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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|---|---|---|---|---|---|---|---|
If lucy is either happy or creative then mary is not generous.
Everyone who is generous or patient is both not strong and not patient.
Everyone who is either wise or curious is tall.
If susan is both quiet and humble then alice is not rich or not strong.
Everyone who is not strong is old and vice versa.
Everyone who is either not old or creative is old or wise and vice versa.
Everyone who is both quiet and generous is either humble or not kind.
If someone is not brave then mary is both strong and rich.
If fred is strong or not curious then lucy is both not tall and not kind and vice versa.
If someone is either creative or not calm then paul is not wise.
Everyone who is creative or brave is both kind and not strong and vice versa.
Everyone who is not creative or quiet is calm or not funny and vice versa.
If someone is both not tall and not humble then lucy is not patient or not happy and vice versa.
Everyone who is calm is happy.
If john is both not calm and humble then fred is either strong or not quiet and vice versa.
If paul is either not strong or not kind then john is either humble or patient.
Someone is either not calm or not happy.
Someone is not wise or quiet.
Someone is either humble or not rich.
Paul is either not quiet or not funny.
Someone is not funny or kind.
Someone is old.
Someone is both tall and calm.
Susan is wise. | Paul is kind. | neutral | (((happy(lucy)<~>creative(lucy)))=>(~generous(mary)))&
(![X]:((generous(X)|patient(X))=>(~strong(X)&~patient(X))))&
(![X]:((wise(X)<~>curious(X))=>tall(X)))&
(((quiet(susan)&humble(susan)))=>((~rich(alice)|~strong(alice))))&
(![X]:(~strong(X)<=>old(X)))&
(![X]:((~old(X)<~>creative(X))<=>(old(X)|wise(X))))&
(![X]:((quiet(X)&generous(X))=>(humble(X)<~>~kind(X))))&
((?[X]:(~brave(X)))=>((strong(mary)&rich(mary))))&
(((strong(fred)|~curious(fred)))<=>((~tall(lucy)&~kind(lucy))))&
((?[X]:((creative(X)<~>~calm(X))))=>(~wise(paul)))&
(![X]:((creative(X)|brave(X))<=>(kind(X)&~strong(X))))&
(![X]:((~creative(X)|quiet(X))<=>(calm(X)|~funny(X))))&
((?[X]:((~tall(X)&~humble(X))))<=>((~patient(lucy)|~happy(lucy))))&
(![X]:(calm(X)=>happy(X)))&
(((~calm(john)&humble(john)))<=>((strong(fred)<~>~quiet(fred))))&
(((~strong(paul)<~>~kind(paul)))=>((humble(john)<~>patient(john))))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:((~wise(X)|quiet(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
((~quiet(paul)<~>~funny(paul)))&
(?[X]:((~funny(X)|kind(X))))&
(?[X]:(old(X)))&
(?[X]:((tall(X)&calm(X))))&
(wise(susan)) | kind(paul) | [] | null | 0 |
If alice is not rich or tall then someone is not brave and vice versa. Everyone who is either not old or not rich is both brave and not rich and vice versa. Everyone who is both curious and not kind is both not calm and not happy and vice versa. Everyone who is rich or curious is not tall or wise and vice versa. If someone is happy or tall then alice is rich and vice versa. If someone is both calm and old then someone is patient. If mary is wise or happy then susan is funny and vice versa. If someone is funny then john is either not humble or old and vice versa. If lucy is either not humble or humble then alice is happy. Everyone who is not patient or not kind is both not tall and not curious and vice versa. If susan is not tall then alice is not humble or patient. Everyone who is either not rich or not creative is not quiet or quiet and vice versa. If lucy is generous then someone is brave or not brave and vice versa. Everyone who is curious or not tall is patient. Everyone who is both not humble and generous is both calm and not patient and vice versa. Everyone who is either not calm or brave is kind and vice versa. Mary is tall. Someone is either calm or not creative. Alice is humble or not kind. Someone is either curious or old. Lucy is not wise. Mary is either not generous or not kind. Mary is not old. | Mary is not wise. | neutral | (((~rich(alice)|tall(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(brave(X)&~rich(X))))&
(![X]:((curious(X)&~kind(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)|curious(X))<=>(~tall(X)|wise(X))))&
((?[X]:((happy(X)|tall(X))))<=>(rich(alice)))&
((?[X]:((calm(X)&old(X))))=>(?[X]:(patient(X))))&
(((wise(mary)|happy(mary)))<=>(funny(susan)))&
((?[X]:(funny(X)))<=>((~humble(john)<~>old(john))))&
(((~humble(lucy)<~>humble(lucy)))=>(happy(alice)))&
(![X]:((~patient(X)|~kind(X))<=>(~tall(X)&~curious(X))))&
((~tall(susan))=>((~humble(alice)|patient(alice))))&
(![X]:((~rich(X)<~>~creative(X))<=>(~quiet(X)|quiet(X))))&
((generous(lucy))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((curious(X)|~tall(X))=>patient(X)))&
(![X]:((~humble(X)&generous(X))<=>(calm(X)&~patient(X))))&
(![X]:((~calm(X)<~>brave(X))<=>kind(X)))&
(tall(mary))&
(?[X]:((calm(X)<~>~creative(X))))&
((humble(alice)|~kind(alice)))&
(?[X]:((curious(X)<~>old(X))))&
(~wise(lucy))&
((~generous(mary)<~>~kind(mary)))&
(~old(mary)) | ~wise(mary) | [] | null | 0 |
Everyone who is either not tall or old is both wise and kind and vice versa. If someone is either not wise or not tall then paul is either brave or not wise and vice versa. Everyone who is both not happy and not creative is not old. Everyone who is not rich or not curious is not old or calm. Everyone who is not generous or strong is creative. Everyone who is creative or not funny is quiet. Everyone who is either happy or not old is not quiet and vice versa. If susan is not quiet then mary is either creative or not strong and vice versa. Everyone who is not old is patient. If alice is either old or not patient then someone is not strong and vice versa. If someone is either not patient or not rich then someone is not rich and vice versa. Everyone who is either not quiet or not funny is both not creative and humble. Everyone who is either tall or calm is not wise or not funny. Everyone who is both not funny and kind is not quiet. Everyone who is patient or not strong is not tall or quiet and vice versa. Someone is not brave or not happy. Alice is either not curious or not quiet. Alice is funny. Someone is not kind. Someone is both not calm and not funny. Lucy is generous. | Mary is not curious. | neutral | (![X]:((~tall(X)<~>old(X))<=>(wise(X)&kind(X))))&
((?[X]:((~wise(X)<~>~tall(X))))<=>((brave(paul)<~>~wise(paul))))&
(![X]:((~happy(X)&~creative(X))=>~old(X)))&
(![X]:((~rich(X)|~curious(X))=>(~old(X)|calm(X))))&
(![X]:((~generous(X)|strong(X))=>creative(X)))&
(![X]:((creative(X)|~funny(X))=>quiet(X)))&
(![X]:((happy(X)<~>~old(X))<=>~quiet(X)))&
((~quiet(susan))<=>((creative(mary)<~>~strong(mary))))&
(![X]:(~old(X)=>patient(X)))&
(((old(alice)<~>~patient(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~creative(X)&humble(X))))&
(![X]:((tall(X)<~>calm(X))=>(~wise(X)|~funny(X))))&
(![X]:((~funny(X)&kind(X))=>~quiet(X)))&
(![X]:((patient(X)|~strong(X))<=>(~tall(X)|quiet(X))))&
(?[X]:((~brave(X)|~happy(X))))&
((~curious(alice)<~>~quiet(alice)))&
(funny(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)&~funny(X))))&
(generous(lucy)) | ~curious(mary) | [] | null | 0 |
Everyone who is both humble and not tall is humble. If lucy is both not quiet and strong then alice is both not calm and wise and vice versa. If fred is either not patient or brave then mary is both happy and not rich. If john is not creative then paul is creative or old and vice versa. If susan is not patient then john is not creative. Everyone who is both not rich and strong is not strong and vice versa. If someone is not funny then someone is either not curious or tall. If someone is not generous then mary is both not happy and not generous and vice versa. Everyone who is either not generous or happy is not rich. If fred is quiet then alice is both not tall and not generous. Everyone who is not rich or calm is either quiet or funny and vice versa. Everyone who is wise is not strong and vice versa. If alice is either rich or strong then alice is both not tall and not funny and vice versa. Everyone who is curious or kind is wise. Someone is tall or not quiet. Someone is rich. Someone is either not patient or creative. Mary is both not happy and not curious. Paul is not wise. Someone is generous or not tall. | Alice is curious. | contradiction | (![X]:((humble(X)&~tall(X))=>humble(X)))&
(((~quiet(lucy)&strong(lucy)))<=>((~calm(alice)&wise(alice))))&
(((~patient(fred)<~>brave(fred)))=>((happy(mary)&~rich(mary))))&
((~creative(john))<=>((creative(paul)|old(paul))))&
((~patient(susan))=>(~creative(john)))&
(![X]:((~rich(X)&strong(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:(~generous(X)))<=>((~happy(mary)&~generous(mary))))&
(![X]:((~generous(X)<~>happy(X))=>~rich(X)))&
((quiet(fred))=>((~tall(alice)&~generous(alice))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(?[X]:((tall(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
((~happy(mary)&~curious(mary)))&
(~wise(paul))&
(?[X]:((generous(X)|~tall(X)))) | curious(alice) | [
"p5",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4492248320031522347596298
% SZS output start Proof for 4492248320031522347596298
6. ! [X0] : ((strong(X0) & ~rich(X0)) <=> ~strong(X0)) [input p5]
12. ! [X0] : (wise(X0) <=> ~strong(X0)) [input p11]
14. ! [X0] : ((kind(X0) | curious(X0)) => wise(X0)) [input p13]
21. curious(alice) [input hypothesis]
23. ! [X0] : (curious(X0) => wise(X0)) [pure predicate removal 14]
31. ! [X0] : (wise(X0) | ~curious(X0)) [ennf transformation 23]
37. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | (~strong(X0) | rich(X0)))) [nnf transformation 6]
38. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | ~strong(X0) | rich(X0))) [flattening 37]
51. ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 12]
78. strong(X0) | strong(X0) [cnf transformation 38]
94. ~strong(X0) | ~wise(X0) [cnf transformation 51]
102. wise(X0) | ~curious(X0) [cnf transformation 31]
111. curious(alice) [cnf transformation 21]
113. strong(X0) [duplicate literal removal 78]
220. ~wise(X0) [subsumption resolution 94,113]
228. ~curious(X0) [subsumption resolution 102,220]
258. $false [subsumption resolution 111,228]
% SZS output end Proof for 4492248320031522347596298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not calm then someone is not patient or not old and vice versa.
Everyone who is patient is brave or not funny and vice versa.
Everyone who is either not brave or not patient is creative or not rich.
If someone is either happy or not creative then john is both patient and not rich and vice versa.
If someone is either not humble or not creative then someone is both strong and not strong.
Everyone who is not happy or not patient is both humble and creative.
If someone is brave then fred is either happy or kind and vice versa.
If someone is not generous or old then someone is rich or happy.
Everyone who is not kind or not strong is happy or not funny.
If someone is kind then paul is not quiet.
Everyone who is not rich is generous and vice versa.
Everyone who is either not funny or not patient is not strong or old and vice versa.
If susan is both wise and not strong then susan is wise or not rich.
If mary is either not creative or not strong then someone is both old and not curious.
Everyone who is both tall and creative is both old and not quiet.
Lucy is either not strong or curious.
Fred is not rich.
Paul is old.
Paul is humble.
Susan is both creative and calm.
Alice is both not brave and not creative.
Someone is both not generous and not humble.
Alice is tall. | Fred is funny. | neutral | ((?[X]:((tall(X)<~>~calm(X))))<=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(patient(X)<=>(brave(X)|~funny(X))))&
(![X]:((~brave(X)<~>~patient(X))=>(creative(X)|~rich(X))))&
((?[X]:((happy(X)<~>~creative(X))))<=>((patient(john)&~rich(john))))&
((?[X]:((~humble(X)<~>~creative(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~happy(X)|~patient(X))=>(humble(X)&creative(X))))&
((?[X]:(brave(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)|~funny(X))))&
((?[X]:(kind(X)))=>(~quiet(paul)))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(~strong(X)|old(X))))&
(((wise(susan)&~strong(susan)))=>((wise(susan)|~rich(susan))))&
(((~creative(mary)<~>~strong(mary)))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)&creative(X))=>(old(X)&~quiet(X))))&
((~strong(lucy)<~>curious(lucy)))&
(~rich(fred))&
(old(paul))&
(humble(paul))&
((creative(susan)&calm(susan)))&
((~brave(alice)&~creative(alice)))&
(?[X]:((~generous(X)&~humble(X))))&
(tall(alice)) | funny(fred) | [] | null | 0 |
If john is both humble and creative then someone is not quiet and vice versa. If someone is not wise then someone is kind. Everyone who is kind or brave is not creative or creative and vice versa. If paul is quiet or not wise then someone is not strong. Everyone who is either not kind or rich is not old or not wise and vice versa. Everyone who is brave is not brave. Everyone who is quiet or not old is either not rich or not wise and vice versa. Everyone who is not quiet or wise is both not rich and not kind and vice versa. If fred is not happy then susan is not wise or calm. If mary is not curious or not generous then someone is both not wise and not brave and vice versa. If mary is either not funny or not humble then mary is not old or strong. Everyone who is either not humble or not rich is both curious and not patient. Everyone who is not brave or calm is not humble or not old. If someone is both creative and calm then mary is either not curious or humble. If john is either quiet or not generous then someone is either strong or not wise and vice versa. If paul is not strong or not patient then alice is creative and vice versa. Someone is both humble and calm. Lucy is either wise or tall. Someone is both not old and not wise. Susan is not generous. Mary is calm. John is both not curious and not wise. John is rich. | Mary is not rich. | contradiction | (((humble(john)&creative(john)))<=>(?[X]:(~quiet(X))))&
((?[X]:(~wise(X)))=>(?[X]:(kind(X))))&
(![X]:((kind(X)|brave(X))<=>(~creative(X)|creative(X))))&
(((quiet(paul)|~wise(paul)))=>(?[X]:(~strong(X))))&
(![X]:((~kind(X)<~>rich(X))<=>(~old(X)|~wise(X))))&
(![X]:(brave(X)=>~brave(X)))&
(![X]:((quiet(X)|~old(X))<=>(~rich(X)<~>~wise(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~rich(X)&~kind(X))))&
((~happy(fred))=>((~wise(susan)|calm(susan))))&
(((~curious(mary)|~generous(mary)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(((~funny(mary)<~>~humble(mary)))=>((~old(mary)|strong(mary))))&
(![X]:((~humble(X)<~>~rich(X))=>(curious(X)&~patient(X))))&
(![X]:((~brave(X)|calm(X))=>(~humble(X)|~old(X))))&
((?[X]:((creative(X)&calm(X))))=>((~curious(mary)<~>humble(mary))))&
(((quiet(john)<~>~generous(john)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
(((~strong(paul)|~patient(paul)))<=>(creative(alice)))&
(?[X]:((humble(X)&calm(X))))&
((wise(lucy)<~>tall(lucy)))&
(?[X]:((~old(X)&~wise(X))))&
(~generous(susan))&
(calm(mary))&
((~curious(john)&~wise(john)))&
(rich(john)) | ~rich(mary) | [
"p2",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 182215251595158198794242
% SZS output start Proof for 182215251595158198794242
3. ! [X0] : ((brave(X0) | kind(X0)) <=> (creative(X0) | ~creative(X0))) [input p2]
5. ! [X0] : ((~kind(X0) <~> rich(X0)) <=> (~wise(X0) | ~old(X0))) [input p4]
6. ! [X0] : (brave(X0) => ~brave(X0)) [input p5]
8. ! [X0] : ((wise(X0) | ~quiet(X0)) <=> (~kind(X0) & ~rich(X0))) [input p7]
24. ~rich(mary) [input hypothesis]
29. ! [X0] : (~brave(X0) | ~brave(X0)) [ennf transformation 6]
44. ! [X0] : (((brave(X0) | kind(X0)) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | (~brave(X0) & ~kind(X0)))) [nnf transformation 3]
45. ! [X0] : ((brave(X0) | kind(X0) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | (~brave(X0) & ~kind(X0)))) [flattening 44]
48. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [nnf transformation 5]
49. ! [X0] : ((((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))))) [flattening 48]
52. ! [X0] : (((wise(X0) | ~quiet(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [nnf transformation 8]
53. ! [X0] : ((wise(X0) | ~quiet(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (~wise(X0) & quiet(X0)))) [flattening 52]
79. brave(X0) | kind(X0) | creative(X0) [cnf transformation 45]
80. ~creative(X0) | kind(X0) | brave(X0) [cnf transformation 45]
86. ~kind(X0) | rich(X0) | wise(X0) [cnf transformation 49]
89. ~brave(X0) | ~brave(X0) [cnf transformation 29]
99. ~kind(X0) | ~wise(X0) [cnf transformation 53]
138. ~rich(mary) [cnf transformation 24]
139. ~brave(X0) [duplicate literal removal 89]
166. brave(X0) | kind(X0) [subsumption resolution 79,80]
287. kind(X0) [resolution 166,139]
288. ~wise(X0) [resolution 287,99]
310. rich(X0) | wise(X0) [resolution 86,287]
313. rich(X0) [subsumption resolution 310,288]
315. $false [resolution 313,138]
% SZS output end Proof for 182215251595158198794242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and creative then lucy is either kind or not calm and vice versa.
If susan is not quiet then paul is strong.
If mary is both old and rich then someone is not rich or not happy and vice versa.
If someone is both old and not funny then someone is both not funny and old.
Everyone who is not creative or tall is either calm or not patient and vice versa.
Everyone who is kind or not quiet is either not brave or not funny and vice versa.
If susan is not old or not generous then paul is creative or not curious and vice versa.
If someone is not creative then someone is both not humble and strong.
If someone is not quiet or not brave then lucy is kind or not funny.
Everyone who is both not wise and patient is either patient or not patient and vice versa.
If fred is both brave and creative then susan is quiet.
Everyone who is both patient and not patient is not generous or creative.
Everyone who is either not rich or tall is old.
Everyone who is either not calm or not wise is not rich or not humble.
Everyone who is either not creative or happy is either funny or not patient and vice versa.
If alice is not humble or happy then someone is either not strong or not quiet.
Someone is not old or not happy.
Someone is both not curious and generous.
Someone is rich or not tall.
Someone is not humble.
Someone is strong or happy.
Someone is not rich or patient. | Mary is not curious. | neutral | ((?[X]:((wise(X)&creative(X))))<=>((kind(lucy)<~>~calm(lucy))))&
((~quiet(susan))=>(strong(paul)))&
(((old(mary)&rich(mary)))<=>(?[X]:((~rich(X)|~happy(X)))))&
((?[X]:((old(X)&~funny(X))))=>(?[X]:((~funny(X)&old(X)))))&
(![X]:((~creative(X)|tall(X))<=>(calm(X)<~>~patient(X))))&
(![X]:((kind(X)|~quiet(X))<=>(~brave(X)<~>~funny(X))))&
(((~old(susan)|~generous(susan)))<=>((creative(paul)|~curious(paul))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)&strong(X)))))&
((?[X]:((~quiet(X)|~brave(X))))=>((kind(lucy)|~funny(lucy))))&
(![X]:((~wise(X)&patient(X))<=>(patient(X)<~>~patient(X))))&
(((brave(fred)&creative(fred)))=>(quiet(susan)))&
(![X]:((patient(X)&~patient(X))=>(~generous(X)|creative(X))))&
(![X]:((~rich(X)<~>tall(X))=>old(X)))&
(![X]:((~calm(X)<~>~wise(X))=>(~rich(X)|~humble(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(funny(X)<~>~patient(X))))&
(((~humble(alice)|happy(alice)))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(?[X]:((~old(X)|~happy(X))))&
(?[X]:((~curious(X)&generous(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:(~humble(X)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((~rich(X)|patient(X)))) | ~curious(mary) | [] | null | 0 |
Everyone who is both not wise and humble is funny or calm and vice versa.
Everyone who is not tall is both not patient and happy and vice versa.
Everyone who is not happy or generous is calm or not brave.
Everyone who is not strong or brave is curious or tall and vice versa.
If susan is rich or kind then lucy is either rich or old.
If someone is curious then susan is patient and vice versa.
If someone is both rich and not humble then someone is kind or not quiet and vice versa.
Everyone who is not kind or strong is either generous or old.
Everyone who is patient or quiet is humble.
If susan is not generous or not old then someone is both not wise and not tall.
Everyone who is both not patient and not old is either not quiet or not brave.
Everyone who is either not wise or not patient is either wise or not kind.
If mary is either not curious or rich then someone is both not rich and not old.
If someone is not calm then someone is curious.
If someone is not tall then someone is either kind or creative.
Fred is not quiet or rich.
Paul is not happy.
Someone is both generous and not tall.
Alice is strong or wise.
Someone is either calm or generous.
Susan is both not happy and not rich.
Someone is not old.
Someone is both calm and not brave. | Susan is not rich. | entailment | (![X]:((~wise(X)&humble(X))<=>(funny(X)|calm(X))))&
(![X]:(~tall(X)<=>(~patient(X)&happy(X))))&
(![X]:((~happy(X)|generous(X))=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|brave(X))<=>(curious(X)|tall(X))))&
(((rich(susan)|kind(susan)))=>((rich(lucy)<~>old(lucy))))&
((?[X]:(curious(X)))<=>(patient(susan)))&
((?[X]:((rich(X)&~humble(X))))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((~kind(X)|strong(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)|quiet(X))=>humble(X)))&
(((~generous(susan)|~old(susan)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((~patient(X)&~old(X))=>(~quiet(X)<~>~brave(X))))&
(![X]:((~wise(X)<~>~patient(X))=>(wise(X)<~>~kind(X))))&
(((~curious(mary)<~>rich(mary)))=>(?[X]:((~rich(X)&~old(X)))))&
((?[X]:(~calm(X)))=>(?[X]:(curious(X))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)<~>creative(X)))))&
((~quiet(fred)|rich(fred)))&
(~happy(paul))&
(?[X]:((generous(X)&~tall(X))))&
((strong(alice)|wise(alice)))&
(?[X]:((calm(X)<~>generous(X))))&
((~happy(susan)&~rich(susan)))&
(?[X]:(~old(X)))&
(?[X]:((calm(X)&~brave(X)))) | ~rich(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1121151542961365971650097
% SZS output start Proof for 1121151542961365971650097
21. ~rich(susan) & ~happy(susan) [input p20]
24. rich(susan) [input hypothesis]
136. ~rich(susan) [cnf transformation 21]
140. rich(susan) [cnf transformation 24]
157. 4 <=> rich(susan) [avatar definition]
295. ~4 [avatar split clause 136,157]
296. 4 [avatar split clause 140,157]
297. $false [avatar sat refutation 295,296]
% SZS output end Proof for 1121151542961365971650097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or quiet is either tall or not old.
If someone is quiet or calm then alice is both wise and not quiet.
If someone is not tall then someone is quiet or not calm.
If someone is not quiet then someone is kind or not calm.
Everyone who is not patient is generous and vice versa.
Everyone who is both strong and not strong is wise or brave and vice versa.
If someone is both humble and happy then john is both not patient and not creative.
Everyone who is not brave is either not curious or patient and vice versa.
Everyone who is not kind or happy is not wise or not rich and vice versa.
Everyone who is both funny and kind is not tall or kind.
If someone is both old and not old then susan is not brave or not strong.
If susan is happy or brave then alice is patient.
Everyone who is patient or creative is both not patient and generous.
Everyone who is not curious or rich is both tall and creative and vice versa.
Everyone who is both kind and humble is not curious.
John is kind.
Paul is not brave.
Someone is either humble or generous.
Someone is kind.
Alice is both not rich and humble.
Fred is funny or not old.
Someone is either funny or quiet. | Fred is wise. | contradiction | (![X]:((~kind(X)<~>quiet(X))=>(tall(X)<~>~old(X))))&
((?[X]:((quiet(X)|calm(X))))=>((wise(alice)&~quiet(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:(~patient(X)<=>generous(X)))&
(![X]:((strong(X)&~strong(X))<=>(wise(X)|brave(X))))&
((?[X]:((humble(X)&happy(X))))=>((~patient(john)&~creative(john))))&
(![X]:(~brave(X)<=>(~curious(X)<~>patient(X))))&
(![X]:((~kind(X)|happy(X))<=>(~wise(X)|~rich(X))))&
(![X]:((funny(X)&kind(X))=>(~tall(X)|kind(X))))&
((?[X]:((old(X)&~old(X))))=>((~brave(susan)|~strong(susan))))&
(((happy(susan)|brave(susan)))=>(patient(alice)))&
(![X]:((patient(X)|creative(X))=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)|rich(X))<=>(tall(X)&creative(X))))&
(![X]:((kind(X)&humble(X))=>~curious(X)))&
(kind(john))&
(~brave(paul))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(kind(X)))&
((~rich(alice)&humble(alice)))&
((funny(fred)|~old(fred)))&
(?[X]:((funny(X)<~>quiet(X)))) | wise(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7779449561296164797621056
% SZS output start Proof for 7779449561296164797621056
6. ! [X0] : ((~strong(X0) & strong(X0)) <=> (brave(X0) | wise(X0))) [input p5]
23. wise(fred) [input hypothesis]
42. ! [X0] : (((~strong(X0) & strong(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 6]
43. ! [X0] : (((~strong(X0) & strong(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | strong(X0) | ~strong(X0))) [flattening 42]
66. strong(X0) | ~wise(X0) [cnf transformation 43]
68. ~strong(X0) | ~wise(X0) [cnf transformation 43]
104. wise(fred) [cnf transformation 23]
120. ~wise(X0) [subsumption resolution 66,68]
167. $false [subsumption resolution 104,120]
% SZS output end Proof for 7779449561296164797621056
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not wise is both calm and humble and vice versa.
Everyone who is not old is creative or not patient.
Everyone who is not old is both generous and not brave and vice versa.
Everyone who is old or not funny is either old or calm.
Everyone who is either rich or not tall is either patient or not brave and vice versa.
Everyone who is both funny and rich is both not calm and not generous and vice versa.
Everyone who is both not calm and curious is either not calm or calm and vice versa.
If fred is both not old and brave then someone is both wise and not quiet.
Everyone who is creative is either not humble or wise.
If someone is old or patient then someone is creative.
If susan is not quiet then someone is either generous or calm and vice versa.
Everyone who is not brave or humble is wise and vice versa.
Everyone who is both not strong and old is either not strong or curious.
If paul is either not kind or quiet then someone is both quiet and patient.
If john is funny then susan is both not curious and creative and vice versa.
If someone is funny or rich then alice is tall or rich.
Someone is not patient.
Mary is not brave.
Alice is not happy.
Someone is not wise or patient.
John is generous.
Someone is kind.
Someone is either creative or curious.
Paul is either not curious or not tall. | Mary is wise. | entailment | (![X]:((~humble(X)|~wise(X))<=>(calm(X)&humble(X))))&
(![X]:(~old(X)=>(creative(X)|~patient(X))))&
(![X]:(~old(X)<=>(generous(X)&~brave(X))))&
(![X]:((old(X)|~funny(X))=>(old(X)<~>calm(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&rich(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~calm(X)&curious(X))<=>(~calm(X)<~>calm(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:(creative(X)=>(~humble(X)<~>wise(X))))&
((?[X]:((old(X)|patient(X))))=>(?[X]:(creative(X))))&
((~quiet(susan))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((~brave(X)|humble(X))<=>wise(X)))&
(![X]:((~strong(X)&old(X))=>(~strong(X)<~>curious(X))))&
(((~kind(paul)<~>quiet(paul)))=>(?[X]:((quiet(X)&patient(X)))))&
((funny(john))<=>((~curious(susan)&creative(susan))))&
((?[X]:((funny(X)|rich(X))))=>((tall(alice)|rich(alice))))&
(?[X]:(~patient(X)))&
(~brave(mary))&
(~happy(alice))&
(?[X]:((~wise(X)|patient(X))))&
(generous(john))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>curious(X))))&
((~curious(paul)<~>~tall(paul))) | wise(mary) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3006441783187230760385605
% SZS output start Proof for 3006441783187230760385605
1. ! [X0] : ((~wise(X0) | ~humble(X0)) <=> (humble(X0) & calm(X0))) [input p0]
12. ! [X0] : ((humble(X0) | ~brave(X0)) <=> wise(X0)) [input p11]
25. ~wise(mary) [input hypothesis]
40. ! [X0] : (((~wise(X0) | ~humble(X0)) | (~humble(X0) | ~calm(X0))) & ((humble(X0) & calm(X0)) | (wise(X0) & humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((~wise(X0) | ~humble(X0) | ~humble(X0) | ~calm(X0)) & ((humble(X0) & calm(X0)) | (wise(X0) & humble(X0)))) [flattening 40]
60. ! [X0] : (((humble(X0) | ~brave(X0)) | ~wise(X0)) & (wise(X0) | (~humble(X0) & brave(X0)))) [nnf transformation 12]
61. ! [X0] : ((humble(X0) | ~brave(X0) | ~wise(X0)) & (wise(X0) | (~humble(X0) & brave(X0)))) [flattening 60]
80. humble(X0) | humble(X0) [cnf transformation 41]
120. wise(X0) | ~humble(X0) [cnf transformation 61]
142. ~wise(mary) [cnf transformation 25]
151. humble(X0) [duplicate literal removal 80]
182. wise(X0) [subsumption resolution 120,151]
234. $false [subsumption resolution 142,182]
% SZS output end Proof for 3006441783187230760385605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or funny then susan is either not rich or humble and vice versa. Everyone who is both rich and creative is not patient. If alice is both not quiet and not tall then someone is kind. If mary is wise or brave then paul is not brave. Everyone who is both kind and not tall is either not wise or humble and vice versa. Everyone who is both not calm and old is old or curious and vice versa. Everyone who is both not old and creative is both not curious and kind and vice versa. If susan is both old and not curious then paul is happy or not generous and vice versa. If mary is both not generous and tall then someone is either not curious or not happy. Everyone who is not curious or not old is both calm and creative and vice versa. If fred is tall or not patient then mary is not rich and vice versa. Everyone who is not generous or generous is either not kind or rich and vice versa. Everyone who is calm is patient and vice versa. If someone is not wise or kind then someone is either happy or wise and vice versa. If someone is not strong or wise then paul is both not tall and humble. If fred is both strong and funny then susan is not quiet and vice versa. Someone is both not brave and not wise. Someone is both not wise and creative. Lucy is either old or not strong. Someone is both strong and not brave. Lucy is not quiet. Someone is either not tall or generous. | Susan is not curious. | contradiction | ((?[X]:((old(X)<~>funny(X))))<=>((~rich(susan)<~>humble(susan))))&
(![X]:((rich(X)&creative(X))=>~patient(X)))&
(((~quiet(alice)&~tall(alice)))=>(?[X]:(kind(X))))&
(((wise(mary)|brave(mary)))=>(~brave(paul)))&
(![X]:((kind(X)&~tall(X))<=>(~wise(X)<~>humble(X))))&
(![X]:((~calm(X)&old(X))<=>(old(X)|curious(X))))&
(![X]:((~old(X)&creative(X))<=>(~curious(X)&kind(X))))&
(((old(susan)&~curious(susan)))<=>((happy(paul)|~generous(paul))))&
(((~generous(mary)&tall(mary)))=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:((~curious(X)|~old(X))<=>(calm(X)&creative(X))))&
(((tall(fred)|~patient(fred)))<=>(~rich(mary)))&
(![X]:((~generous(X)|generous(X))<=>(~kind(X)<~>rich(X))))&
(![X]:(calm(X)<=>patient(X)))&
((?[X]:((~wise(X)|kind(X))))<=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:((~strong(X)|wise(X))))=>((~tall(paul)&humble(paul))))&
(((strong(fred)&funny(fred)))<=>(~quiet(susan)))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:((~wise(X)&creative(X))))&
((old(lucy)<~>~strong(lucy)))&
(?[X]:((strong(X)&~brave(X))))&
(~quiet(lucy))&
(?[X]:((~tall(X)<~>generous(X)))) | ~curious(susan) | [
"p1",
"p5",
"p6",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7517369525443535410639115
% SZS output start Proof for 7517369525443535410639115
2. ! [X0] : ((creative(X0) & rich(X0)) => ~patient(X0)) [input p1]
6. ! [X0] : ((old(X0) & ~calm(X0)) <=> (curious(X0) | old(X0))) [input p5]
7. ! [X0] : ((creative(X0) & ~old(X0)) <=> (kind(X0) & ~curious(X0))) [input p6]
10. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (creative(X0) & calm(X0))) [input p9]
12. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (~kind(X0) <~> rich(X0))) [input p11]
13. ! [X0] : (calm(X0) <=> patient(X0)) [input p12]
23. ~curious(susan) [input hypothesis]
28. ! [X0] : (~patient(X0) | (~creative(X0) | ~rich(X0))) [ennf transformation 2]
29. ! [X0] : (~patient(X0) | ~creative(X0) | ~rich(X0)) [flattening 28]
43. ! [X0] : (((old(X0) & ~calm(X0)) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 6]
44. ! [X0] : (((old(X0) & ~calm(X0)) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | ~old(X0) | calm(X0))) [flattening 43]
45. ! [X0] : (((creative(X0) & ~old(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (~creative(X0) | old(X0)))) [nnf transformation 7]
46. ! [X0] : (((creative(X0) & ~old(X0)) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | ~creative(X0) | old(X0))) [flattening 45]
52. ! [X0] : (((~old(X0) | ~curious(X0)) | (~creative(X0) | ~calm(X0))) & ((creative(X0) & calm(X0)) | (old(X0) & curious(X0)))) [nnf transformation 10]
53. ! [X0] : ((~old(X0) | ~curious(X0) | ~creative(X0) | ~calm(X0)) & ((creative(X0) & calm(X0)) | (old(X0) & curious(X0)))) [flattening 52]
56. ! [X0] : (((generous(X0) | ~generous(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~generous(X0) & generous(X0)))) [nnf transformation 12]
57. ! [X0] : ((generous(X0) | ~generous(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (~generous(X0) & generous(X0)))) [flattening 56]
58. ! [X0] : ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))) [nnf transformation 13]
84. ~patient(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 29]
93. ~calm(X0) | ~old(X0) [cnf transformation 44]
98. ~creative(X0) | kind(X0) | old(X0) [cnf transformation 46]
108. curious(X0) | calm(X0) [cnf transformation 53]
109. calm(X0) | old(X0) [cnf transformation 53]
111. creative(X0) | old(X0) [cnf transformation 53]
116. rich(X0) | ~kind(X0) | generous(X0) [cnf transformation 57]
117. ~generous(X0) | ~kind(X0) | rich(X0) [cnf transformation 57]
122. ~calm(X0) | patient(X0) [cnf transformation 58]
146. ~curious(susan) [cnf transformation 23]
195. 11 <=> curious(susan) [avatar definition]
197. ~curious(susan) <- (~11) [avatar component clause 195]
245. ~kind(X0) | rich(X0) [subsumption resolution 116,117]
333. ~11 [avatar split clause 146,195]
334. calm(susan) <- (~11) [resolution 108,197]
337. ~old(susan) <- (~11) [resolution 334,93]
343. patient(X0) | old(X0) [resolution 122,109]
349. old(X0) | ~creative(X0) | ~rich(X0) [resolution 343,84]
351. old(X0) | ~rich(X0) [subsumption resolution 349,111]
398. kind(X0) | old(X0) | old(X0) [resolution 98,111]
400. kind(X0) | old(X0) [duplicate literal removal 398]
472. old(X3) | rich(X3) [resolution 400,245]
474. old(X3) [subsumption resolution 472,351]
485. $false <- (~11) [subsumption resolution 337,474]
486. 11 [avatar contradiction clause 485]
487. $false [avatar sat refutation 333,486]
% SZS output end Proof for 7517369525443535410639115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not calm then someone is both not patient and not tall and vice versa. If someone is either brave or humble then someone is either not old or not quiet and vice versa. Everyone who is either old or calm is humble and vice versa. Everyone who is not creative is either curious or funny. Everyone who is both not generous and old is creative or calm. Everyone who is either not strong or quiet is both calm and rich and vice versa. If someone is humble then fred is both kind and not creative. Everyone who is tall is not quiet or strong and vice versa. If someone is both happy and not calm then john is both not funny and curious. Everyone who is both tall and rich is both generous and not wise. Everyone who is not funny is both funny and calm and vice versa. If someone is both funny and quiet then someone is both not happy and not kind. If someone is happy or calm then someone is not rich or tall. Everyone who is not humble is both not happy and kind and vice versa. Everyone who is either creative or not brave is not strong. If susan is patient or not wise then someone is either tall or wise. Alice is either brave or not calm. John is either brave or not brave. Someone is both not humble and tall. Lucy is both not kind and strong. Someone is old or not brave. Mary is either not calm or patient. Susan is not happy. | Fred is creative. | contradiction | ((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((brave(X)<~>humble(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((old(X)<~>calm(X))<=>humble(X)))&
(![X]:(~creative(X)=>(curious(X)<~>funny(X))))&
(![X]:((~generous(X)&old(X))=>(creative(X)|calm(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>(calm(X)&rich(X))))&
((?[X]:(humble(X)))=>((kind(fred)&~creative(fred))))&
(![X]:(tall(X)<=>(~quiet(X)|strong(X))))&
((?[X]:((happy(X)&~calm(X))))=>((~funny(john)&curious(john))))&
(![X]:((tall(X)&rich(X))=>(generous(X)&~wise(X))))&
(![X]:(~funny(X)<=>(funny(X)&calm(X))))&
((?[X]:((funny(X)&quiet(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(~humble(X)<=>(~happy(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))=>~strong(X)))&
(((patient(susan)|~wise(susan)))=>(?[X]:((tall(X)<~>wise(X)))))&
((brave(alice)<~>~calm(alice)))&
((brave(john)<~>~brave(john)))&
(?[X]:((~humble(X)&tall(X))))&
((~kind(lucy)&strong(lucy)))&
(?[X]:((old(X)|~brave(X))))&
((~calm(mary)<~>patient(mary)))&
(~happy(susan)) | creative(fred) | [
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8526814817278429320596473
% SZS output start Proof for 8526814817278429320596473
7. ? [X0] : humble(X0) => (~creative(fred) & kind(fred)) [input p6]
14. ! [X0] : (~humble(X0) <=> (kind(X0) & ~happy(X0))) [input p13]
20. strong(lucy) & ~kind(lucy) [input p19]
24. creative(fred) [input hypothesis]
32. (~creative(fred) & kind(fred)) | ! [X0] : ~humble(X0) [ennf transformation 7]
64. ! [X0] : ((~humble(X0) | (~kind(X0) | happy(X0))) & ((kind(X0) & ~happy(X0)) | humble(X0))) [nnf transformation 14]
65. ! [X0] : ((~humble(X0) | ~kind(X0) | happy(X0)) & ((kind(X0) & ~happy(X0)) | humble(X0))) [flattening 64]
103. ~creative(fred) | ~humble(X0) [cnf transformation 32]
118. kind(X0) | humble(X0) [cnf transformation 65]
132. ~kind(lucy) [cnf transformation 20]
138. creative(fred) [cnf transformation 24]
208. 16 <=> ! [X0] : ~humble(X0) [avatar definition]
209. ~humble(X0) <- (16) [avatar component clause 208]
211. 17 <=> creative(fred) [avatar definition]
214. 16 | ~17 [avatar split clause 103,211,208]
313. 17 [avatar split clause 138,211]
319. humble(lucy) [resolution 118,132]
321. $false <- (16) [subsumption resolution 319,209]
322. ~16 [avatar contradiction clause 321]
325. $false [avatar sat refutation 214,313,322]
% SZS output end Proof for 8526814817278429320596473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is creative or patient.
If susan is old then someone is both not kind and happy and vice versa.
If someone is tall then paul is not rich or not old.
If someone is not happy or funny then someone is both not creative and brave and vice versa.
Everyone who is either tall or not tall is generous or old.
If someone is either not calm or old then john is 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.
Alice is wise or strong.
Someone is both not kind and not calm.
Someone is not generous or old.
Lucy is happy.
Mary is both strong and brave.
Someone is either happy or curious.
Paul is kind or happy.
Someone is both not generous and not brave. | Lucy is strong. | neutral | (![X]:(brave(X)=>(creative(X)|patient(X))))&
((old(susan))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:(tall(X)))=>((~rich(paul)|~old(paul))))&
((?[X]:((~happy(X)|funny(X))))<=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:((tall(X)<~>~tall(X))=>(generous(X)|old(X))))&
((?[X]:((~calm(X)<~>old(X))))=>((happy(john)|kind(john))))&
(![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))))&
((wise(alice)|strong(alice)))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((~generous(X)|old(X))))&
(happy(lucy))&
((strong(mary)&brave(mary)))&
(?[X]:((happy(X)<~>curious(X))))&
((kind(paul)|happy(paul)))&
(?[X]:((~generous(X)&~brave(X)))) | strong(lucy) | [] | null | 0 |
If alice is both not rich and strong then someone is both curious and rich.
If john is not old then someone is both creative and wise.
Everyone who is both humble and calm is either humble or rich and vice versa.
Everyone who is tall is both patient and old.
Everyone who is not creative or creative is not quiet.
Everyone who is not strong is both kind and happy and vice versa.
If someone is either not patient or kind then alice is not old or not humble.
If john is curious then someone is both rich and not generous.
If someone is not tall or curious then alice is not kind or not quiet.
Everyone who is both rich and generous is not happy and vice versa.
If alice is creative or funny then susan is old and vice versa.
Everyone who is both calm and funny is not brave or not happy and vice versa.
If someone is strong then alice is either wise or not tall and vice versa.
Everyone who is either quiet or brave is creative and vice versa.
Everyone who is either not tall or not patient is not generous or not creative.
If mary is either not curious or generous then someone is creative and vice versa.
Someone is humble or not strong.
Paul is both happy and brave.
Lucy is calm or generous.
Someone is either not happy or not kind.
John is either generous or not happy.
Someone is curious or not generous.
Someone is either not generous or not kind. | Lucy is happy. | entailment | (((~rich(alice)&strong(alice)))=>(?[X]:((curious(X)&rich(X)))))&
((~old(john))=>(?[X]:((creative(X)&wise(X)))))&
(![X]:((humble(X)&calm(X))<=>(humble(X)<~>rich(X))))&
(![X]:(tall(X)=>(patient(X)&old(X))))&
(![X]:((~creative(X)|creative(X))=>~quiet(X)))&
(![X]:(~strong(X)<=>(kind(X)&happy(X))))&
((?[X]:((~patient(X)<~>kind(X))))=>((~old(alice)|~humble(alice))))&
((curious(john))=>(?[X]:((rich(X)&~generous(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((~kind(alice)|~quiet(alice))))&
(![X]:((rich(X)&generous(X))<=>~happy(X)))&
(((creative(alice)|funny(alice)))<=>(old(susan)))&
(![X]:((calm(X)&funny(X))<=>(~brave(X)|~happy(X))))&
((?[X]:(strong(X)))<=>((wise(alice)<~>~tall(alice))))&
(![X]:((quiet(X)<~>brave(X))<=>creative(X)))&
(![X]:((~tall(X)<~>~patient(X))=>(~generous(X)|~creative(X))))&
(((~curious(mary)<~>generous(mary)))<=>(?[X]:(creative(X))))&
(?[X]:((humble(X)|~strong(X))))&
((happy(paul)&brave(paul)))&
((calm(lucy)|generous(lucy)))&
(?[X]:((~happy(X)<~>~kind(X))))&
((generous(john)<~>~happy(john)))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~generous(X)<~>~kind(X)))) | happy(lucy) | [
"p2",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 989814047620150740466613
% SZS output start Proof for 989814047620150740466613
3. ! [X0] : ((calm(X0) & humble(X0)) <=> (humble(X0) <~> rich(X0))) [input p2]
10. ! [X0] : ((generous(X0) & rich(X0)) <=> ~happy(X0)) [input p9]
12. ! [X0] : ((funny(X0) & calm(X0)) <=> (~happy(X0) | ~brave(X0))) [input p11]
24. ~happy(lucy) [input hypothesis]
41. ! [X0] : (((calm(X0) & humble(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | (~calm(X0) | ~humble(X0)))) [nnf transformation 3]
42. ! [X0] : (((calm(X0) & humble(X0)) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ~calm(X0) | ~humble(X0))) [flattening 41]
48. ! [X0] : (((generous(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (~generous(X0) | ~rich(X0)))) [nnf transformation 10]
49. ! [X0] : (((generous(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | ~generous(X0) | ~rich(X0))) [flattening 48]
52. ! [X0] : (((funny(X0) & calm(X0)) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 12]
53. ! [X0] : (((funny(X0) & calm(X0)) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | ~funny(X0) | ~calm(X0))) [flattening 52]
80. ~rich(X0) | ~humble(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 42]
82. humble(X0) | humble(X0) | ~rich(X0) [cnf transformation 42]
99. happy(X0) | rich(X0) [cnf transformation 49]
106. happy(X0) | calm(X0) [cnf transformation 53]
134. ~happy(lucy) [cnf transformation 24]
135. ~rich(X0) | ~humble(X0) | ~calm(X0) [duplicate literal removal 80]
136. ~rich(X0) | humble(X0) [duplicate literal removal 82]
169. ~calm(X0) | ~rich(X0) [subsumption resolution 135,136]
266. 28 <=> calm(lucy) [avatar definition]
268. calm(lucy) <- (28) [avatar component clause 266]
308. rich(lucy) [resolution 99,134]
311. calm(lucy) [resolution 106,134]
314. ~rich(lucy) <- (28) [resolution 169,268]
315. $false <- (28) [subsumption resolution 314,308]
316. ~28 [avatar contradiction clause 315]
317. 28 [avatar split clause 311,266]
318. $false [avatar sat refutation 316,317]
% SZS output end Proof for 989814047620150740466613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If fred is both calm and not calm then someone is either kind or generous and vice versa.
Everyone who is either kind or happy is calm or kind and vice versa.
If someone is strong or old then someone is either not funny or strong.
Everyone who is strong or wise is patient and vice versa.
If someone is not rich or not generous then alice is not old.
If someone is strong or patient then alice is curious or brave and vice versa.
Everyone who is both not calm and not tall is either not kind or not wise and vice versa.
If someone is not generous or not old then mary is funny and vice versa.
If someone is tall or curious then alice is both patient and not strong.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is not generous or not curious is both kind and patient and vice versa.
Everyone who is either calm or not tall is strong.
Everyone who is tall is both curious and not creative and vice versa.
Everyone who is either not rich or rich is both not wise and old and vice versa.
Everyone who is not creative is either funny or not wise and vice versa.
Someone is not curious or patient.
Someone is not quiet or strong.
Someone is old or not creative.
Someone is either curious or not curious.
Susan is generous or not patient. | Mary is not calm. | entailment | (((calm(fred)&~calm(fred)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((kind(X)<~>happy(X))<=>(calm(X)|kind(X))))&
((?[X]:((strong(X)|old(X))))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((strong(X)|wise(X))<=>patient(X)))&
((?[X]:((~rich(X)|~generous(X))))=>(~old(alice)))&
((?[X]:((strong(X)|patient(X))))<=>((curious(alice)|brave(alice))))&
(![X]:((~calm(X)&~tall(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((~generous(X)|~old(X))))<=>(funny(mary)))&
((?[X]:((tall(X)|curious(X))))=>((patient(alice)&~strong(alice))))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((~generous(X)|~curious(X))<=>(kind(X)&patient(X))))&
(![X]:((calm(X)<~>~tall(X))=>strong(X)))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~wise(X)&old(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~wise(X))))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
((generous(susan)|~patient(susan))) | ~calm(mary) | [
"p0",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 608569109519521794945912
% SZS output start Proof for 608569109519521794945912
1. (~calm(fred) & calm(fred)) <=> ? [X0] : (kind(X0) <~> generous(X0)) [input p0]
5. ? [X0] : (~generous(X0) | ~rich(X0)) => ~old(alice) [input p4]
7. ! [X0] : ((~tall(X0) & ~calm(X0)) <=> (~kind(X0) <~> ~wise(X0))) [input p6]
14. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (old(X0) & ~wise(X0))) [input p13]
21. calm(mary) [input hypothesis]
25. ~old(alice) | ! [X0] : (generous(X0) & rich(X0)) [ennf transformation 5]
28. ((~calm(fred) & calm(fred)) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (? [X0] : ((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | (calm(fred) | ~calm(fred))) [nnf transformation 1]
29. ((~calm(fred) & calm(fred)) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (? [X0] : ((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | calm(fred) | ~calm(fred)) [flattening 28]
30. ((~calm(fred) & calm(fred)) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (? [X1] : ((~generous(X1) | ~kind(X1)) & (generous(X1) | kind(X1))) | calm(fred) | ~calm(fred)) [rectify 29]
31. ? [X1] : ((~generous(X1) | ~kind(X1)) & (generous(X1) | kind(X1))) => ((~generous(sK0) | ~kind(sK0)) & (generous(sK0) | kind(sK0))) [choice axiom]
32. ((~calm(fred) & calm(fred)) | ! [X0] : ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (((~generous(sK0) | ~kind(sK0)) & (generous(sK0) | kind(sK0))) | calm(fred) | ~calm(fred)) [skolemisation 30,31]
46. ! [X0] : (((~tall(X0) & ~calm(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (tall(X0) | calm(X0)))) [nnf transformation 7]
47. ! [X0] : (((~tall(X0) & ~calm(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0)))) & (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | tall(X0) | calm(X0))) [flattening 46]
57. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 14]
58. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 57]
70. calm(fred) | kind(X0) | ~generous(X0) [cnf transformation 32]
72. ~calm(fred) | kind(X0) | ~generous(X0) [cnf transformation 32]
87. ~old(alice) | generous(X0) [cnf transformation 25]
95. ~kind(X0) | ~calm(X0) | wise(X0) [cnf transformation 47]
115. ~wise(X0) | rich(X0) | rich(X0) [cnf transformation 58]
116. ~wise(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
117. old(X0) | rich(X0) | rich(X0) [cnf transformation 58]
118. old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
130. calm(mary) [cnf transformation 21]
131. ~wise(X0) | rich(X0) [duplicate literal removal 115]
132. ~rich(X0) | ~wise(X0) [duplicate literal removal 116]
133. old(X0) | rich(X0) [duplicate literal removal 117]
134. ~rich(X0) | old(X0) [duplicate literal removal 118]
138. 1 <=> ! [X0] : (kind(X0) | ~generous(X0)) [avatar definition]
139. kind(X0) | ~generous(X0) <- (1) [avatar component clause 138]
141. 2 <=> calm(fred) [avatar definition]
144. 1 | ~2 [avatar split clause 72,141,138]
149. 1 | 2 [avatar split clause 70,141,138]
171. 8 <=> ! [X0] : generous(X0) [avatar definition]
172. generous(X0) <- (8) [avatar component clause 171]
174. 9 <=> old(alice) [avatar definition]
176. ~old(alice) <- (~9) [avatar component clause 174]
177. 8 | ~9 [avatar split clause 87,174,171]
217. 18 <=> ! [X1] : old(X1) [avatar definition]
218. old(X1) <- (18) [avatar component clause 217]
239. old(X0) [subsumption resolution 133,134]
240. 18 [avatar split clause 239,217]
241. ~wise(X0) [subsumption resolution 131,132]
257. $false <- (~9, 18) [subsumption resolution 176,218]
258. 9 | ~18 [avatar contradiction clause 257]
259. kind(X0) <- (1, 8) [subsumption resolution 139,172]
273. ~calm(X0) | wise(X0) <- (1, 8) [resolution 95,259]
274. ~calm(X0) <- (1, 8) [subsumption resolution 273,241]
276. $false <- (1, 8) [resolution 274,130]
277. ~1 | ~8 [avatar contradiction clause 276]
278. $false [avatar sat refutation 144,149,177,240,258,277]
% SZS output end Proof for 608569109519521794945912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or tall is wise and vice versa.
Everyone who is either not kind or not old is either quiet or not calm.
If lucy is not creative or kind then someone is either not rich or not old and vice versa.
If someone is kind then someone is not rich or tall and vice versa.
If someone is either not calm or not happy then john is not brave or not quiet and vice versa.
If john is either not funny or kind then susan is both happy and not humble and vice versa.
Everyone who is not wise or not rich is either humble or tall and vice versa.
Everyone who is both curious and not happy is kind and vice versa.
If paul is both tall and brave then someone is either strong or old and vice versa.
Everyone who is humble is both old and happy and vice versa.
Everyone who is quiet is both not curious and not old and vice versa.
If someone is brave then someone is not humble or not brave and vice versa.
If someone is not happy or not calm then paul is either rich or tall and vice versa.
If someone is not creative then john is either tall or curious.
If someone is kind then someone is either generous or not wise and vice versa.
Alice is not humble.
Susan is both creative and brave.
Someone is creative.
Someone is either old or not generous.
Someone is not creative or kind.
Someone is not happy or not humble.
Someone is not kind. | Alice is tall. | entailment | (![X]:((~wise(X)|tall(X))<=>wise(X)))&
(![X]:((~kind(X)<~>~old(X))=>(quiet(X)<~>~calm(X))))&
(((~creative(lucy)|kind(lucy)))<=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:(kind(X)))<=>(?[X]:((~rich(X)|tall(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>((~brave(john)|~quiet(john))))&
(((~funny(john)<~>kind(john)))<=>((happy(susan)&~humble(susan))))&
(![X]:((~wise(X)|~rich(X))<=>(humble(X)<~>tall(X))))&
(![X]:((curious(X)&~happy(X))<=>kind(X)))&
(((tall(paul)&brave(paul)))<=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:(humble(X)<=>(old(X)&happy(X))))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
((?[X]:(~creative(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)<~>~wise(X)))))&
(~humble(alice))&
((creative(susan)&brave(susan)))&
(?[X]:(creative(X)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:(~kind(X))) | tall(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2003670922358084311721849
% SZS output start Proof for 2003670922358084311721849
1. ! [X0] : ((tall(X0) | ~wise(X0)) <=> wise(X0)) [input p0]
23. ~tall(alice) [input hypothesis]
29. ! [X0] : (((tall(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) & wise(X0)))) [nnf transformation 1]
30. ! [X0] : ((tall(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~tall(X0) & wise(X0)))) [flattening 29]
88. wise(X0) | wise(X0) [cnf transformation 30]
90. tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 30]
161. ~tall(alice) [cnf transformation 23]
162. wise(X0) [duplicate literal removal 88]
163. ~wise(X0) | tall(X0) [duplicate literal removal 90]
409. tall(X0) [resolution 163,162]
410. $false [resolution 409,161]
% SZS output end Proof for 2003670922358084311721849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not tall is both not calm and rich. Everyone who is not quiet or not humble is either old or quiet. Everyone who is not generous is funny. If susan is not creative then someone is not brave. Everyone who is calm or not humble is wise. If someone is kind then alice is either quiet or not kind. Everyone who is not old is not brave. Everyone who is humble or not brave is both not happy and happy. Everyone who is not brave or happy is not patient or strong and vice versa. Everyone who is both old and calm is either kind or not patient and vice versa. If someone is either not happy or quiet then someone is curious or funny. Everyone who is both not curious and funny is both wise and not patient. Everyone who is not generous is both funny and curious and vice versa. Everyone who is both not rich and calm is generous or not rich. Everyone who is not rich is both creative and not rich and vice versa. Alice is curious. Someone is either creative or not humble. Someone is not funny. Someone is curious or creative. Someone is not funny or not kind. Susan is curious or not generous. Someone is both kind and funny. | Susan is generous. | neutral | (![X]:((strong(X)|~tall(X))=>(~calm(X)&rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>(old(X)<~>quiet(X))))&
(![X]:(~generous(X)=>funny(X)))&
((~creative(susan))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|~humble(X))=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~curious(X)&funny(X))=>(wise(X)&~patient(X))))&
(![X]:(~generous(X)<=>(funny(X)&curious(X))))&
(![X]:((~rich(X)&calm(X))=>(generous(X)|~rich(X))))&
(![X]:(~rich(X)<=>(creative(X)&~rich(X))))&
(curious(alice))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~funny(X)|~kind(X))))&
((curious(susan)|~generous(susan)))&
(?[X]:((kind(X)&funny(X)))) | generous(susan) | [] | null | 0 |
If paul is calm or rich then john is either kind or not patient and vice versa. Everyone who is not creative or not quiet is not brave. If someone is not tall or not kind then someone is not kind or creative. If someone is not funny then fred is not kind or strong. If someone is both not patient and patient then someone is both not brave and not humble. Everyone who is both wise and patient is both quiet and not happy and vice versa. Everyone who is funny is either tall or rich and vice versa. Everyone who is brave or not curious is not patient and vice versa. Everyone who is not old or not strong is tall or curious and vice versa. If someone is tall then someone is both not quiet and generous and vice versa. If someone is both not strong and strong then someone is not calm or humble and vice versa. Everyone who is both brave and not tall is either not wise or calm. Everyone who is not curious or curious is both happy and not brave and vice versa. Everyone who is either quiet or not patient is both not generous and not calm and vice versa. Everyone who is happy or strong is both not patient and old. Everyone who is either not brave or patient is either not rich or curious. Someone is not wise or wise. Someone is not kind. Someone is both quiet and calm. | Fred is not funny. | entailment | (((calm(paul)|rich(paul)))<=>((kind(john)<~>~patient(john))))&
(![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:(~kind(X)))&
(?[X]:((quiet(X)&calm(X)))) | ~funny(fred) | [
"p6",
"p7",
"p9",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8874704049467842311509806
% SZS output start Proof for 8874704049467842311509806
7. ! [X0] : (funny(X0) <=> (tall(X0) <~> rich(X0))) [input p6]
8. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p7]
10. ? [X0] : tall(X0) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p9]
13. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p12]
14. ! [X0] : ((quiet(X0) <~> ~patient(X0)) <=> (~calm(X0) & ~generous(X0))) [input p13]
15. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p14]
16. ! [X0] : ((~brave(X0) <~> patient(X0)) => (~rich(X0) <~> curious(X0))) [input p15]
20. funny(fred) [input hypothesis]
23. ? [X0] : tall(X0) <=> ? [X1] : (generous(X1) & ~quiet(X1)) [rectify 10]
25. ! [X0] : (funny(X0) => (tall(X0) <~> rich(X0))) [unused predicate definition removal 7]
32. ! [X0] : ((tall(X0) <~> rich(X0)) | ~funny(X0)) [ennf transformation 25]
35. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 15]
36. ! [X0] : ((~rich(X0) <~> curious(X0)) | (~brave(X0) <=> patient(X0))) [ennf transformation 16]
44. ! [X0] : (((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | ~funny(X0)) [nnf transformation 32]
45. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 45]
49. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X1] : (generous(X1) & ~quiet(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 23]
50. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X2] : (generous(X2) & ~quiet(X2)) | ! [X3] : ~tall(X3)) [rectify 49]
51. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
52. ? [X2] : (generous(X2) & ~quiet(X2)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
53. (tall(sK1) | ! [X1] : (~generous(X1) | quiet(X1))) & ((generous(sK2) & ~quiet(sK2)) | ! [X3] : ~tall(X3)) [skolemisation 50,52,51]
60. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 13]
61. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 60]
62. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [nnf transformation 14]
63. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [flattening 62]
64. ! [X0] : (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0)))) [nnf transformation 36]
85. ~funny(X0) | tall(X0) | rich(X0) [cnf transformation 44]
89. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 46]
94. ~quiet(sK2) | ~tall(X3) [cnf transformation 53]
95. generous(sK2) | ~tall(X3) [cnf transformation 53]
104. happy(X0) | curious(X0) [cnf transformation 61]
105. ~curious(X0) | happy(X0) [cnf transformation 61]
106. ~brave(X0) | curious(X0) [cnf transformation 61]
107. ~curious(X0) | ~brave(X0) [cnf transformation 61]
110. ~generous(X0) | quiet(X0) | patient(X0) [cnf transformation 63]
115. ~patient(X0) | ~happy(X0) [cnf transformation 35]
119. curious(X0) | ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 64]
127. funny(fred) [cnf transformation 20]
171. 10 <=> ! [X3] : ~tall(X3) [avatar definition]
172. ~tall(X3) <- (10) [avatar component clause 171]
174. 11 <=> generous(sK2) [avatar definition]
176. generous(sK2) <- (11) [avatar component clause 174]
177. 10 | 11 [avatar split clause 95,174,171]
179. 12 <=> quiet(sK2) [avatar definition]
181. ~quiet(sK2) <- (~12) [avatar component clause 179]
182. 10 | ~12 [avatar split clause 94,179,171]
197. ~brave(X0) [subsumption resolution 106,107]
198. happy(X0) [subsumption resolution 104,105]
200. ~patient(X0) [subsumption resolution 115,198]
201. curious(X0) | ~rich(X0) | brave(X0) [subsumption resolution 119,200]
202. ~rich(X0) | curious(X0) [subsumption resolution 201,197]
210. tall(fred) | rich(fred) [resolution 85,127]
211. rich(fred) <- (10) [subsumption resolution 210,172]
212. curious(fred) <- (10) [resolution 211,202]
216. brave(fred) | patient(fred) <- (10) [resolution 89,212]
217. patient(fred) <- (10) [subsumption resolution 216,197]
218. $false <- (10) [subsumption resolution 217,200]
219. ~10 [avatar contradiction clause 218]
250. quiet(sK2) | patient(sK2) <- (11) [resolution 110,176]
251. patient(sK2) <- (11, ~12) [subsumption resolution 250,181]
252. $false <- (11, ~12) [subsumption resolution 251,200]
253. ~11 | 12 [avatar contradiction clause 252]
254. $false [avatar sat refutation 177,182,219,253]
% SZS output end Proof for 8874704049467842311509806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or curious is both not rich and not kind. Everyone who is generous is not rich and vice versa. If john is not creative then someone is either not generous or not patient and vice versa. Everyone who is both not strong and not wise is not rich and vice versa. Everyone who is either quiet or not kind is not strong or funny. Everyone who is either quiet or humble is either calm or generous and vice versa. If someone is both humble and quiet then fred is both not tall and not generous. Everyone who is kind or brave is either not curious or not funny. If mary is either not creative or strong then susan is both creative and not funny and vice versa. If lucy is not rich or not patient then john is quiet or not curious and vice versa. If lucy is not rich or creative then mary is either patient or not happy. Everyone who is not quiet is both not brave and not calm and vice versa. If lucy is not quiet then mary is not quiet. Everyone who is kind is either creative or not brave. If someone is not tall or quiet then john is either not creative or not curious and vice versa. Everyone who is not patient or generous is both wise and not quiet. Someone is not wise or not rich. Susan is both calm and not creative. Someone is creative or funny. Alice is calm. Alice is either creative or happy. Fred is either not humble or not patient. Someone is not patient or not strong. | Lucy is not humble. | entailment | (![X]:((calm(X)<~>curious(X))=>(~rich(X)&~kind(X))))&
(![X]:(generous(X)<=>~rich(X)))&
((~creative(john))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~wise(X))<=>~rich(X)))&
(![X]:((quiet(X)<~>~kind(X))=>(~strong(X)|funny(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(calm(X)<~>generous(X))))&
((?[X]:((humble(X)&quiet(X))))=>((~tall(fred)&~generous(fred))))&
(![X]:((kind(X)|brave(X))=>(~curious(X)<~>~funny(X))))&
(((~creative(mary)<~>strong(mary)))<=>((creative(susan)&~funny(susan))))&
(((~rich(lucy)|~patient(lucy)))<=>((quiet(john)|~curious(john))))&
(((~rich(lucy)|creative(lucy)))=>((patient(mary)<~>~happy(mary))))&
(![X]:(~quiet(X)<=>(~brave(X)&~calm(X))))&
((~quiet(lucy))=>(~quiet(mary)))&
(![X]:(kind(X)=>(creative(X)<~>~brave(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>((~creative(john)<~>~curious(john))))&
(![X]:((~patient(X)|generous(X))=>(wise(X)&~quiet(X))))&
(?[X]:((~wise(X)|~rich(X))))&
((calm(susan)&~creative(susan)))&
(?[X]:((creative(X)|funny(X))))&
(calm(alice))&
((creative(alice)<~>happy(alice)))&
((~humble(fred)<~>~patient(fred)))&
(?[X]:((~patient(X)|~strong(X)))) | ~humble(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 149286580856203147384793
% SZS output start Proof for 149286580856203147384793
1. ! [X0] : ((calm(X0) <~> curious(X0)) => (~kind(X0) & ~rich(X0))) [input p0]
2. ! [X0] : (generous(X0) <=> ~rich(X0)) [input p1]
4. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> ~rich(X0)) [input p3]
6. ! [X0] : ((quiet(X0) <~> humble(X0)) <=> (calm(X0) <~> generous(X0))) [input p5]
10. (~patient(lucy) | ~rich(lucy)) <=> (~curious(john) | quiet(john)) [input p9]
12. ! [X0] : (~quiet(X0) <=> (~calm(X0) & ~brave(X0))) [input p11]
16. ! [X0] : ((generous(X0) | ~patient(X0)) => (~quiet(X0) & wise(X0))) [input p15]
24. humble(lucy) [input hypothesis]
25. ! [X0] : ((~kind(X0) & ~rich(X0)) | (calm(X0) <=> curious(X0))) [ennf transformation 1]
33. ! [X0] : ((~quiet(X0) & wise(X0)) | (~generous(X0) & patient(X0))) [ennf transformation 16]
34. ! [X0] : ((~kind(X0) & ~rich(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) [nnf transformation 25]
35. ! [X0] : ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))) [nnf transformation 2]
40. ! [X0] : (((~wise(X0) & ~strong(X0)) | rich(X0)) & (~rich(X0) | (wise(X0) | strong(X0)))) [nnf transformation 4]
41. ! [X0] : (((~wise(X0) & ~strong(X0)) | rich(X0)) & (~rich(X0) | wise(X0) | strong(X0))) [flattening 40]
43. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [nnf transformation 6]
47. ((~patient(lucy) | ~rich(lucy)) | (curious(john) & ~quiet(john))) & ((~curious(john) | quiet(john)) | (patient(lucy) & rich(lucy))) [nnf transformation 10]
48. (~patient(lucy) | ~rich(lucy) | (curious(john) & ~quiet(john))) & (~curious(john) | quiet(john) | (patient(lucy) & rich(lucy))) [flattening 47]
50. ! [X0] : ((~quiet(X0) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | quiet(X0))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | quiet(X0))) [flattening 50]
66. ~rich(X0) | calm(X0) | ~curious(X0) [cnf transformation 34]
69. ~generous(X0) | ~rich(X0) [cnf transformation 35]
70. generous(X0) | rich(X0) [cnf transformation 35]
77. ~wise(X0) | rich(X0) [cnf transformation 41]
81. ~humble(X0) | calm(X0) | quiet(X0) | generous(X0) [cnf transformation 43]
102. ~patient(lucy) | ~rich(lucy) | ~quiet(john) [cnf transformation 48]
103. ~patient(lucy) | ~rich(lucy) | curious(john) [cnf transformation 48]
109. ~calm(X0) | quiet(X0) [cnf transformation 51]
121. ~generous(X0) | wise(X0) [cnf transformation 33]
122. ~quiet(X0) | patient(X0) [cnf transformation 33]
134. humble(lucy) [cnf transformation 24]
193. 13 <=> curious(john) [avatar definition]
195. curious(john) <- (13) [avatar component clause 193]
197. 14 <=> rich(lucy) [avatar definition]
199. ~rich(lucy) <- (~14) [avatar component clause 197]
201. 15 <=> patient(lucy) [avatar definition]
204. 13 | ~14 | ~15 [avatar split clause 103,201,197,193]
206. 16 <=> quiet(john) [avatar definition]
208. ~quiet(john) <- (~16) [avatar component clause 206]
209. ~16 | ~14 | ~15 [avatar split clause 102,201,197,206]
229. 20 <=> quiet(lucy) [avatar definition]
230. ~quiet(lucy) <- (~20) [avatar component clause 229]
231. quiet(lucy) <- (20) [avatar component clause 229]
305. wise(X0) | rich(X0) [resolution 121,70]
306. rich(X0) [subsumption resolution 305,77]
315. 34 <=> calm(lucy) [avatar definition]
316. calm(lucy) <- (34) [avatar component clause 315]
317. ~calm(lucy) <- (~34) [avatar component clause 315]
338. ~curious(X0) | calm(X0) [resolution 66,306]
364. $false <- (~14) [subsumption resolution 199,306]
365. 14 [avatar contradiction clause 364]
387. 43 <=> calm(john) [avatar definition]
389. calm(john) <- (43) [avatar component clause 387]
448. calm(lucy) | quiet(lucy) | generous(lucy) [resolution 81,134]
450. quiet(lucy) | generous(lucy) <- (~34) [subsumption resolution 448,317]
451. generous(lucy) <- (~20, ~34) [subsumption resolution 450,230]
459. ~rich(lucy) <- (~20, ~34) [resolution 451,69]
460. $false <- (~20, ~34) [subsumption resolution 459,306]
461. 20 | 34 [avatar contradiction clause 460]
469. quiet(lucy) <- (34) [resolution 316,109]
472. 20 | ~34 [avatar split clause 469,315,229]
478. patient(lucy) <- (20) [resolution 231,122]
526. calm(john) <- (13) [resolution 338,195]
527. 43 | ~13 [avatar split clause 526,193,387]
528. 15 | ~20 [avatar split clause 478,229,201]
542. quiet(john) <- (43) [resolution 389,109]
553. $false <- (~16, 43) [subsumption resolution 542,208]
554. 16 | ~43 [avatar contradiction clause 553]
555. $false [avatar sat refutation 204,209,365,461,472,527,528,554]
% SZS output end Proof for 149286580856203147384793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either not curious or curious and vice versa.
Everyone who is either not curious or not patient is both calm and rich and vice versa.
If someone is either not curious or old then someone is both brave and not old.
If alice is not old then john is old.
If mary is not creative then someone is either patient or not curious.
Everyone who is not curious is not rich and vice versa.
If someone is not humble then someone is either funny or not curious.
If susan is both not rich and not humble then someone is curious or not kind.
If someone is either not humble or happy then someone is either patient or not humble.
Everyone who is not brave is either not rich or not quiet and vice versa.
If someone is happy or not calm then susan is either not quiet or not brave and vice versa.
If someone is not patient or not kind then someone is curious.
If susan is either brave or not tall then susan is strong.
If someone is both not curious and not creative then someone is either not brave or strong.
Everyone who is both not rich and not funny is not quiet.
Everyone who is both creative and strong is not quiet and vice versa.
Someone is both not curious and not old.
Someone is rich.
John is either not wise or old.
Fred is not kind or generous.
Someone is kind.
Fred is both not quiet and not brave.
John is both patient and wise.
Lucy is not humble. | Susan is patient. | contradiction | (![X]:(generous(X)<=>(~curious(X)<~>curious(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(calm(X)&rich(X))))&
((?[X]:((~curious(X)<~>old(X))))=>(?[X]:((brave(X)&~old(X)))))&
((~old(alice))=>(old(john)))&
((~creative(mary))=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>~rich(X)))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)<~>~curious(X)))))&
(((~rich(susan)&~humble(susan)))=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:((~humble(X)<~>happy(X))))=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:(~brave(X)<=>(~rich(X)<~>~quiet(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((~quiet(susan)<~>~brave(susan))))&
((?[X]:((~patient(X)|~kind(X))))=>(?[X]:(curious(X))))&
(((brave(susan)<~>~tall(susan)))=>(strong(susan)))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:((~rich(X)&~funny(X))=>~quiet(X)))&
(![X]:((creative(X)&strong(X))<=>~quiet(X)))&
(?[X]:((~curious(X)&~old(X))))&
(?[X]:(rich(X)))&
((~wise(john)<~>old(john)))&
((~kind(fred)|generous(fred)))&
(?[X]:(kind(X)))&
((~quiet(fred)&~brave(fred)))&
((patient(john)&wise(john)))&
(~humble(lucy)) | patient(susan) | [
"p1",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 136622053425676286395455
% SZS output start Proof for 136622053425676286395455
2. ! [X0] : ((~curious(X0) <~> ~patient(X0)) <=> (rich(X0) & calm(X0))) [input p1]
6. ! [X0] : (~curious(X0) <=> ~rich(X0)) [input p5]
10. ! [X0] : (~brave(X0) <=> (~rich(X0) <~> ~quiet(X0))) [input p9]
11. ? [X0] : (~calm(X0) | happy(X0)) <=> (~quiet(susan) <~> ~brave(susan)) [input p10]
25. patient(susan) [input hypothesis]
46. ! [X0] : ((((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (~rich(X0) | ~calm(X0))) & ((rich(X0) & calm(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0))))) [nnf transformation 2]
47. ! [X0] : ((((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~rich(X0) | ~calm(X0)) & ((rich(X0) & calm(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0))))) [flattening 46]
55. ! [X0] : ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0))) [nnf transformation 6]
66. ! [X0] : ((~brave(X0) | ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0)))) & (((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | brave(X0))) [nnf transformation 10]
67. (? [X0] : (~calm(X0) | happy(X0)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X0] : (calm(X0) & ~happy(X0))) [nnf transformation 11]
68. (? [X0] : (~calm(X0) | happy(X0)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X1] : (calm(X1) & ~happy(X1))) [rectify 67]
69. ? [X0] : (~calm(X0) | happy(X0)) => (~calm(sK5) | happy(sK5)) [choice axiom]
70. ((~calm(sK5) | happy(sK5)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X1] : (calm(X1) & ~happy(X1))) [skolemisation 68,69]
92. ~patient(X0) | rich(X0) | curious(X0) [cnf transformation 47]
94. ~rich(X0) | ~curious(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 47]
103. ~rich(X0) | curious(X0) [cnf transformation 55]
104. ~curious(X0) | rich(X0) [cnf transformation 55]
112. ~quiet(X0) | ~rich(X0) | brave(X0) [cnf transformation 66]
115. ~brave(X0) | ~rich(X0) | quiet(X0) [cnf transformation 66]
117. ~brave(susan) | ~quiet(susan) | calm(X1) [cnf transformation 70]
119. brave(susan) | quiet(susan) | calm(X1) [cnf transformation 70]
144. patient(susan) [cnf transformation 25]
200. 13 <=> rich(susan) [avatar definition]
202. rich(susan) <- (13) [avatar component clause 200]
235. 21 <=> brave(susan) [avatar definition]
236. ~brave(susan) <- (~21) [avatar component clause 235]
237. brave(susan) <- (21) [avatar component clause 235]
239. 22 <=> quiet(susan) [avatar definition]
240. quiet(susan) <- (22) [avatar component clause 239]
253. 25 <=> ! [X1] : calm(X1) [avatar definition]
254. calm(X1) <- (25) [avatar component clause 253]
255. 25 | 22 | 21 [avatar split clause 119,235,239,253]
260. 25 | ~22 | ~21 [avatar split clause 117,235,239,253]
332. 40 <=> curious(susan) [avatar definition]
333. ~curious(susan) <- (~40) [avatar component clause 332]
334. curious(susan) <- (40) [avatar component clause 332]
373. rich(susan) | curious(susan) [resolution 92,144]
399. ~rich(susan) | quiet(susan) <- (21) [resolution 115,237]
415. 22 | ~13 | ~21 [avatar split clause 399,235,200,239]
418. ~rich(susan) | brave(susan) <- (22) [resolution 240,112]
430. ~curious(susan) | ~patient(susan) | ~calm(susan) <- (13) [resolution 94,202]
434. ~patient(susan) | ~calm(susan) <- (13, 40) [subsumption resolution 430,334]
435. ~calm(susan) <- (13, 40) [subsumption resolution 434,144]
436. $false <- (13, 25, 40) [subsumption resolution 435,254]
437. ~13 | ~25 | ~40 [avatar contradiction clause 436]
464. ~rich(susan) <- (~21, 22) [subsumption resolution 418,236]
465. ~13 | 21 | ~22 [avatar split clause 464,239,235,200]
471. rich(susan) [subsumption resolution 373,104]
472. 13 [avatar split clause 471,200]
480. curious(susan) <- (13) [resolution 202,103]
481. $false <- (13, ~40) [subsumption resolution 480,333]
482. ~13 | 40 [avatar contradiction clause 481]
483. $false [avatar sat refutation 255,260,415,437,465,472,482]
% SZS output end Proof for 136622053425676286395455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not strong then someone is either calm or happy.
Everyone who is not old is not kind or brave and vice versa.
Everyone who is either not quiet or patient is not happy and vice versa.
Everyone who is tall is tall or not quiet and vice versa.
If someone is either not brave or quiet then alice is both creative and not rich and vice versa.
Everyone who is both not kind and not humble is not tall and vice versa.
If someone is either quiet or creative then someone is both old and funny.
Everyone who is not creative is rich or not rich and vice versa.
If someone is either not generous or not calm then someone is not patient or not tall and vice versa.
If paul is both tall and not funny then mary is either generous or not humble.
Everyone who is kind is funny.
Everyone who is both not brave and happy is not tall and vice versa.
Everyone who is both brave and happy is both not generous and old.
Everyone who is either calm or not humble is not wise and vice versa.
Everyone who is calm or generous is either not patient or patient and vice versa.
Everyone who is not calm is either funny or tall and vice versa.
Someone is both not humble and old.
Someone is not curious.
Susan is either not quiet or not patient.
Alice is creative or humble.
Mary is both not creative and not brave.
Someone is either not brave or generous.
Susan is not funny or not rich. | Paul is not funny. | neutral | ((?[X]:((~generous(X)&~strong(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(~old(X)<=>(~kind(X)|brave(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>~happy(X)))&
(![X]:(tall(X)<=>(tall(X)|~quiet(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((creative(alice)&~rich(alice))))&
(![X]:((~kind(X)&~humble(X))<=>~tall(X)))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:((old(X)&funny(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~rich(X))))&
((?[X]:((~generous(X)<~>~calm(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(((tall(paul)&~funny(paul)))=>((generous(mary)<~>~humble(mary))))&
(![X]:(kind(X)=>funny(X)))&
(![X]:((~brave(X)&happy(X))<=>~tall(X)))&
(![X]:((brave(X)&happy(X))=>(~generous(X)&old(X))))&
(![X]:((calm(X)<~>~humble(X))<=>~wise(X)))&
(![X]:((calm(X)|generous(X))<=>(~patient(X)<~>patient(X))))&
(![X]:(~calm(X)<=>(funny(X)<~>tall(X))))&
(?[X]:((~humble(X)&old(X))))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>~patient(susan)))&
((creative(alice)|humble(alice)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((~brave(X)<~>generous(X))))&
((~funny(susan)|~rich(susan))) | ~funny(paul) | [] | null | 0 |
If paul is rich then someone is not rich and vice versa.
Everyone who is not tall is not rich and vice versa.
Everyone who is both not humble and not rich is brave and vice versa.
If someone is both not old and strong then someone is either humble or happy and vice versa.
If alice is tall or not wise then someone is either not funny or curious.
If alice is both not curious and not generous then someone is calm or strong.
Everyone who is both brave and creative is either calm or patient and vice versa.
If someone is either patient or not wise then susan is both not patient and rich and vice versa.
If someone is either not old or not quiet then someone is either patient or humble.
Everyone who is either brave or patient is generous or not wise and vice versa.
If paul is funny or not happy then someone is humble.
Everyone who is either not happy or not calm is either kind or calm.
If someone is not tall then alice is both not quiet and not old.
If someone is patient or not strong then susan is both strong and wise and vice versa.
Everyone who is rich is either not old or creative.
Everyone who is not humble or not patient is not kind or curious.
Someone is either humble or quiet.
Someone is both not creative and not curious.
Someone is both not kind and curious.
Mary is generous.
Someone is either not old or not patient.
Someone is either not patient or quiet.
Someone is not humble or creative.
Paul is not creative or not happy. | Alice is old. | contradiction | ((rich(paul))<=>(?[X]:(~rich(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
(![X]:((~humble(X)&~rich(X))<=>brave(X)))&
((?[X]:((~old(X)&strong(X))))<=>(?[X]:((humble(X)<~>happy(X)))))&
(((tall(alice)|~wise(alice)))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((~curious(alice)&~generous(alice)))=>(?[X]:((calm(X)|strong(X)))))&
(![X]:((brave(X)&creative(X))<=>(calm(X)<~>patient(X))))&
((?[X]:((patient(X)<~>~wise(X))))<=>((~patient(susan)&rich(susan))))&
((?[X]:((~old(X)<~>~quiet(X))))=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((brave(X)<~>patient(X))<=>(generous(X)|~wise(X))))&
(((funny(paul)|~happy(paul)))=>(?[X]:(humble(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
((?[X]:(~tall(X)))=>((~quiet(alice)&~old(alice))))&
((?[X]:((patient(X)|~strong(X))))<=>((strong(susan)&wise(susan))))&
(![X]:(rich(X)=>(~old(X)<~>creative(X))))&
(![X]:((~humble(X)|~patient(X))=>(~kind(X)|curious(X))))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:((~kind(X)&curious(X))))&
(generous(mary))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((~humble(X)|creative(X))))&
((~creative(paul)|~happy(paul))) | old(alice) | [
"p0",
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3683893766838695629895132
% SZS output start Proof for 3683893766838695629895132
1. rich(paul) <=> ? [X0] : ~rich(X0) [input p0]
2. ! [X0] : (~tall(X0) <=> ~rich(X0)) [input p1]
13. ? [X0] : ~tall(X0) => (~old(alice) & ~quiet(alice)) [input p12]
25. old(alice) [input hypothesis]
34. (~old(alice) & ~quiet(alice)) | ! [X0] : tall(X0) [ennf transformation 13]
38. (rich(paul) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | ~rich(paul)) [nnf transformation 1]
39. (rich(paul) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | ~rich(paul)) [rectify 38]
40. ? [X1] : ~rich(X1) => ~rich(sK0) [choice axiom]
41. (rich(paul) | ! [X0] : rich(X0)) & (~rich(sK0) | ~rich(paul)) [skolemisation 39,40]
42. ! [X0] : ((~tall(X0) | rich(X0)) & (~rich(X0) | tall(X0))) [nnf transformation 2]
92. ~rich(sK0) | ~rich(paul) [cnf transformation 41]
95. ~tall(X0) | rich(X0) [cnf transformation 42]
139. ~old(alice) | tall(X0) [cnf transformation 34]
162. old(alice) [cnf transformation 25]
166. 1 <=> ! [X0] : rich(X0) [avatar definition]
167. rich(X0) <- (1) [avatar component clause 166]
169. 2 <=> rich(paul) [avatar definition]
170. ~rich(paul) <- (~2) [avatar component clause 169]
174. 3 <=> rich(sK0) [avatar definition]
176. ~rich(sK0) <- (~3) [avatar component clause 174]
177. ~2 | ~3 [avatar split clause 92,174,169]
307. 32 <=> ! [X0] : tall(X0) [avatar definition]
308. tall(X0) <- (32) [avatar component clause 307]
310. 33 <=> old(alice) [avatar definition]
313. 32 | ~33 [avatar split clause 139,310,307]
390. 33 [avatar split clause 162,310]
393. rich(X0) <- (32) [resolution 95,308]
394. 1 | ~32 [avatar split clause 393,307,166]
395. $false <- (1, ~3) [resolution 167,176]
397. ~1 | 3 [avatar contradiction clause 395]
398. $false <- (1, ~2) [subsumption resolution 170,167]
399. ~1 | 2 [avatar contradiction clause 398]
400. $false [avatar sat refutation 177,313,390,394,397,399]
% SZS output end Proof for 3683893766838695629895132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not old or not calm then lucy is either rich or tall and vice versa.
If someone is either not happy or patient then someone is both wise and funny.
Everyone who is brave or not patient is either quiet or not rich.
Everyone who is either old or creative is rich.
Everyone who is both rich and not patient is both not patient and not tall and vice versa.
If paul is funny then john is not humble.
Everyone who is funny or not wise is not funny and vice versa.
If someone is both patient and not humble then susan is brave.
Everyone who is both quiet and creative is either creative or not patient and vice versa.
If alice is either not curious or calm then mary is both not rich and not calm and vice versa.
If susan is either strong or not kind then susan is either rich or calm.
Everyone who is both not funny and not wise is not rich or happy and vice versa.
Everyone who is kind or not happy is not creative and vice versa.
Everyone who is rich or kind is either curious or happy.
Everyone who is either patient or not patient is either not tall or curious and vice versa.
Everyone who is wise is not curious or not brave.
John is not rich or not curious.
Susan is either not old or not strong.
Someone is either not creative or brave.
Fred is both not brave and not tall.
Someone is both not happy and brave.
Susan is either creative or not quiet.
Someone is either not wise or happy. | John is funny. | contradiction | (((~old(mary)|~calm(mary)))<=>((rich(lucy)<~>tall(lucy))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((wise(X)&funny(X)))))&
(![X]:((brave(X)|~patient(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((old(X)<~>creative(X))=>rich(X)))&
(![X]:((rich(X)&~patient(X))<=>(~patient(X)&~tall(X))))&
((funny(paul))=>(~humble(john)))&
(![X]:((funny(X)|~wise(X))<=>~funny(X)))&
((?[X]:((patient(X)&~humble(X))))=>(brave(susan)))&
(![X]:((quiet(X)&creative(X))<=>(creative(X)<~>~patient(X))))&
(((~curious(alice)<~>calm(alice)))<=>((~rich(mary)&~calm(mary))))&
(((strong(susan)<~>~kind(susan)))=>((rich(susan)<~>calm(susan))))&
(![X]:((~funny(X)&~wise(X))<=>(~rich(X)|happy(X))))&
(![X]:((kind(X)|~happy(X))<=>~creative(X)))&
(![X]:((rich(X)|kind(X))=>(curious(X)<~>happy(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~tall(X)<~>curious(X))))&
(![X]:(wise(X)=>(~curious(X)|~brave(X))))&
((~rich(john)|~curious(john)))&
((~old(susan)<~>~strong(susan)))&
(?[X]:((~creative(X)<~>brave(X))))&
((~brave(fred)&~tall(fred)))&
(?[X]:((~happy(X)&brave(X))))&
((creative(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)<~>happy(X)))) | funny(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3723292683459615603515963
% SZS output start Proof for 3723292683459615603515963
7. ! [X0] : ((~wise(X0) | funny(X0)) <=> ~funny(X0)) [input p6]
24. funny(john) [input hypothesis]
45. ! [X0] : (((~wise(X0) | funny(X0)) | funny(X0)) & (~funny(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((~wise(X0) | funny(X0) | funny(X0)) & (~funny(X0) | (wise(X0) & ~funny(X0)))) [flattening 45]
89. ~funny(X0) | ~funny(X0) [cnf transformation 46]
143. funny(john) [cnf transformation 24]
150. ~funny(X0) [duplicate literal removal 89]
288. $false [subsumption resolution 143,150]
% SZS output end Proof for 3723292683459615603515963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then someone is not happy or happy and vice versa. Everyone who is either not old or rich is not kind or curious. If someone is not old or quiet then someone is both not quiet and rich and vice versa. If someone is not wise or strong then someone is both rich and not brave. If someone is both not humble and creative then someone is both brave and not generous. If fred is either not kind or not happy then someone is happy or creative and vice versa. If someone is not strong then someone is both strong and not old and vice versa. If paul is patient then someone is both not kind and not patient and vice versa. Everyone who is brave or not funny is not old. Everyone who is kind is not old. If someone is funny then alice is either not kind or not brave and vice versa. Everyone who is patient is not wise or patient and vice versa. If alice is not funny then fred is curious or happy and vice versa. Everyone who is wise is not strong or not patient. Lucy is both not humble and funny. Someone is humble or not happy. Someone is not kind. Someone is not calm or not patient. Susan is either happy or not funny. Susan is either not kind or happy. Fred is either creative or curious. | Lucy is not quiet. | neutral | ((?[X]:(~humble(X)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~old(X)<~>rich(X))=>(~kind(X)|curious(X))))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:((~wise(X)|strong(X))))=>(?[X]:((rich(X)&~brave(X)))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((brave(X)&~generous(X)))))&
(((~kind(fred)<~>~happy(fred)))<=>(?[X]:((happy(X)|creative(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((strong(X)&~old(X)))))&
((patient(paul))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((brave(X)|~funny(X))=>~old(X)))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:(funny(X)))<=>((~kind(alice)<~>~brave(alice))))&
(![X]:(patient(X)<=>(~wise(X)|patient(X))))&
((~funny(alice))<=>((curious(fred)|happy(fred))))&
(![X]:(wise(X)=>(~strong(X)|~patient(X))))&
((~humble(lucy)&funny(lucy)))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)|~patient(X))))&
((happy(susan)<~>~funny(susan)))&
((~kind(susan)<~>happy(susan)))&
((creative(fred)<~>curious(fred))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is both not kind and not strong is calm or not calm.
If susan is not humble or not patient then someone is old or not calm and vice versa.
If lucy is either creative or calm then lucy is both not wise and not funny and vice versa.
If someone is both strong and not brave then john is either strong or old and vice versa.
Everyone who is either not calm or not curious is either quiet or curious.
If lucy is not brave or not wise then fred is both quiet and not kind.
If someone is both not calm and not brave then fred is either not funny or funny and vice versa.
If susan is both not curious and not funny then paul is both calm and not happy and vice versa.
Everyone who is curious or not tall is either not strong or not happy.
Everyone who is both not happy and not patient is both not quiet and generous and vice versa.
Everyone who is not creative or not calm is both happy and quiet and vice versa.
Everyone who is not curious is either not brave or not strong and vice versa.
Everyone who is quiet or old is humble.
Everyone who is rich is both not quiet and not old and vice versa.
If paul is not old or quiet then someone is brave or quiet.
Everyone who is either creative or not creative is not brave or not humble.
Paul is either curious or not brave.
Alice is both strong and not old.
Alice is both creative and not humble.
Someone is either curious or not rich.
Alice is funny.
Someone is either happy or not brave. | John is not patient. | neutral | (![X]:((~kind(X)&~strong(X))=>(calm(X)|~calm(X))))&
(((~humble(susan)|~patient(susan)))<=>(?[X]:((old(X)|~calm(X)))))&
(((creative(lucy)<~>calm(lucy)))<=>((~wise(lucy)&~funny(lucy))))&
((?[X]:((strong(X)&~brave(X))))<=>((strong(john)<~>old(john))))&
(![X]:((~calm(X)<~>~curious(X))=>(quiet(X)<~>curious(X))))&
(((~brave(lucy)|~wise(lucy)))=>((quiet(fred)&~kind(fred))))&
((?[X]:((~calm(X)&~brave(X))))<=>((~funny(fred)<~>funny(fred))))&
(((~curious(susan)&~funny(susan)))<=>((calm(paul)&~happy(paul))))&
(![X]:((curious(X)|~tall(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~happy(X)&~patient(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~creative(X)|~calm(X))<=>(happy(X)&quiet(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((quiet(X)|old(X))=>humble(X)))&
(![X]:(rich(X)<=>(~quiet(X)&~old(X))))&
(((~old(paul)|quiet(paul)))=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((creative(X)<~>~creative(X))=>(~brave(X)|~humble(X))))&
((curious(paul)<~>~brave(paul)))&
((strong(alice)&~old(alice)))&
((creative(alice)&~humble(alice)))&
(?[X]:((curious(X)<~>~rich(X))))&
(funny(alice))&
(?[X]:((happy(X)<~>~brave(X)))) | ~patient(john) | [] | null | 0 |
Everyone who is not funny or not brave is either not quiet or not curious. Everyone who is either not patient or not creative is both brave and creative and vice versa. If mary is both not old and not funny then mary is not calm and vice versa. Everyone who is both not humble and old is kind. If someone is strong or not rich then someone is either wise or quiet. If mary is both kind and not funny then someone is either not creative or not calm. Everyone who is creative or funny is either not quiet or curious and vice versa. Everyone who is creative is either not calm or creative and vice versa. Everyone who is either curious or generous is both not curious and not brave and vice versa. If lucy is both tall and rich then john is both not rich and not creative and vice versa. If someone is not kind or brave then someone is old. Everyone who is not rich or wise is wise or strong and vice versa. Everyone who is funny or curious is not generous or rich and vice versa. If john is not quiet then someone is not brave or tall. If someone is not creative or humble then paul is both not calm and not patient. Everyone who is strong or humble is not quiet or curious and vice versa. John is not old or patient. Someone is both brave and old. Someone is strong. John is either strong or not wise. Fred is not tall. Susan is either creative or not calm. | John is calm. | entailment | (![X]:((~funny(X)|~brave(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>(brave(X)&creative(X))))&
(((~old(mary)&~funny(mary)))<=>(~calm(mary)))&
(![X]:((~humble(X)&old(X))=>kind(X)))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:((wise(X)<~>quiet(X)))))&
(((kind(mary)&~funny(mary)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((creative(X)|funny(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:(creative(X)<=>(~calm(X)<~>creative(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~curious(X)&~brave(X))))&
(((tall(lucy)&rich(lucy)))<=>((~rich(john)&~creative(john))))&
((?[X]:((~kind(X)|brave(X))))=>(?[X]:(old(X))))&
(![X]:((~rich(X)|wise(X))<=>(wise(X)|strong(X))))&
(![X]:((funny(X)|curious(X))<=>(~generous(X)|rich(X))))&
((~quiet(john))=>(?[X]:((~brave(X)|tall(X)))))&
((?[X]:((~creative(X)|humble(X))))=>((~calm(paul)&~patient(paul))))&
(![X]:((strong(X)|humble(X))<=>(~quiet(X)|curious(X))))&
((~old(john)|patient(john)))&
(?[X]:((brave(X)&old(X))))&
(?[X]:(strong(X)))&
((strong(john)<~>~wise(john)))&
(~tall(fred))&
((creative(susan)<~>~calm(susan))) | calm(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6222008328259985355804899
% SZS output start Proof for 6222008328259985355804899
8. ! [X0] : (creative(X0) <=> (~calm(X0) <~> creative(X0))) [input p7]
23. ~calm(john) [input hypothesis]
49. ! [X0] : ((creative(X0) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~creative(X0))) [nnf transformation 8]
98. ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 49]
99. creative(X0) | creative(X0) | calm(X0) [cnf transformation 49]
139. ~calm(john) [cnf transformation 23]
142. ~creative(X0) | calm(X0) [duplicate literal removal 98]
143. creative(X0) | calm(X0) [duplicate literal removal 99]
193. calm(X0) [subsumption resolution 142,143]
277. $false [subsumption resolution 139,193]
% SZS output end Proof for 6222008328259985355804899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not funny or not rich is not tall.
Everyone who is both not tall and not funny is not wise.
If someone is either funny or old then someone is both not old and strong and vice versa.
If john is strong then someone is either not brave or wise.
Everyone who is rich or generous is not old or happy and vice versa.
Everyone who is both patient and calm is both not patient and wise and vice versa.
If someone is either rich or not old then someone is not happy and vice versa.
If john is either not kind or creative then fred is both patient and not quiet.
If someone is both not old and not calm then someone is either not rich or strong.
Everyone who is either not funny or not wise is not strong.
Everyone who is calm is generous and vice versa.
Everyone who is either curious or not strong is not kind or not wise.
Everyone who is both funny and calm is generous and vice versa.
Everyone who is both not wise and wise is either not patient or wise and vice versa.
Everyone who is tall is not brave or wise and vice versa.
Everyone who is happy or not humble is creative and vice versa.
Alice is not tall.
Someone is generous or not brave.
Mary is both quiet and not tall.
Someone is humble.
Someone is kind or not brave.
Someone is both not happy and brave.
Someone is not rich or strong.
Someone is either not generous or not creative. | Mary is calm. | contradiction | (![X]:((~funny(X)<~>~rich(X))=>~tall(X)))&
(![X]:((~tall(X)&~funny(X))=>~wise(X)))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:((~old(X)&strong(X)))))&
((strong(john))=>(?[X]:((~brave(X)<~>wise(X)))))&
(![X]:((rich(X)|generous(X))<=>(~old(X)|happy(X))))&
(![X]:((patient(X)&calm(X))<=>(~patient(X)&wise(X))))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:(~happy(X))))&
(((~kind(john)<~>creative(john)))=>((patient(fred)&~quiet(fred))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~funny(X)<~>~wise(X))=>~strong(X)))&
(![X]:(calm(X)<=>generous(X)))&
(![X]:((curious(X)<~>~strong(X))=>(~kind(X)|~wise(X))))&
(![X]:((funny(X)&calm(X))<=>generous(X)))&
(![X]:((~wise(X)&wise(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(tall(X)<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)|~humble(X))<=>creative(X)))&
(~tall(alice))&
(?[X]:((generous(X)|~brave(X))))&
((quiet(mary)&~tall(mary)))&
(?[X]:(humble(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((~happy(X)&brave(X))))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((~generous(X)<~>~creative(X)))) | calm(mary) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4408824072366286313787915
% SZS output start Proof for 4408824072366286313787915
6. ! [X0] : ((calm(X0) & patient(X0)) <=> (wise(X0) & ~patient(X0))) [input p5]
14. ! [X0] : ((wise(X0) & ~wise(X0)) <=> (~patient(X0) <~> wise(X0))) [input p13]
25. calm(mary) [input hypothesis]
49. ! [X0] : (((calm(X0) & patient(X0)) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | (~calm(X0) | ~patient(X0)))) [nnf transformation 6]
50. ! [X0] : (((calm(X0) & patient(X0)) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ~calm(X0) | ~patient(X0))) [flattening 49]
66. ! [X0] : (((wise(X0) & ~wise(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~wise(X0) | wise(X0)))) [nnf transformation 14]
67. ! [X0] : (((wise(X0) & ~wise(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ~wise(X0) | wise(X0))) [flattening 66]
100. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 50]
102. patient(X0) | ~wise(X0) | patient(X0) [cnf transformation 50]
127. wise(X0) | wise(X0) | patient(X0) [cnf transformation 67]
146. calm(mary) [cnf transformation 25]
150. wise(X0) | patient(X0) [duplicate literal removal 127]
151. ~calm(X0) | ~patient(X0) [duplicate literal removal 100]
152. patient(X0) | ~wise(X0) [duplicate literal removal 102]
256. patient(X0) [subsumption resolution 150,152]
304. ~patient(mary) [resolution 151,146]
306. $false [subsumption resolution 304,256]
% SZS output end Proof for 4408824072366286313787915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both kind and not rich then someone is not wise or quiet.
Everyone who is either funny or not kind is not rich or not old and vice versa.
Everyone who is not calm or calm is not rich or not quiet.
If someone is generous then someone is not kind and vice versa.
If alice is both curious and calm then someone is not tall and vice versa.
Everyone who is not curious is either strong or creative.
If paul is both not happy and not kind then mary is not happy.
If someone is both not curious and generous then mary is not patient and vice versa.
If someone is calm then someone is both not tall and not humble and vice versa.
If paul is both quiet and not rich then mary is kind or generous and vice versa.
Everyone who is calm or happy is not funny.
Everyone who is old is both wise and generous.
Everyone who is both creative and not creative is happy or not happy.
If someone is either not old or not quiet then someone is quiet or rich and vice versa.
Everyone who is happy or not kind is not wise and vice versa.
Everyone who is either curious or tall is not kind and vice versa.
Someone is either happy or tall.
Alice is wise.
Someone is both not funny and patient.
Paul is both not curious and not generous.
Someone is both generous and wise.
Alice is both not rich and generous.
Someone is wise or kind.
Someone is not tall or funny. | Mary is not calm. | entailment | (((kind(alice)&~rich(alice)))=>(?[X]:((~wise(X)|quiet(X)))))&
(![X]:((funny(X)<~>~kind(X))<=>(~rich(X)|~old(X))))&
(![X]:((~calm(X)|calm(X))=>(~rich(X)|~quiet(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~kind(X))))&
(((curious(alice)&calm(alice)))<=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)=>(strong(X)<~>creative(X))))&
(((~happy(paul)&~kind(paul)))=>(~happy(mary)))&
((?[X]:((~curious(X)&generous(X))))<=>(~patient(mary)))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(((quiet(paul)&~rich(paul)))<=>((kind(mary)|generous(mary))))&
(![X]:((calm(X)|happy(X))=>~funny(X)))&
(![X]:(old(X)=>(wise(X)&generous(X))))&
(![X]:((creative(X)&~creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((happy(X)|~kind(X))<=>~wise(X)))&
(![X]:((curious(X)<~>tall(X))<=>~kind(X)))&
(?[X]:((happy(X)<~>tall(X))))&
(wise(alice))&
(?[X]:((~funny(X)&patient(X))))&
((~curious(paul)&~generous(paul)))&
(?[X]:((generous(X)&wise(X))))&
((~rich(alice)&generous(alice)))&
(?[X]:((wise(X)|kind(X))))&
(?[X]:((~tall(X)|funny(X)))) | ~calm(mary) | [
"p1",
"p4",
"p8",
"p10",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7388184821926986038355021
% SZS output start Proof for 7388184821926986038355021
2. ! [X0] : ((funny(X0) <~> ~kind(X0)) <=> (~old(X0) | ~rich(X0))) [input p1]
5. (calm(alice) & curious(alice)) <=> ? [X0] : ~tall(X0) [input p4]
9. ? [X0] : calm(X0) <=> ? [X0] : (~humble(X0) & ~tall(X0)) [input p8]
11. ! [X0] : ((happy(X0) | calm(X0)) => ~funny(X0)) [input p10]
15. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~wise(X0)) [input p14]
18. wise(alice) [input p17]
22. generous(alice) & ~rich(alice) [input p21]
25. calm(mary) [input hypothesis]
27. ? [X0] : calm(X0) <=> ? [X1] : (~humble(X1) & ~tall(X1)) [rectify 9]
36. ! [X0] : (~funny(X0) | (~happy(X0) & ~calm(X0))) [ennf transformation 11]
42. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [nnf transformation 2]
43. ! [X0] : ((((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0))))) [flattening 42]
49. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (~calm(alice) | ~curious(alice))) [nnf transformation 5]
50. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~calm(alice) | ~curious(alice)) [flattening 49]
51. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~calm(alice) | ~curious(alice)) [rectify 50]
52. ? [X1] : ~tall(X1) => ~tall(sK3) [choice axiom]
53. ((calm(alice) & curious(alice)) | ! [X0] : tall(X0)) & (~tall(sK3) | ~calm(alice) | ~curious(alice)) [skolemisation 51,52]
59. (? [X0] : calm(X0) | ! [X1] : (humble(X1) | tall(X1))) & (? [X1] : (~humble(X1) & ~tall(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 27]
60. (? [X0] : calm(X0) | ! [X1] : (humble(X1) | tall(X1))) & (? [X2] : (~humble(X2) & ~tall(X2)) | ! [X3] : ~calm(X3)) [rectify 59]
61. ? [X0] : calm(X0) => calm(sK5) [choice axiom]
62. ? [X2] : (~humble(X2) & ~tall(X2)) => (~humble(sK6) & ~tall(sK6)) [choice axiom]
63. (calm(sK5) | ! [X1] : (humble(X1) | tall(X1))) & ((~humble(sK6) & ~tall(sK6)) | ! [X3] : ~calm(X3)) [skolemisation 60,62,61]
71. ! [X0] : (((~kind(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 15]
72. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [flattening 71]
88. ~kind(X0) | funny(X0) | rich(X0) [cnf transformation 43]
98. calm(alice) | tall(X0) [cnf transformation 53]
105. ~tall(sK6) | ~calm(X3) [cnf transformation 63]
113. ~calm(X0) | ~funny(X0) [cnf transformation 36]
125. ~wise(X0) | kind(X0) [cnf transformation 72]
133. wise(alice) [cnf transformation 18]
140. ~rich(alice) [cnf transformation 22]
144. calm(mary) [cnf transformation 25]
146. 1 <=> kind(alice) [avatar definition]
147. kind(alice) <- (1) [avatar component clause 146]
150. 2 <=> rich(alice) [avatar definition]
151. ~rich(alice) <- (~2) [avatar component clause 150]
180. 9 <=> ! [X0] : tall(X0) [avatar definition]
181. tall(X0) <- (9) [avatar component clause 180]
183. 10 <=> calm(alice) [avatar definition]
185. calm(alice) <- (10) [avatar component clause 183]
186. 9 | 10 [avatar split clause 98,183,180]
237. 22 <=> ! [X3] : ~calm(X3) [avatar definition]
238. ~calm(X3) <- (22) [avatar component clause 237]
245. 24 <=> tall(sK6) [avatar definition]
247. ~tall(sK6) <- (~24) [avatar component clause 245]
248. 22 | ~24 [avatar split clause 105,245,237]
315. ~2 [avatar split clause 140,150]
331. ~funny(alice) <- (10) [resolution 113,185]
336. kind(alice) [resolution 125,133]
341. 1 [avatar split clause 336,146]
349. funny(alice) | rich(alice) <- (1) [resolution 88,147]
359. rich(alice) <- (1, 10) [subsumption resolution 349,331]
360. $false <- (1, ~2, 10) [subsumption resolution 359,151]
361. ~1 | 2 | ~10 [avatar contradiction clause 360]
363. $false <- (9, ~24) [resolution 181,247]
368. ~9 | 24 [avatar contradiction clause 363]
369. $false <- (22) [resolution 238,144]
372. ~22 [avatar contradiction clause 369]
373. $false [avatar sat refutation 186,248,315,341,361,368,372]
% SZS output end Proof for 7388184821926986038355021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both rich and calm then someone is funny or not calm.
If someone is either not tall or not patient then fred is both kind and not patient.
If fred is not generous or not curious then fred is either not humble or humble and vice versa.
Everyone who is not happy or patient is patient or strong.
If lucy is either happy or generous then someone is either not quiet or not curious.
If lucy is either not strong or not patient then fred is both not quiet and kind and vice versa.
If fred is not funny or not calm then mary is either patient or not wise.
Everyone who is not brave or not kind is quiet or not calm and vice versa.
Everyone who is happy is patient or strong and vice versa.
If someone is either not happy or old then susan is either quiet or brave and vice versa.
Everyone who is brave is happy or humble and vice versa.
If paul is either curious or strong then someone is both not old and not quiet.
If mary is both not brave and rich then fred is both not calm and not tall.
Everyone who is not kind is not calm.
If mary is either not quiet or brave then someone is either funny or brave and vice versa.
If alice is either not happy or curious then alice is either not calm or not rich.
John is either funny or not old.
John is calm or not calm.
Lucy is either tall or not rich.
Someone is funny or not strong.
Someone is creative or strong.
Someone is not strong or not humble.
Alice is not patient.
Mary is either not wise or tall. | Lucy is brave. | entailment | (((rich(john)&calm(john)))=>(?[X]:((funny(X)|~calm(X)))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(fred)&~patient(fred))))&
(((~generous(fred)|~curious(fred)))<=>((~humble(fred)<~>humble(fred))))&
(![X]:((~happy(X)|patient(X))=>(patient(X)|strong(X))))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((~quiet(X)<~>~curious(X)))))&
(((~strong(lucy)<~>~patient(lucy)))<=>((~quiet(fred)&kind(fred))))&
(((~funny(fred)|~calm(fred)))=>((patient(mary)<~>~wise(mary))))&
(![X]:((~brave(X)|~kind(X))<=>(quiet(X)|~calm(X))))&
(![X]:(happy(X)<=>(patient(X)|strong(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>((quiet(susan)<~>brave(susan))))&
(![X]:(brave(X)<=>(happy(X)|humble(X))))&
(((curious(paul)<~>strong(paul)))=>(?[X]:((~old(X)&~quiet(X)))))&
(((~brave(mary)&rich(mary)))=>((~calm(fred)&~tall(fred))))&
(![X]:(~kind(X)=>~calm(X)))&
(((~quiet(mary)<~>brave(mary)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(((~happy(alice)<~>curious(alice)))=>((~calm(alice)<~>~rich(alice))))&
((funny(john)<~>~old(john)))&
((calm(john)|~calm(john)))&
((tall(lucy)<~>~rich(lucy)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((creative(X)|strong(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(~patient(alice))&
((~wise(mary)<~>tall(mary))) | brave(lucy) | [
"p3",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2069091732222612243983177
% SZS output start Proof for 2069091732222612243983177
4. ! [X0] : ((patient(X0) | ~happy(X0)) => (strong(X0) | patient(X0))) [input p3]
9. ! [X0] : (happy(X0) <=> (strong(X0) | patient(X0))) [input p8]
11. ! [X0] : (brave(X0) <=> (humble(X0) | happy(X0))) [input p10]
25. ~brave(lucy) [input hypothesis]
30. ! [X0] : ((strong(X0) | patient(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 4]
31. ! [X0] : (strong(X0) | patient(X0) | (~patient(X0) & happy(X0))) [flattening 30]
52. ! [X0] : ((happy(X0) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | ~happy(X0))) [nnf transformation 9]
53. ! [X0] : ((happy(X0) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | ~happy(X0))) [flattening 52]
58. ! [X0] : ((brave(X0) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | ~brave(X0))) [nnf transformation 11]
59. ! [X0] : ((brave(X0) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | ~brave(X0))) [flattening 58]
86. strong(X0) | patient(X0) | happy(X0) [cnf transformation 31]
106. strong(X0) | patient(X0) | ~happy(X0) [cnf transformation 53]
107. ~patient(X0) | happy(X0) [cnf transformation 53]
108. ~strong(X0) | happy(X0) [cnf transformation 53]
118. ~happy(X0) | brave(X0) [cnf transformation 59]
149. ~brave(lucy) [cnf transformation 25]
259. strong(X0) | patient(X0) [subsumption resolution 106,86]
414. patient(X0) | happy(X0) [resolution 259,108]
418. happy(X0) [subsumption resolution 414,107]
430. brave(X0) [resolution 418,118]
444. $false [resolution 430,149]
% SZS output end Proof for 2069091732222612243983177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or curious is wise.
If paul is either brave or not brave then someone is not wise or old.
If someone is not curious or quiet then alice is either humble or not kind and vice versa.
If someone is not happy then someone is humble.
If someone is not tall or not brave then someone is both not tall and wise and vice versa.
Everyone who is creative or wise is quiet.
If someone is both happy and quiet then alice is either not strong or not creative and vice versa.
Everyone who is not humble or not tall is both not patient and not brave and vice versa.
Everyone who is either curious or not generous is not funny or not curious and vice versa.
If someone is either not rich or rich then paul is either quiet or not rich.
Everyone who is not funny is not happy or quiet and vice versa.
Everyone who is either creative or not humble is generous.
Everyone who is wise is not kind.
Everyone who is either not brave or not quiet is kind and vice versa.
Everyone who is either curious or patient is not tall.
If someone is not old or generous then someone is not brave and vice versa.
Susan is old.
Paul is either quiet or not old.
Someone is wise or not kind.
Mary is either not funny or not creative.
Mary is both not strong and not rich.
Alice is tall. | Mary is humble. | entailment | (![X]:((generous(X)<~>curious(X))=>wise(X)))&
(((brave(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)|old(X)))))&
((?[X]:((~curious(X)|quiet(X))))<=>((humble(alice)<~>~kind(alice))))&
((?[X]:(~happy(X)))=>(?[X]:(humble(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((creative(X)|wise(X))=>quiet(X)))&
((?[X]:((happy(X)&quiet(X))))<=>((~strong(alice)<~>~creative(alice))))&
(![X]:((~humble(X)|~tall(X))<=>(~patient(X)&~brave(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>((quiet(paul)<~>~rich(paul))))&
(![X]:(~funny(X)<=>(~happy(X)|quiet(X))))&
(![X]:((creative(X)<~>~humble(X))=>generous(X)))&
(![X]:(wise(X)=>~kind(X)))&
(![X]:((~brave(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((curious(X)<~>patient(X))=>~tall(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:(~brave(X))))&
(old(susan))&
((quiet(paul)<~>~old(paul)))&
(?[X]:((wise(X)|~kind(X))))&
((~funny(mary)<~>~creative(mary)))&
((~strong(mary)&~rich(mary)))&
(tall(alice)) | humble(mary) | [
"p4",
"p5",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 32026489808986367288481
% SZS output start Proof for 32026489808986367288481
5. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X0] : (wise(X0) & ~tall(X0)) [input p4]
6. ! [X0] : ((wise(X0) | creative(X0)) => quiet(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~brave(X0) & ~patient(X0))) [input p7]
13. ! [X0] : (wise(X0) => ~kind(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) <=> kind(X0)) [input p13]
23. ~humble(mary) [input hypothesis]
25. ? [X0] : (~brave(X0) | ~tall(X0)) <=> ? [X1] : (wise(X1) & ~tall(X1)) [rectify 5]
30. ! [X0] : (quiet(X0) | (~wise(X0) & ~creative(X0))) [ennf transformation 6]
33. ! [X0] : (~kind(X0) | ~wise(X0)) [ennf transformation 13]
46. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X1] : (wise(X1) & ~tall(X1)) | ! [X0] : (brave(X0) & tall(X0))) [nnf transformation 25]
47. (? [X0] : (~brave(X0) | ~tall(X0)) | ! [X1] : (~wise(X1) | tall(X1))) & (? [X2] : (wise(X2) & ~tall(X2)) | ! [X3] : (brave(X3) & tall(X3))) [rectify 46]
48. ? [X0] : (~brave(X0) | ~tall(X0)) => (~brave(sK3) | ~tall(sK3)) [choice axiom]
49. ? [X2] : (wise(X2) & ~tall(X2)) => (wise(sK4) & ~tall(sK4)) [choice axiom]
50. ((~brave(sK3) | ~tall(sK3)) | ! [X1] : (~wise(X1) | tall(X1))) & ((wise(sK4) & ~tall(sK4)) | ! [X3] : (brave(X3) & tall(X3))) [skolemisation 47,49,48]
55. ! [X0] : (((~tall(X0) | ~humble(X0)) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 8]
56. ! [X0] : ((~tall(X0) | ~humble(X0) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | (tall(X0) & humble(X0)))) [flattening 55]
63. ! [X0] : ((((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | ~kind(X0)) & (kind(X0) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0))))) [nnf transformation 14]
86. ~tall(sK4) | brave(X3) [cnf transformation 50]
87. wise(sK4) | tall(X3) [cnf transformation 50]
91. ~wise(X0) | quiet(X0) [cnf transformation 30]
100. ~brave(X0) | humble(X0) [cnf transformation 56]
101. ~brave(X0) | tall(X0) [cnf transformation 56]
118. ~kind(X0) | ~wise(X0) [cnf transformation 33]
119. ~quiet(X0) | kind(X0) | brave(X0) [cnf transformation 63]
137. ~humble(mary) [cnf transformation 23]
209. 15 <=> ! [X3] : brave(X3) [avatar definition]
210. brave(X3) <- (15) [avatar component clause 209]
212. 16 <=> wise(sK4) [avatar definition]
214. wise(sK4) <- (16) [avatar component clause 212]
217. 17 <=> ! [X3] : tall(X3) [avatar definition]
218. tall(X3) <- (17) [avatar component clause 217]
219. 17 | 16 [avatar split clause 87,212,217]
221. 18 <=> tall(sK4) [avatar definition]
223. ~tall(sK4) <- (~18) [avatar component clause 221]
224. 15 | ~18 [avatar split clause 86,221,209]
310. quiet(sK4) <- (16) [resolution 91,214]
333. kind(sK4) | brave(sK4) <- (16) [resolution 119,310]
346. 38 <=> brave(sK4) [avatar definition]
348. brave(sK4) <- (38) [avatar component clause 346]
350. 39 <=> kind(sK4) [avatar definition]
352. kind(sK4) <- (39) [avatar component clause 350]
353. 38 | 39 | ~16 [avatar split clause 333,212,350,346]
430. ~wise(sK4) <- (39) [resolution 352,118]
435. ~16 | ~39 [avatar split clause 430,350,212]
456. $false <- (17, ~18) [resolution 218,223]
459. ~17 | 18 [avatar contradiction clause 456]
470. tall(sK4) <- (38) [resolution 348,101]
474. 18 | ~38 [avatar split clause 470,346,221]
488. humble(X2) <- (15) [resolution 210,100]
499. $false <- (15) [resolution 488,137]
500. ~15 [avatar contradiction clause 499]
501. $false [avatar sat refutation 219,224,353,435,459,474,500]
% SZS output end Proof for 32026489808986367288481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not generous or funny then someone is not quiet or not creative. Everyone who is not patient or old is brave or quiet and vice versa. If lucy is not old then fred is not creative. If someone is either old or not wise then alice is both calm and not humble. Everyone who is not tall or quiet is both creative and not brave. Everyone who is either quiet or not creative is either quiet or not old. If john is not calm then mary is not wise or not creative. If someone is either not tall or happy then mary is not creative or generous and vice versa. If someone is old then john is both creative and happy and vice versa. If someone is either not curious or humble then someone is either not rich or patient. Everyone who is not tall is either not brave or not humble. If mary is not happy or not funny then alice is funny or not calm. If someone is not rich then someone is both not funny and patient. If mary is both not kind and not brave then mary is either not humble or humble and vice versa. If someone is not tall or not wise then lucy is both funny and not rich and vice versa. If someone is not kind or not brave then mary is not funny. Mary is happy. Susan is tall. Someone is not calm or kind. Someone is not wise. Lucy is either tall or not patient. Someone is not creative or not kind. Lucy is rich or not calm. Someone is both brave and happy. | Mary is funny. | contradiction | (((~generous(fred)|funny(fred)))=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~patient(X)|old(X))<=>(brave(X)|quiet(X))))&
((~old(lucy))=>(~creative(fred)))&
((?[X]:((old(X)<~>~wise(X))))=>((calm(alice)&~humble(alice))))&
(![X]:((~tall(X)|quiet(X))=>(creative(X)&~brave(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(quiet(X)<~>~old(X))))&
((~calm(john))=>((~wise(mary)|~creative(mary))))&
((?[X]:((~tall(X)<~>happy(X))))<=>((~creative(mary)|generous(mary))))&
((?[X]:(old(X)))<=>((creative(john)&happy(john))))&
((?[X]:((~curious(X)<~>humble(X))))=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:(~tall(X)=>(~brave(X)<~>~humble(X))))&
(((~happy(mary)|~funny(mary)))=>((funny(alice)|~calm(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((~funny(X)&patient(X)))))&
(((~kind(mary)&~brave(mary)))<=>((~humble(mary)<~>humble(mary))))&
((?[X]:((~tall(X)|~wise(X))))<=>((funny(lucy)&~rich(lucy))))&
((?[X]:((~kind(X)|~brave(X))))=>(~funny(mary)))&
(happy(mary))&
(tall(susan))&
(?[X]:((~calm(X)|kind(X))))&
(?[X]:(~wise(X)))&
((tall(lucy)<~>~patient(lucy)))&
(?[X]:((~creative(X)|~kind(X))))&
((rich(lucy)|~calm(lucy)))&
(?[X]:((brave(X)&happy(X)))) | funny(mary) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8131834208361557794236597
% SZS output start Proof for 8131834208361557794236597
14. (~brave(mary) & ~kind(mary)) <=> (~humble(mary) <~> humble(mary)) [input p13]
16. ? [X0] : (~brave(X0) | ~kind(X0)) => ~funny(mary) [input p15]
25. funny(mary) [input hypothesis]
40. ~funny(mary) | ! [X0] : (brave(X0) & kind(X0)) [ennf transformation 16]
65. ((~brave(mary) & ~kind(mary)) | ((~humble(mary) | ~humble(mary)) & (humble(mary) | humble(mary)))) & (((~humble(mary) | humble(mary)) & (humble(mary) | ~humble(mary))) | (brave(mary) | kind(mary))) [nnf transformation 14]
66. ((~brave(mary) & ~kind(mary)) | ((~humble(mary) | ~humble(mary)) & (humble(mary) | humble(mary)))) & (((~humble(mary) | humble(mary)) & (humble(mary) | ~humble(mary))) | brave(mary) | kind(mary)) [flattening 65]
122. ~kind(mary) | humble(mary) | humble(mary) [cnf transformation 66]
123. ~kind(mary) | ~humble(mary) | ~humble(mary) [cnf transformation 66]
131. ~funny(mary) | kind(X0) [cnf transformation 40]
143. funny(mary) [cnf transformation 25]
144. ~kind(mary) | humble(mary) [duplicate literal removal 122]
145. ~kind(mary) | ~humble(mary) [duplicate literal removal 123]
272. 27 <=> funny(mary) [avatar definition]
299. 33 <=> humble(mary) [avatar definition]
309. 35 <=> kind(mary) [avatar definition]
311. ~kind(mary) <- (~35) [avatar component clause 309]
312. ~33 | ~35 [avatar split clause 145,309,299]
313. 33 | ~35 [avatar split clause 144,309,299]
346. 43 <=> ! [X0] : kind(X0) [avatar definition]
347. kind(X0) <- (43) [avatar component clause 346]
348. 43 | ~27 [avatar split clause 131,272,346]
383. 27 [avatar split clause 143,272]
384. $false <- (~35, 43) [subsumption resolution 311,347]
385. 35 | ~43 [avatar contradiction clause 384]
390. $false [avatar sat refutation 312,313,348,383,385]
% SZS output end Proof for 8131834208361557794236597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not generous is creative or not rich and vice versa.
Everyone who is quiet or patient is not calm and vice versa.
If paul is brave then fred is both not tall and generous and vice versa.
If someone is tall or wise then john is both calm and not calm and vice versa.
Everyone who is curious is either not old or not wise and vice versa.
If john is either happy or calm then susan is either brave or kind and vice versa.
Everyone who is either not curious or not generous is both rich and curious.
Everyone who is brave is either not quiet or not calm and vice versa.
If lucy is either not tall or tall then someone is both rich and not wise and vice versa.
Everyone who is not old is humble or old.
If someone is both not old and generous then someone is both not creative and creative and vice versa.
Everyone who is wise or calm is humble or rich.
Everyone who is not happy is either not tall or not wise and vice versa.
If someone is either not strong or wise then someone is funny and vice versa.
If mary is tall or not patient then someone is quiet or old and vice versa.
Fred is not calm or calm.
Mary is either generous or not rich.
Susan is either not creative or not funny.
John is either not rich or not humble. | Susan is not rich. | neutral | (![X]:((~rich(X)<~>~generous(X))<=>(creative(X)|~rich(X))))&
(![X]:((quiet(X)|patient(X))<=>~calm(X)))&
((brave(paul))<=>((~tall(fred)&generous(fred))))&
((?[X]:((tall(X)|wise(X))))<=>((calm(john)&~calm(john))))&
(![X]:(curious(X)<=>(~old(X)<~>~wise(X))))&
(((happy(john)<~>calm(john)))<=>((brave(susan)<~>kind(susan))))&
(![X]:((~curious(X)<~>~generous(X))=>(rich(X)&curious(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~calm(X))))&
(((~tall(lucy)<~>tall(lucy)))<=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:(~old(X)=>(humble(X)|old(X))))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:((wise(X)|calm(X))=>(humble(X)|rich(X))))&
(![X]:(~happy(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~strong(X)<~>wise(X))))<=>(?[X]:(funny(X))))&
(((tall(mary)|~patient(mary)))<=>(?[X]:((quiet(X)|old(X)))))&
((~calm(fred)|calm(fred)))&
((generous(mary)<~>~rich(mary)))&
((~creative(susan)<~>~funny(susan)))&
((~rich(john)<~>~humble(john))) | ~rich(susan) | [] | null | 0 |
Everyone who is not kind or generous is either not quiet or happy and vice versa.
If someone is either not patient or old then someone is either not creative or wise.
Everyone who is not tall is creative and vice versa.
Everyone who is calm is not strong or not curious.
Everyone who is not quiet is either brave or patient.
If fred is rich or patient then someone is both kind and not brave and vice versa.
Everyone who is both kind and quiet is either not kind or happy.
Everyone who is either not wise or not curious is both not rich and creative and vice versa.
If someone is both creative and calm then someone is not happy or creative and vice versa.
Everyone who is both quiet and not creative is not generous or curious and vice versa.
If alice is not curious or not old then someone is both not rich and humble.
Everyone who is both not happy and rich is creative and vice versa.
Everyone who is kind or patient is both tall and old and vice versa.
Everyone who is either not generous or rich is rich and vice versa.
Everyone who is not quiet is not curious.
If someone is old or brave then paul is not creative and vice versa.
Someone is either old or kind.
John is either not funny or not wise.
Mary is not happy.
Someone is either happy or tall.
Someone is not quiet or brave. | Alice is generous. | entailment | (![X]:((~kind(X)|generous(X))<=>(~quiet(X)<~>happy(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:(~tall(X)<=>creative(X)))&
(![X]:(calm(X)=>(~strong(X)|~curious(X))))&
(![X]:(~quiet(X)=>(brave(X)<~>patient(X))))&
(((rich(fred)|patient(fred)))<=>(?[X]:((kind(X)&~brave(X)))))&
(![X]:((kind(X)&quiet(X))=>(~kind(X)<~>happy(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~rich(X)&creative(X))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((~happy(X)|creative(X)))))&
(![X]:((quiet(X)&~creative(X))<=>(~generous(X)|curious(X))))&
(((~curious(alice)|~old(alice)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~happy(X)&rich(X))<=>creative(X)))&
(![X]:((kind(X)|patient(X))<=>(tall(X)&old(X))))&
(![X]:((~generous(X)<~>rich(X))<=>rich(X)))&
(![X]:(~quiet(X)=>~curious(X)))&
((?[X]:((old(X)|brave(X))))<=>(~creative(paul)))&
(?[X]:((old(X)<~>kind(X))))&
((~funny(john)<~>~wise(john)))&
(~happy(mary))&
(?[X]:((happy(X)<~>tall(X))))&
(?[X]:((~quiet(X)|brave(X)))) | generous(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1821801787993045488113747
% SZS output start Proof for 1821801787993045488113747
14. ! [X0] : ((~generous(X0) <~> rich(X0)) <=> rich(X0)) [input p13]
22. ~generous(alice) [input hypothesis]
62. ! [X0] : ((((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | ~rich(X0)) & (rich(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0))))) [nnf transformation 14]
123. rich(X0) | rich(X0) | generous(X0) [cnf transformation 62]
126. ~rich(X0) | generous(X0) | ~rich(X0) [cnf transformation 62]
139. ~generous(alice) [cnf transformation 22]
140. rich(X0) | generous(X0) [duplicate literal removal 123]
141. ~rich(X0) | generous(X0) [duplicate literal removal 126]
230. generous(X0) [subsumption resolution 140,141]
283. $false [subsumption resolution 139,230]
% SZS output end Proof for 1821801787993045488113747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is both not brave and not calm.
If lucy is generous or strong then someone is either rich or not curious and vice versa.
If someone is not tall or not brave then fred is strong.
If someone is both not old and not rich then someone is not quiet or generous.
If mary is not humble then someone is not patient and vice versa.
If susan is not curious then mary is both not quiet and not creative and vice versa.
Everyone who is humble is both quiet and generous and vice versa.
Everyone who is both not wise and not quiet is either brave or patient and vice versa.
Everyone who is wise is not humble or wise and vice versa.
Everyone who is both not old and tall is both happy and generous and vice versa.
If paul is not curious then susan is both generous and humble.
If someone is both calm and not humble then someone is either not rich or not brave.
Everyone who is both generous and not patient is not generous and vice versa.
Everyone who is not calm or not funny is either creative or generous.
Everyone who is both not creative and old is either patient or brave and vice versa.
Everyone who is quiet is rich.
Someone is either not funny or happy.
Fred is either brave or kind.
Someone is not curious.
Mary is not wise.
Someone is both generous and not creative.
Someone is strong or old.
John is both not curious and brave. | Fred is old. | contradiction | ((?[X]:(funny(X)))=>(?[X]:((~brave(X)&~calm(X)))))&
(((generous(lucy)|strong(lucy)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
((?[X]:((~tall(X)|~brave(X))))=>(strong(fred)))&
((?[X]:((~old(X)&~rich(X))))=>(?[X]:((~quiet(X)|generous(X)))))&
((~humble(mary))<=>(?[X]:(~patient(X))))&
((~curious(susan))<=>((~quiet(mary)&~creative(mary))))&
(![X]:(humble(X)<=>(quiet(X)&generous(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(brave(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~humble(X)|wise(X))))&
(![X]:((~old(X)&tall(X))<=>(happy(X)&generous(X))))&
((~curious(paul))=>((generous(susan)&humble(susan))))&
((?[X]:((calm(X)&~humble(X))))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((generous(X)&~patient(X))<=>~generous(X)))&
(![X]:((~calm(X)|~funny(X))=>(creative(X)<~>generous(X))))&
(![X]:((~creative(X)&old(X))<=>(patient(X)<~>brave(X))))&
(![X]:(quiet(X)=>rich(X)))&
(?[X]:((~funny(X)<~>happy(X))))&
((brave(fred)<~>kind(fred)))&
(?[X]:(~curious(X)))&
(~wise(mary))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:((strong(X)|old(X))))&
((~curious(john)&brave(john))) | old(fred) | [
"p0",
"p6",
"p7",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 246930041785788938612593
% SZS output start Proof for 246930041785788938612593
1. ? [X0] : funny(X0) => ? [X0] : (~calm(X0) & ~brave(X0)) [input p0]
7. ! [X0] : (humble(X0) <=> (generous(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (brave(X0) <~> patient(X0))) [input p7]
9. ! [X0] : (wise(X0) <=> (wise(X0) | ~humble(X0))) [input p8]
13. ! [X0] : ((~patient(X0) & generous(X0)) <=> ~generous(X0)) [input p12]
14. ! [X0] : ((~funny(X0) | ~calm(X0)) => (creative(X0) <~> generous(X0))) [input p13]
15. ! [X0] : ((old(X0) & ~creative(X0)) <=> (patient(X0) <~> brave(X0))) [input p14]
24. old(fred) [input hypothesis]
25. ? [X0] : funny(X0) => ? [X1] : (~calm(X1) & ~brave(X1)) [rectify 1]
28. ? [X1] : (~calm(X1) & ~brave(X1)) | ! [X0] : ~funny(X0) [ennf transformation 25]
33. ! [X0] : ((creative(X0) <~> generous(X0)) | (funny(X0) & calm(X0))) [ennf transformation 14]
35. ? [X0] : (~calm(X0) & ~brave(X0)) | ! [X1] : ~funny(X1) [rectify 28]
36. ? [X0] : (~calm(X0) & ~brave(X0)) => (~calm(sK0) & ~brave(sK0)) [choice axiom]
37. (~calm(sK0) & ~brave(sK0)) | ! [X1] : ~funny(X1) [skolemisation 35,36]
52. ! [X0] : ((humble(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ~humble(X0))) [nnf transformation 7]
53. ! [X0] : ((humble(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ~humble(X0))) [flattening 52]
54. ! [X0] : (((~quiet(X0) & ~wise(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (quiet(X0) | wise(X0)))) [nnf transformation 8]
55. ! [X0] : (((~quiet(X0) & ~wise(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | quiet(X0) | wise(X0))) [flattening 54]
56. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 9]
57. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~wise(X0))) [flattening 56]
64. ! [X0] : (((~patient(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | (patient(X0) | ~generous(X0)))) [nnf transformation 13]
65. ! [X0] : (((~patient(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | patient(X0) | ~generous(X0))) [flattening 64]
66. ! [X0] : (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (funny(X0) & calm(X0))) [nnf transformation 33]
67. ! [X0] : (((old(X0) & ~creative(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~old(X0) | creative(X0)))) [nnf transformation 15]
68. ! [X0] : (((old(X0) & ~creative(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~old(X0) | creative(X0))) [flattening 67]
79. ~brave(sK0) | ~funny(X1) [cnf transformation 37]
95. ~humble(X0) | quiet(X0) [cnf transformation 53]
101. ~wise(X0) | brave(X0) | ~patient(X0) [cnf transformation 55]
103. ~patient(X0) | brave(X0) | ~quiet(X0) [cnf transformation 55]
105. wise(X0) | humble(X0) [cnf transformation 57]
115. ~generous(X0) | patient(X0) | ~generous(X0) [cnf transformation 65]
116. generous(X0) | generous(X0) [cnf transformation 65]
121. ~generous(X0) | ~creative(X0) | funny(X0) [cnf transformation 66]
123. ~patient(X0) | ~brave(X0) | ~old(X0) | creative(X0) [cnf transformation 68]
140. old(fred) [cnf transformation 24]
141. ~generous(X0) | patient(X0) [duplicate literal removal 115]
142. generous(X0) [duplicate literal removal 116]
144. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
145. ~funny(X1) <- (1) [avatar component clause 144]
152. 3 <=> brave(sK0) [avatar definition]
154. ~brave(sK0) <- (~3) [avatar component clause 152]
155. 1 | ~3 [avatar split clause 79,152,144]
185. 10 <=> ! [X0] : brave(X0) [avatar definition]
186. brave(X0) <- (10) [avatar component clause 185]
209. 16 <=> ! [X0] : patient(X0) [avatar definition]
210. patient(X0) <- (16) [avatar component clause 209]
263. patient(X0) [subsumption resolution 141,142]
264. 16 [avatar split clause 263,209]
265. ~creative(X0) | funny(X0) [subsumption resolution 121,142]
308. brave(X0) | ~patient(X0) | humble(X0) [resolution 101,105]
309. humble(X0) | brave(X0) <- (16) [subsumption resolution 308,210]
311. quiet(X1) | brave(X1) <- (16) [resolution 309,95]
317. brave(X0) | ~quiet(X0) <- (16) [resolution 103,210]
318. brave(X0) <- (16) [subsumption resolution 317,311]
319. 10 | ~16 [avatar split clause 318,209,185]
320. $false <- (~3, 10) [resolution 186,154]
321. 3 | ~10 [avatar contradiction clause 320]
339. ~brave(X0) | ~old(X0) | creative(X0) <- (16) [resolution 123,210]
340. ~old(X0) | creative(X0) <- (10, 16) [subsumption resolution 339,186]
341. creative(fred) <- (10, 16) [resolution 340,140]
345. funny(fred) <- (10, 16) [resolution 341,265]
346. $false <- (1, 10, 16) [subsumption resolution 345,145]
347. ~1 | ~10 | ~16 [avatar contradiction clause 346]
348. $false [avatar sat refutation 155,264,319,321,347]
% SZS output end Proof for 246930041785788938612593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or kind then someone is either not wise or humble and vice versa. Everyone who is happy is not old and vice versa. Everyone who is not happy is both generous and calm. Everyone who is old or rich is kind. Everyone who is funny is not creative or not kind. Everyone who is not humble or old is rich or not curious. If lucy is curious then fred is either strong or creative. Everyone who is both humble and generous is both kind and happy. Everyone who is either not generous or not curious is either not brave or not tall and vice versa. Everyone who is not creative is tall or not old and vice versa. Everyone who is humble or generous is humble. Everyone who is both happy and not rich is funny. Everyone who is not wise is quiet or not kind and vice versa. If lucy is either patient or not funny then someone is both not patient and not tall and vice versa. If susan is both quiet and not creative then lucy is both curious and not calm. If someone is not generous then john is either not tall or not patient and vice versa. Someone is not happy or not quiet. John is both not brave and not humble. John is either tall or not generous. Someone is not wise. Susan is both not curious and not kind. Someone is either funny or not calm. Mary is not wise. | Lucy is funny. | neutral | ((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
(![X]:((humble(X)&generous(X))=>(kind(X)&happy(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(tall(X)|~old(X))))&
(![X]:((humble(X)|generous(X))=>humble(X)))&
(![X]:((happy(X)&~rich(X))=>funny(X)))&
(![X]:(~wise(X)<=>(quiet(X)|~kind(X))))&
(((patient(lucy)<~>~funny(lucy)))<=>(?[X]:((~patient(X)&~tall(X)))))&
(((quiet(susan)&~creative(susan)))=>((curious(lucy)&~calm(lucy))))&
((?[X]:(~generous(X)))<=>((~tall(john)<~>~patient(john))))&
(?[X]:((~happy(X)|~quiet(X))))&
((~brave(john)&~humble(john)))&
((tall(john)<~>~generous(john)))&
(?[X]:(~wise(X)))&
((~curious(susan)&~kind(susan)))&
(?[X]:((funny(X)<~>~calm(X))))&
(~wise(mary)) | funny(lucy) | [] | null | 0 |
If someone is not curious or not calm then paul is not old and vice versa. Everyone who is either tall or not rich is humble and vice versa. Everyone who is not humble is creative. If paul is wise then paul is not wise. Everyone who is both rich and not rich is humble or rich. Everyone who is either not patient or not strong is generous and vice versa. Everyone who is curious is either not curious or not kind and vice versa. Everyone who is both not calm and not humble is either not curious or kind. Everyone who is both not curious and rich is both calm and not strong and vice versa. Everyone who is either not curious or not happy is both not old and humble and vice versa. If someone is both brave and not brave then mary is both not old and not tall and vice versa. If someone is not curious or not creative then fred is either not tall or not rich. Everyone who is generous is both wise and not strong. Everyone who is old is either calm or not tall. If someone is not patient or not funny then someone is both not happy and patient. If someone is not generous or not tall then susan is strong. Someone is either wise or not curious. Susan is not funny or happy. Someone is not old or rich. Someone is brave or not strong. Fred is both brave and not tall. Paul is both not tall and curious. Paul is both not happy and calm. | Fred is not kind. | entailment | ((?[X]:((~curious(X)|~calm(X))))<=>(~old(paul)))&
(![X]:((tall(X)<~>~rich(X))<=>humble(X)))&
(![X]:(~humble(X)=>creative(X)))&
((wise(paul))=>(~wise(paul)))&
(![X]:((rich(X)&~rich(X))=>(humble(X)|rich(X))))&
(![X]:((~patient(X)<~>~strong(X))<=>generous(X)))&
(![X]:(curious(X)<=>(~curious(X)<~>~kind(X))))&
(![X]:((~calm(X)&~humble(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~curious(X)&rich(X))<=>(calm(X)&~strong(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>(~old(X)&humble(X))))&
((?[X]:((brave(X)&~brave(X))))<=>((~old(mary)&~tall(mary))))&
((?[X]:((~curious(X)|~creative(X))))=>((~tall(fred)<~>~rich(fred))))&
(![X]:(generous(X)=>(wise(X)&~strong(X))))&
(![X]:(old(X)=>(calm(X)<~>~tall(X))))&
((?[X]:((~patient(X)|~funny(X))))=>(?[X]:((~happy(X)&patient(X)))))&
((?[X]:((~generous(X)|~tall(X))))=>(strong(susan)))&
(?[X]:((wise(X)<~>~curious(X))))&
((~funny(susan)|happy(susan)))&
(?[X]:((~old(X)|rich(X))))&
(?[X]:((brave(X)|~strong(X))))&
((brave(fred)&~tall(fred)))&
((~tall(paul)&curious(paul)))&
((~happy(paul)&calm(paul))) | ~kind(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5137803985820193285457274
% SZS output start Proof for 5137803985820193285457274
7. ! [X0] : (curious(X0) <=> (~curious(X0) <~> ~kind(X0))) [input p6]
24. kind(fred) [input hypothesis]
44. ! [X0] : ((curious(X0) | ((~curious(X0) | kind(X0)) & (~kind(X0) | curious(X0)))) & (((kind(X0) | curious(X0)) & (~kind(X0) | ~curious(X0))) | ~curious(X0))) [nnf transformation 7]
80. ~kind(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 44]
82. curious(X0) | ~kind(X0) | curious(X0) [cnf transformation 44]
123. kind(fred) [cnf transformation 24]
124. ~kind(X0) | ~curious(X0) [duplicate literal removal 80]
125. curious(X0) | ~kind(X0) [duplicate literal removal 82]
149. ~kind(X0) [subsumption resolution 124,125]
243. $false [subsumption resolution 123,149]
% SZS output end Proof for 5137803985820193285457274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is not patient and vice versa.
Everyone who is not tall or not humble is not old or not generous.
Everyone who is either curious or patient is not happy and vice versa.
Everyone who is humble is either patient or not happy.
Everyone who is not humble is not patient.
If paul is either not calm or not old then someone is funny or not humble.
Everyone who is not rich or patient is patient and vice versa.
Everyone who is either not wise or brave is tall and vice versa.
Everyone who is both funny and brave is either not wise or tall.
If susan is not humble or not strong then alice is either not patient or quiet and vice versa.
If john is wise then someone is not patient or not curious and vice versa.
Everyone who is happy or strong is both rich and not brave and vice versa.
Everyone who is both generous and happy is either brave or happy.
If someone is either not humble or strong then someone is not brave and vice versa.
If mary is either happy or not calm then someone is either humble or happy and vice versa.
Everyone who is not quiet or not patient is both not old and kind.
Fred is not brave or happy.
Paul is not calm.
Someone is kind.
Alice is not tall.
Someone is curious or not rich. | Paul is wise. | neutral | (![X]:(old(X)<=>~patient(X)))&
(![X]:((~tall(X)|~humble(X))=>(~old(X)|~generous(X))))&
(![X]:((curious(X)<~>patient(X))<=>~happy(X)))&
(![X]:(humble(X)=>(patient(X)<~>~happy(X))))&
(![X]:(~humble(X)=>~patient(X)))&
(((~calm(paul)<~>~old(paul)))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:((~rich(X)|patient(X))<=>patient(X)))&
(![X]:((~wise(X)<~>brave(X))<=>tall(X)))&
(![X]:((funny(X)&brave(X))=>(~wise(X)<~>tall(X))))&
(((~humble(susan)|~strong(susan)))<=>((~patient(alice)<~>quiet(alice))))&
((wise(john))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((happy(X)|strong(X))<=>(rich(X)&~brave(X))))&
(![X]:((generous(X)&happy(X))=>(brave(X)<~>happy(X))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:(~brave(X))))&
(((happy(mary)<~>~calm(mary)))<=>(?[X]:((humble(X)<~>happy(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(~old(X)&kind(X))))&
((~brave(fred)|happy(fred)))&
(~calm(paul))&
(?[X]:(kind(X)))&
(~tall(alice))&
(?[X]:((curious(X)|~rich(X)))) | wise(paul) | [] | null | 0 |
Everyone who is not calm or not strong is both old and wise and vice versa.
If john is not happy or kind then someone is either not tall or not rich.
Everyone who is not kind or curious is either rich or not kind.
Everyone who is not patient or not quiet is not rich or not funny and vice versa.
Everyone who is brave is rich or quiet and vice versa.
If alice is either not curious or not patient then someone is calm.
If alice is either not patient or calm then someone is both kind and not old.
If paul is patient or quiet then susan is both old and not wise and vice versa.
Everyone who is not strong is both funny and curious and vice versa.
If lucy is generous then someone is either funny or not curious and vice versa.
If john is not happy then fred is calm.
Everyone who is not generous or not creative is both not wise and brave.
Everyone who is not patient is creative and vice versa.
Everyone who is both not happy and not humble is tall.
If paul is both not strong and tall then someone is either not old or patient.
Everyone who is both quiet and curious is happy and vice versa.
Susan is not quiet.
Fred is both creative and not funny.
Someone is either not old or not wise.
Lucy is either not quiet or not funny.
Someone is old or not rich.
John is brave or not old.
Someone is either not happy or old.
John is both not funny and not tall. | Fred is not patient. | entailment | (![X]:((~calm(X)|~strong(X))<=>(old(X)&wise(X))))&
(((~happy(john)|kind(john)))=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~kind(X)|curious(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(~rich(X)|~funny(X))))&
(![X]:(brave(X)<=>(rich(X)|quiet(X))))&
(((~curious(alice)<~>~patient(alice)))=>(?[X]:(calm(X))))&
(((~patient(alice)<~>calm(alice)))=>(?[X]:((kind(X)&~old(X)))))&
(((patient(paul)|quiet(paul)))<=>((old(susan)&~wise(susan))))&
(![X]:(~strong(X)<=>(funny(X)&curious(X))))&
((generous(lucy))<=>(?[X]:((funny(X)<~>~curious(X)))))&
((~happy(john))=>(calm(fred)))&
(![X]:((~generous(X)|~creative(X))=>(~wise(X)&brave(X))))&
(![X]:(~patient(X)<=>creative(X)))&
(![X]:((~happy(X)&~humble(X))=>tall(X)))&
(((~strong(paul)&tall(paul)))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((quiet(X)&curious(X))<=>happy(X)))&
(~quiet(susan))&
((creative(fred)&~funny(fred)))&
(?[X]:((~old(X)<~>~wise(X))))&
((~quiet(lucy)<~>~funny(lucy)))&
(?[X]:((old(X)|~rich(X))))&
((brave(john)|~old(john)))&
(?[X]:((~happy(X)<~>old(X))))&
((~funny(john)&~tall(john))) | ~patient(fred) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 824202642789764930882160
% SZS output start Proof for 824202642789764930882160
13. ! [X0] : (~patient(X0) <=> creative(X0)) [input p12]
18. ~funny(fred) & creative(fred) [input p17]
25. patient(fred) [input hypothesis]
60. ! [X0] : ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))) [nnf transformation 13]
117. ~creative(X0) | ~patient(X0) [cnf transformation 60]
124. creative(fred) [cnf transformation 18]
136. patient(fred) [cnf transformation 25]
321. ~patient(fred) [resolution 117,124]
324. $false [subsumption resolution 321,136]
% SZS output end Proof for 824202642789764930882160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious is both not kind and calm and vice versa.
If fred is both not wise and wise then someone is either not humble or not calm and vice versa.
Everyone who is happy is either funny or not patient and vice versa.
Everyone who is not calm is both kind and patient.
Everyone who is both wise and not generous is tall and vice versa.
Everyone who is either not funny or not patient is either old or not rich and vice versa.
If someone is both not creative and quiet then someone is both funny and not rich.
Everyone who is not creative is either not wise or quiet and vice versa.
If paul is kind or funny then susan is either funny or not quiet and vice versa.
If someone is either not old or not brave then alice is not wise or not humble and vice versa.
Everyone who is not kind or rich is both humble and not humble.
Everyone who is either not generous or not happy is either calm or not calm.
Everyone who is quiet is either rich or old.
If john is both rich and not tall then someone is humble.
Everyone who is not brave is not quiet or not curious and vice versa.
If someone is either not happy or not old then someone is not brave.
John is not happy or not rich.
Someone is either not humble or not old.
Mary is not calm.
Someone is either old or wise.
Lucy is both not funny and not strong.
Someone is quiet. | Lucy is funny. | contradiction | (![X]:((calm(X)|curious(X))<=>(~kind(X)&calm(X))))&
(((~wise(fred)&wise(fred)))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>~patient(X))))&
(![X]:(~calm(X)=>(kind(X)&patient(X))))&
(![X]:((wise(X)&~generous(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((funny(X)&~rich(X)))))&
(![X]:(~creative(X)<=>(~wise(X)<~>quiet(X))))&
(((kind(paul)|funny(paul)))<=>((funny(susan)<~>~quiet(susan))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(alice)|~humble(alice))))&
(![X]:((~kind(X)|rich(X))=>(humble(X)&~humble(X))))&
(![X]:((~generous(X)<~>~happy(X))=>(calm(X)<~>~calm(X))))&
(![X]:(quiet(X)=>(rich(X)<~>old(X))))&
(((rich(john)&~tall(john)))=>(?[X]:(humble(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|~curious(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:(~brave(X))))&
((~happy(john)|~rich(john)))&
(?[X]:((~humble(X)<~>~old(X))))&
(~calm(mary))&
(?[X]:((old(X)<~>wise(X))))&
((~funny(lucy)&~strong(lucy)))&
(?[X]:(quiet(X))) | funny(lucy) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1302891727705028258203777
% SZS output start Proof for 1302891727705028258203777
21. ~strong(lucy) & ~funny(lucy) [input p20]
23. funny(lucy) [input hypothesis]
28. ~funny(lucy) [pure predicate removal 21]
142. ~funny(lucy) [cnf transformation 28]
144. funny(lucy) [cnf transformation 23]
257. $false [subsumption resolution 144,142]
% SZS output end Proof for 1302891727705028258203777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or kind is both not humble and not happy. Everyone who is rich or kind is not generous or funny and vice versa. If someone is either not creative or funny then mary is both not quiet and not curious. If susan is kind or not old then lucy is wise or not curious. Everyone who is not calm or brave is both funny and rich and vice versa. Everyone who is happy or not happy is not creative and vice versa. Everyone who is not tall or rich is both not wise and wise. Everyone who is not old is both not quiet and humble. Everyone who is both humble and not happy is not happy. If someone is curious then mary is curious or creative and vice versa. If someone is patient then someone is not kind or old. Everyone who is not patient is not rich or humble and vice versa. Everyone who is either quiet or not creative is patient or rich. Everyone who is either not brave or not happy is strong or not wise. Alice is not creative. John is curious or not curious. Someone is both quiet and strong. Someone is humble or curious. Someone is both curious and not happy. Alice is not curious. | John is curious. | neutral | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((rich(X)|kind(X))<=>(~generous(X)|funny(X))))&
((?[X]:((~creative(X)<~>funny(X))))=>((~quiet(mary)&~curious(mary))))&
(((kind(susan)|~old(susan)))=>((wise(lucy)|~curious(lucy))))&
(![X]:((~calm(X)|brave(X))<=>(funny(X)&rich(X))))&
(![X]:((happy(X)|~happy(X))<=>~creative(X)))&
(![X]:((~tall(X)|rich(X))=>(~wise(X)&wise(X))))&
(![X]:(~old(X)=>(~quiet(X)&humble(X))))&
(![X]:((humble(X)&~happy(X))=>~happy(X)))&
((?[X]:(curious(X)))<=>((curious(mary)|creative(mary))))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:(~patient(X)<=>(~rich(X)|humble(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(patient(X)|rich(X))))&
(![X]:((~brave(X)<~>~happy(X))=>(strong(X)|~wise(X))))&
(~creative(alice))&
((curious(john)|~curious(john)))&
(?[X]:((quiet(X)&strong(X))))&
(?[X]:((humble(X)|curious(X))))&
(?[X]:((curious(X)&~happy(X))))&
(~curious(alice)) | curious(john) | [] | null | 0 |
Everyone who is both old and curious is not kind or not happy and vice versa.
If paul is either strong or calm then someone is both brave and generous.
If someone is both not humble and quiet then susan is kind and vice versa.
Everyone who is not calm or not kind is not brave.
Everyone who is both tall and not rich is either humble or not old and vice versa.
If alice is not humble then someone is not curious and vice versa.
Everyone who is either humble or rich is either wise or not kind and vice versa.
Everyone who is not wise or not quiet is both tall and generous.
If paul is both quiet and tall then someone is either not rich or not kind and vice versa.
If lucy is both not curious and not brave then someone is funny and vice versa.
Everyone who is both funny and not happy is both calm and strong and vice versa.
Everyone who is funny is both wise and not creative and vice versa.
Everyone who is wise is either generous or not old.
Everyone who is not quiet is not rich or curious.
Everyone who is both not creative and not tall is funny and vice versa.
Everyone who is strong is both not curious and not rich and vice versa.
Susan is either curious or tall.
Susan is not generous.
Someone is either not tall or quiet.
John is both not quiet and not kind.
Fred is either wise or happy.
Someone is rich or not wise.
Paul is brave.
Paul is either not curious or old. | Fred is not funny. | entailment | (![X]:((old(X)&curious(X))<=>(~kind(X)|~happy(X))))&
(((strong(paul)<~>calm(paul)))=>(?[X]:((brave(X)&generous(X)))))&
((?[X]:((~humble(X)&quiet(X))))<=>(kind(susan)))&
(![X]:((~calm(X)|~kind(X))=>~brave(X)))&
(![X]:((tall(X)&~rich(X))<=>(humble(X)<~>~old(X))))&
((~humble(alice))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)<~>rich(X))<=>(wise(X)<~>~kind(X))))&
(![X]:((~wise(X)|~quiet(X))=>(tall(X)&generous(X))))&
(((quiet(paul)&tall(paul)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(((~curious(lucy)&~brave(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)&~happy(X))<=>(calm(X)&strong(X))))&
(![X]:(funny(X)<=>(wise(X)&~creative(X))))&
(![X]:(wise(X)=>(generous(X)<~>~old(X))))&
(![X]:(~quiet(X)=>(~rich(X)|curious(X))))&
(![X]:((~creative(X)&~tall(X))<=>funny(X)))&
(![X]:(strong(X)<=>(~curious(X)&~rich(X))))&
((curious(susan)<~>tall(susan)))&
(~generous(susan))&
(?[X]:((~tall(X)<~>quiet(X))))&
((~quiet(john)&~kind(john)))&
((wise(fred)<~>happy(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(brave(paul))&
((~curious(paul)<~>old(paul))) | ~funny(fred) | [
"p0",
"p10",
"p11",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2050102220595160139882218
% SZS output start Proof for 2050102220595160139882218
1. ! [X0] : ((curious(X0) & old(X0)) <=> (~happy(X0) | ~kind(X0))) [input p0]
11. ! [X0] : ((~happy(X0) & funny(X0)) <=> (strong(X0) & calm(X0))) [input p10]
12. ! [X0] : (funny(X0) <=> (~creative(X0) & wise(X0))) [input p11]
16. ! [X0] : (strong(X0) <=> (~rich(X0) & ~curious(X0))) [input p15]
21. wise(fred) <~> happy(fred) [input p20]
25. funny(fred) [input hypothesis]
32. ! [X0] : (((curious(X0) & old(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 1]
33. ! [X0] : (((curious(X0) & old(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~curious(X0) | ~old(X0))) [flattening 32]
58. ! [X0] : (((~happy(X0) & funny(X0)) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 11]
59. ! [X0] : (((~happy(X0) & funny(X0)) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | happy(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : ((funny(X0) | (creative(X0) | ~wise(X0))) & ((~creative(X0) & wise(X0)) | ~funny(X0))) [nnf transformation 12]
61. ! [X0] : ((funny(X0) | creative(X0) | ~wise(X0)) & ((~creative(X0) & wise(X0)) | ~funny(X0))) [flattening 60]
65. ! [X0] : ((strong(X0) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | ~strong(X0))) [nnf transformation 16]
66. ! [X0] : ((strong(X0) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | ~strong(X0))) [flattening 65]
71. (~happy(fred) | ~wise(fred)) & (happy(fred) | wise(fred)) [nnf transformation 21]
79. happy(X0) | curious(X0) [cnf transformation 33]
119. ~funny(X0) | happy(X0) | strong(X0) [cnf transformation 59]
122. ~funny(X0) | wise(X0) [cnf transformation 61]
131. ~strong(X0) | ~curious(X0) [cnf transformation 66]
142. ~happy(fred) | ~wise(fred) [cnf transformation 71]
147. funny(fred) [cnf transformation 25]
259. 24 <=> wise(fred) [avatar definition]
263. 25 <=> happy(fred) [avatar definition]
265. ~happy(fred) <- (~25) [avatar component clause 263]
266. ~24 | ~25 [avatar split clause 142,263,259]
292. curious(fred) <- (~25) [resolution 79,265]
307. wise(fred) [resolution 122,147]
381. happy(fred) | strong(fred) [resolution 119,147]
383. strong(fred) <- (~25) [subsumption resolution 381,265]
408. ~curious(fred) <- (~25) [resolution 383,131]
409. $false <- (~25) [subsumption resolution 408,292]
410. 25 [avatar contradiction clause 409]
411. 24 [avatar split clause 307,259]
431. $false [avatar sat refutation 266,410,411]
% SZS output end Proof for 2050102220595160139882218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not generous is both not wise and calm and vice versa.
Everyone who is both happy and brave is either not brave or rich and vice versa.
Everyone who is calm is not happy or creative and vice versa.
Everyone who is both not calm and brave is not rich or quiet and vice versa.
Everyone who is both strong and happy is calm or curious.
If someone is not happy then lucy is not funny or calm and vice versa.
Everyone who is both not patient and wise is not rich and vice versa.
Everyone who is both not wise and not funny is both wise and kind and vice versa.
Everyone who is not old is patient.
Everyone who is both brave and not patient is both kind and patient.
If lucy is both not wise and calm then susan is either not creative or humble and vice versa.
If someone is either creative or not calm then someone is not kind or not generous.
Everyone who is either funny or not curious is either funny or generous and vice versa.
If mary is patient or not quiet then paul is either not old or kind and vice versa.
If mary is quiet or brave then someone is not generous or calm and vice versa.
Everyone who is not humble is either kind or quiet and vice versa.
Lucy is calm.
Someone is either not generous or not quiet.
Someone is both patient and not calm.
Someone is not happy.
Someone is not patient or not rich.
Someone is humble or calm.
Someone is not wise or not calm. | Mary is rich. | entailment | (![X]:((wise(X)&~generous(X))<=>(~wise(X)&calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~brave(X)<~>rich(X))))&
(![X]:(calm(X)<=>(~happy(X)|creative(X))))&
(![X]:((~calm(X)&brave(X))<=>(~rich(X)|quiet(X))))&
(![X]:((strong(X)&happy(X))=>(calm(X)|curious(X))))&
((?[X]:(~happy(X)))<=>((~funny(lucy)|calm(lucy))))&
(![X]:((~patient(X)&wise(X))<=>~rich(X)))&
(![X]:((~wise(X)&~funny(X))<=>(wise(X)&kind(X))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((brave(X)&~patient(X))=>(kind(X)&patient(X))))&
(((~wise(lucy)&calm(lucy)))<=>((~creative(susan)<~>humble(susan))))&
((?[X]:((creative(X)<~>~calm(X))))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:((funny(X)<~>~curious(X))<=>(funny(X)<~>generous(X))))&
(((patient(mary)|~quiet(mary)))<=>((~old(paul)<~>kind(paul))))&
(((quiet(mary)|brave(mary)))<=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:(~humble(X)<=>(kind(X)<~>quiet(X))))&
(calm(lucy))&
(?[X]:((~generous(X)<~>~quiet(X))))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~patient(X)|~rich(X))))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:((~wise(X)|~calm(X)))) | rich(mary) | [
"p2",
"p3",
"p6",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3330451108568358766314106
% SZS output start Proof for 3330451108568358766314106
3. ! [X0] : (calm(X0) <=> (creative(X0) | ~happy(X0))) [input p2]
4. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (quiet(X0) | ~rich(X0))) [input p3]
7. ! [X0] : ((wise(X0) & ~patient(X0)) <=> ~rich(X0)) [input p6]
10. ! [X0] : ((~patient(X0) & brave(X0)) => (patient(X0) & kind(X0))) [input p9]
15. (brave(mary) | quiet(mary)) <=> ? [X0] : (calm(X0) | ~generous(X0)) [input p14]
20. ? [X0] : ~happy(X0) [input p19]
24. ~rich(mary) [input hypothesis]
28. ! [X0] : ((patient(X0) & kind(X0)) | (patient(X0) | ~brave(X0))) [ennf transformation 10]
29. ! [X0] : ((patient(X0) & kind(X0)) | patient(X0) | ~brave(X0)) [flattening 28]
35. ! [X0] : ((calm(X0) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | ~calm(X0))) [nnf transformation 3]
36. ! [X0] : ((calm(X0) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ~calm(X0))) [flattening 35]
37. ! [X0] : (((brave(X0) & ~calm(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (~brave(X0) | calm(X0)))) [nnf transformation 4]
38. ! [X0] : (((brave(X0) & ~calm(X0)) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | ~brave(X0) | calm(X0))) [flattening 37]
44. ! [X0] : (((wise(X0) & ~patient(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) | patient(X0)))) [nnf transformation 7]
45. ! [X0] : (((wise(X0) & ~patient(X0)) | rich(X0)) & (~rich(X0) | ~wise(X0) | patient(X0))) [flattening 44]
57. ((brave(mary) | quiet(mary)) | ! [X0] : (~calm(X0) & generous(X0))) & (? [X0] : (calm(X0) | ~generous(X0)) | (~brave(mary) & ~quiet(mary))) [nnf transformation 15]
58. (brave(mary) | quiet(mary) | ! [X0] : (~calm(X0) & generous(X0))) & (? [X0] : (calm(X0) | ~generous(X0)) | (~brave(mary) & ~quiet(mary))) [flattening 57]
59. (brave(mary) | quiet(mary) | ! [X0] : (~calm(X0) & generous(X0))) & (? [X1] : (calm(X1) | ~generous(X1)) | (~brave(mary) & ~quiet(mary))) [rectify 58]
60. ? [X1] : (calm(X1) | ~generous(X1)) => (calm(sK2) | ~generous(sK2)) [choice axiom]
61. (brave(mary) | quiet(mary) | ! [X0] : (~calm(X0) & generous(X0))) & ((calm(sK2) | ~generous(sK2)) | (~brave(mary) & ~quiet(mary))) [skolemisation 59,60]
68. ? [X0] : ~happy(X0) => ~happy(sK5) [choice axiom]
69. ~happy(sK5) [skolemisation 20,68]
87. happy(X0) | calm(X0) [cnf transformation 36]
93. ~quiet(X0) | brave(X0) [cnf transformation 38]
98. ~patient(X0) | rich(X0) [cnf transformation 45]
106. patient(X0) | patient(X0) | ~brave(X0) [cnf transformation 29]
132. brave(mary) | quiet(mary) | ~calm(X0) [cnf transformation 61]
142. ~happy(sK5) [cnf transformation 69]
146. ~rich(mary) [cnf transformation 24]
151. ~brave(X0) | patient(X0) [duplicate literal removal 106]
222. 14 <=> patient(mary) [avatar definition]
224. patient(mary) <- (14) [avatar component clause 222]
235. brave(mary) | ~calm(X0) [subsumption resolution 132,93]
237. 16 <=> ! [X0] : ~calm(X0) [avatar definition]
238. ~calm(X0) <- (16) [avatar component clause 237]
240. 17 <=> brave(mary) [avatar definition]
242. brave(mary) <- (17) [avatar component clause 240]
243. 16 | 17 [avatar split clause 235,240,237]
281. calm(sK5) [resolution 87,142]
290. patient(mary) <- (17) [resolution 151,242]
291. 14 | ~17 [avatar split clause 290,240,222]
292. rich(mary) <- (14) [resolution 224,98]
293. $false <- (14) [subsumption resolution 292,146]
294. ~14 [avatar contradiction clause 293]
296. $false <- (16) [resolution 238,281]
299. ~16 [avatar contradiction clause 296]
301. $false [avatar sat refutation 243,291,294,299]
% SZS output end Proof for 3330451108568358766314106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not kind then someone is rich and vice versa.
If someone is happy or old then john is funny or tall.
If someone is happy or strong then john is funny or humble.
If someone is both happy and curious then paul is curious and vice versa.
Everyone who is either brave or not strong is strong or not humble.
Everyone who is either happy or not quiet is either happy or humble.
Everyone who is creative is strong or not happy.
If someone is either funny or not creative then someone is either old or not patient.
Everyone who is either quiet or curious is not brave.
Everyone who is curious is not funny.
If someone is not patient or not generous then someone is tall and vice versa.
Everyone who is happy is not creative or patient and vice versa.
Everyone who is wise or kind is both old and not brave.
Everyone who is not calm is either kind or happy and vice versa.
Everyone who is both strong and not tall is strong or not strong and vice versa.
Everyone who is not kind or not humble is not happy and vice versa.
Paul is old.
Someone is not strong or not funny.
Someone is not curious.
Someone is rich or not funny. | Paul is strong. | entailment | ((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|old(X))))=>((funny(john)|tall(john))))&
((?[X]:((happy(X)|strong(X))))=>((funny(john)|humble(john))))&
((?[X]:((happy(X)&curious(X))))<=>(curious(paul)))&
(![X]:((brave(X)<~>~strong(X))=>(strong(X)|~humble(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(happy(X)<~>humble(X))))&
(![X]:(creative(X)=>(strong(X)|~happy(X))))&
((?[X]:((funny(X)<~>~creative(X))))=>(?[X]:((old(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>curious(X))=>~brave(X)))&
(![X]:(curious(X)=>~funny(X)))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:(tall(X))))&
(![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((wise(X)|kind(X))=>(old(X)&~brave(X))))&
(![X]:(~calm(X)<=>(kind(X)<~>happy(X))))&
(![X]:((strong(X)&~tall(X))<=>(strong(X)|~strong(X))))&
(![X]:((~kind(X)|~humble(X))<=>~happy(X)))&
(old(paul))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:((rich(X)|~funny(X)))) | strong(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1638264558380699633954376
% SZS output start Proof for 1638264558380699633954376
15. ! [X0] : ((~tall(X0) & strong(X0)) <=> (~strong(X0) | strong(X0))) [input p14]
21. ~strong(paul) [input hypothesis]
62. ! [X0] : (((~tall(X0) & strong(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (tall(X0) | ~strong(X0)))) [nnf transformation 15]
63. ! [X0] : (((~tall(X0) & strong(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | tall(X0) | ~strong(X0))) [flattening 62]
106. strong(X0) | strong(X0) [cnf transformation 63]
116. ~strong(paul) [cnf transformation 21]
118. strong(X0) [duplicate literal removal 106]
240. $false [subsumption resolution 116,118]
% SZS output end Proof for 1638264558380699633954376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or quiet is not funny or wise.
Everyone who is either happy or not humble is generous or strong and vice versa.
If lucy is either not generous or not happy then someone is funny and vice versa.
Everyone who is generous or not rich is not brave or happy and vice versa.
Everyone who is both funny and not tall is both generous and strong and vice versa.
Everyone who is either not calm or not generous is either not kind or brave.
Everyone who is either happy or not rich is both not brave and not strong.
Everyone who is both not rich and not quiet is curious and vice versa.
Everyone who is either happy or humble is brave.
If fred is both not rich and tall then someone is quiet or not patient and vice versa.
If someone is both not curious and not strong then someone is happy or not quiet.
Everyone who is not funny or generous is not kind and vice versa.
Everyone who is both not brave and wise is happy and vice versa.
If lucy is curious then john is patient or not old.
Everyone who is creative is either strong or not happy.
If lucy is creative or not funny then fred is either creative or not generous and vice versa.
Someone is creative or rich.
Mary is strong.
Someone is both not rich and calm.
Someone is quiet or old.
Someone is quiet or not humble.
Someone is quiet.
Someone is both not tall and not patient.
Someone is both not wise and not funny. | Lucy is brave. | neutral | (![X]:((~tall(X)|quiet(X))=>(~funny(X)|wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>(generous(X)|strong(X))))&
(((~generous(lucy)<~>~happy(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((generous(X)|~rich(X))<=>(~brave(X)|happy(X))))&
(![X]:((funny(X)&~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(?[X]:((creative(X)|rich(X))))&
(strong(mary))&
(?[X]:((~rich(X)&calm(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~tall(X)&~patient(X))))&
(?[X]:((~wise(X)&~funny(X)))) | brave(lucy) | [] | null | 0 |
Everyone who is either not wise or wise is not brave or not patient.
If someone is humble then john is both strong and not curious and vice versa.
If fred is patient or not creative then someone is not rich or patient.
Everyone who is both not kind and not quiet is both not generous and creative and vice versa.
Everyone who is not curious is not generous and vice versa.
If lucy is generous or not rich then lucy is both not generous and not old and vice versa.
If someone is either not brave or not old then someone is not patient or strong and vice versa.
Everyone who is either not happy or old is not tall.
Everyone who is old is both not patient and funny.
If lucy is either not curious or humble then alice is both not kind and quiet.
Everyone who is either not tall or not kind is not generous or quiet and vice versa.
Everyone who is both old and not creative is wise.
Everyone who is wise or not wise is either patient or brave and vice versa.
If someone is either quiet or not wise then paul is not generous.
Everyone who is curious is both humble and not tall.
Everyone who is both humble and not wise is creative or humble.
John is either not calm or old.
John is not brave or not happy.
Susan is not kind or not funny.
Paul is both kind and not creative.
Someone is both rich and not quiet.
Someone is not humble.
Mary is kind. | John is curious. | contradiction | (![X]:((~wise(X)<~>wise(X))=>(~brave(X)|~patient(X))))&
((?[X]:(humble(X)))<=>((strong(john)&~curious(john))))&
(((patient(fred)|~creative(fred)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((~kind(X)&~quiet(X))<=>(~generous(X)&creative(X))))&
(![X]:(~curious(X)<=>~generous(X)))&
(((generous(lucy)|~rich(lucy)))<=>((~generous(lucy)&~old(lucy))))&
((?[X]:((~brave(X)<~>~old(X))))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((~happy(X)<~>old(X))=>~tall(X)))&
(![X]:(old(X)=>(~patient(X)&funny(X))))&
(((~curious(lucy)<~>humble(lucy)))=>((~kind(alice)&quiet(alice))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~generous(X)|quiet(X))))&
(![X]:((old(X)&~creative(X))=>wise(X)))&
(![X]:((wise(X)|~wise(X))<=>(patient(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>~wise(X))))=>(~generous(paul)))&
(![X]:(curious(X)=>(humble(X)&~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(creative(X)|humble(X))))&
((~calm(john)<~>old(john)))&
((~brave(john)|~happy(john)))&
((~kind(susan)|~funny(susan)))&
((kind(paul)&~creative(paul)))&
(?[X]:((rich(X)&~quiet(X))))&
(?[X]:(~humble(X)))&
(kind(mary)) | curious(john) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8936267153028029009826609
% SZS output start Proof for 8936267153028029009826609
2. ? [X0] : humble(X0) <=> (~curious(john) & strong(john)) [input p1]
15. ! [X0] : (curious(X0) => (~tall(X0) & humble(X0))) [input p14]
24. curious(john) [input hypothesis]
35. ! [X0] : ((~tall(X0) & humble(X0)) | ~curious(X0)) [ennf transformation 15]
39. (? [X0] : humble(X0) | (curious(john) | ~strong(john))) & ((~curious(john) & strong(john)) | ! [X0] : ~humble(X0)) [nnf transformation 2]
40. (? [X0] : humble(X0) | curious(john) | ~strong(john)) & ((~curious(john) & strong(john)) | ! [X0] : ~humble(X0)) [flattening 39]
41. (? [X0] : humble(X0) | curious(john) | ~strong(john)) & ((~curious(john) & strong(john)) | ! [X1] : ~humble(X1)) [rectify 40]
42. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
43. (humble(sK0) | curious(john) | ~strong(john)) & ((~curious(john) & strong(john)) | ! [X1] : ~humble(X1)) [skolemisation 41,42]
71. ~curious(john) | ~humble(X1) [cnf transformation 43]
115. ~curious(X0) | humble(X0) [cnf transformation 35]
128. curious(john) [cnf transformation 24]
139. 2 <=> curious(john) [avatar definition]
141. curious(john) <- (2) [avatar component clause 139]
148. 4 <=> ! [X1] : ~humble(X1) [avatar definition]
149. ~humble(X1) <- (4) [avatar component clause 148]
150. 4 | ~2 [avatar split clause 71,139,148]
283. 2 [avatar split clause 128,139]
291. humble(john) <- (2) [resolution 115,141]
292. $false <- (2, 4) [subsumption resolution 291,149]
293. ~2 | ~4 [avatar contradiction clause 292]
294. $false [avatar sat refutation 150,283,293]
% SZS output end Proof for 8936267153028029009826609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is either not tall or not wise is either patient or tall and vice versa.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Fred is both not tall and not humble.
Someone is wise.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm. | Susan is patient. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X))) | patient(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 287966822911435048301585
% SZS output start Proof for 287966822911435048301585
1. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> humble(X0)) [input p0]
3. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) <~> tall(X0))) [input p2]
4. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p3]
5. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (brave(X0) | happy(X0))) [input p6]
9. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p8]
16. ~humble(fred) & ~tall(fred) [input p15]
20. ~generous(fred) & ~rich(fred) [input p19]
22. ~patient(susan) [input hypothesis]
24. ! [X0] : ((~curious(X0) <~> generous(X0)) => humble(X0)) [unused predicate definition removal 1]
27. ! [X0] : (humble(X0) | (~curious(X0) <=> generous(X0))) [ennf transformation 24]
28. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 4]
34. ! [X0] : (humble(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 27]
35. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 3]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 5]
38. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 7]
39. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~wise(X0))) [flattening 38]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 9]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
71. humble(X0) | generous(X0) | curious(X0) [cnf transformation 34]
73. tall(X0) | patient(X0) | ~wise(X0) | tall(X0) [cnf transformation 35]
78. ~wise(X0) | ~tall(X0) | patient(X0) | ~tall(X0) [cnf transformation 35]
82. ~curious(X0) | happy(X0) [cnf transformation 28]
84. ~patient(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 36]
90. ~happy(X0) | wise(X0) [cnf transformation 39]
92. creative(fred) | wise(X1) [cnf transformation 44]
122. ~humble(fred) [cnf transformation 16]
127. ~generous(fred) [cnf transformation 20]
129. ~patient(susan) [cnf transformation 22]
132. tall(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 73]
134. ~wise(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 78]
137. ~wise(X0) | patient(X0) [subsumption resolution 132,134]
139. 1 <=> creative(fred) [avatar definition]
152. 4 <=> ! [X1] : wise(X1) [avatar definition]
153. wise(X1) <- (4) [avatar component clause 152]
155. 4 | 1 [avatar split clause 92,139,152]
157. 5 <=> patient(fred) [avatar definition]
159. patient(fred) <- (5) [avatar component clause 157]
277. generous(fred) | curious(fred) [resolution 71,122]
278. curious(fred) [subsumption resolution 277,127]
292. happy(fred) [resolution 278,82]
412. wise(fred) [resolution 292,90]
447. patient(fred) [resolution 412,137]
452. 5 [avatar split clause 447,157]
454. ~happy(fred) | ~creative(fred) <- (5) [resolution 159,84]
457. ~creative(fred) <- (5) [subsumption resolution 454,292]
460. ~1 | ~5 [avatar split clause 457,157,139]
464. patient(X3) <- (4) [resolution 153,137]
481. $false <- (4) [resolution 464,129]
482. ~4 [avatar contradiction clause 481]
484. $false [avatar sat refutation 155,452,460,482]
% SZS output end Proof for 287966822911435048301585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both calm and brave then someone is both calm and not brave and vice versa. If lucy is curious then mary is both generous and curious. If mary is not curious or rich then someone is both not brave and old. If susan is not curious then someone is both not happy and generous and vice versa. If someone is either not patient or not old then someone is both not quiet and not funny and vice versa. Everyone who is both not curious and tall is both patient and not kind and vice versa. Everyone who is both not generous and tall is both not calm and not brave. If fred is not calm or not kind then lucy is both tall and not happy and vice versa. Everyone who is not tall is strong or rich. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Someone is curious. Someone is both calm and not strong. Someone is funny. Someone is either not old or not funny. Someone is kind. Someone is not patient or not humble. Someone is both not funny and humble. Lucy is either not wise or brave. | Susan is generous. | entailment | ((?[X]:((calm(X)&brave(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
((curious(lucy))=>((generous(mary)&curious(mary))))&
(((~curious(mary)|rich(mary)))=>(?[X]:((~brave(X)&old(X)))))&
((~curious(susan))<=>(?[X]:((~happy(X)&generous(X)))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:((~curious(X)&tall(X))<=>(patient(X)&~kind(X))))&
(![X]:((~generous(X)&tall(X))=>(~calm(X)&~brave(X))))&
(((~calm(fred)|~kind(fred)))<=>((tall(lucy)&~happy(lucy))))&
(![X]:(~tall(X)=>(strong(X)|rich(X))))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:(kind(X)))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((~funny(X)&humble(X))))&
((~wise(lucy)<~>brave(lucy))) | generous(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3566158129436364627568330
% SZS output start Proof for 3566158129436364627568330
15. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p14]
25. ~generous(susan) [input hypothesis]
37. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 15]
133. generous(X0) | generous(X0) [cnf transformation 37]
148. ~generous(susan) [cnf transformation 25]
150. generous(X0) [duplicate literal removal 133]
335. $false [subsumption resolution 148,150]
% SZS output end Proof for 3566158129436364627568330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not funny or not curious then someone is both kind and strong. Everyone who is brave is not patient. If someone is either tall or brave then alice is not tall or patient and vice versa. Everyone who is rich or tall is funny or not quiet and vice versa. Everyone who is both not patient and rich is curious or quiet and vice versa. If someone is both not generous and not quiet then someone is tall or patient. If someone is either old or not patient then alice is either rich or brave and vice versa. Everyone who is both not kind and not calm is either funny or not wise. Everyone who is strong or not creative is not creative. If susan is either happy or not calm then someone is tall and vice versa. If someone is either happy or creative then fred is either creative or not calm. Everyone who is either not strong or not patient is either not tall or kind. Everyone who is patient is both not patient and creative and vice versa. Everyone who is creative is creative or not curious and vice versa. If susan is funny or humble then susan is not humble and vice versa. Everyone who is both curious and not curious is either not humble or not old. Paul is not calm or not quiet. Someone is both tall and calm. John is not calm. Mary is either funny or not kind. Someone is not old. Someone is either not wise or humble. | Alice is not brave. | entailment | (((~funny(alice)|~curious(alice)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:(brave(X)=>~patient(X)))&
((?[X]:((tall(X)<~>brave(X))))<=>((~tall(alice)|patient(alice))))&
(![X]:((rich(X)|tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
(![X]:((curious(X)&~curious(X))=>(~humble(X)<~>~old(X))))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
(~calm(john))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~wise(X)<~>humble(X)))) | ~brave(alice) | [
"p4",
"p6",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6791595766648835477197942
% SZS output start Proof for 6791595766648835477197942
5. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (quiet(X0) | curious(X0))) [input p4]
7. ? [X0] : (old(X0) <~> ~patient(X0)) <=> (rich(alice) <~> brave(alice)) [input p6]
13. ! [X0] : (patient(X0) <=> (creative(X0) & ~patient(X0))) [input p12]
14. ! [X0] : (creative(X0) <=> (~curious(X0) | creative(X0))) [input p13]
21. ? [X0] : ~old(X0) [input p20]
23. brave(alice) [input hypothesis]
44. ! [X0] : (((rich(X0) & ~patient(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 5]
45. ! [X0] : (((rich(X0) & ~patient(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | ~rich(X0) | patient(X0))) [flattening 44]
46. (? [X0] : ((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ((rich(alice) | ~brave(alice)) & (brave(alice) | ~rich(alice)))) & (((~brave(alice) | ~rich(alice)) & (brave(alice) | rich(alice))) | ! [X0] : ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) [nnf transformation 7]
47. (? [X0] : ((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ((rich(alice) | ~brave(alice)) & (brave(alice) | ~rich(alice)))) & (((~brave(alice) | ~rich(alice)) & (brave(alice) | rich(alice))) | ! [X1] : ((old(X1) | patient(X1)) & (~patient(X1) | ~old(X1)))) [rectify 46]
48. ? [X0] : ((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) => ((patient(sK2) | ~old(sK2)) & (~patient(sK2) | old(sK2))) [choice axiom]
49. (((patient(sK2) | ~old(sK2)) & (~patient(sK2) | old(sK2))) | ((rich(alice) | ~brave(alice)) & (brave(alice) | ~rich(alice)))) & (((~brave(alice) | ~rich(alice)) & (brave(alice) | rich(alice))) | ! [X1] : ((old(X1) | patient(X1)) & (~patient(X1) | ~old(X1)))) [skolemisation 47,48]
57. ! [X0] : ((patient(X0) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 13]
58. ! [X0] : ((patient(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [flattening 57]
59. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 14]
60. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~creative(X0))) [flattening 59]
67. ? [X0] : ~old(X0) => ~old(sK5) [choice axiom]
68. ~old(sK5) [skolemisation 21,67]
90. ~curious(X0) | rich(X0) [cnf transformation 45]
95. ~brave(alice) | ~rich(alice) | old(X1) | patient(X1) [cnf transformation 49]
116. ~patient(X0) | ~patient(X0) [cnf transformation 58]
118. patient(X0) | ~creative(X0) | patient(X0) [cnf transformation 58]
121. creative(X0) | curious(X0) [cnf transformation 60]
133. ~old(sK5) [cnf transformation 68]
136. brave(alice) [cnf transformation 23]
139. ~patient(X0) [duplicate literal removal 116]
140. ~creative(X0) | patient(X0) [duplicate literal removal 118]
190. 11 <=> brave(alice) [avatar definition]
194. 12 <=> rich(alice) [avatar definition]
195. ~rich(alice) <- (~12) [avatar component clause 194]
210. 15 <=> ! [X1] : (old(X1) | patient(X1)) [avatar definition]
211. old(X1) | patient(X1) <- (15) [avatar component clause 210]
212. 15 | ~12 | ~11 [avatar split clause 95,190,194,210]
296. 11 [avatar split clause 136,190]
304. patient(X0) | curious(X0) [resolution 140,121]
305. curious(X0) [subsumption resolution 304,139]
306. rich(X0) [resolution 305,90]
307. $false <- (~12) [resolution 306,195]
308. 12 [avatar contradiction clause 307]
309. old(X1) <- (15) [subsumption resolution 211,139]
310. $false <- (15) [resolution 309,133]
313. ~15 [avatar contradiction clause 310]
314. $false [avatar sat refutation 212,296,308,313]
% SZS output end Proof for 6791595766648835477197942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not brave or happy and vice versa.
Everyone who is not strong is either calm or kind.
If alice is not curious or rich then someone is either generous or not brave and vice versa.
If someone is both not brave and not funny then someone is not kind and vice versa.
Everyone who is not wise or brave is quiet or not funny.
Everyone who is both not curious and brave is not patient or not calm and vice versa.
If alice is both funny and curious then alice is either not calm or funny.
Everyone who is not happy or not strong is quiet or not calm.
Everyone who is strong or calm is both humble and funny.
If someone is both not curious and calm then alice is not tall or rich and vice versa.
If someone is either wise or not strong then someone is kind or curious and vice versa.
Everyone who is both humble and quiet is both not old and not humble and vice versa.
Everyone who is either not brave or rich is both not curious and not generous.
Everyone who is wise or curious is both not tall and not funny.
If someone is either not kind or not wise then someone is both brave and not curious and vice versa.
Lucy is either happy or not patient.
Someone is either not happy or not wise.
Someone is rich.
Susan is not creative.
Someone is both not strong and not rich.
Someone is not strong or strong.
Alice is either old or not humble. | Susan is not strong. | entailment | (![X]:(humble(X)<=>(~brave(X)|happy(X))))&
(![X]:(~strong(X)=>(calm(X)<~>kind(X))))&
(((~curious(alice)|rich(alice)))<=>(?[X]:((generous(X)<~>~brave(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)|~funny(X))))&
(![X]:((~curious(X)&brave(X))<=>(~patient(X)|~calm(X))))&
(((funny(alice)&curious(alice)))=>((~calm(alice)<~>funny(alice))))&
(![X]:((~happy(X)|~strong(X))=>(quiet(X)|~calm(X))))&
(![X]:((strong(X)|calm(X))=>(humble(X)&funny(X))))&
((?[X]:((~curious(X)&calm(X))))<=>((~tall(alice)|rich(alice))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((humble(X)&quiet(X))<=>(~old(X)&~humble(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~curious(X)&~generous(X))))&
(![X]:((wise(X)|curious(X))=>(~tall(X)&~funny(X))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:((brave(X)&~curious(X)))))&
((happy(lucy)<~>~patient(lucy)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:(rich(X)))&
(~creative(susan))&
(?[X]:((~strong(X)&~rich(X))))&
(?[X]:((~strong(X)|strong(X))))&
((old(alice)<~>~humble(alice))) | ~strong(susan) | [
"p4",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8340433298399520204857461
% SZS output start Proof for 8340433298399520204857461
5. ! [X0] : ((brave(X0) | ~wise(X0)) => (~funny(X0) | quiet(X0))) [input p4]
9. ! [X0] : ((calm(X0) | strong(X0)) => (funny(X0) & humble(X0))) [input p8]
12. ! [X0] : ((quiet(X0) & humble(X0)) <=> (~humble(X0) & ~old(X0))) [input p11]
14. ! [X0] : ((curious(X0) | wise(X0)) => (~funny(X0) & ~tall(X0))) [input p13]
23. strong(susan) [input hypothesis]
29. ! [X0] : ((~funny(X0) | quiet(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 5]
30. ! [X0] : (~funny(X0) | quiet(X0) | (~brave(X0) & wise(X0))) [flattening 29]
35. ! [X0] : ((funny(X0) & humble(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 9]
37. ! [X0] : ((~funny(X0) & ~tall(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 14]
64. ! [X0] : (((quiet(X0) & humble(X0)) | (humble(X0) | old(X0))) & ((~humble(X0) & ~old(X0)) | (~quiet(X0) | ~humble(X0)))) [nnf transformation 12]
65. ! [X0] : (((quiet(X0) & humble(X0)) | humble(X0) | old(X0)) & ((~humble(X0) & ~old(X0)) | ~quiet(X0) | ~humble(X0))) [flattening 64]
97. ~funny(X0) | quiet(X0) | wise(X0) [cnf transformation 30]
108. ~strong(X0) | humble(X0) [cnf transformation 35]
110. ~strong(X0) | funny(X0) [cnf transformation 35]
124. ~humble(X0) | ~quiet(X0) | ~humble(X0) [cnf transformation 65]
133. ~wise(X0) | ~funny(X0) [cnf transformation 37]
151. strong(susan) [cnf transformation 23]
152. ~quiet(X0) | ~humble(X0) [duplicate literal removal 124]
315. humble(susan) [resolution 108,151]
318. funny(susan) [resolution 110,151]
374. quiet(susan) | wise(susan) [resolution 97,318]
378. 39 <=> wise(susan) [avatar definition]
380. wise(susan) <- (39) [avatar component clause 378]
382. 40 <=> quiet(susan) [avatar definition]
384. quiet(susan) <- (40) [avatar component clause 382]
385. 39 | 40 [avatar split clause 374,382,378]
436. ~funny(susan) <- (39) [resolution 380,133]
437. $false <- (39) [subsumption resolution 436,318]
438. ~39 [avatar contradiction clause 437]
439. ~humble(susan) <- (40) [resolution 384,152]
440. $false <- (40) [subsumption resolution 439,315]
441. ~40 [avatar contradiction clause 440]
442. $false [avatar sat refutation 385,438,441]
% SZS output end Proof for 8340433298399520204857461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not creative is kind or creative and vice versa.
If alice is not calm or curious then someone is not curious or not old and vice versa.
Everyone who is humble is either not tall or not old.
If someone is not old then someone is either not brave or quiet and vice versa.
Everyone who is old is both wise and not rich and vice versa.
Everyone who is patient or old is both quiet and not kind.
Everyone who is not patient or not wise is either quiet or old and vice versa.
Everyone who is both not calm and calm is either calm or humble.
Everyone who is calm is either not old or rich.
Everyone who is not curious or rich is either not rich or tall.
Everyone who is not wise or not patient is either kind or humble and vice versa.
Everyone who is happy is either not curious or not old and vice versa.
Everyone who is both not humble and happy is humble or curious and vice versa.
Everyone who is not wise is not curious.
If fred is either calm or not quiet then lucy is both not patient and wise.
Everyone who is not wise is either not kind or not creative and vice versa.
Someone is either creative or strong.
Fred is either not strong or creative.
Alice is not calm.
Fred is not creative.
Susan is either creative or not brave.
Paul is not brave or humble. | Fred is creative. | contradiction | (![X]:((patient(X)|~creative(X))<=>(kind(X)|creative(X))))&
(((~calm(alice)|curious(alice)))<=>(?[X]:((~curious(X)|~old(X)))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
(?[X]:((creative(X)<~>strong(X))))&
((~strong(fred)<~>creative(fred)))&
(~calm(alice))&
(~creative(fred))&
((creative(susan)<~>~brave(susan)))&
((~brave(paul)|humble(paul))) | creative(fred) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1259944148951996892231212
% SZS output start Proof for 1259944148951996892231212
20. ~creative(fred) [input p19]
23. creative(fred) [input hypothesis]
129. ~creative(fred) [cnf transformation 20]
133. creative(fred) [cnf transformation 23]
232. 18 <=> creative(fred) [avatar definition]
238. ~18 [avatar split clause 129,232]
250. 18 [avatar split clause 133,232]
251. $false [avatar sat refutation 238,250]
% SZS output end Proof for 1259944148951996892231212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or not funny then someone is both old and not rich and vice versa.
If someone is quiet or strong then someone is tall or humble.
If someone is both not calm and not generous then mary is either not wise or not humble.
If someone is not brave then paul is not rich and vice versa.
If someone is both generous and not curious then paul is both humble and not calm and vice versa.
Everyone who is wise is either not humble or calm and vice versa.
Everyone who is either not strong or not calm is both old and not creative and vice versa.
Everyone who is kind or not calm is quiet and vice versa.
Everyone who is either brave or not generous is not funny or creative.
Everyone who is both not patient and not curious is both not curious and not old and vice versa.
If mary is either calm or kind then someone is either not humble or not wise and vice versa.
Everyone who is humble is either curious or old and vice versa.
Everyone who is tall is either not quiet or not creative.
If susan is both creative and not quiet then mary is both not brave and not wise and vice versa.
Everyone who is not happy or kind is not calm or patient and vice versa.
Everyone who is happy is not generous.
Mary is both strong and kind.
Lucy is not calm or funny.
Fred is either happy or wise.
Fred is either not kind or tall.
Mary is rich or not quiet.
Someone is creative.
Lucy is quiet.
Someone is either quiet or creative. | Mary is not kind. | contradiction | ((?[X]:((kind(X)|~funny(X))))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((quiet(X)|strong(X))))=>(?[X]:((tall(X)|humble(X)))))&
((?[X]:((~calm(X)&~generous(X))))=>((~wise(mary)<~>~humble(mary))))&
((?[X]:(~brave(X)))<=>(~rich(paul)))&
((?[X]:((generous(X)&~curious(X))))<=>((humble(paul)&~calm(paul))))&
(![X]:(wise(X)<=>(~humble(X)<~>calm(X))))&
(![X]:((~strong(X)<~>~calm(X))<=>(old(X)&~creative(X))))&
(![X]:((kind(X)|~calm(X))<=>quiet(X)))&
(![X]:((brave(X)<~>~generous(X))=>(~funny(X)|creative(X))))&
(![X]:((~patient(X)&~curious(X))<=>(~curious(X)&~old(X))))&
(((calm(mary)<~>kind(mary)))<=>(?[X]:((~humble(X)<~>~wise(X)))))&
(![X]:(humble(X)<=>(curious(X)<~>old(X))))&
(![X]:(tall(X)=>(~quiet(X)<~>~creative(X))))&
(((creative(susan)&~quiet(susan)))<=>((~brave(mary)&~wise(mary))))&
(![X]:((~happy(X)|kind(X))<=>(~calm(X)|patient(X))))&
(![X]:(happy(X)=>~generous(X)))&
((strong(mary)&kind(mary)))&
((~calm(lucy)|funny(lucy)))&
((happy(fred)<~>wise(fred)))&
((~kind(fred)<~>tall(fred)))&
((rich(mary)|~quiet(mary)))&
(?[X]:(creative(X)))&
(quiet(lucy))&
(?[X]:((quiet(X)<~>creative(X)))) | ~kind(mary) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2661632375354433112362901
% SZS output start Proof for 2661632375354433112362901
17. kind(mary) & strong(mary) [input p16]
25. ~kind(mary) [input hypothesis]
135. kind(mary) [cnf transformation 17]
146. ~kind(mary) [cnf transformation 25]
250. 25 <=> kind(mary) [avatar definition]
288. 25 [avatar split clause 135,250]
337. ~25 [avatar split clause 146,250]
338. $false [avatar sat refutation 288,337]
% SZS output end Proof for 2661632375354433112362901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or kind then someone is both quiet and not old and vice versa. If someone is either not brave or not quiet then someone is not generous. Everyone who is both not funny and not brave is calm and vice versa. Everyone who is brave or old is both not rich and curious and vice versa. If mary is wise or not happy then someone is curious or kind. If someone is either not patient or quiet then someone is not calm or creative and vice versa. Everyone who is not wise or patient is either not patient or rich. Everyone who is either not kind or not old is either not rich or quiet. Everyone who is both old and not tall is not humble or not quiet and vice versa. Everyone who is both not rich and calm is both not wise and not creative and vice versa. If susan is both not rich and wise then someone is both tall and quiet and vice versa. Everyone who is both happy and not strong is either creative or not generous and vice versa. If someone is both curious and funny then alice is rich. If someone is both funny and wise then someone is not kind. Everyone who is not brave or strong is either not creative or happy and vice versa. Everyone who is kind or calm is either tall or not calm. Someone is humble. Someone is calm. Someone is not brave or tall. Someone is both not patient and not quiet. Alice is either not kind or creative. Someone is generous or calm. Someone is quiet. | Susan is not wise. | contradiction | ((?[X]:((humble(X)|kind(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>calm(X)))&
(![X]:((brave(X)|old(X))<=>(~rich(X)&curious(X))))&
(((wise(mary)|~happy(mary)))=>(?[X]:((curious(X)|kind(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((~wise(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&~creative(X))))&
(((~rich(susan)&wise(susan)))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:((curious(X)&funny(X))))=>(rich(alice)))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)<~>happy(X))))&
(![X]:((kind(X)|calm(X))=>(tall(X)<~>~calm(X))))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~patient(X)&~quiet(X))))&
((~kind(alice)<~>creative(alice)))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:(quiet(X))) | ~wise(susan) | [
"p8",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 224539890922449754089869
% SZS output start Proof for 224539890922449754089869
9. ! [X0] : ((~tall(X0) & old(X0)) <=> (~quiet(X0) | ~humble(X0))) [input p8]
11. (wise(susan) & ~rich(susan)) <=> ? [X0] : (quiet(X0) & tall(X0)) [input p10]
16. ! [X0] : ((calm(X0) | kind(X0)) => (tall(X0) <~> ~calm(X0))) [input p15]
18. ? [X0] : calm(X0) [input p17]
24. ~wise(susan) [input hypothesis]
35. ! [X0] : ((tall(X0) <~> ~calm(X0)) | (~calm(X0) & ~kind(X0))) [ennf transformation 16]
58. ! [X0] : (((~tall(X0) & old(X0)) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | (tall(X0) | ~old(X0)))) [nnf transformation 9]
59. ! [X0] : (((~tall(X0) & old(X0)) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | tall(X0) | ~old(X0))) [flattening 58]
62. ((wise(susan) & ~rich(susan)) | ! [X0] : (~quiet(X0) | ~tall(X0))) & (? [X0] : (quiet(X0) & tall(X0)) | (~wise(susan) | rich(susan))) [nnf transformation 11]
63. ((wise(susan) & ~rich(susan)) | ! [X0] : (~quiet(X0) | ~tall(X0))) & (? [X0] : (quiet(X0) & tall(X0)) | ~wise(susan) | rich(susan)) [flattening 62]
64. ((wise(susan) & ~rich(susan)) | ! [X0] : (~quiet(X0) | ~tall(X0))) & (? [X1] : (quiet(X1) & tall(X1)) | ~wise(susan) | rich(susan)) [rectify 63]
65. ? [X1] : (quiet(X1) & tall(X1)) => (quiet(sK6) & tall(sK6)) [choice axiom]
66. ((wise(susan) & ~rich(susan)) | ! [X0] : (~quiet(X0) | ~tall(X0))) & ((quiet(sK6) & tall(sK6)) | ~wise(susan) | rich(susan)) [skolemisation 64,65]
74. ! [X0] : (((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | (~calm(X0) & ~kind(X0))) [nnf transformation 35]
77. ? [X0] : calm(X0) => calm(sK9) [choice axiom]
78. calm(sK9) [skolemisation 18,77]
123. ~tall(X0) | quiet(X0) [cnf transformation 59]
131. wise(susan) | ~quiet(X0) | ~tall(X0) [cnf transformation 66]
147. ~calm(X0) | tall(X0) | ~calm(X0) [cnf transformation 74]
151. calm(sK9) [cnf transformation 78]
159. ~wise(susan) [cnf transformation 24]
160. ~calm(X0) | tall(X0) [duplicate literal removal 147]
258. wise(susan) | ~tall(X0) [subsumption resolution 131,123]
260. 23 <=> ! [X0] : ~tall(X0) [avatar definition]
261. ~tall(X0) <- (23) [avatar component clause 260]
263. 24 <=> wise(susan) [avatar definition]
266. 23 | 24 [avatar split clause 258,263,260]
327. ~24 [avatar split clause 159,263]
336. tall(sK9) [resolution 160,151]
337. $false <- (23) [subsumption resolution 336,261]
338. ~23 [avatar contradiction clause 337]
339. $false [avatar sat refutation 266,327,338]
% SZS output end Proof for 224539890922449754089869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either not happy or old and vice versa.
Everyone who is not rich or tall is not creative or old and vice versa.
Everyone who is wise is strong.
Everyone who is tall or kind is not generous or not tall.
If someone is happy or not tall then alice is calm and vice versa.
Everyone who is either not humble or creative is both not curious and not creative.
If fred is not brave then someone is either not strong or brave and vice versa.
Everyone who is not wise is not patient or old and vice versa.
Everyone who is humble or not patient is both strong and not funny and vice versa.
Everyone who is not rich or not kind is both not kind and happy.
If someone is both old and not creative then lucy is happy.
If someone is either kind or not humble then someone is curious.
Everyone who is not creative or funny is either old or strong and vice versa.
Everyone who is both not brave and creative is not creative.
Everyone who is either brave or not tall is either quiet or not humble and vice versa.
Everyone who is both patient and wise is both not patient and patient.
Paul is not happy.
Someone is curious.
John is either generous or quiet.
Someone is either curious or calm.
Lucy is not generous.
Someone is either not tall or tall.
Someone is either not quiet or old.
Lucy is either not quiet or wise. | Paul is not humble. | entailment | (![X]:(funny(X)<=>(~happy(X)<~>old(X))))&
(![X]:((~rich(X)|tall(X))<=>(~creative(X)|old(X))))&
(![X]:(wise(X)=>strong(X)))&
(![X]:((tall(X)|kind(X))=>(~generous(X)|~tall(X))))&
((?[X]:((happy(X)|~tall(X))))<=>(calm(alice)))&
(![X]:((~humble(X)<~>creative(X))=>(~curious(X)&~creative(X))))&
((~brave(fred))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(~wise(X)<=>(~patient(X)|old(X))))&
(![X]:((humble(X)|~patient(X))<=>(strong(X)&~funny(X))))&
(![X]:((~rich(X)|~kind(X))=>(~kind(X)&happy(X))))&
((?[X]:((old(X)&~creative(X))))=>(happy(lucy)))&
((?[X]:((kind(X)<~>~humble(X))))=>(?[X]:(curious(X))))&
(![X]:((~creative(X)|funny(X))<=>(old(X)<~>strong(X))))&
(![X]:((~brave(X)&creative(X))=>~creative(X)))&
(![X]:((brave(X)<~>~tall(X))<=>(quiet(X)<~>~humble(X))))&
(![X]:((patient(X)&wise(X))=>(~patient(X)&patient(X))))&
(~happy(paul))&
(?[X]:(curious(X)))&
((generous(john)<~>quiet(john)))&
(?[X]:((curious(X)<~>calm(X))))&
(~generous(lucy))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~quiet(X)<~>old(X))))&
((~quiet(lucy)<~>wise(lucy))) | ~humble(paul) | [
"p0",
"p5",
"p8",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4268134667993823324469182
% SZS output start Proof for 4268134667993823324469182
1. ! [X0] : (funny(X0) <=> (~happy(X0) <~> old(X0))) [input p0]
6. ! [X0] : ((~humble(X0) <~> creative(X0)) => (~creative(X0) & ~curious(X0))) [input p5]
9. ! [X0] : ((~patient(X0) | humble(X0)) <=> (~funny(X0) & strong(X0))) [input p8]
13. ! [X0] : ((funny(X0) | ~creative(X0)) <=> (old(X0) <~> strong(X0))) [input p12]
17. ~happy(paul) [input p16]
25. humble(paul) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~curious(X0)) | (~humble(X0) <=> creative(X0))) [ennf transformation 6]
38. ! [X0] : ((funny(X0) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0)))) & (((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | ~funny(X0))) [nnf transformation 1]
45. ! [X0] : ((~creative(X0) & ~curious(X0)) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) [nnf transformation 30]
52. ! [X0] : (((~patient(X0) | humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (patient(X0) & ~humble(X0)))) [nnf transformation 9]
53. ! [X0] : ((~patient(X0) | humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (patient(X0) & ~humble(X0)))) [flattening 52]
58. ! [X0] : (((funny(X0) | ~creative(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~funny(X0) & creative(X0)))) [nnf transformation 13]
59. ! [X0] : ((funny(X0) | ~creative(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~funny(X0) & creative(X0)))) [flattening 58]
76. old(X0) | funny(X0) | happy(X0) [cnf transformation 38]
91. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 45]
99. ~humble(X0) | strong(X0) [cnf transformation 53]
101. ~humble(X0) | ~funny(X0) [cnf transformation 53]
113. ~strong(X0) | ~old(X0) | creative(X0) [cnf transformation 59]
128. ~happy(paul) [cnf transformation 17]
141. humble(paul) [cnf transformation 25]
144. ~humble(X0) | ~creative(X0) [duplicate literal removal 91]
241. strong(paul) [resolution 99,141]
242. ~funny(paul) [resolution 101,141]
244. ~creative(paul) [resolution 144,141]
375. ~old(paul) | creative(paul) [resolution 113,241]
378. ~old(paul) [subsumption resolution 375,244]
561. funny(paul) | happy(paul) [resolution 378,76]
562. happy(paul) [subsumption resolution 561,242]
563. $false [subsumption resolution 562,128]
% SZS output end Proof for 4268134667993823324469182
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or old is both not funny and not quiet.
Everyone who is both humble and curious is both not generous and calm and vice versa.
Everyone who is both not brave and not tall is either brave or not creative and vice versa.
Everyone who is not tall is either rich or not curious.
If someone is either not tall or not kind then john is both not humble and old and vice versa.
Everyone who is either not kind or creative is not kind or tall and vice versa.
If alice is either strong or not kind then someone is both not humble and rich.
If fred is either not creative or strong then lucy is both strong and old.
If fred is not kind then paul is calm and vice versa.
If lucy is both happy and not humble then someone is both not quiet and calm and vice versa.
If someone is both not tall and strong then someone is tall.
Everyone who is not rich is both wise and patient and vice versa.
Everyone who is not quiet is either generous or rich.
Everyone who is both funny and not old is not creative.
If mary is both calm and not quiet then someone is calm or not quiet and vice versa.
If alice is either not brave or not generous then someone is humble and vice versa.
Mary is both rich and funny.
Mary is both strong and not patient.
Mary is either not funny or generous.
Lucy is humble or not old.
Someone is either wise or not strong. | John is humble. | neutral | (![X]:((~happy(X)|old(X))=>(~funny(X)&~quiet(X))))&
(![X]:((humble(X)&curious(X))<=>(~generous(X)&calm(X))))&
(![X]:((~brave(X)&~tall(X))<=>(brave(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(rich(X)<~>~curious(X))))&
((?[X]:((~tall(X)<~>~kind(X))))<=>((~humble(john)&old(john))))&
(![X]:((~kind(X)<~>creative(X))<=>(~kind(X)|tall(X))))&
(((strong(alice)<~>~kind(alice)))=>(?[X]:((~humble(X)&rich(X)))))&
(((~creative(fred)<~>strong(fred)))=>((strong(lucy)&old(lucy))))&
((~kind(fred))<=>(calm(paul)))&
(((happy(lucy)&~humble(lucy)))<=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((~tall(X)&strong(X))))=>(?[X]:(tall(X))))&
(![X]:(~rich(X)<=>(wise(X)&patient(X))))&
(![X]:(~quiet(X)=>(generous(X)<~>rich(X))))&
(![X]:((funny(X)&~old(X))=>~creative(X)))&
(((calm(mary)&~quiet(mary)))<=>(?[X]:((calm(X)|~quiet(X)))))&
(((~brave(alice)<~>~generous(alice)))<=>(?[X]:(humble(X))))&
((rich(mary)&funny(mary)))&
((strong(mary)&~patient(mary)))&
((~funny(mary)<~>generous(mary)))&
((humble(lucy)|~old(lucy)))&
(?[X]:((wise(X)<~>~strong(X)))) | humble(john) | [] | null | 0 |
Everyone who is both not brave and calm is brave and vice versa. If john is both not curious and not happy then lucy is both not rich and generous. If someone is not funny then susan is strong. If someone is tall or not funny then lucy is both not curious and tall. Everyone who is not old or not quiet is rich or not calm and vice versa. Everyone who is both humble and not curious is either patient or not old. Everyone who is both not patient and not curious is both rich and not funny and vice versa. If someone is either calm or wise then someone is either humble or tall and vice versa. If mary is both quiet and calm then someone is both happy and not brave and vice versa. If someone is both old and not humble then paul is calm or wise. If someone is either not wise or creative then someone is either not wise or humble and vice versa. If alice is either not generous or not tall then alice is wise. Everyone who is tall or not humble is either kind or brave. Everyone who is either kind or not wise is either funny or tall. If someone is not funny then someone is both not patient and not strong. Everyone who is not rich is both not calm and not funny. John is not old or rich. Fred is either patient or not rich. Fred is not calm. Someone is either not rich or not funny. Lucy is kind. Mary is not wise. Someone is not generous or creative. Someone is both not quiet and old. | Mary is brave. | contradiction | (![X]:((~brave(X)&calm(X))<=>brave(X)))&
(((~curious(john)&~happy(john)))=>((~rich(lucy)&generous(lucy))))&
((?[X]:(~funny(X)))=>(strong(susan)))&
((?[X]:((tall(X)|~funny(X))))=>((~curious(lucy)&tall(lucy))))&
(![X]:((~old(X)|~quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((humble(X)&~curious(X))=>(patient(X)<~>~old(X))))&
(![X]:((~patient(X)&~curious(X))<=>(rich(X)&~funny(X))))&
((?[X]:((calm(X)<~>wise(X))))<=>(?[X]:((humble(X)<~>tall(X)))))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((happy(X)&~brave(X)))))&
((?[X]:((old(X)&~humble(X))))=>((calm(paul)|wise(paul))))&
((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(((~generous(alice)<~>~tall(alice)))=>(wise(alice)))&
(![X]:((tall(X)|~humble(X))=>(kind(X)<~>brave(X))))&
(![X]:((kind(X)<~>~wise(X))=>(funny(X)<~>tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:(~rich(X)=>(~calm(X)&~funny(X))))&
((~old(john)|rich(john)))&
((patient(fred)<~>~rich(fred)))&
(~calm(fred))&
(?[X]:((~rich(X)<~>~funny(X))))&
(kind(lucy))&
(~wise(mary))&
(?[X]:((~generous(X)|creative(X))))&
(?[X]:((~quiet(X)&old(X)))) | brave(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8390087850097357751181726
% SZS output start Proof for 8390087850097357751181726
1. ! [X0] : ((calm(X0) & ~brave(X0)) <=> brave(X0)) [input p0]
25. brave(mary) [input hypothesis]
42. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~calm(X0) | brave(X0)))) [nnf transformation 1]
43. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~calm(X0) | brave(X0))) [flattening 42]
79. ~brave(X0) | ~brave(X0) [cnf transformation 43]
144. brave(mary) [cnf transformation 25]
146. ~brave(X0) [duplicate literal removal 79]
324. $false [subsumption resolution 144,146]
% SZS output end Proof for 8390087850097357751181726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet then fred is strong or not kind. If someone is both not humble and patient then someone is both not patient and not strong. Everyone who is not brave is not calm and vice versa. Everyone who is both not funny and not quiet is not calm. Everyone who is either wise or patient is both funny and not curious. Everyone who is not wise or not calm is not wise and vice versa. Everyone who is either not humble or old is either not curious or not generous and vice versa. If mary is either rich or not wise then paul is either strong or not generous and vice versa. If paul is both not generous and not brave then someone is not patient or not curious and vice versa. Everyone who is both not patient and calm is not calm or not old and vice versa. If paul is patient then john is not wise or not rich. Everyone who is either not kind or not quiet is either old or not tall. Everyone who is not happy is not strong and vice versa. Everyone who is not rich is old or not curious and vice versa. If paul is both humble and quiet then lucy is either strong or calm. Someone is both patient and not generous. Someone is happy or curious. Fred is not funny or not kind. | Lucy is not humble. | contradiction | ((~quiet(paul))=>((strong(fred)|~kind(fred))))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:((~patient(X)&~strong(X)))))&
(![X]:(~brave(X)<=>~calm(X)))&
(![X]:((~funny(X)&~quiet(X))=>~calm(X)))&
(![X]:((wise(X)<~>patient(X))=>(funny(X)&~curious(X))))&
(![X]:((~wise(X)|~calm(X))<=>~wise(X)))&
(![X]:((~humble(X)<~>old(X))<=>(~curious(X)<~>~generous(X))))&
(((rich(mary)<~>~wise(mary)))<=>((strong(paul)<~>~generous(paul))))&
(((~generous(paul)&~brave(paul)))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~patient(X)&calm(X))<=>(~calm(X)|~old(X))))&
((patient(paul))=>((~wise(john)|~rich(john))))&
(![X]:((~kind(X)<~>~quiet(X))=>(old(X)<~>~tall(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(~rich(X)<=>(old(X)|~curious(X))))&
(((humble(paul)&quiet(paul)))=>((strong(lucy)<~>calm(lucy))))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((happy(X)|curious(X))))&
((~funny(fred)|~kind(fred))) | ~humble(lucy) | [
"p1",
"p2",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1923158328983080943555649
% SZS output start Proof for 1923158328983080943555649
2. ? [X0] : (patient(X0) & ~humble(X0)) => ? [X0] : (~strong(X0) & ~patient(X0)) [input p1]
3. ! [X0] : (~brave(X0) <=> ~calm(X0)) [input p2]
9. (~brave(paul) & ~generous(paul)) <=> ? [X0] : (~curious(X0) | ~patient(X0)) [input p8]
10. ! [X0] : ((calm(X0) & ~patient(X0)) <=> (~old(X0) | ~calm(X0))) [input p9]
19. ~humble(lucy) [input hypothesis]
20. ? [X0] : (patient(X0) & ~humble(X0)) => ? [X1] : (~strong(X1) & ~patient(X1)) [rectify 2]
24. ? [X1] : (~strong(X1) & ~patient(X1)) | ! [X0] : (~patient(X0) | humble(X0)) [ennf transformation 20]
34. ? [X0] : (~strong(X0) & ~patient(X0)) | ! [X1] : (~patient(X1) | humble(X1)) [rectify 24]
35. ? [X0] : (~strong(X0) & ~patient(X0)) => (~strong(sK0) & ~patient(sK0)) [choice axiom]
36. (~strong(sK0) & ~patient(sK0)) | ! [X1] : (~patient(X1) | humble(X1)) [skolemisation 34,35]
37. ! [X0] : ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))) [nnf transformation 3]
43. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | (brave(paul) | generous(paul))) [nnf transformation 9]
44. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X0] : (~curious(X0) | ~patient(X0)) | brave(paul) | generous(paul)) [flattening 43]
45. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & (? [X1] : (~curious(X1) | ~patient(X1)) | brave(paul) | generous(paul)) [rectify 44]
46. ? [X1] : (~curious(X1) | ~patient(X1)) => (~curious(sK1) | ~patient(sK1)) [choice axiom]
47. ((~brave(paul) & ~generous(paul)) | ! [X0] : (curious(X0) & patient(X0))) & ((~curious(sK1) | ~patient(sK1)) | brave(paul) | generous(paul)) [skolemisation 45,46]
48. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | (~calm(X0) | patient(X0)))) [nnf transformation 10]
49. ! [X0] : (((calm(X0) & ~patient(X0)) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | ~calm(X0) | patient(X0))) [flattening 48]
59. ~patient(sK0) | ~patient(X1) | humble(X1) [cnf transformation 36]
61. ~calm(X0) | brave(X0) [cnf transformation 37]
90. ~brave(paul) | patient(X0) [cnf transformation 47]
95. calm(X0) | calm(X0) [cnf transformation 49]
112. ~humble(lucy) [cnf transformation 19]
114. calm(X0) [duplicate literal removal 95]
129. 4 <=> ! [X1] : (~patient(X1) | humble(X1)) [avatar definition]
130. ~patient(X1) | humble(X1) <- (4) [avatar component clause 129]
137. 6 <=> patient(sK0) [avatar definition]
139. ~patient(sK0) <- (~6) [avatar component clause 137]
140. 4 | ~6 [avatar split clause 59,137,129]
169. 12 <=> brave(paul) [avatar definition]
171. ~brave(paul) <- (~12) [avatar component clause 169]
174. 13 <=> ! [X0] : patient(X0) [avatar definition]
175. patient(X0) <- (13) [avatar component clause 174]
176. 13 | ~12 [avatar split clause 90,169,174]
226. brave(X0) [resolution 61,114]
227. $false <- (~12) [resolution 226,171]
229. 12 [avatar contradiction clause 227]
230. $false <- (~6, 13) [resolution 175,139]
233. 6 | ~13 [avatar contradiction clause 230]
234. humble(X1) <- (4, 13) [subsumption resolution 130,175]
235. $false <- (4, 13) [resolution 234,112]
238. ~4 | ~13 [avatar contradiction clause 235]
239. $false [avatar sat refutation 140,176,229,233,238]
% SZS output end Proof for 1923158328983080943555649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or curious is both not rich and creative and vice versa.
If susan is quiet or tall then someone is both calm and not rich.
If mary is both not creative and funny then lucy is either not quiet or old and vice versa.
Everyone who is both not creative and tall is both funny and curious.
Everyone who is not patient is either not old or calm and vice versa.
If john is both not creative and happy then mary is either tall or not tall.
Everyone who is happy is not humble or calm.
Everyone who is curious is both tall and happy and vice versa.
Everyone who is wise or not patient is both rich and not curious.
Everyone who is calm or not patient is not brave or quiet and vice versa.
Everyone who is either funny or not strong is curious and vice versa.
If someone is both kind and not kind then someone is either kind or not brave and vice versa.
If someone is both generous and not kind then alice is both not quiet and brave and vice versa.
If someone is either not patient or not funny then john is either patient or not quiet and vice versa.
Everyone who is wise is not creative and vice versa.
If fred is rich or not happy then someone is either quiet or humble and vice versa.
Someone is both not humble and brave.
Someone is both not wise and not humble.
Paul is both quiet and not humble.
Someone is not brave.
Someone is not happy or brave.
Someone is quiet.
Paul is both happy and generous.
John is either humble or kind. | Alice is old. | neutral | (![X]:((kind(X)<~>curious(X))<=>(~rich(X)&creative(X))))&
(((quiet(susan)|tall(susan)))=>(?[X]:((calm(X)&~rich(X)))))&
(((~creative(mary)&funny(mary)))<=>((~quiet(lucy)<~>old(lucy))))&
(![X]:((~creative(X)&tall(X))=>(funny(X)&curious(X))))&
(![X]:(~patient(X)<=>(~old(X)<~>calm(X))))&
(((~creative(john)&happy(john)))=>((tall(mary)<~>~tall(mary))))&
(![X]:(happy(X)=>(~humble(X)|calm(X))))&
(![X]:(curious(X)<=>(tall(X)&happy(X))))&
(![X]:((wise(X)|~patient(X))=>(rich(X)&~curious(X))))&
(![X]:((calm(X)|~patient(X))<=>(~brave(X)|quiet(X))))&
(![X]:((funny(X)<~>~strong(X))<=>curious(X)))&
((?[X]:((kind(X)&~kind(X))))<=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((generous(X)&~kind(X))))<=>((~quiet(alice)&brave(alice))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>((patient(john)<~>~quiet(john))))&
(![X]:(wise(X)<=>~creative(X)))&
(((rich(fred)|~happy(fred)))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(?[X]:((~humble(X)&brave(X))))&
(?[X]:((~wise(X)&~humble(X))))&
((quiet(paul)&~humble(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)|brave(X))))&
(?[X]:(quiet(X)))&
((happy(paul)&generous(paul)))&
((humble(john)<~>kind(john))) | old(alice) | [] | null | 0 |
Everyone who is not calm is not tall and vice versa.
If fred is either not humble or funny then lucy is rich or generous and vice versa.
If fred is not generous then someone is humble or quiet and vice versa.
If susan is both not creative and not wise then susan is not tall and vice versa.
If john is strong then someone is both not calm and not happy and vice versa.
If mary is humble or not strong then someone is not creative and vice versa.
Everyone who is rich is not curious.
If john is not wise or not happy then someone is both not humble and humble and vice versa.
If fred is both not strong and not humble then susan is rich or curious.
Everyone who is not strong is both happy and not curious and vice versa.
If someone is both strong and not calm then someone is both creative and not wise.
If someone is either not rich or not strong then susan is either not kind or generous.
Everyone who is wise or kind is not calm or happy and vice versa.
Everyone who is either strong or brave is both not old and funny.
Everyone who is both strong and not old is either brave or not wise.
Everyone who is both curious and brave is not curious or not patient and vice versa.
Susan is both not happy and tall.
Someone is creative.
Someone is both not generous and not kind.
Someone is curious or wise.
Someone is not old or not curious.
Paul is either not quiet or not wise.
Fred is either kind or quiet. | John is not happy. | contradiction | (![X]:(~calm(X)<=>~tall(X)))&
(((~humble(fred)<~>funny(fred)))<=>((rich(lucy)|generous(lucy))))&
((~generous(fred))<=>(?[X]:((humble(X)|quiet(X)))))&
(((~creative(susan)&~wise(susan)))<=>(~tall(susan)))&
((strong(john))<=>(?[X]:((~calm(X)&~happy(X)))))&
(((humble(mary)|~strong(mary)))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>~curious(X)))&
(((~wise(john)|~happy(john)))<=>(?[X]:((~humble(X)&humble(X)))))&
(((~strong(fred)&~humble(fred)))=>((rich(susan)|curious(susan))))&
(![X]:(~strong(X)<=>(happy(X)&~curious(X))))&
((?[X]:((strong(X)&~calm(X))))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>((~kind(susan)<~>generous(susan))))&
(![X]:((wise(X)|kind(X))<=>(~calm(X)|happy(X))))&
(![X]:((strong(X)<~>brave(X))=>(~old(X)&funny(X))))&
(![X]:((strong(X)&~old(X))=>(brave(X)<~>~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(~curious(X)|~patient(X))))&
((~happy(susan)&tall(susan)))&
(?[X]:(creative(X)))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~old(X)|~curious(X))))&
((~quiet(paul)<~>~wise(paul)))&
((kind(fred)<~>quiet(fred))) | ~happy(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8532033879440811317190859
% SZS output start Proof for 8532033879440811317190859
8. (~happy(john) | ~wise(john)) <=> ? [X0] : (humble(X0) & ~humble(X0)) [input p7]
24. ~happy(john) [input hypothesis]
52. ((~happy(john) | ~wise(john)) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [nnf transformation 8]
53. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X0] : (humble(X0) & ~humble(X0)) | (happy(john) & wise(john))) [flattening 52]
54. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & (? [X1] : (humble(X1) & ~humble(X1)) | (happy(john) & wise(john))) [rectify 53]
55. ? [X1] : (humble(X1) & ~humble(X1)) => (humble(sK3) & ~humble(sK3)) [choice axiom]
56. (~happy(john) | ~wise(john) | ! [X0] : (~humble(X0) | humble(X0))) & ((humble(sK3) & ~humble(sK3)) | (happy(john) & wise(john))) [skolemisation 54,55]
101. ~humble(sK3) | happy(john) [cnf transformation 56]
103. humble(sK3) | happy(john) [cnf transformation 56]
141. ~happy(john) [cnf transformation 24]
239. 21 <=> happy(john) [avatar definition]
243. 22 <=> humble(sK3) [avatar definition]
246. 21 | 22 [avatar split clause 103,243,239]
252. 21 | ~22 [avatar split clause 101,243,239]
322. ~21 [avatar split clause 141,239]
323. $false [avatar sat refutation 246,252,322]
% SZS output end Proof for 8532033879440811317190859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not brave then paul is not patient and vice versa.
If someone is both not calm and strong then john is rich and vice versa.
If paul is either patient or strong then paul is calm or generous.
If paul is strong then lucy is both curious and not brave and vice versa.
Everyone who is either rich or not happy is not wise and vice versa.
If someone is either not curious or patient then someone 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.
If mary is not tall then lucy is both not patient and rich.
If someone is wise or tall then paul is both wise and not happy.
Everyone who is patient or not strong is not rich.
If john is both not patient and brave then john is not strong or not happy.
Everyone who is both not humble and not funny is both not tall and not strong.
Everyone who is calm is humble.
If alice is either not calm or not quiet then someone is both creative and not calm and vice versa.
If susan is both quiet and not strong then john is either generous or patient and vice versa.
Someone is both calm and creative.
Someone is not rich or not quiet.
Someone is either not rich or not brave.
Someone is both creative and funny.
Someone is not rich or not generous.
Mary is not happy or not tall.
Lucy is not calm or happy.
Someone is either not humble or not rich. | John is tall. | neutral | ((?[X]:((quiet(X)<~>~brave(X))))<=>(~patient(paul)))&
((?[X]:((~calm(X)&strong(X))))<=>(rich(john)))&
(((patient(paul)<~>strong(paul)))=>((calm(paul)|generous(paul))))&
((strong(paul))<=>((curious(lucy)&~brave(lucy))))&
(![X]:((rich(X)<~>~happy(X))<=>~wise(X)))&
((?[X]:((~curious(X)<~>patient(X))))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((happy(X)&brave(X))<=>(humble(X)&rich(X))))&
(![X]:(strong(X)<=>(rich(X)&strong(X))))&
((~tall(mary))=>((~patient(lucy)&rich(lucy))))&
((?[X]:((wise(X)|tall(X))))=>((wise(paul)&~happy(paul))))&
(![X]:((patient(X)|~strong(X))=>~rich(X)))&
(((~patient(john)&brave(john)))=>((~strong(john)|~happy(john))))&
(![X]:((~humble(X)&~funny(X))=>(~tall(X)&~strong(X))))&
(![X]:(calm(X)=>humble(X)))&
(((~calm(alice)<~>~quiet(alice)))<=>(?[X]:((creative(X)&~calm(X)))))&
(((quiet(susan)&~strong(susan)))<=>((generous(john)<~>patient(john))))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:((~rich(X)<~>~brave(X))))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((~rich(X)|~generous(X))))&
((~happy(mary)|~tall(mary)))&
((~calm(lucy)|happy(lucy)))&
(?[X]:((~humble(X)<~>~rich(X)))) | tall(john) | [] | null | 0 |
If mary is either not old or kind then susan is both generous and humble.
Everyone who is not rich is either funny or not strong.
Everyone who is both funny and not rich is both not generous and not kind.
Everyone who is calm is both not wise and not quiet.
Everyone who is both not brave and curious is both tall and not creative and vice versa.
Everyone who is happy is brave.
If susan is not kind or not happy then paul is either not creative or not tall.
Everyone who is not wise or not rich is not humble or quiet.
If susan is not happy or not strong then alice is both not kind and calm.
If someone is both humble and not calm then mary is tall and vice versa.
If someone is both not rich and not kind then susan is both not creative and not happy and vice versa.
If john is both humble and happy then lucy is quiet.
If mary is both wise and happy then someone is generous.
Everyone who is not brave or brave is both happy and humble.
If alice is not generous or kind then fred is both calm and not kind and vice versa.
Everyone who is not generous or not rich is both not tall and calm.
Lucy is both curious and not wise.
Someone is quiet or not patient.
Someone is either funny or not tall.
Someone is either not old or not rich.
Someone is either not rich or humble.
John is rich or kind.
Someone is both not old and not strong. | Alice is brave. | entailment | (((~old(mary)<~>kind(mary)))=>((generous(susan)&humble(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>~strong(X))))&
(![X]:((funny(X)&~rich(X))=>(~generous(X)&~kind(X))))&
(![X]:(calm(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~brave(X)&curious(X))<=>(tall(X)&~creative(X))))&
(![X]:(happy(X)=>brave(X)))&
(((~kind(susan)|~happy(susan)))=>((~creative(paul)<~>~tall(paul))))&
(![X]:((~wise(X)|~rich(X))=>(~humble(X)|quiet(X))))&
(((~happy(susan)|~strong(susan)))=>((~kind(alice)&calm(alice))))&
((?[X]:((humble(X)&~calm(X))))<=>(tall(mary)))&
((?[X]:((~rich(X)&~kind(X))))<=>((~creative(susan)&~happy(susan))))&
(((humble(john)&happy(john)))=>(quiet(lucy)))&
(((wise(mary)&happy(mary)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|brave(X))=>(happy(X)&humble(X))))&
(((~generous(alice)|kind(alice)))<=>((calm(fred)&~kind(fred))))&
(![X]:((~generous(X)|~rich(X))=>(~tall(X)&calm(X))))&
((curious(lucy)&~wise(lucy)))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
((rich(john)|kind(john)))&
(?[X]:((~old(X)&~strong(X)))) | brave(alice) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2875563596663134515914591
% SZS output start Proof for 2875563596663134515914591
6. ! [X0] : (happy(X0) => brave(X0)) [input p5]
14. ! [X0] : ((brave(X0) | ~brave(X0)) => (humble(X0) & happy(X0))) [input p13]
24. ~brave(alice) [input hypothesis]
31. ! [X0] : (brave(X0) | ~happy(X0)) [ennf transformation 6]
40. ! [X0] : ((humble(X0) & happy(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 14]
85. ~happy(X0) | brave(X0) [cnf transformation 31]
105. happy(X0) | brave(X0) [cnf transformation 40]
106. ~brave(X0) | happy(X0) [cnf transformation 40]
129. ~brave(alice) [cnf transformation 24]
250. happy(X0) [subsumption resolution 105,106]
307. brave(X0) [resolution 85,250]
308. $false [resolution 307,129]
% SZS output end Proof for 2875563596663134515914591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not curious then someone is either not generous or curious.
Everyone who is both not generous and not old is both not calm and not quiet.
Everyone who is creative is either not kind or kind and vice versa.
Everyone who is quiet is wise.
Everyone who is both creative and brave is both not tall and not happy.
Everyone who is not old is funny.
If someone is creative then susan is either creative or happy and vice versa.
Everyone who is either wise or not strong is not quiet.
Everyone who is both wise and generous is either not generous or creative.
If alice is not creative then someone is humble or old.
If someone is both not calm and not patient then someone is patient and vice versa.
If someone is generous or funny then alice is not creative or rich.
Everyone who is both not curious and not funny is wise and vice versa.
Everyone who is both funny and brave is not quiet or not funny and vice versa.
If fred is kind or not rich then someone is generous or not funny.
Everyone who is curious or not old is either patient or not generous.
Alice is not wise or not calm.
Someone is either rich or not rich.
Someone is kind.
Someone is either tall or not kind.
Someone is not curious.
Someone is either not rich or patient. | Alice is not quiet. | entailment | ((~curious(alice))=>(?[X]:((~generous(X)<~>curious(X)))))&
(![X]:((~generous(X)&~old(X))=>(~calm(X)&~quiet(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
(![X]:(quiet(X)=>wise(X)))&
(![X]:((creative(X)&brave(X))=>(~tall(X)&~happy(X))))&
(![X]:(~old(X)=>funny(X)))&
((?[X]:(creative(X)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((wise(X)<~>~strong(X))=>~quiet(X)))&
(![X]:((wise(X)&generous(X))=>(~generous(X)<~>creative(X))))&
((~creative(alice))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:((~calm(X)&~patient(X))))<=>(?[X]:(patient(X))))&
((?[X]:((generous(X)|funny(X))))=>((~creative(alice)|rich(alice))))&
(![X]:((~curious(X)&~funny(X))<=>wise(X)))&
(![X]:((funny(X)&brave(X))<=>(~quiet(X)|~funny(X))))&
(((kind(fred)|~rich(fred)))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((curious(X)|~old(X))=>(patient(X)<~>~generous(X))))&
((~wise(alice)|~calm(alice)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:(kind(X)))&
(?[X]:((tall(X)<~>~kind(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>patient(X)))) | ~quiet(alice) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3712540760496842442524326
% SZS output start Proof for 3712540760496842442524326
4. ! [X0] : (quiet(X0) => wise(X0)) [input p3]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> wise(X0)) [input p12]
14. ! [X0] : ((brave(X0) & funny(X0)) <=> (~funny(X0) | ~quiet(X0))) [input p13]
23. quiet(alice) [input hypothesis]
30. ! [X0] : (wise(X0) | ~quiet(X0)) [ennf transformation 4]
55. ! [X0] : (((~funny(X0) & ~curious(X0)) | ~wise(X0)) & (wise(X0) | (funny(X0) | curious(X0)))) [nnf transformation 13]
56. ! [X0] : (((~funny(X0) & ~curious(X0)) | ~wise(X0)) & (wise(X0) | funny(X0) | curious(X0))) [flattening 55]
57. ! [X0] : (((brave(X0) & funny(X0)) | (funny(X0) & quiet(X0))) & ((~funny(X0) | ~quiet(X0)) | (~brave(X0) | ~funny(X0)))) [nnf transformation 14]
58. ! [X0] : (((brave(X0) & funny(X0)) | (funny(X0) & quiet(X0))) & (~funny(X0) | ~quiet(X0) | ~brave(X0) | ~funny(X0))) [flattening 57]
81. ~quiet(X0) | wise(X0) [cnf transformation 30]
99. ~funny(X0) | ~wise(X0) [cnf transformation 56]
102. funny(X0) | funny(X0) [cnf transformation 58]
118. quiet(alice) [cnf transformation 23]
120. funny(X0) [duplicate literal removal 102]
197. 15 <=> wise(alice) [avatar definition]
198. wise(alice) <- (15) [avatar component clause 197]
225. wise(alice) [resolution 81,118]
226. 15 [avatar split clause 225,197]
229. ~wise(X0) [resolution 99,120]
230. $false <- (15) [resolution 229,198]
231. ~15 [avatar contradiction clause 230]
232. $false [avatar sat refutation 226,231]
% SZS output end Proof for 3712540760496842442524326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is tall. Everyone who is either not generous or kind is either not funny or strong. If someone is both happy and wise then paul is not curious. If john is creative or tall then lucy is not rich. If someone is quiet or not rich then paul is both humble and patient. If susan is curious or not quiet then lucy is not funny and vice versa. Everyone who is curious or not happy is tall. Everyone who is either calm or not generous is both not curious and not generous. Everyone who is both strong and humble is strong or generous. Everyone who is generous or not kind is kind. Everyone who is either tall or not patient is not strong and vice versa. If susan is both not patient and curious then someone is not curious and vice versa. If paul is both not strong and tall then someone is either not old or rich and vice versa. Everyone who is creative is both not humble and not old. Everyone who is brave is wise and vice versa. If lucy is both not rich and calm then someone is either patient or wise. Someone is both not old and rich. Mary is both not funny and creative. Mary is both wise and curious. Someone is both strong and rich. Mary is wise or not funny. | Paul is not happy. | neutral | ((?[X]:(~strong(X)))=>(?[X]:(tall(X))))&
(![X]:((~generous(X)<~>kind(X))=>(~funny(X)<~>strong(X))))&
((?[X]:((happy(X)&wise(X))))=>(~curious(paul)))&
(((creative(john)|tall(john)))=>(~rich(lucy)))&
((?[X]:((quiet(X)|~rich(X))))=>((humble(paul)&patient(paul))))&
(((curious(susan)|~quiet(susan)))<=>(~funny(lucy)))&
(![X]:((curious(X)|~happy(X))=>tall(X)))&
(![X]:((calm(X)<~>~generous(X))=>(~curious(X)&~generous(X))))&
(![X]:((strong(X)&humble(X))=>(strong(X)|generous(X))))&
(![X]:((generous(X)|~kind(X))=>kind(X)))&
(![X]:((tall(X)<~>~patient(X))<=>~strong(X)))&
(((~patient(susan)&curious(susan)))<=>(?[X]:(~curious(X))))&
(((~strong(paul)&tall(paul)))<=>(?[X]:((~old(X)<~>rich(X)))))&
(![X]:(creative(X)=>(~humble(X)&~old(X))))&
(![X]:(brave(X)<=>wise(X)))&
(((~rich(lucy)&calm(lucy)))=>(?[X]:((patient(X)<~>wise(X)))))&
(?[X]:((~old(X)&rich(X))))&
((~funny(mary)&creative(mary)))&
((wise(mary)&curious(mary)))&
(?[X]:((strong(X)&rich(X))))&
((wise(mary)|~funny(mary))) | ~happy(paul) | [] | null | 0 |
Everyone who is not wise or patient is either not old or not curious and vice versa. Everyone who is generous is either strong or not tall. If lucy is humble then susan is both not funny and not generous and vice versa. Everyone who is both quiet and not funny is patient or tall and vice versa. Everyone who is not wise is either not rich or old. If lucy is either wise or not brave then john is either creative or not creative and vice versa. Everyone who is either not strong or wise is both humble and creative and vice versa. Everyone who is not kind or patient is either brave or calm. If paul is either not brave or wise then someone is both not curious and not old and vice versa. Everyone who is not humble is either not wise or not curious and vice versa. Everyone who is funny is both not kind and not happy. Everyone who is wise is both not curious and patient. Everyone who is either calm or not patient is not kind or humble and vice versa. If john is old then someone is both not wise and not tall. If someone is not rich then mary is strong or funny and vice versa. Everyone who is rich is both not tall and old. Someone is either not rich or not generous. Someone is old or generous. Alice is either funny or rich. John is not happy. Alice is either not rich or quiet. Mary is either not curious or not humble. | Lucy is funny. | contradiction | (![X]:((~wise(X)|patient(X))<=>(~old(X)<~>~curious(X))))&
(![X]:(generous(X)=>(strong(X)<~>~tall(X))))&
((humble(lucy))<=>((~funny(susan)&~generous(susan))))&
(![X]:((quiet(X)&~funny(X))<=>(patient(X)|tall(X))))&
(![X]:(~wise(X)=>(~rich(X)<~>old(X))))&
(((wise(lucy)<~>~brave(lucy)))<=>((creative(john)<~>~creative(john))))&
(![X]:((~strong(X)<~>wise(X))<=>(humble(X)&creative(X))))&
(![X]:((~kind(X)|patient(X))=>(brave(X)<~>calm(X))))&
(((~brave(paul)<~>wise(paul)))<=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:(~humble(X)<=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)=>(~kind(X)&~happy(X))))&
(![X]:(wise(X)=>(~curious(X)&patient(X))))&
(![X]:((calm(X)<~>~patient(X))<=>(~kind(X)|humble(X))))&
((old(john))=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))<=>((strong(mary)|funny(mary))))&
(![X]:(rich(X)=>(~tall(X)&old(X))))&
(?[X]:((~rich(X)<~>~generous(X))))&
(?[X]:((old(X)|generous(X))))&
((funny(alice)<~>rich(alice)))&
(~happy(john))&
((~rich(alice)<~>quiet(alice)))&
((~curious(mary)<~>~humble(mary))) | funny(lucy) | [
"p3",
"p5",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7992962106861173692919841
% SZS output start Proof for 7992962106861173692919841
4. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (tall(X0) | patient(X0))) [input p3]
6. (wise(lucy) <~> ~brave(lucy)) <=> (creative(john) <~> ~creative(john)) [input p5]
8. ! [X0] : ((patient(X0) | ~kind(X0)) => (brave(X0) <~> calm(X0))) [input p7]
11. ! [X0] : (funny(X0) => (~happy(X0) & ~kind(X0))) [input p10]
12. ! [X0] : (wise(X0) => (patient(X0) & ~curious(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> ~patient(X0)) <=> (humble(X0) | ~kind(X0))) [input p12]
23. funny(lucy) [input hypothesis]
24. ! [X0] : (funny(X0) => ~kind(X0)) [pure predicate removal 11]
28. ! [X0] : ((brave(X0) <~> calm(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 8]
29. ! [X0] : (~kind(X0) | ~funny(X0)) [ennf transformation 24]
30. ! [X0] : ((patient(X0) & ~curious(X0)) | ~wise(X0)) [ennf transformation 12]
38. ! [X0] : (((~funny(X0) & quiet(X0)) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 4]
39. ! [X0] : (((~funny(X0) & quiet(X0)) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | funny(X0) | ~quiet(X0))) [flattening 38]
41. (((brave(lucy) | ~wise(lucy)) & (~brave(lucy) | wise(lucy))) | ((creative(john) | creative(john)) & (~creative(john) | ~creative(john)))) & (((creative(john) | ~creative(john)) & (~creative(john) | creative(john))) | ((wise(lucy) | brave(lucy)) & (~brave(lucy) | ~wise(lucy)))) [nnf transformation 6]
44. ! [X0] : (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (~patient(X0) & kind(X0))) [nnf transformation 28]
50. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [nnf transformation 13]
51. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [flattening 50]
81. ~funny(X0) | ~patient(X0) [cnf transformation 39]
89. ~brave(lucy) | wise(lucy) | ~creative(john) | ~creative(john) [cnf transformation 41]
90. ~brave(lucy) | wise(lucy) | creative(john) | creative(john) [cnf transformation 41]
99. calm(X0) | brave(X0) | kind(X0) [cnf transformation 44]
113. ~kind(X0) | ~funny(X0) [cnf transformation 29]
115. ~wise(X0) | patient(X0) [cnf transformation 30]
120. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 51]
138. funny(lucy) [cnf transformation 23]
139. ~brave(lucy) | wise(lucy) | ~creative(john) [duplicate literal removal 89]
140. ~brave(lucy) | wise(lucy) | creative(john) [duplicate literal removal 90]
159. 4 <=> creative(john) [avatar definition]
163. 5 <=> wise(lucy) [avatar definition]
164. wise(lucy) <- (5) [avatar component clause 163]
167. 6 <=> brave(lucy) [avatar definition]
172. 4 | 5 | ~6 [avatar split clause 140,167,163,159]
173. ~4 | 5 | ~6 [avatar split clause 139,167,163,159]
276. ~patient(lucy) [resolution 81,138]
396. patient(X0) | kind(X0) | brave(X0) | kind(X0) [resolution 120,99]
397. kind(X0) | patient(X0) | brave(X0) [duplicate literal removal 396]
402. patient(X0) | brave(X0) | ~funny(X0) [resolution 397,113]
403. ~funny(X0) | brave(X0) [subsumption resolution 402,81]
411. brave(lucy) [resolution 403,138]
426. 6 [avatar split clause 411,167]
428. patient(lucy) <- (5) [resolution 164,115]
429. $false <- (5) [subsumption resolution 428,276]
430. ~5 [avatar contradiction clause 429]
431. $false [avatar sat refutation 172,173,426,430]
% SZS output end Proof for 7992962106861173692919841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and quiet then someone is both tall and not rich and vice versa.
If john is kind or quiet then john is brave or strong and vice versa.
If lucy is both humble and brave then john is tall and vice versa.
If mary is both not curious and not wise then fred is either not brave or not humble.
Everyone who is either brave or not tall is both not patient and not calm.
If someone is either creative or brave then susan is wise or old and vice versa.
If lucy is either curious or not funny then fred is creative and vice versa.
Everyone who is not humble or generous is not calm and vice versa.
Everyone who is tall is brave and vice versa.
If someone is both brave and not brave then someone is either not wise or not creative and vice versa.
Everyone who is both brave and not generous is both not wise and rich.
Everyone who is both humble and not tall is either quiet or not old and vice versa.
Everyone who is either humble or not wise is both not patient and not tall.
Everyone who is not creative or not wise is not old and vice versa.
If someone is generous or quiet then mary is not quiet or funny.
Everyone who is not brave or not strong is patient.
Alice is not curious or not brave.
Someone is both happy and kind.
Someone is either tall or kind.
Someone is creative or quiet.
Fred is not kind.
Someone is not funny. | Susan is not quiet. | entailment | ((?[X]:((old(X)&quiet(X))))<=>(?[X]:((tall(X)&~rich(X)))))&
(((kind(john)|quiet(john)))<=>((brave(john)|strong(john))))&
(((humble(lucy)&brave(lucy)))<=>(tall(john)))&
(((~curious(mary)&~wise(mary)))=>((~brave(fred)<~>~humble(fred))))&
(![X]:((brave(X)<~>~tall(X))=>(~patient(X)&~calm(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((wise(susan)|old(susan))))&
(((curious(lucy)<~>~funny(lucy)))<=>(creative(fred)))&
(![X]:((~humble(X)|generous(X))<=>~calm(X)))&
(![X]:(tall(X)<=>brave(X)))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>~creative(X)))))&
(![X]:((brave(X)&~generous(X))=>(~wise(X)&rich(X))))&
(![X]:((humble(X)&~tall(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((humble(X)<~>~wise(X))=>(~patient(X)&~tall(X))))&
(![X]:((~creative(X)|~wise(X))<=>~old(X)))&
((?[X]:((generous(X)|quiet(X))))=>((~quiet(mary)|funny(mary))))&
(![X]:((~brave(X)|~strong(X))=>patient(X)))&
((~curious(alice)|~brave(alice)))&
(?[X]:((happy(X)&kind(X))))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:((creative(X)|quiet(X))))&
(~kind(fred))&
(?[X]:(~funny(X))) | ~quiet(susan) | [
"p4",
"p5",
"p8",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2257196014526629835438898
% SZS output start Proof for 2257196014526629835438898
5. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (~calm(X0) & ~patient(X0))) [input p4]
6. ? [X0] : (creative(X0) <~> brave(X0)) <=> (old(susan) | wise(susan)) [input p5]
9. ! [X0] : (tall(X0) <=> brave(X0)) [input p8]
10. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X0] : (~wise(X0) <~> ~creative(X0)) [input p9]
12. ! [X0] : ((~tall(X0) & humble(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> ~old(X0)) [input p13]
16. ! [X0] : ((~strong(X0) | ~brave(X0)) => patient(X0)) [input p15]
23. quiet(susan) [input hypothesis]
25. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X1] : (~wise(X1) <~> ~creative(X1)) [rectify 10]
30. ! [X0] : ((~calm(X0) & ~patient(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 5]
38. ! [X0] : (patient(X0) | (strong(X0) & brave(X0))) [ennf transformation 16]
49. ! [X0] : ((~calm(X0) & ~patient(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 30]
50. (? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (~old(susan) & ~wise(susan))) & ((old(susan) | wise(susan)) | ! [X0] : ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0)))) [nnf transformation 6]
51. (? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (~old(susan) & ~wise(susan))) & (old(susan) | wise(susan) | ! [X0] : ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0)))) [flattening 50]
52. (? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | (~old(susan) & ~wise(susan))) & (old(susan) | wise(susan) | ! [X1] : ((creative(X1) | ~brave(X1)) & (brave(X1) | ~creative(X1)))) [rectify 51]
53. ? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) => ((~brave(sK2) | ~creative(sK2)) & (brave(sK2) | creative(sK2))) [choice axiom]
54. (((~brave(sK2) | ~creative(sK2)) & (brave(sK2) | creative(sK2))) | (~old(susan) & ~wise(susan))) & (old(susan) | wise(susan) | ! [X1] : ((creative(X1) | ~brave(X1)) & (brave(X1) | ~creative(X1)))) [skolemisation 52,53]
56. ! [X0] : ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))) [nnf transformation 9]
57. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | creative(X1)) & (~creative(X1) | wise(X1)))) & (? [X1] : ((creative(X1) | wise(X1)) & (~creative(X1) | ~wise(X1))) | ! [X0] : (brave(X0) | ~brave(X0))) [nnf transformation 25]
58. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | creative(X1)) & (~creative(X1) | wise(X1)))) & (? [X2] : ((creative(X2) | wise(X2)) & (~creative(X2) | ~wise(X2))) | ! [X3] : (brave(X3) | ~brave(X3))) [rectify 57]
59. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK3) & brave(sK3)) [choice axiom]
60. ? [X2] : ((creative(X2) | wise(X2)) & (~creative(X2) | ~wise(X2))) => ((creative(sK4) | wise(sK4)) & (~creative(sK4) | ~wise(sK4))) [choice axiom]
61. ((~brave(sK3) & brave(sK3)) | ! [X1] : ((~wise(X1) | creative(X1)) & (~creative(X1) | wise(X1)))) & (((creative(sK4) | wise(sK4)) & (~creative(sK4) | ~wise(sK4))) | ! [X3] : (brave(X3) | ~brave(X3))) [skolemisation 58,60,59]
62. ! [X0] : (((~tall(X0) & humble(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (tall(X0) | ~humble(X0)))) [nnf transformation 12]
63. ! [X0] : (((~tall(X0) & humble(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | tall(X0) | ~humble(X0))) [flattening 62]
65. ! [X0] : (((~wise(X0) | ~creative(X0)) | old(X0)) & (~old(X0) | (wise(X0) & creative(X0)))) [nnf transformation 14]
66. ! [X0] : ((~wise(X0) | ~creative(X0) | old(X0)) & (~old(X0) | (wise(X0) & creative(X0)))) [flattening 65]
90. ~patient(X0) | brave(X0) | tall(X0) [cnf transformation 49]
94. old(susan) | wise(susan) | creative(X1) | ~brave(X1) [cnf transformation 54]
104. ~tall(X0) | brave(X0) [cnf transformation 56]
105. ~brave(X0) | tall(X0) [cnf transformation 56]
108. brave(sK3) | ~creative(X1) | wise(X1) [cnf transformation 61]
109. brave(sK3) | ~wise(X1) | creative(X1) [cnf transformation 61]
110. ~brave(sK3) | ~creative(X1) | wise(X1) [cnf transformation 61]
111. ~brave(sK3) | ~wise(X1) | creative(X1) [cnf transformation 61]
118. ~tall(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 63]
126. ~creative(X0) | ~wise(X0) | old(X0) [cnf transformation 66]
129. patient(X0) | brave(X0) [cnf transformation 38]
138. quiet(susan) [cnf transformation 23]
153. 4 <=> ! [X3] : (~quiet(X3) | ~old(X3)) [avatar definition]
154. ~quiet(X3) | ~old(X3) <- (4) [avatar component clause 153]
219. 18 <=> old(susan) [avatar definition]
220. old(susan) <- (18) [avatar component clause 219]
221. ~old(susan) <- (~18) [avatar component clause 219]
232. 21 <=> wise(susan) [avatar definition]
233. wise(susan) <- (21) [avatar component clause 232]
234. ~wise(susan) <- (~21) [avatar component clause 232]
239. 22 <=> ! [X1] : (creative(X1) | ~brave(X1)) [avatar definition]
240. creative(X1) | ~brave(X1) <- (22) [avatar component clause 239]
241. 22 | 21 | 18 [avatar split clause 94,219,232,239]
263. 27 <=> ! [X1] : (~wise(X1) | creative(X1)) [avatar definition]
264. ~wise(X1) | creative(X1) <- (27) [avatar component clause 263]
266. 28 <=> brave(sK3) [avatar definition]
269. 27 | ~28 [avatar split clause 111,266,263]
271. 29 <=> ! [X1] : (~creative(X1) | wise(X1)) [avatar definition]
272. ~creative(X1) | wise(X1) <- (29) [avatar component clause 271]
273. 29 | ~28 [avatar split clause 110,266,271]
274. 27 | 28 [avatar split clause 109,266,263]
275. 29 | 28 [avatar split clause 108,266,271]
327. ~old(susan) <- (4) [resolution 154,138]
329. $false <- (4, 18) [subsumption resolution 327,220]
330. ~4 | ~18 [avatar contradiction clause 329]
336. creative(susan) <- (21, 27) [resolution 264,233]
350. brave(X1) | tall(X1) | brave(X1) [resolution 90,129]
351. brave(X1) | tall(X1) [duplicate literal removal 350]
353. tall(X1) [subsumption resolution 351,105]
356. brave(X0) [resolution 353,104]
413. ~old(X0) | ~quiet(X0) [resolution 118,353]
415. 4 [avatar split clause 413,153]
463. ~wise(susan) | old(susan) <- (21, 27) [resolution 126,336]
467. old(susan) <- (21, 27) [subsumption resolution 463,233]
468. $false <- (~18, 21, 27) [subsumption resolution 467,221]
469. 18 | ~21 | ~27 [avatar contradiction clause 468]
471. creative(X1) <- (22) [subsumption resolution 240,356]
473. wise(X1) <- (22, 29) [resolution 471,272]
490. $false <- (~21, 22, 29) [resolution 473,234]
491. 21 | ~22 | ~29 [avatar contradiction clause 490]
494. $false [avatar sat refutation 241,269,273,274,275,330,415,469,491]
% SZS output end Proof for 2257196014526629835438898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is not brave.
Everyone who is both not funny and happy is either not tall or old and vice versa.
If someone is either kind or not humble then someone is strong.
Everyone who is both not humble and humble is both kind and tall and vice versa.
If lucy is wise then susan is either not creative or rich and vice versa.
If lucy is not creative then alice is calm and vice versa.
Everyone who is not creative or humble is not wise.
Everyone who is either not strong or not rich is not old.
Everyone who is generous is both not generous and curious.
If someone is both rich and quiet then alice is both not generous and brave.
Everyone who is either not patient or curious is not curious and vice versa.
If fred is calm or curious then fred is not humble or wise and vice versa.
Everyone who is strong or not wise is both quiet and not strong and vice versa.
If someone is not rich then susan is both generous and creative and vice versa.
Everyone who is kind or not patient is not tall.
Everyone who is not curious or old is either not funny or not generous and vice versa.
Someone is not quiet.
John is happy.
Someone is either not tall or calm.
Alice is calm.
Someone is not brave. | Alice is not tall. | entailment | (![X]:((~happy(X)|~curious(X))=>~brave(X)))&
(![X]:((~funny(X)&happy(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((kind(X)<~>~humble(X))))=>(?[X]:(strong(X))))&
(![X]:((~humble(X)&humble(X))<=>(kind(X)&tall(X))))&
((wise(lucy))<=>((~creative(susan)<~>rich(susan))))&
((~creative(lucy))<=>(calm(alice)))&
(![X]:((~creative(X)|humble(X))=>~wise(X)))&
(![X]:((~strong(X)<~>~rich(X))=>~old(X)))&
(![X]:(generous(X)=>(~generous(X)&curious(X))))&
((?[X]:((rich(X)&quiet(X))))=>((~generous(alice)&brave(alice))))&
(![X]:((~patient(X)<~>curious(X))<=>~curious(X)))&
(((calm(fred)|curious(fred)))<=>((~humble(fred)|wise(fred))))&
(![X]:((strong(X)|~wise(X))<=>(quiet(X)&~strong(X))))&
((?[X]:(~rich(X)))<=>((generous(susan)&creative(susan))))&
(![X]:((kind(X)|~patient(X))=>~tall(X)))&
(![X]:((~curious(X)|old(X))<=>(~funny(X)<~>~generous(X))))&
(?[X]:(~quiet(X)))&
(happy(john))&
(?[X]:((~tall(X)<~>calm(X))))&
(calm(alice))&
(?[X]:(~brave(X))) | ~tall(alice) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 410765386937027072769394
% SZS output start Proof for 410765386937027072769394
11. ! [X0] : ((~patient(X0) <~> curious(X0)) <=> ~curious(X0)) [input p10]
15. ! [X0] : ((~patient(X0) | kind(X0)) => ~tall(X0)) [input p14]
22. tall(alice) [input hypothesis]
30. ! [X0] : (~tall(X0) | (patient(X0) & ~kind(X0))) [ennf transformation 15]
42. ! [X0] : ((((~curious(X0) | patient(X0)) & (curious(X0) | ~patient(X0))) | curious(X0)) & (~curious(X0) | ((~patient(X0) | ~curious(X0)) & (curious(X0) | patient(X0))))) [nnf transformation 11]
90. ~curious(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 42]
91. curious(X0) | ~patient(X0) | curious(X0) [cnf transformation 42]
106. ~tall(X0) | patient(X0) [cnf transformation 30]
119. tall(alice) [cnf transformation 22]
122. ~curious(X0) | ~patient(X0) [duplicate literal removal 90]
123. curious(X0) | ~patient(X0) [duplicate literal removal 91]
172. ~patient(X0) [subsumption resolution 122,123]
201. ~tall(X0) [subsumption resolution 106,172]
207. $false [subsumption resolution 119,201]
% SZS output end Proof for 410765386937027072769394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not generous is both quiet and not happy and vice versa.
Everyone who is both not patient and not kind is not strong and vice versa.
Everyone who is patient or rich is curious.
If paul is either kind or not tall then someone is both humble and not curious.
Everyone who is either not patient or quiet is wise or humble and vice versa.
Everyone who is not strong is not old.
Everyone who is either strong or tall is quiet or happy.
Everyone who is either not happy or not strong is both curious and not humble and vice versa.
Everyone who is generous or not brave is either not patient or funny and vice versa.
If fred is both not creative and old then fred is strong or quiet and vice versa.
Everyone who is generous is either not creative or patient.
Everyone who is both not wise and not creative is happy.
Everyone who is not rich or wise is not generous and vice versa.
If someone is quiet or not generous then alice is old and vice versa.
Everyone who is both funny and not kind is both not happy and old.
Everyone who is not creative is not brave and vice versa.
Someone is both not calm and not patient.
Susan is not humble.
Someone is both funny and humble.
Someone is both not wise and not curious.
Susan is tall or not curious.
Someone is both not patient and quiet.
Someone is either wise or patient.
Fred is both wise and quiet. | Paul is old. | neutral | (![X]:((patient(X)&~generous(X))<=>(quiet(X)&~happy(X))))&
(![X]:((~patient(X)&~kind(X))<=>~strong(X)))&
(![X]:((patient(X)|rich(X))=>curious(X)))&
(((kind(paul)<~>~tall(paul)))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>(wise(X)|humble(X))))&
(![X]:(~strong(X)=>~old(X)))&
(![X]:((strong(X)<~>tall(X))=>(quiet(X)|happy(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(curious(X)&~humble(X))))&
(![X]:((generous(X)|~brave(X))<=>(~patient(X)<~>funny(X))))&
(((~creative(fred)&old(fred)))<=>((strong(fred)|quiet(fred))))&
(![X]:(generous(X)=>(~creative(X)<~>patient(X))))&
(![X]:((~wise(X)&~creative(X))=>happy(X)))&
(![X]:((~rich(X)|wise(X))<=>~generous(X)))&
((?[X]:((quiet(X)|~generous(X))))<=>(old(alice)))&
(![X]:((funny(X)&~kind(X))=>(~happy(X)&old(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(~humble(susan))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((tall(susan)|~curious(susan)))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((wise(X)<~>patient(X))))&
((wise(fred)&quiet(fred))) | old(paul) | [] | null | 0 |
If someone is not humble or not funny then susan is both not generous and not funny and vice versa.
Everyone who is humble is either wise or humble and vice versa.
If someone is wise or not calm then fred is either not tall or not brave.
Everyone who is not curious or funny is not tall or not quiet.
Everyone who is either kind or patient is both not rich and kind and vice versa.
Everyone who is not funny is either strong or not wise and vice versa.
If someone is either curious or not patient then someone is brave and vice versa.
If lucy is old or funny then someone is patient and vice versa.
If alice is not brave then mary is creative.
If someone is funny or strong then someone is not quiet and vice versa.
Everyone who is not patient is not calm or kind and vice versa.
Everyone who is rich or curious is either patient or humble and vice versa.
If someone is not old or not happy then mary is either not rich or not brave.
Everyone who is both humble and not brave is tall and vice versa.
If someone is both not happy and not rich then someone is not curious or not strong.
Everyone who is either not wise or quiet is not tall and vice versa.
Someone is either wise or not generous.
Someone is rich.
Fred is either curious or not wise.
Someone is not strong.
Paul is both old and not quiet.
Someone is generous. | Alice is not quiet. | neutral | ((?[X]:((~humble(X)|~funny(X))))<=>((~generous(susan)&~funny(susan))))&
(![X]:(humble(X)<=>(wise(X)<~>humble(X))))&
((?[X]:((wise(X)|~calm(X))))=>((~tall(fred)<~>~brave(fred))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)|~quiet(X))))&
(![X]:((kind(X)<~>patient(X))<=>(~rich(X)&kind(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>~wise(X))))&
((?[X]:((curious(X)<~>~patient(X))))<=>(?[X]:(brave(X))))&
(((old(lucy)|funny(lucy)))<=>(?[X]:(patient(X))))&
((~brave(alice))=>(creative(mary)))&
((?[X]:((funny(X)|strong(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(~patient(X)<=>(~calm(X)|kind(X))))&
(![X]:((rich(X)|curious(X))<=>(patient(X)<~>humble(X))))&
((?[X]:((~old(X)|~happy(X))))=>((~rich(mary)<~>~brave(mary))))&
(![X]:((humble(X)&~brave(X))<=>tall(X)))&
((?[X]:((~happy(X)&~rich(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~tall(X)))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:(rich(X)))&
((curious(fred)<~>~wise(fred)))&
(?[X]:(~strong(X)))&
((old(paul)&~quiet(paul)))&
(?[X]:(generous(X))) | ~quiet(alice) | [] | null | 0 |
If john is humble then someone is both patient and kind.
If paul is both not patient and kind then susan is either not tall or not patient and vice versa.
Everyone who is funny or not curious is funny and vice versa.
If someone is calm then someone is patient and vice versa.
Everyone who is both not patient and wise is both not old and not kind and vice versa.
If someone is either calm or not patient then someone is not funny or kind.
Everyone who is not humble is both old and not creative and vice versa.
Everyone who is both rich and not brave is either not rich or not funny and vice versa.
If someone is old or not quiet then someone is both not brave and funny and vice versa.
If someone is either calm or quiet then someone is either kind or not old and vice versa.
Everyone who is not quiet or not calm is both not quiet and not strong and vice versa.
Everyone who is both not rich and generous is curious.
If someone is both not kind and tall then susan is creative and vice versa.
If someone is patient or strong then susan is either not patient or kind.
If john is not tall or strong then alice is both wise and brave.
Everyone who is both not funny and patient is both quiet and kind.
Someone is both strong and quiet.
Paul is both quiet and not patient.
Someone is both not happy and not curious.
John is either kind or tall.
Susan is either calm or not curious.
Lucy is not rich or not strong.
Fred is humble. | Paul is wise. | contradiction | ((humble(john))=>(?[X]:((patient(X)&kind(X)))))&
(((~patient(paul)&kind(paul)))<=>((~tall(susan)<~>~patient(susan))))&
(![X]:((funny(X)|~curious(X))<=>funny(X)))&
((?[X]:(calm(X)))<=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&wise(X))<=>(~old(X)&~kind(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:(~humble(X)<=>(old(X)&~creative(X))))&
(![X]:((rich(X)&~brave(X))<=>(~rich(X)<~>~funny(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:((~brave(X)&funny(X)))))&
((?[X]:((calm(X)<~>quiet(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(![X]:((~quiet(X)|~calm(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~rich(X)&generous(X))=>curious(X)))&
((?[X]:((~kind(X)&tall(X))))<=>(creative(susan)))&
((?[X]:((patient(X)|strong(X))))=>((~patient(susan)<~>kind(susan))))&
(((~tall(john)|strong(john)))=>((wise(alice)&brave(alice))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&kind(X))))&
(?[X]:((strong(X)&quiet(X))))&
((quiet(paul)&~patient(paul)))&
(?[X]:((~happy(X)&~curious(X))))&
((kind(john)<~>tall(john)))&
((calm(susan)<~>~curious(susan)))&
((~rich(lucy)|~strong(lucy)))&
(humble(fred)) | wise(paul) | [
"p4",
"p7",
"p8",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2679874800294647609379286
% SZS output start Proof for 2679874800294647609379286
5. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (~kind(X0) & ~old(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & rich(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p7]
9. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X0] : (funny(X0) & ~brave(X0)) [input p8]
10. ? [X0] : (calm(X0) <~> quiet(X0)) <=> ? [X0] : (kind(X0) <~> ~old(X0)) [input p9]
11. ! [X0] : ((~calm(X0) | ~quiet(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p10]
18. ~patient(paul) & quiet(paul) [input p17]
24. wise(paul) [input hypothesis]
27. ? [X0] : (~quiet(X0) | old(X0)) <=> ? [X1] : (funny(X1) & ~brave(X1)) [rectify 9]
28. ? [X0] : (calm(X0) <~> quiet(X0)) <=> ? [X1] : (kind(X1) <~> ~old(X1)) [rectify 10]
48. ! [X0] : (((wise(X0) & ~patient(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 5]
49. ! [X0] : (((wise(X0) & ~patient(X0)) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ~wise(X0) | patient(X0))) [flattening 48]
56. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (brave(X0) | ~rich(X0)))) [nnf transformation 8]
57. ! [X0] : (((~brave(X0) & rich(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | brave(X0) | ~rich(X0))) [flattening 56]
58. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X1] : (funny(X1) & ~brave(X1)) | ! [X0] : (quiet(X0) & ~old(X0))) [nnf transformation 27]
59. (? [X0] : (~quiet(X0) | old(X0)) | ! [X1] : (~funny(X1) | brave(X1))) & (? [X2] : (funny(X2) & ~brave(X2)) | ! [X3] : (quiet(X3) & ~old(X3))) [rectify 58]
60. ? [X0] : (~quiet(X0) | old(X0)) => (~quiet(sK4) | old(sK4)) [choice axiom]
61. ? [X2] : (funny(X2) & ~brave(X2)) => (funny(sK5) & ~brave(sK5)) [choice axiom]
62. ((~quiet(sK4) | old(sK4)) | ! [X1] : (~funny(X1) | brave(X1))) & ((funny(sK5) & ~brave(sK5)) | ! [X3] : (quiet(X3) & ~old(X3))) [skolemisation 59,61,60]
63. (? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X1] : ((old(X1) | ~kind(X1)) & (~old(X1) | kind(X1))) | ! [X0] : ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0)))) [nnf transformation 28]
64. (? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) | ! [X3] : ((calm(X3) | ~quiet(X3)) & (quiet(X3) | ~calm(X3)))) [rectify 63]
65. ? [X0] : ((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) => ((~quiet(sK6) | ~calm(sK6)) & (quiet(sK6) | calm(sK6))) [choice axiom]
66. ? [X2] : ((old(X2) | ~kind(X2)) & (~old(X2) | kind(X2))) => ((old(sK7) | ~kind(sK7)) & (~old(sK7) | kind(sK7))) [choice axiom]
67. (((~quiet(sK6) | ~calm(sK6)) & (quiet(sK6) | calm(sK6))) | ! [X1] : ((kind(X1) | old(X1)) & (~old(X1) | ~kind(X1)))) & (((old(sK7) | ~kind(sK7)) & (~old(sK7) | kind(sK7))) | ! [X3] : ((calm(X3) | ~quiet(X3)) & (quiet(X3) | ~calm(X3)))) [skolemisation 64,66,65]
68. ! [X0] : (((~calm(X0) | ~quiet(X0)) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [nnf transformation 11]
69. ! [X0] : ((~calm(X0) | ~quiet(X0) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | (calm(X0) & quiet(X0)))) [flattening 68]
95. ~wise(X0) | ~kind(X0) | patient(X0) [cnf transformation 49]
103. ~funny(X0) | ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
105. rich(X0) | ~funny(X0) | rich(X0) [cnf transformation 57]
109. ~brave(sK5) | ~old(X3) [cnf transformation 62]
110. ~brave(sK5) | quiet(X3) [cnf transformation 62]
111. funny(sK5) | ~old(X3) [cnf transformation 62]
112. funny(sK5) | quiet(X3) [cnf transformation 62]
121. ~quiet(sK6) | ~calm(sK6) | kind(X1) | old(X1) [cnf transformation 67]
123. ~quiet(X0) | calm(X0) [cnf transformation 69]
143. ~patient(paul) [cnf transformation 18]
151. wise(paul) [cnf transformation 24]
152. ~funny(X0) | ~rich(X0) | brave(X0) [duplicate literal removal 103]
153. ~funny(X0) | rich(X0) [duplicate literal removal 105]
183. 7 <=> patient(paul) [avatar definition]
185. ~patient(paul) <- (~7) [avatar component clause 183]
222. ~funny(X0) | brave(X0) [subsumption resolution 152,153]
224. 16 <=> ! [X3] : quiet(X3) [avatar definition]
225. quiet(X3) <- (16) [avatar component clause 224]
227. 17 <=> funny(sK5) [avatar definition]
229. funny(sK5) <- (17) [avatar component clause 227]
230. 16 | 17 [avatar split clause 112,227,224]
232. 18 <=> ! [X3] : ~old(X3) [avatar definition]
233. ~old(X3) <- (18) [avatar component clause 232]
234. 18 | 17 [avatar split clause 111,227,232]
236. 19 <=> brave(sK5) [avatar definition]
238. ~brave(sK5) <- (~19) [avatar component clause 236]
239. 16 | ~19 [avatar split clause 110,236,224]
240. 18 | ~19 [avatar split clause 109,236,232]
242. 20 <=> ! [X1] : (kind(X1) | old(X1)) [avatar definition]
243. kind(X1) | old(X1) <- (20) [avatar component clause 242]
245. 21 <=> calm(sK6) [avatar definition]
247. ~calm(sK6) <- (~21) [avatar component clause 245]
249. 22 <=> quiet(sK6) [avatar definition]
251. ~quiet(sK6) <- (~22) [avatar component clause 249]
252. 20 | ~21 | ~22 [avatar split clause 121,249,245,242]
260. 24 <=> ! [X3] : (calm(X3) | ~quiet(X3)) [avatar definition]
261. ~quiet(X3) | calm(X3) <- (24) [avatar component clause 260]
277. 24 [avatar split clause 123,260]
327. ~7 [avatar split clause 143,183]
366. brave(sK5) <- (17) [resolution 222,229]
369. $false <- (17, ~19) [subsumption resolution 366,238]
370. ~17 | 19 [avatar contradiction clause 369]
371. $false <- (16, ~22) [resolution 225,251]
372. ~16 | 22 [avatar contradiction clause 371]
378. calm(X0) <- (16, 24) [resolution 261,225]
381. $false <- (16, ~21, 24) [resolution 378,247]
382. ~16 | 21 | ~24 [avatar contradiction clause 381]
384. kind(X1) <- (18, 20) [subsumption resolution 243,233]
397. ~kind(paul) | patient(paul) [resolution 95,151]
399. patient(paul) <- (18, 20) [subsumption resolution 397,384]
400. $false <- (~7, 18, 20) [subsumption resolution 399,185]
401. 7 | ~18 | ~20 [avatar contradiction clause 400]
403. $false [avatar sat refutation 230,234,239,240,252,277,327,370,372,382,401]
% SZS output end Proof for 2679874800294647609379286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or brave is brave and vice versa.
If susan is either wise or humble then mary is both strong and brave.
Everyone who is humble is either tall or brave.
Everyone who is not quiet or creative is quiet or not quiet and vice versa.
Everyone who is both creative and patient is both not brave and rich and vice versa.
Everyone who is both wise and not brave is both not brave and calm.
If someone is brave then alice is either not curious or tall and vice versa.
If susan is either strong or not rich then someone is not old or funny.
Everyone who is either not brave or not funny is either kind or not calm.
Everyone who is not tall or kind is either not generous or brave.
Everyone who is not wise or brave is not funny and vice versa.
Everyone who is not tall is either kind or not quiet.
Everyone who is not tall or old is funny.
If someone is both rich and not humble then alice is either curious or not quiet and vice versa.
Everyone who is generous or not patient is not creative.
Everyone who is both not creative and not brave is brave and vice versa.
Lucy is not generous or creative.
Lucy is both kind and curious.
Mary is both old and strong.
Someone is either quiet or not strong.
Fred is both quiet and not old.
Someone is either happy or not brave. | Fred is not curious. | neutral | (![X]:((~strong(X)<~>brave(X))<=>brave(X)))&
(((wise(susan)<~>humble(susan)))=>((strong(mary)&brave(mary))))&
(![X]:(humble(X)=>(tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|creative(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((creative(X)&patient(X))<=>(~brave(X)&rich(X))))&
(![X]:((wise(X)&~brave(X))=>(~brave(X)&calm(X))))&
((?[X]:(brave(X)))<=>((~curious(alice)<~>tall(alice))))&
(((strong(susan)<~>~rich(susan)))=>(?[X]:((~old(X)|funny(X)))))&
(![X]:((~brave(X)<~>~funny(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~tall(X)|kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~wise(X)|brave(X))<=>~funny(X)))&
(![X]:(~tall(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((~tall(X)|old(X))=>funny(X)))&
((?[X]:((rich(X)&~humble(X))))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((generous(X)|~patient(X))=>~creative(X)))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
((~generous(lucy)|creative(lucy)))&
((kind(lucy)&curious(lucy)))&
((old(mary)&strong(mary)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((quiet(fred)&~old(fred)))&
(?[X]:((happy(X)<~>~brave(X)))) | ~curious(fred) | [] | null | 0 |
If someone is either kind or not creative then mary is either not kind or not humble. If someone is both not strong and not kind then someone is both not patient and not rich and vice versa. Everyone who is both old and creative is strong and vice versa. If someone is either not patient or happy then susan is either happy or patient. Everyone who is kind is not curious. If mary is either not rich or funny then paul is not happy and vice versa. If someone is not generous then someone is both happy and wise and vice versa. Everyone who is patient is strong. Everyone who is patient is not rich. If someone is both not creative and not tall then fred is both not brave and not patient. Everyone who is wise is both not quiet and kind. Everyone who is wise or not funny is creative and vice versa. Everyone who is quiet is calm and vice versa. Everyone who is both generous and not curious is not strong. If someone is happy then someone is brave and vice versa. Everyone who is either patient or old is patient and vice versa. Someone is either not funny or happy. Someone is not quiet or happy. Someone is not kind. Fred is funny. Mary is either calm or not patient. Someone is wise. | Mary is old. | contradiction | ((?[X]:((kind(X)<~>~creative(X))))=>((~kind(mary)<~>~humble(mary))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((old(X)&creative(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>happy(X))))=>((happy(susan)<~>patient(susan))))&
(![X]:(kind(X)=>~curious(X)))&
(((~rich(mary)<~>funny(mary)))<=>(~happy(paul)))&
((?[X]:(~generous(X)))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:(patient(X)=>strong(X)))&
(![X]:(patient(X)=>~rich(X)))&
((?[X]:((~creative(X)&~tall(X))))=>((~brave(fred)&~patient(fred))))&
(![X]:(wise(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~funny(X))<=>creative(X)))&
(![X]:(quiet(X)<=>calm(X)))&
(![X]:((generous(X)&~curious(X))=>~strong(X)))&
((?[X]:(happy(X)))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)<~>old(X))<=>patient(X)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:(~kind(X)))&
(funny(fred))&
((calm(mary)<~>~patient(mary)))&
(?[X]:(wise(X))) | old(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 197560378046570313995618
% SZS output start Proof for 197560378046570313995618
16. ! [X0] : ((patient(X0) <~> old(X0)) <=> patient(X0)) [input p15]
23. old(mary) [input hypothesis]
60. ! [X0] : ((((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~patient(X0)) & (patient(X0) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0))))) [nnf transformation 16]
106. patient(X0) | patient(X0) | ~old(X0) [cnf transformation 60]
108. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 60]
117. old(mary) [cnf transformation 23]
118. patient(X0) | ~old(X0) [duplicate literal removal 106]
119. ~old(X0) | ~patient(X0) [duplicate literal removal 108]
235. ~old(X0) [subsumption resolution 118,119]
265. $false [subsumption resolution 117,235]
% SZS output end Proof for 197560378046570313995618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is brave or wise. Everyone who is both curious and happy is not brave. Everyone who is tall or creative is funny. Everyone who is not wise is creative or not brave and vice versa. If someone is both not humble and happy then someone is wise and vice versa. If alice is either not wise or kind then someone is both not happy and happy. If someone is curious or funny then someone is humble. If paul is humble or not patient then someone is both not humble and curious and vice versa. Everyone who is either not quiet or strong is not generous. Everyone who is happy or not patient is not old. Everyone who is happy or not brave is not calm or not wise. Everyone who is not calm is not generous and vice versa. Everyone who is old is either not quiet or brave. If fred is brave then someone is either rich or creative. Everyone who is both not curious and rich is either tall or quiet. If someone is not funny or happy then fred is either not calm or not strong and vice versa. Someone is curious. Someone is quiet. Someone is both tall and humble. Someone is curious or not calm. Someone is not patient. Someone is not kind or not rich. Someone is either not kind or kind. Susan is not generous or strong. | Susan is humble. | neutral | (![X]:(~quiet(X)=>(brave(X)|wise(X))))&
(![X]:((curious(X)&happy(X))=>~brave(X)))&
(![X]:((tall(X)|creative(X))=>funny(X)))&
(![X]:(~wise(X)<=>(creative(X)|~brave(X))))&
((?[X]:((~humble(X)&happy(X))))<=>(?[X]:(wise(X))))&
(((~wise(alice)<~>kind(alice)))=>(?[X]:((~happy(X)&happy(X)))))&
((?[X]:((curious(X)|funny(X))))=>(?[X]:(humble(X))))&
(((humble(paul)|~patient(paul)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((~quiet(X)<~>strong(X))=>~generous(X)))&
(![X]:((happy(X)|~patient(X))=>~old(X)))&
(![X]:((happy(X)|~brave(X))=>(~calm(X)|~wise(X))))&
(![X]:(~calm(X)<=>~generous(X)))&
(![X]:(old(X)=>(~quiet(X)<~>brave(X))))&
((brave(fred))=>(?[X]:((rich(X)<~>creative(X)))))&
(![X]:((~curious(X)&rich(X))=>(tall(X)<~>quiet(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~calm(fred)<~>~strong(fred))))&
(?[X]:(curious(X)))&
(?[X]:(quiet(X)))&
(?[X]:((tall(X)&humble(X))))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((~kind(X)<~>kind(X))))&
((~generous(susan)|strong(susan))) | humble(susan) | [] | null | 0 |
If mary is either generous or not generous then someone is either curious or not brave and vice versa.
Everyone who is not tall is both rich and quiet.
Everyone who is happy is both old and creative and vice versa.
Everyone who is curious is strong or not quiet and vice versa.
Everyone who is strong is wise or funny.
Everyone who is both kind and not kind is either not old or not happy.
Everyone who is both happy and quiet is not curious or quiet.
Everyone who is both wise and patient is either funny or generous.
Everyone who is both not calm and not funny is both not wise and creative.
If alice is old or brave then lucy is both creative and old.
Everyone who is not rich or generous is both not calm and not tall.
If john is quiet or not humble then alice is both kind and not quiet and vice versa.
Everyone who is tall or not kind is either humble or brave and vice versa.
If mary is either not happy or rich then someone is old.
If someone is both rich and not happy then susan is either kind or humble.
Everyone who is either not quiet or not curious is both brave and wise.
Someone is not wise or not rich.
Someone is not strong or funny.
John is calm or brave.
Someone is both not generous and old. | Mary is old. | neutral | (((generous(mary)<~>~generous(mary)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~tall(X)=>(rich(X)&quiet(X))))&
(![X]:(happy(X)<=>(old(X)&creative(X))))&
(![X]:(curious(X)<=>(strong(X)|~quiet(X))))&
(![X]:(strong(X)=>(wise(X)|funny(X))))&
(![X]:((kind(X)&~kind(X))=>(~old(X)<~>~happy(X))))&
(![X]:((happy(X)&quiet(X))=>(~curious(X)|quiet(X))))&
(![X]:((wise(X)&patient(X))=>(funny(X)<~>generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~wise(X)&creative(X))))&
(((old(alice)|brave(alice)))=>((creative(lucy)&old(lucy))))&
(![X]:((~rich(X)|generous(X))=>(~calm(X)&~tall(X))))&
(((quiet(john)|~humble(john)))<=>((kind(alice)&~quiet(alice))))&
(![X]:((tall(X)|~kind(X))<=>(humble(X)<~>brave(X))))&
(((~happy(mary)<~>rich(mary)))=>(?[X]:(old(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(susan)<~>humble(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(brave(X)&wise(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((~strong(X)|funny(X))))&
((calm(john)|brave(john)))&
(?[X]:((~generous(X)&old(X)))) | old(mary) | [] | null | 0 |
If fred is both patient and calm then someone is brave or quiet and vice versa.
Everyone who is either not humble or not happy is both calm and not tall and vice versa.
Everyone who is either not rich or not funny is both generous and not creative.
Everyone who is both curious and not tall is quiet.
If fred is both not rich and creative then someone is both not calm and not wise.
Everyone who is either wise or patient is curious or patient.
Everyone who is wise or generous is both tall and not funny and vice versa.
Everyone who is not wise is not brave or not old and vice versa.
Everyone who is not curious is generous or not creative.
If someone is both not rich and not kind then fred is both not curious and funny and vice versa.
Everyone who is not happy or curious is not kind.
Everyone who is funny is either not tall or not old.
Everyone who is not patient is not wise or generous and vice versa.
If paul is either calm or quiet then paul is strong or quiet and vice versa.
Everyone who is not brave is either quiet or not generous and vice versa.
If someone is not creative or patient then someone is generous.
Someone is either not generous or brave.
John is old or not brave.
Lucy is either quiet or not rich.
Someone is either kind or brave.
Someone is not generous.
Lucy is curious. | John is generous. | neutral | (((patient(fred)&calm(fred)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~happy(X))<=>(calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(generous(X)&~creative(X))))&
(![X]:((curious(X)&~tall(X))=>quiet(X)))&
(((~rich(fred)&creative(fred)))=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:((wise(X)<~>patient(X))=>(curious(X)|patient(X))))&
(![X]:((wise(X)|generous(X))<=>(tall(X)&~funny(X))))&
(![X]:(~wise(X)<=>(~brave(X)|~old(X))))&
(![X]:(~curious(X)=>(generous(X)|~creative(X))))&
((?[X]:((~rich(X)&~kind(X))))<=>((~curious(fred)&funny(fred))))&
(![X]:((~happy(X)|curious(X))=>~kind(X)))&
(![X]:(funny(X)=>(~tall(X)<~>~old(X))))&
(![X]:(~patient(X)<=>(~wise(X)|generous(X))))&
(((calm(paul)<~>quiet(paul)))<=>((strong(paul)|quiet(paul))))&
(![X]:(~brave(X)<=>(quiet(X)<~>~generous(X))))&
((?[X]:((~creative(X)|patient(X))))=>(?[X]:(generous(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
((old(john)|~brave(john)))&
((quiet(lucy)<~>~rich(lucy)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:(~generous(X)))&
(curious(lucy)) | generous(john) | [] | null | 0 |
Everyone who is not tall or not humble is happy or calm and vice versa. Everyone who is rich is not kind. If mary is either not generous or rich then someone is kind or not creative. If someone is both not quiet and rich then alice is both tall and kind and vice versa. Everyone who is either funny or strong is either happy or not generous and vice versa. If john is creative or not happy then mary is wise and vice versa. If john is both not calm and old then someone is both not calm and not tall and vice versa. Everyone who is either not creative or not strong is either not happy or wise. Everyone who is both humble and not wise is not humble. Everyone who is not happy is not rich. Everyone who is either not strong or not creative is happy or curious and vice versa. If paul is either not patient or strong then mary is not humble and vice versa. If fred is either not tall or not wise then someone is not happy. Everyone who is both quiet and not happy is either not tall or not patient and vice versa. If lucy is happy then someone is both creative and not strong and vice versa. If someone is not strong or humble then fred is not quiet or generous and vice versa. Mary is both wise and quiet. Someone is not humble. Lucy is either brave or not quiet. Someone is not patient. Someone is rich or happy. Someone is strong. Susan is old or not brave. Paul is both calm and not generous. | John is not quiet. | neutral | (![X]:((~tall(X)|~humble(X))<=>(happy(X)|calm(X))))&
(![X]:(rich(X)=>~kind(X)))&
(((~generous(mary)<~>rich(mary)))=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((~quiet(X)&rich(X))))<=>((tall(alice)&kind(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(happy(X)<~>~generous(X))))&
(((creative(john)|~happy(john)))<=>(wise(mary)))&
(((~calm(john)&old(john)))<=>(?[X]:((~calm(X)&~tall(X)))))&
(![X]:((~creative(X)<~>~strong(X))=>(~happy(X)<~>wise(X))))&
(![X]:((humble(X)&~wise(X))=>~humble(X)))&
(![X]:(~happy(X)=>~rich(X)))&
(![X]:((~strong(X)<~>~creative(X))<=>(happy(X)|curious(X))))&
(((~patient(paul)<~>strong(paul)))<=>(~humble(mary)))&
(((~tall(fred)<~>~wise(fred)))=>(?[X]:(~happy(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~tall(X)<~>~patient(X))))&
((happy(lucy))<=>(?[X]:((creative(X)&~strong(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>((~quiet(fred)|generous(fred))))&
((wise(mary)&quiet(mary)))&
(?[X]:(~humble(X)))&
((brave(lucy)<~>~quiet(lucy)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|happy(X))))&
(?[X]:(strong(X)))&
((old(susan)|~brave(susan)))&
((calm(paul)&~generous(paul))) | ~quiet(john) | [] | null | 0 |
If mary is funny or not kind then susan is either not happy or kind.
If someone is both not tall and not strong then someone is both old and not humble and vice versa.
Everyone who is both rich and not humble is calm.
If someone is calm then someone is both creative and not tall and vice versa.
Everyone who is patient or not kind is happy.
Everyone who is quiet or strong is either quiet or not kind and vice versa.
Everyone who is not quiet is not tall and vice versa.
Everyone who is both not wise and not patient is quiet or calm.
If someone is both patient and rich then someone is quiet and vice versa.
Everyone who is not tall or not humble is both not calm and humble and vice versa.
Everyone who is both happy and brave is funny or old and vice versa.
If someone is both not strong and creative then someone is either old or quiet.
If someone is generous or not rich then someone is either not generous or wise.
Everyone who is both generous and quiet is strong.
If someone is either not funny or tall then john is both generous and kind.
Someone is not creative.
Someone is not old.
Lucy is not old or curious.
Someone is not funny or not patient.
Someone is not patient. | John is not brave. | neutral | (((funny(mary)|~kind(mary)))=>((~happy(susan)<~>kind(susan))))&
((?[X]:((~tall(X)&~strong(X))))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((rich(X)&~humble(X))=>calm(X)))&
((?[X]:(calm(X)))<=>(?[X]:((creative(X)&~tall(X)))))&
(![X]:((patient(X)|~kind(X))=>happy(X)))&
(![X]:((quiet(X)|strong(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
(![X]:((~wise(X)&~patient(X))=>(quiet(X)|calm(X))))&
((?[X]:((patient(X)&rich(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)|~humble(X))<=>(~calm(X)&humble(X))))&
(![X]:((happy(X)&brave(X))<=>(funny(X)|old(X))))&
((?[X]:((~strong(X)&creative(X))))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((generous(X)&quiet(X))=>strong(X)))&
((?[X]:((~funny(X)<~>tall(X))))=>((generous(john)&kind(john))))&
(?[X]:(~creative(X)))&
(?[X]:(~old(X)))&
((~old(lucy)|curious(lucy)))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | ~brave(john) | [] | null | 0 |
Everyone who is not tall is either old or not humble and vice versa.
Everyone who is both not curious and not creative is either not patient or not brave and vice versa.
If someone is not curious then someone is either brave or not wise and vice versa.
Everyone who is not generous is either not old or tall.
Everyone who is not strong is not funny or not rich and vice versa.
If someone is not happy or rich then fred is either humble or not strong.
Everyone who is both not wise and old is generous or brave and vice versa.
Everyone who is not quiet is not kind.
If susan is either old or not generous then susan is tall.
Everyone who is both rich and humble is creative and vice versa.
Everyone who is either brave or not wise is either not brave or patient and vice versa.
If someone is both quiet and wise then someone is funny.
If someone is either curious or funny then susan is old or wise and vice versa.
Everyone who is both not humble and not funny is brave and vice versa.
Everyone who is either not quiet or not funny is both patient and old.
If fred is both not patient and not old then someone is either brave or curious and vice versa.
Mary is both not quiet and calm.
Fred is not old.
Someone is either not tall or not generous.
Paul is brave.
Someone is not brave or not happy.
Someone is not generous or not creative.
Susan is both not quiet and not kind.
Someone is either brave or not happy. | Susan is humble. | contradiction | (![X]:(~tall(X)<=>(old(X)<~>~humble(X))))&
(![X]:((~curious(X)&~creative(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(~funny(X)|~rich(X))))&
((?[X]:((~happy(X)|rich(X))))=>((humble(fred)<~>~strong(fred))))&
(![X]:((~wise(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(((old(susan)<~>~generous(susan)))=>(tall(susan)))&
(![X]:((rich(X)&humble(X))<=>creative(X)))&
(![X]:((brave(X)<~>~wise(X))<=>(~brave(X)<~>patient(X))))&
((?[X]:((quiet(X)&wise(X))))=>(?[X]:(funny(X))))&
((?[X]:((curious(X)<~>funny(X))))<=>((old(susan)|wise(susan))))&
(![X]:((~humble(X)&~funny(X))<=>brave(X)))&
(![X]:((~quiet(X)<~>~funny(X))=>(patient(X)&old(X))))&
(((~patient(fred)&~old(fred)))<=>(?[X]:((brave(X)<~>curious(X)))))&
((~quiet(mary)&calm(mary)))&
(~old(fred))&
(?[X]:((~tall(X)<~>~generous(X))))&
(brave(paul))&
(?[X]:((~brave(X)|~happy(X))))&
(?[X]:((~generous(X)|~creative(X))))&
((~quiet(susan)&~kind(susan)))&
(?[X]:((brave(X)<~>~happy(X)))) | humble(susan) | [
"p0",
"p3",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3258525246392435699825303
% SZS output start Proof for 3258525246392435699825303
1. ! [X0] : (~tall(X0) <=> (old(X0) <~> ~humble(X0))) [input p0]
4. ! [X0] : (~generous(X0) => (~old(X0) <~> tall(X0))) [input p3]
7. ! [X0] : ((old(X0) & ~wise(X0)) <=> (brave(X0) | generous(X0))) [input p6]
9. (old(susan) <~> ~generous(susan)) => tall(susan) [input p8]
25. humble(susan) [input hypothesis]
31. ! [X0] : ((~old(X0) <~> tall(X0)) | generous(X0)) [ennf transformation 4]
33. tall(susan) | (old(susan) <=> ~generous(susan)) [ennf transformation 9]
36. ! [X0] : ((~tall(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | tall(X0))) [nnf transformation 1]
44. ! [X0] : (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | generous(X0)) [nnf transformation 31]
48. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 7]
49. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | wise(X0))) [flattening 48]
50. tall(susan) | ((old(susan) | generous(susan)) & (~generous(susan) | ~old(susan))) [nnf transformation 33]
82. ~humble(X0) | ~tall(X0) | ~old(X0) [cnf transformation 36]
94. ~old(X0) | tall(X0) | generous(X0) [cnf transformation 44]
95. ~tall(X0) | old(X0) | generous(X0) [cnf transformation 44]
106. ~generous(X0) | old(X0) [cnf transformation 49]
108. tall(susan) | ~generous(susan) | ~old(susan) [cnf transformation 50]
109. tall(susan) | old(susan) | generous(susan) [cnf transformation 50]
151. humble(susan) [cnf transformation 25]
200. old(susan) | generous(susan) [subsumption resolution 109,95]
201. old(susan) [subsumption resolution 200,106]
202. tall(susan) | ~generous(susan) [subsumption resolution 108,201]
204. 11 <=> generous(susan) [avatar definition]
206. ~generous(susan) <- (~11) [avatar component clause 204]
208. 12 <=> tall(susan) [avatar definition]
209. ~tall(susan) <- (~12) [avatar component clause 208]
211. ~11 | 12 [avatar split clause 202,208,204]
324. ~tall(susan) | ~old(susan) [resolution 82,151]
325. ~tall(susan) [subsumption resolution 324,201]
326. ~12 [avatar split clause 325,208]
358. tall(susan) | generous(susan) [resolution 94,201]
361. generous(susan) <- (~12) [subsumption resolution 358,209]
362. $false <- (~11, ~12) [subsumption resolution 361,206]
363. 11 | 12 [avatar contradiction clause 362]
364. $false [avatar sat refutation 211,326,363]
% SZS output end Proof for 3258525246392435699825303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and rich is both not strong and not old and vice versa.
If mary is either not tall or tall then alice is both rich and wise and vice versa.
If someone is not kind or not old then mary is both funny and not strong and vice versa.
If mary is both not humble and wise then someone is both not generous and old.
Everyone who is wise is not quiet and vice versa.
If someone is either not curious or generous then someone is creative or not calm and vice versa.
If someone is both not rich and not strong then someone is happy or not happy and vice versa.
Everyone who is old is creative.
If someone is wise then someone is both generous and calm and vice versa.
If someone is both kind and not rich then someone is either not brave or not kind.
If someone is generous then someone is tall or not curious.
Everyone who is not funny or old is both brave and not kind.
Everyone who is both not creative and humble is not humble and vice versa.
Everyone who is not rich or rich is not old or not kind and vice versa.
Everyone who is not brave or not old is either old or not generous.
John is both not kind and brave.
Paul is either not generous or calm.
Someone is not rich or not happy.
Mary is brave or not humble.
Someone is calm.
Someone is either calm or not creative.
Alice is not curious.
John is either quiet or strong. | Alice is not wise. | contradiction | (![X]:((kind(X)&rich(X))<=>(~strong(X)&~old(X))))&
(((~tall(mary)<~>tall(mary)))<=>((rich(alice)&wise(alice))))&
((?[X]:((~kind(X)|~old(X))))<=>((funny(mary)&~strong(mary))))&
(((~humble(mary)&wise(mary)))=>(?[X]:((~generous(X)&old(X)))))&
(![X]:(wise(X)<=>~quiet(X)))&
((?[X]:((~curious(X)<~>generous(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:(old(X)=>creative(X)))&
((?[X]:(wise(X)))<=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~funny(X)|old(X))=>(brave(X)&~kind(X))))&
(![X]:((~creative(X)&humble(X))<=>~humble(X)))&
(![X]:((~rich(X)|rich(X))<=>(~old(X)|~kind(X))))&
(![X]:((~brave(X)|~old(X))=>(old(X)<~>~generous(X))))&
((~kind(john)&brave(john)))&
((~generous(paul)<~>calm(paul)))&
(?[X]:((~rich(X)|~happy(X))))&
((brave(mary)|~humble(mary)))&
(?[X]:(calm(X)))&
(?[X]:((calm(X)<~>~creative(X))))&
(~curious(alice))&
((quiet(john)<~>strong(john))) | ~wise(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5452834295245114634404192
% SZS output start Proof for 5452834295245114634404192
2. (~tall(mary) <~> tall(mary)) <=> (wise(alice) & rich(alice)) [input p1]
24. ~wise(alice) [input hypothesis]
39. (((~tall(mary) | tall(mary)) & (tall(mary) | ~tall(mary))) | (~wise(alice) | ~rich(alice))) & ((wise(alice) & rich(alice)) | ((~tall(mary) | ~tall(mary)) & (tall(mary) | tall(mary)))) [nnf transformation 2]
40. (((~tall(mary) | tall(mary)) & (tall(mary) | ~tall(mary))) | ~wise(alice) | ~rich(alice)) & ((wise(alice) & rich(alice)) | ((~tall(mary) | ~tall(mary)) & (tall(mary) | tall(mary)))) [flattening 39]
91. wise(alice) | tall(mary) | tall(mary) [cnf transformation 40]
92. wise(alice) | ~tall(mary) | ~tall(mary) [cnf transformation 40]
149. ~wise(alice) [cnf transformation 24]
155. wise(alice) | tall(mary) [duplicate literal removal 91]
156. wise(alice) | ~tall(mary) [duplicate literal removal 92]
158. 1 <=> tall(mary) [avatar definition]
162. 2 <=> wise(alice) [avatar definition]
165. ~1 | 2 [avatar split clause 156,162,158]
166. 1 | 2 [avatar split clause 155,162,158]
348. ~2 [avatar split clause 149,162]
349. $false [avatar sat refutation 165,166,348]
% SZS output end Proof for 5452834295245114634404192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or tall is both kind and old and vice versa.
If paul is either not old or humble then someone is not strong.
Everyone who is not patient or not tall is either not kind or calm and vice versa.
If someone is either not old or kind then someone is both wise and not wise.
Everyone who is either not strong or not creative is either not curious or rich.
If someone is both patient and tall then paul is not humble or not curious.
If john is either wise or not generous then someone is kind or curious.
If someone is both not wise and not happy then someone is tall and vice versa.
Everyone who is both happy and not creative is either not happy or rich.
Everyone who is either rich or humble is both happy and rich and vice versa.
Everyone who is old or creative is both not calm and not strong.
Everyone who is either strong or not generous is either not old or kind and vice versa.
Everyone who is funny is both not wise and happy and vice versa.
If john is either not quiet or not kind then lucy is either wise or not humble and vice versa.
If someone is happy then fred is humble and vice versa.
Someone is creative or strong.
Someone is either wise or happy.
Someone is both not brave and not curious. | Fred is not old. | entailment | (![X]:((~strong(X)|tall(X))<=>(kind(X)&old(X))))&
(((~old(paul)<~>humble(paul)))=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)|~tall(X))<=>(~kind(X)<~>calm(X))))&
((?[X]:((~old(X)<~>kind(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~curious(X)<~>rich(X))))&
((?[X]:((patient(X)&tall(X))))=>((~humble(paul)|~curious(paul))))&
(((wise(john)<~>~generous(john)))=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:((~wise(X)&~happy(X))))<=>(?[X]:(tall(X))))&
(![X]:((happy(X)&~creative(X))=>(~happy(X)<~>rich(X))))&
(![X]:((rich(X)<~>humble(X))<=>(happy(X)&rich(X))))&
(![X]:((old(X)|creative(X))=>(~calm(X)&~strong(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~old(X)<~>kind(X))))&
(![X]:(funny(X)<=>(~wise(X)&happy(X))))&
(((~quiet(john)<~>~kind(john)))<=>((wise(lucy)<~>~humble(lucy))))&
((?[X]:(happy(X)))<=>(humble(fred)))&
(?[X]:((creative(X)|strong(X))))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((~brave(X)&~curious(X)))) | ~old(fred) | [
"p0",
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6775134612918568156394292
% SZS output start Proof for 6775134612918568156394292
1. ! [X0] : ((tall(X0) | ~strong(X0)) <=> (old(X0) & kind(X0))) [input p0]
4. ? [X0] : (~old(X0) <~> kind(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p3]
11. ! [X0] : ((creative(X0) | old(X0)) => (~strong(X0) & ~calm(X0))) [input p10]
19. old(fred) [input hypothesis]
20. ? [X0] : (~old(X0) <~> kind(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 4]
24. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~old(X0) <=> kind(X0)) [ennf transformation 20]
31. ! [X0] : ((~strong(X0) & ~calm(X0)) | (~creative(X0) & ~old(X0))) [ennf transformation 11]
32. ! [X0] : (((tall(X0) | ~strong(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (~tall(X0) & strong(X0)))) [nnf transformation 1]
33. ! [X0] : ((tall(X0) | ~strong(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (~tall(X0) & strong(X0)))) [flattening 32]
39. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))) [nnf transformation 24]
40. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : ((~old(X1) | ~kind(X1)) & (kind(X1) | old(X1))) [rectify 39]
41. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK1) & wise(sK1)) [choice axiom]
42. (~wise(sK1) & wise(sK1)) | ! [X1] : ((~old(X1) | ~kind(X1)) & (kind(X1) | old(X1))) [skolemisation 40,41]
68. kind(X0) | strong(X0) [cnf transformation 33]
70. old(X0) | strong(X0) [cnf transformation 33]
82. wise(sK1) | ~old(X1) | ~kind(X1) [cnf transformation 42]
84. ~wise(sK1) | ~old(X1) | ~kind(X1) [cnf transformation 42]
105. ~old(X0) | ~strong(X0) [cnf transformation 31]
129. old(fred) [cnf transformation 19]
150. 4 <=> ! [X1] : (~old(X1) | ~kind(X1)) [avatar definition]
151. ~old(X1) | ~kind(X1) <- (4) [avatar component clause 150]
153. 5 <=> wise(sK1) [avatar definition]
156. 4 | ~5 [avatar split clause 84,153,150]
161. 4 | 5 [avatar split clause 82,153,150]
271. ~strong(fred) [resolution 105,129]
278. ~kind(X0) | strong(X0) <- (4) [resolution 151,70]
279. strong(X0) <- (4) [subsumption resolution 278,68]
285. $false <- (4) [resolution 279,271]
288. ~4 [avatar contradiction clause 285]
290. $false [avatar sat refutation 156,161,288]
% SZS output end Proof for 6775134612918568156394292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative is not wise. If someone is not strong then someone is not quiet or not strong. Everyone who is calm is either not rich or quiet. Everyone who is either not kind or happy is not strong. If someone is not strong then someone is tall and vice versa. Everyone who is both not old and not curious is kind or not rich and vice versa. Everyone who is not generous or wise is quiet and vice versa. If someone is not old or patient then someone is both not creative and not rich. Everyone who is both not old and not patient is wise. Everyone who is not patient or not kind is both not happy and funny. Everyone who is both funny and wise is both old and not creative. If john is both not kind and not patient then john is curious. Everyone who is tall is either curious or not wise and vice versa. Everyone who is either calm or not patient is strong and vice versa. Everyone who is both not generous and tall is both strong and generous. John is old. Someone is either rich or not generous. Susan is humble or happy. Someone is not kind or rich. | John is generous. | neutral | (![X]:((patient(X)|~creative(X))=>~wise(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~quiet(X)|~strong(X)))))&
(![X]:(calm(X)=>(~rich(X)<~>quiet(X))))&
(![X]:((~kind(X)<~>happy(X))=>~strong(X)))&
((?[X]:(~strong(X)))<=>(?[X]:(tall(X))))&
(![X]:((~old(X)&~curious(X))<=>(kind(X)|~rich(X))))&
(![X]:((~generous(X)|wise(X))<=>quiet(X)))&
((?[X]:((~old(X)|patient(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:((~old(X)&~patient(X))=>wise(X)))&
(![X]:((~patient(X)|~kind(X))=>(~happy(X)&funny(X))))&
(![X]:((funny(X)&wise(X))=>(old(X)&~creative(X))))&
(((~kind(john)&~patient(john)))=>(curious(john)))&
(![X]:(tall(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((calm(X)<~>~patient(X))<=>strong(X)))&
(![X]:((~generous(X)&tall(X))=>(strong(X)&generous(X))))&
(old(john))&
(?[X]:((rich(X)<~>~generous(X))))&
((humble(susan)|happy(susan)))&
(?[X]:((~kind(X)|rich(X)))) | generous(john) | [] | null | 0 |
If someone is funny then john is not wise.
If someone is not happy or patient then john is both not tall and curious and vice versa.
If john is not funny or humble then john is not wise or wise and vice versa.
Everyone who is both not happy and not curious is either not funny or not patient and vice versa.
Everyone who is not tall or not generous is both tall and not old and vice versa.
Everyone who is tall or generous is both not generous and rich.
Everyone who is strong or not quiet is either generous or not strong and vice versa.
If fred is not humble or not generous then mary is either not wise or patient.
Everyone who is not rich is funny and vice versa.
Everyone who is not creative is old or not happy and vice versa.
If someone is both humble and kind then lucy is not strong or tall and vice versa.
Everyone who is either generous or not humble is both generous and curious and vice versa.
If mary is kind or not curious then mary is either not strong or not rich and vice versa.
Everyone who is both not rich and not happy is not kind and vice versa.
If someone is both humble and not generous then someone is not wise and vice versa.
Fred is either brave or not strong.
Alice is wise. | Mary is wise. | contradiction | ((?[X]:(funny(X)))=>(~wise(john)))&
((?[X]:((~happy(X)|patient(X))))<=>((~tall(john)&curious(john))))&
(((~funny(john)|humble(john)))<=>((~wise(john)|wise(john))))&
(![X]:((~happy(X)&~curious(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
(![X]:((strong(X)|~quiet(X))<=>(generous(X)<~>~strong(X))))&
(((~humble(fred)|~generous(fred)))=>((~wise(mary)<~>patient(mary))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:(~creative(X)<=>(old(X)|~happy(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~strong(lucy)|tall(lucy))))&
(![X]:((generous(X)<~>~humble(X))<=>(generous(X)&curious(X))))&
(((kind(mary)|~curious(mary)))<=>((~strong(mary)<~>~rich(mary))))&
(![X]:((~rich(X)&~happy(X))<=>~kind(X)))&
((?[X]:((humble(X)&~generous(X))))<=>(?[X]:(~wise(X))))&
((brave(fred)<~>~strong(fred)))&
(wise(alice)) | wise(mary) | [
"p1",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3255982137605667924519013
% SZS output start Proof for 3255982137605667924519013
2. ? [X0] : (patient(X0) | ~happy(X0)) <=> (curious(john) & ~tall(john)) [input p1]
5. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~old(X0) & tall(X0))) [input p4]
6. ! [X0] : ((generous(X0) | tall(X0)) => (rich(X0) & ~generous(X0))) [input p5]
8. (~generous(fred) | ~humble(fred)) => (~wise(mary) <~> patient(mary)) [input p7]
18. wise(mary) [input hypothesis]
21. ! [X0] : ((rich(X0) & ~generous(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 6]
22. (~wise(mary) <~> patient(mary)) | (generous(fred) & humble(fred)) [ennf transformation 8]
23. (? [X0] : (patient(X0) | ~happy(X0)) | (~curious(john) | tall(john))) & ((curious(john) & ~tall(john)) | ! [X0] : (~patient(X0) & happy(X0))) [nnf transformation 2]
24. (? [X0] : (patient(X0) | ~happy(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X0] : (~patient(X0) & happy(X0))) [flattening 23]
25. (? [X0] : (patient(X0) | ~happy(X0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (~patient(X1) & happy(X1))) [rectify 24]
26. ? [X0] : (patient(X0) | ~happy(X0)) => (patient(sK0) | ~happy(sK0)) [choice axiom]
27. ((patient(sK0) | ~happy(sK0)) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ! [X1] : (~patient(X1) & happy(X1))) [skolemisation 25,26]
32. ! [X0] : (((~generous(X0) | ~tall(X0)) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 5]
33. ! [X0] : ((~generous(X0) | ~tall(X0) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [flattening 32]
36. ((~patient(mary) | wise(mary)) & (patient(mary) | ~wise(mary))) | (generous(fred) & humble(fred)) [nnf transformation 22]
57. ~tall(john) | ~patient(X1) [cnf transformation 27]
71. tall(X0) | tall(X0) [cnf transformation 33]
77. ~generous(X0) | ~generous(X0) [cnf transformation 21]
87. patient(mary) | ~wise(mary) | generous(fred) [cnf transformation 36]
118. wise(mary) [cnf transformation 18]
123. ~generous(X0) [duplicate literal removal 77]
124. tall(X0) [duplicate literal removal 71]
135. 3 <=> tall(john) [avatar definition]
136. ~tall(john) <- (~3) [avatar component clause 135]
152. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
153. ~patient(X1) <- (7) [avatar component clause 152]
159. 7 | ~3 [avatar split clause 57,135,152]
177. 11 <=> wise(mary) [avatar definition]
181. 12 <=> patient(mary) [avatar definition]
182. patient(mary) <- (12) [avatar component clause 181]
190. patient(mary) | ~wise(mary) [subsumption resolution 87,123]
191. ~11 | 12 [avatar split clause 190,181,177]
214. 11 [avatar split clause 118,177]
215. $false <- (~3) [subsumption resolution 136,124]
216. 3 [avatar contradiction clause 215]
219. $false <- (7, 12) [resolution 182,153]
220. ~7 | ~12 [avatar contradiction clause 219]
221. $false [avatar sat refutation 159,191,214,216,220]
% SZS output end Proof for 3255982137605667924519013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is rich then john is both not creative and tall and vice versa.
Everyone who is not strong or tall is either not old or not wise and vice versa.
If someone is either not curious or rich then someone is both happy and not tall and vice versa.
Everyone who is tall or patient is either humble or tall and vice versa.
If mary is both not humble and quiet then mary is not kind.
Everyone who is not funny or creative is not humble and vice versa.
If paul is either creative or curious then someone is not generous or rich.
If someone is either not rich or not calm then fred is not old.
If john is either creative or not strong then someone is not quiet or strong and vice versa.
If someone is brave or kind then mary is curious.
Everyone who is either not strong or tall is both not funny and not kind.
Everyone who is funny or not humble is not wise or not old.
If lucy is not humble or not tall then someone is both not brave and not old.
If fred is funny then someone is both kind and brave and vice versa.
Everyone who is tall is either not generous or curious.
Someone is either brave or not generous.
Someone is either not curious or tall.
Someone is curious.
Lucy is not creative.
Mary is both strong and curious.
Lucy is either not wise or happy.
Lucy is both rich and brave.
Someone is either quiet or not quiet. | John is not humble. | entailment | ((rich(mary))<=>((~creative(john)&tall(john))))&
(![X]:((~strong(X)|tall(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((tall(X)|patient(X))<=>(humble(X)<~>tall(X))))&
(((~humble(mary)&quiet(mary)))=>(~kind(mary)))&
(![X]:((~funny(X)|creative(X))<=>~humble(X)))&
(((creative(paul)<~>curious(paul)))=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((~rich(X)<~>~calm(X))))=>(~old(fred)))&
(((creative(john)<~>~strong(john)))<=>(?[X]:((~quiet(X)|strong(X)))))&
((?[X]:((brave(X)|kind(X))))=>(curious(mary)))&
(![X]:((~strong(X)<~>tall(X))=>(~funny(X)&~kind(X))))&
(![X]:((funny(X)|~humble(X))=>(~wise(X)|~old(X))))&
(((~humble(lucy)|~tall(lucy)))=>(?[X]:((~brave(X)&~old(X)))))&
((funny(fred))<=>(?[X]:((kind(X)&brave(X)))))&
(![X]:(tall(X)=>(~generous(X)<~>curious(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
(?[X]:((~curious(X)<~>tall(X))))&
(?[X]:(curious(X)))&
(~creative(lucy))&
((strong(mary)&curious(mary)))&
((~wise(lucy)<~>happy(lucy)))&
((rich(lucy)&brave(lucy)))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~humble(john) | [
"p3",
"p5",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 36957408206046155682985
% SZS output start Proof for 36957408206046155682985
4. ! [X0] : ((patient(X0) | tall(X0)) <=> (humble(X0) <~> tall(X0))) [input p3]
6. ! [X0] : ((creative(X0) | ~funny(X0)) <=> ~humble(X0)) [input p5]
9. (creative(john) <~> ~strong(john)) <=> ? [X0] : (strong(X0) | ~quiet(X0)) [input p8]
11. ! [X0] : ((~strong(X0) <~> tall(X0)) => (~kind(X0) & ~funny(X0))) [input p10]
20. curious(mary) & strong(mary) [input p19]
24. humble(john) [input hypothesis]
31. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~strong(X0) <=> tall(X0))) [ennf transformation 11]
45. ! [X0] : (((patient(X0) | tall(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~patient(X0) & ~tall(X0)))) [nnf transformation 4]
46. ! [X0] : ((patient(X0) | tall(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~patient(X0) & ~tall(X0)))) [flattening 45]
47. ! [X0] : (((creative(X0) | ~funny(X0)) | humble(X0)) & (~humble(X0) | (~creative(X0) & funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((creative(X0) | ~funny(X0) | humble(X0)) & (~humble(X0) | (~creative(X0) & funny(X0)))) [flattening 47]
53. (((strong(john) | ~creative(john)) & (~strong(john) | creative(john))) | ! [X0] : (~strong(X0) & quiet(X0))) & (? [X0] : (strong(X0) | ~quiet(X0)) | ((creative(john) | strong(john)) & (~strong(john) | ~creative(john)))) [nnf transformation 9]
54. (((strong(john) | ~creative(john)) & (~strong(john) | creative(john))) | ! [X0] : (~strong(X0) & quiet(X0))) & (? [X1] : (strong(X1) | ~quiet(X1)) | ((creative(john) | strong(john)) & (~strong(john) | ~creative(john)))) [rectify 53]
55. ? [X1] : (strong(X1) | ~quiet(X1)) => (strong(sK3) | ~quiet(sK3)) [choice axiom]
56. (((strong(john) | ~creative(john)) & (~strong(john) | creative(john))) | ! [X0] : (~strong(X0) & quiet(X0))) & ((strong(sK3) | ~quiet(sK3)) | ((creative(john) | strong(john)) & (~strong(john) | ~creative(john)))) [skolemisation 54,55]
57. ! [X0] : ((~kind(X0) & ~funny(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) [nnf transformation 31]
94. ~tall(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 46]
99. ~humble(X0) | funny(X0) [cnf transformation 48]
100. ~humble(X0) | ~creative(X0) [cnf transformation 48]
109. ~strong(john) | creative(john) | ~strong(X0) [cnf transformation 56]
114. ~funny(X0) | tall(X0) | strong(X0) [cnf transformation 57]
135. strong(mary) [cnf transformation 20]
143. humble(john) [cnf transformation 24]
144. ~humble(X0) | ~tall(X0) [duplicate literal removal 94]
147. 1 <=> creative(john) [avatar definition]
151. 2 <=> tall(john) [avatar definition]
236. 21 <=> ! [X0] : ~strong(X0) [avatar definition]
237. ~strong(X0) <- (21) [avatar component clause 236]
239. 22 <=> strong(john) [avatar definition]
247. 21 | 1 | ~22 [avatar split clause 109,239,147,236]
340. funny(john) [resolution 99,143]
341. ~creative(john) [resolution 100,143]
342. ~tall(john) [resolution 144,143]
374. tall(john) | strong(john) [resolution 114,340]
379. $false <- (21) [resolution 237,135]
380. ~21 [avatar contradiction clause 379]
381. 22 | 2 [avatar split clause 374,151,239]
387. ~2 [avatar split clause 342,151]
389. ~1 [avatar split clause 341,147]
390. $false [avatar sat refutation 247,380,381,387,389]
% SZS output end Proof for 36957408206046155682985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and quiet then someone is both funny and tall. Everyone who is either not brave or not quiet is both not wise and not funny and vice versa. If someone is both not kind and kind then someone is either generous or creative. Everyone who is not patient is both patient and generous. If alice is both not curious and not quiet then john is either brave or not generous. If fred is either not tall or old then lucy is not tall and vice versa. If someone is either generous or curious then lucy is curious and vice versa. If someone is either old or not funny then someone is either not curious or not kind and vice versa. Everyone who is either generous or not funny is old or not curious and vice versa. Everyone who is either tall or not curious is both not old and funny. Everyone who is patient or not happy is brave and vice versa. Everyone who is both not generous and not patient is both not patient and rich and vice versa. Everyone who is calm or not creative is tall and vice versa. If susan is either not kind or old then lucy is rich or kind and vice versa. If someone is not patient then someone is both curious and not patient. Someone is either not wise or happy. Someone is both not rich and not generous. Someone is curious or not brave. Mary is tall. Mary is either patient or not quiet. Someone is not wise. Someone is either kind or generous. Someone is not kind or not humble. | Fred is not brave. | contradiction | ((?[X]:((kind(X)&quiet(X))))=>(?[X]:((funny(X)&tall(X)))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~wise(X)&~funny(X))))&
((?[X]:((~kind(X)&kind(X))))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~patient(X)=>(patient(X)&generous(X))))&
(((~curious(alice)&~quiet(alice)))=>((brave(john)<~>~generous(john))))&
(((~tall(fred)<~>old(fred)))<=>(~tall(lucy)))&
((?[X]:((generous(X)<~>curious(X))))<=>(curious(lucy)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)|~curious(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((patient(X)|~happy(X))<=>brave(X)))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(![X]:((calm(X)|~creative(X))<=>tall(X)))&
(((~kind(susan)<~>old(susan)))<=>((rich(lucy)|kind(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:((curious(X)&~patient(X)))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:((curious(X)|~brave(X))))&
(tall(mary))&
((patient(mary)<~>~quiet(mary)))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((~kind(X)|~humble(X)))) | ~brave(fred) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9058623588674589707772126
% SZS output start Proof for 9058623588674589707772126
4. ! [X0] : (~patient(X0) => (generous(X0) & patient(X0))) [input p3]
11. ! [X0] : ((~happy(X0) | patient(X0)) <=> brave(X0)) [input p10]
24. ~brave(fred) [input hypothesis]
32. ! [X0] : ((generous(X0) & patient(X0)) | patient(X0)) [ennf transformation 4]
60. ! [X0] : (((~happy(X0) | patient(X0)) | ~brave(X0)) & (brave(X0) | (happy(X0) & ~patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((~happy(X0) | patient(X0) | ~brave(X0)) & (brave(X0) | (happy(X0) & ~patient(X0)))) [flattening 60]
94. patient(X0) | patient(X0) [cnf transformation 32]
124. brave(X0) | ~patient(X0) [cnf transformation 61]
153. ~brave(fred) [cnf transformation 24]
154. patient(X0) [duplicate literal removal 94]
260. brave(X0) [subsumption resolution 124,154]
305. $false [subsumption resolution 153,260]
% SZS output end Proof for 9058623588674589707772126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or funny is old or strong and vice versa.
If someone is not creative or patient then paul is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is generous.
Someone is either not generous or quiet.
Lucy is not funny or strong.
John is not kind or not funny. | Mary is strong. | entailment | (![X]:((~tall(X)<~>funny(X))<=>(old(X)|strong(X))))&
((?[X]:((~creative(X)|patient(X))))<=>(old(paul)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~funny(lucy)|strong(lucy)))&
((~kind(john)|~funny(john))) | strong(mary) | [
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8417761546825758464513820
% SZS output start Proof for 8417761546825758464513820
7. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> rich(X0)) [input p6]
8. ? [X0] : (creative(X0) | ~strong(X0)) <=> ~rich(mary) [input p7]
13. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p12]
15. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p14]
25. ~strong(mary) [input hypothesis]
35. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 13]
48. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [nnf transformation 7]
49. ! [X0] : ((~humble(X0) | ~happy(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [flattening 48]
50. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~creative(X0) & strong(X0))) [nnf transformation 8]
51. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [rectify 50]
52. ? [X0] : (creative(X0) | ~strong(X0)) => (creative(sK1) | ~strong(sK1)) [choice axiom]
53. ((creative(sK1) | ~strong(sK1)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [skolemisation 51,52]
59. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 15]
60. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 59]
95. happy(X0) | rich(X0) [cnf transformation 49]
96. humble(X0) | rich(X0) [cnf transformation 49]
98. ~rich(mary) | strong(X1) [cnf transformation 53]
109. ~humble(X0) | ~old(X0) [cnf transformation 35]
113. ~happy(X0) | old(X0) [cnf transformation 60]
131. ~strong(mary) [cnf transformation 25]
190. 13 <=> rich(mary) [avatar definition]
191. ~rich(mary) <- (~13) [avatar component clause 190]
207. 17 <=> ! [X1] : strong(X1) [avatar definition]
208. strong(X1) <- (17) [avatar component clause 207]
209. 17 | ~13 [avatar split clause 98,190,207]
324. ~old(X0) | rich(X0) [resolution 109,96]
327. old(X0) | rich(X0) [resolution 113,95]
328. rich(X0) [subsumption resolution 327,324]
334. $false <- (~13) [resolution 328,191]
335. 13 [avatar contradiction clause 334]
338. $false <- (17) [resolution 208,131]
343. ~17 [avatar contradiction clause 338]
345. $false [avatar sat refutation 209,335,343]
% SZS output end Proof for 8417761546825758464513820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and kind is not patient.
If someone is either not brave or humble then someone is either not brave or kind.
Everyone who is quiet is both not patient and not wise and vice versa.
If paul is both not happy and not rich then someone is strong or not patient and vice versa.
If someone is not creative or old then someone is either old or not strong and vice versa.
If mary is humble then someone is either strong or creative and vice versa.
If alice is both creative and not patient then alice is not humble or not strong.
If someone is creative or not funny then paul is not funny or not creative and vice versa.
Everyone who is either funny or not brave is not rich and vice versa.
Everyone who is not creative or tall is not quiet and vice versa.
Everyone who is not funny or curious is not generous or not patient and vice versa.
Everyone who is both not calm and not tall is both kind and not quiet.
Everyone who is either not happy or rich is both not curious and curious.
Everyone who is either not rich or tall is funny or not happy and vice versa.
Everyone who is either not kind or not humble is strong and vice versa.
If someone is not old or not funny then lucy is either calm or not creative and vice versa.
Mary is funny or not calm.
Someone is either not brave or not humble.
Paul is both patient and funny.
Alice is either humble or not funny.
Susan is rich.
Someone is happy or not generous.
Someone is either not quiet or not funny.
Someone is old. | Alice is not strong. | entailment | (![X]:((tall(X)&kind(X))=>~patient(X)))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:(quiet(X)<=>(~patient(X)&~wise(X))))&
(((~happy(paul)&~rich(paul)))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((~creative(X)|old(X))))<=>(?[X]:((old(X)<~>~strong(X)))))&
((humble(mary))<=>(?[X]:((strong(X)<~>creative(X)))))&
(((creative(alice)&~patient(alice)))=>((~humble(alice)|~strong(alice))))&
((?[X]:((creative(X)|~funny(X))))<=>((~funny(paul)|~creative(paul))))&
(![X]:((funny(X)<~>~brave(X))<=>~rich(X)))&
(![X]:((~creative(X)|tall(X))<=>~quiet(X)))&
(![X]:((~funny(X)|curious(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((~happy(X)<~>rich(X))=>(~curious(X)&curious(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(funny(X)|~happy(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((calm(lucy)<~>~creative(lucy))))&
((funny(mary)|~calm(mary)))&
(?[X]:((~brave(X)<~>~humble(X))))&
((patient(paul)&funny(paul)))&
((humble(alice)<~>~funny(alice)))&
(rich(susan))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:(old(X))) | ~strong(alice) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 495991433304780285339729
% SZS output start Proof for 495991433304780285339729
4. (~rich(paul) & ~happy(paul)) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p3]
13. ! [X0] : ((~happy(X0) <~> rich(X0)) => (curious(X0) & ~curious(X0))) [input p12]
25. strong(alice) [input hypothesis]
35. ! [X0] : ((curious(X0) & ~curious(X0)) | (~happy(X0) <=> rich(X0))) [ennf transformation 13]
42. ((~rich(paul) & ~happy(paul)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | (rich(paul) | happy(paul))) [nnf transformation 4]
43. ((~rich(paul) & ~happy(paul)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | rich(paul) | happy(paul)) [flattening 42]
44. ((~rich(paul) & ~happy(paul)) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | rich(paul) | happy(paul)) [rectify 43]
45. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
46. ((~rich(paul) & ~happy(paul)) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | rich(paul) | happy(paul)) [skolemisation 44,45]
66. ! [X0] : ((curious(X0) & ~curious(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) [nnf transformation 35]
94. ~happy(paul) | ~strong(X0) [cnf transformation 46]
96. ~rich(paul) | ~strong(X0) [cnf transformation 46]
126. ~curious(X0) | rich(X0) | happy(X0) [cnf transformation 66]
128. curious(X0) | rich(X0) | happy(X0) [cnf transformation 66]
158. strong(alice) [cnf transformation 25]
181. 6 <=> rich(paul) [avatar definition]
183. ~rich(paul) <- (~6) [avatar component clause 181]
186. 7 <=> ! [X0] : ~strong(X0) [avatar definition]
187. ~strong(X0) <- (7) [avatar component clause 186]
188. 7 | ~6 [avatar split clause 96,181,186]
190. 8 <=> happy(paul) [avatar definition]
192. ~happy(paul) <- (~8) [avatar component clause 190]
194. 7 | ~8 [avatar split clause 94,190,186]
273. 27 <=> strong(alice) [avatar definition]
274. strong(alice) <- (27) [avatar component clause 273]
305. rich(X0) | happy(X0) [subsumption resolution 126,128]
379. 27 [avatar split clause 158,273]
388. happy(paul) <- (~6) [resolution 305,183]
390. $false <- (~6, ~8) [subsumption resolution 388,192]
391. 6 | 8 [avatar contradiction clause 390]
396. $false <- (7, 27) [resolution 187,274]
399. ~7 | ~27 [avatar contradiction clause 396]
400. $false [avatar sat refutation 188,194,379,391,399]
% SZS output end Proof for 495991433304780285339729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or funny then someone is not brave.
If mary is not strong or strong then john is calm or 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.
Everyone who is both kind and calm is quiet.
If someone is both rich and curious then john is generous or humble and vice versa.
Someone is both creative and not generous.
Someone is either tall or calm.
Mary is either humble or creative.
Someone is not calm.
Someone is wise.
Someone is not funny or rich.
Someone is both funny and not curious. | John is quiet. | entailment | ((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![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))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
((?[X]:((rich(X)&curious(X))))<=>((generous(john)|humble(john))))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((humble(mary)<~>creative(mary)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:((funny(X)&~curious(X)))) | quiet(john) | [
"p1",
"p4",
"p5",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7583738319827188042753894
% SZS output start Proof for 7583738319827188042753894
2. (strong(mary) | ~strong(mary)) => (generous(john) | calm(john)) [input p1]
5. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p4]
6. ! [X0] : ((kind(X0) | quiet(X0)) <=> (funny(X0) | happy(X0))) [input p5]
10. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p9]
14. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p13]
15. ! [X0] : ((calm(X0) & kind(X0)) => quiet(X0)) [input p14]
24. ~quiet(john) [input hypothesis]
29. (generous(john) | calm(john)) | (~strong(mary) & strong(mary)) [ennf transformation 2]
30. generous(john) | calm(john) | (~strong(mary) & strong(mary)) [flattening 29]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 5]
39. ! [X0] : (quiet(X0) | (~calm(X0) | ~kind(X0))) [ennf transformation 15]
40. ! [X0] : (quiet(X0) | ~calm(X0) | ~kind(X0)) [flattening 39]
47. ! [X0] : (((kind(X0) | quiet(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 6]
48. ! [X0] : ((kind(X0) | quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 47]
60. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 10]
61. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 60]
67. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 14]
68. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 67]
90. generous(john) | calm(john) | strong(mary) [cnf transformation 30]
91. generous(john) | calm(john) | ~strong(mary) [cnf transformation 30]
97. ~patient(X0) | ~generous(X0) [cnf transformation 34]
101. ~funny(X0) | quiet(X0) | kind(X0) [cnf transformation 48]
114. quiet(X0) | funny(X0) [cnf transformation 61]
123. ~kind(X0) | patient(X0) [cnf transformation 68]
126. ~kind(X0) | ~calm(X0) | quiet(X0) [cnf transformation 40]
143. ~quiet(john) [cnf transformation 24]
157. 4 <=> strong(mary) [avatar definition]
161. 5 <=> calm(john) [avatar definition]
165. 6 <=> generous(john) [avatar definition]
167. generous(john) <- (6) [avatar component clause 165]
168. ~4 | 5 | 6 [avatar split clause 91,165,161,157]
169. 4 | 5 | 6 [avatar split clause 90,165,161,157]
308. funny(john) [resolution 114,143]
322. quiet(john) | kind(john) [resolution 101,308]
324. kind(john) [subsumption resolution 322,143]
418. ~calm(john) | quiet(john) [resolution 324,126]
420. patient(john) [resolution 324,123]
425. ~calm(john) [subsumption resolution 418,143]
426. ~5 [avatar split clause 425,161]
522. ~generous(john) [resolution 420,97]
523. $false <- (6) [subsumption resolution 522,167]
524. ~6 [avatar contradiction clause 523]
525. $false [avatar sat refutation 168,169,426,524]
% SZS output end Proof for 7583738319827188042753894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or quiet then paul is either funny or creative.
Everyone who is not strong is humble.
If alice is humble or happy then someone is both humble and not old.
Everyone who is both not wise and not humble is either rich or strong.
Everyone who is both not happy and wise is both not strong and old and vice versa.
If alice is either not wise or patient then alice is funny and vice versa.
Everyone who is either not tall or calm is both old and rich.
If alice is both funny and happy then paul is both rich and creative and vice versa.
If mary is not kind then mary is funny or not patient and vice versa.
If john is either wise or tall then paul is not humble and vice versa.
Everyone who is creative is not strong or happy.
Everyone who is either not generous or brave is both brave and not brave.
Everyone who is both patient and not brave is not calm or wise and vice versa.
If lucy is strong then john is both not patient and not old.
If someone is both not strong and rich then john is both not humble and not strong.
Everyone who is both not old and brave is both not generous and not creative and vice versa.
Mary is brave or funny.
Someone is both tall and not generous.
John is both not patient and not quiet.
Someone is happy or not calm.
Someone is either humble or not wise.
Mary is not strong or curious.
Someone is both not quiet and not patient. | Alice is wise. | neutral | ((?[X]:((~wise(X)|quiet(X))))=>((funny(paul)<~>creative(paul))))&
(![X]:(~strong(X)=>humble(X)))&
(((humble(alice)|happy(alice)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((~wise(X)&~humble(X))=>(rich(X)<~>strong(X))))&
(![X]:((~happy(X)&wise(X))<=>(~strong(X)&old(X))))&
(((~wise(alice)<~>patient(alice)))<=>(funny(alice)))&
(![X]:((~tall(X)<~>calm(X))=>(old(X)&rich(X))))&
(((funny(alice)&happy(alice)))<=>((rich(paul)&creative(paul))))&
((~kind(mary))<=>((funny(mary)|~patient(mary))))&
(((wise(john)<~>tall(john)))<=>(~humble(paul)))&
(![X]:(creative(X)=>(~strong(X)|happy(X))))&
(![X]:((~generous(X)<~>brave(X))=>(brave(X)&~brave(X))))&
(![X]:((patient(X)&~brave(X))<=>(~calm(X)|wise(X))))&
((strong(lucy))=>((~patient(john)&~old(john))))&
((?[X]:((~strong(X)&rich(X))))=>((~humble(john)&~strong(john))))&
(![X]:((~old(X)&brave(X))<=>(~generous(X)&~creative(X))))&
((brave(mary)|funny(mary)))&
(?[X]:((tall(X)&~generous(X))))&
((~patient(john)&~quiet(john)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
((~strong(mary)|curious(mary)))&
(?[X]:((~quiet(X)&~patient(X)))) | wise(alice) | [] | null | 0 |
Everyone who is either strong or not wise is happy and vice versa. Everyone who is curious is calm. Everyone who is either curious or not brave is strong and vice versa. Everyone who is either not wise or not kind is both quiet and brave and vice versa. Everyone who is both curious and not creative is not funny or calm and vice versa. If fred is rich then someone is both not strong and kind. Everyone who is not brave or quiet is quiet and vice versa. If mary is not wise then someone is either not old or brave. Everyone who is not calm or not old is either not generous or calm and vice versa. If fred is calm or not kind then alice is old and vice versa. If someone is either generous or curious then someone is brave. Everyone who is not quiet or not funny is both strong and wise and vice versa. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. If alice is not funny or creative then someone is strong. Lucy is both brave and not kind. Susan is either not old or not happy. Someone is either humble or wise. Someone is not creative. Paul is not curious or not strong. John is both quiet and kind. | Mary is not humble. | neutral | (![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(strong(X))))&
((brave(lucy)&~kind(lucy)))&
((~old(susan)<~>~happy(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
((~curious(paul)|~strong(paul)))&
((quiet(john)&kind(john))) | ~humble(mary) | [] | null | 0 |
Everyone who is both quiet and tall is tall and vice versa.
Everyone who is wise or not tall is not wise or wise and vice versa.
Everyone who is both not rich and calm is either not strong or not funny.
Everyone who is both not humble and generous is brave and vice versa.
Everyone who is either calm or old is patient and vice versa.
If lucy is either not calm or not curious then someone is either happy or curious.
If john is either not wise or not tall then someone is either not curious or strong and vice versa.
Everyone who is funny or not strong is both not rich and humble and vice versa.
If someone is calm then someone is not quiet or brave.
If mary is both not quiet and creative then john is not calm or creative and vice versa.
If someone is both not funny and old then susan is quiet and vice versa.
Everyone who is both patient and happy is not old and vice versa.
Everyone who is humble or not funny is both rich and calm and vice versa.
Everyone who is either funny or patient is old.
Everyone who is both rich and quiet is either calm or creative.
Everyone who is happy or not rich is both not quiet and wise.
Lucy is either not quiet or curious.
Someone is not creative.
Someone is both not curious and wise.
John is happy.
Mary is either happy or not brave.
Susan is either old or not kind. | John is creative. | neutral | (![X]:((quiet(X)&tall(X))<=>tall(X)))&
(![X]:((wise(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~rich(X)&calm(X))=>(~strong(X)<~>~funny(X))))&
(![X]:((~humble(X)&generous(X))<=>brave(X)))&
(![X]:((calm(X)<~>old(X))<=>patient(X)))&
(((~calm(lucy)<~>~curious(lucy)))=>(?[X]:((happy(X)<~>curious(X)))))&
(((~wise(john)<~>~tall(john)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((funny(X)|~strong(X))<=>(~rich(X)&humble(X))))&
((?[X]:(calm(X)))=>(?[X]:((~quiet(X)|brave(X)))))&
(((~quiet(mary)&creative(mary)))<=>((~calm(john)|creative(john))))&
((?[X]:((~funny(X)&old(X))))<=>(quiet(susan)))&
(![X]:((patient(X)&happy(X))<=>~old(X)))&
(![X]:((humble(X)|~funny(X))<=>(rich(X)&calm(X))))&
(![X]:((funny(X)<~>patient(X))=>old(X)))&
(![X]:((rich(X)&quiet(X))=>(calm(X)<~>creative(X))))&
(![X]:((happy(X)|~rich(X))=>(~quiet(X)&wise(X))))&
((~quiet(lucy)<~>curious(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)&wise(X))))&
(happy(john))&
((happy(mary)<~>~brave(mary)))&
((old(susan)<~>~kind(susan))) | creative(john) | [] | null | 0 |
Everyone who is generous or not kind is either not quiet or calm.
Everyone who is either kind or old is both calm and not happy and vice versa.
If paul is either old or not funny then paul is quiet.
Everyone who is both not creative and quiet is not calm or not brave and vice versa.
If lucy is both quiet and kind then someone is both not curious and not wise and vice versa.
Everyone who is both brave and rich is not patient.
If someone is both kind and curious then alice is both not kind and creative.
If someone is both brave and rich then fred is not rich and vice versa.
Everyone who is both rich and funny is not creative or not quiet and vice versa.
Everyone who is not generous is creative and vice versa.
Everyone who is both not funny and not brave is both not patient and not generous.
Everyone who is calm or kind is both humble and not strong and vice versa.
Everyone who is not brave or not funny is either not kind or not creative and vice versa.
Everyone who is both happy and not strong is either not generous or generous and vice versa.
Everyone who is both curious and not generous is either not kind or patient and vice versa.
If someone is either curious or not brave then someone is not kind or patient and vice versa.
John is both not wise and not generous.
Someone is both not wise and curious.
Someone is old.
Fred is not rich.
Someone is humble or not funny.
Someone is tall or not strong.
Mary is either generous or not happy. | Paul is curious. | neutral | (![X]:((generous(X)|~kind(X))=>(~quiet(X)<~>calm(X))))&
(![X]:((kind(X)<~>old(X))<=>(calm(X)&~happy(X))))&
(((old(paul)<~>~funny(paul)))=>(quiet(paul)))&
(![X]:((~creative(X)&quiet(X))<=>(~calm(X)|~brave(X))))&
(((quiet(lucy)&kind(lucy)))<=>(?[X]:((~curious(X)&~wise(X)))))&
(![X]:((brave(X)&rich(X))=>~patient(X)))&
((?[X]:((kind(X)&curious(X))))=>((~kind(alice)&creative(alice))))&
((?[X]:((brave(X)&rich(X))))<=>(~rich(fred)))&
(![X]:((rich(X)&funny(X))<=>(~creative(X)|~quiet(X))))&
(![X]:(~generous(X)<=>creative(X)))&
(![X]:((~funny(X)&~brave(X))=>(~patient(X)&~generous(X))))&
(![X]:((calm(X)|kind(X))<=>(humble(X)&~strong(X))))&
(![X]:((~brave(X)|~funny(X))<=>(~kind(X)<~>~creative(X))))&
(![X]:((happy(X)&~strong(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((curious(X)&~generous(X))<=>(~kind(X)<~>patient(X))))&
((?[X]:((curious(X)<~>~brave(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
((~wise(john)&~generous(john)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(old(X)))&
(~rich(fred))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((tall(X)|~strong(X))))&
((generous(mary)<~>~happy(mary))) | curious(paul) | [] | null | 0 |
Everyone who is either not strong or not happy is not quiet or not tall and vice versa.
If someone is funny then john is not patient or not quiet and vice versa.
Everyone who is not quiet is strong or not calm and vice versa.
Everyone who is calm is not humble and vice versa.
Everyone who is curious is not calm and vice versa.
Everyone who is both not calm and humble is either calm or not old and vice versa.
Everyone who is either calm or tall is either not patient or not kind and vice versa.
Everyone who is funny or quiet is not kind and vice versa.
If someone is not humble or not quiet then paul is either not calm or not strong and vice versa.
Everyone who is tall or not curious is both not patient and not quiet.
Everyone who is both humble and creative is rich or not brave and vice versa.
If someone is both old and tall then someone is creative or not generous.
If someone is funny or kind then susan is curious and vice versa.
If someone is not rich then someone is not curious.
If someone is either not creative or not brave then lucy is both not calm and not happy and vice versa.
Lucy is not old or not humble.
Mary is both brave and curious.
Mary is either not generous or not quiet.
Someone is either not creative or generous.
Someone is either quiet or not creative. | Susan is humble. | entailment | (![X]:((~strong(X)<~>~happy(X))<=>(~quiet(X)|~tall(X))))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:((tall(X)|~curious(X))=>(~patient(X)&~quiet(X))))&
(![X]:((humble(X)&creative(X))<=>(rich(X)|~brave(X))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((creative(X)|~generous(X)))))&
((?[X]:((funny(X)|kind(X))))<=>(curious(susan)))&
((?[X]:(~rich(X)))=>(?[X]:(~curious(X))))&
((?[X]:((~creative(X)<~>~brave(X))))<=>((~calm(lucy)&~happy(lucy))))&
((~old(lucy)|~humble(lucy)))&
((brave(mary)&curious(mary)))&
((~generous(mary)<~>~quiet(mary)))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:((quiet(X)<~>~creative(X)))) | humble(susan) | [
"p1",
"p2",
"p3",
"p4",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6421468682743623874502571
% SZS output start Proof for 6421468682743623874502571
2. ? [X0] : funny(X0) <=> (~quiet(john) | ~patient(john)) [input p1]
3. ! [X0] : (~quiet(X0) <=> (~calm(X0) | strong(X0))) [input p2]
4. ! [X0] : (calm(X0) <=> ~humble(X0)) [input p3]
5. ! [X0] : (curious(X0) <=> ~calm(X0)) [input p4]
10. ! [X0] : ((~curious(X0) | tall(X0)) => (~quiet(X0) & ~patient(X0))) [input p9]
13. ? [X0] : (kind(X0) | funny(X0)) <=> curious(susan) [input p12]
21. ~humble(susan) [input hypothesis]
24. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (curious(X0) & ~tall(X0))) [ennf transformation 10]
29. (? [X0] : funny(X0) | (quiet(john) & patient(john))) & ((~quiet(john) | ~patient(john)) | ! [X0] : ~funny(X0)) [nnf transformation 2]
30. (? [X0] : funny(X0) | (quiet(john) & patient(john))) & (~quiet(john) | ~patient(john) | ! [X0] : ~funny(X0)) [flattening 29]
31. (? [X0] : funny(X0) | (quiet(john) & patient(john))) & (~quiet(john) | ~patient(john) | ! [X1] : ~funny(X1)) [rectify 30]
32. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
33. (funny(sK0) | (quiet(john) & patient(john))) & (~quiet(john) | ~patient(john) | ! [X1] : ~funny(X1)) [skolemisation 31,32]
34. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & ((~calm(X0) | strong(X0)) | quiet(X0))) [nnf transformation 3]
35. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & (~calm(X0) | strong(X0) | quiet(X0))) [flattening 34]
36. ! [X0] : ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))) [nnf transformation 4]
37. ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 5]
52. (? [X0] : (kind(X0) | funny(X0)) | ~curious(susan)) & (curious(susan) | ! [X0] : (~kind(X0) & ~funny(X0))) [nnf transformation 13]
53. (? [X0] : (kind(X0) | funny(X0)) | ~curious(susan)) & (curious(susan) | ! [X1] : (~kind(X1) & ~funny(X1))) [rectify 52]
54. ? [X0] : (kind(X0) | funny(X0)) => (kind(sK3) | funny(sK3)) [choice axiom]
55. ((kind(sK3) | funny(sK3)) | ~curious(susan)) & (curious(susan) | ! [X1] : (~kind(X1) & ~funny(X1))) [skolemisation 53,54]
78. funny(sK0) | patient(john) [cnf transformation 33]
79. funny(sK0) | quiet(john) [cnf transformation 33]
82. ~quiet(X0) | calm(X0) [cnf transformation 35]
84. humble(X0) | calm(X0) [cnf transformation 36]
85. ~curious(X0) | ~calm(X0) [cnf transformation 37]
111. ~patient(X0) | curious(X0) [cnf transformation 24]
120. curious(susan) | ~funny(X1) [cnf transformation 55]
139. ~humble(susan) [cnf transformation 21]
143. 1 <=> quiet(john) [avatar definition]
145. quiet(john) <- (1) [avatar component clause 143]
147. 2 <=> funny(sK0) [avatar definition]
149. funny(sK0) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 79,147,143]
152. 3 <=> patient(john) [avatar definition]
154. patient(john) <- (3) [avatar component clause 152]
155. 3 | 2 [avatar split clause 78,147,152]
157. 4 <=> ! [X1] : ~funny(X1) [avatar definition]
158. ~funny(X1) <- (4) [avatar component clause 157]
192. 11 <=> curious(susan) [avatar definition]
193. curious(susan) <- (11) [avatar component clause 192]
208. 4 | 11 [avatar split clause 120,192,157]
278. calm(susan) [resolution 84,139]
281. ~calm(susan) <- (11) [resolution 85,193]
282. $false <- (11) [subsumption resolution 281,278]
283. ~11 [avatar contradiction clause 282]
284. $false <- (2, 4) [resolution 158,149]
287. ~2 | ~4 [avatar contradiction clause 284]
288. calm(john) <- (1) [resolution 145,82]
294. curious(john) <- (3) [resolution 111,154]
296. ~calm(john) <- (3) [resolution 294,85]
297. $false <- (1, 3) [subsumption resolution 296,288]
298. ~1 | ~3 [avatar contradiction clause 297]
299. $false [avatar sat refutation 150,155,208,283,287,298]
% SZS output end Proof for 6421468682743623874502571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind or not patient then someone is either not kind or creative. If someone is either not tall or not calm then someone is either creative or not old and vice versa. Everyone who is not creative is either humble or wise. If john is both not funny and patient then someone is not happy or kind. If fred is either funny or rich then fred is creative or happy. Everyone who is either wise or humble is wise and vice versa. Everyone who is kind or not old is not quiet. If someone is not strong or happy then someone is either tall or not strong. If fred is tall then someone is calm or humble and vice versa. Everyone who is both tall and not patient is rich and vice versa. If someone is either not generous or not curious then someone is kind. Everyone who is both not patient and brave is not quiet and vice versa. Everyone who is either not generous or not humble is both creative and not happy and vice versa. Everyone who is patient or creative is both humble and not patient and vice versa. Everyone who is both old and not funny is either patient or happy. If john is both not curious and not calm then john is either generous or not strong. John is both not curious and rich. Someone is funny or humble. Paul is happy or kind. Someone is either old or happy. Susan is not brave. Mary is either not old or not humble. Fred is either not quiet or humble. | Alice is generous. | contradiction | (((~kind(alice)|~patient(alice)))=>(?[X]:((~kind(X)<~>creative(X)))))&
((?[X]:((~tall(X)<~>~calm(X))))<=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:(~creative(X)=>(humble(X)<~>wise(X))))&
(((~funny(john)&patient(john)))=>(?[X]:((~happy(X)|kind(X)))))&
(((funny(fred)<~>rich(fred)))=>((creative(fred)|happy(fred))))&
(![X]:((wise(X)<~>humble(X))<=>wise(X)))&
(![X]:((kind(X)|~old(X))=>~quiet(X)))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((tall(X)<~>~strong(X)))))&
((tall(fred))<=>(?[X]:((calm(X)|humble(X)))))&
(![X]:((tall(X)&~patient(X))<=>rich(X)))&
((?[X]:((~generous(X)<~>~curious(X))))=>(?[X]:(kind(X))))&
(![X]:((~patient(X)&brave(X))<=>~quiet(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(creative(X)&~happy(X))))&
(![X]:((patient(X)|creative(X))<=>(humble(X)&~patient(X))))&
(![X]:((old(X)&~funny(X))=>(patient(X)<~>happy(X))))&
(((~curious(john)&~calm(john)))=>((generous(john)<~>~strong(john))))&
((~curious(john)&rich(john)))&
(?[X]:((funny(X)|humble(X))))&
((happy(paul)|kind(paul)))&
(?[X]:((old(X)<~>happy(X))))&
(~brave(susan))&
((~old(mary)<~>~humble(mary)))&
((~quiet(fred)<~>humble(fred))) | generous(alice) | [
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8655217354798846867614430
% SZS output start Proof for 8655217354798846867614430
6. ! [X0] : ((wise(X0) <~> humble(X0)) <=> wise(X0)) [input p5]
13. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~happy(X0) & creative(X0))) [input p12]
14. ! [X0] : ((creative(X0) | patient(X0)) <=> (~patient(X0) & humble(X0))) [input p13]
24. generous(alice) [input hypothesis]
53. ! [X0] : ((((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | ~wise(X0)) & (wise(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0))))) [nnf transformation 6]
70. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (happy(X0) | ~creative(X0))) & ((~happy(X0) & creative(X0)) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 13]
71. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | happy(X0) | ~creative(X0)) & ((~happy(X0) & creative(X0)) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [flattening 70]
72. ! [X0] : (((creative(X0) | patient(X0)) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | (~creative(X0) & ~patient(X0)))) [nnf transformation 14]
73. ! [X0] : ((creative(X0) | patient(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | (~creative(X0) & ~patient(X0)))) [flattening 72]
101. wise(X0) | wise(X0) | ~humble(X0) [cnf transformation 53]
103. ~humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 53]
122. creative(X0) | ~generous(X0) | humble(X0) [cnf transformation 71]
128. humble(X0) | ~creative(X0) [cnf transformation 73]
147. generous(alice) [cnf transformation 24]
150. wise(X0) | ~humble(X0) [duplicate literal removal 101]
151. ~wise(X0) | ~humble(X0) [duplicate literal removal 103]
243. ~humble(X0) [subsumption resolution 150,151]
290. ~generous(X0) | creative(X0) [subsumption resolution 122,243]
291. ~creative(X0) [subsumption resolution 128,243]
340. creative(alice) [resolution 290,147]
341. $false [subsumption resolution 340,291]
% SZS output end Proof for 8655217354798846867614430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is curious or not wise then someone is strong and vice versa. Everyone who is either creative or calm is both not rich and kind. If someone is not brave or tall then lucy is humble or not generous. Everyone who is both not rich and not tall is not funny or old and vice versa. If susan is both not funny and not humble then john is both happy and not kind and vice versa. Everyone who is wise or creative is both not quiet and brave and vice versa. Everyone who is both funny and not strong is either happy or quiet and vice versa. If someone is either wise or old then someone is not rich. If someone is not old or generous then paul is both brave and kind and vice versa. If lucy is both happy and not brave then someone is not rich or not calm and vice versa. If someone is either not old or not brave then someone is not brave. Everyone who is old is not rich and vice versa. If susan is both not happy and curious then alice is not calm or wise and vice versa. Everyone who is both generous and not happy is old or not funny and vice versa. If fred is old or not strong then someone is happy or kind and vice versa. If someone is brave or not creative then lucy is either tall or funny and vice versa. Someone is not patient. Someone is not tall or old. Alice is either brave or not old. Someone is not quiet. John is both wise and not patient. Paul is either not creative or not kind. | Lucy is not calm. | entailment | (((curious(lucy)|~wise(lucy)))<=>(?[X]:(strong(X))))&
(![X]:((creative(X)<~>calm(X))=>(~rich(X)&kind(X))))&
((?[X]:((~brave(X)|tall(X))))=>((humble(lucy)|~generous(lucy))))&
(![X]:((~rich(X)&~tall(X))<=>(~funny(X)|old(X))))&
(((~funny(susan)&~humble(susan)))<=>((happy(john)&~kind(john))))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(?[X]:(~patient(X)))&
(?[X]:((~tall(X)|old(X))))&
((brave(alice)<~>~old(alice)))&
(?[X]:(~quiet(X)))&
((wise(john)&~patient(john)))&
((~creative(paul)<~>~kind(paul))) | ~calm(lucy) | [
"p1",
"p3",
"p5",
"p9",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3204929236476257316868531
% SZS output start Proof for 3204929236476257316868531
2. ! [X0] : ((creative(X0) <~> calm(X0)) => (kind(X0) & ~rich(X0))) [input p1]
4. ! [X0] : ((~tall(X0) & ~rich(X0)) <=> (old(X0) | ~funny(X0))) [input p3]
6. ! [X0] : ((creative(X0) | wise(X0)) <=> (brave(X0) & ~quiet(X0))) [input p5]
10. (~brave(lucy) & happy(lucy)) <=> ? [X0] : (~calm(X0) | ~rich(X0)) [input p9]
12. ! [X0] : (old(X0) <=> ~rich(X0)) [input p11]
14. ! [X0] : ((~happy(X0) & generous(X0)) <=> (~funny(X0) | old(X0))) [input p13]
19. brave(alice) <~> ~old(alice) [input p18]
23. calm(lucy) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~rich(X0)) | (creative(X0) <=> calm(X0))) [ennf transformation 2]
38. ! [X0] : ((kind(X0) & ~rich(X0)) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 28]
39. ! [X0] : (((~tall(X0) & ~rich(X0)) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | (tall(X0) | rich(X0)))) [nnf transformation 4]
40. ! [X0] : (((~tall(X0) & ~rich(X0)) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | tall(X0) | rich(X0))) [flattening 39]
43. ! [X0] : (((creative(X0) | wise(X0)) | (~brave(X0) | quiet(X0))) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 6]
44. ! [X0] : ((creative(X0) | wise(X0) | ~brave(X0) | quiet(X0)) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 43]
56. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | (brave(lucy) | ~happy(lucy))) [nnf transformation 10]
57. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X0] : (~calm(X0) | ~rich(X0)) | brave(lucy) | ~happy(lucy)) [flattening 56]
58. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & (? [X1] : (~calm(X1) | ~rich(X1)) | brave(lucy) | ~happy(lucy)) [rectify 57]
59. ? [X1] : (~calm(X1) | ~rich(X1)) => (~calm(sK3) | ~rich(sK3)) [choice axiom]
60. ((~brave(lucy) & happy(lucy)) | ! [X0] : (calm(X0) & rich(X0))) & ((~calm(sK3) | ~rich(sK3)) | brave(lucy) | ~happy(lucy)) [skolemisation 58,59]
65. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 12]
68. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | (happy(X0) | ~generous(X0)))) [nnf transformation 14]
69. ! [X0] : (((~happy(X0) & generous(X0)) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | happy(X0) | ~generous(X0))) [flattening 68]
81. (old(alice) | ~brave(alice)) & (~old(alice) | brave(alice)) [nnf transformation 19]
89. ~rich(X0) | creative(X0) | ~calm(X0) [cnf transformation 38]
96. ~old(X0) | ~rich(X0) [cnf transformation 40]
106. ~creative(X0) | brave(X0) [cnf transformation 44]
122. happy(lucy) | rich(X0) [cnf transformation 60]
123. happy(lucy) | calm(X0) [cnf transformation 60]
124. ~brave(lucy) | rich(X0) [cnf transformation 60]
125. ~brave(lucy) | calm(X0) [cnf transformation 60]
129. old(X0) | rich(X0) [cnf transformation 65]
138. ~happy(X0) | ~old(X0) [cnf transformation 69]
152. old(alice) | ~brave(alice) [cnf transformation 81]
157. calm(lucy) [cnf transformation 23]
252. 22 <=> ! [X0] : calm(X0) [avatar definition]
253. calm(X0) <- (22) [avatar component clause 252]
255. 23 <=> brave(lucy) [avatar definition]
257. ~brave(lucy) <- (~23) [avatar component clause 255]
258. 22 | ~23 [avatar split clause 125,255,252]
260. 24 <=> ! [X0] : rich(X0) [avatar definition]
261. rich(X0) <- (24) [avatar component clause 260]
262. 24 | ~23 [avatar split clause 124,255,260]
264. 25 <=> happy(lucy) [avatar definition]
266. happy(lucy) <- (25) [avatar component clause 264]
267. 22 | 25 [avatar split clause 123,264,252]
268. 24 | 25 [avatar split clause 122,264,260]
361. 45 <=> brave(alice) [avatar definition]
363. ~brave(alice) <- (~45) [avatar component clause 361]
365. 46 <=> old(alice) [avatar definition]
366. ~old(alice) <- (~46) [avatar component clause 365]
367. old(alice) <- (46) [avatar component clause 365]
368. ~45 | 46 [avatar split clause 152,365,361]
406. ~rich(alice) <- (46) [resolution 367,96]
407. $false <- (24, 46) [subsumption resolution 406,261]
408. ~24 | ~46 [avatar contradiction clause 407]
411. rich(alice) <- (~46) [resolution 129,366]
431. ~old(lucy) <- (25) [resolution 266,138]
434. creative(alice) | ~calm(alice) <- (~46) [resolution 411,89]
437. creative(alice) <- (22, ~46) [subsumption resolution 434,253]
449. 49 <=> creative(lucy) [avatar definition]
451. creative(lucy) <- (49) [avatar component clause 449]
458. rich(lucy) <- (25) [resolution 431,129]
611. brave(alice) <- (22, ~46) [resolution 437,106]
612. $false <- (22, ~45, ~46) [subsumption resolution 611,363]
613. ~22 | 45 | 46 [avatar contradiction clause 612]
696. creative(lucy) | ~calm(lucy) <- (25) [resolution 458,89]
699. creative(lucy) <- (25) [subsumption resolution 696,157]
700. 49 | ~25 [avatar split clause 699,264,449]
702. brave(lucy) <- (49) [resolution 451,106]
703. $false <- (~23, 49) [subsumption resolution 702,257]
704. 23 | ~49 [avatar contradiction clause 703]
705. $false [avatar sat refutation 258,262,267,268,368,408,613,700,704]
% SZS output end Proof for 3204929236476257316868531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is wise or tall and vice versa.
If mary is generous then mary is either not calm or not old.
Everyone who is either happy or not curious is not happy.
Everyone who is both happy and curious is not patient.
Everyone who is creative or humble is either not old or tall and vice versa.
Everyone who is either not funny or not wise is either not quiet or not humble and vice versa.
If someone is both happy and not tall then alice is both not happy and not calm and vice versa.
Everyone who is either creative or not calm is both not strong and strong and vice versa.
Everyone who is not creative or not happy is both not calm and happy.
Everyone who is both not generous and brave is not quiet.
If someone is not funny then someone is not tall.
If fred is patient or not curious then susan is not rich or wise.
Everyone who is both strong and not calm is strong or funny.
Everyone who is either humble or happy is either not kind or tall and vice versa.
If fred is curious or not wise then susan is either wise or strong.
Someone is either kind or not creative.
Someone is rich or patient.
John is not calm.
Lucy is funny.
John is wise or tall. | John is not patient. | neutral | (![X]:(~generous(X)<=>(wise(X)|tall(X))))&
((generous(mary))=>((~calm(mary)<~>~old(mary))))&
(![X]:((happy(X)<~>~curious(X))=>~happy(X)))&
(![X]:((happy(X)&curious(X))=>~patient(X)))&
(![X]:((creative(X)|humble(X))<=>(~old(X)<~>tall(X))))&
(![X]:((~funny(X)<~>~wise(X))<=>(~quiet(X)<~>~humble(X))))&
((?[X]:((happy(X)&~tall(X))))<=>((~happy(alice)&~calm(alice))))&
(![X]:((creative(X)<~>~calm(X))<=>(~strong(X)&strong(X))))&
(![X]:((~creative(X)|~happy(X))=>(~calm(X)&happy(X))))&
(![X]:((~generous(X)&brave(X))=>~quiet(X)))&
((?[X]:(~funny(X)))=>(?[X]:(~tall(X))))&
(((patient(fred)|~curious(fred)))=>((~rich(susan)|wise(susan))))&
(![X]:((strong(X)&~calm(X))=>(strong(X)|funny(X))))&
(![X]:((humble(X)<~>happy(X))<=>(~kind(X)<~>tall(X))))&
(((curious(fred)|~wise(fred)))=>((wise(susan)<~>strong(susan))))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:((rich(X)|patient(X))))&
(~calm(john))&
(funny(lucy))&
((wise(john)|tall(john))) | ~patient(john) | [] | null | 0 |
If fred is generous or not old then someone is humble or not brave and vice versa.
If someone is both brave and strong then someone is not funny or creative.
Everyone who is not humble or old is not funny or funny and vice versa.
Everyone who is either not funny or not happy is either curious or not patient and vice versa.
Everyone who is wise or generous is curious.
Everyone who is both not humble and old is not happy or not patient.
Everyone who is funny or creative is humble.
If john is both old and wise then paul is both funny and patient and vice versa.
If paul is both not quiet and brave then someone is not generous or not tall.
Everyone who is kind is either quiet or rich.
If mary is both not curious and not kind then fred is patient or not old and vice versa.
Everyone who is both not patient and strong is tall or not calm and vice versa.
Everyone who is wise is happy and vice versa.
Everyone who is both happy and not brave is both not strong and wise and vice versa.
Everyone who is humble is not old and vice versa.
If fred is tall then fred is not humble.
Alice is both not patient and not calm.
Paul is both quiet and not strong.
Alice is not rich or old.
Someone is either not wise or wise.
Someone is both calm and not tall.
Someone is happy or old.
Someone is not rich or not creative. | Fred is creative. | contradiction | (((generous(fred)|~old(fred)))<=>(?[X]:((humble(X)|~brave(X)))))&
((?[X]:((brave(X)&strong(X))))=>(?[X]:((~funny(X)|creative(X)))))&
(![X]:((~humble(X)|old(X))<=>(~funny(X)|funny(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((wise(X)|generous(X))=>curious(X)))&
(![X]:((~humble(X)&old(X))=>(~happy(X)|~patient(X))))&
(![X]:((funny(X)|creative(X))=>humble(X)))&
(((old(john)&wise(john)))<=>((funny(paul)&patient(paul))))&
(((~quiet(paul)&brave(paul)))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:(kind(X)=>(quiet(X)<~>rich(X))))&
(((~curious(mary)&~kind(mary)))<=>((patient(fred)|~old(fred))))&
(![X]:((~patient(X)&strong(X))<=>(tall(X)|~calm(X))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((happy(X)&~brave(X))<=>(~strong(X)&wise(X))))&
(![X]:(humble(X)<=>~old(X)))&
((tall(fred))=>(~humble(fred)))&
((~patient(alice)&~calm(alice)))&
((quiet(paul)&~strong(paul)))&
((~rich(alice)|old(alice)))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((~rich(X)|~creative(X)))) | creative(fred) | [
"p2",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4895624119819578973756580
% SZS output start Proof for 4895624119819578973756580
3. ! [X0] : ((old(X0) | ~humble(X0)) <=> (funny(X0) | ~funny(X0))) [input p2]
7. ! [X0] : ((creative(X0) | funny(X0)) => humble(X0)) [input p6]
15. ! [X0] : (humble(X0) <=> ~old(X0)) [input p14]
24. creative(fred) [input hypothesis]
30. ! [X0] : (humble(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 7]
43. ! [X0] : (((old(X0) | ~humble(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 3]
44. ! [X0] : ((old(X0) | ~humble(X0) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | (~old(X0) & humble(X0)))) [flattening 43]
58. ! [X0] : ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))) [nnf transformation 15]
75. old(X0) | ~humble(X0) | funny(X0) [cnf transformation 44]
76. old(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 44]
89. ~creative(X0) | humble(X0) [cnf transformation 30]
113. ~old(X0) | ~humble(X0) [cnf transformation 58]
114. humble(X0) | old(X0) [cnf transformation 58]
127. creative(fred) [cnf transformation 24]
141. 4 <=> ! [X0] : ~humble(X0) [avatar definition]
142. ~humble(X0) <- (4) [avatar component clause 141]
166. old(X0) | ~humble(X0) [subsumption resolution 75,76]
221. old(X0) [subsumption resolution 114,166]
222. ~humble(X0) [subsumption resolution 113,221]
223. 4 [avatar split clause 222,141]
249. humble(fred) [resolution 89,127]
250. $false <- (4) [subsumption resolution 249,142]
251. ~4 [avatar contradiction clause 250]
252. $false [avatar sat refutation 223,251]
% SZS output end Proof for 4895624119819578973756580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is creative then someone is wise or quiet and vice versa.
Everyone who is either rich or old is brave or not happy and vice versa.
If mary is either not funny or funny then lucy is both strong and not creative and vice versa.
If lucy is either not happy or tall then someone is either curious or not quiet.
If someone is both not happy and funny then mary is both curious and tall and vice versa.
Everyone who is either creative or not patient is not creative.
Everyone who is both strong and happy is not old or not tall and vice versa.
Everyone who is either strong or kind is strong or rich.
Everyone who is not generous or not rich is tall.
If someone is tall or not wise then someone is both rich and not creative and vice versa.
If fred is not funny or not creative then susan is brave or rich.
If someone is both strong and not curious then someone is either not humble or not calm.
If someone is not creative then fred is tall or not curious and vice versa.
If alice is either wise or not patient then susan is both patient and humble.
If someone is either not creative or not calm then someone is either creative or not tall and vice versa.
If someone is either tall or happy then someone is not rich and vice versa.
Fred is both kind and old.
Someone is either quiet or not strong.
Susan is either patient or rich.
Mary is either rich or generous.
Someone is both strong and funny.
Paul is either not tall or not strong.
Someone is old.
Fred is both quiet and happy. | John is creative. | entailment | ((creative(john))<=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((rich(X)<~>old(X))<=>(brave(X)|~happy(X))))&
(((~funny(mary)<~>funny(mary)))<=>((strong(lucy)&~creative(lucy))))&
(((~happy(lucy)<~>tall(lucy)))=>(?[X]:((curious(X)<~>~quiet(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((curious(mary)&tall(mary))))&
(![X]:((creative(X)<~>~patient(X))=>~creative(X)))&
(![X]:((strong(X)&happy(X))<=>(~old(X)|~tall(X))))&
(![X]:((strong(X)<~>kind(X))=>(strong(X)|rich(X))))&
(![X]:((~generous(X)|~rich(X))=>tall(X)))&
((?[X]:((tall(X)|~wise(X))))<=>(?[X]:((rich(X)&~creative(X)))))&
(((~funny(fred)|~creative(fred)))=>((brave(susan)|rich(susan))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~creative(X)))<=>((tall(fred)|~curious(fred))))&
(((wise(alice)<~>~patient(alice)))=>((patient(susan)&humble(susan))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((creative(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>happy(X))))<=>(?[X]:(~rich(X))))&
((kind(fred)&old(fred)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((patient(susan)<~>rich(susan)))&
((rich(mary)<~>generous(mary)))&
(?[X]:((strong(X)&funny(X))))&
((~tall(paul)<~>~strong(paul)))&
(?[X]:(old(X)))&
((quiet(fred)&happy(fred))) | creative(john) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4718296125037169502193492
% SZS output start Proof for 4718296125037169502193492
1. creative(john) <=> ? [X0] : (quiet(X0) | wise(X0)) [input p0]
24. happy(fred) & quiet(fred) [input p23]
25. ~creative(john) [input hypothesis]
39. (creative(john) | ! [X0] : (~quiet(X0) & ~wise(X0))) & (? [X0] : (quiet(X0) | wise(X0)) | ~creative(john)) [nnf transformation 1]
40. (creative(john) | ! [X0] : (~quiet(X0) & ~wise(X0))) & (? [X1] : (quiet(X1) | wise(X1)) | ~creative(john)) [rectify 39]
41. ? [X1] : (quiet(X1) | wise(X1)) => (quiet(sK0) | wise(sK0)) [choice axiom]
42. (creative(john) | ! [X0] : (~quiet(X0) & ~wise(X0))) & ((quiet(sK0) | wise(sK0)) | ~creative(john)) [skolemisation 40,41]
96. creative(john) | ~quiet(X0) [cnf transformation 42]
169. quiet(fred) [cnf transformation 24]
171. ~creative(john) [cnf transformation 25]
179. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
180. ~quiet(X0) <- (1) [avatar component clause 179]
182. 2 <=> creative(john) [avatar definition]
185. 1 | 2 [avatar split clause 96,182,179]
450. ~2 [avatar split clause 171,182]
457. $false <- (1) [resolution 180,169]
458. ~1 [avatar contradiction clause 457]
459. $false [avatar sat refutation 185,450,458]
% SZS output end Proof for 4718296125037169502193492
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or not old is either funny or not quiet and vice versa.
If fred is both generous and patient then alice is either not rich or generous and vice versa.
If paul is kind then someone is both not old and not happy and vice versa.
If susan is wise then mary is patient or strong and vice versa.
Everyone who is both kind and humble is not quiet and vice versa.
Everyone who is both happy and wise is not generous.
Everyone who is both not humble and strong is either not humble or kind and vice versa.
If someone is either not funny or not kind then fred is not patient.
Everyone who is not tall or not humble is both not generous and creative.
If someone is not funny then alice is either not brave or kind and vice versa.
Everyone who is not patient or not old is not kind or strong and vice versa.
Everyone who is either brave or patient is both kind and patient.
If fred is either generous or humble then someone is creative or not old and vice versa.
Everyone who is either not patient or tall is quiet or brave and vice versa.
If john is either funny or not happy then someone is kind and vice versa.
If someone is either not kind or tall then alice is not wise or wise.
Fred is strong.
Paul is both curious and not happy.
Alice is both not humble and creative.
Someone is not happy or not calm.
Someone is both not tall and not patient.
Susan is both strong and not wise.
Mary is either not happy or not old. | Fred is not kind. | entailment | (![X]:((old(X)<~>~old(X))<=>(funny(X)<~>~quiet(X))))&
(((generous(fred)&patient(fred)))<=>((~rich(alice)<~>generous(alice))))&
((kind(paul))<=>(?[X]:((~old(X)&~happy(X)))))&
((wise(susan))<=>((patient(mary)|strong(mary))))&
(![X]:((kind(X)&humble(X))<=>~quiet(X)))&
(![X]:((happy(X)&wise(X))=>~generous(X)))&
(![X]:((~humble(X)&strong(X))<=>(~humble(X)<~>kind(X))))&
((?[X]:((~funny(X)<~>~kind(X))))=>(~patient(fred)))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&creative(X))))&
((?[X]:(~funny(X)))<=>((~brave(alice)<~>kind(alice))))&
(![X]:((~patient(X)|~old(X))<=>(~kind(X)|strong(X))))&
(![X]:((brave(X)<~>patient(X))=>(kind(X)&patient(X))))&
(((generous(fred)<~>humble(fred)))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>(quiet(X)|brave(X))))&
(((funny(john)<~>~happy(john)))<=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>((~wise(alice)|wise(alice))))&
(strong(fred))&
((curious(paul)&~happy(paul)))&
((~humble(alice)&creative(alice)))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((~tall(X)&~patient(X))))&
((strong(susan)&~wise(susan)))&
((~happy(mary)<~>~old(mary))) | ~kind(fred) | [
"p6",
"p8",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7326078343743024440657000
% SZS output start Proof for 7326078343743024440657000
7. ! [X0] : ((strong(X0) & ~humble(X0)) <=> (~humble(X0) <~> kind(X0))) [input p6]
9. ! [X0] : ((~humble(X0) | ~tall(X0)) => (creative(X0) & ~generous(X0))) [input p8]
13. (generous(fred) <~> humble(fred)) <=> ? [X0] : (~old(X0) | creative(X0)) [input p12]
19. creative(alice) & ~humble(alice) [input p18]
24. kind(fred) [input hypothesis]
30. ! [X0] : ((creative(X0) & ~generous(X0)) | (humble(X0) & tall(X0))) [ennf transformation 9]
45. ! [X0] : (((strong(X0) & ~humble(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) & (((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | (~strong(X0) | humble(X0)))) [nnf transformation 7]
46. ! [X0] : (((strong(X0) & ~humble(X0)) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0)))) & (((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ~strong(X0) | humble(X0))) [flattening 45]
55. (((~humble(fred) | ~generous(fred)) & (humble(fred) | generous(fred))) | ! [X0] : (old(X0) & ~creative(X0))) & (? [X0] : (~old(X0) | creative(X0)) | ((generous(fred) | ~humble(fred)) & (humble(fred) | ~generous(fred)))) [nnf transformation 13]
56. (((~humble(fred) | ~generous(fred)) & (humble(fred) | generous(fred))) | ! [X0] : (old(X0) & ~creative(X0))) & (? [X1] : (~old(X1) | creative(X1)) | ((generous(fred) | ~humble(fred)) & (humble(fred) | ~generous(fred)))) [rectify 55]
57. ? [X1] : (~old(X1) | creative(X1)) => (~old(sK2) | creative(sK2)) [choice axiom]
58. (((~humble(fred) | ~generous(fred)) & (humble(fred) | generous(fred))) | ! [X0] : (old(X0) & ~creative(X0))) & ((~old(sK2) | creative(sK2)) | ((generous(fred) | ~humble(fred)) & (humble(fred) | ~generous(fred)))) [skolemisation 56,57]
96. ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 46]
102. ~generous(X0) | humble(X0) [cnf transformation 30]
119. humble(fred) | generous(fred) | ~creative(X0) [cnf transformation 58]
138. creative(alice) [cnf transformation 19]
145. kind(fred) [cnf transformation 24]
148. ~humble(X0) | ~kind(X0) [duplicate literal removal 96]
247. 19 <=> ! [X0] : ~creative(X0) [avatar definition]
248. ~creative(X0) <- (19) [avatar component clause 247]
252. 20 <=> humble(fred) [avatar definition]
254. humble(fred) <- (20) [avatar component clause 252]
256. humble(fred) | ~creative(X0) [subsumption resolution 119,102]
257. 19 | 20 [avatar split clause 256,252,247]
299. $false <- (19) [resolution 248,138]
300. ~19 [avatar contradiction clause 299]
308. ~kind(fred) <- (20) [resolution 148,254]
310. $false <- (20) [subsumption resolution 308,145]
311. ~20 [avatar contradiction clause 310]
313. $false [avatar sat refutation 257,300,311]
% SZS output end Proof for 7326078343743024440657000
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and wise is not humble or not patient and vice versa.
Everyone who is both calm and not patient is curious or not patient.
If mary is brave or not quiet then someone is both funny and humble.
Everyone who is not rich or not happy is both not old and not funny.
If mary is old or not tall then someone is both not curious and calm.
Everyone who is not generous or generous is not generous.
If mary is not strong then someone is either funny or not creative.
If someone is kind then someone is either calm or happy.
If someone is both strong and tall then mary is either not creative or strong and vice versa.
If alice is not patient then alice is not calm or kind and vice versa.
Everyone who is both old and not funny is not kind or not old and vice versa.
Everyone who is both not creative and wise is both not old and generous and vice versa.
Everyone who is humble or not wise is curious or not strong.
Everyone who is both not happy and not wise is both not happy and kind.
If mary is not patient or strong then someone is both tall and not curious and vice versa.
Everyone who is tall or old is tall.
Paul is either not funny or rich.
Mary is tall or calm.
Mary is either not humble or tall.
John is humble or quiet.
Susan is not funny or creative. | John is not brave. | neutral | (![X]:((~happy(X)&wise(X))<=>(~humble(X)|~patient(X))))&
(![X]:((calm(X)&~patient(X))=>(curious(X)|~patient(X))))&
(((brave(mary)|~quiet(mary)))=>(?[X]:((funny(X)&humble(X)))))&
(![X]:((~rich(X)|~happy(X))=>(~old(X)&~funny(X))))&
(((old(mary)|~tall(mary)))=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:((~generous(X)|generous(X))=>~generous(X)))&
((~strong(mary))=>(?[X]:((funny(X)<~>~creative(X)))))&
((?[X]:(kind(X)))=>(?[X]:((calm(X)<~>happy(X)))))&
((?[X]:((strong(X)&tall(X))))<=>((~creative(mary)<~>strong(mary))))&
((~patient(alice))<=>((~calm(alice)|kind(alice))))&
(![X]:((old(X)&~funny(X))<=>(~kind(X)|~old(X))))&
(![X]:((~creative(X)&wise(X))<=>(~old(X)&generous(X))))&
(![X]:((humble(X)|~wise(X))=>(curious(X)|~strong(X))))&
(![X]:((~happy(X)&~wise(X))=>(~happy(X)&kind(X))))&
(((~patient(mary)|strong(mary)))<=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:((tall(X)|old(X))=>tall(X)))&
((~funny(paul)<~>rich(paul)))&
((tall(mary)|calm(mary)))&
((~humble(mary)<~>tall(mary)))&
((humble(john)|quiet(john)))&
((~funny(susan)|creative(susan))) | ~brave(john) | [] | null | 0 |
If fred is not creative then lucy is not curious. If someone is patient then someone is not generous or not brave and vice versa. If john is strong or not patient then john is either rich or not wise and vice versa. Everyone who is both not kind and funny is both funny and not kind and vice versa. If someone is happy then someone is either not creative or not curious and vice versa. Everyone who is funny or not patient is both wise and not rich and vice versa. Everyone who is not rich is strong or not quiet and vice versa. If mary is not humble then susan is either wise or strong. If john is either quiet or not old then john is either kind or not curious and vice versa. If mary is either not tall or not rich then lucy is not creative. Everyone who is both tall and humble is not calm. Everyone who is curious or brave is not brave or not happy and vice versa. Everyone who is both quiet and not brave is either generous or not happy and vice versa. If someone is not generous then john is both creative and not funny and vice versa. Everyone who is generous or not creative is creative and vice versa. Everyone who is not creative is generous or not creative. Someone is either not rich or humble. Someone is not kind or tall. Mary is both not curious and not calm. Mary is not generous or wise. Someone is not quiet or wise. John is not humble or humble. | Mary is rich. | neutral | ((~creative(fred))=>(~curious(lucy)))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|~brave(X)))))&
(((strong(john)|~patient(john)))<=>((rich(john)<~>~wise(john))))&
(![X]:((~kind(X)&funny(X))<=>(funny(X)&~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>(strong(X)|~quiet(X))))&
((~humble(mary))=>((wise(susan)<~>strong(susan))))&
(((quiet(john)<~>~old(john)))<=>((kind(john)<~>~curious(john))))&
(((~tall(mary)<~>~rich(mary)))=>(~creative(lucy)))&
(![X]:((tall(X)&humble(X))=>~calm(X)))&
(![X]:((curious(X)|brave(X))<=>(~brave(X)|~happy(X))))&
(![X]:((quiet(X)&~brave(X))<=>(generous(X)<~>~happy(X))))&
((?[X]:(~generous(X)))<=>((creative(john)&~funny(john))))&
(![X]:((generous(X)|~creative(X))<=>creative(X)))&
(![X]:(~creative(X)=>(generous(X)|~creative(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)&~calm(mary)))&
((~generous(mary)|wise(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
((~humble(john)|humble(john))) | rich(mary) | [] | null | 0 |
If someone is both quiet and not rich then someone is both quiet and not curious and vice versa. Everyone who is curious or generous is both rich and not wise and vice versa. If someone is humble then someone is not old or not tall and vice versa. Everyone who is not happy is either brave or generous. Everyone who is not brave or funny is tall and vice versa. Everyone who is humble or not rich is not creative. Everyone who is not wise is either curious or patient. If paul is either curious or brave then john is either curious or generous and vice versa. Everyone who is either not calm or not old is both old and quiet. If someone is both not rich and old then someone is rich and vice versa. If susan is either not rich or wise then someone is both not rich and not humble and vice versa. If fred is either old or not quiet then fred is either not strong or strong. If someone is both rich and generous then someone is both happy and wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. John is both not tall and curious. Paul is both not funny and not creative. Lucy is not rich or not quiet. Someone is strong or old. Someone is either not kind or not funny. Susan is both not tall and not quiet. Someone is strong. Paul is wise. | Paul is not calm. | neutral | ((?[X]:((quiet(X)&~rich(X))))<=>(?[X]:((quiet(X)&~curious(X)))))&
(![X]:((curious(X)|generous(X))<=>(rich(X)&~wise(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:(~happy(X)=>(brave(X)<~>generous(X))))&
(![X]:((~brave(X)|funny(X))<=>tall(X)))&
(![X]:((humble(X)|~rich(X))=>~creative(X)))&
(![X]:(~wise(X)=>(curious(X)<~>patient(X))))&
(((curious(paul)<~>brave(paul)))<=>((curious(john)<~>generous(john))))&
(![X]:((~calm(X)<~>~old(X))=>(old(X)&quiet(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(rich(X))))&
(((~rich(susan)<~>wise(susan)))<=>(?[X]:((~rich(X)&~humble(X)))))&
(((old(fred)<~>~quiet(fred)))=>((~strong(fred)<~>strong(fred))))&
((?[X]:((rich(X)&generous(X))))=>(?[X]:((happy(X)&wise(X)))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
((~tall(john)&curious(john)))&
((~funny(paul)&~creative(paul)))&
((~rich(lucy)|~quiet(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
((~tall(susan)&~quiet(susan)))&
(?[X]:(strong(X)))&
(wise(paul)) | ~calm(paul) | [] | null | 0 |
Everyone who is both wise and not old is both not generous and generous. Everyone who is not kind is both not humble and curious and vice versa. If susan is not brave or calm then someone is not brave and vice versa. Everyone who is funny or not creative is brave or not brave. If someone is not funny or tall then someone is not humble. Everyone who is not humble or not strong is creative or not strong. Everyone who is old is both not old and tall. If someone is not happy then someone is not wise. If someone is either calm or not generous then someone is not wise and vice versa. Everyone who is funny or not patient is either tall or wise. Everyone who is both old and not creative is curious or calm and vice versa. If susan is either calm or old then mary is either not funny or not patient. Everyone who is not brave or not patient is both calm and not patient. If someone is both not tall and not strong then alice is either kind or not generous and vice versa. Everyone who is both not patient and not quiet is either not funny or not strong. Everyone who is both wise and not rich is happy or not tall. Someone is either not rich or humble. Someone is patient. Someone is curious or generous. Someone is both not quiet and generous. Paul is either rich or not curious. Paul is either happy or curious. | Alice is generous. | neutral | (![X]:((wise(X)&~old(X))=>(~generous(X)&generous(X))))&
(![X]:(~kind(X)<=>(~humble(X)&curious(X))))&
(((~brave(susan)|calm(susan)))<=>(?[X]:(~brave(X))))&
(![X]:((funny(X)|~creative(X))=>(brave(X)|~brave(X))))&
((?[X]:((~funny(X)|tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|~strong(X))=>(creative(X)|~strong(X))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|~patient(X))=>(calm(X)&~patient(X))))&
((?[X]:((~tall(X)&~strong(X))))<=>((kind(alice)<~>~generous(alice))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)&~rich(X))=>(happy(X)|~tall(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(patient(X)))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((~quiet(X)&generous(X))))&
((rich(paul)<~>~curious(paul)))&
((happy(paul)<~>curious(paul))) | generous(alice) | [] | null | 0 |
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