premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is both creative and brave is both not strong and calm.
If paul is quiet or not old then someone is both tall and calm and vice versa.
If someone is not creative then someone is either generous or tall and vice versa.
Everyone who is creative or not wise is both not kind and not brave and vice versa.
If someone is not calm or quiet then someone is either curious or brave.
Everyone who is generous is old and vice versa.
Everyone who is not creative is either not creative or not funny.
Everyone who is not brave is either not brave or not old and vice versa.
Everyone who is both quiet and creative is both humble and kind.
Everyone who is not creative or funny is both calm and not kind.
Everyone who is either not creative or tall is kind and vice versa.
If someone is both not rich and not generous then someone is not strong and vice versa.
Everyone who is funny or not brave is either brave or strong.
Everyone who is either not generous or funny is either kind or not happy.
Everyone who is funny or not brave is not quiet or curious.
Someone is either not patient or not old.
Someone is not funny.
Someone is either kind or not happy.
Lucy is brave or funny. | Paul is humble. | neutral | (![X]:((creative(X)&brave(X))=>(~strong(X)&calm(X))))&
(((quiet(paul)|~old(paul)))<=>(?[X]:((tall(X)&calm(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((creative(X)|~wise(X))<=>(~kind(X)&~brave(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~creative(X)=>(~creative(X)<~>~funny(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~old(X))))&
(![X]:((quiet(X)&creative(X))=>(humble(X)&kind(X))))&
(![X]:((~creative(X)|funny(X))=>(calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>tall(X))<=>kind(X)))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(![X]:((~generous(X)<~>funny(X))=>(kind(X)<~>~happy(X))))&
(![X]:((funny(X)|~brave(X))=>(~quiet(X)|curious(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
((brave(lucy)|funny(lucy))) | humble(paul) | [] | null | 0 |
Everyone who is either old or not brave is brave and vice versa. Everyone who is both not strong and not old is both not kind and not funny. Everyone who is kind or wise is either not brave or humble. If someone is not patient or not brave then mary is either not tall or not curious and vice versa. If someone is not brave then someone is funny or not happy. If mary is not creative or not tall then susan is not creative. Everyone who is not curious is either not funny or strong. Everyone who is both old and not tall is either not creative or strong and vice versa. Everyone who is patient is either not creative or not patient and vice versa. If lucy is either generous or not generous then paul is not strong and vice versa. If someone is kind then someone is not kind. Everyone who is both not brave and generous is either not calm or humble. If john is both not kind and old then susan is happy and vice versa. Everyone who is both not creative and strong is both not rich and not old. Everyone who is old or brave is not brave. Everyone who is both funny and not wise is not happy or not kind and vice versa. Paul is not kind or quiet. Someone is not tall. Someone is either not rich or not patient. Alice is both quiet and wise. Someone is both not funny and generous. Someone is both not quiet and not calm. Someone is not funny or not wise. Paul is both generous and not funny. | Lucy is brave. | contradiction | (![X]:((old(X)<~>~brave(X))<=>brave(X)))&
(![X]:((~strong(X)&~old(X))=>(~kind(X)&~funny(X))))&
(![X]:((kind(X)|wise(X))=>(~brave(X)<~>humble(X))))&
((?[X]:((~patient(X)|~brave(X))))<=>((~tall(mary)<~>~curious(mary))))&
((?[X]:(~brave(X)))=>(?[X]:((funny(X)|~happy(X)))))&
(((~creative(mary)|~tall(mary)))=>(~creative(susan)))&
(![X]:(~curious(X)=>(~funny(X)<~>strong(X))))&
(![X]:((old(X)&~tall(X))<=>(~creative(X)<~>strong(X))))&
(![X]:(patient(X)<=>(~creative(X)<~>~patient(X))))&
(((generous(lucy)<~>~generous(lucy)))<=>(~strong(paul)))&
((?[X]:(kind(X)))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)&generous(X))=>(~calm(X)<~>humble(X))))&
(((~kind(john)&old(john)))<=>(happy(susan)))&
(![X]:((~creative(X)&strong(X))=>(~rich(X)&~old(X))))&
(![X]:((old(X)|brave(X))=>~brave(X)))&
(![X]:((funny(X)&~wise(X))<=>(~happy(X)|~kind(X))))&
((~kind(paul)|quiet(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((~rich(X)<~>~patient(X))))&
((quiet(alice)&wise(alice)))&
(?[X]:((~funny(X)&generous(X))))&
(?[X]:((~quiet(X)&~calm(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((generous(paul)&~funny(paul))) | brave(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1752895476555338383689622
% SZS output start Proof for 1752895476555338383689622
15. ! [X0] : ((brave(X0) | old(X0)) => ~brave(X0)) [input p14]
25. brave(lucy) [input hypothesis]
39. ! [X0] : (~brave(X0) | (~brave(X0) & ~old(X0))) [ennf transformation 15]
117. ~brave(X0) | ~brave(X0) [cnf transformation 39]
136. brave(lucy) [cnf transformation 25]
137. ~brave(X0) [duplicate literal removal 117]
254. $false [subsumption resolution 136,137]
% SZS output end Proof for 1752895476555338383689622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or old is not kind or tall and vice versa.
If someone is quiet or wise then someone is not quiet and vice versa.
If someone is both happy and not tall then lucy is calm.
If someone is either funny or not humble then someone is creative or tall.
Everyone who is humble or curious is both patient and wise and vice versa.
Everyone who is either generous or not wise is either strong or funny and vice versa.
Everyone who is either not brave or not tall is not brave.
If john is either humble or quiet then susan is rich or not old.
Everyone who is not brave or not humble is tall or happy.
Everyone who is brave is either brave or not rich.
If john is generous then lucy is not quiet.
Everyone who is either quiet or not quiet is both not old and rich and vice versa.
Everyone who is not curious is both not funny and not brave.
Everyone who is not wise is both tall and wise and vice versa.
Everyone who is not wise is either creative or not funny.
If someone is both not wise and not patient then someone is wise or kind.
Someone is curious.
Someone is curious or not generous.
Fred is either not generous or not curious.
Someone is either strong or wise.
Someone is both not old and calm.
Someone is patient.
Alice is not rich or not tall. | Fred is wise. | entailment | (![X]:((~brave(X)<~>old(X))<=>(~kind(X)|tall(X))))&
((?[X]:((quiet(X)|wise(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((happy(X)&~tall(X))))=>(calm(lucy)))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((humble(X)|curious(X))<=>(patient(X)&wise(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(strong(X)<~>funny(X))))&
(![X]:((~brave(X)<~>~tall(X))=>~brave(X)))&
(((humble(john)<~>quiet(john)))=>((rich(susan)|~old(susan))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)|happy(X))))&
(![X]:(brave(X)=>(brave(X)<~>~rich(X))))&
((generous(john))=>(~quiet(lucy)))&
(![X]:((quiet(X)<~>~quiet(X))<=>(~old(X)&rich(X))))&
(![X]:(~curious(X)=>(~funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(tall(X)&wise(X))))&
(![X]:(~wise(X)=>(creative(X)<~>~funny(X))))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((wise(X)|kind(X)))))&
(?[X]:(curious(X)))&
(?[X]:((curious(X)|~generous(X))))&
((~generous(fred)<~>~curious(fred)))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~old(X)&calm(X))))&
(?[X]:(patient(X)))&
((~rich(alice)|~tall(alice))) | wise(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8152047349685111051531343
% SZS output start Proof for 8152047349685111051531343
14. ! [X0] : (~wise(X0) <=> (wise(X0) & tall(X0))) [input p13]
24. ~wise(fred) [input hypothesis]
59. ! [X0] : ((~wise(X0) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | wise(X0))) [nnf transformation 14]
60. ! [X0] : ((~wise(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | wise(X0))) [flattening 59]
117. wise(X0) | wise(X0) [cnf transformation 60]
131. ~wise(fred) [cnf transformation 24]
132. wise(X0) [duplicate literal removal 117]
230. $false [subsumption resolution 131,132]
% SZS output end Proof for 8152047349685111051531343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not brave is old and vice versa.
Everyone who is both not brave and patient is either not patient or not calm.
If fred is not patient then john is both funny and old.
If someone is either quiet or happy then alice is not strong and vice versa.
If lucy is both not strong and old then someone is both not generous and not kind.
If john is either not calm or creative then someone is either not curious or strong and vice versa.
Everyone who is either funny or not strong is either brave or funny.
If fred is either not brave or creative then someone is generous and vice versa.
Everyone who is either not patient or not kind is not creative or strong and vice versa.
If someone is either curious or happy then alice is strong or not wise and vice versa.
If someone is either not old or brave then mary is not curious.
Everyone who is not patient is both not tall and not brave.
Everyone who is either calm or old is both quiet and not wise.
Everyone who is either not tall or tall is calm and vice versa.
If someone is both quiet and kind then paul is not generous and vice versa.
Everyone who is brave is both wise and happy and vice versa.
Someone is both not generous and strong.
Susan is not happy.
Alice is generous.
Someone is either creative or not creative.
Lucy is rich.
Alice is both old and not kind.
Alice is either strong or not quiet. | Paul is not kind. | neutral | (![X]:((~wise(X)&~brave(X))<=>old(X)))&
(![X]:((~brave(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
((~patient(fred))=>((funny(john)&old(john))))&
((?[X]:((quiet(X)<~>happy(X))))<=>(~strong(alice)))&
(((~strong(lucy)&old(lucy)))=>(?[X]:((~generous(X)&~kind(X)))))&
(((~calm(john)<~>creative(john)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((funny(X)<~>~strong(X))=>(brave(X)<~>funny(X))))&
(((~brave(fred)<~>creative(fred)))<=>(?[X]:(generous(X))))&
(![X]:((~patient(X)<~>~kind(X))<=>(~creative(X)|strong(X))))&
((?[X]:((curious(X)<~>happy(X))))<=>((strong(alice)|~wise(alice))))&
((?[X]:((~old(X)<~>brave(X))))=>(~curious(mary)))&
(![X]:(~patient(X)=>(~tall(X)&~brave(X))))&
(![X]:((calm(X)<~>old(X))=>(quiet(X)&~wise(X))))&
(![X]:((~tall(X)<~>tall(X))<=>calm(X)))&
((?[X]:((quiet(X)&kind(X))))<=>(~generous(paul)))&
(![X]:(brave(X)<=>(wise(X)&happy(X))))&
(?[X]:((~generous(X)&strong(X))))&
(~happy(susan))&
(generous(alice))&
(?[X]:((creative(X)<~>~creative(X))))&
(rich(lucy))&
((old(alice)&~kind(alice)))&
((strong(alice)<~>~quiet(alice))) | ~kind(paul) | [] | null | 0 |
If someone is both old and brave then someone is both funny and not humble. If someone is both not patient and not creative then paul is kind or creative and vice versa. If someone is either happy or not wise then alice is either not quiet or not creative. If someone is not creative then mary is not happy. Everyone who is both calm and strong is both not humble and not strong. Everyone who is either not strong or patient is humble or tall and vice versa. If fred is not kind then lucy is not happy or not brave and vice versa. If paul is either not quiet or calm then alice is both not quiet and not patient. If mary is calm then paul is either humble or not old and vice versa. Everyone who is both happy and not funny is calm or not curious. Everyone who is either not creative or kind is funny or old and vice versa. If someone is rich or kind then mary is not tall. Everyone who is both not generous and not happy is either kind or not rich and vice versa. If someone is creative or kind then someone is tall or quiet and vice versa. Everyone who is not funny is not curious. Someone is not generous. Lucy is either not funny or happy. Someone is not strong. Alice is both calm and not wise. Someone is not old. Someone is not happy. John is both happy and wise. Alice is either not kind or old. | Lucy is funny. | neutral | ((?[X]:((old(X)&brave(X))))=>(?[X]:((funny(X)&~humble(X)))))&
((?[X]:((~patient(X)&~creative(X))))<=>((kind(paul)|creative(paul))))&
((?[X]:((happy(X)<~>~wise(X))))=>((~quiet(alice)<~>~creative(alice))))&
((?[X]:(~creative(X)))=>(~happy(mary)))&
(![X]:((calm(X)&strong(X))=>(~humble(X)&~strong(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|tall(X))))&
((~kind(fred))<=>((~happy(lucy)|~brave(lucy))))&
(((~quiet(paul)<~>calm(paul)))=>((~quiet(alice)&~patient(alice))))&
((calm(mary))<=>((humble(paul)<~>~old(paul))))&
(![X]:((happy(X)&~funny(X))=>(calm(X)|~curious(X))))&
(![X]:((~creative(X)<~>kind(X))<=>(funny(X)|old(X))))&
((?[X]:((rich(X)|kind(X))))=>(~tall(mary)))&
(![X]:((~generous(X)&~happy(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:(~funny(X)=>~curious(X)))&
(?[X]:(~generous(X)))&
((~funny(lucy)<~>happy(lucy)))&
(?[X]:(~strong(X)))&
((calm(alice)&~wise(alice)))&
(?[X]:(~old(X)))&
(?[X]:(~happy(X)))&
((happy(john)&wise(john)))&
((~kind(alice)<~>old(alice))) | funny(lucy) | [] | null | 0 |
Everyone who is rich is either not quiet or quiet and vice versa. If someone is brave or tall then someone is either quiet or calm. Everyone who is either not funny or not rich is not creative and vice versa. If someone is either rich or not calm then someone is either not brave or not humble and vice versa. If someone is either happy or not funny then someone is happy or not kind. Everyone who is humble is both not humble and kind. Everyone who is both old and not curious is curious and vice versa. If someone is both tall and quiet then alice is kind and vice versa. Everyone who is either patient or not quiet is not brave or not curious and vice versa. Everyone who is both not strong and not old is both quiet and funny. Everyone who is both not quiet and humble is either tall or not kind. If lucy is both not rich and not happy then someone is creative and vice versa. If mary is kind or creative then fred is not brave and vice versa. Everyone who is not kind is both not generous and not old. If someone is either not brave or not wise then john is both tall and wise and vice versa. If lucy is happy or kind then someone is both happy and rich. Someone is patient. Paul is both rich and not calm. Alice is both not calm and not tall. Fred is either not creative or wise. Paul is both wise and not kind. Someone is either curious or brave. Alice is both not curious and brave. | Paul is not strong. | contradiction | (![X]:(rich(X)<=>(~quiet(X)<~>quiet(X))))&
((?[X]:((brave(X)|tall(X))))=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:((~funny(X)<~>~rich(X))<=>~creative(X)))&
((?[X]:((rich(X)<~>~calm(X))))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
((?[X]:((happy(X)<~>~funny(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:(humble(X)=>(~humble(X)&kind(X))))&
(![X]:((old(X)&~curious(X))<=>curious(X)))&
((?[X]:((tall(X)&quiet(X))))<=>(kind(alice)))&
(![X]:((patient(X)<~>~quiet(X))<=>(~brave(X)|~curious(X))))&
(![X]:((~strong(X)&~old(X))=>(quiet(X)&funny(X))))&
(![X]:((~quiet(X)&humble(X))=>(tall(X)<~>~kind(X))))&
(((~rich(lucy)&~happy(lucy)))<=>(?[X]:(creative(X))))&
(((kind(mary)|creative(mary)))<=>(~brave(fred)))&
(![X]:(~kind(X)=>(~generous(X)&~old(X))))&
((?[X]:((~brave(X)<~>~wise(X))))<=>((tall(john)&wise(john))))&
(((happy(lucy)|kind(lucy)))=>(?[X]:((happy(X)&rich(X)))))&
(?[X]:(patient(X)))&
((rich(paul)&~calm(paul)))&
((~calm(alice)&~tall(alice)))&
((~creative(fred)<~>wise(fred)))&
((wise(paul)&~kind(paul)))&
(?[X]:((curious(X)<~>brave(X))))&
((~curious(alice)&brave(alice))) | ~strong(paul) | [
"p0",
"p2",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6772034157142956828265447
% SZS output start Proof for 6772034157142956828265447
1. ! [X0] : (rich(X0) <=> (~quiet(X0) <~> quiet(X0))) [input p0]
3. ! [X0] : ((~funny(X0) <~> ~rich(X0)) <=> ~creative(X0)) [input p2]
7. ! [X0] : ((~curious(X0) & old(X0)) <=> curious(X0)) [input p6]
10. ! [X0] : ((~old(X0) & ~strong(X0)) => (funny(X0) & quiet(X0))) [input p9]
12. (~happy(lucy) & ~rich(lucy)) <=> ? [X0] : creative(X0) [input p11]
24. ~strong(paul) [input hypothesis]
32. ! [X0] : ((funny(X0) & quiet(X0)) | (old(X0) | strong(X0))) [ennf transformation 10]
33. ! [X0] : ((funny(X0) & quiet(X0)) | old(X0) | strong(X0)) [flattening 32]
38. ! [X0] : ((rich(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) & (((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ~rich(X0))) [nnf transformation 1]
43. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | creative(X0)) & (~creative(X0) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [nnf transformation 3]
53. ! [X0] : (((~curious(X0) & old(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~old(X0)))) [nnf transformation 7]
54. ! [X0] : (((~curious(X0) & old(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~old(X0))) [flattening 53]
62. ((~happy(lucy) & ~rich(lucy)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (happy(lucy) | rich(lucy))) [nnf transformation 12]
63. ((~happy(lucy) & ~rich(lucy)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | happy(lucy) | rich(lucy)) [flattening 62]
64. ((~happy(lucy) & ~rich(lucy)) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | happy(lucy) | rich(lucy)) [rectify 63]
65. ? [X1] : creative(X1) => creative(sK5) [choice axiom]
66. ((~happy(lucy) & ~rich(lucy)) | ! [X0] : ~creative(X0)) & (creative(sK5) | happy(lucy) | rich(lucy)) [skolemisation 64,65]
84. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
85. rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
92. ~rich(X0) | ~funny(X0) | creative(X0) [cnf transformation 43]
106. curious(X0) | curious(X0) | ~old(X0) [cnf transformation 54]
108. ~curious(X0) | ~curious(X0) [cnf transformation 54]
119. funny(X0) | old(X0) | strong(X0) [cnf transformation 33]
123. ~rich(lucy) | ~creative(X0) [cnf transformation 66]
152. ~strong(paul) [cnf transformation 24]
153. curious(X0) | ~old(X0) [duplicate literal removal 106]
154. ~curious(X0) [duplicate literal removal 108]
156. rich(X0) | quiet(X0) [duplicate literal removal 84]
157. ~quiet(X0) | rich(X0) [duplicate literal removal 85]
158. rich(X0) [subsumption resolution 156,157]
177. ~funny(X0) | creative(X0) [subsumption resolution 92,158]
224. ~old(X0) [subsumption resolution 153,154]
245. strong(X0) | funny(X0) [subsumption resolution 119,224]
248. 19 <=> ! [X0] : ~creative(X0) [avatar definition]
249. ~creative(X0) <- (19) [avatar component clause 248]
255. ~creative(X0) [subsumption resolution 123,158]
256. 19 [avatar split clause 255,248]
333. funny(paul) [resolution 245,152]
336. creative(paul) [resolution 333,177]
337. $false <- (19) [subsumption resolution 336,249]
338. ~19 [avatar contradiction clause 337]
339. $false [avatar sat refutation 256,338]
% SZS output end Proof for 6772034157142956828265447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or strong is calm and vice versa. Everyone who is both calm and not patient is brave. Everyone who is both not calm and rich is not happy or old and vice versa. If someone is not tall then someone is creative or not rich. Everyone who is either generous or not funny is both not quiet and curious. Everyone who is either not old or not curious is patient and vice versa. If someone is patient then someone is not old or not patient and vice versa. Everyone who is curious or strong is patient and vice versa. Everyone who is either not tall or not calm is both not calm and not tall. Everyone who is either not funny or not patient is wise or not humble. If alice is not wise or not strong then someone is both not strong and not quiet. Everyone who is not calm or not kind is not funny and vice versa. Everyone who is happy is wise. If someone is not kind or not patient then someone is either not generous or not brave and vice versa. Everyone who is either not rich or creative is humble or not calm and vice versa. Everyone who is both generous and funny is generous or quiet. Someone is either not funny or not tall. Susan is not strong. Alice is not calm. Someone is both calm and quiet. Someone is either not calm or generous. Fred is not kind. Someone is either humble or creative. | Alice is strong. | neutral | (![X]:((humble(X)<~>strong(X))<=>calm(X)))&
(![X]:((calm(X)&~patient(X))=>brave(X)))&
(![X]:((~calm(X)&rich(X))<=>(~happy(X)|old(X))))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:((generous(X)<~>~funny(X))=>(~quiet(X)&curious(X))))&
(![X]:((~old(X)<~>~curious(X))<=>patient(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((curious(X)|strong(X))<=>patient(X)))&
(![X]:((~tall(X)<~>~calm(X))=>(~calm(X)&~tall(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(wise(X)|~humble(X))))&
(((~wise(alice)|~strong(alice)))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~funny(X)))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((generous(X)&funny(X))=>(generous(X)|quiet(X))))&
(?[X]:((~funny(X)<~>~tall(X))))&
(~strong(susan))&
(~calm(alice))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~calm(X)<~>generous(X))))&
(~kind(fred))&
(?[X]:((humble(X)<~>creative(X)))) | strong(alice) | [] | null | 0 |
If alice is either not generous or strong then someone is funny.
If someone is both generous and not humble then paul is not patient.
Everyone who is happy or not happy is not generous.
If fred is both not rich and curious then someone is not brave and vice versa.
If paul is either funny or happy then fred is generous or wise.
Everyone who is not humble or not happy is not brave and vice versa.
If alice is both brave and old then mary is creative or generous.
If susan is both not wise and curious then someone is old or not kind and vice versa.
If someone is not patient then alice is not rich or not strong.
Everyone who is both old and not happy is not creative or kind.
Everyone who is strong is either strong or patient and vice versa.
Everyone who is not rich is not creative or not old.
Everyone who is funny is not generous.
If someone is curious then someone is old or rich.
Everyone who is kind is both not happy and brave.
Everyone who is either humble or quiet is strong or not patient.
Someone is either humble or not humble.
John is both not funny and not tall.
Someone is either funny or not patient.
Someone is not patient.
Someone is both curious and not wise.
Someone is either generous or not calm. | Susan is kind. | contradiction | (((~generous(alice)<~>strong(alice)))=>(?[X]:(funny(X))))&
((?[X]:((generous(X)&~humble(X))))=>(~patient(paul)))&
(![X]:((happy(X)|~happy(X))=>~generous(X)))&
(((~rich(fred)&curious(fred)))<=>(?[X]:(~brave(X))))&
(((funny(paul)<~>happy(paul)))=>((generous(fred)|wise(fred))))&
(![X]:((~humble(X)|~happy(X))<=>~brave(X)))&
(((brave(alice)&old(alice)))=>((creative(mary)|generous(mary))))&
(((~wise(susan)&curious(susan)))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:(~patient(X)))=>((~rich(alice)|~strong(alice))))&
(![X]:((old(X)&~happy(X))=>(~creative(X)|kind(X))))&
(![X]:(strong(X)<=>(strong(X)<~>patient(X))))&
(![X]:(~rich(X)=>(~creative(X)|~old(X))))&
(![X]:(funny(X)=>~generous(X)))&
((?[X]:(curious(X)))=>(?[X]:((old(X)|rich(X)))))&
(![X]:(kind(X)=>(~happy(X)&brave(X))))&
(![X]:((humble(X)<~>quiet(X))=>(strong(X)|~patient(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
((~funny(john)&~tall(john)))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:((generous(X)<~>~calm(X)))) | kind(susan) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 602714614351429164122911
% SZS output start Proof for 602714614351429164122911
6. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> ~brave(X0)) [input p5]
15. ! [X0] : (kind(X0) => (brave(X0) & ~happy(X0))) [input p14]
23. kind(susan) [input hypothesis]
41. ! [X0] : ((brave(X0) & ~happy(X0)) | ~kind(X0)) [ennf transformation 15]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | brave(X0)) & (~brave(X0) | (happy(X0) & humble(X0)))) [nnf transformation 6]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | brave(X0)) & (~brave(X0) | (happy(X0) & humble(X0)))) [flattening 53]
89. ~brave(X0) | happy(X0) [cnf transformation 54]
106. ~kind(X0) | ~happy(X0) [cnf transformation 41]
107. ~kind(X0) | brave(X0) [cnf transformation 41]
120. kind(susan) [cnf transformation 23]
256. ~happy(susan) [resolution 106,120]
262. brave(susan) [resolution 107,120]
267. happy(susan) [resolution 262,89]
269. $false [subsumption resolution 267,256]
% SZS output end Proof for 602714614351429164122911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not brave then lucy is either brave or not humble and vice versa.
If fred is brave then someone is not wise.
If mary is rich or humble then someone is not funny or not tall.
Everyone who is not brave is kind and vice versa.
Everyone who is both rich and not calm is not wise or humble and vice versa.
If susan is not patient then lucy is either not funny or not brave and vice versa.
If someone is both funny and not generous then paul is rich or brave.
If susan is both not happy and kind then someone is not rich.
Everyone who is not quiet or not tall is either not brave or not strong.
Everyone who is either not quiet or not kind is calm or funny and vice versa.
Everyone who is either not wise or generous is either not creative or quiet and vice versa.
If mary is not kind then someone is not strong and vice versa.
Everyone who is not tall or not wise is not humble.
Everyone who is both wise and tall is not funny.
If fred is not calm then someone is either calm or not kind.
John is either not happy or rich.
Lucy is not patient.
John is both not strong and kind.
Someone is either calm or not wise.
Paul is funny.
Susan is curious.
Someone is funny.
Someone is not funny or happy. | John is quiet. | entailment | ((?[X]:((~generous(X)|~brave(X))))<=>((brave(lucy)<~>~humble(lucy))))&
((brave(fred))=>(?[X]:(~wise(X))))&
(((rich(mary)|humble(mary)))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((rich(X)&~calm(X))<=>(~wise(X)|humble(X))))&
((~patient(susan))<=>((~funny(lucy)<~>~brave(lucy))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(paul)|brave(paul))))&
(((~happy(susan)&kind(susan)))=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)|~tall(X))=>(~brave(X)<~>~strong(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(calm(X)|funny(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~creative(X)<~>quiet(X))))&
((~kind(mary))<=>(?[X]:(~strong(X))))&
(![X]:((~tall(X)|~wise(X))=>~humble(X)))&
(![X]:((wise(X)&tall(X))=>~funny(X)))&
((~calm(fred))=>(?[X]:((calm(X)<~>~kind(X)))))&
((~happy(john)<~>rich(john)))&
(~patient(lucy))&
((~strong(john)&kind(john)))&
(?[X]:((calm(X)<~>~wise(X))))&
(funny(paul))&
(curious(susan))&
(?[X]:(funny(X)))&
(?[X]:((~funny(X)|happy(X)))) | quiet(john) | [
"p3",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 287195984463780564654900
% SZS output start Proof for 287195984463780564654900
4. ! [X0] : (~brave(X0) <=> kind(X0)) [input p3]
9. ! [X0] : ((~tall(X0) | ~quiet(X0)) => (~brave(X0) <~> ~strong(X0))) [input p8]
18. kind(john) & ~strong(john) [input p17]
24. ~quiet(john) [input hypothesis]
32. ! [X0] : ((~brave(X0) <~> ~strong(X0)) | (tall(X0) & quiet(X0))) [ennf transformation 9]
45. ! [X0] : ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))) [nnf transformation 4]
51. ! [X0] : (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (tall(X0) & quiet(X0))) [nnf transformation 32]
80. ~kind(X0) | ~brave(X0) [cnf transformation 45]
94. strong(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
120. ~strong(john) [cnf transformation 18]
121. kind(john) [cnf transformation 18]
127. ~quiet(john) [cnf transformation 24]
282. ~brave(john) [resolution 80,121]
288. brave(john) | quiet(john) [resolution 94,120]
293. quiet(john) [subsumption resolution 288,282]
294. $false [subsumption resolution 293,127]
% SZS output end Proof for 287195984463780564654900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and funny is either generous or not funny. Everyone who is either kind or not funny is not calm or funny and vice versa. If someone is not humble or old then someone is creative. If john is either not curious or not happy then susan is either not generous or not humble. Everyone who is both strong and not quiet is not tall. Everyone who is both humble and not curious is either generous or strong and vice versa. If paul is not quiet or not patient then someone is rich or not brave and vice versa. If someone is calm or not generous then someone is either not quiet or not kind. Everyone who is either funny or not strong is generous or curious and vice versa. Everyone who is curious is either patient or not wise and vice versa. If someone is not old then someone is happy or quiet. If someone is either not humble or not funny then susan is either not curious or happy and vice versa. Everyone who is strong is not funny or tall and vice versa. Everyone who is not quiet is both not wise and not generous. Everyone who is either not humble or not generous is either curious or not happy and vice versa. If mary is either curious or not happy then someone is either funny or tall. Fred is either not creative or funny. Susan is not calm or curious. Someone is happy or not creative. Mary is either not strong or quiet. Someone is wise. Fred is both not quiet and rich. | Fred is not curious. | entailment | (![X]:((~generous(X)&funny(X))=>(generous(X)<~>~funny(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~calm(X)|funny(X))))&
((?[X]:((~humble(X)|old(X))))=>(?[X]:(creative(X))))&
(((~curious(john)<~>~happy(john)))=>((~generous(susan)<~>~humble(susan))))&
(![X]:((strong(X)&~quiet(X))=>~tall(X)))&
(![X]:((humble(X)&~curious(X))<=>(generous(X)<~>strong(X))))&
(((~quiet(paul)|~patient(paul)))<=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:((funny(X)<~>~strong(X))<=>(generous(X)|curious(X))))&
(![X]:(curious(X)<=>(patient(X)<~>~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((happy(X)|quiet(X)))))&
((?[X]:((~humble(X)<~>~funny(X))))<=>((~curious(susan)<~>happy(susan))))&
(![X]:(strong(X)<=>(~funny(X)|tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)&~generous(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(curious(X)<~>~happy(X))))&
(((curious(mary)<~>~happy(mary)))=>(?[X]:((funny(X)<~>tall(X)))))&
((~creative(fred)<~>funny(fred)))&
((~calm(susan)|curious(susan)))&
(?[X]:((happy(X)|~creative(X))))&
((~strong(mary)<~>quiet(mary)))&
(?[X]:(wise(X)))&
((~quiet(fred)&rich(fred))) | ~curious(fred) | [
"p0",
"p5",
"p8",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2660310003829972219665248
% SZS output start Proof for 2660310003829972219665248
1. ! [X0] : ((funny(X0) & ~generous(X0)) => (generous(X0) <~> ~funny(X0))) [input p0]
6. ! [X0] : ((~curious(X0) & humble(X0)) <=> (generous(X0) <~> strong(X0))) [input p5]
9. ! [X0] : ((funny(X0) <~> ~strong(X0)) <=> (curious(X0) | generous(X0))) [input p8]
13. ! [X0] : (strong(X0) <=> (tall(X0) | ~funny(X0))) [input p12]
14. ! [X0] : (~quiet(X0) => (~generous(X0) & ~wise(X0))) [input p13]
22. rich(fred) & ~quiet(fred) [input p21]
23. curious(fred) [input hypothesis]
27. ! [X0] : ((generous(X0) <~> ~funny(X0)) | (~funny(X0) | generous(X0))) [ennf transformation 1]
28. ! [X0] : ((generous(X0) <~> ~funny(X0)) | ~funny(X0) | generous(X0)) [flattening 27]
35. ! [X0] : ((~generous(X0) & ~wise(X0)) | quiet(X0)) [ennf transformation 14]
37. ! [X0] : (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | ~funny(X0) | generous(X0)) [nnf transformation 28]
44. ! [X0] : (((~curious(X0) & humble(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) & (((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (curious(X0) | ~humble(X0)))) [nnf transformation 6]
45. ! [X0] : (((~curious(X0) & humble(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0)))) & (((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | curious(X0) | ~humble(X0))) [flattening 44]
55. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [nnf transformation 9]
56. ! [X0] : ((((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0))))) [flattening 55]
65. ! [X0] : ((strong(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ~strong(X0))) [nnf transformation 13]
66. ! [X0] : ((strong(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~strong(X0))) [flattening 65]
77. ~funny(X0) | generous(X0) | ~funny(X0) | generous(X0) [cnf transformation 37]
97. ~strong(X0) | generous(X0) | ~curious(X0) [cnf transformation 45]
110. strong(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 56]
126. strong(X0) | funny(X0) [cnf transformation 66]
129. ~generous(X0) | quiet(X0) [cnf transformation 35]
149. ~quiet(fred) [cnf transformation 22]
151. curious(fred) [cnf transformation 23]
154. ~funny(X0) | generous(X0) [duplicate literal removal 77]
232. ~funny(X0) | strong(X0) [subsumption resolution 110,154]
276. strong(X0) [subsumption resolution 126,232]
330. ~curious(X0) | generous(X0) [resolution 97,276]
331. generous(fred) [resolution 330,151]
334. quiet(fred) [resolution 331,129]
335. $false [subsumption resolution 334,149]
% SZS output end Proof for 2660310003829972219665248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not humble then someone is either not old or not generous and vice versa.
Everyone who is either strong or old is both not creative and tall and vice versa.
If someone is both calm and not old then alice is either not curious or not rich and vice versa.
Everyone who is both old and generous is strong or rich and vice versa.
Everyone who is not creative is both not patient and not funny.
If someone is not generous or not quiet then someone is both not creative and not old.
Everyone who is curious or kind is either not happy or not old.
Everyone who is either happy or not strong is rich.
If paul is both funny and creative then mary is rich and vice versa.
Everyone who is both humble and patient is tall or not patient and vice versa.
Everyone who is either not funny or not kind is both not funny and old.
If susan is both curious and rich then someone is not rich or not quiet.
Everyone who is brave or creative is either curious or calm.
If someone is either not strong or tall then lucy is old or not calm.
Everyone who is either not brave or not happy is not wise.
Everyone who is not curious or not calm is not wise or rich and vice versa.
Alice is either not old or old.
Someone is creative or not strong.
Susan is brave.
Paul is either funny or humble.
Paul is both old and creative.
Susan is either humble or not quiet. | Susan is kind. | neutral | ((?[X]:(~humble(X)))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((strong(X)<~>old(X))<=>(~creative(X)&tall(X))))&
((?[X]:((calm(X)&~old(X))))<=>((~curious(alice)<~>~rich(alice))))&
(![X]:((old(X)&generous(X))<=>(strong(X)|rich(X))))&
(![X]:(~creative(X)=>(~patient(X)&~funny(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((curious(X)|kind(X))=>(~happy(X)<~>~old(X))))&
(![X]:((happy(X)<~>~strong(X))=>rich(X)))&
(((funny(paul)&creative(paul)))<=>(rich(mary)))&
(![X]:((humble(X)&patient(X))<=>(tall(X)|~patient(X))))&
(![X]:((~funny(X)<~>~kind(X))=>(~funny(X)&old(X))))&
(((curious(susan)&rich(susan)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((brave(X)|creative(X))=>(curious(X)<~>calm(X))))&
((?[X]:((~strong(X)<~>tall(X))))=>((old(lucy)|~calm(lucy))))&
(![X]:((~brave(X)<~>~happy(X))=>~wise(X)))&
(![X]:((~curious(X)|~calm(X))<=>(~wise(X)|rich(X))))&
((~old(alice)<~>old(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(brave(susan))&
((funny(paul)<~>humble(paul)))&
((old(paul)&creative(paul)))&
((humble(susan)<~>~quiet(susan))) | kind(susan) | [] | null | 0 |
Everyone who is either quiet or calm is both creative and generous and vice versa.
Everyone who is both kind and not brave is either not kind or tall.
Everyone who is either not rich or happy is both not generous and not calm.
If john is either not quiet or not tall then mary is both not brave and not humble.
Everyone who is both wise and calm is not humble or calm.
If someone is both brave and not patient then someone is happy or not kind and vice versa.
If someone is not funny then alice is both not calm and tall.
Everyone who is not wise or not quiet is not kind.
Everyone who is both not calm and not humble is either not happy or tall and vice versa.
If mary is either kind or old then someone is either happy or patient and vice versa.
If someone is both not quiet and not happy then fred is either funny or not tall and vice versa.
Everyone who is not brave or not patient is not humble or funny.
If someone is tall or calm then mary is both not patient and strong.
If mary is not brave or tall then someone is both funny and wise and vice versa.
Everyone who is both rich and humble is quiet.
Everyone who is both not wise and quiet is either old or calm and vice versa.
Mary is both happy and tall.
John is tall.
Someone is creative.
Someone is either calm or not calm.
Someone is not rich or quiet.
Someone is not tall.
Paul is either not calm or kind.
Someone is both brave and rich. | Paul is wise. | neutral | (![X]:((quiet(X)<~>calm(X))<=>(creative(X)&generous(X))))&
(![X]:((kind(X)&~brave(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~rich(X)<~>happy(X))=>(~generous(X)&~calm(X))))&
(((~quiet(john)<~>~tall(john)))=>((~brave(mary)&~humble(mary))))&
(![X]:((wise(X)&calm(X))=>(~humble(X)|calm(X))))&
((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((happy(X)|~kind(X)))))&
((?[X]:(~funny(X)))=>((~calm(alice)&tall(alice))))&
(![X]:((~wise(X)|~quiet(X))=>~kind(X)))&
(![X]:((~calm(X)&~humble(X))<=>(~happy(X)<~>tall(X))))&
(((kind(mary)<~>old(mary)))<=>(?[X]:((happy(X)<~>patient(X)))))&
((?[X]:((~quiet(X)&~happy(X))))<=>((funny(fred)<~>~tall(fred))))&
(![X]:((~brave(X)|~patient(X))=>(~humble(X)|funny(X))))&
((?[X]:((tall(X)|calm(X))))=>((~patient(mary)&strong(mary))))&
(((~brave(mary)|tall(mary)))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((rich(X)&humble(X))=>quiet(X)))&
(![X]:((~wise(X)&quiet(X))<=>(old(X)<~>calm(X))))&
((happy(mary)&tall(mary)))&
(tall(john))&
(?[X]:(creative(X)))&
(?[X]:((calm(X)<~>~calm(X))))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:(~tall(X)))&
((~calm(paul)<~>kind(paul)))&
(?[X]:((brave(X)&rich(X)))) | wise(paul) | [] | null | 0 |
Everyone who is not humble is generous. If someone is either tall or not funny then alice is wise or not patient. Everyone who is both not curious and humble is both not generous and brave and vice versa. If someone is either not brave or not tall then lucy is either not kind or not patient. If someone is curious then fred is both funny and not curious and vice versa. If fred is creative or not strong then mary is not wise and vice versa. If fred is either not tall or not old then someone is both not kind and not generous. Everyone who is both strong and not strong is calm or tall and vice versa. Everyone who is old or humble is either not curious or wise and vice versa. If susan is either not humble or not quiet then someone is tall and vice versa. Everyone who is either not strong or tall is not tall or not patient and vice versa. If someone is both not strong and happy then lucy is not brave and vice versa. If someone is not calm or not humble then someone is either not kind or not funny. If someone is both patient and quiet then fred is either brave or generous. Everyone who is not generous or not calm is not wise or rich and vice versa. If mary is wise then mary is tall or creative. Someone is either not kind or quiet. Someone is not brave. Mary is patient. Paul is either not creative or not curious. Susan is either not patient or happy. Someone is not generous. | Paul is wise. | neutral | (![X]:(~humble(X)=>generous(X)))&
((?[X]:((tall(X)<~>~funny(X))))=>((wise(alice)|~patient(alice))))&
(![X]:((~curious(X)&humble(X))<=>(~generous(X)&brave(X))))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~kind(lucy)<~>~patient(lucy))))&
((?[X]:(curious(X)))<=>((funny(fred)&~curious(fred))))&
(((creative(fred)|~strong(fred)))<=>(~wise(mary)))&
(((~tall(fred)<~>~old(fred)))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:((strong(X)&~strong(X))<=>(calm(X)|tall(X))))&
(![X]:((old(X)|humble(X))<=>(~curious(X)<~>wise(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>(?[X]:(tall(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~tall(X)|~patient(X))))&
((?[X]:((~strong(X)&happy(X))))<=>(~brave(lucy)))&
((?[X]:((~calm(X)|~humble(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:((patient(X)&quiet(X))))=>((brave(fred)<~>generous(fred))))&
(![X]:((~generous(X)|~calm(X))<=>(~wise(X)|rich(X))))&
((wise(mary))=>((tall(mary)|creative(mary))))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:(~brave(X)))&
(patient(mary))&
((~creative(paul)<~>~curious(paul)))&
((~patient(susan)<~>happy(susan)))&
(?[X]:(~generous(X))) | wise(paul) | [] | null | 0 |
If lucy is not old or old then john is tall and vice versa. Everyone who is both not old and not patient is either quiet or not old. If someone is not funny or old then someone is either curious or rich. If alice is both old and rich then lucy is not rich and vice versa. Everyone who is both not patient and not rich is either creative or humble and vice versa. Everyone who is funny or generous is both not strong and not kind. If paul is either not old or not rich then paul is not creative and vice versa. Everyone who is not old is both rich and patient and vice versa. Everyone who is not calm is happy and vice versa. Everyone who is both not patient and not happy is both not funny and quiet and vice versa. Everyone who is calm is both not old and not kind and vice versa. If john is both not kind and creative then lucy is both brave and creative and vice versa. If lucy is not wise then paul is quiet. Everyone who is old is either not old or quiet. Everyone who is happy or calm is both creative and not wise. If someone is not rich then john is both not kind and not quiet and vice versa. Susan is not calm. Someone is either curious or not funny. Someone is either not creative or humble. Fred is both curious and not strong. Someone is either brave or generous. Someone is both old and not curious. John is both quiet and generous. | John is not humble. | contradiction | (((~old(lucy)|old(lucy)))<=>(tall(john)))&
(![X]:((~old(X)&~patient(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((curious(X)<~>rich(X)))))&
(((old(alice)&rich(alice)))<=>(~rich(lucy)))&
(![X]:((~patient(X)&~rich(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|generous(X))=>(~strong(X)&~kind(X))))&
(((~old(paul)<~>~rich(paul)))<=>(~creative(paul)))&
(![X]:(~old(X)<=>(rich(X)&patient(X))))&
(![X]:(~calm(X)<=>happy(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~funny(X)&quiet(X))))&
(![X]:(calm(X)<=>(~old(X)&~kind(X))))&
(((~kind(john)&creative(john)))<=>((brave(lucy)&creative(lucy))))&
((~wise(lucy))=>(quiet(paul)))&
(![X]:(old(X)=>(~old(X)<~>quiet(X))))&
(![X]:((happy(X)|calm(X))=>(creative(X)&~wise(X))))&
((?[X]:(~rich(X)))<=>((~kind(john)&~quiet(john))))&
(~calm(susan))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((curious(fred)&~strong(fred)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((old(X)&~curious(X))))&
((quiet(john)&generous(john))) | ~humble(john) | [
"p4",
"p8",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 113863652357324075679408
% SZS output start Proof for 113863652357324075679408
5. ! [X0] : ((~rich(X0) & ~patient(X0)) <=> (creative(X0) <~> humble(X0))) [input p4]
9. ! [X0] : (~calm(X0) <=> happy(X0)) [input p8]
15. ! [X0] : ((calm(X0) | happy(X0)) => (~wise(X0) & creative(X0))) [input p14]
16. ? [X0] : ~rich(X0) <=> (~quiet(john) & ~kind(john)) [input p15]
23. generous(john) & quiet(john) [input p22]
24. ~humble(john) [input hypothesis]
34. ! [X0] : ((~wise(X0) & creative(X0)) | (~calm(X0) & ~happy(X0))) [ennf transformation 15]
44. ! [X0] : (((~rich(X0) & ~patient(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (rich(X0) | patient(X0)))) [nnf transformation 5]
45. ! [X0] : (((~rich(X0) & ~patient(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | rich(X0) | patient(X0))) [flattening 44]
49. ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))) [nnf transformation 9]
57. (? [X0] : ~rich(X0) | (quiet(john) | kind(john))) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [nnf transformation 16]
58. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X0] : rich(X0)) [flattening 57]
59. (? [X0] : ~rich(X0) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [rectify 58]
60. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
61. (~rich(sK1) | quiet(john) | kind(john)) & ((~quiet(john) & ~kind(john)) | ! [X1] : rich(X1)) [skolemisation 59,60]
89. ~creative(X0) | humble(X0) | ~rich(X0) [cnf transformation 45]
100. happy(X0) | calm(X0) [cnf transformation 49]
116. ~happy(X0) | creative(X0) [cnf transformation 34]
117. ~calm(X0) | creative(X0) [cnf transformation 34]
121. ~quiet(john) | rich(X1) [cnf transformation 61]
133. quiet(john) [cnf transformation 23]
135. ~humble(john) [cnf transformation 24]
227. 19 <=> quiet(john) [avatar definition]
236. 21 <=> ! [X1] : rich(X1) [avatar definition]
237. rich(X1) <- (21) [avatar component clause 236]
238. 21 | ~19 [avatar split clause 121,227,236]
270. 19 [avatar split clause 133,227]
276. creative(X0) | calm(X0) [resolution 116,100]
277. creative(X0) [subsumption resolution 276,117]
294. humble(X0) | ~rich(X0) [resolution 89,277]
295. humble(X0) <- (21) [subsumption resolution 294,237]
296. $false <- (21) [resolution 295,135]
298. ~21 [avatar contradiction clause 296]
299. $false [avatar sat refutation 238,270,298]
% SZS output end Proof for 113863652357324075679408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or tall then someone is strong or tall.
Everyone who is not kind or not curious is both generous and wise and vice versa.
If someone is both old and calm then someone is both wise and generous and vice versa.
Everyone who is not kind or creative is funny or patient.
Everyone who is both generous and not tall is either generous or not funny and vice versa.
If fred is old then fred is both calm and old and vice versa.
Everyone who is not quiet is both not humble and not happy.
Everyone who is either not humble or curious is both not humble and not brave and vice versa.
If someone is either creative or not curious then john is funny or generous and vice versa.
Everyone who is rich is either tall or not patient.
Everyone who is not creative or quiet is either not humble or creative and vice versa.
Everyone who is either not brave or not kind is not wise and vice versa.
If someone is both kind and not humble then someone is not curious.
Everyone who is not quiet is either not generous or not strong and vice versa.
Everyone who is funny is kind and vice versa.
Someone is strong or not brave.
Someone is not generous or not brave.
Mary is not brave.
Lucy is either wise or happy.
Someone is either not happy or curious.
Paul is either generous or not old.
Fred is both calm and brave. | Paul is not patient. | neutral | ((?[X]:((creative(X)<~>tall(X))))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(generous(X)&wise(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((~kind(X)|creative(X))=>(funny(X)|patient(X))))&
(![X]:((generous(X)&~tall(X))<=>(generous(X)<~>~funny(X))))&
((old(fred))<=>((calm(fred)&old(fred))))&
(![X]:(~quiet(X)=>(~humble(X)&~happy(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(~humble(X)&~brave(X))))&
((?[X]:((creative(X)<~>~curious(X))))<=>((funny(john)|generous(john))))&
(![X]:(rich(X)=>(tall(X)<~>~patient(X))))&
(![X]:((~creative(X)|quiet(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~brave(X)<~>~kind(X))<=>~wise(X)))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:(~curious(X))))&
(![X]:(~quiet(X)<=>(~generous(X)<~>~strong(X))))&
(![X]:(funny(X)<=>kind(X)))&
(?[X]:((strong(X)|~brave(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(~brave(mary))&
((wise(lucy)<~>happy(lucy)))&
(?[X]:((~happy(X)<~>curious(X))))&
((generous(paul)<~>~old(paul)))&
((calm(fred)&brave(fred))) | ~patient(paul) | [] | null | 0 |
If paul is not strong then someone is both strong and funny and vice versa. Everyone who is either not rich or calm is either patient or not humble. Everyone who is either not tall or creative is generous or creative and vice versa. Everyone who is both calm and humble is not brave and vice versa. Everyone who is both not calm and funny is both curious and not patient and vice versa. If fred is not old then someone is either not patient or not wise. Everyone who is either not tall or strong is not creative and vice versa. If someone is both funny and creative then someone is either not old or not humble. If someone is either not generous or rich then paul is either not patient or rich and vice versa. If john is generous then mary is not creative or curious and vice versa. If someone is not tall or not humble then susan is not calm or not funny and vice versa. Everyone who is either rich or not funny is brave. Everyone who is either not old or wise is not wise and vice versa. If lucy is both not strong and creative then someone is not tall or tall. Everyone who is patient is both patient and not humble and vice versa. Everyone who is strong or quiet is not funny or not old. Alice is either patient or not creative. Mary is both strong and rich. Someone is not tall. Someone is both rich and quiet. Someone is not quiet or strong. Someone is both not tall and rich. Someone is either strong or tall. Susan is either not patient or brave. | Susan is funny. | contradiction | ((~strong(paul))<=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((~rich(X)<~>calm(X))=>(patient(X)<~>~humble(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(generous(X)|creative(X))))&
(![X]:((calm(X)&humble(X))<=>~brave(X)))&
(![X]:((~calm(X)&funny(X))<=>(curious(X)&~patient(X))))&
((~old(fred))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((~tall(X)<~>strong(X))<=>~creative(X)))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:((~old(X)<~>~humble(X)))))&
((?[X]:((~generous(X)<~>rich(X))))<=>((~patient(paul)<~>rich(paul))))&
((generous(john))<=>((~creative(mary)|curious(mary))))&
((?[X]:((~tall(X)|~humble(X))))<=>((~calm(susan)|~funny(susan))))&
(![X]:((rich(X)<~>~funny(X))=>brave(X)))&
(![X]:((~old(X)<~>wise(X))<=>~wise(X)))&
(((~strong(lucy)&creative(lucy)))=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:(patient(X)<=>(patient(X)&~humble(X))))&
(![X]:((strong(X)|quiet(X))=>(~funny(X)|~old(X))))&
((patient(alice)<~>~creative(alice)))&
((strong(mary)&rich(mary)))&
(?[X]:(~tall(X)))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~tall(X)&rich(X))))&
(?[X]:((strong(X)<~>tall(X))))&
((~patient(susan)<~>brave(susan))) | funny(susan) | [
"p3",
"p4",
"p10",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6821163788310576950625406
% SZS output start Proof for 6821163788310576950625406
4. ! [X0] : ((humble(X0) & calm(X0)) <=> ~brave(X0)) [input p3]
5. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (~patient(X0) & curious(X0))) [input p4]
11. ? [X0] : (~humble(X0) | ~tall(X0)) <=> (~funny(susan) | ~calm(susan)) [input p10]
19. ? [X0] : ~tall(X0) [input p18]
24. ~patient(susan) <~> brave(susan) [input p23]
25. funny(susan) [input hypothesis]
42. ! [X0] : (((humble(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) | ~calm(X0)))) [nnf transformation 4]
43. ! [X0] : (((humble(X0) & calm(X0)) | brave(X0)) & (~brave(X0) | ~humble(X0) | ~calm(X0))) [flattening 42]
44. ! [X0] : (((funny(X0) & ~calm(X0)) | (patient(X0) | ~curious(X0))) & ((~patient(X0) & curious(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) & ~calm(X0)) | patient(X0) | ~curious(X0)) & ((~patient(X0) & curious(X0)) | ~funny(X0) | calm(X0))) [flattening 44]
60. (? [X0] : (~humble(X0) | ~tall(X0)) | (funny(susan) & calm(susan))) & ((~funny(susan) | ~calm(susan)) | ! [X0] : (humble(X0) & tall(X0))) [nnf transformation 11]
61. (? [X0] : (~humble(X0) | ~tall(X0)) | (funny(susan) & calm(susan))) & (~funny(susan) | ~calm(susan) | ! [X0] : (humble(X0) & tall(X0))) [flattening 60]
62. (? [X0] : (~humble(X0) | ~tall(X0)) | (funny(susan) & calm(susan))) & (~funny(susan) | ~calm(susan) | ! [X1] : (humble(X1) & tall(X1))) [rectify 61]
63. ? [X0] : (~humble(X0) | ~tall(X0)) => (~humble(sK4) | ~tall(sK4)) [choice axiom]
64. ((~humble(sK4) | ~tall(sK4)) | (funny(susan) & calm(susan))) & (~funny(susan) | ~calm(susan) | ! [X1] : (humble(X1) & tall(X1))) [skolemisation 62,63]
72. ? [X0] : ~tall(X0) => ~tall(sK6) [choice axiom]
73. ~tall(sK6) [skolemisation 19,72]
83. (~brave(susan) | patient(susan)) & (brave(susan) | ~patient(susan)) [nnf transformation 24]
98. brave(X0) | calm(X0) [cnf transformation 43]
101. ~patient(X0) | ~funny(X0) | calm(X0) [cnf transformation 45]
123. ~funny(susan) | ~calm(susan) | tall(X1) [cnf transformation 64]
143. ~tall(sK6) [cnf transformation 73]
152. ~brave(susan) | patient(susan) [cnf transformation 83]
153. funny(susan) [cnf transformation 25]
252. 20 <=> funny(susan) [avatar definition]
254. funny(susan) <- (20) [avatar component clause 252]
265. 23 <=> calm(susan) [avatar definition]
266. ~calm(susan) <- (~23) [avatar component clause 265]
274. 25 <=> ! [X1] : tall(X1) [avatar definition]
275. tall(X1) <- (25) [avatar component clause 274]
276. 25 | ~23 | ~20 [avatar split clause 123,252,265,274]
300. 30 <=> patient(susan) [avatar definition]
302. patient(susan) <- (30) [avatar component clause 300]
304. 31 <=> brave(susan) [avatar definition]
306. ~brave(susan) <- (~31) [avatar component clause 304]
307. 30 | ~31 [avatar split clause 152,304,300]
309. 20 [avatar split clause 153,252]
312. calm(susan) <- (~31) [resolution 98,306]
315. 23 | 31 [avatar split clause 312,304,265]
318. $false <- (25) [resolution 275,143]
321. ~25 [avatar contradiction clause 318]
360. ~funny(susan) | calm(susan) <- (30) [resolution 101,302]
370. calm(susan) <- (20, 30) [subsumption resolution 360,254]
371. $false <- (20, ~23, 30) [subsumption resolution 370,266]
372. ~20 | 23 | ~30 [avatar contradiction clause 371]
373. $false [avatar sat refutation 276,307,309,315,321,372]
% SZS output end Proof for 6821163788310576950625406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not strong is both funny and generous. Everyone who is not curious is not old and vice versa. If john is not old then fred is either not humble or not happy. If lucy is either generous or not funny then someone is quiet. If lucy is rich then someone is both wise and not brave. Everyone who is happy or not strong is either quiet or curious and vice versa. If someone is creative then john is strong or generous and vice versa. If fred is both curious and generous then someone is not quiet and vice versa. Everyone who is both not wise and happy is either not kind or tall. Everyone who is not wise or not happy is not curious or not rich and vice versa. Everyone who is quiet or brave is either curious or kind. Everyone who is not happy is not curious or not funny. If fred is either not generous or humble then susan is patient or not old and vice versa. Everyone who is quiet or strong is either not humble or not brave and vice versa. Everyone who is tall is either rich or not old and vice versa. Everyone who is kind is either not old or not rich. Fred is calm. Alice is not old. Paul is not curious. Mary is not creative. Lucy is rich or not brave. Fred is not curious. Someone is either not wise or quiet. Someone is not humble. | Lucy is not happy. | entailment | (![X]:((creative(X)|~strong(X))=>(funny(X)&generous(X))))&
(![X]:(~curious(X)<=>~old(X)))&
((~old(john))=>((~humble(fred)<~>~happy(fred))))&
(((generous(lucy)<~>~funny(lucy)))=>(?[X]:(quiet(X))))&
((rich(lucy))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>(quiet(X)<~>curious(X))))&
((?[X]:(creative(X)))<=>((strong(john)|generous(john))))&
(((curious(fred)&generous(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:((~wise(X)&happy(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~curious(X)|~rich(X))))&
(![X]:((quiet(X)|brave(X))=>(curious(X)<~>kind(X))))&
(![X]:(~happy(X)=>(~curious(X)|~funny(X))))&
(((~generous(fred)<~>humble(fred)))<=>((patient(susan)|~old(susan))))&
(![X]:((quiet(X)|strong(X))<=>(~humble(X)<~>~brave(X))))&
(![X]:(tall(X)<=>(rich(X)<~>~old(X))))&
(![X]:(kind(X)=>(~old(X)<~>~rich(X))))&
(calm(fred))&
(~old(alice))&
(~curious(paul))&
(~creative(mary))&
((rich(lucy)|~brave(lucy)))&
(~curious(fred))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | ~happy(lucy) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3545876538847440947470807
% SZS output start Proof for 3545876538847440947470807
2. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p1]
6. ! [X0] : ((~strong(X0) | happy(X0)) <=> (quiet(X0) <~> curious(X0))) [input p5]
8. (generous(fred) & curious(fred)) <=> ? [X0] : ~quiet(X0) [input p7]
9. ! [X0] : ((happy(X0) & ~wise(X0)) => (~kind(X0) <~> tall(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~rich(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((brave(X0) | quiet(X0)) => (curious(X0) <~> kind(X0))) [input p10]
15. ! [X0] : (tall(X0) <=> (rich(X0) <~> ~old(X0))) [input p14]
16. ! [X0] : (kind(X0) => (~old(X0) <~> ~rich(X0))) [input p15]
22. ~curious(fred) [input p21]
25. happy(lucy) [input hypothesis]
31. ! [X0] : ((~kind(X0) <~> tall(X0)) | (~happy(X0) | wise(X0))) [ennf transformation 9]
32. ! [X0] : ((~kind(X0) <~> tall(X0)) | ~happy(X0) | wise(X0)) [flattening 31]
33. ! [X0] : ((curious(X0) <~> kind(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 11]
36. ! [X0] : ((~old(X0) <~> ~rich(X0)) | ~kind(X0)) [ennf transformation 16]
37. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 2]
44. ! [X0] : (((~strong(X0) | happy(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~strong(X0) | happy(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (strong(X0) & ~happy(X0)))) [flattening 44]
51. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~generous(fred) | ~curious(fred))) [nnf transformation 8]
52. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~generous(fred) | ~curious(fred)) [flattening 51]
53. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~generous(fred) | ~curious(fred)) [rectify 52]
54. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
55. ((generous(fred) & curious(fred)) | ! [X0] : quiet(X0)) & (~quiet(sK3) | ~generous(fred) | ~curious(fred)) [skolemisation 53,54]
56. ! [X0] : (((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ~happy(X0) | wise(X0)) [nnf transformation 32]
57. ! [X0] : (((~happy(X0) | ~wise(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 10]
58. ! [X0] : ((~happy(X0) | ~wise(X0) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | (happy(X0) & wise(X0)))) [flattening 57]
59. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33]
64. ! [X0] : ((tall(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0))) [nnf transformation 15]
65. ! [X0] : (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 36]
75. ~old(X0) | curious(X0) [cnf transformation 37]
76. ~curious(X0) | old(X0) [cnf transformation 37]
85. ~quiet(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 45]
93. curious(fred) | quiet(X0) [cnf transformation 55]
95. ~kind(X0) | tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 56]
99. ~wise(X0) | ~happy(X0) | curious(X0) [cnf transformation 58]
101. ~quiet(X0) | curious(X0) | kind(X0) [cnf transformation 59]
119. ~tall(X0) | ~rich(X0) | old(X0) [cnf transformation 64]
123. ~kind(X0) | old(X0) | rich(X0) [cnf transformation 65]
128. ~curious(fred) [cnf transformation 22]
132. happy(lucy) [cnf transformation 25]
162. 7 <=> rich(lucy) [avatar definition]
163. rich(lucy) <- (7) [avatar component clause 162]
164. ~rich(lucy) <- (~7) [avatar component clause 162]
190. 13 <=> ! [X0] : quiet(X0) [avatar definition]
191. quiet(X0) <- (13) [avatar component clause 190]
198. 15 <=> curious(fred) [avatar definition]
201. 13 | 15 [avatar split clause 93,198,190]
226. ~15 [avatar split clause 128,198]
249. ~happy(X1) | ~curious(X1) <- (13) [resolution 85,191]
253. ~curious(lucy) <- (13) [resolution 249,132]
259. kind(X1) | curious(X1) <- (13) [resolution 101,191]
283. old(X1) | rich(X1) | curious(X1) <- (13) [resolution 123,259]
284. rich(X1) | old(X1) <- (13) [subsumption resolution 283,76]
288. old(lucy) <- (~7, 13) [resolution 284,164]
292. curious(lucy) <- (~7, 13) [resolution 288,75]
293. $false <- (~7, 13) [subsumption resolution 292,253]
294. 7 | ~13 [avatar contradiction clause 293]
299. 22 <=> tall(lucy) [avatar definition]
301. tall(lucy) <- (22) [avatar component clause 299]
303. 23 <=> old(lucy) [avatar definition]
304. old(lucy) <- (23) [avatar component clause 303]
322. tall(X1) | ~happy(X1) | wise(X1) | curious(X1) <- (13) [resolution 95,259]
323. tall(X1) | ~happy(X1) | curious(X1) <- (13) [subsumption resolution 322,99]
324. ~happy(X1) | tall(X1) <- (13) [subsumption resolution 323,249]
328. tall(lucy) <- (13) [resolution 324,132]
330. 22 | ~13 [avatar split clause 328,190,299]
334. ~rich(lucy) | old(lucy) <- (22) [resolution 301,119]
346. old(lucy) <- (7, 22) [subsumption resolution 334,163]
349. 23 | ~7 | ~22 [avatar split clause 346,299,162,303]
350. curious(lucy) <- (23) [resolution 304,75]
351. $false <- (13, 23) [subsumption resolution 350,253]
352. ~13 | ~23 [avatar contradiction clause 351]
353. $false [avatar sat refutation 201,226,294,330,349,352]
% SZS output end Proof for 3545876538847440947470807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both not tall and not creative and vice versa.
Everyone who is both not kind and humble is either strong or not patient.
Everyone who is either strong or not calm is strong.
Everyone who is either not humble or calm is not curious or calm.
If susan is either not quiet or not humble then susan is either not strong or not generous and vice versa.
Everyone who is not kind or not old is both not funny and old and vice versa.
Everyone who is not quiet is not rich and vice versa.
Everyone who is not strong is not funny and vice versa.
Everyone who is either generous or rich is both funny and old and vice versa.
If fred is not patient or not happy then paul is either kind or humble and vice versa.
If someone is either not creative or happy then someone is either kind or not brave.
Everyone who is not generous or kind is kind and vice versa.
If john is humble then someone is patient and vice versa.
If lucy is not brave or happy then mary is either humble or calm and vice versa.
Everyone who is either not quiet or not happy is both not calm and wise and vice versa.
Everyone who is wise or not rich is generous or funny.
Mary is patient or not strong.
John is either not old or brave.
Fred is either not happy or not old.
Susan is both not rich and happy.
Lucy is both strong and calm.
Someone is not kind. | Susan is not humble. | entailment | (![X]:((creative(X)|brave(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~kind(X)&humble(X))=>(strong(X)<~>~patient(X))))&
(![X]:((strong(X)<~>~calm(X))=>strong(X)))&
(![X]:((~humble(X)<~>calm(X))=>(~curious(X)|calm(X))))&
(((~quiet(susan)<~>~humble(susan)))<=>((~strong(susan)<~>~generous(susan))))&
(![X]:((~kind(X)|~old(X))<=>(~funny(X)&old(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
(![X]:((generous(X)<~>rich(X))<=>(funny(X)&old(X))))&
(((~patient(fred)|~happy(fred)))<=>((kind(paul)<~>humble(paul))))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
(![X]:((~generous(X)|kind(X))<=>kind(X)))&
((humble(john))<=>(?[X]:(patient(X))))&
(((~brave(lucy)|happy(lucy)))<=>((humble(mary)<~>calm(mary))))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~calm(X)&wise(X))))&
(![X]:((wise(X)|~rich(X))=>(generous(X)|funny(X))))&
((patient(mary)|~strong(mary)))&
((~old(john)<~>brave(john)))&
((~happy(fred)<~>~old(fred)))&
((~rich(susan)&happy(susan)))&
((strong(lucy)&calm(lucy)))&
(?[X]:(~kind(X))) | ~humble(susan) | [
"p4",
"p5",
"p6",
"p7",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 684370004649459735762453
% SZS output start Proof for 684370004649459735762453
5. (~quiet(susan) <~> ~humble(susan)) <=> (~strong(susan) <~> ~generous(susan)) [input p4]
6. ! [X0] : ((~old(X0) | ~kind(X0)) <=> (old(X0) & ~funny(X0))) [input p5]
7. ! [X0] : (~quiet(X0) <=> ~rich(X0)) [input p6]
8. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p7]
9. ! [X0] : ((generous(X0) <~> rich(X0)) <=> (old(X0) & funny(X0))) [input p8]
16. ! [X0] : ((~rich(X0) | wise(X0)) => (funny(X0) | generous(X0))) [input p15]
20. happy(susan) & ~rich(susan) [input p19]
23. humble(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) | generous(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 16]
31. ! [X0] : (funny(X0) | generous(X0) | (rich(X0) & ~wise(X0))) [flattening 30]
36. (((humble(susan) | quiet(susan)) & (~humble(susan) | ~quiet(susan))) | ((~strong(susan) | generous(susan)) & (~generous(susan) | strong(susan)))) & (((generous(susan) | strong(susan)) & (~generous(susan) | ~strong(susan))) | ((~quiet(susan) | humble(susan)) & (~humble(susan) | quiet(susan)))) [nnf transformation 5]
37. ! [X0] : (((~old(X0) | ~kind(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [nnf transformation 6]
38. ! [X0] : ((~old(X0) | ~kind(X0) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | (old(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0))) [nnf transformation 7]
40. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 8]
41. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [nnf transformation 9]
42. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [flattening 41]
72. ~generous(susan) | ~strong(susan) | ~humble(susan) | quiet(susan) [cnf transformation 36]
83. old(X0) | old(X0) [cnf transformation 38]
86. ~quiet(X0) | rich(X0) [cnf transformation 39]
87. ~funny(X0) | strong(X0) [cnf transformation 40]
89. ~generous(X0) | rich(X0) | funny(X0) [cnf transformation 42]
93. rich(X0) | generous(X0) | ~old(X0) | ~funny(X0) [cnf transformation 42]
123. funny(X0) | generous(X0) | rich(X0) [cnf transformation 31]
129. ~rich(susan) [cnf transformation 20]
134. humble(susan) [cnf transformation 23]
135. old(X0) [duplicate literal removal 83]
141. 1 <=> generous(susan) [avatar definition]
143. generous(susan) <- (1) [avatar component clause 141]
145. 2 <=> strong(susan) [avatar definition]
147. ~strong(susan) <- (~2) [avatar component clause 145]
149. 3 <=> quiet(susan) [avatar definition]
151. quiet(susan) <- (3) [avatar component clause 149]
153. 4 <=> humble(susan) [avatar definition]
163. 3 | ~4 | ~2 | ~1 [avatar split clause 72,141,145,153,149]
165. rich(X0) | generous(X0) | ~funny(X0) [subsumption resolution 93,135]
238. rich(X0) | generous(X0) [subsumption resolution 123,165]
251. 4 [avatar split clause 134,153]
260. generous(susan) [resolution 238,129]
264. 1 [avatar split clause 260,141]
265. rich(susan) <- (3) [resolution 151,86]
266. $false <- (3) [subsumption resolution 265,129]
267. ~3 [avatar contradiction clause 266]
269. rich(susan) | funny(susan) <- (1) [resolution 89,143]
271. funny(susan) <- (1) [subsumption resolution 269,129]
272. strong(susan) <- (1) [resolution 271,87]
274. $false <- (1, ~2) [subsumption resolution 272,147]
275. ~1 | 2 [avatar contradiction clause 274]
276. $false [avatar sat refutation 163,251,264,267,275]
% SZS output end Proof for 684370004649459735762453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and happy then paul is creative and vice versa.
Everyone who is either creative or not quiet is either not brave or not curious and vice versa.
Everyone who is not generous is wise or creative and vice versa.
Everyone who is not wise or not humble is not funny and vice versa.
If someone is kind then someone is not tall or generous.
Everyone who is not funny or not humble is not generous or humble.
Everyone who is not quiet or generous is either tall or old.
Everyone who is either curious or not curious is not rich or generous.
Everyone who is not creative is not happy or tall.
Everyone who is old or not humble is not old or creative and vice versa.
If someone is not calm or quiet then someone is not strong or funny and vice versa.
If alice is tall or not patient then someone is both not rich and not quiet and vice versa.
If someone is happy or not funny then susan is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
Someone is both not creative and not funny.
Susan is both curious and tall.
Someone is not patient.
Someone is rich or tall.
Someone is either patient or curious.
Lucy is calm or not generous.
Someone is both tall and not wise. | Lucy is calm. | neutral | ((?[X]:((~funny(X)&happy(X))))<=>(creative(paul)))&
(![X]:((creative(X)<~>~quiet(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(~generous(X)<=>(wise(X)|creative(X))))&
(![X]:((~wise(X)|~humble(X))<=>~funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((~funny(X)|~humble(X))=>(~generous(X)|humble(X))))&
(![X]:((~quiet(X)|generous(X))=>(tall(X)<~>old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~rich(X)|generous(X))))&
(![X]:(~creative(X)=>(~happy(X)|tall(X))))&
(![X]:((old(X)|~humble(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(?[X]:((~creative(X)&~funny(X))))&
((curious(susan)&tall(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|tall(X))))&
(?[X]:((patient(X)<~>curious(X))))&
((calm(lucy)|~generous(lucy)))&
(?[X]:((tall(X)&~wise(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not tall or happy is not brave.
Everyone who is not creative or brave is either not creative or funny and vice versa.
If someone is not humble then someone is both not patient and not brave and vice versa.
Everyone who is not humble is both not funny and quiet and vice versa.
Everyone who is both not generous and not creative is not kind or not rich.
Everyone who is both kind and not old is either not generous or quiet.
If fred is funny then mary is both tall and funny and vice versa.
Everyone who is creative or not wise is not tall or calm.
Everyone who is either curious or happy is calm.
If someone is quiet then someone is not humble or curious and vice versa.
Everyone who is rich is either humble or generous.
If someone is curious or happy then someone is both not strong and strong and vice versa.
Everyone who is both not patient and patient is not old and vice versa.
Everyone who is not humble is either not kind or strong and vice versa.
If mary is both generous and not humble then someone is not curious or patient and vice versa.
Everyone who is either humble or not generous is not kind and vice versa.
John is not old or strong.
Someone is both not rich and brave.
Fred is both not patient and not happy.
Someone is both not kind and not curious.
Someone is not rich.
Someone is not kind or not calm.
Alice is both strong and not curious. | Mary is quiet. | entailment | (![X]:((~tall(X)|happy(X))=>~brave(X)))&
(![X]:((~creative(X)|brave(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:(~humble(X)<=>(~funny(X)&quiet(X))))&
(![X]:((~generous(X)&~creative(X))=>(~kind(X)|~rich(X))))&
(![X]:((kind(X)&~old(X))=>(~generous(X)<~>quiet(X))))&
((funny(fred))<=>((tall(mary)&funny(mary))))&
(![X]:((creative(X)|~wise(X))=>(~tall(X)|calm(X))))&
(![X]:((curious(X)<~>happy(X))=>calm(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:(rich(X)=>(humble(X)<~>generous(X))))&
((?[X]:((curious(X)|happy(X))))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((~patient(X)&patient(X))<=>~old(X)))&
(![X]:(~humble(X)<=>(~kind(X)<~>strong(X))))&
(((generous(mary)&~humble(mary)))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((humble(X)<~>~generous(X))<=>~kind(X)))&
((~old(john)|strong(john)))&
(?[X]:((~rich(X)&brave(X))))&
((~patient(fred)&~happy(fred)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)|~calm(X))))&
((strong(alice)&~curious(alice))) | quiet(mary) | [
"p3",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2476822143293129798748163
% SZS output start Proof for 2476822143293129798748163
4. ! [X0] : (~humble(X0) <=> (quiet(X0) & ~funny(X0))) [input p3]
12. ? [X0] : (happy(X0) | curious(X0)) <=> ? [X0] : (strong(X0) & ~strong(X0)) [input p11]
15. (~humble(mary) & generous(mary)) <=> ? [X0] : (patient(X0) | ~curious(X0)) [input p14]
24. ~quiet(mary) [input hypothesis]
27. ? [X0] : (happy(X0) | curious(X0)) <=> ? [X1] : (strong(X1) & ~strong(X1)) [rectify 12]
46. ! [X0] : ((~humble(X0) | (~quiet(X0) | funny(X0))) & ((quiet(X0) & ~funny(X0)) | humble(X0))) [nnf transformation 4]
47. ! [X0] : ((~humble(X0) | ~quiet(X0) | funny(X0)) & ((quiet(X0) & ~funny(X0)) | humble(X0))) [flattening 46]
57. (? [X0] : (happy(X0) | curious(X0)) | ! [X1] : (~strong(X1) | strong(X1))) & (? [X1] : (strong(X1) & ~strong(X1)) | ! [X0] : (~happy(X0) & ~curious(X0))) [nnf transformation 27]
58. (? [X0] : (happy(X0) | curious(X0)) | ! [X1] : (~strong(X1) | strong(X1))) & (? [X2] : (strong(X2) & ~strong(X2)) | ! [X3] : (~happy(X3) & ~curious(X3))) [rectify 57]
59. ? [X0] : (happy(X0) | curious(X0)) => (happy(sK4) | curious(sK4)) [choice axiom]
60. ? [X2] : (strong(X2) & ~strong(X2)) => (strong(sK5) & ~strong(sK5)) [choice axiom]
61. ((happy(sK4) | curious(sK4)) | ! [X1] : (~strong(X1) | strong(X1))) & ((strong(sK5) & ~strong(sK5)) | ! [X3] : (~happy(X3) & ~curious(X3))) [skolemisation 58,60,59]
65. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X0] : (patient(X0) | ~curious(X0)) | (humble(mary) | ~generous(mary))) [nnf transformation 15]
66. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X0] : (patient(X0) | ~curious(X0)) | humble(mary) | ~generous(mary)) [flattening 65]
67. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & (? [X1] : (patient(X1) | ~curious(X1)) | humble(mary) | ~generous(mary)) [rectify 66]
68. ? [X1] : (patient(X1) | ~curious(X1)) => (patient(sK6) | ~curious(sK6)) [choice axiom]
69. ((~humble(mary) & generous(mary)) | ! [X0] : (~patient(X0) & curious(X0))) & ((patient(sK6) | ~curious(sK6)) | humble(mary) | ~generous(mary)) [skolemisation 67,68]
89. quiet(X0) | humble(X0) [cnf transformation 47]
102. ~strong(sK5) | ~curious(X3) [cnf transformation 61]
104. strong(sK5) | ~curious(X3) [cnf transformation 61]
117. ~humble(mary) | curious(X0) [cnf transformation 69]
132. ~quiet(mary) [cnf transformation 24]
172. 9 <=> ! [X1] : ~curious(X1) [avatar definition]
173. ~curious(X1) <- (9) [avatar component clause 172]
196. 15 <=> strong(sK5) [avatar definition]
200. 9 | 15 [avatar split clause 104,196,172]
202. 9 | ~15 [avatar split clause 102,196,172]
208. 17 <=> humble(mary) [avatar definition]
210. ~humble(mary) <- (~17) [avatar component clause 208]
213. 18 <=> ! [X0] : curious(X0) [avatar definition]
214. curious(X0) <- (18) [avatar component clause 213]
215. 18 | ~17 [avatar split clause 117,208,213]
241. $false <- (9, 18) [subsumption resolution 173,214]
242. ~9 | ~18 [avatar contradiction clause 241]
247. humble(mary) [resolution 89,132]
248. $false <- (~17) [subsumption resolution 247,210]
249. 17 [avatar contradiction clause 248]
250. $false [avatar sat refutation 200,202,215,242,249]
% SZS output end Proof for 2476822143293129798748163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not happy and not kind and vice versa. Everyone who is not humble or calm is either not funny or not creative. If someone is both funny and not strong then susan is either not humble or curious. Everyone who is funny is not quiet or not tall and vice versa. Everyone who is both not kind and funny is either not old or quiet. Everyone who is quiet is either not funny or not rich. If someone is not strong or not curious then someone is either kind or not quiet and vice versa. Everyone who is calm or quiet is both not patient and patient and vice versa. If lucy is either curious or not strong then fred is not creative and vice versa. Everyone who is calm or tall is old or generous. If alice is both not patient and not brave then someone is either funny or not strong. If someone is not patient or patient then someone is either strong or not tall. If someone is not brave or wise then someone is old or not rich and vice versa. If susan is not curious then someone is not brave or tall. Everyone who is both not brave and not tall is generous and vice versa. If someone is not strong then someone is not quiet and vice versa. Susan is both not old and rich. Mary is either not wise or not generous. Someone is not humble or calm. Mary is creative. Lucy is brave. Someone is both not brave and old. Paul is both old and generous. Someone is either rich or not strong. | Mary is funny. | entailment | (![X]:(calm(X)<=>(~happy(X)&~kind(X))))&
(![X]:((~humble(X)|calm(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~humble(susan)<~>curious(susan))))&
(![X]:(funny(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((~kind(X)&funny(X))=>(~old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&patient(X))))&
(((curious(lucy)<~>~strong(lucy)))<=>(~creative(fred)))&
(![X]:((calm(X)|tall(X))=>(old(X)|generous(X))))&
(((~patient(alice)&~brave(alice)))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|patient(X))))=>(?[X]:((strong(X)<~>~tall(X)))))&
((?[X]:((~brave(X)|wise(X))))<=>(?[X]:((old(X)|~rich(X)))))&
((~curious(susan))=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((~brave(X)&~tall(X))<=>generous(X)))&
((?[X]:(~strong(X)))<=>(?[X]:(~quiet(X))))&
((~old(susan)&rich(susan)))&
((~wise(mary)<~>~generous(mary)))&
(?[X]:((~humble(X)|calm(X))))&
(creative(mary))&
(brave(lucy))&
(?[X]:((~brave(X)&old(X))))&
((old(paul)&generous(paul)))&
(?[X]:((rich(X)<~>~strong(X)))) | funny(mary) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4133980761907740190359990
% SZS output start Proof for 4133980761907740190359990
4. ! [X0] : (funny(X0) <=> (~tall(X0) | ~quiet(X0))) [input p3]
8. ! [X0] : ((quiet(X0) | calm(X0)) <=> (patient(X0) & ~patient(X0))) [input p7]
25. ~funny(mary) [input hypothesis]
45. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 4]
46. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ~funny(X0))) [flattening 45]
54. ! [X0] : (((quiet(X0) | calm(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((quiet(X0) | calm(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 54]
96. quiet(X0) | funny(X0) [cnf transformation 46]
109. ~patient(X0) | ~quiet(X0) [cnf transformation 55]
111. patient(X0) | ~quiet(X0) [cnf transformation 55]
148. ~funny(mary) [cnf transformation 25]
198. ~quiet(X0) [subsumption resolution 109,111]
315. funny(X0) [resolution 96,198]
316. $false [resolution 315,148]
% SZS output end Proof for 4133980761907740190359990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or funny is wise and vice versa.
Everyone who is either not happy or not funny is generous and vice versa.
If paul is not quiet then fred is either not humble or not strong.
Everyone who is either not calm or quiet is either brave or not happy and vice versa.
Everyone who is not curious or funny is both not tall and calm.
If susan is not strong then someone is generous and vice versa.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
If someone is happy then paul is either not creative or happy.
Someone is creative or happy.
Someone is not quiet or generous.
Someone is not tall.
Fred is not patient.
Someone is either not strong or quiet.
Lucy is not strong or generous. | Fred is not generous. | contradiction | (![X]:((happy(X)<~>funny(X))<=>wise(X)))&
(![X]:((~happy(X)<~>~funny(X))<=>generous(X)))&
((~quiet(paul))=>((~humble(fred)<~>~strong(fred))))&
(![X]:((~calm(X)<~>quiet(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)&calm(X))))&
((~strong(susan))<=>(?[X]:(generous(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(?[X]:((creative(X)|happy(X))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:(~tall(X)))&
(~patient(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~strong(lucy)|generous(lucy))) | ~generous(fred) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p7",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4766530205612118061824811
% SZS output start Proof for 4766530205612118061824811
1. ! [X0] : ((happy(X0) <~> funny(X0)) <=> wise(X0)) [input p0]
2. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> generous(X0)) [input p1]
4. ! [X0] : ((~calm(X0) <~> quiet(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p3]
5. ! [X0] : ((funny(X0) | ~curious(X0)) => (calm(X0) & ~tall(X0))) [input p4]
6. ~strong(susan) <=> ? [X0] : generous(X0) [input p5]
8. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p7]
9. ! [X0] : ((brave(X0) | ~patient(X0)) => (funny(X0) | happy(X0))) [input p8]
11. ? [X0] : (~generous(X0) | funny(X0)) => (~wise(susan) & brave(susan)) [input p10]
19. ~patient(fred) [input p18]
22. ~generous(fred) [input hypothesis]
23. ! [X0] : ((happy(X0) <~> funny(X0)) => wise(X0)) [unused predicate definition removal 1]
25. ! [X0] : (funny(X0) => (calm(X0) & ~tall(X0))) [pure predicate removal 5]
27. ! [X0] : (funny(X0) => calm(X0)) [pure predicate removal 25]
28. ! [X0] : (wise(X0) | (happy(X0) <=> funny(X0))) [ennf transformation 23]
30. ! [X0] : (calm(X0) | ~funny(X0)) [ennf transformation 27]
31. ! [X0] : ((funny(X0) | happy(X0)) | (~brave(X0) & patient(X0))) [ennf transformation 9]
32. ! [X0] : (funny(X0) | happy(X0) | (~brave(X0) & patient(X0))) [flattening 31]
34. (~wise(susan) & brave(susan)) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 11]
37. ! [X0] : (wise(X0) | ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [nnf transformation 28]
38. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ~generous(X0)) & (generous(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [nnf transformation 4]
41. (~strong(susan) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | strong(susan)) [nnf transformation 6]
42. (~strong(susan) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | strong(susan)) [rectify 41]
43. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
44. (~strong(susan) | ! [X0] : ~generous(X0)) & (generous(sK0) | strong(susan)) [skolemisation 42,43]
46. ! [X0] : (((~generous(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (generous(X0) & strong(X0)))) [flattening 46]
61. ~happy(X0) | funny(X0) | wise(X0) [cnf transformation 37]
62. ~funny(X0) | happy(X0) | wise(X0) [cnf transformation 37]
64. ~happy(X0) | generous(X0) | funny(X0) [cnf transformation 38]
73. ~brave(X0) | ~calm(X0) | ~happy(X0) | quiet(X0) [cnf transformation 40]
77. ~funny(X0) | calm(X0) [cnf transformation 30]
79. ~strong(susan) | ~generous(X0) [cnf transformation 44]
88. ~quiet(X0) | strong(X0) [cnf transformation 47]
89. ~quiet(X0) | generous(X0) [cnf transformation 47]
91. patient(X0) | happy(X0) | funny(X0) [cnf transformation 32]
92. ~brave(X0) | happy(X0) | funny(X0) [cnf transformation 32]
97. brave(susan) | ~funny(X0) [cnf transformation 34]
99. ~wise(susan) | ~funny(X0) [cnf transformation 34]
113. ~patient(fred) [cnf transformation 19]
117. ~generous(fred) [cnf transformation 22]
133. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
134. ~generous(X0) <- (4) [avatar component clause 133]
136. 5 <=> strong(susan) [avatar definition]
138. ~strong(susan) <- (~5) [avatar component clause 136]
139. 4 | ~5 [avatar split clause 79,136,133]
149. 8 <=> wise(susan) [avatar definition]
151. ~wise(susan) <- (~8) [avatar component clause 149]
154. 9 <=> ! [X0] : ~funny(X0) [avatar definition]
155. ~funny(X0) <- (9) [avatar component clause 154]
156. 9 | ~8 [avatar split clause 99,149,154]
158. 10 <=> brave(susan) [avatar definition]
160. brave(susan) <- (10) [avatar component clause 158]
162. 9 | 10 [avatar split clause 97,158,154]
227. happy(fred) | funny(fred) [resolution 91,113]
228. happy(fred) <- (9) [subsumption resolution 227,155]
229. generous(fred) | funny(fred) <- (9) [resolution 228,64]
231. funny(fred) <- (9) [subsumption resolution 229,117]
232. $false <- (9) [subsumption resolution 231,155]
233. ~9 [avatar contradiction clause 232]
265. happy(susan) | funny(susan) <- (10) [resolution 92,160]
267. 28 <=> funny(susan) [avatar definition]
269. funny(susan) <- (28) [avatar component clause 267]
271. 29 <=> happy(susan) [avatar definition]
273. happy(susan) <- (29) [avatar component clause 271]
274. 28 | 29 | ~10 [avatar split clause 265,158,271,267]
278. happy(susan) | wise(susan) <- (28) [resolution 269,62]
279. calm(susan) <- (28) [resolution 269,77]
282. happy(susan) <- (~8, 28) [subsumption resolution 278,151]
283. 29 | 8 | ~28 [avatar split clause 282,267,149,271]
287. funny(susan) | wise(susan) <- (29) [resolution 273,61]
308. 33 <=> quiet(susan) [avatar definition]
310. quiet(susan) <- (33) [avatar component clause 308]
320. generous(susan) <- (33) [resolution 310,89]
322. $false <- (4, 33) [subsumption resolution 320,134]
323. ~4 | ~33 [avatar contradiction clause 322]
336. ~calm(susan) | ~happy(susan) | quiet(susan) <- (10) [resolution 73,160]
337. ~happy(susan) | quiet(susan) <- (10, 28) [subsumption resolution 336,279]
338. quiet(susan) <- (10, 28, 29) [subsumption resolution 337,273]
341. 33 | ~10 | ~28 | ~29 [avatar split clause 338,271,267,158,308]
352. strong(susan) <- (33) [resolution 310,88]
353. $false <- (~5, 33) [subsumption resolution 352,138]
354. 5 | ~33 [avatar contradiction clause 353]
368. funny(susan) <- (~8, 29) [subsumption resolution 287,151]
369. 28 | 8 | ~29 [avatar split clause 368,271,149,267]
376. $false [avatar sat refutation 139,156,162,233,274,283,323,341,354,369]
% SZS output end Proof for 4766530205612118061824811
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is not calm or brave.
If someone is either not patient or not strong then someone is generous.
If someone is quiet then someone is generous and vice versa.
If paul is both creative and calm then someone is not generous.
Everyone who is not curious or not brave is not brave or quiet and vice versa.
Everyone who is not tall or not generous is either rich or old.
Everyone who is not kind is not curious and vice versa.
Everyone who is both brave and wise is not kind and vice versa.
Everyone who is both rich and creative is both not patient and curious and vice versa.
If john is happy then someone is rich or patient.
If someone is not strong then someone is both not happy and not calm and vice versa.
Everyone who is both calm and not happy is tall and vice versa.
Everyone who is both not calm and humble is both not tall and not kind and vice versa.
Everyone who is not old or tall is funny.
If mary is curious then susan is calm.
Everyone who is either not rich or calm is not funny or not generous.
Fred is funny.
Someone is not calm or calm.
Lucy is both rich and not kind.
John is quiet or curious.
Susan is either not rich or not creative.
Mary is curious.
Paul is both not kind and not old.
Susan is both not generous and patient. | Lucy is not old. | entailment | (![X]:(~rich(X)=>(~calm(X)|brave(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:(generous(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(generous(X))))&
(((creative(paul)&calm(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)|~brave(X))<=>(~brave(X)|quiet(X))))&
(![X]:((~tall(X)|~generous(X))=>(rich(X)<~>old(X))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:((brave(X)&wise(X))<=>~kind(X)))&
(![X]:((rich(X)&creative(X))<=>(~patient(X)&curious(X))))&
((happy(john))=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((calm(X)&~happy(X))<=>tall(X)))&
(![X]:((~calm(X)&humble(X))<=>(~tall(X)&~kind(X))))&
(![X]:((~old(X)|tall(X))=>funny(X)))&
((curious(mary))=>(calm(susan)))&
(![X]:((~rich(X)<~>calm(X))=>(~funny(X)|~generous(X))))&
(funny(fred))&
(?[X]:((~calm(X)|calm(X))))&
((rich(lucy)&~kind(lucy)))&
((quiet(john)|curious(john)))&
((~rich(susan)<~>~creative(susan)))&
(curious(mary))&
((~kind(paul)&~old(paul)))&
((~generous(susan)&patient(susan))) | ~old(lucy) | [
"p5",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 10586981170367433715008
% SZS output start Proof for 10586981170367433715008
6. ! [X0] : ((~generous(X0) | ~tall(X0)) => (rich(X0) <~> old(X0))) [input p5]
12. ! [X0] : ((~happy(X0) & calm(X0)) <=> tall(X0)) [input p11]
14. ! [X0] : ((tall(X0) | ~old(X0)) => funny(X0)) [input p13]
16. ! [X0] : ((~rich(X0) <~> calm(X0)) => (~generous(X0) | ~funny(X0))) [input p15]
19. ~kind(lucy) & rich(lucy) [input p18]
25. old(lucy) [input hypothesis]
34. ! [X0] : ((rich(X0) <~> old(X0)) | (generous(X0) & tall(X0))) [ennf transformation 6]
36. ! [X0] : (funny(X0) | (~tall(X0) & old(X0))) [ennf transformation 14]
38. ! [X0] : ((~generous(X0) | ~funny(X0)) | (~rich(X0) <=> calm(X0))) [ennf transformation 16]
39. ! [X0] : (~generous(X0) | ~funny(X0) | (~rich(X0) <=> calm(X0))) [flattening 38]
53. ! [X0] : (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (generous(X0) & tall(X0))) [nnf transformation 34]
66. ! [X0] : (((~happy(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 12]
67. ! [X0] : (((~happy(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | happy(X0) | ~calm(X0))) [flattening 66]
70. ! [X0] : (~generous(X0) | ~funny(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) [nnf transformation 39]
86. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 53]
87. ~old(X0) | ~rich(X0) | generous(X0) [cnf transformation 53]
102. ~tall(X0) | calm(X0) [cnf transformation 67]
109. ~tall(X0) | funny(X0) [cnf transformation 36]
112. ~funny(X0) | ~generous(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 70]
115. rich(lucy) [cnf transformation 19]
125. old(lucy) [cnf transformation 25]
312. ~rich(lucy) | tall(lucy) [resolution 86,125]
316. tall(lucy) [subsumption resolution 312,115]
317. funny(lucy) [resolution 316,109]
318. calm(lucy) [resolution 316,102]
319. ~rich(lucy) | generous(lucy) [resolution 87,125]
323. generous(lucy) [subsumption resolution 319,115]
416. ~generous(lucy) | ~rich(lucy) | ~calm(lucy) [resolution 317,112]
418. ~rich(lucy) | ~calm(lucy) [subsumption resolution 416,323]
419. ~calm(lucy) [subsumption resolution 418,115]
420. $false [subsumption resolution 419,318]
% SZS output end Proof for 10586981170367433715008
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is either not quiet or calm and vice versa. Everyone who is either wise or not humble is either not generous or wise and vice versa. Everyone who is not old or generous is either tall or wise and vice versa. Everyone who is not generous or generous is not old and vice versa. Everyone who is either patient or not kind is either quiet or not wise and vice versa. Everyone who is either generous or calm is either not kind or quiet and vice versa. If paul is either not rich or happy then someone is both not quiet and quiet. Everyone who is either not patient or patient is both not old and not quiet. Everyone who is not patient is either not creative or funny and vice versa. If susan is either not happy or kind then susan is either not tall or not old and vice versa. Everyone who is either old or not generous is calm or happy. If someone is not happy or tall then someone is either patient or not kind. If fred is not happy then fred is either brave or not quiet and vice versa. Everyone who is strong is both strong and not quiet and vice versa. If susan is old or patient then alice is both not curious and curious. Someone is both curious and not brave. Someone is not tall or not humble. Paul is not kind. Mary is not creative. Susan is either brave or not happy. | Susan is humble. | entailment | (![X]:((~quiet(X)|humble(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
(![X]:((old(X)<~>~generous(X))=>(calm(X)|happy(X))))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
((~happy(fred))<=>((brave(fred)<~>~quiet(fred))))&
(![X]:(strong(X)<=>(strong(X)&~quiet(X))))&
(((old(susan)|patient(susan)))=>((~curious(alice)&curious(alice))))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~tall(X)|~humble(X))))&
(~kind(paul))&
(~creative(mary))&
((brave(susan)<~>~happy(susan))) | humble(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8807956177035992277611677
% SZS output start Proof for 8807956177035992277611677
1. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> (~quiet(X0) <~> calm(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> (~generous(X0) <~> wise(X0))) [input p1]
3. ! [X0] : ((generous(X0) | ~old(X0)) <=> (tall(X0) <~> wise(X0))) [input p2]
4. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~old(X0)) [input p3]
5. ! [X0] : ((patient(X0) <~> ~kind(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p4]
6. ! [X0] : ((generous(X0) <~> calm(X0)) <=> (~kind(X0) <~> quiet(X0))) [input p5]
8. ! [X0] : ((~patient(X0) <~> patient(X0)) => (~quiet(X0) & ~old(X0))) [input p7]
10. (~happy(susan) <~> kind(susan)) <=> (~tall(susan) <~> ~old(susan)) [input p9]
11. ! [X0] : ((old(X0) <~> ~generous(X0)) => (happy(X0) | calm(X0))) [input p10]
15. (patient(susan) | old(susan)) => (curious(alice) & ~curious(alice)) [input p14]
21. ~humble(susan) [input hypothesis]
24. ! [X0] : ((~quiet(X0) & ~old(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 8]
25. ! [X0] : ((happy(X0) | calm(X0)) | (old(X0) <=> ~generous(X0))) [ennf transformation 11]
26. ! [X0] : (happy(X0) | calm(X0) | (old(X0) <=> ~generous(X0))) [flattening 25]
28. (curious(alice) & ~curious(alice)) | (~patient(susan) & ~old(susan)) [ennf transformation 15]
29. ! [X0] : (((humble(X0) | ~quiet(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~humble(X0) & quiet(X0)))) [nnf transformation 1]
30. ! [X0] : ((humble(X0) | ~quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) & (((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (~humble(X0) & quiet(X0)))) [flattening 29]
31. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 2]
32. ! [X0] : (((generous(X0) | ~old(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [nnf transformation 3]
33. ! [X0] : ((generous(X0) | ~old(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [flattening 32]
34. ! [X0] : (((generous(X0) | ~generous(X0)) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 4]
35. ! [X0] : ((generous(X0) | ~generous(X0) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [flattening 34]
36. ! [X0] : ((((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 6]
41. ! [X0] : ((~quiet(X0) & ~old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 24]
43. (((~kind(susan) | happy(susan)) & (kind(susan) | ~happy(susan))) | ((~tall(susan) | old(susan)) & (~old(susan) | tall(susan)))) & (((old(susan) | tall(susan)) & (~old(susan) | ~tall(susan))) | ((~happy(susan) | ~kind(susan)) & (kind(susan) | happy(susan)))) [nnf transformation 10]
44. ! [X0] : (happy(X0) | calm(X0) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0)))) [nnf transformation 26]
59. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 30]
64. wise(X0) | ~generous(X0) | wise(X0) | humble(X0) [cnf transformation 31]
70. humble(X0) | ~wise(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 31]
73. ~tall(X0) | ~wise(X0) | old(X0) [cnf transformation 33]
77. ~old(X0) | generous(X0) [cnf transformation 35]
78. ~old(X0) | ~generous(X0) [cnf transformation 35]
85. ~kind(X0) | patient(X0) | quiet(X0) | wise(X0) [cnf transformation 36]
88. quiet(X0) | ~kind(X0) | calm(X0) | ~generous(X0) [cnf transformation 37]
92. calm(X0) | generous(X0) | quiet(X0) | kind(X0) [cnf transformation 37]
95. ~calm(X0) | ~generous(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 37]
102. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 41]
103. ~quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 41]
111. old(susan) | tall(susan) | ~happy(susan) | ~kind(susan) [cnf transformation 43]
117. happy(X0) | calm(X0) | old(X0) | generous(X0) [cnf transformation 44]
130. ~curious(alice) | ~patient(susan) [cnf transformation 28]
132. curious(alice) | ~patient(susan) [cnf transformation 28]
140. ~humble(susan) [cnf transformation 21]
143. ~quiet(X0) | patient(X0) [duplicate literal removal 102]
144. ~patient(X0) | ~quiet(X0) [duplicate literal removal 103]
145. wise(X0) | ~generous(X0) | humble(X0) [duplicate literal removal 64]
148. ~generous(X0) | ~wise(X0) | humble(X0) [duplicate literal removal 70]
149. ~calm(X0) | quiet(X0) [duplicate literal removal 59]
152. ~generous(X0) | humble(X0) [subsumption resolution 145,148]
153. ~old(X0) [subsumption resolution 77,78]
154. ~kind(X0) | ~generous(X0) | ~calm(X0) [subsumption resolution 95,149]
155. kind(X0) | quiet(X0) | generous(X0) [subsumption resolution 92,149]
157. ~kind(X0) | quiet(X0) | ~generous(X0) [subsumption resolution 88,154]
174. ~quiet(X0) [subsumption resolution 143,144]
177. 4 <=> tall(susan) [avatar definition]
178. tall(susan) <- (4) [avatar component clause 177]
181. 5 <=> happy(susan) [avatar definition]
182. ~happy(susan) <- (~5) [avatar component clause 181]
185. 6 <=> kind(susan) [avatar definition]
186. kind(susan) <- (6) [avatar component clause 185]
187. ~kind(susan) <- (~6) [avatar component clause 185]
191. tall(susan) | ~happy(susan) | ~kind(susan) [subsumption resolution 111,153]
192. ~6 | ~5 | 4 [avatar split clause 191,177,181,185]
195. happy(X0) | calm(X0) | generous(X0) [subsumption resolution 117,153]
227. 13 <=> patient(susan) [avatar definition]
229. ~patient(susan) <- (~13) [avatar component clause 227]
231. 14 <=> curious(alice) [avatar definition]
234. ~13 | 14 [avatar split clause 132,231,227]
235. ~13 | ~14 [avatar split clause 130,231,227]
261. quiet(susan) | generous(susan) <- (~6) [resolution 155,187]
264. generous(susan) <- (~6) [subsumption resolution 261,174]
288. humble(susan) <- (~6) [resolution 264,152]
289. $false <- (~6) [subsumption resolution 288,140]
290. 6 [avatar contradiction clause 289]
293. quiet(susan) | ~generous(susan) <- (6) [resolution 186,157]
295. ~generous(susan) <- (6) [subsumption resolution 293,174]
297. calm(susan) | generous(susan) <- (~5) [resolution 195,182]
299. calm(susan) <- (~5, 6) [subsumption resolution 297,295]
359. quiet(susan) <- (~5, 6) [resolution 299,149]
360. $false <- (~5, 6) [subsumption resolution 359,174]
361. 5 | ~6 [avatar contradiction clause 360]
366. ~wise(susan) | old(susan) <- (4) [resolution 178,73]
367. ~wise(susan) <- (4) [subsumption resolution 366,153]
407. patient(susan) | quiet(susan) | wise(susan) <- (6) [resolution 85,186]
410. quiet(susan) | wise(susan) <- (6, ~13) [subsumption resolution 407,229]
411. wise(susan) <- (6, ~13) [subsumption resolution 410,174]
412. $false <- (4, 6, ~13) [subsumption resolution 411,367]
413. ~4 | ~6 | 13 [avatar contradiction clause 412]
414. $false [avatar sat refutation 192,234,235,290,361,413]
% SZS output end Proof for 8807956177035992277611677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or strong is strong or patient and vice versa.
Everyone who is both not kind and kind is either patient or creative.
Everyone who is not kind is not rich.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
Everyone who is calm is both curious and humble.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
Everyone who is both not calm and not happy is not brave and vice versa.
Everyone who is not funny is both not funny and calm.
Someone is both not tall and curious.
Paul is not strong.
Mary is either not curious or humble.
Someone is either wise or not calm.
Paul is both not calm and tall.
Someone is either not creative or tall.
Someone is either not kind or not funny.
Someone is both quiet and kind. | Paul is not brave. | contradiction | (![X]:((creative(X)|strong(X))<=>(strong(X)|patient(X))))&
(![X]:((~kind(X)&kind(X))=>(patient(X)<~>creative(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
(![X]:(calm(X)=>(curious(X)&humble(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((~calm(X)&~happy(X))<=>~brave(X)))&
(![X]:(~funny(X)=>(~funny(X)&calm(X))))&
(?[X]:((~tall(X)&curious(X))))&
(~strong(paul))&
((~curious(mary)<~>humble(mary)))&
(?[X]:((wise(X)<~>~calm(X))))&
((~calm(paul)&tall(paul)))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((quiet(X)&kind(X)))) | ~brave(paul) | [
"p3",
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6060078848411174377702493
% SZS output start Proof for 6060078848411174377702493
4. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p3]
5. ! [X0] : (happy(X0) <=> (brave(X0) & ~creative(X0))) [input p4]
21. tall(paul) & ~calm(paul) [input p20]
25. ~brave(paul) [input hypothesis]
39. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 4]
40. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 39]
41. ! [X0] : ((happy(X0) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [nnf transformation 5]
42. ! [X0] : ((happy(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | ~happy(X0))) [flattening 41]
86. calm(X0) | happy(X0) [cnf transformation 40]
89. ~happy(X0) | brave(X0) [cnf transformation 42]
129. ~calm(paul) [cnf transformation 21]
137. ~brave(paul) [cnf transformation 25]
262. happy(paul) [resolution 86,129]
268. brave(paul) [resolution 89,262]
271. $false [subsumption resolution 268,137]
% SZS output end Proof for 6060078848411174377702493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both generous and not patient is both calm and humble. If someone is either not kind or quiet then lucy is either not wise or curious. Everyone who is both not curious and curious is both not happy and funny. If someone is either calm or not generous then alice is not humble and vice versa. Everyone who is brave is both not rich and not happy and vice versa. If john is both generous and not strong then someone is not patient or not rich and vice versa. If someone is both generous and not calm then lucy is not curious or funny and vice versa. If someone is not kind or generous then someone is both funny and not funny and vice versa. Everyone who is either not rich or quiet is calm or tall and vice versa. Everyone who is not strong is either creative or not old and vice versa. Everyone who is wise or curious is rich or funny and vice versa. If someone is both not old and not tall then lucy is humble and vice versa. Everyone who is either calm or not brave is not kind. Everyone who is both not kind and generous is both happy and not patient. If lucy is either not patient or not brave then someone is not humble and vice versa. Someone is not brave. Mary is both rich and creative. Mary is old or not brave. Mary is strong. Someone is creative. Someone is both funny and tall. Fred is not curious. | Fred is not strong. | neutral | (![X]:((generous(X)&~patient(X))=>(calm(X)&humble(X))))&
((?[X]:((~kind(X)<~>quiet(X))))=>((~wise(lucy)<~>curious(lucy))))&
(![X]:((~curious(X)&curious(X))=>(~happy(X)&funny(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(~humble(alice)))&
(![X]:(brave(X)<=>(~rich(X)&~happy(X))))&
(((generous(john)&~strong(john)))<=>(?[X]:((~patient(X)|~rich(X)))))&
((?[X]:((generous(X)&~calm(X))))<=>((~curious(lucy)|funny(lucy))))&
((?[X]:((~kind(X)|generous(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~rich(X)<~>quiet(X))<=>(calm(X)|tall(X))))&
(![X]:(~strong(X)<=>(creative(X)<~>~old(X))))&
(![X]:((wise(X)|curious(X))<=>(rich(X)|funny(X))))&
((?[X]:((~old(X)&~tall(X))))<=>(humble(lucy)))&
(![X]:((calm(X)<~>~brave(X))=>~kind(X)))&
(![X]:((~kind(X)&generous(X))=>(happy(X)&~patient(X))))&
(((~patient(lucy)<~>~brave(lucy)))<=>(?[X]:(~humble(X))))&
(?[X]:(~brave(X)))&
((rich(mary)&creative(mary)))&
((old(mary)|~brave(mary)))&
(strong(mary))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)&tall(X))))&
(~curious(fred)) | ~strong(fred) | [] | null | 0 |
Everyone who is not calm is either humble or not quiet and vice versa.
If someone is either not quiet or humble then john is patient and vice versa.
If paul is either not funny or wise then someone is not curious and vice versa.
Everyone who is both not calm and generous is not strong and vice versa.
If fred is both not creative and not generous then someone is both not strong and not humble and vice versa.
Everyone who is not wise is tall or not creative and vice versa.
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Someone is funny.
Someone is either strong or tall.
John is both funny and not wise.
Someone is calm or not quiet. | Paul is funny. | entailment | (![X]:(~calm(X)<=>(humble(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(patient(john)))&
(((~funny(paul)<~>wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((~calm(X)&generous(X))<=>~strong(X)))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)<~>tall(X))))&
((funny(john)&~wise(john)))&
(?[X]:((calm(X)|~quiet(X)))) | funny(paul) | [
"p2",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8724212782946169970337817
% SZS output start Proof for 8724212782946169970337817
3. (~funny(paul) <~> wise(paul)) <=> ? [X0] : ~curious(X0) [input p2]
8. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) | old(X0)) => (~brave(X0) & curious(X0))) [input p9]
11. (wise(paul) <~> ~old(paul)) => tall(fred) [input p10]
12. ! [X0] : ((~patient(X0) & ~quiet(X0)) => (old(X0) & ~tall(X0))) [input p11]
21. ~funny(paul) [input hypothesis]
25. ! [X0] : ((~brave(X0) & curious(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 10]
26. tall(fred) | (wise(paul) <=> ~old(paul)) [ennf transformation 11]
27. ! [X0] : ((old(X0) & ~tall(X0)) | (patient(X0) | quiet(X0))) [ennf transformation 12]
28. ! [X0] : ((old(X0) & ~tall(X0)) | patient(X0) | quiet(X0)) [flattening 27]
37. (((~wise(paul) | funny(paul)) & (wise(paul) | ~funny(paul))) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ((~funny(paul) | ~wise(paul)) & (wise(paul) | funny(paul)))) [nnf transformation 3]
38. (((~wise(paul) | funny(paul)) & (wise(paul) | ~funny(paul))) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ((~funny(paul) | ~wise(paul)) & (wise(paul) | funny(paul)))) [rectify 37]
39. ? [X1] : ~curious(X1) => ~curious(sK1) [choice axiom]
40. (((~wise(paul) | funny(paul)) & (wise(paul) | ~funny(paul))) | ! [X0] : curious(X0)) & (~curious(sK1) | ((~funny(paul) | ~wise(paul)) & (wise(paul) | funny(paul)))) [skolemisation 38,39]
54. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
55. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 54]
58. tall(fred) | ((wise(paul) | old(paul)) & (~old(paul) | ~wise(paul))) [nnf transformation 26]
81. ~curious(sK1) | wise(paul) | funny(paul) [cnf transformation 40]
99. ~patient(X0) | ~patient(X0) [cnf transformation 55]
101. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 55]
104. curious(X0) | quiet(X0) [cnf transformation 25]
107. tall(fred) | ~old(paul) | ~wise(paul) [cnf transformation 58]
109. ~tall(X0) | patient(X0) | quiet(X0) [cnf transformation 28]
110. old(X0) | patient(X0) | quiet(X0) [cnf transformation 28]
131. ~funny(paul) [cnf transformation 21]
132. ~patient(X0) [duplicate literal removal 99]
133. ~quiet(X0) | patient(X0) [duplicate literal removal 101]
160. 7 <=> funny(paul) [avatar definition]
164. 8 <=> wise(paul) [avatar definition]
170. 9 <=> curious(sK1) [avatar definition]
172. ~curious(sK1) <- (~9) [avatar component clause 170]
174. 7 | 8 | ~9 [avatar split clause 81,170,164,160]
211. 18 <=> ! [X1] : (quiet(X1) | old(X1)) [avatar definition]
212. old(X1) | quiet(X1) <- (18) [avatar component clause 211]
226. 21 <=> old(paul) [avatar definition]
227. ~old(paul) <- (~21) [avatar component clause 226]
230. 22 <=> tall(fred) [avatar definition]
232. tall(fred) <- (22) [avatar component clause 230]
234. ~8 | ~21 | 22 [avatar split clause 107,230,226,164]
235. old(X0) | quiet(X0) [subsumption resolution 110,132]
236. 18 [avatar split clause 235,211]
237. ~tall(X0) | quiet(X0) [subsumption resolution 109,132]
291. ~7 [avatar split clause 131,160]
300. quiet(sK1) <- (~9) [resolution 104,172]
302. patient(sK1) <- (~9) [resolution 133,300]
305. $false <- (~9) [subsumption resolution 302,132]
306. 9 [avatar contradiction clause 305]
317. quiet(paul) <- (18, ~21) [resolution 212,227]
321. patient(paul) <- (18, ~21) [resolution 317,133]
324. $false <- (18, ~21) [subsumption resolution 321,132]
325. ~18 | 21 [avatar contradiction clause 324]
327. quiet(fred) <- (22) [resolution 232,237]
331. patient(fred) <- (22) [resolution 327,133]
334. $false <- (22) [subsumption resolution 331,132]
335. ~22 [avatar contradiction clause 334]
336. $false [avatar sat refutation 174,234,236,291,306,325,335]
% SZS output end Proof for 8724212782946169970337817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not humble is quiet and vice versa.
If fred is creative or not creative then someone is not humble or curious and vice versa.
If susan is not tall or curious then someone is not generous or not creative and vice versa.
Everyone who is either patient or happy is either not curious or tall and vice versa.
Everyone who is both strong and not calm is either not calm or quiet.
Everyone who is either not calm or creative is either not happy or brave.
If alice is both not curious and not happy then someone is calm or quiet.
Everyone who is both old and humble is generous and vice versa.
Everyone who is brave is not calm or not brave and vice versa.
If someone is patient then someone is either not rich or not funny and vice versa.
If someone is both old and wise then alice is not curious and vice versa.
If alice is both not brave and not kind then someone is either not kind or not calm.
If fred is not funny then someone is either strong or old.
Everyone who is strong or creative is not rich and vice versa.
If someone is patient then mary is both calm and not generous and vice versa.
Everyone who is both curious and kind is both not humble and quiet.
Someone is either kind or generous.
Alice is funny.
Someone is not calm or not strong.
Paul is not quiet.
Someone is either not calm or old.
Susan is both not patient and not happy.
Alice is both generous and not creative.
John is not old. | Alice is brave. | entailment | (![X]:((~tall(X)&~humble(X))<=>quiet(X)))&
(((creative(fred)|~creative(fred)))<=>(?[X]:((~humble(X)|curious(X)))))&
(((~tall(susan)|curious(susan)))<=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:((patient(X)<~>happy(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((strong(X)&~calm(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~calm(X)<~>creative(X))=>(~happy(X)<~>brave(X))))&
(((~curious(alice)&~happy(alice)))=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((old(X)&humble(X))<=>generous(X)))&
(![X]:(brave(X)<=>(~calm(X)|~brave(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
((?[X]:((old(X)&wise(X))))<=>(~curious(alice)))&
(((~brave(alice)&~kind(alice)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
((~funny(fred))=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:((strong(X)|creative(X))<=>~rich(X)))&
((?[X]:(patient(X)))<=>((calm(mary)&~generous(mary))))&
(![X]:((curious(X)&kind(X))=>(~humble(X)&quiet(X))))&
(?[X]:((kind(X)<~>generous(X))))&
(funny(alice))&
(?[X]:((~calm(X)|~strong(X))))&
(~quiet(paul))&
(?[X]:((~calm(X)<~>old(X))))&
((~patient(susan)&~happy(susan)))&
((generous(alice)&~creative(alice)))&
(~old(john)) | brave(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8709505187823124454629364
% SZS output start Proof for 8709505187823124454629364
9. ! [X0] : (brave(X0) <=> (~brave(X0) | ~calm(X0))) [input p8]
25. ~brave(alice) [input hypothesis]
56. ! [X0] : ((brave(X0) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 9]
57. ! [X0] : ((brave(X0) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ~brave(X0))) [flattening 56]
119. brave(X0) | brave(X0) [cnf transformation 57]
151. ~brave(alice) [cnf transformation 25]
153. brave(X0) [duplicate literal removal 119]
284. $false [subsumption resolution 151,153]
% SZS output end Proof for 8709505187823124454629364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and wise is not strong and vice versa.
If someone is both not funny and creative then john is curious or brave and vice versa.
If someone is happy or not strong then someone is not creative or humble and vice versa.
If fred is kind or brave then someone is either not brave or funny.
If fred is either curious or calm then alice is not generous and vice versa.
Everyone who is not creative or tall is either not patient or wise.
If someone is happy then someone is not patient and vice versa.
Everyone who is either rich or calm is both not generous and funny and vice versa.
Everyone who is creative is brave or curious.
If mary is not wise then someone is old and vice versa.
Everyone who is quiet is both not generous and kind.
If someone is not calm or not kind then someone is not curious and vice versa.
If paul is quiet then paul is strong.
Everyone who is either wise or not funny is either not quiet or not curious.
Everyone who is both not happy and not old is either kind or rich and vice versa.
If john is both not rich and funny then someone is either not wise or not quiet and vice versa.
Lucy is either calm or rich.
Someone is both humble and not kind.
Someone is either curious or brave.
Paul is either not quiet or not calm.
Lucy is curious.
Lucy is both happy and not patient.
John is both not funny and not tall.
Someone is both not quiet and not old. | Lucy is not strong. | contradiction | (![X]:((funny(X)&wise(X))<=>~strong(X)))&
((?[X]:((~funny(X)&creative(X))))<=>((curious(john)|brave(john))))&
((?[X]:((happy(X)|~strong(X))))<=>(?[X]:((~creative(X)|humble(X)))))&
(((kind(fred)|brave(fred)))=>(?[X]:((~brave(X)<~>funny(X)))))&
(((curious(fred)<~>calm(fred)))<=>(~generous(alice)))&
(![X]:((~creative(X)|tall(X))=>(~patient(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~patient(X))))&
(![X]:((rich(X)<~>calm(X))<=>(~generous(X)&funny(X))))&
(![X]:(creative(X)=>(brave(X)|curious(X))))&
((~wise(mary))<=>(?[X]:(old(X))))&
(![X]:(quiet(X)=>(~generous(X)&kind(X))))&
((?[X]:((~calm(X)|~kind(X))))<=>(?[X]:(~curious(X))))&
((quiet(paul))=>(strong(paul)))&
(![X]:((wise(X)<~>~funny(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((~happy(X)&~old(X))<=>(kind(X)<~>rich(X))))&
(((~rich(john)&funny(john)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
((calm(lucy)<~>rich(lucy)))&
(?[X]:((humble(X)&~kind(X))))&
(?[X]:((curious(X)<~>brave(X))))&
((~quiet(paul)<~>~calm(paul)))&
(curious(lucy))&
((happy(lucy)&~patient(lucy)))&
((~funny(john)&~tall(john)))&
(?[X]:((~quiet(X)&~old(X)))) | ~strong(lucy) | [
"p0",
"p13",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2836158988483391311595217
% SZS output start Proof for 2836158988483391311595217
1. ! [X0] : ((wise(X0) & funny(X0)) <=> ~strong(X0)) [input p0]
14. ! [X0] : ((wise(X0) <~> ~funny(X0)) => (~quiet(X0) <~> ~curious(X0))) [input p13]
16. (funny(john) & ~rich(john)) <=> ? [X0] : (~wise(X0) <~> ~quiet(X0)) [input p15]
21. curious(lucy) [input p20]
23. ~tall(john) & ~funny(john) [input p22]
25. ~strong(lucy) [input hypothesis]
30. ~funny(john) [pure predicate removal 23]
37. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) | (wise(X0) <=> ~funny(X0))) [ennf transformation 14]
38. ! [X0] : (((wise(X0) & funny(X0)) | strong(X0)) & (~strong(X0) | (~wise(X0) | ~funny(X0)))) [nnf transformation 1]
39. ! [X0] : (((wise(X0) & funny(X0)) | strong(X0)) & (~strong(X0) | ~wise(X0) | ~funny(X0))) [flattening 38]
71. ! [X0] : (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) [nnf transformation 37]
74. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (~funny(john) | rich(john))) [nnf transformation 16]
75. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X0] : ((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ~funny(john) | rich(john)) [flattening 74]
76. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) | ~funny(john) | rich(john)) [rectify 75]
77. ? [X1] : ((quiet(X1) | wise(X1)) & (~quiet(X1) | ~wise(X1))) => ((quiet(sK9) | wise(sK9)) & (~quiet(sK9) | ~wise(sK9))) [choice axiom]
78. ((funny(john) & ~rich(john)) | ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0)))) & (((quiet(sK9) | wise(sK9)) & (~quiet(sK9) | ~wise(sK9))) | ~funny(john) | rich(john)) [skolemisation 76,77]
89. strong(X0) | funny(X0) [cnf transformation 39]
90. strong(X0) | wise(X0) [cnf transformation 39]
127. ~quiet(X0) | ~curious(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 71]
142. funny(john) | ~wise(X0) | quiet(X0) [cnf transformation 78]
151. curious(lucy) [cnf transformation 21]
154. ~funny(john) [cnf transformation 30]
157. ~strong(lucy) [cnf transformation 25]
310. 35 <=> ! [X0] : (~wise(X0) | quiet(X0)) [avatar definition]
311. ~wise(X0) | quiet(X0) <- (35) [avatar component clause 310]
313. 36 <=> funny(john) [avatar definition]
316. 35 | 36 [avatar split clause 142,313,310]
363. ~36 [avatar split clause 154,313]
366. funny(lucy) [resolution 89,157]
368. wise(lucy) [resolution 90,157]
373. quiet(lucy) <- (35) [resolution 311,368]
502. ~curious(lucy) | ~funny(lucy) | ~wise(lucy) <- (35) [resolution 127,373]
503. ~funny(lucy) | ~wise(lucy) <- (35) [subsumption resolution 502,151]
504. ~wise(lucy) <- (35) [subsumption resolution 503,366]
505. $false <- (35) [subsumption resolution 504,368]
506. ~35 [avatar contradiction clause 505]
507. $false [avatar sat refutation 316,363,506]
% SZS output end Proof for 2836158988483391311595217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not creative is not kind. Everyone who is not generous is strong. If someone is not generous or curious then fred is either not wise or not old. Everyone who is either old or tall is either creative or not strong. If mary is both not humble and not funny then fred is either not humble or not quiet. If alice is either not curious or not kind then john is not brave or funny and vice versa. If someone is humble then fred is strong and vice versa. If someone is either quiet or not creative then someone is not creative or calm and vice versa. Everyone who is not rich or kind is old or strong. If susan is either humble or not creative then someone is either not old or not patient. If alice is patient or not humble then someone is not happy. Everyone who is not old or quiet is both not wise and not curious and vice versa. Everyone who is old is quiet and vice versa. If someone is either not old or not wise then lucy is not patient. Everyone who is curious is calm or not tall. Everyone who is not calm or calm is curious or not rich. Someone is either not rich or creative. Someone is either generous or not humble. Someone is both calm and old. Alice is creative. Lucy is both not quiet and not brave. Someone is quiet. Someone is not happy or not brave. | Mary is not humble. | neutral | (![X]:((wise(X)|~creative(X))=>~kind(X)))&
(![X]:(~generous(X)=>strong(X)))&
((?[X]:((~generous(X)|curious(X))))=>((~wise(fred)<~>~old(fred))))&
(![X]:((old(X)<~>tall(X))=>(creative(X)<~>~strong(X))))&
(((~humble(mary)&~funny(mary)))=>((~humble(fred)<~>~quiet(fred))))&
(((~curious(alice)<~>~kind(alice)))<=>((~brave(john)|funny(john))))&
((?[X]:(humble(X)))<=>(strong(fred)))&
((?[X]:((quiet(X)<~>~creative(X))))<=>(?[X]:((~creative(X)|calm(X)))))&
(![X]:((~rich(X)|kind(X))=>(old(X)|strong(X))))&
(((humble(susan)<~>~creative(susan)))=>(?[X]:((~old(X)<~>~patient(X)))))&
(((patient(alice)|~humble(alice)))=>(?[X]:(~happy(X))))&
(![X]:((~old(X)|quiet(X))<=>(~wise(X)&~curious(X))))&
(![X]:(old(X)<=>quiet(X)))&
((?[X]:((~old(X)<~>~wise(X))))=>(~patient(lucy)))&
(![X]:(curious(X)=>(calm(X)|~tall(X))))&
(![X]:((~calm(X)|calm(X))=>(curious(X)|~rich(X))))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:((calm(X)&old(X))))&
(creative(alice))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~happy(X)|~brave(X)))) | ~humble(mary) | [] | null | 0 |
If susan is not tall then fred is not strong and vice versa.
Everyone who is both not generous and happy is generous or happy.
If lucy is not rich then someone is quiet or not generous and vice versa.
If paul is wise or not funny then fred is either not kind or humble.
Everyone who is either not patient or not funny is brave and vice versa.
Everyone who is either not old or not creative is not creative and vice versa.
Everyone who is not wise or humble is both rich and calm.
Everyone who is either not old or funny is old.
If fred is both curious and not creative then fred is not quiet or creative.
If fred is both not brave and calm then mary is not patient or rich and vice versa.
Everyone who is generous or humble is kind or quiet and vice versa.
If someone is happy then lucy is either not patient or generous.
If someone is not calm then john is either strong or brave.
Everyone who is either not old or humble is quiet or brave and vice versa.
Everyone who is both not calm and strong is not old.
Everyone who is generous is not happy or quiet and vice versa.
Fred is not patient.
Mary is either patient or not rich.
Someone is patient or not curious.
Someone is both humble and kind.
Paul is either wise or not calm.
Paul is both rich and not curious.
Someone is either not creative or humble.
Mary is both not generous and patient. | Fred is quiet. | neutral | ((~tall(susan))<=>(~strong(fred)))&
(![X]:((~generous(X)&happy(X))=>(generous(X)|happy(X))))&
((~rich(lucy))<=>(?[X]:((quiet(X)|~generous(X)))))&
(((wise(paul)|~funny(paul)))=>((~kind(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>~funny(X))<=>brave(X)))&
(![X]:((~old(X)<~>~creative(X))<=>~creative(X)))&
(![X]:((~wise(X)|humble(X))=>(rich(X)&calm(X))))&
(![X]:((~old(X)<~>funny(X))=>old(X)))&
(((curious(fred)&~creative(fred)))=>((~quiet(fred)|creative(fred))))&
(((~brave(fred)&calm(fred)))<=>((~patient(mary)|rich(mary))))&
(![X]:((generous(X)|humble(X))<=>(kind(X)|quiet(X))))&
((?[X]:(happy(X)))=>((~patient(lucy)<~>generous(lucy))))&
((?[X]:(~calm(X)))=>((strong(john)<~>brave(john))))&
(![X]:((~old(X)<~>humble(X))<=>(quiet(X)|brave(X))))&
(![X]:((~calm(X)&strong(X))=>~old(X)))&
(![X]:(generous(X)<=>(~happy(X)|quiet(X))))&
(~patient(fred))&
((patient(mary)<~>~rich(mary)))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:((humble(X)&kind(X))))&
((wise(paul)<~>~calm(paul)))&
((rich(paul)&~curious(paul)))&
(?[X]:((~creative(X)<~>humble(X))))&
((~generous(mary)&patient(mary))) | quiet(fred) | [] | null | 0 |
Everyone who is both funny and not strong is not funny or calm.
Everyone who is curious or not humble is not rich.
Everyone who is rich is not tall and vice versa.
If someone is both not quiet and strong then someone is not patient or not old.
Everyone who is not rich or old is either strong or not calm.
Everyone who is kind or not generous is either not calm or not funny.
Everyone who is not kind or calm is both not brave and not curious.
If someone is not wise then mary is either brave or not wise and vice versa.
Everyone who is both not curious and not humble is calm and vice versa.
Everyone who is brave is not brave.
If someone is happy then someone is not strong or not happy.
Everyone who is not kind is not wise or not calm and vice versa.
Everyone who is either old or tall is both not quiet and not funny.
If susan is both not kind and funny then someone is not humble and vice versa.
If john is either happy or not humble then susan is both curious and not wise.
Lucy is both quiet and not old.
Alice is not kind or wise.
Someone is strong or not quiet.
Fred is curious or not patient.
Someone is either old or not wise.
Alice is brave or not kind.
Paul is either funny or calm. | Paul is strong. | entailment | (![X]:((funny(X)&~strong(X))=>(~funny(X)|calm(X))))&
(![X]:((curious(X)|~humble(X))=>~rich(X)))&
(![X]:(rich(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((~rich(X)|old(X))=>(strong(X)<~>~calm(X))))&
(![X]:((kind(X)|~generous(X))=>(~calm(X)<~>~funny(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)&~curious(X))))&
((?[X]:(~wise(X)))<=>((brave(mary)<~>~wise(mary))))&
(![X]:((~curious(X)&~humble(X))<=>calm(X)))&
(![X]:(brave(X)=>~brave(X)))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(~kind(X)<=>(~wise(X)|~calm(X))))&
(![X]:((old(X)<~>tall(X))=>(~quiet(X)&~funny(X))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:(~humble(X))))&
(((happy(john)<~>~humble(john)))=>((curious(susan)&~wise(susan))))&
((quiet(lucy)&~old(lucy)))&
((~kind(alice)|wise(alice)))&
(?[X]:((strong(X)|~quiet(X))))&
((curious(fred)|~patient(fred)))&
(?[X]:((old(X)<~>~wise(X))))&
((brave(alice)|~kind(alice)))&
((funny(paul)<~>calm(paul))) | strong(paul) | [
"p0",
"p1",
"p4",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4110242483989338381624225
% SZS output start Proof for 4110242483989338381624225
1. ! [X0] : ((~strong(X0) & funny(X0)) => (calm(X0) | ~funny(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | curious(X0)) => ~rich(X0)) [input p1]
5. ! [X0] : ((old(X0) | ~rich(X0)) => (strong(X0) <~> ~calm(X0))) [input p4]
9. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> calm(X0)) [input p8]
22. funny(paul) <~> calm(paul) [input p21]
23. ~strong(paul) [input hypothesis]
29. ! [X0] : ((calm(X0) | ~funny(X0)) | (strong(X0) | ~funny(X0))) [ennf transformation 1]
30. ! [X0] : (calm(X0) | ~funny(X0) | strong(X0) | ~funny(X0)) [flattening 29]
31. ! [X0] : (~rich(X0) | (humble(X0) & ~curious(X0))) [ennf transformation 2]
32. ! [X0] : ((strong(X0) <~> ~calm(X0)) | (~old(X0) & rich(X0))) [ennf transformation 5]
40. ! [X0] : (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~old(X0) & rich(X0))) [nnf transformation 32]
46. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | (humble(X0) | curious(X0)))) [nnf transformation 9]
47. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | humble(X0) | curious(X0))) [flattening 46]
65. (~calm(paul) | ~funny(paul)) & (calm(paul) | funny(paul)) [nnf transformation 22]
66. calm(X0) | ~funny(X0) | strong(X0) | ~funny(X0) [cnf transformation 30]
68. ~rich(X0) | humble(X0) [cnf transformation 31]
71. ~calm(X0) | strong(X0) | rich(X0) [cnf transformation 40]
87. ~humble(X0) | ~calm(X0) [cnf transformation 47]
111. calm(paul) | funny(paul) [cnf transformation 65]
113. ~strong(paul) [cnf transformation 23]
115. ~funny(X0) | calm(X0) | strong(X0) [duplicate literal removal 66]
206. 20 <=> funny(paul) [avatar definition]
207. funny(paul) <- (20) [avatar component clause 206]
210. 21 <=> calm(paul) [avatar definition]
211. calm(paul) <- (21) [avatar component clause 210]
212. ~calm(paul) <- (~21) [avatar component clause 210]
214. 20 | 21 [avatar split clause 111,210,206]
238. calm(paul) | strong(paul) <- (20) [resolution 115,207]
239. strong(paul) <- (20, ~21) [subsumption resolution 238,212]
240. $false <- (20, ~21) [subsumption resolution 239,113]
241. ~20 | 21 [avatar contradiction clause 240]
255. strong(paul) | rich(paul) <- (21) [resolution 211,71]
256. rich(paul) <- (21) [subsumption resolution 255,113]
267. humble(paul) <- (21) [resolution 256,68]
293. ~calm(paul) <- (21) [resolution 267,87]
294. $false <- (21) [subsumption resolution 293,211]
295. ~21 [avatar contradiction clause 294]
296. $false [avatar sat refutation 214,241,295]
% SZS output end Proof for 4110242483989338381624225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not quiet and kind and vice versa.
Everyone who is calm or humble is not brave and vice versa.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
If mary is both not curious and not humble then mary is either generous or not happy and vice versa.
Everyone who is not generous or not funny is not generous.
Everyone who is both not funny and not old is happy.
If paul is brave then someone is both not quiet and not tall.
Lucy is either funny or not strong.
Someone is either not old or not creative.
John is funny or tall.
Mary is either not quiet or not old. | Paul is not wise. | neutral | (![X]:(kind(X)<=>(~quiet(X)&kind(X))))&
(![X]:((calm(X)|humble(X))<=>~brave(X)))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(((~curious(mary)&~humble(mary)))<=>((generous(mary)<~>~happy(mary))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(![X]:((~funny(X)&~old(X))=>happy(X)))&
((brave(paul))=>(?[X]:((~quiet(X)&~tall(X)))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((~old(X)<~>~creative(X))))&
((funny(john)|tall(john)))&
((~quiet(mary)<~>~old(mary))) | ~wise(paul) | [] | null | 0 |
If someone is both tall and not calm then someone is wise. If john is both not kind and not old then paul is either not rich or not patient. If susan is wise then someone is either not calm or quiet. Everyone who is generous is both not creative and not quiet and vice versa. Everyone who is not rich or not funny is not kind or not old. Everyone who is not kind or not generous is both rich and not tall and vice versa. If alice is both not funny and not strong then paul is creative. If mary is both not strong and not quiet then someone is not old. If someone is either not tall or not humble then someone is not creative and vice versa. If john is either kind or not calm then someone is either strong or quiet. Everyone who is both funny and calm is generous and vice versa. If fred is wise or funny then someone is either not creative or humble. Everyone who is both strong and humble is either not happy or generous and vice versa. Susan is either calm or wise. Mary is not kind or generous. Alice is both not humble and old. Someone is either not funny or patient. Someone is not humble or wise. Susan is not tall. | Fred is not creative. | neutral | ((?[X]:((tall(X)&~calm(X))))=>(?[X]:(wise(X))))&
(((~kind(john)&~old(john)))=>((~rich(paul)<~>~patient(paul))))&
((wise(susan))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(generous(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((~rich(X)|~funny(X))=>(~kind(X)|~old(X))))&
(![X]:((~kind(X)|~generous(X))<=>(rich(X)&~tall(X))))&
(((~funny(alice)&~strong(alice)))=>(creative(paul)))&
(((~strong(mary)&~quiet(mary)))=>(?[X]:(~old(X))))&
((?[X]:((~tall(X)<~>~humble(X))))<=>(?[X]:(~creative(X))))&
(((kind(john)<~>~calm(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((funny(X)&calm(X))<=>generous(X)))&
(((wise(fred)|funny(fred)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((strong(X)&humble(X))<=>(~happy(X)<~>generous(X))))&
((calm(susan)<~>wise(susan)))&
((~kind(mary)|generous(mary)))&
((~humble(alice)&old(alice)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~humble(X)|wise(X))))&
(~tall(susan)) | ~creative(fred) | [] | null | 0 |
Everyone who is not humble or not brave is generous or not kind. Everyone who is both humble and tall is either not wise or not rich and vice versa. Everyone who is not wise or not funny is wise or not generous. Everyone who is generous is not quiet or rich and vice versa. If susan is not calm or not kind then someone is either not funny or calm. If someone is both generous and kind then fred is not quiet or not curious and vice versa. If fred is creative then john is both funny and not rich and vice versa. Everyone who is both not calm and generous is calm and vice versa. If someone is either not kind or not curious then someone is either not old or not tall and vice versa. If someone is funny then alice is either not tall or not humble and vice versa. Everyone who is either not creative or not tall is not strong or not rich and vice versa. If someone is either not kind or strong then someone is not brave or not calm. Everyone who is both not kind and brave is old. If someone is rich then someone is either funny or strong and vice versa. If someone is both wise and not patient then someone is wise or not patient and vice versa. Someone is not wise. John is both funny and not happy. Fred is either funny or not rich. Mary is not old or not brave. Alice is either patient or strong. Susan is not old or calm. | Alice is quiet. | entailment | (![X]:((~humble(X)|~brave(X))=>(generous(X)|~kind(X))))&
(![X]:((humble(X)&tall(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~wise(X)|~funny(X))=>(wise(X)|~generous(X))))&
(![X]:(generous(X)<=>(~quiet(X)|rich(X))))&
(((~calm(susan)|~kind(susan)))=>(?[X]:((~funny(X)<~>calm(X)))))&
((?[X]:((generous(X)&kind(X))))<=>((~quiet(fred)|~curious(fred))))&
((creative(fred))<=>((funny(john)&~rich(john))))&
(![X]:((~calm(X)&generous(X))<=>calm(X)))&
((?[X]:((~kind(X)<~>~curious(X))))<=>(?[X]:((~old(X)<~>~tall(X)))))&
((?[X]:(funny(X)))<=>((~tall(alice)<~>~humble(alice))))&
(![X]:((~creative(X)<~>~tall(X))<=>(~strong(X)|~rich(X))))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~kind(X)&brave(X))=>old(X)))&
((?[X]:(rich(X)))<=>(?[X]:((funny(X)<~>strong(X)))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(?[X]:(~wise(X)))&
((funny(john)&~happy(john)))&
((funny(fred)<~>~rich(fred)))&
((~old(mary)|~brave(mary)))&
((patient(alice)<~>strong(alice)))&
((~old(susan)|calm(susan))) | quiet(alice) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5804123411573760215462677
% SZS output start Proof for 5804123411573760215462677
4. ! [X0] : (generous(X0) <=> (rich(X0) | ~quiet(X0))) [input p3]
8. ! [X0] : ((generous(X0) & ~calm(X0)) <=> calm(X0)) [input p7]
22. ~quiet(alice) [input hypothesis]
38. ! [X0] : ((generous(X0) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | ~generous(X0))) [nnf transformation 4]
39. ! [X0] : ((generous(X0) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | ~generous(X0))) [flattening 38]
50. ! [X0] : (((generous(X0) & ~calm(X0)) | ~calm(X0)) & (calm(X0) | (~generous(X0) | calm(X0)))) [nnf transformation 8]
51. ! [X0] : (((generous(X0) & ~calm(X0)) | ~calm(X0)) & (calm(X0) | ~generous(X0) | calm(X0))) [flattening 50]
92. quiet(X0) | generous(X0) [cnf transformation 39]
106. calm(X0) | ~generous(X0) | calm(X0) [cnf transformation 51]
107. ~calm(X0) | ~calm(X0) [cnf transformation 51]
147. ~quiet(alice) [cnf transformation 22]
148. calm(X0) | ~generous(X0) [duplicate literal removal 106]
149. ~calm(X0) [duplicate literal removal 107]
210. ~generous(X0) [subsumption resolution 148,149]
362. generous(alice) [resolution 92,147]
363. $false [subsumption resolution 362,210]
% SZS output end Proof for 5804123411573760215462677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not happy is either not happy or brave. Everyone who is not kind is both quiet and not brave and vice versa. Everyone who is both strong and happy is rich or creative. If someone is both not old and not humble then lucy is creative. If someone is either not rich or not kind then someone is happy and vice versa. If someone is not tall or not generous then paul is not brave. Everyone who is either not patient or not humble is not brave. If someone is both not patient and not brave then paul is kind or rich and vice versa. Everyone who is not strong is both not tall and tall and vice versa. Everyone who is not old or kind is both not quiet and brave. Everyone who is generous is tall or not happy and vice versa. Everyone who is both strong and kind is creative. Everyone who is both patient and not humble is strong or curious and vice versa. If someone is tall then mary is not humble or not tall and vice versa. Everyone who is kind is not patient. Everyone who is both creative and quiet is either funny or patient. Someone is both not funny and quiet. Lucy is wise or patient. Someone is both curious and not humble. Mary is wise or not quiet. Someone is either not funny or not generous. | Paul is curious. | neutral | (![X]:((quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(![X]:(~kind(X)<=>(quiet(X)&~brave(X))))&
(![X]:((strong(X)&happy(X))=>(rich(X)|creative(X))))&
((?[X]:((~old(X)&~humble(X))))=>(creative(lucy)))&
((?[X]:((~rich(X)<~>~kind(X))))<=>(?[X]:(happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(~brave(paul)))&
(![X]:((~patient(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((kind(paul)|rich(paul))))&
(![X]:(~strong(X)<=>(~tall(X)&tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)&brave(X))))&
(![X]:(generous(X)<=>(tall(X)|~happy(X))))&
(![X]:((strong(X)&kind(X))=>creative(X)))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|curious(X))))&
((?[X]:(tall(X)))<=>((~humble(mary)|~tall(mary))))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((creative(X)&quiet(X))=>(funny(X)<~>patient(X))))&
(?[X]:((~funny(X)&quiet(X))))&
((wise(lucy)|patient(lucy)))&
(?[X]:((curious(X)&~humble(X))))&
((wise(mary)|~quiet(mary)))&
(?[X]:((~funny(X)<~>~generous(X)))) | curious(paul) | [] | null | 0 |
If susan is both wise and not kind then someone is both funny and not wise and vice versa.
Everyone who is both not funny and calm is brave and vice versa.
If someone is not generous or strong then someone is not happy and vice versa.
Everyone who is not patient or generous is wise or quiet.
Everyone who is not old or not happy is either patient or calm.
Everyone who is tall is not kind or tall.
If alice is quiet then john is strong or not kind and vice versa.
If lucy is happy then someone is old and vice versa.
If alice is humble or funny then someone is both calm and wise.
Everyone who is not humble or generous is both not generous and tall and vice versa.
If someone is either not generous or not humble then paul is both not old and generous and vice versa.
If someone is brave then fred is patient and vice versa.
Everyone who is both calm and curious is either old or not curious.
Everyone who is not funny or brave is not rich.
Everyone who is not wise or not calm is generous.
If mary is either wise or quiet then someone is either not rich or not quiet and vice versa.
Someone is both curious and not patient.
Someone is curious or generous.
Someone is humble or not funny.
Someone is not kind or not brave.
Paul is either funny or not rich.
Susan is not humble or not brave.
Alice is either wise or rich.
Someone is both quiet and not happy. | Paul is funny. | neutral | (((wise(susan)&~kind(susan)))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((~funny(X)&calm(X))<=>brave(X)))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)|generous(X))=>(wise(X)|quiet(X))))&
(![X]:((~old(X)|~happy(X))=>(patient(X)<~>calm(X))))&
(![X]:(tall(X)=>(~kind(X)|tall(X))))&
((quiet(alice))<=>((strong(john)|~kind(john))))&
((happy(lucy))<=>(?[X]:(old(X))))&
(((humble(alice)|funny(alice)))=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~humble(X)|generous(X))<=>(~generous(X)&tall(X))))&
((?[X]:((~generous(X)<~>~humble(X))))<=>((~old(paul)&generous(paul))))&
((?[X]:(brave(X)))<=>(patient(fred)))&
(![X]:((calm(X)&curious(X))=>(old(X)<~>~curious(X))))&
(![X]:((~funny(X)|brave(X))=>~rich(X)))&
(![X]:((~wise(X)|~calm(X))=>generous(X)))&
(((wise(mary)<~>quiet(mary)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(?[X]:((curious(X)&~patient(X))))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((~kind(X)|~brave(X))))&
((funny(paul)<~>~rich(paul)))&
((~humble(susan)|~brave(susan)))&
((wise(alice)<~>rich(alice)))&
(?[X]:((quiet(X)&~happy(X)))) | funny(paul) | [] | null | 0 |
If someone is rich then paul is either not strong or not curious.
Everyone who is either not patient or not tall is either not tall or not kind and vice versa.
Everyone who is either not generous or old is calm.
If someone is humble then alice is either not generous or not kind and vice versa.
Everyone who is patient is not generous.
Everyone who is calm is both patient and wise and vice versa.
If someone is both not patient and not kind then lucy is either funny or not kind.
Everyone who is both not funny and not rich is both generous and not calm and vice versa.
Everyone who is both not humble and not rich is either not old or not tall and vice versa.
If someone is both not curious and curious then fred is either not old or rich and vice versa.
Everyone who is not patient is both not patient and not brave and vice versa.
If someone is both curious and not quiet then paul is either strong or not generous and vice versa.
Everyone who is either old or not quiet is not happy and vice versa.
Everyone who is patient is kind.
Everyone who is either tall or calm is both not patient and generous.
Everyone who is both not patient and not happy is both funny and not calm.
Fred is both not wise and not happy.
Someone is calm or creative.
Someone is not generous.
Fred is not brave.
Someone is either generous or quiet.
Someone is not rich or not curious.
Someone is both not wise and tall.
Someone is either not rich or not kind. | Fred is not generous. | entailment | ((?[X]:(rich(X)))=>((~strong(paul)<~>~curious(paul))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~tall(X)<~>~kind(X))))&
(![X]:((~generous(X)<~>old(X))=>calm(X)))&
((?[X]:(humble(X)))<=>((~generous(alice)<~>~kind(alice))))&
(![X]:(patient(X)=>~generous(X)))&
(![X]:(calm(X)<=>(patient(X)&wise(X))))&
((?[X]:((~patient(X)&~kind(X))))=>((funny(lucy)<~>~kind(lucy))))&
(![X]:((~funny(X)&~rich(X))<=>(generous(X)&~calm(X))))&
(![X]:((~humble(X)&~rich(X))<=>(~old(X)<~>~tall(X))))&
((?[X]:((~curious(X)&curious(X))))<=>((~old(fred)<~>rich(fred))))&
(![X]:(~patient(X)<=>(~patient(X)&~brave(X))))&
((?[X]:((curious(X)&~quiet(X))))<=>((strong(paul)<~>~generous(paul))))&
(![X]:((old(X)<~>~quiet(X))<=>~happy(X)))&
(![X]:(patient(X)=>kind(X)))&
(![X]:((tall(X)<~>calm(X))=>(~patient(X)&generous(X))))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)&~calm(X))))&
((~wise(fred)&~happy(fred)))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:(~generous(X)))&
(~brave(fred))&
(?[X]:((generous(X)<~>quiet(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((~wise(X)&tall(X))))&
(?[X]:((~rich(X)<~>~kind(X)))) | ~generous(fred) | [
"p2",
"p4",
"p5",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 889455062520738712667961
% SZS output start Proof for 889455062520738712667961
3. ! [X0] : ((~generous(X0) <~> old(X0)) => calm(X0)) [input p2]
5. ! [X0] : (patient(X0) => ~generous(X0)) [input p4]
6. ! [X0] : (calm(X0) <=> (wise(X0) & patient(X0))) [input p5]
8. ! [X0] : ((~rich(X0) & ~funny(X0)) <=> (~calm(X0) & generous(X0))) [input p7]
10. ? [X0] : (curious(X0) & ~curious(X0)) <=> (~old(fred) <~> rich(fred)) [input p9]
25. generous(fred) [input hypothesis]
28. ! [X0] : (calm(X0) | (~generous(X0) <=> old(X0))) [ennf transformation 3]
29. ! [X0] : (~generous(X0) | ~patient(X0)) [ennf transformation 5]
37. ! [X0] : (calm(X0) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0)))) [nnf transformation 28]
42. ! [X0] : ((calm(X0) | (~wise(X0) | ~patient(X0))) & ((wise(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 6]
43. ! [X0] : ((calm(X0) | ~wise(X0) | ~patient(X0)) & ((wise(X0) & patient(X0)) | ~calm(X0))) [flattening 42]
45. ! [X0] : (((~rich(X0) & ~funny(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (rich(X0) | funny(X0)))) [nnf transformation 8]
46. ! [X0] : (((~rich(X0) & ~funny(X0)) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | rich(X0) | funny(X0))) [flattening 45]
49. (? [X0] : (curious(X0) & ~curious(X0)) | ((~old(fred) | ~rich(fred)) & (rich(fred) | old(fred)))) & (((~rich(fred) | old(fred)) & (rich(fred) | ~old(fred))) | ! [X0] : (~curious(X0) | curious(X0))) [nnf transformation 10]
50. (? [X0] : (curious(X0) & ~curious(X0)) | ((~old(fred) | ~rich(fred)) & (rich(fred) | old(fred)))) & (((~rich(fred) | old(fred)) & (rich(fred) | ~old(fred))) | ! [X1] : (~curious(X1) | curious(X1))) [rectify 49]
51. ? [X0] : (curious(X0) & ~curious(X0)) => (curious(sK1) & ~curious(sK1)) [choice axiom]
52. ((curious(sK1) & ~curious(sK1)) | ((~old(fred) | ~rich(fred)) & (rich(fred) | old(fred)))) & (((~rich(fred) | old(fred)) & (rich(fred) | ~old(fred))) | ! [X1] : (~curious(X1) | curious(X1))) [skolemisation 50,51]
84. ~old(X0) | ~generous(X0) | calm(X0) [cnf transformation 37]
89. ~generous(X0) | ~patient(X0) [cnf transformation 29]
90. ~calm(X0) | patient(X0) [cnf transformation 43]
98. ~generous(X0) | calm(X0) | ~rich(X0) [cnf transformation 46]
107. ~curious(sK1) | rich(fred) | old(fred) [cnf transformation 52]
109. curious(sK1) | rich(fred) | old(fred) [cnf transformation 52]
142. generous(fred) [cnf transformation 25]
197. 11 <=> rich(fred) [avatar definition]
201. 12 <=> old(fred) [avatar definition]
202. old(fred) <- (12) [avatar component clause 201]
205. 13 <=> curious(sK1) [avatar definition]
209. 12 | 11 | 13 [avatar split clause 109,205,197,201]
211. 12 | 11 | ~13 [avatar split clause 107,205,197,201]
263. ~patient(fred) [resolution 89,142]
286. calm(fred) | ~rich(fred) [resolution 98,142]
307. 28 <=> calm(fred) [avatar definition]
309. calm(fred) <- (28) [avatar component clause 307]
310. ~11 | 28 [avatar split clause 286,307,197]
311. ~generous(fred) | calm(fred) <- (12) [resolution 202,84]
312. calm(fred) <- (12) [subsumption resolution 311,142]
313. 28 | ~12 [avatar split clause 312,201,307]
317. patient(fred) <- (28) [resolution 309,90]
321. $false <- (28) [subsumption resolution 317,263]
322. ~28 [avatar contradiction clause 321]
323. $false [avatar sat refutation 209,211,310,313,322]
% SZS output end Proof for 889455062520738712667961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or happy then john is either not tall or not generous and vice versa.
Everyone who is happy or old is not brave or not patient and vice versa.
Everyone who is humble or not quiet is patient and vice versa.
If susan is either funny or brave then lucy is either not wise or not brave and vice versa.
If paul is not curious or not patient then someone is not curious or not generous and vice versa.
If susan is either not patient or not happy then susan is both not patient and generous.
If someone is both not funny and kind then someone is both not funny and not rich.
Everyone who is not happy is curious and vice versa.
Everyone who is old is both old and kind and vice versa.
If mary is funny then someone is either not brave or not funny and vice versa.
Everyone who is not calm or not tall is old or tall and vice versa.
Everyone who is strong or funny is both happy and not creative and vice versa.
If mary is not happy or strong then mary is not rich or brave and vice versa.
If john is not rich then someone is not humble or rich.
Everyone who is both not kind and wise is both wise and not humble.
Everyone who is both not calm and rich is either patient or not patient.
Someone is tall.
Someone is rich or quiet.
Someone is not kind.
Someone is either not curious or not patient.
Someone is not old or patient.
Someone is not wise or funny.
Someone is not old or rich.
John is creative. | Mary is not calm. | neutral | ((?[X]:((curious(X)<~>happy(X))))<=>((~tall(john)<~>~generous(john))))&
(![X]:((happy(X)|old(X))<=>(~brave(X)|~patient(X))))&
(![X]:((humble(X)|~quiet(X))<=>patient(X)))&
(((funny(susan)<~>brave(susan)))<=>((~wise(lucy)<~>~brave(lucy))))&
(((~curious(paul)|~patient(paul)))<=>(?[X]:((~curious(X)|~generous(X)))))&
(((~patient(susan)<~>~happy(susan)))=>((~patient(susan)&generous(susan))))&
((?[X]:((~funny(X)&kind(X))))=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:(~happy(X)<=>curious(X)))&
(![X]:(old(X)<=>(old(X)&kind(X))))&
((funny(mary))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(old(X)|tall(X))))&
(![X]:((strong(X)|funny(X))<=>(happy(X)&~creative(X))))&
(((~happy(mary)|strong(mary)))<=>((~rich(mary)|brave(mary))))&
((~rich(john))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((~kind(X)&wise(X))=>(wise(X)&~humble(X))))&
(![X]:((~calm(X)&rich(X))=>(patient(X)<~>~patient(X))))&
(?[X]:(tall(X)))&
(?[X]:((rich(X)|quiet(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~curious(X)<~>~patient(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~old(X)|rich(X))))&
(creative(john)) | ~calm(mary) | [] | null | 0 |
Everyone who is either not wise or not kind is both wise and not humble and vice versa. Everyone who is not brave or rich is both not kind and happy and vice versa. If someone is rich or not brave then alice is either not wise or funny. If fred is both not patient and strong then someone is both strong and not quiet and vice versa. Everyone who is both calm and kind is not wise or not strong. If mary is happy then paul is not kind or calm and vice versa. Everyone who is both quiet and not patient is not strong or not kind and vice versa. If alice is wise or brave then someone is tall or not generous. If someone is both not tall and not curious then someone is old or not kind and vice versa. If someone is rich or old then susan is not brave or old and vice versa. Everyone who is brave or wise is either not calm or not rich and vice versa. If susan is patient then someone is curious. Everyone who is tall is not creative. Everyone who is either tall or not strong is either not curious or kind and vice versa. Everyone who is either patient or not calm is not happy and vice versa. If lucy is wise then fred is either kind or not calm. Lucy is either not happy or not brave. Someone is either tall or happy. Paul is both rich and strong. Susan is either funny or wise. Someone is creative or curious. Mary is not old or not brave. Susan is not quiet or not wise. Someone is not curious or not generous. | Lucy is not happy. | contradiction | (![X]:((~wise(X)<~>~kind(X))<=>(wise(X)&~humble(X))))&
(![X]:((~brave(X)|rich(X))<=>(~kind(X)&happy(X))))&
((?[X]:((rich(X)|~brave(X))))=>((~wise(alice)<~>funny(alice))))&
(((~patient(fred)&strong(fred)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((calm(X)&kind(X))=>(~wise(X)|~strong(X))))&
((happy(mary))<=>((~kind(paul)|calm(paul))))&
(![X]:((quiet(X)&~patient(X))<=>(~strong(X)|~kind(X))))&
(((wise(alice)|brave(alice)))=>(?[X]:((tall(X)|~generous(X)))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((rich(X)|old(X))))<=>((~brave(susan)|old(susan))))&
(![X]:((brave(X)|wise(X))<=>(~calm(X)<~>~rich(X))))&
((patient(susan))=>(?[X]:(curious(X))))&
(![X]:(tall(X)=>~creative(X)))&
(![X]:((tall(X)<~>~strong(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~happy(X)))&
((wise(lucy))=>((kind(fred)<~>~calm(fred))))&
((~happy(lucy)<~>~brave(lucy)))&
(?[X]:((tall(X)<~>happy(X))))&
((rich(paul)&strong(paul)))&
((funny(susan)<~>wise(susan)))&
(?[X]:((creative(X)|curious(X))))&
((~old(mary)|~brave(mary)))&
((~quiet(susan)|~wise(susan)))&
(?[X]:((~curious(X)|~generous(X)))) | ~happy(lucy) | [
"p0",
"p1",
"p4",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5875191285036042049453607
% SZS output start Proof for 5875191285036042049453607
1. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (~humble(X0) & wise(X0))) [input p0]
2. ! [X0] : ((rich(X0) | ~brave(X0)) <=> (happy(X0) & ~kind(X0))) [input p1]
5. ! [X0] : ((kind(X0) & calm(X0)) => (~strong(X0) | ~wise(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~kind(X0) | ~strong(X0))) [input p6]
11. ! [X0] : ((wise(X0) | brave(X0)) <=> (~calm(X0) <~> ~rich(X0))) [input p10]
15. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> ~happy(X0)) [input p14]
25. ~happy(lucy) [input hypothesis]
30. ! [X0] : ((~strong(X0) | ~wise(X0)) | (~kind(X0) | ~calm(X0))) [ennf transformation 5]
31. ! [X0] : (~strong(X0) | ~wise(X0) | ~kind(X0) | ~calm(X0)) [flattening 30]
35. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 1]
36. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [flattening 35]
37. ! [X0] : (((rich(X0) | ~brave(X0)) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | (~rich(X0) & brave(X0)))) [nnf transformation 2]
38. ! [X0] : ((rich(X0) | ~brave(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | (~rich(X0) & brave(X0)))) [flattening 37]
47. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | (patient(X0) | ~quiet(X0)))) [nnf transformation 7]
48. ! [X0] : (((~patient(X0) & quiet(X0)) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | patient(X0) | ~quiet(X0))) [flattening 47]
59. ! [X0] : (((wise(X0) | brave(X0)) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~wise(X0) & ~brave(X0)))) [nnf transformation 11]
60. ! [X0] : ((wise(X0) | brave(X0) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | (~wise(X0) & ~brave(X0)))) [flattening 59]
64. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | happy(X0)) & (~happy(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 15]
73. wise(X0) | ~kind(X0) | wise(X0) [cnf transformation 36]
81. happy(X0) | brave(X0) [cnf transformation 38]
82. ~rich(X0) | happy(X0) [cnf transformation 38]
92. ~strong(X0) | ~wise(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 31]
99. ~patient(X0) | strong(X0) [cnf transformation 48]
100. ~patient(X0) | kind(X0) [cnf transformation 48]
112. ~brave(X0) | calm(X0) | rich(X0) [cnf transformation 60]
128. ~calm(X0) | patient(X0) | happy(X0) [cnf transformation 64]
143. ~happy(lucy) [cnf transformation 25]
144. ~kind(X0) | wise(X0) [duplicate literal removal 73]
187. ~calm(X0) | ~kind(X0) | ~strong(X0) [subsumption resolution 92,144]
277. 29 <=> happy(lucy) [avatar definition]
279. ~happy(lucy) <- (~29) [avatar component clause 277]
281. 30 <=> brave(lucy) [avatar definition]
282. brave(lucy) <- (30) [avatar component clause 281]
328. ~29 [avatar split clause 143,277]
332. brave(lucy) <- (~29) [resolution 81,279]
334. 30 | 29 [avatar split clause 332,277,281]
338. calm(lucy) | rich(lucy) <- (30) [resolution 112,282]
341. 40 <=> rich(lucy) [avatar definition]
343. rich(lucy) <- (40) [avatar component clause 341]
345. 41 <=> calm(lucy) [avatar definition]
347. calm(lucy) <- (41) [avatar component clause 345]
348. 40 | 41 | ~30 [avatar split clause 338,281,345,341]
358. happy(lucy) <- (40) [resolution 343,82]
360. $false <- (~29, 40) [subsumption resolution 358,279]
361. 29 | ~40 [avatar contradiction clause 360]
404. patient(lucy) | happy(lucy) <- (41) [resolution 347,128]
408. patient(lucy) <- (~29, 41) [subsumption resolution 404,279]
426. ~kind(lucy) | ~strong(lucy) <- (41) [resolution 187,347]
429. 52 <=> strong(lucy) [avatar definition]
431. ~strong(lucy) <- (~52) [avatar component clause 429]
433. 53 <=> kind(lucy) [avatar definition]
436. ~52 | ~53 | ~41 [avatar split clause 426,345,433,429]
589. kind(lucy) <- (~29, 41) [resolution 408,100]
590. strong(lucy) <- (~29, 41) [resolution 408,99]
591. 53 | 29 | ~41 [avatar split clause 589,345,277,433]
592. $false <- (~29, 41, ~52) [subsumption resolution 590,431]
593. 29 | ~41 | 52 [avatar contradiction clause 592]
594. $false [avatar sat refutation 328,334,348,361,436,591,593]
% SZS output end Proof for 5875191285036042049453607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then someone is quiet or happy and vice versa.
If lucy is both not brave and not patient then someone is both humble and happy and vice versa.
Everyone who is both kind and not humble is both calm and not strong and vice versa.
If someone is either tall or not curious then someone is either old or curious and vice versa.
Everyone who is both not quiet and creative is generous or not kind and vice versa.
If someone is wise or funny then john is both strong and happy.
If someone is either brave or not humble then alice is either not calm or quiet and vice versa.
If someone is either not strong or quiet then someone is wise or not old and vice versa.
Everyone who is both not quiet and quiet is happy.
Everyone who is not tall is both not patient and not old.
If mary is either not humble or not curious then someone is both strong and generous and vice versa.
If alice is either wise or not wise then someone is either old or patient.
Everyone who is not rich is both not strong and not creative.
If lucy is either tall or not old then someone is both not quiet and kind and vice versa.
Everyone who is both tall and not wise is strong or not curious and vice versa.
If mary is either not generous or old then lucy is either wise or kind.
Someone is not funny.
Someone is strong.
Mary is either kind or old.
Lucy is strong or not creative.
Someone is patient or not funny.
Mary is either strong or rich.
Someone is not rich.
Someone is kind or not humble. | John is not wise. | entailment | ((?[X]:(old(X)))<=>(?[X]:((quiet(X)|happy(X)))))&
(((~brave(lucy)&~patient(lucy)))<=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((kind(X)&~humble(X))<=>(calm(X)&~strong(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:((~quiet(X)&creative(X))<=>(generous(X)|~kind(X))))&
((?[X]:((wise(X)|funny(X))))=>((strong(john)&happy(john))))&
((?[X]:((brave(X)<~>~humble(X))))<=>((~calm(alice)<~>quiet(alice))))&
((?[X]:((~strong(X)<~>quiet(X))))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~quiet(X)&quiet(X))=>happy(X)))&
(![X]:(~tall(X)=>(~patient(X)&~old(X))))&
(((~humble(mary)<~>~curious(mary)))<=>(?[X]:((strong(X)&generous(X)))))&
(((wise(alice)<~>~wise(alice)))=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(~rich(X)=>(~strong(X)&~creative(X))))&
(((tall(lucy)<~>~old(lucy)))<=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((tall(X)&~wise(X))<=>(strong(X)|~curious(X))))&
(((~generous(mary)<~>old(mary)))=>((wise(lucy)<~>kind(lucy))))&
(?[X]:(~funny(X)))&
(?[X]:(strong(X)))&
((kind(mary)<~>old(mary)))&
((strong(lucy)|~creative(lucy)))&
(?[X]:((patient(X)|~funny(X))))&
((strong(mary)<~>rich(mary)))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)|~humble(X)))) | ~wise(john) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8939376599843209116238930
% SZS output start Proof for 8939376599843209116238930
6. ? [X0] : (funny(X0) | wise(X0)) => (happy(john) & strong(john)) [input p5]
15. ! [X0] : ((~wise(X0) & tall(X0)) <=> (~curious(X0) | strong(X0))) [input p14]
25. wise(john) [input hypothesis]
30. ? [X0] : wise(X0) => (happy(john) & strong(john)) [pure predicate removal 6]
32. (happy(john) & strong(john)) | ! [X0] : ~wise(X0) [ennf transformation 30]
78. ! [X0] : (((~wise(X0) & tall(X0)) | (curious(X0) & ~strong(X0))) & ((~curious(X0) | strong(X0)) | (wise(X0) | ~tall(X0)))) [nnf transformation 15]
79. ! [X0] : (((~wise(X0) & tall(X0)) | (curious(X0) & ~strong(X0))) & (~curious(X0) | strong(X0) | wise(X0) | ~tall(X0))) [flattening 78]
113. strong(john) | ~wise(X0) [cnf transformation 32]
153. ~wise(X0) | ~strong(X0) [cnf transformation 79]
167. wise(john) [cnf transformation 25]
256. 20 <=> ! [X0] : ~wise(X0) [avatar definition]
257. ~wise(X0) <- (20) [avatar component clause 256]
264. 22 <=> strong(john) [avatar definition]
266. strong(john) <- (22) [avatar component clause 264]
267. 20 | 22 [avatar split clause 113,264,256]
447. $false <- (20) [resolution 257,167]
448. ~20 [avatar contradiction clause 447]
462. ~strong(john) [resolution 153,167]
464. $false <- (22) [subsumption resolution 462,266]
465. ~22 [avatar contradiction clause 464]
466. $false [avatar sat refutation 267,448,465]
% SZS output end Proof for 8939376599843209116238930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not rich and vice versa.
If mary is patient or not happy then someone is both not patient and patient and vice versa.
Everyone who is generous is rich.
If someone is happy then someone is both humble and not rich.
If someone is not patient or calm then alice is either not rich or not calm.
If someone is both generous and not wise then someone is not strong or strong and vice versa.
If someone is both calm and curious then someone is wise and vice versa.
If mary is either brave or creative then susan is both not wise and not funny and vice versa.
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
Someone is either not patient or humble.
John is both creative and not generous.
Mary is not funny.
John is both creative and not happy.
Paul is either not tall or generous.
Paul is either creative or rich.
Lucy is both brave and not patient.
Paul is either quiet or not funny. | John is not happy. | entailment | (![X]:(~patient(X)<=>~rich(X)))&
(((patient(mary)|~happy(mary)))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:(generous(X)=>rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((humble(X)&~rich(X)))))&
((?[X]:((~patient(X)|calm(X))))=>((~rich(alice)<~>~calm(alice))))&
((?[X]:((generous(X)&~wise(X))))<=>(?[X]:((~strong(X)|strong(X)))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:(wise(X))))&
(((brave(mary)<~>creative(mary)))<=>((~wise(susan)&~funny(susan))))&
(((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
(?[X]:((~patient(X)<~>humble(X))))&
((creative(john)&~generous(john)))&
(~funny(mary))&
((creative(john)&~happy(john)))&
((~tall(paul)<~>generous(paul)))&
((creative(paul)<~>rich(paul)))&
((brave(lucy)&~patient(lucy)))&
((quiet(paul)<~>~funny(paul))) | ~happy(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8384553258492079945111273
% SZS output start Proof for 8384553258492079945111273
19. ~happy(john) & creative(john) [input p18]
24. happy(john) [input hypothesis]
133. ~happy(john) [cnf transformation 19]
142. happy(john) [cnf transformation 24]
280. 30 <=> happy(john) [avatar definition]
340. ~30 [avatar split clause 133,280]
360. 30 [avatar split clause 142,280]
361. $false [avatar sat refutation 340,360]
% SZS output end Proof for 8384553258492079945111273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either funny or kind then mary is not kind or kind. Everyone who is both not happy and quiet is either quiet or creative. Everyone who is happy or creative is patient and vice versa. If someone is not brave then mary is happy. If someone is both not quiet and not humble then alice is not generous. If fred is not happy then someone is either not curious or not humble and vice versa. Everyone who is either wise or not strong is both happy and not kind and vice versa. Everyone who is either not strong or kind is old or not happy. If someone is not tall or not kind then mary is not happy and vice versa. If fred is rich or generous then lucy is both not creative and curious and vice versa. If someone is generous then someone is both calm and not humble. Everyone who is not patient or funny is not kind or calm and vice versa. If someone is not happy then someone is either not creative or curious and vice versa. Everyone who is both not funny and not happy is generous and vice versa. Everyone who is either not quiet or not creative is happy and vice versa. Everyone who is either humble or not tall is both not patient and kind and vice versa. Lucy is both not tall and rich. Mary is not rich. Lucy is calm. Mary is not happy or not tall. Lucy is both generous and not quiet. Susan is both not strong and generous. Fred is either humble or not curious. John is both kind and humble. | Lucy is calm. | entailment | (((funny(john)<~>kind(john)))=>((~kind(mary)|kind(mary))))&
(![X]:((~happy(X)&quiet(X))=>(quiet(X)<~>creative(X))))&
(![X]:((happy(X)|creative(X))<=>patient(X)))&
((?[X]:(~brave(X)))=>(happy(mary)))&
((?[X]:((~quiet(X)&~humble(X))))=>(~generous(alice)))&
((~happy(fred))<=>(?[X]:((~curious(X)<~>~humble(X)))))&
(![X]:((wise(X)<~>~strong(X))<=>(happy(X)&~kind(X))))&
(![X]:((~strong(X)<~>kind(X))=>(old(X)|~happy(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>(~happy(mary)))&
(((rich(fred)|generous(fred)))<=>((~creative(lucy)&curious(lucy))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((~patient(X)|funny(X))<=>(~kind(X)|calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((~funny(X)&~happy(X))<=>generous(X)))&
(![X]:((~quiet(X)<~>~creative(X))<=>happy(X)))&
(![X]:((humble(X)<~>~tall(X))<=>(~patient(X)&kind(X))))&
((~tall(lucy)&rich(lucy)))&
(~rich(mary))&
(calm(lucy))&
((~happy(mary)|~tall(mary)))&
((generous(lucy)&~quiet(lucy)))&
((~strong(susan)&generous(susan)))&
((humble(fred)<~>~curious(fred)))&
((kind(john)&humble(john))) | calm(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5477829127975359471861265
% SZS output start Proof for 5477829127975359471861265
19. calm(lucy) [input p18]
25. ~calm(lucy) [input hypothesis]
120. calm(lucy) [cnf transformation 19]
130. ~calm(lucy) [cnf transformation 25]
260. $false [subsumption resolution 130,120]
% SZS output end Proof for 5477829127975359471861265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or humble then someone is both old and not humble and vice versa. Everyone who is not kind or happy is both curious and old and vice versa. Everyone who is both creative and strong is either not patient or tall. If someone is not curious or not quiet then someone is generous or not happy. Everyone who is either calm or patient is either not wise or not funny. Everyone who is not happy or quiet is either not rich or tall. Everyone who is not kind is both not funny and calm and vice versa. If someone is not old then someone is both not funny and not brave. If fred is either tall or not rich then paul is either not calm or not funny. Everyone who is either creative or rich is not wise or curious and vice versa. If mary is humble then someone is either rich or brave and vice versa. If someone is kind or not tall then someone is either not creative or not curious. Everyone who is both brave and curious is both strong and brave and vice versa. Everyone who is not quiet is either rich or not kind and vice versa. Everyone who is rich or calm is not kind. If alice is both not brave and quiet then john is not funny and vice versa. Someone is quiet or not generous. Someone is both not patient and not strong. Someone is patient. Susan is both strong and not calm. Fred is quiet or creative. Paul is both strong and not old. Someone is not kind. John is both not generous and not wise. | Paul is tall. | contradiction | ((?[X]:((creative(X)<~>humble(X))))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((~kind(X)|happy(X))<=>(curious(X)&old(X))))&
(![X]:((creative(X)&strong(X))=>(~patient(X)<~>tall(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:((calm(X)<~>patient(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~happy(X)|quiet(X))=>(~rich(X)<~>tall(X))))&
(![X]:(~kind(X)<=>(~funny(X)&calm(X))))&
((?[X]:(~old(X)))=>(?[X]:((~funny(X)&~brave(X)))))&
(((tall(fred)<~>~rich(fred)))=>((~calm(paul)<~>~funny(paul))))&
(![X]:((creative(X)<~>rich(X))<=>(~wise(X)|curious(X))))&
((humble(mary))<=>(?[X]:((rich(X)<~>brave(X)))))&
((?[X]:((kind(X)|~tall(X))))=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((brave(X)&curious(X))<=>(strong(X)&brave(X))))&
(![X]:(~quiet(X)<=>(rich(X)<~>~kind(X))))&
(![X]:((rich(X)|calm(X))=>~kind(X)))&
(((~brave(alice)&quiet(alice)))<=>(~funny(john)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((~patient(X)&~strong(X))))&
(?[X]:(patient(X)))&
((strong(susan)&~calm(susan)))&
((quiet(fred)|creative(fred)))&
((strong(paul)&~old(paul)))&
(?[X]:(~kind(X)))&
((~generous(john)&~wise(john))) | tall(paul) | [
"p1",
"p5",
"p6",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1957785746114926276409393
% SZS output start Proof for 1957785746114926276409393
2. ! [X0] : ((happy(X0) | ~kind(X0)) <=> (old(X0) & curious(X0))) [input p1]
6. ! [X0] : ((quiet(X0) | ~happy(X0)) => (~rich(X0) <~> tall(X0))) [input p5]
7. ! [X0] : (~kind(X0) <=> (calm(X0) & ~funny(X0))) [input p6]
15. ! [X0] : ((calm(X0) | rich(X0)) => ~kind(X0)) [input p14]
22. ~old(paul) & strong(paul) [input p21]
25. tall(paul) [input hypothesis]
34. ! [X0] : ((~rich(X0) <~> tall(X0)) | (~quiet(X0) & happy(X0))) [ennf transformation 6]
38. ! [X0] : (~kind(X0) | (~calm(X0) & ~rich(X0))) [ennf transformation 15]
44. ! [X0] : (((happy(X0) | ~kind(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~happy(X0) & kind(X0)))) [nnf transformation 2]
45. ! [X0] : ((happy(X0) | ~kind(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~happy(X0) & kind(X0)))) [flattening 44]
51. ! [X0] : (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | (~quiet(X0) & happy(X0))) [nnf transformation 34]
52. ! [X0] : ((~kind(X0) | (~calm(X0) | funny(X0))) & ((calm(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 7]
53. ! [X0] : ((~kind(X0) | ~calm(X0) | funny(X0)) & ((calm(X0) & ~funny(X0)) | kind(X0))) [flattening 52]
89. kind(X0) | old(X0) [cnf transformation 45]
90. ~happy(X0) | old(X0) [cnf transformation 45]
102. ~tall(X0) | rich(X0) | happy(X0) [cnf transformation 51]
105. calm(X0) | kind(X0) [cnf transformation 53]
135. ~rich(X0) | ~kind(X0) [cnf transformation 38]
136. ~calm(X0) | ~kind(X0) [cnf transformation 38]
148. ~old(paul) [cnf transformation 22]
152. tall(paul) [cnf transformation 25]
222. 17 <=> calm(paul) [avatar definition]
223. ~calm(paul) <- (~17) [avatar component clause 222]
224. calm(paul) <- (17) [avatar component clause 222]
325. rich(paul) | happy(paul) [resolution 102,152]
328. 35 <=> happy(paul) [avatar definition]
330. happy(paul) <- (35) [avatar component clause 328]
332. 36 <=> rich(paul) [avatar definition]
334. rich(paul) <- (36) [avatar component clause 332]
335. 35 | 36 [avatar split clause 325,332,328]
342. ~kind(paul) <- (17) [resolution 224,136]
345. old(paul) <- (35) [resolution 330,90]
347. $false <- (35) [subsumption resolution 345,148]
348. ~35 [avatar contradiction clause 347]
366. ~kind(paul) <- (36) [resolution 334,135]
378. old(paul) <- (17) [resolution 342,89]
379. $false <- (17) [subsumption resolution 378,148]
380. ~17 [avatar contradiction clause 379]
381. kind(paul) <- (~17) [resolution 223,105]
382. $false <- (~17, 36) [subsumption resolution 381,366]
383. 17 | ~36 [avatar contradiction clause 382]
384. $false [avatar sat refutation 335,348,380,383]
% SZS output end Proof for 1957785746114926276409393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either kind or not kind then lucy is both not kind and not creative.
If someone is not old then someone is both brave and old and vice versa.
Everyone who is either not creative or calm is either not calm or happy and vice versa.
If someone is either brave or not wise then someone is tall or quiet.
Everyone who is not kind is both humble and not quiet.
If lucy is not wise then mary is not old and vice versa.
If someone is not funny or not tall then john is happy.
Everyone who is not curious or not calm is not humble or not generous.
Everyone who is both not curious and not humble is both not old and not strong and vice versa.
Everyone who is not strong or not generous is both humble and rich and vice versa.
If susan is not old then fred is wise.
Everyone who is both not wise and not strong is not quiet or not generous and vice versa.
If someone is not happy then alice is either not patient or not curious.
Everyone who is either old or not quiet is either not brave or not wise.
Everyone who is brave or old is generous.
Mary is both strong and not rich.
Someone is humble or not quiet.
Alice is both not rich and curious.
Someone is old or not calm.
Someone is curious.
Someone is creative or not wise.
Fred is funny.
Susan is either not brave or not curious. | Fred is curious. | entailment | (((kind(john)<~>~kind(john)))=>((~kind(lucy)&~creative(lucy))))&
((?[X]:(~old(X)))<=>(?[X]:((brave(X)&old(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(~calm(X)<~>happy(X))))&
((?[X]:((brave(X)<~>~wise(X))))=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:(~kind(X)=>(humble(X)&~quiet(X))))&
((~wise(lucy))<=>(~old(mary)))&
((?[X]:((~funny(X)|~tall(X))))=>(happy(john)))&
(![X]:((~curious(X)|~calm(X))=>(~humble(X)|~generous(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>(humble(X)&rich(X))))&
((~old(susan))=>(wise(fred)))&
(![X]:((~wise(X)&~strong(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:(~happy(X)))=>((~patient(alice)<~>~curious(alice))))&
(![X]:((old(X)<~>~quiet(X))=>(~brave(X)<~>~wise(X))))&
(![X]:((brave(X)|old(X))=>generous(X)))&
((strong(mary)&~rich(mary)))&
(?[X]:((humble(X)|~quiet(X))))&
((~rich(alice)&curious(alice)))&
(?[X]:((old(X)|~calm(X))))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)|~wise(X))))&
(funny(fred))&
((~brave(susan)<~>~curious(susan))) | curious(fred) | [
"p7",
"p8",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 13682122331015626358720
% SZS output start Proof for 13682122331015626358720
8. ! [X0] : ((~calm(X0) | ~curious(X0)) => (~generous(X0) | ~humble(X0))) [input p7]
9. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (~strong(X0) & ~old(X0))) [input p8]
10. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> (rich(X0) & humble(X0))) [input p9]
12. ! [X0] : ((~strong(X0) & ~wise(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p11]
15. ! [X0] : ((old(X0) | brave(X0)) => generous(X0)) [input p14]
24. ~curious(fred) [input hypothesis]
33. ! [X0] : ((~generous(X0) | ~humble(X0)) | (calm(X0) & curious(X0))) [ennf transformation 8]
34. ! [X0] : (~generous(X0) | ~humble(X0) | (calm(X0) & curious(X0))) [flattening 33]
38. ! [X0] : (generous(X0) | (~old(X0) & ~brave(X0))) [ennf transformation 15]
47. ! [X0] : (((~humble(X0) & ~curious(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 9]
48. ! [X0] : (((~humble(X0) & ~curious(X0)) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | humble(X0) | curious(X0))) [flattening 47]
49. ! [X0] : (((~generous(X0) | ~strong(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (generous(X0) & strong(X0)))) [nnf transformation 10]
50. ! [X0] : ((~generous(X0) | ~strong(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (generous(X0) & strong(X0)))) [flattening 49]
51. ! [X0] : (((~strong(X0) & ~wise(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (strong(X0) | wise(X0)))) [nnf transformation 12]
52. ! [X0] : (((~strong(X0) & ~wise(X0)) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | strong(X0) | wise(X0))) [flattening 51]
83. ~generous(X0) | ~humble(X0) | curious(X0) [cnf transformation 34]
86. ~strong(X0) | humble(X0) | curious(X0) [cnf transformation 48]
88. ~humble(X0) | strong(X0) | old(X0) [cnf transformation 48]
89. strong(X0) | humble(X0) [cnf transformation 50]
99. ~strong(X0) | generous(X0) [cnf transformation 52]
107. ~old(X0) | generous(X0) [cnf transformation 38]
118. ~curious(fred) [cnf transformation 24]
330. humble(X0) | curious(X0) | humble(X0) [resolution 86,89]
332. curious(X0) | humble(X0) [duplicate literal removal 330]
443. humble(fred) [resolution 332,118]
508. strong(fred) | old(fred) [resolution 443,88]
510. 54 <=> old(fred) [avatar definition]
512. old(fred) <- (54) [avatar component clause 510]
514. 55 <=> strong(fred) [avatar definition]
516. strong(fred) <- (55) [avatar component clause 514]
517. 54 | 55 [avatar split clause 508,514,510]
544. generous(fred) <- (55) [resolution 516,99]
554. ~humble(fred) | curious(fred) <- (55) [resolution 544,83]
556. curious(fred) <- (55) [subsumption resolution 554,443]
557. $false <- (55) [subsumption resolution 556,118]
558. ~55 [avatar contradiction clause 557]
560. generous(fred) <- (54) [resolution 512,107]
566. ~humble(fred) | curious(fred) <- (54) [resolution 560,83]
574. curious(fred) <- (54) [subsumption resolution 566,443]
575. $false <- (54) [subsumption resolution 574,118]
576. ~54 [avatar contradiction clause 575]
577. $false [avatar sat refutation 517,558,576]
% SZS output end Proof for 13682122331015626358720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or old then paul is calm or wise. Everyone who is creative is old or not brave and vice versa. If lucy is either not tall or calm then mary is either not brave or not kind and vice versa. Everyone who is either not old or curious is generous. Everyone who is either generous or not brave is either not creative or creative and vice versa. Everyone who is both happy and not wise is not curious. Everyone who is wise is both generous and not generous and vice versa. If john is either not kind or funny then someone is either patient or generous. Everyone who is either not creative or calm is both quiet and not generous and vice versa. If someone is both funny and not wise then fred is not funny or not kind and vice versa. Everyone who is both patient and not happy is not brave. Everyone who is either wise or funny is both generous and calm. If someone is not humble then someone is patient and vice versa. If someone is not happy or creative then someone is both not curious and humble and vice versa. Everyone who is quiet or kind is not old or not strong. If someone is not tall or not strong then someone is either creative or humble. Paul is funny or patient. Mary is both not tall and not rich. Lucy is generous or not patient. Someone is not quiet. John is not humble or generous. Someone is both strong and not brave. Mary is either old or not calm. | Mary is generous. | contradiction | (((~wise(mary)|old(mary)))=>((calm(paul)|wise(paul))))&
(![X]:(creative(X)<=>(old(X)|~brave(X))))&
(((~tall(lucy)<~>calm(lucy)))<=>((~brave(mary)<~>~kind(mary))))&
(![X]:((~old(X)<~>curious(X))=>generous(X)))&
(![X]:((generous(X)<~>~brave(X))<=>(~creative(X)<~>creative(X))))&
(![X]:((happy(X)&~wise(X))=>~curious(X)))&
(![X]:(wise(X)<=>(generous(X)&~generous(X))))&
(((~kind(john)<~>funny(john)))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(quiet(X)&~generous(X))))&
((?[X]:((funny(X)&~wise(X))))<=>((~funny(fred)|~kind(fred))))&
(![X]:((patient(X)&~happy(X))=>~brave(X)))&
(![X]:((wise(X)<~>funny(X))=>(generous(X)&calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(patient(X))))&
((?[X]:((~happy(X)|creative(X))))<=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((quiet(X)|kind(X))=>(~old(X)|~strong(X))))&
((?[X]:((~tall(X)|~strong(X))))=>(?[X]:((creative(X)<~>humble(X)))))&
((funny(paul)|patient(paul)))&
((~tall(mary)&~rich(mary)))&
((generous(lucy)|~patient(lucy)))&
(?[X]:(~quiet(X)))&
((~humble(john)|generous(john)))&
(?[X]:((strong(X)&~brave(X))))&
((old(mary)<~>~calm(mary))) | generous(mary) | [
"p1",
"p4",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4824322512447439069393632
% SZS output start Proof for 4824322512447439069393632
2. ! [X0] : (creative(X0) <=> (~brave(X0) | old(X0))) [input p1]
5. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> (~creative(X0) <~> creative(X0))) [input p4]
9. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> (~generous(X0) & quiet(X0))) [input p8]
23. old(mary) <~> ~calm(mary) [input p22]
24. generous(mary) [input hypothesis]
41. ! [X0] : ((creative(X0) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | ~creative(X0))) [nnf transformation 2]
42. ! [X0] : ((creative(X0) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~creative(X0))) [flattening 41]
45. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 5]
51. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 9]
52. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [flattening 51]
77. (calm(mary) | ~old(mary)) & (~calm(mary) | old(mary)) [nnf transformation 23]
80. ~brave(X0) | old(X0) | ~creative(X0) [cnf transformation 42]
81. ~old(X0) | creative(X0) [cnf transformation 42]
82. brave(X0) | creative(X0) [cnf transformation 42]
97. ~brave(X0) | generous(X0) | creative(X0) | creative(X0) [cnf transformation 45]
100. brave(X0) | ~generous(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 45]
111. ~generous(X0) | calm(X0) | creative(X0) [cnf transformation 52]
112. ~generous(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 52]
145. ~calm(mary) | old(mary) [cnf transformation 77]
146. calm(mary) | ~old(mary) [cnf transformation 77]
147. generous(mary) [cnf transformation 24]
148. ~brave(X0) | generous(X0) | creative(X0) [duplicate literal removal 97]
151. brave(X0) | ~generous(X0) | ~creative(X0) [duplicate literal removal 100]
153. 1 <=> old(mary) [avatar definition]
154. old(mary) <- (1) [avatar component clause 153]
155. ~old(mary) <- (~1) [avatar component clause 153]
175. 6 <=> brave(mary) [avatar definition]
176. brave(mary) <- (6) [avatar component clause 175]
194. ~generous(X0) | brave(X0) [subsumption resolution 151,82]
195. generous(X0) | creative(X0) [subsumption resolution 148,82]
218. creative(X0) | calm(X0) [subsumption resolution 111,195]
332. 38 <=> calm(mary) [avatar definition]
333. ~calm(mary) <- (~38) [avatar component clause 332]
334. calm(mary) <- (38) [avatar component clause 332]
335. ~1 | 38 [avatar split clause 146,332,153]
336. 1 | ~38 [avatar split clause 145,332,153]
346. brave(mary) [resolution 194,147]
349. 6 [avatar split clause 346,175]
360. old(mary) | ~creative(mary) <- (6) [resolution 80,176]
361. ~creative(mary) <- (~1, 6) [subsumption resolution 360,155]
368. calm(mary) <- (~1, 6) [resolution 361,218]
369. $false <- (~1, 6, ~38) [subsumption resolution 368,333]
370. 1 | ~6 | 38 [avatar contradiction clause 369]
372. 39 <=> creative(mary) [avatar definition]
373. creative(mary) <- (39) [avatar component clause 372]
376. creative(mary) <- (1) [resolution 154,81]
377. 39 | ~1 [avatar split clause 376,153,372]
403. ~creative(mary) | ~calm(mary) [resolution 112,147]
406. ~calm(mary) <- (39) [subsumption resolution 403,373]
407. $false <- (38, 39) [subsumption resolution 406,334]
408. ~38 | ~39 [avatar contradiction clause 407]
411. $false [avatar sat refutation 335,336,349,370,377,408]
% SZS output end Proof for 4824322512447439069393632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and happy then lucy is patient or generous.
Everyone who is brave or not rich is not old and vice versa.
If mary is either not quiet or patient then someone is both patient and calm.
If someone is not curious or not happy then susan is tall or old and vice versa.
If fred is humble or not calm then someone is not rich and vice versa.
Everyone who is either not creative or not brave is both humble and not wise and vice versa.
If paul is either not kind or not rich then someone is not creative or calm and vice versa.
Everyone who is either not strong or funny is not funny and vice versa.
Everyone who is both funny and creative is old or patient and vice versa.
Everyone who is not patient or tall is either humble or not curious and vice versa.
If alice is both not generous and creative then someone is either happy or not strong and vice versa.
If alice is either brave or old then fred is patient or wise and vice versa.
If paul is both not happy and kind then someone is either not quiet or tall and vice versa.
If paul is not patient or curious then someone is both curious and not patient and vice versa.
If alice is not happy then john is quiet.
If someone is either humble or not humble then lucy is not happy or not brave.
Susan is either not old or not kind.
Lucy is not happy or patient.
Alice is curious.
Someone is either not humble or funny.
Someone is either not kind or brave.
Someone is not curious.
Someone is tall.
Fred is both not quiet and not generous. | Fred is not strong. | entailment | ((?[X]:((rich(X)&happy(X))))=>((patient(lucy)|generous(lucy))))&
(![X]:((brave(X)|~rich(X))<=>~old(X)))&
(((~quiet(mary)<~>patient(mary)))=>(?[X]:((patient(X)&calm(X)))))&
((?[X]:((~curious(X)|~happy(X))))<=>((tall(susan)|old(susan))))&
(((humble(fred)|~calm(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(humble(X)&~wise(X))))&
(((~kind(paul)<~>~rich(paul)))<=>(?[X]:((~creative(X)|calm(X)))))&
(![X]:((~strong(X)<~>funny(X))<=>~funny(X)))&
(![X]:((funny(X)&creative(X))<=>(old(X)|patient(X))))&
(![X]:((~patient(X)|tall(X))<=>(humble(X)<~>~curious(X))))&
(((~generous(alice)&creative(alice)))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(((brave(alice)<~>old(alice)))<=>((patient(fred)|wise(fred))))&
(((~happy(paul)&kind(paul)))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
(((~patient(paul)|curious(paul)))<=>(?[X]:((curious(X)&~patient(X)))))&
((~happy(alice))=>(quiet(john)))&
((?[X]:((humble(X)<~>~humble(X))))=>((~happy(lucy)|~brave(lucy))))&
((~old(susan)<~>~kind(susan)))&
((~happy(lucy)|patient(lucy)))&
(curious(alice))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((~kind(X)<~>brave(X))))&
(?[X]:(~curious(X)))&
(?[X]:(tall(X)))&
((~quiet(fred)&~generous(fred))) | ~strong(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2357306694221494600690567
% SZS output start Proof for 2357306694221494600690567
8. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> ~funny(X0)) [input p7]
25. strong(fred) [input hypothesis]
53. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | funny(X0)) & (~funny(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 8]
115. ~funny(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 53]
116. funny(X0) | ~strong(X0) | funny(X0) [cnf transformation 53]
167. strong(fred) [cnf transformation 25]
170. ~funny(X0) | ~strong(X0) [duplicate literal removal 115]
171. funny(X0) | ~strong(X0) [duplicate literal removal 116]
276. ~strong(X0) [subsumption resolution 170,171]
417. $false [subsumption resolution 167,276]
% SZS output end Proof for 2357306694221494600690567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or quiet is curious or not wise.
Everyone who is not happy is not old or not creative.
If lucy is calm or wise then paul is either not wise or not brave and vice versa.
If lucy is either humble or happy then susan is not rich or creative.
If susan is not calm or not generous then someone is both generous and quiet and vice versa.
Everyone who is not rich is not generous or creative and vice versa.
If susan is humble or creative then someone is creative and vice versa.
Everyone who is both brave and generous is not calm and vice versa.
Everyone who is not patient is both funny and strong.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Everyone who is both happy and not creative is not quiet or generous and vice versa.
Everyone who is not calm is not funny or old and vice versa.
Alice is either not quiet or not happy.
Someone is not wise.
Alice is either tall or quiet.
Paul is either not happy or funny.
Lucy is both not funny and wise. | John is old. | entailment | (![X]:((~old(X)<~>quiet(X))=>(curious(X)|~wise(X))))&
(![X]:(~happy(X)=>(~old(X)|~creative(X))))&
(((calm(lucy)|wise(lucy)))<=>((~wise(paul)<~>~brave(paul))))&
(((humble(lucy)<~>happy(lucy)))=>((~rich(susan)|creative(susan))))&
(((~calm(susan)|~generous(susan)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~rich(X)<=>(~generous(X)|creative(X))))&
(((humble(susan)|creative(susan)))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)&generous(X))<=>~calm(X)))&
(![X]:(~patient(X)=>(funny(X)&strong(X))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(![X]:((happy(X)&~creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:(~calm(X)<=>(~funny(X)|old(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:(~wise(X)))&
((tall(alice)<~>quiet(alice)))&
((~happy(paul)<~>funny(paul)))&
((~funny(lucy)&wise(lucy))) | old(john) | [
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1655606737647350225813586
% SZS output start Proof for 1655606737647350225813586
11. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p10]
13. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & happy(X0)) <=> (generous(X0) | ~quiet(X0))) [input p14]
22. ~old(john) [input hypothesis]
50. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 11]
51. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 50]
53. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 13]
54. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 53]
55. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 15]
56. ! [X0] : (((~creative(X0) & happy(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | creative(X0) | ~happy(X0))) [flattening 55]
87. ~generous(X0) | creative(X0) | strong(X0) [cnf transformation 51]
89. ~strong(X0) | generous(X0) [cnf transformation 51]
94. ~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0) [cnf transformation 54]
96. strong(X0) | generous(X0) [cnf transformation 54]
102. happy(X0) | ~generous(X0) [cnf transformation 56]
104. ~creative(X0) | ~generous(X0) [cnf transformation 56]
117. ~old(john) [cnf transformation 22]
183. 14 <=> ! [X0] : ~creative(X0) [avatar definition]
184. ~creative(X0) <- (14) [avatar component clause 183]
224. generous(X0) [subsumption resolution 96,89]
225. ~strong(X0) | old(X0) | ~happy(X0) [subsumption resolution 94,224]
226. ~creative(X0) [subsumption resolution 104,224]
227. 14 [avatar split clause 226,183]
228. happy(X0) [subsumption resolution 102,224]
257. creative(X1) | strong(X1) [resolution 87,224]
259. strong(X1) <- (14) [subsumption resolution 257,184]
269. old(X0) | ~happy(X0) <- (14) [resolution 225,259]
271. old(X0) <- (14) [subsumption resolution 269,228]
276. $false <- (14) [resolution 271,117]
277. ~14 [avatar contradiction clause 276]
280. $false [avatar sat refutation 227,277]
% SZS output end Proof for 1655606737647350225813586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both old and not funny then someone is rich or not quiet and vice versa.
If susan is humble then fred is funny or not wise.
Everyone who is humble or tall is either wise or not rich.
If mary is both kind and rich then someone is not humble or not calm and vice versa.
Everyone who is rich is patient or not funny.
Everyone who is humble is rich or curious and vice versa.
If mary is brave or not strong then lucy is either not happy or generous and vice versa.
If someone is both not strong and generous then someone is not happy or not funny and vice versa.
If someone is both creative and not generous then mary is both patient and not funny and vice versa.
Everyone who is not generous or happy is either not humble or generous.
Everyone who is not old is not patient or not kind and vice versa.
If someone is either calm or funny then someone is either not generous or not rich.
If john is not creative or not generous then susan is not rich or not generous.
Everyone who is either quiet or not funny is both not wise and curious.
Everyone who is either wise or not strong is either old or wise.
If someone is both not tall and funny then mary is strong or not strong.
John is old.
Fred is not kind or not rich.
Someone is both calm and generous.
Someone is tall.
Someone is either not calm or not wise.
Someone is both rich and strong.
Someone is patient.
Susan is both humble and kind. | Mary is rich. | neutral | (((old(alice)&~funny(alice)))<=>(?[X]:((rich(X)|~quiet(X)))))&
((humble(susan))=>((funny(fred)|~wise(fred))))&
(![X]:((humble(X)|tall(X))=>(wise(X)<~>~rich(X))))&
(((kind(mary)&rich(mary)))<=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:(rich(X)=>(patient(X)|~funny(X))))&
(![X]:(humble(X)<=>(rich(X)|curious(X))))&
(((brave(mary)|~strong(mary)))<=>((~happy(lucy)<~>generous(lucy))))&
((?[X]:((~strong(X)&generous(X))))<=>(?[X]:((~happy(X)|~funny(X)))))&
((?[X]:((creative(X)&~generous(X))))<=>((patient(mary)&~funny(mary))))&
(![X]:((~generous(X)|happy(X))=>(~humble(X)<~>generous(X))))&
(![X]:(~old(X)<=>(~patient(X)|~kind(X))))&
((?[X]:((calm(X)<~>funny(X))))=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((~creative(john)|~generous(john)))=>((~rich(susan)|~generous(susan))))&
(![X]:((quiet(X)<~>~funny(X))=>(~wise(X)&curious(X))))&
(![X]:((wise(X)<~>~strong(X))=>(old(X)<~>wise(X))))&
((?[X]:((~tall(X)&funny(X))))=>((strong(mary)|~strong(mary))))&
(old(john))&
((~kind(fred)|~rich(fred)))&
(?[X]:((calm(X)&generous(X))))&
(?[X]:(tall(X)))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:((rich(X)&strong(X))))&
(?[X]:(patient(X)))&
((humble(susan)&kind(susan))) | rich(mary) | [] | null | 0 |
If alice is strong then someone is both wise and quiet. If john is creative then someone is both wise and quiet and vice versa. If someone is both happy and old then someone is wise and vice versa. Everyone who is generous is either old or not calm and vice versa. Everyone who is not old is both quiet and strong. If someone is either rich or kind then john is either kind or wise. Everyone who is patient or not happy is calm and vice versa. If alice is calm then someone is wise. Everyone who is rich or creative is happy. If someone is either creative or not generous then mary is either not curious or not creative and vice versa. Everyone who is brave or rich is not quiet. Everyone who is rich or not wise is either not strong or tall and vice versa. Everyone who is strong is not generous or brave and vice versa. Everyone who is both not old and curious is not quiet or rich and vice versa. If someone is not old or not calm then alice is not quiet or creative and vice versa. If someone is either not generous or kind then alice is curious or not kind and vice versa. Someone is not brave. Paul is both not patient and not strong. Someone is either kind or not calm. Susan is brave or not old. Someone is not generous or old. Someone is both not rich and not patient. John is both creative and not tall. | Mary is not wise. | neutral | ((strong(alice))=>(?[X]:((wise(X)&quiet(X)))))&
((creative(john))<=>(?[X]:((wise(X)&quiet(X)))))&
((?[X]:((happy(X)&old(X))))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(old(X)<~>~calm(X))))&
(![X]:(~old(X)=>(quiet(X)&strong(X))))&
((?[X]:((rich(X)<~>kind(X))))=>((kind(john)<~>wise(john))))&
(![X]:((patient(X)|~happy(X))<=>calm(X)))&
((calm(alice))=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~curious(mary)<~>~creative(mary))))&
(![X]:((brave(X)|rich(X))=>~quiet(X)))&
(![X]:((rich(X)|~wise(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(strong(X)<=>(~generous(X)|brave(X))))&
(![X]:((~old(X)&curious(X))<=>(~quiet(X)|rich(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~quiet(alice)|creative(alice))))&
((?[X]:((~generous(X)<~>kind(X))))<=>((curious(alice)|~kind(alice))))&
(?[X]:(~brave(X)))&
((~patient(paul)&~strong(paul)))&
(?[X]:((kind(X)<~>~calm(X))))&
((brave(susan)|~old(susan)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:((~rich(X)&~patient(X))))&
((creative(john)&~tall(john))) | ~wise(mary) | [] | null | 0 |
Everyone who is humble or not creative is either not calm or not rich.
Everyone who is either patient or not creative is both not tall and not kind.
If alice is either humble or not old then paul is both not quiet and funny.
Everyone who is either curious or old is both not kind and brave and vice versa.
If mary is either funny or strong then someone is both humble and not wise.
If someone is not rich then fred is either not creative or tall and vice versa.
If someone is either quiet or not quiet then someone is not wise or creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
Susan is rich or creative.
Fred is both not generous and kind.
Fred is not happy or not rich.
Someone is funny or not rich.
Someone is wise or not calm.
Someone is either not humble or tall.
Someone is not strong or not happy. | Alice is not happy. | contradiction | (![X]:((humble(X)|~creative(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((patient(X)<~>~creative(X))=>(~tall(X)&~kind(X))))&
(((humble(alice)<~>~old(alice)))=>((~quiet(paul)&funny(paul))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((rich(susan)|creative(susan)))&
((~generous(fred)&kind(fred)))&
((~happy(fred)|~rich(fred)))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~strong(X)|~happy(X)))) | ~happy(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2390212737813391032233032
% SZS output start Proof for 2390212737813391032233032
14. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~old(X0) | old(X0))) [input p13]
24. ~happy(alice) [input hypothesis]
65. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~happy(X0) | quiet(X0)))) [nnf transformation 14]
66. ! [X0] : (((happy(X0) & ~quiet(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~happy(X0) | quiet(X0))) [flattening 65]
131. happy(X0) | ~old(X0) [cnf transformation 66]
132. happy(X0) | old(X0) [cnf transformation 66]
148. ~happy(alice) [cnf transformation 24]
260. happy(X0) [subsumption resolution 131,132]
303. $false [subsumption resolution 148,260]
% SZS output end Proof for 2390212737813391032233032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not patient is rich and vice versa.
Everyone who is either patient or creative is either not creative or funny.
If someone is not patient or generous then someone is funny or tall.
If susan is not calm then someone is either humble or not creative and vice versa.
Everyone who is not kind or curious is either creative or not happy and vice versa.
Everyone who is either calm or wise is brave or patient.
Everyone who is both brave and curious is both not humble and not generous and vice versa.
If someone is both not humble and brave then fred is not rich.
If susan is both curious and funny then someone is both brave and wise.
Everyone who is both rich and not quiet is not wise.
Everyone who is generous is not quiet and vice versa.
Everyone who is happy is both not rich and not brave and vice versa.
Everyone who is not old or not wise is not old and vice versa.
Everyone who is not quiet is rich and vice versa.
If fred is calm then someone is not curious or not funny and vice versa.
If paul is patient or calm then john is both kind and not rich.
Mary is either strong or creative.
Lucy is not quiet or calm.
Lucy is not curious.
Someone is both wise and not generous.
Someone is both brave and funny.
Someone is not wise.
Lucy is not brave.
Someone is calm or creative. | Mary is not patient. | neutral | (![X]:((patient(X)&~patient(X))<=>rich(X)))&
(![X]:((patient(X)<~>creative(X))=>(~creative(X)<~>funny(X))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:((funny(X)|tall(X)))))&
((~calm(susan))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)|curious(X))<=>(creative(X)<~>~happy(X))))&
(![X]:((calm(X)<~>wise(X))=>(brave(X)|patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((~humble(X)&brave(X))))=>(~rich(fred)))&
(((curious(susan)&funny(susan)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((rich(X)&~quiet(X))=>~wise(X)))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:(happy(X)<=>(~rich(X)&~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
(![X]:(~quiet(X)<=>rich(X)))&
((calm(fred))<=>(?[X]:((~curious(X)|~funny(X)))))&
(((patient(paul)|calm(paul)))=>((kind(john)&~rich(john))))&
((strong(mary)<~>creative(mary)))&
((~quiet(lucy)|calm(lucy)))&
(~curious(lucy))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~wise(X)))&
(~brave(lucy))&
(?[X]:((calm(X)|creative(X)))) | ~patient(mary) | [] | null | 0 |
Everyone who is curious or happy is both brave and creative.
Everyone who is both not rich and not kind is both patient and not generous.
If someone is not quiet then someone is quiet or creative.
Everyone who is humble is either not quiet or quiet.
Everyone who is not tall is both not brave and creative.
If someone is either curious or humble then someone is calm or rich.
Everyone who is not happy is both rich and brave.
Everyone who is both not creative and not wise is quiet or not patient and vice versa.
Everyone who is either wise or not wise is rich or not old.
Everyone who is both tall and generous is old.
If john is not old then someone is either not kind or quiet.
If someone is not brave then someone is not humble.
Everyone who is both rich and curious is either happy or strong and vice versa.
Everyone who is not quiet is not creative or old.
Everyone who is rich or not rich is calm and vice versa.
Everyone who is not creative or strong is old.
Lucy is not kind or generous.
Someone is not humble or not creative.
Someone is either happy or curious.
Someone is both wise and creative.
Paul is not brave or creative.
Fred is either not rich or humble.
Susan is strong. | Fred is not tall. | contradiction | (![X]:((curious(X)|happy(X))=>(brave(X)&creative(X))))&
(![X]:((~rich(X)&~kind(X))=>(patient(X)&~generous(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(~brave(X)&creative(X))))&
((?[X]:((curious(X)<~>humble(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~happy(X)=>(rich(X)&brave(X))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)|~patient(X))))&
(![X]:((wise(X)<~>~wise(X))=>(rich(X)|~old(X))))&
(![X]:((tall(X)&generous(X))=>old(X)))&
((~old(john))=>(?[X]:((~kind(X)<~>quiet(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~humble(X))))&
(![X]:((rich(X)&curious(X))<=>(happy(X)<~>strong(X))))&
(![X]:(~quiet(X)=>(~creative(X)|old(X))))&
(![X]:((rich(X)|~rich(X))<=>calm(X)))&
(![X]:((~creative(X)|strong(X))=>old(X)))&
((~kind(lucy)|generous(lucy)))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((wise(X)&creative(X))))&
((~brave(paul)|creative(paul)))&
((~rich(fred)<~>humble(fred)))&
(strong(susan)) | ~tall(fred) | [
"p0",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 9086105633278391465142905
% SZS output start Proof for 9086105633278391465142905
1. ! [X0] : ((happy(X0) | curious(X0)) => (creative(X0) & brave(X0))) [input p0]
5. ! [X0] : (~tall(X0) => (creative(X0) & ~brave(X0))) [input p4]
7. ! [X0] : (~happy(X0) => (brave(X0) & rich(X0))) [input p6]
24. ~tall(fred) [input hypothesis]
29. ! [X0] : ((creative(X0) & brave(X0)) | (~happy(X0) & ~curious(X0))) [ennf transformation 1]
34. ! [X0] : ((creative(X0) & ~brave(X0)) | tall(X0)) [ennf transformation 5]
36. ! [X0] : ((brave(X0) & rich(X0)) | happy(X0)) [ennf transformation 7]
76. ~happy(X0) | brave(X0) [cnf transformation 29]
84. ~brave(X0) | tall(X0) [cnf transformation 34]
89. brave(X0) | happy(X0) [cnf transformation 36]
121. ~tall(fred) [cnf transformation 24]
152. brave(X0) [subsumption resolution 89,76]
213. tall(X0) [resolution 84,152]
215. $false [resolution 213,121]
% SZS output end Proof for 9086105633278391465142905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not calm then someone is both not patient and not tall and vice versa. If someone is either brave or humble then someone is either not old or not quiet and vice versa. Everyone who is either old or calm is humble and vice versa. Everyone who is not creative is either curious or funny. Everyone who is both not generous and old is creative or calm. Everyone who is either not strong or quiet is both calm and rich and vice versa. If someone is humble then fred is both kind and not creative. Everyone who is tall is not quiet or strong and vice versa. If someone is both happy and not calm then john is both not funny and curious. Everyone who is both tall and rich is both generous and not wise. Everyone who is not funny is both funny and calm and vice versa. If someone is both funny and quiet then someone is both not happy and not kind. If someone is happy or calm then someone is not rich or tall. Everyone who is not humble is both not happy and kind and vice versa. Everyone who is either creative or not brave is not strong. If susan is patient or not wise then someone is either tall or wise. Alice is either brave or not calm. John is either brave or not brave. Someone is both not humble and tall. Lucy is both not kind and strong. Someone is old or not brave. Mary is either not calm or patient. Susan is not happy. | Fred is not creative. | entailment | ((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((brave(X)<~>humble(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((old(X)<~>calm(X))<=>humble(X)))&
(![X]:(~creative(X)=>(curious(X)<~>funny(X))))&
(![X]:((~generous(X)&old(X))=>(creative(X)|calm(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(calm(X)&rich(X))))&
((?[X]:(humble(X)))=>((kind(fred)&~creative(fred))))&
(![X]:(tall(X)<=>(~quiet(X)|strong(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~funny(john)&curious(john))))&
(![X]:((tall(X)&rich(X))=>(generous(X)&~wise(X))))&
(![X]:(~funny(X)<=>(funny(X)&calm(X))))&
((?[X]:((funny(X)&quiet(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(~humble(X)<=>(~happy(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))=>~strong(X)))&
(((patient(susan)|~wise(susan)))=>(?[X]:((tall(X)<~>wise(X)))))&
((brave(alice)<~>~calm(alice)))&
((brave(john)<~>~brave(john)))&
(?[X]:((~humble(X)&tall(X))))&
((~kind(lucy)&strong(lucy)))&
(?[X]:((old(X)|~brave(X))))&
((~calm(mary)<~>patient(mary)))&
(~happy(susan)) | ~creative(fred) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5749218042858041969681452
% SZS output start Proof for 5749218042858041969681452
7. ? [X0] : humble(X0) => (~creative(fred) & kind(fred)) [input p6]
14. ! [X0] : (~humble(X0) <=> (kind(X0) & ~happy(X0))) [input p13]
20. strong(lucy) & ~kind(lucy) [input p19]
24. creative(fred) [input hypothesis]
32. (~creative(fred) & kind(fred)) | ! [X0] : ~humble(X0) [ennf transformation 7]
64. ! [X0] : ((~humble(X0) | (~kind(X0) | happy(X0))) & ((kind(X0) & ~happy(X0)) | humble(X0))) [nnf transformation 14]
65. ! [X0] : ((~humble(X0) | ~kind(X0) | happy(X0)) & ((kind(X0) & ~happy(X0)) | humble(X0))) [flattening 64]
103. ~creative(fred) | ~humble(X0) [cnf transformation 32]
118. kind(X0) | humble(X0) [cnf transformation 65]
132. ~kind(lucy) [cnf transformation 20]
138. creative(fred) [cnf transformation 24]
208. 16 <=> ! [X0] : ~humble(X0) [avatar definition]
209. ~humble(X0) <- (16) [avatar component clause 208]
211. 17 <=> creative(fred) [avatar definition]
214. 16 | ~17 [avatar split clause 103,211,208]
313. 17 [avatar split clause 138,211]
319. humble(lucy) [resolution 118,132]
321. $false <- (16) [subsumption resolution 319,209]
322. ~16 [avatar contradiction clause 321]
325. $false [avatar sat refutation 214,313,322]
% SZS output end Proof for 5749218042858041969681452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous or funny then paul is either not brave or brave and vice versa.
Everyone who is both not wise and not strong is both not happy and not generous and vice versa.
Everyone who is not creative or calm is both not kind and creative.
Everyone who is either not kind or not happy is either not generous or not brave.
If paul is calm then fred is wise or not wise and vice versa.
Everyone who is not funny is wise or not calm and vice versa.
Everyone who is brave is both not tall and not calm.
Everyone who is either patient or not strong is not generous and vice versa.
If john is both not rich and wise then fred is not happy or not humble and vice versa.
If susan is either not creative or kind then alice is not calm or generous and vice versa.
Everyone who is both generous and strong is generous or quiet.
If someone is wise or patient then someone is either not patient or quiet.
If someone is not old then someone is not quiet.
Everyone who is either rich or curious is both not strong and humble.
If susan is not creative then someone is both curious and not curious.
If someone is not calm then lucy is both creative and not curious.
Someone is not kind or wise.
Someone is brave.
Lucy is either not curious or not wise.
Someone is not funny.
Fred is kind or patient.
John is either generous or patient.
Mary is either old or not wise. | Paul is not wise. | entailment | (((~generous(paul)|funny(paul)))<=>((~brave(paul)<~>brave(paul))))&
(![X]:((~wise(X)&~strong(X))<=>(~happy(X)&~generous(X))))&
(![X]:((~creative(X)|calm(X))=>(~kind(X)&creative(X))))&
(![X]:((~kind(X)<~>~happy(X))=>(~generous(X)<~>~brave(X))))&
((calm(paul))<=>((wise(fred)|~wise(fred))))&
(![X]:(~funny(X)<=>(wise(X)|~calm(X))))&
(![X]:(brave(X)=>(~tall(X)&~calm(X))))&
(![X]:((patient(X)<~>~strong(X))<=>~generous(X)))&
(((~rich(john)&wise(john)))<=>((~happy(fred)|~humble(fred))))&
(((~creative(susan)<~>kind(susan)))<=>((~calm(alice)|generous(alice))))&
(![X]:((generous(X)&strong(X))=>(generous(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((~patient(X)<~>quiet(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~quiet(X))))&
(![X]:((rich(X)<~>curious(X))=>(~strong(X)&humble(X))))&
((~creative(susan))=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((creative(lucy)&~curious(lucy))))&
(?[X]:((~kind(X)|wise(X))))&
(?[X]:(brave(X)))&
((~curious(lucy)<~>~wise(lucy)))&
(?[X]:(~funny(X)))&
((kind(fred)|patient(fred)))&
((generous(john)<~>patient(john)))&
((old(mary)<~>~wise(mary))) | ~wise(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5014127906487609127813044
% SZS output start Proof for 5014127906487609127813044
1. (funny(paul) | ~generous(paul)) <=> (~brave(paul) <~> brave(paul)) [input p0]
2. ! [X0] : ((~strong(X0) & ~wise(X0)) <=> (~generous(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((calm(X0) | ~creative(X0)) => (creative(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~kind(X0) <~> ~happy(X0)) => (~generous(X0) <~> ~brave(X0))) [input p3]
5. calm(paul) <=> (~wise(fred) | wise(fred)) [input p4]
6. ! [X0] : (~funny(X0) <=> (~calm(X0) | wise(X0))) [input p5]
7. ! [X0] : (brave(X0) => (~calm(X0) & ~tall(X0))) [input p6]
24. wise(paul) [input hypothesis]
27. ! [X0] : (brave(X0) => ~calm(X0)) [pure predicate removal 7]
28. ! [X0] : ((creative(X0) & ~kind(X0)) | (~calm(X0) & creative(X0))) [ennf transformation 3]
29. ! [X0] : ((~generous(X0) <~> ~brave(X0)) | (~kind(X0) <=> ~happy(X0))) [ennf transformation 4]
30. ! [X0] : (~calm(X0) | ~brave(X0)) [ennf transformation 27]
38. ((funny(paul) | ~generous(paul)) | ((~brave(paul) | ~brave(paul)) & (brave(paul) | brave(paul)))) & (((~brave(paul) | brave(paul)) & (brave(paul) | ~brave(paul))) | (~funny(paul) & generous(paul))) [nnf transformation 1]
39. (funny(paul) | ~generous(paul) | ((~brave(paul) | ~brave(paul)) & (brave(paul) | brave(paul)))) & (((~brave(paul) | brave(paul)) & (brave(paul) | ~brave(paul))) | (~funny(paul) & generous(paul))) [flattening 38]
40. ! [X0] : (((~strong(X0) & ~wise(X0)) | (generous(X0) | happy(X0))) & ((~generous(X0) & ~happy(X0)) | (strong(X0) | wise(X0)))) [nnf transformation 2]
41. ! [X0] : (((~strong(X0) & ~wise(X0)) | generous(X0) | happy(X0)) & ((~generous(X0) & ~happy(X0)) | strong(X0) | wise(X0))) [flattening 40]
42. ! [X0] : (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) [nnf transformation 29]
43. (calm(paul) | (wise(fred) & ~wise(fred))) & ((~wise(fred) | wise(fred)) | ~calm(paul)) [nnf transformation 5]
44. (calm(paul) | (wise(fred) & ~wise(fred))) & (~wise(fred) | wise(fred) | ~calm(paul)) [flattening 43]
45. ! [X0] : ((~funny(X0) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | funny(X0))) [nnf transformation 6]
46. ! [X0] : ((~funny(X0) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | funny(X0))) [flattening 45]
75. funny(paul) | ~generous(paul) | brave(paul) | brave(paul) [cnf transformation 39]
79. ~wise(X0) | generous(X0) | happy(X0) [cnf transformation 41]
82. ~kind(X0) | ~calm(X0) [cnf transformation 28]
87. ~happy(X0) | generous(X0) | brave(X0) | kind(X0) [cnf transformation 42]
90. calm(paul) | ~wise(fred) [cnf transformation 44]
91. calm(paul) | wise(fred) [cnf transformation 44]
93. ~wise(X0) | ~funny(X0) [cnf transformation 46]
95. ~calm(X0) | ~brave(X0) [cnf transformation 30]
135. wise(paul) [cnf transformation 24]
137. funny(paul) | ~generous(paul) | brave(paul) [duplicate literal removal 75]
140. 1 <=> brave(paul) [avatar definition]
142. ~brave(paul) <- (~1) [avatar component clause 140]
144. 2 <=> generous(paul) [avatar definition]
146. ~generous(paul) <- (~2) [avatar component clause 144]
148. 3 <=> funny(paul) [avatar definition]
152. 1 | ~2 | 3 [avatar split clause 137,148,144,140]
154. 4 <=> wise(fred) [avatar definition]
158. 5 <=> calm(paul) [avatar definition]
160. calm(paul) <- (5) [avatar component clause 158]
161. 4 | 5 [avatar split clause 91,158,154]
162. ~4 | 5 [avatar split clause 90,158,154]
290. ~funny(paul) [resolution 93,135]
293. ~3 [avatar split clause 290,148]
294. ~brave(paul) <- (5) [resolution 95,160]
296. ~1 | ~5 [avatar split clause 294,158,140]
308. generous(paul) | happy(paul) [resolution 79,135]
311. happy(paul) <- (~2) [subsumption resolution 308,146]
373. generous(paul) | brave(paul) | kind(paul) <- (~2) [resolution 87,311]
376. brave(paul) | kind(paul) <- (~2) [subsumption resolution 373,146]
377. kind(paul) <- (~1, ~2) [subsumption resolution 376,142]
399. ~calm(paul) <- (~1, ~2) [resolution 377,82]
400. $false <- (~1, ~2, 5) [subsumption resolution 399,160]
401. 1 | 2 | ~5 [avatar contradiction clause 400]
402. $false [avatar sat refutation 152,161,162,293,296,401]
% SZS output end Proof for 5014127906487609127813044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not quiet then john is both humble and not calm and vice versa.
Everyone who is both not happy and not funny is either old or strong and vice versa.
If someone is generous then someone is either not calm or strong.
Everyone who is generous or not strong is curious or not rich.
Everyone who is both rich and not quiet is brave.
Everyone who is both funny and not tall is either humble or not rich and vice versa.
Everyone who is strong is either patient or old and vice versa.
Everyone who is both not wise and not quiet is not old or creative.
If someone is both not calm and patient then john is both not rich and funny and vice versa.
Everyone who is not strong or not generous is calm or not curious and vice versa.
Everyone who is not generous or not humble is both not happy and humble and vice versa.
Everyone who is brave is calm.
Everyone who is funny or rich is either happy or not strong.
If alice is both not brave and not curious then someone is not patient and vice versa.
If someone is rich then someone is either creative or not kind and vice versa.
If john is both not happy and not tall then alice is either not calm or not brave and vice versa.
Alice is both not tall and generous.
Someone is not creative.
Someone is kind or not kind.
Lucy is not tall or not generous.
Lucy is rich or not brave.
John is not tall or not happy.
Someone is both not brave and creative.
Someone is patient or wise. | John is not quiet. | neutral | ((?[X]:((~strong(X)&~quiet(X))))<=>((humble(john)&~calm(john))))&
(![X]:((~happy(X)&~funny(X))<=>(old(X)<~>strong(X))))&
((?[X]:(generous(X)))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((generous(X)|~strong(X))=>(curious(X)|~rich(X))))&
(![X]:((rich(X)&~quiet(X))=>brave(X)))&
(![X]:((funny(X)&~tall(X))<=>(humble(X)<~>~rich(X))))&
(![X]:(strong(X)<=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)&~quiet(X))=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)&patient(X))))<=>((~rich(john)&funny(john))))&
(![X]:((~strong(X)|~generous(X))<=>(calm(X)|~curious(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~happy(X)&humble(X))))&
(![X]:(brave(X)=>calm(X)))&
(![X]:((funny(X)|rich(X))=>(happy(X)<~>~strong(X))))&
(((~brave(alice)&~curious(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(((~happy(john)&~tall(john)))<=>((~calm(alice)<~>~brave(alice))))&
((~tall(alice)&generous(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((kind(X)|~kind(X))))&
((~tall(lucy)|~generous(lucy)))&
((rich(lucy)|~brave(lucy)))&
((~tall(john)|~happy(john)))&
(?[X]:((~brave(X)&creative(X))))&
(?[X]:((patient(X)|wise(X)))) | ~quiet(john) | [] | null | 0 |
Everyone who is rich or not strong is patient and vice versa.
If someone is both funny and not strong then someone is not happy or old and vice versa.
If mary is quiet then someone is either strong or not strong and vice versa.
Everyone who is curious or not tall is humble or funny.
If someone is calm or rich then someone is both wise and not old.
If someone is either calm or generous then someone is both wise and creative.
Everyone who is either not strong or not funny is not tall and vice versa.
If someone is funny then fred is humble or curious and vice versa.
Everyone who is either not creative or not curious is quiet or patient and vice versa.
Everyone who is humble is not humble.
Everyone who is both calm and creative is both not creative and strong.
Everyone who is not quiet is quiet or brave.
If someone is not old or not wise then alice is quiet.
If alice is either happy or creative then alice is kind or old and vice versa.
If someone is both happy and not funny then someone is not strong or quiet.
If mary is either calm or curious then someone is either not curious or not brave.
Someone is not kind or creative.
Mary is either curious or creative.
Alice is either calm or generous.
Fred is either strong or not curious.
Someone is not happy or strong.
John is not calm.
Someone is happy or patient.
Someone is not generous. | John is not quiet. | neutral | (![X]:((rich(X)|~strong(X))<=>patient(X)))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((~happy(X)|old(X)))))&
((quiet(mary))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((curious(X)|~tall(X))=>(humble(X)|funny(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:((wise(X)&creative(X)))))&
(![X]:((~strong(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(funny(X)))<=>((humble(fred)|curious(fred))))&
(![X]:((~creative(X)<~>~curious(X))<=>(quiet(X)|patient(X))))&
(![X]:(humble(X)=>~humble(X)))&
(![X]:((calm(X)&creative(X))=>(~creative(X)&strong(X))))&
(![X]:(~quiet(X)=>(quiet(X)|brave(X))))&
((?[X]:((~old(X)|~wise(X))))=>(quiet(alice)))&
(((happy(alice)<~>creative(alice)))<=>((kind(alice)|old(alice))))&
((?[X]:((happy(X)&~funny(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(?[X]:((~kind(X)|creative(X))))&
((curious(mary)<~>creative(mary)))&
((calm(alice)<~>generous(alice)))&
((strong(fred)<~>~curious(fred)))&
(?[X]:((~happy(X)|strong(X))))&
(~calm(john))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:(~generous(X))) | ~quiet(john) | [] | null | 0 |
Everyone who is either brave or not rich is either kind or not quiet and vice versa.
If paul is not kind or old then john is rich and vice versa.
Everyone who is quiet is either not happy or generous and vice versa.
Everyone who is both not old and not tall is either not calm or curious and vice versa.
If someone is either not quiet or funny then mary is not brave.
Everyone who is both old and not strong is not wise or old and vice versa.
If paul is either wise or not rich then someone is either not tall or kind.
If someone is wise then someone is not generous.
Everyone who is not calm or kind is generous or brave.
If someone is either not brave or not wise then lucy is not curious or not generous.
Everyone who is both not generous and not quiet is not rich or old and vice versa.
Everyone who is not rich or kind is both not calm and not tall.
If lucy is either not brave or wise then someone is patient or not calm and vice versa.
Everyone who is humble or patient is funny or not happy and vice versa.
Everyone who is not strong or generous is wise or calm and vice versa.
If someone is both funny and quiet then someone is brave or not generous and vice versa.
Someone is either not humble or generous.
Someone is both happy and not funny.
Paul is happy or creative.
Someone is both not brave and not quiet.
John is either wise or not curious.
Susan is either funny or not funny.
Someone is humble or quiet.
Someone is quiet or tall. | Mary is wise. | entailment | (![X]:((brave(X)<~>~rich(X))<=>(kind(X)<~>~quiet(X))))&
(((~kind(paul)|old(paul)))<=>(rich(john)))&
(![X]:(quiet(X)<=>(~happy(X)<~>generous(X))))&
(![X]:((~old(X)&~tall(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((~quiet(X)<~>funny(X))))=>(~brave(mary)))&
(![X]:((old(X)&~strong(X))<=>(~wise(X)|old(X))))&
(((wise(paul)<~>~rich(paul)))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(wise(X)))=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)|kind(X))=>(generous(X)|brave(X))))&
((?[X]:((~brave(X)<~>~wise(X))))=>((~curious(lucy)|~generous(lucy))))&
(![X]:((~generous(X)&~quiet(X))<=>(~rich(X)|old(X))))&
(![X]:((~rich(X)|kind(X))=>(~calm(X)&~tall(X))))&
(((~brave(lucy)<~>wise(lucy)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((humble(X)|patient(X))<=>(funny(X)|~happy(X))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)|calm(X))))&
((?[X]:((funny(X)&quiet(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((happy(X)&~funny(X))))&
((happy(paul)|creative(paul)))&
(?[X]:((~brave(X)&~quiet(X))))&
((wise(john)<~>~curious(john)))&
((funny(susan)<~>~funny(susan)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((quiet(X)|tall(X)))) | wise(mary) | [
"p0",
"p4",
"p5",
"p7",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5878656795294999653388210
% SZS output start Proof for 5878656795294999653388210
1. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (kind(X0) <~> ~quiet(X0))) [input p0]
5. ? [X0] : (~quiet(X0) <~> funny(X0)) => ~brave(mary) [input p4]
6. ! [X0] : ((~strong(X0) & old(X0)) <=> (old(X0) | ~wise(X0))) [input p5]
8. ? [X0] : wise(X0) => ? [X0] : ~generous(X0) [input p7]
11. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (old(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((kind(X0) | ~rich(X0)) => (~tall(X0) & ~calm(X0))) [input p11]
15. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (calm(X0) | wise(X0))) [input p14]
16. ? [X0] : (quiet(X0) & funny(X0)) <=> ? [X0] : (~generous(X0) | brave(X0)) [input p15]
25. ~wise(mary) [input hypothesis]
26. ? [X0] : wise(X0) => ? [X1] : ~generous(X1) [rectify 8]
27. ? [X0] : (quiet(X0) & funny(X0)) <=> ? [X1] : (~generous(X1) | brave(X1)) [rectify 16]
29. ~brave(mary) | ! [X0] : (~quiet(X0) <=> funny(X0)) [ennf transformation 5]
31. ? [X1] : ~generous(X1) | ! [X0] : ~wise(X0) [ennf transformation 26]
36. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~kind(X0) & rich(X0))) [ennf transformation 12]
37. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 1]
43. ~brave(mary) | ! [X0] : ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0))) [nnf transformation 29]
44. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | strong(X0) | ~old(X0))) [flattening 44]
49. ? [X0] : ~generous(X0) | ! [X1] : ~wise(X1) [rectify 31]
50. ? [X0] : ~generous(X0) => ~generous(sK1) [choice axiom]
51. ~generous(sK1) | ! [X1] : ~wise(X1) [skolemisation 49,50]
53. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | quiet(X0) | generous(X0))) [flattening 53]
61. ! [X0] : (((generous(X0) | ~strong(X0)) | (~calm(X0) & ~wise(X0))) & ((calm(X0) | wise(X0)) | (~generous(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((generous(X0) | ~strong(X0) | (~calm(X0) & ~wise(X0))) & (calm(X0) | wise(X0) | (~generous(X0) & strong(X0)))) [flattening 61]
63. (? [X0] : (quiet(X0) & funny(X0)) | ! [X1] : (generous(X1) & ~brave(X1))) & (? [X1] : (~generous(X1) | brave(X1)) | ! [X0] : (~quiet(X0) | ~funny(X0))) [nnf transformation 27]
64. (? [X0] : (quiet(X0) & funny(X0)) | ! [X1] : (generous(X1) & ~brave(X1))) & (? [X2] : (~generous(X2) | brave(X2)) | ! [X3] : (~quiet(X3) | ~funny(X3))) [rectify 63]
65. ? [X0] : (quiet(X0) & funny(X0)) => (quiet(sK3) & funny(sK3)) [choice axiom]
66. ? [X2] : (~generous(X2) | brave(X2)) => (~generous(sK4) | brave(sK4)) [choice axiom]
67. ((quiet(sK3) & funny(sK3)) | ! [X1] : (generous(X1) & ~brave(X1))) & ((~generous(sK4) | brave(sK4)) | ! [X3] : (~quiet(X3) | ~funny(X3))) [skolemisation 64,66,65]
86. ~rich(X0) | brave(X0) | kind(X0) | quiet(X0) [cnf transformation 37]
103. ~brave(mary) | ~quiet(X0) | ~funny(X0) [cnf transformation 43]
105. wise(X0) | old(X0) [cnf transformation 45]
107. ~strong(X0) | wise(X0) [cnf transformation 45]
113. ~generous(sK1) | ~wise(X1) [cnf transformation 51]
120. ~generous(X0) | ~old(X0) [cnf transformation 54]
122. ~old(X0) | ~quiet(X0) [cnf transformation 54]
123. ~calm(X0) | rich(X0) [cnf transformation 36]
124. ~calm(X0) | ~kind(X0) [cnf transformation 36]
137. calm(X0) | wise(X0) | strong(X0) [cnf transformation 62]
143. funny(sK3) | generous(X1) [cnf transformation 67]
145. quiet(sK3) | generous(X1) [cnf transformation 67]
158. ~wise(mary) [cnf transformation 25]
175. 4 <=> ! [X0] : (~quiet(X0) | ~funny(X0)) [avatar definition]
176. ~funny(X0) | ~quiet(X0) <- (4) [avatar component clause 175]
178. 5 <=> brave(mary) [avatar definition]
180. ~brave(mary) <- (~5) [avatar component clause 178]
181. 4 | ~5 [avatar split clause 103,178,175]
207. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
208. ~wise(X1) <- (11) [avatar component clause 207]
210. 12 <=> generous(sK1) [avatar definition]
212. ~generous(sK1) <- (~12) [avatar component clause 210]
213. 11 | ~12 [avatar split clause 113,210,207]
259. wise(X0) | calm(X0) [subsumption resolution 137,107]
261. 23 <=> ! [X1] : generous(X1) [avatar definition]
262. generous(X1) <- (23) [avatar component clause 261]
264. 24 <=> quiet(sK3) [avatar definition]
266. quiet(sK3) <- (24) [avatar component clause 264]
267. 23 | 24 [avatar split clause 145,264,261]
273. 26 <=> funny(sK3) [avatar definition]
275. funny(sK3) <- (26) [avatar component clause 273]
276. 23 | 26 [avatar split clause 143,273,261]
283. 28 <=> generous(sK4) [avatar definition]
284. generous(sK4) <- (28) [avatar component clause 283]
285. ~generous(sK4) <- (~28) [avatar component clause 283]
325. $false <- (~12, 23) [subsumption resolution 212,262]
326. 12 | ~23 [avatar contradiction clause 325]
327. $false <- (23, ~28) [resolution 285,262]
328. ~23 | 28 [avatar contradiction clause 327]
331. old(mary) [resolution 105,158]
338. ~quiet(mary) [resolution 122,331]
341. calm(mary) [resolution 259,158]
357. ~kind(mary) [resolution 341,124]
358. rich(mary) [resolution 341,123]
399. old(X1) <- (11) [resolution 208,105]
415. ~old(sK4) <- (28) [resolution 284,120]
418. $false <- (11, 28) [subsumption resolution 415,399]
419. ~11 | ~28 [avatar contradiction clause 418]
492. brave(mary) | kind(mary) | quiet(mary) [resolution 358,86]
499. kind(mary) | quiet(mary) <- (~5) [subsumption resolution 492,180]
500. quiet(mary) <- (~5) [subsumption resolution 499,357]
501. $false <- (~5) [subsumption resolution 500,338]
502. 5 [avatar contradiction clause 501]
515. ~quiet(sK3) <- (4, 26) [resolution 176,275]
516. $false <- (4, 24, 26) [subsumption resolution 515,266]
517. ~4 | ~24 | ~26 [avatar contradiction clause 516]
518. $false [avatar sat refutation 181,213,267,276,326,328,419,502,517]
% SZS output end Proof for 5878656795294999653388210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not strong then someone is not old or calm.
Everyone who is either strong or not old is funny or not wise and vice versa.
Everyone who is not strong is either brave or not curious.
If someone is both not wise and kind then someone is not creative and vice versa.
Everyone who is both happy and quiet is either curious or not patient.
Everyone who is both old and tall is not rich or not wise.
Everyone who is both not tall and not kind is generous or not strong and vice versa.
If alice is not funny or not rich then someone is not funny.
If fred is not generous then john is patient.
If susan is both not calm and humble then john is generous or wise.
Everyone who is either tall or patient is both not patient and rich and vice versa.
If paul is not funny then lucy is curious or brave and vice versa.
Everyone who is either old or not quiet is both happy and not tall and vice versa.
If someone is not calm or not rich then someone is kind or not funny.
If someone is either not kind or kind then someone is brave and vice versa.
If alice is both old and not generous then someone is not happy or humble.
Someone is either not generous or rich.
Susan is kind.
Someone is either brave or generous.
John is not quiet.
Someone is not happy or wise.
Alice is both funny and not brave. | Alice is quiet. | neutral | (((quiet(paul)|~strong(paul)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((strong(X)<~>~old(X))<=>(funny(X)|~wise(X))))&
(![X]:(~strong(X)=>(brave(X)<~>~curious(X))))&
((?[X]:((~wise(X)&kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((happy(X)&quiet(X))=>(curious(X)<~>~patient(X))))&
(![X]:((old(X)&tall(X))=>(~rich(X)|~wise(X))))&
(![X]:((~tall(X)&~kind(X))<=>(generous(X)|~strong(X))))&
(((~funny(alice)|~rich(alice)))=>(?[X]:(~funny(X))))&
((~generous(fred))=>(patient(john)))&
(((~calm(susan)&humble(susan)))=>((generous(john)|wise(john))))&
(![X]:((tall(X)<~>patient(X))<=>(~patient(X)&rich(X))))&
((~funny(paul))<=>((curious(lucy)|brave(lucy))))&
(![X]:((old(X)<~>~quiet(X))<=>(happy(X)&~tall(X))))&
((?[X]:((~calm(X)|~rich(X))))=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:(brave(X))))&
(((old(alice)&~generous(alice)))=>(?[X]:((~happy(X)|humble(X)))))&
(?[X]:((~generous(X)<~>rich(X))))&
(kind(susan))&
(?[X]:((brave(X)<~>generous(X))))&
(~quiet(john))&
(?[X]:((~happy(X)|wise(X))))&
((funny(alice)&~brave(alice))) | quiet(alice) | [] | null | 0 |
If susan is either not calm or not brave then someone is not creative. If john is not quiet or quiet then mary is rich or not humble and vice versa. Everyone who is both generous and humble is either quiet or wise and vice versa. If someone is humble then john is either not old or not strong. Everyone who is both brave and not patient is either humble or not creative and vice versa. Everyone who is either not quiet or quiet is both not quiet and not humble and vice versa. Everyone who is either funny or not kind is curious or humble. Everyone who is not calm is wise or not patient and vice versa. Everyone who is patient or not quiet is either funny or not quiet. Everyone who is either not rich or not tall is both not brave and happy. If someone is funny or not rich then john is either quiet or old. If someone is both not wise and not rich then someone is either not patient or not tall. Everyone who is either not brave or not old is happy. If john is both kind and not old then someone is kind and vice versa. If someone is either wise or calm then alice is both not curious and not strong. If someone is rich then someone is not old or calm and vice versa. Someone is either not curious or not brave. Someone is generous or not creative. Someone is both not calm and old. Someone is old. Someone is either not wise or not rich. Paul is strong. Someone is both not rich and not humble. | Paul is kind. | contradiction | (((~calm(susan)<~>~brave(susan)))=>(?[X]:(~creative(X))))&
(((~quiet(john)|quiet(john)))<=>((rich(mary)|~humble(mary))))&
(![X]:((generous(X)&humble(X))<=>(quiet(X)<~>wise(X))))&
((?[X]:(humble(X)))=>((~old(john)<~>~strong(john))))&
(![X]:((brave(X)&~patient(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~quiet(X)&~humble(X))))&
(![X]:((funny(X)<~>~kind(X))=>(curious(X)|humble(X))))&
(![X]:(~calm(X)<=>(wise(X)|~patient(X))))&
(![X]:((patient(X)|~quiet(X))=>(funny(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>~tall(X))=>(~brave(X)&happy(X))))&
((?[X]:((funny(X)|~rich(X))))=>((quiet(john)<~>old(john))))&
((?[X]:((~wise(X)&~rich(X))))=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((~brave(X)<~>~old(X))=>happy(X)))&
(((kind(john)&~old(john)))<=>(?[X]:(kind(X))))&
((?[X]:((wise(X)<~>calm(X))))=>((~curious(alice)&~strong(alice))))&
((?[X]:(rich(X)))<=>(?[X]:((~old(X)|calm(X)))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:(old(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(strong(paul))&
(?[X]:((~rich(X)&~humble(X)))) | kind(paul) | [
"p5",
"p10",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3846019352053822581440390
% SZS output start Proof for 3846019352053822581440390
6. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (~humble(X0) & ~quiet(X0))) [input p5]
11. ? [X0] : (~rich(X0) | funny(X0)) => (quiet(john) <~> old(john)) [input p10]
14. (~old(john) & kind(john)) <=> ? [X0] : kind(X0) [input p13]
23. ? [X0] : (~humble(X0) & ~rich(X0)) [input p22]
24. kind(paul) [input hypothesis]
35. (quiet(john) <~> old(john)) | ! [X0] : (rich(X0) & ~funny(X0)) [ennf transformation 11]
48. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [flattening 48]
55. ((~old(john) | ~quiet(john)) & (old(john) | quiet(john))) | ! [X0] : (rich(X0) & ~funny(X0)) [nnf transformation 35]
60. ((~old(john) & kind(john)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | (old(john) | ~kind(john))) [nnf transformation 14]
61. ((~old(john) & kind(john)) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | old(john) | ~kind(john)) [flattening 60]
62. ((~old(john) & kind(john)) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | old(john) | ~kind(john)) [rectify 61]
63. ? [X1] : kind(X1) => kind(sK2) [choice axiom]
64. ((~old(john) & kind(john)) | ! [X0] : ~kind(X0)) & (kind(sK2) | old(john) | ~kind(john)) [skolemisation 62,63]
83. ? [X0] : (~humble(X0) & ~rich(X0)) => (~humble(sK10) & ~rich(sK10)) [choice axiom]
84. ~humble(sK10) & ~rich(sK10) [skolemisation 23,83]
106. ~quiet(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
123. old(john) | quiet(john) | rich(X0) [cnf transformation 55]
130. ~old(john) | ~kind(X0) [cnf transformation 64]
147. ~rich(sK10) [cnf transformation 84]
149. kind(paul) [cnf transformation 24]
152. ~quiet(X0) [duplicate literal removal 106]
189. 8 <=> old(john) [avatar definition]
201. old(john) | rich(X0) [subsumption resolution 123,152]
203. 10 <=> ! [X0] : rich(X0) [avatar definition]
204. rich(X0) <- (10) [avatar component clause 203]
205. 10 | 8 [avatar split clause 201,189,203]
220. 14 <=> ! [X0] : ~kind(X0) [avatar definition]
221. ~kind(X0) <- (14) [avatar component clause 220]
222. 14 | ~8 [avatar split clause 130,189,220]
305. $false <- (14) [resolution 221,149]
306. ~14 [avatar contradiction clause 305]
307. $false <- (10) [resolution 204,147]
308. ~10 [avatar contradiction clause 307]
309. $false [avatar sat refutation 205,222,306,308]
% SZS output end Proof for 3846019352053822581440390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or happy is brave or generous. Everyone who is brave is kind and vice versa. If someone is either happy or not brave then susan is wise or not creative. If someone is either not funny or strong then someone is both tall and creative and vice versa. If someone is both not happy and wise then someone is both not curious and not creative. If someone is both strong and quiet then someone is not generous or not happy and vice versa. Everyone who is not humble is either not funny or not quiet. If someone is not patient or not generous then someone is either not generous or wise and vice versa. Everyone who is either not happy or creative is either not old or not generous. Everyone who is either not strong or not funny is either patient or generous and vice versa. Everyone who is both not curious and happy is funny or not creative. If someone is brave then someone is either patient or creative and vice versa. Everyone who is either not wise or quiet is not funny and vice versa. Everyone who is not calm or not quiet is creative or funny. Everyone who is generous is both not wise and calm. Everyone who is quiet is not strong. Susan is not old. Susan is not strong or not old. Lucy is tall. Someone is either not wise or kind. Someone is not old or tall. Paul is old or not rich. | Lucy is old. | contradiction | (![X]:((funny(X)|happy(X))=>(brave(X)|generous(X))))&
(![X]:(brave(X)<=>kind(X)))&
((?[X]:((happy(X)<~>~brave(X))))=>((wise(susan)|~creative(susan))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:((~curious(X)&~creative(X)))))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(~humble(X)=>(~funny(X)<~>~quiet(X))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~old(X)<~>~generous(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~curious(X)&happy(X))=>(funny(X)|~creative(X))))&
((?[X]:(brave(X)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~funny(X)))&
(![X]:((~calm(X)|~quiet(X))=>(creative(X)|funny(X))))&
(![X]:(generous(X)=>(~wise(X)&calm(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(~old(susan))&
((~strong(susan)|~old(susan)))&
(tall(lucy))&
(?[X]:((~wise(X)<~>kind(X))))&
(?[X]:((~old(X)|tall(X))))&
((old(paul)|~rich(paul))) | old(lucy) | [
"p2",
"p5",
"p7",
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4717413103566575763196046
% SZS output start Proof for 4717413103566575763196046
3. ? [X0] : (happy(X0) <~> ~brave(X0)) => (~creative(susan) | wise(susan)) [input p2]
6. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p5]
8. ? [X0] : (~generous(X0) | ~patient(X0)) <=> ? [X0] : (~generous(X0) <~> wise(X0)) [input p7]
9. ! [X0] : ((~happy(X0) <~> creative(X0)) => (~old(X0) <~> ~generous(X0))) [input p8]
10. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (patient(X0) <~> generous(X0))) [input p9]
12. ? [X0] : brave(X0) <=> ? [X0] : (patient(X0) <~> creative(X0)) [input p11]
13. ! [X0] : ((~wise(X0) <~> quiet(X0)) <=> ~funny(X0)) [input p12]
14. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (funny(X0) | creative(X0))) [input p13]
15. ! [X0] : (generous(X0) => (calm(X0) & ~wise(X0))) [input p14]
16. ! [X0] : (quiet(X0) => ~strong(X0)) [input p15]
23. old(lucy) [input hypothesis]
26. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | ~generous(X1)) [rectify 6]
27. ? [X0] : (~generous(X0) | ~patient(X0)) <=> ? [X1] : (~generous(X1) <~> wise(X1)) [rectify 8]
28. ? [X0] : brave(X0) <=> ? [X1] : (patient(X1) <~> creative(X1)) [rectify 12]
30. ! [X0] : (~quiet(X0) => (funny(X0) | creative(X0))) [pure predicate removal 14]
31. ! [X0] : (generous(X0) => ~wise(X0)) [pure predicate removal 15]
35. (~creative(susan) | wise(susan)) | ! [X0] : (happy(X0) <=> ~brave(X0)) [ennf transformation 3]
36. ~creative(susan) | wise(susan) | ! [X0] : (happy(X0) <=> ~brave(X0)) [flattening 35]
38. ! [X0] : ((~old(X0) <~> ~generous(X0)) | (~happy(X0) <=> creative(X0))) [ennf transformation 9]
41. ! [X0] : ((funny(X0) | creative(X0)) | quiet(X0)) [ennf transformation 30]
42. ! [X0] : (funny(X0) | creative(X0) | quiet(X0)) [flattening 41]
43. ! [X0] : (~wise(X0) | ~generous(X0)) [ennf transformation 31]
44. ! [X0] : (~strong(X0) | ~quiet(X0)) [ennf transformation 16]
46. ~creative(susan) | wise(susan) | ! [X0] : ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))) [nnf transformation 36]
55. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ! [X0] : (~quiet(X0) | ~strong(X0))) [nnf transformation 26]
56. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X2] : (~happy(X2) | ~generous(X2)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [rectify 55]
57. ? [X0] : (quiet(X0) & strong(X0)) => (quiet(sK3) & strong(sK3)) [choice axiom]
58. ? [X2] : (~happy(X2) | ~generous(X2)) => (~happy(sK4) | ~generous(sK4)) [choice axiom]
59. ((quiet(sK3) & strong(sK3)) | ! [X1] : (happy(X1) & generous(X1))) & ((~happy(sK4) | ~generous(sK4)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [skolemisation 56,58,57]
60. (? [X0] : (~generous(X0) | ~patient(X0)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (? [X1] : ((~wise(X1) | generous(X1)) & (wise(X1) | ~generous(X1))) | ! [X0] : (generous(X0) & patient(X0))) [nnf transformation 27]
61. (? [X0] : (~generous(X0) | ~patient(X0)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (? [X2] : ((~wise(X2) | generous(X2)) & (wise(X2) | ~generous(X2))) | ! [X3] : (generous(X3) & patient(X3))) [rectify 60]
62. ? [X0] : (~generous(X0) | ~patient(X0)) => (~generous(sK5) | ~patient(sK5)) [choice axiom]
63. ? [X2] : ((~wise(X2) | generous(X2)) & (wise(X2) | ~generous(X2))) => ((~wise(sK6) | generous(sK6)) & (wise(sK6) | ~generous(sK6))) [choice axiom]
64. ((~generous(sK5) | ~patient(sK5)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (((~wise(sK6) | generous(sK6)) & (wise(sK6) | ~generous(sK6))) | ! [X3] : (generous(X3) & patient(X3))) [skolemisation 61,63,62]
65. ! [X0] : (((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) [nnf transformation 38]
66. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 10]
67. (? [X0] : brave(X0) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1)))) & (? [X1] : ((~creative(X1) | ~patient(X1)) & (creative(X1) | patient(X1))) | ! [X0] : ~brave(X0)) [nnf transformation 28]
68. (? [X0] : brave(X0) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1)))) & (? [X2] : ((~creative(X2) | ~patient(X2)) & (creative(X2) | patient(X2))) | ! [X3] : ~brave(X3)) [rectify 67]
69. ? [X0] : brave(X0) => brave(sK7) [choice axiom]
70. ? [X2] : ((~creative(X2) | ~patient(X2)) & (creative(X2) | patient(X2))) => ((~creative(sK8) | ~patient(sK8)) & (creative(sK8) | patient(sK8))) [choice axiom]
71. (brave(sK7) | ! [X1] : ((patient(X1) | ~creative(X1)) & (creative(X1) | ~patient(X1)))) & (((~creative(sK8) | ~patient(sK8)) & (creative(sK8) | patient(sK8))) | ! [X3] : ~brave(X3)) [skolemisation 68,70,69]
72. ! [X0] : ((((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | funny(X0)) & (~funny(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0))))) [nnf transformation 13]
82. ~creative(susan) | wise(susan) | ~brave(X0) | ~happy(X0) [cnf transformation 46]
93. strong(sK3) | generous(X1) [cnf transformation 59]
95. quiet(sK3) | generous(X1) [cnf transformation 59]
96. quiet(sK3) | happy(X1) [cnf transformation 59]
97. wise(sK6) | ~generous(sK6) | patient(X3) [cnf transformation 64]
104. ~old(X0) | ~generous(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 65]
109. ~patient(X0) | ~generous(X0) | ~funny(X0) | strong(X0) [cnf transformation 66]
118. brave(sK7) | creative(X1) | ~patient(X1) [cnf transformation 71]
120. ~funny(X0) | quiet(X0) | wise(X0) [cnf transformation 72]
123. ~quiet(X0) | wise(X0) | funny(X0) [cnf transformation 72]
124. quiet(X0) | creative(X0) | funny(X0) [cnf transformation 42]
125. ~wise(X0) | ~generous(X0) [cnf transformation 43]
126. ~strong(X0) | ~quiet(X0) [cnf transformation 44]
133. old(lucy) [cnf transformation 23]
138. 2 <=> wise(susan) [avatar definition]
139. ~wise(susan) <- (~2) [avatar component clause 138]
140. wise(susan) <- (2) [avatar component clause 138]
142. 3 <=> creative(susan) [avatar definition]
144. ~creative(susan) <- (~3) [avatar component clause 142]
147. 4 <=> ! [X0] : (~brave(X0) | ~happy(X0)) [avatar definition]
148. ~brave(X0) | ~happy(X0) <- (4) [avatar component clause 147]
149. 4 | 2 | ~3 [avatar split clause 82,142,138,147]
195. 15 <=> ! [X1] : happy(X1) [avatar definition]
196. happy(X1) <- (15) [avatar component clause 195]
198. 16 <=> quiet(sK3) [avatar definition]
200. quiet(sK3) <- (16) [avatar component clause 198]
201. 15 | 16 [avatar split clause 96,198,195]
203. 17 <=> ! [X1] : generous(X1) [avatar definition]
204. generous(X1) <- (17) [avatar component clause 203]
205. 17 | 16 [avatar split clause 95,198,203]
207. 18 <=> strong(sK3) [avatar definition]
208. ~strong(sK3) <- (~18) [avatar component clause 207]
211. 17 | 18 [avatar split clause 93,207,203]
213. 19 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
214. ~quiet(X3) | ~strong(X3) <- (19) [avatar component clause 213]
225. 22 <=> ! [X1] : (~generous(X1) | ~wise(X1)) [avatar definition]
226. ~wise(X1) | ~generous(X1) <- (22) [avatar component clause 225]
241. 26 <=> generous(sK6) [avatar definition]
242. ~generous(sK6) <- (~26) [avatar component clause 241]
245. 27 <=> wise(sK6) [avatar definition]
246. wise(sK6) <- (27) [avatar component clause 245]
250. 28 <=> ! [X3] : patient(X3) [avatar definition]
251. patient(X3) <- (28) [avatar component clause 250]
254. 28 | ~26 | 27 [avatar split clause 97,245,241,250]
259. 30 <=> brave(sK7) [avatar definition]
261. brave(sK7) <- (30) [avatar component clause 259]
264. 31 <=> ! [X1] : (creative(X1) | ~patient(X1)) [avatar definition]
265. ~patient(X1) | creative(X1) <- (31) [avatar component clause 264]
266. 31 | 30 [avatar split clause 118,259,264]
268. 32 <=> ! [X3] : ~brave(X3) [avatar definition]
269. ~brave(X3) <- (32) [avatar component clause 268]
280. 22 [avatar split clause 125,225]
281. 19 [avatar split clause 126,213]
301. $false <- (30, 32) [subsumption resolution 261,269]
302. ~30 | ~32 [avatar contradiction clause 301]
313. ~strong(sK3) <- (16, 19) [resolution 214,200]
316. ~18 | ~16 | ~19 [avatar split clause 313,213,198,207]
317. $false <- (17, ~26) [resolution 204,242]
318. ~17 | 26 [avatar contradiction clause 317]
320. ~generous(sK6) <- (22, 27) [resolution 226,246]
321. $false <- (17, 22, 27) [subsumption resolution 320,204]
322. ~17 | ~22 | ~27 [avatar contradiction clause 321]
326. creative(X0) <- (28, 31) [resolution 265,251]
332. ~generous(susan) <- (2, 22) [resolution 140,226]
333. $false <- (2, 17, 22) [subsumption resolution 332,204]
334. ~2 | ~17 | ~22 [avatar contradiction clause 333]
359. 41 <=> funny(sK3) [avatar definition]
360. funny(sK3) <- (41) [avatar component clause 359]
363. 42 <=> wise(sK3) [avatar definition]
364. wise(sK3) <- (42) [avatar component clause 363]
367. wise(sK3) | funny(sK3) <- (16) [resolution 123,200]
370. creative(X0) | funny(X0) | wise(X0) | funny(X0) [resolution 124,123]
373. creative(X0) | funny(X0) | wise(X0) [duplicate literal removal 370]
375. ~generous(sK3) <- (22, 42) [resolution 364,226]
376. $false <- (17, 22, 42) [subsumption resolution 375,204]
377. ~17 | ~22 | ~42 [avatar contradiction clause 376]
378. 41 | 42 | ~16 [avatar split clause 367,198,363,359]
382. ~generous(lucy) | ~happy(lucy) | ~creative(lucy) [resolution 104,133]
383. ~happy(lucy) | ~creative(lucy) <- (17) [subsumption resolution 382,204]
384. ~creative(lucy) <- (15, 17) [subsumption resolution 383,196]
385. $false <- (15, 17, 28, 31) [subsumption resolution 384,326]
386. ~15 | ~17 | ~28 | ~31 [avatar contradiction clause 385]
387. ~brave(X0) <- (4, 15) [subsumption resolution 148,196]
388. 32 | ~4 | ~15 [avatar split clause 387,195,147,268]
402. funny(susan) | wise(susan) <- (~3) [resolution 373,144]
405. funny(susan) <- (~2, ~3) [subsumption resolution 402,139]
424. ~generous(X0) | ~funny(X0) | strong(X0) <- (28) [resolution 109,251]
425. ~funny(X0) | strong(X0) <- (17, 28) [subsumption resolution 424,204]
427. quiet(susan) | wise(susan) <- (~2, ~3) [resolution 405,120]
429. quiet(susan) <- (~2, ~3) [subsumption resolution 427,139]
506. strong(susan) <- (~2, ~3, 17, 28) [resolution 425,405]
509. strong(sK3) <- (17, 28, 41) [resolution 425,360]
510. $false <- (17, ~18, 28, 41) [subsumption resolution 509,208]
511. ~17 | 18 | ~28 | ~41 [avatar contradiction clause 510]
551. ~strong(susan) <- (~2, ~3, 19) [resolution 429,214]
552. $false <- (~2, ~3, 17, 19, 28) [subsumption resolution 551,506]
553. 2 | 3 | ~17 | ~19 | ~28 [avatar contradiction clause 552]
554. $false [avatar sat refutation 149,201,205,211,254,266,280,281,302,316,318,322,334,377,378,386,388,511,553]
% SZS output end Proof for 4717413103566575763196046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not happy or not old is calm.
Everyone who is either old or curious is both happy and calm.
Everyone who is both not creative and brave is kind.
If someone is generous or tall then someone is patient or not humble and vice versa.
If susan is not old or not quiet then someone is generous and vice versa.
Everyone who is both not generous and quiet is both not quiet and not tall.
Everyone who is both curious and not generous is quiet and vice versa.
Everyone who is either generous or patient is not rich or not brave.
Everyone who is happy or curious is both not tall and not calm.
If someone is both not patient and patient then someone is both not curious and not kind and vice versa.
Everyone who is either old or brave is not curious or happy and vice versa.
If fred is not kind or not quiet then someone is either rich or tall and vice versa.
Everyone who is both strong and not kind is generous or not patient.
Everyone who is not old or not generous is either not curious or strong and vice versa.
If susan is not patient then someone is not brave or generous.
Everyone who is quiet is either curious or not old.
Alice is not patient.
Someone is either rich or not wise.
Someone is both calm and not happy.
Someone is either not happy or not funny.
Someone is not strong or not kind.
Alice is calm.
Someone is either tall or quiet.
Mary is not funny or not humble. | Susan is patient. | neutral | (![X]:((~happy(X)<~>~old(X))=>calm(X)))&
(![X]:((old(X)<~>curious(X))=>(happy(X)&calm(X))))&
(![X]:((~creative(X)&brave(X))=>kind(X)))&
((?[X]:((generous(X)|tall(X))))<=>(?[X]:((patient(X)|~humble(X)))))&
(((~old(susan)|~quiet(susan)))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)&quiet(X))=>(~quiet(X)&~tall(X))))&
(![X]:((curious(X)&~generous(X))<=>quiet(X)))&
(![X]:((generous(X)<~>patient(X))=>(~rich(X)|~brave(X))))&
(![X]:((happy(X)|curious(X))=>(~tall(X)&~calm(X))))&
((?[X]:((~patient(X)&patient(X))))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((old(X)<~>brave(X))<=>(~curious(X)|happy(X))))&
(((~kind(fred)|~quiet(fred)))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:((strong(X)&~kind(X))=>(generous(X)|~patient(X))))&
(![X]:((~old(X)|~generous(X))<=>(~curious(X)<~>strong(X))))&
((~patient(susan))=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:(quiet(X)=>(curious(X)<~>~old(X))))&
(~patient(alice))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(calm(alice))&
(?[X]:((tall(X)<~>quiet(X))))&
((~funny(mary)|~humble(mary))) | patient(susan) | [] | null | 0 |
If paul is generous or creative then lucy is funny or old.
Everyone who is either kind or brave is calm.
Everyone who is either not calm or happy is both brave and humble.
If fred is either wise or strong then paul is not strong and vice versa.
Everyone who is not tall or not happy is both brave and kind.
Everyone who is either strong or funny is both not happy and curious.
If mary is not old then someone is not brave.
Everyone who is both generous and strong is both not old and not rich and vice versa.
If someone is either not curious or quiet then alice is kind or calm and vice versa.
If john is both not tall and not quiet then john is either creative or not kind and vice versa.
If someone is either not wise or not generous then fred is not rich.
If someone is patient then someone is either not brave or not kind.
If someone is either not rich or not wise then someone is not wise and vice versa.
Everyone who is not funny is both not quiet and quiet and vice versa.
Everyone who is both kind and happy is happy and vice versa.
If someone is not old or happy then alice is both patient and not old.
Lucy is not curious or strong.
Lucy is either curious or not old.
Someone is not calm or rich.
Fred is both not curious and rich.
Susan is not happy or not curious.
Susan is both not patient and not curious. | Alice is not old. | contradiction | (((generous(paul)|creative(paul)))=>((funny(lucy)|old(lucy))))&
(![X]:((kind(X)<~>brave(X))=>calm(X)))&
(![X]:((~calm(X)<~>happy(X))=>(brave(X)&humble(X))))&
(((wise(fred)<~>strong(fred)))<=>(~strong(paul)))&
(![X]:((~tall(X)|~happy(X))=>(brave(X)&kind(X))))&
(![X]:((strong(X)<~>funny(X))=>(~happy(X)&curious(X))))&
((~old(mary))=>(?[X]:(~brave(X))))&
(![X]:((generous(X)&strong(X))<=>(~old(X)&~rich(X))))&
((?[X]:((~curious(X)<~>quiet(X))))<=>((kind(alice)|calm(alice))))&
(((~tall(john)&~quiet(john)))<=>((creative(john)<~>~kind(john))))&
((?[X]:((~wise(X)<~>~generous(X))))=>(~rich(fred)))&
((?[X]:(patient(X)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:(~wise(X))))&
(![X]:(~funny(X)<=>(~quiet(X)&quiet(X))))&
(![X]:((kind(X)&happy(X))<=>happy(X)))&
((?[X]:((~old(X)|happy(X))))=>((patient(alice)&~old(alice))))&
((~curious(lucy)|strong(lucy)))&
((curious(lucy)<~>~old(lucy)))&
(?[X]:((~calm(X)|rich(X))))&
((~curious(fred)&rich(fred)))&
((~happy(susan)|~curious(susan)))&
((~patient(susan)&~curious(susan))) | ~old(alice) | [
"p1",
"p2",
"p4",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7368472433102400826366933
% SZS output start Proof for 7368472433102400826366933
2. ! [X0] : ((kind(X0) <~> brave(X0)) => calm(X0)) [input p1]
3. ! [X0] : ((~calm(X0) <~> happy(X0)) => (humble(X0) & brave(X0))) [input p2]
5. ! [X0] : ((~happy(X0) | ~tall(X0)) => (kind(X0) & brave(X0))) [input p4]
12. ? [X0] : patient(X0) => ? [X0] : (~brave(X0) <~> ~kind(X0)) [input p11]
15. ! [X0] : ((happy(X0) & kind(X0)) <=> happy(X0)) [input p14]
16. ? [X0] : (happy(X0) | ~old(X0)) => (~old(alice) & patient(alice)) [input p15]
23. ~old(alice) [input hypothesis]
24. ? [X0] : patient(X0) => ? [X1] : (~brave(X1) <~> ~kind(X1)) [rectify 12]
26. ! [X0] : ((~calm(X0) <~> happy(X0)) => brave(X0)) [pure predicate removal 3]
29. ! [X0] : (calm(X0) | (kind(X0) <=> brave(X0))) [ennf transformation 2]
30. ! [X0] : (brave(X0) | (~calm(X0) <=> happy(X0))) [ennf transformation 26]
31. ! [X0] : ((kind(X0) & brave(X0)) | (happy(X0) & tall(X0))) [ennf transformation 5]
35. ? [X1] : (~brave(X1) <~> ~kind(X1)) | ! [X0] : ~patient(X0) [ennf transformation 24]
36. (~old(alice) & patient(alice)) | ! [X0] : (~happy(X0) & old(X0)) [ennf transformation 16]
37. ! [X0] : (calm(X0) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 29]
38. ! [X0] : (brave(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0)))) [nnf transformation 30]
53. ? [X1] : ((kind(X1) | brave(X1)) & (~kind(X1) | ~brave(X1))) | ! [X0] : ~patient(X0) [nnf transformation 35]
54. ? [X0] : ((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | ! [X1] : ~patient(X1) [rectify 53]
55. ? [X0] : ((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) => ((kind(sK2) | brave(sK2)) & (~kind(sK2) | ~brave(sK2))) [choice axiom]
56. ((kind(sK2) | brave(sK2)) & (~kind(sK2) | ~brave(sK2))) | ! [X1] : ~patient(X1) [skolemisation 54,55]
64. ! [X0] : (((happy(X0) & kind(X0)) | ~happy(X0)) & (happy(X0) | (~happy(X0) | ~kind(X0)))) [nnf transformation 15]
65. ! [X0] : (((happy(X0) & kind(X0)) | ~happy(X0)) & (happy(X0) | ~happy(X0) | ~kind(X0))) [flattening 64]
71. ~kind(X0) | brave(X0) | calm(X0) [cnf transformation 37]
74. ~happy(X0) | ~calm(X0) | brave(X0) [cnf transformation 38]
80. happy(X0) | brave(X0) [cnf transformation 31]
82. happy(X0) | kind(X0) [cnf transformation 31]
106. ~kind(sK2) | ~brave(sK2) | ~patient(X1) [cnf transformation 56]
116. kind(X0) | ~happy(X0) [cnf transformation 65]
118. patient(alice) | old(X0) [cnf transformation 36]
131. ~old(alice) [cnf transformation 23]
239. 23 <=> ! [X1] : ~patient(X1) [avatar definition]
240. ~patient(X1) <- (23) [avatar component clause 239]
242. 24 <=> brave(sK2) [avatar definition]
243. ~brave(sK2) <- (~24) [avatar component clause 242]
246. 25 <=> kind(sK2) [avatar definition]
247. ~kind(sK2) <- (~25) [avatar component clause 246]
250. 23 | ~24 | ~25 [avatar split clause 106,246,242,239]
277. kind(X0) [subsumption resolution 116,82]
282. 33 <=> old(alice) [avatar definition]
284. ~old(alice) <- (~33) [avatar component clause 282]
287. 34 <=> ! [X0] : old(X0) [avatar definition]
288. old(X0) <- (34) [avatar component clause 287]
291. 35 <=> patient(alice) [avatar definition]
293. patient(alice) <- (35) [avatar component clause 291]
295. 34 | 35 [avatar split clause 118,291,287]
327. ~33 [avatar split clause 131,282]
328. $false <- (~33, 34) [subsumption resolution 284,288]
329. 33 | ~34 [avatar contradiction clause 328]
339. $false <- (23, 35) [subsumption resolution 293,240]
340. ~23 | ~35 [avatar contradiction clause 339]
341. $false <- (~25) [subsumption resolution 247,277]
342. 25 [avatar contradiction clause 341]
352. calm(X0) | brave(X0) [resolution 71,277]
358. ~calm(X2) | brave(X2) | brave(X2) [resolution 74,80]
359. ~calm(X2) | brave(X2) [duplicate literal removal 358]
361. brave(X2) [subsumption resolution 359,352]
364. $false <- (~24) [resolution 361,243]
366. 24 [avatar contradiction clause 364]
368. $false [avatar sat refutation 250,295,327,329,340,342,366]
% SZS output end Proof for 7368472433102400826366933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous is not kind or not old and vice versa.
If someone is not creative then fred is not curious.
If paul is rich or not creative then someone is either not tall or not creative.
If alice is not strong or not humble then alice is rich or not curious.
If someone is wise or generous then john is either not humble or rich and vice versa.
Everyone who is creative or not wise is rich and vice versa.
Everyone who is curious or not happy is not tall or not happy and vice versa.
Everyone who is either not curious or brave is both funny and tall and vice versa.
Everyone who is not curious is not kind or humble and vice versa.
Everyone who is old is humble or rich.
Everyone who is creative is either humble or not wise and vice versa.
Everyone who is either not tall or not generous is not happy or strong and vice versa.
If someone is both not strong and not humble then susan is either not generous or not quiet.
If john is both tall and not generous then someone is either brave or not wise and vice versa.
Everyone who is both not rich and not humble is both brave and not old and vice versa.
Everyone who is wise or not generous is either not curious or rich.
Someone is either calm or tall.
Fred is not tall.
Someone is old or not brave.
John is both not old and not calm.
Someone is not tall or generous. | Susan is creative. | entailment | (![X]:((kind(X)|~generous(X))<=>(~kind(X)|~old(X))))&
((?[X]:(~creative(X)))=>(~curious(fred)))&
(((rich(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(((~strong(alice)|~humble(alice)))=>((rich(alice)|~curious(alice))))&
((?[X]:((wise(X)|generous(X))))<=>((~humble(john)<~>rich(john))))&
(![X]:((creative(X)|~wise(X))<=>rich(X)))&
(![X]:((curious(X)|~happy(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(funny(X)&tall(X))))&
(![X]:(~curious(X)<=>(~kind(X)|humble(X))))&
(![X]:(old(X)=>(humble(X)|rich(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~strong(X)&~humble(X))))=>((~generous(susan)<~>~quiet(susan))))&
(((tall(john)&~generous(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)&~old(X))))&
(![X]:((wise(X)|~generous(X))=>(~curious(X)<~>rich(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(~tall(fred))&
(?[X]:((old(X)|~brave(X))))&
((~old(john)&~calm(john)))&
(?[X]:((~tall(X)|generous(X)))) | creative(susan) | [
"p0",
"p1",
"p6",
"p7",
"p8",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 171132441001428827950110
% SZS output start Proof for 171132441001428827950110
1. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~old(X0) | ~kind(X0))) [input p0]
2. ? [X0] : ~creative(X0) => ~curious(fred) [input p1]
7. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~happy(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~curious(X0) <~> brave(X0)) <=> (tall(X0) & funny(X0))) [input p7]
9. ! [X0] : (~curious(X0) <=> (humble(X0) | ~kind(X0))) [input p8]
12. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
15. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (~old(X0) & brave(X0))) [input p14]
18. ~tall(fred) [input p17]
22. ~creative(susan) [input hypothesis]
23. ~curious(fred) | ! [X0] : creative(X0) [ennf transformation 2]
31. ! [X0] : (((~generous(X0) | kind(X0)) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~generous(X0) | kind(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | (generous(X0) & ~kind(X0)))) [flattening 31]
42. ! [X0] : (((~happy(X0) | curious(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : ((~happy(X0) | curious(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | (happy(X0) & ~curious(X0)))) [flattening 42]
44. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (~tall(X0) | ~funny(X0))) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | ~tall(X0) | ~funny(X0)) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [flattening 44]
46. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | curious(X0))) [flattening 46]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 12]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
57. ! [X0] : (((~humble(X0) & ~rich(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 15]
58. ! [X0] : (((~humble(X0) & ~rich(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | humble(X0) | rich(X0))) [flattening 57]
67. ~old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 32]
69. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 32]
71. ~curious(fred) | creative(X0) [cnf transformation 23]
89. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 43]
93. brave(X0) | tall(X0) | curious(X0) [cnf transformation 45]
97. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 47]
99. ~humble(X0) | ~curious(X0) [cnf transformation 47]
109. happy(X0) | tall(X0) | generous(X0) [cnf transformation 50]
122. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 58]
129. ~tall(fred) [cnf transformation 18]
134. ~creative(susan) [cnf transformation 22]
135. ~old(X0) | ~kind(X0) [duplicate literal removal 67]
136. ~generous(X0) | kind(X0) [duplicate literal removal 69]
138. 1 <=> ! [X0] : creative(X0) [avatar definition]
139. creative(X0) <- (1) [avatar component clause 138]
141. 2 <=> curious(fred) [avatar definition]
143. ~curious(fred) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 71,141,138]
375. tall(X0) | generous(X0) | curious(X0) | tall(X0) [resolution 109,89]
377. tall(X0) | generous(X0) | curious(X0) [duplicate literal removal 375]
454. old(X1) | ~humble(X1) | tall(X1) | curious(X1) [resolution 122,93]
478. ~humble(X1) | old(X1) | tall(X1) [subsumption resolution 454,99]
551. generous(fred) | curious(fred) [resolution 377,129]
555. generous(fred) <- (~2) [subsumption resolution 551,143]
618. kind(fred) <- (~2) [resolution 555,136]
620. 62 <=> old(fred) [avatar definition]
622. old(fred) <- (62) [avatar component clause 620]
624. 63 <=> kind(fred) [avatar definition]
626. kind(fred) <- (63) [avatar component clause 624]
628. 63 | 2 [avatar split clause 618,141,624]
667. humble(fred) | curious(fred) <- (63) [resolution 626,97]
668. humble(fred) <- (~2, 63) [subsumption resolution 667,143]
713. old(fred) | tall(fred) <- (~2, 63) [resolution 668,478]
717. old(fred) <- (~2, 63) [subsumption resolution 713,129]
718. 62 | 2 | ~63 [avatar split clause 717,624,141,620]
730. ~kind(fred) <- (62) [resolution 622,135]
740. ~63 | ~62 [avatar split clause 730,620,624]
744. $false <- (1) [resolution 139,134]
749. ~1 [avatar contradiction clause 744]
751. $false [avatar sat refutation 144,628,718,740,749]
% SZS output end Proof for 171132441001428827950110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or funny is not funny.
Everyone who is kind or curious is not happy.
If someone is tall then mary is not brave.
Everyone who is both rich and kind is both strong and creative and vice versa.
If susan is both not creative and not humble then susan is either not brave or not humble.
Everyone who is old or not quiet is both happy and not brave.
Everyone who is funny is both creative and not tall and vice versa.
If someone is either happy or not curious then someone is kind or quiet.
If fred is both not strong and kind then lucy is both not happy and not generous and vice versa.
Everyone who is not humble or curious is both generous and not tall.
Everyone who is either not patient or calm is not creative or not patient and vice versa.
If someone is curious or not strong then someone is not rich or not humble and vice versa.
Everyone who is not generous or not old is not curious or not happy and vice versa.
Everyone who is calm or curious is either not generous or not curious.
Everyone who is both rich and calm is not curious.
If someone is both not generous and not kind then someone is not creative.
Someone is not humble.
Someone is both not funny and happy.
Paul is both not tall and happy.
Someone is not funny or quiet.
Someone is either brave or not rich.
Someone is not strong.
Someone is not kind.
Someone is rich. | Lucy is happy. | neutral | (![X]:((humble(X)|funny(X))=>~funny(X)))&
(![X]:((kind(X)|curious(X))=>~happy(X)))&
((?[X]:(tall(X)))=>(~brave(mary)))&
(![X]:((rich(X)&kind(X))<=>(strong(X)&creative(X))))&
(((~creative(susan)&~humble(susan)))=>((~brave(susan)<~>~humble(susan))))&
(![X]:((old(X)|~quiet(X))=>(happy(X)&~brave(X))))&
(![X]:(funny(X)<=>(creative(X)&~tall(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((kind(X)|quiet(X)))))&
(((~strong(fred)&kind(fred)))<=>((~happy(lucy)&~generous(lucy))))&
(![X]:((~humble(X)|curious(X))=>(generous(X)&~tall(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((curious(X)|~strong(X))))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((~generous(X)|~old(X))<=>(~curious(X)|~happy(X))))&
(![X]:((calm(X)|curious(X))=>(~generous(X)<~>~curious(X))))&
(![X]:((rich(X)&calm(X))=>~curious(X)))&
((?[X]:((~generous(X)&~kind(X))))=>(?[X]:(~creative(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)&happy(X))))&
((~tall(paul)&happy(paul)))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~kind(X)))&
(?[X]:(rich(X))) | happy(lucy) | [] | null | 0 |
Everyone who is both not humble and kind is not old. If john is both not rich and not funny then someone is both not wise and not generous and vice versa. If someone is either not rich or rich then someone is both not wise and not creative. If someone is both creative and calm then john is either tall or wise. If someone is both not brave and creative then mary is either not strong or rich. Everyone who is both not tall and quiet is not humble or not wise and vice versa. If someone is not brave then mary is either tall or strong. If someone is both not creative and not curious then someone is rich or not generous. Everyone who is both brave and not calm is either not generous or happy and vice versa. Everyone who is both not creative and happy is creative and vice versa. If lucy is not generous then someone is both not humble and patient. If lucy is either strong or not strong then someone is quiet and vice versa. Everyone who is curious is either calm or not patient and vice versa. Everyone who is both generous and not funny is not quiet or kind and vice versa. Everyone who is both strong and brave is not strong. Someone is both not old and strong. John is calm. John is both not brave and not curious. Alice is either funny or brave. Lucy is both not creative and not strong. Fred is old. Someone is both not kind and strong. John is old. | Mary is not happy. | entailment | (![X]:((~humble(X)&kind(X))=>~old(X)))&
(((~rich(john)&~funny(john)))<=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~rich(X)<~>rich(X))))=>(?[X]:((~wise(X)&~creative(X)))))&
((?[X]:((creative(X)&calm(X))))=>((tall(john)<~>wise(john))))&
((?[X]:((~brave(X)&creative(X))))=>((~strong(mary)<~>rich(mary))))&
(![X]:((~tall(X)&quiet(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(~brave(X)))=>((tall(mary)<~>strong(mary))))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((brave(X)&~calm(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~creative(X)&happy(X))<=>creative(X)))&
((~generous(lucy))=>(?[X]:((~humble(X)&patient(X)))))&
(((strong(lucy)<~>~strong(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(curious(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((generous(X)&~funny(X))<=>(~quiet(X)|kind(X))))&
(![X]:((strong(X)&brave(X))=>~strong(X)))&
(?[X]:((~old(X)&strong(X))))&
(calm(john))&
((~brave(john)&~curious(john)))&
((funny(alice)<~>brave(alice)))&
((~creative(lucy)&~strong(lucy)))&
(old(fred))&
(?[X]:((~kind(X)&strong(X))))&
(old(john)) | ~happy(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9144822837447231876975942
% SZS output start Proof for 9144822837447231876975942
10. ! [X0] : ((happy(X0) & ~creative(X0)) <=> creative(X0)) [input p9]
24. happy(mary) [input hypothesis]
56. ! [X0] : (((happy(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) | creative(X0)))) [nnf transformation 10]
57. ! [X0] : (((happy(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | ~happy(X0) | creative(X0))) [flattening 56]
99. creative(X0) | ~happy(X0) | creative(X0) [cnf transformation 57]
100. ~creative(X0) | ~creative(X0) [cnf transformation 57]
131. happy(mary) [cnf transformation 24]
135. creative(X0) | ~happy(X0) [duplicate literal removal 99]
136. ~creative(X0) [duplicate literal removal 100]
229. ~happy(X0) [subsumption resolution 135,136]
265. $false [subsumption resolution 131,229]
% SZS output end Proof for 9144822837447231876975942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or quiet is both not quiet and not patient.
If someone is both brave and generous then someone is either not rich or not curious and vice versa.
If someone is not old or not quiet then someone is both not brave and not generous.
Everyone who is both not quiet and not brave is either brave or kind and vice versa.
If someone is either not tall or tall then someone is both not kind and not patient.
If someone is either calm or not funny then paul is not curious.
Everyone who is humble or not humble is both not kind and not happy and vice versa.
If someone is either humble or not strong then someone is not wise and vice versa.
If fred is rich then someone is both not brave and not quiet and vice versa.
Everyone who is kind is not generous.
Everyone who is either not generous or patient is both not curious and strong and vice versa.
Everyone who is both old and not humble is both not generous and creative.
Everyone who is either curious or patient is either not old or not calm and vice versa.
Everyone who is strong is not funny or happy and vice versa.
Someone is old or humble.
John is either curious or not patient.
Someone is either not tall or not quiet.
Someone is either not patient or not strong.
Fred is not strong or not old.
Someone is not old or humble.
Susan is not old or strong. | Fred is curious. | contradiction | (![X]:((~generous(X)<~>quiet(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((brave(X)&generous(X))))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:((~old(X)|~quiet(X))))=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~quiet(X)&~brave(X))<=>(brave(X)<~>kind(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>(?[X]:((~kind(X)&~patient(X)))))&
((?[X]:((calm(X)<~>~funny(X))))=>(~curious(paul)))&
(![X]:((humble(X)|~humble(X))<=>(~kind(X)&~happy(X))))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(~wise(X))))&
((rich(fred))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(![X]:(kind(X)=>~generous(X)))&
(![X]:((~generous(X)<~>patient(X))<=>(~curious(X)&strong(X))))&
(![X]:((old(X)&~humble(X))=>(~generous(X)&creative(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~old(X)<~>~calm(X))))&
(![X]:(strong(X)<=>(~funny(X)|happy(X))))&
(?[X]:((old(X)|humble(X))))&
((curious(john)<~>~patient(john)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
((~strong(fred)|~old(fred)))&
(?[X]:((~old(X)|humble(X))))&
((~old(susan)|strong(susan))) | curious(fred) | [
"p1",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8467780447459931703731587
% SZS output start Proof for 8467780447459931703731587
2. ? [X0] : (generous(X0) & brave(X0)) <=> ? [X0] : (~rich(X0) <~> ~curious(X0)) [input p1]
4. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (brave(X0) <~> kind(X0))) [input p3]
7. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~happy(X0) & ~kind(X0))) [input p6]
9. rich(fred) <=> ? [X0] : (~quiet(X0) & ~brave(X0)) [input p8]
22. curious(fred) [input hypothesis]
23. ? [X0] : (generous(X0) & brave(X0)) <=> ? [X1] : (~rich(X1) <~> ~curious(X1)) [rectify 2]
36. (? [X0] : (generous(X0) & brave(X0)) | ! [X1] : ((~rich(X1) | curious(X1)) & (~curious(X1) | rich(X1)))) & (? [X1] : ((curious(X1) | rich(X1)) & (~curious(X1) | ~rich(X1))) | ! [X0] : (~generous(X0) | ~brave(X0))) [nnf transformation 23]
37. (? [X0] : (generous(X0) & brave(X0)) | ! [X1] : ((~rich(X1) | curious(X1)) & (~curious(X1) | rich(X1)))) & (? [X2] : ((curious(X2) | rich(X2)) & (~curious(X2) | ~rich(X2))) | ! [X3] : (~generous(X3) | ~brave(X3))) [rectify 36]
38. ? [X0] : (generous(X0) & brave(X0)) => (generous(sK0) & brave(sK0)) [choice axiom]
39. ? [X2] : ((curious(X2) | rich(X2)) & (~curious(X2) | ~rich(X2))) => ((curious(sK1) | rich(sK1)) & (~curious(sK1) | ~rich(sK1))) [choice axiom]
40. ((generous(sK0) & brave(sK0)) | ! [X1] : ((~rich(X1) | curious(X1)) & (~curious(X1) | rich(X1)))) & (((curious(sK1) | rich(sK1)) & (~curious(sK1) | ~rich(sK1))) | ! [X3] : (~generous(X3) | ~brave(X3))) [skolemisation 37,39,38]
44. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (brave(X0) | quiet(X0)))) [nnf transformation 4]
45. ! [X0] : (((~brave(X0) & ~quiet(X0)) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) & (((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | brave(X0) | quiet(X0))) [flattening 44]
51. ! [X0] : (((~humble(X0) | humble(X0)) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 7]
52. ! [X0] : ((~humble(X0) | humble(X0) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | (humble(X0) & ~humble(X0)))) [flattening 51]
58. (rich(fred) | ! [X0] : (quiet(X0) | brave(X0))) & (? [X0] : (~quiet(X0) & ~brave(X0)) | ~rich(fred)) [nnf transformation 9]
59. (rich(fred) | ! [X0] : (quiet(X0) | brave(X0))) & (? [X1] : (~quiet(X1) & ~brave(X1)) | ~rich(fred)) [rectify 58]
60. ? [X1] : (~quiet(X1) & ~brave(X1)) => (~quiet(sK6) & ~brave(sK6)) [choice axiom]
61. (rich(fred) | ! [X0] : (quiet(X0) | brave(X0))) & ((~quiet(sK6) & ~brave(sK6)) | ~rich(fred)) [skolemisation 59,60]
84. brave(sK0) | ~curious(X1) | rich(X1) [cnf transformation 40]
92. kind(X0) | brave(X0) | brave(X0) | quiet(X0) [cnf transformation 45]
96. ~brave(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
104. ~kind(X0) | ~humble(X0) [cnf transformation 52]
105. ~kind(X0) | humble(X0) [cnf transformation 52]
114. ~quiet(sK6) | ~rich(fred) [cnf transformation 61]
145. curious(fred) [cnf transformation 22]
150. kind(X0) | brave(X0) | quiet(X0) [duplicate literal removal 92]
151. ~brave(X0) | kind(X0) [duplicate literal removal 96]
162. 3 <=> ! [X1] : (~curious(X1) | rich(X1)) [avatar definition]
163. ~curious(X1) | rich(X1) <- (3) [avatar component clause 162]
166. 4 <=> brave(sK0) [avatar definition]
168. brave(sK0) <- (4) [avatar component clause 166]
170. 3 | 4 [avatar split clause 84,166,162]
185. 8 <=> ! [X1] : quiet(X1) [avatar definition]
186. quiet(X1) <- (8) [avatar component clause 185]
202. kind(X0) | quiet(X0) [subsumption resolution 150,151]
234. ~kind(X0) [subsumption resolution 104,105]
264. 26 <=> rich(fred) [avatar definition]
269. 27 <=> quiet(sK6) [avatar definition]
271. ~quiet(sK6) <- (~27) [avatar component clause 269]
272. ~26 | ~27 [avatar split clause 114,269,264]
348. kind(sK0) <- (4) [resolution 151,168]
349. $false <- (4) [subsumption resolution 348,234]
350. ~4 [avatar contradiction clause 349]
351. rich(fred) <- (3) [resolution 163,145]
354. 26 | ~3 [avatar split clause 351,162,264]
357. quiet(X1) [resolution 202,234]
358. 8 [avatar split clause 357,185]
361. $false <- (8, ~27) [resolution 186,271]
362. ~8 | 27 [avatar contradiction clause 361]
364. $false [avatar sat refutation 170,272,350,354,358,362]
% SZS output end Proof for 8467780447459931703731587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is tall then alice is both not rich and not calm and vice versa. Everyone who is either not curious or not happy is not creative. Everyone who is both patient and not happy is either quiet or not rich. Everyone who is both not humble and tall is calm or not curious and vice versa. If someone is humble then someone is strong. Everyone who is creative or not tall is either not brave or not strong and vice versa. If someone is either quiet or not wise then lucy is both not brave and not old and vice versa. Everyone who is creative or not wise is either not wise or wise. Everyone who is either not tall or not patient is not wise or not brave. Everyone who is not kind is both strong and generous and vice versa. Everyone who is not generous is generous or calm. If mary is both not kind and not calm then alice is tall. If someone is old then someone is either funny or not calm. Everyone who is wise or not quiet is both kind and rich. If someone is both not funny and patient then susan is tall. Alice is either happy or not creative. Someone is old. Susan is brave. Someone is funny. | Lucy is brave. | neutral | ((tall(lucy))<=>((~rich(alice)&~calm(alice))))&
(![X]:((~curious(X)<~>~happy(X))=>~creative(X)))&
(![X]:((patient(X)&~happy(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~humble(X)&tall(X))<=>(calm(X)|~curious(X))))&
((?[X]:(humble(X)))=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~tall(X))<=>(~brave(X)<~>~strong(X))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>((~brave(lucy)&~old(lucy))))&
(![X]:((creative(X)|~wise(X))=>(~wise(X)<~>wise(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~wise(X)|~brave(X))))&
(![X]:(~kind(X)<=>(strong(X)&generous(X))))&
(![X]:(~generous(X)=>(generous(X)|calm(X))))&
(((~kind(mary)&~calm(mary)))=>(tall(alice)))&
((?[X]:(old(X)))=>(?[X]:((funny(X)<~>~calm(X)))))&
(![X]:((wise(X)|~quiet(X))=>(kind(X)&rich(X))))&
((?[X]:((~funny(X)&patient(X))))=>(tall(susan)))&
((happy(alice)<~>~creative(alice)))&
(?[X]:(old(X)))&
(brave(susan))&
(?[X]:(funny(X))) | brave(lucy) | [] | null | 0 |
Everyone who is both not generous and happy is either happy or calm and vice versa. Everyone who is generous is both happy and old. Everyone who is either wise or not rich is quiet or not brave. Everyone who is not curious is old or tall and vice versa. Everyone who is not kind is creative and vice versa. If someone is either creative or not creative then susan is both not humble and happy and vice versa. If someone is either happy or not calm then someone is not curious or not calm. Everyone who is both old and happy is both kind and happy and vice versa. Everyone who is either not old or not patient is both creative and not brave and vice versa. If someone is curious then someone is both not patient and not kind. Everyone who is patient is not funny or not brave. Everyone who is either brave or not happy is not rich. Everyone who is both not humble and not happy is generous. If susan is either patient or not quiet then fred is old or not wise. Everyone who is humble is either strong or not old and vice versa. Everyone who is either not tall or creative is either strong or not kind. Mary is old or not old. Mary is calm. Someone is funny or not calm. Alice is brave or not kind. Someone is not patient. Someone is not patient or rich. Fred is either wise or not tall. Mary is either not happy or not strong. | Mary is humble. | contradiction | (![X]:((~generous(X)&happy(X))<=>(happy(X)<~>calm(X))))&
(![X]:(generous(X)=>(happy(X)&old(X))))&
(![X]:((wise(X)<~>~rich(X))=>(quiet(X)|~brave(X))))&
(![X]:(~curious(X)<=>(old(X)|tall(X))))&
(![X]:(~kind(X)<=>creative(X)))&
((?[X]:((creative(X)<~>~creative(X))))<=>((~humble(susan)&happy(susan))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((old(X)&happy(X))<=>(kind(X)&happy(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(creative(X)&~brave(X))))&
((?[X]:(curious(X)))=>(?[X]:((~patient(X)&~kind(X)))))&
(![X]:(patient(X)=>(~funny(X)|~brave(X))))&
(![X]:((brave(X)<~>~happy(X))=>~rich(X)))&
(![X]:((~humble(X)&~happy(X))=>generous(X)))&
(((patient(susan)<~>~quiet(susan)))=>((old(fred)|~wise(fred))))&
(![X]:(humble(X)<=>(strong(X)<~>~old(X))))&
(![X]:((~tall(X)<~>creative(X))=>(strong(X)<~>~kind(X))))&
((old(mary)|~old(mary)))&
(calm(mary))&
(?[X]:((funny(X)|~calm(X))))&
((brave(alice)|~kind(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)|rich(X))))&
((wise(fred)<~>~tall(fred)))&
((~happy(mary)<~>~strong(mary))) | humble(mary) | [
"p0",
"p1",
"p14",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3229725053877015169547337
% SZS output start Proof for 3229725053877015169547337
1. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (happy(X0) <~> calm(X0))) [input p0]
2. ! [X0] : (generous(X0) => (old(X0) & happy(X0))) [input p1]
15. ! [X0] : (humble(X0) <=> (strong(X0) <~> ~old(X0))) [input p14]
18. calm(mary) [input p17]
24. ~happy(mary) <~> ~strong(mary) [input p23]
25. humble(mary) [input hypothesis]
29. ! [X0] : ((old(X0) & happy(X0)) | ~generous(X0)) [ennf transformation 2]
44. ! [X0] : (((happy(X0) & ~generous(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (~happy(X0) | generous(X0)))) [nnf transformation 1]
45. ! [X0] : (((happy(X0) & ~generous(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ~happy(X0) | generous(X0))) [flattening 44]
66. ! [X0] : ((humble(X0) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) & (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | ~humble(X0))) [nnf transformation 15]
75. (strong(mary) | happy(mary)) & (~strong(mary) | ~happy(mary)) [nnf transformation 24]
77. ~calm(X0) | ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 45]
81. happy(X0) | happy(X0) | ~calm(X0) [cnf transformation 45]
83. ~generous(X0) | old(X0) [cnf transformation 29]
115. ~humble(X0) | strong(X0) | ~old(X0) [cnf transformation 66]
124. calm(mary) [cnf transformation 18]
131. ~strong(mary) | ~happy(mary) [cnf transformation 75]
133. humble(mary) [cnf transformation 25]
138. ~calm(X0) | ~happy(X0) | generous(X0) [duplicate literal removal 77]
139. ~calm(X0) | happy(X0) [duplicate literal removal 81]
140. ~calm(X0) | generous(X0) [subsumption resolution 138,139]
245. 23 <=> happy(mary) [avatar definition]
249. 24 <=> strong(mary) [avatar definition]
253. ~23 | ~24 [avatar split clause 131,249,245]
255. happy(mary) [resolution 139,124]
256. generous(mary) [resolution 140,124]
258. old(mary) [resolution 256,83]
312. strong(mary) | ~old(mary) [resolution 115,133]
323. 23 [avatar split clause 255,245]
324. strong(mary) [subsumption resolution 312,258]
325. 24 [avatar split clause 324,249]
326. $false [avatar sat refutation 253,323,325]
% SZS output end Proof for 3229725053877015169547337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not curious is kind and vice versa.
If someone is not calm then alice is humble and vice versa.
If mary is not generous then someone is kind or calm.
Everyone who is either rich or tall is both happy and not funny and vice versa.
If john is both not happy and creative then mary is old.
If alice is not curious or not patient then someone is either old or not wise.
If someone is either patient or not brave then susan is humble or not humble.
Everyone who is humble is generous and vice versa.
Everyone who is both not generous and strong is not creative and vice versa.
Everyone who is quiet or generous is either not funny or not calm.
If someone is not curious then someone is both wise and not patient and vice versa.
Everyone who is both creative and old is both generous and not humble.
If mary is not calm or not creative then someone is not quiet.
Everyone who is both calm and strong is either not humble or generous and vice versa.
If someone is both creative and not creative then alice is not curious or not tall and vice versa.
Everyone who is both creative and calm is calm or generous.
Susan is not humble.
Fred is humble or not brave.
Someone is rich.
Mary is either happy or generous.
Someone is both patient and not quiet.
Someone is either old or not curious.
Someone is either not calm or not curious. | Alice is not curious. | contradiction | (![X]:((kind(X)&~curious(X))<=>kind(X)))&
((?[X]:(~calm(X)))<=>(humble(alice)))&
((~generous(mary))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((rich(X)<~>tall(X))<=>(happy(X)&~funny(X))))&
(((~happy(john)&creative(john)))=>(old(mary)))&
(((~curious(alice)|~patient(alice)))=>(?[X]:((old(X)<~>~wise(X)))))&
((?[X]:((patient(X)<~>~brave(X))))=>((humble(susan)|~humble(susan))))&
(![X]:(humble(X)<=>generous(X)))&
(![X]:((~generous(X)&strong(X))<=>~creative(X)))&
(![X]:((quiet(X)|generous(X))=>(~funny(X)<~>~calm(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((creative(X)&old(X))=>(generous(X)&~humble(X))))&
(((~calm(mary)|~creative(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((calm(X)&strong(X))<=>(~humble(X)<~>generous(X))))&
((?[X]:((creative(X)&~creative(X))))<=>((~curious(alice)|~tall(alice))))&
(![X]:((creative(X)&calm(X))=>(calm(X)|generous(X))))&
(~humble(susan))&
((humble(fred)|~brave(fred)))&
(?[X]:(rich(X)))&
((happy(mary)<~>generous(mary)))&
(?[X]:((patient(X)&~quiet(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>~curious(X)))) | ~curious(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5681056757153777746289047
% SZS output start Proof for 5681056757153777746289047
15. ? [X0] : (~creative(X0) & creative(X0)) <=> (~tall(alice) | ~curious(alice)) [input p14]
24. ~curious(alice) [input hypothesis]
65. (? [X0] : (~creative(X0) & creative(X0)) | (tall(alice) & curious(alice))) & ((~tall(alice) | ~curious(alice)) | ! [X0] : (creative(X0) | ~creative(X0))) [nnf transformation 15]
66. (? [X0] : (~creative(X0) & creative(X0)) | (tall(alice) & curious(alice))) & (~tall(alice) | ~curious(alice) | ! [X0] : (creative(X0) | ~creative(X0))) [flattening 65]
67. (? [X0] : (~creative(X0) & creative(X0)) | (tall(alice) & curious(alice))) & (~tall(alice) | ~curious(alice) | ! [X1] : (creative(X1) | ~creative(X1))) [rectify 66]
68. ? [X0] : (~creative(X0) & creative(X0)) => (~creative(sK5) & creative(sK5)) [choice axiom]
69. ((~creative(sK5) & creative(sK5)) | (tall(alice) & curious(alice))) & (~tall(alice) | ~curious(alice) | ! [X1] : (creative(X1) | ~creative(X1))) [skolemisation 67,68]
119. creative(sK5) | curious(alice) [cnf transformation 69]
121. ~creative(sK5) | curious(alice) [cnf transformation 69]
134. ~curious(alice) [cnf transformation 24]
188. 13 <=> curious(alice) [avatar definition]
224. 20 <=> creative(sK5) [avatar definition]
228. 13 | ~20 [avatar split clause 121,224,188]
230. 13 | 20 [avatar split clause 119,224,188]
266. ~13 [avatar split clause 134,188]
267. $false [avatar sat refutation 228,230,266]
% SZS output end Proof for 5681056757153777746289047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not funny is not patient or humble. If someone is either not calm or happy then someone is either wise or tall. Everyone who is either not happy or kind is both humble and patient and vice versa. Everyone who is both not rich and funny is both not happy and kind. Everyone who is not wise or not brave is both not quiet and not old and vice versa. If susan is either rich or quiet then fred is both not kind and not brave. Everyone who is patient is not happy or not kind. Everyone who is both not curious and creative is not humble or not strong and vice versa. Everyone who is calm or not quiet is not quiet and vice versa. Everyone who is both not kind and not strong is both not humble and not curious and vice versa. Everyone who is not calm or not old is both tall and humble and vice versa. Everyone who is both not generous and not brave is either not funny or not wise. Everyone who is both not happy and not creative is not calm. If mary is not kind then someone is either not calm or not old. Everyone who is either not brave or not funny is either patient or not funny and vice versa. If someone is both creative and calm then someone is brave or not tall and vice versa. Susan is not generous. Susan is not calm. Someone is either not calm or funny. Someone is happy. Someone is both happy and not generous. Susan is either not generous or not happy. Susan is strong. Someone is not quiet. | Susan is not happy. | contradiction | (![X]:((~generous(X)|~funny(X))=>(~patient(X)|humble(X))))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((~happy(X)<~>kind(X))<=>(humble(X)&patient(X))))&
(![X]:((~rich(X)&funny(X))=>(~happy(X)&kind(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~quiet(X)&~old(X))))&
(((rich(susan)<~>quiet(susan)))=>((~kind(fred)&~brave(fred))))&
(![X]:(patient(X)=>(~happy(X)|~kind(X))))&
(![X]:((~curious(X)&creative(X))<=>(~humble(X)|~strong(X))))&
(![X]:((calm(X)|~quiet(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~strong(X))<=>(~humble(X)&~curious(X))))&
(![X]:((~calm(X)|~old(X))<=>(tall(X)&humble(X))))&
(![X]:((~generous(X)&~brave(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~happy(X)&~creative(X))=>~calm(X)))&
((~kind(mary))=>(?[X]:((~calm(X)<~>~old(X)))))&
(![X]:((~brave(X)<~>~funny(X))<=>(patient(X)<~>~funny(X))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((brave(X)|~tall(X)))))&
(~generous(susan))&
(~calm(susan))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(happy(X)))&
(?[X]:((happy(X)&~generous(X))))&
((~generous(susan)<~>~happy(susan)))&
(strong(susan))&
(?[X]:(~quiet(X))) | ~happy(susan) | [
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3476876977091436878126928
% SZS output start Proof for 3476876977091436878126928
17. ~generous(susan) [input p16]
22. ~generous(susan) <~> ~happy(susan) [input p21]
25. ~happy(susan) [input hypothesis]
75. (happy(susan) | generous(susan)) & (~happy(susan) | ~generous(susan)) [nnf transformation 22]
137. ~generous(susan) [cnf transformation 17]
145. happy(susan) | generous(susan) [cnf transformation 75]
148. ~happy(susan) [cnf transformation 25]
250. happy(susan) [subsumption resolution 145,137]
251. $false [subsumption resolution 148,250]
% SZS output end Proof for 3476876977091436878126928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not kind and quiet then someone is quiet or not tall.
Everyone who is not kind or happy is not tall or rich.
Everyone who is both not humble and not curious is not rich and vice versa.
If someone is both not funny and not rich then someone is either not generous or not old.
If someone is not generous or happy then someone is not creative and vice versa.
Everyone who is rich is both old and happy.
Everyone who is both not kind and kind is either old or tall and vice versa.
Everyone who is both not old and not generous is either generous or old.
Everyone who is either patient or old is either happy or not curious and vice versa.
Everyone who is not kind is both not strong and calm.
Everyone who is not old or generous is not wise or not old and vice versa.
Everyone who is either not happy or brave is either not calm or rich and vice versa.
Everyone who is generous or rich is either old or rich.
If someone is either funny or humble then someone is creative.
If someone is either not quiet or not kind then someone is either humble or not humble.
If someone is not curious or funny then someone is calm.
Someone is either tall or calm.
John is either kind or generous.
Lucy is not strong or not happy.
Someone is not creative or not brave.
Someone is either not creative or not curious.
Mary is not funny or strong.
Someone is either not patient or brave. | John is not happy. | entailment | (((~kind(mary)&quiet(mary)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~kind(X)|happy(X))=>(~tall(X)|rich(X))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((kind(john)<~>generous(john)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~funny(mary)|strong(mary)))&
(?[X]:((~patient(X)<~>brave(X)))) | ~happy(john) | [
"p1",
"p5",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5406235276163839807306942
% SZS output start Proof for 5406235276163839807306942
2. ! [X0] : ((happy(X0) | ~kind(X0)) => (rich(X0) | ~tall(X0))) [input p1]
6. ! [X0] : (rich(X0) => (happy(X0) & old(X0))) [input p5]
7. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (old(X0) <~> tall(X0))) [input p6]
8. ! [X0] : ((~generous(X0) & ~old(X0)) => (generous(X0) <~> old(X0))) [input p7]
13. ! [X0] : ((rich(X0) | generous(X0)) => (old(X0) <~> rich(X0))) [input p12]
24. happy(john) [input hypothesis]
32. ! [X0] : ((rich(X0) | ~tall(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 2]
33. ! [X0] : (rich(X0) | ~tall(X0) | (~happy(X0) & kind(X0))) [flattening 32]
35. ! [X0] : ((happy(X0) & old(X0)) | ~rich(X0)) [ennf transformation 6]
36. ! [X0] : ((generous(X0) <~> old(X0)) | (generous(X0) | old(X0))) [ennf transformation 8]
37. ! [X0] : ((generous(X0) <~> old(X0)) | generous(X0) | old(X0)) [flattening 36]
39. ! [X0] : ((old(X0) <~> rich(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 13]
56. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~kind(X0) | kind(X0)))) [nnf transformation 7]
57. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | ~kind(X0) | kind(X0))) [flattening 56]
58. ! [X0] : (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | generous(X0) | old(X0)) [nnf transformation 37]
63. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 39]
89. ~happy(X0) | ~tall(X0) | rich(X0) [cnf transformation 33]
98. ~rich(X0) | old(X0) [cnf transformation 35]
102. ~kind(X0) | tall(X0) | ~old(X0) [cnf transformation 57]
104. kind(X0) | tall(X0) | ~old(X0) [cnf transformation 57]
106. old(X0) | generous(X0) | generous(X0) | old(X0) [cnf transformation 58]
130. rich(X0) | old(X0) | ~generous(X0) [cnf transformation 63]
133. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 63]
153. happy(john) [cnf transformation 24]
154. ~rich(X0) | ~old(X0) [duplicate literal removal 133]
155. old(X0) | generous(X0) [duplicate literal removal 106]
211. ~old(X0) | tall(X0) [subsumption resolution 102,104]
217. ~rich(X0) [subsumption resolution 154,98]
218. old(X0) | ~generous(X0) [subsumption resolution 130,217]
219. old(X0) [subsumption resolution 218,155]
319. tall(X1) [resolution 211,219]
324. ~tall(john) | rich(john) [resolution 89,153]
325. rich(john) [subsumption resolution 324,319]
326. $false [subsumption resolution 325,217]
% SZS output end Proof for 5406235276163839807306942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or quiet then susan is both creative and not generous and vice versa.
Everyone who is both not patient and not humble is not funny and vice versa.
If susan is either tall or not patient then john is not tall or kind and vice versa.
If paul is funny then someone is tall or wise and vice versa.
Everyone who is either wise or creative is either not old or creative.
Everyone who is happy or not happy is both wise and not rich.
Everyone who is not quiet is both wise and patient.
Everyone who is either not generous or not funny is curious and vice versa.
If someone is curious then fred is strong.
Everyone who is curious or creative is not creative or funny.
Everyone who is both strong and not tall is either creative or not happy.
If someone is either tall or brave then someone is not rich or old and vice versa.
If someone is old or curious then someone is not humble and vice versa.
If someone is creative then susan is either funny or not strong and vice versa.
If fred is both not funny and not happy then paul is funny and vice versa.
Someone is either not generous or curious.
Mary is not curious.
Someone is brave.
Paul is both not calm and creative.
Paul is strong or rich.
Someone is either creative or not brave.
Mary is either humble or not calm. | Susan is wise. | entailment | ((?[X]:((~kind(X)|quiet(X))))<=>((creative(susan)&~generous(susan))))&
(![X]:((~patient(X)&~humble(X))<=>~funny(X)))&
(((tall(susan)<~>~patient(susan)))<=>((~tall(john)|kind(john))))&
((funny(paul))<=>(?[X]:((tall(X)|wise(X)))))&
(![X]:((wise(X)<~>creative(X))=>(~old(X)<~>creative(X))))&
(![X]:((happy(X)|~happy(X))=>(wise(X)&~rich(X))))&
(![X]:(~quiet(X)=>(wise(X)&patient(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>curious(X)))&
((?[X]:(curious(X)))=>(strong(fred)))&
(![X]:((curious(X)|creative(X))=>(~creative(X)|funny(X))))&
(![X]:((strong(X)&~tall(X))=>(creative(X)<~>~happy(X))))&
((?[X]:((tall(X)<~>brave(X))))<=>(?[X]:((~rich(X)|old(X)))))&
((?[X]:((old(X)|curious(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(creative(X)))<=>((funny(susan)<~>~strong(susan))))&
(((~funny(fred)&~happy(fred)))<=>(funny(paul)))&
(?[X]:((~generous(X)<~>curious(X))))&
(~curious(mary))&
(?[X]:(brave(X)))&
((~calm(paul)&creative(paul)))&
((strong(paul)|rich(paul)))&
(?[X]:((creative(X)<~>~brave(X))))&
((humble(mary)<~>~calm(mary))) | wise(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3581425044525497379143442
% SZS output start Proof for 3581425044525497379143442
6. ! [X0] : ((~happy(X0) | happy(X0)) => (~rich(X0) & wise(X0))) [input p5]
23. ~wise(susan) [input hypothesis]
27. ! [X0] : ((~rich(X0) & wise(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 6]
96. wise(X0) | ~happy(X0) [cnf transformation 27]
97. wise(X0) | happy(X0) [cnf transformation 27]
138. ~wise(susan) [cnf transformation 23]
213. wise(X0) [subsumption resolution 96,97]
318. $false [subsumption resolution 138,213]
% SZS output end Proof for 3581425044525497379143442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is both funny and curious and vice versa. If someone is not quiet then someone is strong. Everyone who is not kind is either not wise or not generous. If john is not brave or not strong then paul is not old. Everyone who is not brave is either not happy or strong. Everyone who is not humble is generous. Everyone who is either not strong or not old is not calm or happy. If john is wise or not creative then someone is patient and vice versa. Everyone who is not happy or not curious is not old or not quiet and vice versa. Everyone who is not creative is either calm or not wise and vice versa. If fred is both not rich and old then someone is rich. If someone is calm or not generous then someone is not curious and vice versa. Everyone who is either not rich or not patient is either not wise or patient. Everyone who is creative or not happy is either not strong or rich. Everyone who is either calm or not quiet is both rich and not happy and vice versa. Everyone who is old is either tall or generous. Someone is either not generous or rich. Someone is both not generous and not happy. Someone is not kind. Alice is both not curious and not brave. John is creative. Someone is both patient and not generous. Susan is kind. Someone is funny or not generous. | Paul is old. | neutral | ((?[X]:(brave(X)))<=>(?[X]:((funny(X)&curious(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:(strong(X))))&
(![X]:(~kind(X)=>(~wise(X)<~>~generous(X))))&
(((~brave(john)|~strong(john)))=>(~old(paul)))&
(![X]:(~brave(X)=>(~happy(X)<~>strong(X))))&
(![X]:(~humble(X)=>generous(X)))&
(![X]:((~strong(X)<~>~old(X))=>(~calm(X)|happy(X))))&
(((wise(john)|~creative(john)))<=>(?[X]:(patient(X))))&
(![X]:((~happy(X)|~curious(X))<=>(~old(X)|~quiet(X))))&
(![X]:(~creative(X)<=>(calm(X)<~>~wise(X))))&
(((~rich(fred)&old(fred)))=>(?[X]:(rich(X))))&
((?[X]:((calm(X)|~generous(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~wise(X)<~>patient(X))))&
(![X]:((creative(X)|~happy(X))=>(~strong(X)<~>rich(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(rich(X)&~happy(X))))&
(![X]:(old(X)=>(tall(X)<~>generous(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:(~kind(X)))&
((~curious(alice)&~brave(alice)))&
(creative(john))&
(?[X]:((patient(X)&~generous(X))))&
(kind(susan))&
(?[X]:((funny(X)|~generous(X)))) | old(paul) | [] | null | 0 |
Everyone who is both not old and quiet is rich or generous and vice versa.
If fred is either brave or old then someone is brave or generous and vice versa.
Everyone who is brave is wise or quiet.
If someone is either not rich or patient then paul is not old.
Everyone who is not wise or quiet is brave and vice versa.
Everyone who is both not strong and not calm is both tall and calm.
If lucy is not brave then someone is either patient or not creative.
If someone is both not old and strong then mary is either not strong or not calm and vice versa.
Everyone who is either not rich or creative is either not old or patient.
If someone is either kind or generous then someone is creative or funny.
If paul is not happy then someone is either not rich or brave and vice versa.
If someone is not wise then paul is not creative.
Everyone who is not quiet or quiet is not curious.
If fred is either not patient or calm then someone is both wise and curious.
If someone is either happy or curious then someone is humble and vice versa.
If someone is not quiet or not brave then paul is not quiet and vice versa.
Paul is both not strong and brave.
Someone is brave or wise.
Paul is rich or patient.
Paul is quiet.
John is not curious or not kind.
Alice is not rich.
Susan is either not curious or creative.
Someone is patient or rich. | Paul is not calm. | contradiction | (![X]:((~old(X)&quiet(X))<=>(rich(X)|generous(X))))&
(((brave(fred)<~>old(fred)))<=>(?[X]:((brave(X)|generous(X)))))&
(![X]:(brave(X)=>(wise(X)|quiet(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>(~old(paul)))&
(![X]:((~wise(X)|quiet(X))<=>brave(X)))&
(![X]:((~strong(X)&~calm(X))=>(tall(X)&calm(X))))&
((~brave(lucy))=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((~old(X)&strong(X))))<=>((~strong(mary)<~>~calm(mary))))&
(![X]:((~rich(X)<~>creative(X))=>(~old(X)<~>patient(X))))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:((creative(X)|funny(X)))))&
((~happy(paul))<=>(?[X]:((~rich(X)<~>brave(X)))))&
((?[X]:(~wise(X)))=>(~creative(paul)))&
(![X]:((~quiet(X)|quiet(X))=>~curious(X)))&
(((~patient(fred)<~>calm(fred)))=>(?[X]:((wise(X)&curious(X)))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(~quiet(paul)))&
((~strong(paul)&brave(paul)))&
(?[X]:((brave(X)|wise(X))))&
((rich(paul)|patient(paul)))&
(quiet(paul))&
((~curious(john)|~kind(john)))&
(~rich(alice))&
((~curious(susan)<~>creative(susan)))&
(?[X]:((patient(X)|rich(X)))) | ~calm(paul) | [
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9139417166429602933318055
% SZS output start Proof for 9139417166429602933318055
6. ! [X0] : ((~calm(X0) & ~strong(X0)) => (calm(X0) & tall(X0))) [input p5]
17. brave(paul) & ~strong(paul) [input p16]
25. ~calm(paul) [input hypothesis]
30. ! [X0] : ((~calm(X0) & ~strong(X0)) => calm(X0)) [pure predicate removal 6]
34. ! [X0] : (calm(X0) | (calm(X0) | strong(X0))) [ennf transformation 30]
35. ! [X0] : (calm(X0) | calm(X0) | strong(X0)) [flattening 34]
96. calm(X0) | calm(X0) | strong(X0) [cnf transformation 35]
127. ~strong(paul) [cnf transformation 17]
136. ~calm(paul) [cnf transformation 25]
137. calm(X0) | strong(X0) [duplicate literal removal 96]
340. strong(paul) [resolution 137,136]
342. $false [subsumption resolution 340,127]
% SZS output end Proof for 9139417166429602933318055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not kind is both brave and not creative.
Everyone who is creative is both not happy and strong.
Everyone who is either curious or not funny is old.
If alice is not strong or not generous then someone is kind or not tall.
If mary is not wise then someone is both not tall and not wise.
Everyone who is old is both not strong and curious and vice versa.
Everyone who is brave is quiet or not generous.
If someone is either not old or curious then someone is both not patient and old and vice versa.
Everyone who is funny or not quiet is not rich.
Everyone who is both not kind and calm is kind and vice versa.
If lucy is not kind then paul is either kind or not rich and vice versa.
Everyone who is not funny or funny is both quiet and generous.
If someone is both tall and not creative then someone is patient.
Everyone who is either not curious or not quiet is both not kind and not wise and vice versa.
Everyone who is both not calm and kind is either calm or not happy.
If susan is happy or quiet then john is both strong and not rich.
Fred is rich or not old.
Someone is either not creative or tall.
Mary is either not creative or creative.
Susan is not funny.
Susan is either patient or not rich.
Someone is either rich or generous. | John is not old. | entailment | (![X]:((~strong(X)|~kind(X))=>(brave(X)&~creative(X))))&
(![X]:(creative(X)=>(~happy(X)&strong(X))))&
(![X]:((curious(X)<~>~funny(X))=>old(X)))&
(((~strong(alice)|~generous(alice)))=>(?[X]:((kind(X)|~tall(X)))))&
((~wise(mary))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:(old(X)<=>(~strong(X)&curious(X))))&
(![X]:(brave(X)=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)<~>curious(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((funny(X)|~quiet(X))=>~rich(X)))&
(![X]:((~kind(X)&calm(X))<=>kind(X)))&
((~kind(lucy))<=>((kind(paul)<~>~rich(paul))))&
(![X]:((~funny(X)|funny(X))=>(quiet(X)&generous(X))))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(~kind(X)&~wise(X))))&
(![X]:((~calm(X)&kind(X))=>(calm(X)<~>~happy(X))))&
(((happy(susan)|quiet(susan)))=>((strong(john)&~rich(john))))&
((rich(fred)|~old(fred)))&
(?[X]:((~creative(X)<~>tall(X))))&
((~creative(mary)<~>creative(mary)))&
(~funny(susan))&
((patient(susan)<~>~rich(susan)))&
(?[X]:((rich(X)<~>generous(X)))) | ~old(john) | [
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4276263235974932322396250
% SZS output start Proof for 4276263235974932322396250
6. ! [X0] : (old(X0) <=> (curious(X0) & ~strong(X0))) [input p5]
12. ! [X0] : ((funny(X0) | ~funny(X0)) => (generous(X0) & quiet(X0))) [input p11]
16. (quiet(susan) | happy(susan)) => (~rich(john) & strong(john)) [input p15]
23. old(john) [input hypothesis]
34. ! [X0] : ((generous(X0) & quiet(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 12]
38. (~rich(john) & strong(john)) | (~quiet(susan) & ~happy(susan)) [ennf transformation 16]
44. ! [X0] : ((old(X0) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | ~old(X0))) [nnf transformation 6]
45. ! [X0] : ((old(X0) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | ~old(X0))) [flattening 44]
80. ~old(X0) | ~strong(X0) [cnf transformation 45]
99. quiet(X0) | funny(X0) [cnf transformation 34]
100. quiet(X0) | ~funny(X0) [cnf transformation 34]
113. strong(john) | ~quiet(susan) [cnf transformation 38]
126. old(john) [cnf transformation 23]
200. quiet(X0) [subsumption resolution 99,100]
213. strong(john) [subsumption resolution 113,200]
244. ~strong(john) [resolution 80,126]
246. $false [subsumption resolution 244,213]
% SZS output end Proof for 4276263235974932322396250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both old and not old then fred is not creative and vice versa.
If someone is both tall and not humble then mary is curious or tall.
Everyone who is both not funny and rich is not patient or brave.
Everyone who is calm is not strong.
Everyone who is either not quiet or not patient is not tall.
If lucy is curious or brave then someone is both calm and not generous and vice versa.
Everyone who is calm or not generous is creative or funny and vice versa.
Everyone who is wise is rich.
If mary is happy or funny then lucy is not strong and vice versa.
Everyone who is either not creative or not generous is both not generous and not brave.
If someone is not rich or funny then alice is both not old and not curious.
If someone is happy then fred is both generous and not patient and vice versa.
Everyone who is not calm is both not kind and old and vice versa.
If someone is kind then mary is not creative and vice versa.
If someone is old or not creative then john is tall.
Everyone who is both creative and brave is not strong and vice versa.
Someone is either calm or not humble.
Someone is not tall or humble.
Lucy is not rich.
Someone is wise.
Someone is both not quiet and not brave.
Fred is either not generous or not curious.
Someone is either not old or not calm.
Mary is either curious or happy. | Lucy is not wise. | entailment | (((old(susan)&~old(susan)))<=>(~creative(fred)))&
((?[X]:((tall(X)&~humble(X))))=>((curious(mary)|tall(mary))))&
(![X]:((~funny(X)&rich(X))=>(~patient(X)|brave(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:((~quiet(X)<~>~patient(X))=>~tall(X)))&
(((curious(lucy)|brave(lucy)))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((calm(X)|~generous(X))<=>(creative(X)|funny(X))))&
(![X]:(wise(X)=>rich(X)))&
(((happy(mary)|funny(mary)))<=>(~strong(lucy)))&
(![X]:((~creative(X)<~>~generous(X))=>(~generous(X)&~brave(X))))&
((?[X]:((~rich(X)|funny(X))))=>((~old(alice)&~curious(alice))))&
((?[X]:(happy(X)))<=>((generous(fred)&~patient(fred))))&
(![X]:(~calm(X)<=>(~kind(X)&old(X))))&
((?[X]:(kind(X)))<=>(~creative(mary)))&
((?[X]:((old(X)|~creative(X))))=>(tall(john)))&
(![X]:((creative(X)&brave(X))<=>~strong(X)))&
(?[X]:((calm(X)<~>~humble(X))))&
(?[X]:((~tall(X)|humble(X))))&
(~rich(lucy))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)&~brave(X))))&
((~generous(fred)<~>~curious(fred)))&
(?[X]:((~old(X)<~>~calm(X))))&
((curious(mary)<~>happy(mary))) | ~wise(lucy) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1880704476492477347726603
% SZS output start Proof for 1880704476492477347726603
8. ! [X0] : (wise(X0) => rich(X0)) [input p7]
19. ~rich(lucy) [input p18]
25. wise(lucy) [input hypothesis]
32. ! [X0] : (rich(X0) | ~wise(X0)) [ennf transformation 8]
93. ~wise(X0) | rich(X0) [cnf transformation 32]
121. ~rich(lucy) [cnf transformation 19]
131. wise(lucy) [cnf transformation 25]
293. rich(lucy) [resolution 93,131]
294. $false [subsumption resolution 293,121]
% SZS output end Proof for 1880704476492477347726603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative.
Everyone who is old or humble is old.
Everyone who is quiet is both not old and not strong and vice versa.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
John is not patient or humble.
John is brave or not funny.
Someone is not old.
Lucy is both not old and not rich.
Someone is brave.
Lucy is patient or calm. | Alice is not old. | neutral | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>old(X)))&
(![X]:(quiet(X)<=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
((~patient(john)|humble(john)))&
((brave(john)|~funny(john)))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy)))&
(?[X]:(brave(X)))&
((patient(lucy)|calm(lucy))) | ~old(alice) | [] | null | 0 |
Everyone who is both not generous and not creative is either not tall or quiet.
Everyone who is humble is funny or curious and vice versa.
Everyone who is wise or not funny is quiet and vice versa.
If fred is both tall and brave then someone is rich or humble and vice versa.
If fred is either wise or brave then someone is both not quiet and not strong and vice versa.
If mary is generous then someone is both old and not quiet and vice versa.
Everyone who is either not funny or not patient is both not generous and humble and vice versa.
If someone is either not creative or not happy then someone is both not happy and calm and vice versa.
If someone is both curious and funny then someone is quiet and vice versa.
Everyone who is both not quiet and not patient is old.
If john is both not strong and old then susan is either humble or rich.
Everyone who is not kind or kind is both strong and patient and vice versa.
Everyone who is both not brave and patient is either not calm or not patient.
If someone is either old or kind then someone is creative or not generous and vice versa.
Everyone who is either rich or not brave is both quiet and brave and vice versa.
If someone is both not curious and tall then mary is both not old and old and vice versa.
Someone is generous.
Someone is kind.
Someone is not strong or creative.
Lucy is not curious or not wise.
Someone is either not quiet or not strong.
Someone is not calm or creative.
Mary is both not rich and not happy. | Susan is happy. | neutral | (![X]:((~generous(X)&~creative(X))=>(~tall(X)<~>quiet(X))))&
(![X]:(humble(X)<=>(funny(X)|curious(X))))&
(![X]:((wise(X)|~funny(X))<=>quiet(X)))&
(((tall(fred)&brave(fred)))<=>(?[X]:((rich(X)|humble(X)))))&
(((wise(fred)<~>brave(fred)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
((generous(mary))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~generous(X)&humble(X))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~patient(X))=>old(X)))&
(((~strong(john)&old(john)))=>((humble(susan)<~>rich(susan))))&
(![X]:((~kind(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((~brave(X)&patient(X))=>(~calm(X)<~>~patient(X))))&
((?[X]:((old(X)<~>kind(X))))<=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~curious(X)&tall(X))))<=>((~old(mary)&old(mary))))&
(?[X]:(generous(X)))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)|creative(X))))&
((~curious(lucy)|~wise(lucy)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~calm(X)|creative(X))))&
((~rich(mary)&~happy(mary))) | happy(susan) | [] | null | 0 |
If mary is brave then someone is both not generous and quiet.
Everyone who is both not creative and old is both generous and not creative and vice versa.
Everyone who is patient is old or not kind and vice versa.
If paul is either not quiet or not wise then someone is quiet or not old and vice versa.
Everyone who is calm is both not old and wise and vice versa.
If paul is not wise then someone is not strong or patient.
If john is both calm and rich then someone is either not quiet or happy and vice versa.
Everyone who is either not humble or not strong is either happy or not happy.
Everyone who is both tall and not wise is both curious and not patient.
If someone is quiet or not calm then someone is both not strong and not old.
If someone is either not calm or not tall then someone is generous.
If someone is humble or generous then someone is curious or not kind.
If someone is funny then susan is either not happy or strong and vice versa.
Everyone who is kind or calm is either not happy or brave and vice versa.
If someone is both not brave and quiet then someone is kind or brave and vice versa.
Everyone who is both kind and not happy is kind or patient and vice versa.
Mary is not calm.
Someone is either not funny or not quiet.
Mary is both not generous and not wise.
John is both wise and not calm.
Someone is either creative or not patient. | Susan is funny. | neutral | ((brave(mary))=>(?[X]:((~generous(X)&quiet(X)))))&
(![X]:((~creative(X)&old(X))<=>(generous(X)&~creative(X))))&
(![X]:(patient(X)<=>(old(X)|~kind(X))))&
(((~quiet(paul)<~>~wise(paul)))<=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:(calm(X)<=>(~old(X)&wise(X))))&
((~wise(paul))=>(?[X]:((~strong(X)|patient(X)))))&
(((calm(john)&rich(john)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~humble(X)<~>~strong(X))=>(happy(X)<~>~happy(X))))&
(![X]:((tall(X)&~wise(X))=>(curious(X)&~patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((~strong(X)&~old(X)))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:(generous(X))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:(funny(X)))<=>((~happy(susan)<~>strong(susan))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
(~calm(mary))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((~generous(mary)&~wise(mary)))&
((wise(john)&~calm(john)))&
(?[X]:((creative(X)<~>~patient(X)))) | funny(susan) | [] | null | 0 |
If paul is old then someone is both kind and rich. If someone is patient or not quiet then someone is not brave. Everyone who is either creative or patient is both happy and not funny and vice versa. If susan is not strong then alice is either not humble or not calm and vice versa. If someone is kind then alice is either funny or not patient and vice versa. If mary is generous then someone is not happy and vice versa. Everyone who is generous is both not wise and tall. Everyone who is not old or not patient is both strong and not calm. Everyone who is both not tall and curious is curious. Everyone who is either not rich or generous is either not patient or not humble. Everyone who is happy or old is both patient and not happy and vice versa. Everyone who is both not patient and calm is both not wise and not curious and vice versa. Everyone who is not funny is both quiet and not kind and vice versa. Everyone who is both not quiet and not rich is either not creative or patient and vice versa. If paul is either strong or not wise then fred is wise or humble. If someone is curious or not humble then someone is not quiet or kind. Someone is not humble. Someone is either happy or not creative. Someone is both not strong and creative. Someone is humble. Someone is not brave or not generous. John is both not wise and not brave. Alice is not quiet. | Paul is not creative. | entailment | ((old(paul))=>(?[X]:((kind(X)&rich(X)))))&
((?[X]:((patient(X)|~quiet(X))))=>(?[X]:(~brave(X))))&
(![X]:((creative(X)<~>patient(X))<=>(happy(X)&~funny(X))))&
((~strong(susan))<=>((~humble(alice)<~>~calm(alice))))&
((?[X]:(kind(X)))<=>((funny(alice)<~>~patient(alice))))&
((generous(mary))<=>(?[X]:(~happy(X))))&
(![X]:(generous(X)=>(~wise(X)&tall(X))))&
(![X]:((~old(X)|~patient(X))=>(strong(X)&~calm(X))))&
(![X]:((~tall(X)&curious(X))=>curious(X)))&
(![X]:((~rich(X)<~>generous(X))=>(~patient(X)<~>~humble(X))))&
(![X]:((happy(X)|old(X))<=>(patient(X)&~happy(X))))&
(![X]:((~patient(X)&calm(X))<=>(~wise(X)&~curious(X))))&
(![X]:(~funny(X)<=>(quiet(X)&~kind(X))))&
(![X]:((~quiet(X)&~rich(X))<=>(~creative(X)<~>patient(X))))&
(((strong(paul)<~>~wise(paul)))=>((wise(fred)|humble(fred))))&
((?[X]:((curious(X)|~humble(X))))=>(?[X]:((~quiet(X)|kind(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((~strong(X)&creative(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)|~generous(X))))&
((~wise(john)&~brave(john)))&
(~quiet(alice)) | ~creative(paul) | [
"p0",
"p2",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1609495403110529799845330
% SZS output start Proof for 1609495403110529799845330
1. old(paul) => ? [X0] : (rich(X0) & kind(X0)) [input p0]
3. ! [X0] : ((creative(X0) <~> patient(X0)) <=> (~funny(X0) & happy(X0))) [input p2]
11. ! [X0] : ((old(X0) | happy(X0)) <=> (~happy(X0) & patient(X0))) [input p10]
14. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> (~creative(X0) <~> patient(X0))) [input p13]
24. creative(paul) [input hypothesis]
32. ? [X0] : (rich(X0) & kind(X0)) | ~old(paul) [ennf transformation 1]
39. ? [X0] : (rich(X0) & kind(X0)) => (rich(sK0) & kind(sK0)) [choice axiom]
40. (rich(sK0) & kind(sK0)) | ~old(paul) [skolemisation 32,39]
41. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [nnf transformation 3]
42. ! [X0] : ((((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0))))) [flattening 41]
53. ! [X0] : (((old(X0) | happy(X0)) | (happy(X0) | ~patient(X0))) & ((~happy(X0) & patient(X0)) | (~old(X0) & ~happy(X0)))) [nnf transformation 11]
54. ! [X0] : ((old(X0) | happy(X0) | happy(X0) | ~patient(X0)) & ((~happy(X0) & patient(X0)) | (~old(X0) & ~happy(X0)))) [flattening 53]
59. ! [X0] : (((~rich(X0) & ~quiet(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (rich(X0) | quiet(X0)))) [nnf transformation 14]
60. ! [X0] : (((~rich(X0) & ~quiet(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | rich(X0) | quiet(X0))) [flattening 59]
75. rich(sK0) | ~old(paul) [cnf transformation 40]
76. ~creative(X0) | patient(X0) | happy(X0) [cnf transformation 42]
77. ~patient(X0) | creative(X0) | happy(X0) [cnf transformation 42]
103. ~happy(X0) | ~happy(X0) [cnf transformation 54]
105. old(X0) | happy(X0) | happy(X0) | ~patient(X0) [cnf transformation 54]
117. ~rich(X0) | patient(X0) | creative(X0) [cnf transformation 60]
118. ~creative(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 60]
131. creative(paul) [cnf transformation 24]
132. ~happy(X0) [duplicate literal removal 103]
133. ~patient(X0) | happy(X0) | old(X0) [duplicate literal removal 105]
135. 1 <=> old(paul) [avatar definition]
139. 2 <=> rich(sK0) [avatar definition]
141. rich(sK0) <- (2) [avatar component clause 139]
142. ~1 | 2 [avatar split clause 75,139,135]
253. patient(paul) | happy(paul) [resolution 76,131]
254. patient(paul) [subsumption resolution 253,132]
317. happy(paul) | old(paul) [resolution 133,254]
319. old(paul) [subsumption resolution 317,132]
322. 1 [avatar split clause 319,135]
324. patient(sK0) | creative(sK0) <- (2) [resolution 141,117]
326. 28 <=> creative(sK0) [avatar definition]
327. ~creative(sK0) <- (~28) [avatar component clause 326]
328. creative(sK0) <- (28) [avatar component clause 326]
330. 29 <=> patient(sK0) [avatar definition]
332. patient(sK0) <- (29) [avatar component clause 330]
333. 28 | 29 | ~2 [avatar split clause 324,139,330,326]
350. ~rich(sK0) | ~patient(sK0) <- (28) [resolution 328,118]
352. patient(sK0) | happy(sK0) <- (28) [resolution 328,76]
353. ~patient(sK0) <- (2, 28) [subsumption resolution 350,141]
354. ~29 | ~2 | ~28 [avatar split clause 353,326,139,330]
360. patient(sK0) <- (28) [subsumption resolution 352,132]
361. 29 | ~28 [avatar split clause 360,326,330]
379. creative(sK0) | happy(sK0) <- (29) [resolution 332,77]
390. happy(sK0) <- (~28, 29) [subsumption resolution 379,327]
391. $false <- (~28, 29) [subsumption resolution 390,132]
392. 28 | ~29 [avatar contradiction clause 391]
393. $false [avatar sat refutation 142,322,333,354,361,392]
% SZS output end Proof for 1609495403110529799845330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous is either not old or happy and vice versa.
Everyone who is either rich or quiet is not old or strong.
If someone is both strong and tall then someone is creative.
Everyone who is either not calm or not old is both creative and not patient.
Everyone who is both not calm and not funny is both curious and quiet.
Everyone who is not curious or not kind is not generous or not wise.
If someone is either not kind or not creative then alice is not calm or humble.
Everyone who is either creative or not calm is creative.
If someone is both quiet and not old then lucy is quiet or strong.
Everyone who is both not old and not calm is both not tall and not brave.
Everyone who is both generous and curious is not curious and vice versa.
If someone is funny or not creative then someone is both not calm and happy and vice versa.
Everyone who is not curious is not strong and vice versa.
If mary is both not quiet and humble then someone is both happy and wise and vice versa.
If fred is either happy or not old then someone is not rich or creative and vice versa.
Everyone who is both not rich and not brave is both not calm and not happy and vice versa.
Someone is either strong or old.
Someone is both not happy and not creative.
Someone is not brave or tall.
Susan is either not wise or not humble.
Someone is not humble or quiet.
Someone is not brave.
Someone is either not strong or not patient.
Someone is both curious and rich. | Susan is generous. | contradiction | (![X]:((~kind(X)<~>~generous(X))<=>(~old(X)<~>happy(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~old(X)|strong(X))))&
((?[X]:((strong(X)&tall(X))))=>(?[X]:(creative(X))))&
(![X]:((~calm(X)<~>~old(X))=>(creative(X)&~patient(X))))&
(![X]:((~calm(X)&~funny(X))=>(curious(X)&quiet(X))))&
(![X]:((~curious(X)|~kind(X))=>(~generous(X)|~wise(X))))&
((?[X]:((~kind(X)<~>~creative(X))))=>((~calm(alice)|humble(alice))))&
(![X]:((creative(X)<~>~calm(X))=>creative(X)))&
((?[X]:((quiet(X)&~old(X))))=>((quiet(lucy)|strong(lucy))))&
(![X]:((~old(X)&~calm(X))=>(~tall(X)&~brave(X))))&
(![X]:((generous(X)&curious(X))<=>~curious(X)))&
((?[X]:((funny(X)|~creative(X))))<=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:(~curious(X)<=>~strong(X)))&
(((~quiet(mary)&humble(mary)))<=>(?[X]:((happy(X)&wise(X)))))&
(((happy(fred)<~>~old(fred)))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:((~rich(X)&~brave(X))<=>(~calm(X)&~happy(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:((~brave(X)|tall(X))))&
((~wise(susan)<~>~humble(susan)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((curious(X)&rich(X)))) | generous(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7471518444201721396964665
% SZS output start Proof for 7471518444201721396964665
11. ! [X0] : ((curious(X0) & generous(X0)) <=> ~curious(X0)) [input p10]
25. generous(susan) [input hypothesis]
51. ! [X0] : (((curious(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | ~generous(X0)))) [nnf transformation 11]
52. ! [X0] : (((curious(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | ~generous(X0))) [flattening 51]
113. ~curious(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 52]
115. curious(X0) | curious(X0) [cnf transformation 52]
150. generous(susan) [cnf transformation 25]
151. ~curious(X0) | ~generous(X0) [duplicate literal removal 113]
152. curious(X0) [duplicate literal removal 115]
190. ~generous(X0) [subsumption resolution 151,152]
303. $false [subsumption resolution 150,190]
% SZS output end Proof for 7471518444201721396964665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or happy is tall and vice versa. Everyone who is either not patient or not tall is old or happy. If someone is not old or kind then susan is both wise and tall and vice versa. Everyone who is both not kind and old is not creative. Everyone who is creative or not strong is both strong and curious. If lucy is either not strong or not creative then someone is both not happy and not patient and vice versa. If someone is either quiet or not wise then someone is kind and vice versa. Everyone who is either generous or old is not humble or not wise and vice versa. Everyone who is either patient or curious is either not generous or humble. If fred is not happy then someone is wise or not calm. Everyone who is not patient is not happy and vice versa. Everyone who is both tall and not creative is not generous or not humble and vice versa. If susan is both happy and not strong then someone is either not old or curious and vice versa. Everyone who is either not generous or humble is either not happy or not creative and vice versa. If fred is both not rich and not old then lucy is either not calm or not humble and vice versa. Everyone who is not wise is both calm and old and vice versa. Someone is not humble. Someone is quiet. Fred is either not happy or not quiet. Mary is either not curious or not strong. Susan is not funny. Someone is funny. Alice is both not curious and humble. Susan is brave. | Susan is not old. | contradiction | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((~patient(X)<~>~tall(X))=>(old(X)|happy(X))))&
((?[X]:((~old(X)|kind(X))))<=>((wise(susan)&tall(susan))))&
(![X]:((~kind(X)&old(X))=>~creative(X)))&
(![X]:((creative(X)|~strong(X))=>(strong(X)&curious(X))))&
(((~strong(lucy)<~>~creative(lucy)))<=>(?[X]:((~happy(X)&~patient(X)))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
(![X]:((patient(X)<~>curious(X))=>(~generous(X)<~>humble(X))))&
((~happy(fred))=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((tall(X)&~creative(X))<=>(~generous(X)|~humble(X))))&
(((happy(susan)&~strong(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~happy(X)<~>~creative(X))))&
(((~rich(fred)&~old(fred)))<=>((~calm(lucy)<~>~humble(lucy))))&
(![X]:(~wise(X)<=>(calm(X)&old(X))))&
(?[X]:(~humble(X)))&
(?[X]:(quiet(X)))&
((~happy(fred)<~>~quiet(fred)))&
((~curious(mary)<~>~strong(mary)))&
(~funny(susan))&
(?[X]:(funny(X)))&
((~curious(alice)&humble(alice)))&
(brave(susan)) | ~old(susan) | [
"p0",
"p1",
"p7",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3070621802531024480602185
% SZS output start Proof for 3070621802531024480602185
1. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> tall(X0)) [input p0]
2. ! [X0] : ((~patient(X0) <~> ~tall(X0)) => (happy(X0) | old(X0))) [input p1]
8. ! [X0] : ((generous(X0) <~> old(X0)) <=> (~wise(X0) | ~humble(X0))) [input p7]
11. ! [X0] : (~patient(X0) <=> ~happy(X0)) [input p10]
12. ! [X0] : ((~creative(X0) & tall(X0)) <=> (~humble(X0) | ~generous(X0))) [input p11]
14. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (~happy(X0) <~> ~creative(X0))) [input p13]
25. ~old(susan) [input hypothesis]
28. ! [X0] : ((happy(X0) | old(X0)) | (~patient(X0) <=> ~tall(X0))) [ennf transformation 2]
29. ! [X0] : (happy(X0) | old(X0) | (~patient(X0) <=> ~tall(X0))) [flattening 28]
35. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 1]
36. ! [X0] : (happy(X0) | old(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0)))) [nnf transformation 29]
51. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 51]
56. ! [X0] : ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0))) [nnf transformation 11]
57. ! [X0] : (((~creative(X0) & tall(X0)) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | (creative(X0) | ~tall(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & tall(X0)) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | creative(X0) | ~tall(X0))) [flattening 57]
64. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ((~happy(X0) | creative(X0)) & (~creative(X0) | happy(X0)))) & (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 14]
77. tall(X0) | happy(X0) | happy(X0) [cnf transformation 35]
78. tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 35]
81. happy(X0) | old(X0) | ~tall(X0) | patient(X0) [cnf transformation 36]
105. humble(X0) | generous(X0) | old(X0) [cnf transformation 52]
114. ~happy(X0) | patient(X0) [cnf transformation 56]
115. ~patient(X0) | happy(X0) [cnf transformation 56]
116. ~humble(X0) | ~generous(X0) | creative(X0) | ~tall(X0) [cnf transformation 58]
119. ~creative(X0) | generous(X0) [cnf transformation 58]
120. ~creative(X0) | humble(X0) [cnf transformation 58]
128. ~creative(X0) | ~happy(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 64]
132. humble(X0) | ~generous(X0) | ~happy(X0) | creative(X0) [cnf transformation 64]
134. ~humble(X0) | generous(X0) | ~happy(X0) | creative(X0) [cnf transformation 64]
154. ~old(susan) [cnf transformation 25]
156. tall(X0) | happy(X0) [duplicate literal removal 77]
157. ~happy(X0) | tall(X0) [duplicate literal removal 78]
158. tall(X0) [subsumption resolution 156,157]
159. old(X0) | happy(X0) | patient(X0) [subsumption resolution 81,158]
238. ~humble(X0) | ~generous(X0) | creative(X0) [subsumption resolution 116,158]
241. ~humble(X0) | generous(X0) | ~happy(X0) [subsumption resolution 134,119]
242. ~generous(X0) | ~happy(X0) | creative(X0) [subsumption resolution 132,238]
244. ~creative(X0) | ~happy(X0) | ~humble(X0) [subsumption resolution 128,241]
245. ~creative(X0) | ~happy(X0) [subsumption resolution 244,120]
307. happy(susan) | patient(susan) [resolution 159,154]
310. patient(susan) [subsumption resolution 307,114]
312. happy(susan) [resolution 310,115]
329. generous(X0) | ~happy(X0) | generous(X0) | old(X0) [resolution 241,105]
330. ~happy(X0) | generous(X0) | old(X0) [duplicate literal removal 329]
481. generous(susan) | old(susan) [resolution 330,312]
483. generous(susan) [subsumption resolution 481,154]
535. ~happy(susan) | creative(susan) [resolution 483,242]
548. creative(susan) [subsumption resolution 535,312]
590. ~happy(susan) [resolution 548,245]
594. $false [subsumption resolution 590,312]
% SZS output end Proof for 3070621802531024480602185
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then mary is either not kind or not curious.
Everyone who is tall is calm and vice versa.
Everyone who is funny is both not tall and strong and vice versa.
Everyone who is either wise or humble is both patient and creative and vice versa.
If someone is either humble or brave then mary is not patient or generous.
Everyone who is not generous or not creative is not rich.
If someone is either not rich or curious then someone is either curious or not patient and vice versa.
If someone is both not strong and curious then someone is not tall or brave.
If mary is generous then someone is both not brave and humble.
If someone is creative then someone is both brave and not brave.
Everyone who is not wise or patient is generous or not funny and vice versa.
If someone is not quiet then mary is happy.
If paul is either not happy or not humble then susan is both not generous and not calm.
If someone is old or not patient then someone is either not old or not creative.
If lucy is both calm and curious then someone is either kind or curious and vice versa.
Everyone who is not creative is quiet.
Someone is not calm or funny.
Lucy is either happy or quiet.
Susan is calm or kind.
Someone is wise or humble.
Someone is not funny or happy.
Paul is both not calm and generous. | Lucy is not tall. | neutral | ((?[X]:(old(X)))=>((~kind(mary)<~>~curious(mary))))&
(![X]:(tall(X)<=>calm(X)))&
(![X]:(funny(X)<=>(~tall(X)&strong(X))))&
(![X]:((wise(X)<~>humble(X))<=>(patient(X)&creative(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((~patient(mary)|generous(mary))))&
(![X]:((~generous(X)|~creative(X))=>~rich(X)))&
((?[X]:((~rich(X)<~>curious(X))))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~tall(X)|brave(X)))))&
((generous(mary))=>(?[X]:((~brave(X)&humble(X)))))&
((?[X]:(creative(X)))=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:((~wise(X)|patient(X))<=>(generous(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>(happy(mary)))&
(((~happy(paul)<~>~humble(paul)))=>((~generous(susan)&~calm(susan))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(((calm(lucy)&curious(lucy)))<=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:(~creative(X)=>quiet(X)))&
(?[X]:((~calm(X)|funny(X))))&
((happy(lucy)<~>quiet(lucy)))&
((calm(susan)|kind(susan)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~funny(X)|happy(X))))&
((~calm(paul)&generous(paul))) | ~tall(lucy) | [] | null | 0 |
Everyone who is tall is either creative or not humble.
Everyone who is not kind or not curious is curious and vice versa.
Everyone who is rich is wise or happy and vice versa.
If lucy is both not strong and funny then mary is humble.
If fred is brave or tall then paul is either not wise or not creative and vice versa.
If someone is either tall or not wise then someone is either quiet or humble and vice versa.
If someone is not tall or not funny then someone is either not wise or old and vice versa.
If someone is happy then mary is not patient or creative.
If someone is curious or not creative then someone is both strong and not funny.
Everyone who is either not brave or brave is brave and vice versa.
Everyone who is brave is both quiet and not old.
Everyone who is not happy or generous is not calm and vice versa.
Everyone who is humble is wise and vice versa.
Everyone who is humble or creative is not calm or not funny and vice versa.
If john is either not rich or not happy then someone is tall and vice versa.
Everyone who is either not rich or tall is tall.
Paul is not old or not quiet.
Paul is not patient or quiet.
Someone is not patient.
Fred is wise or not tall.
Someone is either not happy or not kind. | Paul is creative. | neutral | (![X]:(tall(X)=>(creative(X)<~>~humble(X))))&
(![X]:((~kind(X)|~curious(X))<=>curious(X)))&
(![X]:(rich(X)<=>(wise(X)|happy(X))))&
(((~strong(lucy)&funny(lucy)))=>(humble(mary)))&
(((brave(fred)|tall(fred)))<=>((~wise(paul)<~>~creative(paul))))&
((?[X]:((tall(X)<~>~wise(X))))<=>(?[X]:((quiet(X)<~>humble(X)))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
((?[X]:(happy(X)))=>((~patient(mary)|creative(mary))))&
((?[X]:((curious(X)|~creative(X))))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~brave(X)<~>brave(X))<=>brave(X)))&
(![X]:(brave(X)=>(quiet(X)&~old(X))))&
(![X]:((~happy(X)|generous(X))<=>~calm(X)))&
(![X]:(humble(X)<=>wise(X)))&
(![X]:((humble(X)|creative(X))<=>(~calm(X)|~funny(X))))&
(((~rich(john)<~>~happy(john)))<=>(?[X]:(tall(X))))&
(![X]:((~rich(X)<~>tall(X))=>tall(X)))&
((~old(paul)|~quiet(paul)))&
((~patient(paul)|quiet(paul)))&
(?[X]:(~patient(X)))&
((wise(fred)|~tall(fred)))&
(?[X]:((~happy(X)<~>~kind(X)))) | creative(paul) | [] | null | 0 |
If someone is generous or not old then alice is not happy. If mary is happy then lucy is both not creative and wise. If someone is not brave or not kind then alice is not humble and vice versa. Everyone who is either not curious or not humble is both humble and not brave. Everyone who is either not old or not generous is not calm. If paul is not calm or not happy then someone is kind and vice versa. If john is not creative or generous then fred is either not quiet or strong. If paul is either not old or kind then someone is both funny and not wise and vice versa. Everyone who is both wise and not quiet is not humble or not patient and vice versa. Everyone who is generous is both humble and not quiet. Everyone who is both rich and not generous is both brave and not tall and vice versa. If lucy is not quiet then someone is old and vice versa. If susan is both not rich and curious then someone is humble or not happy and vice versa. Everyone who is kind or not creative is old. Everyone who is curious or not kind is both not curious and brave and vice versa. If mary is either not funny or generous then someone is either kind or not calm. John is rich or not strong. Mary is not curious or funny. Someone is either not brave or humble. John is either not rich or not patient. Someone is kind. Someone is not tall. | John is not generous. | entailment | ((?[X]:((generous(X)|~old(X))))=>(~happy(alice)))&
((happy(mary))=>((~creative(lucy)&wise(lucy))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~humble(alice)))&
(![X]:((~curious(X)<~>~humble(X))=>(humble(X)&~brave(X))))&
(![X]:((~old(X)<~>~generous(X))=>~calm(X)))&
(((~calm(paul)|~happy(paul)))<=>(?[X]:(kind(X))))&
(((~creative(john)|generous(john)))=>((~quiet(fred)<~>strong(fred))))&
(((~old(paul)<~>kind(paul)))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((wise(X)&~quiet(X))<=>(~humble(X)|~patient(X))))&
(![X]:(generous(X)=>(humble(X)&~quiet(X))))&
(![X]:((rich(X)&~generous(X))<=>(brave(X)&~tall(X))))&
((~quiet(lucy))<=>(?[X]:(old(X))))&
(((~rich(susan)&curious(susan)))<=>(?[X]:((humble(X)|~happy(X)))))&
(![X]:((kind(X)|~creative(X))=>old(X)))&
(![X]:((curious(X)|~kind(X))<=>(~curious(X)&brave(X))))&
(((~funny(mary)<~>generous(mary)))=>(?[X]:((kind(X)<~>~calm(X)))))&
((rich(john)|~strong(john)))&
((~curious(mary)|funny(mary)))&
(?[X]:((~brave(X)<~>humble(X))))&
((~rich(john)<~>~patient(john)))&
(?[X]:(kind(X)))&
(?[X]:(~tall(X))) | ~generous(john) | [
"p0",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4806681329669590854998634
% SZS output start Proof for 4806681329669590854998634
1. ? [X0] : (~old(X0) | generous(X0)) => ~happy(alice) [input p0]
13. (curious(susan) & ~rich(susan)) <=> ? [X0] : (~happy(X0) | humble(X0)) [input p12]
15. ! [X0] : ((~kind(X0) | curious(X0)) <=> (brave(X0) & ~curious(X0))) [input p14]
23. generous(john) [input hypothesis]
24. ~happy(alice) | ! [X0] : (old(X0) & ~generous(X0)) [ennf transformation 1]
56. ((curious(susan) & ~rich(susan)) | ! [X0] : (happy(X0) & ~humble(X0))) & (? [X0] : (~happy(X0) | humble(X0)) | (~curious(susan) | rich(susan))) [nnf transformation 13]
57. ((curious(susan) & ~rich(susan)) | ! [X0] : (happy(X0) & ~humble(X0))) & (? [X0] : (~happy(X0) | humble(X0)) | ~curious(susan) | rich(susan)) [flattening 56]
58. ((curious(susan) & ~rich(susan)) | ! [X0] : (happy(X0) & ~humble(X0))) & (? [X1] : (~happy(X1) | humble(X1)) | ~curious(susan) | rich(susan)) [rectify 57]
59. ? [X1] : (~happy(X1) | humble(X1)) => (~happy(sK4) | humble(sK4)) [choice axiom]
60. ((curious(susan) & ~rich(susan)) | ! [X0] : (happy(X0) & ~humble(X0))) & ((~happy(sK4) | humble(sK4)) | ~curious(susan) | rich(susan)) [skolemisation 58,59]
61. ! [X0] : (((~kind(X0) | curious(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (kind(X0) & ~curious(X0)))) [nnf transformation 15]
62. ! [X0] : ((~kind(X0) | curious(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (kind(X0) & ~curious(X0)))) [flattening 61]
74. ~happy(alice) | ~generous(X0) [cnf transformation 24]
117. curious(susan) | happy(X0) [cnf transformation 60]
120. ~curious(X0) | ~curious(X0) [cnf transformation 62]
137. generous(john) [cnf transformation 23]
138. ~curious(X0) [duplicate literal removal 120]
145. 2 <=> happy(alice) [avatar definition]
147. ~happy(alice) <- (~2) [avatar component clause 145]
150. 3 <=> ! [X0] : ~generous(X0) [avatar definition]
151. ~generous(X0) <- (3) [avatar component clause 150]
152. 3 | ~2 [avatar split clause 74,145,150]
207. 16 <=> generous(john) [avatar definition]
208. generous(john) <- (16) [avatar component clause 207]
265. 28 <=> ! [X0] : happy(X0) [avatar definition]
266. happy(X0) <- (28) [avatar component clause 265]
268. 29 <=> curious(susan) [avatar definition]
270. curious(susan) <- (29) [avatar component clause 268]
271. 28 | 29 [avatar split clause 117,268,265]
336. 16 [avatar split clause 137,207]
337. $false <- (29) [subsumption resolution 270,138]
338. ~29 [avatar contradiction clause 337]
345. $false <- (~2, 28) [resolution 266,147]
348. 2 | ~28 [avatar contradiction clause 345]
353. $false <- (3, 16) [resolution 151,208]
354. ~3 | ~16 [avatar contradiction clause 353]
355. $false [avatar sat refutation 152,271,336,338,348,354]
% SZS output end Proof for 4806681329669590854998634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not rich then paul is both quiet and curious.
Everyone who is creative is curious or tall.
Everyone who is both not calm and tall is patient or not old.
Everyone who is humble or not creative is brave or curious and vice versa.
If fred is not tall or not happy then someone is both not brave and not generous and vice versa.
Everyone who is generous is strong or not wise.
Everyone who is not curious is either not creative or rich.
If someone is not kind then fred is either not rich or not calm.
If fred is both not kind and curious then someone is not creative or quiet.
Everyone who is not creative is wise.
If lucy is both rich and patient then lucy is strong or tall and vice versa.
Everyone who is either not creative or calm is calm or kind.
If someone is both humble and old then alice is either rich or not tall.
If someone is calm or old then mary is either not curious or funny.
If lucy is both not strong and not generous then fred is both not quiet and not generous and vice versa.
If someone is either kind or happy then alice is both funny and generous and vice versa.
Someone is both not tall and curious.
Lucy is both not creative and not humble.
Someone is both kind and patient.
Someone is not happy.
Alice is calm.
Alice is happy or patient.
Someone is not happy or strong.
Someone is both not quiet and not generous. | Fred is curious. | neutral | ((~rich(fred))=>((quiet(paul)&curious(paul))))&
(![X]:(creative(X)=>(curious(X)|tall(X))))&
(![X]:((~calm(X)&tall(X))=>(patient(X)|~old(X))))&
(![X]:((humble(X)|~creative(X))<=>(brave(X)|curious(X))))&
(((~tall(fred)|~happy(fred)))<=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:(generous(X)=>(strong(X)|~wise(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>rich(X))))&
((?[X]:(~kind(X)))=>((~rich(fred)<~>~calm(fred))))&
(((~kind(fred)&curious(fred)))=>(?[X]:((~creative(X)|quiet(X)))))&
(![X]:(~creative(X)=>wise(X)))&
(((rich(lucy)&patient(lucy)))<=>((strong(lucy)|tall(lucy))))&
(![X]:((~creative(X)<~>calm(X))=>(calm(X)|kind(X))))&
((?[X]:((humble(X)&old(X))))=>((rich(alice)<~>~tall(alice))))&
((?[X]:((calm(X)|old(X))))=>((~curious(mary)<~>funny(mary))))&
(((~strong(lucy)&~generous(lucy)))<=>((~quiet(fred)&~generous(fred))))&
((?[X]:((kind(X)<~>happy(X))))<=>((funny(alice)&generous(alice))))&
(?[X]:((~tall(X)&curious(X))))&
((~creative(lucy)&~humble(lucy)))&
(?[X]:((kind(X)&patient(X))))&
(?[X]:(~happy(X)))&
(calm(alice))&
((happy(alice)|patient(alice)))&
(?[X]:((~happy(X)|strong(X))))&
(?[X]:((~quiet(X)&~generous(X)))) | curious(fred) | [] | null | 0 |
Everyone who is both curious and not quiet is either quiet or not calm and vice versa.
If alice is both curious and not brave then alice is either not humble or humble and vice versa.
If mary is either wise or not calm then someone is either not funny or not brave.
Everyone who is not rich or funny is either brave or not tall and vice versa.
Everyone who is not humble is both curious and not tall and vice versa.
Everyone who is quiet or not old is both not funny and happy and vice versa.
Everyone who is not humble or not kind is either funny or old.
If someone is either not creative or not brave then alice is both old and curious.
If someone is not funny or creative then paul is creative or not curious and vice versa.
If lucy is tall then someone is not rich or not brave and vice versa.
Everyone who is not tall is either not patient or wise and vice versa.
If someone is not wise or not calm then someone is funny or patient.
If someone is funny then susan is generous.
Everyone who is not strong is quiet and vice versa.
Everyone who is either tall or not generous is both not brave and humble and vice versa.
Everyone who is both not calm and old is brave or humble.
Alice is both wise and quiet.
Someone is both not creative and not quiet.
Someone is brave or strong.
Susan is both not tall and not strong.
Someone is kind or creative.
Paul is both generous and not funny.
Someone is both quiet and not funny.
Someone is patient or not kind. | Lucy is humble. | entailment | (![X]:((curious(X)&~quiet(X))<=>(quiet(X)<~>~calm(X))))&
(((curious(alice)&~brave(alice)))<=>((~humble(alice)<~>humble(alice))))&
(((wise(mary)<~>~calm(mary)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~rich(X)|funny(X))<=>(brave(X)<~>~tall(X))))&
(![X]:(~humble(X)<=>(curious(X)&~tall(X))))&
(![X]:((quiet(X)|~old(X))<=>(~funny(X)&happy(X))))&
(![X]:((~humble(X)|~kind(X))=>(funny(X)<~>old(X))))&
((?[X]:((~creative(X)<~>~brave(X))))=>((old(alice)&curious(alice))))&
((?[X]:((~funny(X)|creative(X))))<=>((creative(paul)|~curious(paul))))&
((tall(lucy))<=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:(~tall(X)<=>(~patient(X)<~>wise(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((funny(X)|patient(X)))))&
((?[X]:(funny(X)))=>(generous(susan)))&
(![X]:(~strong(X)<=>quiet(X)))&
(![X]:((tall(X)<~>~generous(X))<=>(~brave(X)&humble(X))))&
(![X]:((~calm(X)&old(X))=>(brave(X)|humble(X))))&
((wise(alice)&quiet(alice)))&
(?[X]:((~creative(X)&~quiet(X))))&
(?[X]:((brave(X)|strong(X))))&
((~tall(susan)&~strong(susan)))&
(?[X]:((kind(X)|creative(X))))&
((generous(paul)&~funny(paul)))&
(?[X]:((quiet(X)&~funny(X))))&
(?[X]:((patient(X)|~kind(X)))) | humble(lucy) | [
"p1",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 413269000422492923965772
% SZS output start Proof for 413269000422492923965772
2. (~brave(alice) & curious(alice)) <=> (~humble(alice) <~> humble(alice)) [input p1]
5. ! [X0] : (~humble(X0) <=> (~tall(X0) & curious(X0))) [input p4]
10. tall(lucy) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p9]
25. ~humble(lucy) [input hypothesis]
36. ((~brave(alice) & curious(alice)) | ((~humble(alice) | ~humble(alice)) & (humble(alice) | humble(alice)))) & (((~humble(alice) | humble(alice)) & (humble(alice) | ~humble(alice))) | (brave(alice) | ~curious(alice))) [nnf transformation 2]
37. ((~brave(alice) & curious(alice)) | ((~humble(alice) | ~humble(alice)) & (humble(alice) | humble(alice)))) & (((~humble(alice) | humble(alice)) & (humble(alice) | ~humble(alice))) | brave(alice) | ~curious(alice)) [flattening 36]
43. ! [X0] : ((~humble(X0) | (tall(X0) | ~curious(X0))) & ((~tall(X0) & curious(X0)) | humble(X0))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | tall(X0) | ~curious(X0)) & ((~tall(X0) & curious(X0)) | humble(X0))) [flattening 43]
54. (tall(lucy) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | ~tall(lucy)) [nnf transformation 10]
55. (tall(lucy) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | ~tall(lucy)) [rectify 54]
56. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK2) | ~rich(sK2)) [choice axiom]
57. (tall(lucy) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK2) | ~rich(sK2)) | ~tall(lucy)) [skolemisation 55,56]
85. ~brave(alice) | humble(alice) | humble(alice) [cnf transformation 37]
86. ~brave(alice) | ~humble(alice) | ~humble(alice) [cnf transformation 37]
98. ~tall(X0) | humble(X0) [cnf transformation 44]
119. tall(lucy) | brave(X0) [cnf transformation 57]
149. ~humble(lucy) [cnf transformation 25]
152. ~brave(alice) | humble(alice) [duplicate literal removal 85]
153. ~brave(alice) | ~humble(alice) [duplicate literal removal 86]
158. 1 <=> humble(alice) [avatar definition]
162. 2 <=> brave(alice) [avatar definition]
164. ~brave(alice) <- (~2) [avatar component clause 162]
165. ~1 | ~2 [avatar split clause 153,162,158]
166. 1 | ~2 [avatar split clause 152,162,158]
238. 17 <=> ! [X0] : brave(X0) [avatar definition]
239. brave(X0) <- (17) [avatar component clause 238]
241. 18 <=> tall(lucy) [avatar definition]
243. tall(lucy) <- (18) [avatar component clause 241]
244. 17 | 18 [avatar split clause 119,241,238]
315. humble(lucy) <- (18) [resolution 98,243]
316. $false <- (18) [subsumption resolution 315,149]
317. ~18 [avatar contradiction clause 316]
318. $false <- (~2, 17) [resolution 239,164]
321. 2 | ~17 [avatar contradiction clause 318]
322. $false [avatar sat refutation 165,166,244,317,321]
% SZS output end Proof for 413269000422492923965772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not kind and not strong then john is generous or not calm and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is either not old or not generous is not generous and vice versa.
Someone is either wise or rich.
Someone is either not happy or brave.
Someone is both not quiet and not humble.
Someone is kind.
Someone is both not funny and not quiet.
Alice is either generous or not generous.
Mary is rich or curious.
Someone is either curious or humble. | Lucy is not curious. | entailment | (((~kind(lucy)&~strong(lucy)))<=>((generous(john)|~calm(john))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>~generous(X)))&
(?[X]:((wise(X)<~>rich(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((~quiet(X)&~humble(X))))&
(?[X]:(kind(X)))&
(?[X]:((~funny(X)&~quiet(X))))&
((generous(alice)<~>~generous(alice)))&
((rich(mary)|curious(mary)))&
(?[X]:((curious(X)<~>humble(X)))) | ~curious(lucy) | [
"p0",
"p1",
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8449751131450921170608840
% SZS output start Proof for 8449751131450921170608840
1. (~strong(lucy) & ~kind(lucy)) <=> (~calm(john) | generous(john)) [input p0]
2. ! [X0] : ((~humble(X0) <~> strong(X0)) => happy(X0)) [input p1]
7. ! [X0] : ((rich(X0) & ~happy(X0)) <=> (curious(X0) | rich(X0))) [input p6]
9. ? [X0] : (generous(X0) | calm(X0)) => ? [X0] : ~old(X0) [input p8]
14. ! [X0] : ((~calm(X0) & humble(X0)) => (kind(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p15]
25. curious(lucy) [input hypothesis]
28. ? [X0] : (generous(X0) | calm(X0)) => ? [X1] : ~old(X1) [rectify 9]
31. ! [X0] : (happy(X0) | (~humble(X0) <=> strong(X0))) [ennf transformation 2]
37. ? [X1] : ~old(X1) | ! [X0] : (~generous(X0) & ~calm(X0)) [ennf transformation 28]
40. ! [X0] : ((kind(X0) & happy(X0)) | (calm(X0) | ~humble(X0))) [ennf transformation 14]
41. ! [X0] : ((kind(X0) & happy(X0)) | calm(X0) | ~humble(X0)) [flattening 40]
43. ((~strong(lucy) & ~kind(lucy)) | (calm(john) & ~generous(john))) & ((~calm(john) | generous(john)) | (strong(lucy) | kind(lucy))) [nnf transformation 1]
44. ((~strong(lucy) & ~kind(lucy)) | (calm(john) & ~generous(john))) & (~calm(john) | generous(john) | strong(lucy) | kind(lucy)) [flattening 43]
45. ! [X0] : (happy(X0) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 31]
56. ! [X0] : (((rich(X0) & ~happy(X0)) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | (~rich(X0) | happy(X0)))) [nnf transformation 7]
57. ! [X0] : (((rich(X0) & ~happy(X0)) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | ~rich(X0) | happy(X0))) [flattening 56]
59. ? [X0] : ~old(X0) | ! [X1] : (~generous(X1) & ~calm(X1)) [rectify 37]
60. ? [X0] : ~old(X0) => ~old(sK3) [choice axiom]
61. ~old(sK3) | ! [X1] : (~generous(X1) & ~calm(X1)) [skolemisation 59,60]
73. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | generous(X0)) & (~generous(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 16]
94. ~strong(lucy) | calm(john) [cnf transformation 44]
95. happy(X0) | strong(X0) | humble(X0) [cnf transformation 45]
108. ~curious(X0) | ~happy(X0) [cnf transformation 57]
115. ~old(sK3) | ~calm(X1) [cnf transformation 61]
128. ~humble(X0) | calm(X0) | happy(X0) [cnf transformation 41]
132. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 73]
135. generous(X0) | old(X0) | generous(X0) [cnf transformation 73]
150. curious(lucy) [cnf transformation 25]
151. ~generous(X0) | old(X0) [duplicate literal removal 132]
152. old(X0) | generous(X0) [duplicate literal removal 135]
155. 1 <=> calm(john) [avatar definition]
157. calm(john) <- (1) [avatar component clause 155]
159. 2 <=> strong(lucy) [avatar definition]
161. ~strong(lucy) <- (~2) [avatar component clause 159]
162. 1 | ~2 [avatar split clause 94,159,155]
242. 21 <=> old(sK3) [avatar definition]
244. ~old(sK3) <- (~21) [avatar component clause 242]
247. 22 <=> ! [X1] : ~calm(X1) [avatar definition]
248. ~calm(X1) <- (22) [avatar component clause 247]
249. 22 | ~21 [avatar split clause 115,242,247]
275. old(X0) [subsumption resolution 151,152]
307. $false <- (~21) [subsumption resolution 244,275]
308. 21 [avatar contradiction clause 307]
310. ~happy(lucy) [resolution 108,150]
316. strong(lucy) | humble(lucy) [resolution 95,310]
321. humble(lucy) <- (~2) [subsumption resolution 316,161]
391. calm(lucy) | happy(lucy) <- (~2) [resolution 128,321]
392. happy(lucy) <- (~2, 22) [subsumption resolution 391,248]
393. $false <- (~2, 22) [subsumption resolution 392,310]
394. 2 | ~22 [avatar contradiction clause 393]
400. $false <- (1, 22) [subsumption resolution 157,248]
401. ~1 | ~22 [avatar contradiction clause 400]
402. $false [avatar sat refutation 162,249,308,394,401]
% SZS output end Proof for 8449751131450921170608840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not calm is both tall and calm and vice versa. Everyone who is either kind or wise is both funny and quiet. Everyone who is not humble is both old and brave and vice versa. If someone is not strong then someone is not funny or wise and vice versa. Everyone who is not kind or old is either wise or brave and vice versa. Everyone who is either humble or creative is either not wise or not kind and vice versa. Everyone who is either not brave or humble is both not rich and not patient and vice versa. Everyone who is not curious or not strong is tall and vice versa. Everyone who is either not happy or not rich is either quiet or curious and vice versa. Everyone who is either not quiet or not rich is happy or not strong. If john is both calm and not old then john is both happy and curious and vice versa. Everyone who is not creative or not wise is humble or brave. If someone is calm or brave then mary is both strong and tall and vice versa. If someone is both not brave and not patient then someone is both happy and not quiet. Everyone who is both creative and not generous is rich or not wise. If someone is both not curious and wise then john is not strong or kind. Someone is either quiet or not generous. Someone is either quiet or curious. Lucy is either not tall or not strong. John is either not quiet or not creative. Someone is either brave or not humble. Mary is both not quiet and strong. Someone is generous. John is not happy. | Mary is not generous. | entailment | (![X]:((generous(X)&~calm(X))<=>(tall(X)&calm(X))))&
(![X]:((kind(X)<~>wise(X))=>(funny(X)&quiet(X))))&
(![X]:(~humble(X)<=>(old(X)&brave(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:((~kind(X)|old(X))<=>(wise(X)<~>brave(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:((~brave(X)<~>humble(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~curious(X)|~strong(X))<=>tall(X)))&
(![X]:((~happy(X)<~>~rich(X))<=>(quiet(X)<~>curious(X))))&
(![X]:((~quiet(X)<~>~rich(X))=>(happy(X)|~strong(X))))&
(((calm(john)&~old(john)))<=>((happy(john)&curious(john))))&
(![X]:((~creative(X)|~wise(X))=>(humble(X)|brave(X))))&
((?[X]:((calm(X)|brave(X))))<=>((strong(mary)&tall(mary))))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((creative(X)&~generous(X))=>(rich(X)|~wise(X))))&
((?[X]:((~curious(X)&wise(X))))=>((~strong(john)|kind(john))))&
(?[X]:((quiet(X)<~>~generous(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
((~tall(lucy)<~>~strong(lucy)))&
((~quiet(john)<~>~creative(john)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~quiet(mary)&strong(mary)))&
(?[X]:(generous(X)))&
(~happy(john)) | ~generous(mary) | [
"p0",
"p2",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2367183155606832276320672
% SZS output start Proof for 2367183155606832276320672
1. ! [X0] : ((~calm(X0) & generous(X0)) <=> (calm(X0) & tall(X0))) [input p0]
3. ! [X0] : (~humble(X0) <=> (brave(X0) & old(X0))) [input p2]
13. ? [X0] : (brave(X0) | calm(X0)) <=> (tall(mary) & strong(mary)) [input p12]
21. ? [X0] : (brave(X0) <~> ~humble(X0)) [input p20]
25. generous(mary) [input hypothesis]
38. ! [X0] : (((~calm(X0) & generous(X0)) | (~calm(X0) | ~tall(X0))) & ((calm(X0) & tall(X0)) | (calm(X0) | ~generous(X0)))) [nnf transformation 1]
39. ! [X0] : (((~calm(X0) & generous(X0)) | ~calm(X0) | ~tall(X0)) & ((calm(X0) & tall(X0)) | calm(X0) | ~generous(X0))) [flattening 38]
41. ! [X0] : ((~humble(X0) | (~brave(X0) | ~old(X0))) & ((brave(X0) & old(X0)) | humble(X0))) [nnf transformation 3]
42. ! [X0] : ((~humble(X0) | ~brave(X0) | ~old(X0)) & ((brave(X0) & old(X0)) | humble(X0))) [flattening 41]
59. (? [X0] : (brave(X0) | calm(X0)) | (~tall(mary) | ~strong(mary))) & ((tall(mary) & strong(mary)) | ! [X0] : (~brave(X0) & ~calm(X0))) [nnf transformation 13]
60. (? [X0] : (brave(X0) | calm(X0)) | ~tall(mary) | ~strong(mary)) & ((tall(mary) & strong(mary)) | ! [X0] : (~brave(X0) & ~calm(X0))) [flattening 59]
61. (? [X0] : (brave(X0) | calm(X0)) | ~tall(mary) | ~strong(mary)) & ((tall(mary) & strong(mary)) | ! [X1] : (~brave(X1) & ~calm(X1))) [rectify 60]
62. ? [X0] : (brave(X0) | calm(X0)) => (brave(sK2) | calm(sK2)) [choice axiom]
63. ((brave(sK2) | calm(sK2)) | ~tall(mary) | ~strong(mary)) & ((tall(mary) & strong(mary)) | ! [X1] : (~brave(X1) & ~calm(X1))) [skolemisation 61,62]
75. ? [X0] : ((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 21]
76. ? [X0] : ((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) => ((humble(sK6) | ~brave(sK6)) & (~humble(sK6) | brave(sK6))) [choice axiom]
77. (humble(sK6) | ~brave(sK6)) & (~humble(sK6) | brave(sK6)) [skolemisation 75,76]
81. calm(X0) | calm(X0) | ~generous(X0) [cnf transformation 39]
83. ~calm(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 39]
89. brave(X0) | humble(X0) [cnf transformation 42]
136. tall(mary) | ~brave(X1) [cnf transformation 63]
150. ~humble(sK6) | brave(sK6) [cnf transformation 77]
151. humble(sK6) | ~brave(sK6) [cnf transformation 77]
156. generous(mary) [cnf transformation 25]
157. ~generous(X0) | calm(X0) [duplicate literal removal 81]
158. ~tall(X0) | ~calm(X0) [duplicate literal removal 83]
210. 12 <=> tall(mary) [avatar definition]
211. tall(mary) <- (12) [avatar component clause 210]
223. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
224. ~brave(X1) <- (15) [avatar component clause 223]
225. 15 | 12 [avatar split clause 136,210,223]
296. humble(sK6) [subsumption resolution 151,89]
297. brave(sK6) [subsumption resolution 150,296]
304. calm(mary) [resolution 157,156]
305. ~calm(mary) <- (12) [resolution 158,211]
308. $false <- (12) [subsumption resolution 305,304]
309. ~12 [avatar contradiction clause 308]
310. $false <- (15) [resolution 224,297]
312. ~15 [avatar contradiction clause 310]
313. $false [avatar sat refutation 225,309,312]
% SZS output end Proof for 2367183155606832276320672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or funny is both patient and not happy.
Everyone who is old or not quiet is not wise.
Everyone who is kind or not wise is both kind and not wise.
Everyone who is not strong or not rich is both not brave and not humble.
Everyone who is either not happy or generous is either humble or generous and vice versa.
Everyone who is either not quiet or strong is not happy and vice versa.
If paul is patient or not funny then someone is not patient.
If lucy is not calm then paul is not strong.
Everyone who is either wise or not old is either creative or not creative and vice versa.
Everyone who is either tall or not old is not strong or not old and vice versa.
Everyone who is either rich or creative is not kind or patient and vice versa.
If someone is strong then someone is either curious or not brave and vice versa.
If mary is strong then john is either brave or quiet and vice versa.
Everyone who is not strong or generous is either wise or kind and vice versa.
Someone is both not creative and rich.
Lucy is either not generous or not old.
Fred is patient or not funny.
Fred is not quiet or rich.
Someone is strong or old.
Paul is curious.
Fred is calm or creative. | John is not patient. | neutral | (![X]:((happy(X)|funny(X))=>(patient(X)&~happy(X))))&
(![X]:((old(X)|~quiet(X))=>~wise(X)))&
(![X]:((kind(X)|~wise(X))=>(kind(X)&~wise(X))))&
(![X]:((~strong(X)|~rich(X))=>(~brave(X)&~humble(X))))&
(![X]:((~happy(X)<~>generous(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>~happy(X)))&
(((patient(paul)|~funny(paul)))=>(?[X]:(~patient(X))))&
((~calm(lucy))=>(~strong(paul)))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~old(X))<=>(~strong(X)|~old(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~kind(X)|patient(X))))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((strong(mary))<=>((brave(john)<~>quiet(john))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)<~>kind(X))))&
(?[X]:((~creative(X)&rich(X))))&
((~generous(lucy)<~>~old(lucy)))&
((patient(fred)|~funny(fred)))&
((~quiet(fred)|rich(fred)))&
(?[X]:((strong(X)|old(X))))&
(curious(paul))&
((calm(fred)|creative(fred))) | ~patient(john) | [] | null | 0 |
Everyone who is either funny or not humble is curious or not wise and vice versa.
Everyone who is curious or wise is both not patient and patient and vice versa.
Everyone who is both rich and patient is strong or old and vice versa.
Everyone who is old is both not curious and generous and vice versa.
If lucy is both patient and generous then paul is either not humble or creative.
If someone is either not old or not strong then someone is not brave and vice versa.
If someone is not rich then susan is generous and vice versa.
Everyone who is generous is funny.
Everyone who is wise is both not kind and brave.
If susan is either patient or not rich then mary is patient or not curious and vice versa.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is kind is either rich or quiet and vice versa.
Someone is strong.
Someone is either rich or not strong.
John is either not happy or funny.
Fred is not tall.
John is not quiet or not brave.
Someone is not wise or curious.
Someone is both humble and not wise.
Someone is both not wise and humble. | Alice is not curious. | entailment | (![X]:((funny(X)<~>~humble(X))<=>(curious(X)|~wise(X))))&
(![X]:((curious(X)|wise(X))<=>(~patient(X)&patient(X))))&
(![X]:((rich(X)&patient(X))<=>(strong(X)|old(X))))&
(![X]:(old(X)<=>(~curious(X)&generous(X))))&
(((patient(lucy)&generous(lucy)))=>((~humble(paul)<~>creative(paul))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~rich(X)))<=>(generous(susan)))&
(![X]:(generous(X)=>funny(X)))&
(![X]:(wise(X)=>(~kind(X)&brave(X))))&
(((patient(susan)<~>~rich(susan)))<=>((patient(mary)|~curious(mary))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(kind(X)<=>(rich(X)<~>quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)<~>~strong(X))))&
((~happy(john)<~>funny(john)))&
(~tall(fred))&
((~quiet(john)|~brave(john)))&
(?[X]:((~wise(X)|curious(X))))&
(?[X]:((humble(X)&~wise(X))))&
(?[X]:((~wise(X)&humble(X)))) | ~curious(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 443521548654777674598631
% SZS output start Proof for 443521548654777674598631
2. ! [X0] : ((wise(X0) | curious(X0)) <=> (patient(X0) & ~patient(X0))) [input p1]
24. curious(alice) [input hypothesis]
35. ! [X0] : (((wise(X0) | curious(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~wise(X0) & ~curious(X0)))) [nnf transformation 2]
36. ! [X0] : ((wise(X0) | curious(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~wise(X0) & ~curious(X0)))) [flattening 35]
84. ~patient(X0) | ~curious(X0) [cnf transformation 36]
86. patient(X0) | ~curious(X0) [cnf transformation 36]
146. curious(alice) [cnf transformation 24]
148. ~curious(X0) [subsumption resolution 84,86]
291. $false [subsumption resolution 146,148]
% SZS output end Proof for 443521548654777674598631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is tall then someone is not calm or not old and vice versa.
If john is either not tall or rich then lucy is old or patient and vice versa.
Everyone who is patient is both humble and rich.
Everyone who is both quiet and not generous is both not rich and curious.
Everyone who is funny is either not happy or not patient.
Everyone who is both calm and not quiet is either not humble or not wise.
If someone is either generous or curious then someone is humble and vice versa.
Everyone who is either tall or kind is wise.
If someone is not calm then john is either funny or not humble.
Everyone who is both not strong and kind is both not humble and brave and vice versa.
Everyone who is creative is generous or not strong and vice versa.
If john is calm then lucy is tall and vice versa.
Everyone who is not humble is either not humble or creative and vice versa.
Everyone who is either not rich or not quiet is creative and vice versa.
If someone is patient or not creative then someone is either old or generous and vice versa.
Everyone who is not brave is strong or not tall and vice versa.
Lucy is tall.
Paul is either wise or not humble.
Someone is either quiet or not rich.
Mary is both not creative and wise.
Lucy is both strong and not rich.
Someone is not brave or not generous. | Lucy is not generous. | entailment | ((tall(lucy))<=>(?[X]:((~calm(X)|~old(X)))))&
(((~tall(john)<~>rich(john)))<=>((old(lucy)|patient(lucy))))&
(![X]:(patient(X)=>(humble(X)&rich(X))))&
(![X]:((quiet(X)&~generous(X))=>(~rich(X)&curious(X))))&
(![X]:(funny(X)=>(~happy(X)<~>~patient(X))))&
(![X]:((calm(X)&~quiet(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)<~>kind(X))=>wise(X)))&
((?[X]:(~calm(X)))=>((funny(john)<~>~humble(john))))&
(![X]:((~strong(X)&kind(X))<=>(~humble(X)&brave(X))))&
(![X]:(creative(X)<=>(generous(X)|~strong(X))))&
((calm(john))<=>(tall(lucy)))&
(![X]:(~humble(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>creative(X)))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(strong(X)|~tall(X))))&
(tall(lucy))&
((wise(paul)<~>~humble(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((~creative(mary)&wise(mary)))&
((strong(lucy)&~rich(lucy)))&
(?[X]:((~brave(X)|~generous(X)))) | ~generous(lucy) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5923471927908132010383250
% SZS output start Proof for 5923471927908132010383250
11. ! [X0] : (creative(X0) <=> (~strong(X0) | generous(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> (~humble(X0) <~> creative(X0))) [input p12]
23. generous(lucy) [input hypothesis]
51. ! [X0] : ((creative(X0) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ~creative(X0))) [nnf transformation 11]
52. ! [X0] : ((creative(X0) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ~creative(X0))) [flattening 51]
54. ! [X0] : ((~humble(X0) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) & (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | humble(X0))) [nnf transformation 13]
99. ~generous(X0) | creative(X0) [cnf transformation 52]
104. ~creative(X0) | humble(X0) | humble(X0) [cnf transformation 54]
106. ~humble(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 54]
130. generous(lucy) [cnf transformation 23]
131. ~creative(X0) | humble(X0) [duplicate literal removal 104]
132. ~humble(X0) | ~creative(X0) [duplicate literal removal 106]
217. ~creative(X0) [subsumption resolution 131,132]
263. creative(lucy) [resolution 99,130]
265. $false [subsumption resolution 263,217]
% SZS output end Proof for 5923471927908132010383250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both old and kind then susan is not brave or not kind and vice versa.
If paul is either old or not patient then someone is not humble or not funny.
If someone is either brave or creative then mary is wise and vice versa.
Everyone who is either not tall or strong is not quiet or not calm.
Everyone who is both kind and not rich is either humble or rich and vice versa.
Everyone who is curious is not humble and vice versa.
Everyone who is either not wise or rich is not old.
Everyone who is either not creative or not tall is both not funny and not humble and vice versa.
Everyone who is wise is both not wise and not calm and vice versa.
If someone is not strong then someone is either wise or rich.
Everyone who is both not strong and not patient is both not calm and old.
If someone is both curious and old then john is not kind and vice versa.
Everyone who is not strong is patient and vice versa.
If someone is patient then someone is not kind or happy.
Everyone who is both kind and generous is both calm and not brave and vice versa.
If mary is either strong or brave then someone is either not humble or creative.
Someone is both not wise and not quiet.
Someone is either not generous or not creative.
Paul is tall.
Someone is not quiet or not calm.
Someone is not strong.
Mary is creative or funny. | Susan is kind. | entailment | (((old(susan)&kind(susan)))<=>((~brave(susan)|~kind(susan))))&
(((old(paul)<~>~patient(paul)))=>(?[X]:((~humble(X)|~funny(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>(wise(mary)))&
(![X]:((~tall(X)<~>strong(X))=>(~quiet(X)|~calm(X))))&
(![X]:((kind(X)&~rich(X))<=>(humble(X)<~>rich(X))))&
(![X]:(curious(X)<=>~humble(X)))&
(![X]:((~wise(X)<~>rich(X))=>~old(X)))&
(![X]:((~creative(X)<~>~tall(X))<=>(~funny(X)&~humble(X))))&
(![X]:(wise(X)<=>(~wise(X)&~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~calm(X)&old(X))))&
((?[X]:((curious(X)&old(X))))<=>(~kind(john)))&
(![X]:(~strong(X)<=>patient(X)))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((kind(X)&generous(X))<=>(calm(X)&~brave(X))))&
(((strong(mary)<~>brave(mary)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(tall(paul))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:(~strong(X)))&
((creative(mary)|funny(mary))) | kind(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5726196654842817561455122
% SZS output start Proof for 5726196654842817561455122
1. (kind(susan) & old(susan)) <=> (~kind(susan) | ~brave(susan)) [input p0]
23. ~kind(susan) [input hypothesis]
36. ((kind(susan) & old(susan)) | (kind(susan) & brave(susan))) & ((~kind(susan) | ~brave(susan)) | (~kind(susan) | ~old(susan))) [nnf transformation 1]
37. ((kind(susan) & old(susan)) | (kind(susan) & brave(susan))) & (~kind(susan) | ~brave(susan) | ~kind(susan) | ~old(susan)) [flattening 36]
78. kind(susan) | kind(susan) [cnf transformation 37]
127. ~kind(susan) [cnf transformation 23]
133. kind(susan) [duplicate literal removal 78]
252. $false [subsumption resolution 127,133]
% SZS output end Proof for 5726196654842817561455122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both curious and humble then susan is not rich or not old.
If someone is not old or kind then someone is either not strong or old.
If susan is either not calm or not kind then someone is curious.
If alice is not rich or curious then john is either calm or wise.
Everyone who is either old or not generous is not tall or quiet.
If someone is either curious or not kind then lucy is quiet or funny.
Everyone who is creative or not curious is not curious and vice versa.
Everyone who is not happy or calm is not quiet.
If someone is not brave or not calm then alice is not wise.
Everyone who is not kind is both brave and strong and vice versa.
Everyone who is either rich or not patient is both not happy and curious.
Everyone who is either not quiet or brave is either rich or not wise.
If someone is not generous or not wise then alice is not old or kind and vice versa.
If alice is both tall and curious then john is creative.
If fred is both not curious and not rich then susan is both brave and funny.
If fred is not tall or old then mary is both not tall and not quiet.
Someone is both not wise and humble.
Someone is either not generous or curious.
Someone is generous.
Paul is both humble and not curious.
Paul is patient.
Someone is brave or old.
Someone is both quiet and not patient.
Someone is creative. | Alice is wise. | contradiction | (((curious(lucy)&humble(lucy)))=>((~rich(susan)|~old(susan))))&
((?[X]:((~old(X)|kind(X))))=>(?[X]:((~strong(X)<~>old(X)))))&
(((~calm(susan)<~>~kind(susan)))=>(?[X]:(curious(X))))&
(((~rich(alice)|curious(alice)))=>((calm(john)<~>wise(john))))&
(![X]:((old(X)<~>~generous(X))=>(~tall(X)|quiet(X))))&
((?[X]:((curious(X)<~>~kind(X))))=>((quiet(lucy)|funny(lucy))))&
(![X]:((creative(X)|~curious(X))<=>~curious(X)))&
(![X]:((~happy(X)|calm(X))=>~quiet(X)))&
((?[X]:((~brave(X)|~calm(X))))=>(~wise(alice)))&
(![X]:(~kind(X)<=>(brave(X)&strong(X))))&
(![X]:((rich(X)<~>~patient(X))=>(~happy(X)&curious(X))))&
(![X]:((~quiet(X)<~>brave(X))=>(rich(X)<~>~wise(X))))&
((?[X]:((~generous(X)|~wise(X))))<=>((~old(alice)|kind(alice))))&
(((tall(alice)&curious(alice)))=>(creative(john)))&
(((~curious(fred)&~rich(fred)))=>((brave(susan)&funny(susan))))&
(((~tall(fred)|old(fred)))=>((~tall(mary)&~quiet(mary))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~generous(X)<~>curious(X))))&
(?[X]:(generous(X)))&
((humble(paul)&~curious(paul)))&
(patient(paul))&
(?[X]:((brave(X)|old(X))))&
(?[X]:((quiet(X)&~patient(X))))&
(?[X]:(creative(X))) | wise(alice) | [
"p7",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4091686423611050820967581
% SZS output start Proof for 4091686423611050820967581
8. ! [X0] : ((calm(X0) | ~happy(X0)) => ~quiet(X0)) [input p7]
9. ? [X0] : (~calm(X0) | ~brave(X0)) => ~wise(alice) [input p8]
23. ? [X0] : (~patient(X0) & quiet(X0)) [input p22]
25. wise(alice) [input hypothesis]
36. ! [X0] : (~quiet(X0) | (~calm(X0) & happy(X0))) [ennf transformation 8]
37. ~wise(alice) | ! [X0] : (calm(X0) & brave(X0)) [ennf transformation 9]
74. ? [X0] : (~patient(X0) & quiet(X0)) => (~patient(sK7) & quiet(sK7)) [choice axiom]
75. ~patient(sK7) & quiet(sK7) [skolemisation 23,74]
95. ~quiet(X0) | ~calm(X0) [cnf transformation 36]
97. ~wise(alice) | calm(X0) [cnf transformation 37]
128. quiet(sK7) [cnf transformation 75]
131. wise(alice) [cnf transformation 25]
202. 16 <=> ! [X0] : calm(X0) [avatar definition]
203. calm(X0) <- (16) [avatar component clause 202]
205. 17 <=> wise(alice) [avatar definition]
208. 16 | ~17 [avatar split clause 97,205,202]
300. 17 [avatar split clause 131,205]
305. ~calm(sK7) [resolution 95,128]
306. $false <- (16) [subsumption resolution 305,203]
307. ~16 [avatar contradiction clause 306]
308. $false [avatar sat refutation 208,300,307]
% SZS output end Proof for 4091686423611050820967581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not generous is creative or not rich and vice versa.
Everyone who is quiet or patient is not calm and vice versa.
If paul is brave then fred is both not tall and generous and vice versa.
If someone is tall or wise then john is both calm and not calm and vice versa.
Everyone who is curious is either not old or not wise and vice versa.
If john is either happy or calm then susan is either brave or kind and vice versa.
Everyone who is either not curious or not generous is both rich and curious.
Everyone who is brave is either not quiet or not calm and vice versa.
If lucy is either not tall or tall then someone is both rich and not wise and vice versa.
Everyone who is not old is humble or old.
If someone is both not old and generous then someone is both not creative and creative and vice versa.
Everyone who is wise or calm is humble or rich.
Everyone who is not happy is either not tall or not wise and vice versa.
If someone is either not strong or wise then someone is funny and vice versa.
If mary is tall or not patient then someone is quiet or old and vice versa.
Fred is not calm or calm.
Mary is either generous or not rich.
Susan is either not creative or not funny.
John is either not rich or not humble. | Mary is not curious. | contradiction | (![X]:((~rich(X)<~>~generous(X))<=>(creative(X)|~rich(X))))&
(![X]:((quiet(X)|patient(X))<=>~calm(X)))&
((brave(paul))<=>((~tall(fred)&generous(fred))))&
((?[X]:((tall(X)|wise(X))))<=>((calm(john)&~calm(john))))&
(![X]:(curious(X)<=>(~old(X)<~>~wise(X))))&
(((happy(john)<~>calm(john)))<=>((brave(susan)<~>kind(susan))))&
(![X]:((~curious(X)<~>~generous(X))=>(rich(X)&curious(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~calm(X))))&
(((~tall(lucy)<~>tall(lucy)))<=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:(~old(X)=>(humble(X)|old(X))))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((wise(X)|calm(X))=>(humble(X)|rich(X))))&
(![X]:(~happy(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~strong(X)<~>wise(X))))<=>(?[X]:(funny(X))))&
(((tall(mary)|~patient(mary)))<=>(?[X]:((quiet(X)|old(X)))))&
((~calm(fred)|calm(fred)))&
((generous(mary)<~>~rich(mary)))&
((~creative(susan)<~>~funny(susan)))&
((~rich(john)<~>~humble(john))) | ~curious(mary) | [
"p0",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5429381143462803204682114
% SZS output start Proof for 5429381143462803204682114
1. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> (~rich(X0) | creative(X0))) [input p0]
7. ! [X0] : ((~curious(X0) <~> ~generous(X0)) => (curious(X0) & rich(X0))) [input p6]
17. generous(mary) <~> ~rich(mary) [input p16]
20. ~curious(mary) [input hypothesis]
23. ! [X0] : ((curious(X0) & rich(X0)) | (~curious(X0) <=> ~generous(X0))) [ennf transformation 7]
28. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (rich(X0) & ~creative(X0))) & ((~rich(X0) | creative(X0)) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 1]
29. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (rich(X0) & ~creative(X0))) & (~rich(X0) | creative(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [flattening 28]
41. ! [X0] : ((curious(X0) & rich(X0)) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) [nnf transformation 23]
63. (rich(mary) | ~generous(mary)) & (~rich(mary) | generous(mary)) [nnf transformation 17]
71. generous(X0) | rich(X0) | rich(X0) [cnf transformation 29]
97. curious(X0) | ~generous(X0) | curious(X0) [cnf transformation 41]
129. ~rich(mary) | generous(mary) [cnf transformation 63]
130. rich(mary) | ~generous(mary) [cnf transformation 63]
135. ~curious(mary) [cnf transformation 20]
141. ~generous(X0) | curious(X0) [duplicate literal removal 97]
143. generous(X0) | rich(X0) [duplicate literal removal 71]
272. rich(mary) [subsumption resolution 130,143]
273. generous(mary) [subsumption resolution 129,272]
300. curious(mary) [resolution 141,273]
301. $false [subsumption resolution 300,135]
% SZS output end Proof for 5429381143462803204682114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is rich.
If john is funny or not strong then someone is not old or patient.
If paul is not wise then alice is both not curious and not calm and vice versa.
Everyone who is not humble is both not calm and brave.
If paul is either patient or not humble then fred is wise or strong.
Everyone who is funny or not wise is rich and vice versa.
Everyone who is either kind or not kind is either not rich or not tall.
Everyone who is tall is both not patient and not wise and vice versa.
Everyone who is either brave or humble is strong or generous.
If paul is not happy then john is both brave and quiet and vice versa.
Everyone who is both not patient and not quiet is both humble and not brave.
Everyone who is not patient or not funny is either not wise or not patient and vice versa.
Everyone who is either not kind or tall is not generous.
Everyone who is not quiet is either rich or not old and vice versa.
Everyone who is both funny and calm is not wise or humble and vice versa.
Mary is not happy or patient.
Susan is both not generous and brave.
Alice is kind.
Fred is both patient and kind.
Fred is either humble or creative.
John is either calm or not tall.
Fred is either strong or not patient. | John is not tall. | entailment | (![X]:(~tall(X)=>rich(X)))&
(((funny(john)|~strong(john)))=>(?[X]:((~old(X)|patient(X)))))&
((~wise(paul))<=>((~curious(alice)&~calm(alice))))&
(![X]:(~humble(X)=>(~calm(X)&brave(X))))&
(((patient(paul)<~>~humble(paul)))=>((wise(fred)|strong(fred))))&
(![X]:((funny(X)|~wise(X))<=>rich(X)))&
(![X]:((kind(X)<~>~kind(X))=>(~rich(X)<~>~tall(X))))&
(![X]:(tall(X)<=>(~patient(X)&~wise(X))))&
(![X]:((brave(X)<~>humble(X))=>(strong(X)|generous(X))))&
((~happy(paul))<=>((brave(john)&quiet(john))))&
(![X]:((~patient(X)&~quiet(X))=>(humble(X)&~brave(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>tall(X))=>~generous(X)))&
(![X]:(~quiet(X)<=>(rich(X)<~>~old(X))))&
(![X]:((funny(X)&calm(X))<=>(~wise(X)|humble(X))))&
((~happy(mary)|patient(mary)))&
((~generous(susan)&brave(susan)))&
(kind(alice))&
((patient(fred)&kind(fred)))&
((humble(fred)<~>creative(fred)))&
((calm(john)<~>~tall(john)))&
((strong(fred)<~>~patient(fred))) | ~tall(john) | [
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1272157575591569145500818
% SZS output start Proof for 1272157575591569145500818
8. ! [X0] : (tall(X0) <=> (~wise(X0) & ~patient(X0))) [input p7]
12. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~wise(X0) <~> ~patient(X0))) [input p11]
23. tall(john) [input hypothesis]
43. ! [X0] : ((tall(X0) | (wise(X0) | patient(X0))) & ((~wise(X0) & ~patient(X0)) | ~tall(X0))) [nnf transformation 8]
44. ! [X0] : ((tall(X0) | wise(X0) | patient(X0)) & ((~wise(X0) & ~patient(X0)) | ~tall(X0))) [flattening 43]
48. ! [X0] : (((~funny(X0) | ~patient(X0)) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (funny(X0) & patient(X0)))) [nnf transformation 12]
49. ! [X0] : ((~funny(X0) | ~patient(X0) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0)))) & (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (funny(X0) & patient(X0)))) [flattening 48]
74. ~patient(X0) | ~tall(X0) [cnf transformation 44]
75. ~wise(X0) | ~tall(X0) [cnf transformation 44]
86. patient(X0) | wise(X0) | patient(X0) [cnf transformation 49]
113. tall(john) [cnf transformation 23]
114. wise(X0) | patient(X0) [duplicate literal removal 86]
213. 20 <=> tall(john) [avatar definition]
215. tall(john) <- (20) [avatar component clause 213]
220. 20 [avatar split clause 113,213]
240. patient(X0) | ~tall(X0) [resolution 114,75]
242. ~tall(X0) [subsumption resolution 240,74]
247. $false <- (20) [resolution 242,215]
248. ~20 [avatar contradiction clause 247]
249. $false [avatar sat refutation 220,248]
% SZS output end Proof for 1272157575591569145500818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not brave and not happy then mary is generous or not patient and vice versa. If someone is both quiet and rich then lucy is not curious and vice versa. Everyone who is both not humble and happy is not brave and vice versa. If john is tall or strong then fred is either curious or not kind. Everyone who is tall is either old or not curious and vice versa. Everyone who is patient is both not funny and brave and vice versa. Everyone who is either not happy or funny is either kind or calm. If mary is wise or not humble then fred is either not old or calm and vice versa. Everyone who is calm or not rich is not happy or funny and vice versa. Everyone who is both not quiet and curious is either not kind or not quiet and vice versa. Everyone who is either curious or not strong is brave and vice versa. If someone is both quiet and not creative then someone is either tall or not old. Everyone who is either not rich or wise is not rich or funny and vice versa. Everyone who is quiet is brave or calm. Everyone who is not humble or humble is both old and not humble and vice versa. Someone is either creative or not kind. Someone is both patient and not creative. Alice is either tall or kind. Fred is both strong and tall. Lucy is brave. Someone is not curious. Someone is either happy or curious. | Alice is brave. | entailment | (((~brave(mary)&~happy(mary)))<=>((generous(mary)|~patient(mary))))&
((?[X]:((quiet(X)&rich(X))))<=>(~curious(lucy)))&
(![X]:((~humble(X)&happy(X))<=>~brave(X)))&
(((tall(john)|strong(john)))=>((curious(fred)<~>~kind(fred))))&
(![X]:(tall(X)<=>(old(X)<~>~curious(X))))&
(![X]:(patient(X)<=>(~funny(X)&brave(X))))&
(![X]:((~happy(X)<~>funny(X))=>(kind(X)<~>calm(X))))&
(((wise(mary)|~humble(mary)))<=>((~old(fred)<~>calm(fred))))&
(![X]:((calm(X)|~rich(X))<=>(~happy(X)|funny(X))))&
(![X]:((~quiet(X)&curious(X))<=>(~kind(X)<~>~quiet(X))))&
(![X]:((curious(X)<~>~strong(X))<=>brave(X)))&
((?[X]:((quiet(X)&~creative(X))))=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((~rich(X)<~>wise(X))<=>(~rich(X)|funny(X))))&
(![X]:(quiet(X)=>(brave(X)|calm(X))))&
(![X]:((~humble(X)|humble(X))<=>(old(X)&~humble(X))))&
(?[X]:((creative(X)<~>~kind(X))))&
(?[X]:((patient(X)&~creative(X))))&
((tall(alice)<~>kind(alice)))&
((strong(fred)&tall(fred)))&
(brave(lucy))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>curious(X)))) | brave(alice) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8903688719717672408196502
% SZS output start Proof for 8903688719717672408196502
3. ! [X0] : ((happy(X0) & ~humble(X0)) <=> ~brave(X0)) [input p2]
5. ! [X0] : (tall(X0) <=> (old(X0) <~> ~curious(X0))) [input p4]
7. ! [X0] : ((~happy(X0) <~> funny(X0)) => (kind(X0) <~> calm(X0))) [input p6]
9. ! [X0] : ((~rich(X0) | calm(X0)) <=> (funny(X0) | ~happy(X0))) [input p8]
10. ! [X0] : ((curious(X0) & ~quiet(X0)) <=> (~kind(X0) <~> ~quiet(X0))) [input p9]
14. ! [X0] : (quiet(X0) => (calm(X0) | brave(X0))) [input p13]
15. ! [X0] : ((humble(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p14]
18. tall(alice) <~> kind(alice) [input p17]
23. ~brave(alice) [input hypothesis]
26. ! [X0] : ((kind(X0) <~> calm(X0)) | (~happy(X0) <=> funny(X0))) [ennf transformation 7]
28. ! [X0] : ((calm(X0) | brave(X0)) | ~quiet(X0)) [ennf transformation 14]
29. ! [X0] : (calm(X0) | brave(X0) | ~quiet(X0)) [flattening 28]
36. ! [X0] : (((happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) | humble(X0)))) [nnf transformation 3]
37. ! [X0] : (((happy(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | ~happy(X0) | humble(X0))) [flattening 36]
39. ! [X0] : ((tall(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) & (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | ~tall(X0))) [nnf transformation 5]
42. ! [X0] : (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | ((~happy(X0) | ~funny(X0)) & (funny(X0) | happy(X0)))) [nnf transformation 26]
45. ! [X0] : (((~rich(X0) | calm(X0)) | (~funny(X0) & happy(X0))) & ((funny(X0) | ~happy(X0)) | (rich(X0) & ~calm(X0)))) [nnf transformation 9]
46. ! [X0] : ((~rich(X0) | calm(X0) | (~funny(X0) & happy(X0))) & (funny(X0) | ~happy(X0) | (rich(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : (((curious(X0) & ~quiet(X0)) | ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0)))) & (((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | (~curious(X0) | quiet(X0)))) [nnf transformation 10]
48. ! [X0] : (((curious(X0) & ~quiet(X0)) | ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0)))) & (((quiet(X0) | kind(X0)) & (~quiet(X0) | ~kind(X0))) | ~curious(X0) | quiet(X0))) [flattening 47]
56. ! [X0] : (((humble(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (~humble(X0) & humble(X0)))) [nnf transformation 15]
57. ! [X0] : ((humble(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (~humble(X0) & humble(X0)))) [flattening 56]
63. (~kind(alice) | ~tall(alice)) & (kind(alice) | tall(alice)) [nnf transformation 18]
79. happy(X0) | brave(X0) [cnf transformation 37]
85. ~old(X0) | curious(X0) | ~tall(X0) [cnf transformation 39]
86. ~old(X0) | ~curious(X0) | tall(X0) [cnf transformation 39]
94. ~calm(X0) | ~kind(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 42]
101. ~calm(X0) | ~happy(X0) | funny(X0) [cnf transformation 46]
106. quiet(X0) | kind(X0) | ~curious(X0) | quiet(X0) [cnf transformation 48]
107. ~quiet(X0) | ~quiet(X0) | kind(X0) [cnf transformation 48]
110. ~kind(X0) | curious(X0) | quiet(X0) [cnf transformation 48]
123. ~quiet(X0) | brave(X0) | calm(X0) [cnf transformation 29]
124. old(X0) | humble(X0) [cnf transformation 57]
127. ~humble(X0) | ~humble(X0) [cnf transformation 57]
133. kind(alice) | tall(alice) [cnf transformation 63]
134. ~kind(alice) | ~tall(alice) [cnf transformation 63]
141. ~brave(alice) [cnf transformation 23]
142. ~humble(X0) [duplicate literal removal 127]
146. quiet(X0) | kind(X0) | ~curious(X0) [duplicate literal removal 106]
147. ~quiet(X0) | kind(X0) [duplicate literal removal 107]
229. ~curious(X0) | kind(X0) [subsumption resolution 146,147]
244. old(X0) [subsumption resolution 124,142]
256. 22 <=> tall(alice) [avatar definition]
257. tall(alice) <- (22) [avatar component clause 256]
258. ~tall(alice) <- (~22) [avatar component clause 256]
260. 23 <=> kind(alice) [avatar definition]
261. kind(alice) <- (23) [avatar component clause 260]
262. ~kind(alice) <- (~23) [avatar component clause 260]
263. ~22 | ~23 [avatar split clause 134,260,256]
264. 22 | 23 [avatar split clause 133,260,256]
299. ~tall(X0) | curious(X0) [resolution 85,244]
301. curious(alice) <- (22) [resolution 299,257]
305. ~curious(X0) | tall(X0) [resolution 86,244]
306. kind(alice) <- (22) [resolution 301,229]
307. $false <- (22, ~23) [subsumption resolution 306,262]
308. ~22 | 23 [avatar contradiction clause 307]
389. curious(alice) | quiet(alice) <- (23) [resolution 110,261]
392. 37 <=> quiet(alice) [avatar definition]
394. quiet(alice) <- (37) [avatar component clause 392]
396. 38 <=> curious(alice) [avatar definition]
398. curious(alice) <- (38) [avatar component clause 396]
399. 37 | 38 | ~23 [avatar split clause 389,260,396,392]
450. brave(alice) | calm(alice) <- (37) [resolution 123,394]
456. calm(alice) <- (37) [subsumption resolution 450,141]
491. ~kind(alice) | ~happy(alice) | ~funny(alice) <- (37) [resolution 456,94]
493. ~happy(alice) | funny(alice) <- (37) [resolution 456,101]
494. ~happy(alice) | ~funny(alice) <- (23, 37) [subsumption resolution 491,261]
496. 46 <=> funny(alice) [avatar definition]
500. 47 <=> happy(alice) [avatar definition]
502. ~happy(alice) <- (~47) [avatar component clause 500]
503. ~46 | ~47 | ~23 | ~37 [avatar split clause 494,392,260,500,496]
506. 46 | ~47 | ~37 [avatar split clause 493,392,500,496]
508. tall(alice) <- (38) [resolution 398,305]
510. $false <- (~22, 38) [subsumption resolution 508,258]
511. 22 | ~38 [avatar contradiction clause 510]
537. brave(alice) <- (~47) [resolution 502,79]
538. $false <- (~47) [subsumption resolution 537,141]
539. 47 [avatar contradiction clause 538]
540. $false [avatar sat refutation 263,264,308,399,503,506,511,539]
% SZS output end Proof for 8903688719717672408196502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or humble is happy.
If someone is both wise and not curious then someone is tall.
If mary is wise or not tall then someone is both not happy and not patient.
Everyone who is creative is both curious and not quiet.
If someone is quiet then mary is rich or calm and vice versa.
Everyone who is patient is not patient or happy and vice versa.
If paul is both kind and tall then susan is either not calm or creative and vice versa.
Everyone who is not old or creative is both calm and not brave and vice versa.
Everyone who is creative or not happy is strong.
If alice is both not patient and quiet then someone is either not quiet or not generous and vice versa.
Everyone who is not rich or not curious is not tall and vice versa.
If someone is both rich and generous then someone is both generous and not funny and vice versa.
If susan is both strong and old then mary is tall or not strong.
Everyone who is not wise is happy or humble.
Everyone who is not tall is both not creative and not happy.
If someone is both funny and not humble then someone is both not happy and generous and vice versa.
Someone is either not happy or wise.
Someone is both brave and not generous.
Paul is both not old and tall.
Alice is old or kind.
John is tall.
Fred is not kind.
Someone is both not brave and quiet.
Someone is either not curious or not calm. | Paul is happy. | entailment | (![X]:((~happy(X)<~>humble(X))=>happy(X)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(tall(X))))&
(((wise(mary)|~tall(mary)))=>(?[X]:((~happy(X)&~patient(X)))))&
(![X]:(creative(X)=>(curious(X)&~quiet(X))))&
((?[X]:(quiet(X)))<=>((rich(mary)|calm(mary))))&
(![X]:(patient(X)<=>(~patient(X)|happy(X))))&
(((kind(paul)&tall(paul)))<=>((~calm(susan)<~>creative(susan))))&
(![X]:((~old(X)|creative(X))<=>(calm(X)&~brave(X))))&
(![X]:((creative(X)|~happy(X))=>strong(X)))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~rich(X)|~curious(X))<=>~tall(X)))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
(((strong(susan)&old(susan)))=>((tall(mary)|~strong(mary))))&
(![X]:(~wise(X)=>(happy(X)|humble(X))))&
(![X]:(~tall(X)=>(~creative(X)&~happy(X))))&
((?[X]:((funny(X)&~humble(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((brave(X)&~generous(X))))&
((~old(paul)&tall(paul)))&
((old(alice)|kind(alice)))&
(tall(john))&
(~kind(fred))&
(?[X]:((~brave(X)&quiet(X))))&
(?[X]:((~curious(X)<~>~calm(X)))) | happy(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7711919116908449541812869
% SZS output start Proof for 7711919116908449541812869
6. ! [X0] : (patient(X0) <=> (happy(X0) | ~patient(X0))) [input p5]
25. ~happy(paul) [input hypothesis]
50. ! [X0] : ((patient(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 6]
51. ! [X0] : ((patient(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~patient(X0))) [flattening 50]
95. happy(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
96. patient(X0) | patient(X0) [cnf transformation 51]
145. ~happy(paul) [cnf transformation 25]
146. happy(X0) | ~patient(X0) [duplicate literal removal 95]
147. patient(X0) [duplicate literal removal 96]
195. happy(X0) [subsumption resolution 146,147]
304. $false [subsumption resolution 145,195]
% SZS output end Proof for 7711919116908449541812869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and humble is not generous or happy and vice versa.
If susan is humble then fred is either not strong or not kind and vice versa.
Everyone who is generous or not patient is quiet or brave and vice versa.
Everyone who is not humble is either not creative or not patient.
If alice is happy or not quiet then fred is not kind or not quiet and vice versa.
If someone is both not quiet and curious then someone is wise or not wise.
If someone is humble or patient then john is not rich or kind and vice versa.
Everyone who is old is humble.
Everyone who is quiet or not patient is strong and vice versa.
If someone is both not generous and funny then someone is not generous or not rich and vice versa.
Everyone who is not quiet is either not tall or rich and vice versa.
Everyone who is quiet is both not curious and not old.
If someone is not kind or not strong then alice is both kind and rich.
Everyone who is calm is both kind and funny and vice versa.
Everyone who is not generous or calm is tall or not brave and vice versa.
If someone is not generous or creative then john is both creative and not tall.
Alice is either not brave or not funny.
Someone is both not kind and not generous.
Someone is both not calm and curious.
John is kind or not strong.
Susan is both funny and not curious.
Susan is either happy or curious.
Alice is humble or not strong. | Alice is curious. | neutral | (![X]:((strong(X)&humble(X))<=>(~generous(X)|happy(X))))&
((humble(susan))<=>((~strong(fred)<~>~kind(fred))))&
(![X]:((generous(X)|~patient(X))<=>(quiet(X)|brave(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~patient(X))))&
(((happy(alice)|~quiet(alice)))<=>((~kind(fred)|~quiet(fred))))&
((?[X]:((~quiet(X)&curious(X))))=>(?[X]:((wise(X)|~wise(X)))))&
((?[X]:((humble(X)|patient(X))))<=>((~rich(john)|kind(john))))&
(![X]:(old(X)=>humble(X)))&
(![X]:((quiet(X)|~patient(X))<=>strong(X)))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>rich(X))))&
(![X]:(quiet(X)=>(~curious(X)&~old(X))))&
((?[X]:((~kind(X)|~strong(X))))=>((kind(alice)&rich(alice))))&
(![X]:(calm(X)<=>(kind(X)&funny(X))))&
(![X]:((~generous(X)|calm(X))<=>(tall(X)|~brave(X))))&
((?[X]:((~generous(X)|creative(X))))=>((creative(john)&~tall(john))))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~calm(X)&curious(X))))&
((kind(john)|~strong(john)))&
((funny(susan)&~curious(susan)))&
((happy(susan)<~>curious(susan)))&
((humble(alice)|~strong(alice))) | curious(alice) | [] | null | 0 |
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