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 someone is both not rich and not generous then paul is patient or not rich and vice versa.
Everyone who is both patient and not kind is both not strong and curious and vice versa.
Everyone who is both happy and not humble is either not happy or not kind and vice versa.
If someone is not calm or calm then fred is both old and not creative and vice versa.
Everyone who is both not patient and funny is both curious and strong and vice versa.
Everyone who is not funny is both funny and not brave.
Everyone who is not wise is not rich or generous and vice versa.
Everyone who is both brave and not patient is happy.
Everyone who is not wise is calm.
If someone is humble or not quiet then someone is both not generous and not strong and vice versa.
Everyone who is either patient or not humble is funny or rich.
Everyone who is not wise is strong.
Everyone who is not humble is either not wise or wise.
Everyone who is both funny and old is both not strong and not generous.
If someone is both not generous and not funny then lucy is not creative.
Everyone who is either humble or not strong is both not quiet and rich and vice versa.
Lucy is both not generous and patient.
Alice is not humble or tall.
Susan is patient.
Someone is not generous.
Someone is rich or not wise.
Alice is not creative. | Paul is not curious. | neutral | ((?[X]:((~rich(X)&~generous(X))))<=>((patient(paul)|~rich(paul))))&
(![X]:((patient(X)&~kind(X))<=>(~strong(X)&curious(X))))&
(![X]:((happy(X)&~humble(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:((~calm(X)|calm(X))))<=>((old(fred)&~creative(fred))))&
(![X]:((~patient(X)&funny(X))<=>(curious(X)&strong(X))))&
(![X]:(~funny(X)=>(funny(X)&~brave(X))))&
(![X]:(~wise(X)<=>(~rich(X)|generous(X))))&
(![X]:((brave(X)&~patient(X))=>happy(X)))&
(![X]:(~wise(X)=>calm(X)))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((patient(X)<~>~humble(X))=>(funny(X)|rich(X))))&
(![X]:(~wise(X)=>strong(X)))&
(![X]:(~humble(X)=>(~wise(X)<~>wise(X))))&
(![X]:((funny(X)&old(X))=>(~strong(X)&~generous(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(~creative(lucy)))&
(![X]:((humble(X)<~>~strong(X))<=>(~quiet(X)&rich(X))))&
((~generous(lucy)&patient(lucy)))&
((~humble(alice)|tall(alice)))&
(patient(susan))&
(?[X]:(~generous(X)))&
(?[X]:((rich(X)|~wise(X))))&
(~creative(alice)) | ~curious(paul) | [] | null | 0 |
Everyone who is either kind or rich is tall or not strong and vice versa. If someone is not happy or not curious then john is not humble. If someone is not rich then someone is either tall or not wise. Everyone who is either happy or curious is creative and vice versa. Everyone who is both not creative and humble is both not old and curious and vice versa. If someone is not happy or not kind then john is both generous and not quiet. Everyone who is not wise is not patient or happy. Everyone who is curious or not strong is either not old or wise. Everyone who is wise or not wise is both not curious and not wise. Everyone who is not strong is not quiet or not rich and vice versa. If paul is creative then someone is both rich and curious. Everyone who is both not generous and old is patient or funny and vice versa. If mary is either brave or not funny then someone is kind or not funny and vice versa. Everyone who is humble or not curious is both calm and generous. Everyone who is either not old or not funny is both kind and not patient. Someone is not kind or calm. Someone is either not old or funny. Alice is either creative or not calm. Someone is either brave or quiet. Lucy is not wise or not strong. Susan is not curious. | Paul is not old. | neutral | (![X]:((kind(X)<~>rich(X))<=>(tall(X)|~strong(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~rich(X))))&
((creative(paul))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~generous(X)&old(X))<=>(patient(X)|funny(X))))&
(((brave(mary)<~>~funny(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((humble(X)|~curious(X))=>(calm(X)&generous(X))))&
(![X]:((~old(X)<~>~funny(X))=>(kind(X)&~patient(X))))&
(?[X]:((~kind(X)|calm(X))))&
(?[X]:((~old(X)<~>funny(X))))&
((creative(alice)<~>~calm(alice)))&
(?[X]:((brave(X)<~>quiet(X))))&
((~wise(lucy)|~strong(lucy)))&
(~curious(susan)) | ~old(paul) | [] | null | 0 |
If alice is funny then someone is old or not happy. If someone is calm then fred is either not rich or not calm. Everyone who is not brave or strong is either not strong or patient and vice versa. Everyone who is both not creative and not humble is either quiet or old. If paul is both happy and not funny then someone is either tall or strong and vice versa. If alice is either quiet or not strong then someone is both not calm and old. If someone is not generous then john is both tall and generous and vice versa. Everyone who is not curious is either old or not funny. If lucy is patient or not strong then someone is either rich or curious. Everyone who is either happy or not patient is rich. If fred is both creative and kind then someone is either generous or not strong and vice versa. If someone is either not old or not funny then lucy is either not happy or not brave. Everyone who is either calm or not rich is not creative and vice versa. Everyone who is curious or calm is happy or rich. If john is rich or not humble then lucy is both not creative and not calm. If someone is not funny or old then lucy is calm or brave. John is both humble and not curious. Alice is either not humble or tall. Susan is not brave. Someone is either not kind or tall. Fred is patient or curious. Alice is either not brave or tall. Someone is not patient or old. Someone is curious or not brave. | Susan is brave. | contradiction | ((funny(alice))=>(?[X]:((old(X)|~happy(X)))))&
((?[X]:(calm(X)))=>((~rich(fred)<~>~calm(fred))))&
(![X]:((~brave(X)|strong(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~creative(X)&~humble(X))=>(quiet(X)<~>old(X))))&
(((happy(paul)&~funny(paul)))<=>(?[X]:((tall(X)<~>strong(X)))))&
(((quiet(alice)<~>~strong(alice)))=>(?[X]:((~calm(X)&old(X)))))&
((?[X]:(~generous(X)))<=>((tall(john)&generous(john))))&
(![X]:(~curious(X)=>(old(X)<~>~funny(X))))&
(((patient(lucy)|~strong(lucy)))=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((happy(X)<~>~patient(X))=>rich(X)))&
(((creative(fred)&kind(fred)))<=>(?[X]:((generous(X)<~>~strong(X)))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~happy(lucy)<~>~brave(lucy))))&
(![X]:((calm(X)<~>~rich(X))<=>~creative(X)))&
(![X]:((curious(X)|calm(X))=>(happy(X)|rich(X))))&
(((rich(john)|~humble(john)))=>((~creative(lucy)&~calm(lucy))))&
((?[X]:((~funny(X)|old(X))))=>((calm(lucy)|brave(lucy))))&
((humble(john)&~curious(john)))&
((~humble(alice)<~>tall(alice)))&
(~brave(susan))&
(?[X]:((~kind(X)<~>tall(X))))&
((patient(fred)|curious(fred)))&
((~brave(alice)<~>tall(alice)))&
(?[X]:((~patient(X)|old(X))))&
(?[X]:((curious(X)|~brave(X)))) | brave(susan) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 857989642744187198483540
% SZS output start Proof for 857989642744187198483540
19. ~brave(susan) [input p18]
25. brave(susan) [input hypothesis]
138. ~brave(susan) [cnf transformation 19]
146. brave(susan) [cnf transformation 25]
389. $false [subsumption resolution 146,138]
% SZS output end Proof for 857989642744187198483540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is both quiet and not tall.
Everyone who is not curious is not kind or creative.
Everyone who is not curious or rich is either not curious or humble.
Everyone who is happy is not happy.
Everyone who is calm or tall is either funny or not humble and vice versa.
If someone is either not happy or not generous then fred is creative and vice versa.
Everyone who is not humble or not happy is either kind or not old.
If someone is rich or not strong then someone is not funny and vice versa.
Everyone who is quiet or not creative is either not calm or humble and vice versa.
If john is happy or kind then someone is either happy or not strong.
Everyone who is either kind or not happy is both generous and wise and vice versa.
Everyone who is both not quiet and not old is both strong and not curious and vice versa.
If fred is humble or tall then someone is both happy and not generous.
Everyone who is either not strong or not tall is happy or curious.
Everyone who is funny or not happy is funny or creative and vice versa.
If fred is both generous and wise then paul is either not creative or patient.
Someone is old.
Alice is both not creative and old.
Someone is happy or not patient.
Someone is both brave and not wise.
Lucy is either tall or funny.
Alice is brave or humble. | Paul is not funny. | neutral | ((?[X]:(generous(X)))=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:(~curious(X)=>(~kind(X)|creative(X))))&
(![X]:((~curious(X)|rich(X))=>(~curious(X)<~>humble(X))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((calm(X)|tall(X))<=>(funny(X)<~>~humble(X))))&
((?[X]:((~happy(X)<~>~generous(X))))<=>(creative(fred)))&
(![X]:((~humble(X)|~happy(X))=>(kind(X)<~>~old(X))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)<~>humble(X))))&
(((happy(john)|kind(john)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:((kind(X)<~>~happy(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(strong(X)&~curious(X))))&
(((humble(fred)|tall(fred)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))<=>(funny(X)|creative(X))))&
(((generous(fred)&wise(fred)))=>((~creative(paul)<~>patient(paul))))&
(?[X]:(old(X)))&
((~creative(alice)&old(alice)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((brave(X)&~wise(X))))&
((tall(lucy)<~>funny(lucy)))&
((brave(alice)|humble(alice))) | ~funny(paul) | [] | null | 0 |
Everyone who is not humble or not funny is both old and not rich and vice versa.
Everyone who is both not wise and not creative is either not creative or calm.
Everyone who is either not old or not funny is both brave and creative and vice versa.
Everyone who is both not calm and not creative is either funny or not creative.
Everyone who is either not rich or not brave is either not tall or brave.
If alice is happy or not brave then fred is either wise or creative.
Everyone who is both not creative and not patient is tall and vice versa.
Everyone who is either not happy or not patient is both not calm and not brave.
Everyone who is either not generous or humble is patient and vice versa.
If fred is both kind and curious then someone is not humble.
Everyone who is not tall is both not funny and not humble and vice versa.
Everyone who is both curious and not funny is not humble or humble.
If alice is either curious or generous then someone is not patient and vice versa.
If someone is either not generous or not calm then someone is not patient or not brave.
Everyone who is either kind or humble is either tall or not funny.
If alice is both not calm and creative then someone is not calm or not generous.
Someone is both kind and not patient.
Someone is either not curious or not humble.
Someone is not wise or calm.
Alice is either not wise or strong.
Fred is either not rich or not creative.
Fred is generous or tall. | Fred is not calm. | contradiction | (![X]:((~humble(X)|~funny(X))<=>(old(X)&~rich(X))))&
(![X]:((~wise(X)&~creative(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(brave(X)&creative(X))))&
(![X]:((~calm(X)&~creative(X))=>(funny(X)<~>~creative(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(~tall(X)<~>brave(X))))&
(((happy(alice)|~brave(alice)))=>((wise(fred)<~>creative(fred))))&
(![X]:((~creative(X)&~patient(X))<=>tall(X)))&
(![X]:((~happy(X)<~>~patient(X))=>(~calm(X)&~brave(X))))&
(![X]:((~generous(X)<~>humble(X))<=>patient(X)))&
(((kind(fred)&curious(fred)))=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)<=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&~funny(X))=>(~humble(X)|humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((kind(X)<~>humble(X))=>(tall(X)<~>~funny(X))))&
(((~calm(alice)&creative(alice)))=>(?[X]:((~calm(X)|~generous(X)))))&
(?[X]:((kind(X)&~patient(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((~wise(X)|calm(X))))&
((~wise(alice)<~>strong(alice)))&
((~rich(fred)<~>~creative(fred)))&
((generous(fred)|tall(fred))) | ~calm(fred) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6212732077415002573599082
% SZS output start Proof for 6212732077415002573599082
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~rich(X0) & old(X0))) [input p0]
3. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> (creative(X0) & brave(X0))) [input p2]
4. ! [X0] : ((~creative(X0) & ~calm(X0)) => (funny(X0) <~> ~creative(X0))) [input p3]
5. ! [X0] : ((~rich(X0) <~> ~brave(X0)) => (~tall(X0) <~> brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> tall(X0)) [input p6]
11. ! [X0] : (~tall(X0) <=> (~humble(X0) & ~funny(X0))) [input p10]
21. ~rich(fred) <~> ~creative(fred) [input p20]
23. ~calm(fred) [input hypothesis]
27. ! [X0] : ((funny(X0) <~> ~creative(X0)) | (creative(X0) | calm(X0))) [ennf transformation 4]
28. ! [X0] : ((funny(X0) <~> ~creative(X0)) | creative(X0) | calm(X0)) [flattening 27]
29. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~rich(X0) <=> ~brave(X0))) [ennf transformation 5]
40. ! [X0] : (((~funny(X0) | ~humble(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((~funny(X0) | ~humble(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (funny(X0) & humble(X0)))) [flattening 40]
43. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 3]
44. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [flattening 43]
45. ! [X0] : (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | creative(X0) | calm(X0)) [nnf transformation 28]
46. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0)))) [nnf transformation 29]
48. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (patient(X0) | creative(X0)))) [nnf transformation 7]
49. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | patient(X0) | creative(X0))) [flattening 48]
54. ! [X0] : ((~tall(X0) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [nnf transformation 11]
55. ! [X0] : ((~tall(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [flattening 54]
75. (creative(fred) | rich(fred)) & (~creative(fred) | ~rich(fred)) [nnf transformation 21]
77. old(X0) | funny(X0) [cnf transformation 41]
84. brave(X0) | ~old(X0) | funny(X0) [cnf transformation 44]
86. creative(X0) | ~old(X0) | funny(X0) [cnf transformation 44]
90. creative(X0) | ~funny(X0) | creative(X0) | calm(X0) [cnf transformation 45]
93. ~brave(X0) | tall(X0) | ~brave(X0) | rich(X0) [cnf transformation 46]
100. ~tall(X0) | ~creative(X0) [cnf transformation 49]
111. ~funny(X0) | tall(X0) [cnf transformation 55]
133. ~creative(fred) | ~rich(fred) [cnf transformation 75]
136. ~calm(fred) [cnf transformation 23]
138. ~brave(X0) | tall(X0) | rich(X0) [duplicate literal removal 93]
139. creative(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 90]
141. creative(X0) | funny(X0) [subsumption resolution 86,77]
143. brave(X0) | funny(X0) [subsumption resolution 84,77]
145. calm(X0) | creative(X0) [subsumption resolution 139,141]
155. 3 <=> creative(fred) [avatar definition]
156. creative(fred) <- (3) [avatar component clause 155]
259. 25 <=> rich(fred) [avatar definition]
260. ~rich(fred) <- (~25) [avatar component clause 259]
263. ~25 | ~3 [avatar split clause 133,155,259]
275. creative(fred) [resolution 145,136]
381. tall(X1) | rich(X1) | funny(X1) [resolution 138,143]
383. tall(X1) | rich(X1) [subsumption resolution 381,111]
429. ~creative(X3) | rich(X3) [resolution 383,100]
502. rich(fred) <- (3) [resolution 429,156]
506. $false <- (3, ~25) [subsumption resolution 502,260]
507. ~3 | 25 [avatar contradiction clause 506]
509. 3 [avatar split clause 275,155]
510. $false [avatar sat refutation 263,507,509]
% SZS output end Proof for 6212732077415002573599082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then someone is generous or not funny.
Everyone who is both not patient and brave is both not rich and tall.
If susan is both funny and kind then someone is creative and vice versa.
Everyone who is either happy or quiet is brave or old and vice versa.
If mary is either not rich or not calm then mary is not tall and vice versa.
Everyone who is both humble and not generous is happy or not wise.
If someone is not tall or creative then someone is not tall.
Everyone who is not old or not quiet is both creative and calm and vice versa.
Everyone who is both calm and not wise is either not curious or not strong and vice versa.
Everyone who is either not humble or not creative is either old or not tall.
Everyone who is both generous and quiet is not curious.
If mary is both not wise and rich then someone is strong.
Everyone who is either not calm or wise is not old and vice versa.
Everyone who is both funny and not wise is either not wise or rich.
If paul is generous or not wise then alice is either kind or wise and vice versa.
If mary is either tall or old then fred is humble and vice versa.
Susan is humble or rich.
Someone is both not patient and creative.
Someone is not kind.
Susan is both not curious and generous.
Susan is not creative.
Lucy is old.
Someone is both not kind and not curious.
Fred is tall or not strong. | Susan is rich. | neutral | ((?[X]:(~kind(X)))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((~patient(X)&brave(X))=>(~rich(X)&tall(X))))&
(((funny(susan)&kind(susan)))<=>(?[X]:(creative(X))))&
(![X]:((happy(X)<~>quiet(X))<=>(brave(X)|old(X))))&
(((~rich(mary)<~>~calm(mary)))<=>(~tall(mary)))&
(![X]:((humble(X)&~generous(X))=>(happy(X)|~wise(X))))&
((?[X]:((~tall(X)|creative(X))))=>(?[X]:(~tall(X))))&
(![X]:((~old(X)|~quiet(X))<=>(creative(X)&calm(X))))&
(![X]:((calm(X)&~wise(X))<=>(~curious(X)<~>~strong(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(old(X)<~>~tall(X))))&
(![X]:((generous(X)&quiet(X))=>~curious(X)))&
(((~wise(mary)&rich(mary)))=>(?[X]:(strong(X))))&
(![X]:((~calm(X)<~>wise(X))<=>~old(X)))&
(![X]:((funny(X)&~wise(X))=>(~wise(X)<~>rich(X))))&
(((generous(paul)|~wise(paul)))<=>((kind(alice)<~>wise(alice))))&
(((tall(mary)<~>old(mary)))<=>(humble(fred)))&
((humble(susan)|rich(susan)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:(~kind(X)))&
((~curious(susan)&generous(susan)))&
(~creative(susan))&
(old(lucy))&
(?[X]:((~kind(X)&~curious(X))))&
((tall(fred)|~strong(fred))) | rich(susan) | [] | null | 0 |
If someone is either creative or not wise then someone is happy and vice versa. Everyone who is not calm or not brave is kind or funny. Everyone who is not patient is either not humble or quiet. Everyone who is not strong is happy and vice versa. Everyone who is wise or brave is both curious and patient. If someone is both not generous and happy then someone is either not patient or rich. If lucy is either not old or rich then lucy is not strong or generous and vice versa. If someone is calm or not curious then lucy is either not strong or not quiet and vice versa. If paul is not wise or not patient then someone is not funny or not kind. If someone is not funny or humble then lucy is either brave or not brave. If someone is either old or not calm then john is not patient. Everyone who is both happy and wise is wise or not brave and vice versa. If someone is rich or quiet then fred is quiet. If alice is not curious or not brave then someone is not happy or not calm. If susan is happy or not humble then susan is tall or not curious and vice versa. If john is happy or not generous then fred is strong or humble. Someone is humble or brave. Susan is both brave and not happy. Someone is both strong and humble. Someone is not brave or rich. Someone is kind or not quiet. Someone is both wise and happy. Someone is both creative and generous. Someone is not quiet. | Lucy is not patient. | contradiction | ((?[X]:((creative(X)<~>~wise(X))))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|~brave(X))=>(kind(X)|funny(X))))&
(![X]:(~patient(X)=>(~humble(X)<~>quiet(X))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:((wise(X)|brave(X))=>(curious(X)&patient(X))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(((~old(lucy)<~>rich(lucy)))<=>((~strong(lucy)|generous(lucy))))&
((?[X]:((calm(X)|~curious(X))))<=>((~strong(lucy)<~>~quiet(lucy))))&
(((~wise(paul)|~patient(paul)))=>(?[X]:((~funny(X)|~kind(X)))))&
((?[X]:((~funny(X)|humble(X))))=>((brave(lucy)<~>~brave(lucy))))&
((?[X]:((old(X)<~>~calm(X))))=>(~patient(john)))&
(![X]:((happy(X)&wise(X))<=>(wise(X)|~brave(X))))&
((?[X]:((rich(X)|quiet(X))))=>(quiet(fred)))&
(((~curious(alice)|~brave(alice)))=>(?[X]:((~happy(X)|~calm(X)))))&
(((happy(susan)|~humble(susan)))<=>((tall(susan)|~curious(susan))))&
(((happy(john)|~generous(john)))=>((strong(fred)|humble(fred))))&
(?[X]:((humble(X)|brave(X))))&
((brave(susan)&~happy(susan)))&
(?[X]:((strong(X)&humble(X))))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:((kind(X)|~quiet(X))))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:(~quiet(X))) | ~patient(lucy) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7314264857600285441284752
% SZS output start Proof for 7314264857600285441284752
5. ! [X0] : ((brave(X0) | wise(X0)) => (patient(X0) & curious(X0))) [input p4]
12. ! [X0] : ((wise(X0) & happy(X0)) <=> (~brave(X0) | wise(X0))) [input p11]
25. ~patient(lucy) [input hypothesis]
31. ! [X0] : ((patient(X0) & curious(X0)) | (~brave(X0) & ~wise(X0))) [ennf transformation 5]
61. ! [X0] : (((wise(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | (~wise(X0) | ~happy(X0)))) [nnf transformation 12]
62. ! [X0] : (((wise(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | ~wise(X0) | ~happy(X0))) [flattening 61]
93. ~wise(X0) | patient(X0) [cnf transformation 31]
94. ~brave(X0) | patient(X0) [cnf transformation 31]
121. brave(X0) | wise(X0) [cnf transformation 62]
144. ~patient(lucy) [cnf transformation 25]
370. wise(X0) | patient(X0) [resolution 121,94]
372. patient(X0) [subsumption resolution 370,93]
386. $false [resolution 372,144]
% SZS output end Proof for 7314264857600285441284752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is wise or not tall then someone is both happy and generous and vice versa.
If paul is either patient or quiet then someone is both old and not quiet.
If alice is both wise and generous then someone is not humble.
If paul is generous or tall then someone is either strong or quiet and vice versa.
If mary is not strong or not funny then alice is either not brave or not kind.
Everyone who is not creative is either not patient or not calm.
If someone is not strong then john is quiet.
If fred is not strong or funny then paul is not rich and vice versa.
Everyone who is not rich or old is either generous or rich.
If alice is kind or not old then fred is humble and vice versa.
Everyone who is curious is both tall and not strong.
Everyone who is not rich or humble is not humble and vice versa.
If someone is not generous or creative then alice is not strong or not curious and vice versa.
Everyone who is not wise is not creative and vice versa.
Everyone who is not curious is both strong and tall and vice versa.
Everyone who is kind or not quiet is either not funny or not creative.
John is both tall and quiet.
Someone is both curious and calm.
Someone is tall.
Someone is both patient and not curious.
Mary is calm or not happy.
Someone is both not patient and strong. | Mary is not happy. | neutral | (((wise(alice)|~tall(alice)))<=>(?[X]:((happy(X)&generous(X)))))&
(((patient(paul)<~>quiet(paul)))=>(?[X]:((old(X)&~quiet(X)))))&
(((wise(alice)&generous(alice)))=>(?[X]:(~humble(X))))&
(((generous(paul)|tall(paul)))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(((~strong(mary)|~funny(mary)))=>((~brave(alice)<~>~kind(alice))))&
(![X]:(~creative(X)=>(~patient(X)<~>~calm(X))))&
((?[X]:(~strong(X)))=>(quiet(john)))&
(((~strong(fred)|funny(fred)))<=>(~rich(paul)))&
(![X]:((~rich(X)|old(X))=>(generous(X)<~>rich(X))))&
(((kind(alice)|~old(alice)))<=>(humble(fred)))&
(![X]:(curious(X)=>(tall(X)&~strong(X))))&
(![X]:((~rich(X)|humble(X))<=>~humble(X)))&
((?[X]:((~generous(X)|creative(X))))<=>((~strong(alice)|~curious(alice))))&
(![X]:(~wise(X)<=>~creative(X)))&
(![X]:(~curious(X)<=>(strong(X)&tall(X))))&
(![X]:((kind(X)|~quiet(X))=>(~funny(X)<~>~creative(X))))&
((tall(john)&quiet(john)))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:(tall(X)))&
(?[X]:((patient(X)&~curious(X))))&
((calm(mary)|~happy(mary)))&
(?[X]:((~patient(X)&strong(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is either happy or not quiet is strong or not quiet and vice versa. Everyone who is either happy or not old is either not calm or creative and vice versa. Everyone who is either quiet or strong is not brave or wise. Everyone who is not happy is both happy and curious and vice versa. Everyone who is both not funny and patient is not generous or not creative. If john is brave or rich then someone is not kind. Everyone who is strong or old is either not patient or not quiet and vice versa. Everyone who is patient is quiet or not calm. Everyone who is both not quiet and not brave is kind or generous and vice versa. If someone is curious then someone is not old. Everyone who is either not brave or patient is not strong. Everyone who is both patient and not patient is humble and vice versa. If fred is calm then fred is strong or not old. Everyone who is either not old or not creative is both brave and not generous. Everyone who is either patient or creative is either brave or generous and vice versa. Someone is old. Someone is wise. Someone is rich. Mary is not funny or tall. | John is generous. | contradiction | (![X]:((happy(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)<~>~old(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~brave(X)|wise(X))))&
(![X]:(~happy(X)<=>(happy(X)&curious(X))))&
(![X]:((~funny(X)&patient(X))=>(~generous(X)|~creative(X))))&
(((brave(john)|rich(john)))=>(?[X]:(~kind(X))))&
(![X]:((strong(X)|old(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(patient(X)=>(quiet(X)|~calm(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(kind(X)|generous(X))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)<~>patient(X))=>~strong(X)))&
(![X]:((patient(X)&~patient(X))<=>humble(X)))&
((calm(fred))=>((strong(fred)|~old(fred))))&
(![X]:((~old(X)<~>~creative(X))=>(brave(X)&~generous(X))))&
(![X]:((patient(X)<~>creative(X))<=>(brave(X)<~>generous(X))))&
(?[X]:(old(X)))&
(?[X]:(wise(X)))&
(?[X]:(rich(X)))&
((~funny(mary)|tall(mary))) | generous(john) | [
"p0",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8411458693460024009756912
% SZS output start Proof for 8411458693460024009756912
1. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (~quiet(X0) | strong(X0))) [input p0]
4. ! [X0] : (~happy(X0) <=> (curious(X0) & happy(X0))) [input p3]
9. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (generous(X0) | kind(X0))) [input p8]
20. generous(john) [input hypothesis]
34. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 1]
35. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 34]
37. ! [X0] : ((~happy(X0) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | happy(X0))) [nnf transformation 4]
38. ! [X0] : ((~happy(X0) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | happy(X0))) [flattening 37]
43. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (~generous(X0) & ~kind(X0))) & ((generous(X0) | kind(X0)) | (brave(X0) | quiet(X0)))) [nnf transformation 9]
44. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (~generous(X0) & ~kind(X0))) & (generous(X0) | kind(X0) | brave(X0) | quiet(X0))) [flattening 43]
60. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 35]
69. happy(X0) | happy(X0) [cnf transformation 38]
83. ~generous(X0) | ~quiet(X0) [cnf transformation 44]
104. generous(john) [cnf transformation 20]
105. happy(X0) [duplicate literal removal 69]
108. ~happy(X0) | quiet(X0) [duplicate literal removal 60]
149. ~quiet(john) [resolution 83,104]
153. quiet(X0) [resolution 108,105]
154. $false [resolution 153,149]
% SZS output end Proof for 8411458693460024009756912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is tall then someone is creative or rich.
Everyone who is kind or not happy is either strong or happy.
If lucy is not funny or not humble then susan is both not humble and not calm and vice versa.
If someone is creative or kind then paul is either generous or curious and vice versa.
Everyone who is curious is either not wise or not creative and vice versa.
If mary is not quiet or tall then mary is not creative or not tall and vice versa.
If someone is patient or not curious then paul is not happy and vice versa.
Everyone who is generous or not funny is kind or not patient.
If someone is either not generous or not funny then lucy is curious.
If someone is not funny or not calm then fred is curious.
If lucy is not rich then mary is funny or not curious and vice versa.
If fred is not rich then someone is either rich or not happy.
Everyone who is both rich and not kind is creative or brave and vice versa.
If someone is both not wise and brave then someone is creative or wise.
Everyone who is not creative or funny is generous or not generous.
If paul is happy or not brave then lucy is not happy and vice versa.
Someone is calm.
Alice is both not kind and curious.
Lucy is both not kind and generous.
Susan is either not strong or strong.
John is not calm.
Someone is either calm or not funny.
Lucy is not strong.
Lucy is not kind. | Paul is strong. | entailment | ((tall(mary))=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((kind(X)|~happy(X))=>(strong(X)<~>happy(X))))&
(((~funny(lucy)|~humble(lucy)))<=>((~humble(susan)&~calm(susan))))&
((?[X]:((creative(X)|kind(X))))<=>((generous(paul)<~>curious(paul))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
(((~quiet(mary)|tall(mary)))<=>((~creative(mary)|~tall(mary))))&
((?[X]:((patient(X)|~curious(X))))<=>(~happy(paul)))&
(![X]:((generous(X)|~funny(X))=>(kind(X)|~patient(X))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(curious(lucy)))&
((?[X]:((~funny(X)|~calm(X))))=>(curious(fred)))&
((~rich(lucy))<=>((funny(mary)|~curious(mary))))&
((~rich(fred))=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((rich(X)&~kind(X))<=>(creative(X)|brave(X))))&
((?[X]:((~wise(X)&brave(X))))=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~creative(X)|funny(X))=>(generous(X)|~generous(X))))&
(((happy(paul)|~brave(paul)))<=>(~happy(lucy)))&
(?[X]:(calm(X)))&
((~kind(alice)&curious(alice)))&
((~kind(lucy)&generous(lucy)))&
((~strong(susan)<~>strong(susan)))&
(~calm(john))&
(?[X]:((calm(X)<~>~funny(X))))&
(~strong(lucy))&
(~kind(lucy)) | strong(paul) | [
"p1",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2401576447485656462969542
% SZS output start Proof for 2401576447485656462969542
2. ! [X0] : ((~happy(X0) | kind(X0)) => (strong(X0) <~> happy(X0))) [input p1]
16. (~brave(paul) | happy(paul)) <=> ~happy(lucy) [input p15]
23. ~strong(lucy) [input p22]
25. ~strong(paul) [input hypothesis]
28. ! [X0] : ((strong(X0) <~> happy(X0)) | (happy(X0) & ~kind(X0))) [ennf transformation 2]
39. ! [X0] : (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (happy(X0) & ~kind(X0))) [nnf transformation 28]
64. ((~brave(paul) | happy(paul)) | happy(lucy)) & (~happy(lucy) | (brave(paul) & ~happy(paul))) [nnf transformation 16]
65. (~brave(paul) | happy(paul) | happy(lucy)) & (~happy(lucy) | (brave(paul) & ~happy(paul))) [flattening 64]
74. happy(X0) | strong(X0) | happy(X0) [cnf transformation 39]
118. ~happy(lucy) | ~happy(paul) [cnf transformation 65]
131. ~strong(lucy) [cnf transformation 23]
133. ~strong(paul) [cnf transformation 25]
136. strong(X0) | happy(X0) [duplicate literal removal 74]
212. 16 <=> happy(paul) [avatar definition]
213. ~happy(paul) <- (~16) [avatar component clause 212]
298. 36 <=> happy(lucy) [avatar definition]
299. ~happy(lucy) <- (~36) [avatar component clause 298]
307. ~16 | ~36 [avatar split clause 118,298,212]
319. happy(lucy) [resolution 136,131]
320. happy(paul) [resolution 136,133]
321. $false <- (~36) [subsumption resolution 319,299]
322. 36 [avatar contradiction clause 321]
323. $false <- (~16) [subsumption resolution 320,213]
324. 16 [avatar contradiction clause 323]
325. $false [avatar sat refutation 307,322,324]
% SZS output end Proof for 2401576447485656462969542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is wise or creative then lucy is both calm and not brave. Everyone who is not strong or not curious is either not tall or not brave. If susan is both happy and calm then paul is creative. If someone is patient or not curious then someone is not old or patient. Everyone who is both quiet and rich is not creative and vice versa. If susan is brave then john is not kind or wise. Everyone who is both humble and not calm is calm and vice versa. Everyone who is either not wise or not old is not old or not funny and vice versa. If someone is either old or not funny then someone is either not calm or happy and vice versa. Everyone who is brave is not rich or not curious and vice versa. Everyone who is either happy or humble is either strong or tall and vice versa. Everyone who is both curious and not humble is either funny or patient and vice versa. Everyone who is not patient or not happy is not old and vice versa. If paul is creative or not patient then mary is humble and vice versa. Someone is both curious and not strong. Someone is both not brave and not happy. Fred is both not curious and generous. Someone is both not calm and wise. Someone is either funny or not strong. Someone is either not patient or not wise. Someone is generous or funny. | Alice is not generous. | neutral | (((wise(alice)|creative(alice)))=>((calm(lucy)&~brave(lucy))))&
(![X]:((~strong(X)|~curious(X))=>(~tall(X)<~>~brave(X))))&
(((happy(susan)&calm(susan)))=>(creative(paul)))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((quiet(X)&rich(X))<=>~creative(X)))&
((brave(susan))=>((~kind(john)|wise(john))))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~old(X)|~funny(X))))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(brave(X)<=>(~rich(X)|~curious(X))))&
(![X]:((happy(X)<~>humble(X))<=>(strong(X)<~>tall(X))))&
(![X]:((curious(X)&~humble(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~patient(X)|~happy(X))<=>~old(X)))&
(((creative(paul)|~patient(paul)))<=>(humble(mary)))&
(?[X]:((curious(X)&~strong(X))))&
(?[X]:((~brave(X)&~happy(X))))&
((~curious(fred)&generous(fred)))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((generous(X)|funny(X)))) | ~generous(alice) | [] | null | 0 |
If someone is both not quiet and not happy then someone is brave or not creative and vice versa.
Everyone who is both not patient and not creative is either tall or generous.
If mary is not rich then mary is both not tall and not brave and vice versa.
Everyone who is both not kind and not wise is tall.
Everyone who is either patient or funny is either curious or not humble.
If alice is humble then paul is not rich or happy and vice versa.
If someone is either calm or old then john is both not happy and not quiet.
If paul is not kind or calm then john is calm or not happy.
Everyone who is both tall and not old is not rich and vice versa.
Everyone who is not funny is kind or happy and vice versa.
Everyone who is not tall or not patient is either calm or brave.
Everyone who is either patient or not humble is not old or not kind.
If alice is not old then susan is wise or rich.
Everyone who is old or kind is not curious or not brave and vice versa.
Everyone who is generous is not calm.
Everyone who is both not wise and calm is either happy or calm and vice versa.
Lucy is either not humble or generous.
Susan is either not funny or not curious.
Someone is curious or not old.
Mary is not happy.
Fred is both not brave and not happy.
Susan is both kind and not generous.
Someone is both not strong and calm.
Someone is either old or wise. | Fred is not brave. | entailment | ((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((~patient(X)&~creative(X))=>(tall(X)<~>generous(X))))&
((~rich(mary))<=>((~tall(mary)&~brave(mary))))&
(![X]:((~kind(X)&~wise(X))=>tall(X)))&
(![X]:((patient(X)<~>funny(X))=>(curious(X)<~>~humble(X))))&
((humble(alice))<=>((~rich(paul)|happy(paul))))&
((?[X]:((calm(X)<~>old(X))))=>((~happy(john)&~quiet(john))))&
(((~kind(paul)|calm(paul)))=>((calm(john)|~happy(john))))&
(![X]:((tall(X)&~old(X))<=>~rich(X)))&
(![X]:(~funny(X)<=>(kind(X)|happy(X))))&
(![X]:((~tall(X)|~patient(X))=>(calm(X)<~>brave(X))))&
(![X]:((patient(X)<~>~humble(X))=>(~old(X)|~kind(X))))&
((~old(alice))=>((wise(susan)|rich(susan))))&
(![X]:((old(X)|kind(X))<=>(~curious(X)|~brave(X))))&
(![X]:(generous(X)=>~calm(X)))&
(![X]:((~wise(X)&calm(X))<=>(happy(X)<~>calm(X))))&
((~humble(lucy)<~>generous(lucy)))&
((~funny(susan)<~>~curious(susan)))&
(?[X]:((curious(X)|~old(X))))&
(~happy(mary))&
((~brave(fred)&~happy(fred)))&
((kind(susan)&~generous(susan)))&
(?[X]:((~strong(X)&calm(X))))&
(?[X]:((old(X)<~>wise(X)))) | ~brave(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1720517795801837011465103
% SZS output start Proof for 1720517795801837011465103
21. ~happy(fred) & ~brave(fred) [input p20]
25. brave(fred) [input hypothesis]
127. ~brave(fred) [cnf transformation 21]
134. brave(fred) [cnf transformation 25]
282. $false [subsumption resolution 134,127]
% SZS output end Proof for 1720517795801837011465103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then lucy is old or not humble and vice versa.
If john is either quiet or curious then mary is both not funny and generous.
Everyone who is either not tall or old is happy.
If someone is either brave or curious then paul is either curious or generous and vice versa.
If someone is both creative and old then lucy is not kind.
Everyone who is not curious is both not funny and quiet.
Everyone who is quiet or tall is both brave and creative.
If someone is either happy or not calm then someone is brave or not creative.
If someone is not happy or not calm then someone is both brave and strong and vice versa.
If mary is not wise or not calm then someone is either not wise or old.
Everyone who is either generous or strong is both not patient and not quiet.
If someone is either funny or quiet then someone is both tall and not creative and vice versa.
Everyone who is both kind and curious is both not curious and not creative.
If someone is either curious or old then someone is either old or humble.
Everyone who is happy is either not curious or not kind.
If susan is either not curious or creative then mary is not creative.
Paul is not happy or not generous.
Mary is both strong and funny.
Someone is both not old and strong.
Someone is old or not quiet.
Lucy is tall.
Susan is not curious or not quiet.
Someone is not humble or quiet.
Someone is wise or patient. | John is brave. | entailment | ((?[X]:(~calm(X)))<=>((old(lucy)|~humble(lucy))))&
(((quiet(john)<~>curious(john)))=>((~funny(mary)&generous(mary))))&
(![X]:((~tall(X)<~>old(X))=>happy(X)))&
((?[X]:((brave(X)<~>curious(X))))<=>((curious(paul)<~>generous(paul))))&
((?[X]:((creative(X)&old(X))))=>(~kind(lucy)))&
(![X]:(~curious(X)=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(brave(X)&creative(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((brave(X)|~creative(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(((~wise(mary)|~calm(mary)))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((generous(X)<~>strong(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((funny(X)<~>quiet(X))))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((kind(X)&curious(X))=>(~curious(X)&~creative(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:(happy(X)=>(~curious(X)<~>~kind(X))))&
(((~curious(susan)<~>creative(susan)))=>(~creative(mary)))&
((~happy(paul)|~generous(paul)))&
((strong(mary)&funny(mary)))&
(?[X]:((~old(X)&strong(X))))&
(?[X]:((old(X)|~quiet(X))))&
(tall(lucy))&
((~curious(susan)|~quiet(susan)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((wise(X)|patient(X)))) | brave(john) | [
"p1",
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3358739308453350914201234
% SZS output start Proof for 3358739308453350914201234
2. (quiet(john) <~> curious(john)) => (generous(mary) & ~funny(mary)) [input p1]
6. ! [X0] : (~curious(X0) => (quiet(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((tall(X0) | quiet(X0)) => (creative(X0) & brave(X0))) [input p6]
18. funny(mary) & strong(mary) [input p17]
25. ~brave(john) [input hypothesis]
30. (generous(mary) & ~funny(mary)) | (quiet(john) <=> curious(john)) [ennf transformation 2]
33. ! [X0] : ((quiet(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 6]
34. ! [X0] : ((creative(X0) & brave(X0)) | (~tall(X0) & ~quiet(X0))) [ennf transformation 7]
48. (generous(mary) & ~funny(mary)) | ((quiet(john) | ~curious(john)) & (curious(john) | ~quiet(john))) [nnf transformation 30]
90. ~funny(mary) | quiet(john) | ~curious(john) [cnf transformation 48]
105. curious(X0) | quiet(X0) [cnf transformation 33]
106. ~quiet(X0) | brave(X0) [cnf transformation 34]
143. funny(mary) [cnf transformation 18]
151. ~brave(john) [cnf transformation 25]
172. 5 <=> curious(john) [avatar definition]
174. ~curious(john) <- (~5) [avatar component clause 172]
176. 6 <=> quiet(john) [avatar definition]
177. ~quiet(john) <- (~6) [avatar component clause 176]
178. quiet(john) <- (6) [avatar component clause 176]
186. 8 <=> funny(mary) [avatar definition]
189. ~5 | 6 | ~8 [avatar split clause 90,186,176,172]
347. 8 [avatar split clause 143,186]
389. quiet(john) <- (~5) [resolution 105,174]
392. $false <- (~5, ~6) [subsumption resolution 389,177]
393. 5 | 6 [avatar contradiction clause 392]
394. brave(john) <- (6) [resolution 106,178]
395. $false <- (6) [subsumption resolution 394,151]
396. ~6 [avatar contradiction clause 395]
397. $false [avatar sat refutation 189,347,393,396]
% SZS output end Proof for 3358739308453350914201234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not wise is both wise and calm and vice versa. If john is rich then someone is not tall and vice versa. If someone is both tall and not rich then someone is quiet or patient. Everyone who is not creative is both not quiet and brave. If mary is both creative and quiet then someone is both kind and humble and vice versa. If someone is not rich or not old then someone is either not funny or not brave. Everyone who is both not calm and wise is both not strong and curious and vice versa. If alice is both strong and old then susan is calm. Everyone who is both generous and not calm is not brave. Everyone who is either not kind or tall is either not strong or tall and vice versa. If someone is either tall or calm then john is either not creative or wise. If lucy is both not kind and not humble then fred is both not generous and not curious. Everyone who is either patient or tall is strong or not tall and vice versa. Everyone who is not quiet is not wise or not calm. Everyone who is either not wise or tall is both not rich and not quiet. If mary is calm or not curious then mary is not old. Lucy is both strong and not calm. Lucy is either old or tall. Someone is calm. Someone is both generous and not curious. Someone is either not wise or not strong. Someone is not humble or kind. Someone is not wise or calm. | Lucy is not humble. | neutral | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
((rich(john))<=>(?[X]:(~tall(X))))&
((?[X]:((tall(X)&~rich(X))))=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:(~creative(X)=>(~quiet(X)&brave(X))))&
(((creative(mary)&quiet(mary)))<=>(?[X]:((kind(X)&humble(X)))))&
((?[X]:((~rich(X)|~old(X))))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~calm(X)&wise(X))<=>(~strong(X)&curious(X))))&
(((strong(alice)&old(alice)))=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
((strong(lucy)&~calm(lucy)))&
((old(lucy)<~>tall(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((generous(X)&~curious(X))))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:((~wise(X)|calm(X)))) | ~humble(lucy) | [] | null | 0 |
Everyone who is both not brave and not generous is either not strong or generous.
If fred is not quiet or old then mary is quiet or humble.
Everyone who is tall is happy.
If fred is wise then susan is both not funny and not happy and vice versa.
Everyone who is either not old or funny is either curious or patient and vice versa.
If lucy is creative or not quiet then susan is generous.
Everyone who is not kind or kind is humble or strong.
If someone is not quiet or not old then someone is both not humble and not funny and vice versa.
Everyone who is not patient is creative or tall and vice versa.
Everyone who is both generous and creative is not curious or not quiet and vice versa.
If someone is both not curious and not creative then alice is generous or brave and vice versa.
Everyone who is kind or not humble is not calm or humble and vice versa.
If someone is not funny then alice is not humble or not curious.
If mary is either wise or creative then someone is wise and vice versa.
Everyone who is either kind or brave is not patient.
Susan is funny or not funny.
Someone is not humble.
Susan is not curious or happy.
Lucy is kind or quiet.
Alice is quiet or patient.
Fred is either happy or quiet. | Mary is not old. | contradiction | (![X]:((~brave(X)&~generous(X))=>(~strong(X)<~>generous(X))))&
(((~quiet(fred)|old(fred)))=>((quiet(mary)|humble(mary))))&
(![X]:(tall(X)=>happy(X)))&
((wise(fred))<=>((~funny(susan)&~happy(susan))))&
(![X]:((~old(X)<~>funny(X))<=>(curious(X)<~>patient(X))))&
(((creative(lucy)|~quiet(lucy)))=>(generous(susan)))&
(![X]:((~kind(X)|kind(X))=>(humble(X)|strong(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:(~patient(X)<=>(creative(X)|tall(X))))&
(![X]:((generous(X)&creative(X))<=>(~curious(X)|~quiet(X))))&
((?[X]:((~curious(X)&~creative(X))))<=>((generous(alice)|brave(alice))))&
(![X]:((kind(X)|~humble(X))<=>(~calm(X)|humble(X))))&
((?[X]:(~funny(X)))=>((~humble(alice)|~curious(alice))))&
(((wise(mary)<~>creative(mary)))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)<~>brave(X))=>~patient(X)))&
((funny(susan)|~funny(susan)))&
(?[X]:(~humble(X)))&
((~curious(susan)|happy(susan)))&
((kind(lucy)|quiet(lucy)))&
((quiet(alice)|patient(alice)))&
((happy(fred)<~>quiet(fred))) | ~old(mary) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5269175755696393386835818
% SZS output start Proof for 5269175755696393386835818
1. ! [X0] : ((~generous(X0) & ~brave(X0)) => (~strong(X0) <~> generous(X0))) [input p0]
7. ! [X0] : ((kind(X0) | ~kind(X0)) => (strong(X0) | humble(X0))) [input p6]
8. ? [X0] : (~old(X0) | ~quiet(X0)) <=> ? [X0] : (~funny(X0) & ~humble(X0)) [input p7]
10. ! [X0] : ((creative(X0) & generous(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p9]
11. ? [X0] : (~creative(X0) & ~curious(X0)) <=> (brave(alice) | generous(alice)) [input p10]
13. ? [X0] : ~funny(X0) => (~curious(alice) | ~humble(alice)) [input p12]
22. ~old(mary) [input hypothesis]
23. ? [X0] : (~old(X0) | ~quiet(X0)) <=> ? [X1] : (~funny(X1) & ~humble(X1)) [rectify 8]
24. ! [X0] : ((~strong(X0) <~> generous(X0)) | (generous(X0) | brave(X0))) [ennf transformation 1]
25. ! [X0] : ((~strong(X0) <~> generous(X0)) | generous(X0) | brave(X0)) [flattening 24]
30. ! [X0] : ((strong(X0) | humble(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 7]
31. ! [X0] : (strong(X0) | humble(X0) | (~kind(X0) & kind(X0))) [flattening 30]
32. (~curious(alice) | ~humble(alice)) | ! [X0] : funny(X0) [ennf transformation 13]
33. ~curious(alice) | ~humble(alice) | ! [X0] : funny(X0) [flattening 32]
35. ! [X0] : (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | generous(X0) | brave(X0)) [nnf transformation 25]
39. (? [X0] : (~old(X0) | ~quiet(X0)) | ! [X1] : (funny(X1) | humble(X1))) & (? [X1] : (~funny(X1) & ~humble(X1)) | ! [X0] : (old(X0) & quiet(X0))) [nnf transformation 23]
40. (? [X0] : (~old(X0) | ~quiet(X0)) | ! [X1] : (funny(X1) | humble(X1))) & (? [X2] : (~funny(X2) & ~humble(X2)) | ! [X3] : (old(X3) & quiet(X3))) [rectify 39]
41. ? [X0] : (~old(X0) | ~quiet(X0)) => (~old(sK0) | ~quiet(sK0)) [choice axiom]
42. ? [X2] : (~funny(X2) & ~humble(X2)) => (~funny(sK1) & ~humble(sK1)) [choice axiom]
43. ((~old(sK0) | ~quiet(sK0)) | ! [X1] : (funny(X1) | humble(X1))) & ((~funny(sK1) & ~humble(sK1)) | ! [X3] : (old(X3) & quiet(X3))) [skolemisation 40,42,41]
46. ! [X0] : (((creative(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | (~creative(X0) | ~generous(X0)))) [nnf transformation 10]
47. ! [X0] : (((creative(X0) & generous(X0)) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ~creative(X0) | ~generous(X0))) [flattening 46]
48. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & ((brave(alice) | generous(alice)) | ! [X0] : (creative(X0) | curious(X0))) [nnf transformation 11]
49. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X0] : (creative(X0) | curious(X0))) [flattening 48]
50. (? [X0] : (~creative(X0) & ~curious(X0)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X1] : (creative(X1) | curious(X1))) [rectify 49]
51. ? [X0] : (~creative(X0) & ~curious(X0)) => (~creative(sK2) & ~curious(sK2)) [choice axiom]
52. ((~creative(sK2) & ~curious(sK2)) | (~brave(alice) & ~generous(alice))) & (brave(alice) | generous(alice) | ! [X1] : (creative(X1) | curious(X1))) [skolemisation 50,51]
63. generous(X0) | ~strong(X0) | generous(X0) | brave(X0) [cnf transformation 35]
81. strong(X0) | humble(X0) | kind(X0) [cnf transformation 31]
82. ~kind(X0) | humble(X0) | strong(X0) [cnf transformation 31]
86. ~funny(sK1) | old(X3) [cnf transformation 43]
92. curious(X0) | generous(X0) [cnf transformation 47]
94. creative(X0) | curious(X0) [cnf transformation 47]
97. ~curious(sK2) | ~generous(alice) [cnf transformation 52]
98. ~curious(sK2) | ~brave(alice) [cnf transformation 52]
99. ~creative(sK2) | ~generous(alice) [cnf transformation 52]
100. ~creative(sK2) | ~brave(alice) [cnf transformation 52]
105. ~curious(alice) | ~humble(alice) | funny(X0) [cnf transformation 33]
119. ~old(mary) [cnf transformation 22]
122. ~strong(X0) | generous(X0) | brave(X0) [duplicate literal removal 63]
170. humble(X0) | strong(X0) [subsumption resolution 81,82]
184. 14 <=> ! [X3] : old(X3) [avatar definition]
185. old(X3) <- (14) [avatar component clause 184]
187. 15 <=> funny(sK1) [avatar definition]
189. ~funny(sK1) <- (~15) [avatar component clause 187]
190. 14 | ~15 [avatar split clause 86,187,184]
202. 18 <=> brave(alice) [avatar definition]
206. 19 <=> creative(sK2) [avatar definition]
208. ~creative(sK2) <- (~19) [avatar component clause 206]
209. ~18 | ~19 [avatar split clause 100,206,202]
211. 20 <=> generous(alice) [avatar definition]
213. ~generous(alice) <- (~20) [avatar component clause 211]
214. ~20 | ~19 [avatar split clause 99,206,211]
216. 21 <=> curious(sK2) [avatar definition]
218. ~curious(sK2) <- (~21) [avatar component clause 216]
219. ~18 | ~21 [avatar split clause 98,216,202]
220. ~20 | ~21 [avatar split clause 97,216,211]
222. 22 <=> ! [X0] : funny(X0) [avatar definition]
223. funny(X0) <- (22) [avatar component clause 222]
225. 23 <=> humble(alice) [avatar definition]
227. ~humble(alice) <- (~23) [avatar component clause 225]
229. 24 <=> curious(alice) [avatar definition]
231. ~curious(alice) <- (~24) [avatar component clause 229]
232. 22 | ~23 | ~24 [avatar split clause 105,229,225,222]
294. strong(alice) <- (~23) [resolution 170,227]
320. generous(alice) | brave(alice) <- (~23) [resolution 122,294]
323. brave(alice) <- (~20, ~23) [subsumption resolution 320,213]
344. 18 | 20 | 23 [avatar split clause 323,225,211,202]
345. $false <- (14) [resolution 185,119]
348. ~14 [avatar contradiction clause 345]
354. curious(sK2) <- (~19) [resolution 208,94]
364. $false <- (~19, ~21) [subsumption resolution 354,218]
365. 19 | 21 [avatar contradiction clause 364]
370. generous(alice) <- (~24) [resolution 231,92]
371. $false <- (~20, ~24) [subsumption resolution 370,213]
372. 20 | 24 [avatar contradiction clause 371]
373. $false <- (~15, 22) [resolution 223,189]
374. 15 | ~22 [avatar contradiction clause 373]
375. $false [avatar sat refutation 190,209,214,219,220,232,344,348,365,372,374]
% SZS output end Proof for 5269175755696393386835818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not funny and not tall. If someone is either not happy or not funny then someone is both not curious and not old. Everyone who is not quiet or creative is funny and vice versa. Everyone who is not old is both generous and not kind and vice versa. If susan is either strong or not calm then someone is not humble or patient and vice versa. If someone is both not old and not kind then john is either not curious or not strong. If someone is not patient then someone is either rich or not patient. If someone is either not old or wise then someone is calm or creative. Everyone who is happy or not calm is either strong or not brave and vice versa. Everyone who is either wise or quiet is either not creative or wise. Everyone who is either not creative or not wise is both not kind and quiet and vice versa. If someone is wise or not rich then susan is either not curious or not happy and vice versa. Everyone who is both not strong and not rich is patient and vice versa. Everyone who is not humble is not kind or funny and vice versa. If someone is either creative or not quiet then someone is strong and vice versa. Everyone who is brave or not curious is humble or happy and vice versa. Fred is creative or not calm. Mary is both not patient and not kind. Someone is both not brave and humble. Mary is not strong. Someone is generous or not generous. Someone is both humble and not wise. John is not patient. Someone is not funny. | Fred is calm. | neutral | (![X]:(~wise(X)=>(~funny(X)&~tall(X))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((~quiet(X)|creative(X))<=>funny(X)))&
(![X]:(~old(X)<=>(generous(X)&~kind(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:((~humble(X)|patient(X)))))&
((?[X]:((~old(X)&~kind(X))))=>((~curious(john)<~>~strong(john))))&
((?[X]:(~patient(X)))=>(?[X]:((rich(X)<~>~patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))=>(?[X]:((calm(X)|creative(X)))))&
(![X]:((happy(X)|~calm(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~kind(X)&quiet(X))))&
((?[X]:((wise(X)|~rich(X))))<=>((~curious(susan)<~>~happy(susan))))&
(![X]:((~strong(X)&~rich(X))<=>patient(X)))&
(![X]:(~humble(X)<=>(~kind(X)|funny(X))))&
((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(humble(X)|happy(X))))&
((creative(fred)|~calm(fred)))&
((~patient(mary)&~kind(mary)))&
(?[X]:((~brave(X)&humble(X))))&
(~strong(mary))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((humble(X)&~wise(X))))&
(~patient(john))&
(?[X]:(~funny(X))) | calm(fred) | [] | null | 0 |
Everyone who is both not happy and not old is humble or brave.
Everyone who is both not humble and not patient is humble and vice versa.
If susan is both old and happy then fred is quiet or not curious and vice versa.
Everyone who is not happy or wise is both not strong and not brave and vice versa.
If paul is either kind or tall then mary is both kind and old.
If john is both happy and brave then someone is both kind and not funny.
If someone is not tall then paul is curious.
Everyone who is old is funny.
Everyone who is either old or not brave is both not patient and not rich and vice versa.
Everyone who is kind is both patient and not creative.
If john is creative or not humble then someone is brave and vice versa.
If john is not curious or not kind then john is creative.
If someone is either curious or old then john is either not quiet or wise and vice versa.
If alice is both creative and not humble then paul is both rich and not old.
Everyone who is either not tall or not brave is both quiet and wise and vice versa.
If paul is both not calm and old then someone is both creative and not creative.
Someone is not funny or curious.
Susan is either wise or quiet.
Paul is strong or happy.
Someone is both not calm and creative.
Mary is both not old and curious.
Someone is either not happy or strong.
Someone is either creative or not funny.
Someone is generous or strong. | Mary is not tall. | contradiction | (![X]:((~happy(X)&~old(X))=>(humble(X)|brave(X))))&
(![X]:((~humble(X)&~patient(X))<=>humble(X)))&
(((old(susan)&happy(susan)))<=>((quiet(fred)|~curious(fred))))&
(![X]:((~happy(X)|wise(X))<=>(~strong(X)&~brave(X))))&
(((kind(paul)<~>tall(paul)))=>((kind(mary)&old(mary))))&
(((happy(john)&brave(john)))=>(?[X]:((kind(X)&~funny(X)))))&
((?[X]:(~tall(X)))=>(curious(paul)))&
(![X]:(old(X)=>funny(X)))&
(![X]:((old(X)<~>~brave(X))<=>(~patient(X)&~rich(X))))&
(![X]:(kind(X)=>(patient(X)&~creative(X))))&
(((creative(john)|~humble(john)))<=>(?[X]:(brave(X))))&
(((~curious(john)|~kind(john)))=>(creative(john)))&
((?[X]:((curious(X)<~>old(X))))<=>((~quiet(john)<~>wise(john))))&
(((creative(alice)&~humble(alice)))=>((rich(paul)&~old(paul))))&
(![X]:((~tall(X)<~>~brave(X))<=>(quiet(X)&wise(X))))&
(((~calm(paul)&old(paul)))=>(?[X]:((creative(X)&~creative(X)))))&
(?[X]:((~funny(X)|curious(X))))&
((wise(susan)<~>quiet(susan)))&
((strong(paul)|happy(paul)))&
(?[X]:((~calm(X)&creative(X))))&
((~old(mary)&curious(mary)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((generous(X)|strong(X)))) | ~tall(mary) | [
"p1",
"p3",
"p8",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8715268252349742185499770
% SZS output start Proof for 8715268252349742185499770
2. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> humble(X0)) [input p1]
4. ! [X0] : ((wise(X0) | ~happy(X0)) <=> (~brave(X0) & ~strong(X0))) [input p3]
9. ! [X0] : ((old(X0) <~> ~brave(X0)) <=> (~rich(X0) & ~patient(X0))) [input p8]
15. ! [X0] : ((~tall(X0) <~> ~brave(X0)) <=> (wise(X0) & quiet(X0))) [input p14]
21. curious(mary) & ~old(mary) [input p20]
25. ~tall(mary) [input hypothesis]
40. ! [X0] : (((~patient(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | (patient(X0) | humble(X0)))) [nnf transformation 2]
41. ! [X0] : (((~patient(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | patient(X0) | humble(X0))) [flattening 40]
44. ! [X0] : (((wise(X0) | ~happy(X0)) | (brave(X0) | strong(X0))) & ((~brave(X0) & ~strong(X0)) | (~wise(X0) & happy(X0)))) [nnf transformation 4]
45. ! [X0] : ((wise(X0) | ~happy(X0) | brave(X0) | strong(X0)) & ((~brave(X0) & ~strong(X0)) | (~wise(X0) & happy(X0)))) [flattening 44]
49. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | (rich(X0) | patient(X0))) & ((~rich(X0) & ~patient(X0)) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [nnf transformation 9]
50. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | rich(X0) | patient(X0)) & ((~rich(X0) & ~patient(X0)) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [flattening 49]
60. ! [X0] : ((((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | (~wise(X0) | ~quiet(X0))) & ((wise(X0) & quiet(X0)) | ((~tall(X0) | brave(X0)) & (~brave(X0) | tall(X0))))) [nnf transformation 15]
61. ! [X0] : ((((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ~wise(X0) | ~quiet(X0)) & ((wise(X0) & quiet(X0)) | ((~tall(X0) | brave(X0)) & (~brave(X0) | tall(X0))))) [flattening 60]
76. humble(X0) | patient(X0) | humble(X0) [cnf transformation 41]
77. ~humble(X0) | ~humble(X0) [cnf transformation 41]
87. ~wise(X0) | ~brave(X0) [cnf transformation 45]
98. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 50]
122. wise(X0) | ~brave(X0) | tall(X0) [cnf transformation 61]
134. ~old(mary) [cnf transformation 21]
140. ~tall(mary) [cnf transformation 25]
141. humble(X0) | patient(X0) [duplicate literal removal 76]
142. ~humble(X0) [duplicate literal removal 77]
143. patient(X0) [subsumption resolution 141,142]
174. 7 <=> old(mary) [avatar definition]
175. ~old(mary) <- (~7) [avatar component clause 174]
209. brave(X0) | old(X0) [subsumption resolution 98,143]
273. ~brave(X0) | tall(X0) [subsumption resolution 122,87]
304. ~7 [avatar split clause 134,174]
342. tall(X0) | old(X0) [resolution 273,209]
399. old(mary) [resolution 342,140]
402. $false <- (~7) [subsumption resolution 399,175]
403. 7 [avatar contradiction clause 402]
404. $false [avatar sat refutation 304,403]
% SZS output end Proof for 8715268252349742185499770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not old or not creative then susan is creative.
If lucy is both not wise and funny then someone is not patient.
Everyone who is either not strong or kind is not curious.
Everyone who is both curious and not quiet is funny and vice versa.
Everyone who is happy or not calm is either not happy or not creative and vice versa.
If susan is not quiet then someone is not generous.
If someone is kind then lucy is either generous or not calm and vice versa.
If someone is both rich and calm then someone is wise or not creative and vice versa.
Everyone who is both not curious and strong is not kind or old.
Everyone who is kind is either strong or not kind.
Everyone who is not quiet or generous is both quiet and calm and vice versa.
If fred is not brave then lucy is strong.
Everyone who is both wise and tall is calm.
If someone is either funny or kind then lucy is not brave and vice versa.
If someone is either rich or kind then paul is both not quiet and not tall.
If susan is either not curious or brave then someone is either not generous or not wise.
Someone is creative or quiet.
Alice is both not happy and quiet.
Someone is happy.
Someone is either rich or not creative.
Mary is curious or not funny.
Someone is both not happy and not curious.
Someone is either generous or creative.
Susan is both not humble and not happy. | Mary is not quiet. | contradiction | (((~old(susan)|~creative(susan)))=>(creative(susan)))&
(((~wise(lucy)&funny(lucy)))=>(?[X]:(~patient(X))))&
(![X]:((~strong(X)<~>kind(X))=>~curious(X)))&
(![X]:((curious(X)&~quiet(X))<=>funny(X)))&
(![X]:((happy(X)|~calm(X))<=>(~happy(X)<~>~creative(X))))&
((~quiet(susan))=>(?[X]:(~generous(X))))&
((?[X]:(kind(X)))<=>((generous(lucy)<~>~calm(lucy))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:((~curious(X)&strong(X))=>(~kind(X)|old(X))))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
(![X]:((~quiet(X)|generous(X))<=>(quiet(X)&calm(X))))&
((~brave(fred))=>(strong(lucy)))&
(![X]:((wise(X)&tall(X))=>calm(X)))&
((?[X]:((funny(X)<~>kind(X))))<=>(~brave(lucy)))&
((?[X]:((rich(X)<~>kind(X))))=>((~quiet(paul)&~tall(paul))))&
(((~curious(susan)<~>brave(susan)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
(?[X]:((creative(X)|quiet(X))))&
((~happy(alice)&quiet(alice)))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)<~>~creative(X))))&
((curious(mary)|~funny(mary)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((generous(X)<~>creative(X))))&
((~humble(susan)&~happy(susan))) | ~quiet(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4580496886294674154420593
% SZS output start Proof for 4580496886294674154420593
11. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (calm(X0) & quiet(X0))) [input p10]
25. ~quiet(mary) [input hypothesis]
57. ! [X0] : (((generous(X0) | ~quiet(X0)) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 11]
58. ! [X0] : ((generous(X0) | ~quiet(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | (~generous(X0) & quiet(X0)))) [flattening 57]
103. quiet(X0) | quiet(X0) [cnf transformation 58]
131. ~quiet(mary) [cnf transformation 25]
132. quiet(X0) [duplicate literal removal 103]
269. $false [subsumption resolution 131,132]
% SZS output end Proof for 4580496886294674154420593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Alice is not tall. | contradiction | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | ~tall(alice) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9195473130737454851362058
% SZS output start Proof for 9195473130737454851362058
2. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X0] : (~happy(X0) <~> creative(X0)) [input p1]
3. ! [X0] : ((kind(X0) & funny(X0)) => ~strong(X0)) [input p2]
4. ! [X0] : ((calm(X0) | tall(X0)) <=> (creative(X0) & ~calm(X0))) [input p3]
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> (quiet(X0) & curious(X0))) [input p6]
12. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> strong(X0)) [input p11]
14. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p13]
22. ~tall(alice) [input hypothesis]
23. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X1] : (~happy(X1) <~> creative(X1)) [rectify 2]
27. ! [X0] : (~strong(X0) | (~kind(X0) | ~funny(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | ~kind(X0) | ~funny(X0)) [flattening 27]
35. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X1] : ((~creative(X1) | happy(X1)) & (creative(X1) | ~happy(X1))) | ! [X0] : (~curious(X0) | brave(X0))) [nnf transformation 23]
36. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) | ! [X3] : (~curious(X3) | brave(X3))) [rectify 35]
37. ? [X0] : (curious(X0) & ~brave(X0)) => (curious(sK0) & ~brave(sK0)) [choice axiom]
38. ? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) => ((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) [choice axiom]
39. ((curious(sK0) & ~brave(sK0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) | ! [X3] : (~curious(X3) | brave(X3))) [skolemisation 36,38,37]
40. ! [X0] : (((calm(X0) | tall(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : ((calm(X0) | tall(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [flattening 40]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
46. ! [X0] : (((~generous(X0) & brave(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | generous(X0) | ~brave(X0))) [flattening 46]
55. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~strong(X0)) & (strong(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 14]
59. ! [X0] : ((~creative(X0) | ~strong(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [flattening 58]
73. ~brave(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
75. curious(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
77. ~kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 28]
79. ~calm(X0) | ~calm(X0) [cnf transformation 41]
82. calm(X0) | tall(X0) | ~creative(X0) | calm(X0) [cnf transformation 41]
89. ~strong(X0) | funny(X0) [cnf transformation 45]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | happy(X0) | happy(X0) | strong(X0) [cnf transformation 45]
95. ~quiet(X0) | brave(X0) | ~curious(X0) [cnf transformation 47]
108. ~strong(X0) | kind(X0) | quiet(X0) [cnf transformation 55]
116. funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 59]
134. ~tall(alice) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
136. ~funny(X0) | happy(X0) | strong(X0) [duplicate literal removal 92]
137. ~calm(X0) [duplicate literal removal 79]
138. ~creative(X0) | tall(X0) | calm(X0) [duplicate literal removal 82]
143. 2 <=> curious(sK0) [avatar definition]
145. curious(sK0) <- (2) [avatar component clause 143]
148. 3 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
149. creative(X1) | happy(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 75,143,148]
152. 4 <=> brave(sK0) [avatar definition]
154. ~brave(sK0) <- (~4) [avatar component clause 152]
156. 3 | ~4 [avatar split clause 73,152,148]
242. ~curious(X0) | funny(X0) [subsumption resolution 116,89]
345. creative(X1) <- (3) [subsumption resolution 149,135]
380. tall(X0) | calm(X0) <- (3) [resolution 138,345]
382. tall(X0) <- (3) [subsumption resolution 380,137]
396. $false <- (3) [resolution 382,134]
401. ~3 [avatar contradiction clause 396]
405. funny(sK0) <- (2) [resolution 145,242]
411. 35 <=> strong(sK0) [avatar definition]
412. strong(sK0) <- (35) [avatar component clause 411]
416. 36 <=> funny(sK0) [avatar definition]
418. funny(sK0) <- (36) [avatar component clause 416]
422. 36 | ~2 [avatar split clause 405,143,416]
438. happy(sK0) | strong(sK0) <- (36) [resolution 418,136]
441. strong(sK0) <- (36) [subsumption resolution 438,135]
442. 35 | ~36 [avatar split clause 441,416,411]
443. kind(sK0) | quiet(sK0) <- (35) [resolution 412,108]
446. 38 <=> quiet(sK0) [avatar definition]
448. quiet(sK0) <- (38) [avatar component clause 446]
450. 39 <=> kind(sK0) [avatar definition]
452. kind(sK0) <- (39) [avatar component clause 450]
453. 38 | 39 | ~35 [avatar split clause 443,411,450,446]
471. ~strong(sK0) | ~funny(sK0) <- (39) [resolution 452,77]
472. ~funny(sK0) <- (35, 39) [subsumption resolution 471,412]
473. $false <- (35, 36, 39) [subsumption resolution 472,418]
474. ~35 | ~36 | ~39 [avatar contradiction clause 473]
478. brave(sK0) | ~curious(sK0) <- (38) [resolution 448,95]
481. ~curious(sK0) <- (~4, 38) [subsumption resolution 478,154]
482. $false <- (2, ~4, 38) [subsumption resolution 481,145]
483. ~2 | 4 | ~38 [avatar contradiction clause 482]
484. $false [avatar sat refutation 150,156,401,422,442,453,474,483]
% SZS output end Proof for 9195473130737454851362058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not strong or generous then someone is either patient or wise. Everyone who is not tall or strong is not curious or quiet. If john is not tall then someone is quiet and vice versa. If lucy is not wise then mary is either not rich or not generous. Everyone who is not kind or not rich is both happy and not old and vice versa. Everyone who is happy or not rich is both happy and not happy and vice versa. Everyone who is both generous and not funny is both brave and happy. Everyone who is not rich is either not quiet or not happy and vice versa. Everyone who is either not happy or not quiet is both not rich and not curious. If someone is funny then someone is both strong and curious. If john is either tall or creative then someone is not strong or rich and vice versa. Everyone who is generous is either rich or not generous and vice versa. Everyone who is both happy and not happy is both kind and not wise. If mary is not curious then alice is either kind or not old and vice versa. If paul is both not curious and old then susan is both not creative and not humble and vice versa. Someone is either not tall or not quiet. Someone is not patient or not quiet. Someone is not brave or not calm. Lucy is not wise or not quiet. Mary is both curious and not brave. Someone is not curious. | John is generous. | contradiction | (((~strong(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)<~>wise(X)))))&
(![X]:((~tall(X)|strong(X))=>(~curious(X)|quiet(X))))&
((~tall(john))<=>(?[X]:(quiet(X))))&
((~wise(lucy))=>((~rich(mary)<~>~generous(mary))))&
(![X]:((~kind(X)|~rich(X))<=>(happy(X)&~old(X))))&
(![X]:((happy(X)|~rich(X))<=>(happy(X)&~happy(X))))&
(![X]:((generous(X)&~funny(X))=>(brave(X)&happy(X))))&
(![X]:(~rich(X)<=>(~quiet(X)<~>~happy(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(~rich(X)&~curious(X))))&
((?[X]:(funny(X)))=>(?[X]:((strong(X)&curious(X)))))&
(((tall(john)<~>creative(john)))<=>(?[X]:((~strong(X)|rich(X)))))&
(![X]:(generous(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((happy(X)&~happy(X))=>(kind(X)&~wise(X))))&
((~curious(mary))<=>((kind(alice)<~>~old(alice))))&
(((~curious(paul)&old(paul)))<=>((~creative(susan)&~humble(susan))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~brave(X)|~calm(X))))&
((~wise(lucy)|~quiet(lucy)))&
((curious(mary)&~brave(mary)))&
(?[X]:(~curious(X))) | generous(john) | [
"p1",
"p4",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6689764353562021839544517
% SZS output start Proof for 6689764353562021839544517
2. ! [X0] : ((strong(X0) | ~tall(X0)) => (quiet(X0) | ~curious(X0))) [input p1]
5. ! [X0] : ((~rich(X0) | ~kind(X0)) <=> (~old(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | happy(X0)) <=> (~happy(X0) & happy(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & generous(X0)) => (happy(X0) & brave(X0))) [input p6]
9. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) => (~curious(X0) & ~rich(X0))) [input p8]
10. ? [X0] : funny(X0) => ? [X0] : (curious(X0) & strong(X0)) [input p9]
22. generous(john) [input hypothesis]
23. ? [X0] : funny(X0) => ? [X1] : (curious(X1) & strong(X1)) [rectify 10]
26. ! [X0] : ((quiet(X0) | ~curious(X0)) | (~strong(X0) & tall(X0))) [ennf transformation 2]
27. ! [X0] : (quiet(X0) | ~curious(X0) | (~strong(X0) & tall(X0))) [flattening 26]
29. ! [X0] : ((happy(X0) & brave(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 7]
30. ! [X0] : ((happy(X0) & brave(X0)) | funny(X0) | ~generous(X0)) [flattening 29]
31. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~happy(X0) <=> ~quiet(X0))) [ennf transformation 9]
32. ? [X1] : (curious(X1) & strong(X1)) | ! [X0] : ~funny(X0) [ennf transformation 23]
43. ! [X0] : (((~rich(X0) | ~kind(X0)) | (old(X0) | ~happy(X0))) & ((~old(X0) & happy(X0)) | (rich(X0) & kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((~rich(X0) | ~kind(X0) | old(X0) | ~happy(X0)) & ((~old(X0) & happy(X0)) | (rich(X0) & kind(X0)))) [flattening 43]
45. ! [X0] : (((~rich(X0) | happy(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 6]
46. ! [X0] : ((~rich(X0) | happy(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (rich(X0) & ~happy(X0)))) [flattening 45]
48. ! [X0] : ((~curious(X0) & ~rich(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) [nnf transformation 31]
49. ? [X0] : (curious(X0) & strong(X0)) | ! [X1] : ~funny(X1) [rectify 32]
50. ? [X0] : (curious(X0) & strong(X0)) => (curious(sK2) & strong(sK2)) [choice axiom]
51. (curious(sK2) & strong(sK2)) | ! [X1] : ~funny(X1) [skolemisation 49,50]
72. ~curious(X0) | quiet(X0) | ~strong(X0) [cnf transformation 27]
78. happy(X0) | rich(X0) [cnf transformation 44]
84. ~happy(X0) | ~happy(X0) [cnf transformation 46]
85. ~happy(X0) | rich(X0) [cnf transformation 46]
88. happy(X0) | funny(X0) | ~generous(X0) [cnf transformation 30]
93. ~rich(X0) | ~quiet(X0) | happy(X0) [cnf transformation 48]
97. strong(sK2) | ~funny(X1) [cnf transformation 51]
98. curious(sK2) | ~funny(X1) [cnf transformation 51]
126. generous(john) [cnf transformation 22]
129. ~happy(X0) [duplicate literal removal 84]
152. 5 <=> ! [X0] : ~quiet(X0) [avatar definition]
153. ~quiet(X0) <- (5) [avatar component clause 152]
178. rich(X0) [subsumption resolution 85,78]
179. ~generous(X0) | funny(X0) [subsumption resolution 88,129]
184. ~quiet(X0) | happy(X0) [subsumption resolution 93,178]
185. ~quiet(X0) [subsumption resolution 184,129]
186. 5 [avatar split clause 185,152]
188. 11 <=> ! [X1] : ~funny(X1) [avatar definition]
189. ~funny(X1) <- (11) [avatar component clause 188]
191. 12 <=> curious(sK2) [avatar definition]
193. curious(sK2) <- (12) [avatar component clause 191]
194. 11 | 12 [avatar split clause 98,191,188]
196. 13 <=> strong(sK2) [avatar definition]
198. strong(sK2) <- (13) [avatar component clause 196]
199. 11 | 13 [avatar split clause 97,196,188]
277. funny(john) [resolution 179,126]
278. $false <- (11) [subsumption resolution 277,189]
279. ~11 [avatar contradiction clause 278]
285. quiet(sK2) | ~strong(sK2) <- (12) [resolution 72,193]
287. ~strong(sK2) <- (5, 12) [subsumption resolution 285,153]
288. $false <- (5, 12, 13) [subsumption resolution 287,198]
289. ~5 | ~12 | ~13 [avatar contradiction clause 288]
290. $false [avatar sat refutation 186,194,199,279,289]
% SZS output end Proof for 6689764353562021839544517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or happy then alice is kind or not creative and vice versa. Everyone who is both not happy and not strong is both old and curious. If someone is curious then susan is not curious. If lucy is old then someone is either curious or not quiet. If paul is either tall or patient then someone is both funny and wise. Everyone who is both happy and not calm is patient and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. If someone is not curious or not generous then fred is both creative and old and vice versa. Someone is either funny or not calm. Lucy is not wise or calm. Susan is rich. Susan is not calm. Someone is both humble and rich. Someone is generous or wise. Paul is not strong or not generous. Alice is not generous. | Lucy is not old. | entailment | ((?[X]:((wise(X)<~>happy(X))))<=>((kind(alice)|~creative(alice))))&
(![X]:((~happy(X)&~strong(X))=>(old(X)&curious(X))))&
((?[X]:(curious(X)))=>(~curious(susan)))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(((tall(paul)<~>patient(paul)))=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((happy(X)&~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X))))&
((~strong(paul)|~generous(paul)))&
(~generous(alice)) | ~old(lucy) | [
"p7",
"p11",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8629614356929483579866662
% SZS output start Proof for 8629614356929483579866662
8. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p7]
12. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p11]
16. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p15]
24. ~generous(alice) [input p23]
25. old(lucy) [input hypothesis]
35. ! [X0] : ((tall(X0) & ~curious(X0)) | (~old(X0) & ~generous(X0))) [ennf transformation 8]
58. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 12]
59. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 58]
66. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 16]
67. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 66]
68. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 67]
69. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK4) | ~curious(sK4)) [choice axiom]
70. ((~generous(sK4) | ~curious(sK4)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 68,69]
101. ~old(X0) | tall(X0) [cnf transformation 35]
117. ~tall(lucy) | ~old(fred) [cnf transformation 59]
132. old(fred) | generous(X1) [cnf transformation 70]
141. ~generous(alice) [cnf transformation 24]
142. old(lucy) [cnf transformation 25]
180. 9 <=> old(lucy) [avatar definition]
181. old(lucy) <- (9) [avatar component clause 180]
252. 24 <=> old(fred) [avatar definition]
256. 25 <=> tall(lucy) [avatar definition]
258. ~tall(lucy) <- (~25) [avatar component clause 256]
259. ~24 | ~25 [avatar split clause 117,256,252]
267. 27 <=> ! [X1] : generous(X1) [avatar definition]
268. generous(X1) <- (27) [avatar component clause 267]
269. 27 | 24 [avatar split clause 132,252,267]
310. 9 [avatar split clause 142,180]
323. $false <- (27) [resolution 268,141]
324. ~27 [avatar contradiction clause 323]
329. tall(lucy) <- (9) [resolution 101,181]
331. $false <- (9, ~25) [subsumption resolution 329,258]
332. ~9 | 25 [avatar contradiction clause 331]
333. $false [avatar sat refutation 259,269,310,324,332]
% SZS output end Proof for 8629614356929483579866662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and not generous is not kind. Everyone who is both not funny and not quiet is rich. Everyone who is either happy or calm is either not old or not kind and vice versa. If someone is either curious or humble then lucy is not funny or not rich and vice versa. Everyone who is not rich is either generous or not strong. Everyone who is not kind or not calm is rich and vice versa. If someone is not patient or not kind then susan is not wise. If someone is generous or not curious then fred is both strong and curious. Everyone who is not patient or not strong is both happy and not quiet. Everyone who is either not rich or strong is curious or not funny and vice versa. Everyone who is not funny is happy and vice versa. If someone is not brave then lucy is either not brave or humble and vice versa. Everyone who is both humble and wise is either not old or tall. Everyone who is either not rich or kind is quiet or old. If alice is not happy or kind then someone is patient and vice versa. If someone is not brave or happy then someone is not brave or not curious and vice versa. Someone is not brave. Alice is creative. Someone is not quiet. Someone is old. Alice is both not funny and not humble. Someone is old or not strong. Someone is not happy. | Alice is not old. | entailment | (![X]:((~rich(X)&~generous(X))=>~kind(X)))&
(![X]:((~funny(X)&~quiet(X))=>rich(X)))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~kind(X))))&
((?[X]:((curious(X)<~>humble(X))))<=>((~funny(lucy)|~rich(lucy))))&
(![X]:(~rich(X)=>(generous(X)<~>~strong(X))))&
(![X]:((~kind(X)|~calm(X))<=>rich(X)))&
((?[X]:((~patient(X)|~kind(X))))=>(~wise(susan)))&
((?[X]:((generous(X)|~curious(X))))=>((strong(fred)&curious(fred))))&
(![X]:((~patient(X)|~strong(X))=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)<~>strong(X))<=>(curious(X)|~funny(X))))&
(![X]:(~funny(X)<=>happy(X)))&
((?[X]:(~brave(X)))<=>((~brave(lucy)<~>humble(lucy))))&
(![X]:((humble(X)&wise(X))=>(~old(X)<~>tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(quiet(X)|old(X))))&
(((~happy(alice)|kind(alice)))<=>(?[X]:(patient(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:((~brave(X)|~curious(X)))))&
(?[X]:(~brave(X)))&
(creative(alice))&
(?[X]:(~quiet(X)))&
(?[X]:(old(X)))&
((~funny(alice)&~humble(alice)))&
(?[X]:((old(X)|~strong(X))))&
(?[X]:(~happy(X))) | ~old(alice) | [
"p1",
"p2",
"p5",
"p8",
"p9",
"p10",
"p14",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8095984089939915747490296
% SZS output start Proof for 8095984089939915747490296
2. ! [X0] : ((~quiet(X0) & ~funny(X0)) => rich(X0)) [input p1]
3. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (~old(X0) <~> ~kind(X0))) [input p2]
6. ! [X0] : ((~calm(X0) | ~kind(X0)) <=> rich(X0)) [input p5]
9. ! [X0] : ((~strong(X0) | ~patient(X0)) => (~quiet(X0) & happy(X0))) [input p8]
10. ! [X0] : ((~rich(X0) <~> strong(X0)) <=> (~funny(X0) | curious(X0))) [input p9]
11. ! [X0] : (~funny(X0) <=> happy(X0)) [input p10]
15. (kind(alice) | ~happy(alice)) <=> ? [X0] : patient(X0) [input p14]
21. ~humble(alice) & ~funny(alice) [input p20]
23. ? [X0] : ~happy(X0) [input p22]
24. old(alice) [input hypothesis]
31. ! [X0] : (rich(X0) | (quiet(X0) | funny(X0))) [ennf transformation 2]
32. ! [X0] : (rich(X0) | quiet(X0) | funny(X0)) [flattening 31]
35. ! [X0] : ((~quiet(X0) & happy(X0)) | (strong(X0) & patient(X0))) [ennf transformation 9]
38. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) & (((kind(X0) | old(X0)) & (~kind(X0) | ~old(X0))) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 3]
45. ! [X0] : (((~calm(X0) | ~kind(X0)) | ~rich(X0)) & (rich(X0) | (calm(X0) & kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~calm(X0) | ~kind(X0) | ~rich(X0)) & (rich(X0) | (calm(X0) & kind(X0)))) [flattening 45]
47. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [nnf transformation 10]
48. ! [X0] : ((((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))))) [flattening 47]
49. ! [X0] : ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0))) [nnf transformation 11]
55. ((kind(alice) | ~happy(alice)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~kind(alice) & happy(alice))) [nnf transformation 15]
56. (kind(alice) | ~happy(alice) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~kind(alice) & happy(alice))) [flattening 55]
57. (kind(alice) | ~happy(alice) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | (~kind(alice) & happy(alice))) [rectify 56]
58. ? [X1] : patient(X1) => patient(sK2) [choice axiom]
59. (kind(alice) | ~happy(alice) | ! [X0] : ~patient(X0)) & (patient(sK2) | (~kind(alice) & happy(alice))) [skolemisation 57,58]
73. ? [X0] : ~happy(X0) => ~happy(sK9) [choice axiom]
74. ~happy(sK9) [skolemisation 23,73]
76. quiet(X0) | rich(X0) | funny(X0) [cnf transformation 32]
77. ~old(X0) | ~kind(X0) | calm(X0) | ~happy(X0) [cnf transformation 38]
95. ~calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 46]
100. patient(X0) | happy(X0) [cnf transformation 35]
103. ~quiet(X0) | strong(X0) [cnf transformation 35]
107. ~rich(X0) | strong(X0) | funny(X0) [cnf transformation 48]
109. ~strong(X0) | rich(X0) | funny(X0) [cnf transformation 48]
110. happy(X0) | funny(X0) [cnf transformation 49]
120. kind(alice) | ~happy(alice) | ~patient(X0) [cnf transformation 59]
128. ~funny(alice) [cnf transformation 21]
131. ~happy(sK9) [cnf transformation 74]
132. old(alice) [cnf transformation 24]
199. 15 <=> ! [X0] : ~patient(X0) [avatar definition]
200. ~patient(X0) <- (15) [avatar component clause 199]
202. 16 <=> happy(alice) [avatar definition]
203. happy(alice) <- (16) [avatar component clause 202]
204. ~happy(alice) <- (~16) [avatar component clause 202]
206. 17 <=> kind(alice) [avatar definition]
208. kind(alice) <- (17) [avatar component clause 206]
209. 15 | ~16 | 17 [avatar split clause 120,206,202,199]
251. happy(X0) <- (15) [resolution 100,200]
253. $false <- (15) [resolution 251,131]
254. ~15 [avatar contradiction clause 253]
256. funny(alice) <- (~16) [resolution 110,204]
257. $false <- (~16) [subsumption resolution 256,128]
258. 16 [avatar contradiction clause 257]
269. rich(X0) | funny(X0) | strong(X0) [resolution 76,103]
301. strong(X0) | funny(X0) [subsumption resolution 269,107]
312. 32 <=> rich(alice) [avatar definition]
313. ~rich(alice) <- (~32) [avatar component clause 312]
333. ~kind(alice) | calm(alice) | ~happy(alice) [resolution 77,132]
348. calm(alice) | ~happy(alice) <- (17) [subsumption resolution 333,208]
349. calm(alice) <- (16, 17) [subsumption resolution 348,203]
429. ~kind(alice) | ~rich(alice) <- (16, 17) [resolution 349,95]
430. ~rich(alice) <- (16, 17) [subsumption resolution 429,208]
433. ~32 | ~16 | ~17 [avatar split clause 430,206,202,312]
446. funny(X1) | rich(X1) | funny(X1) [resolution 301,109]
449. funny(X1) | rich(X1) [duplicate literal removal 446]
538. rich(alice) [resolution 449,128]
545. $false <- (~32) [subsumption resolution 538,313]
546. 32 [avatar contradiction clause 545]
549. $false [avatar sat refutation 209,254,258,433,546]
% SZS output end Proof for 8095984089939915747490296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not funny then someone is not calm or not tall. If john is both old and creative then someone is either rich or not wise. Everyone who is wise is both not humble and humble and vice versa. Everyone who is not wise or curious is either kind or happy. Everyone who is both kind and not patient is not humble or curious. Everyone who is not humble is patient or rich and vice versa. If someone is both not calm and rich then susan is either wise or not creative. If susan is both not creative and not strong then someone is both not humble and not strong and vice versa. Everyone who is either strong or quiet is both not generous and not strong and vice versa. Everyone who is not rich is both not rich and not wise. If someone is either not strong or not quiet then fred is rich or not quiet. Everyone who is quiet is wise and vice versa. Everyone who is quiet is either not tall or curious and vice versa. If alice is either curious or kind then someone is both not funny and not quiet. If mary is both wise and patient then someone is not brave or not calm and vice versa. Everyone who is not wise or creative is both tall and happy. Someone is brave. Susan is happy. Someone is funny. | Mary is kind. | contradiction | ((?[X]:((funny(X)&~funny(X))))=>(?[X]:((~calm(X)|~tall(X)))))&
(((old(john)&creative(john)))=>(?[X]:((rich(X)<~>~wise(X)))))&
(![X]:(wise(X)<=>(~humble(X)&humble(X))))&
(![X]:((~wise(X)|curious(X))=>(kind(X)<~>happy(X))))&
(![X]:((kind(X)&~patient(X))=>(~humble(X)|curious(X))))&
(![X]:(~humble(X)<=>(patient(X)|rich(X))))&
((?[X]:((~calm(X)&rich(X))))=>((wise(susan)<~>~creative(susan))))&
(((~creative(susan)&~strong(susan)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((strong(X)<~>quiet(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~rich(X)=>(~rich(X)&~wise(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))=>((rich(fred)|~quiet(fred))))&
(![X]:(quiet(X)<=>wise(X)))&
(![X]:(quiet(X)<=>(~tall(X)<~>curious(X))))&
(((curious(alice)<~>kind(alice)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((wise(mary)&patient(mary)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(tall(X)&happy(X))))&
(?[X]:(brave(X)))&
(happy(susan))&
(?[X]:(funny(X))) | kind(mary) | [
"p2",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 531057274409650658882229
% SZS output start Proof for 531057274409650658882229
3. ! [X0] : (wise(X0) <=> (humble(X0) & ~humble(X0))) [input p2]
4. ! [X0] : ((curious(X0) | ~wise(X0)) => (kind(X0) <~> happy(X0))) [input p3]
16. ! [X0] : ((creative(X0) | ~wise(X0)) => (happy(X0) & tall(X0))) [input p15]
20. kind(mary) [input hypothesis]
24. ! [X0] : ((kind(X0) <~> happy(X0)) | (~curious(X0) & wise(X0))) [ennf transformation 4]
32. ! [X0] : ((happy(X0) & tall(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 16]
36. ! [X0] : ((wise(X0) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | ~wise(X0))) [nnf transformation 3]
37. ! [X0] : ((wise(X0) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | ~wise(X0))) [flattening 36]
38. ! [X0] : (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~curious(X0) & wise(X0))) [nnf transformation 24]
65. ~humble(X0) | ~wise(X0) [cnf transformation 37]
66. ~wise(X0) | humble(X0) [cnf transformation 37]
70. ~happy(X0) | ~kind(X0) | wise(X0) [cnf transformation 38]
109. happy(X0) | wise(X0) [cnf transformation 32]
114. kind(mary) [cnf transformation 20]
117. ~wise(X0) [subsumption resolution 65,66]
118. ~happy(X0) | ~kind(X0) [subsumption resolution 70,117]
193. happy(X0) [subsumption resolution 109,117]
195. ~kind(X0) [resolution 118,193]
197. $false [resolution 195,114]
% SZS output end Proof for 531057274409650658882229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not rich is not curious.
If lucy is either not rich or strong then alice is either not patient or not kind and vice versa.
If someone is creative then alice is quiet or not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
If alice is not tall or not wise then someone is both not creative and tall.
If someone is both tall and quiet then john is either not patient or wise and vice versa.
Someone is patient.
Lucy is both humble and not happy.
Paul is either not funny or not tall.
Alice is calm or not creative.
Someone is not kind.
Someone is not calm or not brave.
Someone is both not patient and not funny. | John is not old. | contradiction | (![X]:((~generous(X)<~>~rich(X))=>~curious(X)))&
(((~rich(lucy)<~>strong(lucy)))<=>((~patient(alice)<~>~kind(alice))))&
((?[X]:(creative(X)))<=>((quiet(alice)|~rich(alice))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(((~tall(alice)|~wise(alice)))=>(?[X]:((~creative(X)&tall(X)))))&
((?[X]:((tall(X)&quiet(X))))<=>((~patient(john)<~>wise(john))))&
(?[X]:(patient(X)))&
((humble(lucy)&~happy(lucy)))&
((~funny(paul)<~>~tall(paul)))&
((calm(alice)|~creative(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)|~brave(X))))&
(?[X]:((~patient(X)&~funny(X)))) | ~old(john) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8784229505308502283572789
% SZS output start Proof for 8784229505308502283572789
10. ! [X0] : ((~old(X0) | rich(X0)) => (old(X0) & tall(X0))) [input p9]
24. ~old(john) [input hypothesis]
31. ! [X0] : ((old(X0) & tall(X0)) | (old(X0) & ~rich(X0))) [ennf transformation 10]
120. old(X0) | old(X0) [cnf transformation 31]
148. ~old(john) [cnf transformation 24]
149. old(X0) [duplicate literal removal 120]
359. $false [subsumption resolution 148,149]
% SZS output end Proof for 8784229505308502283572789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not calm is not kind and vice versa.
Everyone who is either funny or not quiet is happy or not wise and vice versa.
Everyone who is old or brave is both tall and not humble and vice versa.
Everyone who is either not happy or happy is both not curious and quiet.
Everyone who is not calm is both curious and not strong and vice versa.
Everyone who is not kind or not brave is either creative or not wise and vice versa.
Everyone who is both calm and wise is not old or not generous and vice versa.
Everyone who is old is not humble.
Everyone who is not funny or not brave is either not rich or brave.
Everyone who is calm or not curious is not kind and vice versa.
Everyone who is not funny or not quiet is quiet or not funny.
Everyone who is not brave is either rich or not generous and vice versa.
Everyone who is both calm and not creative is wise.
Everyone who is not tall or rich is tall or creative and vice versa.
If mary is both not humble and not happy then paul is both happy and not generous.
Someone is either patient or calm.
Someone is not brave or not funny.
Lucy is humble or calm.
Fred is either humble or brave.
Paul is not happy or not curious. | Lucy is not wise. | contradiction | (![X]:((~brave(X)|~calm(X))<=>~kind(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>(happy(X)|~wise(X))))&
(![X]:((old(X)|brave(X))<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)<~>happy(X))=>(~curious(X)&quiet(X))))&
(![X]:(~calm(X)<=>(curious(X)&~strong(X))))&
(![X]:((~kind(X)|~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((calm(X)&wise(X))<=>(~old(X)|~generous(X))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~funny(X)|~brave(X))=>(~rich(X)<~>brave(X))))&
(![X]:((calm(X)|~curious(X))<=>~kind(X)))&
(![X]:((~funny(X)|~quiet(X))=>(quiet(X)|~funny(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((calm(X)&~creative(X))=>wise(X)))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|creative(X))))&
(((~humble(mary)&~happy(mary)))=>((happy(paul)&~generous(paul))))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~brave(X)|~funny(X))))&
((humble(lucy)|calm(lucy)))&
((humble(fred)<~>brave(fred)))&
((~happy(paul)|~curious(paul))) | ~wise(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6741666468567595783905164
% SZS output start Proof for 6741666468567595783905164
1. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> ~kind(X0)) [input p0]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (~strong(X0) & curious(X0))) [input p4]
7. ! [X0] : ((wise(X0) & calm(X0)) <=> (~generous(X0) | ~old(X0))) [input p6]
9. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~rich(X0) <~> brave(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | calm(X0)) <=> ~kind(X0)) [input p9]
12. ! [X0] : (~brave(X0) <=> (rich(X0) <~> ~generous(X0))) [input p11]
21. ~wise(lucy) [input hypothesis]
22. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 4]
24. ! [X0] : ((~rich(X0) <~> brave(X0)) | (brave(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : (((~calm(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [nnf transformation 1]
32. ! [X0] : ((~calm(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [flattening 31]
37. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 22]
38. ! [X0] : ((~calm(X0) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | calm(X0))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | calm(X0))) [flattening 38]
42. ! [X0] : (((wise(X0) & calm(X0)) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | (~wise(X0) | ~calm(X0)))) [nnf transformation 7]
43. ! [X0] : (((wise(X0) & calm(X0)) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | ~wise(X0) | ~calm(X0))) [flattening 42]
44. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (brave(X0) & funny(X0))) [nnf transformation 24]
45. ! [X0] : (((~curious(X0) | calm(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~curious(X0) | calm(X0) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : ((~brave(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | brave(X0))) [nnf transformation 12]
58. ~calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 32]
70. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 37]
71. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 37]
74. curious(X0) | calm(X0) [cnf transformation 39]
87. generous(X0) | wise(X0) [cnf transformation 43]
90. brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 44]
94. ~kind(X0) | curious(X0) [cnf transformation 46]
98. ~generous(X0) | rich(X0) | brave(X0) [cnf transformation 47]
100. ~brave(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 47]
116. ~wise(lucy) [cnf transformation 21]
120. ~rich(X0) | brave(X0) [duplicate literal removal 90]
121. ~curious(X0) | happy(X0) [duplicate literal removal 70]
122. ~curious(X0) | ~happy(X0) [duplicate literal removal 71]
126. ~curious(X0) [subsumption resolution 121,122]
127. calm(X0) [subsumption resolution 74,126]
131. ~kind(X0) [subsumption resolution 94,126]
132. ~rich(X0) | ~generous(X0) [subsumption resolution 100,120]
133. ~generous(X0) | brave(X0) [subsumption resolution 98,132]
178. wise(X0) | brave(X0) [resolution 133,87]
179. ~brave(X0) | kind(X0) [resolution 58,127]
180. ~brave(X0) [subsumption resolution 179,131]
186. brave(lucy) [resolution 178,116]
187. $false [subsumption resolution 186,180]
% SZS output end Proof for 6741666468567595783905164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is not rich then someone is either patient or not patient. If lucy is both funny and not kind then someone is either not tall or not humble and vice versa. Everyone who is strong or not wise is both not tall and not generous and vice versa. Everyone who is either old or not old is not patient. Everyone who is wise is not funny or calm and vice versa. Everyone who is either old or quiet is not happy and vice versa. Everyone who is not creative is both quiet and not quiet and vice versa. Everyone who is not curious or generous is either kind or rich and vice versa. If someone is both not kind and not generous then mary is either rich or brave. Everyone who is not patient is funny or rich. If lucy is either happy or old then susan is either not old or wise and vice versa. If someone is not patient or not funny then alice is either not rich or strong. If paul is either funny or generous then lucy is funny or not quiet. Everyone who is quiet or old is both not funny and not kind and vice versa. Everyone who is happy or patient is either humble or old and vice versa. Someone is not quiet. Lucy is both not quiet and humble. Someone is calm. Someone is both brave and not calm. Someone is both not kind and funny. Someone is not funny. Someone is either humble or not patient. Someone is either patient or happy. | Paul is generous. | neutral | ((~rich(mary))=>(?[X]:((patient(X)<~>~patient(X)))))&
(((funny(lucy)&~kind(lucy)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((strong(X)|~wise(X))<=>(~tall(X)&~generous(X))))&
(![X]:((old(X)<~>~old(X))=>~patient(X)))&
(![X]:(wise(X)<=>(~funny(X)|calm(X))))&
(![X]:((old(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(~creative(X)<=>(quiet(X)&~quiet(X))))&
(![X]:((~curious(X)|generous(X))<=>(kind(X)<~>rich(X))))&
((?[X]:((~kind(X)&~generous(X))))=>((rich(mary)<~>brave(mary))))&
(![X]:(~patient(X)=>(funny(X)|rich(X))))&
(((happy(lucy)<~>old(lucy)))<=>((~old(susan)<~>wise(susan))))&
((?[X]:((~patient(X)|~funny(X))))=>((~rich(alice)<~>strong(alice))))&
(((funny(paul)<~>generous(paul)))=>((funny(lucy)|~quiet(lucy))))&
(![X]:((quiet(X)|old(X))<=>(~funny(X)&~kind(X))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)<~>old(X))))&
(?[X]:(~quiet(X)))&
((~quiet(lucy)&humble(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)<~>~patient(X))))&
(?[X]:((patient(X)<~>happy(X)))) | generous(paul) | [] | null | 0 |
Everyone who is either not tall or kind is not old or strong. Everyone who is both not humble and not creative is not patient or old. If susan is both not old and not tall then someone is both not happy and old. Everyone who is patient or rich is not patient and vice versa. If mary is not generous or patient then someone is either quiet or funny. Everyone who is not generous or strong is rich or not old. If alice is either not funny or happy then someone is either brave or not wise and vice versa. If someone is not rich then alice is not brave and vice versa. Everyone who is either not creative or quiet is humble or not patient. Everyone who is not old is both not brave and old and vice versa. Everyone who is either patient or tall is both curious and not rich and vice versa. Everyone who is both calm and patient is either not calm or patient. Everyone who is either not happy or kind is calm. Everyone who is wise or generous is not strong or curious and vice versa. Everyone who is either not old or old is not strong. Someone is not funny or strong. Someone is both creative and not calm. John is not tall or brave. Someone is both not creative and not generous. Susan is not happy. Alice is both not creative and kind. | John is creative. | neutral | (![X]:((~tall(X)<~>kind(X))=>(~old(X)|strong(X))))&
(![X]:((~humble(X)&~creative(X))=>(~patient(X)|old(X))))&
(((~old(susan)&~tall(susan)))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((patient(X)|rich(X))<=>~patient(X)))&
(((~generous(mary)|patient(mary)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~generous(X)|strong(X))=>(rich(X)|~old(X))))&
(((~funny(alice)<~>happy(alice)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:(~old(X)<=>(~brave(X)&old(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
(![X]:((~happy(X)<~>kind(X))=>calm(X)))&
(![X]:((wise(X)|generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((~old(X)<~>old(X))=>~strong(X)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~tall(john)|brave(john)))&
(?[X]:((~creative(X)&~generous(X))))&
(~happy(susan))&
((~creative(alice)&kind(alice))) | creative(john) | [] | null | 0 |
Everyone who is both not quiet and happy is generous. If someone is not funny then paul is both not quiet and not patient and vice versa. If john is both rich and not humble then mary is both not generous and tall. Everyone who is not calm or not curious is either not quiet or funny and vice versa. If fred is both not funny and old then john is not calm or wise. Everyone who is kind is kind or brave and vice versa. Everyone who is both quiet and calm is both tall and old and vice versa. Everyone who is not generous or funny is tall and vice versa. If someone is not calm or strong then paul is either generous or brave. If someone is both not brave and not humble then someone is either not calm or happy and vice versa. Everyone who is either not humble or strong is either curious or creative. If someone is either patient or not creative then someone is not rich. Everyone who is both not rich and quiet is not rich or kind and vice versa. Everyone who is either not strong or not rich is both not wise and not kind. If someone is not brave or tall then someone is curious and vice versa. If alice is not funny or not rich then someone is not funny. Fred is either not wise or not kind. Someone is both not funny and curious. Someone is not generous or not strong. John is both not kind and patient. Alice is either kind or creative. Someone is not rich. Someone is not curious or creative. Lucy is not funny. | Paul is not brave. | entailment | (![X]:((~quiet(X)&happy(X))=>generous(X)))&
((?[X]:(~funny(X)))<=>((~quiet(paul)&~patient(paul))))&
(((rich(john)&~humble(john)))=>((~generous(mary)&tall(mary))))&
(![X]:((~calm(X)|~curious(X))<=>(~quiet(X)<~>funny(X))))&
(((~funny(fred)&old(fred)))=>((~calm(john)|wise(john))))&
(![X]:(kind(X)<=>(kind(X)|brave(X))))&
(![X]:((quiet(X)&calm(X))<=>(tall(X)&old(X))))&
(![X]:((~generous(X)|funny(X))<=>tall(X)))&
((?[X]:((~calm(X)|strong(X))))=>((generous(paul)<~>brave(paul))))&
((?[X]:((~brave(X)&~humble(X))))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(curious(X)<~>creative(X))))&
((?[X]:((patient(X)<~>~creative(X))))=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)&quiet(X))<=>(~rich(X)|kind(X))))&
(![X]:((~strong(X)<~>~rich(X))=>(~wise(X)&~kind(X))))&
((?[X]:((~brave(X)|tall(X))))<=>(?[X]:(curious(X))))&
(((~funny(alice)|~rich(alice)))=>(?[X]:(~funny(X))))&
((~wise(fred)<~>~kind(fred)))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((~kind(john)&patient(john)))&
((kind(alice)<~>creative(alice)))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)|creative(X))))&
(~funny(lucy)) | ~brave(paul) | [
"p1",
"p5",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2825289547587975310400420
% SZS output start Proof for 2825289547587975310400420
2. ? [X0] : ~funny(X0) <=> (~patient(paul) & ~quiet(paul)) [input p1]
6. ! [X0] : (kind(X0) <=> (brave(X0) | kind(X0))) [input p5]
13. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (kind(X0) | ~rich(X0))) [input p12]
24. ~funny(lucy) [input p23]
25. brave(paul) [input hypothesis]
40. (? [X0] : ~funny(X0) | (patient(paul) | quiet(paul))) & ((~patient(paul) & ~quiet(paul)) | ! [X0] : funny(X0)) [nnf transformation 2]
41. (? [X0] : ~funny(X0) | patient(paul) | quiet(paul)) & ((~patient(paul) & ~quiet(paul)) | ! [X0] : funny(X0)) [flattening 40]
42. (? [X0] : ~funny(X0) | patient(paul) | quiet(paul)) & ((~patient(paul) & ~quiet(paul)) | ! [X1] : funny(X1)) [rectify 41]
43. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
44. (~funny(sK0) | patient(paul) | quiet(paul)) & ((~patient(paul) & ~quiet(paul)) | ! [X1] : funny(X1)) [skolemisation 42,43]
47. ! [X0] : ((kind(X0) | (~brave(X0) & ~kind(X0))) & ((brave(X0) | kind(X0)) | ~kind(X0))) [nnf transformation 6]
48. ! [X0] : ((kind(X0) | (~brave(X0) & ~kind(X0))) & (brave(X0) | kind(X0) | ~kind(X0))) [flattening 47]
64. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~kind(X0) & rich(X0))) & ((kind(X0) | ~rich(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 13]
65. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~kind(X0) & rich(X0))) & (kind(X0) | ~rich(X0) | ~quiet(X0) | rich(X0))) [flattening 64]
85. ~quiet(paul) | funny(X1) [cnf transformation 44]
99. ~brave(X0) | kind(X0) [cnf transformation 48]
127. ~kind(X0) | quiet(X0) [cnf transformation 65]
148. ~funny(lucy) [cnf transformation 24]
149. brave(paul) [cnf transformation 25]
151. 1 <=> quiet(paul) [avatar definition]
164. 4 <=> ! [X1] : funny(X1) [avatar definition]
165. funny(X1) <- (4) [avatar component clause 164]
167. 4 | ~1 [avatar split clause 85,151,164]
211. 15 <=> brave(paul) [avatar definition]
212. brave(paul) <- (15) [avatar component clause 211]
341. 15 [avatar split clause 149,211]
342. kind(paul) <- (15) [resolution 99,212]
351. quiet(paul) <- (15) [resolution 127,342]
354. 1 | ~15 [avatar split clause 351,211,151]
356. $false <- (4) [resolution 165,148]
363. ~4 [avatar contradiction clause 356]
364. $false [avatar sat refutation 167,341,354,363]
% SZS output end Proof for 2825289547587975310400420
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not old then someone is both brave and curious and vice versa.
If john is either curious or not humble then susan is both wise and not generous.
Everyone who is rich or not patient is not kind.
Everyone who is not creative or not happy is both not kind and quiet and vice versa.
Everyone who is funny or not old is quiet and vice versa.
Everyone who is patient is both patient and not funny.
Everyone who is both humble and not quiet is wise.
Everyone who is old is patient.
If fred is not brave then susan is either funny or strong.
Everyone who is happy is funny or quiet.
If someone is not happy then someone is both tall and rich.
Everyone who is old is curious.
Everyone who is either wise or calm is both rich and not funny and vice versa.
If alice is both old and not humble then susan is either not curious or not patient.
Everyone who is both creative and generous is both not wise and not humble.
Someone is either not generous or creative.
Someone is either not quiet or not tall.
John is both brave and strong.
Fred is not calm or not kind.
Alice is funny.
Someone is not generous.
Fred is not tall or not funny.
Alice is not old or generous. | Alice is generous. | neutral | ((~old(john))<=>(?[X]:((brave(X)&curious(X)))))&
(((curious(john)<~>~humble(john)))=>((wise(susan)&~generous(susan))))&
(![X]:((rich(X)|~patient(X))=>~kind(X)))&
(![X]:((~creative(X)|~happy(X))<=>(~kind(X)&quiet(X))))&
(![X]:((funny(X)|~old(X))<=>quiet(X)))&
(![X]:(patient(X)=>(patient(X)&~funny(X))))&
(![X]:((humble(X)&~quiet(X))=>wise(X)))&
(![X]:(old(X)=>patient(X)))&
((~brave(fred))=>((funny(susan)<~>strong(susan))))&
(![X]:(happy(X)=>(funny(X)|quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:(old(X)=>curious(X)))&
(![X]:((wise(X)<~>calm(X))<=>(rich(X)&~funny(X))))&
(((old(alice)&~humble(alice)))=>((~curious(susan)<~>~patient(susan))))&
(![X]:((creative(X)&generous(X))=>(~wise(X)&~humble(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((~quiet(X)<~>~tall(X))))&
((brave(john)&strong(john)))&
((~calm(fred)|~kind(fred)))&
(funny(alice))&
(?[X]:(~generous(X)))&
((~tall(fred)|~funny(fred)))&
((~old(alice)|generous(alice))) | generous(alice) | [] | null | 0 |
If paul is both happy and not calm then someone is happy or not old. Everyone who is either curious or kind is either kind or quiet and vice versa. Everyone who is tall is funny or generous and vice versa. Everyone who is brave is creative or not strong and vice versa. Everyone who is either kind or humble is both not kind and not creative. If john is not brave or not patient then someone is strong or humble and vice versa. If lucy is both not wise and wise then someone is not rich or not generous. If paul is not creative or not funny then someone is rich. Everyone who is not funny or humble is not strong. Everyone who is either happy or not funny is both patient and not humble. Everyone who is not brave is either rich or not quiet and vice versa. Everyone who is both kind and generous is both not generous and not strong. Everyone who is both funny and not calm is either tall or not calm. Everyone who is either not humble or old is brave. Everyone who is either patient or kind is either not curious or not tall. If mary is both not old and humble then john is not curious or quiet. John is calm or kind. Mary is not calm. Someone is both brave and strong. Paul is not old. Someone is not tall or happy. Someone is patient. Someone is generous or not kind. Mary is both old and not wise. | John is rich. | neutral | (((happy(paul)&~calm(paul)))=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((curious(X)<~>kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:(tall(X)<=>(funny(X)|generous(X))))&
(![X]:(brave(X)<=>(creative(X)|~strong(X))))&
(![X]:((kind(X)<~>humble(X))=>(~kind(X)&~creative(X))))&
(((~brave(john)|~patient(john)))<=>(?[X]:((strong(X)|humble(X)))))&
(((~wise(lucy)&wise(lucy)))=>(?[X]:((~rich(X)|~generous(X)))))&
(((~creative(paul)|~funny(paul)))=>(?[X]:(rich(X))))&
(![X]:((~funny(X)|humble(X))=>~strong(X)))&
(![X]:((happy(X)<~>~funny(X))=>(patient(X)&~humble(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:((kind(X)&generous(X))=>(~generous(X)&~strong(X))))&
(![X]:((funny(X)&~calm(X))=>(tall(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>old(X))=>brave(X)))&
(![X]:((patient(X)<~>kind(X))=>(~curious(X)<~>~tall(X))))&
(((~old(mary)&humble(mary)))=>((~curious(john)|quiet(john))))&
((calm(john)|kind(john)))&
(~calm(mary))&
(?[X]:((brave(X)&strong(X))))&
(~old(paul))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:(patient(X)))&
(?[X]:((generous(X)|~kind(X))))&
((old(mary)&~wise(mary))) | rich(john) | [] | null | 0 |
Everyone who is patient or not quiet is both kind and quiet.
If someone is quiet or not happy then mary is happy.
If susan is either not kind or not generous then lucy is generous.
If lucy is not tall then someone is not creative.
Everyone who is patient is both not wise and not quiet and vice versa.
Everyone who is not generous or kind is not quiet.
If someone is both not generous and wise then mary is both wise and curious.
Everyone who is old or not kind is both not strong and not creative.
If someone is not creative then someone is rich and vice versa.
If someone is both not curious and not humble then someone is either brave or rich and vice versa.
Everyone who is tall or brave is both humble and not old and vice versa.
Everyone who is either tall or not funny is both not generous and strong.
Everyone who is not kind or curious is not patient.
If someone is not curious then fred is either not humble or not brave.
If someone is both not happy and kind then susan is either not patient or not funny.
Everyone who is humble or not quiet is rich or quiet and vice versa.
Someone is both curious and funny.
Someone is either brave or funny.
Someone is creative or not tall.
Someone is happy.
Someone is both not brave and not happy.
Susan is not happy.
Paul is not old or kind. | Fred is not strong. | entailment | (![X]:((patient(X)|~quiet(X))=>(kind(X)&quiet(X))))&
((?[X]:((quiet(X)|~happy(X))))=>(happy(mary)))&
(((~kind(susan)<~>~generous(susan)))=>(generous(lucy)))&
((~tall(lucy))=>(?[X]:(~creative(X))))&
(![X]:(patient(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((~generous(X)|kind(X))=>~quiet(X)))&
((?[X]:((~generous(X)&wise(X))))=>((wise(mary)&curious(mary))))&
(![X]:((old(X)|~kind(X))=>(~strong(X)&~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)&~humble(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:((tall(X)|brave(X))<=>(humble(X)&~old(X))))&
(![X]:((tall(X)<~>~funny(X))=>(~generous(X)&strong(X))))&
(![X]:((~kind(X)|curious(X))=>~patient(X)))&
((?[X]:(~curious(X)))=>((~humble(fred)<~>~brave(fred))))&
((?[X]:((~happy(X)&kind(X))))=>((~patient(susan)<~>~funny(susan))))&
(![X]:((humble(X)|~quiet(X))<=>(rich(X)|quiet(X))))&
(?[X]:((curious(X)&funny(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)&~happy(X))))&
(~happy(susan))&
((~old(paul)|kind(paul))) | ~strong(fred) | [
"p0",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3008115867631044402164090
% SZS output start Proof for 3008115867631044402164090
1. ! [X0] : ((~quiet(X0) | patient(X0)) => (quiet(X0) & kind(X0))) [input p0]
6. ! [X0] : ((kind(X0) | ~generous(X0)) => ~quiet(X0)) [input p5]
8. ! [X0] : ((~kind(X0) | old(X0)) => (~creative(X0) & ~strong(X0))) [input p7]
24. strong(fred) [input hypothesis]
27. ! [X0] : ((quiet(X0) & kind(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 1]
31. ! [X0] : (~quiet(X0) | (~kind(X0) & generous(X0))) [ennf transformation 6]
33. ! [X0] : ((~creative(X0) & ~strong(X0)) | (kind(X0) & ~old(X0))) [ennf transformation 8]
74. quiet(X0) | quiet(X0) [cnf transformation 27]
84. ~quiet(X0) | ~kind(X0) [cnf transformation 31]
88. ~strong(X0) | kind(X0) [cnf transformation 33]
128. strong(fred) [cnf transformation 24]
131. quiet(X0) [duplicate literal removal 74]
166. ~kind(X0) [subsumption resolution 84,131]
169. ~strong(X0) [subsumption resolution 88,166]
232. $false [subsumption resolution 128,169]
% SZS output end Proof for 3008115867631044402164090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not strong is not curious or funny and vice versa.
Everyone who is not creative is both not patient and not strong.
If someone is not old or creative then someone is either funny or patient and vice versa.
Everyone who is wise is not rich or funny and vice versa.
If someone is not rich or curious then paul is not strong or generous and vice versa.
Everyone who is tall or wise is patient and vice versa.
Everyone who is creative or tall is not brave or not calm and vice versa.
Everyone who is not curious or not quiet is not curious or tall and vice versa.
If someone is not rich then lucy is both not quiet and wise.
Everyone who is not tall is quiet or old and vice versa.
If someone is both rich and tall then someone is both not old and rich.
Everyone who is brave or not brave is not calm and vice versa.
If mary is both quiet and wise then someone is either not curious or curious.
Everyone who is tall or curious is both strong and tall.
Everyone who is either not creative or humble is not strong or not brave.
Everyone who is both not humble and rich is not creative or not tall and vice versa.
Lucy is both not calm and rich. | Mary is old. | contradiction | (![X]:((curious(X)&~strong(X))<=>(~curious(X)|funny(X))))&
(![X]:(~creative(X)=>(~patient(X)&~strong(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((funny(X)<~>patient(X)))))&
(![X]:(wise(X)<=>(~rich(X)|funny(X))))&
((?[X]:((~rich(X)|curious(X))))<=>((~strong(paul)|generous(paul))))&
(![X]:((tall(X)|wise(X))<=>patient(X)))&
(![X]:((creative(X)|tall(X))<=>(~brave(X)|~calm(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(~curious(X)|tall(X))))&
((?[X]:(~rich(X)))=>((~quiet(lucy)&wise(lucy))))&
(![X]:(~tall(X)<=>(quiet(X)|old(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((brave(X)|~brave(X))<=>~calm(X)))&
(((quiet(mary)&wise(mary)))=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:((tall(X)|curious(X))=>(strong(X)&tall(X))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|~brave(X))))&
(![X]:((~humble(X)&rich(X))<=>(~creative(X)|~tall(X))))&
((~calm(lucy)&rich(lucy))) | old(mary) | [
"p0",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1101148453798483881657232
% SZS output start Proof for 1101148453798483881657232
1. ! [X0] : ((~strong(X0) & curious(X0)) <=> (funny(X0) | ~curious(X0))) [input p0]
10. ! [X0] : (~tall(X0) <=> (old(X0) | quiet(X0))) [input p9]
14. ! [X0] : ((curious(X0) | tall(X0)) => (tall(X0) & strong(X0))) [input p13]
18. old(mary) [input hypothesis]
26. ! [X0] : ((tall(X0) & strong(X0)) | (~curious(X0) & ~tall(X0))) [ennf transformation 14]
29. ! [X0] : (((~strong(X0) & curious(X0)) | (~funny(X0) & curious(X0))) & ((funny(X0) | ~curious(X0)) | (strong(X0) | ~curious(X0)))) [nnf transformation 1]
30. ! [X0] : (((~strong(X0) & curious(X0)) | (~funny(X0) & curious(X0))) & (funny(X0) | ~curious(X0) | strong(X0) | ~curious(X0))) [flattening 29]
49. ! [X0] : ((~tall(X0) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | tall(X0))) [nnf transformation 10]
50. ! [X0] : ((~tall(X0) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | tall(X0))) [flattening 49]
63. curious(X0) | curious(X0) [cnf transformation 30]
97. ~tall(X0) | ~old(X0) [cnf transformation 50]
108. tall(X0) | ~curious(X0) [cnf transformation 26]
118. old(mary) [cnf transformation 18]
120. curious(X0) [duplicate literal removal 63]
196. tall(X0) [subsumption resolution 108,120]
217. ~old(X0) [resolution 97,196]
218. $false [resolution 217,118]
% SZS output end Proof for 1101148453798483881657232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not wise then mary is both not humble and humble and vice versa.
If someone is both not old and tall then someone is either brave or not tall and vice versa.
If someone is either kind or not happy then someone is curious.
If someone is curious or rich then alice is curious or not strong.
Everyone who is patient or humble is not kind.
Everyone who is not funny or wise is either not old or not generous.
Everyone who is either strong or not calm is not humble and vice versa.
If someone is either humble or kind then mary is both not quiet and not creative and vice versa.
If john is either tall or kind then lucy is not wise or not generous and vice versa.
Everyone who is either humble or calm is strong or not strong.
Everyone who is creative or not rich is both generous and old.
Everyone who is quiet is tall and vice versa.
Everyone who is either humble or brave is either not strong or rich and vice versa.
Everyone who is both patient and not tall is not kind and vice versa.
If susan is both not wise and calm then paul is both calm and not happy.
Everyone who is either not kind or strong is not humble.
Someone is humble.
Paul is either not brave or wise.
Someone is strong.
Susan is both brave and not strong.
Someone is happy or not curious.
Paul is both quiet and curious.
Someone is wise or not humble.
Someone is not rich or wise. | Susan is not generous. | contradiction | ((~wise(fred))<=>((~humble(mary)&humble(mary))))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:((brave(X)<~>~tall(X)))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:(curious(X))))&
((?[X]:((curious(X)|rich(X))))=>((curious(alice)|~strong(alice))))&
(![X]:((patient(X)|humble(X))=>~kind(X)))&
(![X]:((~funny(X)|wise(X))=>(~old(X)<~>~generous(X))))&
(![X]:((strong(X)<~>~calm(X))<=>~humble(X)))&
((?[X]:((humble(X)<~>kind(X))))<=>((~quiet(mary)&~creative(mary))))&
(((tall(john)<~>kind(john)))<=>((~wise(lucy)|~generous(lucy))))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)|~strong(X))))&
(![X]:((creative(X)|~rich(X))=>(generous(X)&old(X))))&
(![X]:(quiet(X)<=>tall(X)))&
(![X]:((humble(X)<~>brave(X))<=>(~strong(X)<~>rich(X))))&
(![X]:((patient(X)&~tall(X))<=>~kind(X)))&
(((~wise(susan)&calm(susan)))=>((calm(paul)&~happy(paul))))&
(![X]:((~kind(X)<~>strong(X))=>~humble(X)))&
(?[X]:(humble(X)))&
((~brave(paul)<~>wise(paul)))&
(?[X]:(strong(X)))&
((brave(susan)&~strong(susan)))&
(?[X]:((happy(X)|~curious(X))))&
((quiet(paul)&curious(paul)))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:((~rich(X)|wise(X)))) | ~generous(susan) | [
"p4",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 753862617685840338348514
% SZS output start Proof for 753862617685840338348514
5. ! [X0] : ((humble(X0) | patient(X0)) => ~kind(X0)) [input p4]
11. ! [X0] : ((~rich(X0) | creative(X0)) => (old(X0) & generous(X0))) [input p10]
13. ! [X0] : ((humble(X0) <~> brave(X0)) <=> (~strong(X0) <~> rich(X0))) [input p12]
16. ! [X0] : ((~kind(X0) <~> strong(X0)) => ~humble(X0)) [input p15]
20. ~strong(susan) & brave(susan) [input p19]
25. ~generous(susan) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 5]
36. ! [X0] : ((old(X0) & generous(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 11]
39. ! [X0] : (~humble(X0) | (~kind(X0) <=> strong(X0))) [ennf transformation 16]
62. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) & (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 13]
65. ! [X0] : (~humble(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) [nnf transformation 39]
91. ~kind(X0) | ~humble(X0) [cnf transformation 32]
113. generous(X0) | rich(X0) [cnf transformation 36]
121. ~rich(X0) | strong(X0) | humble(X0) | ~brave(X0) [cnf transformation 62]
131. ~humble(X0) | strong(X0) | kind(X0) [cnf transformation 65]
137. brave(susan) [cnf transformation 20]
138. ~strong(susan) [cnf transformation 20]
144. ~generous(susan) [cnf transformation 25]
285. ~humble(X0) | strong(X0) [subsumption resolution 131,91]
323. rich(susan) [resolution 113,144]
427. strong(susan) | humble(susan) | ~brave(susan) [resolution 121,323]
430. humble(susan) | ~brave(susan) [subsumption resolution 427,138]
431. humble(susan) [subsumption resolution 430,137]
517. strong(susan) [resolution 431,285]
521. $false [subsumption resolution 517,138]
% SZS output end Proof for 753862617685840338348514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or funny then someone is both not strong and quiet and vice versa.
If someone is either strong or curious then fred is not kind and vice versa.
If susan is not rich then john is quiet or patient.
If mary is either not tall or generous then someone is not happy or kind.
If paul is both humble and not kind then someone is both funny and not strong and vice versa.
If someone is not old or tall then alice is not humble and vice versa.
Everyone who is both not humble and brave is either rich or not tall and vice versa.
Everyone who is both not strong and old is calm or quiet and vice versa.
If someone is either not patient or old then someone is not brave.
If someone is tall or rich then someone is calm and vice versa.
Everyone who is both not calm and funny is patient or brave and vice versa.
Everyone who is both rich and not humble is both old and not strong.
If alice is both quiet and rich then alice is not calm and vice versa.
If someone is not calm then someone is wise or calm.
Everyone who is old is not humble.
If someone is humble then someone is not humble and vice versa.
Alice is not patient or not strong.
John is strong.
Susan is both calm and wise.
Someone is wise or funny.
Someone is not creative.
Mary is not humble.
Someone is either strong or calm.
Someone is not kind. | Alice is not strong. | entailment | ((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((~strong(X)&quiet(X)))))&
((?[X]:((strong(X)<~>curious(X))))<=>(~kind(fred)))&
((~rich(susan))=>((quiet(john)|patient(john))))&
(((~tall(mary)<~>generous(mary)))=>(?[X]:((~happy(X)|kind(X)))))&
(((humble(paul)&~kind(paul)))<=>(?[X]:((funny(X)&~strong(X)))))&
((?[X]:((~old(X)|tall(X))))<=>(~humble(alice)))&
(![X]:((~humble(X)&brave(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~strong(X)&old(X))<=>(calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:(~brave(X))))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((~calm(X)&funny(X))<=>(patient(X)|brave(X))))&
(![X]:((rich(X)&~humble(X))=>(old(X)&~strong(X))))&
(((quiet(alice)&rich(alice)))<=>(~calm(alice)))&
((?[X]:(~calm(X)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(old(X)=>~humble(X)))&
((?[X]:(humble(X)))<=>(?[X]:(~humble(X))))&
((~patient(alice)|~strong(alice)))&
(strong(john))&
((calm(susan)&wise(susan)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:(~creative(X)))&
(~humble(mary))&
(?[X]:((strong(X)<~>calm(X))))&
(?[X]:(~kind(X))) | ~strong(alice) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2104700736330419505366476
% SZS output start Proof for 2104700736330419505366476
8. ! [X0] : ((old(X0) & ~strong(X0)) <=> (quiet(X0) | calm(X0))) [input p7]
13. (rich(alice) & quiet(alice)) <=> ~calm(alice) [input p12]
25. strong(alice) [input hypothesis]
62. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (~old(X0) | strong(X0)))) [nnf transformation 8]
63. ! [X0] : (((old(X0) & ~strong(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | ~old(X0) | strong(X0))) [flattening 62]
75. ((rich(alice) & quiet(alice)) | calm(alice)) & (~calm(alice) | (~rich(alice) | ~quiet(alice))) [nnf transformation 13]
76. ((rich(alice) & quiet(alice)) | calm(alice)) & (~calm(alice) | ~rich(alice) | ~quiet(alice)) [flattening 75]
112. ~strong(X0) | ~calm(X0) [cnf transformation 63]
113. ~quiet(X0) | ~strong(X0) [cnf transformation 63]
129. quiet(alice) | calm(alice) [cnf transformation 76]
141. strong(alice) [cnf transformation 25]
286. 34 <=> calm(alice) [avatar definition]
295. 36 <=> quiet(alice) [avatar definition]
297. quiet(alice) <- (36) [avatar component clause 295]
298. 34 | 36 [avatar split clause 129,295,286]
321. 42 <=> strong(alice) [avatar definition]
322. strong(alice) <- (42) [avatar component clause 321]
334. 42 [avatar split clause 141,321]
352. ~calm(alice) <- (42) [resolution 112,322]
358. ~34 | ~42 [avatar split clause 352,321,286]
361. ~strong(alice) <- (36) [resolution 113,297]
364. $false <- (36, 42) [subsumption resolution 361,322]
365. ~36 | ~42 [avatar contradiction clause 364]
366. $false [avatar sat refutation 298,334,358,365]
% SZS output end Proof for 2104700736330419505366476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is tall then susan is both quiet and not strong.
Everyone who is not wise is not wise or not quiet.
If someone is both curious and not quiet then someone is curious.
If someone is not old then someone is both quiet and curious and vice versa.
Everyone who is either not calm or not old is either old or patient.
Everyone who is not calm or old is not strong or quiet and vice versa.
If paul is either rich or not generous then someone is patient or tall and vice versa.
Everyone who is not quiet is either not happy or quiet and vice versa.
If susan is happy or rich then paul is tall and vice versa.
If someone is not brave or not creative then paul is humble and vice versa.
If someone is not quiet or creative then paul is both kind and not curious and vice versa.
Everyone who is both kind and patient is either not happy or not rich.
Everyone who is either curious or old is both not brave and happy.
Everyone who is both not happy and not curious is both not kind and humble and vice versa.
If someone is patient or calm then mary is either not calm or not funny.
If someone is both not humble and rich then paul is humble and vice versa.
John is either not strong or not wise.
Someone is either quiet or not patient.
Someone is quiet or tall.
Susan is generous.
Someone is not funny or not old.
Paul is either not wise or quiet.
Someone is both old and not humble. | Paul is not humble. | contradiction | ((tall(fred))=>((quiet(susan)&~strong(susan))))&
(![X]:(~wise(X)=>(~wise(X)|~quiet(X))))&
((?[X]:((curious(X)&~quiet(X))))=>(?[X]:(curious(X))))&
((?[X]:(~old(X)))<=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((~calm(X)<~>~old(X))=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)|old(X))<=>(~strong(X)|quiet(X))))&
(((rich(paul)<~>~generous(paul)))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>quiet(X))))&
(((happy(susan)|rich(susan)))<=>(tall(paul)))&
((?[X]:((~brave(X)|~creative(X))))<=>(humble(paul)))&
((?[X]:((~quiet(X)|creative(X))))<=>((kind(paul)&~curious(paul))))&
(![X]:((kind(X)&patient(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((curious(X)<~>old(X))=>(~brave(X)&happy(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~kind(X)&humble(X))))&
((?[X]:((patient(X)|calm(X))))=>((~calm(mary)<~>~funny(mary))))&
((?[X]:((~humble(X)&rich(X))))<=>(humble(paul)))&
((~strong(john)<~>~wise(john)))&
(?[X]:((quiet(X)<~>~patient(X))))&
(?[X]:((quiet(X)|tall(X))))&
(generous(susan))&
(?[X]:((~funny(X)|~old(X))))&
((~wise(paul)<~>quiet(paul)))&
(?[X]:((old(X)&~humble(X)))) | ~humble(paul) | [
"p7",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2998288509395646095696522
% SZS output start Proof for 2998288509395646095696522
8. ! [X0] : (~quiet(X0) <=> (~happy(X0) <~> quiet(X0))) [input p7]
10. ? [X0] : (~creative(X0) | ~brave(X0)) <=> humble(paul) [input p9]
11. ? [X0] : (creative(X0) | ~quiet(X0)) <=> (~curious(paul) & kind(paul)) [input p10]
14. ! [X0] : ((~curious(X0) & ~happy(X0)) <=> (humble(X0) & ~kind(X0))) [input p13]
24. ~humble(paul) [input hypothesis]
51. ! [X0] : ((~quiet(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | quiet(X0))) [nnf transformation 8]
54. (? [X0] : (~creative(X0) | ~brave(X0)) | ~humble(paul)) & (humble(paul) | ! [X0] : (creative(X0) & brave(X0))) [nnf transformation 10]
55. (? [X0] : (~creative(X0) | ~brave(X0)) | ~humble(paul)) & (humble(paul) | ! [X1] : (creative(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (~creative(X0) | ~brave(X0)) => (~creative(sK4) | ~brave(sK4)) [choice axiom]
57. ((~creative(sK4) | ~brave(sK4)) | ~humble(paul)) & (humble(paul) | ! [X1] : (creative(X1) & brave(X1))) [skolemisation 55,56]
58. (? [X0] : (creative(X0) | ~quiet(X0)) | (curious(paul) | ~kind(paul))) & ((~curious(paul) & kind(paul)) | ! [X0] : (~creative(X0) & quiet(X0))) [nnf transformation 11]
59. (? [X0] : (creative(X0) | ~quiet(X0)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X0] : (~creative(X0) & quiet(X0))) [flattening 58]
60. (? [X0] : (creative(X0) | ~quiet(X0)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X1] : (~creative(X1) & quiet(X1))) [rectify 59]
61. ? [X0] : (creative(X0) | ~quiet(X0)) => (creative(sK5) | ~quiet(sK5)) [choice axiom]
62. ((creative(sK5) | ~quiet(sK5)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X1] : (~creative(X1) & quiet(X1))) [skolemisation 60,61]
65. ! [X0] : (((~curious(X0) & ~happy(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (curious(X0) | happy(X0)))) [nnf transformation 14]
66. ! [X0] : (((~curious(X0) & ~happy(X0)) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | curious(X0) | happy(X0))) [flattening 65]
104. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 51]
107. ~quiet(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 51]
112. humble(paul) | creative(X1) [cnf transformation 57]
117. ~curious(paul) | ~creative(X1) [cnf transformation 62]
126. humble(X0) | curious(X0) | happy(X0) [cnf transformation 66]
147. ~humble(paul) [cnf transformation 24]
148. quiet(X0) | ~happy(X0) [duplicate literal removal 104]
149. ~happy(X0) | ~quiet(X0) [duplicate literal removal 107]
223. ~happy(X0) [subsumption resolution 148,149]
236. 19 <=> humble(paul) [avatar definition]
238. ~humble(paul) <- (~19) [avatar component clause 236]
249. 22 <=> ! [X1] : creative(X1) [avatar definition]
250. creative(X1) <- (22) [avatar component clause 249]
251. 22 | 19 [avatar split clause 112,236,249]
261. 25 <=> curious(paul) [avatar definition]
274. 28 <=> ! [X1] : ~creative(X1) [avatar definition]
275. ~creative(X1) <- (28) [avatar component clause 274]
276. 28 | ~25 [avatar split clause 117,261,274]
286. humble(X0) | curious(X0) [subsumption resolution 126,223]
365. ~19 [avatar split clause 147,236]
380. curious(paul) <- (~19) [resolution 286,238]
383. 25 | 19 [avatar split clause 380,236,261]
384. $false <- (22, 28) [subsumption resolution 275,250]
385. ~22 | ~28 [avatar contradiction clause 384]
386. $false [avatar sat refutation 251,276,365,383,385]
% SZS output end Proof for 2998288509395646095696522
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or kind is rich or funny. Everyone who is either not calm or strong is strong and vice versa. Everyone who is either not creative or not wise is either not rich or humble and vice versa. Everyone who is both not old and strong is not patient. Everyone who is both not strong and tall is not creative. Everyone who is both not creative and patient is wise. Everyone who is either old or not wise is both not old and not brave. Everyone who is both not kind and old is either strong or not curious and vice versa. Everyone who is both tall and strong is not quiet or not old and vice versa. If alice is rich then paul is happy and vice versa. Everyone who is happy or wise is not creative and vice versa. If someone is either not tall or not brave then someone is creative or patient and vice versa. If mary is calm or not tall then someone is either tall or not quiet. Everyone who is either not brave or not patient is both not calm and not tall. Everyone who is funny or happy is both wise and not tall and vice versa. If mary is either rich or brave then someone is both not creative and not patient and vice versa. Someone is not patient or not curious. Alice is both not creative and not patient. Someone is either generous or tall. Fred is brave. Someone is not kind or not creative. Lucy is either kind or not quiet. | Fred is not creative. | contradiction | (![X]:((~old(X)<~>kind(X))=>(rich(X)|funny(X))))&
(![X]:((~calm(X)<~>strong(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((~old(X)&strong(X))=>~patient(X)))&
(![X]:((~strong(X)&tall(X))=>~creative(X)))&
(![X]:((~creative(X)&patient(X))=>wise(X)))&
(![X]:((old(X)<~>~wise(X))=>(~old(X)&~brave(X))))&
(![X]:((~kind(X)&old(X))<=>(strong(X)<~>~curious(X))))&
(![X]:((tall(X)&strong(X))<=>(~quiet(X)|~old(X))))&
((rich(alice))<=>(happy(paul)))&
(![X]:((happy(X)|wise(X))<=>~creative(X)))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(?[X]:((creative(X)|patient(X)))))&
(((calm(mary)|~tall(mary)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>(~calm(X)&~tall(X))))&
(![X]:((funny(X)|happy(X))<=>(wise(X)&~tall(X))))&
(((rich(mary)<~>brave(mary)))<=>(?[X]:((~creative(X)&~patient(X)))))&
(?[X]:((~patient(X)|~curious(X))))&
((~creative(alice)&~patient(alice)))&
(?[X]:((generous(X)<~>tall(X))))&
(brave(fred))&
(?[X]:((~kind(X)|~creative(X))))&
((kind(lucy)<~>~quiet(lucy))) | ~creative(fred) | [
"p1",
"p3",
"p5",
"p6",
"p8",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1242538496991385173156204
% SZS output start Proof for 1242538496991385173156204
2. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> strong(X0)) [input p1]
4. ! [X0] : ((strong(X0) & ~old(X0)) => ~patient(X0)) [input p3]
6. ! [X0] : ((patient(X0) & ~creative(X0)) => wise(X0)) [input p5]
7. ! [X0] : ((old(X0) <~> ~wise(X0)) => (~brave(X0) & ~old(X0))) [input p6]
9. ! [X0] : ((strong(X0) & tall(X0)) <=> (~old(X0) | ~quiet(X0))) [input p8]
14. ! [X0] : ((~brave(X0) <~> ~patient(X0)) => (~tall(X0) & ~calm(X0))) [input p13]
20. brave(fred) [input p19]
23. ~creative(fred) [input hypothesis]
27. ! [X0] : (~patient(X0) | (~strong(X0) | old(X0))) [ennf transformation 4]
28. ! [X0] : (~patient(X0) | ~strong(X0) | old(X0)) [flattening 27]
31. ! [X0] : (wise(X0) | (~patient(X0) | creative(X0))) [ennf transformation 6]
32. ! [X0] : (wise(X0) | ~patient(X0) | creative(X0)) [flattening 31]
33. ! [X0] : ((~brave(X0) & ~old(X0)) | (old(X0) <=> ~wise(X0))) [ennf transformation 7]
35. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~brave(X0) <=> ~patient(X0))) [ennf transformation 14]
37. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | ~strong(X0)) & (strong(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 2]
39. ! [X0] : ((~brave(X0) & ~old(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) [nnf transformation 33]
42. ! [X0] : (((strong(X0) & tall(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 9]
43. ! [X0] : (((strong(X0) & tall(X0)) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | ~strong(X0) | ~tall(X0))) [flattening 42]
55. ! [X0] : ((~tall(X0) & ~calm(X0)) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) [nnf transformation 35]
72. strong(X0) | strong(X0) | calm(X0) [cnf transformation 37]
75. ~strong(X0) | calm(X0) | ~strong(X0) [cnf transformation 37]
84. ~patient(X0) | ~strong(X0) | old(X0) [cnf transformation 28]
86. ~patient(X0) | wise(X0) | creative(X0) [cnf transformation 32]
87. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 39]
101. strong(X0) | old(X0) [cnf transformation 43]
118. ~calm(X0) | ~brave(X0) | patient(X0) [cnf transformation 55]
137. brave(fred) [cnf transformation 20]
141. ~creative(fred) [cnf transformation 23]
142. ~wise(X0) | ~old(X0) [duplicate literal removal 87]
143. strong(X0) | calm(X0) [duplicate literal removal 72]
144. ~strong(X0) | calm(X0) [duplicate literal removal 75]
145. calm(X0) [subsumption resolution 143,144]
212. ~brave(X0) | patient(X0) [subsumption resolution 118,145]
286. patient(fred) [resolution 212,137]
292. ~strong(fred) | old(fred) [resolution 84,286]
293. old(fred) [subsumption resolution 292,101]
316. wise(fred) | creative(fred) [resolution 86,286]
317. wise(fred) [subsumption resolution 316,141]
319. ~old(fred) [resolution 317,142]
321. $false [subsumption resolution 319,293]
% SZS output end Proof for 1242538496991385173156204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both wise and creative. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. If susan is not kind then susan is both generous and not old and vice versa. Everyone who is funny or tall is patient and vice versa. Everyone who is either happy or humble is either not brave or not calm. Someone is not humble or not kind. Someone is both funny and strong. Paul is wise. Someone is not humble. Someone is humble. Someone is generous. Mary is not generous. Lucy is both creative and not patient. | Lucy is wise. | entailment | (![X]:((patient(X)&generous(X))=>(wise(X)&creative(X))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:((funny(X)&strong(X))))&
(wise(paul))&
(?[X]:(~humble(X)))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(~generous(mary))&
((creative(lucy)&~patient(lucy))) | wise(lucy) | [
"p3",
"p8",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 438800609950123576226366
% SZS output start Proof for 438800609950123576226366
4. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> funny(X0)) [input p3]
9. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~humble(X0) & curious(X0))) [input p8]
15. ! [X0] : ((tall(X0) | funny(X0)) <=> patient(X0)) [input p14]
24. ~patient(lucy) & creative(lucy) [input p23]
25. ~wise(lucy) [input hypothesis]
26. ! [X0] : ((tall(X0) | funny(X0)) => patient(X0)) [unused predicate definition removal 15]
38. ! [X0] : (patient(X0) | (~tall(X0) & ~funny(X0))) [ennf transformation 26]
42. ! [X0] : (((~humble(X0) | ~creative(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) & creative(X0)))) [nnf transformation 4]
43. ! [X0] : ((~humble(X0) | ~creative(X0) | ~funny(X0)) & (funny(X0) | (humble(X0) & creative(X0)))) [flattening 42]
51. ! [X0] : (((quiet(X0) | ~wise(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 9]
52. ! [X0] : ((quiet(X0) | ~wise(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [flattening 51]
76. funny(X0) | humble(X0) [cnf transformation 43]
91. ~humble(X0) | wise(X0) [cnf transformation 52]
107. ~funny(X0) | patient(X0) [cnf transformation 38]
122. ~patient(lucy) [cnf transformation 24]
123. ~wise(lucy) [cnf transformation 25]
243. humble(X0) | patient(X0) [resolution 107,76]
311. wise(X0) | patient(X0) [resolution 243,91]
322. patient(lucy) [resolution 311,123]
323. $false [subsumption resolution 322,122]
% SZS output end Proof for 438800609950123576226366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is not tall.
If paul is either curious or patient then paul is both not happy and rich and vice versa.
If john is either patient or not brave then mary is either not generous or not calm and vice versa.
If lucy is both not kind and curious then someone is creative or not quiet.
Everyone who is either not strong or not patient is both not strong and not happy and vice versa.
If someone is both happy and not creative then mary is quiet and vice versa.
If paul is not happy or not tall then someone is happy or humble and vice versa.
Everyone who is either curious or not happy is both curious and kind and vice versa.
Everyone who is both not calm and tall is calm and vice versa.
Everyone who is both tall and funny is either funny or quiet.
If fred is either not strong or not kind then someone is funny or rich.
Everyone who is both not creative and not patient is either not old or not wise and vice versa.
If paul is tall then fred is happy and vice versa.
Everyone who is either not creative or quiet is either curious or not patient.
If someone is kind then paul is humble.
If someone is both humble and strong then paul is either tall or not strong and vice versa.
Someone is not kind or not generous.
Someone is quiet.
Someone is strong.
Mary is both not tall and humble.
Alice is wise.
Mary is brave. | Fred is humble. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~tall(X))))&
(((curious(paul)<~>patient(paul)))<=>((~happy(paul)&rich(paul))))&
(((patient(john)<~>~brave(john)))<=>((~generous(mary)<~>~calm(mary))))&
(((~kind(lucy)&curious(lucy)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((happy(X)&~creative(X))))<=>(quiet(mary)))&
(((~happy(paul)|~tall(paul)))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(curious(X)&kind(X))))&
(![X]:((~calm(X)&tall(X))<=>calm(X)))&
(![X]:((tall(X)&funny(X))=>(funny(X)<~>quiet(X))))&
(((~strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~old(X)<~>~wise(X))))&
((tall(paul))<=>(happy(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(kind(X)))=>(humble(paul)))&
((?[X]:((humble(X)&strong(X))))<=>((tall(paul)<~>~strong(paul))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
((~tall(mary)&humble(mary)))&
(wise(alice))&
(brave(mary)) | humble(fred) | [] | null | 0 |
Everyone who is either humble or quiet is not strong or not happy and vice versa.
Everyone who is not brave is both happy and generous and vice versa.
Everyone who is either not generous or not creative is both humble and tall.
Everyone who is either not funny or brave is curious or not curious and vice versa.
Everyone who is not strong or generous is not humble or not curious.
Everyone who is either not quiet or calm is both old and calm and vice versa.
If someone is either humble or brave then mary is humble or not kind.
Everyone who is both not rich and calm is strong or not rich and vice versa.
If mary is not patient or not kind then mary is not generous.
Everyone who is both not humble and not old is both not calm and brave.
Everyone who is tall is not brave or happy.
If mary is both curious and not quiet then lucy is not wise or not creative.
Everyone who is either rich or not creative is generous and vice versa.
If john is generous then someone is both not calm and patient and vice versa.
Everyone who is not funny or tall is not calm or rich and vice versa.
If paul is not rich then someone is both not kind and not generous and vice versa.
Someone is brave.
Alice is creative.
Someone is happy or not calm.
Someone is not curious or not patient.
Someone is either not creative or rich.
Mary is both patient and not humble.
Someone is not quiet or not wise.
Fred is strong or not funny. | Paul is not rich. | contradiction | (![X]:((humble(X)<~>quiet(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)&generous(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(humble(X)&tall(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)|~curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)|~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(old(X)&calm(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((humble(mary)|~kind(mary))))&
(![X]:((~rich(X)&calm(X))<=>(strong(X)|~rich(X))))&
(((~patient(mary)|~kind(mary)))=>(~generous(mary)))&
(![X]:((~humble(X)&~old(X))=>(~calm(X)&brave(X))))&
(![X]:(tall(X)=>(~brave(X)|happy(X))))&
(((curious(mary)&~quiet(mary)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:((rich(X)<~>~creative(X))<=>generous(X)))&
((generous(john))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~calm(X)|rich(X))))&
((~rich(paul))<=>(?[X]:((~kind(X)&~generous(X)))))&
(?[X]:(brave(X)))&
(creative(alice))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((patient(mary)&~humble(mary)))&
(?[X]:((~quiet(X)|~wise(X))))&
((strong(fred)|~funny(fred))) | ~rich(paul) | [
"p2",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4976175185473529109179740
% SZS output start Proof for 4976175185473529109179740
3. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (tall(X0) & humble(X0))) [input p2]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~rich(X0) | strong(X0))) [input p7]
13. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> generous(X0)) [input p12]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
25. ~rich(paul) [input hypothesis]
28. ! [X0] : ((tall(X0) & humble(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 3]
42. ! [X0] : ((tall(X0) & humble(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 28]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : (((tall(X0) | ~funny(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | ~funny(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | (~tall(X0) & funny(X0)))) [flattening 55]
81. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 42]
82. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 42]
103. rich(X0) | calm(X0) [cnf transformation 49]
110. rich(X0) | generous(X0) | creative(X0) [cnf transformation 50]
111. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
116. rich(X0) | ~calm(X0) | funny(X0) [cnf transformation 56]
117. rich(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 56]
119. ~rich(X0) | ~funny(X0) | tall(X0) [cnf transformation 56]
132. ~rich(paul) [cnf transformation 25]
182. ~tall(X0) | rich(X0) [subsumption resolution 117,103]
183. rich(X0) | funny(X0) [subsumption resolution 116,103]
188. 12 <=> rich(paul) [avatar definition]
190. ~rich(paul) <- (~12) [avatar component clause 188]
241. ~12 [avatar split clause 132,188]
257. funny(paul) <- (~12) [resolution 183,190]
452. 48 <=> creative(paul) [avatar definition]
454. creative(paul) <- (48) [avatar component clause 452]
456. 49 <=> generous(paul) [avatar definition]
498. rich(paul) | ~generous(paul) <- (48) [resolution 454,111]
499. tall(paul) | generous(paul) <- (48) [resolution 454,81]
501. ~generous(paul) <- (~12, 48) [subsumption resolution 498,190]
502. ~49 | 12 | ~48 [avatar split clause 501,452,188,456]
504. 52 <=> tall(paul) [avatar definition]
506. tall(paul) <- (52) [avatar component clause 504]
507. 49 | 52 | ~48 [avatar split clause 499,452,504,456]
572. ~funny(X0) | tall(X0) | generous(X0) | creative(X0) [resolution 119,110]
577. ~funny(X0) | tall(X0) | creative(X0) [subsumption resolution 572,82]
737. tall(paul) | creative(paul) <- (~12) [resolution 577,257]
758. rich(paul) <- (52) [resolution 506,182]
760. $false <- (~12, 52) [subsumption resolution 758,190]
761. 12 | ~52 [avatar contradiction clause 760]
762. 48 | 52 | 12 [avatar split clause 737,188,504,452]
763. $false [avatar sat refutation 241,502,507,761,762]
% SZS output end Proof for 4976175185473529109179740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or strong is not rich or wise and vice versa. If mary is both not funny and curious then someone is not funny or strong and vice versa. Everyone who is either calm or wise is tall and vice versa. Everyone who is both not curious and wise is not funny. Everyone who is not wise or not kind is quiet or not wise and vice versa. Everyone who is either humble or not curious is creative. Everyone who is both rich and curious is either old or funny and vice versa. Everyone who is not funny or not calm is funny or patient and vice versa. If paul is both kind and not kind then fred is both not kind and not calm. If someone is not kind or tall then john is not happy or kind. Everyone who is both brave and tall is not funny or creative and vice versa. If someone is old or not creative then someone is humble. Everyone who is not brave or kind is quiet or kind and vice versa. If lucy is both not patient and happy then someone is curious or not curious. If alice is not brave then susan is not wise and vice versa. Everyone who is either wise or tall is generous or rich and vice versa. Fred is not rich. Fred is happy. Someone is either generous or rich. Alice is both happy and not generous. John is not wise. Susan is either quiet or happy. Paul is calm or rich. Alice is both not creative and funny. | Paul is not rich. | neutral | (![X]:((happy(X)<~>strong(X))<=>(~rich(X)|wise(X))))&
(((~funny(mary)&curious(mary)))<=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:((calm(X)<~>wise(X))<=>tall(X)))&
(![X]:((~curious(X)&wise(X))=>~funny(X)))&
(![X]:((~wise(X)|~kind(X))<=>(quiet(X)|~wise(X))))&
(![X]:((humble(X)<~>~curious(X))=>creative(X)))&
(![X]:((rich(X)&curious(X))<=>(old(X)<~>funny(X))))&
(![X]:((~funny(X)|~calm(X))<=>(funny(X)|patient(X))))&
(((kind(paul)&~kind(paul)))=>((~kind(fred)&~calm(fred))))&
((?[X]:((~kind(X)|tall(X))))=>((~happy(john)|kind(john))))&
(![X]:((brave(X)&tall(X))<=>(~funny(X)|creative(X))))&
((?[X]:((old(X)|~creative(X))))=>(?[X]:(humble(X))))&
(![X]:((~brave(X)|kind(X))<=>(quiet(X)|kind(X))))&
(((~patient(lucy)&happy(lucy)))=>(?[X]:((curious(X)|~curious(X)))))&
((~brave(alice))<=>(~wise(susan)))&
(![X]:((wise(X)<~>tall(X))<=>(generous(X)|rich(X))))&
(~rich(fred))&
(happy(fred))&
(?[X]:((generous(X)<~>rich(X))))&
((happy(alice)&~generous(alice)))&
(~wise(john))&
((quiet(susan)<~>happy(susan)))&
((calm(paul)|rich(paul)))&
((~creative(alice)&funny(alice))) | ~rich(paul) | [] | null | 0 |
If someone is both quiet and not strong then paul is both not old and not patient. Everyone who is either not strong or not tall is either not calm or not strong. Everyone who is strong is either not old or humble. Everyone who is not creative or not humble is both not old and not tall. If someone is not brave or not strong then fred is patient or tall. Everyone who is either wise or strong is not calm and vice versa. Everyone who is either strong or not strong is both not creative and curious and vice versa. If paul is not generous or tall then paul is not happy or not quiet and vice versa. Everyone who is funny is not funny or not calm and vice versa. Everyone who is not brave is creative or tall and vice versa. Everyone who is funny is both happy and not quiet and vice versa. Everyone who is both not rich and creative is either humble or not funny and vice versa. If paul is not wise then someone is both not humble and not tall. Everyone who is both generous and brave is both not calm and rich and vice versa. If someone is rich then someone is both happy and funny and vice versa. Fred is either tall or not wise. Susan is not tall. Lucy is either rich or not humble. Someone is both not quiet and not wise. Someone is not wise or patient. | Paul is generous. | contradiction | ((?[X]:((quiet(X)&~strong(X))))=>((~old(paul)&~patient(paul))))&
(![X]:((~strong(X)<~>~tall(X))=>(~calm(X)<~>~strong(X))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
((tall(fred)<~>~wise(fred)))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~wise(X)|patient(X)))) | generous(paul) | [
"p3",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 802757295812408619576666
% SZS output start Proof for 802757295812408619576666
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
8. (tall(paul) | ~generous(paul)) <=> (~quiet(paul) | ~happy(paul)) [input p7]
9. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~quiet(X0) & happy(X0))) [input p10]
21. generous(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
33. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 7]
34. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 33]
35. ((tall(paul) | ~generous(paul)) | (quiet(paul) & happy(paul))) & ((~quiet(paul) | ~happy(paul)) | (~tall(paul) & generous(paul))) [nnf transformation 8]
36. (tall(paul) | ~generous(paul) | (quiet(paul) & happy(paul))) & (~quiet(paul) | ~happy(paul) | (~tall(paul) & generous(paul))) [flattening 35]
37. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 9]
38. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 37]
41. ! [X0] : ((funny(X0) | (quiet(X0) | ~happy(X0))) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [nnf transformation 11]
42. ! [X0] : ((funny(X0) | quiet(X0) | ~happy(X0)) & ((~quiet(X0) & happy(X0)) | ~funny(X0))) [flattening 41]
70. ~tall(X0) | creative(X0) [cnf transformation 26]
78. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 34]
79. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 34]
87. tall(paul) | ~generous(paul) | quiet(paul) [cnf transformation 36]
89. funny(X0) | funny(X0) [cnf transformation 38]
95. ~quiet(X0) | ~funny(X0) [cnf transformation 42]
120. generous(paul) [cnf transformation 21]
122. funny(X0) [duplicate literal removal 89]
123. ~creative(X0) | ~strong(X0) [duplicate literal removal 78]
124. ~creative(X0) | strong(X0) [duplicate literal removal 79]
159. ~creative(X0) [subsumption resolution 123,124]
161. 8 <=> quiet(paul) [avatar definition]
163. quiet(paul) <- (8) [avatar component clause 161]
165. 9 <=> generous(paul) [avatar definition]
169. 10 <=> tall(paul) [avatar definition]
171. tall(paul) <- (10) [avatar component clause 169]
172. 8 | ~9 | 10 [avatar split clause 87,169,165,161]
182. ~quiet(X0) [subsumption resolution 95,122]
215. 9 [avatar split clause 120,165]
218. creative(paul) <- (10) [resolution 70,171]
219. $false <- (10) [subsumption resolution 218,159]
220. ~10 [avatar contradiction clause 219]
221. $false <- (8) [subsumption resolution 163,182]
222. ~8 [avatar contradiction clause 221]
223. $false [avatar sat refutation 172,215,220,222]
% SZS output end Proof for 802757295812408619576666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not kind is quiet and vice versa.
Everyone who is either not calm or creative is not brave or not strong and vice versa.
Everyone who is quiet is not quiet or calm.
If someone is not brave then someone is curious and vice versa.
If someone is patient then someone is both wise and happy and vice versa.
If fred is both kind and not patient then someone is either funny or curious.
Everyone who is old or quiet is both creative and not curious and vice versa.
If fred is not calm or not kind then someone is both creative and not patient.
If lucy is creative or not generous then fred is both not rich and not humble and vice versa.
Everyone who is either brave or rich is not old.
Everyone who is rich is either not humble or tall and vice versa.
Everyone who is not quiet or rich is kind and vice versa.
If someone is either not humble or not funny then susan is strong or not kind.
If fred is brave or not wise then mary is not creative.
If john is either not old or kind then lucy is not kind and vice versa.
If mary is calm or not patient then someone is either wise or not funny and vice versa.
Someone is both not old and strong.
Mary is tall.
Someone is not quiet or old.
Someone is old.
Someone is either not tall or kind.
Someone is both curious and generous. | Fred is not kind. | contradiction | (![X]:((curious(X)&~kind(X))<=>quiet(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~brave(X)|~strong(X))))&
(![X]:(quiet(X)=>(~quiet(X)|calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(curious(X))))&
((?[X]:(patient(X)))<=>(?[X]:((wise(X)&happy(X)))))&
(((kind(fred)&~patient(fred)))=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((old(X)|quiet(X))<=>(creative(X)&~curious(X))))&
(((~calm(fred)|~kind(fred)))=>(?[X]:((creative(X)&~patient(X)))))&
(((creative(lucy)|~generous(lucy)))<=>((~rich(fred)&~humble(fred))))&
(![X]:((brave(X)<~>rich(X))=>~old(X)))&
(![X]:(rich(X)<=>(~humble(X)<~>tall(X))))&
(![X]:((~quiet(X)|rich(X))<=>kind(X)))&
((?[X]:((~humble(X)<~>~funny(X))))=>((strong(susan)|~kind(susan))))&
(((brave(fred)|~wise(fred)))=>(~creative(mary)))&
(((~old(john)<~>kind(john)))<=>(~kind(lucy)))&
(((calm(mary)|~patient(mary)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
(?[X]:((~old(X)&strong(X))))&
(tall(mary))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
(?[X]:((curious(X)&generous(X)))) | ~kind(fred) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3592097907471459035183557
% SZS output start Proof for 3592097907471459035183557
1. ! [X0] : ((~kind(X0) & curious(X0)) <=> quiet(X0)) [input p0]
7. ! [X0] : ((quiet(X0) | old(X0)) <=> (~curious(X0) & creative(X0))) [input p6]
12. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> kind(X0)) [input p11]
23. ~kind(fred) [input hypothesis]
35. ! [X0] : (((~kind(X0) & curious(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | ~curious(X0)))) [nnf transformation 1]
36. ! [X0] : (((~kind(X0) & curious(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | ~curious(X0))) [flattening 35]
52. ! [X0] : (((quiet(X0) | old(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 7]
53. ! [X0] : ((quiet(X0) | old(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 52]
60. ! [X0] : (((rich(X0) | ~quiet(X0)) | ~kind(X0)) & (kind(X0) | (~rich(X0) & quiet(X0)))) [nnf transformation 12]
61. ! [X0] : ((rich(X0) | ~quiet(X0) | ~kind(X0)) & (kind(X0) | (~rich(X0) & quiet(X0)))) [flattening 60]
81. curious(X0) | ~quiet(X0) [cnf transformation 36]
100. ~curious(X0) | ~quiet(X0) [cnf transformation 53]
117. kind(X0) | quiet(X0) [cnf transformation 61]
143. ~kind(fred) [cnf transformation 23]
201. ~quiet(X0) [subsumption resolution 100,81]
239. kind(X0) [subsumption resolution 117,201]
299. $false [subsumption resolution 143,239]
% SZS output end Proof for 3592097907471459035183557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both strong and not creative is both not funny and not happy and vice versa.
Everyone who is rich or wise is not calm.
If susan is brave then someone is both not quiet and curious and vice versa.
Everyone who is either brave or kind is not tall.
If mary is not calm or patient then someone is both not brave and not strong.
Everyone who is not curious is not generous or not old and vice versa.
If mary is both not happy and not brave then fred is not patient and vice versa.
Everyone who is not curious or not wise is both curious and not patient.
If john is not strong or rich then alice is creative or tall and vice versa.
Everyone who is both happy and wise is wise or not strong and vice versa.
Everyone who is both not funny and old is either brave or not generous and vice versa.
If someone is both creative and not happy then lucy is both not calm and rich.
Everyone who is not strong is both creative and not wise.
Everyone who is rich is not calm and vice versa.
Someone is not humble.
Fred is both tall and not creative.
John is either not funny or not kind.
Paul is not creative.
Someone is both kind and not patient.
Someone is not kind or wise.
John is calm or kind.
Someone is brave. | Fred is not funny. | entailment | (![X]:((strong(X)&~creative(X))<=>(~funny(X)&~happy(X))))&
(![X]:((rich(X)|wise(X))=>~calm(X)))&
((brave(susan))<=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:((brave(X)<~>kind(X))=>~tall(X)))&
(((~calm(mary)|patient(mary)))=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|~old(X))))&
(((~happy(mary)&~brave(mary)))<=>(~patient(fred)))&
(![X]:((~curious(X)|~wise(X))=>(curious(X)&~patient(X))))&
(((~strong(john)|rich(john)))<=>((creative(alice)|tall(alice))))&
(![X]:((happy(X)&wise(X))<=>(wise(X)|~strong(X))))&
(![X]:((~funny(X)&old(X))<=>(brave(X)<~>~generous(X))))&
((?[X]:((creative(X)&~happy(X))))=>((~calm(lucy)&rich(lucy))))&
(![X]:(~strong(X)=>(creative(X)&~wise(X))))&
(![X]:(rich(X)<=>~calm(X)))&
(?[X]:(~humble(X)))&
((tall(fred)&~creative(fred)))&
((~funny(john)<~>~kind(john)))&
(~creative(paul))&
(?[X]:((kind(X)&~patient(X))))&
(?[X]:((~kind(X)|wise(X))))&
((calm(john)|kind(john)))&
(?[X]:(brave(X))) | ~funny(fred) | [
"p0",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5617968440378334318591681
% SZS output start Proof for 5617968440378334318591681
1. ! [X0] : ((~creative(X0) & strong(X0)) <=> (~happy(X0) & ~funny(X0))) [input p0]
10. ! [X0] : ((wise(X0) & happy(X0)) <=> (~strong(X0) | wise(X0))) [input p9]
13. ! [X0] : (~strong(X0) => (~wise(X0) & creative(X0))) [input p12]
16. ~creative(fred) & tall(fred) [input p15]
23. funny(fred) [input hypothesis]
30. ! [X0] : ((~wise(X0) & creative(X0)) | strong(X0)) [ennf transformation 13]
31. ! [X0] : (((~creative(X0) & strong(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 1]
32. ! [X0] : (((~creative(X0) & strong(X0)) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | creative(X0) | ~strong(X0))) [flattening 31]
46. ! [X0] : (((wise(X0) & happy(X0)) | (strong(X0) & ~wise(X0))) & ((~strong(X0) | wise(X0)) | (~wise(X0) | ~happy(X0)))) [nnf transformation 10]
47. ! [X0] : (((wise(X0) & happy(X0)) | (strong(X0) & ~wise(X0))) & (~strong(X0) | wise(X0) | ~wise(X0) | ~happy(X0))) [flattening 46]
58. ~funny(X0) | creative(X0) | ~strong(X0) [cnf transformation 32]
91. wise(X0) | strong(X0) [cnf transformation 47]
101. ~wise(X0) | strong(X0) [cnf transformation 30]
105. ~creative(fred) [cnf transformation 16]
114. funny(fred) [cnf transformation 23]
202. strong(X0) [subsumption resolution 101,91]
242. creative(fred) | ~strong(fred) [resolution 58,114]
243. ~strong(fred) [subsumption resolution 242,105]
244. $false [subsumption resolution 243,202]
% SZS output end Proof for 5617968440378334318591681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not curious and patient then someone is either not quiet or not wise.
If mary is not generous then someone is not old or tall and vice versa.
If paul is not wise or not patient then someone is kind or calm.
Everyone who is strong or generous is not tall or not wise and vice versa.
Everyone who is both not creative and not wise is patient and vice versa.
Everyone who is either not creative or generous is both generous and not quiet.
Everyone who is either kind or not wise is patient or tall and vice versa.
Everyone who is not old is either not creative or not strong and vice versa.
If john is not strong or not quiet then paul is both not tall and patient.
Everyone who is both not kind and not curious is either not happy or funny and vice versa.
Everyone who is both not generous and not humble is both generous and not humble and vice versa.
If susan is both not happy and rich then fred is calm or old and vice versa.
If someone is funny then lucy is humble and vice versa.
Everyone who is either not calm or not happy is creative and vice versa.
If mary is both tall and not kind then someone is either not tall or quiet and vice versa.
Everyone who is either not patient or not tall is either not happy or not kind and vice versa.
Someone is not funny.
Someone is not patient.
Someone is not rich.
Susan is not creative or tall.
John is both not tall and quiet.
Lucy is either brave or not strong.
Someone is humble.
Susan is either not tall or not creative. | Susan is tall. | entailment | (((~curious(paul)&patient(paul)))=>(?[X]:((~quiet(X)<~>~wise(X)))))&
((~generous(mary))<=>(?[X]:((~old(X)|tall(X)))))&
(((~wise(paul)|~patient(paul)))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((strong(X)|generous(X))<=>(~tall(X)|~wise(X))))&
(![X]:((~creative(X)&~wise(X))<=>patient(X)))&
(![X]:((~creative(X)<~>generous(X))=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(patient(X)|tall(X))))&
(![X]:(~old(X)<=>(~creative(X)<~>~strong(X))))&
(((~strong(john)|~quiet(john)))=>((~tall(paul)&patient(paul))))&
(![X]:((~kind(X)&~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~generous(X)&~humble(X))<=>(generous(X)&~humble(X))))&
(((~happy(susan)&rich(susan)))<=>((calm(fred)|old(fred))))&
((?[X]:(funny(X)))<=>(humble(lucy)))&
(![X]:((~calm(X)<~>~happy(X))<=>creative(X)))&
(((tall(mary)&~kind(mary)))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~happy(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
(?[X]:(~patient(X)))&
(?[X]:(~rich(X)))&
((~creative(susan)|tall(susan)))&
((~tall(john)&quiet(john)))&
((brave(lucy)<~>~strong(lucy)))&
(?[X]:(humble(X)))&
((~tall(susan)<~>~creative(susan))) | tall(susan) | [
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7884778243806187069869252
% SZS output start Proof for 7884778243806187069869252
20. tall(susan) | ~creative(susan) [input p19]
24. ~tall(susan) <~> ~creative(susan) [input p23]
25. ~tall(susan) [input hypothesis]
74. (creative(susan) | tall(susan)) & (~creative(susan) | ~tall(susan)) [nnf transformation 24]
145. tall(susan) | ~creative(susan) [cnf transformation 20]
152. creative(susan) | tall(susan) [cnf transformation 74]
153. ~tall(susan) [cnf transformation 25]
284. 26 <=> creative(susan) [avatar definition]
288. 27 <=> tall(susan) [avatar definition]
291. ~26 | 27 [avatar split clause 145,288,284]
303. 27 | 26 [avatar split clause 152,284,288]
305. ~27 [avatar split clause 153,288]
306. $false [avatar sat refutation 291,303,305]
% SZS output end Proof for 7884778243806187069869252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or rich is both not funny and not patient.
Everyone who is both calm and humble is funny and vice versa.
Everyone who is either strong or not curious is both humble and not patient and vice versa.
Everyone who is happy is both not calm and not strong.
Everyone who is not happy or not curious is old and vice versa.
Everyone who is either creative or not happy is not strong or patient.
If mary is happy or not wise then someone is either calm or kind.
If someone is either happy or not creative then someone is not rich and vice versa.
If mary is either not patient or happy then someone is either generous or not strong and vice versa.
Everyone who is both not creative and not quiet is kind or creative and vice versa.
Everyone who is not happy is not happy or not patient and vice versa.
If someone is both happy and not rich then paul is not strong.
Everyone who is not creative is old and vice versa.
Everyone who is not generous is strong or not quiet.
Everyone who is not creative is both humble and not calm and vice versa.
If someone is either not wise or tall then john is either tall or rich and vice versa.
Someone is either brave or creative.
Someone is either curious or not patient.
Someone is either quiet or not strong.
Someone is either strong or humble.
Susan is both not brave and not tall.
Mary is both not calm and not strong.
Mary is both old and not calm.
Someone is either tall or not quiet. | Susan is happy. | contradiction | (![X]:((creative(X)<~>rich(X))=>(~funny(X)&~patient(X))))&
(![X]:((calm(X)&humble(X))<=>funny(X)))&
(![X]:((strong(X)<~>~curious(X))<=>(humble(X)&~patient(X))))&
(![X]:(happy(X)=>(~calm(X)&~strong(X))))&
(![X]:((~happy(X)|~curious(X))<=>old(X)))&
(![X]:((creative(X)<~>~happy(X))=>(~strong(X)|patient(X))))&
(((happy(mary)|~wise(mary)))=>(?[X]:((calm(X)<~>kind(X)))))&
((?[X]:((happy(X)<~>~creative(X))))<=>(?[X]:(~rich(X))))&
(((~patient(mary)<~>happy(mary)))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~creative(X)&~quiet(X))<=>(kind(X)|creative(X))))&
(![X]:(~happy(X)<=>(~happy(X)|~patient(X))))&
((?[X]:((happy(X)&~rich(X))))=>(~strong(paul)))&
(![X]:(~creative(X)<=>old(X)))&
(![X]:(~generous(X)=>(strong(X)|~quiet(X))))&
(![X]:(~creative(X)<=>(humble(X)&~calm(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((tall(john)<~>rich(john))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((strong(X)<~>humble(X))))&
((~brave(susan)&~tall(susan)))&
((~calm(mary)&~strong(mary)))&
((old(mary)&~calm(mary)))&
(?[X]:((tall(X)<~>~quiet(X)))) | happy(susan) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7184699532503897933490746
% SZS output start Proof for 7184699532503897933490746
3. ! [X0] : ((strong(X0) <~> ~curious(X0)) <=> (~patient(X0) & humble(X0))) [input p2]
4. ! [X0] : (happy(X0) => (~strong(X0) & ~calm(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> old(X0)) [input p4]
10. ! [X0] : ((~quiet(X0) & ~creative(X0)) <=> (creative(X0) | kind(X0))) [input p9]
11. ! [X0] : (~happy(X0) <=> (~patient(X0) | ~happy(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> old(X0)) [input p12]
25. happy(susan) [input hypothesis]
31. ! [X0] : ((~strong(X0) & ~calm(X0)) | ~happy(X0)) [ennf transformation 4]
39. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [nnf transformation 3]
40. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [flattening 39]
41. ! [X0] : (((~curious(X0) | ~happy(X0)) | ~old(X0)) & (old(X0) | (curious(X0) & happy(X0)))) [nnf transformation 5]
42. ! [X0] : ((~curious(X0) | ~happy(X0) | ~old(X0)) & (old(X0) | (curious(X0) & happy(X0)))) [flattening 41]
56. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~creative(X0) & ~kind(X0))) & ((creative(X0) | kind(X0)) | (quiet(X0) | creative(X0)))) [nnf transformation 10]
57. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~creative(X0) & ~kind(X0))) & (creative(X0) | kind(X0) | quiet(X0) | creative(X0))) [flattening 56]
58. ! [X0] : ((~happy(X0) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | happy(X0))) [nnf transformation 11]
59. ! [X0] : ((~happy(X0) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | happy(X0))) [flattening 58]
60. ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))) [nnf transformation 13]
90. ~patient(X0) | strong(X0) | curious(X0) [cnf transformation 40]
94. ~happy(X0) | ~strong(X0) [cnf transformation 31]
97. ~old(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 42]
118. ~creative(X0) | ~creative(X0) [cnf transformation 57]
123. ~happy(X0) | patient(X0) [cnf transformation 59]
125. old(X0) | creative(X0) [cnf transformation 60]
155. happy(susan) [cnf transformation 25]
157. ~creative(X0) [duplicate literal removal 118]
239. old(X0) [subsumption resolution 125,157]
307. ~strong(susan) [resolution 94,155]
308. patient(susan) [resolution 123,155]
321. strong(susan) | curious(susan) [resolution 90,308]
322. curious(susan) [subsumption resolution 321,307]
327. ~happy(X2) | ~curious(X2) [resolution 97,239]
328. ~curious(susan) [resolution 327,155]
329. $false [subsumption resolution 328,322]
% SZS output end Proof for 7184699532503897933490746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is both quiet and happy.
Everyone who is not creative is not calm or calm and vice versa.
Everyone who is not quiet or not generous is either not brave or humble and vice versa.
Everyone who is not humble or not strong is not old or not curious and vice versa.
If mary is either curious or brave then someone is old and vice versa.
If someone is both not old and kind then mary is curious or happy.
Everyone who is both not curious and not kind is not brave or old and vice versa.
If mary is generous then john is both funny and not calm and vice versa.
Everyone who is happy is calm or not funny.
Everyone who is funny is creative.
Everyone who is rich or wise is both strong and happy and vice versa.
Everyone who is brave or not calm is both tall and generous.
If someone is both not funny and old then someone is both not strong and generous.
Everyone who is rich or not humble is either not funny or not happy.
If someone is both happy and not quiet then susan is not brave or generous.
Alice is either not happy or strong.
Someone is not funny.
Fred is both patient and not curious.
Paul is happy.
Someone is kind or curious.
Someone is wise or creative.
Someone is both quiet and calm. | Paul is old. | contradiction | (![X]:((strong(X)|~rich(X))=>(quiet(X)&happy(X))))&
(![X]:(~creative(X)<=>(~calm(X)|calm(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~humble(X)|~strong(X))<=>(~old(X)|~curious(X))))&
(((curious(mary)<~>brave(mary)))<=>(?[X]:(old(X))))&
((?[X]:((~old(X)&kind(X))))=>((curious(mary)|happy(mary))))&
(![X]:((~curious(X)&~kind(X))<=>(~brave(X)|old(X))))&
((generous(mary))<=>((funny(john)&~calm(john))))&
(![X]:(happy(X)=>(calm(X)|~funny(X))))&
(![X]:(funny(X)=>creative(X)))&
(![X]:((rich(X)|wise(X))<=>(strong(X)&happy(X))))&
(![X]:((brave(X)|~calm(X))=>(tall(X)&generous(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:((rich(X)|~humble(X))=>(~funny(X)<~>~happy(X))))&
((?[X]:((happy(X)&~quiet(X))))=>((~brave(susan)|generous(susan))))&
((~happy(alice)<~>strong(alice)))&
(?[X]:(~funny(X)))&
((patient(fred)&~curious(fred)))&
(happy(paul))&
(?[X]:((kind(X)|curious(X))))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:((quiet(X)&calm(X)))) | old(paul) | [
"p1",
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 896767815062796358279773
% SZS output start Proof for 896767815062796358279773
2. ! [X0] : (~creative(X0) <=> (calm(X0) | ~calm(X0))) [input p1]
5. (curious(mary) <~> brave(mary)) <=> ? [X0] : old(X0) [input p4]
7. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (old(X0) | ~brave(X0))) [input p6]
8. generous(mary) <=> (~calm(john) & funny(john)) [input p7]
10. ! [X0] : (funny(X0) => creative(X0)) [input p9]
12. ! [X0] : ((~calm(X0) | brave(X0)) => (generous(X0) & tall(X0))) [input p11]
23. old(paul) [input hypothesis]
25. ! [X0] : ((calm(X0) | ~calm(X0)) => ~creative(X0)) [unused predicate definition removal 2]
27. ! [X0] : ((~calm(X0) | brave(X0)) => generous(X0)) [pure predicate removal 12]
29. ! [X0] : (~creative(X0) | (~calm(X0) & calm(X0))) [ennf transformation 25]
34. ! [X0] : (creative(X0) | ~funny(X0)) [ennf transformation 10]
35. ! [X0] : (generous(X0) | (calm(X0) & ~brave(X0))) [ennf transformation 27]
44. (((~brave(mary) | ~curious(mary)) & (brave(mary) | curious(mary))) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | ((curious(mary) | ~brave(mary)) & (brave(mary) | ~curious(mary)))) [nnf transformation 5]
45. (((~brave(mary) | ~curious(mary)) & (brave(mary) | curious(mary))) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | ((curious(mary) | ~brave(mary)) & (brave(mary) | ~curious(mary)))) [rectify 44]
46. ? [X1] : old(X1) => old(sK0) [choice axiom]
47. (((~brave(mary) | ~curious(mary)) & (brave(mary) | curious(mary))) | ! [X0] : ~old(X0)) & (old(sK0) | ((curious(mary) | ~brave(mary)) & (brave(mary) | ~curious(mary)))) [skolemisation 45,46]
48. ! [X0] : (((~kind(X0) & ~curious(X0)) | (~old(X0) & brave(X0))) & ((old(X0) | ~brave(X0)) | (kind(X0) | curious(X0)))) [nnf transformation 7]
49. ! [X0] : (((~kind(X0) & ~curious(X0)) | (~old(X0) & brave(X0))) & (old(X0) | ~brave(X0) | kind(X0) | curious(X0))) [flattening 48]
50. (generous(mary) | (calm(john) | ~funny(john))) & ((~calm(john) & funny(john)) | ~generous(mary)) [nnf transformation 8]
51. (generous(mary) | calm(john) | ~funny(john)) & ((~calm(john) & funny(john)) | ~generous(mary)) [flattening 50]
71. ~creative(X0) | calm(X0) [cnf transformation 29]
72. ~calm(X0) | ~creative(X0) [cnf transformation 29]
85. brave(mary) | curious(mary) | ~old(X0) [cnf transformation 47]
89. ~curious(X0) | brave(X0) [cnf transformation 49]
93. funny(john) | ~generous(mary) [cnf transformation 51]
97. creative(X0) | ~funny(X0) [cnf transformation 34]
103. ~brave(X0) | generous(X0) [cnf transformation 35]
121. old(paul) [cnf transformation 23]
122. ~creative(X0) [subsumption resolution 71,72]
124. 1 <=> ! [X0] : ~old(X0) [avatar definition]
125. ~old(X0) <- (1) [avatar component clause 124]
127. 2 <=> curious(mary) [avatar definition]
128. curious(mary) <- (2) [avatar component clause 127]
131. 3 <=> brave(mary) [avatar definition]
132. brave(mary) <- (3) [avatar component clause 131]
133. ~brave(mary) <- (~3) [avatar component clause 131]
135. 1 | 2 | 3 [avatar split clause 85,131,127,124]
151. 7 <=> funny(john) [avatar definition]
152. funny(john) <- (7) [avatar component clause 151]
159. 9 <=> generous(mary) [avatar definition]
164. ~9 | 7 [avatar split clause 93,151,159]
165. ~funny(X0) [subsumption resolution 97,122]
194. brave(mary) <- (2) [resolution 89,128]
195. $false <- (2, ~3) [subsumption resolution 194,133]
196. ~2 | 3 [avatar contradiction clause 195]
206. generous(mary) <- (3) [resolution 103,132]
210. 9 | ~3 [avatar split clause 206,131,159]
211. $false <- (7) [subsumption resolution 152,165]
212. ~7 [avatar contradiction clause 211]
213. $false <- (1) [resolution 125,121]
216. ~1 [avatar contradiction clause 213]
217. $false [avatar sat refutation 135,164,196,210,212,216]
% SZS output end Proof for 896767815062796358279773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is both creative and not brave and vice versa.
Everyone who is both not quiet and not rich is either not strong or wise.
Everyone who is kind is either not wise or not kind and vice versa.
Everyone who is happy is not quiet or old and vice versa.
If someone is not wise then someone is tall.
If alice is not quiet or not generous then someone is not wise or humble and vice versa.
Everyone who is both tall and not kind is not happy or not patient.
Everyone who is brave or not calm is either generous or old and vice versa.
If someone is not humble or not strong then susan is either funny or generous.
Everyone who is not old or generous is both wise and not strong and vice versa.
If susan is funny then alice is not wise or calm and vice versa.
Everyone who is either funny or not brave is either not calm or humble and vice versa.
Everyone who is not funny or not curious is either patient or not happy.
Everyone who is not tall or wise is both happy and curious.
If paul is not old then fred is wise.
Everyone who is both not humble and funny is both generous and rich and vice versa.
Mary is both not humble and not quiet.
Someone is both funny and not kind.
Paul is either old or tall.
Alice is either not quiet or generous.
Someone is not curious.
Mary is either not rich or tall.
Paul is not creative. | Alice is not old. | contradiction | ((?[X]:(~happy(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((~quiet(X)&~rich(X))=>(~strong(X)<~>wise(X))))&
(![X]:(kind(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:(happy(X)<=>(~quiet(X)|old(X))))&
((?[X]:(~wise(X)))=>(?[X]:(tall(X))))&
(((~quiet(alice)|~generous(alice)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((tall(X)&~kind(X))=>(~happy(X)|~patient(X))))&
(![X]:((brave(X)|~calm(X))<=>(generous(X)<~>old(X))))&
((?[X]:((~humble(X)|~strong(X))))=>((funny(susan)<~>generous(susan))))&
(![X]:((~old(X)|generous(X))<=>(wise(X)&~strong(X))))&
((funny(susan))<=>((~wise(alice)|calm(alice))))&
(![X]:((funny(X)<~>~brave(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~funny(X)|~curious(X))=>(patient(X)<~>~happy(X))))&
(![X]:((~tall(X)|wise(X))=>(happy(X)&curious(X))))&
((~old(paul))=>(wise(fred)))&
(![X]:((~humble(X)&funny(X))<=>(generous(X)&rich(X))))&
((~humble(mary)&~quiet(mary)))&
(?[X]:((funny(X)&~kind(X))))&
((old(paul)<~>tall(paul)))&
((~quiet(alice)<~>generous(alice)))&
(?[X]:(~curious(X)))&
((~rich(mary)<~>tall(mary)))&
(~creative(paul)) | ~old(alice) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4268050698621512849561745
% SZS output start Proof for 4268050698621512849561745
3. ! [X0] : (kind(X0) <=> (~wise(X0) <~> ~kind(X0))) [input p2]
10. ! [X0] : ((generous(X0) | ~old(X0)) <=> (~strong(X0) & wise(X0))) [input p9]
24. ~old(alice) [input hypothesis]
42. ! [X0] : ((kind(X0) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0)))) & (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | ~kind(X0))) [nnf transformation 3]
56. ! [X0] : (((generous(X0) | ~old(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (~generous(X0) & old(X0)))) [nnf transformation 10]
57. ! [X0] : ((generous(X0) | ~old(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (~generous(X0) & old(X0)))) [flattening 56]
76. ~kind(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 42]
79. kind(X0) | ~wise(X0) | kind(X0) [cnf transformation 42]
99. wise(X0) | old(X0) [cnf transformation 57]
140. ~old(alice) [cnf transformation 24]
141. ~kind(X0) | ~wise(X0) [duplicate literal removal 76]
142. kind(X0) | ~wise(X0) [duplicate literal removal 79]
164. ~wise(X0) [subsumption resolution 141,142]
199. old(X0) [subsumption resolution 99,164]
221. $false [subsumption resolution 140,199]
% SZS output end Proof for 4268050698621512849561745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not tall or not strong then someone is tall or strong.
If someone is either strong or rich then alice is both not creative and not funny.
Everyone who is old is rich.
Everyone who is brave is both not funny and not wise and vice versa.
If someone is both not humble and kind then john is not patient.
Everyone who is not patient or not funny is either not humble or not strong and vice versa.
Everyone who is either happy or patient is both humble and funny and vice versa.
Everyone who is both happy and old is either calm or not humble.
Everyone who is rich is not funny and vice versa.
Everyone who is both not rich and funny is not funny or tall and vice versa.
Everyone who is both creative and not creative is patient.
If alice is either not tall or old then fred is not generous.
If someone is strong or not generous then lucy is not generous or curious and vice versa.
If lucy is either not tall or not generous then paul is both curious and not funny and vice versa.
Everyone who is calm is happy or rich and vice versa.
Someone is either not rich or not kind.
Someone is calm.
Someone is brave or not wise.
Lucy is either rich or not quiet.
Alice is humble.
Someone is both not wise and not curious. | Fred is curious. | neutral | ((?[X]:((~tall(X)|~strong(X))))=>(?[X]:((tall(X)|strong(X)))))&
((?[X]:((strong(X)<~>rich(X))))=>((~creative(alice)&~funny(alice))))&
(![X]:(old(X)=>rich(X)))&
(![X]:(brave(X)<=>(~funny(X)&~wise(X))))&
((?[X]:((~humble(X)&kind(X))))=>(~patient(john)))&
(![X]:((~patient(X)|~funny(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:((happy(X)<~>patient(X))<=>(humble(X)&funny(X))))&
(![X]:((happy(X)&old(X))=>(calm(X)<~>~humble(X))))&
(![X]:(rich(X)<=>~funny(X)))&
(![X]:((~rich(X)&funny(X))<=>(~funny(X)|tall(X))))&
(![X]:((creative(X)&~creative(X))=>patient(X)))&
(((~tall(alice)<~>old(alice)))=>(~generous(fred)))&
((?[X]:((strong(X)|~generous(X))))<=>((~generous(lucy)|curious(lucy))))&
(((~tall(lucy)<~>~generous(lucy)))<=>((curious(paul)&~funny(paul))))&
(![X]:(calm(X)<=>(happy(X)|rich(X))))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)|~wise(X))))&
((rich(lucy)<~>~quiet(lucy)))&
(humble(alice))&
(?[X]:((~wise(X)&~curious(X)))) | curious(fred) | [] | null | 0 |
If someone is not patient or not strong then paul is not rich or old. If fred is not brave then someone is not creative or not funny and vice versa. If fred is either not wise or old then someone is both not funny and not tall. Everyone who is old is not wise or not patient. If lucy is either not patient or not creative then someone is brave or wise and vice versa. Everyone who is not rich is not humble or strong and vice versa. If paul is not strong then mary is not funny or not happy. Everyone who is not creative or not curious is both not strong and not patient and vice versa. If paul is either not curious or humble then someone is generous. If mary is not rich then someone is either generous or not rich. Everyone who is either quiet or not strong is either humble or quiet. If someone is quiet then alice is either not creative or creative and vice versa. If mary is not kind then lucy is happy or not kind. Everyone who is either kind or not strong is not calm or patient. If someone is old then someone is both old and not kind. Everyone who is funny or not brave is not calm or old. Someone is either not curious or generous. Fred is funny. Susan is both creative and tall. Someone is not wise or generous. Someone is both quiet and funny. Fred is rich or calm. Alice is kind or not tall. | Mary is funny. | neutral | ((?[X]:((~patient(X)|~strong(X))))=>((~rich(paul)|old(paul))))&
((~brave(fred))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((~wise(fred)<~>old(fred)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(old(X)=>(~wise(X)|~patient(X))))&
(((~patient(lucy)<~>~creative(lucy)))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(~rich(X)<=>(~humble(X)|strong(X))))&
((~strong(paul))=>((~funny(mary)|~happy(mary))))&
(![X]:((~creative(X)|~curious(X))<=>(~strong(X)&~patient(X))))&
(((~curious(paul)<~>humble(paul)))=>(?[X]:(generous(X))))&
((~rich(mary))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:((quiet(X)<~>~strong(X))=>(humble(X)<~>quiet(X))))&
((?[X]:(quiet(X)))<=>((~creative(alice)<~>creative(alice))))&
((~kind(mary))=>((happy(lucy)|~kind(lucy))))&
(![X]:((kind(X)<~>~strong(X))=>(~calm(X)|patient(X))))&
((?[X]:(old(X)))=>(?[X]:((old(X)&~kind(X)))))&
(![X]:((funny(X)|~brave(X))=>(~calm(X)|old(X))))&
(?[X]:((~curious(X)<~>generous(X))))&
(funny(fred))&
((creative(susan)&tall(susan)))&
(?[X]:((~wise(X)|generous(X))))&
(?[X]:((quiet(X)&funny(X))))&
((rich(fred)|calm(fred)))&
((kind(alice)|~tall(alice))) | funny(mary) | [] | null | 0 |
If alice is not generous or not patient then alice is quiet or happy and vice versa.
If someone is both not tall and not generous then someone is both curious and not rich and vice versa.
If paul is either not curious or quiet then susan is both not wise and not curious.
Everyone who is either curious or funny is funny and vice versa.
If alice is either quiet or wise then someone is both curious and not rich and vice versa.
Everyone who is not wise is both brave and generous and vice versa.
If john is not kind or not quiet then someone is not wise or not kind.
If someone is either not calm or not happy then someone is kind or rich and vice versa.
Everyone who is both brave and creative is either tall or generous.
If susan is not creative or kind then paul is happy and vice versa.
If someone is both patient and not curious then paul is brave.
If someone is not rich or wise then paul is strong or not tall.
Everyone who is either not brave or not happy is creative or brave and vice versa.
If someone is wise or happy then someone is not tall and vice versa.
If someone is not creative or not strong then paul is either strong or kind and vice versa.
If mary is both not humble and curious then someone is not brave or creative.
John is either patient or curious.
John is both not wise and not humble.
Someone is either funny or patient.
Someone is kind or tall.
Someone is not curious or not strong.
Someone is not quiet.
Someone is not happy or generous. | Alice is not patient. | neutral | (((~generous(alice)|~patient(alice)))<=>((quiet(alice)|happy(alice))))&
((?[X]:((~tall(X)&~generous(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(((~curious(paul)<~>quiet(paul)))=>((~wise(susan)&~curious(susan))))&
(![X]:((curious(X)<~>funny(X))<=>funny(X)))&
(((quiet(alice)<~>wise(alice)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~wise(X)<=>(brave(X)&generous(X))))&
(((~kind(john)|~quiet(john)))=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&creative(X))=>(tall(X)<~>generous(X))))&
(((~creative(susan)|kind(susan)))<=>(happy(paul)))&
((?[X]:((patient(X)&~curious(X))))=>(brave(paul)))&
((?[X]:((~rich(X)|wise(X))))=>((strong(paul)|~tall(paul))))&
(![X]:((~brave(X)<~>~happy(X))<=>(creative(X)|brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((strong(paul)<~>kind(paul))))&
(((~humble(mary)&curious(mary)))=>(?[X]:((~brave(X)|creative(X)))))&
((patient(john)<~>curious(john)))&
((~wise(john)&~humble(john)))&
(?[X]:((funny(X)<~>patient(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)|generous(X)))) | ~patient(alice) | [] | null | 0 |
If john is not old then someone is both generous and not curious and vice versa.
Everyone who is both wise and strong is not wise and vice versa.
Everyone who is not wise or not generous is both not creative and not kind.
Everyone who is patient is either kind or not brave.
If mary is either strong or creative then someone is quiet or old.
Everyone who is tall is both not calm and not funny and vice versa.
Everyone who is not brave or not curious is funny and vice versa.
If paul is not calm then mary is either patient or not creative and vice versa.
Everyone who is either creative or happy is rich and vice versa.
If fred is both not generous and happy then someone is either not quiet or calm.
Everyone who is quiet or funny is not curious or old.
If lucy is not rich or old then fred is both patient and not quiet and vice versa.
If someone is not strong then susan is either rich or old.
Everyone who is either not patient or not calm is quiet or not happy and vice versa.
If fred is both not humble and brave then someone is both brave and funny.
Everyone who is both creative and not calm is both tall and curious.
Mary is happy.
Someone is wise.
Someone is patient or strong.
Someone is both old and patient.
Someone is kind.
John is either not old or not creative.
Alice is either not patient or not rich.
Paul is either wise or kind. | Mary is not wise. | contradiction | ((~old(john))<=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((wise(X)&strong(X))<=>~wise(X)))&
(![X]:((~wise(X)|~generous(X))=>(~creative(X)&~kind(X))))&
(![X]:(patient(X)=>(kind(X)<~>~brave(X))))&
(((strong(mary)<~>creative(mary)))=>(?[X]:((quiet(X)|old(X)))))&
(![X]:(tall(X)<=>(~calm(X)&~funny(X))))&
(![X]:((~brave(X)|~curious(X))<=>funny(X)))&
((~calm(paul))<=>((patient(mary)<~>~creative(mary))))&
(![X]:((creative(X)<~>happy(X))<=>rich(X)))&
(((~generous(fred)&happy(fred)))=>(?[X]:((~quiet(X)<~>calm(X)))))&
(![X]:((quiet(X)|funny(X))=>(~curious(X)|old(X))))&
(((~rich(lucy)|old(lucy)))<=>((patient(fred)&~quiet(fred))))&
((?[X]:(~strong(X)))=>((rich(susan)<~>old(susan))))&
(![X]:((~patient(X)<~>~calm(X))<=>(quiet(X)|~happy(X))))&
(((~humble(fred)&brave(fred)))=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((creative(X)&~calm(X))=>(tall(X)&curious(X))))&
(happy(mary))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)|strong(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:(kind(X)))&
((~old(john)<~>~creative(john)))&
((~patient(alice)<~>~rich(alice)))&
((wise(paul)<~>kind(paul))) | ~wise(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5464860491396579611328971
% SZS output start Proof for 5464860491396579611328971
2. ! [X0] : ((strong(X0) & wise(X0)) <=> ~wise(X0)) [input p1]
25. ~wise(mary) [input hypothesis]
45. ! [X0] : (((strong(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 2]
46. ! [X0] : (((strong(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | ~strong(X0) | ~wise(X0))) [flattening 45]
76. wise(X0) | wise(X0) [cnf transformation 46]
129. ~wise(mary) [cnf transformation 25]
131. wise(X0) [duplicate literal removal 76]
246. $false [subsumption resolution 129,131]
% SZS output end Proof for 5464860491396579611328971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not rich then alice is funny or not humble and vice versa.
Everyone who is quiet or not quiet is both not wise and generous.
If fred is generous or not kind then someone is either wise or humble and vice versa.
Everyone who is strong is quiet.
If susan is generous or not happy then fred is not quiet.
Everyone who is either funny or not rich is kind or wise.
Everyone who is not creative is quiet and vice versa.
Everyone who is not creative is not quiet or not rich.
If someone is both not creative and kind then fred is old.
Everyone who is not humble or not wise is both not strong and not tall.
Everyone who is not generous or not calm is either old or humble and vice versa.
If someone is either not generous or not brave then fred is not generous.
If john is both not humble and happy then someone is wise or patient and vice versa.
Everyone who is either tall or not tall is patient or creative and vice versa.
Everyone who is not brave or not rich is not rich and vice versa.
Everyone who is not calm or curious is both funny and not rich.
Mary is either happy or funny.
Lucy is humble.
Someone is both not curious and not calm.
Someone is quiet or not tall.
Someone is either not calm or old.
John is quiet or not creative.
Someone is both not happy and humble. | John is happy. | entailment | ((?[X]:((curious(X)|~rich(X))))<=>((funny(alice)|~humble(alice))))&
(![X]:((quiet(X)|~quiet(X))=>(~wise(X)&generous(X))))&
(((generous(fred)|~kind(fred)))<=>(?[X]:((wise(X)<~>humble(X)))))&
(![X]:(strong(X)=>quiet(X)))&
(((generous(susan)|~happy(susan)))=>(~quiet(fred)))&
(![X]:((funny(X)<~>~rich(X))=>(kind(X)|wise(X))))&
(![X]:(~creative(X)<=>quiet(X)))&
(![X]:(~creative(X)=>(~quiet(X)|~rich(X))))&
((?[X]:((~creative(X)&kind(X))))=>(old(fred)))&
(![X]:((~humble(X)|~wise(X))=>(~strong(X)&~tall(X))))&
(![X]:((~generous(X)|~calm(X))<=>(old(X)<~>humble(X))))&
((?[X]:((~generous(X)<~>~brave(X))))=>(~generous(fred)))&
(((~humble(john)&happy(john)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((tall(X)<~>~tall(X))<=>(patient(X)|creative(X))))&
(![X]:((~brave(X)|~rich(X))<=>~rich(X)))&
(![X]:((~calm(X)|curious(X))=>(funny(X)&~rich(X))))&
((happy(mary)<~>funny(mary)))&
(humble(lucy))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((~calm(X)<~>old(X))))&
((quiet(john)|~creative(john)))&
(?[X]:((~happy(X)&humble(X)))) | happy(john) | [
"p1",
"p6",
"p9",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7785501810331951132871292
% SZS output start Proof for 7785501810331951132871292
2. ! [X0] : ((~quiet(X0) | quiet(X0)) => (generous(X0) & ~wise(X0))) [input p1]
7. ! [X0] : (~creative(X0) <=> quiet(X0)) [input p6]
10. ! [X0] : ((~wise(X0) | ~humble(X0)) => (~tall(X0) & ~strong(X0))) [input p9]
13. (happy(john) & ~humble(john)) <=> ? [X0] : (patient(X0) | wise(X0)) [input p12]
14. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (creative(X0) | patient(X0))) [input p13]
22. ~creative(john) | quiet(john) [input p21]
24. ~happy(john) [input hypothesis]
25. ! [X0] : ((~wise(X0) | ~humble(X0)) => ~tall(X0)) [pure predicate removal 10]
27. ! [X0] : ((generous(X0) & ~wise(X0)) | (quiet(X0) & ~quiet(X0))) [ennf transformation 2]
34. ! [X0] : (~tall(X0) | (wise(X0) & humble(X0))) [ennf transformation 25]
48. ! [X0] : ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0))) [nnf transformation 7]
52. ((happy(john) & ~humble(john)) | ! [X0] : (~patient(X0) & ~wise(X0))) & (? [X0] : (patient(X0) | wise(X0)) | (~happy(john) | humble(john))) [nnf transformation 13]
53. ((happy(john) & ~humble(john)) | ! [X0] : (~patient(X0) & ~wise(X0))) & (? [X0] : (patient(X0) | wise(X0)) | ~happy(john) | humble(john)) [flattening 52]
54. ((happy(john) & ~humble(john)) | ! [X0] : (~patient(X0) & ~wise(X0))) & (? [X1] : (patient(X1) | wise(X1)) | ~happy(john) | humble(john)) [rectify 53]
55. ? [X1] : (patient(X1) | wise(X1)) => (patient(sK2) | wise(sK2)) [choice axiom]
56. ((happy(john) & ~humble(john)) | ! [X0] : (~patient(X0) & ~wise(X0))) & ((patient(sK2) | wise(sK2)) | ~happy(john) | humble(john)) [skolemisation 54,55]
57. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~creative(X0) & ~patient(X0))) & ((creative(X0) | patient(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 14]
58. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (~creative(X0) & ~patient(X0))) & (creative(X0) | patient(X0) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [flattening 57]
75. ~wise(X0) | ~quiet(X0) [cnf transformation 27]
76. ~wise(X0) | quiet(X0) [cnf transformation 27]
90. ~creative(X0) | ~quiet(X0) [cnf transformation 48]
94. ~tall(X0) | wise(X0) [cnf transformation 34]
107. happy(john) | ~patient(X0) [cnf transformation 56]
109. creative(X0) | patient(X0) | tall(X0) | tall(X0) [cnf transformation 58]
129. ~creative(john) | quiet(john) [cnf transformation 22]
132. ~happy(john) [cnf transformation 24]
134. creative(X0) | patient(X0) | tall(X0) [duplicate literal removal 109]
162. ~wise(X0) [subsumption resolution 75,76]
198. ~tall(X0) [subsumption resolution 94,162]
204. 13 <=> ! [X0] : ~patient(X0) [avatar definition]
205. ~patient(X0) <- (13) [avatar component clause 204]
207. 14 <=> happy(john) [avatar definition]
210. 13 | 14 [avatar split clause 107,207,204]
222. patient(X0) | creative(X0) [subsumption resolution 134,198]
243. ~creative(john) [subsumption resolution 129,90]
244. ~14 [avatar split clause 132,207]
249. creative(X0) <- (13) [resolution 222,205]
250. $false <- (13) [resolution 249,243]
252. ~13 [avatar contradiction clause 250]
253. $false [avatar sat refutation 210,244,252]
% SZS output end Proof for 7785501810331951132871292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not quiet then paul is creative.
Everyone who is both not old and not calm is not calm or not humble and vice versa.
If someone is both curious and happy then someone is not brave and vice versa.
Everyone who is patient or creative is not quiet.
Everyone who is both not brave and not creative is not creative or not calm.
If paul is not calm or happy then fred is not patient or old.
If fred is either brave or quiet then someone is both not creative and not calm and vice versa.
If someone is quiet or not quiet then someone is old and vice versa.
Everyone who is either wise or not quiet is not brave and vice versa.
Everyone who is not rich is either happy or not funny and vice versa.
If fred is not rich or kind then paul is calm.
If mary is both calm and old then someone is either creative or kind and vice versa.
If someone is generous then someone is both old and not funny and vice versa.
If someone is either wise or strong then mary is both quiet and not wise.
If paul is both calm and not curious then someone is both not kind and not wise and vice versa.
Everyone who is funny or not brave is either not brave or kind and vice versa.
Someone is not rich or humble.
Mary is either funny or strong.
Alice is not wise or creative.
Alice is either kind or brave.
Someone is either humble or not calm.
Paul is creative or not strong.
Someone is patient or not patient.
Someone is kind. | Mary is calm. | neutral | (((brave(paul)|~quiet(paul)))=>(creative(paul)))&
(![X]:((~old(X)&~calm(X))<=>(~calm(X)|~humble(X))))&
((?[X]:((curious(X)&happy(X))))<=>(?[X]:(~brave(X))))&
(![X]:((patient(X)|creative(X))=>~quiet(X)))&
(![X]:((~brave(X)&~creative(X))=>(~creative(X)|~calm(X))))&
(((~calm(paul)|happy(paul)))=>((~patient(fred)|old(fred))))&
(((brave(fred)<~>quiet(fred)))<=>(?[X]:((~creative(X)&~calm(X)))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:(old(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>~brave(X)))&
(![X]:(~rich(X)<=>(happy(X)<~>~funny(X))))&
(((~rich(fred)|kind(fred)))=>(calm(paul)))&
(((calm(mary)&old(mary)))<=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((old(X)&~funny(X)))))&
((?[X]:((wise(X)<~>strong(X))))=>((quiet(mary)&~wise(mary))))&
(((calm(paul)&~curious(paul)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((funny(X)|~brave(X))<=>(~brave(X)<~>kind(X))))&
(?[X]:((~rich(X)|humble(X))))&
((funny(mary)<~>strong(mary)))&
((~wise(alice)|creative(alice)))&
((kind(alice)<~>brave(alice)))&
(?[X]:((humble(X)<~>~calm(X))))&
((creative(paul)|~strong(paul)))&
(?[X]:((patient(X)|~patient(X))))&
(?[X]:(kind(X))) | calm(mary) | [] | null | 0 |
Everyone who is wise or not creative is both not strong and not happy and vice versa.
Everyone who is both not strong and not curious is happy or calm and vice versa.
Everyone who is funny is patient and vice versa.
Everyone who is not humble or strong is not patient and vice versa.
Everyone who is either not brave or kind is brave and vice versa.
If someone is either not patient or not curious then lucy is not wise or happy and vice versa.
If paul is either not rich or not happy then paul is either not kind or not strong.
Everyone who is patient or creative is either happy or strong.
Everyone who is not creative is both patient and not curious.
Everyone who is curious or not funny is not generous or strong and vice versa.
If someone is wise then paul is brave and vice versa.
If someone is rich or not funny then mary is not happy.
If paul is creative or strong then someone is not happy or kind and vice versa.
Everyone who is either not generous or not humble is both not patient and not creative.
If lucy is both old and not happy then someone is not tall or not kind and vice versa.
If someone is both humble and not strong then someone is either generous or brave.
Mary is either tall or not old.
Someone is strong.
Someone is wise or not curious.
Susan is creative or humble.
Mary is either not tall or not humble.
Alice is either brave or kind.
Someone is either not quiet or not creative. | Paul is wise. | contradiction | (![X]:((wise(X)|~creative(X))<=>(~strong(X)&~happy(X))))&
(![X]:((~strong(X)&~curious(X))<=>(happy(X)|calm(X))))&
(![X]:(funny(X)<=>patient(X)))&
(![X]:((~humble(X)|strong(X))<=>~patient(X)))&
(![X]:((~brave(X)<~>kind(X))<=>brave(X)))&
((?[X]:((~patient(X)<~>~curious(X))))<=>((~wise(lucy)|happy(lucy))))&
(((~rich(paul)<~>~happy(paul)))=>((~kind(paul)<~>~strong(paul))))&
(![X]:((patient(X)|creative(X))=>(happy(X)<~>strong(X))))&
(![X]:(~creative(X)=>(patient(X)&~curious(X))))&
(![X]:((curious(X)|~funny(X))<=>(~generous(X)|strong(X))))&
((?[X]:(wise(X)))<=>(brave(paul)))&
((?[X]:((rich(X)|~funny(X))))=>(~happy(mary)))&
(((creative(paul)|strong(paul)))<=>(?[X]:((~happy(X)|kind(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(~patient(X)&~creative(X))))&
(((old(lucy)&~happy(lucy)))<=>(?[X]:((~tall(X)|~kind(X)))))&
((?[X]:((humble(X)&~strong(X))))=>(?[X]:((generous(X)<~>brave(X)))))&
((tall(mary)<~>~old(mary)))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)|~curious(X))))&
((creative(susan)|humble(susan)))&
((~tall(mary)<~>~humble(mary)))&
((brave(alice)<~>kind(alice)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | wise(paul) | [
"p0",
"p3",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7096235419497441343537904
% SZS output start Proof for 7096235419497441343537904
1. ! [X0] : ((~creative(X0) | wise(X0)) <=> (~happy(X0) & ~strong(X0))) [input p0]
4. ! [X0] : ((strong(X0) | ~humble(X0)) <=> ~patient(X0)) [input p3]
8. ! [X0] : ((creative(X0) | patient(X0)) => (happy(X0) <~> strong(X0))) [input p7]
9. ! [X0] : (~creative(X0) => (~curious(X0) & patient(X0))) [input p8]
24. wise(paul) [input hypothesis]
27. ! [X0] : ((happy(X0) <~> strong(X0)) | (~creative(X0) & ~patient(X0))) [ennf transformation 8]
28. ! [X0] : ((~curious(X0) & patient(X0)) | creative(X0)) [ennf transformation 9]
32. ! [X0] : (((~creative(X0) | wise(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (creative(X0) & ~wise(X0)))) [nnf transformation 1]
33. ! [X0] : ((~creative(X0) | wise(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (creative(X0) & ~wise(X0)))) [flattening 32]
37. ! [X0] : (((strong(X0) | ~humble(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) & humble(X0)))) [nnf transformation 4]
38. ! [X0] : ((strong(X0) | ~humble(X0) | patient(X0)) & (~patient(X0) | (~strong(X0) & humble(X0)))) [flattening 37]
46. ! [X0] : (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~creative(X0) & ~patient(X0))) [nnf transformation 27]
78. ~strong(X0) | ~wise(X0) [cnf transformation 33]
80. ~happy(X0) | ~wise(X0) [cnf transformation 33]
81. ~happy(X0) | creative(X0) [cnf transformation 33]
91. ~patient(X0) | ~strong(X0) [cnf transformation 38]
107. strong(X0) | happy(X0) | ~patient(X0) [cnf transformation 46]
108. ~creative(X0) | happy(X0) | strong(X0) [cnf transformation 46]
111. patient(X0) | creative(X0) [cnf transformation 28]
147. wise(paul) [cnf transformation 24]
192. ~patient(X0) | happy(X0) [subsumption resolution 107,91]
203. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
204. ~wise(X1) <- (11) [avatar component clause 203]
307. happy(X0) | creative(X0) [resolution 192,111]
308. creative(X0) [subsumption resolution 307,81]
322. happy(X0) | strong(X0) [resolution 108,308]
350. strong(X2) | ~wise(X2) [resolution 322,80]
351. ~wise(X2) [subsumption resolution 350,78]
352. 11 [avatar split clause 351,203]
353. $false <- (11) [resolution 204,147]
356. ~11 [avatar contradiction clause 353]
357. $false [avatar sat refutation 352,356]
% SZS output end Proof for 7096235419497441343537904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both quiet and not quiet. Everyone who is either patient or not wise is not funny or curious. Everyone who is both old and not calm is either not curious or not calm and vice versa. Everyone who is quiet or curious is not kind or old and vice versa. Everyone who is either not happy or quiet is either not happy or not wise. Everyone who is either creative or humble is old or not rich. If paul is both not quiet and funny then someone is either creative or not humble. Everyone who is not brave or wise is both not quiet and not calm and vice versa. If paul is either not quiet or wise then someone is both rich and not quiet and vice versa. Everyone who is not old or tall is both happy and not calm and vice versa. Everyone who is either old or not kind is both kind and patient. Everyone who is strong is either not funny or not curious. Everyone who is not calm or not rich is not tall and vice versa. If someone is both not old and tall then someone is not humble and vice versa. If alice is not quiet then someone is patient or wise and vice versa. If lucy is either not brave or not old then someone is not tall. Someone is either curious or quiet. Fred is not kind or not calm. Alice is not old or brave. Someone is calm. Someone is quiet or brave. Mary is happy or rich. Fred is both kind and strong. | Alice is brave. | neutral | (![X]:(rich(X)=>(quiet(X)&~quiet(X))))&
(![X]:((patient(X)<~>~wise(X))=>(~funny(X)|curious(X))))&
(![X]:((old(X)&~calm(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((quiet(X)|curious(X))<=>(~kind(X)|old(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(~happy(X)<~>~wise(X))))&
(![X]:((creative(X)<~>humble(X))=>(old(X)|~rich(X))))&
(((~quiet(paul)&funny(paul)))=>(?[X]:((creative(X)<~>~humble(X)))))&
(![X]:((~brave(X)|wise(X))<=>(~quiet(X)&~calm(X))))&
(((~quiet(paul)<~>wise(paul)))<=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:((~old(X)|tall(X))<=>(happy(X)&~calm(X))))&
(![X]:((old(X)<~>~kind(X))=>(kind(X)&patient(X))))&
(![X]:(strong(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((~calm(X)|~rich(X))<=>~tall(X)))&
((?[X]:((~old(X)&tall(X))))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>(?[X]:((patient(X)|wise(X)))))&
(((~brave(lucy)<~>~old(lucy)))=>(?[X]:(~tall(X))))&
(?[X]:((curious(X)<~>quiet(X))))&
((~kind(fred)|~calm(fred)))&
((~old(alice)|brave(alice)))&
(?[X]:(calm(X)))&
(?[X]:((quiet(X)|brave(X))))&
((happy(mary)|rich(mary)))&
((kind(fred)&strong(fred))) | brave(alice) | [] | null | 0 |
If lucy is both not patient and not quiet then mary is not kind.
Everyone who is wise or not humble is not happy and vice versa.
If someone is both not wise and curious then alice is humble.
If someone is not humble or not patient then someone is not calm and vice versa.
Everyone who is not happy is patient.
If lucy is both not curious and not happy then someone is either strong or kind.
If fred is tall or not tall then someone is both strong and kind and vice versa.
If paul is both tall and humble then lucy is either not humble or kind.
Everyone who is not quiet or humble is both wise and not old and vice versa.
Everyone who is not rich is both patient and not kind and vice versa.
If susan is both not strong and not kind then someone is both not creative and calm and vice versa.
Everyone who is both old and patient is old or not strong.
Everyone who is both not funny and happy is either kind or not strong.
Everyone who is both not tall and wise is either happy or strong and vice versa.
If john is both generous and not funny then paul is either strong or not kind.
Everyone who is not rich is either patient or rich.
Lucy is humble.
Someone is calm.
Someone is rich or patient.
Fred is either not creative or wise.
Alice is both rich and tall.
Susan is not curious or not humble.
Fred is wise or old.
Paul is patient or wise. | Alice is not strong. | entailment | (((~patient(lucy)&~quiet(lucy)))=>(~kind(mary)))&
(![X]:((wise(X)|~humble(X))<=>~happy(X)))&
((?[X]:((~wise(X)&curious(X))))=>(humble(alice)))&
((?[X]:((~humble(X)|~patient(X))))<=>(?[X]:(~calm(X))))&
(![X]:(~happy(X)=>patient(X)))&
(((~curious(lucy)&~happy(lucy)))=>(?[X]:((strong(X)<~>kind(X)))))&
(((tall(fred)|~tall(fred)))<=>(?[X]:((strong(X)&kind(X)))))&
(((tall(paul)&humble(paul)))=>((~humble(lucy)<~>kind(lucy))))&
(![X]:((~quiet(X)|humble(X))<=>(wise(X)&~old(X))))&
(![X]:(~rich(X)<=>(patient(X)&~kind(X))))&
(((~strong(susan)&~kind(susan)))<=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:((old(X)&patient(X))=>(old(X)|~strong(X))))&
(![X]:((~funny(X)&happy(X))=>(kind(X)<~>~strong(X))))&
(![X]:((~tall(X)&wise(X))<=>(happy(X)<~>strong(X))))&
(((generous(john)&~funny(john)))=>((strong(paul)<~>~kind(paul))))&
(![X]:(~rich(X)=>(patient(X)<~>rich(X))))&
(humble(lucy))&
(?[X]:(calm(X)))&
(?[X]:((rich(X)|patient(X))))&
((~creative(fred)<~>wise(fred)))&
((rich(alice)&tall(alice)))&
((~curious(susan)|~humble(susan)))&
((wise(fred)|old(fred)))&
((patient(paul)|wise(paul))) | ~strong(alice) | [
"p1",
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 50377892870940123712678
% SZS output start Proof for 50377892870940123712678
2. ! [X0] : ((~humble(X0) | wise(X0)) <=> ~happy(X0)) [input p1]
9. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> (~old(X0) & wise(X0))) [input p8]
14. ! [X0] : ((wise(X0) & ~tall(X0)) <=> (happy(X0) <~> strong(X0))) [input p13]
21. tall(alice) & rich(alice) [input p20]
25. strong(alice) [input hypothesis]
40. ! [X0] : (((~humble(X0) | wise(X0)) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [nnf transformation 2]
41. ! [X0] : ((~humble(X0) | wise(X0) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [flattening 40]
56. ! [X0] : (((humble(X0) | ~quiet(X0)) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | (~humble(X0) & quiet(X0)))) [nnf transformation 9]
57. ! [X0] : ((humble(X0) | ~quiet(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | (~humble(X0) & quiet(X0)))) [flattening 56]
65. ! [X0] : (((wise(X0) & ~tall(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (~wise(X0) | tall(X0)))) [nnf transformation 14]
66. ! [X0] : (((wise(X0) & ~tall(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | ~wise(X0) | tall(X0))) [flattening 65]
74. ~happy(X0) | ~wise(X0) [cnf transformation 41]
75. ~happy(X0) | humble(X0) [cnf transformation 41]
92. ~humble(X0) | wise(X0) [cnf transformation 57]
107. ~tall(X0) | happy(X0) | ~strong(X0) [cnf transformation 66]
118. tall(alice) [cnf transformation 21]
122. strong(alice) [cnf transformation 25]
141. 5 <=> humble(alice) [avatar definition]
143. humble(alice) <- (5) [avatar component clause 141]
282. wise(alice) <- (5) [resolution 92,143]
303. happy(alice) | ~strong(alice) [resolution 107,118]
304. happy(alice) [subsumption resolution 303,122]
306. humble(alice) [resolution 304,75]
307. ~wise(alice) [resolution 304,74]
308. $false <- (5) [subsumption resolution 307,282]
309. ~5 [avatar contradiction clause 308]
310. 5 [avatar split clause 306,141]
311. $false [avatar sat refutation 309,310]
% SZS output end Proof for 50377892870940123712678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not rich or calm and vice versa.
If someone is not calm or wise then someone is not creative or not strong.
If susan is not calm or calm then lucy is either not curious or wise and vice versa.
If mary is kind then someone is either strong or not generous and vice versa.
If someone is not funny then someone is kind or not kind.
Everyone who is kind is not kind.
Everyone who is creative or not wise is either not wise or curious.
Everyone who is either funny or not rich is calm or kind and vice versa.
Everyone who is tall or old is not tall or not funny.
If john is both happy and not quiet then someone is wise and vice versa.
Everyone who is both not happy and humble is happy or rich and vice versa.
Everyone who is either kind or not creative is kind.
If susan is not creative then john is not creative or not old.
If fred is old or tall then paul is either happy or curious and vice versa.
If lucy is both funny and curious then someone is either curious or humble.
If someone is both not wise and strong then susan is either funny or not happy.
Mary is not wise.
Someone is both old and not wise.
Someone is either not quiet or calm.
Someone is either quiet or not creative.
Fred is either not tall or wise.
Someone is not strong.
Someone is either not funny or not wise. | Fred is not tall. | entailment | (![X]:(~generous(X)<=>(~rich(X)|calm(X))))&
((?[X]:((~calm(X)|wise(X))))=>(?[X]:((~creative(X)|~strong(X)))))&
(((~calm(susan)|calm(susan)))<=>((~curious(lucy)<~>wise(lucy))))&
((kind(mary))<=>(?[X]:((strong(X)<~>~generous(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:(kind(X)=>~kind(X)))&
(![X]:((creative(X)|~wise(X))=>(~wise(X)<~>curious(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(calm(X)|kind(X))))&
(![X]:((tall(X)|old(X))=>(~tall(X)|~funny(X))))&
(((happy(john)&~quiet(john)))<=>(?[X]:(wise(X))))&
(![X]:((~happy(X)&humble(X))<=>(happy(X)|rich(X))))&
(![X]:((kind(X)<~>~creative(X))=>kind(X)))&
((~creative(susan))=>((~creative(john)|~old(john))))&
(((old(fred)|tall(fred)))<=>((happy(paul)<~>curious(paul))))&
(((funny(lucy)&curious(lucy)))=>(?[X]:((curious(X)<~>humble(X)))))&
((?[X]:((~wise(X)&strong(X))))=>((funny(susan)<~>~happy(susan))))&
(~wise(mary))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:((quiet(X)<~>~creative(X))))&
((~tall(fred)<~>wise(fred)))&
(?[X]:(~strong(X)))&
(?[X]:((~funny(X)<~>~wise(X)))) | ~tall(fred) | [
"p9",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 703159696512596248742166
% SZS output start Proof for 703159696512596248742166
10. (~quiet(john) & happy(john)) <=> ? [X0] : wise(X0) [input p9]
11. ! [X0] : ((humble(X0) & ~happy(X0)) <=> (rich(X0) | happy(X0))) [input p10]
21. ~tall(fred) <~> wise(fred) [input p20]
24. tall(fred) [input hypothesis]
56. ((~quiet(john) & happy(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | (quiet(john) | ~happy(john))) [nnf transformation 10]
57. ((~quiet(john) & happy(john)) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | quiet(john) | ~happy(john)) [flattening 56]
58. ((~quiet(john) & happy(john)) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | quiet(john) | ~happy(john)) [rectify 57]
59. ? [X1] : wise(X1) => wise(sK3) [choice axiom]
60. ((~quiet(john) & happy(john)) | ! [X0] : ~wise(X0)) & (wise(sK3) | quiet(john) | ~happy(john)) [skolemisation 58,59]
61. ! [X0] : (((humble(X0) & ~happy(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (~humble(X0) | happy(X0)))) [nnf transformation 11]
62. ! [X0] : (((humble(X0) & ~happy(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | ~humble(X0) | happy(X0))) [flattening 61]
78. (~wise(fred) | tall(fred)) & (wise(fred) | ~tall(fred)) [nnf transformation 21]
114. happy(john) | ~wise(X0) [cnf transformation 60]
117. ~happy(X0) | ~happy(X0) [cnf transformation 62]
141. wise(fred) | ~tall(fred) [cnf transformation 78]
146. tall(fred) [cnf transformation 24]
149. ~happy(X0) [duplicate literal removal 117]
154. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
155. ~wise(X1) <- (1) [avatar component clause 154]
215. 14 <=> happy(john) [avatar definition]
217. happy(john) <- (14) [avatar component clause 215]
218. 1 | 14 [avatar split clause 114,215,154]
236. 18 <=> tall(fred) [avatar definition]
279. 26 <=> wise(fred) [avatar definition]
280. wise(fred) <- (26) [avatar component clause 279]
283. ~18 | 26 [avatar split clause 141,279,236]
294. 18 [avatar split clause 146,236]
295. $false <- (14) [subsumption resolution 217,149]
296. ~14 [avatar contradiction clause 295]
303. $false <- (1, 26) [resolution 280,155]
304. ~1 | ~26 [avatar contradiction clause 303]
305. $false [avatar sat refutation 218,283,294,296,304]
% SZS output end Proof for 703159696512596248742166
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not strong is humble or not generous.
Everyone who is not curious is either kind or not calm and vice versa.
If someone is rich then someone is either tall or rich and vice versa.
If someone is either old or not brave then john is not strong or wise and vice versa.
Everyone who is funny or not creative is patient or not tall.
If someone is old or quiet then fred is not creative or strong and vice versa.
Everyone who is both not calm and wise is wise.
Everyone who is either not generous or calm is both calm and not funny and vice versa.
If someone is rich or not tall then someone is either not tall or not curious and vice versa.
Everyone who is not kind is not brave.
Everyone who is either not rich or not patient is either rich or brave and vice versa.
If someone is not old then someone is curious.
Everyone who is quiet is not brave and vice versa.
If lucy is both not generous and not patient then lucy is brave or not quiet.
Everyone who is both wise and humble is patient.
Everyone who is humble or calm is both not quiet and not calm.
Someone is either calm or strong.
Lucy is humble or not funny.
John is either not patient or funny.
Susan is not wise.
Someone is either kind or quiet.
Someone is either quiet or patient.
Lucy is either not strong or creative. | Lucy is kind. | entailment | (![X]:((quiet(X)|~strong(X))=>(humble(X)|~generous(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((tall(X)<~>rich(X)))))&
((?[X]:((old(X)<~>~brave(X))))<=>((~strong(john)|wise(john))))&
(![X]:((funny(X)|~creative(X))=>(patient(X)|~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>((~creative(fred)|strong(fred))))&
(![X]:((~calm(X)&wise(X))=>wise(X)))&
(![X]:((~generous(X)<~>calm(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
(![X]:(~kind(X)=>~brave(X)))&
(![X]:((~rich(X)<~>~patient(X))<=>(rich(X)<~>brave(X))))&
((?[X]:(~old(X)))=>(?[X]:(curious(X))))&
(![X]:(quiet(X)<=>~brave(X)))&
(((~generous(lucy)&~patient(lucy)))=>((brave(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&humble(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(~quiet(X)&~calm(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((humble(lucy)|~funny(lucy)))&
((~patient(john)<~>funny(john)))&
(~wise(susan))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
((~strong(lucy)<~>creative(lucy))) | kind(lucy) | [
"p0",
"p7",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1385682699804420676322343
% SZS output start Proof for 1385682699804420676322343
1. ! [X0] : ((~strong(X0) | quiet(X0)) => (~generous(X0) | humble(X0))) [input p0]
8. ! [X0] : ((~generous(X0) <~> calm(X0)) <=> (~funny(X0) & calm(X0))) [input p7]
10. ! [X0] : (~kind(X0) => ~brave(X0)) [input p9]
13. ! [X0] : (quiet(X0) <=> ~brave(X0)) [input p12]
16. ! [X0] : ((calm(X0) | humble(X0)) => (~calm(X0) & ~quiet(X0))) [input p15]
24. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((~generous(X0) | humble(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 1]
29. ! [X0] : (~generous(X0) | humble(X0) | (strong(X0) & ~quiet(X0))) [flattening 28]
34. ! [X0] : (~brave(X0) | kind(X0)) [ennf transformation 10]
40. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 16]
57. ! [X0] : ((((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))))) [nnf transformation 8]
58. ! [X0] : ((((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | ((~generous(X0) | ~calm(X0)) & (calm(X0) | generous(X0))))) [flattening 57]
68. ! [X0] : ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0))) [nnf transformation 13]
80. ~generous(X0) | humble(X0) | ~quiet(X0) [cnf transformation 29]
103. calm(X0) | calm(X0) | generous(X0) [cnf transformation 58]
115. ~brave(X0) | kind(X0) [cnf transformation 34]
126. brave(X0) | quiet(X0) [cnf transformation 68]
129. ~humble(X0) | ~quiet(X0) [cnf transformation 40]
132. ~calm(X0) | ~calm(X0) [cnf transformation 40]
145. ~kind(lucy) [cnf transformation 24]
146. ~calm(X0) [duplicate literal removal 132]
151. calm(X0) | generous(X0) [duplicate literal removal 103]
225. 17 <=> ! [X1] : ~quiet(X1) [avatar definition]
226. ~quiet(X1) <- (17) [avatar component clause 225]
346. kind(X1) | quiet(X1) [resolution 126,115]
347. generous(X0) [resolution 151,146]
351. humble(X0) | ~quiet(X0) [resolution 80,347]
352. ~quiet(X0) [subsumption resolution 351,129]
353. 17 [avatar split clause 352,225]
362. quiet(lucy) [resolution 346,145]
365. $false <- (17) [subsumption resolution 362,226]
366. ~17 [avatar contradiction clause 365]
369. $false [avatar sat refutation 353,366]
% SZS output end Proof for 1385682699804420676322343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not calm is tall.
Everyone who is not tall is either not tall or not quiet and vice versa.
If fred is either not brave or not quiet then someone is both not old and not kind.
Everyone who is humble is not rich or wise and vice versa.
Everyone who is not rich or rich is happy or curious.
If someone is curious or not generous then someone is not brave and vice versa.
If alice is not wise or wise then someone is either generous or rich.
If someone is strong then john is either funny or not generous.
Everyone who is either humble or not brave is either humble or calm and vice versa.
Everyone who is either funny or not generous is both not calm and not curious and vice versa.
Everyone who is wise or quiet is not curious and vice versa.
Everyone who is not calm or tall is either not wise or not creative.
If alice is both kind and brave then paul is not generous and vice versa.
If someone is calm or strong then mary is both curious and tall and vice versa.
Everyone who is old is both not rich and kind.
Everyone who is not quiet or not creative is generous and vice versa.
Fred is curious or brave.
Someone is either not funny or old.
Someone is either curious or not curious.
Mary is brave.
Someone is both not patient and tall.
Susan is either not curious or not humble. | Paul is not old. | neutral | (![X]:((patient(X)<~>~calm(X))=>tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)<~>~quiet(X))))&
(((~brave(fred)<~>~quiet(fred)))=>(?[X]:((~old(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~rich(X)|wise(X))))&
(![X]:((~rich(X)|rich(X))=>(happy(X)|curious(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:(~brave(X))))&
(((~wise(alice)|wise(alice)))=>(?[X]:((generous(X)<~>rich(X)))))&
((?[X]:(strong(X)))=>((funny(john)<~>~generous(john))))&
(![X]:((humble(X)<~>~brave(X))<=>(humble(X)<~>calm(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~calm(X)&~curious(X))))&
(![X]:((wise(X)|quiet(X))<=>~curious(X)))&
(![X]:((~calm(X)|tall(X))=>(~wise(X)<~>~creative(X))))&
(((kind(alice)&brave(alice)))<=>(~generous(paul)))&
((?[X]:((calm(X)|strong(X))))<=>((curious(mary)&tall(mary))))&
(![X]:(old(X)=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)|~creative(X))<=>generous(X)))&
((curious(fred)|brave(fred)))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(brave(mary))&
(?[X]:((~patient(X)&tall(X))))&
((~curious(susan)<~>~humble(susan))) | ~old(paul) | [] | null | 0 |
Everyone who is happy is both not generous and not quiet and vice versa.
Everyone who is kind or rich is both not generous and not brave.
Everyone who is both rich and not brave is not tall or not strong.
If paul is not patient then someone is not kind or patient.
Everyone who is either not creative or curious is not kind or not humble.
Everyone who is either quiet or not brave is not strong or wise and vice versa.
Everyone who is either rich or old is not rich.
If mary is either curious or not wise then someone is either not wise or tall and vice versa.
If lucy is not curious then susan is calm or not funny.
If someone is either not quiet or not old then someone is both wise and not wise and vice versa.
Everyone who is not strong is not patient.
If lucy is both not creative and not patient then alice is either tall or not calm and vice versa.
Everyone who is not old or kind is either not brave or funny and vice versa.
Everyone who is both patient and rich is either not brave or brave and vice versa.
If lucy is both creative and old then fred is either brave or not rich.
Fred is not wise.
Someone is either not brave or not strong.
Someone is not brave.
Someone is not curious.
Someone is either old or tall.
Susan is both calm and not funny. | Paul is not old. | contradiction | (![X]:(happy(X)<=>(~generous(X)&~quiet(X))))&
(![X]:((kind(X)|rich(X))=>(~generous(X)&~brave(X))))&
(![X]:((rich(X)&~brave(X))=>(~tall(X)|~strong(X))))&
((~patient(paul))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((~creative(X)<~>curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)|wise(X))))&
(![X]:((rich(X)<~>old(X))=>~rich(X)))&
(((curious(mary)<~>~wise(mary)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~curious(lucy))=>((calm(susan)|~funny(susan))))&
((?[X]:((~quiet(X)<~>~old(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~strong(X)=>~patient(X)))&
(((~creative(lucy)&~patient(lucy)))<=>((tall(alice)<~>~calm(alice))))&
(![X]:((~old(X)|kind(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((patient(X)&rich(X))<=>(~brave(X)<~>brave(X))))&
(((creative(lucy)&old(lucy)))=>((brave(fred)<~>~rich(fred))))&
(~wise(fred))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)<~>tall(X))))&
((calm(susan)&~funny(susan))) | ~old(paul) | [
"p1",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1216395291061022305687224
% SZS output start Proof for 1216395291061022305687224
2. ! [X0] : ((rich(X0) | kind(X0)) => (~brave(X0) & ~generous(X0))) [input p1]
7. ! [X0] : ((rich(X0) <~> old(X0)) => ~rich(X0)) [input p6]
14. ! [X0] : ((rich(X0) & patient(X0)) <=> (~brave(X0) <~> brave(X0))) [input p13]
22. ~old(paul) [input hypothesis]
24. ! [X0] : ((rich(X0) | kind(X0)) => ~brave(X0)) [pure predicate removal 2]
26. ! [X0] : (~brave(X0) | (~rich(X0) & ~kind(X0))) [ennf transformation 24]
30. ! [X0] : (~rich(X0) | (rich(X0) <=> old(X0))) [ennf transformation 7]
40. ! [X0] : (~rich(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 30]
54. ! [X0] : (((rich(X0) & patient(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (~rich(X0) | ~patient(X0)))) [nnf transformation 14]
55. ! [X0] : (((rich(X0) & patient(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~rich(X0) | ~patient(X0))) [flattening 54]
68. ~brave(X0) | ~rich(X0) [cnf transformation 26]
77. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 40]
111. rich(X0) | brave(X0) | brave(X0) [cnf transformation 55]
112. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 55]
124. ~old(paul) [cnf transformation 22]
127. rich(X0) | brave(X0) [duplicate literal removal 111]
128. rich(X0) | ~brave(X0) [duplicate literal removal 112]
129. ~rich(X0) | old(X0) [duplicate literal removal 77]
225. ~brave(X0) [subsumption resolution 128,68]
226. rich(X0) [subsumption resolution 127,225]
251. old(X0) [resolution 129,226]
252. $false [resolution 251,124]
% SZS output end Proof for 1216395291061022305687224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then john is either not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Fred is brave. | contradiction | ((?[X]:(kind(X)))<=>((~quiet(john)<~>humble(john))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | brave(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 35803350791638291303972
% SZS output start Proof for 35803350791638291303972
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. brave(fred) [input hypothesis]
59. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 59]
112. ~brave(X0) | ~brave(X0) [cnf transformation 60]
124. brave(fred) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
254. $false [subsumption resolution 124,126]
% SZS output end Proof for 35803350791638291303972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and tall then someone is both old and not strong and vice versa.
Everyone who is not kind or not funny is either not old or humble and vice versa.
Everyone who is creative is tall.
Everyone who is either creative or funny is either not brave or tall and vice versa.
Everyone who is funny is both not curious and brave and vice versa.
Everyone who is strong or happy is creative or not strong and vice versa.
If someone is patient then someone is either not kind or creative and vice versa.
Everyone who is both not tall and not generous is both generous and funny.
If fred is both not kind and generous then someone is both patient and not brave and vice versa.
If john is either kind or not strong then alice is calm and vice versa.
Everyone who is either tall or strong is not brave and vice versa.
If someone is either calm or happy then someone is not happy.
If someone is either calm or quiet then someone is creative.
Everyone who is both funny and quiet is either not curious or not humble and vice versa.
If someone is quiet or not old then someone is both generous and happy.
Everyone who is either not happy or not curious is wise.
Susan is creative.
Someone is both happy and not strong.
Paul is not strong or not creative.
Susan is not funny.
Someone is old or brave.
Someone is not quiet.
Someone is not strong. | Susan is not humble. | contradiction | ((?[X]:((curious(X)&tall(X))))<=>(?[X]:((old(X)&~strong(X)))))&
(![X]:((~kind(X)|~funny(X))<=>(~old(X)<~>humble(X))))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~brave(X)<~>tall(X))))&
(![X]:(funny(X)<=>(~curious(X)&brave(X))))&
(![X]:((strong(X)|happy(X))<=>(creative(X)|~strong(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:((~tall(X)&~generous(X))=>(generous(X)&funny(X))))&
(((~kind(fred)&generous(fred)))<=>(?[X]:((patient(X)&~brave(X)))))&
(((kind(john)<~>~strong(john)))<=>(calm(alice)))&
(![X]:((tall(X)<~>strong(X))<=>~brave(X)))&
((?[X]:((calm(X)<~>happy(X))))=>(?[X]:(~happy(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:(creative(X))))&
(![X]:((funny(X)&quiet(X))<=>(~curious(X)<~>~humble(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((~happy(X)<~>~curious(X))=>wise(X)))&
(creative(susan))&
(?[X]:((happy(X)&~strong(X))))&
((~strong(paul)|~creative(paul)))&
(~funny(susan))&
(?[X]:((old(X)|brave(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(~strong(X))) | ~humble(susan) | [
"p2",
"p3",
"p4",
"p13",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 552897370108769135593167
% SZS output start Proof for 552897370108769135593167
3. ! [X0] : (creative(X0) => tall(X0)) [input p2]
4. ! [X0] : ((creative(X0) <~> funny(X0)) <=> (~brave(X0) <~> tall(X0))) [input p3]
5. ! [X0] : (funny(X0) <=> (brave(X0) & ~curious(X0))) [input p4]
14. ! [X0] : ((quiet(X0) & funny(X0)) <=> (~curious(X0) <~> ~humble(X0))) [input p13]
17. creative(susan) [input p16]
20. ~funny(susan) [input p19]
24. ~humble(susan) [input hypothesis]
31. ! [X0] : (tall(X0) | ~creative(X0)) [ennf transformation 3]
44. ! [X0] : ((((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0)))) & (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0))))) [nnf transformation 4]
45. ! [X0] : ((funny(X0) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | ~funny(X0))) [nnf transformation 5]
46. ! [X0] : ((funny(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | ~funny(X0))) [flattening 45]
69. ! [X0] : (((quiet(X0) & funny(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | (~quiet(X0) | ~funny(X0)))) [nnf transformation 14]
70. ! [X0] : (((quiet(X0) & funny(X0)) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | ~quiet(X0) | ~funny(X0))) [flattening 69]
92. ~creative(X0) | tall(X0) [cnf transformation 31]
95. ~tall(X0) | brave(X0) | funny(X0) | ~creative(X0) [cnf transformation 44]
101. ~funny(X0) | ~curious(X0) [cnf transformation 46]
103. ~brave(X0) | funny(X0) | curious(X0) [cnf transformation 46]
133. funny(X0) | ~curious(X0) | humble(X0) [cnf transformation 70]
140. creative(susan) [cnf transformation 17]
144. ~funny(susan) [cnf transformation 20]
148. ~humble(susan) [cnf transformation 24]
180. ~creative(X0) | funny(X0) | brave(X0) [subsumption resolution 95,92]
270. ~curious(X0) | humble(X0) [subsumption resolution 133,101]
498. funny(susan) | brave(susan) [resolution 180,140]
501. brave(susan) [subsumption resolution 498,144]
506. funny(susan) | curious(susan) [resolution 501,103]
508. curious(susan) [subsumption resolution 506,144]
638. humble(susan) [resolution 508,270]
642. $false [subsumption resolution 638,148]
% SZS output end Proof for 552897370108769135593167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.048 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both humble and not humble then someone is both strong and humble and vice versa.
Everyone who is old or brave is both wise and not curious and vice versa.
If alice is both kind and generous then someone is either generous or not curious and vice versa.
If someone is wise or not creative then fred is either generous or humble and vice versa.
Everyone who is brave is both not happy and not old and vice versa.
Everyone who is not tall or quiet is not quiet or humble.
If someone is not creative then someone is not wise.
Everyone who is not brave is kind or not quiet and vice versa.
Everyone who is not generous or generous is both not strong and creative and vice versa.
If lucy is either not humble or creative then someone is not creative.
If someone is wise then someone is not old or not kind.
Everyone who is not humble or not brave is not happy or brave.
Everyone who is either generous or not calm is either curious or wise.
If mary is both not happy and quiet then someone is either not brave or not generous.
Everyone who is both patient and brave is wise or calm.
Someone is happy or not happy.
Alice is either patient or calm.
Lucy is either happy or not quiet.
Paul is either not generous or not tall.
Lucy is not kind.
Mary is both not happy and not curious.
Fred is old. | Fred is brave. | contradiction | (((humble(alice)&~humble(alice)))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((old(X)|brave(X))<=>(wise(X)&~curious(X))))&
(((kind(alice)&generous(alice)))<=>(?[X]:((generous(X)<~>~curious(X)))))&
((?[X]:((wise(X)|~creative(X))))<=>((generous(fred)<~>humble(fred))))&
(![X]:(brave(X)<=>(~happy(X)&~old(X))))&
(![X]:((~tall(X)|quiet(X))=>(~quiet(X)|humble(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)<=>(kind(X)|~quiet(X))))&
(![X]:((~generous(X)|generous(X))<=>(~strong(X)&creative(X))))&
(((~humble(lucy)<~>creative(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((~humble(X)|~brave(X))=>(~happy(X)|brave(X))))&
(![X]:((generous(X)<~>~calm(X))=>(curious(X)<~>wise(X))))&
(((~happy(mary)&quiet(mary)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((patient(X)&brave(X))=>(wise(X)|calm(X))))&
(?[X]:((happy(X)|~happy(X))))&
((patient(alice)<~>calm(alice)))&
((happy(lucy)<~>~quiet(lucy)))&
((~generous(paul)<~>~tall(paul)))&
(~kind(lucy))&
((~happy(mary)&~curious(mary)))&
(old(fred)) | brave(fred) | [
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5559926840394018025825432
% SZS output start Proof for 5559926840394018025825432
5. ! [X0] : (brave(X0) <=> (~old(X0) & ~happy(X0))) [input p4]
22. old(fred) [input p21]
23. brave(fred) [input hypothesis]
54. ! [X0] : ((brave(X0) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | ~brave(X0))) [nnf transformation 5]
55. ! [X0] : ((brave(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | ~brave(X0))) [flattening 54]
100. ~brave(X0) | ~old(X0) [cnf transformation 55]
135. old(fred) [cnf transformation 22]
136. brave(fred) [cnf transformation 23]
281. ~old(fred) [resolution 100,136]
282. $false [subsumption resolution 281,135]
% SZS output end Proof for 5559926840394018025825432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either not kind or creative then someone is either not patient or old.
Everyone who is brave is not tall or generous and vice versa.
Everyone who is generous or calm is either happy or tall.
If someone is either not curious or rich then paul is creative or not curious and vice versa.
Everyone who is either creative or old is not patient or quiet.
If susan is curious or not generous then fred is both not patient and tall and vice versa.
Everyone who is either not generous or not happy is either not creative or brave and vice versa.
Everyone who is calm or rich is both not creative and not strong and vice versa.
Everyone who is not old or not generous is both happy and wise.
If someone is either kind or not kind then mary is either generous or not wise and vice versa.
Everyone who is either not patient or not funny is either creative or calm and vice versa.
If alice is either not wise or patient then john is not generous or not calm and vice versa.
Everyone who is either not patient or creative is both kind and strong and vice versa.
Everyone who is either not happy or not generous is patient or humble and vice versa.
Everyone who is not quiet or kind is not kind or quiet.
Everyone who is funny or not brave is rich.
Someone is funny.
Fred is not old or not funny.
Someone is either not brave or quiet.
Susan is either not creative or curious.
John is both curious and not quiet.
Someone is not kind.
Fred is curious or quiet.
Lucy is not happy. | Susan is not creative. | entailment | ((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)&~strong(X))))&
(![X]:((~old(X)|~generous(X))=>(happy(X)&wise(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((generous(mary)<~>~wise(mary))))&
(![X]:((~patient(X)<~>~funny(X))<=>(creative(X)<~>calm(X))))&
(((~wise(alice)<~>patient(alice)))<=>((~generous(john)|~calm(john))))&
(![X]:((~patient(X)<~>creative(X))<=>(kind(X)&strong(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)|humble(X))))&
(![X]:((~quiet(X)|kind(X))=>(~kind(X)|quiet(X))))&
(![X]:((funny(X)|~brave(X))=>rich(X)))&
(?[X]:(funny(X)))&
((~old(fred)|~funny(fred)))&
(?[X]:((~brave(X)<~>quiet(X))))&
((~creative(susan)<~>curious(susan)))&
((curious(john)&~quiet(john)))&
(?[X]:(~kind(X)))&
((curious(fred)|quiet(fred)))&
(~happy(lucy)) | ~creative(susan) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6284829217037943587523550
% SZS output start Proof for 6284829217037943587523550
2. ! [X0] : (brave(X0) <=> (generous(X0) | ~tall(X0))) [input p1]
3. ! [X0] : ((calm(X0) | generous(X0)) => (happy(X0) <~> tall(X0))) [input p2]
6. (~generous(susan) | curious(susan)) <=> (tall(fred) & ~patient(fred)) [input p5]
7. ! [X0] : ((~generous(X0) <~> ~happy(X0)) <=> (~creative(X0) <~> brave(X0))) [input p6]
8. ! [X0] : ((rich(X0) | calm(X0)) <=> (~strong(X0) & ~creative(X0))) [input p7]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (creative(X0) <~> calm(X0))) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (strong(X0) & kind(X0))) [input p12]
16. ! [X0] : ((~brave(X0) | funny(X0)) => rich(X0)) [input p15]
20. ~creative(susan) <~> curious(susan) [input p19]
25. creative(susan) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> tall(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 3]
34. ! [X0] : (rich(X0) | (brave(X0) & ~funny(X0))) [ennf transformation 16]
39. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 28]
48. ((~generous(susan) | curious(susan)) | (~tall(fred) | patient(fred))) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [nnf transformation 6]
49. (~generous(susan) | curious(susan) | ~tall(fred) | patient(fred)) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [flattening 48]
50. ! [X0] : ((((happy(X0) | generous(X0)) & (~happy(X0) | ~generous(X0))) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))))) [nnf transformation 7]
51. ! [X0] : (((rich(X0) | calm(X0)) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((rich(X0) | calm(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 51]
57. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 60]
69. (~curious(susan) | creative(susan)) & (curious(susan) | ~creative(susan)) [nnf transformation 20]
76. ~tall(X0) | generous(X0) | ~brave(X0) [cnf transformation 40]
78. ~generous(X0) | brave(X0) [cnf transformation 40]
81. ~happy(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 41]
91. ~patient(fred) | ~curious(susan) [cnf transformation 49]
93. tall(fred) | ~curious(susan) [cnf transformation 49]
99. ~brave(X0) | creative(X0) | ~generous(X0) | happy(X0) [cnf transformation 50]
102. happy(X0) | generous(X0) | brave(X0) | creative(X0) [cnf transformation 50]
104. ~calm(X0) | ~creative(X0) [cnf transformation 52]
105. ~rich(X0) | ~creative(X0) [cnf transformation 52]
107. ~strong(X0) | ~rich(X0) [cnf transformation 52]
127. funny(X0) | patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 57]
128. funny(X0) | patient(X0) | creative(X0) | ~calm(X0) [cnf transformation 57]
137. strong(X0) | creative(X0) | patient(X0) [cnf transformation 61]
149. ~funny(X0) | rich(X0) [cnf transformation 34]
150. rich(X0) | brave(X0) [cnf transformation 34]
155. curious(susan) | ~creative(susan) [cnf transformation 69]
162. creative(susan) [cnf transformation 25]
216. 11 <=> patient(fred) [avatar definition]
217. ~patient(fred) <- (~11) [avatar component clause 216]
220. 12 <=> tall(fred) [avatar definition]
221. tall(fred) <- (12) [avatar component clause 220]
224. 13 <=> curious(susan) [avatar definition]
233. ~13 | 12 [avatar split clause 93,220,224]
235. ~13 | ~11 [avatar split clause 91,216,224]
236. happy(X0) | brave(X0) | creative(X0) [subsumption resolution 102,78]
238. ~generous(X0) | creative(X0) | happy(X0) [subsumption resolution 99,236]
262. ~calm(X0) | patient(X0) | funny(X0) [subsumption resolution 128,104]
263. ~creative(X0) | patient(X0) | funny(X0) [subsumption resolution 127,262]
295. 24 <=> funny(fred) [avatar definition]
296. funny(fred) <- (24) [avatar component clause 295]
297. ~funny(fred) <- (~24) [avatar component clause 295]
310. 27 <=> creative(susan) [avatar definition]
314. ~27 | 13 [avatar split clause 155,224,310]
324. 27 [avatar split clause 162,310]
338. generous(fred) | ~brave(fred) <- (12) [resolution 76,221]
341. 30 <=> brave(fred) [avatar definition]
343. ~brave(fred) <- (~30) [avatar component clause 341]
345. 31 <=> generous(fred) [avatar definition]
347. generous(fred) <- (31) [avatar component clause 345]
348. ~30 | 31 | ~12 [avatar split clause 338,220,345,341]
385. creative(X0) | patient(X0) | ~rich(X0) [resolution 137,107]
387. ~rich(X0) | patient(X0) [subsumption resolution 385,105]
473. rich(fred) <- (24) [resolution 296,149]
592. brave(X0) | patient(X0) [resolution 387,150]
593. patient(fred) <- (24) [resolution 387,473]
595. $false <- (~11, 24) [subsumption resolution 593,217]
596. 11 | ~24 [avatar contradiction clause 595]
602. 51 <=> creative(fred) [avatar definition]
604. creative(fred) <- (51) [avatar component clause 602]
607. 52 <=> happy(fred) [avatar definition]
609. happy(fred) <- (52) [avatar component clause 607]
763. patient(fred) <- (~30) [resolution 592,343]
764. $false <- (~11, ~30) [subsumption resolution 763,217]
765. 11 | 30 [avatar contradiction clause 764]
771. creative(fred) | happy(fred) <- (31) [resolution 347,238]
783. patient(fred) | funny(fred) <- (51) [resolution 604,263]
785. funny(fred) <- (~11, 51) [subsumption resolution 783,217]
786. $false <- (~11, ~24, 51) [subsumption resolution 785,297]
787. 11 | 24 | ~51 [avatar contradiction clause 786]
788. 52 | 51 | ~31 [avatar split clause 771,345,602,607]
794. ~tall(fred) | ~generous(fred) <- (52) [resolution 609,81]
796. ~generous(fred) <- (12, 52) [subsumption resolution 794,221]
797. $false <- (12, 31, 52) [subsumption resolution 796,347]
798. ~12 | ~31 | ~52 [avatar contradiction clause 797]
799. $false [avatar sat refutation 233,235,314,324,348,596,765,787,788,798]
% SZS output end Proof for 6284829217037943587523550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is kind or brave.
If mary is either not strong or not quiet then someone is not wise.
If paul is not rich then alice is not curious or not strong and vice versa.
If mary is both not creative and not tall then someone is not happy and vice versa.
If john is both happy and not quiet then someone is not curious and vice versa.
Everyone who is funny is either not happy or humble and vice versa.
If someone is either quiet or not patient then john is brave and vice versa.
If lucy is either curious or not old then fred is not kind or funny and vice versa.
If someone is generous or not patient then lucy is generous and vice versa.
If someone is either strong or not funny then mary is rich or quiet.
Everyone who is generous or brave is not generous.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Everyone who is either not brave or generous is both not old and rich and vice versa.
If john is not patient then lucy is not funny or not quiet.
Fred is both not funny and not generous.
Mary is either rich or not happy.
John is not creative or not humble.
Alice is wise.
Someone is strong.
Lucy is both not generous and happy.
Someone is either not funny or humble.
Alice is not generous or not curious. | Mary is not happy. | contradiction | ((?[X]:(~generous(X)))=>(?[X]:((kind(X)|brave(X)))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:(~wise(X))))&
((~rich(paul))<=>((~curious(alice)|~strong(alice))))&
(((~creative(mary)&~tall(mary)))<=>(?[X]:(~happy(X))))&
(((happy(john)&~quiet(john)))<=>(?[X]:(~curious(X))))&
(![X]:(funny(X)<=>(~happy(X)<~>humble(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(brave(john)))&
(((curious(lucy)<~>~old(lucy)))<=>((~kind(fred)|funny(fred))))&
((?[X]:((generous(X)|~patient(X))))<=>(generous(lucy)))&
((?[X]:((strong(X)<~>~funny(X))))=>((rich(mary)|quiet(mary))))&
(![X]:((generous(X)|brave(X))=>~generous(X)))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
((~patient(john))=>((~funny(lucy)|~quiet(lucy))))&
((~funny(fred)&~generous(fred)))&
((rich(mary)<~>~happy(mary)))&
((~creative(john)|~humble(john)))&
(wise(alice))&
(?[X]:(strong(X)))&
((~generous(lucy)&happy(lucy)))&
(?[X]:((~funny(X)<~>humble(X))))&
((~generous(alice)|~curious(alice))) | ~happy(mary) | [
"p3",
"p10",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6958443250298167952760448
% SZS output start Proof for 6958443250298167952760448
4. (~tall(mary) & ~creative(mary)) <=> ? [X0] : ~happy(X0) [input p3]
11. ! [X0] : ((brave(X0) | generous(X0)) => ~generous(X0)) [input p10]
13. ! [X0] : ((~rich(X0) | ~strong(X0)) <=> (tall(X0) | ~brave(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> generous(X0)) <=> (rich(X0) & ~old(X0))) [input p14]
18. rich(mary) <~> ~happy(mary) [input p17]
25. ~happy(mary) [input hypothesis]
31. ! [X0] : (~generous(X0) | (~brave(X0) & ~generous(X0))) [ennf transformation 11]
42. ((~tall(mary) & ~creative(mary)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (tall(mary) | creative(mary))) [nnf transformation 4]
43. ((~tall(mary) & ~creative(mary)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | tall(mary) | creative(mary)) [flattening 42]
44. ((~tall(mary) & ~creative(mary)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | tall(mary) | creative(mary)) [rectify 43]
45. ? [X1] : ~happy(X1) => ~happy(sK2) [choice axiom]
46. ((~tall(mary) & ~creative(mary)) | ! [X0] : happy(X0)) & (~happy(sK2) | tall(mary) | creative(mary)) [skolemisation 44,45]
66. ! [X0] : (((~rich(X0) | ~strong(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (rich(X0) & strong(X0)))) [nnf transformation 13]
67. ! [X0] : ((~rich(X0) | ~strong(X0) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | (rich(X0) & strong(X0)))) [flattening 66]
73. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [nnf transformation 15]
74. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [flattening 73]
75. (happy(mary) | ~rich(mary)) & (~happy(mary) | rich(mary)) [nnf transformation 18]
89. ~tall(mary) | happy(X0) [cnf transformation 46]
112. ~generous(X0) | ~generous(X0) [cnf transformation 31]
119. ~brave(X0) | tall(X0) | rich(X0) [cnf transformation 67]
128. rich(X0) | generous(X0) | brave(X0) [cnf transformation 74]
136. happy(mary) | ~rich(mary) [cnf transformation 75]
145. ~happy(mary) [cnf transformation 25]
146. ~generous(X0) [duplicate literal removal 112]
189. 10 <=> ! [X0] : happy(X0) [avatar definition]
190. happy(X0) <- (10) [avatar component clause 189]
192. 11 <=> tall(mary) [avatar definition]
195. 10 | ~11 [avatar split clause 89,192,189]
286. 31 <=> ! [X1] : ~generous(X1) [avatar definition]
287. ~generous(X1) <- (31) [avatar component clause 286]
293. 33 <=> rich(mary) [avatar definition]
294. ~rich(mary) <- (~33) [avatar component clause 293]
301. 31 [avatar split clause 146,286]
333. 41 <=> happy(mary) [avatar definition]
334. ~happy(mary) <- (~41) [avatar component clause 333]
336. ~33 | 41 [avatar split clause 136,333,293]
363. ~41 [avatar split clause 145,333]
423. generous(mary) | brave(mary) <- (~33) [resolution 128,294]
430. brave(mary) <- (31, ~33) [subsumption resolution 423,287]
432. tall(mary) | rich(mary) <- (31, ~33) [resolution 430,119]
441. tall(mary) <- (31, ~33) [subsumption resolution 432,294]
442. 11 | ~31 | 33 [avatar split clause 441,293,286,192]
445. $false <- (10, ~41) [resolution 190,334]
446. ~10 | 41 [avatar contradiction clause 445]
449. $false [avatar sat refutation 195,301,336,363,442,446]
% SZS output end Proof for 6958443250298167952760448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both strong and not happy and vice versa. If john is either rich or tall then paul is old. If someone is both not happy and not curious then lucy is not curious. If mary is either not creative or not patient then paul is patient. If john is both calm and not strong then paul is not humble or funny. If someone is not happy or not quiet then fred is both not happy and old and vice versa. Everyone who is not calm is quiet or strong and vice versa. If fred is either not tall or curious then lucy is either not brave or not tall and vice versa. If lucy is either not calm or happy then mary is not kind and vice versa. Everyone who is creative is not humble. Everyone who is either not rich or not curious is happy. If mary is curious then john is both curious and humble. Everyone who is either patient or happy is creative or not kind and vice versa. If alice is both not wise and not patient then fred is happy. If someone is not happy or not curious then someone is both not brave and not rich and vice versa. Everyone who is either quiet or not kind is not quiet. Lucy is both not curious and not tall. Lucy is wise or not tall. Someone is either not humble or funny. Lucy is not strong. Someone is either wise or not old. Someone is kind or quiet. John is either not curious or funny. Someone is not rich or not funny. | Fred is happy. | contradiction | (![X]:(~wise(X)<=>(strong(X)&~happy(X))))&
(((rich(john)<~>tall(john)))=>(old(paul)))&
((?[X]:((~happy(X)&~curious(X))))=>(~curious(lucy)))&
(((~creative(mary)<~>~patient(mary)))=>(patient(paul)))&
(((calm(john)&~strong(john)))=>((~humble(paul)|funny(paul))))&
((?[X]:((~happy(X)|~quiet(X))))<=>((~happy(fred)&old(fred))))&
(![X]:(~calm(X)<=>(quiet(X)|strong(X))))&
(((~tall(fred)<~>curious(fred)))<=>((~brave(lucy)<~>~tall(lucy))))&
(((~calm(lucy)<~>happy(lucy)))<=>(~kind(mary)))&
(![X]:(creative(X)=>~humble(X)))&
(![X]:((~rich(X)<~>~curious(X))=>happy(X)))&
((curious(mary))=>((curious(john)&humble(john))))&
(![X]:((patient(X)<~>happy(X))<=>(creative(X)|~kind(X))))&
(((~wise(alice)&~patient(alice)))=>(happy(fred)))&
((?[X]:((~happy(X)|~curious(X))))<=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((quiet(X)<~>~kind(X))=>~quiet(X)))&
((~curious(lucy)&~tall(lucy)))&
((wise(lucy)|~tall(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~strong(lucy))&
(?[X]:((wise(X)<~>~old(X))))&
(?[X]:((kind(X)|quiet(X))))&
((~curious(john)<~>funny(john)))&
(?[X]:((~rich(X)|~funny(X)))) | happy(fred) | [
"p5",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2142523594919433107836835
% SZS output start Proof for 2142523594919433107836835
6. ? [X0] : (~quiet(X0) | ~happy(X0)) <=> (old(fred) & ~happy(fred)) [input p5]
7. ! [X0] : (~calm(X0) <=> (strong(X0) | quiet(X0))) [input p6]
9. (~calm(lucy) <~> happy(lucy)) <=> ~kind(mary) [input p8]
16. ! [X0] : ((quiet(X0) <~> ~kind(X0)) => ~quiet(X0)) [input p15]
25. happy(fred) [input hypothesis]
37. ! [X0] : (~quiet(X0) | (quiet(X0) <=> ~kind(X0))) [ennf transformation 16]
42. (? [X0] : (~quiet(X0) | ~happy(X0)) | (~old(fred) | happy(fred))) & ((old(fred) & ~happy(fred)) | ! [X0] : (quiet(X0) & happy(X0))) [nnf transformation 6]
43. (? [X0] : (~quiet(X0) | ~happy(X0)) | ~old(fred) | happy(fred)) & ((old(fred) & ~happy(fred)) | ! [X0] : (quiet(X0) & happy(X0))) [flattening 42]
44. (? [X0] : (~quiet(X0) | ~happy(X0)) | ~old(fred) | happy(fred)) & ((old(fred) & ~happy(fred)) | ! [X1] : (quiet(X1) & happy(X1))) [rectify 43]
45. ? [X0] : (~quiet(X0) | ~happy(X0)) => (~quiet(sK0) | ~happy(sK0)) [choice axiom]
46. ((~quiet(sK0) | ~happy(sK0)) | ~old(fred) | happy(fred)) & ((old(fred) & ~happy(fred)) | ! [X1] : (quiet(X1) & happy(X1))) [skolemisation 44,45]
47. ! [X0] : ((~calm(X0) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | calm(X0))) [nnf transformation 7]
48. ! [X0] : ((~calm(X0) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | calm(X0))) [flattening 47]
50. (((~happy(lucy) | calm(lucy)) & (happy(lucy) | ~calm(lucy))) | kind(mary)) & (~kind(mary) | ((~calm(lucy) | ~happy(lucy)) & (happy(lucy) | calm(lucy)))) [nnf transformation 9]
59. ! [X0] : (~quiet(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) [nnf transformation 37]
80. ~happy(fred) | happy(X1) [cnf transformation 46]
81. ~happy(fred) | quiet(X1) [cnf transformation 46]
86. ~quiet(X0) | ~calm(X0) [cnf transformation 48]
99. ~happy(lucy) | calm(lucy) | kind(mary) [cnf transformation 50]
117. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 59]
131. happy(fred) [cnf transformation 25]
132. ~kind(X0) | ~quiet(X0) [duplicate literal removal 117]
187. 13 <=> happy(fred) [avatar definition]
204. 17 <=> ! [X1] : quiet(X1) [avatar definition]
205. quiet(X1) <- (17) [avatar component clause 204]
208. 18 <=> ! [X1] : happy(X1) [avatar definition]
209. happy(X1) <- (18) [avatar component clause 208]
211. 17 | ~13 [avatar split clause 81,187,204]
212. 18 | ~13 [avatar split clause 80,187,208]
238. 23 <=> kind(mary) [avatar definition]
240. kind(mary) <- (23) [avatar component clause 238]
242. 24 <=> calm(lucy) [avatar definition]
244. calm(lucy) <- (24) [avatar component clause 242]
246. 25 <=> happy(lucy) [avatar definition]
248. ~happy(lucy) <- (~25) [avatar component clause 246]
249. 23 | 24 | ~25 [avatar split clause 99,246,242,238]
354. 13 [avatar split clause 131,187]
355. $false <- (18, ~25) [resolution 248,209]
356. ~18 | 25 [avatar contradiction clause 355]
362. ~calm(X0) <- (17) [resolution 86,205]
363. ~quiet(mary) <- (23) [resolution 132,240]
365. $false <- (17, 23) [subsumption resolution 363,205]
366. ~17 | ~23 [avatar contradiction clause 365]
369. $false <- (17, 24) [subsumption resolution 244,362]
370. ~17 | ~24 [avatar contradiction clause 369]
371. $false [avatar sat refutation 211,212,249,354,356,366,370]
% SZS output end Proof for 2142523594919433107836835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or not creative then someone is strong.
If someone is both not kind and rich then john is either not happy or quiet and vice versa.
If someone is both calm and generous then lucy is both quiet and not brave.
Everyone who is old is either not brave or not calm.
Everyone who is both strong and not calm is not brave and vice versa.
If someone is patient or not strong then fred is not calm and vice versa.
Everyone who is either creative or happy is both kind and not happy.
If someone is not kind or not old then someone is either not tall or not rich and vice versa.
Everyone who is not creative or not patient is both not generous and not patient and vice versa.
Everyone who is either wise or not calm is both not rich and not tall.
Everyone who is either strong or not calm is both not happy and not tall and vice versa.
If someone is both tall and old then someone is either quiet or funny and vice versa.
Everyone who is either not tall or quiet is not strong or creative and vice versa.
Everyone who is both humble and not happy is calm or humble and vice versa.
If someone is curious or not wise then someone is both patient and not humble and vice versa.
If someone is both patient and happy then john is both not rich and calm and vice versa.
Lucy is not tall.
Someone is either brave or calm.
Someone is either not tall or calm.
Paul is both funny and not calm.
John is patient or not wise.
Someone is either not generous or funny.
Someone is either not strong or humble.
Fred is either funny or rich. | Paul is creative. | entailment | ((?[X]:((wise(X)|~creative(X))))=>(?[X]:(strong(X))))&
((?[X]:((~kind(X)&rich(X))))<=>((~happy(john)<~>quiet(john))))&
((?[X]:((calm(X)&generous(X))))=>((quiet(lucy)&~brave(lucy))))&
(![X]:(old(X)=>(~brave(X)<~>~calm(X))))&
(![X]:((strong(X)&~calm(X))<=>~brave(X)))&
((?[X]:((patient(X)|~strong(X))))<=>(~calm(fred)))&
(![X]:((creative(X)<~>happy(X))=>(kind(X)&~happy(X))))&
((?[X]:((~kind(X)|~old(X))))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(~generous(X)&~patient(X))))&
(![X]:((wise(X)<~>~calm(X))=>(~rich(X)&~tall(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(~happy(X)&~tall(X))))&
((?[X]:((tall(X)&old(X))))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~strong(X)|creative(X))))&
(![X]:((humble(X)&~happy(X))<=>(calm(X)|humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((~rich(john)&calm(john))))&
(~tall(lucy))&
(?[X]:((brave(X)<~>calm(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
((funny(paul)&~calm(paul)))&
((patient(john)|~wise(john)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
((funny(fred)<~>rich(fred))) | creative(paul) | [
"p3",
"p4",
"p6",
"p10",
"p11",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 594238824068428862816568
% SZS output start Proof for 594238824068428862816568
4. ! [X0] : (old(X0) => (~brave(X0) <~> ~calm(X0))) [input p3]
5. ! [X0] : ((~calm(X0) & strong(X0)) <=> ~brave(X0)) [input p4]
7. ! [X0] : ((creative(X0) <~> happy(X0)) => (~happy(X0) & kind(X0))) [input p6]
11. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> (~tall(X0) & ~happy(X0))) [input p10]
12. ? [X0] : (old(X0) & tall(X0)) <=> ? [X0] : (quiet(X0) <~> funny(X0)) [input p11]
13. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (creative(X0) | ~strong(X0))) [input p12]
20. ~calm(paul) & funny(paul) [input p19]
25. ~creative(paul) [input hypothesis]
28. ? [X0] : (old(X0) & tall(X0)) <=> ? [X1] : (quiet(X1) <~> funny(X1)) [rectify 12]
32. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | ~old(X0)) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & kind(X0)) | (creative(X0) <=> happy(X0))) [ennf transformation 7]
42. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | ~old(X0)) [nnf transformation 32]
43. ! [X0] : (((~calm(X0) & strong(X0)) | brave(X0)) & (~brave(X0) | (calm(X0) | ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : (((~calm(X0) & strong(X0)) | brave(X0)) & (~brave(X0) | calm(X0) | ~strong(X0))) [flattening 43]
49. ! [X0] : ((~happy(X0) & kind(X0)) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0)))) [nnf transformation 33]
58. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (tall(X0) | happy(X0))) & ((~tall(X0) & ~happy(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 11]
59. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | tall(X0) | happy(X0)) & ((~tall(X0) & ~happy(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [flattening 58]
60. (? [X0] : (old(X0) & tall(X0)) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) & (? [X1] : ((~funny(X1) | ~quiet(X1)) & (funny(X1) | quiet(X1))) | ! [X0] : (~old(X0) | ~tall(X0))) [nnf transformation 28]
61. (? [X0] : (old(X0) & tall(X0)) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) & (? [X2] : ((~funny(X2) | ~quiet(X2)) & (funny(X2) | quiet(X2))) | ! [X3] : (~old(X3) | ~tall(X3))) [rectify 60]
62. ? [X0] : (old(X0) & tall(X0)) => (old(sK5) & tall(sK5)) [choice axiom]
63. ? [X2] : ((~funny(X2) | ~quiet(X2)) & (funny(X2) | quiet(X2))) => ((~funny(sK6) | ~quiet(sK6)) & (funny(sK6) | quiet(sK6))) [choice axiom]
64. ((old(sK5) & tall(sK5)) | ! [X1] : ((quiet(X1) | ~funny(X1)) & (funny(X1) | ~quiet(X1)))) & (((~funny(sK6) | ~quiet(sK6)) & (funny(sK6) | quiet(sK6))) | ! [X3] : (~old(X3) | ~tall(X3))) [skolemisation 61,63,62]
65. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 13]
66. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 65]
102. ~old(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 42]
103. ~old(X0) | brave(X0) | calm(X0) [cnf transformation 42]
104. ~brave(X0) | calm(X0) | ~strong(X0) [cnf transformation 44]
106. ~calm(X0) | brave(X0) [cnf transformation 44]
113. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 49]
132. ~tall(X0) | strong(X0) | calm(X0) [cnf transformation 59]
134. ~strong(X0) | calm(X0) | tall(X0) | happy(X0) [cnf transformation 59]
138. tall(sK5) | quiet(X1) | ~funny(X1) [cnf transformation 64]
140. old(sK5) | quiet(X1) | ~funny(X1) [cnf transformation 64]
142. ~tall(X0) | ~strong(X0) | creative(X0) | ~quiet(X0) [cnf transformation 66]
145. ~quiet(X0) | tall(X0) | strong(X0) [cnf transformation 66]
166. funny(paul) [cnf transformation 20]
167. ~calm(paul) [cnf transformation 20]
175. ~creative(paul) [cnf transformation 25]
176. ~happy(X0) | creative(X0) [duplicate literal removal 113]
283. 25 <=> ! [X1] : (quiet(X1) | ~funny(X1)) [avatar definition]
284. ~funny(X1) | quiet(X1) <- (25) [avatar component clause 283]
286. 26 <=> old(sK5) [avatar definition]
288. old(sK5) <- (26) [avatar component clause 286]
289. 25 | 26 [avatar split clause 140,286,283]
295. 28 <=> tall(sK5) [avatar definition]
297. tall(sK5) <- (28) [avatar component clause 295]
298. 25 | 28 [avatar split clause 138,295,283]
428. quiet(paul) <- (25) [resolution 284,166]
529. tall(paul) | strong(paul) <- (25) [resolution 145,428]
532. 66 <=> strong(paul) [avatar definition]
534. strong(paul) <- (66) [avatar component clause 532]
536. 67 <=> tall(paul) [avatar definition]
537. ~tall(paul) <- (~67) [avatar component clause 536]
538. tall(paul) <- (67) [avatar component clause 536]
539. 66 | 67 | ~25 [avatar split clause 529,283,536,532]
616. strong(paul) | calm(paul) <- (67) [resolution 538,132]
617. ~strong(paul) | creative(paul) | ~quiet(paul) <- (67) [resolution 538,142]
622. strong(paul) <- (67) [subsumption resolution 616,167]
623. 66 | ~67 [avatar split clause 622,536,532]
624. ~strong(paul) | ~quiet(paul) <- (67) [subsumption resolution 617,175]
625. ~strong(paul) <- (25, 67) [subsumption resolution 624,428]
626. ~66 | ~25 | ~67 [avatar split clause 625,536,283,532]
628. calm(paul) | tall(paul) | happy(paul) <- (66) [resolution 534,134]
629. tall(paul) | happy(paul) <- (66) [subsumption resolution 628,167]
630. happy(paul) <- (66, ~67) [subsumption resolution 629,537]
715. creative(paul) <- (66, ~67) [resolution 630,176]
716. $false <- (66, ~67) [subsumption resolution 715,175]
717. ~66 | 67 [avatar contradiction clause 716]
729. brave(sK5) | calm(sK5) <- (26) [resolution 288,103]
730. ~brave(sK5) | ~calm(sK5) <- (26) [resolution 288,102]
731. brave(sK5) <- (26) [subsumption resolution 729,106]
732. ~calm(sK5) <- (26) [subsumption resolution 730,731]
736. strong(sK5) | calm(sK5) <- (28) [resolution 297,132]
742. strong(sK5) <- (26, 28) [subsumption resolution 736,732]
775. calm(sK5) | ~strong(sK5) <- (26) [resolution 731,104]
776. ~strong(sK5) <- (26) [subsumption resolution 775,732]
777. $false <- (26, 28) [subsumption resolution 776,742]
778. ~26 | ~28 [avatar contradiction clause 777]
779. $false [avatar sat refutation 289,298,539,623,626,717,778]
% SZS output end Proof for 594238824068428862816568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or patient is not curious or rich and vice versa.
Everyone who is brave or creative is both not brave and not curious and vice versa.
Everyone who is strong or happy is tall and vice versa.
If alice is both not old and not tall then someone is either patient or humble and vice versa.
Everyone who is both not happy and not calm is generous or brave.
Everyone who is not calm or happy is either not creative or not quiet and vice versa.
If someone is both old and not wise then someone is both not kind and not quiet.
If someone is either not tall or patient then fred is both not kind and strong and vice versa.
Everyone who is not rich is tall and vice versa.
If someone is generous then someone is either not curious or not humble.
If someone is strong then mary is not wise.
If fred is both calm and creative then susan is either not strong or calm.
If someone is both patient and not quiet then someone is creative and vice versa.
If someone is both wise and not brave then lucy is both not patient and not funny and vice versa.
If someone is humble then paul is both generous and not funny and vice versa.
If someone is both curious and not strong then someone is not creative or wise.
Fred is either not funny or not old.
Alice is both not strong and kind.
Lucy is either wise or not creative.
Someone is old.
Alice is creative or curious.
Paul is not rich.
Susan is both funny and strong. | Susan is strong. | entailment | (![X]:((~rich(X)<~>patient(X))<=>(~curious(X)|rich(X))))&
(![X]:((brave(X)|creative(X))<=>(~brave(X)&~curious(X))))&
(![X]:((strong(X)|happy(X))<=>tall(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~happy(X)&~calm(X))=>(generous(X)|brave(X))))&
(![X]:((~calm(X)|happy(X))<=>(~creative(X)<~>~quiet(X))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((~kind(X)&~quiet(X)))))&
((?[X]:((~tall(X)<~>patient(X))))<=>((~kind(fred)&strong(fred))))&
(![X]:(~rich(X)<=>tall(X)))&
((?[X]:(generous(X)))=>(?[X]:((~curious(X)<~>~humble(X)))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(((calm(fred)&creative(fred)))=>((~strong(susan)<~>calm(susan))))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:(creative(X))))&
((?[X]:((wise(X)&~brave(X))))<=>((~patient(lucy)&~funny(lucy))))&
((?[X]:(humble(X)))<=>((generous(paul)&~funny(paul))))&
((?[X]:((curious(X)&~strong(X))))=>(?[X]:((~creative(X)|wise(X)))))&
((~funny(fred)<~>~old(fred)))&
((~strong(alice)&kind(alice)))&
((wise(lucy)<~>~creative(lucy)))&
(?[X]:(old(X)))&
((creative(alice)|curious(alice)))&
(~rich(paul))&
((funny(susan)&strong(susan))) | strong(susan) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4887879853627794059808567
% SZS output start Proof for 4887879853627794059808567
23. strong(susan) & funny(susan) [input p22]
24. ~strong(susan) [input hypothesis]
149. strong(susan) [cnf transformation 23]
150. ~strong(susan) [cnf transformation 24]
256. 23 <=> strong(susan) [avatar definition]
365. 23 [avatar split clause 149,256]
366. ~23 [avatar split clause 150,256]
367. $false [avatar sat refutation 365,366]
% SZS output end Proof for 4887879853627794059808567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not funny is rich. If john is either strong or not curious then paul is either not calm or not curious and vice versa. If alice is either brave or not creative then alice is both curious and not generous. Everyone who is strong is old or rich and vice versa. Everyone who is not brave or happy is both not kind and funny. Everyone who is both not kind and happy is creative or not kind. Everyone who is either strong or not brave is either not old or not wise and vice versa. If someone is either old or not tall then someone is both generous and patient and vice versa. If susan is funny then someone is not rich or not wise and vice versa. Everyone who is both not patient and rich is happy or humble. Everyone who is both not strong and quiet is either curious or not strong. Everyone who is wise is both patient and quiet and vice versa. If john is quiet then paul is either creative or calm and vice versa. Everyone who is brave is both not creative and rich and vice versa. If someone is tall or rich then john is not brave or humble and vice versa. Everyone who is both quiet and not quiet is either not humble or calm and vice versa. Fred is either happy or not generous. Fred is both rich and kind. Mary is curious or not rich. Someone is not creative or generous. Paul is both not humble and not funny. Mary is both not wise and not quiet. Lucy is old or not rich. Someone is both not funny and calm. | Mary is not generous. | neutral | (![X]:((strong(X)<~>~funny(X))=>rich(X)))&
(((strong(john)<~>~curious(john)))<=>((~calm(paul)<~>~curious(paul))))&
(((brave(alice)<~>~creative(alice)))=>((curious(alice)&~generous(alice))))&
(![X]:(strong(X)<=>(old(X)|rich(X))))&
(![X]:((~brave(X)|happy(X))=>(~kind(X)&funny(X))))&
(![X]:((~kind(X)&happy(X))=>(creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:((generous(X)&patient(X)))))&
((funny(susan))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((~patient(X)&rich(X))=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&quiet(X))=>(curious(X)<~>~strong(X))))&
(![X]:(wise(X)<=>(patient(X)&quiet(X))))&
((quiet(john))<=>((creative(paul)<~>calm(paul))))&
(![X]:(brave(X)<=>(~creative(X)&rich(X))))&
((?[X]:((tall(X)|rich(X))))<=>((~brave(john)|humble(john))))&
(![X]:((quiet(X)&~quiet(X))<=>(~humble(X)<~>calm(X))))&
((happy(fred)<~>~generous(fred)))&
((rich(fred)&kind(fred)))&
((curious(mary)|~rich(mary)))&
(?[X]:((~creative(X)|generous(X))))&
((~humble(paul)&~funny(paul)))&
((~wise(mary)&~quiet(mary)))&
((old(lucy)|~rich(lucy)))&
(?[X]:((~funny(X)&calm(X)))) | ~generous(mary) | [] | null | 0 |
Everyone who is old is not funny or funny.
If john is old or not generous then mary is both old and brave and vice versa.
Everyone who is strong or not strong is tall and vice versa.
If someone is both not curious and wise then someone is not brave and vice versa.
Everyone who is humble is not tall or not kind and vice versa.
Everyone who is strong or not patient is not strong and vice versa.
If paul is not funny or not quiet then fred is patient or not humble.
If someone is either patient or humble then lucy is not tall or not curious and vice versa.
Everyone who is not calm is wise or not creative.
If someone is not quiet then mary is not generous and vice versa.
If lucy is brave then someone is either not creative or quiet and vice versa.
If lucy is either happy or not wise then someone is both wise and not generous.
Everyone who is both funny and not curious is both not old and calm.
Everyone who is either quiet or not brave is not old.
Everyone who is happy or old is both not rich and old.
If someone is either not generous or not wise then paul is either kind or not happy.
Someone is either not rich or not happy.
Alice is either not tall or not wise.
Someone is either wise or creative.
Fred is both not brave and wise.
John is both not happy and not rich.
Someone is both not calm and not strong.
Someone is not creative or not kind.
Mary is not rich or not humble. | Mary is not patient. | entailment | (![X]:(old(X)=>(~funny(X)|funny(X))))&
(((old(john)|~generous(john)))<=>((old(mary)&brave(mary))))&
(![X]:((strong(X)|~strong(X))<=>tall(X)))&
((?[X]:((~curious(X)&wise(X))))<=>(?[X]:(~brave(X))))&
(![X]:(humble(X)<=>(~tall(X)|~kind(X))))&
(![X]:((strong(X)|~patient(X))<=>~strong(X)))&
(((~funny(paul)|~quiet(paul)))=>((patient(fred)|~humble(fred))))&
((?[X]:((patient(X)<~>humble(X))))<=>((~tall(lucy)|~curious(lucy))))&
(![X]:(~calm(X)=>(wise(X)|~creative(X))))&
((?[X]:(~quiet(X)))<=>(~generous(mary)))&
((brave(lucy))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((happy(lucy)<~>~wise(lucy)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:((funny(X)&~curious(X))=>(~old(X)&calm(X))))&
(![X]:((quiet(X)<~>~brave(X))=>~old(X)))&
(![X]:((happy(X)|old(X))=>(~rich(X)&old(X))))&
((?[X]:((~generous(X)<~>~wise(X))))=>((kind(paul)<~>~happy(paul))))&
(?[X]:((~rich(X)<~>~happy(X))))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((wise(X)<~>creative(X))))&
((~brave(fred)&wise(fred)))&
((~happy(john)&~rich(john)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((~creative(X)|~kind(X))))&
((~rich(mary)|~humble(mary))) | ~patient(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4031827854943730405294809
% SZS output start Proof for 4031827854943730405294809
6. ! [X0] : ((~patient(X0) | strong(X0)) <=> ~strong(X0)) [input p5]
25. patient(mary) [input hypothesis]
50. ! [X0] : (((~patient(X0) | strong(X0)) | strong(X0)) & (~strong(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 6]
51. ! [X0] : ((~patient(X0) | strong(X0) | strong(X0)) & (~strong(X0) | (patient(X0) & ~strong(X0)))) [flattening 50]
96. ~strong(X0) | ~strong(X0) [cnf transformation 51]
98. ~patient(X0) | strong(X0) | strong(X0) [cnf transformation 51]
144. patient(mary) [cnf transformation 25]
145. ~strong(X0) [duplicate literal removal 96]
146. ~patient(X0) | strong(X0) [duplicate literal removal 98]
351. strong(mary) [resolution 146,144]
353. $false [subsumption resolution 351,145]
% SZS output end Proof for 4031827854943730405294809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both curious and not old. If someone is not happy then paul is quiet or humble. If paul is generous then someone is either rich or not humble and vice versa. If john is not humble or not old then someone is old or generous. Everyone who is both not patient and not calm is calm or not creative. If someone is either strong or funny then someone is happy or not old and vice versa. Everyone who is not creative is both calm and not rich. Everyone who is kind or not funny is either creative or not quiet. If someone is creative or kind then alice is either not humble or old. Everyone who is not humble is tall. If someone is either humble or not creative then someone is both not rich and funny and vice versa. If fred is both old and happy then someone is either not funny or not strong and vice versa. Everyone who is not funny is not generous and vice versa. If fred is either not wise or patient then lucy is either not kind or old and vice versa. If fred is humble then someone is not kind or not rich. Everyone who is both calm and not tall is not humble or generous and vice versa. Mary is both rich and quiet. Alice is either humble or rich. Paul is creative or quiet. Someone is calm or generous. Someone is either not patient or tall. Mary is either quiet or not happy. | Fred is not wise. | neutral | (![X]:(~old(X)=>(curious(X)&~old(X))))&
((?[X]:(~happy(X)))=>((quiet(paul)|humble(paul))))&
((generous(paul))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~humble(john)|~old(john)))=>(?[X]:((old(X)|generous(X)))))&
(![X]:((~patient(X)&~calm(X))=>(calm(X)|~creative(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((happy(X)|~old(X)))))&
(![X]:(~creative(X)=>(calm(X)&~rich(X))))&
(![X]:((kind(X)|~funny(X))=>(creative(X)<~>~quiet(X))))&
((?[X]:((creative(X)|kind(X))))=>((~humble(alice)<~>old(alice))))&
(![X]:(~humble(X)=>tall(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((~rich(X)&funny(X)))))&
(((old(fred)&happy(fred)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~funny(X)<=>~generous(X)))&
(((~wise(fred)<~>patient(fred)))<=>((~kind(lucy)<~>old(lucy))))&
((humble(fred))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:((calm(X)&~tall(X))<=>(~humble(X)|generous(X))))&
((rich(mary)&quiet(mary)))&
((humble(alice)<~>rich(alice)))&
((creative(paul)|quiet(paul)))&
(?[X]:((calm(X)|generous(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((quiet(mary)<~>~happy(mary))) | ~wise(fred) | [] | null | 0 |
Everyone who is generous or humble is either not strong or not old.
If someone is funny then susan is both not happy and not strong.
Everyone who is quiet or not humble is not quiet.
If alice is not brave or not patient then someone is not curious and vice versa.
If someone is not kind then someone is quiet and vice versa.
If paul is both not funny and not wise then mary is both not old and kind and vice versa.
If someone is not curious or not old then fred is either not happy or funny.
If john is both happy and not quiet then someone is either not tall or calm and vice versa.
Everyone who is both humble and quiet is either tall or not quiet.
If lucy is tall then alice is wise or creative and vice versa.
If susan is both patient and strong then someone is either not curious or old and vice versa.
If someone is both not quiet and funny then someone is not humble or humble.
Everyone who is both not happy and not patient is calm.
Everyone who is both happy and not happy is either not wise or not quiet.
Everyone who is both not tall and strong is either creative or funny and vice versa.
If mary is wise then someone is not generous.
Someone is strong or not strong.
Someone is brave.
John is not brave or not calm.
Someone is either rich or humble.
John is not quiet or quiet. | Mary is wise. | neutral | (![X]:((generous(X)|humble(X))=>(~strong(X)<~>~old(X))))&
((?[X]:(funny(X)))=>((~happy(susan)&~strong(susan))))&
(![X]:((quiet(X)|~humble(X))=>~quiet(X)))&
(((~brave(alice)|~patient(alice)))<=>(?[X]:(~curious(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(quiet(X))))&
(((~funny(paul)&~wise(paul)))<=>((~old(mary)&kind(mary))))&
((?[X]:((~curious(X)|~old(X))))=>((~happy(fred)<~>funny(fred))))&
(((happy(john)&~quiet(john)))<=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:((humble(X)&quiet(X))=>(tall(X)<~>~quiet(X))))&
((tall(lucy))<=>((wise(alice)|creative(alice))))&
(((patient(susan)&strong(susan)))<=>(?[X]:((~curious(X)<~>old(X)))))&
((?[X]:((~quiet(X)&funny(X))))=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:((~happy(X)&~patient(X))=>calm(X)))&
(![X]:((happy(X)&~happy(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~tall(X)&strong(X))<=>(creative(X)<~>funny(X))))&
((wise(mary))=>(?[X]:(~generous(X))))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(brave(X)))&
((~brave(john)|~calm(john)))&
(?[X]:((rich(X)<~>humble(X))))&
((~quiet(john)|quiet(john))) | wise(mary) | [] | null | 0 |
Everyone who is either generous or not generous is both strong and curious and vice versa. If someone is both brave and not quiet then fred is both not generous and not humble. Everyone who is either not kind or not wise is both not creative and calm. Everyone who is both not calm and not quiet is both not happy and not rich and vice versa. Everyone who is not happy is either not funny or not humble and vice versa. Everyone who is either not tall or not generous is tall and vice versa. If someone is either not creative or not rich then someone is either not humble or generous and vice versa. Everyone who is wise or not old is curious or patient. If someone is both not brave and happy then someone is both funny and patient and vice versa. Everyone who is humble or kind is rich or creative and vice versa. Everyone who is both calm and quiet is both old and not calm. If alice is both not wise and humble then lucy is not tall or happy. Everyone who is either happy or not quiet is strong and vice versa. If someone is patient or not old then alice is humble and vice versa. Everyone who is not quiet or not wise is both generous and calm. Everyone who is either not curious or not patient is either rich or old. Mary is funny. Someone is not brave or creative. Susan is funny or happy. Mary is funny or not humble. Susan is either not creative or not tall. | Susan is not wise. | contradiction | (![X]:((generous(X)<~>~generous(X))<=>(strong(X)&curious(X))))&
((?[X]:((brave(X)&~quiet(X))))=>((~generous(fred)&~humble(fred))))&
(![X]:((~kind(X)<~>~wise(X))=>(~creative(X)&calm(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~happy(X)&~rich(X))))&
(![X]:(~happy(X)<=>(~funny(X)<~>~humble(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>tall(X)))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(![X]:((wise(X)|~old(X))=>(curious(X)|patient(X))))&
((?[X]:((~brave(X)&happy(X))))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:((humble(X)|kind(X))<=>(rich(X)|creative(X))))&
(![X]:((calm(X)&quiet(X))=>(old(X)&~calm(X))))&
(((~wise(alice)&humble(alice)))=>((~tall(lucy)|happy(lucy))))&
(![X]:((happy(X)<~>~quiet(X))<=>strong(X)))&
((?[X]:((patient(X)|~old(X))))<=>(humble(alice)))&
(![X]:((~quiet(X)|~wise(X))=>(generous(X)&calm(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(rich(X)<~>old(X))))&
(funny(mary))&
(?[X]:((~brave(X)|creative(X))))&
((funny(susan)|happy(susan)))&
((funny(mary)|~humble(mary)))&
((~creative(susan)<~>~tall(susan))) | ~wise(susan) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 148957370872000859678758
% SZS output start Proof for 148957370872000859678758
6. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> tall(X0)) [input p5]
15. ! [X0] : ((~wise(X0) | ~quiet(X0)) => (calm(X0) & generous(X0))) [input p14]
22. ~wise(susan) [input hypothesis]
33. ! [X0] : ((calm(X0) & generous(X0)) | (wise(X0) & quiet(X0))) [ennf transformation 15]
41. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 6]
83. tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 41]
85. ~generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
116. generous(X0) | wise(X0) [cnf transformation 33]
129. ~wise(susan) [cnf transformation 22]
131. tall(X0) | ~generous(X0) [duplicate literal removal 83]
132. ~generous(X0) | ~tall(X0) [duplicate literal removal 85]
152. ~generous(X0) [subsumption resolution 131,132]
244. wise(X0) [subsumption resolution 116,152]
276. $false [subsumption resolution 129,244]
% SZS output end Proof for 148957370872000859678758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or creative is not old and vice versa.
Everyone who is not creative is brave.
Everyone who is not humble or not creative is both not kind and humble and vice versa.
Everyone who is either not tall or happy is both happy and rich and vice versa.
Everyone who is both not happy and generous is either not strong or not calm and vice versa.
If mary is either generous or not old then mary is both humble and not quiet and vice versa.
If john is not creative then lucy is brave or not rich and vice versa.
If someone is not brave or not humble then paul is rich or not old and vice versa.
Everyone who is either not humble or wise is not rich or tall and vice versa.
Everyone who is creative is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Someone is humble or not curious.
Someone is not funny.
Someone is not humble or tall.
Someone is either quiet or not patient. | Susan is kind. | entailment | (![X]:((humble(X)|creative(X))<=>~old(X)))&
(![X]:(~creative(X)=>brave(X)))&
(![X]:((~humble(X)|~creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&generous(X))<=>(~strong(X)<~>~calm(X))))&
(((generous(mary)<~>~old(mary)))<=>((humble(mary)&~quiet(mary))))&
((~creative(john))<=>((brave(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((~humble(X)<~>wise(X))<=>(~rich(X)|tall(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | kind(susan) | [
"p2",
"p4",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1107022552469647984154316
% SZS output start Proof for 1107022552469647984154316
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (humble(X0) & ~kind(X0))) [input p2]
5. ! [X0] : ((generous(X0) & ~happy(X0)) <=> (~strong(X0) <~> ~calm(X0))) [input p4]
11. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (~wise(X0) | strong(X0))) [input p10]
14. ! [X0] : ((~patient(X0) <~> patient(X0)) => (strong(X0) | creative(X0))) [input p13]
16. ! [X0] : ((~happy(X0) | generous(X0)) => ~humble(X0)) [input p15]
21. ~kind(susan) [input hypothesis]
24. ! [X0] : ((strong(X0) | creative(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 14]
25. ! [X0] : (strong(X0) | creative(X0) | (~patient(X0) <=> patient(X0))) [flattening 24]
28. ! [X0] : (~humble(X0) | (happy(X0) & ~generous(X0))) [ennf transformation 16]
31. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
32. ! [X0] : ((~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [flattening 31]
35. ! [X0] : (((generous(X0) & ~happy(X0)) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | (~generous(X0) | happy(X0)))) [nnf transformation 5]
36. ! [X0] : (((generous(X0) & ~happy(X0)) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ~generous(X0) | happy(X0))) [flattening 35]
49. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & ((~wise(X0) | strong(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 11]
50. ! [X0] : (((~calm(X0) & quiet(X0)) | (wise(X0) & ~strong(X0))) & (~wise(X0) | strong(X0) | calm(X0) | ~quiet(X0))) [flattening 49]
55. ! [X0] : (strong(X0) | creative(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 25]
73. humble(X0) | humble(X0) [cnf transformation 32]
75. ~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0) [cnf transformation 32]
85. ~strong(X0) | ~happy(X0) | calm(X0) [cnf transformation 36]
114. ~calm(X0) | ~strong(X0) [cnf transformation 50]
124. strong(X0) | creative(X0) | patient(X0) | patient(X0) [cnf transformation 55]
125. strong(X0) | creative(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 55]
129. ~humble(X0) | happy(X0) [cnf transformation 28]
135. ~kind(susan) [cnf transformation 21]
136. strong(X0) | creative(X0) | patient(X0) [duplicate literal removal 124]
137. ~patient(X0) | creative(X0) | strong(X0) [duplicate literal removal 125]
140. humble(X0) [duplicate literal removal 73]
141. ~creative(X0) | ~humble(X0) | kind(X0) [duplicate literal removal 75]
212. strong(X0) | creative(X0) [subsumption resolution 136,137]
231. happy(X0) [subsumption resolution 129,140]
258. ~happy(X0) | calm(X0) | creative(X0) [resolution 85,212]
259. calm(X0) | creative(X0) [subsumption resolution 258,231]
266. creative(X3) | ~strong(X3) [resolution 259,114]
267. creative(X3) [subsumption resolution 266,212]
310. ~humble(X0) | kind(X0) [resolution 141,267]
316. kind(X0) [subsumption resolution 310,140]
377. $false [resolution 316,135]
% SZS output end Proof for 1107022552469647984154316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not tall then someone is either not strong or rich.
Everyone who is strong is both brave and not rich.
Everyone who is not rich or strong is not humble and vice versa.
Everyone who is patient is both not kind and generous.
Everyone who is both strong and not calm is either not wise or not humble.
Everyone who is either not brave or not wise is both not patient and not humble.
Everyone who is happy or quiet is not rich or not wise.
Everyone who is not patient or generous is both not quiet and curious.
If susan is either tall or strong then fred is either not rich or not kind.
Everyone who is not calm or not patient is generous or curious and vice versa.
If alice is either creative or generous then someone is not old.
Everyone who is strong or not kind is both not happy and not wise and vice versa.
Everyone who is not calm or not wise is both tall and not curious.
Everyone who is quiet is not generous or patient.
If someone is either humble or tall then someone is old.
Someone is curious.
Someone is patient or tall.
Fred is either strong or not brave.
Lucy is not happy. | Alice is calm. | entailment | ((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:(strong(X)=>(brave(X)&~rich(X))))&
(![X]:((~rich(X)|strong(X))<=>~humble(X)))&
(![X]:(patient(X)=>(~kind(X)&generous(X))))&
(![X]:((strong(X)&~calm(X))=>(~wise(X)<~>~humble(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~patient(X)&~humble(X))))&
(![X]:((happy(X)|quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)&curious(X))))&
(((tall(susan)<~>strong(susan)))=>((~rich(fred)<~>~kind(fred))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)|curious(X))))&
(((creative(alice)<~>generous(alice)))=>(?[X]:(~old(X))))&
(![X]:((strong(X)|~kind(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~calm(X)|~wise(X))=>(tall(X)&~curious(X))))&
(![X]:(quiet(X)=>(~generous(X)|patient(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(old(X))))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)|tall(X))))&
((strong(fred)<~>~brave(fred)))&
(~happy(lucy)) | calm(alice) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7566133256655031330143814
% SZS output start Proof for 7566133256655031330143814
8. ! [X0] : ((generous(X0) | ~patient(X0)) => (curious(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (curious(X0) | generous(X0))) [input p9]
13. ! [X0] : ((~wise(X0) | ~calm(X0)) => (~curious(X0) & tall(X0))) [input p12]
20. ~calm(alice) [input hypothesis]
23. ! [X0] : ((generous(X0) | ~patient(X0)) => curious(X0)) [pure predicate removal 8]
34. ! [X0] : (curious(X0) | (~generous(X0) & patient(X0))) [ennf transformation 23]
37. ! [X0] : ((~curious(X0) & tall(X0)) | (wise(X0) & calm(X0))) [ennf transformation 13]
48. ! [X0] : (((~patient(X0) | ~calm(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 10]
49. ! [X0] : ((~patient(X0) | ~calm(X0) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | (patient(X0) & calm(X0)))) [flattening 48]
81. curious(X0) | ~generous(X0) [cnf transformation 34]
86. curious(X0) | generous(X0) | calm(X0) [cnf transformation 49]
99. ~curious(X0) | calm(X0) [cnf transformation 37]
108. ~calm(alice) [cnf transformation 20]
145. curious(X0) | calm(X0) [subsumption resolution 86,81]
160. calm(X0) [subsumption resolution 99,145]
191. $false [subsumption resolution 108,160]
% SZS output end Proof for 7566133256655031330143814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not curious then john is both happy and not curious and vice versa. If someone is not curious or rich then someone is rich or wise. Everyone who is rich or creative is both happy and not strong and vice versa. If fred is both funny and not tall then someone is either brave or kind and vice versa. Everyone who is both calm and not happy is not happy and vice versa. If susan is either not old or old then alice is not funny or strong and vice versa. If someone is both tall and calm then paul is either humble or curious. If paul is rich or not tall then someone is rich. Everyone who is generous or wise is both not quiet and not wise and vice versa. Everyone who is not generous is either strong or not funny. If fred is not creative then someone is either old or not brave. Everyone who is not rich or not patient is not funny or calm. If someone is both tall and brave then susan is either not brave or patient and vice versa. If john is either humble or wise then someone is rich or kind and vice versa. Everyone who is either calm or not quiet is not patient and vice versa. Everyone who is both not curious and calm is curious or rich and vice versa. Someone is not humble. Lucy is both not quiet and rich. Susan is not funny. Susan is either not patient or calm. | Susan is not happy. | contradiction | ((?[X]:((~old(X)<~>~curious(X))))<=>((happy(john)&~curious(john))))&
((?[X]:((~curious(X)|rich(X))))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((rich(X)|creative(X))<=>(happy(X)&~strong(X))))&
(((funny(fred)&~tall(fred)))<=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((calm(X)&~happy(X))<=>~happy(X)))&
(((~old(susan)<~>old(susan)))<=>((~funny(alice)|strong(alice))))&
((?[X]:((tall(X)&calm(X))))=>((humble(paul)<~>curious(paul))))&
(((rich(paul)|~tall(paul)))=>(?[X]:(rich(X))))&
(![X]:((generous(X)|wise(X))<=>(~quiet(X)&~wise(X))))&
(![X]:(~generous(X)=>(strong(X)<~>~funny(X))))&
((~creative(fred))=>(?[X]:((old(X)<~>~brave(X)))))&
(![X]:((~rich(X)|~patient(X))=>(~funny(X)|calm(X))))&
((?[X]:((tall(X)&brave(X))))<=>((~brave(susan)<~>patient(susan))))&
(((humble(john)<~>wise(john)))<=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>~patient(X)))&
(![X]:((~curious(X)&calm(X))<=>(curious(X)|rich(X))))&
(?[X]:(~humble(X)))&
((~quiet(lucy)&rich(lucy)))&
(~funny(susan))&
((~patient(susan)<~>calm(susan))) | ~happy(susan) | [
"p2",
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7895036240539014055964913
% SZS output start Proof for 7895036240539014055964913
3. ! [X0] : ((creative(X0) | rich(X0)) <=> (~strong(X0) & happy(X0))) [input p2]
5. ! [X0] : ((~happy(X0) & calm(X0)) <=> ~happy(X0)) [input p4]
16. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (rich(X0) | curious(X0))) [input p15]
21. ~happy(susan) [input hypothesis]
38. ! [X0] : (((creative(X0) | rich(X0)) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | (~creative(X0) & ~rich(X0)))) [nnf transformation 3]
39. ! [X0] : ((creative(X0) | rich(X0) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | (~creative(X0) & ~rich(X0)))) [flattening 38]
45. ! [X0] : (((~happy(X0) & calm(X0)) | happy(X0)) & (~happy(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 5]
46. ! [X0] : (((~happy(X0) & calm(X0)) | happy(X0)) & (~happy(X0) | happy(X0) | ~calm(X0))) [flattening 45]
67. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 16]
68. ! [X0] : (((calm(X0) & ~curious(X0)) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~calm(X0) | curious(X0))) [flattening 67]
80. ~rich(X0) | happy(X0) [cnf transformation 39]
92. calm(X0) | happy(X0) [cnf transformation 46]
131. rich(X0) | curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 68]
132. ~curious(X0) | ~curious(X0) [cnf transformation 68]
142. ~happy(susan) [cnf transformation 21]
143. rich(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 131]
144. ~curious(X0) [duplicate literal removal 132]
322. ~calm(X0) | rich(X0) [subsumption resolution 143,144]
351. rich(X0) | happy(X0) [resolution 322,92]
355. happy(X0) [subsumption resolution 351,80]
374. $false [resolution 355,142]
% SZS output end Proof for 7895036240539014055964913
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or funny is not old or old and vice versa.
Everyone who is either not funny or not curious is both not curious and not brave and vice versa.
Everyone who is both brave and not creative is both not creative and creative and vice versa.
If someone is either not old or rich then someone is either not curious or humble.
If alice is wise or not generous then john is either kind or quiet.
Everyone who is patient is not humble and vice versa.
Everyone who is both not quiet and not tall is happy.
Everyone who is either not brave or strong is not old or not strong and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is strong or not kind is both old and calm.
Everyone who is either not strong or generous is both not wise and humble.
Everyone who is either not humble or not quiet is not brave and vice versa.
Everyone who is humble is strong or not quiet.
Everyone who is not happy is not wise and vice versa.
If someone is not curious then someone is either not creative or happy.
John is both not patient and not curious.
Paul is not patient or quiet.
Someone is wise or tall.
Someone is not brave or not rich.
Someone is either not funny or not quiet.
Mary is not humble.
Someone is either not kind or not curious. | John is quiet. | contradiction | (![X]:((old(X)<~>funny(X))<=>(~old(X)|old(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(~curious(X)&~brave(X))))&
(![X]:((brave(X)&~creative(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~old(X)<~>rich(X))))=>(?[X]:((~curious(X)<~>humble(X)))))&
(((wise(alice)|~generous(alice)))=>((kind(john)<~>quiet(john))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((~quiet(X)&~tall(X))=>happy(X)))&
(![X]:((~brave(X)<~>strong(X))<=>(~old(X)|~strong(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((strong(X)|~kind(X))=>(old(X)&calm(X))))&
(![X]:((~strong(X)<~>generous(X))=>(~wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>~brave(X)))&
(![X]:(humble(X)=>(strong(X)|~quiet(X))))&
(![X]:(~happy(X)<=>~wise(X)))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)<~>happy(X)))))&
((~patient(john)&~curious(john)))&
((~patient(paul)|quiet(paul)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~funny(X)<~>~quiet(X))))&
(~humble(mary))&
(?[X]:((~kind(X)<~>~curious(X)))) | quiet(john) | [
"p5",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8688818516622621725734119
% SZS output start Proof for 8688818516622621725734119
6. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p5]
8. ! [X0] : ((~brave(X0) <~> strong(X0)) <=> (~strong(X0) | ~old(X0))) [input p7]
10. ! [X0] : ((~kind(X0) | strong(X0)) => (calm(X0) & old(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> ~quiet(X0)) <=> ~brave(X0)) [input p11]
16. ~curious(john) & ~patient(john) [input p15]
23. quiet(john) [input hypothesis]
26. ! [X0] : (~humble(X0) => patient(X0)) [unused predicate definition removal 6]
27. ! [X0] : ((~kind(X0) | strong(X0)) => old(X0)) [pure predicate removal 10]
32. ! [X0] : (patient(X0) | humble(X0)) [ennf transformation 26]
33. ! [X0] : (old(X0) | (kind(X0) & ~strong(X0))) [ennf transformation 27]
49. ! [X0] : ((((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (strong(X0) & old(X0))) & ((~strong(X0) | ~old(X0)) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))))) [nnf transformation 8]
50. ! [X0] : ((((~strong(X0) | brave(X0)) & (strong(X0) | ~brave(X0))) | (strong(X0) & old(X0))) & (~strong(X0) | ~old(X0) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))))) [flattening 49]
53. ! [X0] : ((((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | brave(X0)) & (~brave(X0) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))))) [nnf transformation 12]
91. patient(X0) | humble(X0) [cnf transformation 32]
93. ~strong(X0) | ~old(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 50]
95. strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 50]
100. ~strong(X0) | old(X0) [cnf transformation 33]
108. ~quiet(X0) | ~humble(X0) | brave(X0) [cnf transformation 53]
115. ~patient(john) [cnf transformation 16]
124. quiet(john) [cnf transformation 23]
125. ~strong(X0) | ~old(X0) | ~brave(X0) [duplicate literal removal 93]
126. ~brave(X0) | strong(X0) [duplicate literal removal 95]
162. 7 <=> quiet(john) [avatar definition]
163. quiet(john) <- (7) [avatar component clause 162]
173. ~brave(X0) | ~old(X0) [subsumption resolution 125,126]
225. 7 [avatar split clause 124,162]
226. humble(john) [resolution 91,115]
251. ~humble(john) | brave(john) <- (7) [resolution 108,163]
252. brave(john) <- (7) [subsumption resolution 251,226]
255. ~old(john) <- (7) [resolution 252,173]
257. strong(john) <- (7) [resolution 252,126]
315. old(john) <- (7) [resolution 257,100]
325. $false <- (7) [subsumption resolution 315,255]
326. ~7 [avatar contradiction clause 325]
327. $false [avatar sat refutation 225,326]
% SZS output end Proof for 8688818516622621725734119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and wise is not wise or rich and vice versa.
Everyone who is either not quiet or not patient is not calm or not quiet and vice versa.
Everyone who is either not curious or not old is either generous or not happy and vice versa.
Everyone who is either curious or brave is creative or brave and vice versa.
Everyone who is not kind or old is not brave or not kind.
Everyone who is both humble and strong is creative or not wise and vice versa.
Everyone who is not funny or not wise is both not creative and old.
Everyone who is either not tall or quiet is either generous or kind and vice versa.
Everyone who is both not rich and happy is curious or not quiet.
If someone is rich or not calm then susan is not old or not tall and vice versa.
Everyone who is either not humble or tall is both old and not quiet and vice versa.
If alice is both not patient and not generous then mary is curious or not patient and vice versa.
If paul is not humble then john is not happy.
Everyone who is both rich and humble is not tall and vice versa.
If john is not humble then paul is rich and vice versa.
If someone is not brave then someone is both not calm and not patient.
Someone is both not kind and not brave.
Paul is either not calm or not brave.
Fred is either creative or not curious.
Someone is both old and not strong.
Someone is either tall or not wise.
Paul is happy or not curious.
Lucy is both not patient and not happy. | John is not creative. | neutral | (![X]:((~curious(X)&wise(X))<=>(~wise(X)|rich(X))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(~calm(X)|~quiet(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(generous(X)<~>~happy(X))))&
(![X]:((curious(X)<~>brave(X))<=>(creative(X)|brave(X))))&
(![X]:((~kind(X)|old(X))=>(~brave(X)|~kind(X))))&
(![X]:((humble(X)&strong(X))<=>(creative(X)|~wise(X))))&
(![X]:((~funny(X)|~wise(X))=>(~creative(X)&old(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(generous(X)<~>kind(X))))&
(![X]:((~rich(X)&happy(X))=>(curious(X)|~quiet(X))))&
((?[X]:((rich(X)|~calm(X))))<=>((~old(susan)|~tall(susan))))&
(![X]:((~humble(X)<~>tall(X))<=>(old(X)&~quiet(X))))&
(((~patient(alice)&~generous(alice)))<=>((curious(mary)|~patient(mary))))&
((~humble(paul))=>(~happy(john)))&
(![X]:((rich(X)&humble(X))<=>~tall(X)))&
((~humble(john))<=>(rich(paul)))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)&~patient(X)))))&
(?[X]:((~kind(X)&~brave(X))))&
((~calm(paul)<~>~brave(paul)))&
((creative(fred)<~>~curious(fred)))&
(?[X]:((old(X)&~strong(X))))&
(?[X]:((tall(X)<~>~wise(X))))&
((happy(paul)|~curious(paul)))&
((~patient(lucy)&~happy(lucy))) | ~creative(john) | [] | null | 0 |
If mary is brave then someone is not wise or humble and vice versa.
If alice is both patient and not curious then fred is not generous.
If someone is either calm or brave then fred is both not calm and tall.
If someone is both happy and not creative then fred is both not strong and not funny.
Everyone who is not rich or quiet is not brave and vice versa.
Everyone who is not kind is not curious and vice versa.
If susan is either not old or strong then john is creative or not humble.
Everyone who is not rich or not calm is both strong and not brave.
If john is both funny and old then susan is not generous.
Everyone who is old is both strong and patient and vice versa.
If someone is either wise or rich then someone is not brave and vice versa.
Everyone who is not funny or quiet is both not happy and generous and vice versa.
If john is either not quiet or happy then someone is either rich or not rich.
If paul is either not kind or curious then paul is both not rich and not calm.
Everyone who is brave or not curious is not curious and vice versa.
Everyone who is not quiet or happy is tall or old.
Someone is both not creative and generous.
Mary is either creative or wise.
Mary is both rich and not tall.
Fred is both kind and not creative.
Someone is rich.
Alice is either tall or not humble.
Someone is quiet or not tall.
Mary is either not wise or calm. | Mary is wise. | entailment | ((brave(mary))<=>(?[X]:((~wise(X)|humble(X)))))&
(((patient(alice)&~curious(alice)))=>(~generous(fred)))&
((?[X]:((calm(X)<~>brave(X))))=>((~calm(fred)&tall(fred))))&
((?[X]:((happy(X)&~creative(X))))=>((~strong(fred)&~funny(fred))))&
(![X]:((~rich(X)|quiet(X))<=>~brave(X)))&
(![X]:(~kind(X)<=>~curious(X)))&
(((~old(susan)<~>strong(susan)))=>((creative(john)|~humble(john))))&
(![X]:((~rich(X)|~calm(X))=>(strong(X)&~brave(X))))&
(((funny(john)&old(john)))=>(~generous(susan)))&
(![X]:(old(X)<=>(strong(X)&patient(X))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)|quiet(X))<=>(~happy(X)&generous(X))))&
(((~quiet(john)<~>happy(john)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(((~kind(paul)<~>curious(paul)))=>((~rich(paul)&~calm(paul))))&
(![X]:((brave(X)|~curious(X))<=>~curious(X)))&
(![X]:((~quiet(X)|happy(X))=>(tall(X)|old(X))))&
(?[X]:((~creative(X)&generous(X))))&
((creative(mary)<~>wise(mary)))&
((rich(mary)&~tall(mary)))&
((kind(fred)&~creative(fred)))&
(?[X]:(rich(X)))&
((tall(alice)<~>~humble(alice)))&
(?[X]:((quiet(X)|~tall(X))))&
((~wise(mary)<~>calm(mary))) | wise(mary) | [
"p0",
"p7",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4575911148043963707917148
% SZS output start Proof for 4575911148043963707917148
1. brave(mary) <=> ? [X0] : (humble(X0) | ~wise(X0)) [input p0]
8. ! [X0] : ((~calm(X0) | ~rich(X0)) => (~brave(X0) & strong(X0))) [input p7]
24. ~wise(mary) <~> calm(mary) [input p23]
25. ~wise(mary) [input hypothesis]
33. ! [X0] : ((~brave(X0) & strong(X0)) | (calm(X0) & rich(X0))) [ennf transformation 8]
40. (brave(mary) | ! [X0] : (~humble(X0) & wise(X0))) & (? [X0] : (humble(X0) | ~wise(X0)) | ~brave(mary)) [nnf transformation 1]
41. (brave(mary) | ! [X0] : (~humble(X0) & wise(X0))) & (? [X1] : (humble(X1) | ~wise(X1)) | ~brave(mary)) [rectify 40]
42. ? [X1] : (humble(X1) | ~wise(X1)) => (humble(sK0) | ~wise(sK0)) [choice axiom]
43. (brave(mary) | ! [X0] : (~humble(X0) & wise(X0))) & ((humble(sK0) | ~wise(sK0)) | ~brave(mary)) [skolemisation 41,42]
72. (~calm(mary) | wise(mary)) & (calm(mary) | ~wise(mary)) [nnf transformation 24]
74. brave(mary) | wise(X0) [cnf transformation 43]
93. ~brave(X0) | calm(X0) [cnf transformation 33]
133. ~calm(mary) | wise(mary) [cnf transformation 72]
134. ~wise(mary) [cnf transformation 25]
139. 2 <=> brave(mary) [avatar definition]
141. brave(mary) <- (2) [avatar component clause 139]
144. 3 <=> ! [X0] : wise(X0) [avatar definition]
145. wise(X0) <- (3) [avatar component clause 144]
146. 3 | 2 [avatar split clause 74,139,144]
170. 9 <=> ! [X0] : (calm(X0) | ~brave(X0)) [avatar definition]
171. ~brave(X0) | calm(X0) <- (9) [avatar component clause 170]
218. 9 [avatar split clause 93,170]
282. 33 <=> wise(mary) [avatar definition]
284. ~wise(mary) <- (~33) [avatar component clause 282]
307. 38 <=> calm(mary) [avatar definition]
309. ~calm(mary) <- (~38) [avatar component clause 307]
310. 33 | ~38 [avatar split clause 133,307,282]
312. ~33 [avatar split clause 134,282]
330. calm(mary) <- (2, 9) [resolution 171,141]
331. $false <- (2, 9, ~38) [subsumption resolution 330,309]
332. ~2 | ~9 | 38 [avatar contradiction clause 331]
334. $false <- (3, ~33) [resolution 145,284]
335. ~3 | 33 [avatar contradiction clause 334]
337. $false [avatar sat refutation 146,218,310,312,332,335]
% SZS output end Proof for 4575911148043963707917148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either curious or quiet then lucy is either strong or calm and vice versa. Everyone who is either not quiet or old is both quiet and generous and vice versa. Everyone who is both generous and old is generous or humble. Everyone who is not funny is creative or not brave and vice versa. If alice is either curious or not tall then lucy is not wise and vice versa. If fred is not kind or not happy then mary is either kind or not rich and vice versa. Everyone who is brave or tall is both not tall and kind and vice versa. Everyone who is either curious or calm is either not rich or not funny and vice versa. Everyone who is either not tall or not generous is both humble and not old and vice versa. If someone is wise or not tall then someone is both quiet and not kind and vice versa. If someone is either curious or tall then someone is either happy or funny and vice versa. If fred is either not funny or not quiet then fred is not calm or not brave. If someone is strong then fred is not rich or not wise and vice versa. If fred is not old or generous then someone is either generous or calm and vice versa. If susan is calm or happy then someone is both not wise and not quiet. If mary is curious or kind then mary is both not creative and rich and vice versa. Lucy is happy or not brave. Someone is both not tall and brave. Susan is not funny. Someone is either not rich or not tall. Someone is not wise or not old. Someone is not curious. Paul is either tall or not happy. Mary is old. | Paul is not generous. | entailment | (((curious(john)<~>quiet(john)))<=>((strong(lucy)<~>calm(lucy))))&
(![X]:((~quiet(X)<~>old(X))<=>(quiet(X)&generous(X))))&
(![X]:((generous(X)&old(X))=>(generous(X)|humble(X))))&
(![X]:(~funny(X)<=>(creative(X)|~brave(X))))&
(((curious(alice)<~>~tall(alice)))<=>(~wise(lucy)))&
(((~kind(fred)|~happy(fred)))<=>((kind(mary)<~>~rich(mary))))&
(![X]:((brave(X)|tall(X))<=>(~tall(X)&kind(X))))&
(![X]:((curious(X)<~>calm(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(humble(X)&~old(X))))&
((?[X]:((wise(X)|~tall(X))))<=>(?[X]:((quiet(X)&~kind(X)))))&
((?[X]:((curious(X)<~>tall(X))))<=>(?[X]:((happy(X)<~>funny(X)))))&
(((~funny(fred)<~>~quiet(fred)))=>((~calm(fred)|~brave(fred))))&
((?[X]:(strong(X)))<=>((~rich(fred)|~wise(fred))))&
(((~old(fred)|generous(fred)))<=>(?[X]:((generous(X)<~>calm(X)))))&
(((calm(susan)|happy(susan)))=>(?[X]:((~wise(X)&~quiet(X)))))&
(((curious(mary)|kind(mary)))<=>((~creative(mary)&rich(mary))))&
((happy(lucy)|~brave(lucy)))&
(?[X]:((~tall(X)&brave(X))))&
(~funny(susan))&
(?[X]:((~rich(X)<~>~tall(X))))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:(~curious(X)))&
((tall(paul)<~>~happy(paul)))&
(old(mary)) | ~generous(paul) | [
"p1",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5438997555867764216219999
% SZS output start Proof for 5438997555867764216219999
2. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (generous(X0) & quiet(X0))) [input p1]
7. ! [X0] : ((tall(X0) | brave(X0)) <=> (kind(X0) & ~tall(X0))) [input p6]
9. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (~old(X0) & humble(X0))) [input p8]
25. generous(paul) [input hypothesis]
34. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 2]
35. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 34]
41. ! [X0] : (((tall(X0) | brave(X0)) | (~kind(X0) | tall(X0))) & ((kind(X0) & ~tall(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((tall(X0) | brave(X0) | ~kind(X0) | tall(X0)) & ((kind(X0) & ~tall(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 41]
44. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 9]
45. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 44]
89. quiet(X0) | old(X0) | quiet(X0) [cnf transformation 35]
93. old(X0) | ~quiet(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 35]
110. ~tall(X0) | ~tall(X0) [cnf transformation 42]
124. ~old(X0) | ~generous(X0) | tall(X0) [cnf transformation 45]
172. generous(paul) [cnf transformation 25]
173. ~tall(X0) [duplicate literal removal 110]
175. old(X0) | quiet(X0) [duplicate literal removal 89]
176. ~generous(X0) | ~quiet(X0) | old(X0) [duplicate literal removal 93]
240. ~generous(X0) | ~old(X0) [subsumption resolution 124,173]
397. ~old(paul) [resolution 240,172]
398. quiet(paul) [resolution 397,175]
434. ~quiet(paul) | old(paul) [resolution 176,172]
437. old(paul) [subsumption resolution 434,398]
438. $false [subsumption resolution 437,397]
% SZS output end Proof for 5438997555867764216219999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is not tall or not creative then fred is either not humble or humble and vice versa.
Everyone who is both not curious and tall is not strong or kind and vice versa.
Everyone who is not funny or generous is both kind and not curious.
If someone is not patient or not happy then someone is tall or brave and vice versa.
If someone is either old or quiet then alice is brave or generous and vice versa.
Everyone who is funny is not wise or happy.
If fred is both not wise and not brave then someone is not strong.
If paul is either tall or quiet then someone is both generous and not creative and vice versa.
If john is quiet then mary is either not calm or not old and vice versa.
Everyone who is both strong and not curious is not calm.
Everyone who is not kind is not rich or not quiet.
Everyone who is brave or old is funny or not tall and vice versa.
Everyone who is either brave or not curious is not calm or not generous and vice versa.
If lucy is both not patient and patient then someone is either not strong or not quiet and vice versa.
If paul is not humble then someone is both humble and tall.
Everyone who is calm is both not generous and not calm and vice versa.
Someone is both not wise and patient.
Someone is either not creative or kind.
Lucy is not wise or funny.
Someone is both not wise and not strong.
Susan is both kind and not strong.
Mary is both old and not happy. | Mary is not calm. | entailment | (((~tall(susan)|~creative(susan)))<=>((~humble(fred)<~>humble(fred))))&
(![X]:((~curious(X)&tall(X))<=>(~strong(X)|kind(X))))&
(![X]:((~funny(X)|generous(X))=>(kind(X)&~curious(X))))&
((?[X]:((~patient(X)|~happy(X))))<=>(?[X]:((tall(X)|brave(X)))))&
((?[X]:((old(X)<~>quiet(X))))<=>((brave(alice)|generous(alice))))&
(![X]:(funny(X)=>(~wise(X)|happy(X))))&
(((~wise(fred)&~brave(fred)))=>(?[X]:(~strong(X))))&
(((tall(paul)<~>quiet(paul)))<=>(?[X]:((generous(X)&~creative(X)))))&
((quiet(john))<=>((~calm(mary)<~>~old(mary))))&
(![X]:((strong(X)&~curious(X))=>~calm(X)))&
(![X]:(~kind(X)=>(~rich(X)|~quiet(X))))&
(![X]:((brave(X)|old(X))<=>(funny(X)|~tall(X))))&
(![X]:((brave(X)<~>~curious(X))<=>(~calm(X)|~generous(X))))&
(((~patient(lucy)&patient(lucy)))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((~humble(paul))=>(?[X]:((humble(X)&tall(X)))))&
(![X]:(calm(X)<=>(~generous(X)&~calm(X))))&
(?[X]:((~wise(X)&patient(X))))&
(?[X]:((~creative(X)<~>kind(X))))&
((~wise(lucy)|funny(lucy)))&
(?[X]:((~wise(X)&~strong(X))))&
((kind(susan)&~strong(susan)))&
((old(mary)&~happy(mary))) | ~calm(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8917010924029910439813066
% SZS output start Proof for 8917010924029910439813066
16. ! [X0] : (calm(X0) <=> (~calm(X0) & ~generous(X0))) [input p15]
23. calm(mary) [input hypothesis]
66. ! [X0] : ((calm(X0) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ~calm(X0))) [nnf transformation 16]
67. ! [X0] : ((calm(X0) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~calm(X0))) [flattening 66]
132. ~calm(X0) | ~calm(X0) [cnf transformation 67]
145. calm(mary) [cnf transformation 23]
146. ~calm(X0) [duplicate literal removal 132]
328. $false [subsumption resolution 145,146]
% SZS output end Proof for 8917010924029910439813066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not happy is old and vice versa.
Everyone who is not kind or brave is either not strong or not brave.
Everyone who is not calm is both not calm and wise.
Everyone who is kind or not happy is either not calm or brave and vice versa.
Everyone who is calm or wise is both strong and not rich.
Everyone who is funny is tall.
If john is either not quiet or wise then alice is either not generous or funny.
Everyone who is quiet or tall is both not creative and rich.
If john is funny then someone is both funny and not tall and vice versa.
Everyone who is not tall or not generous is either quiet or old and vice versa.
If susan is both not tall and wise then someone is rich or not funny and vice versa.
If someone is not calm then lucy is not creative or not strong.
Everyone who is strong is either not curious or creative.
Everyone who is tall or rich is not old or not brave.
Everyone who is both funny and not strong is both not wise and not rich.
Everyone who is curious is patient and vice versa.
Fred is not kind.
Lucy is not brave or not humble.
Someone is either kind or wise.
Someone is not rich or strong.
Someone is not curious or not happy.
Alice is kind.
Someone is either not happy or humble. | Fred is not rich. | entailment | (![X]:((kind(X)<~>~happy(X))<=>old(X)))&
(![X]:((~kind(X)|brave(X))=>(~strong(X)<~>~brave(X))))&
(![X]:(~calm(X)=>(~calm(X)&wise(X))))&
(![X]:((kind(X)|~happy(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((calm(X)|wise(X))=>(strong(X)&~rich(X))))&
(![X]:(funny(X)=>tall(X)))&
(((~quiet(john)<~>wise(john)))=>((~generous(alice)<~>funny(alice))))&
(![X]:((quiet(X)|tall(X))=>(~creative(X)&rich(X))))&
((funny(john))<=>(?[X]:((funny(X)&~tall(X)))))&
(![X]:((~tall(X)|~generous(X))<=>(quiet(X)<~>old(X))))&
(((~tall(susan)&wise(susan)))<=>(?[X]:((rich(X)|~funny(X)))))&
((?[X]:(~calm(X)))=>((~creative(lucy)|~strong(lucy))))&
(![X]:(strong(X)=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)|rich(X))=>(~old(X)|~brave(X))))&
(![X]:((funny(X)&~strong(X))=>(~wise(X)&~rich(X))))&
(![X]:(curious(X)<=>patient(X)))&
(~kind(fred))&
((~brave(lucy)|~humble(lucy)))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((~curious(X)|~happy(X))))&
(kind(alice))&
(?[X]:((~happy(X)<~>humble(X)))) | ~rich(fred) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7182024333905188052214493
% SZS output start Proof for 7182024333905188052214493
3. ! [X0] : (~calm(X0) => (wise(X0) & ~calm(X0))) [input p2]
5. ! [X0] : ((wise(X0) | calm(X0)) => (~rich(X0) & strong(X0))) [input p4]
24. rich(fred) [input hypothesis]
26. ! [X0] : ((wise(X0) & ~calm(X0)) | calm(X0)) [ennf transformation 3]
27. ! [X0] : ((~rich(X0) & strong(X0)) | (~wise(X0) & ~calm(X0))) [ennf transformation 5]
75. wise(X0) | calm(X0) [cnf transformation 26]
84. ~rich(X0) | ~calm(X0) [cnf transformation 27]
85. ~rich(X0) | ~wise(X0) [cnf transformation 27]
127. rich(fred) [cnf transformation 24]
256. ~calm(fred) [resolution 84,127]
257. ~wise(fred) [resolution 85,127]
260. calm(fred) [resolution 257,75]
261. $false [subsumption resolution 260,256]
% SZS output end Proof for 7182024333905188052214493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is both creative and generous and vice versa.
Everyone who is either funny or tall is both creative and not brave and vice versa.
If someone is not kind then someone is both not wise and not tall.
Everyone who is either generous or rich is either not tall or tall and vice versa.
If lucy is both not curious and strong then fred is quiet and vice versa.
Everyone who is tall is both not patient and not humble.
If someone is not calm then someone is not old or not brave and vice versa.
If lucy is not quiet or calm then someone is not rich or not funny.
If susan is both happy and not kind then someone is not funny and vice versa.
Everyone who is not strong or brave is not kind.
If someone is either not humble or tall then someone is both not rich and wise and vice versa.
If someone is not humble or tall then susan is funny or generous.
Everyone who is both not rich and tall is quiet and vice versa.
If fred is both brave and not brave then someone is both not quiet and generous and vice versa.
Everyone who is both happy and patient is either funny or generous and vice versa.
Everyone who is both quiet and not funny is both tall and quiet and vice versa.
Fred is both wise and not tall.
Someone is wise or not humble.
Someone is both humble and not patient.
Someone is happy.
John is not humble or not creative. | Susan is rich. | entailment | (![X]:((~patient(X)<~>~calm(X))<=>(creative(X)&generous(X))))&
(![X]:((funny(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>tall(X))))&
(((~curious(lucy)&strong(lucy)))<=>(quiet(fred)))&
(![X]:(tall(X)=>(~patient(X)&~humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~quiet(lucy)|calm(lucy)))=>(?[X]:((~rich(X)|~funny(X)))))&
(((happy(susan)&~kind(susan)))<=>(?[X]:(~funny(X))))&
(![X]:((~strong(X)|brave(X))=>~kind(X)))&
((?[X]:((~humble(X)<~>tall(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((~humble(X)|tall(X))))=>((funny(susan)|generous(susan))))&
(![X]:((~rich(X)&tall(X))<=>quiet(X)))&
(((brave(fred)&~brave(fred)))<=>(?[X]:((~quiet(X)&generous(X)))))&
(![X]:((happy(X)&patient(X))<=>(funny(X)<~>generous(X))))&
(![X]:((quiet(X)&~funny(X))<=>(tall(X)&quiet(X))))&
((wise(fred)&~tall(fred)))&
(?[X]:((wise(X)|~humble(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:(happy(X)))&
((~humble(john)|~creative(john))) | rich(susan) | [
"p3",
"p5",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7346644534287886324434531
% SZS output start Proof for 7346644534287886324434531
4. ! [X0] : ((generous(X0) <~> rich(X0)) <=> (~tall(X0) <~> tall(X0))) [input p3]
6. ! [X0] : (tall(X0) => (~humble(X0) & ~patient(X0))) [input p5]
13. ! [X0] : ((tall(X0) & ~rich(X0)) <=> quiet(X0)) [input p12]
14. (~brave(fred) & brave(fred)) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p13]
15. ! [X0] : ((patient(X0) & happy(X0)) <=> (funny(X0) <~> generous(X0))) [input p14]
16. ! [X0] : ((~funny(X0) & quiet(X0)) <=> (quiet(X0) & tall(X0))) [input p15]
22. ~rich(susan) [input hypothesis]
27. ! [X0] : ((~humble(X0) & ~patient(X0)) | ~tall(X0)) [ennf transformation 6]
39. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [nnf transformation 4]
59. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (~tall(X0) | rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((tall(X0) & ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | ~tall(X0) | rich(X0))) [flattening 59]
61. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | (brave(fred) | ~brave(fred))) [nnf transformation 14]
62. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X0] : (generous(X0) & ~quiet(X0)) | brave(fred) | ~brave(fred)) [flattening 61]
63. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & (? [X1] : (generous(X1) & ~quiet(X1)) | brave(fred) | ~brave(fred)) [rectify 62]
64. ? [X1] : (generous(X1) & ~quiet(X1)) => (generous(sK7) & ~quiet(sK7)) [choice axiom]
65. ((~brave(fred) & brave(fred)) | ! [X0] : (~generous(X0) | quiet(X0))) & ((generous(sK7) & ~quiet(sK7)) | brave(fred) | ~brave(fred)) [skolemisation 63,64]
66. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 15]
67. ! [X0] : (((patient(X0) & happy(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | ~patient(X0) | ~happy(X0))) [flattening 66]
68. ! [X0] : (((~funny(X0) & quiet(X0)) | (~quiet(X0) | ~tall(X0))) & ((quiet(X0) & tall(X0)) | (funny(X0) | ~quiet(X0)))) [nnf transformation 16]
69. ! [X0] : (((~funny(X0) & quiet(X0)) | ~quiet(X0) | ~tall(X0)) & ((quiet(X0) & tall(X0)) | funny(X0) | ~quiet(X0))) [flattening 68]
94. rich(X0) | generous(X0) | tall(X0) | tall(X0) [cnf transformation 39]
95. rich(X0) | generous(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 39]
101. ~tall(X0) | ~patient(X0) [cnf transformation 27]
123. ~quiet(X0) | tall(X0) [cnf transformation 60]
126. brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
127. ~brave(fred) | ~generous(X0) | quiet(X0) [cnf transformation 65]
133. ~generous(X0) | funny(X0) | patient(X0) [cnf transformation 67]
137. ~funny(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 69]
145. ~rich(susan) [cnf transformation 22]
146. rich(X0) | generous(X0) | tall(X0) [duplicate literal removal 94]
147. rich(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 95]
164. rich(X0) | generous(X0) [subsumption resolution 146,147]
272. 28 <=> funny(susan) [avatar definition]
273. ~funny(susan) <- (~28) [avatar component clause 272]
276. 29 <=> generous(susan) [avatar definition]
278. generous(susan) <- (29) [avatar component clause 276]
285. 31 <=> ! [X0] : (~generous(X0) | quiet(X0)) [avatar definition]
286. ~generous(X0) | quiet(X0) <- (31) [avatar component clause 285]
288. 32 <=> brave(fred) [avatar definition]
291. 31 | ~32 [avatar split clause 127,288,285]
292. 31 | 32 [avatar split clause 126,288,285]
293. ~quiet(X0) | ~funny(X0) [subsumption resolution 137,123]
315. generous(susan) [resolution 164,145]
318. 29 [avatar split clause 315,276]
328. quiet(susan) <- (29, 31) [resolution 286,278]
331. ~funny(susan) <- (29, 31) [resolution 328,293]
332. tall(susan) <- (29, 31) [resolution 328,123]
336. ~28 | ~29 | ~31 [avatar split clause 331,285,276,272]
341. ~patient(susan) <- (29, 31) [resolution 332,101]
382. funny(susan) | patient(susan) <- (29) [resolution 133,278]
385. patient(susan) <- (~28, 29) [subsumption resolution 382,273]
386. $false <- (~28, 29, 31) [subsumption resolution 385,341]
387. 28 | ~29 | ~31 [avatar contradiction clause 386]
392. $false [avatar sat refutation 291,292,318,336,387]
% SZS output end Proof for 7346644534287886324434531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or old is either kind or tall and vice versa.
Everyone who is both not rich and brave is either patient or creative and vice versa.
If paul is not strong or not generous then susan is not creative.
If alice is either tall or not humble then susan is patient and vice versa.
Everyone who is not creative is quiet.
If fred is not calm or not curious then john is not generous or patient.
Everyone who is not patient or not curious is not kind or not humble.
Everyone who is either not humble or not generous is both not creative and wise and vice versa.
Everyone who is not old or not strong is either creative or old.
Everyone who is not strong or not quiet is not humble and vice versa.
Everyone who is not generous or not happy is not old.
If someone is either not humble or quiet then paul is not generous.
Everyone who is quiet is either strong or not funny.
Everyone who is wise or rich is humble or funny.
If john is calm then someone is either not humble or not strong.
Someone is both quiet and not humble.
Someone is both not kind and curious.
Someone is not calm.
Lucy is both curious and brave.
Someone is funny or calm.
Someone is not generous or not brave.
Someone is both happy and not kind. | Paul is old. | contradiction | (![X]:((funny(X)<~>old(X))<=>(kind(X)<~>tall(X))))&
(![X]:((~rich(X)&brave(X))<=>(patient(X)<~>creative(X))))&
(((~strong(paul)|~generous(paul)))=>(~creative(susan)))&
(((tall(alice)<~>~humble(alice)))<=>(patient(susan)))&
(![X]:(~creative(X)=>quiet(X)))&
(((~calm(fred)|~curious(fred)))=>((~generous(john)|patient(john))))&
(![X]:((~patient(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~creative(X)&wise(X))))&
(![X]:((~old(X)|~strong(X))=>(creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~humble(X)))&
(![X]:((~generous(X)|~happy(X))=>~old(X)))&
((?[X]:((~humble(X)<~>quiet(X))))=>(~generous(paul)))&
(![X]:(quiet(X)=>(strong(X)<~>~funny(X))))&
(![X]:((wise(X)|rich(X))=>(humble(X)|funny(X))))&
((calm(john))=>(?[X]:((~humble(X)<~>~strong(X)))))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((~kind(X)&curious(X))))&
(?[X]:(~calm(X)))&
((curious(lucy)&brave(lucy)))&
(?[X]:((funny(X)|calm(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((happy(X)&~kind(X)))) | old(paul) | [
"p7",
"p9",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6565776624862980950876932
% SZS output start Proof for 6565776624862980950876932
8. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (wise(X0) & ~creative(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> ~humble(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | ~generous(X0)) => ~old(X0)) [input p10]
12. ? [X0] : (~humble(X0) <~> quiet(X0)) => ~generous(paul) [input p11]
13. ! [X0] : (quiet(X0) => (strong(X0) <~> ~funny(X0))) [input p12]
14. ! [X0] : ((rich(X0) | wise(X0)) => (funny(X0) | humble(X0))) [input p13]
23. old(paul) [input hypothesis]
24. ! [X0] : (~generous(X0) => ~old(X0)) [pure predicate removal 11]
37. ! [X0] : (~old(X0) | generous(X0)) [ennf transformation 24]
38. ~generous(paul) | ! [X0] : (~humble(X0) <=> quiet(X0)) [ennf transformation 12]
39. ! [X0] : ((strong(X0) <~> ~funny(X0)) | ~quiet(X0)) [ennf transformation 13]
40. ! [X0] : ((funny(X0) | humble(X0)) | (~rich(X0) & ~wise(X0))) [ennf transformation 14]
41. ! [X0] : (funny(X0) | humble(X0) | (~rich(X0) & ~wise(X0))) [flattening 40]
47. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 8]
48. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [flattening 47]
50. ! [X0] : (((~quiet(X0) | ~strong(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 10]
51. ! [X0] : ((~quiet(X0) | ~strong(X0) | humble(X0)) & (~humble(X0) | (quiet(X0) & strong(X0)))) [flattening 50]
52. ~generous(paul) | ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))) [nnf transformation 38]
53. ! [X0] : (((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ~quiet(X0)) [nnf transformation 39]
94. ~generous(X0) | wise(X0) | humble(X0) [cnf transformation 48]
103. ~humble(X0) | quiet(X0) [cnf transformation 51]
104. ~quiet(X0) | ~strong(X0) | humble(X0) [cnf transformation 51]
105. ~old(X0) | generous(X0) [cnf transformation 37]
106. ~generous(paul) | quiet(X0) | humble(X0) [cnf transformation 52]
107. ~generous(paul) | ~humble(X0) | ~quiet(X0) [cnf transformation 52]
108. ~quiet(X0) | strong(X0) | ~funny(X0) [cnf transformation 53]
110. ~wise(X0) | humble(X0) | funny(X0) [cnf transformation 41]
122. old(paul) [cnf transformation 23]
125. 1 <=> generous(paul) [avatar definition]
127. generous(paul) <- (1) [avatar component clause 125]
167. ~generous(paul) | ~humble(X0) [subsumption resolution 107,103]
169. 10 <=> ! [X0] : ~humble(X0) [avatar definition]
170. ~humble(X0) <- (10) [avatar component clause 169]
171. 10 | ~1 [avatar split clause 167,125,169]
172. ~generous(paul) | quiet(X0) [subsumption resolution 106,103]
174. 11 <=> ! [X0] : quiet(X0) [avatar definition]
175. quiet(X0) <- (11) [avatar component clause 174]
176. 11 | ~1 [avatar split clause 172,125,174]
211. generous(paul) [resolution 105,122]
214. 1 [avatar split clause 211,125]
227. wise(paul) | humble(paul) <- (1) [resolution 94,127]
229. wise(paul) <- (1, 10) [subsumption resolution 227,170]
233. ~strong(X0) | humble(X0) <- (11) [resolution 104,175]
236. ~strong(X0) <- (10, 11) [subsumption resolution 233,170]
238. strong(X0) | ~funny(X0) <- (11) [resolution 108,175]
241. ~funny(X0) <- (10, 11) [subsumption resolution 238,236]
247. humble(paul) | funny(paul) <- (1, 10) [resolution 110,229]
249. funny(paul) <- (1, 10) [subsumption resolution 247,170]
250. $false <- (1, 10, 11) [subsumption resolution 249,241]
251. ~1 | ~10 | ~11 [avatar contradiction clause 250]
255. $false [avatar sat refutation 171,176,214,251]
% SZS output end Proof for 6565776624862980950876932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and kind is curious or old.
If someone is either generous or not strong then susan is either creative or patient.
If paul is both not quiet and funny then fred is not wise and vice versa.
Everyone who is either old or not brave is not kind or not strong.
Everyone who is strong is not humble and vice versa.
Everyone who is wise or calm is either not rich or not humble and vice versa.
Everyone who is either wise or not brave is both curious and patient.
If alice is not rich or not strong then john is both not happy and not tall.
Everyone who is not happy or brave is both humble and strong and vice versa.
Everyone who is not strong is either old or happy.
Everyone who is both not rich and tall is not quiet and vice versa.
If fred is calm or not old then someone is tall and vice versa.
If alice is either not curious or wise then someone is both not creative and quiet.
Everyone who is not kind or not happy is not strong.
Everyone who is wise or curious is either curious or not rich and vice versa.
Someone is curious or patient.
Someone is both humble and not brave.
Someone is patient or not rich.
Alice is either patient or wise.
Mary is either quiet or not tall.
Paul is not patient or not old.
Someone is humble. | Paul is not happy. | contradiction | (![X]:((creative(X)&kind(X))=>(curious(X)|old(X))))&
((?[X]:((generous(X)<~>~strong(X))))=>((creative(susan)<~>patient(susan))))&
(((~quiet(paul)&funny(paul)))<=>(~wise(fred)))&
(![X]:((old(X)<~>~brave(X))=>(~kind(X)|~strong(X))))&
(![X]:(strong(X)<=>~humble(X)))&
(![X]:((wise(X)|calm(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((wise(X)<~>~brave(X))=>(curious(X)&patient(X))))&
(((~rich(alice)|~strong(alice)))=>((~happy(john)&~tall(john))))&
(![X]:((~happy(X)|brave(X))<=>(humble(X)&strong(X))))&
(![X]:(~strong(X)=>(old(X)<~>happy(X))))&
(![X]:((~rich(X)&tall(X))<=>~quiet(X)))&
(((calm(fred)|~old(fred)))<=>(?[X]:(tall(X))))&
(((~curious(alice)<~>wise(alice)))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~kind(X)|~happy(X))=>~strong(X)))&
(![X]:((wise(X)|curious(X))<=>(curious(X)<~>~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:((patient(X)|~rich(X))))&
((patient(alice)<~>wise(alice)))&
((quiet(mary)<~>~tall(mary)))&
((~patient(paul)|~old(paul)))&
(?[X]:(humble(X))) | ~happy(paul) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5162380212595698689148645
% SZS output start Proof for 5162380212595698689148645
9. ! [X0] : ((brave(X0) | ~happy(X0)) <=> (strong(X0) & humble(X0))) [input p8]
14. ! [X0] : ((~happy(X0) | ~kind(X0)) => ~strong(X0)) [input p13]
23. ~happy(paul) [input hypothesis]
33. ! [X0] : (~strong(X0) | (happy(X0) & kind(X0))) [ennf transformation 14]
42. ! [X0] : (((brave(X0) | ~happy(X0)) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | (~brave(X0) & happy(X0)))) [nnf transformation 9]
43. ! [X0] : ((brave(X0) | ~happy(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | (~brave(X0) & happy(X0)))) [flattening 42]
95. strong(X0) | happy(X0) [cnf transformation 43]
111. ~strong(X0) | happy(X0) [cnf transformation 33]
128. ~happy(paul) [cnf transformation 23]
223. happy(X0) [subsumption resolution 111,95]
259. $false [subsumption resolution 128,223]
% SZS output end Proof for 5162380212595698689148645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is both not strong and not wise and vice versa.
Everyone who is both strong and not creative is both not brave and not rich and vice versa.
If someone is both not wise and not kind then mary is not quiet or not wise and vice versa.
Everyone who is not tall is funny and vice versa.
Everyone who is curious or not kind is both tall and not brave.
If lucy is not brave or funny then paul is either not strong or brave.
Everyone who is either wise or not happy is both brave and not funny.
Everyone who is tall is both not tall and old and vice versa.
Everyone who is wise is not calm and vice versa.
Everyone who is not kind is not funny.
Everyone who is calm is not funny.
Everyone who is either brave or patient is not old or patient and vice versa.
If mary is not wise then lucy is both rich and calm.
Everyone who is both not wise and curious is both rich and not kind and vice versa.
Someone is both brave and rich.
Susan is either not rich or humble.
Susan is either old or kind.
Someone is either patient or calm.
Susan is either brave or happy.
Alice is either not tall or strong.
Someone is both not brave and strong.
Someone is patient or not rich. | Susan is not wise. | contradiction | ((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((strong(X)&~creative(X))<=>(~brave(X)&~rich(X))))&
((?[X]:((~wise(X)&~kind(X))))<=>((~quiet(mary)|~wise(mary))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((curious(X)|~kind(X))=>(tall(X)&~brave(X))))&
(((~brave(lucy)|funny(lucy)))=>((~strong(paul)<~>brave(paul))))&
(![X]:((wise(X)<~>~happy(X))=>(brave(X)&~funny(X))))&
(![X]:(tall(X)<=>(~tall(X)&old(X))))&
(![X]:(wise(X)<=>~calm(X)))&
(![X]:(~kind(X)=>~funny(X)))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:((brave(X)<~>patient(X))<=>(~old(X)|patient(X))))&
((~wise(mary))=>((rich(lucy)&calm(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(rich(X)&~kind(X))))&
(?[X]:((brave(X)&rich(X))))&
((~rich(susan)<~>humble(susan)))&
((old(susan)<~>kind(susan)))&
(?[X]:((patient(X)<~>calm(X))))&
((brave(susan)<~>happy(susan)))&
((~tall(alice)<~>strong(alice)))&
(?[X]:((~brave(X)&strong(X))))&
(?[X]:((patient(X)|~rich(X)))) | ~wise(susan) | [
"p3",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5585495199675740339821580
% SZS output start Proof for 5585495199675740339821580
4. ! [X0] : (~tall(X0) <=> funny(X0)) [input p3]
8. ! [X0] : (tall(X0) <=> (old(X0) & ~tall(X0))) [input p7]
9. ! [X0] : (wise(X0) <=> ~calm(X0)) [input p8]
11. ! [X0] : (calm(X0) => ~funny(X0)) [input p10]
23. ~wise(susan) [input hypothesis]
29. ! [X0] : (~funny(X0) | ~calm(X0)) [ennf transformation 11]
43. ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 4]
46. ! [X0] : ((tall(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~tall(X0))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~tall(X0))) [flattening 46]
48. ! [X0] : ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))) [nnf transformation 9]
78. funny(X0) | tall(X0) [cnf transformation 43]
92. ~tall(X0) | ~tall(X0) [cnf transformation 47]
96. calm(X0) | wise(X0) [cnf transformation 48]
98. ~calm(X0) | ~funny(X0) [cnf transformation 29]
126. ~wise(susan) [cnf transformation 23]
129. ~tall(X0) [duplicate literal removal 92]
274. ~funny(X0) | wise(X0) [resolution 98,96]
276. wise(X0) | tall(X0) [resolution 274,78]
278. wise(X0) [subsumption resolution 276,129]
320. $false [resolution 278,126]
% SZS output end Proof for 5585495199675740339821580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not patient then someone is both funny and not quiet and vice versa.
Everyone who is either funny or wise is either kind or tall.
Everyone who is not old is not happy.
If someone is not humble or not quiet then someone is not brave.
Everyone who is wise or patient is strong.
If susan is not strong then john is happy.
Everyone who is patient is either not creative or humble.
If susan is both generous and not generous then someone is both happy and creative.
If mary is both rich and old then fred is not strong or quiet.
Everyone who is old or not calm is either not strong or happy.
Everyone who is not patient is calm and vice versa.
Everyone who is tall is either not quiet or not calm and vice versa.
If someone is patient or not old then alice is humble and vice versa.
Everyone who is not quiet or not wise is both generous and calm.
Everyone who is either not curious or not patient is either rich or old.
If susan is both funny and not creative then lucy is not happy or humble.
Someone is either not brave or not funny.
Fred is both not humble and not old.
Someone is either not humble or generous.
Fred is rich.
Susan is not tall or not old.
Someone is both not rich and not patient.
John is calm or not humble.
Someone is either tall or not quiet. | Fred is patient. | contradiction | ((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(![X]:((funny(X)<~>wise(X))=>(kind(X)<~>tall(X))))&
(![X]:(~old(X)=>~happy(X)))&
((?[X]:((~humble(X)|~quiet(X))))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|patient(X))=>strong(X)))&
((~strong(susan))=>(happy(john)))&
(![X]:(patient(X)=>(~creative(X)<~>humble(X))))&
(((generous(susan)&~generous(susan)))=>(?[X]:((happy(X)&creative(X)))))&
(((rich(mary)&old(mary)))=>((~strong(fred)|quiet(fred))))&
(![X]:((old(X)|~calm(X))=>(~strong(X)<~>happy(X))))&
(![X]:(~patient(X)<=>calm(X)))&
(![X]:(tall(X)<=>(~quiet(X)<~>~calm(X))))&
((?[X]:((patient(X)|~old(X))))<=>(humble(alice)))&
(![X]:((~quiet(X)|~wise(X))=>(generous(X)&calm(X))))&
(![X]:((~curious(X)<~>~patient(X))=>(rich(X)<~>old(X))))&
(((funny(susan)&~creative(susan)))=>((~happy(lucy)|humble(lucy))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((~humble(fred)&~old(fred)))&
(?[X]:((~humble(X)<~>generous(X))))&
(rich(fred))&
((~tall(susan)|~old(susan)))&
(?[X]:((~rich(X)&~patient(X))))&
((calm(john)|~humble(john)))&
(?[X]:((tall(X)<~>~quiet(X)))) | patient(fred) | [
"p2",
"p4",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6473142949924506389788071
% SZS output start Proof for 6473142949924506389788071
3. ! [X0] : (~old(X0) => ~happy(X0)) [input p2]
5. ! [X0] : ((patient(X0) | wise(X0)) => strong(X0)) [input p4]
10. ! [X0] : ((~calm(X0) | old(X0)) => (~strong(X0) <~> happy(X0))) [input p9]
11. ! [X0] : (~patient(X0) <=> calm(X0)) [input p10]
18. ~old(fred) & ~humble(fred) [input p17]
25. patient(fred) [input hypothesis]
29. ! [X0] : (~happy(X0) | old(X0)) [ennf transformation 3]
31. ! [X0] : (strong(X0) | (~patient(X0) & ~wise(X0))) [ennf transformation 5]
38. ! [X0] : ((~strong(X0) <~> happy(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 10]
55. ! [X0] : (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (calm(X0) & ~old(X0))) [nnf transformation 38]
56. ! [X0] : ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0))) [nnf transformation 11]
83. ~happy(X0) | old(X0) [cnf transformation 29]
87. ~patient(X0) | strong(X0) [cnf transformation 31]
95. ~strong(X0) | happy(X0) | calm(X0) [cnf transformation 55]
99. ~calm(X0) | ~patient(X0) [cnf transformation 56]
119. ~old(fred) [cnf transformation 18]
129. patient(fred) [cnf transformation 25]
190. 15 <=> strong(fred) [avatar definition]
191. strong(fred) <- (15) [avatar component clause 190]
287. strong(fred) [resolution 87,129]
288. 15 [avatar split clause 287,190]
315. happy(fred) | calm(fred) <- (15) [resolution 95,191]
327. 40 <=> calm(fred) [avatar definition]
329. calm(fred) <- (40) [avatar component clause 327]
331. 41 <=> happy(fred) [avatar definition]
333. happy(fred) <- (41) [avatar component clause 331]
334. 40 | 41 | ~15 [avatar split clause 315,190,331,327]
344. ~patient(fred) <- (40) [resolution 329,99]
345. $false <- (40) [subsumption resolution 344,129]
346. ~40 [avatar contradiction clause 345]
356. old(fred) <- (41) [resolution 333,83]
357. $false <- (41) [subsumption resolution 356,119]
358. ~41 [avatar contradiction clause 357]
359. $false [avatar sat refutation 288,334,346,358]
% SZS output end Proof for 6473142949924506389788071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or humble then someone is both kind and not wise. Everyone who is humble is funny or humble and vice versa. Everyone who is old or not wise is quiet or not quiet and vice versa. If susan is either not tall or not brave then alice is either tall or not funny and vice versa. Everyone who is happy or strong is both strong and humble and vice versa. Everyone who is not patient or tall is funny. Everyone who is either not creative or not patient is quiet or kind. Everyone who is both not kind and not generous is both strong and not strong and vice versa. If someone is quiet or creative then someone is both not funny and not brave. If someone is old then john is either creative or tall and vice versa. If john is not tall or tall then lucy is either not creative or not generous and vice versa. Everyone who is both not quiet and tall is not happy and vice versa. Everyone who is either not brave or not wise is not curious or not funny and vice versa. Everyone who is not calm or tall is either kind or not funny. Everyone who is either not tall or wise is happy or brave and vice versa. If someone is not tall then someone is either not calm or not tall. Someone is both not quiet and happy. Someone is both brave and not happy. Someone is either old or strong. John is either not patient or not wise. John is creative or calm. Someone is both funny and patient. Someone is brave or funny. Someone is either happy or not brave. | John is creative. | contradiction | ((?[X]:((~funny(X)|humble(X))))=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:(humble(X)<=>(funny(X)|humble(X))))&
(![X]:((old(X)|~wise(X))<=>(quiet(X)|~quiet(X))))&
(((~tall(susan)<~>~brave(susan)))<=>((tall(alice)<~>~funny(alice))))&
(![X]:((happy(X)|strong(X))<=>(strong(X)&humble(X))))&
(![X]:((~patient(X)|tall(X))=>funny(X)))&
(![X]:((~creative(X)<~>~patient(X))=>(quiet(X)|kind(X))))&
(![X]:((~kind(X)&~generous(X))<=>(strong(X)&~strong(X))))&
((?[X]:((quiet(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
((?[X]:(old(X)))<=>((creative(john)<~>tall(john))))&
(((~tall(john)|tall(john)))<=>((~creative(lucy)<~>~generous(lucy))))&
(![X]:((~quiet(X)&tall(X))<=>~happy(X)))&
(![X]:((~brave(X)<~>~wise(X))<=>(~curious(X)|~funny(X))))&
(![X]:((~calm(X)|tall(X))=>(kind(X)<~>~funny(X))))&
(![X]:((~tall(X)<~>wise(X))<=>(happy(X)|brave(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((brave(X)&~happy(X))))&
(?[X]:((old(X)<~>strong(X))))&
((~patient(john)<~>~wise(john)))&
((creative(john)|calm(john)))&
(?[X]:((funny(X)&patient(X))))&
(?[X]:((brave(X)|funny(X))))&
(?[X]:((happy(X)<~>~brave(X)))) | creative(john) | [
"p5",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 720822769629390952974165
% SZS output start Proof for 720822769629390952974165
6. ! [X0] : ((tall(X0) | ~patient(X0)) => funny(X0)) [input p5]
9. ? [X0] : (creative(X0) | quiet(X0)) => ? [X0] : (~brave(X0) & ~funny(X0)) [input p8]
12. ! [X0] : ((tall(X0) & ~quiet(X0)) <=> ~happy(X0)) [input p11]
13. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~funny(X0) | ~curious(X0))) [input p12]
15. ! [X0] : ((~tall(X0) <~> wise(X0)) <=> (brave(X0) | happy(X0))) [input p14]
25. creative(john) [input hypothesis]
27. ? [X0] : (creative(X0) | quiet(X0)) => ? [X1] : (~brave(X1) & ~funny(X1)) [rectify 9]
30. ! [X0] : (funny(X0) | (~tall(X0) & patient(X0))) [ennf transformation 6]
33. ? [X1] : (~brave(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & ~quiet(X0)) [ennf transformation 27]
49. ? [X0] : (~brave(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & ~quiet(X1)) [rectify 33]
50. ? [X0] : (~brave(X0) & ~funny(X0)) => (~brave(sK1) & ~funny(sK1)) [choice axiom]
51. (~brave(sK1) & ~funny(sK1)) | ! [X1] : (~creative(X1) & ~quiet(X1)) [skolemisation 49,50]
58. ! [X0] : (((tall(X0) & ~quiet(X0)) | happy(X0)) & (~happy(X0) | (~tall(X0) | quiet(X0)))) [nnf transformation 12]
59. ! [X0] : (((tall(X0) & ~quiet(X0)) | happy(X0)) & (~happy(X0) | ~tall(X0) | quiet(X0))) [flattening 58]
60. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & curious(X0))) & ((~funny(X0) | ~curious(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 13]
61. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & curious(X0))) & (~funny(X0) | ~curious(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 60]
63. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0))))) [flattening 63]
109. ~tall(X0) | funny(X0) [cnf transformation 30]
117. ~funny(sK1) | ~creative(X1) [cnf transformation 51]
119. ~brave(sK1) | ~creative(X1) [cnf transformation 51]
132. happy(X0) | tall(X0) [cnf transformation 59]
138. brave(X0) | wise(X0) | funny(X0) [cnf transformation 61]
147. ~wise(X0) | tall(X0) | ~happy(X0) [cnf transformation 64]
165. creative(john) [cnf transformation 25]
211. 9 <=> ! [X1] : ~creative(X1) [avatar definition]
212. ~creative(X1) <- (9) [avatar component clause 211]
214. 10 <=> brave(sK1) [avatar definition]
216. ~brave(sK1) <- (~10) [avatar component clause 214]
217. 9 | ~10 [avatar split clause 119,214,211]
223. 12 <=> funny(sK1) [avatar definition]
225. ~funny(sK1) <- (~12) [avatar component clause 223]
226. 9 | ~12 [avatar split clause 117,223,211]
233. 14 <=> creative(john) [avatar definition]
235. creative(john) <- (14) [avatar component clause 233]
260. ~wise(X0) | tall(X0) [subsumption resolution 147,132]
319. 14 [avatar split clause 165,233]
371. wise(sK1) | funny(sK1) <- (~10) [resolution 138,216]
374. wise(sK1) <- (~10, ~12) [subsumption resolution 371,225]
376. tall(sK1) <- (~10, ~12) [resolution 374,260]
470. funny(sK1) <- (~10, ~12) [resolution 376,109]
471. $false <- (~10, ~12) [subsumption resolution 470,225]
472. 10 | 12 [avatar contradiction clause 471]
473. $false <- (9, 14) [resolution 212,235]
476. ~9 | ~14 [avatar contradiction clause 473]
477. $false [avatar sat refutation 217,226,319,472,476]
% SZS output end Proof for 720822769629390952974165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is both not tall and tall. If lucy is calm then paul is not generous. Everyone who is either not curious or rich is calm. Everyone who is rich is either not creative or not funny. If someone is either not brave or quiet then someone is curious. Everyone who is not wise or not patient is both funny and not funny and vice versa. If someone is kind then someone is rich or curious and vice versa. If fred is either not brave or rich then susan is both not kind and calm. If john is both strong and not calm then paul is either generous or not humble and vice versa. Everyone who is both not quiet and not happy is not curious and vice versa. Everyone who is both rich and not rich is either patient or not rich. If someone is both not rich and kind then someone is generous and vice versa. Everyone who is humble or not rich is creative or not rich and vice versa. Everyone who is patient is not calm or not generous and vice versa. If susan is both not kind and not quiet then susan is brave or strong and vice versa. Mary is not generous or humble. Mary is both funny and not kind. Someone is either tall or wise. Someone is not kind. Fred is brave or not happy. | Paul is not humble. | contradiction | (![X]:(kind(X)=>(~tall(X)&tall(X))))&
((calm(lucy))=>(~generous(paul)))&
(![X]:((~curious(X)<~>rich(X))=>calm(X)))&
(![X]:(rich(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|curious(X)))))&
(((~brave(fred)<~>rich(fred)))=>((~kind(susan)&calm(susan))))&
(((strong(john)&~calm(john)))<=>((generous(paul)<~>~humble(paul))))&
(![X]:((~quiet(X)&~happy(X))<=>~curious(X)))&
(![X]:((rich(X)&~rich(X))=>(patient(X)<~>~rich(X))))&
((?[X]:((~rich(X)&kind(X))))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|~rich(X))<=>(creative(X)|~rich(X))))&
(![X]:(patient(X)<=>(~calm(X)|~generous(X))))&
(((~kind(susan)&~quiet(susan)))<=>((brave(susan)|strong(susan))))&
((~generous(mary)|humble(mary)))&
((funny(mary)&~kind(mary)))&
(?[X]:((tall(X)<~>wise(X))))&
(?[X]:(~kind(X)))&
((brave(fred)|~happy(fred))) | ~humble(paul) | [
"p0",
"p2",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7180430506538439439301892
% SZS output start Proof for 7180430506538439439301892
1. ! [X0] : (kind(X0) => (tall(X0) & ~tall(X0))) [input p0]
3. ! [X0] : ((~curious(X0) <~> rich(X0)) => calm(X0)) [input p2]
7. ? [X0] : kind(X0) <=> ? [X0] : (curious(X0) | rich(X0)) [input p6]
9. (~calm(john) & strong(john)) <=> (generous(paul) <~> ~humble(paul)) [input p8]
12. ? [X0] : (kind(X0) & ~rich(X0)) <=> ? [X0] : generous(X0) [input p11]
21. ~humble(paul) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : (curious(X1) | rich(X1)) [rectify 7]
24. ? [X0] : (kind(X0) & ~rich(X0)) <=> ? [X1] : generous(X1) [rectify 12]
25. ! [X0] : ((tall(X0) & ~tall(X0)) | ~kind(X0)) [ennf transformation 1]
27. ! [X0] : (calm(X0) | (~curious(X0) <=> rich(X0))) [ennf transformation 3]
33. ! [X0] : (calm(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) [nnf transformation 27]
41. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X1] : (curious(X1) | rich(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 23]
42. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X2] : (curious(X2) | rich(X2)) | ! [X3] : ~kind(X3)) [rectify 41]
43. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
44. ? [X2] : (curious(X2) | rich(X2)) => (curious(sK2) | rich(sK2)) [choice axiom]
45. (kind(sK1) | ! [X1] : (~curious(X1) & ~rich(X1))) & ((curious(sK2) | rich(sK2)) | ! [X3] : ~kind(X3)) [skolemisation 42,44,43]
47. ((~calm(john) & strong(john)) | ((generous(paul) | humble(paul)) & (~humble(paul) | ~generous(paul)))) & (((humble(paul) | ~generous(paul)) & (~humble(paul) | generous(paul))) | (calm(john) | ~strong(john))) [nnf transformation 9]
48. ((~calm(john) & strong(john)) | ((generous(paul) | humble(paul)) & (~humble(paul) | ~generous(paul)))) & (((humble(paul) | ~generous(paul)) & (~humble(paul) | generous(paul))) | calm(john) | ~strong(john)) [flattening 47]
52. (? [X0] : (kind(X0) & ~rich(X0)) | ! [X1] : ~generous(X1)) & (? [X1] : generous(X1) | ! [X0] : (~kind(X0) | rich(X0))) [nnf transformation 24]
53. (? [X0] : (kind(X0) & ~rich(X0)) | ! [X1] : ~generous(X1)) & (? [X2] : generous(X2) | ! [X3] : (~kind(X3) | rich(X3))) [rectify 52]
54. ? [X0] : (kind(X0) & ~rich(X0)) => (kind(sK3) & ~rich(sK3)) [choice axiom]
55. ? [X2] : generous(X2) => generous(sK4) [choice axiom]
56. ((kind(sK3) & ~rich(sK3)) | ! [X1] : ~generous(X1)) & (generous(sK4) | ! [X3] : (~kind(X3) | rich(X3))) [skolemisation 53,55,54]
68. ~tall(X0) | ~kind(X0) [cnf transformation 25]
69. ~kind(X0) | tall(X0) [cnf transformation 25]
71. rich(X0) | calm(X0) | curious(X0) [cnf transformation 33]
83. kind(sK1) | ~rich(X1) [cnf transformation 45]
84. kind(sK1) | ~curious(X1) [cnf transformation 45]
94. ~calm(john) | generous(paul) | humble(paul) [cnf transformation 48]
102. kind(sK3) | ~generous(X1) [cnf transformation 56]
122. ~humble(paul) [cnf transformation 21]
125. ~kind(X0) [subsumption resolution 68,69]
131. 2 <=> generous(paul) [avatar definition]
132. generous(paul) <- (2) [avatar component clause 131]
149. ~curious(X1) [subsumption resolution 84,125]
150. ~rich(X1) [subsumption resolution 83,125]
162. 8 <=> humble(paul) [avatar definition]
166. 9 <=> calm(john) [avatar definition]
168. ~calm(john) <- (~9) [avatar component clause 166]
169. 8 | 2 | ~9 [avatar split clause 94,166,131,162]
181. ~generous(X1) [subsumption resolution 102,125]
194. ~8 [avatar split clause 122,162]
197. $false <- (2) [subsumption resolution 132,181]
198. ~2 [avatar contradiction clause 197]
202. calm(X0) | curious(X0) [resolution 71,150]
203. calm(X0) [subsumption resolution 202,149]
207. $false <- (~9) [resolution 203,168]
208. 9 [avatar contradiction clause 207]
210. $false [avatar sat refutation 169,194,198,208]
% SZS output end Proof for 7180430506538439439301892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not calm then paul is either not kind or funny. If fred is not brave then paul is not generous or tall. Everyone who is kind is both rich and not creative. Everyone who is generous or not rich is either patient or not happy and vice versa. If someone is both not brave and humble then someone is either not kind or not strong and vice versa. Everyone who is not calm or not kind is both strong and not curious and vice versa. If someone is either calm or not old then someone is either not happy or creative. Everyone who is not calm or wise is not wise and vice versa. If someone is either funny or not old then someone is not rich or not curious. If someone is both not kind and not creative then lucy is not brave and vice versa. Everyone who is not curious is both not rich and happy. If lucy is either brave or not humble then someone is kind or calm and vice versa. Everyone who is both not brave and not rich is not kind or not curious. If paul is curious or not creative then paul is both not kind and not brave and vice versa. If someone is both curious and tall then paul is both wise and not calm and vice versa. Everyone who is kind is either strong or not kind. Susan is not funny or quiet. Susan is brave or wise. Lucy is tall or not happy. Someone is both not creative and old. Someone is both not tall and strong. Mary is both not wise and humble. Someone is not happy or not creative. Fred is brave or rich. | Fred is not patient. | contradiction | ((?[X]:((~funny(X)|~calm(X))))=>((~kind(paul)<~>funny(paul))))&
((~brave(fred))=>((~generous(paul)|tall(paul))))&
(![X]:(kind(X)=>(rich(X)&~creative(X))))&
(![X]:((generous(X)|~rich(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:((~calm(X)|~kind(X))<=>(strong(X)&~curious(X))))&
((?[X]:((calm(X)<~>~old(X))))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))<=>~wise(X)))&
((?[X]:((funny(X)<~>~old(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~kind(X)&~creative(X))))<=>(~brave(lucy)))&
(![X]:(~curious(X)=>(~rich(X)&happy(X))))&
(((brave(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~brave(X)&~rich(X))=>(~kind(X)|~curious(X))))&
(((curious(paul)|~creative(paul)))<=>((~kind(paul)&~brave(paul))))&
((?[X]:((curious(X)&tall(X))))<=>((wise(paul)&~calm(paul))))&
(![X]:(kind(X)=>(strong(X)<~>~kind(X))))&
((~funny(susan)|quiet(susan)))&
((brave(susan)|wise(susan)))&
((tall(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((~tall(X)&strong(X))))&
((~wise(mary)&humble(mary)))&
(?[X]:((~happy(X)|~creative(X))))&
((brave(fred)|rich(fred))) | ~patient(fred) | [
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5722418256688308780712569
% SZS output start Proof for 5722418256688308780712569
3. ! [X0] : (kind(X0) => (~creative(X0) & rich(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | generous(X0)) <=> (patient(X0) <~> ~happy(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> (~curious(X0) & strong(X0))) [input p5]
8. ! [X0] : ((wise(X0) | ~calm(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : (~curious(X0) => (happy(X0) & ~rich(X0))) [input p10]
12. (brave(lucy) <~> ~humble(lucy)) <=> ? [X0] : (calm(X0) | kind(X0)) [input p11]
25. ~patient(fred) [input hypothesis]
33. ! [X0] : ((~creative(X0) & rich(X0)) | ~kind(X0)) [ennf transformation 3]
36. ! [X0] : ((happy(X0) & ~rich(X0)) | curious(X0)) [ennf transformation 11]
41. ! [X0] : (((~rich(X0) | generous(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (rich(X0) & ~generous(X0)))) [nnf transformation 4]
42. ! [X0] : ((~rich(X0) | generous(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) & (((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (rich(X0) & ~generous(X0)))) [flattening 41]
48. ! [X0] : (((~kind(X0) | ~calm(X0)) | (curious(X0) | ~strong(X0))) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | ~calm(X0) | curious(X0) | ~strong(X0)) & ((~curious(X0) & strong(X0)) | (kind(X0) & calm(X0)))) [flattening 48]
54. ! [X0] : (((wise(X0) | ~calm(X0)) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [nnf transformation 8]
55. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0)) & (~wise(X0) | (~wise(X0) & calm(X0)))) [flattening 54]
64. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X0] : (calm(X0) | kind(X0)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [nnf transformation 12]
65. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X1] : (calm(X1) | kind(X1)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [rectify 64]
66. ? [X1] : (calm(X1) | kind(X1)) => (calm(sK5) | kind(sK5)) [choice axiom]
67. (((humble(lucy) | ~brave(lucy)) & (~humble(lucy) | brave(lucy))) | ! [X0] : (~calm(X0) & ~kind(X0))) & ((calm(sK5) | kind(sK5)) | ((brave(lucy) | humble(lucy)) & (~humble(lucy) | ~brave(lucy)))) [skolemisation 65,66]
87. ~kind(X0) | rich(X0) [cnf transformation 33]
90. ~happy(X0) | patient(X0) | rich(X0) [cnf transformation 42]
103. ~curious(X0) | calm(X0) [cnf transformation 49]
104. ~curious(X0) | kind(X0) [cnf transformation 49]
111. ~wise(X0) | ~wise(X0) [cnf transformation 55]
112. wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 55]
118. ~rich(X0) | curious(X0) [cnf transformation 36]
119. curious(X0) | happy(X0) [cnf transformation 36]
120. calm(sK5) | kind(sK5) | ~humble(lucy) | ~brave(lucy) [cnf transformation 67]
121. calm(sK5) | kind(sK5) | brave(lucy) | humble(lucy) [cnf transformation 67]
122. ~humble(lucy) | brave(lucy) | ~kind(X0) [cnf transformation 67]
124. humble(lucy) | ~brave(lucy) | ~kind(X0) [cnf transformation 67]
148. ~patient(fred) [cnf transformation 25]
150. ~wise(X0) [duplicate literal removal 111]
151. ~calm(X0) | wise(X0) [duplicate literal removal 112]
249. 23 <=> brave(lucy) [avatar definition]
270. 28 <=> humble(lucy) [avatar definition]
275. 29 <=> ! [X0] : ~kind(X0) [avatar definition]
276. ~kind(X0) <- (29) [avatar component clause 275]
277. 29 | ~23 | 28 [avatar split clause 124,270,249,275]
279. 29 | 23 | ~28 [avatar split clause 122,270,249,275]
281. 30 <=> kind(sK5) [avatar definition]
283. kind(sK5) <- (30) [avatar component clause 281]
285. 31 <=> calm(sK5) [avatar definition]
286. ~calm(sK5) <- (~31) [avatar component clause 285]
287. calm(sK5) <- (31) [avatar component clause 285]
288. 28 | 23 | 30 | 31 [avatar split clause 121,285,281,249,270]
289. ~23 | ~28 | 30 | 31 [avatar split clause 120,285,281,270,249]
342. 41 <=> rich(fred) [avatar definition]
344. rich(fred) <- (41) [avatar component clause 342]
357. happy(X0) | kind(X0) [resolution 119,104]
359. happy(X0) <- (29) [subsumption resolution 357,276]
382. patient(X0) | rich(X0) <- (29) [resolution 90,359]
409. rich(fred) <- (29) [resolution 382,148]
413. 41 | ~29 [avatar split clause 409,275,342]
415. curious(fred) <- (41) [resolution 344,118]
418. calm(fred) <- (41) [resolution 415,103]
433. wise(sK5) <- (31) [resolution 287,151]
434. $false <- (31) [subsumption resolution 433,150]
435. ~31 [avatar contradiction clause 434]
436. rich(sK5) <- (30) [resolution 283,87]
461. curious(sK5) <- (30) [resolution 436,118]
485. wise(fred) <- (41) [resolution 418,151]
486. $false <- (41) [subsumption resolution 485,150]
487. ~41 [avatar contradiction clause 486]
490. calm(sK5) <- (30) [resolution 461,103]
491. $false <- (30, ~31) [subsumption resolution 490,286]
492. ~30 | 31 [avatar contradiction clause 491]
493. $false [avatar sat refutation 277,279,288,289,413,435,487,492]
% SZS output end Proof for 5722418256688308780712569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then paul is tall or not calm.
If john is quiet or not generous then alice is creative.
If fred is funny or not kind then someone is rich or quiet and vice versa.
Everyone who is tall or not tall is not funny and vice versa.
If someone is not patient then someone is not generous and vice versa.
Everyone who is both not kind and not patient is not wise or not happy and vice versa.
If alice is either quiet or not patient then someone is old.
Everyone who is either old or not strong is old or funny.
Everyone who is both happy and not curious is either creative or kind and vice versa.
If someone is not kind then someone is either curious or not wise.
If john is not old or happy then mary is wise.
Everyone who is not strong or kind is not happy and vice versa.
Everyone who is either not humble or humble is not calm.
Everyone who is patient or not old is either not creative or wise.
If someone is either calm or kind then mary is not generous or not creative.
Everyone who is calm is curious.
John is either kind or patient.
Susan is old.
Someone is old or not old.
Someone is funny or humble.
Paul is not brave.
Fred is either not calm or patient.
Alice is creative or generous. | Susan is rich. | neutral | ((?[X]:(old(X)))=>((tall(paul)|~calm(paul))))&
(((quiet(john)|~generous(john)))=>(creative(alice)))&
(((funny(fred)|~kind(fred)))<=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((tall(X)|~tall(X))<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(~generous(X))))&
(![X]:((~kind(X)&~patient(X))<=>(~wise(X)|~happy(X))))&
(((quiet(alice)<~>~patient(alice)))=>(?[X]:(old(X))))&
(![X]:((old(X)<~>~strong(X))=>(old(X)|funny(X))))&
(![X]:((happy(X)&~curious(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~old(john)|happy(john)))=>(wise(mary)))&
(![X]:((~strong(X)|kind(X))<=>~happy(X)))&
(![X]:((~humble(X)<~>humble(X))=>~calm(X)))&
(![X]:((patient(X)|~old(X))=>(~creative(X)<~>wise(X))))&
((?[X]:((calm(X)<~>kind(X))))=>((~generous(mary)|~creative(mary))))&
(![X]:(calm(X)=>curious(X)))&
((kind(john)<~>patient(john)))&
(old(susan))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((funny(X)|humble(X))))&
(~brave(paul))&
((~calm(fred)<~>patient(fred)))&
((creative(alice)|generous(alice))) | rich(susan) | [] | null | 0 |
Everyone who is both calm and quiet is both not happy and curious and vice versa. Everyone who is not wise is quiet and vice versa. If someone is not rich or not quiet then susan is both not patient and not generous. If paul is not quiet then someone is old and vice versa. If paul is both not humble and old then john is wise or not patient. If fred is not tall then paul is humble and vice versa. If mary is tall or not creative then lucy is both not quiet and not humble. Everyone who is not humble is both not tall and not generous. If someone is both not brave and not wise then someone is both not rich and not humble. If someone is happy then susan is not brave or not kind and vice versa. Everyone who is generous or creative is not wise and vice versa. Everyone who is brave or funny is rich or not tall and vice versa. Everyone who is either not creative or not quiet is either happy or not kind and vice versa. Everyone who is not funny is either not humble or not strong and vice versa. If paul is calm then mary is humble or kind. Everyone who is funny or not humble is either happy or not brave and vice versa. Mary is either not happy or wise. Someone is not strong or not quiet. Someone is either brave or not kind. John is either generous or not happy. Someone is both not old and not strong. Someone is either generous or not kind. Fred is not happy or not creative. | Paul is not humble. | neutral | (![X]:((calm(X)&quiet(X))<=>(~happy(X)&curious(X))))&
(![X]:(~wise(X)<=>quiet(X)))&
((?[X]:((~rich(X)|~quiet(X))))=>((~patient(susan)&~generous(susan))))&
((~quiet(paul))<=>(?[X]:(old(X))))&
(((~humble(paul)&old(paul)))=>((wise(john)|~patient(john))))&
((~tall(fred))<=>(humble(paul)))&
(((tall(mary)|~creative(mary)))=>((~quiet(lucy)&~humble(lucy))))&
(![X]:(~humble(X)=>(~tall(X)&~generous(X))))&
((?[X]:((~brave(X)&~wise(X))))=>(?[X]:((~rich(X)&~humble(X)))))&
((?[X]:(happy(X)))<=>((~brave(susan)|~kind(susan))))&
(![X]:((generous(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((generous(john)<~>~happy(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred))) | ~humble(paul) | [] | null | 0 |
If someone is either brave or patient then susan is not patient and vice versa.
Everyone who is either not strong or not patient is both rich and curious and vice versa.
Everyone who is both strong and not kind is funny and vice versa.
Everyone who is not curious is either not brave or not rich and vice versa.
Everyone who is both humble and brave is both generous and kind.
Everyone who is both not funny and generous is either wise or not curious.
If someone is calm then someone is not happy or tall.
If lucy is both happy and brave then fred is curious.
Everyone who is both quiet and kind is curious.
If fred is either kind or not curious then someone is either not kind or not humble.
If susan is not happy or not curious then someone is both not funny and not creative and vice versa.
If someone is either not brave or strong then someone is either generous or curious and vice versa.
Everyone who is not wise or not tall is tall and vice versa.
Everyone who is strong is either tall or generous and vice versa.
Everyone who is funny or not generous is not wise or quiet.
Everyone who is both kind and generous is not curious and vice versa.
Mary is not kind.
Someone is either humble or not wise.
Someone is not funny.
Alice is not kind.
Alice is quiet.
Susan is old. | Susan is not curious. | neutral | ((?[X]:((brave(X)<~>patient(X))))<=>(~patient(susan)))&
(![X]:((~strong(X)<~>~patient(X))<=>(rich(X)&curious(X))))&
(![X]:((strong(X)&~kind(X))<=>funny(X)))&
(![X]:(~curious(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((humble(X)&brave(X))=>(generous(X)&kind(X))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)<~>~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~happy(X)|tall(X)))))&
(((happy(lucy)&brave(lucy)))=>(curious(fred)))&
(![X]:((quiet(X)&kind(X))=>curious(X)))&
(((kind(fred)<~>~curious(fred)))=>(?[X]:((~kind(X)<~>~humble(X)))))&
(((~happy(susan)|~curious(susan)))<=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~wise(X)|~tall(X))<=>tall(X)))&
(![X]:(strong(X)<=>(tall(X)<~>generous(X))))&
(![X]:((funny(X)|~generous(X))=>(~wise(X)|quiet(X))))&
(![X]:((kind(X)&generous(X))<=>~curious(X)))&
(~kind(mary))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
(~kind(alice))&
(quiet(alice))&
(old(susan)) | ~curious(susan) | [] | null | 0 |
Everyone who is not happy is either rich or not curious and vice versa. Everyone who is either brave or funny is not kind. Everyone who is not funny or generous is both not happy and happy and vice versa. Everyone who is quiet or wise is rich or not curious and vice versa. Everyone who is quiet is either quiet or happy and vice versa. Everyone who is brave is both happy and not rich. Everyone who is either tall or not humble is both not curious and patient and vice versa. Everyone who is either creative or not rich is curious. If mary is creative or not old then someone is either tall or not old. If someone is both creative and not calm then someone is both quiet and not quiet and vice versa. If someone is either not curious or not old then mary is not brave or not curious. Everyone who is patient or quiet is both not kind and not strong and vice versa. If fred is generous then fred is not tall or creative and vice versa. Everyone who is either not calm or not strong is either kind or not rich and vice versa. If someone is both not kind and old then someone is not humble and vice versa. Everyone who is either not quiet or not calm is both not strong and quiet and vice versa. Fred is funny or patient. Paul is rich. Lucy is not patient or rich. Someone is tall or funny. Paul is funny or not calm. John is not quiet. Someone is not tall. | John is not rich. | contradiction | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>funny(X))=>~kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)|wise(X))<=>(rich(X)|~curious(X))))&
(![X]:(quiet(X)<=>(quiet(X)<~>happy(X))))&
(![X]:(brave(X)=>(happy(X)&~rich(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(~curious(X)&patient(X))))&
(![X]:((creative(X)<~>~rich(X))=>curious(X)))&
(((creative(mary)|~old(mary)))=>(?[X]:((tall(X)<~>~old(X)))))&
((?[X]:((creative(X)&~calm(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>((~brave(mary)|~curious(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~kind(X)&~strong(X))))&
((generous(fred))<=>((~tall(fred)|creative(fred))))&
(![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)&quiet(X))))&
((funny(fred)|patient(fred)))&
(rich(paul))&
((~patient(lucy)|rich(lucy)))&
(?[X]:((tall(X)|funny(X))))&
((funny(paul)|~calm(paul)))&
(~quiet(john))&
(?[X]:(~tall(X))) | ~rich(john) | [
"p0",
"p4",
"p7",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3279151519511320577670316
% SZS output start Proof for 3279151519511320577670316
1. ! [X0] : (~happy(X0) <=> (rich(X0) <~> ~curious(X0))) [input p0]
5. ! [X0] : (quiet(X0) <=> (quiet(X0) <~> happy(X0))) [input p4]
8. ! [X0] : ((creative(X0) <~> ~rich(X0)) => curious(X0)) [input p7]
10. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p9]
12. ! [X0] : ((quiet(X0) | patient(X0)) <=> (~strong(X0) & ~kind(X0))) [input p11]
16. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p15]
24. ~rich(john) [input hypothesis]
25. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 10]
29. ! [X0] : (curious(X0) | (creative(X0) <=> ~rich(X0))) [ennf transformation 8]
33. ! [X0] : ((~happy(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | happy(X0))) [nnf transformation 1]
39. ! [X0] : ((quiet(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ~quiet(X0))) [nnf transformation 5]
42. ! [X0] : (curious(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 29]
46. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : (calm(X0) | ~creative(X0))) [nnf transformation 25]
47. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : (calm(X3) | ~creative(X3))) [rectify 46]
48. ? [X0] : (~calm(X0) & creative(X0)) => (~calm(sK1) & creative(sK1)) [choice axiom]
49. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK2) & quiet(sK2)) [choice axiom]
50. ((~calm(sK1) & creative(sK1)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK2) & quiet(sK2)) | ! [X3] : (calm(X3) | ~creative(X3))) [skolemisation 47,49,48]
52. ! [X0] : (((quiet(X0) | patient(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 12]
53. ! [X0] : ((quiet(X0) | patient(X0) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [flattening 52]
62. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 16]
63. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 62]
68. ~curious(X0) | rich(X0) | happy(X0) [cnf transformation 33]
84. ~happy(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 39]
86. quiet(X0) | quiet(X0) | ~happy(X0) [cnf transformation 39]
96. creative(X0) | curious(X0) | rich(X0) [cnf transformation 42]
101. quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 50]
102. ~quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 50]
110. ~strong(X0) | ~quiet(X0) [cnf transformation 53]
128. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 63]
130. ~calm(X0) | ~quiet(X0) | ~quiet(X0) | strong(X0) [cnf transformation 63]
139. ~rich(john) [cnf transformation 24]
140. quiet(X0) | ~calm(X0) [duplicate literal removal 128]
141. ~calm(X0) | ~quiet(X0) | strong(X0) [duplicate literal removal 130]
142. ~happy(X0) | ~quiet(X0) [duplicate literal removal 84]
143. ~happy(X0) | quiet(X0) [duplicate literal removal 86]
146. ~happy(X0) [subsumption resolution 142,143]
169. 5 <=> ! [X3] : (calm(X3) | ~creative(X3)) [avatar definition]
170. calm(X3) | ~creative(X3) <- (5) [avatar component clause 169]
172. 6 <=> quiet(sK2) [avatar definition]
175. 5 | ~6 [avatar split clause 102,172,169]
176. 5 | 6 [avatar split clause 101,172,169]
200. ~calm(X0) | ~quiet(X0) [subsumption resolution 141,110]
201. ~calm(X0) [subsumption resolution 140,200]
211. ~creative(X3) <- (5) [subsumption resolution 170,201]
280. curious(X1) | rich(X1) <- (5) [resolution 96,211]
326. rich(X2) | rich(X2) | happy(X2) <- (5) [resolution 280,68]
327. rich(X2) | happy(X2) <- (5) [duplicate literal removal 326]
328. rich(X2) <- (5) [subsumption resolution 327,146]
333. $false <- (5) [resolution 328,139]
334. ~5 [avatar contradiction clause 333]
337. $false [avatar sat refutation 175,176,334]
% SZS output end Proof for 3279151519511320577670316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not humble is both not brave and quiet and vice versa.
If paul is curious or not brave then alice is not kind or not humble.
If someone is both not calm and rich then someone is either patient or wise.
If susan is not wise then fred is not humble or funny and vice versa.
If lucy is both curious and old then someone is not brave or not funny and vice versa.
If susan is not calm then susan is both not tall and not old and vice versa.
If paul is both not kind and not funny then lucy is either not generous or not creative and vice versa.
Everyone who is not tall is not calm.
If someone is curious or strong then john is curious or tall.
If someone is kind then someone is either not curious or rich and vice versa.
Everyone who is not wise or creative is both humble and patient.
If someone is humble then alice is either old or humble.
Everyone who is either not kind or not funny is not rich or strong and vice versa.
Everyone who is kind or not tall is not wise or brave and vice versa.
Everyone who is both not calm and patient is both calm and creative.
If lucy is generous then susan is not humble or not happy and vice versa.
Someone is not old or not humble.
Someone is not generous or generous.
Susan is not patient or not happy.
Susan is rich.
Someone is not rich or not creative.
Someone is strong.
Fred is both funny and not creative. | Paul is tall. | entailment | (![X]:((wise(X)|~humble(X))<=>(~brave(X)&quiet(X))))&
(((curious(paul)|~brave(paul)))=>((~kind(alice)|~humble(alice))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((patient(X)<~>wise(X)))))&
((~wise(susan))<=>((~humble(fred)|funny(fred))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:((~brave(X)|~funny(X)))))&
((~calm(susan))<=>((~tall(susan)&~old(susan))))&
(((~kind(paul)&~funny(paul)))<=>((~generous(lucy)<~>~creative(lucy))))&
(![X]:(~tall(X)=>~calm(X)))&
((?[X]:((curious(X)|strong(X))))=>((curious(john)|tall(john))))&
((?[X]:(kind(X)))<=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((~wise(X)|creative(X))=>(humble(X)&patient(X))))&
((?[X]:(humble(X)))=>((old(alice)<~>humble(alice))))&
(![X]:((~kind(X)<~>~funny(X))<=>(~rich(X)|strong(X))))&
(![X]:((kind(X)|~tall(X))<=>(~wise(X)|brave(X))))&
(![X]:((~calm(X)&patient(X))=>(calm(X)&creative(X))))&
((generous(lucy))<=>((~humble(susan)|~happy(susan))))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~generous(X)|generous(X))))&
((~patient(susan)|~happy(susan)))&
(rich(susan))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(strong(X)))&
((funny(fred)&~creative(fred))) | tall(paul) | [
"p0",
"p7",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6796361773747210753954034
% SZS output start Proof for 6796361773747210753954034
1. ! [X0] : ((~humble(X0) | wise(X0)) <=> (quiet(X0) & ~brave(X0))) [input p0]
8. ! [X0] : (~tall(X0) => ~calm(X0)) [input p7]
11. ! [X0] : ((creative(X0) | ~wise(X0)) => (patient(X0) & humble(X0))) [input p10]
14. ! [X0] : ((~tall(X0) | kind(X0)) <=> (brave(X0) | ~wise(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~calm(X0)) => (creative(X0) & calm(X0))) [input p14]
24. ~tall(paul) [input hypothesis]
30. ! [X0] : (~calm(X0) | tall(X0)) [ennf transformation 8]
33. ! [X0] : ((patient(X0) & humble(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 11]
35. ! [X0] : ((creative(X0) & calm(X0)) | (~patient(X0) | calm(X0))) [ennf transformation 15]
36. ! [X0] : ((creative(X0) & calm(X0)) | ~patient(X0) | calm(X0)) [flattening 35]
37. ! [X0] : (((~humble(X0) | wise(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [nnf transformation 1]
38. ! [X0] : ((~humble(X0) | wise(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (humble(X0) & ~wise(X0)))) [flattening 37]
62. ! [X0] : (((~tall(X0) | kind(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (tall(X0) & ~kind(X0)))) [nnf transformation 14]
63. ! [X0] : ((~tall(X0) | kind(X0) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | (tall(X0) & ~kind(X0)))) [flattening 62]
74. ~brave(X0) | ~wise(X0) [cnf transformation 38]
100. ~calm(X0) | tall(X0) [cnf transformation 30]
109. patient(X0) | wise(X0) [cnf transformation 33]
120. brave(X0) | ~wise(X0) | tall(X0) [cnf transformation 63]
123. calm(X0) | ~patient(X0) | calm(X0) [cnf transformation 36]
136. ~tall(paul) [cnf transformation 24]
137. ~patient(X0) | calm(X0) [duplicate literal removal 123]
298. ~wise(X0) | tall(X0) [subsumption resolution 120,74]
339. calm(X0) | wise(X0) [resolution 137,109]
461. wise(X0) | tall(X0) [resolution 339,100]
463. tall(X0) [subsumption resolution 461,298]
467. $false [resolution 463,136]
% SZS output end Proof for 6796361773747210753954034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and creative is not rich or strong and vice versa. If fred is not strong then fred is both happy and not brave. Everyone who is either not wise or not humble is not happy. Everyone who is not kind or not curious is either not generous or not kind. Everyone who is not happy or creative is either not strong or curious. Everyone who is not curious is both humble and rich. If lucy is tall or calm then john is quiet or patient and vice versa. If someone is either not quiet or not rich then someone is either tall or not tall. Everyone who is not calm is happy or not patient. Everyone who is calm is not kind or not curious. Everyone who is rich or not strong is not brave or not kind and vice versa. Everyone who is not kind or patient is both not brave and not tall. Everyone who is creative is rich and vice versa. 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. Someone is not strong or not calm. Lucy is either patient or generous. Someone is either curious or not curious. Paul is not creative or funny. Someone is rich or not kind. Someone is humble. Paul is wise. Lucy is curious or not happy. | Mary is not curious. | entailment | (![X]:((happy(X)&creative(X))<=>(~rich(X)|strong(X))))&
((~strong(fred))=>((happy(fred)&~brave(fred))))&
(![X]:((~wise(X)<~>~humble(X))=>~happy(X)))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~kind(X))))&
(![X]:((~happy(X)|creative(X))=>(~strong(X)<~>curious(X))))&
(![X]:(~curious(X)=>(humble(X)&rich(X))))&
(((tall(lucy)|calm(lucy)))<=>((quiet(john)|patient(john))))&
((?[X]:((~quiet(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:(~calm(X)=>(happy(X)|~patient(X))))&
(![X]:(calm(X)=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(?[X]:((~strong(X)|~calm(X))))&
((patient(lucy)<~>generous(lucy)))&
(?[X]:((curious(X)<~>~curious(X))))&
((~creative(paul)|funny(paul)))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:(humble(X)))&
(wise(paul))&
((curious(lucy)|~happy(lucy))) | ~curious(mary) | [
"p0",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7593377431452282353828851
% SZS output start Proof for 7593377431452282353828851
1. ! [X0] : ((creative(X0) & happy(X0)) <=> (strong(X0) | ~rich(X0))) [input p0]
5. ! [X0] : ((creative(X0) | ~happy(X0)) => (~strong(X0) <~> curious(X0))) [input p4]
13. ! [X0] : (creative(X0) <=> rich(X0)) [input p12]
14. rich(alice) <=> (~happy(mary) & patient(mary)) [input p13]
25. curious(mary) [input hypothesis]
32. ! [X0] : ((~strong(X0) <~> curious(X0)) | (~creative(X0) & happy(X0))) [ennf transformation 5]
41. ! [X0] : (((creative(X0) & happy(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (~creative(X0) | ~happy(X0)))) [nnf transformation 1]
42. ! [X0] : (((creative(X0) & happy(X0)) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ~creative(X0) | ~happy(X0))) [flattening 41]
45. ! [X0] : (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | (~creative(X0) & happy(X0))) [nnf transformation 32]
54. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 13]
55. (rich(alice) | (happy(mary) | ~patient(mary))) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [nnf transformation 14]
56. (rich(alice) | happy(mary) | ~patient(mary)) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [flattening 55]
71. ~strong(X0) | happy(X0) [cnf transformation 42]
72. rich(X0) | creative(X0) [cnf transformation 42]
84. ~curious(X0) | strong(X0) | happy(X0) [cnf transformation 45]
106. rich(X0) | ~creative(X0) [cnf transformation 54]
107. creative(X0) | ~rich(X0) [cnf transformation 54]
109. ~happy(mary) | ~rich(alice) [cnf transformation 56]
122. curious(mary) [cnf transformation 25]
134. ~curious(X0) | happy(X0) [subsumption resolution 84,71]
156. creative(X0) [subsumption resolution 107,72]
157. rich(X0) [subsumption resolution 106,156]
158. ~happy(mary) [subsumption resolution 109,157]
207. happy(mary) [resolution 134,122]
210. $false [subsumption resolution 207,158]
% SZS output end Proof for 7593377431452282353828851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either brave or not rich and vice versa. If john is funny or not old then someone is not tall and vice versa. If someone is both funny and not wise then someone is either kind or quiet. Everyone who is not funny or generous is not creative and vice versa. Everyone who is old or not humble is either strong or brave. If paul is either curious or calm then someone is both patient and not happy and vice versa. If someone is either not creative or quiet then susan is either not tall or creative. If john is creative then john is both kind and not calm. If lucy is either not rich or not humble then alice is not generous or not happy and vice versa. If susan is not quiet or generous then someone is not happy. Everyone who is both generous and humble is either tall or old and vice versa. If someone is not kind or not curious then fred is either kind or not funny and vice versa. If someone is not happy then lucy is not rich or not humble and vice versa. If mary is generous then someone is both rich and humble and vice versa. If lucy is rich then someone is both not calm and not kind and vice versa. If someone is not wise then someone is curious or not brave and vice versa. Someone is both calm and creative. Mary is either not brave or not generous. John is not happy or not calm. Someone is not quiet. Someone is patient. Susan is both not patient and generous. Fred is not patient. Someone is either not strong or not funny. | Susan is generous. | entailment | (![X]:((patient(X)|generous(X))<=>(brave(X)<~>~rich(X))))&
(((funny(john)|~old(john)))<=>(?[X]:(~tall(X))))&
((?[X]:((funny(X)&~wise(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~creative(X)))&
(![X]:((old(X)|~humble(X))=>(strong(X)<~>brave(X))))&
(((curious(paul)<~>calm(paul)))<=>(?[X]:((patient(X)&~happy(X)))))&
((?[X]:((~creative(X)<~>quiet(X))))=>((~tall(susan)<~>creative(susan))))&
((creative(john))=>((kind(john)&~calm(john))))&
(((~rich(lucy)<~>~humble(lucy)))<=>((~generous(alice)|~happy(alice))))&
(((~quiet(susan)|generous(susan)))=>(?[X]:(~happy(X))))&
(![X]:((generous(X)&humble(X))<=>(tall(X)<~>old(X))))&
((?[X]:((~kind(X)|~curious(X))))<=>((kind(fred)<~>~funny(fred))))&
((?[X]:(~happy(X)))<=>((~rich(lucy)|~humble(lucy))))&
((generous(mary))<=>(?[X]:((rich(X)&humble(X)))))&
((rich(lucy))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((curious(X)|~brave(X)))))&
(?[X]:((calm(X)&creative(X))))&
((~brave(mary)<~>~generous(mary)))&
((~happy(john)|~calm(john)))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
((~patient(susan)&generous(susan)))&
(~patient(fred))&
(?[X]:((~strong(X)<~>~funny(X)))) | generous(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 252114141346491182658714
% SZS output start Proof for 252114141346491182658714
22. generous(susan) & ~patient(susan) [input p21]
25. ~generous(susan) [input hypothesis]
160. generous(susan) [cnf transformation 22]
164. ~generous(susan) [cnf transformation 25]
276. 24 <=> generous(susan) [avatar definition]
394. 24 [avatar split clause 160,276]
405. ~24 [avatar split clause 164,276]
406. $false [avatar sat refutation 394,405]
% SZS output end Proof for 252114141346491182658714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is tall or not generous and vice versa.
Everyone who is not humble or not old is not calm or not strong.
If alice is either not strong or old then someone is both not funny and not wise and vice versa.
Everyone who is not kind or not wise is not tall or not old and vice versa.
Everyone who is both humble and generous is not generous or creative and vice versa.
Everyone who is either old or creative is both not generous and quiet.
If someone is not curious then paul is either not happy or funny and vice versa.
If someone is both old and not curious then someone is both humble and not funny.
Everyone who is either quiet or calm is either not funny or curious and vice versa.
Everyone who is either not brave or creative is tall.
Everyone who is not creative is both not rich and not wise and vice versa.
If john is both generous and curious then someone is not calm or not creative and vice versa.
Everyone who is either not funny or brave is either wise or not creative and vice versa.
Everyone who is not old or not generous is happy or brave and vice versa.
If someone is not old then susan is either not old or not strong.
If someone is either happy or wise then mary is both funny and not brave.
Someone is strong or curious.
Someone is rich or not tall.
Alice is either brave or not strong.
Someone is either calm or not calm.
Someone is either not wise or not curious. | Susan is tall. | contradiction | (![X]:(creative(X)<=>(tall(X)|~generous(X))))&
(![X]:((~humble(X)|~old(X))=>(~calm(X)|~strong(X))))&
(((~strong(alice)<~>old(alice)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~kind(X)|~wise(X))<=>(~tall(X)|~old(X))))&
(![X]:((humble(X)&generous(X))<=>(~generous(X)|creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~generous(X)&quiet(X))))&
((?[X]:(~curious(X)))<=>((~happy(paul)<~>funny(paul))))&
((?[X]:((old(X)&~curious(X))))=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~brave(X)<~>creative(X))=>tall(X)))&
(![X]:(~creative(X)<=>(~rich(X)&~wise(X))))&
(((generous(john)&curious(john)))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((~funny(X)<~>brave(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~old(X)|~generous(X))<=>(happy(X)|brave(X))))&
((?[X]:(~old(X)))=>((~old(susan)<~>~strong(susan))))&
((?[X]:((happy(X)<~>wise(X))))=>((funny(mary)&~brave(mary))))&
(?[X]:((strong(X)|curious(X))))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
(?[X]:((~wise(X)<~>~curious(X)))) | tall(susan) | [
"p0",
"p3",
"p4",
"p5",
"p9",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5780951732842752872151324
% SZS output start Proof for 5780951732842752872151324
1. ! [X0] : (creative(X0) <=> (~generous(X0) | tall(X0))) [input p0]
4. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> (~old(X0) | ~tall(X0))) [input p3]
5. ! [X0] : ((generous(X0) & humble(X0)) <=> (creative(X0) | ~generous(X0))) [input p4]
6. ! [X0] : ((old(X0) <~> creative(X0)) => (quiet(X0) & ~generous(X0))) [input p5]
10. ! [X0] : ((~brave(X0) <~> creative(X0)) => tall(X0)) [input p9]
11. ! [X0] : (~creative(X0) <=> (~wise(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> (wise(X0) <~> ~creative(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | ~old(X0)) <=> (brave(X0) | happy(X0))) [input p13]
16. ? [X0] : (happy(X0) <~> wise(X0)) => (~brave(mary) & funny(mary)) [input p15]
22. tall(susan) [input hypothesis]
26. ! [X0] : ((quiet(X0) & ~generous(X0)) | (old(X0) <=> creative(X0))) [ennf transformation 6]
28. ! [X0] : (tall(X0) | (~brave(X0) <=> creative(X0))) [ennf transformation 10]
30. (~brave(mary) & funny(mary)) | ! [X0] : (happy(X0) <=> wise(X0)) [ennf transformation 16]
31. ! [X0] : ((creative(X0) | (generous(X0) & ~tall(X0))) & ((~generous(X0) | tall(X0)) | ~creative(X0))) [nnf transformation 1]
32. ! [X0] : ((creative(X0) | (generous(X0) & ~tall(X0))) & (~generous(X0) | tall(X0) | ~creative(X0))) [flattening 31]
37. ! [X0] : (((~wise(X0) | ~kind(X0)) | (old(X0) & tall(X0))) & ((~old(X0) | ~tall(X0)) | (wise(X0) & kind(X0)))) [nnf transformation 4]
38. ! [X0] : ((~wise(X0) | ~kind(X0) | (old(X0) & tall(X0))) & (~old(X0) | ~tall(X0) | (wise(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : (((generous(X0) & humble(X0)) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | (~generous(X0) | ~humble(X0)))) [nnf transformation 5]
40. ! [X0] : (((generous(X0) & humble(X0)) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ~generous(X0) | ~humble(X0))) [flattening 39]
41. ! [X0] : ((quiet(X0) & ~generous(X0)) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) [nnf transformation 26]
50. ! [X0] : (tall(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) [nnf transformation 28]
51. ! [X0] : ((~creative(X0) | (wise(X0) | rich(X0))) & ((~wise(X0) & ~rich(X0)) | creative(X0))) [nnf transformation 11]
52. ! [X0] : ((~creative(X0) | wise(X0) | rich(X0)) & ((~wise(X0) & ~rich(X0)) | creative(X0))) [flattening 51]
58. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | ((wise(X0) | creative(X0)) & (~creative(X0) | ~wise(X0)))) & (((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 13]
59. ! [X0] : (((~generous(X0) | ~old(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (generous(X0) & old(X0)))) [nnf transformation 14]
60. ! [X0] : ((~generous(X0) | ~old(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | (generous(X0) & old(X0)))) [flattening 59]
62. (~brave(mary) & funny(mary)) | ! [X0] : ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))) [nnf transformation 30]
74. ~generous(X0) | tall(X0) | ~creative(X0) [cnf transformation 32]
75. ~tall(X0) | creative(X0) [cnf transformation 32]
76. generous(X0) | creative(X0) [cnf transformation 32]
86. ~old(X0) | ~tall(X0) | wise(X0) [cnf transformation 38]
93. generous(X0) | ~creative(X0) [cnf transformation 40]
95. ~generous(X0) | old(X0) | ~creative(X0) [cnf transformation 41]
112. tall(X0) | creative(X0) | brave(X0) [cnf transformation 50]
115. ~wise(X0) | creative(X0) [cnf transformation 52]
126. brave(X0) | ~funny(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 58]
132. ~generous(X0) | ~old(X0) | ~happy(X0) [cnf transformation 60]
137. funny(mary) | happy(X0) | ~wise(X0) [cnf transformation 62]
139. ~brave(mary) | happy(X0) | ~wise(X0) [cnf transformation 62]
148. tall(susan) [cnf transformation 22]
176. generous(X0) [subsumption resolution 93,76]
178. ~creative(X0) | old(X0) [subsumption resolution 95,176]
212. brave(X0) | creative(X0) [subsumption resolution 112,75]
238. ~wise(X0) | ~funny(X0) | brave(X0) [subsumption resolution 126,115]
241. ~happy(X0) | ~old(X0) [subsumption resolution 132,176]
246. 19 <=> old(susan) [avatar definition]
248. old(susan) <- (19) [avatar component clause 246]
256. 21 <=> ! [X0] : (happy(X0) | ~wise(X0)) [avatar definition]
257. ~wise(X0) | happy(X0) <- (21) [avatar component clause 256]
259. 22 <=> brave(mary) [avatar definition]
261. ~brave(mary) <- (~22) [avatar component clause 259]
262. 21 | ~22 [avatar split clause 139,259,256]
268. 24 <=> funny(mary) [avatar definition]
270. funny(mary) <- (24) [avatar component clause 268]
271. 21 | 24 [avatar split clause 137,268,256]
311. creative(susan) [resolution 75,148]
316. old(susan) [resolution 178,311]
359. creative(mary) <- (~22) [resolution 261,212]
360. old(mary) <- (~22) [resolution 359,178]
363. ~creative(X1) | tall(X1) [resolution 74,176]
421. ~tall(susan) | wise(susan) <- (19) [resolution 86,248]
424. wise(susan) <- (19) [subsumption resolution 421,148]
435. ~tall(mary) | wise(mary) <- (~22) [resolution 360,86]
439. 42 <=> wise(mary) [avatar definition]
441. wise(mary) <- (42) [avatar component clause 439]
443. 43 <=> tall(mary) [avatar definition]
446. 42 | ~43 | 22 [avatar split clause 435,259,443,439]
592. tall(mary) <- (~22) [resolution 363,359]
602. 43 | 22 [avatar split clause 592,259,443]
612. ~funny(mary) | brave(mary) <- (42) [resolution 441,238]
614. brave(mary) <- (24, 42) [subsumption resolution 612,270]
615. $false <- (~22, 24, 42) [subsumption resolution 614,261]
616. 22 | ~24 | ~42 [avatar contradiction clause 615]
631. happy(susan) <- (19, 21) [resolution 257,424]
636. ~old(susan) <- (19, 21) [resolution 631,241]
637. $false <- (19, 21) [subsumption resolution 636,248]
638. ~19 | ~21 [avatar contradiction clause 637]
653. 19 [avatar split clause 316,246]
654. $false [avatar sat refutation 262,271,446,602,616,638,653]
% SZS output end Proof for 5780951732842752872151324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or generous is both tall and not curious and vice versa.
If susan is not happy then someone is either happy or creative.
Everyone who is strong is either not creative or not happy and vice versa.
If someone is kind then someone is calm and vice versa.
Everyone who is either quiet or old is not rich and vice versa.
If someone is both not old and happy then someone is not old or old.
If someone is not old then susan is happy or not curious and vice versa.
Everyone who is creative or old is not funny or not patient and vice versa.
If alice is not patient or curious then john is strong and vice versa.
Everyone who is either funny or generous is rich.
Everyone who is either not humble or not old is old.
Everyone who is either not generous or kind is creative and vice versa.
If someone is not kind then someone is not patient and vice versa.
Everyone who is calm is both not tall and not brave and vice versa.
If paul is both not tall and not strong then someone is not patient.
If someone is curious then alice is either not generous or creative.
Lucy is not strong or brave.
Someone is either not curious or not old.
Susan is either curious or creative.
Fred is either old or humble.
John is both rich and quiet.
Someone is either not quiet or not patient.
Susan is either not curious or calm. | Lucy is strong. | neutral | (![X]:((curious(X)|generous(X))<=>(tall(X)&~curious(X))))&
((~happy(susan))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:(strong(X)<=>(~creative(X)<~>~happy(X))))&
((?[X]:(kind(X)))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)<~>old(X))<=>~rich(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((~old(X)|old(X)))))&
((?[X]:(~old(X)))<=>((happy(susan)|~curious(susan))))&
(![X]:((creative(X)|old(X))<=>(~funny(X)|~patient(X))))&
(((~patient(alice)|curious(alice)))<=>(strong(john)))&
(![X]:((funny(X)<~>generous(X))=>rich(X)))&
(![X]:((~humble(X)<~>~old(X))=>old(X)))&
(![X]:((~generous(X)<~>kind(X))<=>creative(X)))&
((?[X]:(~kind(X)))<=>(?[X]:(~patient(X))))&
(![X]:(calm(X)<=>(~tall(X)&~brave(X))))&
(((~tall(paul)&~strong(paul)))=>(?[X]:(~patient(X))))&
((?[X]:(curious(X)))=>((~generous(alice)<~>creative(alice))))&
((~strong(lucy)|brave(lucy)))&
(?[X]:((~curious(X)<~>~old(X))))&
((curious(susan)<~>creative(susan)))&
((old(fred)<~>humble(fred)))&
((rich(john)&quiet(john)))&
(?[X]:((~quiet(X)<~>~patient(X))))&
((~curious(susan)<~>calm(susan))) | strong(lucy) | [] | null | 0 |
Everyone who is happy or not humble is brave and vice versa.
If fred is not curious or kind then someone is either not rich or not quiet and vice versa.
Everyone who is both not humble and humble is either not humble or funny.
If john is both not curious and brave then someone is either old or curious and vice versa.
If fred is not curious then someone is strong and vice versa.
If someone is both quiet and creative then someone is curious or quiet and vice versa.
If someone is either calm or not kind then mary is not brave or not happy.
If someone is not creative then paul is curious or old.
Everyone who is creative or rich is either humble or quiet and vice versa.
Everyone who is both not kind and kind is curious.
Everyone who is not wise or not quiet is not brave.
Everyone who is both wise and not rich is either rich or not calm and vice versa.
If someone is both strong and happy then paul is tall.
If paul is not kind then someone is strong or kind and vice versa.
Everyone who is creative or not kind is brave and vice versa.
Everyone who is not happy is not brave or not happy and vice versa.
Someone is not brave.
Someone is humble.
Someone is funny.
Someone is not kind or not happy.
Someone is both not generous and not calm.
Someone is calm.
Alice is not kind or not brave. | Mary is happy. | contradiction | (![X]:((happy(X)|~humble(X))<=>brave(X)))&
(((~curious(fred)|kind(fred)))<=>(?[X]:((~rich(X)<~>~quiet(X)))))&
(![X]:((~humble(X)&humble(X))=>(~humble(X)<~>funny(X))))&
(((~curious(john)&brave(john)))<=>(?[X]:((old(X)<~>curious(X)))))&
((~curious(fred))<=>(?[X]:(strong(X))))&
((?[X]:((quiet(X)&creative(X))))<=>(?[X]:((curious(X)|quiet(X)))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~brave(mary)|~happy(mary))))&
((?[X]:(~creative(X)))=>((curious(paul)|old(paul))))&
(![X]:((creative(X)|rich(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((~kind(X)&kind(X))=>curious(X)))&
(![X]:((~wise(X)|~quiet(X))=>~brave(X)))&
(![X]:((wise(X)&~rich(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((strong(X)&happy(X))))=>(tall(paul)))&
((~kind(paul))<=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((creative(X)|~kind(X))<=>brave(X)))&
(![X]:(~happy(X)<=>(~brave(X)|~happy(X))))&
(?[X]:(~brave(X)))&
(?[X]:(humble(X)))&
(?[X]:(funny(X)))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:(calm(X)))&
((~kind(alice)|~brave(alice))) | happy(mary) | [
"p0",
"p6",
"p10",
"p11",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3342540948511582744526644
% SZS output start Proof for 3342540948511582744526644
1. ! [X0] : ((~humble(X0) | happy(X0)) <=> brave(X0)) [input p0]
7. ? [X0] : (calm(X0) <~> ~kind(X0)) => (~happy(mary) | ~brave(mary)) [input p6]
11. ! [X0] : ((~quiet(X0) | ~wise(X0)) => ~brave(X0)) [input p10]
12. ! [X0] : ((~rich(X0) & wise(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p11]
14. ~kind(paul) <=> ? [X0] : (kind(X0) | strong(X0)) [input p13]
15. ! [X0] : ((~kind(X0) | creative(X0)) <=> brave(X0)) [input p14]
21. ? [X0] : (~calm(X0) & ~generous(X0)) [input p20]
24. happy(mary) [input hypothesis]
26. ? [X0] : ~calm(X0) [pure predicate removal 21]
30. (~happy(mary) | ~brave(mary)) | ! [X0] : (calm(X0) <=> ~kind(X0)) [ennf transformation 7]
31. ~happy(mary) | ~brave(mary) | ! [X0] : (calm(X0) <=> ~kind(X0)) [flattening 30]
36. ! [X0] : (~brave(X0) | (quiet(X0) & wise(X0))) [ennf transformation 11]
37. ! [X0] : (((~humble(X0) | happy(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) & ~happy(X0)))) [nnf transformation 1]
38. ! [X0] : ((~humble(X0) | happy(X0) | ~brave(X0)) & (brave(X0) | (humble(X0) & ~happy(X0)))) [flattening 37]
59. ~happy(mary) | ~brave(mary) | ! [X0] : ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0))) [nnf transformation 31]
62. ! [X0] : (((~rich(X0) & wise(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (rich(X0) | ~wise(X0)))) [nnf transformation 12]
63. ! [X0] : (((~rich(X0) & wise(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | rich(X0) | ~wise(X0))) [flattening 62]
64. (~kind(paul) | ! [X0] : (~kind(X0) & ~strong(X0))) & (? [X0] : (kind(X0) | strong(X0)) | kind(paul)) [nnf transformation 14]
65. (~kind(paul) | ! [X0] : (~kind(X0) & ~strong(X0))) & (? [X1] : (kind(X1) | strong(X1)) | kind(paul)) [rectify 64]
66. ? [X1] : (kind(X1) | strong(X1)) => (kind(sK5) | strong(sK5)) [choice axiom]
67. (~kind(paul) | ! [X0] : (~kind(X0) & ~strong(X0))) & ((kind(sK5) | strong(sK5)) | kind(paul)) [skolemisation 65,66]
68. ! [X0] : (((~kind(X0) | creative(X0)) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~creative(X0)))) [nnf transformation 15]
69. ! [X0] : ((~kind(X0) | creative(X0) | ~brave(X0)) & (brave(X0) | (kind(X0) & ~creative(X0)))) [flattening 68]
80. ? [X0] : ~calm(X0) => ~calm(sK10) [choice axiom]
81. ~calm(sK10) [skolemisation 26,80]
84. ~happy(X0) | brave(X0) [cnf transformation 38]
109. ~happy(mary) | ~brave(mary) | calm(X0) | kind(X0) [cnf transformation 59]
118. ~brave(X0) | wise(X0) [cnf transformation 36]
120. ~calm(X0) | rich(X0) | rich(X0) | ~wise(X0) [cnf transformation 63]
124. ~rich(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 63]
128. ~kind(paul) | ~kind(X0) [cnf transformation 67]
130. kind(X0) | brave(X0) [cnf transformation 69]
139. ~calm(sK10) [cnf transformation 81]
142. happy(mary) [cnf transformation 24]
143. ~calm(X0) | rich(X0) | ~wise(X0) [duplicate literal removal 120]
144. ~calm(X0) | ~rich(X0) [duplicate literal removal 124]
242. ~happy(mary) | calm(X0) | kind(X0) [subsumption resolution 109,84]
244. 22 <=> ! [X0] : (calm(X0) | kind(X0)) [avatar definition]
245. calm(X0) | kind(X0) <- (22) [avatar component clause 244]
247. 23 <=> happy(mary) [avatar definition]
250. 22 | ~23 [avatar split clause 242,247,244]
268. ~wise(X0) | ~calm(X0) [subsumption resolution 143,144]
270. 28 <=> ! [X0] : ~kind(X0) [avatar definition]
271. ~kind(X0) <- (28) [avatar component clause 270]
273. 29 <=> kind(paul) [avatar definition]
275. ~kind(paul) <- (~29) [avatar component clause 273]
276. 28 | ~29 [avatar split clause 128,273,270]
305. 23 [avatar split clause 142,247]
306. calm(X0) <- (22, 28) [subsumption resolution 245,271]
316. $false <- (22, 28) [resolution 306,139]
317. ~22 | ~28 [avatar contradiction clause 316]
334. brave(paul) <- (~29) [resolution 130,275]
361. wise(paul) <- (~29) [resolution 334,118]
571. ~calm(paul) <- (~29) [resolution 361,268]
656. kind(paul) <- (22, ~29) [resolution 571,245]
657. $false <- (22, ~29) [subsumption resolution 656,275]
658. ~22 | 29 [avatar contradiction clause 657]
659. $false [avatar sat refutation 250,276,305,317,658]
% SZS output end Proof for 3342540948511582744526644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
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