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 either not tall or not humble is either brave or not humble and vice versa.
Everyone who is not wise or not quiet is kind.
Everyone who is both not generous and not funny is either wise or humble and vice versa.
If john is both curious and not strong then lucy is calm or strong and vice versa.
Everyone who is not calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
If fred is not generous then fred is either not tall or patient and vice versa.
Someone is not brave or happy.
Susan is not patient.
Fred is calm.
Alice is both kind and humble.
Someone is both kind and patient. | Mary is quiet. | entailment | (![X]:((~tall(X)<~>~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)<~>humble(X))))&
(((curious(john)&~strong(john)))<=>((calm(lucy)|strong(lucy))))&
(![X]:(~calm(X)<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(?[X]:((~brave(X)|happy(X))))&
(~patient(susan))&
(calm(fred))&
((kind(alice)&humble(alice)))&
(?[X]:((kind(X)&patient(X)))) | quiet(mary) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 52575586648430574276968
% SZS output start Proof for 52575586648430574276968
9. ! [X0] : ((~calm(X0) | ~strong(X0)) => (quiet(X0) & calm(X0))) [input p8]
14. ? [X0] : (calm(X0) | ~calm(X0)) <=> ~strong(mary) [input p13]
21. ~quiet(mary) [input hypothesis]
29. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & strong(X0))) [ennf transformation 9]
51. (? [X0] : (calm(X0) | ~calm(X0)) | strong(mary)) & (~strong(mary) | ! [X0] : (~calm(X0) & calm(X0))) [nnf transformation 14]
52. (? [X0] : (calm(X0) | ~calm(X0)) | strong(mary)) & (~strong(mary) | ! [X1] : (~calm(X1) & calm(X1))) [rectify 51]
53. ? [X0] : (calm(X0) | ~calm(X0)) => (calm(sK1) | ~calm(sK1)) [choice axiom]
54. ((calm(sK1) | ~calm(sK1)) | strong(mary)) & (~strong(mary) | ! [X1] : (~calm(X1) & calm(X1))) [skolemisation 52,53]
93. calm(X0) | calm(X0) [cnf transformation 29]
94. strong(X0) | quiet(X0) [cnf transformation 29]
111. ~strong(mary) | ~calm(X1) [cnf transformation 54]
124. ~quiet(mary) [cnf transformation 21]
127. calm(X0) [duplicate literal removal 93]
209. ~strong(mary) [subsumption resolution 111,127]
233. quiet(mary) [resolution 94,209]
234. $false [subsumption resolution 233,124]
% SZS output end Proof for 52575586648430574276968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is patient or not wise then fred is either not strong or patient.
Everyone who is not humble is not generous or quiet.
Everyone who is not wise or not quiet is both not brave and wise and vice versa.
Everyone who is kind or quiet is not quiet or tall.
Everyone who is quiet is both not creative and not calm and vice versa.
If alice is not kind then alice is both not kind and calm and vice versa.
Everyone who is both not happy and not patient is either not kind or not humble and vice versa.
Everyone who is generous or kind is creative and vice versa.
Everyone who is either not funny or not generous is not wise or funny.
If paul is either strong or brave then someone is both brave and quiet and vice versa.
If someone is both rich and not calm then someone is either curious or funny and vice versa.
Everyone who is either humble or patient is either not funny or curious.
If someone is both humble and not happy then susan is both humble and curious.
Everyone who is not calm is both not quiet and not generous.
If someone is quiet then someone is not calm or not rich.
Everyone who is both not curious and not wise is both not happy and not brave and vice versa.
Someone is either not rich or happy.
Paul is not generous.
Lucy is both not patient and funny.
Mary is not kind or wise.
Paul is either not creative or not curious.
Lucy is either not strong or funny. | Mary is not quiet. | entailment | (((patient(mary)|~wise(mary)))=>((~strong(fred)<~>patient(fred))))&
(![X]:(~humble(X)=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)&wise(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|tall(X))))&
(![X]:(quiet(X)<=>(~creative(X)&~calm(X))))&
((~kind(alice))<=>((~kind(alice)&calm(alice))))&
(![X]:((~happy(X)&~patient(X))<=>(~kind(X)<~>~humble(X))))&
(![X]:((generous(X)|kind(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~generous(X))=>(~wise(X)|funny(X))))&
(((strong(paul)<~>brave(paul)))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)<~>patient(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((humble(X)&~happy(X))))=>((humble(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(~happy(X)&~brave(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(~generous(paul))&
((~patient(lucy)&funny(lucy)))&
((~kind(mary)|wise(mary)))&
((~creative(paul)<~>~curious(paul)))&
((~strong(lucy)<~>funny(lucy))) | ~quiet(mary) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7058992262402513054397732
% SZS output start Proof for 7058992262402513054397732
5. ! [X0] : (quiet(X0) <=> (~calm(X0) & ~creative(X0))) [input p4]
14. ! [X0] : (~calm(X0) => (~generous(X0) & ~quiet(X0))) [input p13]
23. quiet(mary) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~quiet(X0)) | calm(X0)) [ennf transformation 14]
39. ! [X0] : ((quiet(X0) | (calm(X0) | creative(X0))) & ((~calm(X0) & ~creative(X0)) | ~quiet(X0))) [nnf transformation 5]
40. ! [X0] : ((quiet(X0) | calm(X0) | creative(X0)) & ((~calm(X0) & ~creative(X0)) | ~quiet(X0))) [flattening 39]
79. ~calm(X0) | ~quiet(X0) [cnf transformation 40]
113. ~quiet(X0) | calm(X0) [cnf transformation 34]
130. quiet(mary) [cnf transformation 23]
235. ~quiet(X0) [subsumption resolution 113,79]
258. $false [subsumption resolution 130,235]
% SZS output end Proof for 7058992262402513054397732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not humble and humble then mary is both brave and not kind.
If lucy is generous or curious then lucy is not tall.
Everyone who is both generous and not wise is tall.
If fred is humble or not patient then lucy is old and vice versa.
Everyone who is either not rich or not patient is either patient or not humble and vice versa.
If mary is either old or patient then someone is patient or curious.
Everyone who is either not quiet or not rich is not rich.
Everyone who is both wise and not old is calm or kind.
If john is both calm and not brave then someone is either not quiet or happy and vice versa.
If fred is either tall or calm then someone is not old.
Everyone who is not curious is either not calm or quiet.
If someone is both generous and not generous then fred is either not creative or not rich.
Everyone who is not old or quiet is both not old and not tall.
Everyone who is not happy is both not funny and not rich and vice versa.
If someone is quiet then paul is not funny or old and vice versa.
Everyone who is both not patient and funny is both rich and not old and vice versa.
Someone is not brave or generous.
Someone is patient.
Fred is not tall or calm.
Susan is either humble or not humble.
Someone is not curious or not tall.
Someone is calm.
Paul is patient or creative. | Mary is generous. | neutral | (((~humble(john)&humble(john)))=>((brave(mary)&~kind(mary))))&
(((generous(lucy)|curious(lucy)))=>(~tall(lucy)))&
(![X]:((generous(X)&~wise(X))=>tall(X)))&
(((humble(fred)|~patient(fred)))<=>(old(lucy)))&
(![X]:((~rich(X)<~>~patient(X))<=>(patient(X)<~>~humble(X))))&
(((old(mary)<~>patient(mary)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((~quiet(X)<~>~rich(X))=>~rich(X)))&
(![X]:((wise(X)&~old(X))=>(calm(X)|kind(X))))&
(((calm(john)&~brave(john)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((tall(fred)<~>calm(fred)))=>(?[X]:(~old(X))))&
(![X]:(~curious(X)=>(~calm(X)<~>quiet(X))))&
((?[X]:((generous(X)&~generous(X))))=>((~creative(fred)<~>~rich(fred))))&
(![X]:((~old(X)|quiet(X))=>(~old(X)&~tall(X))))&
(![X]:(~happy(X)<=>(~funny(X)&~rich(X))))&
((?[X]:(quiet(X)))<=>((~funny(paul)|old(paul))))&
(![X]:((~patient(X)&funny(X))<=>(rich(X)&~old(X))))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:(patient(X)))&
((~tall(fred)|calm(fred)))&
((humble(susan)<~>~humble(susan)))&
(?[X]:((~curious(X)|~tall(X))))&
(?[X]:(calm(X)))&
((patient(paul)|creative(paul))) | generous(mary) | [] | null | 0 |
Everyone who is both old and not quiet is either quiet or not happy and vice versa.
Everyone who is either not patient or strong is not wise and vice versa.
Everyone who is not kind is either rich or old.
Everyone who is funny is not wise or patient and vice versa.
If someone is not calm or not rich then someone is both funny and kind and vice versa.
If john is not tall or old then someone is both old and not patient and vice versa.
If alice is either happy or not rich then someone is both not tall and not curious.
Everyone who is calm is either not old or not calm and vice versa.
Everyone who is both happy and brave is not wise or wise and vice versa.
If lucy is generous then susan is either curious or kind.
Everyone who is both not generous and not creative is both quiet and humble.
Everyone who is both not curious and quiet is either funny or not generous and vice versa.
Everyone who is both creative and kind is either not wise or kind.
Someone is calm.
Someone is kind or not curious.
Someone is either not quiet or not kind.
Susan is not kind or not wise.
Susan is old or not calm.
John is both strong and patient.
Someone is not curious or curious.
Someone is creative. | John is not humble. | neutral | (![X]:((old(X)&~quiet(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((~patient(X)<~>strong(X))<=>~wise(X)))&
(![X]:(~kind(X)=>(rich(X)<~>old(X))))&
(![X]:(funny(X)<=>(~wise(X)|patient(X))))&
((?[X]:((~calm(X)|~rich(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(((~tall(john)|old(john)))<=>(?[X]:((old(X)&~patient(X)))))&
(((happy(alice)<~>~rich(alice)))=>(?[X]:((~tall(X)&~curious(X)))))&
(![X]:(calm(X)<=>(~old(X)<~>~calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~wise(X)|wise(X))))&
((generous(lucy))=>((curious(susan)<~>kind(susan))))&
(![X]:((~generous(X)&~creative(X))=>(quiet(X)&humble(X))))&
(![X]:((~curious(X)&quiet(X))<=>(funny(X)<~>~generous(X))))&
(![X]:((creative(X)&kind(X))=>(~wise(X)<~>kind(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~kind(susan)|~wise(susan)))&
((old(susan)|~calm(susan)))&
((strong(john)&patient(john)))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:(creative(X))) | ~humble(john) | [] | null | 0 |
Everyone who is not calm is both not calm and not strong.
If someone is either not kind or creative then paul is both funny and not wise.
If someone is not old or not creative then alice is creative or old and vice versa.
Everyone who is old is either not happy or kind.
Everyone who is old or not funny is both not curious and patient.
Everyone who is not wise or brave is not funny or not brave.
If lucy is both tall and not generous then lucy is both not brave and calm.
If someone is generous then fred is not old or funny and vice versa.
Everyone who is creative is not tall or happy.
Everyone who is both not strong and not kind is either not curious or patient.
If someone is calm or happy then someone is not humble or not creative and vice versa.
If mary is either not tall or not curious then someone is not curious or curious and vice versa.
Everyone who is both calm and kind is both not quiet and not old and vice versa.
If someone is not curious then someone is humble and vice versa.
If someone is not old or not wise then lucy is both brave and quiet and vice versa.
If john is both quiet and brave then someone is either not old or happy.
Fred is strong.
Someone is either not happy or not quiet.
Paul is both humble and curious.
Mary is brave.
Paul is not creative.
Someone is not strong or not creative.
Someone is either not funny or not quiet.
Someone is not quiet. | Lucy is not patient. | contradiction | (![X]:(~calm(X)=>(~calm(X)&~strong(X))))&
((?[X]:((~kind(X)<~>creative(X))))=>((funny(paul)&~wise(paul))))&
((?[X]:((~old(X)|~creative(X))))<=>((creative(alice)|old(alice))))&
(![X]:(old(X)=>(~happy(X)<~>kind(X))))&
(![X]:((old(X)|~funny(X))=>(~curious(X)&patient(X))))&
(![X]:((~wise(X)|brave(X))=>(~funny(X)|~brave(X))))&
(((tall(lucy)&~generous(lucy)))=>((~brave(lucy)&calm(lucy))))&
((?[X]:(generous(X)))<=>((~old(fred)|funny(fred))))&
(![X]:(creative(X)=>(~tall(X)|happy(X))))&
(![X]:((~strong(X)&~kind(X))=>(~curious(X)<~>patient(X))))&
((?[X]:((calm(X)|happy(X))))<=>(?[X]:((~humble(X)|~creative(X)))))&
(((~tall(mary)<~>~curious(mary)))<=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:((calm(X)&kind(X))<=>(~quiet(X)&~old(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(humble(X))))&
((?[X]:((~old(X)|~wise(X))))<=>((brave(lucy)&quiet(lucy))))&
(((quiet(john)&brave(john)))=>(?[X]:((~old(X)<~>happy(X)))))&
(strong(fred))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((humble(paul)&curious(paul)))&
(brave(mary))&
(~creative(paul))&
(?[X]:((~strong(X)|~creative(X))))&
(?[X]:((~funny(X)<~>~quiet(X))))&
(?[X]:(~quiet(X))) | ~patient(lucy) | [
"p4",
"p5",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8612969258971242516370764
% SZS output start Proof for 8612969258971242516370764
5. ! [X0] : ((~funny(X0) | old(X0)) => (patient(X0) & ~curious(X0))) [input p4]
6. ! [X0] : ((brave(X0) | ~wise(X0)) => (~brave(X0) | ~funny(X0))) [input p5]
15. ? [X0] : (~wise(X0) | ~old(X0)) <=> (quiet(lucy) & brave(lucy)) [input p14]
19. curious(paul) & humble(paul) [input p18]
25. ~patient(lucy) [input hypothesis]
31. ! [X0] : ((patient(X0) & ~curious(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 5]
32. ! [X0] : ((~brave(X0) | ~funny(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 6]
33. ! [X0] : (~brave(X0) | ~funny(X0) | (~brave(X0) & wise(X0))) [flattening 32]
71. (? [X0] : (~wise(X0) | ~old(X0)) | (~quiet(lucy) | ~brave(lucy))) & ((quiet(lucy) & brave(lucy)) | ! [X0] : (wise(X0) & old(X0))) [nnf transformation 15]
72. (? [X0] : (~wise(X0) | ~old(X0)) | ~quiet(lucy) | ~brave(lucy)) & ((quiet(lucy) & brave(lucy)) | ! [X0] : (wise(X0) & old(X0))) [flattening 71]
73. (? [X0] : (~wise(X0) | ~old(X0)) | ~quiet(lucy) | ~brave(lucy)) & ((quiet(lucy) & brave(lucy)) | ! [X1] : (wise(X1) & old(X1))) [rectify 72]
74. ? [X0] : (~wise(X0) | ~old(X0)) => (~wise(sK7) | ~old(sK7)) [choice axiom]
75. ((~wise(sK7) | ~old(sK7)) | ~quiet(lucy) | ~brave(lucy)) & ((quiet(lucy) & brave(lucy)) | ! [X1] : (wise(X1) & old(X1))) [skolemisation 73,74]
101. ~curious(X0) | ~old(X0) [cnf transformation 31]
104. patient(X0) | funny(X0) [cnf transformation 31]
106. ~brave(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 33]
131. brave(lucy) | old(X1) [cnf transformation 75]
142. curious(paul) [cnf transformation 19]
149. ~patient(lucy) [cnf transformation 25]
150. ~brave(X0) | ~funny(X0) [duplicate literal removal 106]
192. 10 <=> ! [X1] : old(X1) [avatar definition]
193. old(X1) <- (10) [avatar component clause 192]
209. 14 <=> brave(lucy) [avatar definition]
210. brave(lucy) <- (14) [avatar component clause 209]
310. 10 | 14 [avatar split clause 131,209,192]
367. ~old(paul) [resolution 101,142]
372. funny(lucy) [resolution 104,149]
374. ~funny(lucy) <- (14) [resolution 150,210]
377. $false <- (14) [subsumption resolution 374,372]
378. ~14 [avatar contradiction clause 377]
380. $false <- (10) [resolution 193,367]
385. ~10 [avatar contradiction clause 380]
386. $false [avatar sat refutation 310,378,385]
% SZS output end Proof for 8612969258971242516370764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or kind is both tall and rich.
If someone is either humble or not kind then someone is humble or not wise and vice versa.
Everyone who is not happy is either not brave or patient and vice versa.
If someone is not happy or strong then fred is wise or not generous.
If someone is either brave or happy then john is both not quiet and quiet.
Everyone who is generous is either happy or creative and vice versa.
Everyone who is humble or not rich is generous or not humble.
If alice is either not calm or not funny then someone is kind.
Everyone who is both patient and quiet is not humble.
Everyone who is not creative is not tall or not funny and vice versa.
If someone is either not creative or wise then someone is both creative and wise.
If alice is not tall then fred is humble or not kind and vice versa.
Everyone who is not strong is either not strong or calm and vice versa.
Everyone who is both not generous and brave is both rich and not humble and vice versa.
If john is both humble and quiet then alice is either not generous or wise and vice versa.
If alice is not happy then someone is both not calm and not generous and vice versa.
John is tall or rich.
John is either humble or not generous.
Someone is both tall and rich.
Someone is not kind.
Someone is both not humble and quiet.
Someone is either not rich or not creative.
Someone is either generous or not happy.
Someone is not curious. | Fred is humble. | neutral | (![X]:((calm(X)<~>kind(X))=>(tall(X)&rich(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(~happy(X)<=>(~brave(X)<~>patient(X))))&
((?[X]:((~happy(X)|strong(X))))=>((wise(fred)|~generous(fred))))&
((?[X]:((brave(X)<~>happy(X))))=>((~quiet(john)&quiet(john))))&
(![X]:(generous(X)<=>(happy(X)<~>creative(X))))&
(![X]:((humble(X)|~rich(X))=>(generous(X)|~humble(X))))&
(((~calm(alice)<~>~funny(alice)))=>(?[X]:(kind(X))))&
(![X]:((patient(X)&quiet(X))=>~humble(X)))&
(![X]:(~creative(X)<=>(~tall(X)|~funny(X))))&
((?[X]:((~creative(X)<~>wise(X))))=>(?[X]:((creative(X)&wise(X)))))&
((~tall(alice))<=>((humble(fred)|~kind(fred))))&
(![X]:(~strong(X)<=>(~strong(X)<~>calm(X))))&
(![X]:((~generous(X)&brave(X))<=>(rich(X)&~humble(X))))&
(((humble(john)&quiet(john)))<=>((~generous(alice)<~>wise(alice))))&
((~happy(alice))<=>(?[X]:((~calm(X)&~generous(X)))))&
((tall(john)|rich(john)))&
((humble(john)<~>~generous(john)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~humble(X)&quiet(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>~happy(X))))&
(?[X]:(~curious(X))) | humble(fred) | [] | null | 0 |
If alice is not funny then fred is both not curious and creative.
If john is either tall or quiet then someone is either not calm or not curious.
If fred is either not brave or tall then paul is calm.
Everyone who is not kind or not rich is either calm or wise.
Everyone who is either not generous or rich is both quiet and old.
If susan is both not kind and not calm then susan is either old or not happy.
Everyone who is both not funny and rich is both not happy and patient and vice versa.
If someone is both brave and tall then someone is quiet or not calm.
Everyone who is not rich or patient is both old and not happy and vice versa.
If someone is both quiet and strong then someone is not brave or old and vice versa.
If someone is not strong then alice is both happy and not brave.
Everyone who is both humble and funny is old.
Everyone who is either quiet or rich is happy and vice versa.
Everyone who is not happy or not wise is not strong or not quiet and vice versa.
Someone is not patient or creative.
Lucy is not brave or not old.
Lucy is not humble or happy.
Someone is either not wise or curious. | John is generous. | contradiction | ((~funny(alice))=>((~curious(fred)&creative(fred))))&
(((tall(john)<~>quiet(john)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
(((~brave(fred)<~>tall(fred)))=>(calm(paul)))&
(![X]:((~kind(X)|~rich(X))=>(calm(X)<~>wise(X))))&
(![X]:((~generous(X)<~>rich(X))=>(quiet(X)&old(X))))&
(((~kind(susan)&~calm(susan)))=>((old(susan)<~>~happy(susan))))&
(![X]:((~funny(X)&rich(X))<=>(~happy(X)&patient(X))))&
((?[X]:((brave(X)&tall(X))))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:((~rich(X)|patient(X))<=>(old(X)&~happy(X))))&
((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:(~strong(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:((quiet(X)<~>rich(X))<=>happy(X)))&
(![X]:((~happy(X)|~wise(X))<=>(~strong(X)|~quiet(X))))&
(?[X]:((~patient(X)|creative(X))))&
((~brave(lucy)|~old(lucy)))&
((~humble(lucy)|happy(lucy)))&
(?[X]:((~wise(X)<~>curious(X)))) | generous(john) | [
"p4",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5190463749741855213948917
% SZS output start Proof for 5190463749741855213948917
5. ! [X0] : ((~generous(X0) <~> rich(X0)) => (old(X0) & quiet(X0))) [input p4]
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~happy(X0) & old(X0))) [input p8]
10. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X0] : (old(X0) | ~brave(X0)) [input p9]
11. ? [X0] : ~strong(X0) => (~brave(alice) & happy(alice)) [input p10]
13. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> happy(X0)) [input p12]
14. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p13]
19. generous(john) [input hypothesis]
21. ? [X0] : (strong(X0) & quiet(X0)) <=> ? [X1] : (old(X1) | ~brave(X1)) [rectify 10]
32. ! [X0] : ((old(X0) & quiet(X0)) | (~generous(X0) <=> rich(X0))) [ennf transformation 5]
34. (~brave(alice) & happy(alice)) | ! [X0] : strong(X0) [ennf transformation 11]
40. ! [X0] : ((old(X0) & quiet(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) [nnf transformation 32]
46. ! [X0] : (((patient(X0) | ~rich(X0)) | (happy(X0) | ~old(X0))) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
47. ! [X0] : ((patient(X0) | ~rich(X0) | happy(X0) | ~old(X0)) & ((~happy(X0) & old(X0)) | (~patient(X0) & rich(X0)))) [flattening 46]
48. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X1] : (old(X1) | ~brave(X1)) | ! [X0] : (~strong(X0) | ~quiet(X0))) [nnf transformation 21]
49. (? [X0] : (strong(X0) & quiet(X0)) | ! [X1] : (~old(X1) & brave(X1))) & (? [X2] : (old(X2) | ~brave(X2)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [rectify 48]
50. ? [X0] : (strong(X0) & quiet(X0)) => (strong(sK2) & quiet(sK2)) [choice axiom]
51. ? [X2] : (old(X2) | ~brave(X2)) => (old(sK3) | ~brave(sK3)) [choice axiom]
52. ((strong(sK2) & quiet(sK2)) | ! [X1] : (~old(X1) & brave(X1))) & ((old(sK3) | ~brave(sK3)) | ! [X3] : (~strong(X3) | ~quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~happy(X0)) & (happy(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 13]
54. ! [X0] : (((~wise(X0) | ~happy(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (wise(X0) & happy(X0)))) [nnf transformation 14]
55. ! [X0] : ((~wise(X0) | ~happy(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | (wise(X0) & happy(X0)))) [flattening 54]
69. ~generous(X0) | quiet(X0) | ~rich(X0) [cnf transformation 40]
77. old(X0) | rich(X0) [cnf transformation 47]
79. ~happy(X0) | rich(X0) [cnf transformation 47]
83. quiet(sK2) | brave(X1) [cnf transformation 52]
84. quiet(sK2) | ~old(X1) [cnf transformation 52]
85. strong(sK2) | brave(X1) [cnf transformation 52]
88. ~brave(alice) | strong(X0) [cnf transformation 34]
92. ~rich(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 53]
93. ~quiet(X0) | ~strong(X0) | happy(X0) [cnf transformation 55]
100. generous(john) [cnf transformation 19]
157. 13 <=> ! [X1] : ~old(X1) [avatar definition]
158. ~old(X1) <- (13) [avatar component clause 157]
160. 14 <=> strong(sK2) [avatar definition]
162. strong(sK2) <- (14) [avatar component clause 160]
165. 15 <=> ! [X1] : brave(X1) [avatar definition]
166. brave(X1) <- (15) [avatar component clause 165]
167. 15 | 14 [avatar split clause 85,160,165]
169. 16 <=> quiet(sK2) [avatar definition]
171. quiet(sK2) <- (16) [avatar component clause 169]
172. 13 | 16 [avatar split clause 84,169,157]
173. 15 | 16 [avatar split clause 83,169,165]
175. 17 <=> ! [X3] : (~strong(X3) | ~quiet(X3)) [avatar definition]
176. ~strong(X3) | ~quiet(X3) <- (17) [avatar component clause 175]
187. 20 <=> ! [X0] : strong(X0) [avatar definition]
188. strong(X0) <- (20) [avatar component clause 187]
190. 21 <=> brave(alice) [avatar definition]
192. ~brave(alice) <- (~21) [avatar component clause 190]
193. 20 | ~21 [avatar split clause 88,190,187]
199. ~happy(X0) | ~quiet(X0) [subsumption resolution 92,79]
202. ~quiet(X0) | ~strong(X0) [subsumption resolution 93,199]
203. 17 [avatar split clause 202,175]
223. ~quiet(X3) <- (17, 20) [subsumption resolution 176,188]
226. rich(X0) <- (13) [resolution 77,158]
231. quiet(john) | ~rich(john) [resolution 69,100]
234. ~rich(john) <- (17, 20) [subsumption resolution 231,223]
235. $false <- (13, 17, 20) [subsumption resolution 234,226]
236. ~13 | ~17 | ~20 [avatar contradiction clause 235]
246. $false <- (16, 17, 20) [subsumption resolution 171,223]
247. ~16 | ~17 | ~20 [avatar contradiction clause 246]
253. $false <- (15, ~21) [subsumption resolution 192,166]
254. ~15 | 21 [avatar contradiction clause 253]
261. ~quiet(sK2) <- (14, 17) [resolution 176,162]
262. $false <- (14, 16, 17) [subsumption resolution 261,171]
263. ~14 | ~16 | ~17 [avatar contradiction clause 262]
264. $false [avatar sat refutation 167,172,173,193,203,236,247,254,263]
% SZS output end Proof for 5190463749741855213948917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both not patient and rich. If someone is either not kind or not creative then someone is not patient or old and vice versa. If mary is both creative and not funny then susan is not tall and vice versa. Everyone who is either not happy or not kind is curious or funny. Everyone who is both not old and calm is not creative or curious and vice versa. Everyone who is either not brave or creative is both humble and brave. Everyone who is not quiet is either not calm or old and vice versa. If lucy is not creative then lucy is both not happy and old. Everyone who is either not generous or not happy is not curious. Everyone who is either not brave or wise is either quiet or happy and vice versa. Everyone who is both not funny and not quiet is both curious and not generous and vice versa. Everyone who is not strong is not rich or not strong and vice versa. If someone is not happy or brave then someone is not curious. Everyone who is both strong and not brave is both not strong and not tall. If someone is not wise then someone is either not calm or not patient and vice versa. Everyone who is either curious or not funny is either not humble or not curious and vice versa. Paul is both not brave and not curious. Someone is wise or calm. Someone is not creative or happy. Someone is not quiet. Someone is both not generous and rich. Lucy is either not kind or calm. Someone is both not tall and not funny. Paul is curious or not curious. | Paul is generous. | neutral | (![X]:(~old(X)=>(~patient(X)&rich(X))))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(?[X]:((~patient(X)|old(X)))))&
(((creative(mary)&~funny(mary)))<=>(~tall(susan)))&
(![X]:((~happy(X)<~>~kind(X))=>(curious(X)|funny(X))))&
(![X]:((~old(X)&calm(X))<=>(~creative(X)|curious(X))))&
(![X]:((~brave(X)<~>creative(X))=>(humble(X)&brave(X))))&
(![X]:(~quiet(X)<=>(~calm(X)<~>old(X))))&
((~creative(lucy))=>((~happy(lucy)&old(lucy))))&
(![X]:((~generous(X)<~>~happy(X))=>~curious(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((~funny(X)&~quiet(X))<=>(curious(X)&~generous(X))))&
(![X]:(~strong(X)<=>(~rich(X)|~strong(X))))&
((?[X]:((~happy(X)|brave(X))))=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~strong(X)&~tall(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(~humble(X)<~>~curious(X))))&
((~brave(paul)&~curious(paul)))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:((~creative(X)|happy(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)&rich(X))))&
((~kind(lucy)<~>calm(lucy)))&
(?[X]:((~tall(X)&~funny(X))))&
((curious(paul)|~curious(paul))) | generous(paul) | [] | null | 0 |
If someone is either kind or not happy then lucy is both not rich and old and vice versa. Everyone who is rich or not kind is both not happy and not creative and vice versa. If someone is curious or generous then susan is either patient or old. Everyone who is humble or not old is not humble or happy. If paul is not rich then paul is either not patient or not kind. Everyone who is calm or not happy is humble or wise. If someone is strong or wise then someone is either not calm or calm and vice versa. Everyone who is not old or rich is patient. Everyone who is either patient or not patient is both not brave and not wise and vice versa. Everyone who is kind or not creative is both happy and not calm. If lucy is both not quiet and wise then someone is not wise. If lucy is either not calm or not humble then paul is both generous and not wise. Everyone who is both not happy and not old is either humble or creative and vice versa. Fred is not humble or old. Someone is not patient or funny. Someone is both not old and funny. Fred is either funny or rich. Fred is either generous or not humble. | Paul is patient. | contradiction | ((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(((~calm(lucy)<~>~humble(lucy)))=>((generous(paul)&~wise(paul))))&
(![X]:((~happy(X)&~old(X))<=>(humble(X)<~>creative(X))))&
((~humble(fred)|old(fred)))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((~old(X)&funny(X))))&
((funny(fred)<~>rich(fred)))&
((generous(fred)<~>~humble(fred))) | patient(paul) | [
"p1",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 268756937511168027206677
% SZS output start Proof for 268756937511168027206677
2. ! [X0] : ((~kind(X0) | rich(X0)) <=> (~creative(X0) & ~happy(X0))) [input p1]
5. ~rich(paul) => (~patient(paul) <~> ~kind(paul)) [input p4]
10. ! [X0] : ((~creative(X0) | kind(X0)) => (~calm(X0) & happy(X0))) [input p9]
19. patient(paul) [input hypothesis]
26. (~patient(paul) <~> ~kind(paul)) | rich(paul) [ennf transformation 5]
30. ! [X0] : ((~calm(X0) & happy(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 10]
37. ! [X0] : (((~kind(X0) | rich(X0)) | (creative(X0) | happy(X0))) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~kind(X0) | rich(X0) | creative(X0) | happy(X0)) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [flattening 37]
40. ((kind(paul) | patient(paul)) & (~kind(paul) | ~patient(paul))) | rich(paul) [nnf transformation 26]
63. ~rich(X0) | ~happy(X0) [cnf transformation 38]
64. ~happy(X0) | kind(X0) [cnf transformation 38]
65. ~creative(X0) | ~rich(X0) [cnf transformation 38]
66. ~creative(X0) | kind(X0) [cnf transformation 38]
72. ~kind(paul) | ~patient(paul) | rich(paul) [cnf transformation 40]
91. creative(X0) | happy(X0) [cnf transformation 30]
112. patient(paul) [cnf transformation 19]
162. 10 <=> rich(paul) [avatar definition]
164. rich(paul) <- (10) [avatar component clause 162]
166. 11 <=> patient(paul) [avatar definition]
170. 12 <=> kind(paul) [avatar definition]
171. ~kind(paul) <- (~12) [avatar component clause 170]
174. 10 | ~11 | ~12 [avatar split clause 72,170,166,162]
243. 11 [avatar split clause 112,166]
245. happy(X0) | kind(X0) [resolution 91,66]
246. happy(X1) | ~rich(X1) [resolution 91,65]
247. kind(X0) [subsumption resolution 245,64]
248. ~rich(X1) [subsumption resolution 246,63]
250. $false <- (~12) [resolution 247,171]
252. 12 [avatar contradiction clause 250]
254. $false <- (10) [subsumption resolution 164,248]
255. ~10 [avatar contradiction clause 254]
256. $false [avatar sat refutation 174,243,252,255]
% SZS output end Proof for 268756937511168027206677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and tall then fred is calm or not wise.
If someone is either not calm or not funny then someone is both calm and not humble and vice versa.
Everyone who is not wise is strong or happy.
Everyone who is not tall or not creative is both not rich and strong and vice versa.
Everyone who is either not old or creative is both not kind and not curious and vice versa.
If john is either not quiet or not happy then fred is both not strong and not wise.
Everyone who is both curious and not humble is either brave or happy.
Everyone who is kind is either kind or not happy and vice versa.
If someone is both funny and happy then john is creative.
Everyone who is patient or calm is either quiet or not rich.
Everyone who is both not tall and not rich is either happy or not calm and vice versa.
Everyone who is old is brave.
If lucy is not creative or wise then paul is calm or not rich.
Everyone who is not calm or not curious is old or not happy and vice versa.
If someone is humble then john is both happy and not humble and vice versa.
If someone is both not happy and humble then someone is not rich or curious and vice versa.
Someone is either not tall or not calm.
Paul is old.
Someone is not brave or not humble.
Mary is quiet or old.
Mary is creative or rich.
Someone is humble. | Fred is tall. | entailment | (((~kind(john)&tall(john)))=>((calm(fred)|~wise(fred))))&
((?[X]:((~calm(X)<~>~funny(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~wise(X)=>(strong(X)|happy(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:((~rich(X)|curious(X)))))&
(?[X]:((~tall(X)<~>~calm(X))))&
(old(paul))&
(?[X]:((~brave(X)|~humble(X))))&
((quiet(mary)|old(mary)))&
((creative(mary)|rich(mary)))&
(?[X]:(humble(X))) | tall(fred) | [
"p3",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5589957791967067718272016
% SZS output start Proof for 5589957791967067718272016
4. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (strong(X0) & ~rich(X0))) [input p3]
8. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p7]
16. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X0] : (curious(X0) | ~rich(X0)) [input p15]
23. ~tall(fred) [input hypothesis]
25. ? [X0] : (humble(X0) & ~happy(X0)) <=> ? [X1] : (curious(X1) | ~rich(X1)) [rectify 16]
44. ! [X0] : (((~creative(X0) | ~tall(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (creative(X0) & tall(X0)))) [nnf transformation 4]
45. ! [X0] : ((~creative(X0) | ~tall(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (creative(X0) & tall(X0)))) [flattening 44]
50. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 8]
61. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X1] : (curious(X1) | ~rich(X1)) | ! [X0] : (~humble(X0) | happy(X0))) [nnf transformation 25]
62. (? [X0] : (humble(X0) & ~happy(X0)) | ! [X1] : (~curious(X1) & rich(X1))) & (? [X2] : (curious(X2) | ~rich(X2)) | ! [X3] : (~humble(X3) | happy(X3))) [rectify 61]
63. ? [X0] : (humble(X0) & ~happy(X0)) => (humble(sK3) & ~happy(sK3)) [choice axiom]
64. ? [X2] : (curious(X2) | ~rich(X2)) => (curious(sK4) | ~rich(sK4)) [choice axiom]
65. ((humble(sK3) & ~happy(sK3)) | ! [X1] : (~curious(X1) & rich(X1))) & ((curious(sK4) | ~rich(sK4)) | ! [X3] : (~humble(X3) | happy(X3))) [skolemisation 62,64,63]
81. ~rich(X0) | tall(X0) [cnf transformation 45]
99. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 50]
101. kind(X0) | kind(X0) | happy(X0) [cnf transformation 50]
122. ~happy(sK3) | rich(X1) [cnf transformation 65]
133. ~tall(fred) [cnf transformation 23]
134. happy(X0) | ~kind(X0) [duplicate literal removal 99]
135. kind(X0) | happy(X0) [duplicate literal removal 101]
200. happy(X0) [subsumption resolution 134,135]
255. 25 <=> ! [X1] : rich(X1) [avatar definition]
256. rich(X1) <- (25) [avatar component clause 255]
260. rich(X1) [subsumption resolution 122,200]
261. 25 [avatar split clause 260,255]
284. tall(X0) <- (25) [resolution 81,256]
285. $false <- (25) [resolution 284,133]
286. ~25 [avatar contradiction clause 285]
287. $false [avatar sat refutation 261,286]
% SZS output end Proof for 5589957791967067718272016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not calm is either not brave or funny.
Everyone who is either patient or not tall is both brave and strong and vice versa.
If mary is either not quiet or not humble then susan is either happy or not rich and vice versa.
If someone is not creative then someone is not generous.
If susan is not rich or not strong then someone is either not calm or generous.
Everyone who is not curious or creative is curious and vice versa.
If alice is not creative or creative then alice is either wise or not rich.
Everyone who is either funny or not rich is not strong and vice versa.
If john is both patient and not old then someone is creative or not happy.
Everyone who is either not generous or generous is either not creative or old and vice versa.
If fred is both not rich and not wise then someone is not kind or not creative.
Everyone who is either not rich or rich is both not brave and not wise and vice versa.
Everyone who is either curious or not creative is funny and vice versa.
If fred is patient then someone is not tall.
Everyone who is strong or curious is funny or not calm.
Someone is both generous and strong.
Susan is rich.
Someone is wise or strong.
Someone is either wise or not wise.
Someone is not patient. | John is wise. | contradiction | (![X]:((~generous(X)<~>~calm(X))=>(~brave(X)<~>funny(X))))&
(![X]:((patient(X)<~>~tall(X))<=>(brave(X)&strong(X))))&
(((~quiet(mary)<~>~humble(mary)))<=>((happy(susan)<~>~rich(susan))))&
((?[X]:(~creative(X)))=>(?[X]:(~generous(X))))&
(((~rich(susan)|~strong(susan)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~curious(X)|creative(X))<=>curious(X)))&
(((~creative(alice)|creative(alice)))=>((wise(alice)<~>~rich(alice))))&
(![X]:((funny(X)<~>~rich(X))<=>~strong(X)))&
(((patient(john)&~old(john)))=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:((~generous(X)<~>generous(X))<=>(~creative(X)<~>old(X))))&
(((~rich(fred)&~wise(fred)))=>(?[X]:((~kind(X)|~creative(X)))))&
(![X]:((~rich(X)<~>rich(X))<=>(~brave(X)&~wise(X))))&
(![X]:((curious(X)<~>~creative(X))<=>funny(X)))&
((patient(fred))=>(?[X]:(~tall(X))))&
(![X]:((strong(X)|curious(X))=>(funny(X)|~calm(X))))&
(?[X]:((generous(X)&strong(X))))&
(rich(susan))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:((wise(X)<~>~wise(X))))&
(?[X]:(~patient(X))) | wise(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4659614938033615481524536
% SZS output start Proof for 4659614938033615481524536
12. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (~wise(X0) & ~brave(X0))) [input p11]
21. wise(john) [input hypothesis]
50. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 12]
51. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 50]
109. ~wise(X0) | rich(X0) | rich(X0) [cnf transformation 51]
110. ~wise(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 51]
127. wise(john) [cnf transformation 21]
130. ~wise(X0) | rich(X0) [duplicate literal removal 109]
131. ~wise(X0) | ~rich(X0) [duplicate literal removal 110]
221. ~wise(X0) [subsumption resolution 130,131]
236. $false [subsumption resolution 127,221]
% SZS output end Proof for 4659614938033615481524536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either kind or happy and vice versa.
Everyone who is both calm and not brave is not funny or not brave.
Everyone who is not creative is not patient.
Everyone who is both funny and not tall is both kind and not brave.
If someone is both rich and not creative then paul is both not calm and wise and vice versa.
If paul is not funny or old then fred is not rich and vice versa.
If someone is quiet then susan is both funny and not old and vice versa.
If susan is both not funny and humble then alice is both not tall and wise.
Everyone who is humble or not patient is funny.
Everyone who is both funny and calm is either strong or creative and vice versa.
If susan is generous or not kind then someone is either strong or not curious.
If alice is both not kind and quiet then someone is patient or old and vice versa.
Everyone who is not funny is either not rich or quiet and vice versa.
If someone is either not old or quiet then someone is not happy or not creative and vice versa.
If lucy is either quiet or not humble then someone is both tall and strong.
Everyone who is either old or calm is both old and kind.
Someone is both old and not quiet.
John is both humble and kind.
Someone is both brave and not funny.
Someone is either brave or happy.
Fred is tall or wise.
Someone is quiet or not quiet.
Someone is strong.
Someone is both rich and not funny. | Paul is not creative. | neutral | (![X]:(strong(X)<=>(kind(X)<~>happy(X))))&
(![X]:((calm(X)&~brave(X))=>(~funny(X)|~brave(X))))&
(![X]:(~creative(X)=>~patient(X)))&
(![X]:((funny(X)&~tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~calm(paul)&wise(paul))))&
(((~funny(paul)|old(paul)))<=>(~rich(fred)))&
((?[X]:(quiet(X)))<=>((funny(susan)&~old(susan))))&
(((~funny(susan)&humble(susan)))=>((~tall(alice)&wise(alice))))&
(![X]:((humble(X)|~patient(X))=>funny(X)))&
(![X]:((funny(X)&calm(X))<=>(strong(X)<~>creative(X))))&
(((generous(susan)|~kind(susan)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(((~kind(alice)&quiet(alice)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:(~funny(X)<=>(~rich(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(((quiet(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(?[X]:((old(X)&~quiet(X))))&
((humble(john)&kind(john)))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((tall(fred)|wise(fred)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)&~funny(X)))) | ~creative(paul) | [] | null | 0 |
If someone is not happy then paul is not old. Everyone who is both not tall and quiet is wise or humble and vice versa. Everyone who is not humble or not quiet is both tall and funny. Everyone who is either not strong or tall is both brave and not brave and vice versa. If mary is both not patient and not quiet then paul is not creative or not quiet and vice versa. If someone is either not patient or not happy then someone is not curious and vice versa. Everyone who is curious is either brave or not rich and vice versa. Everyone who is quiet is not kind and vice versa. Everyone who is either not rich or generous is wise or quiet and vice versa. Everyone who is both not brave and strong is either not curious or not quiet. Everyone who is both kind and not patient is brave or happy and vice versa. If alice is not strong or patient then someone is either not quiet or not patient and vice versa. If fred is not strong or kind then paul is either old or not patient. Everyone who is not quiet is not tall or old. Everyone who is both wise and tall is both quiet and generous and vice versa. If someone is not wise then lucy is either happy or not humble and vice versa. Someone is not curious or calm. Lucy is not happy. Someone is quiet or humble. Someone is both quiet and not brave. Alice is either not creative or generous. | Fred is quiet. | neutral | ((?[X]:(~happy(X)))=>(~old(paul)))&
(![X]:((~tall(X)&quiet(X))<=>(wise(X)|humble(X))))&
(![X]:((~humble(X)|~quiet(X))=>(tall(X)&funny(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(brave(X)&~brave(X))))&
(((~patient(mary)&~quiet(mary)))<=>((~creative(paul)|~quiet(paul))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
(![X]:((~rich(X)<~>generous(X))<=>(wise(X)|quiet(X))))&
(![X]:((~brave(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:((kind(X)&~patient(X))<=>(brave(X)|happy(X))))&
(((~strong(alice)|patient(alice)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(((~strong(fred)|kind(fred)))=>((old(paul)<~>~patient(paul))))&
(![X]:(~quiet(X)=>(~tall(X)|old(X))))&
(![X]:((wise(X)&tall(X))<=>(quiet(X)&generous(X))))&
((?[X]:(~wise(X)))<=>((happy(lucy)<~>~humble(lucy))))&
(?[X]:((~curious(X)|calm(X))))&
(~happy(lucy))&
(?[X]:((quiet(X)|humble(X))))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(alice)<~>generous(alice))) | quiet(fred) | [] | null | 0 |
If mary is both funny and generous then lucy is not humble or humble. Everyone who is both wise and not happy is not rich or not happy and vice versa. Everyone who is generous is both not calm and not brave and vice versa. Everyone who is either strong or not patient is either tall or wise and vice versa. Everyone who is not brave is not wise or funny and vice versa. If paul is both not calm and curious then fred is quiet or not strong. Everyone who is not wise is not kind. Everyone who is not funny or not humble is curious or not old. Everyone who is both not funny and not old is both not funny and not tall and vice versa. Everyone who is not humble is not old and vice versa. Everyone who is both not creative and generous is happy or not brave. Everyone who is funny or old is wise and vice versa. If someone is both brave and funny then someone is funny or curious and vice versa. If someone is not rich then lucy is either happy or generous. Everyone who is either old or strong is either not tall or brave. If lucy is old then someone is kind. Alice is not generous or not happy. Fred is either not generous or not wise. Paul is either tall or creative. Someone is quiet. | Paul is patient. | neutral | (((funny(mary)&generous(mary)))=>((~humble(lucy)|humble(lucy))))&
(![X]:((wise(X)&~happy(X))<=>(~rich(X)|~happy(X))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
(![X]:((~creative(X)&generous(X))=>(happy(X)|~brave(X))))&
(![X]:((funny(X)|old(X))<=>wise(X)))&
((?[X]:((brave(X)&funny(X))))<=>(?[X]:((funny(X)|curious(X)))))&
((?[X]:(~rich(X)))=>((happy(lucy)<~>generous(lucy))))&
(![X]:((old(X)<~>strong(X))=>(~tall(X)<~>brave(X))))&
((old(lucy))=>(?[X]:(kind(X))))&
((~generous(alice)|~happy(alice)))&
((~generous(fred)<~>~wise(fred)))&
((tall(paul)<~>creative(paul)))&
(?[X]:(quiet(X))) | patient(paul) | [] | null | 0 |
If susan is both tall and not funny then fred is patient or not brave.
If paul is either not curious or creative then mary is either not quiet or not happy and vice versa.
If someone is either not kind or wise then someone is either kind or patient.
Everyone who is brave is funny or not old.
Everyone who is not generous or not creative is both funny and not strong.
Everyone who is both not brave and funny is both strong and not kind.
Everyone who is not strong or not patient is both not creative and kind and vice versa.
If someone is not curious then someone is humble and vice versa.
If paul is either kind or rich then someone is brave and vice versa.
Everyone who is either generous or not creative is funny or calm and vice versa.
Everyone who is both not wise and humble is either curious or quiet.
Everyone who is either generous or rich is either not humble or not strong and vice versa.
If alice is rich or funny then alice is both brave and not creative and vice versa.
If someone is not calm or not rich then paul is patient or calm and vice versa.
Everyone who is calm is not kind or patient and vice versa.
If someone is not creative then lucy is generous and vice versa.
Someone is either not curious or not brave.
Someone is both not kind and not quiet.
Mary is not creative or generous.
Someone is not generous.
Alice is not wise.
Mary is strong.
Susan is not creative.
Someone is either not quiet or not old. | Lucy is strong. | entailment | (((tall(susan)&~funny(susan)))=>((patient(fred)|~brave(fred))))&
(((~curious(paul)<~>creative(paul)))<=>((~quiet(mary)<~>~happy(mary))))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:(brave(X)=>(funny(X)|~old(X))))&
(![X]:((~generous(X)|~creative(X))=>(funny(X)&~strong(X))))&
(![X]:((~brave(X)&funny(X))=>(strong(X)&~kind(X))))&
(![X]:((~strong(X)|~patient(X))<=>(~creative(X)&kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(humble(X))))&
(((kind(paul)<~>rich(paul)))<=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~creative(X))<=>(funny(X)|calm(X))))&
(![X]:((~wise(X)&humble(X))=>(curious(X)<~>quiet(X))))&
(![X]:((generous(X)<~>rich(X))<=>(~humble(X)<~>~strong(X))))&
(((rich(alice)|funny(alice)))<=>((brave(alice)&~creative(alice))))&
((?[X]:((~calm(X)|~rich(X))))<=>((patient(paul)|calm(paul))))&
(![X]:(calm(X)<=>(~kind(X)|patient(X))))&
((?[X]:(~creative(X)))<=>(generous(lucy)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((~kind(X)&~quiet(X))))&
((~creative(mary)|generous(mary)))&
(?[X]:(~generous(X)))&
(~wise(alice))&
(strong(mary))&
(~creative(susan))&
(?[X]:((~quiet(X)<~>~old(X)))) | strong(lucy) | [
"p4",
"p6",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 258823245565359841613038
% SZS output start Proof for 258823245565359841613038
5. ! [X0] : ((~creative(X0) | ~generous(X0)) => (~strong(X0) & funny(X0))) [input p4]
7. ! [X0] : ((~patient(X0) | ~strong(X0)) <=> (kind(X0) & ~creative(X0))) [input p6]
10. ! [X0] : ((generous(X0) <~> ~creative(X0)) <=> (calm(X0) | funny(X0))) [input p9]
16. ? [X0] : ~creative(X0) <=> generous(lucy) [input p15]
23. ~creative(susan) [input p22]
25. ~strong(lucy) [input hypothesis]
32. ! [X0] : ((~strong(X0) & funny(X0)) | (creative(X0) & generous(X0))) [ennf transformation 5]
42. ! [X0] : (((~patient(X0) | ~strong(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (patient(X0) & strong(X0)))) [nnf transformation 7]
43. ! [X0] : ((~patient(X0) | ~strong(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | (patient(X0) & strong(X0)))) [flattening 42]
53. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [nnf transformation 10]
54. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [flattening 53]
66. (? [X0] : ~creative(X0) | ~generous(lucy)) & (generous(lucy) | ! [X0] : creative(X0)) [nnf transformation 16]
67. (? [X0] : ~creative(X0) | ~generous(lucy)) & (generous(lucy) | ! [X1] : creative(X1)) [rectify 66]
68. ? [X0] : ~creative(X0) => ~creative(sK5) [choice axiom]
69. (~creative(sK5) | ~generous(lucy)) & (generous(lucy) | ! [X1] : creative(X1)) [skolemisation 67,68]
94. creative(X0) | funny(X0) [cnf transformation 32]
99. ~creative(X0) | strong(X0) [cnf transformation 43]
114. creative(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 54]
138. generous(lucy) | creative(X1) [cnf transformation 69]
148. ~creative(susan) [cnf transformation 23]
151. ~strong(lucy) [cnf transformation 25]
229. ~generous(X0) | creative(X0) [subsumption resolution 114,94]
285. 27 <=> generous(lucy) [avatar definition]
286. generous(lucy) <- (27) [avatar component clause 285]
294. 29 <=> ! [X1] : creative(X1) [avatar definition]
295. creative(X1) <- (29) [avatar component clause 294]
296. 29 | 27 [avatar split clause 138,285,294]
345. creative(lucy) <- (27) [resolution 229,286]
349. strong(lucy) <- (27) [resolution 345,99]
350. $false <- (27) [subsumption resolution 349,151]
351. ~27 [avatar contradiction clause 350]
355. $false <- (29) [resolution 295,148]
360. ~29 [avatar contradiction clause 355]
361. $false [avatar sat refutation 296,351,360]
% SZS output end Proof for 258823245565359841613038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then mary is both brave and happy and vice versa.
If lucy is not strong then lucy is both not happy and not funny.
If someone is rich or quiet then paul is either not tall or tall and vice versa.
Everyone who is both curious and creative is either curious or not tall.
Everyone who is funny or not funny is either not happy or kind.
If fred is both patient and not kind then susan is both creative and calm.
Everyone who is generous is either not humble or not generous.
Everyone who is both not patient and strong is not kind.
Everyone who is not tall is not wise or old and vice versa.
If someone is both not patient and curious then someone is both not strong and not calm.
Everyone who is not wise or humble is both not brave and not rich and vice versa.
If someone is either not rich or not funny then someone is either not quiet or humble and vice versa.
Everyone who is brave or not tall is either not funny or not wise and vice versa.
If someone is either tall or not creative then susan is not tall and vice versa.
If someone is not funny then mary is either kind or brave.
If someone is curious then someone is both not old and kind.
Someone is both old and humble.
Alice is both patient and not humble.
Fred is wise.
Susan is humble.
Someone is both not funny and not generous.
Lucy is not humble or not calm.
Paul is quiet or happy.
Someone is either kind or calm. | Susan is creative. | neutral | ((?[X]:(rich(X)))<=>((brave(mary)&happy(mary))))&
((~strong(lucy))=>((~happy(lucy)&~funny(lucy))))&
((?[X]:((rich(X)|quiet(X))))<=>((~tall(paul)<~>tall(paul))))&
(![X]:((curious(X)&creative(X))=>(curious(X)<~>~tall(X))))&
(![X]:((funny(X)|~funny(X))=>(~happy(X)<~>kind(X))))&
(((patient(fred)&~kind(fred)))=>((creative(susan)&calm(susan))))&
(![X]:(generous(X)=>(~humble(X)<~>~generous(X))))&
(![X]:((~patient(X)&strong(X))=>~kind(X)))&
(![X]:(~tall(X)<=>(~wise(X)|old(X))))&
((?[X]:((~patient(X)&curious(X))))=>(?[X]:((~strong(X)&~calm(X)))))&
(![X]:((~wise(X)|humble(X))<=>(~brave(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~funny(X))))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((brave(X)|~tall(X))<=>(~funny(X)<~>~wise(X))))&
((?[X]:((tall(X)<~>~creative(X))))<=>(~tall(susan)))&
((?[X]:(~funny(X)))=>((kind(mary)<~>brave(mary))))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)&kind(X)))))&
(?[X]:((old(X)&humble(X))))&
((patient(alice)&~humble(alice)))&
(wise(fred))&
(humble(susan))&
(?[X]:((~funny(X)&~generous(X))))&
((~humble(lucy)|~calm(lucy)))&
((quiet(paul)|happy(paul)))&
(?[X]:((kind(X)<~>calm(X)))) | creative(susan) | [] | null | 0 |
If john is either funny or not funny then someone is funny and vice versa.
If alice is either generous or not humble then john is either not calm or quiet and vice versa.
If someone is either not happy or funny then susan is strong and vice versa.
If fred is either tall or quiet then someone is both creative and calm and vice versa.
Everyone who is both not humble and old is kind or wise and vice versa.
If someone is not curious or brave then fred is strong.
Everyone who is happy or not calm is generous or funny.
If lucy is not happy then someone is either not calm or tall.
If lucy is either not funny or not happy then someone is either not rich or kind and vice versa.
Everyone who is calm or not old is patient and vice versa.
Everyone who is either generous or patient is brave or not funny.
If john is calm then john is brave and vice versa.
If someone is both not creative and humble then alice is both not generous and not brave.
If fred is creative then someone is both not creative and not happy.
Everyone who is not wise or not calm is not kind and vice versa.
Everyone who is generous or not kind is both not tall and wise.
Paul is either rich or humble.
Someone is not humble.
Someone is strong.
John is not patient or rich.
Mary is tall.
Alice is not quiet or brave.
Susan is both curious and calm.
Paul is creative. | John is not old. | contradiction | (((funny(john)<~>~funny(john)))<=>(?[X]:(funny(X))))&
(((generous(alice)<~>~humble(alice)))<=>((~calm(john)<~>quiet(john))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(strong(susan)))&
(((tall(fred)<~>quiet(fred)))<=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((~humble(X)&old(X))<=>(kind(X)|wise(X))))&
((?[X]:((~curious(X)|brave(X))))=>(strong(fred)))&
(![X]:((happy(X)|~calm(X))=>(generous(X)|funny(X))))&
((~happy(lucy))=>(?[X]:((~calm(X)<~>tall(X)))))&
(((~funny(lucy)<~>~happy(lucy)))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((calm(X)|~old(X))<=>patient(X)))&
(![X]:((generous(X)<~>patient(X))=>(brave(X)|~funny(X))))&
((calm(john))<=>(brave(john)))&
((?[X]:((~creative(X)&humble(X))))=>((~generous(alice)&~brave(alice))))&
((creative(fred))=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:((~wise(X)|~calm(X))<=>~kind(X)))&
(![X]:((generous(X)|~kind(X))=>(~tall(X)&wise(X))))&
((rich(paul)<~>humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:(strong(X)))&
((~patient(john)|rich(john)))&
(tall(mary))&
((~quiet(alice)|brave(alice)))&
((curious(susan)&calm(susan)))&
(creative(paul)) | ~old(john) | [
"p4",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7922371383710959575607379
% SZS output start Proof for 7922371383710959575607379
5. ! [X0] : ((old(X0) & ~humble(X0)) <=> (wise(X0) | kind(X0))) [input p4]
15. ! [X0] : ((~calm(X0) | ~wise(X0)) <=> ~kind(X0)) [input p14]
16. ! [X0] : ((~kind(X0) | generous(X0)) => (wise(X0) & ~tall(X0))) [input p15]
25. ~old(john) [input hypothesis]
36. ! [X0] : ((wise(X0) & ~tall(X0)) | (kind(X0) & ~generous(X0))) [ennf transformation 16]
50. ! [X0] : (((old(X0) & ~humble(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (~old(X0) | humble(X0)))) [nnf transformation 5]
51. ! [X0] : (((old(X0) & ~humble(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | ~old(X0) | humble(X0))) [flattening 50]
65. ! [X0] : (((~calm(X0) | ~wise(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) & wise(X0)))) [nnf transformation 15]
66. ! [X0] : ((~calm(X0) | ~wise(X0) | kind(X0)) & (~kind(X0) | (calm(X0) & wise(X0)))) [flattening 65]
98. ~wise(X0) | old(X0) [cnf transformation 51]
123. ~kind(X0) | wise(X0) [cnf transformation 66]
129. wise(X0) | kind(X0) [cnf transformation 36]
139. ~old(john) [cnf transformation 25]
300. wise(X0) [subsumption resolution 129,123]
326. old(X0) [resolution 98,300]
327. $false [resolution 326,139]
% SZS output end Proof for 7922371383710959575607379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not old and brave then susan is both generous and curious and vice versa.
If someone is not humble then someone is brave.
If someone is either not strong or wise then someone is either generous or kind.
Everyone who is either not wise or tall is both not happy and not creative.
Everyone who is both not humble and not kind is either not quiet or not generous.
If alice is both humble and kind then someone is not rich or not strong and vice versa.
If someone is both not happy and happy then fred is curious or wise and vice versa.
Everyone who is patient or old is both humble and rich.
If john is both not strong and not wise then someone is strong or not wise.
Everyone who is creative is both wise and happy.
Everyone who is both not wise and quiet is either humble or not old and vice versa.
If john is both not brave and not kind then susan is tall or not generous and vice versa.
Everyone who is not calm or funny is both creative and not funny.
If someone is either not strong or not rich then someone is both old and not happy.
Everyone who is not tall or not creative is both not quiet and calm and vice versa.
Everyone who is both happy and not brave is patient.
Someone is both rich and patient.
Someone is brave or not rich.
Someone is either not funny or tall.
Lucy is creative.
Mary is both not generous and wise.
Paul is both not happy and not tall.
Someone is either humble or not creative. | Alice is funny. | contradiction | (((~old(mary)&brave(mary)))<=>((generous(susan)&curious(susan))))&
((?[X]:(~humble(X)))=>(?[X]:(brave(X))))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((~wise(X)<~>tall(X))=>(~happy(X)&~creative(X))))&
(![X]:((~humble(X)&~kind(X))=>(~quiet(X)<~>~generous(X))))&
(((humble(alice)&kind(alice)))<=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((~happy(X)&happy(X))))<=>((curious(fred)|wise(fred))))&
(![X]:((patient(X)|old(X))=>(humble(X)&rich(X))))&
(((~strong(john)&~wise(john)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:(creative(X)=>(wise(X)&happy(X))))&
(![X]:((~wise(X)&quiet(X))<=>(humble(X)<~>~old(X))))&
(((~brave(john)&~kind(john)))<=>((tall(susan)|~generous(susan))))&
(![X]:((~calm(X)|funny(X))=>(creative(X)&~funny(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((old(X)&~happy(X)))))&
(![X]:((~tall(X)|~creative(X))<=>(~quiet(X)&calm(X))))&
(![X]:((happy(X)&~brave(X))=>patient(X)))&
(?[X]:((rich(X)&patient(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(creative(lucy))&
((~generous(mary)&wise(mary)))&
((~happy(paul)&~tall(paul)))&
(?[X]:((humble(X)<~>~creative(X)))) | funny(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5731801963744706215510322
% SZS output start Proof for 5731801963744706215510322
13. ! [X0] : ((funny(X0) | ~calm(X0)) => (~funny(X0) & creative(X0))) [input p12]
24. funny(alice) [input hypothesis]
37. ! [X0] : ((~funny(X0) & creative(X0)) | (~funny(X0) & calm(X0))) [ennf transformation 13]
130. ~funny(X0) | ~funny(X0) [cnf transformation 37]
153. funny(alice) [cnf transformation 24]
154. ~funny(X0) [duplicate literal removal 130]
320. $false [subsumption resolution 153,154]
% SZS output end Proof for 5731801963744706215510322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both not curious and wise.
Everyone who is both old and not calm is not brave or wise and vice versa.
If someone is not generous or not tall then mary is rich or quiet.
If someone is both not quiet and creative then someone is not funny.
Everyone who is not tall or not rich is either humble or creative.
If someone is either not quiet or not old then someone is not curious.
If someone is not wise or creative then someone is curious or brave and vice versa.
If someone is wise or not calm then someone is not creative and vice versa.
Everyone who is not humble is either not kind or not happy and vice versa.
Everyone who is not strong or tall is either funny or strong and vice versa.
If someone is not rich or not tall then someone is calm or patient and vice versa.
If alice is not brave then mary is not generous and vice versa.
If someone is both calm and rich then someone is not brave.
Everyone who is not patient is both not happy and old.
Everyone who is either strong or not old is either funny or not generous and vice versa.
Everyone who is not tall is curious and vice versa.
Someone is both quiet and not happy.
Someone is either brave or not patient.
Lucy is not funny or not rich.
Alice is not calm.
Fred is tall.
Someone is not creative.
Someone is both curious and not strong.
Someone is both not happy and not old. | Fred is not curious. | entailment | (![X]:(creative(X)=>(~curious(X)&wise(X))))&
(![X]:((old(X)&~calm(X))<=>(~brave(X)|wise(X))))&
((?[X]:((~generous(X)|~tall(X))))=>((rich(mary)|quiet(mary))))&
((?[X]:((~quiet(X)&creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|~rich(X))=>(humble(X)<~>creative(X))))&
((?[X]:((~quiet(X)<~>~old(X))))=>(?[X]:(~curious(X))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((curious(X)|brave(X)))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~humble(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:((~strong(X)|tall(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((calm(X)|patient(X)))))&
((~brave(alice))<=>(~generous(mary)))&
((?[X]:((calm(X)&rich(X))))=>(?[X]:(~brave(X))))&
(![X]:(~patient(X)=>(~happy(X)&old(X))))&
(![X]:((strong(X)<~>~old(X))<=>(funny(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>curious(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((brave(X)<~>~patient(X))))&
((~funny(lucy)|~rich(lucy)))&
(~calm(alice))&
(tall(fred))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)&~strong(X))))&
(?[X]:((~happy(X)&~old(X)))) | ~curious(fred) | [
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7196846445411604008391174
% SZS output start Proof for 7196846445411604008391174
16. ! [X0] : (~tall(X0) <=> curious(X0)) [input p15]
21. tall(fred) [input p20]
25. curious(fred) [input hypothesis]
73. ! [X0] : ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))) [nnf transformation 16]
136. ~tall(X0) | ~curious(X0) [cnf transformation 73]
143. tall(fred) [cnf transformation 21]
149. curious(fred) [cnf transformation 25]
320. ~curious(fred) [resolution 136,143]
322. $false [subsumption resolution 320,149]
% SZS output end Proof for 7196846445411604008391174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or patient is not quiet.
Everyone who is old or curious is not rich and vice versa.
Everyone who is either not wise or not calm is both not old and tall.
If susan is not generous then someone is happy or wise.
Everyone who is both creative and not quiet is both not patient and not generous.
Everyone who is either creative or not humble is either curious or not curious and vice versa.
If someone is both not patient and not happy then susan is either not rich or not kind and vice versa.
Everyone who is either rich or not wise is either brave or curious and vice versa.
Everyone who is brave or not patient is old.
Everyone who is not humble is creative or kind and vice versa.
If someone is funny or not funny then someone is either kind or funny.
Everyone who is either not curious or not funny is either curious or brave.
If susan is not humble or not rich then someone is happy and vice versa.
If fred is rich or happy then alice is both not tall and not curious and vice versa.
If someone is not quiet then alice is both calm and not generous and vice versa.
If someone is both strong and not strong then susan is both creative and not kind.
Someone is funny.
Lucy is curious.
Susan is old or generous.
Someone is either not quiet or not humble.
Mary is both not happy and curious.
John is both curious and strong.
Someone is both not creative and not old. | Susan is kind. | entailment | (![X]:((~funny(X)|patient(X))=>~quiet(X)))&
(![X]:((old(X)|curious(X))<=>~rich(X)))&
(![X]:((~wise(X)<~>~calm(X))=>(~old(X)&tall(X))))&
((~generous(susan))=>(?[X]:((happy(X)|wise(X)))))&
(![X]:((creative(X)&~quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(curious(X)<~>~curious(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:((rich(X)<~>~wise(X))<=>(brave(X)<~>curious(X))))&
(![X]:((brave(X)|~patient(X))=>old(X)))&
(![X]:(~humble(X)<=>(creative(X)|kind(X))))&
((?[X]:((funny(X)|~funny(X))))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((~curious(X)<~>~funny(X))=>(curious(X)<~>brave(X))))&
(((~humble(susan)|~rich(susan)))<=>(?[X]:(happy(X))))&
(((rich(fred)|happy(fred)))<=>((~tall(alice)&~curious(alice))))&
((?[X]:(~quiet(X)))<=>((calm(alice)&~generous(alice))))&
((?[X]:((strong(X)&~strong(X))))=>((creative(susan)&~kind(susan))))&
(?[X]:(funny(X)))&
(curious(lucy))&
((old(susan)|generous(susan)))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((~happy(mary)&curious(mary)))&
((curious(john)&strong(john)))&
(?[X]:((~creative(X)&~old(X)))) | kind(susan) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8819521295173540812242432
% SZS output start Proof for 8819521295173540812242432
6. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p5]
10. ! [X0] : (~humble(X0) <=> (kind(X0) | creative(X0))) [input p9]
24. ~kind(susan) [input hypothesis]
40. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 6]
46. ! [X0] : ((~humble(X0) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | humble(X0))) [nnf transformation 10]
47. ! [X0] : ((~humble(X0) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | humble(X0))) [flattening 46]
88. ~humble(X0) | creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 40]
89. ~humble(X0) | creative(X0) | curious(X0) | curious(X0) [cnf transformation 40]
90. humble(X0) | ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 40]
91. humble(X0) | ~creative(X0) | curious(X0) | curious(X0) [cnf transformation 40]
108. kind(X0) | creative(X0) | humble(X0) [cnf transformation 47]
109. ~humble(X0) | ~creative(X0) [cnf transformation 47]
143. ~kind(susan) [cnf transformation 24]
146. ~humble(X0) | creative(X0) | ~curious(X0) [duplicate literal removal 88]
147. ~humble(X0) | creative(X0) | curious(X0) [duplicate literal removal 89]
148. humble(X0) | ~creative(X0) | ~curious(X0) [duplicate literal removal 90]
149. humble(X0) | ~creative(X0) | curious(X0) [duplicate literal removal 91]
164. ~creative(X0) | humble(X0) [subsumption resolution 148,149]
165. ~humble(X0) | creative(X0) [subsumption resolution 146,147]
167. 4 <=> kind(susan) [avatar definition]
168. ~kind(susan) <- (~4) [avatar component clause 167]
195. ~creative(X0) [subsumption resolution 109,164]
196. kind(X0) | humble(X0) [subsumption resolution 108,195]
219. 14 <=> humble(susan) [avatar definition]
220. humble(susan) <- (14) [avatar component clause 219]
221. ~humble(susan) <- (~14) [avatar component clause 219]
283. ~4 [avatar split clause 143,167]
290. creative(susan) <- (14) [resolution 165,220]
291. $false <- (14) [subsumption resolution 290,195]
292. ~14 [avatar contradiction clause 291]
298. humble(susan) <- (~4) [resolution 196,168]
300. $false <- (~4, ~14) [subsumption resolution 298,221]
301. 4 | 14 [avatar contradiction clause 300]
302. $false [avatar sat refutation 283,292,301]
% SZS output end Proof for 8819521295173540812242432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is kind then mary is not curious or rich.
Everyone who is both rich and tall is not happy or tall.
If someone is not strong or strong then john is both not tall and not wise.
Everyone who is not patient is either old or curious.
Everyone who is happy or not wise is both not funny and old.
If someone is curious or not strong then fred is either old or not patient and vice versa.
If someone is both not strong and funny then lucy is not old.
Everyone who is not quiet is either patient or rich.
Everyone who is old or not happy is either creative or not quiet and vice versa.
If someone is not humble or not creative then someone is not tall.
Everyone who is rich is both not tall and not old.
Everyone who is not quiet is not patient or brave and vice versa.
Everyone who is brave is quiet.
If paul is both funny and tall then someone is both not kind and not old and vice versa.
If alice is both patient and not curious then someone is not rich or not humble.
Everyone who is either generous or not quiet is both not creative and happy and vice versa.
Paul is either funny or not patient.
John is either quiet or funny.
Someone is either calm or not happy.
Someone is curious or not rich.
Paul is tall or curious.
Someone is not wise.
Someone is strong or happy.
Paul is both not strong and not curious. | Paul is patient. | entailment | ((kind(paul))=>((~curious(mary)|rich(mary))))&
(![X]:((rich(X)&tall(X))=>(~happy(X)|tall(X))))&
((?[X]:((~strong(X)|strong(X))))=>((~tall(john)&~wise(john))))&
(![X]:(~patient(X)=>(old(X)<~>curious(X))))&
(![X]:((happy(X)|~wise(X))=>(~funny(X)&old(X))))&
((?[X]:((curious(X)|~strong(X))))<=>((old(fred)<~>~patient(fred))))&
((?[X]:((~strong(X)&funny(X))))=>(~old(lucy)))&
(![X]:(~quiet(X)=>(patient(X)<~>rich(X))))&
(![X]:((old(X)|~happy(X))<=>(creative(X)<~>~quiet(X))))&
((?[X]:((~humble(X)|~creative(X))))=>(?[X]:(~tall(X))))&
(![X]:(rich(X)=>(~tall(X)&~old(X))))&
(![X]:(~quiet(X)<=>(~patient(X)|brave(X))))&
(![X]:(brave(X)=>quiet(X)))&
(((funny(paul)&tall(paul)))<=>(?[X]:((~kind(X)&~old(X)))))&
(((patient(alice)&~curious(alice)))=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~creative(X)&happy(X))))&
((funny(paul)<~>~patient(paul)))&
((quiet(john)<~>funny(john)))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((curious(X)|~rich(X))))&
((tall(paul)|curious(paul)))&
(?[X]:(~wise(X)))&
(?[X]:((strong(X)|happy(X))))&
((~strong(paul)&~curious(paul))) | patient(paul) | [
"p7",
"p10",
"p11",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5023972365016483467983310
% SZS output start Proof for 5023972365016483467983310
8. ! [X0] : (~quiet(X0) => (patient(X0) <~> rich(X0))) [input p7]
11. ! [X0] : (rich(X0) => (~old(X0) & ~tall(X0))) [input p10]
12. ! [X0] : (~quiet(X0) <=> (brave(X0) | ~patient(X0))) [input p11]
21. curious(paul) | tall(paul) [input p20]
24. ~curious(paul) & ~strong(paul) [input p23]
25. ~patient(paul) [input hypothesis]
35. ! [X0] : ((patient(X0) <~> rich(X0)) | quiet(X0)) [ennf transformation 8]
37. ! [X0] : ((~old(X0) & ~tall(X0)) | ~rich(X0)) [ennf transformation 11]
46. ! [X0] : (((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | quiet(X0)) [nnf transformation 35]
52. ! [X0] : ((~quiet(X0) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | quiet(X0))) [nnf transformation 12]
53. ! [X0] : ((~quiet(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | quiet(X0))) [flattening 52]
93. quiet(X0) | patient(X0) | rich(X0) [cnf transformation 46]
103. ~tall(X0) | ~rich(X0) [cnf transformation 37]
106. ~quiet(X0) | patient(X0) [cnf transformation 53]
127. curious(paul) | tall(paul) [cnf transformation 21]
131. ~curious(paul) [cnf transformation 24]
132. ~patient(paul) [cnf transformation 25]
214. 19 <=> tall(paul) [avatar definition]
216. tall(paul) <- (19) [avatar component clause 214]
252. 27 <=> patient(paul) [avatar definition]
253. ~patient(paul) <- (~27) [avatar component clause 252]
287. 34 <=> curious(paul) [avatar definition]
290. 19 | 34 [avatar split clause 127,287,214]
300. ~34 [avatar split clause 131,287]
301. ~27 [avatar split clause 132,252]
304. ~rich(paul) <- (19) [resolution 103,216]
330. patient(X0) | rich(X0) | patient(X0) [resolution 93,106]
331. patient(X0) | rich(X0) [duplicate literal removal 330]
367. rich(paul) <- (~27) [resolution 331,253]
370. $false <- (19, ~27) [subsumption resolution 367,304]
371. ~19 | 27 [avatar contradiction clause 370]
373. $false [avatar sat refutation 290,300,301,371]
% SZS output end Proof for 5023972365016483467983310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both kind and not strong and vice versa.
Everyone who is rich or old is both not quiet and not curious.
If someone is not calm or not tall then susan is both not kind and not funny.
If lucy is both not happy and not patient then someone is either curious or not creative and vice versa.
If someone is both not funny and rich then lucy is not strong and vice versa.
Everyone who is either humble or not creative is not curious.
If someone is either kind or tall then lucy is either humble or not quiet.
If someone is both tall and wise then alice is both not rich and quiet and vice versa.
If someone is wise then someone is rich or old and vice versa.
If john is both tall and not curious then someone is not brave and vice versa.
Everyone who is old is not happy.
Everyone who is funny is either generous or kind.
Everyone who is happy is either not quiet or patient.
If someone is both old and funny then someone is funny and vice versa.
Everyone who is both kind and not tall is both brave and creative and vice versa.
Everyone who is either generous or kind is either humble or not old and vice versa.
Fred is both brave and funny.
Paul is either not calm or curious.
Someone is rich.
Paul is old.
Someone is either not old or calm.
Fred is creative or not humble.
Susan is either generous or not brave. | Paul is not funny. | neutral | (![X]:((~rich(X)<~>~brave(X))<=>(kind(X)&~strong(X))))&
(![X]:((rich(X)|old(X))=>(~quiet(X)&~curious(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~kind(susan)&~funny(susan))))&
(((~happy(lucy)&~patient(lucy)))<=>(?[X]:((curious(X)<~>~creative(X)))))&
((?[X]:((~funny(X)&rich(X))))<=>(~strong(lucy)))&
(![X]:((humble(X)<~>~creative(X))=>~curious(X)))&
((?[X]:((kind(X)<~>tall(X))))=>((humble(lucy)<~>~quiet(lucy))))&
((?[X]:((tall(X)&wise(X))))<=>((~rich(alice)&quiet(alice))))&
((?[X]:(wise(X)))<=>(?[X]:((rich(X)|old(X)))))&
(((tall(john)&~curious(john)))<=>(?[X]:(~brave(X))))&
(![X]:(old(X)=>~happy(X)))&
(![X]:(funny(X)=>(generous(X)<~>kind(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>patient(X))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((kind(X)&~tall(X))<=>(brave(X)&creative(X))))&
(![X]:((generous(X)<~>kind(X))<=>(humble(X)<~>~old(X))))&
((brave(fred)&funny(fred)))&
((~calm(paul)<~>curious(paul)))&
(?[X]:(rich(X)))&
(old(paul))&
(?[X]:((~old(X)<~>calm(X))))&
((creative(fred)|~humble(fred)))&
((generous(susan)<~>~brave(susan))) | ~funny(paul) | [] | null | 0 |
Everyone who is both not rich and not patient is both not wise and not patient and vice versa.
Everyone who is not tall is rich.
If someone is either calm or not funny then someone is patient.
If someone is either happy or strong then someone is happy.
If alice is funny then someone is either humble or wise and vice versa.
Everyone who is not tall is both not quiet and not patient.
Everyone who is either calm or patient is not quiet and vice versa.
Everyone who is not old is humble or not patient and vice versa.
If fred is either happy or humble then alice is not patient or brave.
If someone is either not kind or calm then paul is both humble and curious.
If someone is either strong or tall then someone is both old and not calm.
If someone is not funny or humble then someone is not tall.
Everyone who is either not wise or brave is either brave or not curious.
Everyone who is not old is either quiet or patient and vice versa.
If paul is both wise and quiet then someone is either not calm or creative.
If mary is either not strong or not humble then someone is not generous or quiet.
Alice is funny or happy.
Someone is calm or not strong.
Alice is generous or wise.
Susan is not generous.
Mary is not quiet or wise.
Susan is either not calm or not tall.
Someone is not creative or calm.
John is both not brave and generous. | Mary is not tall. | contradiction | (![X]:((~rich(X)&~patient(X))<=>(~wise(X)&~patient(X))))&
(![X]:(~tall(X)=>rich(X)))&
((?[X]:((calm(X)<~>~funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((happy(X)<~>strong(X))))=>(?[X]:(happy(X))))&
((funny(alice))<=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:(~tall(X)=>(~quiet(X)&~patient(X))))&
(![X]:((calm(X)<~>patient(X))<=>~quiet(X)))&
(![X]:(~old(X)<=>(humble(X)|~patient(X))))&
(((happy(fred)<~>humble(fred)))=>((~patient(alice)|brave(alice))))&
((?[X]:((~kind(X)<~>calm(X))))=>((humble(paul)&curious(paul))))&
((?[X]:((strong(X)<~>tall(X))))=>(?[X]:((old(X)&~calm(X)))))&
((?[X]:((~funny(X)|humble(X))))=>(?[X]:(~tall(X))))&
(![X]:((~wise(X)<~>brave(X))=>(brave(X)<~>~curious(X))))&
(![X]:(~old(X)<=>(quiet(X)<~>patient(X))))&
(((wise(paul)&quiet(paul)))=>(?[X]:((~calm(X)<~>creative(X)))))&
(((~strong(mary)<~>~humble(mary)))=>(?[X]:((~generous(X)|quiet(X)))))&
((funny(alice)|happy(alice)))&
(?[X]:((calm(X)|~strong(X))))&
((generous(alice)|wise(alice)))&
(~generous(susan))&
((~quiet(mary)|wise(mary)))&
((~calm(susan)<~>~tall(susan)))&
(?[X]:((~creative(X)|calm(X))))&
((~brave(john)&generous(john))) | ~tall(mary) | [
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 172072335260244874722950
% SZS output start Proof for 172072335260244874722950
6. ! [X0] : (~tall(X0) => (~patient(X0) & ~quiet(X0))) [input p5]
8. ! [X0] : (~old(X0) <=> (~patient(X0) | humble(X0))) [input p7]
14. ! [X0] : (~old(X0) <=> (quiet(X0) <~> patient(X0))) [input p13]
25. ~tall(mary) [input hypothesis]
33. ! [X0] : ((~patient(X0) & ~quiet(X0)) | tall(X0)) [ennf transformation 6]
58. ! [X0] : ((~old(X0) | (patient(X0) & ~humble(X0))) & ((~patient(X0) | humble(X0)) | old(X0))) [nnf transformation 8]
59. ! [X0] : ((~old(X0) | (patient(X0) & ~humble(X0))) & (~patient(X0) | humble(X0) | old(X0))) [flattening 58]
70. ! [X0] : ((~old(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | old(X0))) [nnf transformation 14]
95. ~quiet(X0) | tall(X0) [cnf transformation 33]
96. ~patient(X0) | tall(X0) [cnf transformation 33]
103. ~old(X0) | patient(X0) [cnf transformation 59]
120. patient(X0) | quiet(X0) | old(X0) [cnf transformation 70]
123. ~old(X0) | quiet(X0) | ~patient(X0) [cnf transformation 70]
138. ~tall(mary) [cnf transformation 25]
253. ~old(X0) | quiet(X0) [subsumption resolution 123,103]
254. quiet(X0) | patient(X0) [subsumption resolution 120,253]
352. patient(X0) | tall(X0) [resolution 254,95]
353. tall(X0) [subsumption resolution 352,96]
399. $false [resolution 353,138]
% SZS output end Proof for 172072335260244874722950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or quiet then susan is either not quiet or not strong.
Everyone who is old or patient is not strong or quiet.
Everyone who is both not old and not wise is kind and vice versa.
If someone is either not wise or kind then john is either not tall or calm.
If someone is not creative or not strong then lucy is quiet or rich.
If someone is not calm or not rich then someone is happy or brave.
If alice is either not calm or not funny then susan is not patient or quiet and vice versa.
If someone is both creative and curious then paul is not kind or not happy.
If lucy is both not calm and not generous then someone is wise or not humble.
Everyone who is happy is both not quiet and not humble.
If paul is both wise and not funny then someone is happy.
If someone is both humble and not generous then fred is kind and vice versa.
Everyone who is either not kind or not tall is both old and rich and vice versa.
If someone is either kind or not strong then fred is strong.
If someone is not old then john is tall.
Everyone who is happy or not humble is either strong or not brave and vice versa.
Susan is not quiet or creative.
Someone is both calm and not funny.
Lucy is kind.
John is both happy and funny.
Someone is either patient or not happy.
Someone is either not tall or not humble.
Someone is both brave and quiet. | Lucy is not tall. | contradiction | ((?[X]:((~quiet(X)<~>quiet(X))))=>((~quiet(susan)<~>~strong(susan))))&
(![X]:((old(X)|patient(X))=>(~strong(X)|quiet(X))))&
(![X]:((~old(X)&~wise(X))<=>kind(X)))&
((?[X]:((~wise(X)<~>kind(X))))=>((~tall(john)<~>calm(john))))&
((?[X]:((~creative(X)|~strong(X))))=>((quiet(lucy)|rich(lucy))))&
((?[X]:((~calm(X)|~rich(X))))=>(?[X]:((happy(X)|brave(X)))))&
(((~calm(alice)<~>~funny(alice)))<=>((~patient(susan)|quiet(susan))))&
((?[X]:((creative(X)&curious(X))))=>((~kind(paul)|~happy(paul))))&
(((~calm(lucy)&~generous(lucy)))=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:(happy(X)=>(~quiet(X)&~humble(X))))&
(((wise(paul)&~funny(paul)))=>(?[X]:(happy(X))))&
((?[X]:((humble(X)&~generous(X))))<=>(kind(fred)))&
(![X]:((~kind(X)<~>~tall(X))<=>(old(X)&rich(X))))&
((?[X]:((kind(X)<~>~strong(X))))=>(strong(fred)))&
((?[X]:(~old(X)))=>(tall(john)))&
(![X]:((happy(X)|~humble(X))<=>(strong(X)<~>~brave(X))))&
((~quiet(susan)|creative(susan)))&
(?[X]:((calm(X)&~funny(X))))&
(kind(lucy))&
((happy(john)&funny(john)))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
(?[X]:((brave(X)&quiet(X)))) | ~tall(lucy) | [
"p2",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8905403988687991308971469
% SZS output start Proof for 8905403988687991308971469
3. ! [X0] : ((~wise(X0) & ~old(X0)) <=> kind(X0)) [input p2]
13. ! [X0] : ((~kind(X0) <~> ~tall(X0)) <=> (rich(X0) & old(X0))) [input p12]
19. kind(lucy) [input p18]
24. ~tall(lucy) [input hypothesis]
44. ! [X0] : (((~wise(X0) & ~old(X0)) | ~kind(X0)) & (kind(X0) | (wise(X0) | old(X0)))) [nnf transformation 3]
45. ! [X0] : (((~wise(X0) & ~old(X0)) | ~kind(X0)) & (kind(X0) | wise(X0) | old(X0))) [flattening 44]
60. ! [X0] : ((((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0))))) [nnf transformation 13]
61. ! [X0] : ((((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0))))) [flattening 60]
82. ~kind(X0) | ~old(X0) [cnf transformation 45]
105. old(X0) | ~kind(X0) | tall(X0) [cnf transformation 61]
121. kind(lucy) [cnf transformation 19]
130. ~tall(lucy) [cnf transformation 24]
261. ~kind(X0) | tall(X0) [subsumption resolution 105,82]
311. tall(lucy) [resolution 261,121]
314. $false [subsumption resolution 311,130]
% SZS output end Proof for 8905403988687991308971469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then someone is not happy. Everyone who is kind is tall or not tall and vice versa. Everyone who is curious is both humble and not kind and vice versa. If someone is quiet or tall then someone is not creative and vice versa. Everyone who is either patient or not patient is not brave and vice versa. Everyone who is brave or strong is not calm. If someone is not wise or patient then someone is not rich. Everyone who is either old or brave is not funny. Everyone who is not rich or curious is wise or kind and vice versa. Everyone who is not happy or rich is not patient or rich and vice versa. Everyone who is happy or not strong is either not curious or not patient. If someone is both happy and brave then someone is not brave. Everyone who is wise is not creative and vice versa. If fred is both humble and brave then alice is either not creative or not curious and vice versa. Everyone who is either happy or curious is either old or strong. If someone is either strong or not quiet then someone is both humble and happy and vice versa. Someone is strong. Lucy is old. Someone is generous or brave. Someone is not wise or not calm. Someone is not humble or curious. Alice is quiet or creative. | Alice is not quiet. | contradiction | ((quiet(mary))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)<=>(tall(X)|~tall(X))))&
(![X]:(curious(X)<=>(humble(X)&~kind(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((brave(X)|strong(X))=>~calm(X)))&
((?[X]:((~wise(X)|patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)<~>brave(X))=>~funny(X)))&
(![X]:((~rich(X)|curious(X))<=>(wise(X)|kind(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((?[X]:((happy(X)&brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(wise(X)<=>~creative(X)))&
(((humble(fred)&brave(fred)))<=>((~creative(alice)<~>~curious(alice))))&
(![X]:((happy(X)<~>curious(X))=>(old(X)<~>strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(?[X]:((humble(X)&happy(X)))))&
(?[X]:(strong(X)))&
(old(lucy))&
(?[X]:((generous(X)|brave(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~humble(X)|curious(X))))&
((quiet(alice)|creative(alice))) | ~quiet(alice) | [
"p1",
"p2",
"p4",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 36490660627732859580136
% SZS output start Proof for 36490660627732859580136
2. ! [X0] : (kind(X0) <=> (~tall(X0) | tall(X0))) [input p1]
3. ! [X0] : (curious(X0) <=> (~kind(X0) & humble(X0))) [input p2]
5. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> ~brave(X0)) [input p4]
14. (brave(fred) & humble(fred)) <=> (~creative(alice) <~> ~curious(alice)) [input p13]
22. creative(alice) | quiet(alice) [input p21]
23. ~quiet(alice) [input hypothesis]
39. ! [X0] : ((kind(X0) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | ~kind(X0))) [nnf transformation 2]
40. ! [X0] : ((kind(X0) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ~kind(X0))) [flattening 39]
41. ! [X0] : ((curious(X0) | (kind(X0) | ~humble(X0))) & ((~kind(X0) & humble(X0)) | ~curious(X0))) [nnf transformation 3]
42. ! [X0] : ((curious(X0) | kind(X0) | ~humble(X0)) & ((~kind(X0) & humble(X0)) | ~curious(X0))) [flattening 41]
48. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | brave(X0)) & (~brave(X0) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 5]
61. ((brave(fred) & humble(fred)) | ((~creative(alice) | curious(alice)) & (~curious(alice) | creative(alice)))) & (((curious(alice) | creative(alice)) & (~curious(alice) | ~creative(alice))) | (~brave(fred) | ~humble(fred))) [nnf transformation 14]
62. ((brave(fred) & humble(fred)) | ((~creative(alice) | curious(alice)) & (~curious(alice) | creative(alice)))) & (((curious(alice) | creative(alice)) & (~curious(alice) | ~creative(alice))) | ~brave(fred) | ~humble(fred)) [flattening 61]
75. kind(X0) | ~tall(X0) [cnf transformation 40]
76. kind(X0) | tall(X0) [cnf transformation 40]
78. ~kind(X0) | ~curious(X0) [cnf transformation 42]
83. ~brave(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 48]
84. ~brave(X0) | patient(X0) | patient(X0) [cnf transformation 48]
109. brave(fred) | ~creative(alice) | curious(alice) [cnf transformation 62]
123. creative(alice) | quiet(alice) [cnf transformation 22]
124. ~quiet(alice) [cnf transformation 23]
125. ~brave(X0) | ~patient(X0) [duplicate literal removal 83]
126. ~brave(X0) | patient(X0) [duplicate literal removal 84]
136. kind(X0) [subsumption resolution 75,76]
137. ~curious(X0) [subsumption resolution 78,136]
162. ~brave(X0) [subsumption resolution 125,126]
180. ~creative(alice) | curious(alice) [subsumption resolution 109,162]
181. ~creative(alice) [subsumption resolution 180,137]
216. quiet(alice) [subsumption resolution 123,181]
217. $false [subsumption resolution 124,216]
% SZS output end Proof for 36490660627732859580136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then alice is both rich and patient and vice versa. Everyone who is either calm or rich is either not funny or kind. Everyone who is either generous or not tall is quiet or not funny and vice versa. If someone is generous then someone is not creative and vice versa. If someone is not quiet then paul is either funny or generous and vice versa. Everyone who is generous is not humble and vice versa. If paul is both patient and not rich then fred is not patient and vice versa. Everyone who is both not generous and not wise is not kind or quiet. If john is both not tall and not generous then paul is not curious or not funny and vice versa. If someone is funny then someone is not tall or kind. If lucy is old or creative then someone is both not brave and not calm. If someone is not wise or not kind then paul is either not happy or rich. Everyone who is calm is both patient and kind. Everyone who is both not creative and not brave is kind and vice versa. Everyone who is humble is not happy and vice versa. If someone is happy or creative then alice is not wise or humble and vice versa. Fred is either wise or humble. Lucy is either not humble or not creative. Fred is either not strong or creative. Susan is rich or curious. Someone is both kind and calm. Someone is both quiet and not funny. Someone is wise. Someone is both not generous and not kind. | Paul is calm. | neutral | ((calm(paul))<=>((rich(alice)&patient(alice))))&
(![X]:((calm(X)<~>rich(X))=>(~funny(X)<~>kind(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(quiet(X)|~funny(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~creative(X))))&
((?[X]:(~quiet(X)))<=>((funny(paul)<~>generous(paul))))&
(![X]:(generous(X)<=>~humble(X)))&
(((patient(paul)&~rich(paul)))<=>(~patient(fred)))&
(![X]:((~generous(X)&~wise(X))=>(~kind(X)|quiet(X))))&
(((~tall(john)&~generous(john)))<=>((~curious(paul)|~funny(paul))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)|kind(X)))))&
(((old(lucy)|creative(lucy)))=>(?[X]:((~brave(X)&~calm(X)))))&
((?[X]:((~wise(X)|~kind(X))))=>((~happy(paul)<~>rich(paul))))&
(![X]:(calm(X)=>(patient(X)&kind(X))))&
(![X]:((~creative(X)&~brave(X))<=>kind(X)))&
(![X]:(humble(X)<=>~happy(X)))&
((?[X]:((happy(X)|creative(X))))<=>((~wise(alice)|humble(alice))))&
((wise(fred)<~>humble(fred)))&
((~humble(lucy)<~>~creative(lucy)))&
((~strong(fred)<~>creative(fred)))&
((rich(susan)|curious(susan)))&
(?[X]:((kind(X)&calm(X))))&
(?[X]:((quiet(X)&~funny(X))))&
(?[X]:(wise(X)))&
(?[X]:((~generous(X)&~kind(X)))) | calm(paul) | [] | null | 0 |
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
If fred is both brave and rich then someone is either not old or not humble and vice versa.
Everyone who is not humble or tall is either calm or patient.
Everyone who is strong is wise and vice versa.
Fred is strong or quiet.
Lucy is humble or not tall.
Someone is creative or strong.
Alice is either strong or calm.
Lucy is either not brave or funny.
Fred is both patient and not happy. | Fred is not humble. | contradiction | (![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(((brave(fred)&rich(fred)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|tall(X))=>(calm(X)<~>patient(X))))&
(![X]:(strong(X)<=>wise(X)))&
((strong(fred)|quiet(fred)))&
((humble(lucy)|~tall(lucy)))&
(?[X]:((creative(X)|strong(X))))&
((strong(alice)<~>calm(alice)))&
((~brave(lucy)<~>funny(lucy)))&
((patient(fred)&~happy(fred))) | ~humble(fred) | [
"p7",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 891669948529478738913772
% SZS output start Proof for 891669948529478738913772
8. ! [X0] : ((calm(X0) & funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p7]
14. ! [X0] : ((tall(X0) | ~humble(X0)) => (calm(X0) <~> patient(X0))) [input p13]
21. ~happy(fred) & patient(fred) [input p20]
22. ~humble(fred) [input hypothesis]
27. ! [X0] : ((calm(X0) <~> patient(X0)) | (~tall(X0) & humble(X0))) [ennf transformation 14]
45. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~calm(X0) | ~funny(X0)))) [nnf transformation 8]
46. ! [X0] : (((calm(X0) & funny(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~calm(X0) | ~funny(X0))) [flattening 45]
62. ! [X0] : (((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~tall(X0) & humble(X0))) [nnf transformation 27]
95. calm(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 46]
96. calm(X0) | tall(X0) | tall(X0) [cnf transformation 46]
123. ~patient(X0) | ~calm(X0) | humble(X0) [cnf transformation 62]
134. patient(fred) [cnf transformation 21]
136. ~humble(fred) [cnf transformation 22]
139. calm(X0) | ~tall(X0) [duplicate literal removal 95]
140. tall(X0) | calm(X0) [duplicate literal removal 96]
178. calm(X0) [subsumption resolution 139,140]
233. ~patient(X0) | humble(X0) [subsumption resolution 123,178]
282. humble(fred) [resolution 233,134]
286. $false [subsumption resolution 282,136]
% SZS output end Proof for 891669948529478738913772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not funny is either not brave or not calm.
Everyone who is rich or not rich is either creative or happy and vice versa.
If fred is either not quiet or generous then lucy is humble.
If mary is not generous or curious then someone is both not creative and tall and vice versa.
Everyone who is either curious or wise is either not old or brave and vice versa.
Everyone who is happy is both not curious and not tall.
If lucy is either old or not funny then paul is both happy and curious and vice versa.
If paul is either patient or not wise then lucy is not calm.
If someone is kind or not brave then someone is both rich and not generous.
Everyone who is not strong or wise is either quiet or curious and vice versa.
If john is both rich and not brave then mary is not quiet or strong.
Everyone who is wise is either quiet or not curious and vice versa.
If someone is either not rich or calm then someone is not strong and vice versa.
If susan is not brave or not curious then alice is not wise and vice versa.
Everyone who is not brave is not kind or not patient.
If someone is creative then susan is either not kind or quiet.
Alice is either brave or calm.
Someone is not rich.
Susan is not tall.
Susan is either happy or brave.
Mary is quiet.
Susan is either not strong or not calm.
Someone is rich.
Fred is either funny or calm. | John is not strong. | entailment | (![X]:((~creative(X)<~>~funny(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(creative(X)<~>happy(X))))&
(((~quiet(fred)<~>generous(fred)))=>(humble(lucy)))&
(((~generous(mary)|curious(mary)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((curious(X)<~>wise(X))<=>(~old(X)<~>brave(X))))&
(![X]:(happy(X)=>(~curious(X)&~tall(X))))&
(((old(lucy)<~>~funny(lucy)))<=>((happy(paul)&curious(paul))))&
(((patient(paul)<~>~wise(paul)))=>(~calm(lucy)))&
((?[X]:((kind(X)|~brave(X))))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~strong(X)|wise(X))<=>(quiet(X)<~>curious(X))))&
(((rich(john)&~brave(john)))=>((~quiet(mary)|strong(mary))))&
(![X]:(wise(X)<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(~strong(X))))&
(((~brave(susan)|~curious(susan)))<=>(~wise(alice)))&
(![X]:(~brave(X)=>(~kind(X)|~patient(X))))&
((?[X]:(creative(X)))=>((~kind(susan)<~>quiet(susan))))&
((brave(alice)<~>calm(alice)))&
(?[X]:(~rich(X)))&
(~tall(susan))&
((happy(susan)<~>brave(susan)))&
(quiet(mary))&
((~strong(susan)<~>~calm(susan)))&
(?[X]:(rich(X)))&
((funny(fred)<~>calm(fred))) | ~strong(john) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2460709675468998041349766
% SZS output start Proof for 2460709675468998041349766
10. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (quiet(X0) <~> curious(X0))) [input p9]
12. ! [X0] : (wise(X0) <=> (quiet(X0) <~> ~curious(X0))) [input p11]
25. strong(john) [input hypothesis]
53. ! [X0] : (((wise(X0) | ~strong(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [nnf transformation 10]
54. ! [X0] : ((wise(X0) | ~strong(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [flattening 53]
55. ! [X0] : ((wise(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) & (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ~wise(X0))) [nnf transformation 12]
110. ~wise(X0) | quiet(X0) | curious(X0) [cnf transformation 54]
112. ~wise(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 54]
113. ~strong(X0) | wise(X0) | curious(X0) | ~quiet(X0) [cnf transformation 54]
114. ~strong(X0) | wise(X0) | quiet(X0) | ~curious(X0) [cnf transformation 54]
116. ~curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 55]
117. curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 55]
118. wise(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 55]
119. wise(X0) | quiet(X0) | curious(X0) [cnf transformation 55]
142. strong(john) [cnf transformation 25]
238. curious(X0) | quiet(X0) [subsumption resolution 119,110]
239. ~curious(X0) | ~quiet(X0) [subsumption resolution 118,112]
240. ~wise(X0) | curious(X0) [subsumption resolution 117,110]
241. ~wise(X0) | quiet(X0) [subsumption resolution 116,110]
394. wise(john) | curious(john) | ~quiet(john) [resolution 113,142]
398. wise(john) | ~quiet(john) [subsumption resolution 394,239]
400. 40 <=> quiet(john) [avatar definition]
401. quiet(john) <- (40) [avatar component clause 400]
402. ~quiet(john) <- (~40) [avatar component clause 400]
404. 41 <=> wise(john) [avatar definition]
406. wise(john) <- (41) [avatar component clause 404]
407. ~40 | 41 [avatar split clause 398,404,400]
411. wise(john) | quiet(john) | ~curious(john) [resolution 114,142]
415. wise(john) | ~curious(john) <- (~40) [subsumption resolution 411,402]
417. 42 <=> curious(john) [avatar definition]
418. curious(john) <- (42) [avatar component clause 417]
419. ~curious(john) <- (~42) [avatar component clause 417]
420. ~42 | 41 | 40 [avatar split clause 415,400,404,417]
515. quiet(john) <- (~42) [resolution 419,238]
518. 40 | 42 [avatar split clause 515,417,400]
523. quiet(john) <- (41) [resolution 406,241]
524. curious(john) <- (41) [resolution 406,240]
533. 42 | ~41 [avatar split clause 524,404,417]
536. 40 | ~41 [avatar split clause 523,404,400]
539. ~quiet(john) <- (42) [resolution 418,239]
541. $false <- (40, 42) [subsumption resolution 539,401]
542. ~40 | ~42 [avatar contradiction clause 541]
543. $false [avatar sat refutation 407,420,518,533,536,542]
% SZS output end Proof for 2460709675468998041349766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is either calm or humble and vice versa.
If alice is not funny or old then paul is not funny.
Everyone who is not rich or humble is both funny and not wise.
If someone is both wise and funny then someone is either not tall or strong.
Everyone who is not rich or not creative is rich or not calm.
Everyone who is happy is not brave and vice versa.
Everyone who is both not humble and rich is either not quiet or not creative and vice versa.
Everyone who is either not calm or happy is either curious or happy.
If susan is both creative and happy then someone is either not brave or humble.
If alice is either curious or generous then someone is old or happy and vice versa.
If susan is quiet or old then paul is both not old and curious and vice versa.
Everyone who is not creative is either wise or creative.
Everyone who is tall or not kind is both happy and wise.
Everyone who is creative is calm or not funny.
Everyone who is wise is not strong or not rich and vice versa.
If someone is patient or not funny then fred is both not generous and patient.
Paul is either not curious or not humble.
Someone is both patient and brave.
Someone is both generous and not happy.
Susan is either kind or brave.
Someone is not quiet or rich.
Someone is both not humble and generous.
Alice is not wise. | Alice is not tall. | entailment | ((?[X]:(~generous(X)))<=>(?[X]:((calm(X)<~>humble(X)))))&
(((~funny(alice)|old(alice)))=>(~funny(paul)))&
(![X]:((~rich(X)|humble(X))=>(funny(X)&~wise(X))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
((~curious(paul)<~>~humble(paul)))&
(?[X]:((patient(X)&brave(X))))&
(?[X]:((generous(X)&~happy(X))))&
((kind(susan)<~>brave(susan)))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~wise(alice)) | ~tall(alice) | [
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8330755539385708550877833
% SZS output start Proof for 8330755539385708550877833
13. ! [X0] : ((~kind(X0) | tall(X0)) => (wise(X0) & happy(X0))) [input p12]
23. ~wise(alice) [input p22]
24. tall(alice) [input hypothesis]
36. ! [X0] : ((wise(X0) & happy(X0)) | (kind(X0) & ~tall(X0))) [ennf transformation 13]
118. ~tall(X0) | wise(X0) [cnf transformation 36]
139. ~wise(alice) [cnf transformation 23]
140. tall(alice) [cnf transformation 24]
324. wise(alice) [resolution 118,140]
325. $false [subsumption resolution 324,139]
% SZS output end Proof for 8330755539385708550877833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is wise or not brave then someone is creative or not wise and vice versa.
Everyone who is not kind is tall and vice versa.
Everyone who is not happy is not generous.
Everyone who is either not rich or creative is either not creative or funny and vice versa.
If someone is either not tall or humble then fred is either not old or not tall and vice versa.
If alice is either not brave or not creative then someone is either tall or not old and vice versa.
Everyone who is not patient or not quiet is tall or not patient.
If susan is both not tall and strong then mary is not humble.
If someone is not generous then someone is patient and vice versa.
If someone is either not happy or not patient then mary is either wise or kind.
Everyone who is either wise or brave is not kind or not rich and vice versa.
If alice is both curious and not brave then someone is both not brave and not quiet and vice versa.
Everyone who is quiet or not happy is either kind or generous.
Everyone who is old is either old or not happy and vice versa.
If someone is not funny or brave then fred is either not old or happy and vice versa.
Everyone who is either not quiet or not tall is either calm or not happy.
Someone is not brave.
Lucy is wise or happy.
Someone is either strong or not kind.
Someone is either generous or not creative.
Lucy is either rich or humble.
John is not kind.
Someone is not strong.
Mary is either not rich or strong. | Alice is not brave. | neutral | (((wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(~kind(X)<=>tall(X)))&
(![X]:(~happy(X)=>~generous(X)))&
(![X]:((~rich(X)<~>creative(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>humble(X))))<=>((~old(fred)<~>~tall(fred))))&
(((~brave(alice)<~>~creative(alice)))<=>(?[X]:((tall(X)<~>~old(X)))))&
(![X]:((~patient(X)|~quiet(X))=>(tall(X)|~patient(X))))&
(((~tall(susan)&strong(susan)))=>(~humble(mary)))&
((?[X]:(~generous(X)))<=>(?[X]:(patient(X))))&
((?[X]:((~happy(X)<~>~patient(X))))=>((wise(mary)<~>kind(mary))))&
(![X]:((wise(X)<~>brave(X))<=>(~kind(X)|~rich(X))))&
(((curious(alice)&~brave(alice)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
(![X]:((quiet(X)|~happy(X))=>(kind(X)<~>generous(X))))&
(![X]:(old(X)<=>(old(X)<~>~happy(X))))&
((?[X]:((~funny(X)|brave(X))))<=>((~old(fred)<~>happy(fred))))&
(![X]:((~quiet(X)<~>~tall(X))=>(calm(X)<~>~happy(X))))&
(?[X]:(~brave(X)))&
((wise(lucy)|happy(lucy)))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:((generous(X)<~>~creative(X))))&
((rich(lucy)<~>humble(lucy)))&
(~kind(john))&
(?[X]:(~strong(X)))&
((~rich(mary)<~>strong(mary))) | ~brave(alice) | [] | null | 0 |
If someone is curious then someone is either old or not calm and vice versa.
If someone is both tall and creative then paul is not strong or brave and vice versa.
If someone is either funny or calm then someone is both creative and quiet.
If someone is either brave or strong then someone is not tall or not wise.
Everyone who is wise is not humble.
Everyone who is humble or wise is either not funny or not strong and vice versa.
If someone is not rich then someone is both not rich and old and vice versa.
Everyone who is quiet or funny is either not creative or brave and vice versa.
Everyone who is both not tall and not humble is not happy or not brave and vice versa.
Everyone who is quiet is tall and vice versa.
Everyone who is strong is not old and vice versa.
If someone is either not funny or not generous then someone is not calm.
Everyone who is both not rich and not curious is either not funny or creative.
Everyone who is brave is not patient or not funny.
If someone is either not old or not wise then fred is not generous and vice versa.
Everyone who is generous is both funny and rich.
Someone is either happy or old.
Someone is either generous or funny.
Alice is either not funny or not strong.
Lucy is either old or generous.
Alice is not old or not creative.
Someone is either calm or not creative.
Someone is not wise or not brave.
Paul is wise. | Paul is not humble. | entailment | ((?[X]:(curious(X)))<=>(?[X]:((old(X)<~>~calm(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~strong(paul)|brave(paul))))&
((?[X]:((funny(X)<~>calm(X))))=>(?[X]:((creative(X)&quiet(X)))))&
((?[X]:((brave(X)<~>strong(X))))=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))<=>(~funny(X)<~>~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~happy(X)|~brave(X))))&
(![X]:(quiet(X)<=>tall(X)))&
(![X]:(strong(X)<=>~old(X)))&
((?[X]:((~funny(X)<~>~generous(X))))=>(?[X]:(~calm(X))))&
(![X]:((~rich(X)&~curious(X))=>(~funny(X)<~>creative(X))))&
(![X]:(brave(X)=>(~patient(X)|~funny(X))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(~generous(fred)))&
(![X]:(generous(X)=>(funny(X)&rich(X))))&
(?[X]:((happy(X)<~>old(X))))&
(?[X]:((generous(X)<~>funny(X))))&
((~funny(alice)<~>~strong(alice)))&
((old(lucy)<~>generous(lucy)))&
((~old(alice)|~creative(alice)))&
(?[X]:((calm(X)<~>~creative(X))))&
(?[X]:((~wise(X)|~brave(X))))&
(wise(paul)) | ~humble(paul) | [
"p4",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3082818489064160399128180
% SZS output start Proof for 3082818489064160399128180
5. ! [X0] : (wise(X0) => ~humble(X0)) [input p4]
24. wise(paul) [input p23]
25. humble(paul) [input hypothesis]
34. ! [X0] : (~humble(X0) | ~wise(X0)) [ennf transformation 5]
107. ~humble(X0) | ~wise(X0) [cnf transformation 34]
154. wise(paul) [cnf transformation 24]
155. humble(paul) [cnf transformation 25]
365. ~wise(paul) [resolution 107,155]
366. $false [subsumption resolution 365,154]
% SZS output end Proof for 3082818489064160399128180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not funny is either not creative or funny and vice versa.
Everyone who is both old and calm is either not strong or humble and vice versa.
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.
Someone is either not funny or calm.
Someone is either not generous or strong.
Someone is both quiet and not curious.
Lucy is either patient or humble.
Susan is not creative or wise.
Someone is both not old and not calm. | Mary is brave. | entailment | (![X]:((~rich(X)|~funny(X))<=>(~creative(X)<~>funny(X))))&
(![X]:((old(X)&calm(X))<=>(~strong(X)<~>humble(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))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~generous(X)<~>strong(X))))&
(?[X]:((quiet(X)&~curious(X))))&
((patient(lucy)<~>humble(lucy)))&
((~creative(susan)|wise(susan)))&
(?[X]:((~old(X)&~calm(X)))) | brave(mary) | [
"p1",
"p3",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7888504832146385134520718
% SZS output start Proof for 7888504832146385134520718
2. ! [X0] : ((calm(X0) & old(X0)) <=> (~strong(X0) <~> humble(X0))) [input p1]
4. ! [X0] : ((humble(X0) & ~curious(X0)) <=> (brave(X0) & ~generous(X0))) [input p3]
7. (~strong(fred) | creative(fred)) <=> ~wise(mary) [input p6]
9. ! [X0] : ((~strong(X0) & strong(X0)) <=> (tall(X0) | calm(X0))) [input p8]
10. ! [X0] : ((humble(X0) | old(X0)) <=> (~curious(X0) <~> wise(X0))) [input p9]
12. ! [X0] : ((~strong(X0) <~> tall(X0)) <=> (~patient(X0) | ~tall(X0))) [input p11]
23. ~brave(mary) [input hypothesis]
33. ! [X0] : (((calm(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~calm(X0) | ~old(X0)))) [nnf transformation 2]
34. ! [X0] : (((calm(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~calm(X0) | ~old(X0))) [flattening 33]
36. ! [X0] : (((humble(X0) & ~curious(X0)) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | (~humble(X0) | curious(X0)))) [nnf transformation 4]
37. ! [X0] : (((humble(X0) & ~curious(X0)) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | ~humble(X0) | curious(X0))) [flattening 36]
44. ((~strong(fred) | creative(fred)) | wise(mary)) & (~wise(mary) | (strong(fred) & ~creative(fred))) [nnf transformation 7]
45. (~strong(fred) | creative(fred) | wise(mary)) & (~wise(mary) | (strong(fred) & ~creative(fred))) [flattening 44]
49. ! [X0] : (((~strong(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 9]
50. ! [X0] : (((~strong(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | strong(X0) | ~strong(X0))) [flattening 49]
51. ! [X0] : (((humble(X0) | old(X0)) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~humble(X0) & ~old(X0)))) [nnf transformation 10]
52. ! [X0] : ((humble(X0) | old(X0) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) & (((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | (~humble(X0) & ~old(X0)))) [flattening 51]
57. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (patient(X0) & tall(X0))) & ((~patient(X0) | ~tall(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [nnf transformation 12]
58. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (patient(X0) & tall(X0))) & (~patient(X0) | ~tall(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [flattening 57]
89. humble(X0) | old(X0) | strong(X0) [cnf transformation 34]
91. humble(X0) | calm(X0) | strong(X0) [cnf transformation 34]
96. ~humble(X0) | brave(X0) | curious(X0) [cnf transformation 37]
107. ~wise(mary) | strong(fred) [cnf transformation 45]
114. strong(X0) | ~calm(X0) [cnf transformation 50]
115. strong(X0) | ~tall(X0) [cnf transformation 50]
116. ~strong(X0) | ~calm(X0) [cnf transformation 50]
117. ~tall(X0) | ~strong(X0) [cnf transformation 50]
118. ~curious(X0) | wise(X0) | ~old(X0) [cnf transformation 52]
119. ~curious(X0) | wise(X0) | ~humble(X0) [cnf transformation 52]
130. tall(X0) | ~strong(X0) | tall(X0) [cnf transformation 58]
158. ~brave(mary) [cnf transformation 23]
160. tall(X0) | ~strong(X0) [duplicate literal removal 130]
216. 13 <=> wise(mary) [avatar definition]
217. ~wise(mary) <- (~13) [avatar component clause 216]
224. 15 <=> strong(fred) [avatar definition]
225. strong(fred) <- (15) [avatar component clause 224]
228. 15 | ~13 [avatar split clause 107,216,224]
250. ~tall(X0) [subsumption resolution 115,117]
251. ~calm(X0) [subsumption resolution 114,116]
265. ~strong(X0) [subsumption resolution 160,250]
360. brave(X0) | curious(X0) | calm(X0) | strong(X0) [resolution 96,91]
383. brave(X0) | curious(X0) | strong(X0) [subsumption resolution 360,251]
384. brave(X0) | curious(X0) [subsumption resolution 383,265]
504. curious(mary) [resolution 384,158]
511. wise(mary) | ~humble(mary) [resolution 504,119]
512. wise(mary) | ~old(mary) [resolution 504,118]
513. ~humble(mary) <- (~13) [subsumption resolution 511,217]
514. ~old(mary) <- (~13) [subsumption resolution 512,217]
516. old(mary) | strong(mary) <- (~13) [resolution 513,89]
520. strong(mary) <- (~13) [subsumption resolution 516,514]
521. $false <- (~13) [subsumption resolution 520,265]
522. 13 [avatar contradiction clause 521]
535. $false <- (15) [subsumption resolution 225,265]
536. ~15 [avatar contradiction clause 535]
537. $false [avatar sat refutation 228,522,536]
% SZS output end Proof for 7888504832146385134520718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not wise is creative.
If lucy is not generous or tall then paul is humble or not humble and vice versa.
Everyone who is either not brave or not tall is not brave or not tall.
Everyone who is either not kind or calm is both curious and not humble and vice versa.
If someone is both not humble and not tall then someone is both not brave and not creative and vice versa.
If someone is both tall and patient then alice is humble.
If fred is not happy or not kind then someone is either not rich or funny and vice versa.
Everyone who is either kind or funny is not wise and vice versa.
Everyone who is both not old and quiet is both not quiet and patient and vice versa.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Everyone who is quiet or old is patient and vice versa.
Alice is either wise or curious.
Someone is not creative or not strong.
Susan is both not tall and not generous.
Alice is either not funny or strong.
Someone is both not kind and not humble.
Someone is either tall or quiet.
Someone is not humble. | Fred is patient. | contradiction | (![X]:((~brave(X)<~>~wise(X))=>creative(X)))&
(((~generous(lucy)|tall(lucy)))<=>((humble(paul)|~humble(paul))))&
(![X]:((~brave(X)<~>~tall(X))=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(curious(X)&~humble(X))))&
((?[X]:((~humble(X)&~tall(X))))<=>(?[X]:((~brave(X)&~creative(X)))))&
((?[X]:((tall(X)&patient(X))))=>(humble(alice)))&
(((~happy(fred)|~kind(fred)))<=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((kind(X)<~>funny(X))<=>~wise(X)))&
(![X]:((~old(X)&quiet(X))<=>(~quiet(X)&patient(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
((wise(alice)<~>curious(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
((~tall(susan)&~generous(susan)))&
((~funny(alice)<~>strong(alice)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | patient(fred) | [
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1828422459963037361855370
% SZS output start Proof for 1828422459963037361855370
9. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (patient(X0) & ~quiet(X0))) [input p8]
15. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X0] : (~patient(X0) <~> ~old(X0)) [input p14]
16. ! [X0] : ((old(X0) | quiet(X0)) <=> patient(X0)) [input p15]
24. patient(fred) [input hypothesis]
26. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X1] : (~patient(X1) <~> ~old(X1)) [rectify 15]
51. ! [X0] : (((quiet(X0) & ~old(X0)) | (~patient(X0) | quiet(X0))) & ((patient(X0) & ~quiet(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 9]
52. ! [X0] : (((quiet(X0) & ~old(X0)) | ~patient(X0) | quiet(X0)) & ((patient(X0) & ~quiet(X0)) | ~quiet(X0) | old(X0))) [flattening 51]
56. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X1] : ((old(X1) | patient(X1)) & (~old(X1) | ~patient(X1))) | ! [X0] : (~brave(X0) & ~patient(X0))) [nnf transformation 26]
57. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) | ! [X3] : (~brave(X3) & ~patient(X3))) [rectify 56]
58. ? [X0] : (brave(X0) | patient(X0)) => (brave(sK3) | patient(sK3)) [choice axiom]
59. ? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) => ((old(sK4) | patient(sK4)) & (~old(sK4) | ~patient(sK4))) [choice axiom]
60. ((brave(sK3) | patient(sK3)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (((old(sK4) | patient(sK4)) & (~old(sK4) | ~patient(sK4))) | ! [X3] : (~brave(X3) & ~patient(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((old(X0) | quiet(X0)) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((old(X0) | quiet(X0) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [flattening 61]
103. ~quiet(X0) | ~quiet(X0) | old(X0) [cnf transformation 52]
106. quiet(X0) | ~patient(X0) | quiet(X0) [cnf transformation 52]
120. ~old(sK4) | ~patient(sK4) | ~patient(X3) [cnf transformation 60]
122. old(sK4) | patient(sK4) | ~patient(X3) [cnf transformation 60]
127. patient(X0) | ~old(X0) [cnf transformation 62]
141. patient(fred) [cnf transformation 24]
142. ~quiet(X0) | old(X0) [duplicate literal removal 103]
143. ~patient(X0) | quiet(X0) [duplicate literal removal 106]
248. 24 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
249. ~old(X1) | patient(X1) <- (24) [avatar component clause 248]
255. 26 <=> patient(sK4) [avatar definition]
256. ~patient(sK4) <- (~26) [avatar component clause 255]
257. patient(sK4) <- (26) [avatar component clause 255]
259. 27 <=> old(sK4) [avatar definition]
260. ~old(sK4) <- (~27) [avatar component clause 259]
261. old(sK4) <- (27) [avatar component clause 259]
264. 28 <=> ! [X3] : ~patient(X3) [avatar definition]
265. ~patient(X3) <- (28) [avatar component clause 264]
266. 28 | 26 | 27 [avatar split clause 122,259,255,264]
268. 28 | ~26 | ~27 [avatar split clause 120,259,255,264]
269. 24 [avatar split clause 127,248]
315. quiet(sK4) <- (26) [resolution 143,257]
323. old(sK4) <- (26) [resolution 315,142]
326. $false <- (26, ~27) [subsumption resolution 323,260]
327. ~26 | 27 [avatar contradiction clause 326]
330. patient(sK4) <- (24, 27) [resolution 249,261]
331. $false <- (24, ~26, 27) [subsumption resolution 330,256]
332. ~24 | 26 | ~27 [avatar contradiction clause 331]
333. $false <- (28) [resolution 265,141]
336. ~28 [avatar contradiction clause 333]
337. $false [avatar sat refutation 266,268,269,327,332,336]
% SZS output end Proof for 1828422459963037361855370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and calm then lucy is either not humble or not funny. If someone is either humble or funny then susan is either happy or not strong and vice versa. Everyone who is creative is not wise. If someone is brave then someone is kind and vice versa. Everyone who is generous is both not strong and calm. If someone is quiet or not wise then someone is either not tall or wise and vice versa. If susan is generous then susan is not curious or old and vice versa. If fred is both not strong and not quiet then someone is either curious or not brave. If someone is patient then someone is either humble or funny. If someone is not calm or not old then paul is either not calm or not humble and vice versa. If lucy is either not curious or not rich then someone is both not creative and not humble. Everyone who is not wise is tall or happy and vice versa. Everyone who is either curious or calm is both not humble and not funny. Everyone who is rich is either happy or old and vice versa. Everyone who is kind or not happy is both rich and not tall. If someone is either not quiet or not tall then paul is either humble or not calm and vice versa. Someone is not wise. Someone is either not old or kind. John is either not happy or happy. John is both not humble and not happy. Susan is not tall or not brave. Someone is either not humble or funny. Susan is not generous. Paul is not old. | Susan is wise. | contradiction | ((?[X]:((creative(X)&calm(X))))=>((~humble(lucy)<~>~funny(lucy))))&
((?[X]:((humble(X)<~>funny(X))))<=>((happy(susan)<~>~strong(susan))))&
(![X]:(creative(X)=>~wise(X)))&
((?[X]:(brave(X)))<=>(?[X]:(kind(X))))&
(![X]:(generous(X)=>(~strong(X)&calm(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~tall(X)<~>wise(X)))))&
((generous(susan))<=>((~curious(susan)|old(susan))))&
(((~strong(fred)&~quiet(fred)))=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>funny(X)))))&
((?[X]:((~calm(X)|~old(X))))<=>((~calm(paul)<~>~humble(paul))))&
(((~curious(lucy)<~>~rich(lucy)))=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|happy(X))))&
(![X]:((curious(X)<~>calm(X))=>(~humble(X)&~funny(X))))&
(![X]:(rich(X)<=>(happy(X)<~>old(X))))&
(![X]:((kind(X)|~happy(X))=>(rich(X)&~tall(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>((humble(paul)<~>~calm(paul))))&
(?[X]:(~wise(X)))&
(?[X]:((~old(X)<~>kind(X))))&
((~happy(john)<~>happy(john)))&
((~humble(john)&~happy(john)))&
((~tall(susan)|~brave(susan)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~generous(susan))&
(~old(paul)) | wise(susan) | [
"p6",
"p11",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3881909339007516006383474
% SZS output start Proof for 3881909339007516006383474
7. generous(susan) <=> (old(susan) | ~curious(susan)) [input p6]
12. ! [X0] : (~wise(X0) <=> (happy(X0) | tall(X0))) [input p11]
14. ! [X0] : (rich(X0) <=> (happy(X0) <~> old(X0))) [input p13]
15. ! [X0] : ((~happy(X0) | kind(X0)) => (~tall(X0) & rich(X0))) [input p14]
23. ~generous(susan) [input p22]
25. wise(susan) [input hypothesis]
38. ! [X0] : ((~tall(X0) & rich(X0)) | (happy(X0) & ~kind(X0))) [ennf transformation 15]
53. (generous(susan) | (~old(susan) & curious(susan))) & ((old(susan) | ~curious(susan)) | ~generous(susan)) [nnf transformation 7]
54. (generous(susan) | (~old(susan) & curious(susan))) & (old(susan) | ~curious(susan) | ~generous(susan)) [flattening 53]
65. ! [X0] : ((~wise(X0) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | wise(X0))) [nnf transformation 12]
66. ! [X0] : ((~wise(X0) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | wise(X0))) [flattening 65]
68. ! [X0] : ((rich(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | ~rich(X0))) [nnf transformation 14]
102. generous(susan) | ~old(susan) [cnf transformation 54]
115. ~wise(X0) | ~happy(X0) [cnf transformation 66]
120. ~rich(X0) | happy(X0) | old(X0) [cnf transformation 68]
125. rich(X0) | happy(X0) [cnf transformation 38]
146. ~generous(susan) [cnf transformation 23]
148. wise(susan) [cnf transformation 25]
154. 2 <=> happy(susan) [avatar definition]
230. 19 <=> old(susan) [avatar definition]
232. ~old(susan) <- (~19) [avatar component clause 230]
234. 20 <=> generous(susan) [avatar definition]
237. ~19 | 20 [avatar split clause 102,234,230]
356. ~20 [avatar split clause 146,234]
361. ~happy(susan) [resolution 115,148]
410. happy(X0) | old(X0) | happy(X0) [resolution 120,125]
411. old(X0) | happy(X0) [duplicate literal removal 410]
488. happy(susan) <- (~19) [resolution 411,232]
495. 2 | 19 [avatar split clause 488,230,154]
496. ~2 [avatar split clause 361,154]
497. $false [avatar sat refutation 237,356,495,496]
% SZS output end Proof for 3881909339007516006383474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or humble is both creative and brave and vice versa. If someone is either tall or not strong then someone is both not curious and calm. If lucy is both not generous and not kind then someone is either not funny or calm and vice versa. If someone is either not curious or not funny then lucy is not curious and vice versa. Everyone who is old or generous is both not patient and old and vice versa. Everyone who is humble is both not calm and not funny. If someone is either strong or not calm then john is both not rich and kind and vice versa. If lucy is not generous or quiet then someone is not calm and vice versa. Everyone who is either not kind or humble is not rich or not wise and vice versa. If someone is either calm or not rich then someone is kind or not old. Everyone who is not wise or not rich is either not old or not creative and vice versa. Everyone who is generous is either generous or not kind. If someone is not wise or not quiet then mary is quiet or humble and vice versa. If mary is either not quiet or not patient then someone is either happy or curious. Everyone who is not curious is not generous and vice versa. Everyone who is not patient is not quiet or not brave. Someone is not generous or generous. Someone is rich. Susan is either not old or not rich. Someone is wise. Someone is both wise and not tall. Paul is both not strong and not humble. Someone is either not creative or calm. | Paul is old. | neutral | (![X]:((~old(X)<~>humble(X))<=>(creative(X)&brave(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>(?[X]:((~curious(X)&calm(X)))))&
(((~generous(lucy)&~kind(lucy)))<=>(?[X]:((~funny(X)<~>calm(X)))))&
((?[X]:((~curious(X)<~>~funny(X))))<=>(~curious(lucy)))&
(![X]:((old(X)|generous(X))<=>(~patient(X)&old(X))))&
(![X]:(humble(X)=>(~calm(X)&~funny(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>((~rich(john)&kind(john))))&
(((~generous(lucy)|quiet(lucy)))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(~rich(X)|~wise(X))))&
((?[X]:((calm(X)<~>~rich(X))))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((~wise(X)|~rich(X))<=>(~old(X)<~>~creative(X))))&
(![X]:(generous(X)=>(generous(X)<~>~kind(X))))&
((?[X]:((~wise(X)|~quiet(X))))<=>((quiet(mary)|humble(mary))))&
(((~quiet(mary)<~>~patient(mary)))=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:(~curious(X)<=>~generous(X)))&
(![X]:(~patient(X)=>(~quiet(X)|~brave(X))))&
(?[X]:((~generous(X)|generous(X))))&
(?[X]:(rich(X)))&
((~old(susan)<~>~rich(susan)))&
(?[X]:(wise(X)))&
(?[X]:((wise(X)&~tall(X))))&
((~strong(paul)&~humble(paul)))&
(?[X]:((~creative(X)<~>calm(X)))) | old(paul) | [] | null | 0 |
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.
Everyone who is both not strong and generous is quiet and vice versa.
Everyone who is both kind and not old is either not strong or not funny and vice versa.
If john is either kind or quiet then paul is either kind or tall.
Everyone who is both not brave and happy is both tall and wise.
Everyone who is either old or tall is old and vice versa.
Everyone who is not humble or tall is not wise.
Someone is kind or not happy.
Someone is not kind.
Lucy is either calm or happy.
Paul is not funny or generous.
Someone is generous. | Alice is not calm. | neutral | ((?[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]:((~strong(X)&generous(X))<=>quiet(X)))&
(![X]:((kind(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(((kind(john)<~>quiet(john)))=>((kind(paul)<~>tall(paul))))&
(![X]:((~brave(X)&happy(X))=>(tall(X)&wise(X))))&
(![X]:((old(X)<~>tall(X))<=>old(X)))&
(![X]:((~humble(X)|tall(X))=>~wise(X)))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:(~kind(X)))&
((calm(lucy)<~>happy(lucy)))&
((~funny(paul)|generous(paul)))&
(?[X]:(generous(X))) | ~calm(alice) | [] | null | 0 |
If someone is either old or wise then lucy is old.
If fred is both not creative and not happy then susan is either not patient or curious and vice versa.
Everyone who is both not quiet and curious is either wise or kind and vice versa.
If someone is calm then alice is both creative and tall and vice versa.
Everyone who is both not patient and funny is either brave or funny.
Everyone who is either tall or not generous is not calm or not happy.
Everyone who is either not humble or strong is rich.
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Someone is humble or not happy.
John is either not humble or humble.
Paul is both not calm and not creative.
Mary is not calm or not funny. | Paul is not old. | neutral | ((?[X]:((old(X)<~>wise(X))))=>(old(lucy)))&
(((~creative(fred)&~happy(fred)))<=>((~patient(susan)<~>curious(susan))))&
(![X]:((~quiet(X)&curious(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(?[X]:((humble(X)|~happy(X))))&
((~humble(john)<~>humble(john)))&
((~calm(paul)&~creative(paul)))&
((~calm(mary)|~funny(mary))) | ~old(paul) | [] | null | 0 |
If someone is both not generous and not calm then mary is both not happy and rich and vice versa. Everyone who is either patient or generous is not generous and vice versa. Everyone who is either not calm or not brave is not old or not tall. If someone is either curious or quiet then fred is not kind or not calm. Everyone who is both not quiet and not rich is not wise. If someone is quiet or brave then mary is happy or rich. If mary is not wise or not curious then someone is not creative. Everyone who is not funny or old is both quiet and creative. If someone is not curious then someone is both not creative and wise. Everyone who is either not creative or old is not calm or not quiet. If someone is both rich and humble then someone is not wise or not humble and vice versa. If john is either not strong or not happy then someone is either not rich or not funny and vice versa. Everyone who is not old or not generous is not wise. Everyone who is not wise or humble is both not strong and rich and vice versa. Everyone who is not happy or creative is both not creative and not brave. Everyone who is both quiet and not tall is both not funny and not creative and vice versa. Someone is both not quiet and not generous. Alice is curious or calm. Lucy is not brave. Mary is not quiet or not happy. Someone is both not happy and humble. Alice is rich or not strong. Someone is brave. | John is brave. | contradiction | ((?[X]:((~generous(X)&~calm(X))))<=>((~happy(mary)&rich(mary))))&
(![X]:((patient(X)<~>generous(X))<=>~generous(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(~old(X)|~tall(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>((~kind(fred)|~calm(fred))))&
(![X]:((~quiet(X)&~rich(X))=>~wise(X)))&
((?[X]:((quiet(X)|brave(X))))=>((happy(mary)|rich(mary))))&
(((~wise(mary)|~curious(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|old(X))=>(quiet(X)&creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((~creative(X)<~>old(X))=>(~calm(X)|~quiet(X))))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((~wise(X)|~humble(X)))))&
(((~strong(john)<~>~happy(john)))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((~old(X)|~generous(X))=>~wise(X)))&
(![X]:((~wise(X)|humble(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|creative(X))=>(~creative(X)&~brave(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~funny(X)&~creative(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
((curious(alice)|calm(alice)))&
(~brave(lucy))&
((~quiet(mary)|~happy(mary)))&
(?[X]:((~happy(X)&humble(X))))&
((rich(alice)|~strong(alice)))&
(?[X]:(brave(X))) | brave(john) | [
"p7",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7879126480460521951982685
% SZS output start Proof for 7879126480460521951982685
8. ! [X0] : ((old(X0) | ~funny(X0)) => (creative(X0) & quiet(X0))) [input p7]
12. (~strong(john) <~> ~happy(john)) <=> ? [X0] : (~rich(X0) <~> ~funny(X0)) [input p11]
13. ! [X0] : ((~generous(X0) | ~old(X0)) => ~wise(X0)) [input p12]
14. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (rich(X0) & ~strong(X0))) [input p13]
15. ! [X0] : ((creative(X0) | ~happy(X0)) => (~brave(X0) & ~creative(X0))) [input p14]
24. brave(john) [input hypothesis]
38. ! [X0] : ((creative(X0) & quiet(X0)) | (~old(X0) & funny(X0))) [ennf transformation 8]
41. ! [X0] : (~wise(X0) | (generous(X0) & old(X0))) [ennf transformation 13]
42. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 15]
58. (((happy(john) | strong(john)) & (~happy(john) | ~strong(john))) | ! [X0] : ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (? [X0] : ((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | ((~strong(john) | happy(john)) & (~happy(john) | strong(john)))) [nnf transformation 12]
59. (((happy(john) | strong(john)) & (~happy(john) | ~strong(john))) | ! [X0] : ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (? [X1] : ((funny(X1) | rich(X1)) & (~funny(X1) | ~rich(X1))) | ((~strong(john) | happy(john)) & (~happy(john) | strong(john)))) [rectify 58]
60. ? [X1] : ((funny(X1) | rich(X1)) & (~funny(X1) | ~rich(X1))) => ((funny(sK4) | rich(sK4)) & (~funny(sK4) | ~rich(sK4))) [choice axiom]
61. (((happy(john) | strong(john)) & (~happy(john) | ~strong(john))) | ! [X0] : ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(sK4) | rich(sK4)) & (~funny(sK4) | ~rich(sK4))) | ((~strong(john) | happy(john)) & (~happy(john) | strong(john)))) [skolemisation 59,60]
62. ! [X0] : (((humble(X0) | ~wise(X0)) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 14]
63. ! [X0] : ((humble(X0) | ~wise(X0) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | (~humble(X0) & wise(X0)))) [flattening 62]
88. funny(X0) | creative(X0) [cnf transformation 38]
89. ~old(X0) | creative(X0) [cnf transformation 38]
97. ~funny(sK4) | ~rich(sK4) | ~happy(john) | strong(john) [cnf transformation 61]
105. ~wise(X0) | old(X0) [cnf transformation 41]
107. ~strong(X0) | wise(X0) [cnf transformation 63]
109. wise(X0) | rich(X0) [cnf transformation 63]
113. ~creative(X0) | ~creative(X0) [cnf transformation 42]
114. ~brave(X0) | happy(X0) [cnf transformation 42]
128. brave(john) [cnf transformation 24]
129. ~creative(X0) [duplicate literal removal 113]
210. 18 <=> strong(john) [avatar definition]
212. strong(john) <- (18) [avatar component clause 210]
214. 19 <=> happy(john) [avatar definition]
225. 21 <=> rich(sK4) [avatar definition]
226. ~rich(sK4) <- (~21) [avatar component clause 225]
229. 22 <=> funny(sK4) [avatar definition]
230. ~funny(sK4) <- (~22) [avatar component clause 229]
235. 18 | ~19 | ~21 | ~22 [avatar split clause 97,229,225,214,210]
265. old(X1) | rich(X1) [resolution 109,105]
269. happy(john) [resolution 114,128]
272. 19 [avatar split clause 269,214]
273. creative(sK4) <- (~22) [resolution 230,88]
275. $false <- (~22) [subsumption resolution 273,129]
276. 22 [avatar contradiction clause 275]
280. wise(john) <- (18) [resolution 212,107]
282. old(john) <- (18) [resolution 280,105]
302. creative(john) <- (18) [resolution 282,89]
304. $false <- (18) [subsumption resolution 302,129]
305. ~18 [avatar contradiction clause 304]
340. rich(X1) | creative(X1) [resolution 265,89]
342. rich(X1) [subsumption resolution 340,129]
344. $false <- (~21) [resolution 342,226]
345. 21 [avatar contradiction clause 344]
346. $false [avatar sat refutation 235,272,276,305,345]
% SZS output end Proof for 7879126480460521951982685
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either not wise or not kind and vice versa.
Everyone who is either not wise or not curious is both wise and not curious and vice versa.
If fred is both not generous and calm then someone is not old.
If someone is creative then someone is generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Everyone who is kind or quiet is both strong and patient and vice versa.
Alice is either not curious or not wise.
Paul is not creative.
Someone is not tall.
Fred is not kind.
Paul is both not generous and not creative.
Alice is not creative.
Someone is not calm. | John is quiet. | entailment | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(wise(X)&~curious(X))))&
(((~generous(fred)&calm(fred)))=>(?[X]:(~old(X))))&
((?[X]:(creative(X)))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
((~curious(alice)<~>~wise(alice)))&
(~creative(paul))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~generous(paul)&~creative(paul)))&
(~creative(alice))&
(?[X]:(~calm(X))) | quiet(john) | [
"p3",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2518454728430288574641352
% SZS output start Proof for 2518454728430288574641352
4. ? [X0] : creative(X0) => ? [X0] : generous(X0) [input p3]
7. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p6]
8. ! [X0] : ((kind(X0) | quiet(X0)) <=> (funny(X0) | happy(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p15]
24. ~quiet(john) [input hypothesis]
25. ? [X0] : creative(X0) => ? [X1] : generous(X1) [rectify 4]
30. ? [X1] : generous(X1) | ! [X0] : ~creative(X0) [ennf transformation 25]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 7]
42. ? [X0] : generous(X0) | ! [X1] : ~creative(X1) [rectify 30]
43. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
44. generous(sK0) | ! [X1] : ~creative(X1) [skolemisation 42,43]
48. ! [X0] : (((kind(X0) | quiet(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 48]
61. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 12]
62. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 61]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
83. generous(sK0) | ~creative(X1) [cnf transformation 44]
89. ~patient(X0) | ~generous(X0) [cnf transformation 34]
93. ~funny(X0) | quiet(X0) | kind(X0) [cnf transformation 49]
105. quiet(X0) | creative(X0) [cnf transformation 62]
106. funny(X0) | quiet(X0) [cnf transformation 62]
115. ~kind(X0) | patient(X0) [cnf transformation 69]
116. ~quiet(X0) | patient(X0) [cnf transformation 69]
126. ~quiet(john) [cnf transformation 24]
132. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
133. ~creative(X1) <- (1) [avatar component clause 132]
135. 2 <=> generous(sK0) [avatar definition]
137. generous(sK0) <- (2) [avatar component clause 135]
138. 1 | 2 [avatar split clause 83,135,132]
231. creative(john) [resolution 105,126]
242. quiet(X0) | kind(X0) | quiet(X0) [resolution 93,106]
243. quiet(X0) | kind(X0) [duplicate literal removal 242]
314. kind(X1) | patient(X1) [resolution 243,116]
317. patient(X1) [subsumption resolution 314,115]
341. ~generous(X2) [resolution 317,89]
381. $false <- (2) [resolution 341,137]
382. ~2 [avatar contradiction clause 381]
383. $false <- (1) [resolution 133,231]
384. ~1 [avatar contradiction clause 383]
385. $false [avatar sat refutation 138,382,384]
% SZS output end Proof for 2518454728430288574641352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is generous and vice versa. If someone is quiet then someone is either happy or brave and vice versa. If fred is both wise and rich then lucy is calm or not brave and vice versa. Everyone who is both not wise and strong is either patient or wise and vice versa. Everyone who is either not curious or not creative is both happy and not old and vice versa. If paul is either creative or not creative then someone is not tall and vice versa. Everyone who is funny or quiet is creative or patient and vice versa. Everyone who is not kind or calm is either curious or creative and vice versa. If someone is not calm then someone is not strong. Everyone who is both strong and old is kind or calm. Everyone who is either funny or old is either not wise or not generous and vice versa. If someone is either wise or brave then someone is either tall or curious. If someone is not rich or rich then paul is either brave or not humble and vice versa. If lucy is either funny or old then someone is not curious or kind and vice versa. If someone is not happy or not old then paul is not patient. Mary is both humble and curious. Someone is either calm or not humble. Someone is strong or not humble. Someone is patient or not humble. Someone is tall or not calm. | Fred is not creative. | entailment | (![X]:(wise(X)<=>generous(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((happy(X)<~>brave(X)))))&
(((wise(fred)&rich(fred)))<=>((calm(lucy)|~brave(lucy))))&
(![X]:((~wise(X)&strong(X))<=>(patient(X)<~>wise(X))))&
(![X]:((~curious(X)<~>~creative(X))<=>(happy(X)&~old(X))))&
(((creative(paul)<~>~creative(paul)))<=>(?[X]:(~tall(X))))&
(![X]:((funny(X)|quiet(X))<=>(creative(X)|patient(X))))&
(![X]:((~kind(X)|calm(X))<=>(curious(X)<~>creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~strong(X))))&
(![X]:((strong(X)&old(X))=>(kind(X)|calm(X))))&
(![X]:((funny(X)<~>old(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:((wise(X)<~>brave(X))))=>(?[X]:((tall(X)<~>curious(X)))))&
((?[X]:((~rich(X)|rich(X))))<=>((brave(paul)<~>~humble(paul))))&
(((funny(lucy)<~>old(lucy)))<=>(?[X]:((~curious(X)|kind(X)))))&
((?[X]:((~happy(X)|~old(X))))=>(~patient(paul)))&
((humble(mary)&curious(mary)))&
(?[X]:((calm(X)<~>~humble(X))))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((tall(X)|~calm(X)))) | ~creative(fred) | [
"p0",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 114947212967696470382131
% SZS output start Proof for 114947212967696470382131
1. ! [X0] : (wise(X0) <=> generous(X0)) [input p0]
8. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (curious(X0) <~> creative(X0))) [input p7]
11. ! [X0] : ((funny(X0) <~> old(X0)) <=> (~wise(X0) <~> ~generous(X0))) [input p10]
14. (funny(lucy) <~> old(lucy)) <=> ? [X0] : (kind(X0) | ~curious(X0)) [input p13]
21. creative(fred) [input hypothesis]
30. ! [X0] : ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0))) [nnf transformation 1]
48. ! [X0] : (((calm(X0) | ~kind(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~calm(X0) & kind(X0)))) [nnf transformation 8]
49. ! [X0] : ((calm(X0) | ~kind(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~calm(X0) & kind(X0)))) [flattening 48]
53. ! [X0] : ((((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) & (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0))))) [nnf transformation 11]
62. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & (? [X0] : (kind(X0) | ~curious(X0)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [nnf transformation 14]
63. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & (? [X1] : (kind(X1) | ~curious(X1)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [rectify 62]
64. ? [X1] : (kind(X1) | ~curious(X1)) => (kind(sK6) | ~curious(sK6)) [choice axiom]
65. (((~old(lucy) | ~funny(lucy)) & (old(lucy) | funny(lucy))) | ! [X0] : (~kind(X0) & curious(X0))) & ((kind(sK6) | ~curious(sK6)) | ((funny(lucy) | ~old(lucy)) & (old(lucy) | ~funny(lucy)))) [skolemisation 63,64]
75. ~wise(X0) | generous(X0) [cnf transformation 30]
76. ~generous(X0) | wise(X0) [cnf transformation 30]
108. ~creative(X0) | ~curious(X0) | kind(X0) [cnf transformation 49]
114. ~generous(X0) | ~wise(X0) | old(X0) | ~funny(X0) [cnf transformation 53]
115. ~generous(X0) | ~wise(X0) | funny(X0) | ~old(X0) [cnf transformation 53]
116. generous(X0) | wise(X0) | old(X0) | ~funny(X0) [cnf transformation 53]
117. generous(X0) | wise(X0) | funny(X0) | ~old(X0) [cnf transformation 53]
134. old(lucy) | funny(lucy) | curious(X0) [cnf transformation 65]
135. old(lucy) | funny(lucy) | ~kind(X0) [cnf transformation 65]
136. ~old(lucy) | ~funny(lucy) | curious(X0) [cnf transformation 65]
137. ~old(lucy) | ~funny(lucy) | ~kind(X0) [cnf transformation 65]
147. creative(fred) [cnf transformation 21]
217. ~old(X0) | funny(X0) | wise(X0) [subsumption resolution 117,76]
218. ~funny(X0) | old(X0) | wise(X0) [subsumption resolution 116,76]
219. ~old(X0) | funny(X0) | ~generous(X0) [subsumption resolution 115,217]
220. ~funny(X0) | old(X0) | ~generous(X0) [subsumption resolution 114,218]
258. 23 <=> ! [X0] : ~kind(X0) [avatar definition]
259. ~kind(X0) <- (23) [avatar component clause 258]
261. 24 <=> funny(lucy) [avatar definition]
262. funny(lucy) <- (24) [avatar component clause 261]
263. ~funny(lucy) <- (~24) [avatar component clause 261]
265. 25 <=> old(lucy) [avatar definition]
266. old(lucy) <- (25) [avatar component clause 265]
267. ~old(lucy) <- (~25) [avatar component clause 265]
268. 23 | ~24 | ~25 [avatar split clause 137,265,261,258]
270. 26 <=> ! [X0] : curious(X0) [avatar definition]
271. curious(X0) <- (26) [avatar component clause 270]
272. 26 | ~24 | ~25 [avatar split clause 136,265,261,270]
273. 23 | 24 | 25 [avatar split clause 135,265,261,258]
274. 26 | 24 | 25 [avatar split clause 134,265,261,270]
399. ~curious(fred) | kind(fred) [resolution 108,147]
407. funny(lucy) | wise(lucy) <- (25) [resolution 217,266]
408. wise(lucy) <- (~24, 25) [subsumption resolution 407,263]
452. funny(lucy) | ~generous(lucy) <- (25) [resolution 219,266]
453. ~generous(lucy) <- (~24, 25) [subsumption resolution 452,263]
456. generous(lucy) <- (~24, 25) [resolution 408,75]
460. $false <- (~24, 25) [subsumption resolution 456,453]
461. 24 | ~25 [avatar contradiction clause 460]
466. kind(fred) <- (26) [subsumption resolution 399,271]
467. $false <- (23, 26) [subsumption resolution 466,259]
468. ~23 | ~26 [avatar contradiction clause 467]
471. old(lucy) | wise(lucy) <- (24) [resolution 262,218]
473. wise(lucy) <- (24, ~25) [subsumption resolution 471,267]
474. old(lucy) | ~generous(lucy) <- (24) [resolution 220,262]
475. ~generous(lucy) <- (24, ~25) [subsumption resolution 474,267]
505. generous(lucy) <- (24, ~25) [resolution 473,75]
506. $false <- (24, ~25) [subsumption resolution 505,475]
507. ~24 | 25 [avatar contradiction clause 506]
508. $false [avatar sat refutation 268,272,273,274,461,468,507]
% SZS output end Proof for 114947212967696470382131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not old and vice versa.
If john is both calm and not calm then lucy is not wise.
If someone is both not patient and kind then mary is either not calm or not wise.
Everyone who is not funny or not generous is both happy and brave.
Everyone who is kind or not wise is either not tall or not generous.
Everyone who is not humble is either strong or creative.
Everyone who is kind or not wise is quiet or wise and vice versa.
Everyone who is either curious or strong is happy.
Everyone who is not curious is both not generous and not strong and vice versa.
If fred is quiet then fred is both happy and not creative and vice versa.
Everyone who is both rich and not old is both rich and strong.
Everyone who is old is quiet or happy and vice versa.
Everyone who is either not creative or curious is brave.
Everyone who is not wise or kind is both curious and generous and vice versa.
If someone is both rich and kind then someone is both tall and funny and vice versa.
Everyone who is tall is either not old or rich.
Alice is not funny or not old.
Someone is either generous or tall. | Alice is not funny. | entailment | (![X]:(quiet(X)<=>~old(X)))&
(((calm(john)&~calm(john)))=>(~wise(lucy)))&
((?[X]:((~patient(X)&kind(X))))=>((~calm(mary)<~>~wise(mary))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&brave(X))))&
(![X]:((kind(X)|~wise(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~humble(X)=>(strong(X)<~>creative(X))))&
(![X]:((kind(X)|~wise(X))<=>(quiet(X)|wise(X))))&
(![X]:((curious(X)<~>strong(X))=>happy(X)))&
(![X]:(~curious(X)<=>(~generous(X)&~strong(X))))&
((quiet(fred))<=>((happy(fred)&~creative(fred))))&
(![X]:((rich(X)&~old(X))=>(rich(X)&strong(X))))&
(![X]:(old(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>curious(X))=>brave(X)))&
(![X]:((~wise(X)|kind(X))<=>(curious(X)&generous(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(tall(X)=>(~old(X)<~>rich(X))))&
((~funny(alice)|~old(alice)))&
(?[X]:((generous(X)<~>tall(X)))) | ~funny(alice) | [
"p0",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7412660645708879342758806
% SZS output start Proof for 7412660645708879342758806
1. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p0]
12. ! [X0] : (old(X0) <=> (happy(X0) | quiet(X0))) [input p11]
17. ~old(alice) | ~funny(alice) [input p16]
19. funny(alice) [input hypothesis]
33. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 1]
42. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | ~old(X0))) [nnf transformation 12]
43. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~old(X0))) [flattening 42]
55. ~old(X0) | ~quiet(X0) [cnf transformation 33]
56. old(X0) | quiet(X0) [cnf transformation 33]
79. old(X0) | ~quiet(X0) [cnf transformation 43]
92. ~old(alice) | ~funny(alice) [cnf transformation 17]
95. funny(alice) [cnf transformation 19]
113. ~quiet(X0) [subsumption resolution 79,55]
142. 10 <=> funny(alice) [avatar definition]
146. 11 <=> old(alice) [avatar definition]
148. ~old(alice) <- (~11) [avatar component clause 146]
149. ~10 | ~11 [avatar split clause 92,146,142]
160. 10 [avatar split clause 95,142]
161. quiet(alice) <- (~11) [resolution 56,148]
163. $false <- (~11) [subsumption resolution 161,113]
164. 11 [avatar contradiction clause 163]
165. $false [avatar sat refutation 149,160,164]
% SZS output end Proof for 7412660645708879342758806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or patient then mary is either wise or happy and vice versa. If someone is quiet or not quiet then someone is not brave or not funny. Everyone who is old or not strong is both generous and not happy. Everyone who is either rich or quiet is quiet or not old. Everyone who is happy or not tall is either not brave or not kind and vice versa. If paul is either not rich or generous then alice is not strong or kind and vice versa. If someone is both not strong and not rich then alice is both quiet and curious and vice versa. If someone is old or not old then someone is wise. Everyone who is either not patient or kind is not wise or not patient and vice versa. Everyone who is not patient is not creative. Everyone who is generous is not quiet. If susan is either funny or wise then someone is either not curious or not old. If mary is not humble then john is strong. Everyone who is either not creative or not happy is both tall and not brave and vice versa. If susan is not strong or not creative then lucy is patient or curious and vice versa. Everyone who is both generous and not rich is rich and vice versa. Someone is not quiet. Someone is either not funny or quiet. Someone is not tall or not happy. Someone is either happy or curious. Someone is strong. Someone is either not wise or calm. Fred is either old or not rich. | Paul is not generous. | entailment | ((?[X]:((~wise(X)<~>patient(X))))<=>((wise(mary)<~>happy(mary))))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((old(X)|~strong(X))=>(generous(X)&~happy(X))))&
(![X]:((rich(X)<~>quiet(X))=>(quiet(X)|~old(X))))&
(![X]:((happy(X)|~tall(X))<=>(~brave(X)<~>~kind(X))))&
(((~rich(paul)<~>generous(paul)))<=>((~strong(alice)|kind(alice))))&
((?[X]:((~strong(X)&~rich(X))))<=>((quiet(alice)&curious(alice))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:(wise(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~wise(X)|~patient(X))))&
(![X]:(~patient(X)=>~creative(X)))&
(![X]:(generous(X)=>~quiet(X)))&
(((funny(susan)<~>wise(susan)))=>(?[X]:((~curious(X)<~>~old(X)))))&
((~humble(mary))=>(strong(john)))&
(![X]:((~creative(X)<~>~happy(X))<=>(tall(X)&~brave(X))))&
(((~strong(susan)|~creative(susan)))<=>((patient(lucy)|curious(lucy))))&
(![X]:((generous(X)&~rich(X))<=>rich(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)<~>calm(X))))&
((old(fred)<~>~rich(fred))) | ~generous(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4327491342633007980783179
% SZS output start Proof for 4327491342633007980783179
16. ! [X0] : ((~rich(X0) & generous(X0)) <=> rich(X0)) [input p15]
24. generous(paul) [input hypothesis]
65. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) | ~generous(X0)))) [nnf transformation 16]
66. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | rich(X0) | ~generous(X0))) [flattening 65]
139. rich(X0) | rich(X0) | ~generous(X0) [cnf transformation 66]
141. ~rich(X0) | ~rich(X0) [cnf transformation 66]
153. generous(paul) [cnf transformation 24]
154. rich(X0) | ~generous(X0) [duplicate literal removal 139]
155. ~rich(X0) [duplicate literal removal 141]
303. ~generous(X0) [subsumption resolution 154,155]
344. $false [subsumption resolution 153,303]
% SZS output end Proof for 4327491342633007980783179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or kind is both not kind and calm and vice versa.
Everyone who is either not old or happy is either not happy or curious.
Everyone who is not patient is not brave and vice versa.
Everyone who is either curious or not brave is either not old or not wise and vice versa.
If someone is quiet then someone is either not quiet or not kind.
Everyone who is either creative or rich is happy or kind.
Everyone who is either quiet or happy is either generous or tall and vice versa.
If someone is not humble then someone is both not brave and not curious.
If paul is both not funny and not creative then alice is both generous and not old and vice versa.
Everyone who is either not creative or tall is either not tall or tall.
If someone is both not calm and wise then someone is not generous or calm and vice versa.
Everyone who is brave is either happy or tall and vice versa.
Everyone who is funny is not humble.
If alice is both not humble and creative then lucy is either tall or not generous and vice versa.
Everyone who is tall or not generous is both old and not quiet.
Everyone who is not old is not wise.
Paul is not old.
Mary is generous or not happy.
Someone is happy or generous.
Someone is not wise or strong.
Someone is both kind and not brave.
Lucy is not kind.
Someone is either calm or generous. | Alice is generous. | neutral | (![X]:((tall(X)<~>kind(X))<=>(~kind(X)&calm(X))))&
(![X]:((~old(X)<~>happy(X))=>(~happy(X)<~>curious(X))))&
(![X]:(~patient(X)<=>~brave(X)))&
(![X]:((curious(X)<~>~brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~quiet(X)<~>~kind(X)))))&
(![X]:((creative(X)<~>rich(X))=>(happy(X)|kind(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(generous(X)<~>tall(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~brave(X)&~curious(X)))))&
(((~funny(paul)&~creative(paul)))<=>((generous(alice)&~old(alice))))&
(![X]:((~creative(X)<~>tall(X))=>(~tall(X)<~>tall(X))))&
((?[X]:((~calm(X)&wise(X))))<=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:(brave(X)<=>(happy(X)<~>tall(X))))&
(![X]:(funny(X)=>~humble(X)))&
(((~humble(alice)&creative(alice)))<=>((tall(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)|~generous(X))=>(old(X)&~quiet(X))))&
(![X]:(~old(X)=>~wise(X)))&
(~old(paul))&
((generous(mary)|~happy(mary)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:((kind(X)&~brave(X))))&
(~kind(lucy))&
(?[X]:((calm(X)<~>generous(X)))) | generous(alice) | [] | null | 0 |
Everyone who is either wise or not humble is kind and vice versa.
Everyone who is quiet is both not wise and not creative.
Everyone who is wise or strong is calm.
Everyone who is not patient or funny is both old and not old and vice versa.
Everyone who is both not funny and patient is not tall and vice versa.
Everyone who is wise is not curious or patient.
Everyone who is both not creative and not curious is happy.
Everyone who is both rich and curious is both not strong and funny.
Everyone who is not patient or not strong is both calm and not generous.
If someone is generous or kind then someone is curious or brave and vice versa.
Everyone who is not quiet is both old and humble and vice versa.
Everyone who is calm is either calm or creative and vice versa.
Everyone who is generous is not old or not humble.
If mary is not generous then susan is both creative and not kind and vice versa.
Everyone who is not brave or not strong is funny and vice versa.
Fred is both humble and generous.
Someone is either wise or generous.
Someone is funny or not generous.
John is quiet.
Alice is either not calm or brave.
John is both not creative and not kind. | John is not calm. | contradiction | (![X]:((wise(X)<~>~humble(X))<=>kind(X)))&
(![X]:(quiet(X)=>(~wise(X)&~creative(X))))&
(![X]:((wise(X)|strong(X))=>calm(X)))&
(![X]:((~patient(X)|funny(X))<=>(old(X)&~old(X))))&
(![X]:((~funny(X)&patient(X))<=>~tall(X)))&
(![X]:(wise(X)=>(~curious(X)|patient(X))))&
(![X]:((~creative(X)&~curious(X))=>happy(X)))&
(![X]:((rich(X)&curious(X))=>(~strong(X)&funny(X))))&
(![X]:((~patient(X)|~strong(X))=>(calm(X)&~generous(X))))&
((?[X]:((generous(X)|kind(X))))<=>(?[X]:((curious(X)|brave(X)))))&
(![X]:(~quiet(X)<=>(old(X)&humble(X))))&
(![X]:(calm(X)<=>(calm(X)<~>creative(X))))&
(![X]:(generous(X)=>(~old(X)|~humble(X))))&
((~generous(mary))<=>((creative(susan)&~kind(susan))))&
(![X]:((~brave(X)|~strong(X))<=>funny(X)))&
((humble(fred)&generous(fred)))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((funny(X)|~generous(X))))&
(quiet(john))&
((~calm(alice)<~>brave(alice)))&
((~creative(john)&~kind(john))) | ~calm(john) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 398556749564206221933766
% SZS output start Proof for 398556749564206221933766
3. ! [X0] : ((strong(X0) | wise(X0)) => calm(X0)) [input p2]
9. ! [X0] : ((~strong(X0) | ~patient(X0)) => (~generous(X0) & calm(X0))) [input p8]
22. ~calm(john) [input hypothesis]
27. ! [X0] : (calm(X0) | (~strong(X0) & ~wise(X0))) [ennf transformation 3]
30. ! [X0] : ((~generous(X0) & calm(X0)) | (strong(X0) & patient(X0))) [ennf transformation 9]
61. calm(X0) | ~strong(X0) [cnf transformation 27]
69. calm(X0) | strong(X0) [cnf transformation 30]
100. ~calm(john) [cnf transformation 22]
105. calm(X0) [subsumption resolution 69,61]
163. $false [subsumption resolution 100,105]
% SZS output end Proof for 398556749564206221933766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then someone is both old and not old. If someone is either not strong or not patient then someone is both not patient and not curious and vice versa. If susan is kind or not strong then susan is not wise or generous and vice versa. Everyone who is not curious is both calm and not kind. If someone is not strong then paul is rich or not kind. Everyone who is both not generous and strong is patient and vice versa. If someone is both not creative and strong then someone is either not quiet or old. If lucy is strong then john is either curious or rich and vice versa. Everyone who is rich or tall is not curious or not brave. Everyone who is not patient or not humble is brave. If someone is old then paul is not creative or generous. Everyone who is humble is not brave. Everyone who is both not happy and brave is either not old or humble. Everyone who is both not calm and quiet is not patient or not happy and vice versa. Everyone who is not generous or humble is not quiet or wise and vice versa. Everyone who is both old and quiet is both not happy and not brave and vice versa. John is both not happy and creative. Lucy is not rich. Fred is not happy or calm. Someone is both not humble and curious. Someone is either strong or wise. Someone is not humble or not patient. | Fred is not strong. | neutral | ((?[X]:(calm(X)))=>(?[X]:((old(X)&~old(X)))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((kind(susan)|~strong(susan)))<=>((~wise(susan)|generous(susan))))&
(![X]:(~curious(X)=>(calm(X)&~kind(X))))&
((?[X]:(~strong(X)))=>((rich(paul)|~kind(paul))))&
(![X]:((~generous(X)&strong(X))<=>patient(X)))&
((?[X]:((~creative(X)&strong(X))))=>(?[X]:((~quiet(X)<~>old(X)))))&
((strong(lucy))<=>((curious(john)<~>rich(john))))&
(![X]:((rich(X)|tall(X))=>(~curious(X)|~brave(X))))&
(![X]:((~patient(X)|~humble(X))=>brave(X)))&
((?[X]:(old(X)))=>((~creative(paul)|generous(paul))))&
(![X]:(humble(X)=>~brave(X)))&
(![X]:((~happy(X)&brave(X))=>(~old(X)<~>humble(X))))&
(![X]:((~calm(X)&quiet(X))<=>(~patient(X)|~happy(X))))&
(![X]:((~generous(X)|humble(X))<=>(~quiet(X)|wise(X))))&
(![X]:((old(X)&quiet(X))<=>(~happy(X)&~brave(X))))&
((~happy(john)&creative(john)))&
(~rich(lucy))&
((~happy(fred)|calm(fred)))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((strong(X)<~>wise(X))))&
(?[X]:((~humble(X)|~patient(X)))) | ~strong(fred) | [] | null | 0 |
Everyone who is either curious or old is both rich and brave and vice versa.
If mary is either calm or not quiet then someone is brave or not creative and vice versa.
Everyone who is both not creative and not tall is humble and vice versa.
If lucy is either kind or calm then paul is not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
If lucy is both curious and patient then lucy is not tall.
If someone is either not strong or funny then someone is not generous or humble and vice versa.
Everyone who is not funny or creative is both not humble and wise and vice versa.
Everyone who is both not patient and old is both funny and not humble.
Everyone who is either not strong or not happy is old or not humble.
Everyone who is either not happy or tall is not curious or creative and vice versa.
Everyone who is calm or not old is patient and vice versa.
Everyone who is both not curious and wise is both tall and not strong and vice versa.
Everyone who is brave or old is both not tall and not kind.
If someone is not kind or rich then someone is not old or not creative and vice versa.
Everyone who is either rich or not funny is both not curious and happy and vice versa.
Someone is both strong and not rich.
Paul is patient or not calm.
Alice is not wise.
Fred is both humble and brave.
John is both quiet and old.
Alice is not old or patient.
Paul is either not happy or brave.
Paul is not creative or not kind. | Fred is not old. | contradiction | (![X]:((curious(X)<~>old(X))<=>(rich(X)&brave(X))))&
(((calm(mary)<~>~quiet(mary)))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((~creative(X)&~tall(X))<=>humble(X)))&
(((kind(lucy)<~>calm(lucy)))=>(~quiet(paul)))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(((curious(lucy)&patient(lucy)))=>(~tall(lucy)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~funny(X)|creative(X))<=>(~humble(X)&wise(X))))&
(![X]:((~patient(X)&old(X))=>(funny(X)&~humble(X))))&
(![X]:((~strong(X)<~>~happy(X))=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((calm(X)|~old(X))<=>patient(X)))&
(![X]:((~curious(X)&wise(X))<=>(tall(X)&~strong(X))))&
(![X]:((brave(X)|old(X))=>(~tall(X)&~kind(X))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~curious(X)&happy(X))))&
(?[X]:((strong(X)&~rich(X))))&
((patient(paul)|~calm(paul)))&
(~wise(alice))&
((humble(fred)&brave(fred)))&
((quiet(john)&old(john)))&
((~old(alice)|patient(alice)))&
((~happy(paul)<~>brave(paul)))&
((~creative(paul)|~kind(paul))) | ~old(fred) | [
"p0",
"p2",
"p4",
"p7",
"p9",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7514122576211875858202114
% SZS output start Proof for 7514122576211875858202114
1. ! [X0] : ((curious(X0) <~> old(X0)) <=> (brave(X0) & rich(X0))) [input p0]
3. ! [X0] : ((~tall(X0) & ~creative(X0)) <=> humble(X0)) [input p2]
5. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p4]
8. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (wise(X0) & ~humble(X0))) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~happy(X0)) => (~humble(X0) | old(X0))) [input p9]
11. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> (creative(X0) | ~curious(X0))) [input p10]
16. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (happy(X0) & ~curious(X0))) [input p15]
20. brave(fred) & humble(fred) [input p19]
25. ~old(fred) [input hypothesis]
33. ! [X0] : ((~humble(X0) | old(X0)) | (~strong(X0) <=> ~happy(X0))) [ennf transformation 10]
34. ! [X0] : (~humble(X0) | old(X0) | (~strong(X0) <=> ~happy(X0))) [flattening 33]
36. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [flattening 36]
42. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | (tall(X0) | creative(X0)))) [nnf transformation 3]
43. ! [X0] : (((~tall(X0) & ~creative(X0)) | ~humble(X0)) & (humble(X0) | tall(X0) | creative(X0))) [flattening 42]
45. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 45]
52. ! [X0] : (((creative(X0) | ~funny(X0)) | (~wise(X0) | humble(X0))) & ((wise(X0) & ~humble(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 8]
53. ! [X0] : ((creative(X0) | ~funny(X0) | ~wise(X0) | humble(X0)) & ((wise(X0) & ~humble(X0)) | (~creative(X0) & funny(X0)))) [flattening 52]
54. ! [X0] : (~humble(X0) | old(X0) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) [nnf transformation 34]
55. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [flattening 55]
66. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 16]
67. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [flattening 66]
71. ~curious(X0) | old(X0) | rich(X0) [cnf transformation 37]
85. ~humble(X0) | ~tall(X0) [cnf transformation 43]
89. ~funny(X0) | strong(X0) [cnf transformation 46]
100. ~humble(X0) | funny(X0) [cnf transformation 53]
108. ~strong(X0) | old(X0) | ~humble(X0) | happy(X0) [cnf transformation 54]
111. ~happy(X0) | tall(X0) | curious(X0) [cnf transformation 56]
130. ~funny(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 67]
140. humble(fred) [cnf transformation 20]
148. ~old(fred) [cnf transformation 25]
292. ~tall(fred) [resolution 85,140]
293. funny(fred) [resolution 100,140]
295. strong(fred) [resolution 293,89]
326. ~curious(fred) | ~rich(fred) [resolution 130,293]
329. 35 <=> rich(fred) [avatar definition]
331. ~rich(fred) <- (~35) [avatar component clause 329]
333. 36 <=> curious(fred) [avatar definition]
334. curious(fred) <- (36) [avatar component clause 333]
336. ~35 | ~36 [avatar split clause 326,333,329]
403. old(fred) | ~humble(fred) | happy(fred) [resolution 108,295]
424. ~humble(fred) | happy(fred) [subsumption resolution 403,148]
425. happy(fred) [subsumption resolution 424,140]
717. tall(fred) | curious(fred) [resolution 425,111]
721. curious(fred) [subsumption resolution 717,292]
722. 36 [avatar split clause 721,333]
726. old(fred) | rich(fred) <- (36) [resolution 334,71]
727. rich(fred) <- (36) [subsumption resolution 726,148]
728. $false <- (~35, 36) [subsumption resolution 727,331]
729. 35 | ~36 [avatar contradiction clause 728]
730. $false [avatar sat refutation 336,722,729]
% SZS output end Proof for 7514122576211875858202114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or creative is either old or not curious.
If alice is both not brave and funny then someone is either not rich or brave and vice versa.
Everyone who is both old and not kind is quiet or wise.
Everyone who is humble or curious is both not calm and old and vice versa.
If fred is either happy or not patient then fred is either brave or not strong.
Everyone who is either old or not generous is either strong or old.
If mary is not strong or not quiet then john is not patient.
Everyone who is both not patient and patient is old or calm and vice versa.
If someone is generous then lucy is either happy or tall and vice versa.
Everyone who is either old or not happy is both quiet and not old.
Everyone who is either old or not old is both funny and not happy.
Everyone who is either curious or old is brave and vice versa.
Everyone who is either not quiet or not humble is not rich.
If john is both not quiet and brave then someone is either not wise or quiet and vice versa.
If someone is both not wise and not strong then fred is both not old and not kind.
Everyone who is quiet is both not curious and not patient.
Lucy is kind.
Fred is either wise or quiet.
Mary is not kind.
Paul is quiet or not humble.
Someone is both strong and not generous.
Susan is quiet or not patient.
Mary is patient or not brave. | Fred is not strong. | entailment | (![X]:((generous(X)|creative(X))=>(old(X)<~>~curious(X))))&
(((~brave(alice)&funny(alice)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((old(X)&~kind(X))=>(quiet(X)|wise(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&old(X))))&
(((happy(fred)<~>~patient(fred)))=>((brave(fred)<~>~strong(fred))))&
(![X]:((old(X)<~>~generous(X))=>(strong(X)<~>old(X))))&
(((~strong(mary)|~quiet(mary)))=>(~patient(john)))&
(![X]:((~patient(X)&patient(X))<=>(old(X)|calm(X))))&
((?[X]:(generous(X)))<=>((happy(lucy)<~>tall(lucy))))&
(![X]:((old(X)<~>~happy(X))=>(quiet(X)&~old(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&~happy(X))))&
(![X]:((curious(X)<~>old(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~humble(X))=>~rich(X)))&
(((~quiet(john)&brave(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
((?[X]:((~wise(X)&~strong(X))))=>((~old(fred)&~kind(fred))))&
(![X]:(quiet(X)=>(~curious(X)&~patient(X))))&
(kind(lucy))&
((wise(fred)<~>quiet(fred)))&
(~kind(mary))&
((quiet(paul)|~humble(paul)))&
(?[X]:((strong(X)&~generous(X))))&
((quiet(susan)|~patient(susan)))&
((patient(mary)|~brave(mary))) | ~strong(fred) | [
"p4",
"p7",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6784901556308390475474280
% SZS output start Proof for 6784901556308390475474280
5. (happy(fred) <~> ~patient(fred)) => (brave(fred) <~> ~strong(fred)) [input p4]
8. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (calm(X0) | old(X0))) [input p7]
10. ! [X0] : ((old(X0) <~> ~happy(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((old(X0) <~> ~old(X0)) => (~happy(X0) & funny(X0))) [input p10]
12. ! [X0] : ((curious(X0) <~> old(X0)) <=> brave(X0)) [input p11]
16. ! [X0] : (quiet(X0) => (~patient(X0) & ~curious(X0))) [input p15]
24. strong(fred) [input hypothesis]
29. (brave(fred) <~> ~strong(fred)) | (happy(fred) <=> ~patient(fred)) [ennf transformation 5]
32. ! [X0] : ((~old(X0) & quiet(X0)) | (old(X0) <=> ~happy(X0))) [ennf transformation 10]
33. ! [X0] : ((~happy(X0) & funny(X0)) | (old(X0) <=> ~old(X0))) [ennf transformation 11]
36. ! [X0] : ((~patient(X0) & ~curious(X0)) | ~quiet(X0)) [ennf transformation 16]
45. ((strong(fred) | ~brave(fred)) & (~strong(fred) | brave(fred))) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred))) [nnf transformation 29]
47. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((patient(X0) & ~patient(X0)) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ~patient(X0) | patient(X0))) [flattening 47]
53. ! [X0] : ((~old(X0) & quiet(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 32]
54. ! [X0] : ((~happy(X0) & funny(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) [nnf transformation 33]
55. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0)) & (brave(X0) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 12]
80. ~strong(fred) | brave(fred) | happy(fred) | patient(fred) [cnf transformation 45]
90. ~patient(X0) | ~old(X0) [cnf transformation 48]
92. ~old(X0) | patient(X0) [cnf transformation 48]
99. quiet(X0) | old(X0) | happy(X0) [cnf transformation 53]
105. ~happy(X0) | old(X0) | old(X0) [cnf transformation 54]
108. old(X0) | curious(X0) | ~brave(X0) [cnf transformation 55]
120. ~quiet(X0) | ~curious(X0) [cnf transformation 36]
121. ~patient(X0) | ~quiet(X0) [cnf transformation 36]
131. strong(fred) [cnf transformation 24]
135. ~happy(X0) | old(X0) [duplicate literal removal 105]
168. 7 <=> patient(fred) [avatar definition]
170. patient(fred) <- (7) [avatar component clause 168]
172. 8 <=> happy(fred) [avatar definition]
174. happy(fred) <- (8) [avatar component clause 172]
176. 9 <=> brave(fred) [avatar definition]
177. brave(fred) <- (9) [avatar component clause 176]
180. 10 <=> strong(fred) [avatar definition]
185. 7 | 8 | 9 | ~10 [avatar split clause 80,180,176,172,168]
202. ~old(X0) [subsumption resolution 90,92]
222. happy(X0) | quiet(X0) [subsumption resolution 99,202]
223. ~happy(X0) [subsumption resolution 135,202]
225. ~brave(X0) | curious(X0) [subsumption resolution 108,202]
291. 10 [avatar split clause 131,180]
292. ~quiet(fred) <- (7) [resolution 121,170]
293. quiet(X0) [resolution 222,223]
295. ~curious(X0) [resolution 293,120]
302. $false <- (7) [subsumption resolution 292,293]
303. ~7 [avatar contradiction clause 302]
305. curious(fred) <- (9) [resolution 177,225]
306. $false <- (9) [subsumption resolution 305,295]
307. ~9 [avatar contradiction clause 306]
308. $false <- (8) [subsumption resolution 174,223]
309. ~8 [avatar contradiction clause 308]
310. $false [avatar sat refutation 185,291,303,307,309]
% SZS output end Proof for 6784901556308390475474280
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both strong and tall and vice versa.
Everyone who is both quiet and not funny is curious or not funny.
Everyone who is calm is both not humble and generous.
Everyone who is not brave or tall is either not brave or calm.
If someone is not tall or wise then lucy is both curious and not curious and vice versa.
Everyone who is either not old or calm is both not curious and humble and vice versa.
If paul is creative or not kind then someone is either rich or not tall and vice versa.
Everyone who is patient is both not funny and not quiet and vice versa.
Everyone who is humble is wise or tall and vice versa.
Everyone who is both curious and not kind is either not creative or not tall and vice versa.
Everyone who is both brave and not strong is either happy or generous and vice versa.
Everyone who is funny or humble is either humble or not kind.
If susan is either not happy or not strong then susan is old or curious.
If paul is either quiet or patient then fred is either not strong or not creative and vice versa.
Everyone who is not happy or not brave is not wise and vice versa.
Everyone who is both not calm and wise is either brave or curious.
Paul is either tall or not kind.
Susan is not funny or not strong.
John is kind or quiet.
Mary is both not happy and not generous.
Someone is both tall and happy.
Susan is rich or not old. | Mary is not wise. | entailment | (![X]:(funny(X)<=>(strong(X)&tall(X))))&
(![X]:((quiet(X)&~funny(X))=>(curious(X)|~funny(X))))&
(![X]:(calm(X)=>(~humble(X)&generous(X))))&
(![X]:((~brave(X)|tall(X))=>(~brave(X)<~>calm(X))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&humble(X))))&
(((creative(paul)|~kind(paul)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(patient(X)<=>(~funny(X)&~quiet(X))))&
(![X]:(humble(X)<=>(wise(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((brave(X)&~strong(X))<=>(happy(X)<~>generous(X))))&
(![X]:((funny(X)|humble(X))=>(humble(X)<~>~kind(X))))&
(((~happy(susan)<~>~strong(susan)))=>((old(susan)|curious(susan))))&
(((quiet(paul)<~>patient(paul)))<=>((~strong(fred)<~>~creative(fred))))&
(![X]:((~happy(X)|~brave(X))<=>~wise(X)))&
(![X]:((~calm(X)&wise(X))=>(brave(X)<~>curious(X))))&
((tall(paul)<~>~kind(paul)))&
((~funny(susan)|~strong(susan)))&
((kind(john)|quiet(john)))&
((~happy(mary)&~generous(mary)))&
(?[X]:((tall(X)&happy(X))))&
((rich(susan)|~old(susan))) | ~wise(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3077333654719771419620295
% SZS output start Proof for 3077333654719771419620295
5. ? [X0] : (wise(X0) | ~tall(X0)) <=> (~curious(lucy) & curious(lucy)) [input p4]
23. wise(mary) [input hypothesis]
36. (? [X0] : (wise(X0) | ~tall(X0)) | (curious(lucy) | ~curious(lucy))) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [nnf transformation 5]
37. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [flattening 36]
38. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [rectify 37]
39. ? [X0] : (wise(X0) | ~tall(X0)) => (wise(sK0) | ~tall(sK0)) [choice axiom]
40. ((wise(sK0) | ~tall(sK0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [skolemisation 38,39]
76. curious(lucy) | ~wise(X1) [cnf transformation 40]
78. ~curious(lucy) | ~wise(X1) [cnf transformation 40]
138. wise(mary) [cnf transformation 23]
142. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
143. ~wise(X1) <- (1) [avatar component clause 142]
145. 2 <=> curious(lucy) [avatar definition]
148. 1 | ~2 [avatar split clause 78,145,142]
153. 1 | 2 [avatar split clause 76,145,142]
251. $false <- (1) [resolution 143,138]
252. ~1 [avatar contradiction clause 251]
253. $false [avatar sat refutation 148,153,252]
% SZS output end Proof for 3077333654719771419620295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is both not curious and not rich and vice versa.
Everyone who is either not old or funny is not brave and vice versa.
Everyone who is not funny or old is both generous and creative.
If john is either calm or not strong then alice is funny.
Everyone who is not old is both not quiet and not generous and vice versa.
Everyone who is either wise or curious is not brave or not strong and vice versa.
Everyone who is generous is either kind or patient.
Everyone who is both not generous and not tall is wise or not old and vice versa.
Everyone who is curious is both humble and not rich.
If mary is old or not funny then susan is either not wise or happy and vice versa.
Everyone who is not kind or not strong is rich and vice versa.
If alice is not wise or calm then mary is both not calm and not funny and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
If susan is both not humble and creative then fred is not humble or generous.
If paul is both quiet and rich then lucy is generous or rich.
Someone is quiet or funny.
Someone is strong or wise.
Lucy is both not strong and not humble.
Someone is humble. | Fred is rich. | neutral | (![X]:((~creative(X)<~>brave(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)<~>funny(X))<=>~brave(X)))&
(![X]:((~funny(X)|old(X))=>(generous(X)&creative(X))))&
(((calm(john)<~>~strong(john)))=>(funny(alice)))&
(![X]:(~old(X)<=>(~quiet(X)&~generous(X))))&
(![X]:((wise(X)<~>curious(X))<=>(~brave(X)|~strong(X))))&
(![X]:(generous(X)=>(kind(X)<~>patient(X))))&
(![X]:((~generous(X)&~tall(X))<=>(wise(X)|~old(X))))&
(![X]:(curious(X)=>(humble(X)&~rich(X))))&
(((old(mary)|~funny(mary)))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((~kind(X)|~strong(X))<=>rich(X)))&
(((~wise(alice)|calm(alice)))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(((~humble(susan)&creative(susan)))=>((~humble(fred)|generous(fred))))&
(((quiet(paul)&rich(paul)))=>((generous(lucy)|rich(lucy))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((strong(X)|wise(X))))&
((~strong(lucy)&~humble(lucy)))&
(?[X]:(humble(X))) | rich(fred) | [] | null | 0 |
Everyone who is not strong or not humble is both not happy and not rich. Everyone who is either not old or happy is not tall. Everyone who is not brave or not happy is old or not tall and vice versa. Everyone who is kind or generous is either creative or not strong and vice versa. Everyone who is both humble and not generous is both not patient and not humble. Everyone who is patient or not quiet is not patient and vice versa. Everyone who is either not brave or quiet is both generous and not curious. Everyone who is both not curious and old is not wise or not brave and vice versa. If mary is either not happy or curious then john is rich or not brave. Everyone who is old is both strong and not humble. Everyone who is not happy or not creative is funny or calm and vice versa. Everyone who is both not quiet and creative is both creative and quiet and vice versa. If someone is either not funny or not rich then mary is both generous and quiet and vice versa. If someone is both not funny and not brave then someone is either brave or not kind and vice versa. Everyone who is not quiet is curious or rich and vice versa. Everyone who is quiet is generous and vice versa. John is either not tall or not creative. Lucy is brave or not generous. Susan is not rich. Someone is not old or not creative. | Susan is not brave. | contradiction | (![X]:((~strong(X)|~humble(X))=>(~happy(X)&~rich(X))))&
(![X]:((~old(X)<~>happy(X))=>~tall(X)))&
(![X]:((~brave(X)|~happy(X))<=>(old(X)|~tall(X))))&
(![X]:((kind(X)|generous(X))<=>(creative(X)<~>~strong(X))))&
(![X]:((humble(X)&~generous(X))=>(~patient(X)&~humble(X))))&
(![X]:((patient(X)|~quiet(X))<=>~patient(X)))&
(![X]:((~brave(X)<~>quiet(X))=>(generous(X)&~curious(X))))&
(![X]:((~curious(X)&old(X))<=>(~wise(X)|~brave(X))))&
(((~happy(mary)<~>curious(mary)))=>((rich(john)|~brave(john))))&
(![X]:(old(X)=>(strong(X)&~humble(X))))&
(![X]:((~happy(X)|~creative(X))<=>(funny(X)|calm(X))))&
(![X]:((~quiet(X)&creative(X))<=>(creative(X)&quiet(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>((generous(mary)&quiet(mary))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:(~quiet(X)<=>(curious(X)|rich(X))))&
(![X]:(quiet(X)<=>generous(X)))&
((~tall(john)<~>~creative(john)))&
((brave(lucy)|~generous(lucy)))&
(~rich(susan))&
(?[X]:((~old(X)|~creative(X)))) | ~brave(susan) | [
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8970238455253101103886561
% SZS output start Proof for 8970238455253101103886561
6. ! [X0] : ((~quiet(X0) | patient(X0)) <=> ~patient(X0)) [input p5]
7. ! [X0] : ((~brave(X0) <~> quiet(X0)) => (~curious(X0) & generous(X0))) [input p6]
16. ! [X0] : (quiet(X0) <=> generous(X0)) [input p15]
21. ~brave(susan) [input hypothesis]
27. ! [X0] : ((~curious(X0) & generous(X0)) | (~brave(X0) <=> quiet(X0))) [ennf transformation 7]
36. ! [X0] : (((~quiet(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 6]
37. ! [X0] : ((~quiet(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~patient(X0)))) [flattening 36]
38. ! [X0] : ((~curious(X0) & generous(X0)) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) [nnf transformation 27]
58. ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))) [nnf transformation 16]
80. ~patient(X0) | ~patient(X0) [cnf transformation 37]
82. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 37]
83. quiet(X0) | generous(X0) | brave(X0) [cnf transformation 38]
120. ~generous(X0) | quiet(X0) [cnf transformation 58]
126. ~brave(susan) [cnf transformation 21]
129. ~patient(X0) [duplicate literal removal 80]
130. ~quiet(X0) | patient(X0) [duplicate literal removal 82]
249. generous(X0) | brave(X0) | patient(X0) [resolution 83,130]
255. generous(X0) | brave(X0) [subsumption resolution 249,129]
258. quiet(X1) | brave(X1) [resolution 255,120]
293. brave(X1) | patient(X1) [resolution 258,130]
298. brave(X1) [subsumption resolution 293,129]
302. $false [resolution 298,126]
% SZS output end Proof for 8970238455253101103886561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is humble or not funny then paul is curious or humble. Everyone who is patient is both not tall and funny. Everyone who is both not generous and not creative is both quiet and not funny and vice versa. Everyone who is both not rich and creative is both not brave and brave and vice versa. If someone is kind or happy then someone is calm. If someone is either old or not curious then alice is either old or wise. If someone is either not rich or not happy then someone is either old or not creative. Everyone who is happy is funny and vice versa. If paul is not humble then alice is both not creative and quiet and vice versa. If someone is curious then lucy is strong or kind and vice versa. Everyone who is rich is both curious and not rich and vice versa. Everyone who is humble is both not rich and brave and vice versa. If someone is not wise then susan is generous or not curious and vice versa. If someone is both not generous and calm then paul is not generous and vice versa. If paul is both quiet and not humble then someone is either not creative or not patient. Everyone who is not tall or not happy is either funny or not curious and vice versa. Alice is both not brave and not strong. Susan is quiet. Susan is not old or rich. Someone is funny or not calm. Someone is both not rich and not tall. Fred is both happy and kind. | Lucy is old. | neutral | (((humble(lucy)|~funny(lucy)))=>((curious(paul)|humble(paul))))&
(![X]:(patient(X)=>(~tall(X)&funny(X))))&
(![X]:((~generous(X)&~creative(X))<=>(quiet(X)&~funny(X))))&
(![X]:((~rich(X)&creative(X))<=>(~brave(X)&brave(X))))&
((?[X]:((kind(X)|happy(X))))=>(?[X]:(calm(X))))&
((?[X]:((old(X)<~>~curious(X))))=>((old(alice)<~>wise(alice))))&
((?[X]:((~rich(X)<~>~happy(X))))=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:(happy(X)<=>funny(X)))&
((~humble(paul))<=>((~creative(alice)&quiet(alice))))&
((?[X]:(curious(X)))<=>((strong(lucy)|kind(lucy))))&
(![X]:(rich(X)<=>(curious(X)&~rich(X))))&
(![X]:(humble(X)<=>(~rich(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((generous(susan)|~curious(susan))))&
((?[X]:((~generous(X)&calm(X))))<=>(~generous(paul)))&
(((quiet(paul)&~humble(paul)))=>(?[X]:((~creative(X)<~>~patient(X)))))&
(![X]:((~tall(X)|~happy(X))<=>(funny(X)<~>~curious(X))))&
((~brave(alice)&~strong(alice)))&
(quiet(susan))&
((~old(susan)|rich(susan)))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:((~rich(X)&~tall(X))))&
((happy(fred)&kind(fred))) | old(lucy) | [] | null | 0 |
Everyone who is not creative or not happy is either funny or creative.
If someone is calm then someone is both humble and patient and vice versa.
Everyone who is either not humble or generous is both humble and not creative.
Everyone who is not rich or not strong is both not funny and humble and vice versa.
If someone is both not creative and not generous then someone is not generous or not strong.
If susan is patient or quiet then fred is either not old or not calm and vice versa.
Everyone who is not strong is either quiet or not happy and vice versa.
If mary is both kind and patient then alice is both strong and calm and vice versa.
Everyone who is funny is either old or not happy and vice versa.
Everyone who is both not kind and not creative is not funny.
Everyone who is not humble or patient is both not humble and quiet.
If john is kind then paul is either not generous or old.
If john is not strong then someone is both not quiet and not wise and vice versa.
If someone is either not curious or not brave then susan is either strong or humble and vice versa.
If paul is either not patient or old then someone is not creative.
Everyone who is funny is not humble or patient.
Someone is generous.
John is not wise.
Alice is both old and not generous.
John is humble.
John is not patient.
Someone is both not rich and humble.
Fred is quiet or not wise.
Fred is not brave or not curious. | Alice is not funny. | entailment | (![X]:((~creative(X)|~happy(X))=>(funny(X)<~>creative(X))))&
((?[X]:(calm(X)))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((~humble(X)<~>generous(X))=>(humble(X)&~creative(X))))&
(![X]:((~rich(X)|~strong(X))<=>(~funny(X)&humble(X))))&
((?[X]:((~creative(X)&~generous(X))))=>(?[X]:((~generous(X)|~strong(X)))))&
(((patient(susan)|quiet(susan)))<=>((~old(fred)<~>~calm(fred))))&
(![X]:(~strong(X)<=>(quiet(X)<~>~happy(X))))&
(((kind(mary)&patient(mary)))<=>((strong(alice)&calm(alice))))&
(![X]:(funny(X)<=>(old(X)<~>~happy(X))))&
(![X]:((~kind(X)&~creative(X))=>~funny(X)))&
(![X]:((~humble(X)|patient(X))=>(~humble(X)&quiet(X))))&
((kind(john))=>((~generous(paul)<~>old(paul))))&
((~strong(john))<=>(?[X]:((~quiet(X)&~wise(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((strong(susan)<~>humble(susan))))&
(((~patient(paul)<~>old(paul)))=>(?[X]:(~creative(X))))&
(![X]:(funny(X)=>(~humble(X)|patient(X))))&
(?[X]:(generous(X)))&
(~wise(john))&
((old(alice)&~generous(alice)))&
(humble(john))&
(~patient(john))&
(?[X]:((~rich(X)&humble(X))))&
((quiet(fred)|~wise(fred)))&
((~brave(fred)|~curious(fred))) | ~funny(alice) | [
"p2",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 18972346137875891582768
% SZS output start Proof for 18972346137875891582768
3. ! [X0] : ((~humble(X0) <~> generous(X0)) => (~creative(X0) & humble(X0))) [input p2]
11. ! [X0] : ((patient(X0) | ~humble(X0)) => (quiet(X0) & ~humble(X0))) [input p10]
16. ! [X0] : (funny(X0) => (patient(X0) | ~humble(X0))) [input p15]
19. ~generous(alice) & old(alice) [input p18]
25. funny(alice) [input hypothesis]
29. ! [X0] : ((~creative(X0) & humble(X0)) | (~humble(X0) <=> generous(X0))) [ennf transformation 3]
33. ! [X0] : ((quiet(X0) & ~humble(X0)) | (~patient(X0) & humble(X0))) [ennf transformation 11]
36. ! [X0] : ((patient(X0) | ~humble(X0)) | ~funny(X0)) [ennf transformation 16]
37. ! [X0] : (patient(X0) | ~humble(X0) | ~funny(X0)) [flattening 36]
44. ! [X0] : ((~creative(X0) & humble(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) [nnf transformation 29]
79. humble(X0) | generous(X0) | humble(X0) [cnf transformation 44]
109. ~humble(X0) | ~patient(X0) [cnf transformation 33]
127. ~humble(X0) | patient(X0) | ~funny(X0) [cnf transformation 37]
131. ~generous(alice) [cnf transformation 19]
138. funny(alice) [cnf transformation 25]
139. generous(X0) | humble(X0) [duplicate literal removal 79]
142. 1 <=> ! [X1] : (~patient(X1) | ~humble(X1)) [avatar definition]
143. ~patient(X1) | ~humble(X1) <- (1) [avatar component clause 142]
217. 1 [avatar split clause 109,142]
325. humble(alice) [resolution 139,131]
415. patient(alice) | ~funny(alice) [resolution 127,325]
421. patient(alice) [subsumption resolution 415,138]
468. ~humble(alice) <- (1) [resolution 421,143]
470. $false <- (1) [subsumption resolution 468,325]
471. ~1 [avatar contradiction clause 470]
473. $false [avatar sat refutation 217,471]
% SZS output end Proof for 18972346137875891582768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either strong or generous then john is quiet and vice versa. If fred is either happy or funny then someone is either brave or not brave and vice versa. Everyone who is rich is both old and not old. If someone is either not wise or strong then someone is either calm or not old. If someone is not funny or quiet then lucy is not patient. Everyone who is both not strong and funny is both not wise and not calm and vice versa. Everyone who is either not creative or curious is either not tall or not rich. Everyone who is rich or humble is both quiet and brave. Everyone who is happy or brave is not brave and vice versa. If someone is wise or calm then someone is both happy and old and vice versa. If someone is not generous or generous then someone is funny. If mary is patient or calm then fred is not strong. Everyone who is kind is both happy and not humble and vice versa. If fred is either not creative or wise then someone is not happy or not patient and vice versa. If lucy is brave or not wise then someone is humble or strong and vice versa. Everyone who is not brave is happy. Someone is either humble or strong. Someone is not brave or funny. Someone is either curious or not calm. Someone is kind. Someone is not kind or not quiet. Someone is either not humble or not funny. Someone is either patient or tall. Fred is quiet. | Fred is not funny. | entailment | (((strong(mary)<~>generous(mary)))<=>(quiet(john)))&
(((happy(fred)<~>funny(fred)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:(rich(X)=>(old(X)&~old(X))))&
((?[X]:((~wise(X)<~>strong(X))))=>(?[X]:((calm(X)<~>~old(X)))))&
((?[X]:((~funny(X)|quiet(X))))=>(~patient(lucy)))&
(![X]:((~strong(X)&funny(X))<=>(~wise(X)&~calm(X))))&
(![X]:((~creative(X)<~>curious(X))=>(~tall(X)<~>~rich(X))))&
(![X]:((rich(X)|humble(X))=>(quiet(X)&brave(X))))&
(![X]:((happy(X)|brave(X))<=>~brave(X)))&
((?[X]:((wise(X)|calm(X))))<=>(?[X]:((happy(X)&old(X)))))&
((?[X]:((~generous(X)|generous(X))))=>(?[X]:(funny(X))))&
(((patient(mary)|calm(mary)))=>(~strong(fred)))&
(![X]:(kind(X)<=>(happy(X)&~humble(X))))&
(((~creative(fred)<~>wise(fred)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(((brave(lucy)|~wise(lucy)))<=>(?[X]:((humble(X)|strong(X)))))&
(![X]:(~brave(X)=>happy(X)))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((~kind(X)|~quiet(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((patient(X)<~>tall(X))))&
(quiet(fred)) | ~funny(fred) | [
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5248748425487819870780872
% SZS output start Proof for 5248748425487819870780872
2. (happy(fred) <~> funny(fred)) <=> ? [X0] : (brave(X0) <~> ~brave(X0)) [input p1]
9. ! [X0] : ((brave(X0) | happy(X0)) <=> ~brave(X0)) [input p8]
25. funny(fred) [input hypothesis]
38. (((~funny(fred) | ~happy(fred)) & (funny(fred) | happy(fred))) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X0] : ((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ((happy(fred) | ~funny(fred)) & (funny(fred) | ~happy(fred)))) [nnf transformation 2]
39. (((~funny(fred) | ~happy(fred)) & (funny(fred) | happy(fred))) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) | ((happy(fred) | ~funny(fred)) & (funny(fred) | ~happy(fred)))) [rectify 38]
40. ? [X1] : ((brave(X1) | ~brave(X1)) & (~brave(X1) | brave(X1))) => ((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) [choice axiom]
41. (((~funny(fred) | ~happy(fred)) & (funny(fred) | happy(fred))) | ! [X0] : ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(sK0) | ~brave(sK0)) & (~brave(sK0) | brave(sK0))) | ((happy(fred) | ~funny(fred)) & (funny(fred) | ~happy(fred)))) [skolemisation 39,40]
49. ! [X0] : (((brave(X0) | happy(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : ((brave(X0) | happy(X0) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~happy(X0)))) [flattening 49]
99. ~funny(fred) | ~happy(fred) | brave(X0) | brave(X0) [cnf transformation 41]
121. ~brave(X0) | ~brave(X0) [cnf transformation 50]
122. brave(X0) | happy(X0) | brave(X0) [cnf transformation 50]
158. funny(fred) [cnf transformation 25]
159. ~brave(X0) [duplicate literal removal 121]
160. brave(X0) | happy(X0) [duplicate literal removal 122]
164. ~funny(fred) | ~happy(fred) | brave(X0) [duplicate literal removal 99]
182. 4 <=> ! [X0] : brave(X0) [avatar definition]
183. brave(X0) <- (4) [avatar component clause 182]
185. 5 <=> happy(fred) [avatar definition]
187. ~happy(fred) <- (~5) [avatar component clause 185]
189. 6 <=> funny(fred) [avatar definition]
192. 4 | ~5 | ~6 [avatar split clause 164,189,185,182]
194. 7 <=> ! [X0] : ~brave(X0) [avatar definition]
195. ~brave(X0) <- (7) [avatar component clause 194]
232. 7 [avatar split clause 159,194]
302. 31 <=> ! [X0] : happy(X0) [avatar definition]
303. happy(X0) <- (31) [avatar component clause 302]
401. 6 [avatar split clause 158,189]
426. happy(X1) <- (7) [resolution 160,195]
429. 31 | ~7 [avatar split clause 426,194,302]
430. $false <- (~5, 31) [resolution 303,187]
431. 5 | ~31 [avatar contradiction clause 430]
432. $false <- (4, 7) [subsumption resolution 183,195]
433. ~4 | ~7 [avatar contradiction clause 432]
434. $false [avatar sat refutation 192,232,401,429,431,433]
% SZS output end Proof for 5248748425487819870780872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or funny is tall and vice versa.
If alice is both not calm and not patient then someone is either not patient or quiet.
If alice is either not patient or kind then someone is either patient or generous.
Everyone who is either tall or happy is not rich or not tall and vice versa.
Everyone who is both old and not quiet is either creative or generous and vice versa.
Everyone who is both not tall and old is either strong or generous and vice versa.
Everyone who is happy or tall is humble and vice versa.
Everyone who is not kind is either not brave or not funny and vice versa.
If fred is both old and not generous then someone is both rich and brave and vice versa.
Everyone who is not humble or brave is both brave and tall.
If someone is either strong or curious then susan is quiet and vice versa.
If someone is either not strong or funny then someone is not funny and vice versa.
If susan is not tall or old then someone is both not calm and not funny.
Everyone who is not tall or not strong is either kind or not kind and vice versa.
Everyone who is both not quiet and strong is not patient and vice versa.
Everyone who is not brave or quiet is not old.
Someone is either creative or not old.
Susan is funny or brave.
Alice is both quiet and rich.
Paul is strong or rich.
Someone is either not patient or not strong.
John is funny.
Someone is tall or generous.
Alice is not kind or not generous. | John is creative. | neutral | (![X]:((~strong(X)|funny(X))<=>tall(X)))&
(((~calm(alice)&~patient(alice)))=>(?[X]:((~patient(X)<~>quiet(X)))))&
(((~patient(alice)<~>kind(alice)))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((tall(X)<~>happy(X))<=>(~rich(X)|~tall(X))))&
(![X]:((old(X)&~quiet(X))<=>(creative(X)<~>generous(X))))&
(![X]:((~tall(X)&old(X))<=>(strong(X)<~>generous(X))))&
(![X]:((happy(X)|tall(X))<=>humble(X)))&
(![X]:(~kind(X)<=>(~brave(X)<~>~funny(X))))&
(((old(fred)&~generous(fred)))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~humble(X)|brave(X))=>(brave(X)&tall(X))))&
((?[X]:((strong(X)<~>curious(X))))<=>(quiet(susan)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:(~funny(X))))&
(((~tall(susan)|old(susan)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((~quiet(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)|quiet(X))=>~old(X)))&
(?[X]:((creative(X)<~>~old(X))))&
((funny(susan)|brave(susan)))&
((quiet(alice)&rich(alice)))&
((strong(paul)|rich(paul)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(funny(john))&
(?[X]:((tall(X)|generous(X))))&
((~kind(alice)|~generous(alice))) | creative(john) | [] | null | 0 |
If someone is both not wise and not funny then paul is not creative or generous. If someone is quiet or not quiet then someone is not patient or strong and vice versa. Everyone who is creative or not generous is either not quiet or old and vice versa. If someone is both not strong and funny then someone is not strong or happy. Everyone who is both generous and happy is both not kind and old. If john is not funny or not tall then someone is not rich and vice versa. If someone is quiet or not rich then someone is calm or not calm. Everyone who is either wise or calm is not strong or rich and vice versa. If mary is not generous or creative then someone is not funny or humble and vice versa. Everyone who is either not quiet or humble is not humble or not rich and vice versa. Everyone who is not generous or wise is both rich and quiet. Everyone who is calm or not strong is both not patient and not old. Everyone who is both funny and not tall is either not old or not happy. Everyone who is not kind is not strong and vice versa. If someone is not humble or curious then john is not patient. Everyone who is either not wise or not generous is both not calm and generous. Alice is patient or not calm. Susan is either funny or curious. Someone is both quiet and curious. Paul is wise or quiet. Paul is both curious and quiet. Alice is both curious and not patient. | Paul is not strong. | contradiction | ((?[X]:((~wise(X)&~funny(X))))=>((~creative(paul)|generous(paul))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((creative(X)|~generous(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:((~strong(X)&funny(X))))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((generous(X)&happy(X))=>(~kind(X)&old(X))))&
(((~funny(john)|~tall(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(~strong(X)|rich(X))))&
(((~generous(mary)|creative(mary)))<=>(?[X]:((~funny(X)|humble(X)))))&
(![X]:((~quiet(X)<~>humble(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~generous(X)|wise(X))=>(rich(X)&quiet(X))))&
(![X]:((calm(X)|~strong(X))=>(~patient(X)&~old(X))))&
(![X]:((funny(X)&~tall(X))=>(~old(X)<~>~happy(X))))&
(![X]:(~kind(X)<=>~strong(X)))&
((?[X]:((~humble(X)|curious(X))))=>(~patient(john)))&
(![X]:((~wise(X)<~>~generous(X))=>(~calm(X)&generous(X))))&
((patient(alice)|~calm(alice)))&
((funny(susan)<~>curious(susan)))&
(?[X]:((quiet(X)&curious(X))))&
((wise(paul)|quiet(paul)))&
((curious(paul)&quiet(paul)))&
((curious(alice)&~patient(alice))) | ~strong(paul) | [
"p7",
"p9",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7073078518852950833145788
% SZS output start Proof for 7073078518852950833145788
8. ! [X0] : ((wise(X0) <~> calm(X0)) <=> (rich(X0) | ~strong(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) <~> humble(X0)) <=> (~rich(X0) | ~humble(X0))) [input p9]
11. ! [X0] : ((wise(X0) | ~generous(X0)) => (quiet(X0) & rich(X0))) [input p10]
16. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (generous(X0) & ~calm(X0))) [input p15]
20. quiet(paul) | wise(paul) [input p19]
23. ~strong(paul) [input hypothesis]
34. ! [X0] : ((quiet(X0) & rich(X0)) | (~wise(X0) & generous(X0))) [ennf transformation 11]
40. ! [X0] : ((generous(X0) & ~calm(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 16]
59. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [nnf transformation 8]
60. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [flattening 59]
66. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (rich(X0) & humble(X0))) & ((~rich(X0) | ~humble(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [nnf transformation 10]
67. ! [X0] : ((((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (rich(X0) & humble(X0))) & (~rich(X0) | ~humble(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0))))) [flattening 66]
69. ! [X0] : ((generous(X0) & ~calm(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 40]
94. calm(X0) | wise(X0) | strong(X0) [cnf transformation 60]
103. ~rich(X0) | ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 67]
104. humble(X0) | ~quiet(X0) | humble(X0) [cnf transformation 67]
108. rich(X0) | generous(X0) [cnf transformation 34]
109. ~wise(X0) | rich(X0) [cnf transformation 34]
110. quiet(X0) | generous(X0) [cnf transformation 34]
111. ~wise(X0) | quiet(X0) [cnf transformation 34]
121. ~calm(X0) | ~generous(X0) | wise(X0) [cnf transformation 69]
130. quiet(paul) | wise(paul) [cnf transformation 20]
135. ~strong(paul) [cnf transformation 23]
137. ~rich(X0) | ~humble(X0) | ~quiet(X0) [duplicate literal removal 103]
138. ~quiet(X0) | humble(X0) [duplicate literal removal 104]
223. ~rich(X0) | ~quiet(X0) [subsumption resolution 137,138]
247. quiet(paul) [subsumption resolution 130,111]
252. ~quiet(X0) | generous(X0) [resolution 223,108]
253. generous(X0) [subsumption resolution 252,110]
297. ~generous(X0) | wise(X0) | wise(X0) | strong(X0) [resolution 121,94]
298. ~generous(X0) | wise(X0) | strong(X0) [duplicate literal removal 297]
299. strong(X0) | wise(X0) [subsumption resolution 298,253]
325. wise(paul) [resolution 299,135]
333. rich(paul) [resolution 325,109]
381. ~quiet(paul) [resolution 333,223]
382. $false [subsumption resolution 381,247]
% SZS output end Proof for 7073078518852950833145788
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or funny is tall. Everyone who is not patient is humble or curious and vice versa. Everyone who is both strong and rich is both not funny and patient. If someone is either kind or brave then someone is not quiet or not kind. Everyone who is happy or kind is both generous and not generous and vice versa. Everyone who is generous or strong is not calm or not humble and vice versa. If john is both not creative and tall then someone is both generous and curious and vice versa. Everyone who is either not rich or not generous is either not wise or rich and vice versa. If someone is either not calm or not wise then lucy is both not kind and not strong and vice versa. Everyone who is both rich and not humble is both tall and rich and vice versa. If john is generous or humble then alice is both not generous and not brave and vice versa. Everyone who is either brave or rich is not generous or quiet. If someone is brave or not calm then someone is not patient or not old and vice versa. Everyone who is humble or not humble is either not happy or not funny and vice versa. Everyone who is not wise is not old or not creative and vice versa. Everyone who is either not strong or wise is either curious or not wise and vice versa. Susan is either not generous or rich. Someone is not humble. Lucy is strong. Mary is calm or not kind. Susan is not patient or not calm. John is either tall or not creative. Lucy is either old or not quiet. | Lucy is calm. | entailment | (![X]:((~wise(X)|funny(X))=>tall(X)))&
(![X]:(~patient(X)<=>(humble(X)|curious(X))))&
(![X]:((strong(X)&rich(X))=>(~funny(X)&patient(X))))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((~quiet(X)|~kind(X)))))&
(![X]:((happy(X)|kind(X))<=>(generous(X)&~generous(X))))&
(![X]:((generous(X)|strong(X))<=>(~calm(X)|~humble(X))))&
(((~creative(john)&tall(john)))<=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((~kind(lucy)&~strong(lucy))))&
(![X]:((rich(X)&~humble(X))<=>(tall(X)&rich(X))))&
(((generous(john)|humble(john)))<=>((~generous(alice)&~brave(alice))))&
(![X]:((brave(X)<~>rich(X))=>(~generous(X)|quiet(X))))&
((?[X]:((brave(X)|~calm(X))))<=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((humble(X)|~humble(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:(~wise(X)<=>(~old(X)|~creative(X))))&
(![X]:((~strong(X)<~>wise(X))<=>(curious(X)<~>~wise(X))))&
((~generous(susan)<~>rich(susan)))&
(?[X]:(~humble(X)))&
(strong(lucy))&
((calm(mary)|~kind(mary)))&
((~patient(susan)|~calm(susan)))&
((tall(john)<~>~creative(john)))&
((old(lucy)<~>~quiet(lucy))) | calm(lucy) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"p13",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3668102769125470603828175
% SZS output start Proof for 3668102769125470603828175
1. ! [X0] : ((funny(X0) | ~wise(X0)) => tall(X0)) [input p0]
5. ! [X0] : ((kind(X0) | happy(X0)) <=> (~generous(X0) & generous(X0))) [input p4]
7. (tall(john) & ~creative(john)) <=> ? [X0] : (curious(X0) & generous(X0)) [input p6]
8. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> (~wise(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~calm(X0) <~> ~wise(X0)) <=> (~strong(lucy) & ~kind(lucy)) [input p8]
14. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p15]
19. strong(lucy) [input p18]
22. tall(john) <~> ~creative(john) [input p21]
24. ~calm(lucy) [input hypothesis]
27. ! [X0] : (tall(X0) | (~funny(X0) & wise(X0))) [ennf transformation 1]
39. ! [X0] : (((kind(X0) | happy(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [nnf transformation 5]
40. ! [X0] : ((kind(X0) | happy(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (~kind(X0) & ~happy(X0)))) [flattening 39]
43. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | (~tall(john) | creative(john))) [nnf transformation 7]
44. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X0] : (curious(X0) & generous(X0)) | ~tall(john) | creative(john)) [flattening 43]
45. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & (? [X1] : (curious(X1) & generous(X1)) | ~tall(john) | creative(john)) [rectify 44]
46. ? [X1] : (curious(X1) & generous(X1)) => (curious(sK1) & generous(sK1)) [choice axiom]
47. ((tall(john) & ~creative(john)) | ! [X0] : (~curious(X0) | ~generous(X0))) & ((curious(sK1) & generous(sK1)) | ~tall(john) | creative(john)) [skolemisation 45,46]
48. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0)))) & (((~rich(X0) | wise(X0)) & (rich(X0) | ~wise(X0))) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 8]
49. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (strong(lucy) | kind(lucy))) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [nnf transformation 9]
50. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X0] : ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) [flattening 49]
51. (? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [rectify 50]
52. ? [X0] : ((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) => ((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) [choice axiom]
53. (((wise(sK2) | calm(sK2)) & (~wise(sK2) | ~calm(sK2))) | strong(lucy) | kind(lucy)) & ((~strong(lucy) & ~kind(lucy)) | ! [X1] : ((~calm(X1) | wise(X1)) & (~wise(X1) | calm(X1)))) [skolemisation 51,52]
64. ! [X0] : (((~humble(X0) | humble(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [nnf transformation 14]
65. ! [X0] : ((~humble(X0) | humble(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (humble(X0) & ~humble(X0)))) [flattening 64]
68. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 16]
72. (creative(john) | ~tall(john)) & (~creative(john) | tall(john)) [nnf transformation 22]
75. ~funny(X0) | tall(X0) [cnf transformation 27]
83. generous(X0) | ~happy(X0) [cnf transformation 40]
85. ~generous(X0) | ~happy(X0) [cnf transformation 40]
94. ~creative(john) | ~curious(X0) | ~generous(X0) [cnf transformation 47]
99. ~rich(X0) | wise(X0) | ~rich(X0) | generous(X0) [cnf transformation 48]
102. generous(X0) | rich(X0) | rich(X0) | wise(X0) [cnf transformation 48]
106. ~strong(lucy) | ~wise(X1) | calm(X1) [cnf transformation 53]
127. funny(X0) | happy(X0) | ~humble(X0) [cnf transformation 65]
128. funny(X0) | happy(X0) | humble(X0) [cnf transformation 65]
135. ~wise(X0) | curious(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 68]
139. wise(X0) | ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 68]
145. strong(lucy) [cnf transformation 19]
149. creative(john) | ~tall(john) [cnf transformation 72]
152. ~calm(lucy) [cnf transformation 24]
153. ~wise(X0) | curious(X0) | ~strong(X0) [duplicate literal removal 135]
155. ~strong(X0) | wise(X0) | curious(X0) [duplicate literal removal 139]
158. ~rich(X0) | wise(X0) | generous(X0) [duplicate literal removal 99]
160. generous(X0) | rich(X0) | wise(X0) [duplicate literal removal 102]
178. ~happy(X0) [subsumption resolution 83,85]
180. 5 <=> ! [X0] : (~curious(X0) | ~generous(X0)) [avatar definition]
181. ~generous(X0) | ~curious(X0) <- (5) [avatar component clause 180]
183. 6 <=> tall(john) [avatar definition]
184. ~tall(john) <- (~6) [avatar component clause 183]
188. 7 <=> creative(john) [avatar definition]
191. 5 | ~7 [avatar split clause 94,188,180]
202. generous(X0) | wise(X0) [subsumption resolution 158,160]
206. 10 <=> strong(lucy) [avatar definition]
208. strong(lucy) <- (10) [avatar component clause 206]
225. 14 <=> ! [X1] : (~wise(X1) | calm(X1)) [avatar definition]
226. ~wise(X1) | calm(X1) <- (14) [avatar component clause 225]
227. 14 | ~10 [avatar split clause 106,206,225]
281. humble(X0) | funny(X0) [subsumption resolution 128,178]
282. funny(X0) | ~humble(X0) [subsumption resolution 127,178]
283. funny(X0) [subsumption resolution 282,281]
285. ~strong(X0) | curious(X0) [subsumption resolution 153,155]
296. 10 [avatar split clause 145,206]
306. ~6 | 7 [avatar split clause 149,188,183]
319. tall(X0) [resolution 75,283]
320. $false <- (~6) [resolution 319,184]
321. 6 [avatar contradiction clause 320]
327. ~curious(X0) | wise(X0) <- (5) [resolution 202,181]
347. curious(lucy) <- (10) [resolution 285,208]
491. wise(lucy) <- (5, 10) [resolution 327,347]
515. calm(lucy) <- (5, 10, 14) [resolution 491,226]
518. $false <- (5, 10, 14) [subsumption resolution 515,152]
519. ~5 | ~10 | ~14 [avatar contradiction clause 518]
522. $false [avatar sat refutation 191,227,296,306,321,519]
% SZS output end Proof for 3668102769125470603828175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then mary is both not tall and strong.
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.
Everyone who is strong is both old and not patient and vice versa.
If susan is not strong or happy then someone is funny or creative.
Someone is either curious or wise.
Someone is happy or not curious.
Someone is not tall or happy.
Someone is not creative.
Someone is not patient.
Someone is both not curious and not creative.
Paul is not calm or brave.
Alice is either calm or humble. | Paul is not rich. | entailment | ((?[X]:(old(X)))=>((~tall(mary)&strong(mary))))&
(![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]:(strong(X)<=>(old(X)&~patient(X))))&
(((~strong(susan)|happy(susan)))=>(?[X]:((funny(X)|creative(X)))))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~curious(X)&~creative(X))))&
((~calm(paul)|brave(paul)))&
((calm(alice)<~>humble(alice))) | ~rich(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2317693841137398198692430
% SZS output start Proof for 2317693841137398198692430
4. ! [X0] : ((~creative(X0) | ~generous(X0)) => ~rich(X0)) [input p3]
8. ? [X0] : creative(X0) => ? [X0] : (~brave(X0) & brave(X0)) [input p7]
25. rich(paul) [input hypothesis]
28. ? [X0] : creative(X0) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 8]
39. ! [X0] : (~rich(X0) | (creative(X0) & generous(X0))) [ennf transformation 4]
41. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : ~creative(X0) [ennf transformation 28]
56. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ~creative(X1) [rectify 41]
57. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK3) & brave(sK3)) [choice axiom]
58. (~brave(sK3) & brave(sK3)) | ! [X1] : ~creative(X1) [skolemisation 56,57]
95. ~rich(X0) | creative(X0) [cnf transformation 39]
106. brave(sK3) | ~creative(X1) [cnf transformation 58]
107. ~brave(sK3) | ~creative(X1) [cnf transformation 58]
140. rich(paul) [cnf transformation 25]
212. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
213. ~creative(X1) <- (17) [avatar component clause 212]
215. 18 <=> brave(sK3) [avatar definition]
218. 17 | ~18 [avatar split clause 107,215,212]
219. 17 | 18 [avatar split clause 106,215,212]
340. creative(paul) [resolution 95,140]
341. $false <- (17) [subsumption resolution 340,213]
342. ~17 [avatar contradiction clause 341]
343. $false [avatar sat refutation 218,219,342]
% SZS output end Proof for 2317693841137398198692430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is funny then mary is not happy or not creative and vice versa.
If someone is either funny or rich then someone is strong or not creative.
If someone is both not rich and kind then fred is not calm.
If someone is not patient or not quiet then susan is not strong.
Everyone who is either happy or not curious is tall.
If paul is either tall or not kind then fred is both old and not rich and vice versa.
Everyone who is humble is both humble and not curious and vice versa.
If someone is not tall then paul is tall or not generous and vice versa.
Everyone who is both not calm and funny is not old or rich and vice versa.
Everyone who is not old is either kind or rich and vice versa.
If someone is not humble or not kind then someone is brave and vice versa.
Everyone who is not old is not tall or not wise.
If someone is both not tall and not funny then lucy is both not rich and brave and vice versa.
If lucy is either not brave or patient then paul is either not rich or creative.
If alice is both not humble and not curious then someone is happy or curious.
Everyone who is not old is tall.
Someone is both not wise and not rich.
Someone is not kind.
Someone is humble.
Someone is either not patient or curious.
Someone is not wise.
Someone is both not creative and quiet.
Susan is wise.
Lucy is both wise and not quiet. | Susan is not old. | contradiction | ((funny(lucy))<=>((~happy(mary)|~creative(mary))))&
((?[X]:((funny(X)<~>rich(X))))=>(?[X]:((strong(X)|~creative(X)))))&
((?[X]:((~rich(X)&kind(X))))=>(~calm(fred)))&
((?[X]:((~patient(X)|~quiet(X))))=>(~strong(susan)))&
(![X]:((happy(X)<~>~curious(X))=>tall(X)))&
(((tall(paul)<~>~kind(paul)))<=>((old(fred)&~rich(fred))))&
(![X]:(humble(X)<=>(humble(X)&~curious(X))))&
((?[X]:(~tall(X)))<=>((tall(paul)|~generous(paul))))&
(![X]:((~calm(X)&funny(X))<=>(~old(X)|rich(X))))&
(![X]:(~old(X)<=>(kind(X)<~>rich(X))))&
((?[X]:((~humble(X)|~kind(X))))<=>(?[X]:(brave(X))))&
(![X]:(~old(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>((~rich(lucy)&brave(lucy))))&
(((~brave(lucy)<~>patient(lucy)))=>((~rich(paul)<~>creative(paul))))&
(((~humble(alice)&~curious(alice)))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~old(X)=>tall(X)))&
(?[X]:((~wise(X)&~rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:(humble(X)))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~creative(X)&quiet(X))))&
(wise(susan))&
((wise(lucy)&~quiet(lucy))) | ~old(susan) | [
"p11",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9046720951508853947337191
% SZS output start Proof for 9046720951508853947337191
12. ! [X0] : (~old(X0) => (~wise(X0) | ~tall(X0))) [input p11]
16. ! [X0] : (~old(X0) => tall(X0)) [input p15]
23. wise(susan) [input p22]
25. ~old(susan) [input hypothesis]
32. ! [X0] : ((~wise(X0) | ~tall(X0)) | old(X0)) [ennf transformation 12]
33. ! [X0] : (~wise(X0) | ~tall(X0) | old(X0)) [flattening 32]
37. ! [X0] : (tall(X0) | old(X0)) [ennf transformation 16]
117. ~wise(X0) | ~tall(X0) | old(X0) [cnf transformation 33]
127. old(X0) | tall(X0) [cnf transformation 37]
137. wise(susan) [cnf transformation 23]
140. ~old(susan) [cnf transformation 25]
323. tall(susan) [resolution 127,140]
390. ~tall(susan) | old(susan) [resolution 117,137]
392. old(susan) [subsumption resolution 390,323]
393. $false [subsumption resolution 392,140]
% SZS output end Proof for 9046720951508853947337191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not brave and not kind then john is not rich or not generous. If someone is either not calm or not tall then someone is not quiet or not patient and vice versa. Everyone who is both not humble and not quiet is either not old or strong. If alice is not rich then someone is either not generous or strong. Everyone who is patient or rich is not strong or not calm and vice versa. If susan is not tall then alice is both kind and not strong and vice versa. If someone is not wise then someone is strong and vice versa. Everyone who is both humble and strong is patient and vice versa. If someone is either not creative or funny then someone is both not strong and not patient and vice versa. If mary is both not quiet and not brave then someone is both not creative and tall. Everyone who is not patient or kind is either not strong or strong. Everyone who is not funny or humble is both calm and wise and vice versa. If someone is either humble or funny then lucy is not rich or curious. Everyone who is both not generous and not humble is either patient or tall and vice versa. Everyone who is not kind or not calm is either not quiet or not patient. Everyone who is either not quiet or not generous is both generous and not rich. Alice is either wise or calm. Someone is either not wise or not curious. Someone is both not humble and quiet. Susan is not rich. John is not humble. Susan is happy. John is kind or curious. Someone is both not patient and not quiet. | Mary is not patient. | entailment | (((~brave(alice)&~kind(alice)))=>((~rich(john)|~generous(john))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((~quiet(X)|~patient(X)))))&
(![X]:((~humble(X)&~quiet(X))=>(~old(X)<~>strong(X))))&
((~rich(alice))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:((patient(X)|rich(X))<=>(~strong(X)|~calm(X))))&
((~tall(susan))<=>((kind(alice)&~strong(alice))))&
((?[X]:(~wise(X)))<=>(?[X]:(strong(X))))&
(![X]:((humble(X)&strong(X))<=>patient(X)))&
((?[X]:((~creative(X)<~>funny(X))))<=>(?[X]:((~strong(X)&~patient(X)))))&
(((~quiet(mary)&~brave(mary)))=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((~patient(X)|kind(X))=>(~strong(X)<~>strong(X))))&
(![X]:((~funny(X)|humble(X))<=>(calm(X)&wise(X))))&
((?[X]:((humble(X)<~>funny(X))))=>((~rich(lucy)|curious(lucy))))&
(![X]:((~generous(X)&~humble(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~kind(X)|~calm(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>(generous(X)&~rich(X))))&
((wise(alice)<~>calm(alice)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((~humble(X)&quiet(X))))&
(~rich(susan))&
(~humble(john))&
(happy(susan))&
((kind(john)|curious(john)))&
(?[X]:((~patient(X)&~quiet(X)))) | ~patient(mary) | [
"p4",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 586821225505811763951225
% SZS output start Proof for 586821225505811763951225
5. ! [X0] : ((rich(X0) | patient(X0)) <=> (~calm(X0) | ~strong(X0))) [input p4]
8. ! [X0] : ((strong(X0) & humble(X0)) <=> patient(X0)) [input p7]
12. ! [X0] : ((humble(X0) | ~funny(X0)) <=> (wise(X0) & calm(X0))) [input p11]
25. patient(mary) [input hypothesis]
49. ! [X0] : (((rich(X0) | patient(X0)) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | (~rich(X0) & ~patient(X0)))) [nnf transformation 5]
50. ! [X0] : ((rich(X0) | patient(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | (~rich(X0) & ~patient(X0)))) [flattening 49]
58. ! [X0] : (((strong(X0) & humble(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) | ~humble(X0)))) [nnf transformation 8]
59. ! [X0] : (((strong(X0) & humble(X0)) | ~patient(X0)) & (patient(X0) | ~strong(X0) | ~humble(X0))) [flattening 58]
66. ! [X0] : (((humble(X0) | ~funny(X0)) | (~wise(X0) | ~calm(X0))) & ((wise(X0) & calm(X0)) | (~humble(X0) & funny(X0)))) [nnf transformation 12]
67. ! [X0] : ((humble(X0) | ~funny(X0) | ~wise(X0) | ~calm(X0)) & ((wise(X0) & calm(X0)) | (~humble(X0) & funny(X0)))) [flattening 66]
91. ~strong(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 50]
101. ~patient(X0) | humble(X0) [cnf transformation 59]
102. ~patient(X0) | strong(X0) [cnf transformation 59]
114. ~humble(X0) | calm(X0) [cnf transformation 67]
145. patient(mary) [cnf transformation 25]
308. humble(mary) [resolution 101,145]
309. strong(mary) [resolution 102,145]
313. calm(mary) [resolution 114,308]
319. ~calm(mary) | ~patient(mary) [resolution 91,309]
329. ~patient(mary) [subsumption resolution 319,313]
330. $false [subsumption resolution 329,145]
% SZS output end Proof for 586821225505811763951225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not brave is both tall and not curious and vice versa. Everyone who is both not kind and funny is happy or not creative. Everyone who is both funny and creative is both not tall and generous. If someone is creative or kind then fred is not calm. Everyone who is both not old and not happy is strong or curious and vice versa. If john is either humble or not funny then someone is both not happy and not brave. Everyone who is not calm or not happy is not brave or not humble and vice versa. Everyone who is tall is not happy. If john is both old and brave then fred is not calm and vice versa. If lucy is both not calm and not tall then someone is either humble or not creative and vice versa. If alice is not funny or rich then someone is generous and vice versa. Everyone who is either not kind or not funny is either not wise or not brave. Everyone who is generous is both not calm and not curious and vice versa. Everyone who is both not old and not strong is either quiet or not brave and vice versa. Everyone who is not creative is not rich. Everyone who is either generous or rich is both strong and not wise and vice versa. Someone is rich or kind. Someone is either wise or generous. Someone is not generous or calm. Susan is either curious or old. Someone is not funny. Someone is both not brave and funny. Someone is curious or not funny. Mary is both creative and curious. | Mary is not happy. | entailment | (![X]:((creative(X)&~brave(X))<=>(tall(X)&~curious(X))))&
(![X]:((~kind(X)&funny(X))=>(happy(X)|~creative(X))))&
(![X]:((funny(X)&creative(X))=>(~tall(X)&generous(X))))&
((?[X]:((creative(X)|kind(X))))=>(~calm(fred)))&
(![X]:((~old(X)&~happy(X))<=>(strong(X)|curious(X))))&
(((humble(john)<~>~funny(john)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(~brave(X)|~humble(X))))&
(![X]:(tall(X)=>~happy(X)))&
(((old(john)&brave(john)))<=>(~calm(fred)))&
(((~calm(lucy)&~tall(lucy)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((~funny(alice)|rich(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~wise(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~calm(X)&~curious(X))))&
(![X]:((~old(X)&~strong(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:(~creative(X)=>~rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>(strong(X)&~wise(X))))&
(?[X]:((rich(X)|kind(X))))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~generous(X)|calm(X))))&
((curious(susan)<~>old(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((curious(X)|~funny(X))))&
((creative(mary)&curious(mary))) | ~happy(mary) | [
"p4",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 353537087894717734113618
% SZS output start Proof for 353537087894717734113618
5. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (curious(X0) | strong(X0))) [input p4]
24. curious(mary) & creative(mary) [input p23]
25. happy(mary) [input hypothesis]
37. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (happy(X0) | old(X0)))) [nnf transformation 5]
38. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | happy(X0) | old(X0))) [flattening 37]
90. ~happy(X0) | ~curious(X0) [cnf transformation 38]
143. curious(mary) [cnf transformation 24]
144. happy(mary) [cnf transformation 25]
273. ~curious(mary) [resolution 90,144]
274. $false [subsumption resolution 273,143]
% SZS output end Proof for 353537087894717734113618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or calm is both tall and not happy. Everyone who is not kind or not brave is either brave or calm and vice versa. Everyone who is generous or happy is tall or quiet and vice versa. If susan is patient then someone is not funny. Everyone who is not tall or not old is not funny or funny and vice versa. If mary is both not calm and not humble then fred is wise and vice versa. Everyone who is either strong or tall is not rich and vice versa. If mary is either not kind or funny then someone is both not rich and not funny and vice versa. Everyone who is both not happy and not wise is not generous or curious. Everyone who is not old is either not strong or patient. Everyone who is not humble or not patient is either not funny or not tall and vice versa. If someone is not quiet then someone is calm and vice versa. Everyone who is brave or not tall is brave. Everyone who is humble or old is funny. Everyone who is either happy or old is old or calm. Everyone who is kind or funny is not humble or old and vice versa. Fred is patient. Someone is strong. Lucy is strong. Mary is both not patient and quiet. Someone is both not patient and wise. Someone is not wise or old. Someone is not generous or brave. | Fred is not wise. | entailment | (![X]:((funny(X)<~>calm(X))=>(tall(X)&~happy(X))))&
(![X]:((~kind(X)|~brave(X))<=>(brave(X)<~>calm(X))))&
(![X]:((generous(X)|happy(X))<=>(tall(X)|quiet(X))))&
((patient(susan))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|~old(X))<=>(~funny(X)|funny(X))))&
(((~calm(mary)&~humble(mary)))<=>(wise(fred)))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
(((~kind(mary)<~>funny(mary)))<=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~happy(X)&~wise(X))=>(~generous(X)|curious(X))))&
(![X]:(~old(X)=>(~strong(X)<~>patient(X))))&
(![X]:((~humble(X)|~patient(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)|~tall(X))=>brave(X)))&
(![X]:((humble(X)|old(X))=>funny(X)))&
(![X]:((happy(X)<~>old(X))=>(old(X)|calm(X))))&
(![X]:((kind(X)|funny(X))<=>(~humble(X)|old(X))))&
(patient(fred))&
(?[X]:(strong(X)))&
(strong(lucy))&
((~patient(mary)&quiet(mary)))&
(?[X]:((~patient(X)&wise(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~generous(X)|brave(X)))) | ~wise(fred) | [
"p0",
"p1",
"p5",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6029533244524015963436638
% SZS output start Proof for 6029533244524015963436638
1. ! [X0] : ((funny(X0) <~> calm(X0)) => (~happy(X0) & tall(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | ~kind(X0)) <=> (brave(X0) <~> calm(X0))) [input p1]
6. (~humble(mary) & ~calm(mary)) <=> wise(fred) [input p5]
11. ! [X0] : ((~patient(X0) | ~humble(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p10]
14. ! [X0] : ((old(X0) | humble(X0)) => funny(X0)) [input p13]
16. ! [X0] : ((funny(X0) | kind(X0)) <=> (old(X0) | ~humble(X0))) [input p15]
24. wise(fred) [input hypothesis]
27. ! [X0] : ((~happy(X0) & tall(X0)) | (funny(X0) <=> calm(X0))) [ennf transformation 1]
31. ! [X0] : (funny(X0) | (~old(X0) & ~humble(X0))) [ennf transformation 14]
34. ! [X0] : ((~happy(X0) & tall(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0)))) [nnf transformation 27]
35. ! [X0] : (((~brave(X0) | ~kind(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (brave(X0) & kind(X0)))) [nnf transformation 2]
36. ! [X0] : ((~brave(X0) | ~kind(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (brave(X0) & kind(X0)))) [flattening 35]
43. ((~humble(mary) & ~calm(mary)) | ~wise(fred)) & (wise(fred) | (humble(mary) | calm(mary))) [nnf transformation 6]
44. ((~humble(mary) & ~calm(mary)) | ~wise(fred)) & (wise(fred) | humble(mary) | calm(mary)) [flattening 43]
51. ! [X0] : (((~patient(X0) | ~humble(X0)) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (patient(X0) & humble(X0)))) [nnf transformation 11]
52. ! [X0] : ((~patient(X0) | ~humble(X0) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | (patient(X0) & humble(X0)))) [flattening 51]
59. ! [X0] : (((funny(X0) | kind(X0)) | (~old(X0) & humble(X0))) & ((old(X0) | ~humble(X0)) | (~funny(X0) & ~kind(X0)))) [nnf transformation 16]
60. ! [X0] : ((funny(X0) | kind(X0) | (~old(X0) & humble(X0))) & (old(X0) | ~humble(X0) | (~funny(X0) & ~kind(X0)))) [flattening 59]
69. ~funny(X0) | calm(X0) | tall(X0) [cnf transformation 34]
74. calm(X0) | brave(X0) | brave(X0) [cnf transformation 36]
77. ~brave(X0) | ~kind(X0) | calm(X0) | ~brave(X0) [cnf transformation 36]
89. ~calm(mary) | ~wise(fred) [cnf transformation 44]
90. ~humble(mary) | ~wise(fred) [cnf transformation 44]
103. ~tall(X0) | ~funny(X0) | humble(X0) [cnf transformation 52]
113. ~humble(X0) | funny(X0) [cnf transformation 31]
119. funny(X0) | kind(X0) | humble(X0) [cnf transformation 60]
130. wise(fred) [cnf transformation 24]
132. brave(X0) | calm(X0) [duplicate literal removal 74]
133. ~brave(X0) | ~kind(X0) | calm(X0) [duplicate literal removal 77]
145. 3 <=> wise(fred) [avatar definition]
149. 4 <=> humble(mary) [avatar definition]
151. ~humble(mary) <- (~4) [avatar component clause 149]
152. ~3 | ~4 [avatar split clause 90,149,145]
154. 5 <=> calm(mary) [avatar definition]
156. ~calm(mary) <- (~5) [avatar component clause 154]
157. ~3 | ~5 [avatar split clause 89,154,145]
163. 7 <=> kind(mary) [avatar definition]
164. ~kind(mary) <- (~7) [avatar component clause 163]
165. kind(mary) <- (7) [avatar component clause 163]
167. 8 <=> funny(mary) [avatar definition]
168. funny(mary) <- (8) [avatar component clause 167]
169. ~funny(mary) <- (~8) [avatar component clause 167]
200. kind(X0) | funny(X0) [subsumption resolution 119,113]
220. 3 [avatar split clause 130,145]
223. funny(mary) <- (~7) [resolution 200,164]
224. $false <- (~7, ~8) [subsumption resolution 223,169]
225. 7 | 8 [avatar contradiction clause 224]
226. calm(mary) | tall(mary) <- (8) [resolution 69,168]
227. tall(mary) <- (~5, 8) [subsumption resolution 226,156]
319. ~funny(mary) | humble(mary) <- (~5, 8) [resolution 103,227]
321. humble(mary) <- (~5, 8) [subsumption resolution 319,168]
322. $false <- (~4, ~5, 8) [subsumption resolution 321,151]
323. 4 | 5 | ~8 [avatar contradiction clause 322]
377. ~kind(X0) | calm(X0) | calm(X0) [resolution 133,132]
379. ~kind(X0) | calm(X0) [duplicate literal removal 377]
444. calm(mary) <- (7) [resolution 379,165]
445. $false <- (~5, 7) [subsumption resolution 444,156]
446. 5 | ~7 [avatar contradiction clause 445]
447. $false [avatar sat refutation 152,157,220,225,323,446]
% SZS output end Proof for 6029533244524015963436638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is curious then john is not calm. Everyone who is not curious is both patient and kind and vice versa. Everyone who is not generous or quiet is not humble or brave and vice versa. Everyone who is both tall and not generous is generous or tall and vice versa. Everyone who is both calm and not happy is either not brave or rich. Everyone who is either brave or kind is either happy or quiet. If someone is both strong and quiet then lucy is both not creative and quiet and vice versa. Everyone who is kind or not funny is wise or not creative and vice versa. Everyone who is both not generous and not strong is either patient or not tall and vice versa. Everyone who is either not kind or not wise is both not kind and creative and vice versa. Everyone who is either rich or calm is both calm and patient and vice versa. Everyone who is either not happy or not old is either not patient or not funny. If susan is not tall or rich then someone is both calm and brave and vice versa. If alice is not happy then john is either creative or not happy and vice versa. Everyone who is both happy and brave is both humble and rich and vice versa. Everyone who is strong is both rich and strong and vice versa. Alice is not tall or rich. Fred is rich or not wise. Someone is both happy and brave. Someone is both brave and not quiet. Someone is either humble or tall. Susan is both not calm and not brave. Someone is both rich and creative. John is old or not curious. | Susan is curious. | entailment | ((curious(paul))=>(~calm(john)))&
(![X]:(~curious(X)<=>(patient(X)&kind(X))))&
(![X]:((~generous(X)|quiet(X))<=>(~humble(X)|brave(X))))&
(![X]:((tall(X)&~generous(X))<=>(generous(X)|tall(X))))&
(![X]:((calm(X)&~happy(X))=>(~brave(X)<~>rich(X))))&
(![X]:((brave(X)<~>kind(X))=>(happy(X)<~>quiet(X))))&
((?[X]:((strong(X)&quiet(X))))<=>((~creative(lucy)&quiet(lucy))))&
(![X]:((kind(X)|~funny(X))<=>(wise(X)|~creative(X))))&
(![X]:((~generous(X)&~strong(X))<=>(patient(X)<~>~tall(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~kind(X)&creative(X))))&
(![X]:((rich(X)<~>calm(X))<=>(calm(X)&patient(X))))&
(![X]:((~happy(X)<~>~old(X))=>(~patient(X)<~>~funny(X))))&
(((~tall(susan)|rich(susan)))<=>(?[X]:((calm(X)&brave(X)))))&
((~happy(alice))<=>((creative(john)<~>~happy(john))))&
(![X]:((happy(X)&brave(X))<=>(humble(X)&rich(X))))&
(![X]:(strong(X)<=>(rich(X)&strong(X))))&
((~tall(alice)|rich(alice)))&
((rich(fred)|~wise(fred)))&
(?[X]:((happy(X)&brave(X))))&
(?[X]:((brave(X)&~quiet(X))))&
(?[X]:((humble(X)<~>tall(X))))&
((~calm(susan)&~brave(susan)))&
(?[X]:((rich(X)&creative(X))))&
((old(john)|~curious(john))) | curious(susan) | [
"p1",
"p3",
"p8",
"p10",
"p12",
"p14",
"p15",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1730945312227003108315032
% SZS output start Proof for 1730945312227003108315032
2. ! [X0] : (~curious(X0) <=> (kind(X0) & patient(X0))) [input p1]
4. ! [X0] : ((~generous(X0) & tall(X0)) <=> (tall(X0) | generous(X0))) [input p3]
9. ! [X0] : ((~strong(X0) & ~generous(X0)) <=> (patient(X0) <~> ~tall(X0))) [input p8]
11. ! [X0] : ((rich(X0) <~> calm(X0)) <=> (patient(X0) & calm(X0))) [input p10]
13. (rich(susan) | ~tall(susan)) <=> ? [X0] : (brave(X0) & calm(X0)) [input p12]
15. ! [X0] : ((brave(X0) & happy(X0)) <=> (rich(X0) & humble(X0))) [input p14]
16. ! [X0] : (strong(X0) <=> (strong(X0) & rich(X0))) [input p15]
19. ? [X0] : (brave(X0) & happy(X0)) [input p18]
22. ~brave(susan) & ~calm(susan) [input p21]
25. ~curious(susan) [input hypothesis]
26. ! [X0] : (~curious(X0) => (kind(X0) & patient(X0))) [unused predicate definition removal 2]
28. ! [X0] : ((kind(X0) & patient(X0)) | curious(X0)) [ennf transformation 26]
35. ! [X0] : (((~generous(X0) & tall(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 4]
36. ! [X0] : (((~generous(X0) & tall(X0)) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | generous(X0) | ~tall(X0))) [flattening 35]
46. ! [X0] : (((~strong(X0) & ~generous(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (strong(X0) | generous(X0)))) [nnf transformation 9]
47. ! [X0] : (((~strong(X0) & ~generous(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0)))) & (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | strong(X0) | generous(X0))) [flattening 46]
50. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [nnf transformation 11]
51. ! [X0] : ((((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0))))) [flattening 50]
53. ((rich(susan) | ~tall(susan)) | ! [X0] : (~brave(X0) | ~calm(X0))) & (? [X0] : (brave(X0) & calm(X0)) | (~rich(susan) & tall(susan))) [nnf transformation 13]
54. (rich(susan) | ~tall(susan) | ! [X0] : (~brave(X0) | ~calm(X0))) & (? [X0] : (brave(X0) & calm(X0)) | (~rich(susan) & tall(susan))) [flattening 53]
55. (rich(susan) | ~tall(susan) | ! [X0] : (~brave(X0) | ~calm(X0))) & (? [X1] : (brave(X1) & calm(X1)) | (~rich(susan) & tall(susan))) [rectify 54]
56. ? [X1] : (brave(X1) & calm(X1)) => (brave(sK1) & calm(sK1)) [choice axiom]
57. (rich(susan) | ~tall(susan) | ! [X0] : (~brave(X0) | ~calm(X0))) & ((brave(sK1) & calm(sK1)) | (~rich(susan) & tall(susan))) [skolemisation 55,56]
59. ! [X0] : (((brave(X0) & happy(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~brave(X0) | ~happy(X0)))) [nnf transformation 15]
60. ! [X0] : (((brave(X0) & happy(X0)) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | ~brave(X0) | ~happy(X0))) [flattening 59]
61. ! [X0] : ((strong(X0) | (~strong(X0) | ~rich(X0))) & ((strong(X0) & rich(X0)) | ~strong(X0))) [nnf transformation 16]
62. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0)) & ((strong(X0) & rich(X0)) | ~strong(X0))) [flattening 61]
63. ? [X0] : (brave(X0) & happy(X0)) => (brave(sK2) & happy(sK2)) [choice axiom]
64. brave(sK2) & happy(sK2) [skolemisation 19,63]
73. patient(X0) | curious(X0) [cnf transformation 28]
82. ~generous(X0) | ~generous(X0) [cnf transformation 36]
99. tall(X0) | ~patient(X0) | strong(X0) | generous(X0) [cnf transformation 47]
110. calm(X0) | calm(X0) | ~rich(X0) [cnf transformation 51]
115. ~calm(X0) | ~rich(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 51]
124. rich(susan) | ~tall(susan) | ~brave(X0) | ~calm(X0) [cnf transformation 57]
130. ~happy(X0) | ~brave(X0) | rich(X0) [cnf transformation 60]
133. ~strong(X0) | rich(X0) [cnf transformation 62]
138. happy(sK2) [cnf transformation 64]
139. brave(sK2) [cnf transformation 64]
144. ~calm(susan) [cnf transformation 22]
149. ~curious(susan) [cnf transformation 25]
150. ~rich(X0) | calm(X0) [duplicate literal removal 110]
151. ~rich(X0) | ~calm(X0) | ~patient(X0) [duplicate literal removal 115]
155. ~generous(X0) [duplicate literal removal 82]
188. ~patient(X0) | tall(X0) | strong(X0) [subsumption resolution 99,155]
193. 8 <=> ! [X0] : (~brave(X0) | ~calm(X0)) [avatar definition]
194. ~brave(X0) | ~calm(X0) <- (8) [avatar component clause 193]
196. 9 <=> tall(susan) [avatar definition]
198. ~tall(susan) <- (~9) [avatar component clause 196]
200. 10 <=> rich(susan) [avatar definition]
202. rich(susan) <- (10) [avatar component clause 200]
203. 8 | ~9 | 10 [avatar split clause 124,200,196,193]
275. ~calm(sK2) <- (8) [resolution 194,139]
322. ~brave(sK2) | rich(sK2) [resolution 130,138]
323. rich(sK2) [subsumption resolution 322,139]
325. calm(sK2) [resolution 323,150]
327. $false <- (8) [subsumption resolution 325,275]
328. ~8 [avatar contradiction clause 327]
330. calm(susan) <- (10) [resolution 202,150]
332. $false <- (10) [subsumption resolution 330,144]
333. ~10 [avatar contradiction clause 332]
380. strong(X0) | tall(X0) | curious(X0) [resolution 188,73]
598. rich(X2) | curious(X2) | tall(X2) [resolution 380,133]
815. curious(X1) | tall(X1) | ~calm(X1) | ~patient(X1) [resolution 598,151]
819. curious(X5) | tall(X5) | calm(X5) [resolution 598,150]
822. curious(X1) | tall(X1) | ~calm(X1) [subsumption resolution 815,73]
823. tall(X5) | curious(X5) [subsumption resolution 819,822]
829. curious(susan) <- (~9) [resolution 823,198]
831. $false <- (~9) [subsumption resolution 829,149]
832. 9 [avatar contradiction clause 831]
834. $false [avatar sat refutation 203,328,333,832]
% SZS output end Proof for 1730945312227003108315032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and kind is not curious or not old and vice versa. If someone is either not funny or quiet then paul is both calm and kind. Everyone who is not tall or not patient is both humble and not generous. If someone is patient or old then someone is not strong or not happy and vice versa. Everyone who is not generous or calm is rich and vice versa. Everyone who is either not quiet or not wise is calm. If someone is not generous then someone is either patient or calm and vice versa. If alice is patient then someone is not wise or not tall and vice versa. If fred is not quiet or strong then fred is either not curious or not strong and vice versa. If someone is not tall then someone is quiet. Everyone who is both not funny and not kind is calm or not happy and vice versa. If someone is kind then susan is both not quiet and not strong and vice versa. Everyone who is generous is not happy or calm and vice versa. Everyone who is creative is both not funny and not strong. If someone is both not old and calm then someone is generous. If mary is patient then lucy is either old or not brave and vice versa. Lucy is not calm. Someone is both not quiet and not tall. John is both patient and not strong. Paul is not brave. Mary is tall or not strong. Someone is either not kind or not curious. Someone is either creative or not quiet. | Alice is curious. | entailment | (![X]:((~happy(X)&kind(X))<=>(~curious(X)|~old(X))))&
((?[X]:((~funny(X)<~>quiet(X))))=>((calm(paul)&kind(paul))))&
(![X]:((~tall(X)|~patient(X))=>(humble(X)&~generous(X))))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((~generous(X)|calm(X))<=>rich(X)))&
(![X]:((~quiet(X)<~>~wise(X))=>calm(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)<~>calm(X)))))&
((patient(alice))<=>(?[X]:((~wise(X)|~tall(X)))))&
(((~quiet(fred)|strong(fred)))<=>((~curious(fred)<~>~strong(fred))))&
((?[X]:(~tall(X)))=>(?[X]:(quiet(X))))&
(![X]:((~funny(X)&~kind(X))<=>(calm(X)|~happy(X))))&
((?[X]:(kind(X)))<=>((~quiet(susan)&~strong(susan))))&
(![X]:(generous(X)<=>(~happy(X)|calm(X))))&
(![X]:(creative(X)=>(~funny(X)&~strong(X))))&
((?[X]:((~old(X)&calm(X))))=>(?[X]:(generous(X))))&
((patient(mary))<=>((old(lucy)<~>~brave(lucy))))&
(~calm(lucy))&
(?[X]:((~quiet(X)&~tall(X))))&
((patient(john)&~strong(john)))&
(~brave(paul))&
((tall(mary)|~strong(mary)))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((creative(X)<~>~quiet(X)))) | curious(alice) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6089908761826225952338349
% SZS output start Proof for 6089908761826225952338349
1. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~old(X0) | ~curious(X0))) [input p0]
11. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (~happy(X0) | calm(X0))) [input p10]
24. ~curious(alice) [input hypothesis]
36. ! [X0] : (((kind(X0) & ~happy(X0)) | (old(X0) & curious(X0))) & ((~old(X0) | ~curious(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 1]
37. ! [X0] : (((kind(X0) & ~happy(X0)) | (old(X0) & curious(X0))) & (~old(X0) | ~curious(X0) | ~kind(X0) | happy(X0))) [flattening 36]
59. ! [X0] : (((~kind(X0) & ~funny(X0)) | (happy(X0) & ~calm(X0))) & ((~happy(X0) | calm(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 11]
60. ! [X0] : (((~kind(X0) & ~funny(X0)) | (happy(X0) & ~calm(X0))) & (~happy(X0) | calm(X0) | kind(X0) | funny(X0))) [flattening 59]
81. ~happy(X0) | curious(X0) [cnf transformation 37]
83. curious(X0) | kind(X0) [cnf transformation 37]
115. ~kind(X0) | happy(X0) [cnf transformation 60]
140. ~curious(alice) [cnf transformation 24]
334. kind(alice) [resolution 83,140]
347. happy(alice) [resolution 115,334]
363. curious(alice) [resolution 347,81]
364. $false [subsumption resolution 363,140]
% SZS output end Proof for 6089908761826225952338349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and funny is either not tall or not strong and vice versa.
If someone is both funny and not old then someone is quiet.
Everyone who is not curious or not humble is old.
Everyone who is both tall and rich is either kind or creative and vice versa.
Everyone who is either happy or not calm is old and vice versa.
Everyone who is quiet is not old or not strong and vice versa.
Everyone who is both not quiet and humble is not funny or not strong and vice versa.
If someone is not happy or calm then someone is both not generous and happy and vice versa.
Everyone who is both not quiet and not generous is either not wise or not old and vice versa.
Everyone who is either strong or patient is either not tall or not patient.
If someone is not brave then someone is either not calm or old.
Everyone who is both not brave and not humble is not strong or tall.
Everyone who is either not brave or calm is either calm or not calm.
If alice is wise then mary is curious.
Everyone who is either not calm or not creative is calm and vice versa.
If someone is both not brave and not curious then fred is either tall or kind and vice versa.
Mary is either not happy or happy.
Someone is both humble and old.
Someone is both calm and not patient.
Alice is either not kind or not curious.
Mary is strong.
Susan is kind or patient. | Fred is not strong. | contradiction | (![X]:((~wise(X)&funny(X))<=>(~tall(X)<~>~strong(X))))&
((?[X]:((funny(X)&~old(X))))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)|~humble(X))=>old(X)))&
(![X]:((tall(X)&rich(X))<=>(kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>~calm(X))<=>old(X)))&
(![X]:(quiet(X)<=>(~old(X)|~strong(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~funny(X)|~strong(X))))&
((?[X]:((~happy(X)|calm(X))))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((strong(X)<~>patient(X))=>(~tall(X)<~>~patient(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:((~brave(X)&~humble(X))=>(~strong(X)|tall(X))))&
(![X]:((~brave(X)<~>calm(X))=>(calm(X)<~>~calm(X))))&
((wise(alice))=>(curious(mary)))&
(![X]:((~calm(X)<~>~creative(X))<=>calm(X)))&
((?[X]:((~brave(X)&~curious(X))))<=>((tall(fred)<~>kind(fred))))&
((~happy(mary)<~>happy(mary)))&
(?[X]:((humble(X)&old(X))))&
(?[X]:((calm(X)&~patient(X))))&
((~kind(alice)<~>~curious(alice)))&
(strong(mary))&
((kind(susan)|patient(susan))) | ~strong(fred) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1307960087438483815790374
% SZS output start Proof for 1307960087438483815790374
6. ! [X0] : (quiet(X0) <=> (~strong(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (~strong(X0) | ~funny(X0))) [input p6]
23. ~strong(fred) [input hypothesis]
43. ! [X0] : ((quiet(X0) | (strong(X0) & old(X0))) & ((~strong(X0) | ~old(X0)) | ~quiet(X0))) [nnf transformation 6]
44. ! [X0] : ((quiet(X0) | (strong(X0) & old(X0))) & (~strong(X0) | ~old(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((humble(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 7]
46. ! [X0] : (((humble(X0) & ~quiet(X0)) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ~humble(X0) | quiet(X0))) [flattening 45]
92. quiet(X0) | strong(X0) [cnf transformation 44]
95. ~quiet(X0) | strong(X0) [cnf transformation 46]
141. ~strong(fred) [cnf transformation 23]
158. strong(X0) [subsumption resolution 95,92]
261. $false [subsumption resolution 141,158]
% SZS output end Proof for 1307960087438483815790374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is old and vice versa. If paul is wise or not happy then mary is not curious or quiet and vice versa. If mary is either old or tall then alice is not rich. If mary is either curious or not wise then someone is happy or not happy and vice versa. Everyone who is both not patient and not tall is both calm and not quiet. Everyone who is both not calm and kind is not kind or brave and vice versa. Everyone who is either not humble or happy is either curious or brave. If john is tall or not patient then someone is not brave or kind and vice versa. If someone is both not kind and funny then john is both not funny and kind and vice versa. Everyone who is tall or not humble is both humble and not curious and vice versa. Everyone who is either kind or humble is not brave. Everyone who is not calm is both not wise and not creative. If someone is not funny or not quiet then lucy is not humble or patient and vice versa. Everyone who is either not old or calm is both humble and not happy. If someone is both not happy and not old then paul is either brave or not strong. If john is either not patient or generous then someone is both not tall and kind. John is rich. Someone is both not happy and curious. Susan is either humble or brave. Someone is not curious or tall. Mary is not generous. Alice is either wise or strong. | Mary is not brave. | neutral | (![X]:(creative(X)<=>old(X)))&
(((wise(paul)|~happy(paul)))<=>((~curious(mary)|quiet(mary))))&
(((old(mary)<~>tall(mary)))=>(~rich(alice)))&
(((curious(mary)<~>~wise(mary)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~patient(X)&~tall(X))=>(calm(X)&~quiet(X))))&
(![X]:((~calm(X)&kind(X))<=>(~kind(X)|brave(X))))&
(![X]:((~humble(X)<~>happy(X))=>(curious(X)<~>brave(X))))&
(((tall(john)|~patient(john)))<=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:((~kind(X)&funny(X))))<=>((~funny(john)&kind(john))))&
(![X]:((tall(X)|~humble(X))<=>(humble(X)&~curious(X))))&
(![X]:((kind(X)<~>humble(X))=>~brave(X)))&
(![X]:(~calm(X)=>(~wise(X)&~creative(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>((~humble(lucy)|patient(lucy))))&
(![X]:((~old(X)<~>calm(X))=>(humble(X)&~happy(X))))&
((?[X]:((~happy(X)&~old(X))))=>((brave(paul)<~>~strong(paul))))&
(((~patient(john)<~>generous(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(rich(john))&
(?[X]:((~happy(X)&curious(X))))&
((humble(susan)<~>brave(susan)))&
(?[X]:((~curious(X)|tall(X))))&
(~generous(mary))&
((wise(alice)<~>strong(alice))) | ~brave(mary) | [] | null | 0 |
If someone is either not funny or not quiet then susan is not humble. Everyone who is not old or not tall is brave. If someone is not kind then someone is either not old or kind and vice versa. If mary is not rich then someone is either happy or not patient and vice versa. Everyone who is either not strong or creative is funny or not curious and vice versa. If susan is strong then alice is generous and vice versa. Everyone who is not humble or not funny is not rich. If someone is either happy or not tall then someone is humble or not tall. Everyone who is not curious is old. If susan is rich then lucy is brave and vice versa. Everyone who is strong or not old is both not brave and not funny and vice versa. Everyone who is either old or not brave is humble. If someone is not tall or not brave then lucy is creative. Everyone who is either happy or generous is either not old or quiet and vice versa. If susan is either not calm or not funny then john is tall or quiet and vice versa. If someone is either not happy or not generous then alice is calm or not quiet and vice versa. John is not curious. Someone is either not curious or not generous. John is both not brave and not humble. Someone is both not patient and not generous. Paul is kind. Mary is patient or happy. Someone is generous or not curious. | Mary is not happy. | neutral | ((?[X]:((~funny(X)<~>~quiet(X))))=>(~humble(susan)))&
(![X]:((~old(X)|~tall(X))=>brave(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~old(X)<~>kind(X)))))&
((~rich(mary))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>(funny(X)|~curious(X))))&
((strong(susan))<=>(generous(alice)))&
(![X]:((~humble(X)|~funny(X))=>~rich(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:(~curious(X)=>old(X)))&
((rich(susan))<=>(brave(lucy)))&
(![X]:((strong(X)|~old(X))<=>(~brave(X)&~funny(X))))&
(![X]:((old(X)<~>~brave(X))=>humble(X)))&
((?[X]:((~tall(X)|~brave(X))))=>(creative(lucy)))&
(![X]:((happy(X)<~>generous(X))<=>(~old(X)<~>quiet(X))))&
(((~calm(susan)<~>~funny(susan)))<=>((tall(john)|quiet(john))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>((calm(alice)|~quiet(alice))))&
(~curious(john))&
(?[X]:((~curious(X)<~>~generous(X))))&
((~brave(john)&~humble(john)))&
(?[X]:((~patient(X)&~generous(X))))&
(kind(paul))&
((patient(mary)|happy(mary)))&
(?[X]:((generous(X)|~curious(X)))) | ~happy(mary) | [] | null | 0 |
If fred is creative or not funny then lucy is patient and vice versa.
Everyone who is not strong or old is both tall and patient and vice versa.
Everyone who is funny or curious is not rich.
Everyone who is not happy or not patient is either rich or funny and vice versa.
If someone is kind then someone is wise or rich and vice versa.
If someone is either not curious or rich then someone is both kind and creative.
Everyone who is not wise is both quiet and patient.
Everyone who is either brave or not humble is both not humble and strong and vice versa.
Everyone who is either generous or tall is patient or calm and vice versa.
If lucy is either rich or not creative then someone is not strong or not old and vice versa.
If paul is humble or calm then someone is both kind and not patient.
Everyone who is rich or not curious is not funny and vice versa.
Everyone who is not brave or not strong is either rich or not curious.
If someone is generous or not happy then someone is rich or not tall.
Everyone who is quiet is both calm and brave.
Everyone who is either not kind or not old is both rich and not wise and vice versa.
Lucy is happy.
Susan is humble or brave.
Susan is both humble and not old.
Fred is patient.
Someone is kind.
Paul is humble or not brave. | Susan is kind. | contradiction | (((creative(fred)|~funny(fred)))<=>(patient(lucy)))&
(![X]:((~strong(X)|old(X))<=>(tall(X)&patient(X))))&
(![X]:((funny(X)|curious(X))=>~rich(X)))&
(![X]:((~happy(X)|~patient(X))<=>(rich(X)<~>funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(~wise(X)=>(quiet(X)&patient(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(~humble(X)&strong(X))))&
(![X]:((generous(X)<~>tall(X))<=>(patient(X)|calm(X))))&
(((rich(lucy)<~>~creative(lucy)))<=>(?[X]:((~strong(X)|~old(X)))))&
(((humble(paul)|calm(paul)))=>(?[X]:((kind(X)&~patient(X)))))&
(![X]:((rich(X)|~curious(X))<=>~funny(X)))&
(![X]:((~brave(X)|~strong(X))=>(rich(X)<~>~curious(X))))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:(quiet(X)=>(calm(X)&brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(rich(X)&~wise(X))))&
(happy(lucy))&
((humble(susan)|brave(susan)))&
((humble(susan)&~old(susan)))&
(patient(fred))&
(?[X]:(kind(X)))&
((humble(paul)|~brave(paul))) | kind(susan) | [
"p2",
"p7",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4674849253522032561379632
% SZS output start Proof for 4674849253522032561379632
3. ! [X0] : ((curious(X0) | funny(X0)) => ~rich(X0)) [input p2]
8. ! [X0] : ((brave(X0) <~> ~humble(X0)) <=> (strong(X0) & ~humble(X0))) [input p7]
13. ! [X0] : ((~strong(X0) | ~brave(X0)) => (rich(X0) <~> ~curious(X0))) [input p12]
16. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> (~wise(X0) & rich(X0))) [input p15]
19. ~old(susan) & humble(susan) [input p18]
23. kind(susan) [input hypothesis]
27. ! [X0] : (~rich(X0) | (~curious(X0) & ~funny(X0))) [ennf transformation 3]
31. ! [X0] : ((rich(X0) <~> ~curious(X0)) | (strong(X0) & brave(X0))) [ennf transformation 13]
49. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (~strong(X0) | humble(X0))) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | ~strong(X0) | humble(X0)) & ((strong(X0) & ~humble(X0)) | ((brave(X0) | humble(X0)) & (~humble(X0) | ~brave(X0))))) [flattening 49]
61. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (strong(X0) & brave(X0))) [nnf transformation 31]
65. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 16]
66. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [flattening 65]
78. ~rich(X0) | ~curious(X0) [cnf transformation 27]
94. ~humble(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 50]
121. curious(X0) | ~rich(X0) | brave(X0) [cnf transformation 61]
128. ~kind(X0) | rich(X0) | old(X0) [cnf transformation 66]
135. humble(susan) [cnf transformation 19]
136. ~old(susan) [cnf transformation 19]
140. kind(susan) [cnf transformation 23]
141. ~humble(X0) | ~brave(X0) [duplicate literal removal 94]
247. ~rich(X0) | brave(X0) [subsumption resolution 121,78]
267. 27 <=> humble(susan) [avatar definition]
269. humble(susan) <- (27) [avatar component clause 267]
271. 28 <=> brave(susan) [avatar definition]
272. ~brave(susan) <- (~28) [avatar component clause 271]
275. 27 [avatar split clause 135,267]
283. ~brave(susan) <- (27) [resolution 141,269]
284. ~28 | ~27 [avatar split clause 283,267,271]
327. rich(susan) | old(susan) [resolution 128,140]
331. rich(susan) [subsumption resolution 327,136]
367. brave(susan) [resolution 331,247]
372. $false <- (~28) [subsumption resolution 367,272]
373. 28 [avatar contradiction clause 372]
374. $false [avatar sat refutation 275,284,373]
% SZS output end Proof for 4674849253522032561379632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or calm then paul is not tall or tall and vice versa.
If someone is kind or happy then lucy is not rich or kind and vice versa.
If lucy is kind then someone is either rich or not humble and vice versa.
Everyone who is either old or not curious is both not strong and patient.
Everyone who is happy is both kind and not old and vice versa.
Everyone who is either not funny or not tall is both patient and rich and vice versa.
If fred is either not humble or quiet then susan is both rich and wise and vice versa.
If susan is not happy or old then someone is both creative and rich and vice versa.
Everyone who is creative is either not kind or kind and vice versa.
If someone is both not brave and not tall then lucy is rich or not curious.
If alice is not generous then paul is both not rich and not tall.
If someone is both quiet and not funny then mary is not happy or strong.
If someone is rich or patient then someone is not curious or tall and vice versa.
Everyone who is both not kind and not funny is not funny.
If john is curious or not creative then someone is calm or curious and vice versa.
Everyone who is not tall or curious is either not curious or not creative and vice versa.
Someone is funny.
Someone is old or kind.
Paul is either not humble or calm.
Paul is both patient and not tall.
Lucy is kind or not tall.
Alice is both not curious and not wise.
Mary is not patient or not quiet. | Alice is not strong. | neutral | ((?[X]:((strong(X)|calm(X))))<=>((~tall(paul)|tall(paul))))&
((?[X]:((kind(X)|happy(X))))<=>((~rich(lucy)|kind(lucy))))&
((kind(lucy))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((old(X)<~>~curious(X))=>(~strong(X)&patient(X))))&
(![X]:(happy(X)<=>(kind(X)&~old(X))))&
(![X]:((~funny(X)<~>~tall(X))<=>(patient(X)&rich(X))))&
(((~humble(fred)<~>quiet(fred)))<=>((rich(susan)&wise(susan))))&
(((~happy(susan)|old(susan)))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
((?[X]:((~brave(X)&~tall(X))))=>((rich(lucy)|~curious(lucy))))&
((~generous(alice))=>((~rich(paul)&~tall(paul))))&
((?[X]:((quiet(X)&~funny(X))))=>((~happy(mary)|strong(mary))))&
((?[X]:((rich(X)|patient(X))))<=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~kind(X)&~funny(X))=>~funny(X)))&
(((curious(john)|~creative(john)))<=>(?[X]:((calm(X)|curious(X)))))&
(![X]:((~tall(X)|curious(X))<=>(~curious(X)<~>~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((old(X)|kind(X))))&
((~humble(paul)<~>calm(paul)))&
((patient(paul)&~tall(paul)))&
((kind(lucy)|~tall(lucy)))&
((~curious(alice)&~wise(alice)))&
((~patient(mary)|~quiet(mary))) | ~strong(alice) | [] | null | 0 |
If someone is both not brave and curious then lucy is quiet and vice versa. If someone is rich or curious then john is not old and vice versa. If someone is either not wise or not strong then lucy is funny and vice versa. If someone is kind or creative then mary is both quiet and not wise and vice versa. Everyone who is not curious is funny or not funny and vice versa. Everyone who is not tall is wise or old and vice versa. Everyone who is both humble and not generous is either not wise or generous. Everyone who is tall or happy is not funny or not tall. Everyone who is both happy and not curious is both not curious and not patient. Everyone who is generous or not creative is tall. Everyone who is not patient or calm is either not quiet or happy and vice versa. Everyone who is not strong is either tall or not old and vice versa. If fred is both not generous and not funny then someone is wise or brave and vice versa. If someone is either not calm or calm then fred is either not generous or not brave. If someone is both not rich and not happy then someone is both calm and creative. Everyone who is either not rich or happy is either patient or calm. Someone is either not creative or rich. Susan is both not curious and not tall. Fred is not quiet. Paul is tall or brave. Someone is either not rich or not old. Someone is brave. | Lucy is not funny. | contradiction | ((?[X]:((~brave(X)&curious(X))))<=>(quiet(lucy)))&
((?[X]:((rich(X)|curious(X))))<=>(~old(john)))&
((?[X]:((~wise(X)<~>~strong(X))))<=>(funny(lucy)))&
((?[X]:((kind(X)|creative(X))))<=>((quiet(mary)&~wise(mary))))&
(![X]:(~curious(X)<=>(funny(X)|~funny(X))))&
(![X]:(~tall(X)<=>(wise(X)|old(X))))&
(![X]:((humble(X)&~generous(X))=>(~wise(X)<~>generous(X))))&
(![X]:((tall(X)|happy(X))=>(~funny(X)|~tall(X))))&
(![X]:((happy(X)&~curious(X))=>(~curious(X)&~patient(X))))&
(![X]:((generous(X)|~creative(X))=>tall(X)))&
(![X]:((~patient(X)|calm(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:(~strong(X)<=>(tall(X)<~>~old(X))))&
(((~generous(fred)&~funny(fred)))<=>(?[X]:((wise(X)|brave(X)))))&
((?[X]:((~calm(X)<~>calm(X))))=>((~generous(fred)<~>~brave(fred))))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((calm(X)&creative(X)))))&
(![X]:((~rich(X)<~>happy(X))=>(patient(X)<~>calm(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((~curious(susan)&~tall(susan)))&
(~quiet(fred))&
((tall(paul)|brave(paul)))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:(brave(X))) | ~funny(lucy) | [
"p2",
"p3",
"p5",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8089805653529059674311914
% SZS output start Proof for 8089805653529059674311914
3. ? [X0] : (~wise(X0) <~> ~strong(X0)) <=> funny(lucy) [input p2]
4. ? [X0] : (creative(X0) | kind(X0)) <=> (~wise(mary) & quiet(mary)) [input p3]
6. ! [X0] : (~tall(X0) <=> (old(X0) | wise(X0))) [input p5]
10. ! [X0] : ((~creative(X0) | generous(X0)) => tall(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (tall(X0) <~> ~old(X0))) [input p11]
18. ~tall(susan) & ~curious(susan) [input p17]
23. ~funny(lucy) [input hypothesis]
30. ! [X0] : (tall(X0) | (creative(X0) & ~generous(X0))) [ennf transformation 10]
42. (? [X0] : ((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~funny(lucy)) & (funny(lucy) | ! [X0] : ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) [nnf transformation 3]
43. (? [X0] : ((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~funny(lucy)) & (funny(lucy) | ! [X1] : ((~wise(X1) | strong(X1)) & (~strong(X1) | wise(X1)))) [rectify 42]
44. ? [X0] : ((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) => ((strong(sK2) | wise(sK2)) & (~strong(sK2) | ~wise(sK2))) [choice axiom]
45. (((strong(sK2) | wise(sK2)) & (~strong(sK2) | ~wise(sK2))) | ~funny(lucy)) & (funny(lucy) | ! [X1] : ((~wise(X1) | strong(X1)) & (~strong(X1) | wise(X1)))) [skolemisation 43,44]
46. (? [X0] : (creative(X0) | kind(X0)) | (wise(mary) | ~quiet(mary))) & ((~wise(mary) & quiet(mary)) | ! [X0] : (~creative(X0) & ~kind(X0))) [nnf transformation 4]
47. (? [X0] : (creative(X0) | kind(X0)) | wise(mary) | ~quiet(mary)) & ((~wise(mary) & quiet(mary)) | ! [X0] : (~creative(X0) & ~kind(X0))) [flattening 46]
48. (? [X0] : (creative(X0) | kind(X0)) | wise(mary) | ~quiet(mary)) & ((~wise(mary) & quiet(mary)) | ! [X1] : (~creative(X1) & ~kind(X1))) [rectify 47]
49. ? [X0] : (creative(X0) | kind(X0)) => (creative(sK3) | kind(sK3)) [choice axiom]
50. ((creative(sK3) | kind(sK3)) | wise(mary) | ~quiet(mary)) & ((~wise(mary) & quiet(mary)) | ! [X1] : (~creative(X1) & ~kind(X1))) [skolemisation 48,49]
53. ! [X0] : ((~tall(X0) | (~old(X0) & ~wise(X0))) & ((old(X0) | wise(X0)) | tall(X0))) [nnf transformation 6]
54. ! [X0] : ((~tall(X0) | (~old(X0) & ~wise(X0))) & (old(X0) | wise(X0) | tall(X0))) [flattening 53]
57. ! [X0] : ((~strong(X0) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0)))) & (((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | strong(X0))) [nnf transformation 12]
82. funny(lucy) | ~strong(X1) | wise(X1) [cnf transformation 45]
83. funny(lucy) | ~wise(X1) | strong(X1) [cnf transformation 45]
89. ~wise(mary) | ~creative(X1) [cnf transformation 50]
94. tall(X0) | wise(X0) | old(X0) [cnf transformation 54]
96. ~tall(X0) | ~old(X0) [cnf transformation 54]
102. tall(X0) | creative(X0) [cnf transformation 30]
109. ~old(X0) | tall(X0) | strong(X0) [cnf transformation 57]
110. old(X0) | ~tall(X0) | strong(X0) [cnf transformation 57]
131. ~tall(susan) [cnf transformation 18]
137. ~funny(lucy) [cnf transformation 23]
183. 10 <=> funny(lucy) [avatar definition]
197. 13 <=> ! [X1] : (~wise(X1) | strong(X1)) [avatar definition]
198. ~wise(X1) | strong(X1) <- (13) [avatar component clause 197]
199. 13 | 10 [avatar split clause 83,183,197]
201. 14 <=> ! [X1] : (~strong(X1) | wise(X1)) [avatar definition]
202. ~strong(X1) | wise(X1) <- (14) [avatar component clause 201]
203. 14 | 10 [avatar split clause 82,183,201]
209. 16 <=> wise(mary) [avatar definition]
210. ~wise(mary) <- (~16) [avatar component clause 209]
222. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
223. ~creative(X1) <- (19) [avatar component clause 222]
224. 19 | ~16 [avatar split clause 89,209,222]
233. ~tall(X0) | strong(X0) [subsumption resolution 110,96]
234. ~old(X0) | strong(X0) [subsumption resolution 109,96]
318. ~10 [avatar split clause 137,183]
326. creative(susan) [resolution 102,131]
340. wise(X0) | old(X0) | strong(X0) [resolution 94,233]
354. old(X0) | strong(X0) <- (13) [subsumption resolution 340,198]
355. strong(X0) <- (13) [subsumption resolution 354,234]
368. wise(X0) <- (13, 14) [resolution 355,202]
381. $false <- (19) [resolution 223,326]
384. ~19 [avatar contradiction clause 381]
393. $false <- (13, 14, ~16) [resolution 368,210]
395. ~13 | ~14 | 16 [avatar contradiction clause 393]
396. $false [avatar sat refutation 199,203,224,318,384,395]
% SZS output end Proof for 8089805653529059674311914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not brave then mary is both brave and kind and vice versa. If someone is happy or strong then john is both kind and not creative and vice versa. Everyone who is not rich is both funny and strong. Everyone who is both wise and tall is either not humble or not curious and vice versa. Everyone who is brave or creative is kind or creative. If lucy is not patient or not curious then mary is both rich and funny. Everyone who is not strong or not calm is not patient. Everyone who is wise or not happy is not strong or not patient. Everyone who is either not humble or happy is not creative. If someone is not happy or not rich then paul is not happy and vice versa. Everyone who is brave or tall is tall or not patient and vice versa. Everyone who is both not generous and strong is either wise or not calm. Everyone who is both not tall and not wise is both brave and kind and vice versa. Everyone who is calm or strong is kind and vice versa. Everyone who is both strong and not tall is not quiet or not calm and vice versa. If someone is not patient or not tall then someone is both tall and not generous and vice versa. Someone is both not happy and rich. Lucy is either not curious or not humble. Someone is both generous and not happy. Paul is either not old or patient. Someone is either not tall or curious. Someone is not calm. Someone is funny or not funny. Mary is happy or calm. | Paul is not old. | entailment | ((?[X]:((humble(X)&~brave(X))))<=>((brave(mary)&kind(mary))))&
((?[X]:((happy(X)|strong(X))))<=>((kind(john)&~creative(john))))&
(![X]:(~rich(X)=>(funny(X)&strong(X))))&
(![X]:((wise(X)&tall(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((brave(X)|creative(X))=>(kind(X)|creative(X))))&
(((~patient(lucy)|~curious(lucy)))=>((rich(mary)&funny(mary))))&
(![X]:((~strong(X)|~calm(X))=>~patient(X)))&
(![X]:((wise(X)|~happy(X))=>(~strong(X)|~patient(X))))&
(![X]:((~humble(X)<~>happy(X))=>~creative(X)))&
((?[X]:((~happy(X)|~rich(X))))<=>(~happy(paul)))&
(![X]:((brave(X)|tall(X))<=>(tall(X)|~patient(X))))&
(![X]:((~generous(X)&strong(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~tall(X)&~wise(X))<=>(brave(X)&kind(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
(![X]:((strong(X)&~tall(X))<=>(~quiet(X)|~calm(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(?[X]:((~happy(X)&rich(X))))&
((~curious(lucy)<~>~humble(lucy)))&
(?[X]:((generous(X)&~happy(X))))&
((~old(paul)<~>patient(paul)))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:(~calm(X)))&
(?[X]:((funny(X)|~funny(X))))&
((happy(mary)|calm(mary))) | ~old(paul) | [
"p6",
"p7",
"p9",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8116076012752754570147830
% SZS output start Proof for 8116076012752754570147830
7. ! [X0] : ((~calm(X0) | ~strong(X0)) => ~patient(X0)) [input p6]
8. ! [X0] : ((~happy(X0) | wise(X0)) => (~patient(X0) | ~strong(X0))) [input p7]
10. ? [X0] : (~rich(X0) | ~happy(X0)) <=> ~happy(paul) [input p9]
17. ? [X0] : (rich(X0) & ~happy(X0)) [input p16]
20. ~old(paul) <~> patient(paul) [input p19]
25. old(paul) [input hypothesis]
31. ! [X0] : (~patient(X0) | (calm(X0) & strong(X0))) [ennf transformation 7]
32. ! [X0] : ((~patient(X0) | ~strong(X0)) | (happy(X0) & ~wise(X0))) [ennf transformation 8]
33. ! [X0] : (~patient(X0) | ~strong(X0) | (happy(X0) & ~wise(X0))) [flattening 32]
50. (? [X0] : (~rich(X0) | ~happy(X0)) | happy(paul)) & (~happy(paul) | ! [X0] : (rich(X0) & happy(X0))) [nnf transformation 10]
51. (? [X0] : (~rich(X0) | ~happy(X0)) | happy(paul)) & (~happy(paul) | ! [X1] : (rich(X1) & happy(X1))) [rectify 50]
52. ? [X0] : (~rich(X0) | ~happy(X0)) => (~rich(sK2) | ~happy(sK2)) [choice axiom]
53. ((~rich(sK2) | ~happy(sK2)) | happy(paul)) & (~happy(paul) | ! [X1] : (rich(X1) & happy(X1))) [skolemisation 51,52]
68. ? [X0] : (rich(X0) & ~happy(X0)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
69. rich(sK5) & ~happy(sK5) [skolemisation 17,68]
73. (~patient(paul) | old(paul)) & (patient(paul) | ~old(paul)) [nnf transformation 20]
104. ~patient(X0) | strong(X0) [cnf transformation 31]
107. ~patient(X0) | ~strong(X0) | happy(X0) [cnf transformation 33]
110. ~happy(paul) | happy(X1) [cnf transformation 53]
136. ~happy(sK5) [cnf transformation 69]
142. patient(paul) | ~old(paul) [cnf transformation 73]
149. old(paul) [cnf transformation 25]
220. ~patient(X0) | happy(X0) [subsumption resolution 107,104]
223. 16 <=> happy(paul) [avatar definition]
240. 20 <=> ! [X1] : happy(X1) [avatar definition]
241. happy(X1) <- (20) [avatar component clause 240]
242. 20 | ~16 [avatar split clause 110,223,240]
280. 29 <=> old(paul) [avatar definition]
284. 30 <=> patient(paul) [avatar definition]
285. patient(paul) <- (30) [avatar component clause 284]
288. ~29 | 30 [avatar split clause 142,284,280]
308. 29 [avatar split clause 149,280]
340. happy(paul) <- (30) [resolution 220,285]
345. 16 | ~30 [avatar split clause 340,284,223]
347. $false <- (20) [resolution 241,136]
350. ~20 [avatar contradiction clause 347]
352. $false [avatar sat refutation 242,288,308,345,350]
% SZS output end Proof for 8116076012752754570147830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not creative then someone is either not humble or not strong.
If someone is calm or old then someone is not wise or wise and vice versa.
Everyone who is not funny or rich is both not calm and tall.
Everyone who is not old is kind and vice versa.
If john is not strong then someone is creative or not patient and vice versa.
If paul is either not curious or not rich then lucy is both not kind and humble and vice versa.
If someone is not humble then john is not funny and vice versa.
Everyone who is not humble is either not strong or not humble and vice versa.
Everyone who is either generous or not funny is strong and vice versa.
Everyone who is either not quiet or strong is both not calm and not old.
If someone is either not old or not generous then john is both brave and not generous.
If lucy is not brave or tall then someone is not strong or not rich.
If john is both not quiet and curious then alice is both humble and generous and vice versa.
Everyone who is calm is both calm and wise.
Everyone who is either not calm or creative is both strong and not patient and vice versa.
If lucy is both not quiet and old then someone is not funny or wise and vice versa.
Someone is either humble or not generous.
Alice is both funny and not kind.
John is old or patient.
Mary is rich or wise. | Lucy is not humble. | contradiction | ((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>~strong(X)))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:((~wise(X)|wise(X)))))&
(![X]:((~funny(X)|rich(X))=>(~calm(X)&tall(X))))&
(![X]:(~old(X)<=>kind(X)))&
((~strong(john))<=>(?[X]:((creative(X)|~patient(X)))))&
(((~curious(paul)<~>~rich(paul)))<=>((~kind(lucy)&humble(lucy))))&
((?[X]:(~humble(X)))<=>(~funny(john)))&
(![X]:(~humble(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((generous(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~quiet(X)<~>strong(X))=>(~calm(X)&~old(X))))&
((?[X]:((~old(X)<~>~generous(X))))=>((brave(john)&~generous(john))))&
(((~brave(lucy)|tall(lucy)))=>(?[X]:((~strong(X)|~rich(X)))))&
(((~quiet(john)&curious(john)))<=>((humble(alice)&generous(alice))))&
(![X]:(calm(X)=>(calm(X)&wise(X))))&
(![X]:((~calm(X)<~>creative(X))<=>(strong(X)&~patient(X))))&
(((~quiet(lucy)&old(lucy)))<=>(?[X]:((~funny(X)|wise(X)))))&
(?[X]:((humble(X)<~>~generous(X))))&
((funny(alice)&~kind(alice)))&
((old(john)|patient(john)))&
((rich(mary)|wise(mary))) | ~humble(lucy) | [
"p2",
"p4",
"p6",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5242102492198859153351986
% SZS output start Proof for 5242102492198859153351986
3. ! [X0] : ((rich(X0) | ~funny(X0)) => (tall(X0) & ~calm(X0))) [input p2]
5. ~strong(john) <=> ? [X0] : (~patient(X0) | creative(X0)) [input p4]
7. ? [X0] : ~humble(X0) <=> ~funny(john) [input p6]
8. ! [X0] : (~humble(X0) <=> (~strong(X0) <~> ~humble(X0))) [input p7]
15. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~patient(X0) & strong(X0))) [input p14]
21. ~humble(lucy) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~calm(X0)) | (~rich(X0) & funny(X0))) [ennf transformation 3]
42. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & (? [X0] : (~patient(X0) | creative(X0)) | strong(john)) [nnf transformation 5]
43. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & (? [X1] : (~patient(X1) | creative(X1)) | strong(john)) [rectify 42]
44. ? [X1] : (~patient(X1) | creative(X1)) => (~patient(sK3) | creative(sK3)) [choice axiom]
45. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & ((~patient(sK3) | creative(sK3)) | strong(john)) [skolemisation 43,44]
48. (? [X0] : ~humble(X0) | funny(john)) & (~funny(john) | ! [X0] : humble(X0)) [nnf transformation 7]
49. (? [X0] : ~humble(X0) | funny(john)) & (~funny(john) | ! [X1] : humble(X1)) [rectify 48]
50. ? [X0] : ~humble(X0) => ~humble(sK4) [choice axiom]
51. (~humble(sK4) | funny(john)) & (~funny(john) | ! [X1] : humble(X1)) [skolemisation 49,50]
52. ! [X0] : ((~humble(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | humble(X0))) [nnf transformation 8]
60. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [flattening 60]
78. ~calm(X0) | funny(X0) [cnf transformation 27]
85. ~strong(john) | ~creative(X0) [cnf transformation 45]
86. ~strong(john) | patient(X0) [cnf transformation 45]
93. ~funny(john) | humble(X1) [cnf transformation 51]
96. humble(X0) | strong(X0) | humble(X0) [cnf transformation 52]
97. ~humble(X0) | ~humble(X0) | strong(X0) [cnf transformation 52]
118. ~patient(X0) | creative(X0) | calm(X0) [cnf transformation 61]
133. ~humble(lucy) [cnf transformation 21]
134. humble(X0) | strong(X0) [duplicate literal removal 96]
135. ~humble(X0) | strong(X0) [duplicate literal removal 97]
171. 9 <=> ! [X0] : patient(X0) [avatar definition]
172. patient(X0) <- (9) [avatar component clause 171]
174. 10 <=> strong(john) [avatar definition]
176. ~strong(john) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 86,174,171]
179. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
180. ~creative(X0) <- (11) [avatar component clause 179]
181. 11 | ~10 [avatar split clause 85,174,179]
196. 15 <=> humble(lucy) [avatar definition]
198. ~humble(lucy) <- (~15) [avatar component clause 196]
214. 18 <=> funny(john) [avatar definition]
215. ~funny(john) <- (~18) [avatar component clause 214]
223. 20 <=> ! [X1] : humble(X1) [avatar definition]
224. humble(X1) <- (20) [avatar component clause 223]
225. 20 | ~18 [avatar split clause 93,214,223]
226. strong(X0) [subsumption resolution 134,135]
281. 31 <=> ! [X0] : funny(X0) [avatar definition]
282. funny(X0) <- (31) [avatar component clause 281]
328. ~15 [avatar split clause 133,196]
329. $false <- (~10) [subsumption resolution 176,226]
330. 10 [avatar contradiction clause 329]
348. creative(X0) | calm(X0) <- (9) [resolution 118,172]
349. calm(X0) <- (9, 11) [subsumption resolution 348,180]
352. funny(X1) <- (9, 11) [resolution 349,78]
356. 31 | ~9 | ~11 [avatar split clause 352,179,171,281]
357. $false <- (~18, 31) [resolution 282,215]
361. 18 | ~31 [avatar contradiction clause 357]
365. $false <- (~15, 20) [resolution 224,198]
372. 15 | ~20 [avatar contradiction clause 365]
373. $false [avatar sat refutation 177,181,225,328,330,356,361,372]
% SZS output end Proof for 5242102492198859153351986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or kind is not brave. Everyone who is not rich or kind is either not kind or brave. If someone is curious or not humble then lucy is not funny and vice versa. If someone is either not calm or not curious then someone is either happy or not patient and vice versa. Everyone who is either not humble or calm is both wise and quiet. Everyone who is not happy or not curious is both happy and kind and vice versa. Everyone who is not kind is not funny or not patient. If alice is not humble or not funny then someone is both not quiet and creative. If someone is patient or wise then paul is both not happy and patient. If alice is either strong or not patient then someone is not funny or not creative. Everyone who is either brave or not patient is not curious or calm. If fred is not strong then someone is brave or happy. Everyone who is either not kind or humble is not old. If someone is tall or not generous then alice is not curious and vice versa. If alice is brave or rich then lucy is not humble. Mary is both not patient and rich. Mary is either strong or quiet. Someone is both not kind and not humble. Someone is strong or not calm. Susan is not kind or calm. Someone is both quiet and not patient. Someone is not wise or curious. | Lucy is old. | contradiction | (![X]:((~creative(X)|kind(X))=>~brave(X)))&
(![X]:((~rich(X)|kind(X))=>(~kind(X)<~>brave(X))))&
((?[X]:((curious(X)|~humble(X))))<=>(~funny(lucy)))&
((?[X]:((~calm(X)<~>~curious(X))))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:((~humble(X)<~>calm(X))=>(wise(X)&quiet(X))))&
(![X]:((~happy(X)|~curious(X))<=>(happy(X)&kind(X))))&
(![X]:(~kind(X)=>(~funny(X)|~patient(X))))&
(((~humble(alice)|~funny(alice)))=>(?[X]:((~quiet(X)&creative(X)))))&
((?[X]:((patient(X)|wise(X))))=>((~happy(paul)&patient(paul))))&
(((strong(alice)<~>~patient(alice)))=>(?[X]:((~funny(X)|~creative(X)))))&
(![X]:((brave(X)<~>~patient(X))=>(~curious(X)|calm(X))))&
((~strong(fred))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~kind(X)<~>humble(X))=>~old(X)))&
((?[X]:((tall(X)|~generous(X))))<=>(~curious(alice)))&
(((brave(alice)|rich(alice)))=>(~humble(lucy)))&
((~patient(mary)&rich(mary)))&
((strong(mary)<~>quiet(mary)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((strong(X)|~calm(X))))&
((~kind(susan)|calm(susan)))&
(?[X]:((quiet(X)&~patient(X))))&
(?[X]:((~wise(X)|curious(X)))) | old(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2902781506209873001451200
% SZS output start Proof for 2902781506209873001451200
1. ! [X0] : ((kind(X0) | ~creative(X0)) => ~brave(X0)) [input p0]
2. ! [X0] : ((kind(X0) | ~rich(X0)) => (~kind(X0) <~> brave(X0))) [input p1]
4. ? [X0] : (~calm(X0) <~> ~curious(X0)) <=> ? [X0] : (happy(X0) <~> ~patient(X0)) [input p3]
5. ! [X0] : ((~humble(X0) <~> calm(X0)) => (quiet(X0) & wise(X0))) [input p4]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (kind(X0) & happy(X0))) [input p5]
9. ? [X0] : (wise(X0) | patient(X0)) => (patient(paul) & ~happy(paul)) [input p8]
13. ! [X0] : ((~kind(X0) <~> humble(X0)) => ~old(X0)) [input p12]
23. old(lucy) [input hypothesis]
24. ? [X0] : (~calm(X0) <~> ~curious(X0)) <=> ? [X1] : (happy(X1) <~> ~patient(X1)) [rectify 4]
25. ! [X0] : (~brave(X0) | (~kind(X0) & creative(X0))) [ennf transformation 1]
26. ! [X0] : ((~kind(X0) <~> brave(X0)) | (~kind(X0) & rich(X0))) [ennf transformation 2]
27. ! [X0] : ((quiet(X0) & wise(X0)) | (~humble(X0) <=> calm(X0))) [ennf transformation 5]
31. (patient(paul) & ~happy(paul)) | ! [X0] : (~wise(X0) & ~patient(X0)) [ennf transformation 9]
36. ! [X0] : (~old(X0) | (~kind(X0) <=> humble(X0))) [ennf transformation 13]
38. ! [X0] : (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | (~kind(X0) & rich(X0))) [nnf transformation 26]
43. (? [X0] : ((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ! [X1] : ((happy(X1) | patient(X1)) & (~patient(X1) | ~happy(X1)))) & (? [X1] : ((patient(X1) | ~happy(X1)) & (~patient(X1) | happy(X1))) | ! [X0] : ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0)))) [nnf transformation 24]
44. (? [X0] : ((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ! [X1] : ((happy(X1) | patient(X1)) & (~patient(X1) | ~happy(X1)))) & (? [X2] : ((patient(X2) | ~happy(X2)) & (~patient(X2) | happy(X2))) | ! [X3] : ((~calm(X3) | curious(X3)) & (~curious(X3) | calm(X3)))) [rectify 43]
45. ? [X0] : ((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) => ((curious(sK1) | calm(sK1)) & (~curious(sK1) | ~calm(sK1))) [choice axiom]
46. ? [X2] : ((patient(X2) | ~happy(X2)) & (~patient(X2) | happy(X2))) => ((patient(sK2) | ~happy(sK2)) & (~patient(sK2) | happy(sK2))) [choice axiom]
47. (((curious(sK1) | calm(sK1)) & (~curious(sK1) | ~calm(sK1))) | ! [X1] : ((happy(X1) | patient(X1)) & (~patient(X1) | ~happy(X1)))) & (((patient(sK2) | ~happy(sK2)) & (~patient(sK2) | happy(sK2))) | ! [X3] : ((~calm(X3) | curious(X3)) & (~curious(X3) | calm(X3)))) [skolemisation 44,46,45]
48. ! [X0] : ((quiet(X0) & wise(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) [nnf transformation 27]
49. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 6]
50. ! [X0] : ((~curious(X0) | ~happy(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | (curious(X0) & happy(X0)))) [flattening 49]
59. ! [X0] : (~old(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0)))) [nnf transformation 36]
74. ~brave(X0) | ~kind(X0) [cnf transformation 25]
76. brave(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 38]
84. patient(sK2) | ~happy(sK2) | ~curious(X3) | calm(X3) [cnf transformation 47]
91. ~calm(X0) | ~humble(X0) | wise(X0) [cnf transformation 48]
96. kind(X0) | happy(X0) [cnf transformation 50]
97. kind(X0) | curious(X0) [cnf transformation 50]
104. ~happy(paul) | ~patient(X0) [cnf transformation 31]
105. ~happy(paul) | ~wise(X0) [cnf transformation 31]
113. ~old(X0) | humble(X0) | kind(X0) [cnf transformation 59]
131. old(lucy) [cnf transformation 23]
134. brave(X0) | ~kind(X0) [duplicate literal removal 76]
136. ~kind(X0) [subsumption resolution 134,74]
180. 11 <=> happy(sK2) [avatar definition]
182. ~happy(sK2) <- (~11) [avatar component clause 180]
184. 12 <=> patient(sK2) [avatar definition]
186. patient(sK2) <- (12) [avatar component clause 184]
189. 13 <=> ! [X3] : (~curious(X3) | calm(X3)) [avatar definition]
190. ~curious(X3) | calm(X3) <- (13) [avatar component clause 189]
191. 13 | ~11 | 12 [avatar split clause 84,184,180,189]
194. curious(X0) [subsumption resolution 97,136]
195. happy(X0) [subsumption resolution 96,136]
218. 18 <=> ! [X0] : ~wise(X0) [avatar definition]
219. ~wise(X0) <- (18) [avatar component clause 218]
226. 20 <=> ! [X0] : ~patient(X0) [avatar definition]
227. ~patient(X0) <- (20) [avatar component clause 226]
229. ~wise(X0) [subsumption resolution 105,195]
230. 18 [avatar split clause 229,218]
231. ~patient(X0) [subsumption resolution 104,195]
232. 20 [avatar split clause 231,226]
253. ~old(X0) | humble(X0) [subsumption resolution 113,136]
261. 26 <=> humble(lucy) [avatar definition]
262. humble(lucy) <- (26) [avatar component clause 261]
289. $false <- (~11) [subsumption resolution 182,195]
290. 11 [avatar contradiction clause 289]
293. $false <- (12, 20) [subsumption resolution 186,227]
294. ~12 | ~20 [avatar contradiction clause 293]
295. calm(X3) <- (13) [subsumption resolution 190,194]
300. humble(lucy) [resolution 253,131]
303. 26 [avatar split clause 300,261]
305. ~humble(X0) | wise(X0) <- (13) [resolution 91,295]
306. ~humble(X0) <- (13, 18) [subsumption resolution 305,219]
309. $false <- (13, 18, 26) [resolution 306,262]
310. ~13 | ~18 | ~26 [avatar contradiction clause 309]
311. $false [avatar sat refutation 191,230,232,290,294,303,310]
% SZS output end Proof for 2902781506209873001451200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not creative then someone is either quiet or kind and vice versa.
If mary is not creative then someone is either not humble or not creative and vice versa.
Everyone who is not humble or not creative is both not old and curious and vice versa.
Everyone who is not patient or calm is either humble or not patient and vice versa.
If paul is either brave or quiet then someone is not curious and vice versa.
If someone is calm or not generous then someone is both happy and wise.
If someone is not strong then someone is wise.
Everyone who is kind is both not brave and humble and vice versa.
Everyone who is either curious or not curious is patient or creative.
If someone is funny then someone is creative.
Everyone who is curious is not funny and vice versa.
If someone is both not generous and happy then someone is patient or not humble.
Everyone who is curious or funny is rich or strong.
If alice is either quiet or not funny then someone is both funny and not wise and vice versa.
Everyone who is not strong is creative and vice versa.
If fred is either kind or curious then someone is either not rich or not brave and vice versa.
Lucy is either not strong or humble.
Someone is tall.
Fred is either rich or old.
John is not old or tall.
Lucy is either patient or curious.
Paul is both strong and not old.
Someone is not tall or funny. | Lucy is patient. | contradiction | ((?[X]:((calm(X)|~creative(X))))<=>(?[X]:((quiet(X)<~>kind(X)))))&
((~creative(mary))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((~humble(X)|~creative(X))<=>(~old(X)&curious(X))))&
(![X]:((~patient(X)|calm(X))<=>(humble(X)<~>~patient(X))))&
(((brave(paul)<~>quiet(paul)))<=>(?[X]:(~curious(X))))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:((happy(X)&wise(X)))))&
((?[X]:(~strong(X)))=>(?[X]:(wise(X))))&
(![X]:(kind(X)<=>(~brave(X)&humble(X))))&
(![X]:((curious(X)<~>~curious(X))=>(patient(X)|creative(X))))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(![X]:(curious(X)<=>~funny(X)))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((curious(X)|funny(X))=>(rich(X)|strong(X))))&
(((quiet(alice)<~>~funny(alice)))<=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:(~strong(X)<=>creative(X)))&
(((kind(fred)<~>curious(fred)))<=>(?[X]:((~rich(X)<~>~brave(X)))))&
((~strong(lucy)<~>humble(lucy)))&
(?[X]:(tall(X)))&
((rich(fred)<~>old(fred)))&
((~old(john)|tall(john)))&
((patient(lucy)<~>curious(lucy)))&
((strong(paul)&~old(paul)))&
(?[X]:((~tall(X)|funny(X)))) | patient(lucy) | [
"p2",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 815634466882502835322737
% SZS output start Proof for 815634466882502835322737
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (curious(X0) & ~old(X0))) [input p2]
15. ! [X0] : (~strong(X0) <=> creative(X0)) [input p14]
17. ~strong(lucy) <~> humble(lucy) [input p16]
21. patient(lucy) <~> curious(lucy) [input p20]
24. patient(lucy) [input hypothesis]
49. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
50. ! [X0] : ((~creative(X0) | ~humble(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | (creative(X0) & humble(X0)))) [flattening 49]
74. ! [X0] : ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))) [nnf transformation 15]
79. (~humble(lucy) | strong(lucy)) & (humble(lucy) | ~strong(lucy)) [nnf transformation 17]
83. (~curious(lucy) | ~patient(lucy)) & (curious(lucy) | patient(lucy)) [nnf transformation 21]
98. curious(X0) | humble(X0) [cnf transformation 50]
99. curious(X0) | creative(X0) [cnf transformation 50]
130. ~strong(X0) | ~creative(X0) [cnf transformation 74]
140. ~humble(lucy) | strong(lucy) [cnf transformation 79]
146. ~curious(lucy) | ~patient(lucy) [cnf transformation 83]
150. patient(lucy) [cnf transformation 24]
308. 34 <=> strong(lucy) [avatar definition]
310. strong(lucy) <- (34) [avatar component clause 308]
312. 35 <=> humble(lucy) [avatar definition]
315. 34 | ~35 [avatar split clause 140,312,308]
337. 40 <=> patient(lucy) [avatar definition]
341. 41 <=> curious(lucy) [avatar definition]
343. ~curious(lucy) <- (~41) [avatar component clause 341]
344. ~40 | ~41 [avatar split clause 146,341,337]
355. 40 [avatar split clause 150,337]
364. humble(lucy) <- (~41) [resolution 98,343]
367. creative(lucy) <- (~41) [resolution 99,343]
390. ~creative(lucy) <- (34) [resolution 310,130]
391. $false <- (34, ~41) [subsumption resolution 390,367]
392. ~34 | 41 [avatar contradiction clause 391]
393. 35 | 41 [avatar split clause 364,341,312]
394. $false [avatar sat refutation 315,344,355,392,393]
% SZS output end Proof for 815634466882502835322737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not kind.
Everyone who is either calm or humble is either not happy or humble and vice versa.
Everyone who is either not creative or calm is not creative.
Everyone who is both not creative and not rich is either happy or humble.
Everyone who is both calm and not wise is either not strong or not happy and vice versa.
If someone is either curious or strong then someone is either kind or curious.
If someone is both generous and not happy then susan is generous.
Everyone who is either tall or not old is generous or not old and vice versa.
If someone is not generous or not funny then someone is either not kind or not patient and vice versa.
Everyone who is generous or humble is not wise.
Everyone who is not patient or strong is not calm.
If someone is not curious or brave then someone is either not wise or not curious.
If someone is either not brave or not tall then someone is either wise or patient and vice versa.
Everyone who is not wise is both wise and not happy and vice versa.
Everyone who is either creative or not brave is kind or not funny.
If fred is either not creative or not kind then alice is not tall and vice versa.
Someone is wise or generous.
Someone is humble or not patient.
Lucy is creative or quiet.
Fred is creative.
Fred is funny or creative.
Mary is either not funny or not kind. | Alice is generous. | contradiction | (![X]:(~calm(X)=>~kind(X)))&
(![X]:((calm(X)<~>humble(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((~creative(X)<~>calm(X))=>~creative(X)))&
(![X]:((~creative(X)&~rich(X))=>(happy(X)<~>humble(X))))&
(![X]:((calm(X)&~wise(X))<=>(~strong(X)<~>~happy(X))))&
((?[X]:((curious(X)<~>strong(X))))=>(?[X]:((kind(X)<~>curious(X)))))&
((?[X]:((generous(X)&~happy(X))))=>(generous(susan)))&
(![X]:((tall(X)<~>~old(X))<=>(generous(X)|~old(X))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((generous(X)|humble(X))=>~wise(X)))&
(![X]:((~patient(X)|strong(X))=>~calm(X)))&
((?[X]:((~curious(X)|brave(X))))=>(?[X]:((~wise(X)<~>~curious(X)))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:(~wise(X)<=>(wise(X)&~happy(X))))&
(![X]:((creative(X)<~>~brave(X))=>(kind(X)|~funny(X))))&
(((~creative(fred)<~>~kind(fred)))<=>(~tall(alice)))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:((humble(X)|~patient(X))))&
((creative(lucy)|quiet(lucy)))&
(creative(fred))&
((funny(fred)|creative(fred)))&
((~funny(mary)<~>~kind(mary))) | generous(alice) | [
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 872260737769053705729399
% SZS output start Proof for 872260737769053705729399
10. ! [X0] : ((humble(X0) | generous(X0)) => ~wise(X0)) [input p9]
14. ! [X0] : (~wise(X0) <=> (~happy(X0) & wise(X0))) [input p13]
23. generous(alice) [input hypothesis]
34. ! [X0] : (~wise(X0) | (~humble(X0) & ~generous(X0))) [ennf transformation 10]
63. ! [X0] : ((~wise(X0) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | wise(X0))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | wise(X0))) [flattening 63]
106. ~generous(X0) | ~wise(X0) [cnf transformation 34]
122. wise(X0) | wise(X0) [cnf transformation 64]
137. generous(alice) [cnf transformation 23]
138. wise(X0) [duplicate literal removal 122]
309. ~wise(alice) [resolution 106,137]
310. $false [subsumption resolution 309,138]
% SZS output end Proof for 872260737769053705729399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both strong and creative then someone is not quiet and vice versa. Everyone who is not tall is both not tall and not happy and vice versa. Everyone who is either not strong or not generous is old or not brave. If paul is either not wise or patient then someone is either old or not generous and vice versa. Everyone who is both not humble and kind is either calm or not kind. If alice is generous or calm then lucy is both not tall and brave. Everyone who is wise or quiet is either quiet or not happy and vice versa. If fred is both not patient and not generous then alice is not humble and vice versa. If someone is both not old and rich then fred is not humble and vice versa. Everyone who is either kind or not kind is either curious or not tall and vice versa. If susan is brave then john is not kind. If someone is not humble or not strong then mary is both kind and not funny and vice versa. Everyone who is creative is both not strong and generous and vice versa. Everyone who is either funny or brave is either not quiet or patient and vice versa. If someone is either curious or patient then someone is strong and vice versa. Everyone who is both not wise and not old is both not wise and brave. Susan is either not strong or funny. Someone is strong. Someone is both happy and wise. John is either rich or generous. Mary is both not humble and quiet. Someone is both not humble and patient. Paul is either not generous or not patient. Lucy is both not humble and patient. | Fred is not calm. | neutral | (((strong(fred)&creative(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:(~tall(X)<=>(~tall(X)&~happy(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(old(X)|~brave(X))))&
(((~wise(paul)<~>patient(paul)))<=>(?[X]:((old(X)<~>~generous(X)))))&
(![X]:((~humble(X)&kind(X))=>(calm(X)<~>~kind(X))))&
(((generous(alice)|calm(alice)))=>((~tall(lucy)&brave(lucy))))&
(![X]:((wise(X)|quiet(X))<=>(quiet(X)<~>~happy(X))))&
(((~patient(fred)&~generous(fred)))<=>(~humble(alice)))&
((?[X]:((~old(X)&rich(X))))<=>(~humble(fred)))&
(![X]:((kind(X)<~>~kind(X))<=>(curious(X)<~>~tall(X))))&
((brave(susan))=>(~kind(john)))&
((?[X]:((~humble(X)|~strong(X))))<=>((kind(mary)&~funny(mary))))&
(![X]:(creative(X)<=>(~strong(X)&generous(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~quiet(X)<~>patient(X))))&
((?[X]:((curious(X)<~>patient(X))))<=>(?[X]:(strong(X))))&
(![X]:((~wise(X)&~old(X))=>(~wise(X)&brave(X))))&
((~strong(susan)<~>funny(susan)))&
(?[X]:(strong(X)))&
(?[X]:((happy(X)&wise(X))))&
((rich(john)<~>generous(john)))&
((~humble(mary)&quiet(mary)))&
(?[X]:((~humble(X)&patient(X))))&
((~generous(paul)<~>~patient(paul)))&
((~humble(lucy)&patient(lucy))) | ~calm(fred) | [] | null | 0 |
If paul is either kind or not curious then someone is creative or patient.
Everyone who is either not creative or rich is brave or not wise and vice versa.
If susan is funny or happy then john is either not strong or not rich and vice versa.
Everyone who is either not funny or calm is not brave or rich and vice versa.
Everyone who is not calm is funny or brave and vice versa.
Everyone who is not patient is either rich or not curious.
Everyone who is not quiet is generous or not generous.
If alice is rich or not patient then someone is not funny or not patient and vice versa.
Everyone who is not strong or creative is wise and vice versa.
Everyone who is creative is not old.
If fred is quiet or not funny then alice is both wise and not happy.
Everyone who is either not wise or not tall is either patient or not strong.
Everyone who is not brave is not wise and vice versa.
If paul is not wise or happy then someone is not quiet and vice versa.
Everyone who is either not kind or funny is both funny and not tall and vice versa.
Everyone who is kind or patient is either not rich or wise.
Susan is both wise and not curious.
Someone is tall.
Paul is both happy and not rich.
Someone is not happy.
Mary is not generous.
Someone is not wise or old.
John is either brave or not quiet.
Someone is either calm or tall. | Paul is not funny. | contradiction | (((kind(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~creative(X)<~>rich(X))<=>(brave(X)|~wise(X))))&
(((funny(susan)|happy(susan)))<=>((~strong(john)<~>~rich(john))))&
(![X]:((~funny(X)<~>calm(X))<=>(~brave(X)|rich(X))))&
(![X]:(~calm(X)<=>(funny(X)|brave(X))))&
(![X]:(~patient(X)=>(rich(X)<~>~curious(X))))&
(![X]:(~quiet(X)=>(generous(X)|~generous(X))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~strong(X)|creative(X))<=>wise(X)))&
(![X]:(creative(X)=>~old(X)))&
(((quiet(fred)|~funny(fred)))=>((wise(alice)&~happy(alice))))&
(![X]:((~wise(X)<~>~tall(X))=>(patient(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>~wise(X)))&
(((~wise(paul)|happy(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(funny(X)&~tall(X))))&
(![X]:((kind(X)|patient(X))=>(~rich(X)<~>wise(X))))&
((wise(susan)&~curious(susan)))&
(?[X]:(tall(X)))&
((happy(paul)&~rich(paul)))&
(?[X]:(~happy(X)))&
(~generous(mary))&
(?[X]:((~wise(X)|old(X))))&
((brave(john)<~>~quiet(john)))&
(?[X]:((calm(X)<~>tall(X)))) | ~funny(paul) | [
"p3",
"p4",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4341724547938282490558998
% SZS output start Proof for 4341724547938282490558998
4. ! [X0] : ((~funny(X0) <~> calm(X0)) <=> (rich(X0) | ~brave(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (brave(X0) | funny(X0))) [input p4]
13. ! [X0] : (~brave(X0) <=> ~wise(X0)) [input p12]
15. ! [X0] : ((~kind(X0) <~> funny(X0)) <=> (~tall(X0) & funny(X0))) [input p14]
16. ! [X0] : ((patient(X0) | kind(X0)) => (~rich(X0) <~> wise(X0))) [input p15]
19. ~rich(paul) & happy(paul) [input p18]
25. ~funny(paul) [input hypothesis]
33. ! [X0] : ((~rich(X0) <~> wise(X0)) | (~patient(X0) & ~kind(X0))) [ennf transformation 16]
41. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & ((rich(X0) | ~brave(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & (rich(X0) | ~brave(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [flattening 41]
43. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | calm(X0))) [nnf transformation 5]
44. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | calm(X0))) [flattening 43]
54. ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))) [nnf transformation 13]
60. ! [X0] : ((((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))))) [flattening 60]
62. ! [X0] : (((~wise(X0) | rich(X0)) & (wise(X0) | ~rich(X0))) | (~patient(X0) & ~kind(X0))) [nnf transformation 33]
89. ~funny(X0) | calm(X0) | brave(X0) [cnf transformation 42]
91. ~calm(X0) | funny(X0) | brave(X0) [cnf transformation 42]
93. brave(X0) | funny(X0) | calm(X0) [cnf transformation 44]
94. ~calm(X0) | ~funny(X0) [cnf transformation 44]
116. ~brave(X0) | wise(X0) [cnf transformation 54]
120. funny(X0) | funny(X0) | kind(X0) [cnf transformation 61]
128. ~wise(X0) | rich(X0) | ~kind(X0) [cnf transformation 62]
134. ~rich(paul) [cnf transformation 19]
142. ~funny(paul) [cnf transformation 25]
143. funny(X0) | kind(X0) [duplicate literal removal 120]
150. 2 <=> kind(paul) [avatar definition]
152. kind(paul) <- (2) [avatar component clause 150]
185. calm(X0) | brave(X0) [subsumption resolution 93,89]
290. kind(paul) [resolution 143,142]
295. ~funny(X1) | brave(X1) [resolution 185,94]
335. funny(X0) | brave(X0) | brave(X0) [resolution 91,185]
336. funny(X0) | brave(X0) [duplicate literal removal 335]
340. brave(X0) [subsumption resolution 336,295]
344. wise(X2) [resolution 340,116]
401. ~kind(X0) | rich(X0) [resolution 128,344]
504. rich(paul) <- (2) [resolution 401,152]
508. $false <- (2) [subsumption resolution 504,134]
509. ~2 [avatar contradiction clause 508]
510. 2 [avatar split clause 290,150]
511. $false [avatar sat refutation 509,510]
% SZS output end Proof for 4341724547938282490558998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise is creative.
Everyone who is not kind or patient is not quiet or brave.
Everyone who is either not patient or not wise is both brave and quiet.
Everyone who is not quiet is old.
If lucy is either not wise or quiet then alice is rich and vice versa.
If john is either not tall or funny then someone is not strong or strong.
If someone is both brave and humble then alice is both calm and strong and vice versa.
Everyone who is both not wise and not old is both strong and generous and vice versa.
If someone is wise then someone is either calm or old.
Everyone who is either kind or funny is both not funny and not patient.
Everyone who is either strong or patient is either not generous or old.
If someone is not old or not quiet then paul is either not creative or not generous and vice versa.
If alice is either strong or old then fred is both not rich and rich.
Everyone who is patient is both quiet and not generous.
If someone is both funny and tall then someone is not old and vice versa.
Everyone who is old is both quiet and happy and vice versa.
Alice is both curious and rich.
Someone is either not wise or not happy.
Someone is both generous and wise.
Someone is both not generous and not calm.
Fred is both funny and not brave.
Someone is either not kind or wise.
Mary is either not humble or not brave. | Fred is not wise. | entailment | (![X]:((creative(X)<~>~wise(X))=>creative(X)))&
(![X]:((~kind(X)|patient(X))=>(~quiet(X)|brave(X))))&
(![X]:((~patient(X)<~>~wise(X))=>(brave(X)&quiet(X))))&
(![X]:(~quiet(X)=>old(X)))&
(((~wise(lucy)<~>quiet(lucy)))<=>(rich(alice)))&
(((~tall(john)<~>funny(john)))=>(?[X]:((~strong(X)|strong(X)))))&
((?[X]:((brave(X)&humble(X))))<=>((calm(alice)&strong(alice))))&
(![X]:((~wise(X)&~old(X))<=>(strong(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((calm(X)<~>old(X)))))&
(![X]:((kind(X)<~>funny(X))=>(~funny(X)&~patient(X))))&
(![X]:((strong(X)<~>patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~creative(paul)<~>~generous(paul))))&
(((strong(alice)<~>old(alice)))=>((~rich(fred)&rich(fred))))&
(![X]:(patient(X)=>(quiet(X)&~generous(X))))&
((?[X]:((funny(X)&tall(X))))<=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>(quiet(X)&happy(X))))&
((curious(alice)&rich(alice)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((generous(X)&wise(X))))&
(?[X]:((~generous(X)&~calm(X))))&
((funny(fred)&~brave(fred)))&
(?[X]:((~kind(X)<~>wise(X))))&
((~humble(mary)<~>~brave(mary))) | ~wise(fred) | [
"p1",
"p2",
"p3",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5539279311827663294972506
% SZS output start Proof for 5539279311827663294972506
2. ! [X0] : ((patient(X0) | ~kind(X0)) => (brave(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((~patient(X0) <~> ~wise(X0)) => (quiet(X0) & brave(X0))) [input p2]
4. ! [X0] : (~quiet(X0) => old(X0)) [input p3]
16. ! [X0] : (old(X0) <=> (happy(X0) & quiet(X0))) [input p15]
21. ~brave(fred) & funny(fred) [input p20]
24. wise(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) | ~quiet(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 2]
30. ! [X0] : (brave(X0) | ~quiet(X0) | (~patient(X0) & kind(X0))) [flattening 29]
31. ! [X0] : ((quiet(X0) & brave(X0)) | (~patient(X0) <=> ~wise(X0))) [ennf transformation 3]
32. ! [X0] : (old(X0) | quiet(X0)) [ennf transformation 4]
40. ! [X0] : ((quiet(X0) & brave(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) [nnf transformation 31]
68. ! [X0] : ((old(X0) | (~happy(X0) | ~quiet(X0))) & ((happy(X0) & quiet(X0)) | ~old(X0))) [nnf transformation 16]
69. ! [X0] : ((old(X0) | ~happy(X0) | ~quiet(X0)) & ((happy(X0) & quiet(X0)) | ~old(X0))) [flattening 68]
84. ~quiet(X0) | brave(X0) | ~patient(X0) [cnf transformation 30]
85. ~wise(X0) | brave(X0) | patient(X0) [cnf transformation 40]
89. old(X0) | quiet(X0) [cnf transformation 32]
129. quiet(X0) | ~old(X0) [cnf transformation 69]
140. ~brave(fred) [cnf transformation 21]
145. wise(fred) [cnf transformation 24]
221. 16 <=> ! [X1] : quiet(X1) [avatar definition]
222. quiet(X1) <- (16) [avatar component clause 221]
261. quiet(X0) [subsumption resolution 129,89]
262. 16 [avatar split clause 261,221]
322. ~patient(X0) | brave(X0) <- (16) [resolution 84,222]
327. brave(fred) | patient(fred) [resolution 85,145]
332. patient(fred) [subsumption resolution 327,140]
432. brave(fred) <- (16) [resolution 322,332]
434. $false <- (16) [subsumption resolution 432,140]
435. ~16 [avatar contradiction clause 434]
436. $false [avatar sat refutation 262,435]
% SZS output end Proof for 5539279311827663294972506
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not calm is either not tall or not happy and vice versa. Everyone who is not kind or not funny is either wise or not funny and vice versa. Everyone who is either happy or not calm is either not happy or not calm. Everyone who is not curious is not strong. If alice is quiet or not kind then susan is either not generous or not rich and vice versa. If someone is not brave then john is happy and vice versa. If john is not curious then someone is not tall and vice versa. Everyone who is old is both not old and not kind. Everyone who is either not kind or happy is not wise or not happy and vice versa. If susan is both brave and tall then someone is either not curious or not tall and vice versa. If alice is not calm or not kind then mary is brave. Everyone who is either generous or not creative is both not happy and happy. Everyone who is not strong or not curious is both humble and quiet. Everyone who is not kind is funny and vice versa. Everyone who is both not generous and not funny is not brave or not rich and vice versa. If someone is either not kind or not calm then alice is brave and vice versa. Someone is either kind or not quiet. Someone is both not calm and rich. Someone is either not old or tall. Susan is rich or not patient. John is generous or not rich. Someone is either curious or funny. Someone is either not old or brave. | Mary is not strong. | entailment | (![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:((~kind(X)|~funny(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~calm(X))=>(~happy(X)<~>~calm(X))))&
(![X]:(~curious(X)=>~strong(X)))&
(((quiet(alice)|~kind(alice)))<=>((~generous(susan)<~>~rich(susan))))&
((?[X]:(~brave(X)))<=>(happy(john)))&
((~curious(john))<=>(?[X]:(~tall(X))))&
(![X]:(old(X)=>(~old(X)&~kind(X))))&
(![X]:((~kind(X)<~>happy(X))<=>(~wise(X)|~happy(X))))&
(((brave(susan)&tall(susan)))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(((~calm(alice)|~kind(alice)))=>(brave(mary)))&
(![X]:((generous(X)<~>~creative(X))=>(~happy(X)&happy(X))))&
(![X]:((~strong(X)|~curious(X))=>(humble(X)&quiet(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:((~generous(X)&~funny(X))<=>(~brave(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))<=>(brave(alice)))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~old(X)<~>tall(X))))&
((rich(susan)|~patient(susan)))&
((generous(john)|~rich(john)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~old(X)<~>brave(X)))) | ~strong(mary) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5546247909389695596575403
% SZS output start Proof for 5546247909389695596575403
1. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p0]
3. ! [X0] : ((happy(X0) <~> ~calm(X0)) => (~happy(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : (~curious(X0) => ~strong(X0)) [input p3]
8. ! [X0] : (old(X0) => (~kind(X0) & ~old(X0))) [input p7]
10. (tall(susan) & brave(susan)) <=> ? [X0] : (~curious(X0) <~> ~tall(X0)) [input p9]
24. strong(mary) [input hypothesis]
27. ! [X0] : ((~happy(X0) <~> ~calm(X0)) | (happy(X0) <=> ~calm(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | curious(X0)) [ennf transformation 4]
29. ! [X0] : ((~kind(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 8]
33. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (calm(X0) | old(X0)))) [nnf transformation 1]
34. ! [X0] : (((~calm(X0) & ~old(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | calm(X0) | old(X0))) [flattening 33]
37. ! [X0] : (((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) [nnf transformation 27]
50. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X0] : ((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~tall(susan) | ~brave(susan))) [nnf transformation 10]
51. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X0] : ((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | ~tall(susan) | ~brave(susan)) [flattening 50]
52. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) | ~tall(susan) | ~brave(susan)) [rectify 51]
53. ? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) => ((tall(sK2) | curious(sK2)) & (~tall(sK2) | ~curious(sK2))) [choice axiom]
54. ((tall(susan) & brave(susan)) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(sK2) | curious(sK2)) & (~tall(sK2) | ~curious(sK2))) | ~tall(susan) | ~brave(susan)) [skolemisation 52,53]
77. ~happy(X0) | ~tall(X0) | calm(X0) | old(X0) [cnf transformation 34]
82. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 34]
89. ~calm(X0) | ~happy(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 37]
92. calm(X0) | happy(X0) | happy(X0) | calm(X0) [cnf transformation 37]
93. ~strong(X0) | curious(X0) [cnf transformation 28]
104. ~old(X0) | ~old(X0) [cnf transformation 29]
117. tall(susan) | ~curious(X0) | tall(X0) [cnf transformation 54]
148. strong(mary) [cnf transformation 24]
151. ~old(X0) [duplicate literal removal 104]
152. ~happy(X0) | ~calm(X0) [duplicate literal removal 89]
153. happy(X0) | calm(X0) [duplicate literal removal 92]
206. 11 <=> ! [X0] : (~curious(X0) | tall(X0)) [avatar definition]
207. ~curious(X0) | tall(X0) <- (11) [avatar component clause 206]
209. 12 <=> tall(susan) [avatar definition]
211. tall(susan) <- (12) [avatar component clause 209]
212. 11 | 12 [avatar split clause 117,209,206]
298. curious(mary) [resolution 93,148]
324. tall(mary) <- (11) [resolution 207,298]
353. ~calm(mary) | happy(mary) <- (11) [resolution 82,324]
356. happy(mary) <- (11) [subsumption resolution 353,153]
396. ~calm(mary) <- (11) [resolution 356,152]
405. ~tall(X0) | calm(X0) | old(X0) | calm(X0) [resolution 77,153]
414. ~tall(X0) | calm(X0) | old(X0) [duplicate literal removal 405]
415. ~tall(X0) | calm(X0) [subsumption resolution 414,151]
463. calm(mary) <- (11) [resolution 415,324]
468. $false <- (11) [subsumption resolution 463,396]
469. ~11 [avatar contradiction clause 468]
474. calm(susan) <- (12) [resolution 211,415]
475. ~calm(susan) | happy(susan) <- (12) [resolution 211,82]
496. happy(susan) <- (12) [subsumption resolution 475,474]
505. ~calm(susan) <- (12) [resolution 496,152]
506. $false <- (12) [subsumption resolution 505,474]
507. ~12 [avatar contradiction clause 506]
508. $false [avatar sat refutation 212,469,507]
% SZS output end Proof for 5546247909389695596575403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich then someone is strong and vice versa. Everyone who is both not brave and tall is curious or not tall. If someone is not brave then someone is either tall or not strong. Everyone who is either happy or not funny is kind or not old and vice versa. Everyone who is both not tall and rich is not calm or happy and vice versa. Everyone who is not generous is creative or not strong and vice versa. Everyone who is happy is not funny or tall and vice versa. If mary is either strong or tall then mary is either not tall or not brave. If someone is both rich and funny then lucy is not calm or generous. Everyone who is both not curious and not brave is wise or not humble and vice versa. Everyone who is not patient or not kind is either not brave or not patient and vice versa. If fred is both old and not calm then lucy is either not patient or not generous. Everyone who is not rich is not brave and vice versa. If someone is either not strong or happy then paul is not tall and vice versa. If someone is either strong or generous then someone is not funny and vice versa. If someone is either patient or not creative then alice is not old. Someone is not wise or not old. Someone is both not quiet and creative. Alice is either calm or not wise. Fred is not calm. Fred is either strong or not tall. Susan is not brave. Alice is both wise and not quiet. | Susan is not creative. | entailment | ((~rich(lucy))<=>(?[X]:(strong(X))))&
(![X]:((~brave(X)&tall(X))=>(curious(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((happy(X)<~>~funny(X))<=>(kind(X)|~old(X))))&
(![X]:((~tall(X)&rich(X))<=>(~calm(X)|happy(X))))&
(![X]:(~generous(X)<=>(creative(X)|~strong(X))))&
(![X]:(happy(X)<=>(~funny(X)|tall(X))))&
(((strong(mary)<~>tall(mary)))=>((~tall(mary)<~>~brave(mary))))&
((?[X]:((rich(X)&funny(X))))=>((~calm(lucy)|generous(lucy))))&
(![X]:((~curious(X)&~brave(X))<=>(wise(X)|~humble(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~brave(X)<~>~patient(X))))&
(((old(fred)&~calm(fred)))=>((~patient(lucy)<~>~generous(lucy))))&
(![X]:(~rich(X)<=>~brave(X)))&
((?[X]:((~strong(X)<~>happy(X))))<=>(~tall(paul)))&
((?[X]:((strong(X)<~>generous(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((patient(X)<~>~creative(X))))=>(~old(alice)))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:((~quiet(X)&creative(X))))&
((calm(alice)<~>~wise(alice)))&
(~calm(fred))&
((strong(fred)<~>~tall(fred)))&
(~brave(susan))&
((wise(alice)&~quiet(alice))) | ~creative(susan) | [
"p3",
"p4",
"p6",
"p9",
"p10",
"p12",
"p15",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3422662454818955285997935
% SZS output start Proof for 3422662454818955285997935
4. ! [X0] : ((happy(X0) <~> ~funny(X0)) <=> (~old(X0) | kind(X0))) [input p3]
5. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (happy(X0) | ~calm(X0))) [input p4]
7. ! [X0] : (happy(X0) <=> (tall(X0) | ~funny(X0))) [input p6]
10. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~humble(X0) | wise(X0))) [input p9]
11. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (~brave(X0) <~> ~patient(X0))) [input p10]
13. ! [X0] : (~rich(X0) <=> ~brave(X0)) [input p12]
16. ? [X0] : (patient(X0) <~> ~creative(X0)) => ~old(alice) [input p15]
22. ~brave(susan) [input p21]
23. ~quiet(alice) & wise(alice) [input p22]
24. creative(susan) [input hypothesis]
28. wise(alice) [pure predicate removal 23]
37. ~old(alice) | ! [X0] : (patient(X0) <=> ~creative(X0)) [ennf transformation 16]
46. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (old(X0) & ~kind(X0))) & ((~old(X0) | kind(X0)) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [nnf transformation 4]
47. ! [X0] : ((((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (old(X0) & ~kind(X0))) & (~old(X0) | kind(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0))))) [flattening 46]
48. ! [X0] : (((rich(X0) & ~tall(X0)) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 5]
49. ! [X0] : (((rich(X0) & ~tall(X0)) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ~rich(X0) | tall(X0))) [flattening 48]
52. ! [X0] : ((happy(X0) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | ~happy(X0))) [nnf transformation 7]
53. ! [X0] : ((happy(X0) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~happy(X0))) [flattening 52]
55. ! [X0] : (((~brave(X0) & ~curious(X0)) | (humble(X0) & ~wise(X0))) & ((~humble(X0) | wise(X0)) | (brave(X0) | curious(X0)))) [nnf transformation 10]
56. ! [X0] : (((~brave(X0) & ~curious(X0)) | (humble(X0) & ~wise(X0))) & (~humble(X0) | wise(X0) | brave(X0) | curious(X0))) [flattening 55]
57. ! [X0] : (((~kind(X0) | ~patient(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (kind(X0) & patient(X0)))) [nnf transformation 11]
58. ! [X0] : ((~kind(X0) | ~patient(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) & (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | (kind(X0) & patient(X0)))) [flattening 57]
60. ! [X0] : ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0))) [nnf transformation 13]
70. ~old(alice) | ! [X0] : ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0))) [nnf transformation 37]
85. ~funny(X0) | happy(X0) | old(X0) [cnf transformation 47]
92. ~happy(X0) | rich(X0) [cnf transformation 49]
97. funny(X0) | happy(X0) [cnf transformation 53]
107. ~wise(X0) | ~brave(X0) [cnf transformation 56]
111. patient(X0) | brave(X0) | patient(X0) [cnf transformation 58]
112. patient(X0) | brave(X0) | kind(X0) [cnf transformation 58]
113. ~kind(X0) | ~patient(X0) | ~patient(X0) | brave(X0) [cnf transformation 58]
118. ~rich(X0) | brave(X0) [cnf transformation 60]
127. ~old(alice) | ~creative(X0) | ~patient(X0) [cnf transformation 70]
136. ~brave(susan) [cnf transformation 22]
137. wise(alice) [cnf transformation 28]
138. creative(susan) [cnf transformation 24]
139. patient(X0) | brave(X0) [duplicate literal removal 111]
140. ~patient(X0) | ~kind(X0) | brave(X0) [duplicate literal removal 113]
247. 23 <=> old(alice) [avatar definition]
249. ~old(alice) <- (~23) [avatar component clause 247]
252. 24 <=> ! [X0] : (~creative(X0) | ~patient(X0)) [avatar definition]
253. ~patient(X0) | ~creative(X0) <- (24) [avatar component clause 252]
254. 24 | ~23 [avatar split clause 127,247,252]
269. 28 <=> wise(alice) [avatar definition]
271. wise(alice) <- (28) [avatar component clause 269]
276. 28 [avatar split clause 137,269]
289. ~brave(alice) <- (28) [resolution 107,271]
298. happy(X0) | old(X0) | happy(X0) [resolution 85,97]
299. old(X0) | happy(X0) [duplicate literal removal 298]
349. ~kind(X1) | brave(X1) | brave(X1) [resolution 140,139]
350. ~kind(X1) | brave(X1) [duplicate literal removal 349]
373. 31 <=> rich(alice) [avatar definition]
374. rich(alice) <- (31) [avatar component clause 373]
377. 32 <=> happy(alice) [avatar definition]
379. happy(alice) <- (32) [avatar component clause 377]
397. happy(alice) <- (~23) [resolution 299,249]
406. 32 | 23 [avatar split clause 397,247,377]
415. rich(alice) <- (32) [resolution 379,92]
420. 31 | ~32 [avatar split clause 415,377,373]
421. brave(alice) <- (31) [resolution 374,118]
422. $false <- (28, 31) [subsumption resolution 421,289]
423. ~28 | ~31 [avatar contradiction clause 422]
429. ~creative(X1) | brave(X1) | kind(X1) <- (24) [resolution 253,112]
431. ~creative(X1) | brave(X1) <- (24) [subsumption resolution 429,350]
442. brave(susan) <- (24) [resolution 431,138]
446. $false <- (24) [subsumption resolution 442,136]
447. ~24 [avatar contradiction clause 446]
448. $false [avatar sat refutation 254,276,406,420,423,447]
% SZS output end Proof for 3422662454818955285997935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not kind then john is generous.
Everyone who is patient or strong is both humble and not kind and vice versa.
If someone is funny then someone is not strong and vice versa.
Everyone who is either not happy or happy is both not tall and strong and vice versa.
Everyone who is not quiet is either not kind or calm.
Everyone who is both curious and creative is not quiet or not rich.
If someone is quiet or wise then someone is both not tall and humble.
Everyone who is not creative is not wise or not humble and vice versa.
If paul is curious then fred is wise or old.
If john is humble or quiet then john is either not rich or not old.
Everyone who is generous or not happy is not calm and vice versa.
If someone is old or not quiet then someone is both happy and funny.
Everyone who is both not humble and funny is both not patient and funny.
Everyone who is not quiet or old is funny or creative and vice versa.
If mary is not curious then someone is both kind and not tall.
Someone is funny or not generous.
Someone is wise or not creative.
Lucy is rich.
Paul is not generous or curious. | Lucy is rich. | entailment | ((?[X]:((wise(X)&~kind(X))))=>(generous(john)))&
(![X]:((patient(X)|strong(X))<=>(humble(X)&~kind(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~tall(X)&strong(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>calm(X))))&
(![X]:((curious(X)&creative(X))=>(~quiet(X)|~rich(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:(~creative(X)<=>(~wise(X)|~humble(X))))&
((curious(paul))=>((wise(fred)|old(fred))))&
(((humble(john)|quiet(john)))=>((~rich(john)<~>~old(john))))&
(![X]:((generous(X)|~happy(X))<=>~calm(X)))&
((?[X]:((old(X)|~quiet(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~humble(X)&funny(X))=>(~patient(X)&funny(X))))&
(![X]:((~quiet(X)|old(X))<=>(funny(X)|creative(X))))&
((~curious(mary))=>(?[X]:((kind(X)&~tall(X)))))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((wise(X)|~creative(X))))&
(rich(lucy))&
((~generous(paul)|curious(paul))) | rich(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4117101829838086648721740
% SZS output start Proof for 4117101829838086648721740
18. rich(lucy) [input p17]
20. ~rich(lucy) [input hypothesis]
111. rich(lucy) [cnf transformation 18]
113. ~rich(lucy) [cnf transformation 20]
231. $false [subsumption resolution 113,111]
% SZS output end Proof for 4117101829838086648721740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not curious or happy. If someone is generous or not wise then alice is not kind. If john is patient or not rich then mary is not patient. If someone is patient or not happy then mary is both funny and not old and vice versa. Everyone who is both not happy and not patient is curious or not patient. If susan is calm or strong then someone is not curious or not patient. Everyone who is either rich or not old is not funny or not wise. Everyone who is not calm or strong is not humble or humble. If lucy is not rich then someone is both kind and not quiet and vice versa. If someone is not generous then someone is not humble or creative and vice versa. Everyone who is not wise is either brave or old and vice versa. If someone is generous then alice is either not strong or creative. If someone is not creative then lucy is either kind or wise. Everyone who is funny is not patient or funny and vice versa. If someone is humble then someone is both not curious and not creative. Everyone who is either brave or not strong is tall. Mary is not curious or rich. Alice is both generous and not patient. Paul is not humble. Someone is not tall. Someone is either not happy or not calm. Someone is quiet or not brave. Lucy is not happy or not calm. | Paul is not calm. | neutral | (![X]:(quiet(X)=>(~curious(X)|happy(X))))&
((?[X]:((generous(X)|~wise(X))))=>(~kind(alice)))&
(((patient(john)|~rich(john)))=>(~patient(mary)))&
((?[X]:((patient(X)|~happy(X))))<=>((funny(mary)&~old(mary))))&
(![X]:((~happy(X)&~patient(X))=>(curious(X)|~patient(X))))&
(((calm(susan)|strong(susan)))=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:((rich(X)<~>~old(X))=>(~funny(X)|~wise(X))))&
(![X]:((~calm(X)|strong(X))=>(~humble(X)|humble(X))))&
((~rich(lucy))<=>(?[X]:((kind(X)&~quiet(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(~wise(X)<=>(brave(X)<~>old(X))))&
((?[X]:(generous(X)))=>((~strong(alice)<~>creative(alice))))&
((?[X]:(~creative(X)))=>((kind(lucy)<~>wise(lucy))))&
(![X]:(funny(X)<=>(~patient(X)|funny(X))))&
((?[X]:(humble(X)))=>(?[X]:((~curious(X)&~creative(X)))))&
(![X]:((brave(X)<~>~strong(X))=>tall(X)))&
((~curious(mary)|rich(mary)))&
((generous(alice)&~patient(alice)))&
(~humble(paul))&
(?[X]:(~tall(X)))&
(?[X]:((~happy(X)<~>~calm(X))))&
(?[X]:((quiet(X)|~brave(X))))&
((~happy(lucy)|~calm(lucy))) | ~calm(paul) | [] | null | 0 |
Everyone who is creative is either not old or not quiet.
Everyone who is either not creative or not wise is both rich and not kind.
If paul is both rich and not wise then someone is rich.
If alice is funny then someone is either curious or not funny.
If alice is not tall then someone is not old and vice versa.
If lucy is both patient and not rich then someone is either not wise or not generous and vice versa.
If someone is not old then someone is not quiet and vice versa.
If someone is either not kind or creative then alice is not curious.
If someone is kind or creative then mary is both happy and not happy and vice versa.
Everyone who is old or not patient is both not tall and not brave.
Everyone who is either brave or not rich is either not patient or wise and vice versa.
Everyone who is patient is either not wise or old and vice versa.
Everyone who is rich is not rich or not funny and vice versa.
Everyone who is both strong and not generous is not kind and vice versa.
Everyone who is either quiet or tall is both not humble and old and vice versa.
Everyone who is either tall or patient is not happy or kind.
Mary is not generous.
Someone is not calm or not old.
Alice is either happy or not old.
Mary is quiet or curious.
Susan is not creative or not curious. | Mary is not happy. | neutral | (![X]:(creative(X)=>(~old(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(rich(X)&~kind(X))))&
(((rich(paul)&~wise(paul)))=>(?[X]:(rich(X))))&
((funny(alice))=>(?[X]:((curious(X)<~>~funny(X)))))&
((~tall(alice))<=>(?[X]:(~old(X))))&
(((patient(lucy)&~rich(lucy)))<=>(?[X]:((~wise(X)<~>~generous(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~kind(X)<~>creative(X))))=>(~curious(alice)))&
((?[X]:((kind(X)|creative(X))))<=>((happy(mary)&~happy(mary))))&
(![X]:((old(X)|~patient(X))=>(~tall(X)&~brave(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>old(X))))&
(![X]:(rich(X)<=>(~rich(X)|~funny(X))))&
(![X]:((strong(X)&~generous(X))<=>~kind(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(~humble(X)&old(X))))&
(![X]:((tall(X)<~>patient(X))=>(~happy(X)|kind(X))))&
(~generous(mary))&
(?[X]:((~calm(X)|~old(X))))&
((happy(alice)<~>~old(alice)))&
((quiet(mary)|curious(mary)))&
((~creative(susan)|~curious(susan))) | ~happy(mary) | [] | null | 0 |
If someone is funny then paul is creative or not humble.
Everyone who is either kind or not patient is either creative or not rich and vice versa.
Everyone who is quiet is not curious or not happy and vice versa.
Everyone who is either tall or not tall is both patient and not generous and vice versa.
Everyone who is either not quiet or not tall is both not humble and not generous and vice versa.
Everyone who is not humble is both not patient and not wise and vice versa.
Everyone who is both strong and not strong is both wise and not curious.
If someone is either generous or not tall then lucy is either not calm or not funny.
If someone is not wise then someone is both patient and not creative and vice versa.
If alice is either strong or rich then someone is humble or quiet and vice versa.
Everyone who is either patient or brave is both not quiet and humble.
If lucy is both not strong and not quiet then someone is both tall and funny and vice versa.
Everyone who is either not happy or not wise is both not funny and not creative.
If someone is patient then someone is either not patient or not rich and vice versa.
If someone is not happy or calm then susan is either not kind or not rich and vice versa.
Everyone who is either not old or wise is both rich and generous.
Someone is either quiet or happy.
Paul is rich.
Someone is not kind.
Someone is not brave.
Alice is either not patient or rich.
Susan is not funny or brave. | Susan is old. | neutral | ((?[X]:(funny(X)))=>((creative(paul)|~humble(paul))))&
(![X]:((kind(X)<~>~patient(X))<=>(creative(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>(~curious(X)|~happy(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(patient(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~humble(X)&~generous(X))))&
(![X]:(~humble(X)<=>(~patient(X)&~wise(X))))&
(![X]:((strong(X)&~strong(X))=>(wise(X)&~curious(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>((~calm(lucy)<~>~funny(lucy))))&
((?[X]:(~wise(X)))<=>(?[X]:((patient(X)&~creative(X)))))&
(((strong(alice)<~>rich(alice)))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:((patient(X)<~>brave(X))=>(~quiet(X)&humble(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~happy(X)<~>~wise(X))=>(~funny(X)&~creative(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|calm(X))))<=>((~kind(susan)<~>~rich(susan))))&
(![X]:((~old(X)<~>wise(X))=>(rich(X)&generous(X))))&
(?[X]:((quiet(X)<~>happy(X))))&
(rich(paul))&
(?[X]:(~kind(X)))&
(?[X]:(~brave(X)))&
((~patient(alice)<~>rich(alice)))&
((~funny(susan)|brave(susan))) | old(susan) | [] | null | 0 |
Everyone who is either not patient or not calm is both creative and generous and vice versa.
Everyone who is either funny or tall is both creative and not brave and vice versa.
If someone is not kind then someone is both not wise and not tall.
Everyone who is either generous or rich is either not tall or tall and vice versa.
If lucy is both not curious and strong then fred is quiet and vice versa.
Everyone who is tall is both not patient and not humble.
If someone is not calm then someone is not old or not brave and vice versa.
If lucy is not quiet or calm then someone is not rich or not funny.
If susan is both happy and not kind then someone is not funny and vice versa.
Everyone who is not strong or brave is not kind.
If someone is either not humble or tall then someone is both not rich and wise and vice versa.
If someone is not humble or tall then susan is funny or generous.
Everyone who is both not rich and tall is quiet and vice versa.
If fred is both brave and not brave then someone is both not quiet and generous and vice versa.
Everyone who is both happy and patient is either funny or generous and vice versa.
Everyone who is both quiet and not funny is both tall and quiet and vice versa.
Fred is both wise and not tall.
Someone is wise or not humble.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative. | Fred is not calm. | neutral | (![X]:((~patient(X)<~>~calm(X))<=>(creative(X)&generous(X))))&
(![X]:((funny(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>tall(X))))&
(((~curious(lucy)&strong(lucy)))<=>(quiet(fred)))&
(![X]:(tall(X)=>(~patient(X)&~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~quiet(lucy)|calm(lucy)))=>(?[X]:((~rich(X)|~funny(X)))))&
(((happy(susan)&~kind(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)|brave(X))=>~kind(X)))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((~humble(X)|tall(X))))=>((funny(susan)|generous(susan))))&
(![X]:((~rich(X)&tall(X))<=>quiet(X)))&
(((brave(fred)&~brave(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((happy(X)&patient(X))<=>(funny(X)<~>generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(tall(X)&quiet(X))))&
((wise(fred)&~tall(fred)))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john))) | ~calm(fred) | [] | null | 0 |
Everyone who is happy or not brave is humble and vice versa.
Everyone who is strong is either not calm or quiet.
Everyone who is either happy or not tall is either humble or not patient and vice versa.
Everyone who is either not rich or curious is not strong or patient and vice versa.
If someone is curious or not generous then someone is both not brave and not curious.
Everyone who is humble or not funny is not strong or rich and vice versa.
Everyone who is both not patient and generous is wise.
If someone is not happy or not calm then someone is both not brave and patient and vice versa.
If someone is rich then john is tall.
Everyone who is kind or not happy is not quiet and vice versa.
If someone is not wise or not old then someone is not tall or generous and vice versa.
If someone is either not wise or wise then lucy is kind or wise and vice versa.
Everyone who is not old or generous is not old.
Everyone who is both patient and not happy is either not tall or not rich.
If someone is either generous or not patient then someone is both not kind and curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
John is either not old or humble.
Mary is both not funny and not patient.
Lucy is humble.
Someone is either not rich or not creative.
Someone is either strong or old.
Someone is not patient or not quiet.
Someone is generous or not funny.
Lucy is either creative or not kind. | Mary is not tall. | neutral | (![X]:((happy(X)|~brave(X))<=>humble(X)))&
(![X]:(strong(X)=>(~calm(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)|patient(X))))&
((?[X]:((curious(X)|~generous(X))))=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((humble(X)|~funny(X))<=>(~strong(X)|rich(X))))&
(![X]:((~patient(X)&generous(X))=>wise(X)))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((~brave(X)&patient(X)))))&
((?[X]:(rich(X)))=>(tall(john)))&
(![X]:((kind(X)|~happy(X))<=>~quiet(X)))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((kind(lucy)|wise(lucy))))&
(![X]:((~old(X)|generous(X))=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(~tall(X)<~>~rich(X))))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
((~old(john)<~>humble(john)))&
((~funny(mary)&~patient(mary)))&
(humble(lucy))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((generous(X)|~funny(X))))&
((creative(lucy)<~>~kind(lucy))) | ~tall(mary) | [] | null | 0 |
Everyone who is either not brave or not strong is not humble or not brave and vice versa.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
If fred is either not quiet or quiet then alice is not tall and vice versa.
Everyone who is both not wise and curious is both not quiet and not old.
If susan is both not brave and curious then lucy is both calm and not strong.
Someone is not happy.
Fred is creative.
John is both creative and not generous.
Mary is both brave and funny.
Alice is rich or not curious. | Mary is not wise. | contradiction | (![X]:((~brave(X)<~>~strong(X))<=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
(((~quiet(fred)<~>quiet(fred)))<=>(~tall(alice)))&
(![X]:((~wise(X)&curious(X))=>(~quiet(X)&~old(X))))&
(((~brave(susan)&curious(susan)))=>((calm(lucy)&~strong(lucy))))&
(?[X]:(~happy(X)))&
(creative(fred))&
((creative(john)&~generous(john)))&
((brave(mary)&funny(mary)))&
((rich(alice)|~curious(alice))) | ~wise(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 415720150785916023402415
% SZS output start Proof for 415720150785916023402415
11. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p10]
21. ~wise(mary) [input hypothesis]
57. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 11]
58. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 57]
111. ~tall(X0) | wise(X0) [cnf transformation 58]
113. tall(X0) | wise(X0) [cnf transformation 58]
131. ~wise(mary) [cnf transformation 21]
228. wise(X0) [subsumption resolution 111,113]
253. $false [subsumption resolution 131,228]
% SZS output end Proof for 415720150785916023402415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or creative is wise or not wise and vice versa.
If someone is not calm or not kind then susan is wise and vice versa.
If someone is either tall or not tall then mary is either not quiet or tall.
Everyone who is either not brave or patient is not patient or not old and vice versa.
Everyone who is either brave or kind is not strong.
If someone is tall or not generous then someone is not curious or curious.
If lucy is generous or wise then someone is wise or not creative.
If john is not patient or quiet then someone is either not calm or not humble.
If someone is tall then alice is not patient.
Everyone who is not happy is not calm.
Everyone who is not tall or humble is not curious and vice versa.
If someone is either kind or old then someone is brave.
If someone is not quiet then susan is both brave and curious and vice versa.
If john is not happy then lucy is either brave or wise.
Everyone who is both not strong and not old is either not calm or not creative and vice versa.
Everyone who is either not brave or patient is both not happy and old and vice versa.
Someone is either kind or not rich.
Someone is tall or brave.
Someone is both not calm and not humble.
Someone is not humble or curious.
Someone is not generous.
Someone is generous or not rich.
Someone is not kind or not wise.
Fred is not calm or old. | Susan is kind. | entailment | (![X]:((~brave(X)|creative(X))<=>(wise(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))<=>(wise(susan)))&
((?[X]:((tall(X)<~>~tall(X))))=>((~quiet(mary)<~>tall(mary))))&
(![X]:((~brave(X)<~>patient(X))<=>(~patient(X)|~old(X))))&
(![X]:((brave(X)<~>kind(X))=>~strong(X)))&
((?[X]:((tall(X)|~generous(X))))=>(?[X]:((~curious(X)|curious(X)))))&
(((generous(lucy)|wise(lucy)))=>(?[X]:((wise(X)|~creative(X)))))&
(((~patient(john)|quiet(john)))=>(?[X]:((~calm(X)<~>~humble(X)))))&
((?[X]:(tall(X)))=>(~patient(alice)))&
(![X]:(~happy(X)=>~calm(X)))&
(![X]:((~tall(X)|humble(X))<=>~curious(X)))&
((?[X]:((kind(X)<~>old(X))))=>(?[X]:(brave(X))))&
((?[X]:(~quiet(X)))<=>((brave(susan)&curious(susan))))&
((~happy(john))=>((brave(lucy)<~>wise(lucy))))&
(![X]:((~strong(X)&~old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(~happy(X)&old(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((~kind(X)|~wise(X))))&
((~calm(fred)|old(fred))) | kind(susan) | [
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6192713252246781395587599
% SZS output start Proof for 6192713252246781395587599
4. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (~old(X0) | ~patient(X0))) [input p3]
12. ? [X0] : (kind(X0) <~> old(X0)) => ? [X0] : brave(X0) [input p11]
16. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (old(X0) & ~happy(X0))) [input p15]
25. ~kind(susan) [input hypothesis]
27. ? [X0] : (kind(X0) <~> old(X0)) => ? [X1] : brave(X1) [rectify 12]
35. ? [X1] : brave(X1) | ! [X0] : (kind(X0) <=> old(X0)) [ennf transformation 27]
44. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 4]
45. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 44]
57. ? [X1] : brave(X1) | ! [X0] : ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))) [nnf transformation 35]
58. ? [X0] : brave(X0) | ! [X1] : ((kind(X1) | ~old(X1)) & (old(X1) | ~kind(X1))) [rectify 57]
59. ? [X0] : brave(X0) => brave(sK4) [choice axiom]
60. brave(sK4) | ! [X1] : ((kind(X1) | ~old(X1)) & (old(X1) | ~kind(X1))) [skolemisation 58,59]
69. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (~old(X0) | happy(X0))) & ((old(X0) & ~happy(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 16]
70. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | ~old(X0) | happy(X0)) & ((old(X0) & ~happy(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 69]
98. ~old(X0) | ~patient(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 45]
99. patient(X0) | ~brave(X0) | patient(X0) [cnf transformation 45]
102. ~patient(X0) | brave(X0) | old(X0) [cnf transformation 45]
119. brave(sK4) | kind(X1) | ~old(X1) [cnf transformation 60]
133. old(X0) | patient(X0) | brave(X0) [cnf transformation 70]
134. old(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 70]
147. ~kind(susan) [cnf transformation 25]
148. ~old(X0) | ~patient(X0) | ~brave(X0) [duplicate literal removal 98]
149. ~brave(X0) | patient(X0) [duplicate literal removal 99]
169. 4 <=> ! [X1] : kind(X1) [avatar definition]
170. kind(X1) <- (4) [avatar component clause 169]
194. ~old(X0) | ~brave(X0) [subsumption resolution 148,149]
239. 19 <=> ! [X1] : (kind(X1) | ~old(X1)) [avatar definition]
240. kind(X1) | ~old(X1) <- (19) [avatar component clause 239]
242. 20 <=> brave(sK4) [avatar definition]
244. brave(sK4) <- (20) [avatar component clause 242]
245. 19 | 20 [avatar split clause 119,242,239]
279. ~patient(X0) | old(X0) [subsumption resolution 134,102]
280. old(X0) | patient(X0) [subsumption resolution 133,149]
281. old(X0) [subsumption resolution 280,279]
324. $false <- (4) [resolution 170,147]
325. ~4 [avatar contradiction clause 324]
332. ~brave(X0) [resolution 194,281]
337. $false <- (20) [resolution 332,244]
340. ~20 [avatar contradiction clause 337]
341. kind(X1) <- (19) [subsumption resolution 240,281]
342. 4 | ~19 [avatar split clause 341,239,169]
343. $false [avatar sat refutation 245,325,340,342]
% SZS output end Proof for 6192713252246781395587599
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then someone is kind or generous. If alice is either tall or curious then alice is curious or humble and vice versa. If someone is either not generous or humble then someone is patient. If paul is either not creative or old then lucy is either brave or not humble and vice versa. If lucy is either creative or not strong then mary is kind and vice versa. Everyone who is either not calm or patient is old or rich and vice versa. If susan is not creative then someone is old or not creative and vice versa. Everyone who is not strong or not funny is both not humble and generous and vice versa. If someone is not tall or not curious then someone is either brave or not wise and vice versa. If fred is both old and not tall then lucy is humble and vice versa. Everyone who is either not strong or not creative is not creative and vice versa. If paul is not strong then someone is quiet. Everyone who is not curious is not strong and vice versa. Everyone who is strong is both creative and not quiet and vice versa. Everyone who is both not curious and strong is either strong or rich. Everyone who is both quiet and not calm is both curious and not strong. Someone is either not rich or not tall. Someone is both strong and not brave. Alice is not rich. Alice is patient. Someone is either happy or not wise. | Fred is funny. | neutral | ((humble(paul))=>(?[X]:((kind(X)|generous(X)))))&
(((tall(alice)<~>curious(alice)))<=>((curious(alice)|humble(alice))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:(patient(X))))&
(((~creative(paul)<~>old(paul)))<=>((brave(lucy)<~>~humble(lucy))))&
(((creative(lucy)<~>~strong(lucy)))<=>(kind(mary)))&
(![X]:((~calm(X)<~>patient(X))<=>(old(X)|rich(X))))&
((~creative(susan))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~humble(X)&generous(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((old(fred)&~tall(fred)))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
(?[X]:((strong(X)&~brave(X))))&
(~rich(alice))&
(patient(alice))&
(?[X]:((happy(X)<~>~wise(X)))) | funny(fred) | [] | null | 0 |
Everyone who is either not curious or curious is either not quiet or kind. Everyone who is strong is either happy or not humble. Everyone who is both not generous and not curious is tall and vice versa. If someone is not old then john is both humble and not kind and vice versa. If alice is not old or brave then lucy is either calm or wise. Everyone who is either patient or not humble is not patient and vice versa. Everyone who is patient is both rich and happy and vice versa. Everyone who is funny or not rich is generous and vice versa. If someone is not curious then paul is either happy or patient. If someone is either rich or not rich then mary is not wise. If mary is rich or happy then fred is strong. If someone is both creative and not tall then lucy is kind or quiet and vice versa. If someone is not strong or not wise then alice is happy. If alice is both strong and creative then john is humble and vice versa. Everyone who is funny is both not strong and not humble. Everyone who is both not rich and not tall is not creative or strong. Someone is not happy. Susan is either kind or not generous. Alice is both not generous and happy. Lucy is not strong or not humble. Someone is curious or quiet. Lucy is either tall or not humble. | Lucy is old. | entailment | (![X]:((~curious(X)<~>curious(X))=>(~quiet(X)<~>kind(X))))&
(![X]:(strong(X)=>(happy(X)<~>~humble(X))))&
(![X]:((~generous(X)&~curious(X))<=>tall(X)))&
((?[X]:(~old(X)))<=>((humble(john)&~kind(john))))&
(((~old(alice)|brave(alice)))=>((calm(lucy)<~>wise(lucy))))&
(![X]:((patient(X)<~>~humble(X))<=>~patient(X)))&
(![X]:(patient(X)<=>(rich(X)&happy(X))))&
(![X]:((funny(X)|~rich(X))<=>generous(X)))&
((?[X]:(~curious(X)))=>((happy(paul)<~>patient(paul))))&
((?[X]:((rich(X)<~>~rich(X))))=>(~wise(mary)))&
(((rich(mary)|happy(mary)))=>(strong(fred)))&
((?[X]:((creative(X)&~tall(X))))<=>((kind(lucy)|quiet(lucy))))&
((?[X]:((~strong(X)|~wise(X))))=>(happy(alice)))&
(((strong(alice)&creative(alice)))<=>(humble(john)))&
(![X]:(funny(X)=>(~strong(X)&~humble(X))))&
(![X]:((~rich(X)&~tall(X))=>(~creative(X)|strong(X))))&
(?[X]:(~happy(X)))&
((kind(susan)<~>~generous(susan)))&
((~generous(alice)&happy(alice)))&
((~strong(lucy)|~humble(lucy)))&
(?[X]:((curious(X)|quiet(X))))&
((tall(lucy)<~>~humble(lucy))) | old(lucy) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1829097839034119049358514
% SZS output start Proof for 1829097839034119049358514
4. ? [X0] : ~old(X0) <=> (~kind(john) & humble(john)) [input p3]
6. ! [X0] : ((patient(X0) <~> ~humble(X0)) <=> ~patient(X0)) [input p5]
23. ~old(lucy) [input hypothesis]
39. (? [X0] : ~old(X0) | (kind(john) | ~humble(john))) & ((~kind(john) & humble(john)) | ! [X0] : old(X0)) [nnf transformation 4]
40. (? [X0] : ~old(X0) | kind(john) | ~humble(john)) & ((~kind(john) & humble(john)) | ! [X0] : old(X0)) [flattening 39]
41. (? [X0] : ~old(X0) | kind(john) | ~humble(john)) & ((~kind(john) & humble(john)) | ! [X1] : old(X1)) [rectify 40]
42. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
43. (~old(sK0) | kind(john) | ~humble(john)) & ((~kind(john) & humble(john)) | ! [X1] : old(X1)) [skolemisation 41,42]
45. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | patient(X0)) & (~patient(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [nnf transformation 6]
74. humble(john) | old(X1) [cnf transformation 43]
79. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 45]
81. ~humble(X0) | patient(X0) | patient(X0) [cnf transformation 45]
117. ~old(lucy) [cnf transformation 23]
120. ~patient(X0) | ~humble(X0) [duplicate literal removal 79]
121. ~humble(X0) | patient(X0) [duplicate literal removal 81]
129. 1 <=> humble(john) [avatar definition]
130. humble(john) <- (1) [avatar component clause 129]
142. 4 <=> ! [X1] : old(X1) [avatar definition]
143. old(X1) <- (4) [avatar component clause 142]
145. 4 | 1 [avatar split clause 74,129,142]
160. ~humble(X0) [subsumption resolution 120,121]
270. $false <- (4) [resolution 143,117]
271. ~4 [avatar contradiction clause 270]
272. $false <- (1) [subsumption resolution 130,160]
273. ~1 [avatar contradiction clause 272]
274. $false [avatar sat refutation 145,271,273]
% SZS output end Proof for 1829097839034119049358514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not tall or not happy then fred is not humble.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
If susan is either calm or brave then alice is both old and not kind.
If someone is either not wise or not humble then lucy is rich or not funny.
Everyone who is not funny is either calm or not rich.
Everyone who is generous or kind is calm.
If susan is not brave or generous then alice is both creative and not old and vice versa.
Everyone who is not calm or not curious is either tall or kind and vice versa.
Everyone who is not humble is both creative and not humble and vice versa.
If lucy is either strong or kind then someone is not calm.
Fred is either not tall or not calm.
Fred is either quiet or not strong.
John is both tall and not calm.
Mary is kind.
Someone is not generous.
Someone is either curious or not rich. | Fred is not strong. | neutral | (((~tall(susan)<~>~happy(susan)))=>(~humble(fred)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(((calm(susan)<~>brave(susan)))=>((old(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>~humble(X))))=>((rich(lucy)|~funny(lucy))))&
(![X]:(~funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((generous(X)|kind(X))=>calm(X)))&
(((~brave(susan)|generous(susan)))<=>((creative(alice)&~old(alice))))&
(![X]:((~calm(X)|~curious(X))<=>(tall(X)<~>kind(X))))&
(![X]:(~humble(X)<=>(creative(X)&~humble(X))))&
(((strong(lucy)<~>kind(lucy)))=>(?[X]:(~calm(X))))&
((~tall(fred)<~>~calm(fred)))&
((quiet(fred)<~>~strong(fred)))&
((tall(john)&~calm(john)))&
(kind(mary))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>~rich(X)))) | ~strong(fred) | [] | null | 0 |
If someone is either not generous or happy then someone is not kind. Everyone who is not calm or rich is either not rich or not happy and vice versa. If someone is not patient then paul is both not kind and not old. If paul is not humble then someone is either not rich or happy. Everyone who is both funny and wise is not wise and vice versa. If someone is patient or generous then paul is either patient or old. Everyone who is either rich or calm is either not old or not creative. Everyone who is either not brave or funny is both wise and not curious. If paul is either not generous or not funny then someone is both not tall and patient. Everyone who is either kind or not humble is both not quiet and not tall. Everyone who is both happy and not strong is both creative and not calm and vice versa. Everyone who is either not creative or creative is generous or creative and vice versa. Everyone who is old is not tall and vice versa. If someone is humble then paul is either tall or wise. If paul is both not quiet and not old then someone is both not quiet and calm. Everyone who is not tall or tall is both brave and not happy. Paul is rich. Susan is strong. Someone is both not kind and not strong. Paul is not rich or not humble. Someone is generous. Someone is curious or wise. Someone is not rich or not wise. | Paul is calm. | entailment | ((?[X]:((~generous(X)<~>happy(X))))=>(?[X]:(~kind(X))))&
(![X]:((~calm(X)|rich(X))<=>(~rich(X)<~>~happy(X))))&
((?[X]:(~patient(X)))=>((~kind(paul)&~old(paul))))&
((~humble(paul))=>(?[X]:((~rich(X)<~>happy(X)))))&
(![X]:((funny(X)&wise(X))<=>~wise(X)))&
((?[X]:((patient(X)|generous(X))))=>((patient(paul)<~>old(paul))))&
(![X]:((rich(X)<~>calm(X))=>(~old(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>funny(X))=>(wise(X)&~curious(X))))&
(((~generous(paul)<~>~funny(paul)))=>(?[X]:((~tall(X)&patient(X)))))&
(![X]:((kind(X)<~>~humble(X))=>(~quiet(X)&~tall(X))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)&~calm(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(generous(X)|creative(X))))&
(![X]:(old(X)<=>~tall(X)))&
((?[X]:(humble(X)))=>((tall(paul)<~>wise(paul))))&
(((~quiet(paul)&~old(paul)))=>(?[X]:((~quiet(X)&calm(X)))))&
(![X]:((~tall(X)|tall(X))=>(brave(X)&~happy(X))))&
(rich(paul))&
(strong(susan))&
(?[X]:((~kind(X)&~strong(X))))&
((~rich(paul)|~humble(paul)))&
(?[X]:(generous(X)))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~rich(X)|~wise(X)))) | calm(paul) | [
"p2",
"p5",
"p6",
"p10",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3190893553269413926360092
% SZS output start Proof for 3190893553269413926360092
3. ? [X0] : ~patient(X0) => (~old(paul) & ~kind(paul)) [input p2]
6. ? [X0] : (generous(X0) | patient(X0)) => (patient(paul) <~> old(paul)) [input p5]
7. ! [X0] : ((rich(X0) <~> calm(X0)) => (~old(X0) <~> ~creative(X0))) [input p6]
11. ! [X0] : ((~strong(X0) & happy(X0)) <=> (~calm(X0) & creative(X0))) [input p10]
16. ! [X0] : ((tall(X0) | ~tall(X0)) => (~happy(X0) & brave(X0))) [input p15]
17. rich(paul) [input p16]
21. ? [X0] : generous(X0) [input p20]
24. ~calm(paul) [input hypothesis]
27. (~old(paul) & ~kind(paul)) | ! [X0] : patient(X0) [ennf transformation 3]
29. (patient(paul) <~> old(paul)) | ! [X0] : (~generous(X0) & ~patient(X0)) [ennf transformation 6]
30. ! [X0] : ((~old(X0) <~> ~creative(X0)) | (rich(X0) <=> calm(X0))) [ennf transformation 7]
37. ! [X0] : ((~happy(X0) & brave(X0)) | (~tall(X0) & tall(X0))) [ennf transformation 16]
49. ((~old(paul) | ~patient(paul)) & (old(paul) | patient(paul))) | ! [X0] : (~generous(X0) & ~patient(X0)) [nnf transformation 29]
50. ! [X0] : (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) [nnf transformation 30]
56. ! [X0] : (((~strong(X0) & happy(X0)) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | (strong(X0) | ~happy(X0)))) [nnf transformation 11]
57. ! [X0] : (((~strong(X0) & happy(X0)) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | strong(X0) | ~happy(X0))) [flattening 56]
66. ? [X0] : generous(X0) => generous(sK5) [choice axiom]
67. generous(sK5) [skolemisation 21,66]
81. ~old(paul) | patient(X0) [cnf transformation 27]
90. ~old(paul) | ~patient(paul) | ~generous(X0) [cnf transformation 49]
93. ~rich(X0) | old(X0) | calm(X0) | creative(X0) [cnf transformation 50]
109. ~creative(X0) | calm(X0) | happy(X0) [cnf transformation 57]
125. ~happy(X0) | tall(X0) [cnf transformation 37]
126. ~tall(X0) | ~happy(X0) [cnf transformation 37]
127. rich(paul) [cnf transformation 17]
132. generous(sK5) [cnf transformation 67]
135. ~calm(paul) [cnf transformation 24]
157. 4 <=> ! [X0] : patient(X0) [avatar definition]
158. patient(X0) <- (4) [avatar component clause 157]
160. 5 <=> old(paul) [avatar definition]
162. ~old(paul) <- (~5) [avatar component clause 160]
163. 4 | ~5 [avatar split clause 81,160,157]
187. 10 <=> ! [X0] : ~generous(X0) [avatar definition]
188. ~generous(X0) <- (10) [avatar component clause 187]
190. 11 <=> patient(paul) [avatar definition]
192. ~patient(paul) <- (~11) [avatar component clause 190]
193. 10 | ~11 | ~5 [avatar split clause 90,160,190,187]
240. ~happy(X0) [subsumption resolution 125,126]
245. $false <- (4, ~11) [resolution 192,158]
246. ~4 | 11 [avatar contradiction clause 245]
249. $false <- (10) [resolution 188,132]
250. ~10 [avatar contradiction clause 249]
314. old(paul) | calm(paul) | creative(paul) [resolution 93,127]
317. calm(paul) | creative(paul) <- (~5) [subsumption resolution 314,162]
318. creative(paul) <- (~5) [subsumption resolution 317,135]
322. calm(paul) | happy(paul) <- (~5) [resolution 318,109]
323. happy(paul) <- (~5) [subsumption resolution 322,135]
324. $false <- (~5) [subsumption resolution 323,240]
325. 5 [avatar contradiction clause 324]
326. $false [avatar sat refutation 163,193,246,250,325]
% SZS output end Proof for 3190893553269413926360092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or calm is both humble and wise and vice versa.
Everyone who is not brave is both strong and not tall and vice versa.
If alice is both creative and not quiet then lucy is strong and vice versa.
Everyone who is both old and humble is rich or brave and vice versa.
If alice is either curious or not brave then someone is both not creative and curious.
If john is either happy or patient then someone is brave and vice versa.
If fred is funny then john is both not quiet and rich and vice versa.
If someone is both not curious and strong then someone is not quiet and vice versa.
If someone is creative then john is quiet or old.
Everyone who is not creative or strong is either not quiet or humble and vice versa.
Everyone who is not brave is creative and vice versa.
Everyone who is not funny or humble is both calm and rich.
If john is either not quiet or not generous then john is creative.
If someone is both not brave and patient then fred is both kind and not humble and vice versa.
If someone is either not funny or not rich then fred is both humble and rich.
Everyone who is not wise is not creative.
Someone is either humble or curious.
Someone is rich or not kind.
Someone is not happy or generous.
Paul is either not generous or not old.
Someone is not patient or patient.
Alice is either humble or not creative.
Mary is not wise. | Fred is funny. | contradiction | (![X]:((~kind(X)<~>calm(X))<=>(humble(X)&wise(X))))&
(![X]:(~brave(X)<=>(strong(X)&~tall(X))))&
(((creative(alice)&~quiet(alice)))<=>(strong(lucy)))&
(![X]:((old(X)&humble(X))<=>(rich(X)|brave(X))))&
(((curious(alice)<~>~brave(alice)))=>(?[X]:((~creative(X)&curious(X)))))&
(((happy(john)<~>patient(john)))<=>(?[X]:(brave(X))))&
((funny(fred))<=>((~quiet(john)&rich(john))))&
((?[X]:((~curious(X)&strong(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(creative(X)))=>((quiet(john)|old(john))))&
(![X]:((~creative(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(![X]:((~funny(X)|humble(X))=>(calm(X)&rich(X))))&
(((~quiet(john)<~>~generous(john)))=>(creative(john)))&
((?[X]:((~brave(X)&patient(X))))<=>((kind(fred)&~humble(fred))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((humble(fred)&rich(fred))))&
(![X]:(~wise(X)=>~creative(X)))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~happy(X)|generous(X))))&
((~generous(paul)<~>~old(paul)))&
(?[X]:((~patient(X)|patient(X))))&
((humble(alice)<~>~creative(alice)))&
(~wise(mary)) | funny(fred) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4536789923394520527399328
% SZS output start Proof for 4536789923394520527399328
2. ! [X0] : (~brave(X0) <=> (~tall(X0) & strong(X0))) [input p1]
4. ! [X0] : ((humble(X0) & old(X0)) <=> (brave(X0) | rich(X0))) [input p3]
7. funny(fred) <=> (rich(john) & ~quiet(john)) [input p6]
10. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~quiet(X0) <~> humble(X0))) [input p9]
11. ! [X0] : (~brave(X0) <=> creative(X0)) [input p10]
24. funny(fred) [input hypothesis]
35. ! [X0] : ((~brave(X0) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | brave(X0))) [nnf transformation 2]
36. ! [X0] : ((~brave(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | brave(X0))) [flattening 35]
39. ! [X0] : (((humble(X0) & old(X0)) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | (~humble(X0) | ~old(X0)))) [nnf transformation 4]
40. ! [X0] : (((humble(X0) & old(X0)) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ~humble(X0) | ~old(X0))) [flattening 39]
48. (funny(fred) | (~rich(john) | quiet(john))) & ((rich(john) & ~quiet(john)) | ~funny(fred)) [nnf transformation 7]
49. (funny(fred) | ~rich(john) | quiet(john)) & ((rich(john) & ~quiet(john)) | ~funny(fred)) [flattening 48]
55. ! [X0] : (((strong(X0) | ~creative(X0)) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [nnf transformation 10]
56. ! [X0] : ((strong(X0) | ~creative(X0) | ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) & (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & creative(X0)))) [flattening 55]
57. ! [X0] : ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))) [nnf transformation 11]
82. strong(X0) | brave(X0) [cnf transformation 36]
91. ~rich(X0) | humble(X0) [cnf transformation 40]
101. ~quiet(john) | ~funny(fred) [cnf transformation 49]
102. rich(john) | ~funny(fred) [cnf transformation 49]
110. ~humble(X0) | quiet(X0) | creative(X0) [cnf transformation 56]
111. ~strong(X0) | quiet(X0) | ~humble(X0) [cnf transformation 56]
115. ~creative(X0) | ~brave(X0) [cnf transformation 57]
141. funny(fred) [cnf transformation 24]
197. 12 <=> quiet(john) [avatar definition]
198. ~quiet(john) <- (~12) [avatar component clause 197]
201. 13 <=> rich(john) [avatar definition]
202. rich(john) <- (13) [avatar component clause 201]
205. 14 <=> funny(fred) [avatar definition]
209. ~14 | 13 [avatar split clause 102,201,205]
210. ~14 | ~12 [avatar split clause 101,197,205]
245. 23 <=> creative(john) [avatar definition]
247. creative(john) <- (23) [avatar component clause 245]
335. 14 [avatar split clause 141,205]
348. humble(john) <- (13) [resolution 91,202]
457. quiet(john) | creative(john) <- (13) [resolution 110,348]
461. creative(john) <- (~12, 13) [subsumption resolution 457,198]
462. 23 | 12 | ~13 [avatar split clause 461,201,197,245]
494. ~brave(john) <- (23) [resolution 247,115]
504. ~humble(X0) | quiet(X0) | brave(X0) [resolution 111,82]
602. quiet(john) | brave(john) <- (13) [resolution 504,348]
609. brave(john) <- (~12, 13) [subsumption resolution 602,198]
610. $false <- (~12, 13, 23) [subsumption resolution 609,494]
611. 12 | ~13 | ~23 [avatar contradiction clause 610]
612. $false [avatar sat refutation 209,210,335,462,611]
% SZS output end Proof for 4536789923394520527399328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then mary is not tall or not kind.
If lucy is both not tall and not creative then fred is not rich or not kind and vice versa.
Everyone who is patient is not funny and vice versa.
If lucy is both not patient and old then fred is not brave.
If someone is not kind then john is both wise and old.
Everyone who is not quiet or strong is quiet or not creative and vice versa.
Everyone who is not humble is strong and vice versa.
Everyone who is not strong or old is not kind and vice versa.
Everyone who is not patient or not brave is either funny or happy and vice versa.
Everyone who is both not humble and kind is both kind and rich and vice versa.
If john is strong or quiet then someone is not patient.
Everyone who is creative is both not rich and wise and vice versa.
Everyone who is funny or tall is tall and vice versa.
Everyone who is not old or not funny is both not humble and not quiet.
If lucy is humble then alice is either not generous or tall and vice versa.
If someone is both not calm and funny then someone is not funny or brave and vice versa.
Paul is not curious.
Someone is strong.
Someone is either wise or funny.
Mary is either wise or not quiet.
John is quiet.
Fred is not generous.
Someone is not happy.
Someone is tall. | John is funny. | entailment | ((?[X]:(funny(X)))=>((~tall(mary)|~kind(mary))))&
(((~tall(lucy)&~creative(lucy)))<=>((~rich(fred)|~kind(fred))))&
(![X]:(patient(X)<=>~funny(X)))&
(((~patient(lucy)&old(lucy)))=>(~brave(fred)))&
((?[X]:(~kind(X)))=>((wise(john)&old(john))))&
(![X]:((~quiet(X)|strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)<=>strong(X)))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~patient(X)|~brave(X))<=>(funny(X)<~>happy(X))))&
(![X]:((~humble(X)&kind(X))<=>(kind(X)&rich(X))))&
(((strong(john)|quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:(creative(X)<=>(~rich(X)&wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(~curious(paul))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)<~>funny(X))))&
((wise(mary)<~>~quiet(mary)))&
(quiet(john))&
(~generous(fred))&
(?[X]:(~happy(X)))&
(?[X]:(tall(X))) | funny(john) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6433574997699387889388096
% SZS output start Proof for 6433574997699387889388096
14. ! [X0] : ((~funny(X0) | ~old(X0)) => (~quiet(X0) & ~humble(X0))) [input p13]
21. quiet(john) [input p20]
25. ~funny(john) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & ~humble(X0)) | (funny(X0) & old(X0))) [ennf transformation 14]
110. ~quiet(X0) | funny(X0) [cnf transformation 34]
125. quiet(john) [cnf transformation 21]
129. ~funny(john) [cnf transformation 25]
194. 14 <=> quiet(john) [avatar definition]
195. quiet(john) <- (14) [avatar component clause 194]
273. 14 [avatar split clause 125,194]
291. funny(john) <- (14) [resolution 110,195]
292. $false <- (14) [subsumption resolution 291,129]
293. ~14 [avatar contradiction clause 292]
294. $false [avatar sat refutation 273,293]
% SZS output end Proof for 6433574997699387889388096
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both brave and generous.
If mary is either not patient or not strong then someone is old or rich and vice versa.
If fred is both not old and rich then alice is wise and vice versa.
Everyone who is both not kind and creative is both not funny and brave.
If mary is not rich then someone is either not generous or old and vice versa.
If someone is funny or not creative then someone is both not calm and not funny.
If susan is either not happy or strong then someone is happy.
Everyone who is either not kind or generous is not brave or humble and vice versa.
Everyone who is calm or not curious is both not patient and not wise.
Everyone who is either funny or not patient is humble.
Everyone who is curious is both not old and kind and vice versa.
Everyone who is not creative or not quiet is both generous and patient.
If lucy is both funny and happy then susan is not happy and vice versa.
Everyone who is either not happy or not brave is wise.
If someone is both creative and generous then lucy is not strong and vice versa.
Everyone who is both not brave and patient is either not quiet or not rich and vice versa.
Susan is creative or humble.
Mary is either not quiet or not kind.
Someone is not happy or not brave.
Susan is tall or old.
Alice is both calm and not wise.
Susan is old or not creative.
Someone is both not calm and not brave.
Mary is both brave and not rich. | Alice is not creative. | contradiction | (![X]:(~happy(X)=>(brave(X)&generous(X))))&
(((~patient(mary)<~>~strong(mary)))<=>(?[X]:((old(X)|rich(X)))))&
(((~old(fred)&rich(fred)))<=>(wise(alice)))&
(![X]:((~kind(X)&creative(X))=>(~funny(X)&brave(X))))&
((~rich(mary))<=>(?[X]:((~generous(X)<~>old(X)))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:((~calm(X)&~funny(X)))))&
(((~happy(susan)<~>strong(susan)))=>(?[X]:(happy(X))))&
(![X]:((~kind(X)<~>generous(X))<=>(~brave(X)|humble(X))))&
(![X]:((calm(X)|~curious(X))=>(~patient(X)&~wise(X))))&
(![X]:((funny(X)<~>~patient(X))=>humble(X)))&
(![X]:(curious(X)<=>(~old(X)&kind(X))))&
(![X]:((~creative(X)|~quiet(X))=>(generous(X)&patient(X))))&
(((funny(lucy)&happy(lucy)))<=>(~happy(susan)))&
(![X]:((~happy(X)<~>~brave(X))=>wise(X)))&
((?[X]:((creative(X)&generous(X))))<=>(~strong(lucy)))&
(![X]:((~brave(X)&patient(X))<=>(~quiet(X)<~>~rich(X))))&
((creative(susan)|humble(susan)))&
((~quiet(mary)<~>~kind(mary)))&
(?[X]:((~happy(X)|~brave(X))))&
((tall(susan)|old(susan)))&
((calm(alice)&~wise(alice)))&
((old(susan)|~creative(susan)))&
(?[X]:((~calm(X)&~brave(X))))&
((brave(mary)&~rich(mary))) | ~creative(alice) | [
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 420804915422750917910929
% SZS output start Proof for 420804915422750917910929
9. ! [X0] : ((~curious(X0) | calm(X0)) => (~wise(X0) & ~patient(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | ~creative(X0)) => (patient(X0) & generous(X0))) [input p11]
21. ~wise(alice) & calm(alice) [input p20]
25. ~creative(alice) [input hypothesis]
34. ! [X0] : ((~wise(X0) & ~patient(X0)) | (curious(X0) & ~calm(X0))) [ennf transformation 9]
37. ! [X0] : ((patient(X0) & generous(X0)) | (quiet(X0) & creative(X0))) [ennf transformation 12]
101. ~calm(X0) | ~patient(X0) [cnf transformation 34]
111. creative(X0) | patient(X0) [cnf transformation 37]
131. calm(alice) [cnf transformation 21]
138. ~creative(alice) [cnf transformation 25]
306. ~patient(alice) [resolution 101,131]
317. patient(alice) [resolution 111,138]
319. $false [subsumption resolution 317,306]
% SZS output end Proof for 420804915422750917910929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both old and creative.
Everyone who is either not generous or not humble is not tall or not happy.
Everyone who is both generous and not humble is both strong and curious and vice versa.
If someone is both not patient and not creative then someone is not brave and vice versa.
If paul is happy or strong then alice is patient or creative and vice versa.
Everyone who is old or not calm is patient or funny and vice versa.
If someone is not rich then mary is calm or not strong.
Everyone who is either not calm or old is both not rich and rich and vice versa.
Everyone who is not creative or not calm is calm or not tall and vice versa.
Everyone who is either not calm or old is strong or patient and vice versa.
If john is not creative then alice is either not generous or not quiet.
If paul is calm then someone is both not creative and calm and vice versa.
If susan is funny or calm then someone is not old and vice versa.
If john is generous then someone is quiet and vice versa.
Everyone who is not brave or quiet is not curious and vice versa.
If lucy is either patient or kind then lucy is funny and vice versa.
Someone is not rich or happy.
Paul is not old or not wise.
Fred is not rich or tall.
Someone is wise or brave.
Alice is either kind or generous.
Paul is either not strong or not wise.
Alice is both not kind and not calm. | Fred is not curious. | neutral | (![X]:(~tall(X)=>(old(X)&creative(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(~tall(X)|~happy(X))))&
(![X]:((generous(X)&~humble(X))<=>(strong(X)&curious(X))))&
((?[X]:((~patient(X)&~creative(X))))<=>(?[X]:(~brave(X))))&
(((happy(paul)|strong(paul)))<=>((patient(alice)|creative(alice))))&
(![X]:((old(X)|~calm(X))<=>(patient(X)|funny(X))))&
((?[X]:(~rich(X)))=>((calm(mary)|~strong(mary))))&
(![X]:((~calm(X)<~>old(X))<=>(~rich(X)&rich(X))))&
(![X]:((~creative(X)|~calm(X))<=>(calm(X)|~tall(X))))&
(![X]:((~calm(X)<~>old(X))<=>(strong(X)|patient(X))))&
((~creative(john))=>((~generous(alice)<~>~quiet(alice))))&
((calm(paul))<=>(?[X]:((~creative(X)&calm(X)))))&
(((funny(susan)|calm(susan)))<=>(?[X]:(~old(X))))&
((generous(john))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|quiet(X))<=>~curious(X)))&
(((patient(lucy)<~>kind(lucy)))<=>(funny(lucy)))&
(?[X]:((~rich(X)|happy(X))))&
((~old(paul)|~wise(paul)))&
((~rich(fred)|tall(fred)))&
(?[X]:((wise(X)|brave(X))))&
((kind(alice)<~>generous(alice)))&
((~strong(paul)<~>~wise(paul)))&
((~kind(alice)&~calm(alice))) | ~curious(fred) | [] | null | 0 |
Everyone who is both not quiet and tall is both not wise and curious.
If lucy is both not curious and not happy then someone is either not happy or not rich.
Everyone who is not funny is either not patient or rich and vice versa.
If someone is not happy or strong then susan is either kind or quiet.
Everyone who is funny or humble is either not funny or brave.
Everyone who is not funny is both quiet and kind.
If someone is both not calm and not strong then john is both not quiet and generous and vice versa.
If john is not tall then someone is both tall and strong and vice versa.
Everyone who is both not wise and curious is either not wise or not quiet.
If lucy is both not creative and not rich then alice is both creative and not old and vice versa.
If lucy is both not humble and rich then someone is both humble and not generous and vice versa.
If someone is both generous and curious then someone is kind or old.
Everyone who is not patient is brave and vice versa.
Everyone who is either funny or rich is either not brave or not funny.
Everyone who is not quiet is patient or not happy.
Everyone who is either not tall or funny is brave.
Fred is either generous or not kind.
Someone is either tall or not creative.
Fred is either old or not calm.
Mary is both not patient and not generous.
Mary is not wise or brave.
Fred is tall or not happy.
Someone is either rich or not generous.
Someone is not wise or not happy. | Alice is patient. | contradiction | (![X]:((~quiet(X)&tall(X))=>(~wise(X)&curious(X))))&
(((~curious(lucy)&~happy(lucy)))=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:(~funny(X)<=>(~patient(X)<~>rich(X))))&
((?[X]:((~happy(X)|strong(X))))=>((kind(susan)<~>quiet(susan))))&
(![X]:((funny(X)|humble(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~funny(X)=>(quiet(X)&kind(X))))&
((?[X]:((~calm(X)&~strong(X))))<=>((~quiet(john)&generous(john))))&
((~tall(john))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(((~creative(lucy)&~rich(lucy)))<=>((creative(alice)&~old(alice))))&
(((~humble(lucy)&rich(lucy)))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((generous(X)&curious(X))))=>(?[X]:((kind(X)|old(X)))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:((funny(X)<~>rich(X))=>(~brave(X)<~>~funny(X))))&
(![X]:(~quiet(X)=>(patient(X)|~happy(X))))&
(![X]:((~tall(X)<~>funny(X))=>brave(X)))&
((generous(fred)<~>~kind(fred)))&
(?[X]:((tall(X)<~>~creative(X))))&
((old(fred)<~>~calm(fred)))&
((~patient(mary)&~generous(mary)))&
((~wise(mary)|brave(mary)))&
((tall(fred)|~happy(fred)))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~wise(X)|~happy(X)))) | patient(alice) | [
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4051365351666346751828638
% SZS output start Proof for 4051365351666346751828638
3. ! [X0] : (~funny(X0) <=> (~patient(X0) <~> rich(X0))) [input p2]
5. ! [X0] : ((humble(X0) | funny(X0)) => (~funny(X0) <~> brave(X0))) [input p4]
13. ! [X0] : (~patient(X0) <=> brave(X0)) [input p12]
14. ! [X0] : ((funny(X0) <~> rich(X0)) => (~brave(X0) <~> ~funny(X0))) [input p13]
25. patient(alice) [input hypothesis]
32. ! [X0] : ((~funny(X0) <~> brave(X0)) | (~humble(X0) & ~funny(X0))) [ennf transformation 5]
37. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (funny(X0) <=> rich(X0))) [ennf transformation 14]
44. ! [X0] : ((~funny(X0) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | funny(X0))) [nnf transformation 3]
46. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~humble(X0) & ~funny(X0))) [nnf transformation 32]
67. ! [X0] : ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0))) [nnf transformation 13]
68. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) [nnf transformation 37]
84. ~patient(X0) | rich(X0) | funny(X0) [cnf transformation 44]
92. brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
117. ~brave(X0) | ~patient(X0) [cnf transformation 67]
118. ~funny(X0) | ~brave(X0) | rich(X0) | ~funny(X0) [cnf transformation 68]
121. funny(X0) | brave(X0) | funny(X0) | ~rich(X0) [cnf transformation 68]
138. patient(alice) [cnf transformation 25]
139. ~funny(X0) | ~brave(X0) | rich(X0) [duplicate literal removal 118]
140. funny(X0) | brave(X0) | ~rich(X0) [duplicate literal removal 121]
142. ~funny(X0) | brave(X0) [duplicate literal removal 92]
271. ~rich(X0) | brave(X0) [subsumption resolution 140,142]
272. ~funny(X0) | rich(X0) [subsumption resolution 139,142]
366. rich(alice) | funny(alice) [resolution 84,138]
367. rich(alice) [subsumption resolution 366,272]
375. brave(alice) [resolution 367,271]
385. ~patient(alice) [resolution 375,117]
387. $false [subsumption resolution 385,138]
% SZS output end Proof for 4051365351666346751828638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both funny and not funny then someone is not rich and vice versa.
If someone is both tall and not quiet then mary is either humble or rich and vice versa.
If susan is both not brave and not strong then mary is either curious or patient.
Everyone who is either not calm or strong is both not happy and rich and vice versa.
Everyone who is both creative and strong is both not wise and not humble.
If john is both wise and not calm then mary is not humble or not generous and vice versa.
If susan is humble then lucy is not strong and vice versa.
Everyone who is not happy or kind is both old and not generous and vice versa.
If mary is either not creative or not rich then someone is either not calm or quiet and vice versa.
Everyone who is creative is not patient or not tall.
Everyone who is both not happy and kind is either not rich or old.
Everyone who is both not generous and not rich is either not kind or funny.
If mary is not tall or calm then alice is either creative or calm.
Everyone who is both kind and not curious is wise.
Everyone who is not brave or strong is not quiet.
Everyone who is both old and brave is not calm and vice versa.
Someone is both not kind and not humble.
John is either happy or not quiet.
Someone is not old.
Paul is not kind or funny.
Susan is quiet or not humble.
Someone is wise.
Susan is either curious or not generous.
Susan is not generous or calm. | Susan is humble. | neutral | (((funny(susan)&~funny(susan)))<=>(?[X]:(~rich(X))))&
((?[X]:((tall(X)&~quiet(X))))<=>((humble(mary)<~>rich(mary))))&
(((~brave(susan)&~strong(susan)))=>((curious(mary)<~>patient(mary))))&
(![X]:((~calm(X)<~>strong(X))<=>(~happy(X)&rich(X))))&
(![X]:((creative(X)&strong(X))=>(~wise(X)&~humble(X))))&
(((wise(john)&~calm(john)))<=>((~humble(mary)|~generous(mary))))&
((humble(susan))<=>(~strong(lucy)))&
(![X]:((~happy(X)|kind(X))<=>(old(X)&~generous(X))))&
(((~creative(mary)<~>~rich(mary)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(creative(X)=>(~patient(X)|~tall(X))))&
(![X]:((~happy(X)&kind(X))=>(~rich(X)<~>old(X))))&
(![X]:((~generous(X)&~rich(X))=>(~kind(X)<~>funny(X))))&
(((~tall(mary)|calm(mary)))=>((creative(alice)<~>calm(alice))))&
(![X]:((kind(X)&~curious(X))=>wise(X)))&
(![X]:((~brave(X)|strong(X))=>~quiet(X)))&
(![X]:((old(X)&brave(X))<=>~calm(X)))&
(?[X]:((~kind(X)&~humble(X))))&
((happy(john)<~>~quiet(john)))&
(?[X]:(~old(X)))&
((~kind(paul)|funny(paul)))&
((quiet(susan)|~humble(susan)))&
(?[X]:(wise(X)))&
((curious(susan)<~>~generous(susan)))&
((~generous(susan)|calm(susan))) | humble(susan) | [] | null | 0 |
Everyone who is either not creative or generous is either not humble or not creative. If fred is funny then lucy is generous or not kind and vice versa. Everyone who is either not rich or quiet is both generous and not strong. Everyone who is patient or creative is either not patient or not generous and vice versa. Everyone who is not wise is not tall. If someone is both humble and not brave then lucy is tall and vice versa. Everyone who is old or not kind is not patient. Everyone who is both kind and old is both creative and calm. If someone is generous or patient then fred is either not old or wise and vice versa. Everyone who is both not old and strong is either happy or not creative. If paul is not old then someone is both wise and not tall. If john is either wise or creative then susan is quiet or patient. If mary is not funny or wise then mary is rich or calm. If someone is patient then mary is not kind. Everyone who is either rich or humble is generous or creative and vice versa. Mary is either tall or not patient. Someone is either humble or old. John is either not generous or not funny. Someone is calm or creative. Someone is either not happy or not creative. Alice is creative or calm. Someone is kind or not wise. Someone is tall or old. | Mary is not strong. | neutral | (![X]:((~creative(X)<~>generous(X))=>(~humble(X)<~>~creative(X))))&
((funny(fred))<=>((generous(lucy)|~kind(lucy))))&
(![X]:((~rich(X)<~>quiet(X))=>(generous(X)&~strong(X))))&
(![X]:((patient(X)|creative(X))<=>(~patient(X)<~>~generous(X))))&
(![X]:(~wise(X)=>~tall(X)))&
((?[X]:((humble(X)&~brave(X))))<=>(tall(lucy)))&
(![X]:((old(X)|~kind(X))=>~patient(X)))&
(![X]:((kind(X)&old(X))=>(creative(X)&calm(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~old(fred)<~>wise(fred))))&
(![X]:((~old(X)&strong(X))=>(happy(X)<~>~creative(X))))&
((~old(paul))=>(?[X]:((wise(X)&~tall(X)))))&
(((wise(john)<~>creative(john)))=>((quiet(susan)|patient(susan))))&
(((~funny(mary)|wise(mary)))=>((rich(mary)|calm(mary))))&
((?[X]:(patient(X)))=>(~kind(mary)))&
(![X]:((rich(X)<~>humble(X))<=>(generous(X)|creative(X))))&
((tall(mary)<~>~patient(mary)))&
(?[X]:((humble(X)<~>old(X))))&
((~generous(john)<~>~funny(john)))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((~happy(X)<~>~creative(X))))&
((creative(alice)|calm(alice)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((tall(X)|old(X)))) | ~strong(mary) | [] | null | 0 |
Everyone who is either humble or quiet is not strong or not happy and vice versa.
Everyone who is not brave is both happy and generous and vice versa.
Everyone who is either not generous or not creative is both humble and tall.
Everyone who is either not funny or brave is curious or not curious and vice versa.
Everyone who is not strong or generous is not humble or not curious.
Everyone who is either not quiet or calm is both old and calm and vice versa.
If someone is either humble or brave then mary is humble or not kind.
Everyone who is both not rich and calm is strong or not rich and vice versa.
If mary is not patient or not kind then mary is not generous.
Everyone who is both not humble and not old is both not calm and brave.
Everyone who is tall is not brave or happy.
If mary is both curious and not quiet then lucy is not wise or not creative.
Everyone who is either rich or not creative is generous and vice versa.
If john is generous then someone is both not calm and patient and vice versa.
Everyone who is not funny or tall is not calm or rich and vice versa.
If paul is not rich then someone is both not kind and not generous and vice versa.
Someone is brave.
Alice is creative.
Someone is happy or not calm.
Someone is not curious or not patient.
Someone is either not creative or rich.
Mary is both patient and not humble.
Someone is not quiet or not wise.
Fred is strong or not funny. | Fred is humble. | contradiction | (![X]:((humble(X)<~>quiet(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)&generous(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(humble(X)&tall(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)|~curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)|~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(old(X)&calm(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((humble(mary)|~kind(mary))))&
(![X]:((~rich(X)&calm(X))<=>(strong(X)|~rich(X))))&
(((~patient(mary)|~kind(mary)))=>(~generous(mary)))&
(![X]:((~humble(X)&~old(X))=>(~calm(X)&brave(X))))&
(![X]:(tall(X)=>(~brave(X)|happy(X))))&
(((curious(mary)&~quiet(mary)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:((rich(X)<~>~creative(X))<=>generous(X)))&
((generous(john))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~calm(X)|rich(X))))&
((~rich(paul))<=>(?[X]:((~kind(X)&~generous(X)))))&
(?[X]:(brave(X)))&
(creative(alice))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((patient(mary)&~humble(mary)))&
(?[X]:((~quiet(X)|~wise(X))))&
((strong(fred)|~funny(fred))) | humble(fred) | [
"p1",
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"p12",
"p14",
"p15",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4641908691391428314910905
% SZS output start Proof for 4641908691391428314910905
2. ! [X0] : (~brave(X0) <=> (generous(X0) & happy(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (tall(X0) & humble(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> (~curious(X0) | curious(X0))) [input p3]
7. ? [X0] : (humble(X0) <~> brave(X0)) => (~kind(mary) | humble(mary)) [input p6]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~rich(X0) | strong(X0))) [input p7]
9. (~kind(mary) | ~patient(mary)) => ~generous(mary) [input p8]
11. ! [X0] : (tall(X0) => (happy(X0) | ~brave(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> generous(X0)) [input p12]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
16. ~rich(paul) <=> ? [X0] : (~generous(X0) & ~kind(X0)) [input p15]
22. ~humble(mary) & patient(mary) [input p21]
24. ~funny(fred) | strong(fred) [input p23]
25. humble(fred) [input hypothesis]
28. ! [X0] : ((tall(X0) & humble(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 3]
31. (~kind(mary) | humble(mary)) | ! [X0] : (humble(X0) <=> brave(X0)) [ennf transformation 7]
32. ~kind(mary) | humble(mary) | ! [X0] : (humble(X0) <=> brave(X0)) [flattening 31]
33. ~generous(mary) | (kind(mary) & patient(mary)) [ennf transformation 9]
36. ! [X0] : ((happy(X0) | ~brave(X0)) | ~tall(X0)) [ennf transformation 11]
37. ! [X0] : (happy(X0) | ~brave(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : ((~brave(X0) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | brave(X0))) [nnf transformation 2]
41. ! [X0] : ((~brave(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | brave(X0))) [flattening 40]
42. ! [X0] : ((tall(X0) & humble(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 28]
43. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [flattening 43]
47. ~kind(mary) | humble(mary) | ! [X0] : ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))) [nnf transformation 32]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : (((tall(X0) | ~funny(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | ~funny(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | (~tall(X0) & funny(X0)))) [flattening 55]
57. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X0] : (~generous(X0) & ~kind(X0)) | rich(paul)) [nnf transformation 16]
58. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & (? [X1] : (~generous(X1) & ~kind(X1)) | rich(paul)) [rectify 57]
59. ? [X1] : (~generous(X1) & ~kind(X1)) => (~generous(sK1) & ~kind(sK1)) [choice axiom]
60. (~rich(paul) | ! [X0] : (generous(X0) | kind(X0))) & ((~generous(sK1) & ~kind(sK1)) | rich(paul)) [skolemisation 58,59]
76. brave(X0) | happy(X0) [cnf transformation 41]
77. generous(X0) | brave(X0) [cnf transformation 41]
78. ~generous(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 41]
81. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 42]
82. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 42]
85. brave(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 44]
86. ~funny(X0) | brave(X0) | curious(X0) [cnf transformation 44]
87. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
88. ~brave(X0) | funny(X0) | curious(X0) [cnf transformation 44]
97. ~kind(mary) | humble(mary) | brave(X0) | ~humble(X0) [cnf transformation 47]
100. ~rich(X0) | ~strong(X0) [cnf transformation 49]
103. rich(X0) | calm(X0) [cnf transformation 49]
105. ~generous(mary) | kind(mary) [cnf transformation 33]
108. happy(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 37]
110. rich(X0) | generous(X0) | creative(X0) [cnf transformation 50]
111. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
112. ~rich(X0) | creative(X0) | ~generous(X0) [cnf transformation 50]
116. rich(X0) | ~calm(X0) | funny(X0) [cnf transformation 56]
117. rich(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 56]
119. ~rich(X0) | ~funny(X0) | tall(X0) [cnf transformation 56]
122. ~rich(paul) | generous(X0) | kind(X0) [cnf transformation 60]
130. ~humble(mary) [cnf transformation 22]
131. ~funny(fred) | strong(fred) [cnf transformation 24]
132. humble(fred) [cnf transformation 25]
135. ~brave(X0) | funny(X0) [subsumption resolution 87,88]
136. ~funny(X0) | brave(X0) [subsumption resolution 85,86]
141. 2 <=> humble(mary) [avatar definition]
145. 3 <=> kind(mary) [avatar definition]
147. ~kind(mary) <- (~3) [avatar component clause 145]
150. 4 <=> ! [X0] : (brave(X0) | ~humble(X0)) [avatar definition]
151. ~humble(X0) | brave(X0) <- (4) [avatar component clause 150]
152. 4 | 2 | ~3 [avatar split clause 97,145,141,150]
154. 5 <=> generous(mary) [avatar definition]
156. ~generous(mary) <- (~5) [avatar component clause 154]
157. 3 | ~5 [avatar split clause 105,154,145]
163. ~tall(X0) | happy(X0) [subsumption resolution 108,76]
182. ~tall(X0) | rich(X0) [subsumption resolution 117,103]
183. rich(X0) | funny(X0) [subsumption resolution 116,103]
185. 11 <=> ! [X0] : (generous(X0) | kind(X0)) [avatar definition]
186. kind(X0) | generous(X0) <- (11) [avatar component clause 185]
188. 12 <=> rich(paul) [avatar definition]
190. ~rich(paul) <- (~12) [avatar component clause 188]
191. 11 | ~12 [avatar split clause 122,188,185]
230. ~2 [avatar split clause 130,141]
233. 21 <=> strong(fred) [avatar definition]
237. 22 <=> funny(fred) [avatar definition]
238. funny(fred) <- (22) [avatar component clause 237]
239. ~funny(fred) <- (~22) [avatar component clause 237]
240. 21 | ~22 [avatar split clause 131,237,233]
248. funny(X0) | happy(X0) [resolution 135,76]
451. 48 <=> creative(paul) [avatar definition]
452. ~creative(paul) <- (~48) [avatar component clause 451]
453. creative(paul) <- (48) [avatar component clause 451]
455. 49 <=> generous(paul) [avatar definition]
456. ~generous(paul) <- (~49) [avatar component clause 455]
457. generous(paul) <- (49) [avatar component clause 455]
464. generous(mary) <- (~3, 11) [resolution 186,147]
466. $false <- (~3, ~5, 11) [subsumption resolution 464,156]
467. 3 | 5 | ~11 [avatar contradiction clause 466]
515. brave(fred) <- (4) [resolution 151,132]
534. ~generous(X1) | creative(X1) | funny(X1) [resolution 112,183]
564. ~funny(X0) | tall(X0) | generous(X0) | creative(X0) [resolution 119,110]
569. ~funny(X0) | tall(X0) | creative(X0) [subsumption resolution 564,82]
571. 60 <=> tall(paul) [avatar definition]
572. ~tall(paul) <- (~60) [avatar component clause 571]
573. tall(paul) <- (60) [avatar component clause 571]
575. 61 <=> funny(paul) [avatar definition]
576. funny(paul) <- (61) [avatar component clause 575]
642. funny(fred) <- (4) [resolution 515,135]
646. 22 | ~4 [avatar split clause 642,150,237]
755. 75 <=> generous(fred) [avatar definition]
759. 76 <=> creative(fred) [avatar definition]
761. creative(fred) <- (76) [avatar component clause 759]
764. creative(X0) | funny(X0) | brave(X0) [resolution 534,77]
770. funny(X0) | creative(X0) [subsumption resolution 764,135]
785. tall(X0) | creative(X0) | happy(X0) [resolution 569,248]
786. tall(fred) | creative(fred) <- (22) [resolution 569,238]
788. creative(X0) | happy(X0) [subsumption resolution 785,163]
790. 77 <=> tall(fred) [avatar definition]
792. tall(fred) <- (77) [avatar component clause 790]
793. 76 | 77 | ~22 [avatar split clause 786,237,790,759]
834. rich(paul) <- (60) [resolution 573,182]
868. rich(fred) | ~generous(fred) <- (76) [resolution 761,111]
869. tall(fred) | generous(fred) <- (76) [resolution 761,81]
1008. 75 | 77 | ~76 [avatar split clause 869,759,790,755]
1010. 86 <=> rich(fred) [avatar definition]
1012. rich(fred) <- (86) [avatar component clause 1010]
1013. ~75 | 86 | ~76 [avatar split clause 868,759,1010,755]
1015. rich(fred) <- (77) [resolution 792,182]
1017. 86 | ~77 [avatar split clause 1015,790,1010]
1048. ~strong(fred) <- (86) [resolution 1012,100]
1110. 12 | ~60 [avatar split clause 834,571,188]
1115. ~21 | ~86 [avatar split clause 1048,1010,233]
1150. generous(paul) | creative(paul) <- (~12) [resolution 190,110]
1151. funny(paul) <- (~12) [resolution 190,183]
1156. 61 | 12 [avatar split clause 1151,188,575]
1160. creative(fred) <- (~22) [resolution 239,770]
1166. 76 | 22 [avatar split clause 1160,237,759]
1169. rich(paul) | ~generous(paul) <- (48) [resolution 453,111]
1172. ~generous(paul) <- (~12, 48) [subsumption resolution 1169,190]
1173. $false <- (~12, 48, 49) [subsumption resolution 1172,457]
1174. 12 | ~48 | ~49 [avatar contradiction clause 1173]
1175. happy(paul) <- (~48) [resolution 452,788]
1181. ~brave(paul) | ~happy(paul) <- (49) [resolution 457,78]
1182. ~brave(paul) <- (~48, 49) [subsumption resolution 1181,1175]
1191. brave(paul) <- (61) [resolution 576,136]
1194. $false <- (~48, 49, 61) [subsumption resolution 1191,1182]
1195. 48 | ~49 | ~61 [avatar contradiction clause 1194]
1196. 48 | 49 | 12 [avatar split clause 1150,188,455,451]
1200. tall(paul) | generous(paul) <- (48) [resolution 453,81]
1202. generous(paul) <- (48, ~60) [subsumption resolution 1200,572]
1203. $false <- (48, ~49, ~60) [subsumption resolution 1202,456]
1204. ~48 | 49 | 60 [avatar contradiction clause 1203]
1205. $false [avatar sat refutation 152,157,191,230,240,467,646,793,1008,1013,1017,1110,1115,1156,1166,1174,1195,1196,1204]
% SZS output end Proof for 4641908691391428314910905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or tall then someone is not wise or curious.
Everyone who is either not wise or patient is strong and vice versa.
If someone is not tall then alice is either creative or not old and vice versa.
If someone is not creative then susan is both not kind and rich.
If someone is not tall or not curious then someone is not kind or funny.
If someone is not generous or happy then fred is funny.
Everyone who is strong or calm is both happy and old.
Everyone who is old is strong and vice versa.
Everyone who is both not brave and not curious is both strong and happy and vice versa.
Everyone who is both not humble and tall is both not kind and not humble.
Everyone who is not strong is patient or not curious.
Everyone who is not calm or not curious is both not humble and brave.
Everyone who is old is both not rich and not tall.
Everyone who is either old or not generous is either tall or curious and vice versa.
If someone is either not happy or old then lucy is either not generous or patient.
Everyone who is wise or not brave is either patient or quiet and vice versa.
Someone is both kind and not generous.
Someone is either generous or rich.
Someone is either generous or brave.
John is either not funny or happy. | Alice is not rich. | neutral | ((?[X]:((~strong(X)|tall(X))))=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>strong(X)))&
((?[X]:(~tall(X)))<=>((creative(alice)<~>~old(alice))))&
((?[X]:(~creative(X)))=>((~kind(susan)&rich(susan))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((~generous(X)|happy(X))))=>(funny(fred)))&
(![X]:((strong(X)|calm(X))=>(happy(X)&old(X))))&
(![X]:(old(X)<=>strong(X)))&
(![X]:((~brave(X)&~curious(X))<=>(strong(X)&happy(X))))&
(![X]:((~humble(X)&tall(X))=>(~kind(X)&~humble(X))))&
(![X]:(~strong(X)=>(patient(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~humble(X)&brave(X))))&
(![X]:(old(X)=>(~rich(X)&~tall(X))))&
(![X]:((old(X)<~>~generous(X))<=>(tall(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>old(X))))=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((wise(X)|~brave(X))<=>(patient(X)<~>quiet(X))))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((generous(X)<~>brave(X))))&
((~funny(john)<~>happy(john))) | ~rich(alice) | [] | null | 0 |
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