyone who is not calm or creative is either not wise or not happy. If someone is either not rich or calm then someone is both not happy and not creative. If mary is either not calm or strong then mary is both curious and quiet and vice versa. Everyone who is patient is either not patient or not calm and vice versa. Everyone who is either not strong or not tall is not tall and vice versa. Everyone who is quiet or not generous is patient or not kind and vice versa. If someone is not humble or not tall then someone is not funny or not happy. If susan is both patient and happy then mary is both tall and not brave and vice versa. If someone is generous or brave then lucy is either not generous or not strong. Someone is both not happy and curious. Paul is not quiet or not rich. Someone is not wise or not patient. Someone is either generous or brave. Fred is both tall and not old. John is both not tall and not funny. Someone is either not quiet or brave. Paul is not brave or happy. | John is not wise. | entailment | (((quiet(mary)<~>brave(mary)))=>(?[X]:((happy(X)|patient(X)))))&
(((happy(john)<~>calm(john)))<=>((~happy(fred)|~old(fred))))&
(![X]:((~brave(X)<~>~generous(X))<=>(~patient(X)<~>~creative(X))))&
(((~happy(fred)<~>~tall(fred)))<=>((strong(fred)<~>~generous(fred))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~generous(X)<~>~funny(X)))))&
((?[X]:((~kind(X)&~rich(X))))=>((~patient(paul)|~quiet(paul))))&
(((~wise(mary)&old(mary)))=>((rich(fred)<~>creative(fred))))&
(![X]:((~calm(X)|creative(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>(?[X]:((~happy(X)&~creative(X)))))&
(((~calm(mary)<~>strong(mary)))<=>((curious(mary)&quiet(mary))))&
(![X]:(patient(X)<=>(~patient(X)<~>~calm(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>~tall(X)))&
(![X]:((quiet(X)|~generous(X))<=>(patient(X)|~kind(X))))&
((?[X]:((~humble(X)|~tall(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(((patient(susan)&happy(susan)))<=>((tall(mary)&~brave(mary))))&
((?[X]:((generous(X)|brave(X))))=>((~generous(lucy)<~>~strong(lucy))))&
(?[X]:((~happy(X)&curious(X))))&
((~quiet(paul)|~rich(paul)))&
(?[X]:((~wise(X)|~patient(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((tall(fred)&~old(fred)))&
((~tall(john)&~funny(john)))&
(?[X]:((~quiet(X)<~>brave(X))))&
((~brave(paul)|happy(paul))) | ~wise(john) | [
"p1",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4195679516500482168583621
% SZS output start Proof for 4195679516500482168583621
2. (happy(john) <~> calm(john)) <=> (~old(fred) | ~happy(fred)) [input p1]
8. ! [X0] : ((creative(X0) | ~calm(X0)) => (~wise(X0) <~> ~happy(X0))) [input p7]
11. ! [X0] : (patient(X0) <=> (~patient(X0) <~> ~calm(X0))) [input p10]
21. ~old(fred) & tall(fred) [input p20]
25. wise(john) [input hypothesis]
36. ! [X0] : ((~wise(X0) <~> ~happy(X0)) | (~creative(X0) & calm(X0))) [ennf transformation 8]
43. (((~calm(john) | ~happy(john)) & (calm(john) | happy(john))) | (old(fred) & happy(fred))) & ((~old(fred) | ~happy(fred)) | ((happy(john) | ~calm(john)) & (calm(john) | ~happy(john)))) [nnf transformation 2]
44. (((~calm(john) | ~happy(john)) & (calm(john) | happy(john))) | (old(fred) & happy(fred))) & (~old(fred) | ~happy(fred) | ((happy(john) | ~calm(john)) & (calm(john) | ~happy(john)))) [flattening 43]
52. ! [X0] : (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~creative(X0) & calm(X0))) [nnf transformation 36]
59. ! [X0] : ((patient(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~patient(X0))) [nnf transformation 11]
84. calm(john) | happy(john) | old(fred) [cnf transformation 44]
110. ~wise(X0) | ~happy(X0) | calm(X0) [cnf transformation 52]
124. ~calm(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 59]
126. patient(X0) | ~calm(X0) | patient(X0) [cnf transformation 59]
152. ~old(fred) [cnf transformation 21]
158. wise(john) [cnf transformation 25]
161. ~calm(X0) | ~patient(X0) [duplicate literal removal 124]
162. ~calm(X0) | patient(X0) [duplicate literal removal 126]
182. 5 <=> old(fred) [avatar definition]
186. 6 <=> happy(john) [avatar definition]
190. 7 <=> calm(john) [avatar definition]
191. calm(john) <- (7) [avatar component clause 190]
199. 5 | 6 | 7 [avatar split clause 84,190,186,182]
307. ~calm(X0) [subsumption resolution 161,162]
369. ~5 [avatar split clause 152,182]
394. ~happy(john) | calm(john) [resolution 110,158]
398. ~happy(john) [subsumption resolution 394,307]
399. ~6 [avatar split clause 398,186]
400. $false <- (7) [subsumption resolution 191,307]
401. ~7 [avatar contradiction clause 400]
402. $false [avatar sat refutation 199,369,399,401]
% SZS output end Proof for 4195679516500482168583621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and patient then someone is either rich or not funny.
Everyone who is not curious or not patient is both not old and not brave and vice versa.
If lucy is wise or not happy then john is happy and vice versa.
If alice is both not rich and calm then someone is either not creative or not calm.
Everyone who is not strong or not brave is not strong and vice versa.
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Everyone who is both patient and humble is not patient and vice versa.
Everyone who is not happy or humble is wise.
Everyone who is either brave or not quiet is not brave and vice versa.
Someone is either humble or wise.
Paul is both not old and not rich.
Someone is both not wise and not quiet.
Someone is either not brave or curious.
Someone is old. | John is rich. | neutral | ((?[X]:((~curious(X)&patient(X))))=>(?[X]:((rich(X)<~>~funny(X)))))&
(![X]:((~curious(X)|~patient(X))<=>(~old(X)&~brave(X))))&
(((wise(lucy)|~happy(lucy)))<=>(happy(john)))&
(((~rich(alice)&calm(alice)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~strong(X)|~brave(X))<=>~strong(X)))&
((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((patient(X)&humble(X))<=>~patient(X)))&
(![X]:((~happy(X)|humble(X))=>wise(X)))&
(![X]:((brave(X)<~>~quiet(X))<=>~brave(X)))&
(?[X]:((humble(X)<~>wise(X))))&
((~old(paul)&~rich(paul)))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:(old(X))) | rich(john) | [] | null | 0 |
If susan is both patient and quiet then someone is not rich or tall.
If john is either patient or not patient then susan is not strong or not curious and vice versa.
If someone is either kind or strong then someone is both not creative and not patient.
If john is either wise or generous then someone is not wise or not calm and vice versa.
Everyone who is not wise or creative is both not happy and not rich.
Everyone who is either generous or not curious is not calm.
If fred is either not rich or old then paul is either not calm or not kind.
Everyone who is humble is curious or tall and vice versa.
Everyone who is strong is not curious and vice versa.
If john is both not funny and funny then someone is generous.
Everyone who is not wise or funny is not brave or humble and vice versa.
Everyone who is both curious and not patient is either not funny or not rich.
Everyone who is both creative and kind is not patient and vice versa.
If fred is not humble then someone is either not kind or not rich and vice versa.
If mary is either curious or humble then someone is not generous or not happy and vice versa.
If someone is rich or not old then someone is either wise or humble and vice versa.
Fred is humble or not wise.
Susan is generous.
Paul is patient or not wise.
Someone is either curious or not generous.
Mary is wise or not quiet.
Susan is both brave and wise.
John is either generous or tall.
Fred is not rich or not generous. | Mary is kind. | entailment | (((patient(susan)&quiet(susan)))=>(?[X]:((~rich(X)|tall(X)))))&
(((patient(john)<~>~patient(john)))<=>((~strong(susan)|~curious(susan))))&
((?[X]:((kind(X)<~>strong(X))))=>(?[X]:((~creative(X)&~patient(X)))))&
(((wise(john)<~>generous(john)))<=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(~happy(X)&~rich(X))))&
(![X]:((generous(X)<~>~curious(X))=>~calm(X)))&
(((~rich(fred)<~>old(fred)))=>((~calm(paul)<~>~kind(paul))))&
(![X]:(humble(X)<=>(curious(X)|tall(X))))&
(![X]:(strong(X)<=>~curious(X)))&
(((~funny(john)&funny(john)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~patient(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((creative(X)&kind(X))<=>~patient(X)))&
((~humble(fred))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(((curious(mary)<~>humble(mary)))<=>(?[X]:((~generous(X)|~happy(X)))))&
((?[X]:((rich(X)|~old(X))))<=>(?[X]:((wise(X)<~>humble(X)))))&
((humble(fred)|~wise(fred)))&
(generous(susan))&
((patient(paul)|~wise(paul)))&
(?[X]:((curious(X)<~>~generous(X))))&
((wise(mary)|~quiet(mary)))&
((brave(susan)&wise(susan)))&
((generous(john)<~>tall(john)))&
((~rich(fred)|~generous(fred))) | kind(mary) | [
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1849878695405105102363991
% SZS output start Proof for 1849878695405105102363991
3. ? [X0] : (kind(X0) <~> strong(X0)) => ? [X0] : (~patient(X0) & ~creative(X0)) [input p2]
4. (wise(john) <~> generous(john)) <=> ? [X0] : (~calm(X0) | ~wise(X0)) [input p3]
5. ! [X0] : ((creative(X0) | ~wise(X0)) => (~rich(X0) & ~happy(X0))) [input p4]
6. ! [X0] : ((generous(X0) <~> ~curious(X0)) => ~calm(X0)) [input p5]
8. ! [X0] : (humble(X0) <=> (tall(X0) | curious(X0))) [input p7]
9. ! [X0] : (strong(X0) <=> ~curious(X0)) [input p8]
13. ! [X0] : ((kind(X0) & creative(X0)) <=> ~patient(X0)) [input p12]
15. (curious(mary) <~> humble(mary)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p14]
25. ~kind(mary) [input hypothesis]
26. ? [X0] : (kind(X0) <~> strong(X0)) => ? [X1] : (~patient(X1) & ~creative(X1)) [rectify 3]
30. ? [X1] : (~patient(X1) & ~creative(X1)) | ! [X0] : (kind(X0) <=> strong(X0)) [ennf transformation 26]
31. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 5]
32. ! [X0] : (~calm(X0) | (generous(X0) <=> ~curious(X0))) [ennf transformation 6]
40. ? [X1] : (~patient(X1) & ~creative(X1)) | ! [X0] : ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0))) [nnf transformation 30]
41. ? [X0] : (~patient(X0) & ~creative(X0)) | ! [X1] : ((kind(X1) | ~strong(X1)) & (strong(X1) | ~kind(X1))) [rectify 40]
42. ? [X0] : (~patient(X0) & ~creative(X0)) => (~patient(sK0) & ~creative(sK0)) [choice axiom]
43. (~patient(sK0) & ~creative(sK0)) | ! [X1] : ((kind(X1) | ~strong(X1)) & (strong(X1) | ~kind(X1))) [skolemisation 41,42]
44. (((~generous(john) | ~wise(john)) & (generous(john) | wise(john))) | ! [X0] : (calm(X0) & wise(X0))) & (? [X0] : (~calm(X0) | ~wise(X0)) | ((wise(john) | ~generous(john)) & (generous(john) | ~wise(john)))) [nnf transformation 4]
45. (((~generous(john) | ~wise(john)) & (generous(john) | wise(john))) | ! [X0] : (calm(X0) & wise(X0))) & (? [X1] : (~calm(X1) | ~wise(X1)) | ((wise(john) | ~generous(john)) & (generous(john) | ~wise(john)))) [rectify 44]
46. ? [X1] : (~calm(X1) | ~wise(X1)) => (~calm(sK1) | ~wise(sK1)) [choice axiom]
47. (((~generous(john) | ~wise(john)) & (generous(john) | wise(john))) | ! [X0] : (calm(X0) & wise(X0))) & ((~calm(sK1) | ~wise(sK1)) | ((wise(john) | ~generous(john)) & (generous(john) | ~wise(john)))) [skolemisation 45,46]
48. ! [X0] : (~calm(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0)))) [nnf transformation 32]
50. ! [X0] : ((humble(X0) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | ~humble(X0))) [nnf transformation 8]
51. ! [X0] : ((humble(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | ~humble(X0))) [flattening 50]
52. ! [X0] : ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))) [nnf transformation 9]
58. ! [X0] : (((kind(X0) & creative(X0)) | patient(X0)) & (~patient(X0) | (~kind(X0) | ~creative(X0)))) [nnf transformation 13]
59. ! [X0] : (((kind(X0) & creative(X0)) | patient(X0)) & (~patient(X0) | ~kind(X0) | ~creative(X0))) [flattening 58]
64. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & (? [X0] : (~happy(X0) | ~generous(X0)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [nnf transformation 15]
65. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [rectify 64]
66. ? [X1] : (~happy(X1) | ~generous(X1)) => (~happy(sK4) | ~generous(sK4)) [choice axiom]
67. (((~humble(mary) | ~curious(mary)) & (humble(mary) | curious(mary))) | ! [X0] : (happy(X0) & generous(X0))) & ((~happy(sK4) | ~generous(sK4)) | ((curious(mary) | ~humble(mary)) & (humble(mary) | ~curious(mary)))) [skolemisation 65,66]
84. ~creative(sK0) | kind(X1) | ~strong(X1) [cnf transformation 43]
86. ~patient(sK0) | kind(X1) | ~strong(X1) [cnf transformation 43]
92. ~generous(john) | ~wise(john) | calm(X0) [cnf transformation 47]
93. ~happy(X0) | wise(X0) [cnf transformation 31]
97. ~calm(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 48]
104. ~curious(X0) | humble(X0) [cnf transformation 51]
107. curious(X0) | strong(X0) [cnf transformation 52]
116. creative(X0) | patient(X0) [cnf transformation 59]
126. ~humble(mary) | ~curious(mary) | generous(X0) [cnf transformation 67]
127. ~humble(mary) | ~curious(mary) | happy(X0) [cnf transformation 67]
144. ~kind(mary) [cnf transformation 25]
162. 4 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
163. ~strong(X1) | kind(X1) <- (4) [avatar component clause 162]
165. 5 <=> patient(sK0) [avatar definition]
167. ~patient(sK0) <- (~5) [avatar component clause 165]
168. 4 | ~5 [avatar split clause 86,165,162]
174. 7 <=> creative(sK0) [avatar definition]
176. ~creative(sK0) <- (~7) [avatar component clause 174]
177. 4 | ~7 [avatar split clause 84,174,162]
180. 8 <=> ! [X0] : calm(X0) [avatar definition]
181. calm(X0) <- (8) [avatar component clause 180]
183. 9 <=> wise(john) [avatar definition]
185. ~wise(john) <- (~9) [avatar component clause 183]
187. 10 <=> generous(john) [avatar definition]
189. ~generous(john) <- (~10) [avatar component clause 187]
190. 8 | ~9 | ~10 [avatar split clause 92,187,183,180]
192. 11 <=> ! [X0] : wise(X0) [avatar definition]
193. wise(X0) <- (11) [avatar component clause 192]
249. ~curious(mary) | happy(X0) [subsumption resolution 127,104]
251. 23 <=> ! [X0] : happy(X0) [avatar definition]
252. happy(X0) <- (23) [avatar component clause 251]
254. 24 <=> curious(mary) [avatar definition]
255. curious(mary) <- (24) [avatar component clause 254]
256. ~curious(mary) <- (~24) [avatar component clause 254]
257. 23 | ~24 [avatar split clause 249,254,251]
258. ~curious(mary) | generous(X0) [subsumption resolution 126,104]
260. 25 <=> ! [X0] : generous(X0) [avatar definition]
261. generous(X0) <- (25) [avatar component clause 260]
262. 25 | ~24 [avatar split clause 258,254,260]
354. strong(mary) <- (~24) [resolution 107,256]
357. patient(sK0) <- (~7) [resolution 116,176]
359. $false <- (~5, ~7) [subsumption resolution 357,167]
360. 5 | 7 [avatar contradiction clause 359]
364. kind(mary) <- (4, ~24) [resolution 163,354]
365. $false <- (4, ~24) [subsumption resolution 364,144]
366. ~4 | 24 [avatar contradiction clause 365]
368. wise(X1) <- (23) [resolution 252,93]
369. 11 | ~23 [avatar split clause 368,251,192]
370. $false <- (~9, 11) [resolution 193,185]
375. 9 | ~11 [avatar contradiction clause 370]
388. ~curious(X0) | ~generous(X0) <- (8) [resolution 97,181]
389. ~curious(X0) <- (8, 25) [subsumption resolution 388,261]
407. $false <- (8, 24, 25) [resolution 389,255]
410. ~8 | ~24 | ~25 [avatar contradiction clause 407]
420. $false <- (~10, 25) [subsumption resolution 189,261]
421. 10 | ~25 [avatar contradiction clause 420]
422. $false [avatar sat refutation 168,177,190,257,262,360,366,369,375,410,421]
% SZS output end Proof for 1849878695405105102363991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not funny then fred is both happy and creative.
If john is not creative then someone is either not happy or not patient and vice versa.
If someone is not kind or not curious then someone is quiet and vice versa.
If paul is both not creative and rich then someone is not happy.
If paul is not kind or not happy then someone is either creative or not quiet and vice versa.
If someone is both not humble and patient then susan is not calm or strong and vice versa.
Everyone who is brave or not generous is funny or wise and vice versa.
Everyone who is either strong or brave is both not curious and generous and vice versa.
If fred is either not old or wise then mary is either not wise or kind.
Everyone who is either not curious or not creative is not old or not kind.
If someone is rich or wise then alice is both not strong and not generous.
If someone is both creative and patient then alice is either not wise or patient.
Everyone who is calm or strong is both calm and not brave.
Everyone who is both brave and not humble is either not happy or generous.
If fred is either rich or wise then alice is not wise and vice versa.
Everyone who is tall or not wise is either not strong or not brave and vice versa.
Someone is either not old or not brave.
John is brave.
Someone is either strong or quiet.
Someone is not calm.
Someone is both not patient and curious.
Someone is not happy.
Fred is both tall and kind.
John is both kind and not curious. | Alice is not wise. | contradiction | ((?[X]:((~curious(X)|~funny(X))))=>((happy(fred)&creative(fred))))&
((~creative(john))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:(quiet(X))))&
(((~creative(paul)&rich(paul)))=>(?[X]:(~happy(X))))&
(((~kind(paul)|~happy(paul)))<=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:((~humble(X)&patient(X))))<=>((~calm(susan)|strong(susan))))&
(![X]:((brave(X)|~generous(X))<=>(funny(X)|wise(X))))&
(![X]:((strong(X)<~>brave(X))<=>(~curious(X)&generous(X))))&
(((~old(fred)<~>wise(fred)))=>((~wise(mary)<~>kind(mary))))&
(![X]:((~curious(X)<~>~creative(X))=>(~old(X)|~kind(X))))&
((?[X]:((rich(X)|wise(X))))=>((~strong(alice)&~generous(alice))))&
((?[X]:((creative(X)&patient(X))))=>((~wise(alice)<~>patient(alice))))&
(![X]:((calm(X)|strong(X))=>(calm(X)&~brave(X))))&
(![X]:((brave(X)&~humble(X))=>(~happy(X)<~>generous(X))))&
(((rich(fred)<~>wise(fred)))<=>(~wise(alice)))&
(![X]:((tall(X)|~wise(X))<=>(~strong(X)<~>~brave(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
(brave(john))&
(?[X]:((strong(X)<~>quiet(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~patient(X)&curious(X))))&
(?[X]:(~happy(X)))&
((tall(fred)&kind(fred)))&
((kind(john)&~curious(john))) | ~wise(alice) | [
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2931762589962529409493029
% SZS output start Proof for 2931762589962529409493029
8. ! [X0] : ((strong(X0) <~> brave(X0)) <=> (generous(X0) & ~curious(X0))) [input p7]
11. ? [X0] : (wise(X0) | rich(X0)) => (~generous(alice) & ~strong(alice)) [input p10]
15. (rich(fred) <~> wise(fred)) <=> ~wise(alice) [input p14]
16. ! [X0] : ((~wise(X0) | tall(X0)) <=> (~strong(X0) <~> ~brave(X0))) [input p15]
25. ~wise(alice) [input hypothesis]
33. (~generous(alice) & ~strong(alice)) | ! [X0] : (~wise(X0) & ~rich(X0)) [ennf transformation 11]
61. ! [X0] : ((((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))))) [nnf transformation 8]
62. ! [X0] : ((((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))))) [flattening 61]
67. (((~wise(fred) | ~rich(fred)) & (wise(fred) | rich(fred))) | wise(alice)) & (~wise(alice) | ((rich(fred) | ~wise(fred)) & (wise(fred) | ~rich(fred)))) [nnf transformation 15]
68. ! [X0] : (((~wise(X0) | tall(X0)) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (wise(X0) & ~tall(X0)))) [nnf transformation 16]
69. ! [X0] : ((~wise(X0) | tall(X0) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) & (((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) | (wise(X0) & ~tall(X0)))) [flattening 68]
112. ~brave(X0) | strong(X0) | generous(X0) [cnf transformation 62]
121. ~strong(alice) | ~rich(X0) [cnf transformation 33]
122. ~strong(alice) | ~wise(X0) [cnf transformation 33]
123. ~generous(alice) | ~rich(X0) [cnf transformation 33]
124. ~generous(alice) | ~wise(X0) [cnf transformation 33]
135. wise(fred) | rich(fred) | wise(alice) [cnf transformation 67]
140. wise(X0) | strong(X0) | brave(X0) [cnf transformation 69]
156. ~wise(alice) [cnf transformation 25]
284. 29 <=> wise(fred) [avatar definition]
285. wise(fred) <- (29) [avatar component clause 284]
304. 33 <=> ! [X0] : ~wise(X0) [avatar definition]
305. ~wise(X0) <- (33) [avatar component clause 304]
307. 34 <=> generous(alice) [avatar definition]
310. 33 | ~34 [avatar split clause 124,307,304]
312. 35 <=> ! [X0] : ~rich(X0) [avatar definition]
313. ~rich(X0) <- (35) [avatar component clause 312]
314. 35 | ~34 [avatar split clause 123,307,312]
316. 36 <=> strong(alice) [avatar definition]
318. ~strong(alice) <- (~36) [avatar component clause 316]
319. 33 | ~36 [avatar split clause 122,316,304]
320. 35 | ~36 [avatar split clause 121,316,312]
325. 38 <=> wise(alice) [avatar definition]
326. ~wise(alice) <- (~38) [avatar component clause 325]
335. 40 <=> rich(fred) [avatar definition]
336. rich(fred) <- (40) [avatar component clause 335]
339. 38 | 40 | 29 [avatar split clause 135,284,335,325]
364. ~38 [avatar split clause 156,325]
435. strong(alice) | brave(alice) <- (~38) [resolution 140,326]
438. brave(alice) <- (~36, ~38) [subsumption resolution 435,318]
452. strong(alice) | generous(alice) <- (~36, ~38) [resolution 438,112]
457. generous(alice) <- (~36, ~38) [subsumption resolution 452,318]
462. 34 | 36 | 38 [avatar split clause 457,325,316,307]
463. $false <- (29, 33) [resolution 305,285]
468. ~29 | ~33 [avatar contradiction clause 463]
470. $false <- (35, 40) [subsumption resolution 336,313]
471. ~35 | ~40 [avatar contradiction clause 470]
472. $false [avatar sat refutation 310,314,319,320,339,364,462,468,471]
% SZS output end Proof for 2931762589962529409493029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both generous and not brave.
Everyone who is not curious or not brave is both wise and not generous.
Everyone who is tall or brave is not curious or not rich.
If alice is calm or patient then alice is quiet or calm.
Everyone who is not brave or funny is either rich or kind and vice versa.
If someone is humble then alice is patient or not happy.
If paul is not tall or not patient then lucy is brave or not funny and vice versa.
Everyone who is both humble and not quiet is both wise and not humble and vice versa.
Everyone who is either not rich or brave is either quiet or happy and vice versa.
Everyone who is not old or humble is not rich or strong and vice versa.
If john is either not patient or funny then someone is both not tall and generous and vice versa.
If someone is both not funny and not curious then john is both calm and not kind.
If alice is both not humble and not creative then paul is both not generous and not funny and vice versa.
If someone is curious or not quiet then susan is either not funny or not wise.
Everyone who is both not old and not tall is not generous and vice versa.
If someone is both curious and quiet then someone is humble or not kind.
Paul is either strong or old.
Someone is not quiet or not strong.
Fred is quiet.
Someone is either not patient or happy.
Fred is not old or old.
Someone is either not tall or not quiet.
Alice is creative.
Susan is either wise or happy. | Susan is funny. | entailment | (![X]:(~generous(X)=>(generous(X)&~brave(X))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)&~generous(X))))&
(![X]:((tall(X)|brave(X))=>(~curious(X)|~rich(X))))&
(((calm(alice)|patient(alice)))=>((quiet(alice)|calm(alice))))&
(![X]:((~brave(X)|funny(X))<=>(rich(X)<~>kind(X))))&
((?[X]:(humble(X)))=>((patient(alice)|~happy(alice))))&
(((~tall(paul)|~patient(paul)))<=>((brave(lucy)|~funny(lucy))))&
(![X]:((humble(X)&~quiet(X))<=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~rich(X)|strong(X))))&
(((~patient(john)<~>funny(john)))<=>(?[X]:((~tall(X)&generous(X)))))&
((?[X]:((~funny(X)&~curious(X))))=>((calm(john)&~kind(john))))&
(((~humble(alice)&~creative(alice)))<=>((~generous(paul)&~funny(paul))))&
((?[X]:((curious(X)|~quiet(X))))=>((~funny(susan)<~>~wise(susan))))&
(![X]:((~old(X)&~tall(X))<=>~generous(X)))&
((?[X]:((curious(X)&quiet(X))))=>(?[X]:((humble(X)|~kind(X)))))&
((strong(paul)<~>old(paul)))&
(?[X]:((~quiet(X)|~strong(X))))&
(quiet(fred))&
(?[X]:((~patient(X)<~>happy(X))))&
((~old(fred)|old(fred)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(creative(alice))&
((wise(susan)<~>happy(susan))) | funny(susan) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1609307538593566629962635
% SZS output start Proof for 1609307538593566629962635
1. ! [X0] : (~generous(X0) => (~brave(X0) & generous(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~curious(X0)) => (~generous(X0) & wise(X0))) [input p1]
3. ! [X0] : ((brave(X0) | tall(X0)) => (~rich(X0) | ~curious(X0))) [input p2]
8. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (~humble(X0) & wise(X0))) [input p7]
9. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (quiet(X0) <~> happy(X0))) [input p8]
14. ? [X0] : (~quiet(X0) | curious(X0)) => (~funny(susan) <~> ~wise(susan)) [input p13]
24. wise(susan) <~> happy(susan) [input p23]
25. ~funny(susan) [input hypothesis]
27. ! [X0] : ((~brave(X0) & generous(X0)) | generous(X0)) [ennf transformation 1]
28. ! [X0] : ((~generous(X0) & wise(X0)) | (brave(X0) & curious(X0))) [ennf transformation 2]
29. ! [X0] : ((~rich(X0) | ~curious(X0)) | (~brave(X0) & ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~rich(X0) | ~curious(X0) | (~brave(X0) & ~tall(X0))) [flattening 29]
36. (~funny(susan) <~> ~wise(susan)) | ! [X0] : (quiet(X0) & ~curious(X0)) [ennf transformation 14]
42. ! [X0] : (((~quiet(X0) & humble(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 8]
43. ! [X0] : (((~quiet(X0) & humble(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | quiet(X0) | ~humble(X0))) [flattening 42]
44. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 9]
53. ((wise(susan) | funny(susan)) & (~wise(susan) | ~funny(susan))) | ! [X0] : (quiet(X0) & ~curious(X0)) [nnf transformation 36]
68. (~happy(susan) | ~wise(susan)) & (happy(susan) | wise(susan)) [nnf transformation 24]
69. generous(X0) | generous(X0) [cnf transformation 27]
73. ~generous(X0) | curious(X0) [cnf transformation 28]
74. ~generous(X0) | brave(X0) [cnf transformation 28]
76. ~rich(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 30]
91. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 43]
92. humble(X0) | humble(X0) | ~wise(X0) [cnf transformation 43]
100. ~brave(X0) | rich(X0) | happy(X0) | ~quiet(X0) [cnf transformation 44]
120. wise(susan) | funny(susan) | ~curious(X0) [cnf transformation 53]
137. ~happy(susan) | ~wise(susan) [cnf transformation 68]
138. ~funny(susan) [cnf transformation 25]
139. ~humble(X0) | quiet(X0) [duplicate literal removal 91]
140. ~wise(X0) | humble(X0) [duplicate literal removal 92]
141. generous(X0) [duplicate literal removal 69]
142. brave(X0) [subsumption resolution 74,141]
143. curious(X0) [subsumption resolution 73,141]
144. ~rich(X0) | ~brave(X0) [subsumption resolution 76,143]
145. ~rich(X0) [subsumption resolution 144,142]
187. rich(X0) | happy(X0) | ~quiet(X0) [subsumption resolution 100,142]
188. ~quiet(X0) | happy(X0) [subsumption resolution 187,145]
230. 17 <=> funny(susan) [avatar definition]
234. 18 <=> wise(susan) [avatar definition]
236. wise(susan) <- (18) [avatar component clause 234]
238. wise(susan) | funny(susan) [subsumption resolution 120,143]
239. 17 | 18 [avatar split clause 238,234,230]
298. 30 <=> happy(susan) [avatar definition]
300. ~happy(susan) <- (~30) [avatar component clause 298]
301. ~18 | ~30 [avatar split clause 137,298,234]
303. ~17 [avatar split clause 138,230]
305. humble(susan) <- (18) [resolution 140,236]
306. quiet(susan) <- (18) [resolution 305,139]
308. happy(susan) <- (18) [resolution 188,306]
309. $false <- (18, ~30) [subsumption resolution 308,300]
310. ~18 | 30 [avatar contradiction clause 309]
311. $false [avatar sat refutation 239,301,303,310]
% SZS output end Proof for 1609307538593566629962635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and not tall is not humble. If someone is happy then someone is both not patient and not wise and vice versa. Everyone who is not generous is both not tall and strong. Everyone who is either happy or not quiet is not tall and vice versa. Everyone who is both not old and strong is wise. Everyone who is quiet is both not quiet and not creative and vice versa. If someone is rich then paul is both curious and calm. Everyone who is both humble and curious is both not generous and not creative. If john is either creative or not old then someone is not rich. Everyone who is not rich or quiet is both curious and not wise and vice versa. If john is old then lucy is both not tall and strong. Everyone who is calm is patient and vice versa. Everyone who is not patient is kind. If someone is creative then someone is not curious or not kind and vice versa. Everyone who is both not generous and not strong is either not humble or not rich. Alice is brave or strong. Alice is not quiet or not rich. Someone is rich. Paul is curious or not patient. Paul is either old or quiet. Someone is both not old and kind. Paul is not old or calm. | Paul is patient. | entailment | (![X]:((happy(X)&~tall(X))=>~humble(X)))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:(~generous(X)=>(~tall(X)&strong(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>~tall(X)))&
(![X]:((~old(X)&strong(X))=>wise(X)))&
(![X]:(quiet(X)<=>(~quiet(X)&~creative(X))))&
((?[X]:(rich(X)))=>((curious(paul)&calm(paul))))&
(![X]:((humble(X)&curious(X))=>(~generous(X)&~creative(X))))&
(((creative(john)<~>~old(john)))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)|quiet(X))<=>(curious(X)&~wise(X))))&
((old(john))=>((~tall(lucy)&strong(lucy))))&
(![X]:(calm(X)<=>patient(X)))&
(![X]:(~patient(X)=>kind(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((~generous(X)&~strong(X))=>(~humble(X)<~>~rich(X))))&
((brave(alice)|strong(alice)))&
((~quiet(alice)|~rich(alice)))&
(?[X]:(rich(X)))&
((curious(paul)|~patient(paul)))&
((old(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&kind(X))))&
((~old(paul)|calm(paul))) | patient(paul) | [
"p5",
"p11",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5606878472520667692186453
% SZS output start Proof for 5606878472520667692186453
6. ! [X0] : (quiet(X0) <=> (~creative(X0) & ~quiet(X0))) [input p5]
12. ! [X0] : (calm(X0) <=> patient(X0)) [input p11]
20. old(paul) <~> quiet(paul) [input p19]
22. calm(paul) | ~old(paul) [input p21]
23. ~patient(paul) [input hypothesis]
26. ! [X0] : (calm(X0) => patient(X0)) [unused predicate definition removal 12]
38. ! [X0] : (patient(X0) | ~calm(X0)) [ennf transformation 26]
48. ! [X0] : ((quiet(X0) | (creative(X0) | quiet(X0))) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((quiet(X0) | creative(X0) | quiet(X0)) & ((~creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 48]
63. (~quiet(paul) | ~old(paul)) & (quiet(paul) | old(paul)) [nnf transformation 20]
77. ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
93. ~calm(X0) | patient(X0) [cnf transformation 38]
103. quiet(paul) | old(paul) [cnf transformation 63]
107. calm(paul) | ~old(paul) [cnf transformation 22]
108. ~patient(paul) [cnf transformation 23]
109. ~quiet(X0) [duplicate literal removal 77]
136. 7 <=> calm(paul) [avatar definition]
138. calm(paul) <- (7) [avatar component clause 136]
195. 20 <=> patient(paul) [avatar definition]
197. ~patient(paul) <- (~20) [avatar component clause 195]
199. old(paul) [subsumption resolution 103,109]
200. calm(paul) [subsumption resolution 107,199]
201. 7 [avatar split clause 200,136]
202. ~20 [avatar split clause 108,195]
207. patient(paul) <- (7) [resolution 93,138]
208. $false <- (7, ~20) [subsumption resolution 207,197]
209. ~7 | 20 [avatar contradiction clause 208]
210. $false [avatar sat refutation 201,202,209]
% SZS output end Proof for 5606878472520667692186453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not wise and not humble and vice versa.
Everyone who is either not rich or not quiet is either wise or brave.
Everyone who is either not calm or not strong is curious or old and vice versa.
Everyone who is humble is either funny or humble and vice versa.
If alice is either brave or not generous then someone is not wise.
Everyone who is not funny or not wise is either patient or not old and vice versa.
Everyone who is either not rich or not wise is either not generous or curious and vice versa.
If lucy is strong or curious then someone is not strong and vice versa.
Everyone who is either rich or not kind is either old or not brave and vice versa.
If someone is brave or calm then mary is not brave.
If someone is either rich or brave then someone is not calm.
Everyone who is both funny and kind is not creative or strong and vice versa.
If john is either not curious or not creative then someone is both not creative and curious.
If fred is not happy then someone is not quiet or calm.
If alice is both quiet and not strong then paul is calm or not patient and vice versa.
Someone is wise.
Mary is not humble or rich.
Alice is humble.
Lucy is either quiet or not curious.
Someone is old.
Someone is humble or not generous. | Paul is not generous. | neutral | (![X]:(~wise(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(curious(X)|old(X))))&
(![X]:(humble(X)<=>(funny(X)<~>humble(X))))&
(((brave(alice)<~>~generous(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~generous(X)<~>curious(X))))&
(((strong(lucy)|curious(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(old(X)<~>~brave(X))))&
((?[X]:((brave(X)|calm(X))))=>(~brave(mary)))&
((?[X]:((rich(X)<~>brave(X))))=>(?[X]:(~calm(X))))&
(![X]:((funny(X)&kind(X))<=>(~creative(X)|strong(X))))&
(((~curious(john)<~>~creative(john)))=>(?[X]:((~creative(X)&curious(X)))))&
((~happy(fred))=>(?[X]:((~quiet(X)|calm(X)))))&
(((quiet(alice)&~strong(alice)))<=>((calm(paul)|~patient(paul))))&
(?[X]:(wise(X)))&
((~humble(mary)|rich(mary)))&
(humble(alice))&
((quiet(lucy)<~>~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:((humble(X)|~generous(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is either strong or quiet is both patient and funny and vice versa.
Everyone who is either curious or brave is either not creative or funny.
Everyone who is not brave is either wise or not generous and vice versa.
If someone is wise or not wise then paul is either not funny or not creative.
Everyone who is not calm or brave is not tall or kind.
Everyone who is not funny or calm is humble or not quiet and vice versa.
Everyone who is either quiet or not humble is both wise and not generous and vice versa.
Everyone who is not curious or not rich is humble.
Everyone who is either calm or not tall is not patient or not rich.
Everyone who is either not patient or happy is both not humble and not generous and vice versa.
If someone is not wise or not happy then someone is quiet.
If someone is both quiet and tall then someone is both not funny and tall.
If mary is strong then paul is both happy and not funny and vice versa.
If someone is either not kind or funny then someone is not old.
Everyone who is not curious or not creative is both quiet and calm and vice versa.
Everyone who is either quiet or humble is tall and vice versa.
Alice is either curious or funny.
Someone is not brave or funny.
Someone is both not funny and not curious.
Someone is not happy or not rich.
Someone is wise.
Someone is both not patient and strong.
Mary is both creative and kind.
Alice is not funny. | Alice is old. | neutral | (![X]:((strong(X)<~>quiet(X))<=>(patient(X)&funny(X))))&
(![X]:((curious(X)<~>brave(X))=>(~creative(X)<~>funny(X))))&
(![X]:(~brave(X)<=>(wise(X)<~>~generous(X))))&
((?[X]:((wise(X)|~wise(X))))=>((~funny(paul)<~>~creative(paul))))&
(![X]:((~calm(X)|brave(X))=>(~tall(X)|kind(X))))&
(![X]:((~funny(X)|calm(X))<=>(humble(X)|~quiet(X))))&
(![X]:((quiet(X)<~>~humble(X))<=>(wise(X)&~generous(X))))&
(![X]:((~curious(X)|~rich(X))=>humble(X)))&
(![X]:((calm(X)<~>~tall(X))=>(~patient(X)|~rich(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((~wise(X)|~happy(X))))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&tall(X))))=>(?[X]:((~funny(X)&tall(X)))))&
((strong(mary))<=>((happy(paul)&~funny(paul))))&
((?[X]:((~kind(X)<~>funny(X))))=>(?[X]:(~old(X))))&
(![X]:((~curious(X)|~creative(X))<=>(quiet(X)&calm(X))))&
(![X]:((quiet(X)<~>humble(X))<=>tall(X)))&
((curious(alice)<~>funny(alice)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((~happy(X)|~rich(X))))&
(?[X]:(wise(X)))&
(?[X]:((~patient(X)&strong(X))))&
((creative(mary)&kind(mary)))&
(~funny(alice)) | old(alice) | [] | null | 0 |
If someone is not creative then alice is either not tall or not patient.
If someone is not calm then paul is both not rich and kind.
If fred is happy or calm then someone is not old or happy.
Everyone who is either not strong or calm is happy.
Everyone who is either not old or wise is either kind or wise.
If someone is not patient or humble then lucy is both happy and not calm and vice versa.
Everyone who is either not kind or kind is both not humble and patient.
If susan is generous or curious then john is not strong.
If mary is not generous then john is creative or not tall and vice versa.
Everyone who is either not strong or not tall is either humble or curious.
If someone is not patient or wise then paul is either not rich or brave and vice versa.
Everyone who is not kind is both not happy and not old and vice versa.
Everyone who is brave is old or wise.
If susan is not old or creative then paul is either not strong or calm.
Everyone who is either quiet or strong is either curious or old.
If paul is both not brave and quiet then paul is both kind and happy.
Susan is either not strong or not tall.
Someone is both not tall and quiet.
Paul is not kind or generous.
Someone is both not wise and not happy.
Lucy is not calm.
Someone is both curious and not kind.
Alice is calm. | Lucy is not humble. | entailment | ((?[X]:(~creative(X)))=>((~tall(alice)<~>~patient(alice))))&
((?[X]:(~calm(X)))=>((~rich(paul)&kind(paul))))&
(((happy(fred)|calm(fred)))=>(?[X]:((~old(X)|happy(X)))))&
(![X]:((~strong(X)<~>calm(X))=>happy(X)))&
(![X]:((~old(X)<~>wise(X))=>(kind(X)<~>wise(X))))&
((?[X]:((~patient(X)|humble(X))))<=>((happy(lucy)&~calm(lucy))))&
(![X]:((~kind(X)<~>kind(X))=>(~humble(X)&patient(X))))&
(((generous(susan)|curious(susan)))=>(~strong(john)))&
((~generous(mary))<=>((creative(john)|~tall(john))))&
(![X]:((~strong(X)<~>~tall(X))=>(humble(X)<~>curious(X))))&
((?[X]:((~patient(X)|wise(X))))<=>((~rich(paul)<~>brave(paul))))&
(![X]:(~kind(X)<=>(~happy(X)&~old(X))))&
(![X]:(brave(X)=>(old(X)|wise(X))))&
(((~old(susan)|creative(susan)))=>((~strong(paul)<~>calm(paul))))&
(![X]:((quiet(X)<~>strong(X))=>(curious(X)<~>old(X))))&
(((~brave(paul)&quiet(paul)))=>((kind(paul)&happy(paul))))&
((~strong(susan)<~>~tall(susan)))&
(?[X]:((~tall(X)&quiet(X))))&
((~kind(paul)|generous(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(~calm(lucy))&
(?[X]:((curious(X)&~kind(X))))&
(calm(alice)) | ~humble(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6596244738142687172856560
% SZS output start Proof for 6596244738142687172856560
7. ! [X0] : ((~kind(X0) <~> kind(X0)) => (patient(X0) & ~humble(X0))) [input p6]
24. humble(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) & ~humble(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 7]
49. ! [X0] : ((patient(X0) & ~humble(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 30]
85. ~humble(X0) | kind(X0) | kind(X0) [cnf transformation 49]
86. ~humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 49]
129. humble(lucy) [cnf transformation 24]
130. ~humble(X0) | kind(X0) [duplicate literal removal 85]
131. ~humble(X0) | ~kind(X0) [duplicate literal removal 86]
198. 15 <=> ! [X1] : ~humble(X1) [avatar definition]
199. ~humble(X1) <- (15) [avatar component clause 198]
209. ~humble(X0) [subsumption resolution 130,131]
210. 15 [avatar split clause 209,198]
311. $false <- (15) [resolution 199,129]
312. ~15 [avatar contradiction clause 311]
313. $false [avatar sat refutation 210,312]
% SZS output end Proof for 6596244738142687172856560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not brave or not rich then paul is both not wise and not generous. Everyone who is quiet is either not curious or not creative and vice versa. If someone is generous or curious then someone is rich or patient and vice versa. If fred is not rich then someone is either tall or not wise and vice versa. Everyone who is both not happy and not humble is funny. If mary is both quiet and wise then someone is curious or not creative. If john is both brave and not curious then someone is both brave and old and vice versa. Everyone who is either creative or not quiet is either old or funny. Everyone who is not tall or not wise is not humble or not tall and vice versa. If someone is not old then mary is either not humble or not wise. Everyone who is either creative or not curious is calm. If susan is calm or not calm then fred is quiet and vice versa. Everyone who is not happy or not humble is both not patient and not happy and vice versa. If someone is both not strong and humble then susan is brave. Everyone who is generous is both old and funny. Everyone who is strong or tall is kind or not kind. Someone is both not brave and wise. Someone is creative. Lucy is either not quiet or not calm. Fred is not patient. Paul is wise or generous. Susan is not creative. Someone is both kind and creative. Someone is not quiet. | John is not curious. | neutral | ((?[X]:((~brave(X)<~>~rich(X))))=>((~wise(paul)&~generous(paul))))&
(![X]:(quiet(X)<=>(~curious(X)<~>~creative(X))))&
((?[X]:((generous(X)|curious(X))))<=>(?[X]:((rich(X)|patient(X)))))&
((~rich(fred))<=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((~happy(X)&~humble(X))=>funny(X)))&
(((quiet(mary)&wise(mary)))=>(?[X]:((curious(X)|~creative(X)))))&
(((brave(john)&~curious(john)))<=>(?[X]:((brave(X)&old(X)))))&
(![X]:((creative(X)<~>~quiet(X))=>(old(X)<~>funny(X))))&
(![X]:((~tall(X)|~wise(X))<=>(~humble(X)|~tall(X))))&
((?[X]:(~old(X)))=>((~humble(mary)<~>~wise(mary))))&
(![X]:((creative(X)<~>~curious(X))=>calm(X)))&
(((calm(susan)|~calm(susan)))<=>(quiet(fred)))&
(![X]:((~happy(X)|~humble(X))<=>(~patient(X)&~happy(X))))&
((?[X]:((~strong(X)&humble(X))))=>(brave(susan)))&
(![X]:(generous(X)=>(old(X)&funny(X))))&
(![X]:((strong(X)|tall(X))=>(kind(X)|~kind(X))))&
(?[X]:((~brave(X)&wise(X))))&
(?[X]:(creative(X)))&
((~quiet(lucy)<~>~calm(lucy)))&
(~patient(fred))&
((wise(paul)|generous(paul)))&
(~creative(susan))&
(?[X]:((kind(X)&creative(X))))&
(?[X]:(~quiet(X))) | ~curious(john) | [] | null | 0 |
Everyone who is either not strong or not patient is rich.
If someone is either tall or not patient then someone is strong.
If paul is old or not calm then someone is not quiet or creative and vice versa.
Everyone who is both not curious and old is creative.
If someone is both humble and not kind then lucy is either not creative or kind.
Everyone who is both wise and patient is not calm or curious and vice versa.
If susan is both humble and generous then john is not rich and vice versa.
Everyone who is quiet or kind is funny or not generous and vice versa.
If someone is not tall then lucy is creative or not brave and vice versa.
If susan is not old then someone is both funny and calm.
Everyone who is either brave or not wise is both not generous and funny and vice versa.
Everyone who is either not kind or kind is either not curious or not happy and vice versa.
Everyone who is curious or creative is either not wise or wise.
Everyone who is both wise and old is generous and vice versa.
Everyone who is either wise or not generous is both funny and rich and vice versa.
Everyone who is generous is not old.
John is either calm or not curious.
Susan is either not wise or wise.
Lucy is not calm.
Alice is not rich.
Someone is not tall or old.
Someone is old or not calm.
Someone is creative or not old. | Susan is not happy. | neutral | (![X]:((~strong(X)<~>~patient(X))=>rich(X)))&
((?[X]:((tall(X)<~>~patient(X))))=>(?[X]:(strong(X))))&
(((old(paul)|~calm(paul)))<=>(?[X]:((~quiet(X)|creative(X)))))&
(![X]:((~curious(X)&old(X))=>creative(X)))&
((?[X]:((humble(X)&~kind(X))))=>((~creative(lucy)<~>kind(lucy))))&
(![X]:((wise(X)&patient(X))<=>(~calm(X)|curious(X))))&
(((humble(susan)&generous(susan)))<=>(~rich(john)))&
(![X]:((quiet(X)|kind(X))<=>(funny(X)|~generous(X))))&
((?[X]:(~tall(X)))<=>((creative(lucy)|~brave(lucy))))&
((~old(susan))=>(?[X]:((funny(X)&calm(X)))))&
(![X]:((brave(X)<~>~wise(X))<=>(~generous(X)&funny(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~curious(X)<~>~happy(X))))&
(![X]:((curious(X)|creative(X))=>(~wise(X)<~>wise(X))))&
(![X]:((wise(X)&old(X))<=>generous(X)))&
(![X]:((wise(X)<~>~generous(X))<=>(funny(X)&rich(X))))&
(![X]:(generous(X)=>~old(X)))&
((calm(john)<~>~curious(john)))&
((~wise(susan)<~>wise(susan)))&
(~calm(lucy))&
(~rich(alice))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((old(X)|~calm(X))))&
(?[X]:((creative(X)|~old(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is both not generous and creative is either not patient or not generous and vice versa.
If mary is either patient or kind then someone is both brave and strong.
If someone is creative or not generous then mary is both not brave and not creative and vice versa.
If someone is not happy then alice is both happy and not quiet and vice versa.
Everyone who is not happy or patient is both quiet and not quiet.
If someone is rich or brave then paul is creative or kind.
If john is not calm or old then fred is either creative or not rich and vice versa.
If paul is both rich and generous then someone is either not humble or not tall and vice versa.
Everyone who is not kind is either not tall or not happy.
If lucy is either funny or not brave then susan is either wise or not curious and vice versa.
Everyone who is either wise or not wise is not strong or not tall.
If lucy is not funny then someone is calm and vice versa.
If susan is either creative or calm then fred is both curious and not calm.
Everyone who is both wise and patient is both tall and rich and vice versa.
If someone is both not curious and not wise then paul is not wise or not brave.
Fred is curious or not funny.
Mary is either brave or not generous.
Someone is both kind and not generous.
Someone is not patient.
Paul is old.
Paul is either not happy or happy.
Lucy is either not humble or generous. | Mary is generous. | contradiction | (![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(((patient(mary)<~>kind(mary)))=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:((creative(X)|~generous(X))))<=>((~brave(mary)&~creative(mary))))&
((?[X]:(~happy(X)))<=>((happy(alice)&~quiet(alice))))&
(![X]:((~happy(X)|patient(X))=>(quiet(X)&~quiet(X))))&
((?[X]:((rich(X)|brave(X))))=>((creative(paul)|kind(paul))))&
(((~calm(john)|old(john)))<=>((creative(fred)<~>~rich(fred))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
((~funny(lucy))<=>(?[X]:(calm(X))))&
(((creative(susan)<~>calm(susan)))=>((curious(fred)&~calm(fred))))&
(![X]:((wise(X)&patient(X))<=>(tall(X)&rich(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((~wise(paul)|~brave(paul))))&
((curious(fred)|~funny(fred)))&
((brave(mary)<~>~generous(mary)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:(~patient(X)))&
(old(paul))&
((~happy(paul)<~>happy(paul)))&
((~humble(lucy)<~>generous(lucy))) | generous(mary) | [
"p2",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6216536910818401071639844
% SZS output start Proof for 6216536910818401071639844
3. ? [X0] : (~generous(X0) | creative(X0)) <=> (~creative(mary) & ~brave(mary)) [input p2]
17. brave(mary) <~> ~generous(mary) [input p16]
18. ? [X0] : (~generous(X0) & kind(X0)) [input p17]
23. generous(mary) [input hypothesis]
39. (? [X0] : (~generous(X0) | creative(X0)) | (creative(mary) | brave(mary))) & ((~creative(mary) & ~brave(mary)) | ! [X0] : (generous(X0) & ~creative(X0))) [nnf transformation 3]
40. (? [X0] : (~generous(X0) | creative(X0)) | creative(mary) | brave(mary)) & ((~creative(mary) & ~brave(mary)) | ! [X0] : (generous(X0) & ~creative(X0))) [flattening 39]
41. (? [X0] : (~generous(X0) | creative(X0)) | creative(mary) | brave(mary)) & ((~creative(mary) & ~brave(mary)) | ! [X1] : (generous(X1) & ~creative(X1))) [rectify 40]
42. ? [X0] : (~generous(X0) | creative(X0)) => (~generous(sK1) | creative(sK1)) [choice axiom]
43. ((~generous(sK1) | creative(sK1)) | creative(mary) | brave(mary)) & ((~creative(mary) & ~brave(mary)) | ! [X1] : (generous(X1) & ~creative(X1))) [skolemisation 41,42]
66. (generous(mary) | ~brave(mary)) & (~generous(mary) | brave(mary)) [nnf transformation 17]
67. ? [X0] : (~generous(X0) & kind(X0)) => (~generous(sK5) & kind(sK5)) [choice axiom]
68. ~generous(sK5) & kind(sK5) [skolemisation 18,67]
84. ~brave(mary) | generous(X1) [cnf transformation 43]
133. ~generous(mary) | brave(mary) [cnf transformation 66]
136. ~generous(sK5) [cnf transformation 68]
143. generous(mary) [cnf transformation 23]
170. 5 <=> brave(mary) [avatar definition]
187. 9 <=> ! [X1] : generous(X1) [avatar definition]
188. generous(X1) <- (9) [avatar component clause 187]
194. 9 | ~5 [avatar split clause 84,170,187]
356. 43 <=> generous(mary) [avatar definition]
360. 5 | ~43 [avatar split clause 133,356,170]
371. 43 [avatar split clause 143,356]
376. $false <- (9) [resolution 188,136]
377. ~9 [avatar contradiction clause 376]
378. $false [avatar sat refutation 194,360,371,377]
% SZS output end Proof for 6216536910818401071639844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is brave.
Everyone who is both not wise and humble is generous.
Everyone who is both curious and not wise is both creative and not generous.
Everyone who is either patient or quiet is either not creative or not brave and vice versa.
If someone is either not kind or not quiet then mary is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Paul is not calm.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is not rich. | entailment | (![X]:(generous(X)=>brave(X)))&
(![X]:((~wise(X)&humble(X))=>generous(X)))&
(![X]:((curious(X)&~wise(X))=>(creative(X)&~generous(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(~calm(mary)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(~calm(paul))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | ~rich(paul) | [
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8883796526308734250331165
% SZS output start Proof for 8883796526308734250331165
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
11. ! [X0] : (rich(X0) => (brave(X0) | calm(X0))) [input p10]
21. ~calm(paul) [input p20]
25. rich(paul) [input hypothesis]
35. ! [X0] : ((brave(X0) | calm(X0)) | ~rich(X0)) [ennf transformation 11]
36. ! [X0] : (brave(X0) | calm(X0) | ~rich(X0)) [flattening 35]
45. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
46. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 45]
94. ~brave(X0) | calm(X0) [cnf transformation 46]
104. brave(X0) | calm(X0) | ~rich(X0) [cnf transformation 36]
123. ~calm(paul) [cnf transformation 21]
128. rich(paul) [cnf transformation 25]
180. ~rich(X0) | calm(X0) [subsumption resolution 104,94]
237. 25 <=> calm(paul) [avatar definition]
239. ~calm(paul) <- (~25) [avatar component clause 237]
246. 27 <=> rich(paul) [avatar definition]
247. rich(paul) <- (27) [avatar component clause 246]
290. ~25 [avatar split clause 123,237]
310. 27 [avatar split clause 128,246]
332. calm(paul) <- (27) [resolution 180,247]
333. $false <- (~25, 27) [subsumption resolution 332,239]
334. 25 | ~27 [avatar contradiction clause 333]
335. $false [avatar sat refutation 290,310,334]
% SZS output end Proof for 8883796526308734250331165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is quiet or not kind then someone is either wise or not kind and vice versa. Everyone who is both patient and not wise is strong. Everyone who is both rich and not quiet is not old or creative and vice versa. Everyone who is both happy and not kind is not humble or not tall and vice versa. Everyone who is both calm and tall is humble or old and vice versa. Everyone who is not funny is rich and vice versa. Everyone who is both not kind and not quiet is both strong and not rich and vice versa. Everyone who is curious is both rich and not curious. If someone is both not quiet and wise then fred is not strong or kind and vice versa. Everyone who is both kind and not humble is not curious or not tall. Everyone who is either not brave or curious is not happy or strong. Everyone who is either calm or not funny is either not strong or funny. Everyone who is both not old and humble is both humble and patient. If someone is both not brave and not generous then someone is creative or not strong. If someone is generous or creative then fred is both humble and creative and vice versa. Everyone who is either not generous or wise is either not kind or not curious. Lucy is patient. Someone is not wise. Someone is kind or wise. Paul is either not creative or not curious. John is either calm or brave. Someone is quiet or calm. Someone is both old and rich. | Fred is not curious. | entailment | (((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
(![X]:((~old(X)&humble(X))=>(humble(X)&patient(X))))&
((?[X]:((~brave(X)&~generous(X))))=>(?[X]:((creative(X)|~strong(X)))))&
((?[X]:((generous(X)|creative(X))))<=>((humble(fred)&creative(fred))))&
(![X]:((~generous(X)<~>wise(X))=>(~kind(X)<~>~curious(X))))&
(patient(lucy))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|wise(X))))&
((~creative(paul)<~>~curious(paul)))&
((calm(john)<~>brave(john)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((old(X)&rich(X)))) | ~curious(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8816892841181373760784791
% SZS output start Proof for 8816892841181373760784791
8. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p7]
24. curious(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 8]
107. ~curious(X0) | ~curious(X0) [cnf transformation 28]
142. curious(fred) [cnf transformation 24]
145. ~curious(X0) [duplicate literal removal 107]
269. $false [subsumption resolution 142,145]
% SZS output end Proof for 8816892841181373760784791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and brave then john is quiet and vice versa.
Everyone who is funny is either calm or not curious and vice versa.
Everyone who is both not quiet and not brave is either humble or not happy and vice versa.
Everyone who is both not generous and patient is either rich or not old and vice versa.
If someone is either not kind or not happy then someone is calm or strong and vice versa.
Everyone who is not creative is rich and vice versa.
If mary is not generous then someone is both rich and not calm and vice versa.
Everyone who is either calm or kind is calm.
Everyone who is brave or not quiet is both kind and humble.
Everyone who is both kind and brave is both calm and strong and vice versa.
If someone is strong then lucy is both happy and not patient and vice versa.
Everyone who is not humble or not strong is not calm and vice versa.
If someone is kind or not calm then someone is generous or not patient.
If someone is patient then someone is either not old or funny.
Everyone who is both not tall and brave is not happy.
Everyone who is either tall or generous is not patient and vice versa.
Fred is both creative and humble.
Someone is both not wise and brave.
John is either not strong or tall.
Fred is either patient or humble.
Someone is both kind and not rich.
Someone is either not creative or patient.
Paul is not quiet or not wise. | Lucy is humble. | contradiction | ((?[X]:((~generous(X)&brave(X))))<=>(quiet(john)))&
(![X]:(funny(X)<=>(calm(X)<~>~curious(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((~generous(X)&patient(X))<=>(rich(X)<~>~old(X))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(![X]:(~creative(X)<=>rich(X)))&
((~generous(mary))<=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((calm(X)<~>kind(X))=>calm(X)))&
(![X]:((brave(X)|~quiet(X))=>(kind(X)&humble(X))))&
(![X]:((kind(X)&brave(X))<=>(calm(X)&strong(X))))&
((?[X]:(strong(X)))<=>((happy(lucy)&~patient(lucy))))&
(![X]:((~humble(X)|~strong(X))<=>~calm(X)))&
((?[X]:((kind(X)|~calm(X))))=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:(patient(X)))=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((~tall(X)&brave(X))=>~happy(X)))&
(![X]:((tall(X)<~>generous(X))<=>~patient(X)))&
((creative(fred)&humble(fred)))&
(?[X]:((~wise(X)&brave(X))))&
((~strong(john)<~>tall(john)))&
((patient(fred)<~>humble(fred)))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
((~quiet(paul)|~wise(paul))) | humble(lucy) | [
"p2",
"p7",
"p8",
"p9",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5638858086510221084410022
% SZS output start Proof for 5638858086510221084410022
3. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (humble(X0) <~> ~happy(X0))) [input p2]
8. ! [X0] : ((calm(X0) <~> kind(X0)) => calm(X0)) [input p7]
9. ! [X0] : ((~quiet(X0) | brave(X0)) => (humble(X0) & kind(X0))) [input p8]
10. ! [X0] : ((brave(X0) & kind(X0)) <=> (strong(X0) & calm(X0))) [input p9]
11. ? [X0] : strong(X0) <=> (~patient(lucy) & happy(lucy)) [input p10]
12. ! [X0] : ((~strong(X0) | ~humble(X0)) <=> ~calm(X0)) [input p11]
18. ? [X0] : (brave(X0) & ~wise(X0)) [input p17]
24. humble(lucy) [input hypothesis]
28. ? [X0] : brave(X0) [pure predicate removal 18]
30. ! [X0] : (calm(X0) | (calm(X0) <=> kind(X0))) [ennf transformation 8]
31. ! [X0] : ((humble(X0) & kind(X0)) | (quiet(X0) & ~brave(X0))) [ennf transformation 9]
41. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0)))) & (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | (brave(X0) | quiet(X0)))) [nnf transformation 3]
42. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0)))) & (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | brave(X0) | quiet(X0))) [flattening 41]
55. ! [X0] : (calm(X0) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0)))) [nnf transformation 30]
56. ! [X0] : (((brave(X0) & kind(X0)) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | (~brave(X0) | ~kind(X0)))) [nnf transformation 10]
57. ! [X0] : (((brave(X0) & kind(X0)) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | ~brave(X0) | ~kind(X0))) [flattening 56]
58. (? [X0] : strong(X0) | (patient(lucy) | ~happy(lucy))) & ((~patient(lucy) & happy(lucy)) | ! [X0] : ~strong(X0)) [nnf transformation 11]
59. (? [X0] : strong(X0) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X0] : ~strong(X0)) [flattening 58]
60. (? [X0] : strong(X0) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X1] : ~strong(X1)) [rectify 59]
61. ? [X0] : strong(X0) => strong(sK4) [choice axiom]
62. (strong(sK4) | patient(lucy) | ~happy(lucy)) & ((~patient(lucy) & happy(lucy)) | ! [X1] : ~strong(X1)) [skolemisation 60,61]
63. ! [X0] : (((~strong(X0) | ~humble(X0)) | calm(X0)) & (~calm(X0) | (strong(X0) & humble(X0)))) [nnf transformation 12]
64. ! [X0] : ((~strong(X0) | ~humble(X0) | calm(X0)) & (~calm(X0) | (strong(X0) & humble(X0)))) [flattening 63]
73. ? [X0] : brave(X0) => brave(sK7) [choice axiom]
74. brave(sK7) [skolemisation 28,73]
91. ~happy(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 42]
93. ~happy(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 42]
113. calm(X0) | calm(X0) | ~kind(X0) [cnf transformation 55]
114. ~brave(X0) | kind(X0) [cnf transformation 31]
115. kind(X0) | quiet(X0) [cnf transformation 31]
119. strong(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 57]
121. ~strong(X0) | brave(X0) | ~calm(X0) [cnf transformation 57]
122. happy(lucy) | ~strong(X1) [cnf transformation 62]
126. ~calm(X0) | strong(X0) [cnf transformation 64]
139. brave(sK7) [cnf transformation 74]
148. humble(lucy) [cnf transformation 24]
149. ~kind(X0) | calm(X0) [duplicate literal removal 113]
169. 5 <=> ! [X1] : ~strong(X1) [avatar definition]
170. ~strong(X1) <- (5) [avatar component clause 169]
220. ~brave(X0) | strong(X0) [subsumption resolution 119,114]
222. 17 <=> happy(lucy) [avatar definition]
223. happy(lucy) <- (17) [avatar component clause 222]
235. 5 | 17 [avatar split clause 122,222,169]
297. calm(X0) | quiet(X0) [resolution 149,115]
317. strong(sK7) [resolution 220,139]
354. ~quiet(lucy) | ~humble(lucy) <- (17) [resolution 91,223]
355. ~quiet(lucy) <- (17) [subsumption resolution 354,148]
356. ~brave(lucy) | ~humble(lucy) <- (17) [resolution 93,223]
357. ~brave(lucy) <- (17) [subsumption resolution 356,148]
561. strong(X1) | quiet(X1) [resolution 297,126]
599. quiet(X1) | brave(X1) | ~calm(X1) [resolution 561,121]
601. quiet(X1) | brave(X1) [subsumption resolution 599,297]
647. brave(lucy) <- (17) [resolution 601,355]
649. $false <- (17) [subsumption resolution 647,357]
650. ~17 [avatar contradiction clause 649]
662. $false <- (5) [resolution 170,317]
667. ~5 [avatar contradiction clause 662]
670. $false [avatar sat refutation 235,650,667]
% SZS output end Proof for 5638858086510221084410022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or patient then someone is both wise and strong and vice versa. Everyone who is not calm is both generous and not brave and vice versa. If fred is either not happy or quiet then someone is both not rich and tall. If someone is both patient and kind then alice is wise or not old. Everyone who is either not happy or rich is both generous and not old. If paul is either not wise or quiet then mary is not wise or not kind. Everyone who is not happy is brave or humble. Everyone who is quiet or happy is not humble. If someone is not calm or rich then lucy is both calm and not calm. If fred is both not curious and not calm then someone is both happy and not funny. If someone is both not wise and not quiet then someone is both calm and not old and vice versa. Everyone who is either not kind or calm is humble. Everyone who is not happy or not calm is not old and vice versa. Everyone who is patient is curious or tall. Everyone who is either strong or tall is both wise and not quiet and vice versa. Everyone who is either not calm or funny is both not tall and kind and vice versa. Someone is not tall. John is not happy. Someone is not rich or not wise. John is either not quiet or not tall. Someone is either quiet or strong. Susan is either not calm or kind. | Mary is not calm. | contradiction | ((?[X]:((quiet(X)|patient(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~calm(X)<=>(generous(X)&~brave(X))))&
(((~happy(fred)<~>quiet(fred)))=>(?[X]:((~rich(X)&tall(X)))))&
((?[X]:((patient(X)&kind(X))))=>((wise(alice)|~old(alice))))&
(![X]:((~happy(X)<~>rich(X))=>(generous(X)&~old(X))))&
(((~wise(paul)<~>quiet(paul)))=>((~wise(mary)|~kind(mary))))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((quiet(X)|happy(X))=>~humble(X)))&
((?[X]:((~calm(X)|rich(X))))=>((calm(lucy)&~calm(lucy))))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((happy(X)&~funny(X)))))&
((?[X]:((~wise(X)&~quiet(X))))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((~kind(X)<~>calm(X))=>humble(X)))&
(![X]:((~happy(X)|~calm(X))<=>~old(X)))&
(![X]:(patient(X)=>(curious(X)|tall(X))))&
(![X]:((strong(X)<~>tall(X))<=>(wise(X)&~quiet(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~tall(X)&kind(X))))&
(?[X]:(~tall(X)))&
(~happy(john))&
(?[X]:((~rich(X)|~wise(X))))&
((~quiet(john)<~>~tall(john)))&
(?[X]:((quiet(X)<~>strong(X))))&
((~calm(susan)<~>kind(susan))) | ~calm(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6084044090091080096504648
% SZS output start Proof for 6084044090091080096504648
9. ? [X0] : (rich(X0) | ~calm(X0)) => (~calm(lucy) & calm(lucy)) [input p8]
23. ~calm(mary) [input hypothesis]
37. (~calm(lucy) & calm(lucy)) | ! [X0] : (~rich(X0) & calm(X0)) [ennf transformation 9]
94. calm(lucy) | calm(X0) [cnf transformation 37]
96. ~calm(lucy) | calm(X0) [cnf transformation 37]
128. ~calm(mary) [cnf transformation 23]
213. 20 <=> calm(lucy) [avatar definition]
218. 21 <=> ! [X0] : calm(X0) [avatar definition]
219. calm(X0) <- (21) [avatar component clause 218]
220. 21 | ~20 [avatar split clause 96,213,218]
222. 21 | 20 [avatar split clause 94,213,218]
290. $false <- (21) [resolution 219,128]
291. ~21 [avatar contradiction clause 290]
292. $false [avatar sat refutation 220,222,291]
% SZS output end Proof for 6084044090091080096504648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both not curious and not kind and vice versa.
If someone is both not strong and not creative then someone is not strong or rich.
If paul is either not tall or rich then someone is either not curious or kind and vice versa.
Everyone who is not patient is funny or creative and vice versa.
Everyone who is happy or not curious is not strong and vice versa.
If someone is not strong or funny then john is both not strong and not calm.
If someone is kind then someone is not humble or humble and vice versa.
If john is either not curious or calm then alice is either not rich or not strong and vice versa.
If someone is humble then someone is not rich or not brave and vice versa.
If someone is both quiet and old then john is not quiet or not humble.
If someone is not quiet then lucy is creative.
Everyone who is not happy is calm or not strong and vice versa.
Everyone who is not calm or happy is not funny or rich and vice versa.
Everyone who is old or creative is either not kind or calm and vice versa.
Everyone who is not calm is both wise and not strong.
If paul is either tall or old then mary is not quiet or not rich and vice versa.
Susan is not kind or wise.
Someone is both creative and not tall.
Susan is either not happy or not tall.
Paul is funny or calm.
Paul is either creative or calm.
Paul is old or humble.
Someone is both not wise and not patient. | John is quiet. | neutral | (![X]:(old(X)<=>(~curious(X)&~kind(X))))&
((?[X]:((~strong(X)&~creative(X))))=>(?[X]:((~strong(X)|rich(X)))))&
(((~tall(paul)<~>rich(paul)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:(~patient(X)<=>(funny(X)|creative(X))))&
(![X]:((happy(X)|~curious(X))<=>~strong(X)))&
((?[X]:((~strong(X)|funny(X))))=>((~strong(john)&~calm(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)|humble(X)))))&
(((~curious(john)<~>calm(john)))<=>((~rich(alice)<~>~strong(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)|~brave(X)))))&
((?[X]:((quiet(X)&old(X))))=>((~quiet(john)|~humble(john))))&
((?[X]:(~quiet(X)))=>(creative(lucy)))&
(![X]:(~happy(X)<=>(calm(X)|~strong(X))))&
(![X]:((~calm(X)|happy(X))<=>(~funny(X)|rich(X))))&
(![X]:((old(X)|creative(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(~calm(X)=>(wise(X)&~strong(X))))&
(((tall(paul)<~>old(paul)))<=>((~quiet(mary)|~rich(mary))))&
((~kind(susan)|wise(susan)))&
(?[X]:((creative(X)&~tall(X))))&
((~happy(susan)<~>~tall(susan)))&
((funny(paul)|calm(paul)))&
((creative(paul)<~>calm(paul)))&
((old(paul)|humble(paul)))&
(?[X]:((~wise(X)&~patient(X)))) | quiet(john) | [] | null | 0 |
If paul is either patient or curious then lucy is both funny and tall and vice versa.
Everyone who is both creative and not quiet is both not wise and brave and vice versa.
If lucy is either quiet or not wise then alice is not brave and vice versa.
Everyone who is both not creative and quiet is both not funny and kind.
If someone is either not calm or not tall then mary is both not strong and kind.
If someone is both not brave and not patient then someone is either not tall or not brave and vice versa.
Everyone who is strong or not rich is not tall or tall and vice versa.
If paul is curious then lucy is generous.
Everyone who is either old or not rich is either not patient or strong.
If paul is both calm and patient then alice is patient or not old.
If alice is not kind then someone is not strong and vice versa.
Everyone who is either creative or not happy is not calm and vice versa.
If paul is calm or rich then someone is creative and vice versa.
Everyone who is either not humble or creative is both not brave and funny and vice versa.
If alice is quiet or not tall then fred is both rich and not humble and vice versa.
Everyone who is both not wise and funny is tall or brave and vice versa.
Someone is both humble and curious.
Alice is not creative or wise.
John is not funny.
Someone is both not happy and humble.
Someone is either not calm or calm.
Someone is both not old and not creative.
Someone is either not creative or generous.
Susan is either not old or not humble. | Alice is brave. | contradiction | (((patient(paul)<~>curious(paul)))<=>((funny(lucy)&tall(lucy))))&
(![X]:((creative(X)&~quiet(X))<=>(~wise(X)&brave(X))))&
(((quiet(lucy)<~>~wise(lucy)))<=>(~brave(alice)))&
(![X]:((~creative(X)&quiet(X))=>(~funny(X)&kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>((~strong(mary)&kind(mary))))&
((?[X]:((~brave(X)&~patient(X))))<=>(?[X]:((~tall(X)<~>~brave(X)))))&
(![X]:((strong(X)|~rich(X))<=>(~tall(X)|tall(X))))&
((curious(paul))=>(generous(lucy)))&
(![X]:((old(X)<~>~rich(X))=>(~patient(X)<~>strong(X))))&
(((calm(paul)&patient(paul)))=>((patient(alice)|~old(alice))))&
((~kind(alice))<=>(?[X]:(~strong(X))))&
(![X]:((creative(X)<~>~happy(X))<=>~calm(X)))&
(((calm(paul)|rich(paul)))<=>(?[X]:(creative(X))))&
(![X]:((~humble(X)<~>creative(X))<=>(~brave(X)&funny(X))))&
(((quiet(alice)|~tall(alice)))<=>((rich(fred)&~humble(fred))))&
(![X]:((~wise(X)&funny(X))<=>(tall(X)|brave(X))))&
(?[X]:((humble(X)&curious(X))))&
((~creative(alice)|wise(alice)))&
(~funny(john))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((~old(X)&~creative(X))))&
(?[X]:((~creative(X)<~>generous(X))))&
((~old(susan)<~>~humble(susan))) | brave(alice) | [
"p1",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1235114290128297826621547
% SZS output start Proof for 1235114290128297826621547
2. ! [X0] : ((~quiet(X0) & creative(X0)) <=> (brave(X0) & ~wise(X0))) [input p1]
16. ! [X0] : ((funny(X0) & ~wise(X0)) <=> (brave(X0) | tall(X0))) [input p15]
18. wise(alice) | ~creative(alice) [input p17]
25. brave(alice) [input hypothesis]
36. ! [X0] : (((~quiet(X0) & creative(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (quiet(X0) | ~creative(X0)))) [nnf transformation 2]
37. ! [X0] : (((~quiet(X0) & creative(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | quiet(X0) | ~creative(X0))) [flattening 36]
62. ! [X0] : (((funny(X0) & ~wise(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (~funny(X0) | wise(X0)))) [nnf transformation 16]
63. ! [X0] : (((funny(X0) & ~wise(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | ~funny(X0) | wise(X0))) [flattening 62]
85. ~brave(X0) | creative(X0) | wise(X0) [cnf transformation 37]
135. ~brave(X0) | ~wise(X0) [cnf transformation 63]
140. wise(alice) | ~creative(alice) [cnf transformation 18]
152. brave(alice) [cnf transformation 25]
176. 5 <=> brave(alice) [avatar definition]
178. brave(alice) <- (5) [avatar component clause 176]
310. 33 <=> creative(alice) [avatar definition]
312. ~creative(alice) <- (~33) [avatar component clause 310]
314. 34 <=> wise(alice) [avatar definition]
315. ~wise(alice) <- (~34) [avatar component clause 314]
317. ~33 | 34 [avatar split clause 140,314,310]
338. 5 [avatar split clause 152,176]
339. ~wise(alice) <- (5) [resolution 135,178]
340. ~34 | ~5 [avatar split clause 339,176,314]
357. creative(alice) | wise(alice) <- (5) [resolution 85,178]
358. wise(alice) <- (5, ~33) [subsumption resolution 357,312]
359. $false <- (5, ~33, ~34) [subsumption resolution 358,315]
360. ~5 | 33 | 34 [avatar contradiction clause 359]
361. $false [avatar sat refutation 317,338,340,360]
% SZS output end Proof for 1235114290128297826621547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not strong or not humble then someone is not kind or not patient.
Everyone who is either not funny or creative is wise and vice versa.
Everyone who is both not rich and humble is not funny or not quiet and vice versa.
Everyone who is not creative is not rich and vice versa.
Everyone who is not humble is not wise and vice versa.
Everyone who is either creative or not kind is either curious or wise.
If someone is either not rich or not wise then lucy is patient or not humble and vice versa.
If mary is brave then john is both not kind and not brave.
Everyone who is both not tall and not brave is not creative or rich and vice versa.
Everyone who is not wise is not patient and vice versa.
Everyone who is not old is both not funny and patient.
Everyone who is calm or funny is patient.
Everyone who is both wise and not kind is rich and vice versa.
Everyone who is both funny and not wise is tall or brave and vice versa.
If someone is both happy and not happy then paul is either not quiet or humble and vice versa.
If someone is wise or not creative then someone is not strong or generous.
Alice is either not humble or not quiet.
Someone is calm.
Paul is not old.
Mary is generous or not happy.
Someone is happy or generous.
Paul is both curious and not generous.
Someone is not wise or strong. | Alice is not funny. | entailment | (((~strong(lucy)<~>~humble(lucy)))=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>wise(X)))&
(![X]:((~rich(X)&humble(X))<=>(~funny(X)|~quiet(X))))&
(![X]:(~creative(X)<=>~rich(X)))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((patient(lucy)|~humble(lucy))))&
((brave(mary))=>((~kind(john)&~brave(john))))&
(![X]:((~tall(X)&~brave(X))<=>(~creative(X)|rich(X))))&
(![X]:(~wise(X)<=>~patient(X)))&
(![X]:(~old(X)=>(~funny(X)&patient(X))))&
(![X]:((calm(X)|funny(X))=>patient(X)))&
(![X]:((wise(X)&~kind(X))<=>rich(X)))&
(![X]:((funny(X)&~wise(X))<=>(tall(X)|brave(X))))&
((?[X]:((happy(X)&~happy(X))))<=>((~quiet(paul)<~>humble(paul))))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~strong(X)|generous(X)))))&
((~humble(alice)<~>~quiet(alice)))&
(?[X]:(calm(X)))&
(~old(paul))&
((generous(mary)|~happy(mary)))&
(?[X]:((happy(X)|generous(X))))&
((curious(paul)&~generous(paul)))&
(?[X]:((~wise(X)|strong(X)))) | ~funny(alice) | [
"p1",
"p2",
"p3",
"p4",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3672939005935618114925010
% SZS output start Proof for 3672939005935618114925010
2. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~rich(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p2]
4. ! [X0] : (~creative(X0) <=> ~rich(X0)) [input p3]
5. ! [X0] : (~humble(X0) <=> ~wise(X0)) [input p4]
10. ! [X0] : (~wise(X0) <=> ~patient(X0)) [input p9]
12. ! [X0] : ((funny(X0) | calm(X0)) => patient(X0)) [input p11]
17. ~humble(alice) <~> ~quiet(alice) [input p16]
24. funny(alice) [input hypothesis]
30. ! [X0] : (patient(X0) | (~funny(X0) & ~calm(X0))) [ennf transformation 12]
35. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | ~wise(X0)) & (wise(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 2]
36. ! [X0] : (((humble(X0) & ~rich(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~humble(X0) | rich(X0)))) [nnf transformation 3]
37. ! [X0] : (((humble(X0) & ~rich(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~humble(X0) | rich(X0))) [flattening 36]
38. ! [X0] : ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))) [nnf transformation 4]
39. ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 5]
48. ! [X0] : ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))) [nnf transformation 10]
60. (quiet(alice) | humble(alice)) & (~quiet(alice) | ~humble(alice)) [nnf transformation 17]
71. ~wise(X0) | ~funny(X0) | creative(X0) [cnf transformation 35]
75. ~rich(X0) | quiet(X0) [cnf transformation 37]
79. ~creative(X0) | rich(X0) [cnf transformation 38]
80. ~wise(X0) | humble(X0) [cnf transformation 39]
99. ~patient(X0) | wise(X0) [cnf transformation 48]
104. ~funny(X0) | patient(X0) [cnf transformation 30]
121. ~quiet(alice) | ~humble(alice) [cnf transformation 60]
130. funny(alice) [cnf transformation 24]
219. 20 <=> humble(alice) [avatar definition]
223. 21 <=> quiet(alice) [avatar definition]
225. ~quiet(alice) <- (~21) [avatar component clause 223]
226. ~20 | ~21 [avatar split clause 121,223,219]
265. patient(alice) [resolution 104,130]
268. wise(alice) [resolution 265,99]
386. ~funny(alice) | creative(alice) [resolution 268,71]
388. humble(alice) [resolution 268,80]
390. 42 <=> rich(alice) [avatar definition]
392. rich(alice) <- (42) [avatar component clause 390]
398. creative(alice) [subsumption resolution 386,130]
401. 20 [avatar split clause 388,219]
511. rich(alice) [resolution 398,79]
512. 42 [avatar split clause 511,390]
516. quiet(alice) <- (42) [resolution 392,75]
520. $false <- (~21, 42) [subsumption resolution 516,225]
521. 21 | ~42 [avatar contradiction clause 520]
522. $false [avatar sat refutation 226,401,512,521]
% SZS output end Proof for 3672939005935618114925010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not funny or humble then alice is both not creative and strong.
Everyone who is not tall is both not quiet and creative.
If susan is not tall or brave then fred is brave or not creative.
If lucy is both not brave and creative then someone is either not brave or calm and vice versa.
If someone is rich then lucy is either not brave or not kind and vice versa.
If someone is generous or not strong then someone is rich or strong.
Everyone who is not wise is quiet or not calm.
Everyone who is quiet or not old is either not creative or not old and vice versa.
If fred is curious or not patient then someone is either rich or not quiet.
Everyone who is both quiet and not kind is both not kind and funny and vice versa.
Everyone who is not brave or strong is both brave and not quiet and vice versa.
If john is either not funny or not old then mary is either not patient or not happy and vice versa.
Everyone who is not rich is not brave or not humble.
Everyone who is not kind is rich and vice versa.
Everyone who is both creative and not quiet is both calm and strong.
If someone is strong then susan is humble or not quiet and vice versa.
Someone is rich or funny.
Someone is either not generous or humble.
Lucy is not tall or generous. | John is not old. | neutral | (((~funny(paul)<~>humble(paul)))=>((~creative(alice)&strong(alice))))&
(![X]:(~tall(X)=>(~quiet(X)&creative(X))))&
(((~tall(susan)|brave(susan)))=>((brave(fred)|~creative(fred))))&
(((~brave(lucy)&creative(lucy)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
((?[X]:(rich(X)))<=>((~brave(lucy)<~>~kind(lucy))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:(~wise(X)=>(quiet(X)|~calm(X))))&
(![X]:((quiet(X)|~old(X))<=>(~creative(X)<~>~old(X))))&
(((curious(fred)|~patient(fred)))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~kind(X)&funny(X))))&
(![X]:((~brave(X)|strong(X))<=>(brave(X)&~quiet(X))))&
(((~funny(john)<~>~old(john)))<=>((~patient(mary)<~>~happy(mary))))&
(![X]:(~rich(X)=>(~brave(X)|~humble(X))))&
(![X]:(~kind(X)<=>rich(X)))&
(![X]:((creative(X)&~quiet(X))=>(calm(X)&strong(X))))&
((?[X]:(strong(X)))<=>((humble(susan)|~quiet(susan))))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~generous(X)<~>humble(X))))&
((~tall(lucy)|generous(lucy))) | ~old(john) | [] | null | 0 |
Everyone who is both strong and kind is not strong and vice versa.
If someone is either not curious or not quiet then paul is funny or not tall and vice versa.
If fred is not rich or not brave then mary is either rich or old.
Everyone who is not creative is not rich or not generous and vice versa.
If alice is both not quiet and not happy then someone is calm or not strong and vice versa.
Everyone who is not calm or happy is not funny or rich and vice versa.
Everyone who is old or creative is either not kind or calm and vice versa.
Everyone who is not calm is both wise and not strong.
If paul is either tall or old then mary is not quiet or not rich and vice versa.
If someone is either not calm or not brave then mary is happy.
Everyone who is both creative and not tall is either not humble or not old.
If paul is funny or calm then paul is either creative or calm and vice versa.
Everyone who is not wise is either not strong or generous.
Everyone who is not wise or humble is brave or not kind and vice versa.
If john is either calm or old then someone is not quiet or not tall.
Someone is patient.
Someone is not happy or humble.
Paul is not kind.
Someone is brave. | Mary is not strong. | contradiction | (![X]:((strong(X)&kind(X))<=>~strong(X)))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((funny(paul)|~tall(paul))))&
(((~rich(fred)|~brave(fred)))=>((rich(mary)<~>old(mary))))&
(![X]:(~creative(X)<=>(~rich(X)|~generous(X))))&
(((~quiet(alice)&~happy(alice)))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((~calm(X)|happy(X))<=>(~funny(X)|rich(X))))&
(![X]:((old(X)|creative(X))<=>(~kind(X)<~>calm(X))))&
(![X]:(~calm(X)=>(wise(X)&~strong(X))))&
(((tall(paul)<~>old(paul)))<=>((~quiet(mary)|~rich(mary))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(happy(mary)))&
(![X]:((creative(X)&~tall(X))=>(~humble(X)<~>~old(X))))&
(((funny(paul)|calm(paul)))<=>((creative(paul)<~>calm(paul))))&
(![X]:(~wise(X)=>(~strong(X)<~>generous(X))))&
(![X]:((~wise(X)|humble(X))<=>(brave(X)|~kind(X))))&
(((calm(john)<~>old(john)))=>(?[X]:((~quiet(X)|~tall(X)))))&
(?[X]:(patient(X)))&
(?[X]:((~happy(X)|humble(X))))&
(~kind(paul))&
(?[X]:(brave(X))) | ~strong(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1072865270172442235238022
% SZS output start Proof for 1072865270172442235238022
1. ! [X0] : ((kind(X0) & strong(X0)) <=> ~strong(X0)) [input p0]
20. ~strong(mary) [input hypothesis]
29. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | ~strong(X0)))) [nnf transformation 1]
30. ! [X0] : (((kind(X0) & strong(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | ~strong(X0))) [flattening 29]
65. strong(X0) | strong(X0) [cnf transformation 30]
124. ~strong(mary) [cnf transformation 20]
128. strong(X0) [duplicate literal removal 65]
249. $false [subsumption resolution 124,128]
% SZS output end Proof for 1072865270172442235238022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave or tall then someone is either rich or kind. If someone is either not calm or not quiet then fred is either humble or not kind and vice versa. If someone is humble or generous then someone is both not tall and wise. Everyone who is either not generous or not happy is both not curious and humble. Everyone who is not happy or not kind is not curious or curious and vice versa. Everyone who is either curious or not funny is both not old and rich. Everyone who is rich is happy or wise and vice versa. Everyone who is not calm or not curious is both not generous and old and vice versa. If fred is humble then someone is not generous or calm. If someone is both not strong and not old then someone is happy. If someone is both wise and happy then john is either humble or creative. If someone is both not curious and not wise then paul is either happy or not old. Everyone who is either not kind or old is both not brave and not tall and vice versa. Everyone who is not tall is both patient and not creative. If lucy is not humble then john is either not rich or wise and vice versa. If someone is not creative then fred is either patient or old and vice versa. Someone is curious. Someone is patient. Someone is not wise or not happy. Susan is humble. Fred is either not strong or not wise. John is not strong. Someone is not patient or happy. Paul is both not patient and brave. | Paul is not tall. | contradiction | ((?[X]:((brave(X)|tall(X))))=>(?[X]:((rich(X)<~>kind(X)))))&
((?[X]:((~calm(X)<~>~quiet(X))))<=>((humble(fred)<~>~kind(fred))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((~generous(X)<~>~happy(X))=>(~curious(X)&humble(X))))&
(![X]:((~happy(X)|~kind(X))<=>(~curious(X)|curious(X))))&
(![X]:((curious(X)<~>~funny(X))=>(~old(X)&rich(X))))&
(![X]:(rich(X)<=>(happy(X)|wise(X))))&
(![X]:((~calm(X)|~curious(X))<=>(~generous(X)&old(X))))&
((humble(fred))=>(?[X]:((~generous(X)|calm(X)))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:(happy(X))))&
((?[X]:((wise(X)&happy(X))))=>((humble(john)<~>creative(john))))&
((?[X]:((~curious(X)&~wise(X))))=>((happy(paul)<~>~old(paul))))&
(![X]:((~kind(X)<~>old(X))<=>(~brave(X)&~tall(X))))&
(![X]:(~tall(X)=>(patient(X)&~creative(X))))&
((~humble(lucy))<=>((~rich(john)<~>wise(john))))&
((?[X]:(~creative(X)))<=>((patient(fred)<~>old(fred))))&
(?[X]:(curious(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|~happy(X))))&
(humble(susan))&
((~strong(fred)<~>~wise(fred)))&
(~strong(john))&
(?[X]:((~patient(X)|happy(X))))&
((~patient(paul)&brave(paul))) | ~tall(paul) | [
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 538469143603020656775696
% SZS output start Proof for 538469143603020656775696
14. ! [X0] : (~tall(X0) => (~creative(X0) & patient(X0))) [input p13]
24. brave(paul) & ~patient(paul) [input p23]
25. ~tall(paul) [input hypothesis]
37. ! [X0] : ((~creative(X0) & patient(X0)) | tall(X0)) [ennf transformation 14]
128. patient(X0) | tall(X0) [cnf transformation 37]
146. ~patient(paul) [cnf transformation 24]
148. ~tall(paul) [cnf transformation 25]
317. tall(paul) [resolution 128,146]
320. $false [subsumption resolution 317,148]
% SZS output end Proof for 538469143603020656775696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either quiet or not curious. If someone is old or kind then someone is funny and vice versa. If someone is brave or generous then someone is either not patient or kind. Everyone who is strong or patient is calm. Everyone who is either humble or wise is not calm. If mary is either quiet or not calm then someone is both not generous and brave and vice versa. Everyone who is both not funny and old is either wise or rich. If lucy is curious or not generous then paul is either tall or not kind. Everyone who is rich or not rich is both wise and curious and vice versa. Everyone who is either kind or not curious is both quiet and not quiet. Everyone who is both funny and happy is either creative or funny. Everyone who is either not curious or not generous is strong and vice versa. Everyone who is creative is funny or not curious. Everyone who is either strong or not strong is funny and vice versa. Everyone who is not generous or tall is strong. Someone is either not happy or brave. John is both brave and patient. Someone is either calm or rich. Someone is funny or not funny. Alice is either not brave or curious. Lucy is not kind or wise. Someone is both humble and brave. | Paul is rich. | neutral | (![X]:(~happy(X)=>(quiet(X)<~>~curious(X))))&
((?[X]:((old(X)|kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)|patient(X))=>calm(X)))&
(![X]:((humble(X)<~>wise(X))=>~calm(X)))&
(((quiet(mary)<~>~calm(mary)))<=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((~funny(X)&old(X))=>(wise(X)<~>rich(X))))&
(((curious(lucy)|~generous(lucy)))=>((tall(paul)<~>~kind(paul))))&
(![X]:((rich(X)|~rich(X))<=>(wise(X)&curious(X))))&
(![X]:((kind(X)<~>~curious(X))=>(quiet(X)&~quiet(X))))&
(![X]:((funny(X)&happy(X))=>(creative(X)<~>funny(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>strong(X)))&
(![X]:(creative(X)=>(funny(X)|~curious(X))))&
(![X]:((strong(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~generous(X)|tall(X))=>strong(X)))&
(?[X]:((~happy(X)<~>brave(X))))&
((brave(john)&patient(john)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((funny(X)|~funny(X))))&
((~brave(alice)<~>curious(alice)))&
((~kind(lucy)|wise(lucy)))&
(?[X]:((humble(X)&brave(X)))) | rich(paul) | [] | null | 0 |
Everyone who is rich or generous is quiet or not tall. Everyone who is either happy or kind is either not quiet or not happy and vice versa. If alice is not generous then someone is either old or not happy. Everyone who is either brave or not generous is either not curious or rich. Everyone who is both strong and brave is brave and vice versa. If someone is either not wise or strong then someone is not calm and vice versa. If susan is either not old or kind then paul is either not calm or rich and vice versa. Everyone who is kind or old is humble or quiet and vice versa. If someone is either not generous or funny then someone is strong or not creative and vice versa. Everyone who is old or not kind is either not rich or not generous and vice versa. If fred is not rich then someone is both humble and not strong and vice versa. If susan is not quiet then someone is kind or not funny and vice versa. If someone is either tall or generous then mary is both tall and brave. Everyone who is calm or not humble is either tall or not humble. Everyone who is not kind is not wise. Everyone who is not brave or not generous is both patient and strong. Someone is either tall or not wise. Someone is kind or not humble. Someone is creative or funny. Lucy is not tall. Someone is brave or not humble. Someone is tall. Paul is brave or tall. | Alice is not rich. | neutral | (![X]:((rich(X)|generous(X))=>(quiet(X)|~tall(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~quiet(X)<~>~happy(X))))&
((~generous(alice))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)<~>rich(X))))&
(![X]:((strong(X)&brave(X))<=>brave(X)))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
(((~old(susan)<~>kind(susan)))<=>((~calm(paul)<~>rich(paul))))&
(![X]:((kind(X)|old(X))<=>(humble(X)|quiet(X))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((old(X)|~kind(X))<=>(~rich(X)<~>~generous(X))))&
((~rich(fred))<=>(?[X]:((humble(X)&~strong(X)))))&
((~quiet(susan))<=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((tall(mary)&brave(mary))))&
(![X]:((calm(X)|~humble(X))=>(tall(X)<~>~humble(X))))&
(![X]:(~kind(X)=>~wise(X)))&
(![X]:((~brave(X)|~generous(X))=>(patient(X)&strong(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:((creative(X)|funny(X))))&
(~tall(lucy))&
(?[X]:((brave(X)|~humble(X))))&
(?[X]:(tall(X)))&
((brave(paul)|tall(paul))) | ~rich(alice) | [] | null | 0 |
If someone is both tall and not brave then someone is not tall and vice versa.
If someone is either creative or not curious then someone is either not creative or wise.
Everyone who is both not kind and generous is rich.
Everyone who is either creative or not calm is both not kind and not wise and vice versa.
If someone is patient then someone is both not tall and patient.
Everyone who is funny is both happy and creative.
Everyone who is both not calm and not quiet is either funny or calm.
Everyone who is not patient is not rich and vice versa.
If someone is rich then someone is both not quiet and generous and vice versa.
If lucy is both creative and not funny then paul is creative or calm.
If someone is either not calm or not humble then someone is not wise or not quiet and vice versa.
If someone is not humble then fred is both not tall and not strong.
If someone is funny then fred is either wise or brave.
Everyone who is both tall and not kind is not wise and vice versa.
Everyone who is quiet or not calm is either not kind or kind and vice versa.
Everyone who is both humble and not humble is generous.
Paul is not brave or not funny.
Someone is both brave and kind.
Someone is brave.
Someone is both not patient and creative.
Someone is funny or creative.
Someone is not tall or curious.
Mary is both creative and quiet.
Susan is not quiet or not creative. | Mary is happy. | neutral | ((?[X]:((tall(X)&~brave(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((creative(X)<~>~curious(X))))=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((~kind(X)&generous(X))=>rich(X)))&
(![X]:((creative(X)<~>~calm(X))<=>(~kind(X)&~wise(X))))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:(funny(X)=>(happy(X)&creative(X))))&
(![X]:((~calm(X)&~quiet(X))=>(funny(X)<~>calm(X))))&
(![X]:(~patient(X)<=>~rich(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(((creative(lucy)&~funny(lucy)))=>((creative(paul)|calm(paul))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
((?[X]:(~humble(X)))=>((~tall(fred)&~strong(fred))))&
((?[X]:(funny(X)))=>((wise(fred)<~>brave(fred))))&
(![X]:((tall(X)&~kind(X))<=>~wise(X)))&
(![X]:((quiet(X)|~calm(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((humble(X)&~humble(X))=>generous(X)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((~tall(X)|curious(X))))&
((creative(mary)&quiet(mary)))&
((~quiet(susan)|~creative(susan))) | happy(mary) | [] | null | 0 |
Everyone who is both not humble and quiet is either not humble or quiet and vice versa.
If someone is either humble or not happy then someone is old and vice versa.
If someone is both strong and not patient then paul is rich or not wise.
If someone is not happy then someone is happy or calm and vice versa.
Everyone who is either funny or calm is either not funny or wise and vice versa.
If someone is both patient and rich then someone is not tall.
If fred is either tall or not tall then someone is not quiet and vice versa.
Everyone who is generous or funny is both not calm and not strong and vice versa.
If fred is not calm then someone is calm or creative.
If someone is not happy or humble then someone is tall or not quiet.
If paul is both not calm and not rich then lucy is not patient and vice versa.
Everyone who is not calm is either not patient or not wise and vice versa.
Everyone who is either happy or patient is either not quiet or not kind.
Everyone who is either calm or strong is not quiet or patient.
If someone is happy then someone is not patient or strong.
Paul is patient or humble.
Someone is strong or not funny.
Fred is rich or not rich. | Paul is patient. | contradiction | (![X]:((~humble(X)&quiet(X))<=>(~humble(X)<~>quiet(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:(old(X))))&
((?[X]:((strong(X)&~patient(X))))=>((rich(paul)|~wise(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((funny(X)<~>calm(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:(~tall(X))))&
(((tall(fred)<~>~tall(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(~calm(X)&~strong(X))))&
((~calm(fred))=>(?[X]:((calm(X)|creative(X)))))&
((?[X]:((~happy(X)|humble(X))))=>(?[X]:((tall(X)|~quiet(X)))))&
(((~calm(paul)&~rich(paul)))<=>(~patient(lucy)))&
(![X]:(~calm(X)<=>(~patient(X)<~>~wise(X))))&
(![X]:((happy(X)<~>patient(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:((calm(X)<~>strong(X))=>(~quiet(X)|patient(X))))&
((?[X]:(happy(X)))=>(?[X]:((~patient(X)|strong(X)))))&
((patient(paul)|humble(paul)))&
(?[X]:((strong(X)|~funny(X))))&
((rich(fred)|~rich(fred))) | patient(paul) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6964475471900760462418946
% SZS output start Proof for 6964475471900760462418946
5. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~funny(X0) <~> wise(X0))) [input p4]
12. ! [X0] : (~calm(X0) <=> (~patient(X0) <~> ~wise(X0))) [input p11]
19. patient(paul) [input hypothesis]
46. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0)))) & (((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 5]
61. ! [X0] : ((~calm(X0) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) & (((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | calm(X0))) [nnf transformation 12]
83. wise(X0) | ~funny(X0) | calm(X0) | ~funny(X0) [cnf transformation 46]
86. ~wise(X0) | funny(X0) | funny(X0) | ~calm(X0) [cnf transformation 46]
87. calm(X0) | funny(X0) | wise(X0) | funny(X0) [cnf transformation 46]
90. ~calm(X0) | ~funny(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 46]
106. ~wise(X0) | ~patient(X0) | calm(X0) [cnf transformation 61]
109. ~calm(X0) | ~patient(X0) | wise(X0) [cnf transformation 61]
120. patient(paul) [cnf transformation 19]
123. wise(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 83]
124. ~wise(X0) | funny(X0) | ~calm(X0) [duplicate literal removal 86]
125. calm(X0) | funny(X0) | wise(X0) [duplicate literal removal 87]
126. ~calm(X0) | ~funny(X0) | ~wise(X0) [duplicate literal removal 90]
192. ~wise(X0) | ~calm(X0) [subsumption resolution 124,126]
193. wise(X0) | calm(X0) [subsumption resolution 123,125]
213. ~patient(X0) | wise(X0) [subsumption resolution 109,193]
214. ~wise(X0) | ~patient(X0) [subsumption resolution 106,192]
215. ~patient(X0) [subsumption resolution 214,213]
220. $false [subsumption resolution 120,215]
% SZS output end Proof for 6964475471900760462418946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not humble then someone is both not quiet and kind and vice versa. If paul is either not strong or not wise then fred is either not creative or old and vice versa. Everyone who is not generous or not happy is either not humble or kind. Everyone who is either happy or not creative is not quiet and vice versa. Everyone who is either kind or not wise is both not curious and not funny. Everyone who is generous or not curious is either not creative or not funny and vice versa. If someone is not patient or patient then someone is either not curious or tall and vice versa. If someone is both happy and generous then paul is both not patient and not tall and vice versa. If someone is either strong or not wise then someone is not creative or not calm. Everyone who is humble is both not wise and not brave. Everyone who is wise is either rich or not happy. Everyone who is calm is either not tall or happy and vice versa. Everyone who is quiet or calm is both not rich and quiet and vice versa. Everyone who is either not creative or not wise is not patient and vice versa. Everyone who is either not creative or not brave is either not humble or not old. Susan is not wise. Someone is not generous or funny. Someone is kind or generous. Fred is either not humble or happy. Someone is not patient or not wise. Fred is either not humble or not quiet. Someone is curious or not funny. Paul is both tall and humble. | Paul is not strong. | neutral | ((?[X]:((~kind(X)|~humble(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
(((~strong(paul)<~>~wise(paul)))<=>((~creative(fred)<~>old(fred))))&
(![X]:((~generous(X)|~happy(X))=>(~humble(X)<~>kind(X))))&
(![X]:((happy(X)<~>~creative(X))<=>~quiet(X)))&
(![X]:((kind(X)<~>~wise(X))=>(~curious(X)&~funny(X))))&
(![X]:((generous(X)|~curious(X))<=>(~creative(X)<~>~funny(X))))&
((?[X]:((~patient(X)|patient(X))))<=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:((happy(X)&generous(X))))<=>((~patient(paul)&~tall(paul))))&
((?[X]:((strong(X)<~>~wise(X))))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:(humble(X)=>(~wise(X)&~brave(X))))&
(![X]:(wise(X)=>(rich(X)<~>~happy(X))))&
(![X]:(calm(X)<=>(~tall(X)<~>happy(X))))&
(![X]:((quiet(X)|calm(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>~patient(X)))&
(![X]:((~creative(X)<~>~brave(X))=>(~humble(X)<~>~old(X))))&
(~wise(susan))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((kind(X)|generous(X))))&
((~humble(fred)<~>happy(fred)))&
(?[X]:((~patient(X)|~wise(X))))&
((~humble(fred)<~>~quiet(fred)))&
(?[X]:((curious(X)|~funny(X))))&
((tall(paul)&humble(paul))) | ~strong(paul) | [] | null | 0 |
If someone is calm then alice is both creative and tall and vice versa. Everyone who is both not patient and funny is either brave or funny. Everyone who is either tall or not generous is not calm or not happy. Everyone who is either not humble or strong is rich. Everyone who is quiet or not patient is creative. If john is not patient then someone is both wise and not kind and vice versa. If fred is not humble then someone is curious. If alice is not patient then fred is either not strong or not quiet and vice versa. Everyone who is strong or not rich is both creative and not patient. Everyone who is both not happy and quiet is either not old or not happy and vice versa. Everyone who is both funny and not creative is not quiet or not wise and vice versa. If someone is quiet or not wise then someone is both not old and not rich and vice versa. Everyone who is either strong or old is not kind or humble. Everyone who is quiet is old or not funny and vice versa. If someone is either not curious or kind then paul is both not calm and not creative and vice versa. Mary is not calm or not funny. Fred is either not old or humble. Someone is not happy. Someone is not creative or not patient. Fred is patient. | John is not happy. | entailment | ((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
((~calm(mary)|~funny(mary)))&
((~old(fred)<~>humble(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)|~patient(X))))&
(patient(fred)) | ~happy(john) | [
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4156446111287752915612320
% SZS output start Proof for 4156446111287752915612320
9. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p9]
11. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p10]
12. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p11]
14. ! [X0] : (quiet(X0) <=> (~funny(X0) | old(X0))) [input p13]
21. happy(john) [input hypothesis]
22. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 12]
30. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 9]
48. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 10]
49. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 48]
50. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 11]
51. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 50]
52. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 22]
53. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 52]
54. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK3) | quiet(sK3)) [choice axiom]
55. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK4) & ~old(sK4)) [choice axiom]
56. ((~wise(sK3) | quiet(sK3)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK4) & ~old(sK4)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 53,55,54]
58. ! [X0] : ((quiet(X0) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ~quiet(X0))) [nnf transformation 14]
59. ! [X0] : ((quiet(X0) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ~quiet(X0))) [flattening 58]
90. rich(X0) | creative(X0) [cnf transformation 30]
94. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 49]
95. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 49]
102. ~creative(X0) | quiet(X0) [cnf transformation 51]
104. ~old(sK4) | ~quiet(X3) [cnf transformation 56]
106. ~rich(sK4) | ~quiet(X3) [cnf transformation 56]
112. ~old(X0) | quiet(X0) [cnf transformation 59]
126. happy(john) [cnf transformation 21]
127. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 94]
128. ~happy(X0) | old(X0) [duplicate literal removal 95]
191. ~quiet(X0) | old(X0) [subsumption resolution 127,128]
208. 18 <=> rich(sK4) [avatar definition]
210. ~rich(sK4) <- (~18) [avatar component clause 208]
213. 19 <=> ! [X3] : ~quiet(X3) [avatar definition]
214. ~quiet(X3) <- (19) [avatar component clause 213]
215. 19 | ~18 [avatar split clause 106,208,213]
217. 20 <=> old(sK4) [avatar definition]
219. ~old(sK4) <- (~20) [avatar component clause 217]
221. 19 | ~20 [avatar split clause 104,217,213]
278. creative(sK4) <- (~18) [resolution 90,210]
286. quiet(sK4) <- (~18) [resolution 102,278]
288. old(john) [resolution 128,126]
289. quiet(john) [resolution 288,112]
293. old(sK4) <- (~18) [resolution 191,286]
294. $false <- (~18, ~20) [subsumption resolution 293,219]
295. 18 | 20 [avatar contradiction clause 294]
318. $false <- (19) [resolution 289,214]
321. ~19 [avatar contradiction clause 318]
322. $false [avatar sat refutation 215,221,295,321]
% SZS output end Proof for 4156446111287752915612320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then alice is either wise or not generous and vice versa.
If fred is calm then someone is not kind.
Everyone who is generous is both not brave and not rich and vice versa.
If john is not rich then lucy is both not generous and creative and vice versa.
Everyone who is calm or not quiet is not old or wise and vice versa.
Everyone who is either not happy or rich is either not old or not generous and vice versa.
If alice is either tall or not funny then someone is humble.
Everyone who is either not patient or brave is both not brave and quiet.
If someone is either not tall or funny then someone is either not old or patient and vice versa.
Everyone who is not kind is both patient and creative and vice versa.
If someone is generous or not patient then susan is not happy or not tall.
Everyone who is both not creative and not generous is patient and vice versa.
If paul is old then paul is both not kind and not calm.
Everyone who is either not happy or kind is strong or not generous and vice versa.
If someone is either not wise or not kind then fred is either old or not quiet.
If mary is not happy or not funny then someone is brave or not rich and vice versa.
Fred is not brave.
Someone is both not brave and tall.
Someone is either kind or wise.
Lucy is old.
Fred is funny or old.
Someone is both calm and not rich.
Alice is quiet or not rich.
Lucy is not curious or not tall. | Lucy is happy. | entailment | ((?[X]:(happy(X)))<=>((wise(alice)<~>~generous(alice))))&
((calm(fred))=>(?[X]:(~kind(X))))&
(![X]:(generous(X)<=>(~brave(X)&~rich(X))))&
((~rich(john))<=>((~generous(lucy)&creative(lucy))))&
(![X]:((calm(X)|~quiet(X))<=>(~old(X)|wise(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~old(X)<~>~generous(X))))&
(((tall(alice)<~>~funny(alice)))=>(?[X]:(humble(X))))&
(![X]:((~patient(X)<~>brave(X))=>(~brave(X)&quiet(X))))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:(~kind(X)<=>(patient(X)&creative(X))))&
((?[X]:((generous(X)|~patient(X))))=>((~happy(susan)|~tall(susan))))&
(![X]:((~creative(X)&~generous(X))<=>patient(X)))&
((old(paul))=>((~kind(paul)&~calm(paul))))&
(![X]:((~happy(X)<~>kind(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~wise(X)<~>~kind(X))))=>((old(fred)<~>~quiet(fred))))&
(((~happy(mary)|~funny(mary)))<=>(?[X]:((brave(X)|~rich(X)))))&
(~brave(fred))&
(?[X]:((~brave(X)&tall(X))))&
(?[X]:((kind(X)<~>wise(X))))&
(old(lucy))&
((funny(fred)|old(fred)))&
(?[X]:((calm(X)&~rich(X))))&
((quiet(alice)|~rich(alice)))&
((~curious(lucy)|~tall(lucy))) | happy(lucy) | [
"p2",
"p5",
"p9",
"p11",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8148968973482234842158977
% SZS output start Proof for 8148968973482234842158977
3. ! [X0] : (generous(X0) <=> (~rich(X0) & ~brave(X0))) [input p2]
6. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (~old(X0) <~> ~generous(X0))) [input p5]
10. ! [X0] : (~kind(X0) <=> (creative(X0) & patient(X0))) [input p9]
12. ! [X0] : ((~generous(X0) & ~creative(X0)) <=> patient(X0)) [input p11]
14. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> (~generous(X0) | strong(X0))) [input p13]
20. old(lucy) [input p19]
25. ~happy(lucy) [input hypothesis]
41. ! [X0] : ((generous(X0) | (rich(X0) | brave(X0))) & ((~rich(X0) & ~brave(X0)) | ~generous(X0))) [nnf transformation 3]
42. ! [X0] : ((generous(X0) | rich(X0) | brave(X0)) & ((~rich(X0) & ~brave(X0)) | ~generous(X0))) [flattening 41]
47. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0)))) & (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 6]
54. ! [X0] : ((~kind(X0) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | kind(X0))) [nnf transformation 10]
55. ! [X0] : ((~kind(X0) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | kind(X0))) [flattening 54]
56. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | (generous(X0) | creative(X0)))) [nnf transformation 12]
57. ! [X0] : (((~generous(X0) & ~creative(X0)) | ~patient(X0)) & (patient(X0) | generous(X0) | creative(X0))) [flattening 56]
58. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [flattening 58]
79. ~rich(X0) | ~generous(X0) [cnf transformation 42]
88. ~generous(X0) | ~old(X0) | rich(X0) | happy(X0) [cnf transformation 47]
95. ~rich(X0) | happy(X0) | ~old(X0) | generous(X0) [cnf transformation 47]
108. patient(X0) | kind(X0) [cnf transformation 55]
109. creative(X0) | kind(X0) [cnf transformation 55]
114. ~patient(X0) | ~creative(X0) [cnf transformation 57]
123. ~kind(X0) | happy(X0) | generous(X0) [cnf transformation 59]
137. old(lucy) [cnf transformation 20]
142. ~happy(lucy) [cnf transformation 25]
173. 7 <=> generous(lucy) [avatar definition]
174. ~generous(lucy) <- (~7) [avatar component clause 173]
187. ~old(X0) | happy(X0) | ~rich(X0) [subsumption resolution 95,79]
190. ~old(X0) | ~generous(X0) | happy(X0) [subsumption resolution 88,187]
326. ~creative(X0) | kind(X0) [resolution 114,108]
327. kind(X0) [subsumption resolution 326,109]
454. generous(X0) | happy(X0) [resolution 123,327]
493. ~generous(lucy) | happy(lucy) [resolution 190,137]
500. ~generous(lucy) [subsumption resolution 493,142]
501. ~7 [avatar split clause 500,173]
618. happy(lucy) <- (~7) [resolution 454,174]
625. $false <- (~7) [subsumption resolution 618,142]
626. 7 [avatar contradiction clause 625]
627. $false [avatar sat refutation 501,626]
% SZS output end Proof for 8148968973482234842158977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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