premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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stringlengths 684
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Everyone who is both quiet and not creative is strong. If someone is patient then someone is either old or generous. Everyone who is rich or funny is happy or not humble and vice versa. If someone is either not rich or brave then someone is either not strong or generous and vice versa. Everyone who is both humble and not funny is either curious or not quiet. If mary is old or tall then lucy is either not generous or tall and vice versa. Everyone who is not happy or kind is creative or generous and vice versa. Everyone who is either not patient or brave is calm or happy. Everyone who is both not strong and curious is not brave and vice versa. Everyone who is quiet or old is rich or old and vice versa. Everyone who is both not wise and not humble is either not tall or not calm. If lucy is not brave or creative then someone is both rich and not calm. Everyone who is not funny or brave is both funny and not quiet. Everyone who is both happy and not happy is curious. Everyone who is not funny or humble is either wise or not humble and vice versa. If someone is brave then lucy is both curious and old. Fred is quiet. Alice is creative or patient. Lucy is creative. Someone is curious. Someone is both rich and tall. Someone is funny or happy. Someone is not wise or old. Lucy is both patient and strong. | Alice is creative. | neutral | (![X]:((quiet(X)&~creative(X))=>strong(X)))&
((?[X]:(patient(X)))=>(?[X]:((old(X)<~>generous(X)))))&
(![X]:((rich(X)|funny(X))<=>(happy(X)|~humble(X))))&
((?[X]:((~rich(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((humble(X)&~funny(X))=>(curious(X)<~>~quiet(X))))&
(((old(mary)|tall(mary)))<=>((~generous(lucy)<~>tall(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(creative(X)|generous(X))))&
(![X]:((~patient(X)<~>brave(X))=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&curious(X))<=>~brave(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)|old(X))))&
(![X]:((~wise(X)&~humble(X))=>(~tall(X)<~>~calm(X))))&
(((~brave(lucy)|creative(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~funny(X)|brave(X))=>(funny(X)&~quiet(X))))&
(![X]:((happy(X)&~happy(X))=>curious(X)))&
(![X]:((~funny(X)|humble(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:(brave(X)))=>((curious(lucy)&old(lucy))))&
(quiet(fred))&
((creative(alice)|patient(alice)))&
(creative(lucy))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:((~wise(X)|old(X))))&
((patient(lucy)&strong(lucy))) | creative(alice) | [] | null | 0 |
Everyone who is not curious or calm is either humble or patient and vice versa. Everyone who is both tall and curious is either calm or humble. Everyone who is strong or not tall is either not rich or generous. If alice is not happy or not funny then someone is calm or not wise. Everyone who is not old or humble is not calm or patient and vice versa. If susan is both wise and funny then john is both strong and generous and vice versa. If someone is both rich and tall then someone is both generous and wise and vice versa. If lucy is not rich or funny then alice is either happy or not generous and vice versa. Everyone who is both not old and not creative is both brave and rich and vice versa. If alice is rich then fred is either not kind or not humble and vice versa. Everyone who is either not old or not kind is either quiet or not wise and vice versa. Everyone who is both kind and not brave is generous and vice versa. Everyone who is both strong and not creative is patient or old and vice versa. If someone is not humble then someone is both quiet and humble and vice versa. If susan is both not brave and not kind then john is not funny. Mary is quiet. Paul is not creative or kind. Alice is not quiet or not old. Someone is either not humble or brave. Lucy is creative or not funny. John is not tall. Paul is happy or not funny. Someone is not happy. | Alice is not tall. | neutral | (![X]:((~curious(X)|calm(X))<=>(humble(X)<~>patient(X))))&
(![X]:((tall(X)&curious(X))=>(calm(X)<~>humble(X))))&
(![X]:((strong(X)|~tall(X))=>(~rich(X)<~>generous(X))))&
(((~happy(alice)|~funny(alice)))=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~old(X)|humble(X))<=>(~calm(X)|patient(X))))&
(((wise(susan)&funny(susan)))<=>((strong(john)&generous(john))))&
((?[X]:((rich(X)&tall(X))))<=>(?[X]:((generous(X)&wise(X)))))&
(((~rich(lucy)|funny(lucy)))<=>((happy(alice)<~>~generous(alice))))&
(![X]:((~old(X)&~creative(X))<=>(brave(X)&rich(X))))&
((rich(alice))<=>((~kind(fred)<~>~humble(fred))))&
(![X]:((~old(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((kind(X)&~brave(X))<=>generous(X)))&
(![X]:((strong(X)&~creative(X))<=>(patient(X)|old(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)&humble(X)))))&
(((~brave(susan)&~kind(susan)))=>(~funny(john)))&
(quiet(mary))&
((~creative(paul)|kind(paul)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((~humble(X)<~>brave(X))))&
((creative(lucy)|~funny(lucy)))&
(~tall(john))&
((happy(paul)|~funny(paul)))&
(?[X]:(~happy(X))) | ~tall(alice) | [] | null | 0 |
If paul is either kind or rich then alice is kind or not generous.
If someone is not brave or quiet then lucy is either not generous or creative and vice versa.
If someone is humble then alice is not brave.
If someone is curious then mary is not old and vice versa.
If john is not strong or not wise then john is either not wise or humble and vice versa.
Everyone who is either creative or not brave is either not brave or not humble.
Everyone who is both not quiet and strong is not kind and vice versa.
If susan is both tall and not creative then someone is creative or not calm and vice versa.
If mary is wise then john is not calm.
If someone is either strong or rich then john is not curious and vice versa.
Everyone who is kind or not quiet is both not kind and strong and vice versa.
If someone is both not humble and tall then someone is curious.
Everyone who is both brave and not creative is both not brave and wise and vice versa.
If someone is either not generous or generous then fred is both not old and not funny.
If someone is either not tall or not brave then mary is curious and vice versa.
Everyone who is both rich and not brave is both rich and not wise and vice versa.
Someone is either wise or not kind.
Someone is not old or not rich.
Someone is both humble and calm.
Someone is curious.
Alice is not curious or kind.
Alice is not brave.
Susan is either not calm or not old. | Mary is calm. | neutral | (((kind(paul)<~>rich(paul)))=>((kind(alice)|~generous(alice))))&
((?[X]:((~brave(X)|quiet(X))))<=>((~generous(lucy)<~>creative(lucy))))&
((?[X]:(humble(X)))=>(~brave(alice)))&
((?[X]:(curious(X)))<=>(~old(mary)))&
(((~strong(john)|~wise(john)))<=>((~wise(john)<~>humble(john))))&
(![X]:((creative(X)<~>~brave(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((~quiet(X)&strong(X))<=>~kind(X)))&
(((tall(susan)&~creative(susan)))<=>(?[X]:((creative(X)|~calm(X)))))&
((wise(mary))=>(~calm(john)))&
((?[X]:((strong(X)<~>rich(X))))<=>(~curious(john)))&
(![X]:((kind(X)|~quiet(X))<=>(~kind(X)&strong(X))))&
((?[X]:((~humble(X)&tall(X))))=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~creative(X))<=>(~brave(X)&wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>((~old(fred)&~funny(fred))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>(curious(mary)))&
(![X]:((rich(X)&~brave(X))<=>(rich(X)&~wise(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((humble(X)&calm(X))))&
(?[X]:(curious(X)))&
((~curious(alice)|kind(alice)))&
(~brave(alice))&
((~calm(susan)<~>~old(susan))) | calm(mary) | [] | null | 0 |
If someone is either generous or kind then someone is generous or not brave and vice versa.
Everyone who is not creative is either calm or not generous and vice versa.
If alice is both not happy and humble then someone is curious.
Everyone who is calm or not humble is both humble and wise and vice versa.
If someone is patient then someone is either not quiet or curious.
Everyone who is generous or not funny is either happy or strong.
Everyone who is either wise or patient is humble or not patient and vice versa.
If paul is both rich and not kind then someone is not creative or wise and vice versa.
Everyone who is generous or calm is not funny and vice versa.
If someone is either not rich or not curious then someone is both generous and curious.
If someone is patient or not curious then lucy is kind and vice versa.
Everyone who is calm or not old is both not curious and not happy.
Everyone who is not quiet or not funny is both wise and not tall and vice versa.
Everyone who is quiet is either tall or not patient and vice versa.
If someone is either happy or not generous then someone is either not old or not generous and vice versa.
If someone is not happy then someone is either calm or curious.
Mary is quiet.
Paul is not humble or brave.
Alice is not wise.
Someone is curious.
Susan is either not happy or not rich. | Alice is humble. | entailment | ((?[X]:((generous(X)<~>kind(X))))<=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:(~creative(X)<=>(calm(X)<~>~generous(X))))&
(((~happy(alice)&humble(alice)))=>(?[X]:(curious(X))))&
(![X]:((calm(X)|~humble(X))<=>(humble(X)&wise(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>curious(X)))))&
(![X]:((generous(X)|~funny(X))=>(happy(X)<~>strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>(humble(X)|~patient(X))))&
(((rich(paul)&~kind(paul)))<=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((generous(X)|calm(X))<=>~funny(X)))&
((?[X]:((~rich(X)<~>~curious(X))))=>(?[X]:((generous(X)&curious(X)))))&
((?[X]:((patient(X)|~curious(X))))<=>(kind(lucy)))&
(![X]:((calm(X)|~old(X))=>(~curious(X)&~happy(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(wise(X)&~tall(X))))&
(![X]:(quiet(X)<=>(tall(X)<~>~patient(X))))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)<~>curious(X)))))&
(quiet(mary))&
((~humble(paul)|brave(paul)))&
(~wise(alice))&
(?[X]:(curious(X)))&
((~happy(susan)<~>~rich(susan))) | humble(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 256492165703615418245093
% SZS output start Proof for 256492165703615418245093
4. ! [X0] : ((~humble(X0) | calm(X0)) <=> (wise(X0) & humble(X0))) [input p3]
22. ~humble(alice) [input hypothesis]
43. ! [X0] : (((~humble(X0) | calm(X0)) | (~wise(X0) | ~humble(X0))) & ((wise(X0) & humble(X0)) | (humble(X0) & ~calm(X0)))) [nnf transformation 4]
44. ! [X0] : ((~humble(X0) | calm(X0) | ~wise(X0) | ~humble(X0)) & ((wise(X0) & humble(X0)) | (humble(X0) & ~calm(X0)))) [flattening 43]
94. humble(X0) | humble(X0) [cnf transformation 44]
154. ~humble(alice) [cnf transformation 22]
157. humble(X0) [duplicate literal removal 94]
344. $false [subsumption resolution 154,157]
% SZS output end Proof for 256492165703615418245093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not humble then susan is strong. If someone is strong then someone is both tall and calm and vice versa. If someone is either creative or not funny then alice is not kind or humble and vice versa. Everyone who is either not funny or not generous is both funny and brave. If lucy is not curious or old then someone is brave or not brave and vice versa. Everyone who is either not happy or tall is both kind and not funny and vice versa. If mary is not calm then someone is either not patient or curious and vice versa. Everyone who is rich or funny is not quiet or old and vice versa. Everyone who is either wise or quiet is both humble and rich and vice versa. If alice is calm or rich then fred is not humble or curious and vice versa. Everyone who is generous or not happy is both tall and wise and vice versa. Everyone who is both not rich and creative is creative or funny. Everyone who is either not quiet or patient is both humble and not tall. Everyone who is brave is not strong and vice versa. If paul is kind then someone is wise. Everyone who is both strong and not kind is patient. Alice is both not rich and not patient. Someone is either strong or quiet. Someone is both not funny and not humble. Someone is either happy or quiet. Susan is creative. Someone is not wise. Alice is creative. | Fred is not humble. | neutral | ((?[X]:((~creative(X)|~humble(X))))=>(strong(susan)))&
((?[X]:(strong(X)))<=>(?[X]:((tall(X)&calm(X)))))&
((?[X]:((creative(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(![X]:((wise(X)<~>quiet(X))<=>(humble(X)&rich(X))))&
(((calm(alice)|rich(alice)))<=>((~humble(fred)|curious(fred))))&
(![X]:((generous(X)|~happy(X))<=>(tall(X)&wise(X))))&
(![X]:((~rich(X)&creative(X))=>(creative(X)|funny(X))))&
(![X]:((~quiet(X)<~>patient(X))=>(humble(X)&~tall(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((kind(paul))=>(?[X]:(wise(X))))&
(![X]:((strong(X)&~kind(X))=>patient(X)))&
((~rich(alice)&~patient(alice)))&
(?[X]:((strong(X)<~>quiet(X))))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((happy(X)<~>quiet(X))))&
(creative(susan))&
(?[X]:(~wise(X)))&
(creative(alice)) | ~humble(fred) | [] | null | 0 |
Everyone who is both not rich and not funny is either old or rich and vice versa.
Everyone who is either happy or not old is either brave or not happy.
If lucy is both not funny and kind then someone is either patient or wise.
If john is either not tall or not quiet then someone is not funny or curious and vice versa.
Everyone who is not brave is patient.
Everyone who is either not kind or generous is either not happy or wise.
Everyone who is both curious and not patient is generous or patient and vice versa.
Everyone who is either not funny or wise is not humble or humble.
Everyone who is not strong is either not generous or not kind and vice versa.
Everyone who is patient is not curious.
Everyone who is both not quiet and curious is not generous or humble and vice versa.
If mary is either happy or not brave then paul is not old.
Everyone who is quiet is not patient or not wise.
Everyone who is either not generous or calm is either patient or not brave and vice versa.
Everyone who is strong is either creative or rich.
Everyone who is strong is brave or calm.
Someone is not rich or creative.
Someone is old or not patient.
Someone is not quiet.
Someone is happy.
John is rich.
Someone is creative. | Paul is not old. | neutral | (![X]:((~rich(X)&~funny(X))<=>(old(X)<~>rich(X))))&
(![X]:((happy(X)<~>~old(X))=>(brave(X)<~>~happy(X))))&
(((~funny(lucy)&kind(lucy)))=>(?[X]:((patient(X)<~>wise(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:(~brave(X)=>patient(X)))&
(![X]:((~kind(X)<~>generous(X))=>(~happy(X)<~>wise(X))))&
(![X]:((curious(X)&~patient(X))<=>(generous(X)|patient(X))))&
(![X]:((~funny(X)<~>wise(X))=>(~humble(X)|humble(X))))&
(![X]:(~strong(X)<=>(~generous(X)<~>~kind(X))))&
(![X]:(patient(X)=>~curious(X)))&
(![X]:((~quiet(X)&curious(X))<=>(~generous(X)|humble(X))))&
(((happy(mary)<~>~brave(mary)))=>(~old(paul)))&
(![X]:(quiet(X)=>(~patient(X)|~wise(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(patient(X)<~>~brave(X))))&
(![X]:(strong(X)=>(creative(X)<~>rich(X))))&
(![X]:(strong(X)=>(brave(X)|calm(X))))&
(?[X]:((~rich(X)|creative(X))))&
(?[X]:((old(X)|~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(happy(X)))&
(rich(john))&
(?[X]:(creative(X))) | ~old(paul) | [] | null | 0 |
Everyone who is either tall or generous is not happy or strong.
Everyone who is brave is both not funny and not kind.
Everyone who is either not patient or patient is both old and not patient and vice versa.
If someone is either not curious or not humble then someone is either generous or humble and vice versa.
If someone is tall then alice is both brave and not humble and vice versa.
If someone is either not tall or not wise then someone is both calm and not curious.
If someone is patient then someone is both not kind and humble and vice versa.
If alice is tall then lucy is either strong or not happy and vice versa.
Everyone who is not funny is kind or generous and vice versa.
Everyone who is both quiet and not happy is either not patient or creative and vice versa.
Everyone who is either generous or happy is not old.
If someone is kind or not funny then someone is either kind or generous.
If alice is not wise then john is either not curious or tall and vice versa.
Everyone who is calm is both tall and curious.
Everyone who is either not happy or old is not strong or rich and vice versa.
Everyone who is not strong or not kind is both generous and patient.
Lucy is either not calm or not humble.
Fred is not rich or calm.
John is both not calm and not generous.
Lucy is not generous or tall.
John is not quiet.
Paul is not brave.
Someone is not patient or old. | Fred is happy. | contradiction | (![X]:((tall(X)<~>generous(X))=>(~happy(X)|strong(X))))&
(![X]:(brave(X)=>(~funny(X)&~kind(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(old(X)&~patient(X))))&
((?[X]:((~curious(X)<~>~humble(X))))<=>(?[X]:((generous(X)<~>humble(X)))))&
((?[X]:(tall(X)))<=>((brave(alice)&~humble(alice))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((calm(X)&~curious(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~kind(X)&humble(X)))))&
((tall(alice))<=>((strong(lucy)<~>~happy(lucy))))&
(![X]:(~funny(X)<=>(kind(X)|generous(X))))&
(![X]:((quiet(X)&~happy(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((generous(X)<~>happy(X))=>~old(X)))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
((~wise(alice))<=>((~curious(john)<~>tall(john))))&
(![X]:(calm(X)=>(tall(X)&curious(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~strong(X)|rich(X))))&
(![X]:((~strong(X)|~kind(X))=>(generous(X)&patient(X))))&
((~calm(lucy)<~>~humble(lucy)))&
((~rich(fred)|calm(fred)))&
((~calm(john)&~generous(john)))&
((~generous(lucy)|tall(lucy)))&
(~quiet(john))&
(~brave(paul))&
(?[X]:((~patient(X)|old(X)))) | happy(fred) | [
"p1",
"p2",
"p4",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6273452276521468835159134
% SZS output start Proof for 6273452276521468835159134
2. ! [X0] : (brave(X0) => (~kind(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> (~patient(X0) & old(X0))) [input p2]
5. ? [X0] : tall(X0) <=> (~humble(alice) & brave(alice)) [input p4]
14. ! [X0] : (calm(X0) => (curious(X0) & tall(X0))) [input p13]
15. ! [X0] : ((~happy(X0) <~> old(X0)) <=> (rich(X0) | ~strong(X0))) [input p14]
16. ! [X0] : ((~kind(X0) | ~strong(X0)) => (patient(X0) & generous(X0))) [input p15]
18. calm(fred) | ~rich(fred) [input p17]
24. happy(fred) [input hypothesis]
31. ! [X0] : ((~kind(X0) & ~funny(X0)) | ~brave(X0)) [ennf transformation 2]
35. ! [X0] : ((curious(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 14]
36. ! [X0] : ((patient(X0) & generous(X0)) | (kind(X0) & strong(X0))) [ennf transformation 16]
38. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 3]
39. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [flattening 38]
45. (? [X0] : tall(X0) | (humble(alice) | ~brave(alice))) & ((~humble(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [nnf transformation 5]
46. (? [X0] : tall(X0) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X0] : ~tall(X0)) [flattening 45]
47. (? [X0] : tall(X0) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [rectify 46]
48. ? [X0] : tall(X0) => tall(sK2) [choice axiom]
49. (tall(sK2) | humble(alice) | ~brave(alice)) & ((~humble(alice) & brave(alice)) | ! [X1] : ~tall(X1)) [skolemisation 47,48]
70. ! [X0] : ((((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0))))) [nnf transformation 15]
71. ! [X0] : ((((~old(X0) | happy(X0)) & (old(X0) | ~happy(X0))) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | ((~happy(X0) | ~old(X0)) & (old(X0) | happy(X0))))) [flattening 70]
78. ~kind(X0) | ~brave(X0) [cnf transformation 31]
79. old(X0) | patient(X0) | patient(X0) [cnf transformation 39]
82. ~patient(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 39]
93. brave(alice) | ~tall(X1) [cnf transformation 49]
126. ~calm(X0) | tall(X0) [cnf transformation 35]
129. rich(X0) | ~strong(X0) | ~happy(X0) | ~old(X0) [cnf transformation 71]
136. patient(X0) | strong(X0) [cnf transformation 36]
137. patient(X0) | kind(X0) [cnf transformation 36]
140. calm(fred) | ~rich(fred) [cnf transformation 18]
147. happy(fred) [cnf transformation 24]
148. old(X0) | patient(X0) [duplicate literal removal 79]
151. ~patient(X0) [duplicate literal removal 82]
154. old(X0) [subsumption resolution 148,151]
192. 9 <=> brave(alice) [avatar definition]
193. brave(alice) <- (9) [avatar component clause 192]
205. 12 <=> ! [X1] : ~tall(X1) [avatar definition]
206. ~tall(X1) <- (12) [avatar component clause 205]
208. 12 | 9 [avatar split clause 93,192,205]
285. ~strong(X0) | rich(X0) | ~happy(X0) [subsumption resolution 129,154]
286. kind(X0) [subsumption resolution 137,151]
287. strong(X0) [subsumption resolution 136,151]
299. 29 <=> rich(fred) [avatar definition]
303. 30 <=> calm(fred) [avatar definition]
305. calm(fred) <- (30) [avatar component clause 303]
306. ~29 | 30 [avatar split clause 140,303,299]
318. ~brave(X0) [resolution 78,286]
319. $false <- (9) [resolution 318,193]
320. ~9 [avatar contradiction clause 319]
340. ~happy(X1) | rich(X1) [resolution 285,287]
343. rich(fred) [resolution 340,147]
347. 29 [avatar split clause 343,299]
350. tall(fred) <- (30) [resolution 305,126]
351. $false <- (12, 30) [subsumption resolution 350,206]
352. ~12 | ~30 [avatar contradiction clause 351]
353. $false [avatar sat refutation 208,306,320,347,352]
% SZS output end Proof for 6273452276521468835159134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Fred is strong. | entailment | ((?[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)))) | strong(fred) | [
"p3",
"p5",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6074386381565248739606063
% SZS output start Proof for 6074386381565248739606063
4. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p3]
6. ! [X0] : ((wise(X0) <~> strong(X0)) <=> ~calm(X0)) [input p5]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p6]
9. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p8]
16. tall(fred) <~> ~wise(fred) [input p15]
21. ~strong(fred) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 4]
32. ! [X0] : ((((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | calm(X0)) & (~calm(X0) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))))) [nnf transformation 6]
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]
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]
54. (wise(fred) | ~tall(fred)) & (~wise(fred) | tall(fred)) [nnf transformation 16]
70. ~tall(X0) | creative(X0) [cnf transformation 26]
76. wise(X0) | strong(X0) | calm(X0) [cnf transformation 32]
78. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 34]
79. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 34]
88. ~calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 38]
89. funny(X0) | funny(X0) [cnf transformation 38]
112. ~wise(fred) | tall(fred) [cnf transformation 54]
120. ~strong(fred) [cnf transformation 21]
121. ~calm(X0) | ~funny(X0) [duplicate literal removal 88]
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]
150. 6 <=> tall(fred) [avatar definition]
152. tall(fred) <- (6) [avatar component clause 150]
159. ~creative(X0) [subsumption resolution 123,124]
180. ~calm(X0) [subsumption resolution 121,122]
200. 14 <=> wise(fred) [avatar definition]
201. ~wise(fred) <- (~14) [avatar component clause 200]
204. 6 | ~14 [avatar split clause 112,200,150]
222. strong(fred) | calm(fred) <- (~14) [resolution 76,201]
226. calm(fred) <- (~14) [subsumption resolution 222,120]
227. $false <- (~14) [subsumption resolution 226,180]
228. 14 [avatar contradiction clause 227]
232. creative(fred) <- (6) [resolution 152,70]
235. $false <- (6) [subsumption resolution 232,159]
236. ~6 [avatar contradiction clause 235]
237. $false [avatar sat refutation 204,228,236]
% SZS output end Proof for 6074386381565248739606063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and creative is not creative and vice versa.
Everyone who is not strong or not creative is both strong and kind and vice versa.
If mary is patient or not humble then mary is both not tall and humble.
Everyone who is quiet is not rich or not patient.
If someone is either not old or tall then alice is both funny and not quiet.
Everyone who is both wise and humble is both not strong and not quiet.
Everyone who is either rich or old is happy or not tall and vice versa.
Everyone who is not funny or patient is either quiet or rich and vice versa.
Everyone who is not funny or happy is either not old or not patient.
If fred is either not calm or kind then john is either rich or not brave and vice versa.
Everyone who is both patient and generous is both not brave and not curious and vice versa.
Everyone who is either not brave or not quiet is both not brave and funny and vice versa.
If someone is either curious or tall then john is either not wise or generous and vice versa.
If john is not kind or creative then someone is both curious and quiet.
Everyone who is either not funny or kind is either patient or quiet.
Someone is brave.
Someone is both generous and tall.
Mary is generous or rich.
Alice is brave.
Someone is both creative and not rich.
Someone is creative. | Alice is not curious. | neutral | (![X]:((~calm(X)&creative(X))<=>~creative(X)))&
(![X]:((~strong(X)|~creative(X))<=>(strong(X)&kind(X))))&
(((patient(mary)|~humble(mary)))=>((~tall(mary)&humble(mary))))&
(![X]:(quiet(X)=>(~rich(X)|~patient(X))))&
((?[X]:((~old(X)<~>tall(X))))=>((funny(alice)&~quiet(alice))))&
(![X]:((wise(X)&humble(X))=>(~strong(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))<=>(happy(X)|~tall(X))))&
(![X]:((~funny(X)|patient(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~funny(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(((~calm(fred)<~>kind(fred)))<=>((rich(john)<~>~brave(john))))&
(![X]:((patient(X)&generous(X))<=>(~brave(X)&~curious(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~brave(X)&funny(X))))&
((?[X]:((curious(X)<~>tall(X))))<=>((~wise(john)<~>generous(john))))&
(((~kind(john)|creative(john)))=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((~funny(X)<~>kind(X))=>(patient(X)<~>quiet(X))))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)&tall(X))))&
((generous(mary)|rich(mary)))&
(brave(alice))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:(creative(X))) | ~curious(alice) | [] | null | 0 |
Everyone who is not humble or kind is curious or not curious and vice versa.
If lucy is both wise and curious then paul is either funny or tall and vice versa.
If paul is not tall or not kind then mary is tall.
Everyone who is either not calm or not old is both not humble and humble and vice versa.
Everyone who is funny is both humble and patient and vice versa.
If alice is not quiet or not happy then alice is either not funny or curious and vice versa.
Everyone who is not old is old.
Everyone who is tall or not happy is either not humble or not happy.
If someone is either curious or quiet then someone is not funny.
Everyone who is either not kind or not patient is both happy and not happy.
Everyone who is both creative and not brave is not brave or not wise.
Everyone who is either curious or generous is not wise or kind and vice versa.
If mary is both not funny and wise then fred is both not wise and not old and vice versa.
If someone is curious then susan is not strong and vice versa.
If someone is both kind and not strong then someone is both not humble and not funny and vice versa.
Everyone who is funny is not curious or not strong.
Mary is generous or not curious.
Paul is both old and generous.
Fred is curious.
Alice is strong.
Someone is patient.
Someone is brave or patient.
Someone is funny or not kind. | Mary is not funny. | neutral | (![X]:((~humble(X)|kind(X))<=>(curious(X)|~curious(X))))&
(((wise(lucy)&curious(lucy)))<=>((funny(paul)<~>tall(paul))))&
(((~tall(paul)|~kind(paul)))=>(tall(mary)))&
(![X]:((~calm(X)<~>~old(X))<=>(~humble(X)&humble(X))))&
(![X]:(funny(X)<=>(humble(X)&patient(X))))&
(((~quiet(alice)|~happy(alice)))<=>((~funny(alice)<~>curious(alice))))&
(![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)|~happy(X))=>(~humble(X)<~>~happy(X))))&
((?[X]:((curious(X)<~>quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>~patient(X))=>(happy(X)&~happy(X))))&
(![X]:((creative(X)&~brave(X))=>(~brave(X)|~wise(X))))&
(![X]:((curious(X)<~>generous(X))<=>(~wise(X)|kind(X))))&
(((~funny(mary)&wise(mary)))<=>((~wise(fred)&~old(fred))))&
((?[X]:(curious(X)))<=>(~strong(susan)))&
((?[X]:((kind(X)&~strong(X))))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:(funny(X)=>(~curious(X)|~strong(X))))&
((generous(mary)|~curious(mary)))&
((old(paul)&generous(paul)))&
(curious(fred))&
(strong(alice))&
(?[X]:(patient(X)))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:((funny(X)|~kind(X)))) | ~funny(mary) | [] | null | 0 |
If john is either brave or not happy then someone is both happy and not generous.
If fred is either funny or rich then alice is wise or generous.
Everyone who is either not funny or strong is either creative or kind and vice versa.
If lucy is both rich and not funny then someone is generous or brave.
If someone is not rich then someone is either not happy or not humble and vice versa.
Everyone who is either humble or not calm is both kind and not rich and vice versa.
Everyone who is either strong or tall is not patient or not humble.
Everyone who is both not humble and not patient is creative.
If someone is either tall or not curious then fred is not generous.
Everyone who is either not quiet or not generous is both creative and kind.
Everyone who is both kind and not calm is either rich or not brave and vice versa.
If lucy is calm or generous then mary is either quiet or not old and vice versa.
Everyone who is both not quiet and not brave is either not wise or not generous.
If john is not creative or not funny then someone is either humble or creative.
Everyone who is either quiet or rich is not curious and vice versa.
If paul is either not quiet or not patient then john is either not curious or strong and vice versa.
Someone is both not funny and patient.
Mary is tall or quiet.
Lucy is both generous and not old.
Paul is happy or quiet.
Alice is both not creative and rich.
Someone is both strong and not old.
Someone is both humble and rich. | John is not happy. | neutral | (((brave(john)<~>~happy(john)))=>(?[X]:((happy(X)&~generous(X)))))&
(((funny(fred)<~>rich(fred)))=>((wise(alice)|generous(alice))))&
(![X]:((~funny(X)<~>strong(X))<=>(creative(X)<~>kind(X))))&
(((rich(lucy)&~funny(lucy)))=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>~calm(X))<=>(kind(X)&~rich(X))))&
(![X]:((strong(X)<~>tall(X))=>(~patient(X)|~humble(X))))&
(![X]:((~humble(X)&~patient(X))=>creative(X)))&
((?[X]:((tall(X)<~>~curious(X))))=>(~generous(fred)))&
(![X]:((~quiet(X)<~>~generous(X))=>(creative(X)&kind(X))))&
(![X]:((kind(X)&~calm(X))<=>(rich(X)<~>~brave(X))))&
(((calm(lucy)|generous(lucy)))<=>((quiet(mary)<~>~old(mary))))&
(![X]:((~quiet(X)&~brave(X))=>(~wise(X)<~>~generous(X))))&
(((~creative(john)|~funny(john)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~curious(X)))&
(((~quiet(paul)<~>~patient(paul)))<=>((~curious(john)<~>strong(john))))&
(?[X]:((~funny(X)&patient(X))))&
((tall(mary)|quiet(mary)))&
((generous(lucy)&~old(lucy)))&
((happy(paul)|quiet(paul)))&
((~creative(alice)&rich(alice)))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:((humble(X)&rich(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is either not brave or old is not humble.
If someone 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.
If someone is both funny and quiet then fred is not kind or not calm.
Everyone who is both not quiet and not rich is not wise.
If someone is quiet or brave then mary is happy or rich.
If mary is not wise or not curious then someone is not creative.
Everyone who is not funny or old is both quiet and creative.
If someone is not curious then someone is both not creative and wise.
Everyone who is either not creative or old is not calm or not quiet.
Someone is rich.
Mary is not kind or not happy.
Someone is both kind and funny.
Someone is both brave and not old.
Someone is not curious.
Alice is kind.
Someone is either brave or patient. | Alice is not calm. | entailment | (![X]:((~brave(X)<~>old(X))=>~humble(X)))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(?[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]:((funny(X)&quiet(X))))=>((~kind(fred)|~calm(fred))))&
(![X]:((~quiet(X)&~rich(X))=>~wise(X)))&
((?[X]:((quiet(X)|brave(X))))=>((happy(mary)|rich(mary))))&
(((~wise(mary)|~curious(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)|old(X))=>(quiet(X)&creative(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:((~creative(X)<~>old(X))=>(~calm(X)|~quiet(X))))&
(?[X]:(rich(X)))&
((~kind(mary)|~happy(mary)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:(~curious(X)))&
(kind(alice))&
(?[X]:((brave(X)<~>patient(X)))) | ~calm(alice) | [
"p2",
"p7",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 344272004383052436243472
% SZS output start Proof for 344272004383052436243472
3. ! [X0] : ((tall(X0) | ~old(X0)) <=> (~calm(X0) & happy(X0))) [input p2]
8. ~quiet(alice) <=> ? [X0] : (wise(X0) | patient(X0)) [input p7]
14. ! [X0] : ((old(X0) | ~funny(X0)) => (creative(X0) & quiet(X0))) [input p13]
15. ? [X0] : ~curious(X0) => ? [X0] : (wise(X0) & ~creative(X0)) [input p14]
21. ? [X0] : ~curious(X0) [input p20]
24. calm(alice) [input hypothesis]
27. ? [X0] : ~curious(X0) => ? [X1] : (wise(X1) & ~creative(X1)) [rectify 15]
39. ! [X0] : ((creative(X0) & quiet(X0)) | (~old(X0) & funny(X0))) [ennf transformation 14]
40. ? [X1] : (wise(X1) & ~creative(X1)) | ! [X0] : curious(X0) [ennf transformation 27]
49. ! [X0] : (((tall(X0) | ~old(X0)) | (calm(X0) | ~happy(X0))) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [nnf transformation 3]
50. ! [X0] : ((tall(X0) | ~old(X0) | calm(X0) | ~happy(X0)) & ((~calm(X0) & happy(X0)) | (~tall(X0) & old(X0)))) [flattening 49]
59. (~quiet(alice) | ! [X0] : (~wise(X0) & ~patient(X0))) & (? [X0] : (wise(X0) | patient(X0)) | quiet(alice)) [nnf transformation 8]
60. (~quiet(alice) | ! [X0] : (~wise(X0) & ~patient(X0))) & (? [X1] : (wise(X1) | patient(X1)) | quiet(alice)) [rectify 59]
61. ? [X1] : (wise(X1) | patient(X1)) => (wise(sK4) | patient(sK4)) [choice axiom]
62. (~quiet(alice) | ! [X0] : (~wise(X0) & ~patient(X0))) & ((wise(sK4) | patient(sK4)) | quiet(alice)) [skolemisation 60,61]
68. ? [X0] : (wise(X0) & ~creative(X0)) | ! [X1] : curious(X1) [rectify 40]
69. ? [X0] : (wise(X0) & ~creative(X0)) => (wise(sK7) & ~creative(sK7)) [choice axiom]
70. (wise(sK7) & ~creative(sK7)) | ! [X1] : curious(X1) [skolemisation 68,69]
78. ? [X0] : ~curious(X0) => ~curious(sK11) [choice axiom]
79. ~curious(sK11) [skolemisation 21,78]
93. ~calm(X0) | old(X0) [cnf transformation 50]
108. ~quiet(alice) | ~wise(X0) [cnf transformation 62]
118. ~old(X0) | quiet(X0) [cnf transformation 39]
122. wise(sK7) | curious(X1) [cnf transformation 70]
131. ~curious(sK11) [cnf transformation 79]
135. calm(alice) [cnf transformation 24]
172. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
173. ~wise(X0) <- (8) [avatar component clause 172]
175. 9 <=> quiet(alice) [avatar definition]
177. ~quiet(alice) <- (~9) [avatar component clause 175]
178. 8 | ~9 [avatar split clause 108,175,172]
235. 23 <=> ! [X1] : curious(X1) [avatar definition]
236. curious(X1) <- (23) [avatar component clause 235]
238. 24 <=> wise(sK7) [avatar definition]
240. wise(sK7) <- (24) [avatar component clause 238]
241. 23 | 24 [avatar split clause 122,238,235]
269. $false <- (23) [resolution 236,131]
270. ~23 [avatar contradiction clause 269]
271. $false <- (8, 24) [subsumption resolution 240,173]
272. ~8 | ~24 [avatar contradiction clause 271]
275. old(alice) [resolution 93,135]
277. quiet(alice) [resolution 118,275]
278. $false <- (~9) [subsumption resolution 277,177]
279. 9 [avatar contradiction clause 278]
280. $false [avatar sat refutation 178,241,270,272,279]
% SZS output end Proof for 344272004383052436243472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either rich or not humble then fred is both not kind and not tall and vice versa. If susan is generous then someone is both not funny and funny and vice versa. If someone is quiet or not kind then paul is both funny and not funny. If susan is not old then someone is not old or happy and vice versa. If someone is either tall or not kind then fred is either not patient or rich. Everyone who is both not creative and tall is not generous. Everyone who is tall is both brave and rich. Everyone who is both patient and not quiet is humble and vice versa. Everyone who is either kind or not kind is strong or not old and vice versa. If alice is wise or humble then someone is not funny or patient and vice versa. Everyone who is not old or not strong is both not funny and not generous and vice versa. If paul is not creative or wise then someone is quiet. Everyone who is both generous and not strong is both calm and brave. Everyone who is either old or not kind is tall and vice versa. If someone is either old or curious then someone is not happy and vice versa. Everyone who is both not strong and funny is not humble and vice versa. Someone is either brave or not humble. Susan is not tall or curious. Someone is rich or quiet. Fred is either wise or not calm. Someone is not quiet or not generous. | Alice is not kind. | contradiction | (((rich(lucy)<~>~humble(lucy)))<=>((~kind(fred)&~tall(fred))))&
((generous(susan))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((quiet(X)|~kind(X))))=>((funny(paul)&~funny(paul))))&
((~old(susan))<=>(?[X]:((~old(X)|happy(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>((~patient(fred)<~>rich(fred))))&
(![X]:((~creative(X)&tall(X))=>~generous(X)))&
(![X]:(tall(X)=>(brave(X)&rich(X))))&
(![X]:((patient(X)&~quiet(X))<=>humble(X)))&
(![X]:((kind(X)<~>~kind(X))<=>(strong(X)|~old(X))))&
(((wise(alice)|humble(alice)))<=>(?[X]:((~funny(X)|patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~funny(X)&~generous(X))))&
(((~creative(paul)|wise(paul)))=>(?[X]:(quiet(X))))&
(![X]:((generous(X)&~strong(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)<~>~kind(X))<=>tall(X)))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)&funny(X))<=>~humble(X)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~tall(susan)|curious(susan)))&
(?[X]:((rich(X)|quiet(X))))&
((wise(fred)<~>~calm(fred)))&
(?[X]:((~quiet(X)|~generous(X)))) | ~kind(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4464135426108719300108113
% SZS output start Proof for 4464135426108719300108113
3. ? [X0] : (~kind(X0) | quiet(X0)) => (~funny(paul) & funny(paul)) [input p2]
22. ~kind(alice) [input hypothesis]
26. (~funny(paul) & funny(paul)) | ! [X0] : (kind(X0) & ~quiet(X0)) [ennf transformation 3]
82. funny(paul) | kind(X0) [cnf transformation 26]
84. ~funny(paul) | kind(X0) [cnf transformation 26]
133. ~kind(alice) [cnf transformation 22]
169. 7 <=> ! [X0] : kind(X0) [avatar definition]
170. kind(X0) <- (7) [avatar component clause 169]
172. 8 <=> funny(paul) [avatar definition]
175. 7 | ~8 [avatar split clause 84,172,169]
180. 7 | 8 [avatar split clause 82,172,169]
332. $false <- (7) [resolution 170,133]
333. ~7 [avatar contradiction clause 332]
334. $false [avatar sat refutation 175,180,333]
% SZS output end Proof for 4464135426108719300108113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or happy then john is both curious and not happy.
Everyone who is not wise or generous is generous or not kind and vice versa.
If susan is not quiet or not humble then john is brave or humble.
If mary is both not humble and not patient then lucy is calm.
If someone is either quiet or tall then someone is either not quiet or brave and vice versa.
Everyone who is either funny or not funny is both funny and not rich and vice versa.
Everyone who is happy is not strong.
If someone is both humble and generous then susan is funny.
If someone is either rich or strong then someone is funny.
If susan is not kind then alice is not kind or not quiet.
If susan is both not humble and funny then someone is not funny or generous and vice versa.
If someone is not kind then someone is either not happy or calm and vice versa.
Everyone who is both not quiet and not generous is patient or not quiet and vice versa.
If someone is either not brave or generous then someone is rich.
Everyone who is not creative is creative or not generous and vice versa.
Everyone who is both not wise and not strong is both rich and happy.
Someone is either creative or wise.
Someone is either calm or not generous.
Susan is either not patient or not rich.
Paul is calm or not happy.
Fred is not patient or funny.
Someone is wise or strong. | Alice is brave. | entailment | ((?[X]:((curious(X)|happy(X))))=>((curious(john)&~happy(john))))&
(![X]:((~wise(X)|generous(X))<=>(generous(X)|~kind(X))))&
(((~quiet(susan)|~humble(susan)))=>((brave(john)|humble(john))))&
(((~humble(mary)&~patient(mary)))=>(calm(lucy)))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
(![X]:((funny(X)<~>~funny(X))<=>(funny(X)&~rich(X))))&
(![X]:(happy(X)=>~strong(X)))&
((?[X]:((humble(X)&generous(X))))=>(funny(susan)))&
((?[X]:((rich(X)<~>strong(X))))=>(?[X]:(funny(X))))&
((~kind(susan))=>((~kind(alice)|~quiet(alice))))&
(((~humble(susan)&funny(susan)))<=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(patient(X)|~quiet(X))))&
((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:(rich(X))))&
(![X]:(~creative(X)<=>(creative(X)|~generous(X))))&
(![X]:((~wise(X)&~strong(X))=>(rich(X)&happy(X))))&
(?[X]:((creative(X)<~>wise(X))))&
(?[X]:((calm(X)<~>~generous(X))))&
((~patient(susan)<~>~rich(susan)))&
((calm(paul)|~happy(paul)))&
((~patient(fred)|funny(fred)))&
(?[X]:((wise(X)|strong(X)))) | brave(alice) | [
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5889886743584461011621228
% SZS output start Proof for 5889886743584461011621228
6. ! [X0] : ((funny(X0) <~> ~funny(X0)) <=> (~rich(X0) & funny(X0))) [input p5]
14. ? [X0] : (~brave(X0) <~> generous(X0)) => ? [X0] : rich(X0) [input p13]
15. ! [X0] : (~creative(X0) <=> (~generous(X0) | creative(X0))) [input p14]
23. ~brave(alice) [input hypothesis]
27. ? [X0] : (~brave(X0) <~> generous(X0)) => ? [X1] : rich(X1) [rectify 14]
38. ? [X1] : rich(X1) | ! [X0] : (~brave(X0) <=> generous(X0)) [ennf transformation 27]
48. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | (rich(X0) | ~funny(X0))) & ((~rich(X0) & funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [nnf transformation 6]
49. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | rich(X0) | ~funny(X0)) & ((~rich(X0) & funny(X0)) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [flattening 48]
66. ? [X1] : rich(X1) | ! [X0] : ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))) [nnf transformation 38]
67. ? [X0] : rich(X0) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1))) [rectify 66]
68. ? [X0] : rich(X0) => rich(sK6) [choice axiom]
69. rich(sK6) | ! [X1] : ((~brave(X1) | ~generous(X1)) & (generous(X1) | brave(X1))) [skolemisation 67,68]
70. ! [X0] : ((~creative(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | creative(X0))) [nnf transformation 15]
71. ! [X0] : ((~creative(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | creative(X0))) [flattening 70]
102. ~rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 49]
103. ~rich(X0) | funny(X0) | funny(X0) [cnf transformation 49]
125. rich(sK6) | generous(X1) | brave(X1) [cnf transformation 69]
127. ~generous(X0) | creative(X0) | creative(X0) [cnf transformation 71]
128. ~creative(X0) | ~creative(X0) [cnf transformation 71]
141. ~brave(alice) [cnf transformation 23]
142. ~generous(X0) | creative(X0) [duplicate literal removal 127]
143. ~creative(X0) [duplicate literal removal 128]
146. ~rich(X0) | ~funny(X0) [duplicate literal removal 102]
147. ~rich(X0) | funny(X0) [duplicate literal removal 103]
235. ~rich(X0) [subsumption resolution 146,147]
250. 23 <=> ! [X0] : ~generous(X0) [avatar definition]
251. ~generous(X0) <- (23) [avatar component clause 250]
286. brave(X1) | generous(X1) [subsumption resolution 125,235]
287. ~generous(X0) [subsumption resolution 142,143]
288. 23 [avatar split clause 287,250]
315. generous(alice) [resolution 286,141]
318. $false <- (23) [subsumption resolution 315,251]
319. ~23 [avatar contradiction clause 318]
322. $false [avatar sat refutation 288,319]
% SZS output end Proof for 5889886743584461011621228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then lucy is both strong and rich.
Everyone who is both not old and rich is both not tall and not kind.
If someone is both humble and patient then susan is both not quiet and curious and vice versa.
Everyone who is both not generous and not humble is either happy or calm and vice versa.
Everyone who is either strong or funny is rich.
Everyone who is not brave is generous or quiet.
If lucy is either old or generous then paul is both wise and not rich and vice versa.
Everyone who is both patient and not humble is not wise or not curious.
Everyone who is not creative is either generous or wise.
If lucy is not patient or not strong then paul is both not kind and not brave and vice versa.
If someone is not funny or not happy then someone is both not generous and not strong and vice versa.
Everyone who is not kind or not calm is either rich or not creative and vice versa.
Everyone who is patient or not strong is funny or humble.
Everyone who is not rich or not brave is not humble or not generous and vice versa.
If john is old or not kind then someone is not patient.
If susan is kind or rich then someone is creative and vice versa.
John is both not humble and not happy.
Mary is tall.
Someone is both not rich and not wise.
Fred is either patient or not funny.
Paul is either happy or not happy.
Someone is both not wise and calm.
John is not quiet or not patient.
Mary is both humble and happy. | Mary is calm. | entailment | ((?[X]:(funny(X)))=>((strong(lucy)&rich(lucy))))&
(![X]:((~old(X)&rich(X))=>(~tall(X)&~kind(X))))&
((?[X]:((humble(X)&patient(X))))<=>((~quiet(susan)&curious(susan))))&
(![X]:((~generous(X)&~humble(X))<=>(happy(X)<~>calm(X))))&
(![X]:((strong(X)<~>funny(X))=>rich(X)))&
(![X]:(~brave(X)=>(generous(X)|quiet(X))))&
(((old(lucy)<~>generous(lucy)))<=>((wise(paul)&~rich(paul))))&
(![X]:((patient(X)&~humble(X))=>(~wise(X)|~curious(X))))&
(![X]:(~creative(X)=>(generous(X)<~>wise(X))))&
(((~patient(lucy)|~strong(lucy)))<=>((~kind(paul)&~brave(paul))))&
((?[X]:((~funny(X)|~happy(X))))<=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((patient(X)|~strong(X))=>(funny(X)|humble(X))))&
(![X]:((~rich(X)|~brave(X))<=>(~humble(X)|~generous(X))))&
(((old(john)|~kind(john)))=>(?[X]:(~patient(X))))&
(((kind(susan)|rich(susan)))<=>(?[X]:(creative(X))))&
((~humble(john)&~happy(john)))&
(tall(mary))&
(?[X]:((~rich(X)&~wise(X))))&
((patient(fred)<~>~funny(fred)))&
((happy(paul)<~>~happy(paul)))&
(?[X]:((~wise(X)&calm(X))))&
((~quiet(john)|~patient(john)))&
((humble(mary)&happy(mary))) | calm(mary) | [
"p3",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7557936544811585032588650
% SZS output start Proof for 7557936544811585032588650
4. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (happy(X0) <~> calm(X0))) [input p3]
24. happy(mary) & humble(mary) [input p23]
25. ~calm(mary) [input hypothesis]
44. ! [X0] : (((~humble(X0) & ~generous(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (humble(X0) | generous(X0)))) [nnf transformation 4]
45. ! [X0] : (((~humble(X0) & ~generous(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | humble(X0) | generous(X0))) [flattening 44]
86. ~happy(X0) | calm(X0) | ~humble(X0) [cnf transformation 45]
139. humble(mary) [cnf transformation 24]
140. happy(mary) [cnf transformation 24]
141. ~calm(mary) [cnf transformation 25]
320. calm(mary) | ~humble(mary) [resolution 86,140]
321. ~humble(mary) [subsumption resolution 320,141]
322. $false [subsumption resolution 321,139]
% SZS output end Proof for 7557936544811585032588650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not kind is either rich or not creative and vice versa.
Everyone who is not brave is happy or not rich and vice versa.
If susan is both humble and not strong then paul is both not rich and not curious and vice versa.
Everyone who is rich or quiet is not old or brave and vice versa.
Everyone who is either not quiet or kind is either creative or not calm and vice versa.
Everyone who is tall is not quiet.
If john is either not quiet or not rich then alice is either tall or calm.
If someone is funny or creative then paul is not generous and vice versa.
If someone is both brave and not calm then lucy is both quiet and not strong.
If john is either rich or wise then mary is not generous.
If someone is calm or not generous then someone is kind or wise.
Everyone who is either patient or not old is not wise or not calm and vice versa.
If lucy is not rich then mary is curious or not funny and vice versa.
If susan is both not calm and brave then someone is either not creative or not humble and vice versa.
Everyone who is not generous or not strong is both rich and not curious.
Everyone who is both not tall and not brave is not tall.
Lucy is not funny.
Someone is not patient or quiet.
Someone is both strong and happy.
Susan is both not tall and patient.
Someone is either brave or curious.
Fred is brave or not funny.
Someone is rich or not humble. | Alice is not humble. | neutral | (![X]:((generous(X)<~>~kind(X))<=>(rich(X)<~>~creative(X))))&
(![X]:(~brave(X)<=>(happy(X)|~rich(X))))&
(((humble(susan)&~strong(susan)))<=>((~rich(paul)&~curious(paul))))&
(![X]:((rich(X)|quiet(X))<=>(~old(X)|brave(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(creative(X)<~>~calm(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(((~quiet(john)<~>~rich(john)))=>((tall(alice)<~>calm(alice))))&
((?[X]:((funny(X)|creative(X))))<=>(~generous(paul)))&
((?[X]:((brave(X)&~calm(X))))=>((quiet(lucy)&~strong(lucy))))&
(((rich(john)<~>wise(john)))=>(~generous(mary)))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((patient(X)<~>~old(X))<=>(~wise(X)|~calm(X))))&
((~rich(lucy))<=>((curious(mary)|~funny(mary))))&
(((~calm(susan)&brave(susan)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~generous(X)|~strong(X))=>(rich(X)&~curious(X))))&
(![X]:((~tall(X)&~brave(X))=>~tall(X)))&
(~funny(lucy))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((strong(X)&happy(X))))&
((~tall(susan)&patient(susan)))&
(?[X]:((brave(X)<~>curious(X))))&
((brave(fred)|~funny(fred)))&
(?[X]:((rich(X)|~humble(X)))) | ~humble(alice) | [] | null | 0 |
If lucy is either not generous or not strong then someone is calm. Everyone who is old is happy 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. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Someone is either not rich or not patient. John is kind. Someone is not patient or not humble. Someone is both not funny and humble. Lucy is either not wise or brave. Someone is not old. Someone is either not tall or kind. Mary is both not curious and not creative. | Alice is not funny. | entailment | (((~generous(lucy)<~>~strong(lucy)))=>(?[X]:(calm(X))))&
(![X]:(old(X)<=>happy(X)))&
((?[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]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(?[X]:((~rich(X)<~>~patient(X))))&
(kind(john))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((~funny(X)&humble(X))))&
((~wise(lucy)<~>brave(lucy)))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)<~>kind(X))))&
((~curious(mary)&~creative(mary))) | ~funny(alice) | [
"p1",
"p7",
"p8",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5610523374549071215669239
% SZS output start Proof for 5610523374549071215669239
2. ! [X0] : (old(X0) <=> happy(X0)) [input p1]
8. ! [X0] : (creative(X0) <=> rich(X0)) [input p7]
9. rich(alice) <=> (~happy(mary) & patient(mary)) [input p8]
15. ! [X0] : ((creative(X0) <~> ~happy(X0)) => (happy(X0) | old(X0))) [input p14]
16. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p15]
24. ~creative(mary) & ~curious(mary) [input p23]
25. funny(alice) [input hypothesis]
38. ! [X0] : ((happy(X0) | old(X0)) | (creative(X0) <=> ~happy(X0))) [ennf transformation 15]
39. ! [X0] : (happy(X0) | old(X0) | (creative(X0) <=> ~happy(X0))) [flattening 38]
43. ! [X0] : ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))) [nnf transformation 2]
50. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 8]
51. (rich(alice) | (happy(mary) | ~patient(mary))) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [nnf transformation 9]
52. (rich(alice) | happy(mary) | ~patient(mary)) & ((~happy(mary) & patient(mary)) | ~rich(alice)) [flattening 51]
59. ! [X0] : (happy(X0) | old(X0) | ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) [nnf transformation 39]
60. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 16]
61. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 60]
77. ~old(X0) | happy(X0) [cnf transformation 43]
78. ~happy(X0) | old(X0) [cnf transformation 43]
93. ~creative(X0) | rich(X0) [cnf transformation 50]
96. ~happy(mary) | ~rich(alice) [cnf transformation 52]
114. happy(X0) | old(X0) | creative(X0) | happy(X0) [cnf transformation 59]
119. ~funny(X0) | ~happy(X0) [cnf transformation 61]
132. ~creative(mary) [cnf transformation 24]
133. funny(alice) [cnf transformation 25]
134. happy(X0) | old(X0) | creative(X0) [duplicate literal removal 114]
155. 5 <=> happy(mary) [avatar definition]
159. 6 <=> rich(alice) [avatar definition]
160. ~rich(alice) <- (~6) [avatar component clause 159]
163. ~6 | ~5 [avatar split clause 96,155,159]
179. creative(X0) | old(X0) [subsumption resolution 134,78]
224. ~happy(alice) [resolution 119,133]
225. old(mary) [resolution 179,132]
226. rich(X0) | old(X0) [resolution 179,93]
227. happy(mary) [resolution 225,77]
228. 5 [avatar split clause 227,155]
232. old(alice) <- (~6) [resolution 226,160]
234. happy(alice) <- (~6) [resolution 232,77]
235. $false <- (~6) [subsumption resolution 234,224]
236. 6 [avatar contradiction clause 235]
237. $false [avatar sat refutation 163,228,236]
% SZS output end Proof for 5610523374549071215669239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet then john is either not old or brave and vice versa. If someone is both kind and patient then someone is not funny or wise and vice versa. Everyone who is not strong is both not old and patient and vice versa. Everyone who is not strong is calm and vice versa. If alice is both not brave and not tall then someone is creative or brave. Everyone who is either humble or generous is old. If john is both old and not calm then mary is both not funny and not old and vice versa. If alice is rich or not rich then alice is both humble and not quiet. Everyone who is either brave or not strong is both calm and brave and vice versa. Everyone who is either patient or quiet is not humble or not tall and vice versa. Everyone who is either not creative or not happy is either quiet or not creative. Everyone who is humble or patient is either rich or not brave. If alice is not old then fred is not kind or tall. If john is not patient or brave then mary is not funny and vice versa. Everyone who is not funny is creative or not kind and vice versa. If someone is quiet then someone is not calm or old. Fred is both rich and not kind. Mary is both curious and happy. Susan is not curious. Paul is either not quiet or not tall. John is both quiet and kind. Mary is curious or brave. | Alice is kind. | neutral | ((~quiet(john))<=>((~old(john)<~>brave(john))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|old(X)))))&
((rich(fred)&~kind(fred)))&
((curious(mary)&happy(mary)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((quiet(john)&kind(john)))&
((curious(mary)|brave(mary))) | kind(alice) | [] | null | 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Mary is not generous. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~generous(mary) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9136943802870318198549633
% SZS output start Proof for 9136943802870318198549633
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p1]
3. ? [X0] : ~old(X0) <=> ~calm(susan) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) => ~curious(X0)) [input p3]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
8. ? [X0] : brave(X0) <=> (~rich(fred) & kind(fred)) [input p7]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> old(X0)) => (humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (~strong(X0) => brave(X0)) [input p11]
21. ~generous(mary) [input hypothesis]
22. ! [X0] : (~curious(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> generous(X0)) | (~creative(X0) <=> old(X0))) [ennf transformation 10]
24. ! [X0] : (brave(X0) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
30. ! [X0] : (((~humble(X0) | ~curious(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | ~curious(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [flattening 30]
32. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X0] : old(X0)) [nnf transformation 3]
33. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [rectify 32]
34. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
35. (~old(sK0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [skolemisation 33,34]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
45. (? [X0] : brave(X0) | (rich(fred) | ~kind(fred))) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
46. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
49. (brave(sK2) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 23]
66. brave(X0) | generous(X0) | rich(X0) [cnf transformation 29]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
68. brave(X0) | calm(X0) | rich(X0) [cnf transformation 29]
70. ~creative(X0) | ~calm(X0) | curious(X0) [cnf transformation 31]
76. ~calm(susan) | old(X1) [cnf transformation 35]
77. ~old(sK0) | calm(susan) [cnf transformation 35]
78. ~strong(X0) | ~curious(X0) [cnf transformation 22]
80. old(X0) | humble(X0) | brave(X0) | rich(X0) [cnf transformation 37]
83. ~old(X0) | ~rich(X0) | brave(X0) [cnf transformation 37]
85. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
97. kind(fred) | ~brave(X1) [cnf transformation 49]
98. ~rich(fred) | ~brave(X1) [cnf transformation 49]
99. brave(sK2) | rich(fred) | ~kind(fred) [cnf transformation 49]
101. ~funny(X0) | old(X0) [cnf transformation 51]
102. ~brave(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~generous(X0) | old(X0) | creative(X0) [cnf transformation 52]
113. strong(X0) | brave(X0) [cnf transformation 24]
132. ~generous(mary) [cnf transformation 21]
134. 1 <=> calm(susan) [avatar definition]
138. 2 <=> old(sK0) [avatar definition]
140. ~old(sK0) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 77,138,134]
143. 3 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (3) [avatar component clause 143]
145. 3 | ~1 [avatar split clause 76,134,143]
151. 5 <=> generous(mary) [avatar definition]
152. ~generous(mary) <- (~5) [avatar component clause 151]
175. 10 <=> kind(fred) [avatar definition]
179. 11 <=> rich(fred) [avatar definition]
183. 12 <=> brave(sK2) [avatar definition]
185. brave(sK2) <- (12) [avatar component clause 183]
186. ~10 | 11 | 12 [avatar split clause 99,183,179,175]
188. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (13) [avatar component clause 188]
190. 13 | ~11 [avatar split clause 98,179,188]
191. 13 | 10 [avatar split clause 97,175,188]
265. ~5 [avatar split clause 132,151]
273. old(sK2) <- (12) [resolution 102,185]
274. ~curious(X0) | brave(X0) [resolution 113,78]
288. ~rich(sK2) | generous(sK2) <- (12) [resolution 67,185]
292. ~rich(sK2) <- (12) [subsumption resolution 288,87]
343. rich(sK2) | ~brave(sK2) <- (12) [resolution 85,273]
350. ~brave(sK2) <- (12) [subsumption resolution 343,292]
351. $false <- (12) [subsumption resolution 350,185]
352. ~12 [avatar contradiction clause 351]
357. rich(X0) | calm(X0) <- (13) [resolution 189,68]
358. rich(X1) | generous(X1) <- (13) [resolution 189,66]
434. humble(sK0) | brave(sK0) | rich(sK0) <- (~2) [resolution 80,140]
441. humble(sK0) | rich(sK0) <- (~2, 13) [subsumption resolution 434,189]
443. 40 <=> rich(sK0) [avatar definition]
444. ~rich(sK0) <- (~40) [avatar component clause 443]
445. rich(sK0) <- (40) [avatar component clause 443]
447. 41 <=> humble(sK0) [avatar definition]
449. humble(sK0) <- (41) [avatar component clause 447]
450. 40 | 41 | 2 | ~13 [avatar split clause 441,188,138,447,443]
454. funny(sK0) <- (40) [resolution 445,88]
458. 42 <=> generous(sK0) [avatar definition]
459. generous(sK0) <- (42) [avatar component clause 458]
462. 43 <=> calm(sK0) [avatar definition]
463. calm(sK0) <- (43) [avatar component clause 462]
481. old(sK0) <- (40) [resolution 454,101]
482. $false <- (~2, 40) [subsumption resolution 481,140]
483. 2 | ~40 [avatar contradiction clause 482]
511. ~generous(sK0) | old(sK0) | creative(sK0) <- (41) [resolution 449,105]
527. 50 <=> curious(sK0) [avatar definition]
528. ~curious(sK0) <- (~50) [avatar component clause 527]
529. curious(sK0) <- (50) [avatar component clause 527]
590. calm(sK0) <- (13, ~40) [resolution 357,444]
593. 43 | ~13 | 40 [avatar split clause 590,443,188,462]
599. generous(sK0) <- (13, ~40) [resolution 358,444]
606. 42 | ~13 | 40 [avatar split clause 599,443,188,458]
607. ~generous(sK0) | creative(sK0) <- (~2, 41) [subsumption resolution 511,140]
611. creative(sK0) <- (~2, 41, 42) [subsumption resolution 607,459]
642. brave(sK0) <- (50) [resolution 529,274]
644. $false <- (13, 50) [subsumption resolution 642,189]
645. ~13 | ~50 [avatar contradiction clause 644]
733. ~calm(sK0) | curious(sK0) <- (~2, 41, 42) [resolution 611,70]
734. curious(sK0) <- (~2, 41, 42, 43) [subsumption resolution 733,463]
735. $false <- (~2, 41, 42, 43, ~50) [subsumption resolution 734,528]
736. 2 | ~41 | ~42 | ~43 | 50 [avatar contradiction clause 735]
747. ~rich(X4) | brave(X4) <- (3) [resolution 144,83]
750. ~rich(X4) <- (3, 13) [subsumption resolution 747,189]
755. generous(X0) <- (3, 13) [resolution 750,358]
767. $false <- (3, ~5, 13) [resolution 755,152]
768. ~3 | 5 | ~13 [avatar contradiction clause 767]
769. $false [avatar sat refutation 141,145,186,190,191,265,352,450,483,593,606,645,736,768]
% SZS output end Proof for 9136943802870318198549633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not happy is not creative or not tall and vice versa. Everyone who is either not rich or strong is not brave and vice versa. Everyone who is not calm is both not rich and not wise. If paul is rich or wise then susan is calm or not quiet. If paul is both tall and not curious then paul is strong or not generous. If someone is both not strong and not quiet then someone is both not creative and not quiet. If lucy is not humble then someone is not old or tall and vice versa. If susan is either patient or kind then paul is both curious and funny. If john is not funny then someone is either curious or tall. Everyone who is either not strong or not kind is not funny and vice versa. If someone is either not patient or not funny then lucy is not humble and vice versa. Everyone who is brave is not tall and vice versa. If someone is not funny then someone is brave. Everyone who is not generous is curious or funny. Everyone who is kind is happy. If susan is not patient or not brave then someone is either not old or not humble and vice versa. Someone is either not tall or not creative. Someone is both not happy and not humble. Fred is not creative. Susan is not calm. John is not wise or not funny. Someone is not rich or wise. Mary is either not happy or not humble. | John is wise. | neutral | (![X]:((~kind(X)&~happy(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>~brave(X)))&
(![X]:(~calm(X)=>(~rich(X)&~wise(X))))&
(((rich(paul)|wise(paul)))=>((calm(susan)|~quiet(susan))))&
(((tall(paul)&~curious(paul)))=>((strong(paul)|~generous(paul))))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
((~humble(lucy))<=>(?[X]:((~old(X)|tall(X)))))&
(((patient(susan)<~>kind(susan)))=>((curious(paul)&funny(paul))))&
((~funny(john))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~strong(X)<~>~kind(X))<=>~funny(X)))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(~humble(lucy)))&
(![X]:(brave(X)<=>~tall(X)))&
((?[X]:(~funny(X)))=>(?[X]:(brave(X))))&
(![X]:(~generous(X)=>(curious(X)|funny(X))))&
(![X]:(kind(X)=>happy(X)))&
(((~patient(susan)|~brave(susan)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((~happy(X)&~humble(X))))&
(~creative(fred))&
(~calm(susan))&
((~wise(john)|~funny(john)))&
(?[X]:((~rich(X)|wise(X))))&
((~happy(mary)<~>~humble(mary))) | wise(john) | [] | null | 0 |
If someone is generous or not brave then someone is either creative or curious.
If mary is not happy or funny then someone is both not rich and not creative.
If john is wise then someone is tall.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
If someone is not old or not creative then someone is not quiet or wise.
Everyone who is both not old and tall is not tall.
Everyone who is curious is both not old and not tall and vice versa.
If mary is not funny then mary is either not rich or creative and vice versa.
Someone is not curious.
Paul is either not generous or funny.
Susan is happy.
Someone is not quiet or not generous.
Someone is either not rich or brave.
Someone is creative or not wise.
Someone is both humble and not quiet. | Fred is not funny. | entailment | ((?[X]:((generous(X)|~brave(X))))=>(?[X]:((creative(X)<~>curious(X)))))&
(((~happy(mary)|funny(mary)))=>(?[X]:((~rich(X)&~creative(X)))))&
((wise(john))=>(?[X]:(tall(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((~old(X)&tall(X))=>~tall(X)))&
(![X]:(curious(X)<=>(~old(X)&~tall(X))))&
((~funny(mary))<=>((~rich(mary)<~>creative(mary))))&
(?[X]:(~curious(X)))&
((~generous(paul)<~>funny(paul)))&
(happy(susan))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((humble(X)&~quiet(X)))) | ~funny(fred) | [
"p3",
"p5",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2499729625763202582308409
% SZS output start Proof for 2499729625763202582308409
4. ! [X0] : ((funny(X0) | curious(X0)) => (rich(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p5]
8. ? [X0] : (~quiet(X0) | ~curious(X0)) => rich(fred) [input p7]
11. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p10]
17. ? [X0] : ~curious(X0) [input p16]
24. funny(fred) [input hypothesis]
32. ! [X0] : ((rich(X0) <~> quiet(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 6]
36. rich(fred) | ! [X0] : (quiet(X0) & curious(X0)) [ennf transformation 8]
38. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 11]
50. ! [X0] : (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 32]
52. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 34]
58. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 38]
69. ? [X0] : ~curious(X0) => ~curious(sK6) [choice axiom]
70. ~curious(sK6) [skolemisation 17,69]
93. ~quiet(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 50]
96. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 52]
97. ~patient(X0) | brave(X0) | quiet(X0) [cnf transformation 52]
104. rich(fred) | curious(X0) [cnf transformation 36]
113. ~funny(X0) | brave(X0) | patient(X0) [cnf transformation 58]
114. ~patient(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 58]
133. ~curious(sK6) [cnf transformation 70]
142. funny(fred) [cnf transformation 24]
208. 15 <=> rich(fred) [avatar definition]
213. 16 <=> ! [X0] : curious(X0) [avatar definition]
214. curious(X0) <- (16) [avatar component clause 213]
215. 16 | 15 [avatar split clause 104,208,213]
217. 17 <=> brave(fred) [avatar definition]
218. ~brave(fred) <- (~17) [avatar component clause 217]
219. brave(fred) <- (17) [avatar component clause 217]
365. brave(fred) | patient(fred) [resolution 113,142]
367. 43 <=> patient(fred) [avatar definition]
369. patient(fred) <- (43) [avatar component clause 367]
370. 43 | 17 [avatar split clause 365,217,367]
371. patient(fred) | quiet(fred) <- (17) [resolution 219,96]
373. 44 <=> quiet(fred) [avatar definition]
374. ~quiet(fred) <- (~44) [avatar component clause 373]
375. quiet(fred) <- (44) [avatar component clause 373]
376. 44 | 43 | ~17 [avatar split clause 371,217,367,373]
377. ~brave(fred) | ~funny(fred) <- (43) [resolution 369,114]
379. ~funny(fred) <- (17, 43) [subsumption resolution 377,219]
380. $false <- (17, 43) [subsumption resolution 379,142]
381. ~17 | ~43 [avatar contradiction clause 380]
385. ~rich(fred) | ~funny(fred) <- (44) [resolution 375,93]
396. ~rich(fred) <- (44) [subsumption resolution 385,142]
397. ~15 | ~44 [avatar split clause 396,373,208]
413. $false <- (16) [resolution 214,133]
414. ~16 [avatar contradiction clause 413]
419. brave(fred) | quiet(fred) <- (43) [resolution 369,97]
420. quiet(fred) <- (~17, 43) [subsumption resolution 419,218]
421. $false <- (~17, 43, ~44) [subsumption resolution 420,374]
422. 17 | ~43 | 44 [avatar contradiction clause 421]
423. $false [avatar sat refutation 215,370,376,381,397,414,422]
% SZS output end Proof for 2499729625763202582308409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not wise and not kind then paul is either not curious or old. If someone is either funny or not strong then lucy is both humble and calm and vice versa. If john is both brave and not brave then alice is either not wise or not tall and vice versa. If someone is curious or not kind then john is not kind or not happy. Everyone who is both creative and not wise is either not brave or not patient and vice versa. Everyone who is both rich and kind is calm or patient and vice versa. If someone is both not calm and not curious then susan is not quiet or tall. If fred is curious then paul is not tall. Everyone who is either wise or curious is not funny or tall. Everyone who is both not old and not strong is either tall or brave. If someone is either not wise or not curious then paul is not creative. Everyone who is either not kind or patient is both patient and calm and vice versa. Everyone who is not patient is both tall and not funny and vice versa. Everyone who is either not humble or calm is both not curious and not creative and vice versa. Everyone who is not curious or not patient is either not wise or not quiet. Everyone who is not creative or not humble is either not quiet or wise and vice versa. Someone is either brave or generous. Alice is not patient or not tall. Someone is not rich. Someone is either strong or funny. Alice is generous or wise. John is either brave or creative. | Lucy is humble. | neutral | (((~wise(john)&~kind(john)))=>((~curious(paul)<~>old(paul))))&
((?[X]:((funny(X)<~>~strong(X))))<=>((humble(lucy)&calm(lucy))))&
(((brave(john)&~brave(john)))<=>((~wise(alice)<~>~tall(alice))))&
((?[X]:((curious(X)|~kind(X))))=>((~kind(john)|~happy(john))))&
(![X]:((creative(X)&~wise(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:((rich(X)&kind(X))<=>(calm(X)|patient(X))))&
((?[X]:((~calm(X)&~curious(X))))=>((~quiet(susan)|tall(susan))))&
((curious(fred))=>(~tall(paul)))&
(![X]:((wise(X)<~>curious(X))=>(~funny(X)|tall(X))))&
(![X]:((~old(X)&~strong(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~wise(X)<~>~curious(X))))=>(~creative(paul)))&
(![X]:((~kind(X)<~>patient(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(tall(X)&~funny(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~curious(X)&~creative(X))))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~creative(X)|~humble(X))<=>(~quiet(X)<~>wise(X))))&
(?[X]:((brave(X)<~>generous(X))))&
((~patient(alice)|~tall(alice)))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)<~>funny(X))))&
((generous(alice)|wise(alice)))&
((brave(john)<~>creative(john))) | humble(lucy) | [] | null | 0 |
If lucy is not creative or not humble then john is not curious and vice versa. If paul is quiet then someone is both kind and not strong. If john is both not old and not patient then lucy is either rich or not wise. If someone is not funny or not creative then someone is both not kind and not rich. Everyone who is both tall and happy is patient and vice versa. Everyone who is either humble or tall is not old or not happy and vice versa. If someone is either generous or old then susan is both not patient and brave and vice versa. If lucy is not patient or patient then someone is either tall or not wise and vice versa. If john is either not rich or rich then someone is tall or not patient and vice versa. Everyone who is either not patient or not tall is not kind and vice versa. Everyone who is rich is both not patient and not kind and vice versa. If someone is rich or not patient then someone is either not wise or not rich and vice versa. If someone is either happy or not patient then paul is not rich and vice versa. Everyone who is not kind is either not old or tall and vice versa. Everyone who is either wise or creative is not funny. Paul is both wise and not quiet. Lucy is curious or funny. Someone is both quiet and funny. Someone is not calm or calm. | Paul is rich. | contradiction | (((~creative(lucy)|~humble(lucy)))<=>(~curious(john)))&
((quiet(paul))=>(?[X]:((kind(X)&~strong(X)))))&
(((~old(john)&~patient(john)))=>((rich(lucy)<~>~wise(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((tall(X)&happy(X))<=>patient(X)))&
(![X]:((humble(X)<~>tall(X))<=>(~old(X)|~happy(X))))&
((?[X]:((generous(X)<~>old(X))))<=>((~patient(susan)&brave(susan))))&
(((~patient(lucy)|patient(lucy)))<=>(?[X]:((tall(X)<~>~wise(X)))))&
(((~rich(john)<~>rich(john)))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>~kind(X)))&
(![X]:(rich(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~rich(paul)))&
(![X]:(~kind(X)<=>(~old(X)<~>tall(X))))&
(![X]:((wise(X)<~>creative(X))=>~funny(X)))&
((wise(paul)&~quiet(paul)))&
((curious(lucy)|funny(lucy)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((~calm(X)|calm(X)))) | rich(paul) | [
"p4",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3700969317578904886436253
% SZS output start Proof for 3700969317578904886436253
5. ! [X0] : ((happy(X0) & tall(X0)) <=> patient(X0)) [input p4]
10. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> ~kind(X0)) [input p9]
11. ! [X0] : (rich(X0) <=> (~kind(X0) & ~patient(X0))) [input p10]
13. ? [X0] : (happy(X0) <~> ~patient(X0)) <=> ~rich(paul) [input p12]
20. rich(paul) [input hypothesis]
37. ! [X0] : (((happy(X0) & tall(X0)) | ~patient(X0)) & (patient(X0) | (~happy(X0) | ~tall(X0)))) [nnf transformation 5]
38. ! [X0] : (((happy(X0) & tall(X0)) | ~patient(X0)) & (patient(X0) | ~happy(X0) | ~tall(X0))) [flattening 37]
55. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | kind(X0)) & (~kind(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 10]
56. ! [X0] : ((rich(X0) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | ~rich(X0))) [nnf transformation 11]
57. ! [X0] : ((rich(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | ~rich(X0))) [flattening 56]
63. (? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | rich(paul)) & (~rich(paul) | ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) [nnf transformation 13]
64. (? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | rich(paul)) & (~rich(paul) | ! [X1] : ((happy(X1) | patient(X1)) & (~patient(X1) | ~happy(X1)))) [rectify 63]
65. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) => ((patient(sK7) | ~happy(sK7)) & (~patient(sK7) | happy(sK7))) [choice axiom]
66. (((patient(sK7) | ~happy(sK7)) & (~patient(sK7) | happy(sK7))) | rich(paul)) & (~rich(paul) | ! [X1] : ((happy(X1) | patient(X1)) & (~patient(X1) | ~happy(X1)))) [skolemisation 64,65]
83. ~happy(X0) | patient(X0) | ~tall(X0) [cnf transformation 38]
84. ~patient(X0) | tall(X0) [cnf transformation 38]
85. ~patient(X0) | happy(X0) [cnf transformation 38]
113. tall(X0) | patient(X0) | kind(X0) [cnf transformation 55]
115. ~rich(X0) | ~kind(X0) [cnf transformation 57]
123. ~rich(paul) | ~patient(X1) | ~happy(X1) [cnf transformation 66]
124. ~rich(paul) | happy(X1) | patient(X1) [cnf transformation 66]
139. rich(paul) [cnf transformation 20]
246. tall(X0) | kind(X0) [subsumption resolution 113,84]
282. 30 <=> rich(paul) [avatar definition]
284. rich(paul) <- (30) [avatar component clause 282]
294. ~rich(paul) | happy(X1) [subsumption resolution 124,85]
296. 33 <=> ! [X1] : happy(X1) [avatar definition]
297. happy(X1) <- (33) [avatar component clause 296]
298. 33 | ~30 [avatar split clause 294,282,296]
299. ~rich(paul) | ~patient(X1) [subsumption resolution 123,85]
301. 34 <=> ! [X1] : ~patient(X1) [avatar definition]
302. ~patient(X1) <- (34) [avatar component clause 301]
303. 34 | ~30 [avatar split clause 299,282,301]
316. 30 [avatar split clause 139,282]
318. ~kind(paul) <- (30) [resolution 115,284]
331. patient(X0) | ~tall(X0) <- (33) [resolution 83,297]
332. ~tall(X0) <- (33, 34) [subsumption resolution 331,302]
336. kind(X2) <- (33, 34) [resolution 332,246]
340. $false <- (30, 33, 34) [resolution 336,318]
341. ~30 | ~33 | ~34 [avatar contradiction clause 340]
342. $false [avatar sat refutation 298,303,316,341]
% SZS output end Proof for 3700969317578904886436253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or calm is both quiet and happy. Everyone who is either patient or not happy is not generous or strong and vice versa. Everyone who is either funny or not humble is rich. If someone is not strong then someone is not quiet or old and vice versa. If john is either not strong or rich then someone is old and vice versa. Everyone who is both generous and not old is both not humble and not generous and vice versa. If paul is both calm and not calm then someone is not calm. If someone is either generous or not quiet then susan is creative. If lucy is not quiet or not generous then someone is not funny or not humble. If fred is either strong or quiet then someone is either not strong or not patient. If someone is both funny and not humble then someone is either humble or generous. If lucy is generous then someone is both calm and funny. Everyone who is not strong is strong. If someone is tall or not calm then susan is not patient or old and vice versa. Everyone who is not kind is rich and vice versa. If lucy is both not old and not strong then someone is both calm and strong. Someone is humble or strong. Someone is creative or strong. Someone is not rich or funny. Susan is not creative or not generous. Someone is rich or not old. | Susan is strong. | entailment | (![X]:((~curious(X)|calm(X))=>(quiet(X)&happy(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(~generous(X)|strong(X))))&
(![X]:((funny(X)<~>~humble(X))=>rich(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~quiet(X)|old(X)))))&
(((~strong(john)<~>rich(john)))<=>(?[X]:(old(X))))&
(![X]:((generous(X)&~old(X))<=>(~humble(X)&~generous(X))))&
(((calm(paul)&~calm(paul)))=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(creative(susan)))&
(((~quiet(lucy)|~generous(lucy)))=>(?[X]:((~funny(X)|~humble(X)))))&
(((strong(fred)<~>quiet(fred)))=>(?[X]:((~strong(X)<~>~patient(X)))))&
((?[X]:((funny(X)&~humble(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((generous(lucy))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((tall(X)|~calm(X))))<=>((~patient(susan)|old(susan))))&
(![X]:(~kind(X)<=>rich(X)))&
(((~old(lucy)&~strong(lucy)))=>(?[X]:((calm(X)&strong(X)))))&
(?[X]:((humble(X)|strong(X))))&
(?[X]:((creative(X)|strong(X))))&
(?[X]:((~rich(X)|funny(X))))&
((~creative(susan)|~generous(susan)))&
(?[X]:((rich(X)|~old(X)))) | strong(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1081509760462259965263780
% SZS output start Proof for 1081509760462259965263780
13. ! [X0] : (~strong(X0) => strong(X0)) [input p12]
22. ~strong(susan) [input hypothesis]
35. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 13]
115. strong(X0) | strong(X0) [cnf transformation 35]
127. ~strong(susan) [cnf transformation 22]
128. strong(X0) [duplicate literal removal 115]
144. 4 <=> ! [X3] : strong(X3) [avatar definition]
145. strong(X3) <- (4) [avatar component clause 144]
243. 4 [avatar split clause 128,144]
331. $false <- (4) [resolution 145,127]
332. ~4 [avatar contradiction clause 331]
333. $false [avatar sat refutation 243,332]
% SZS output end Proof for 1081509760462259965263780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not humble or calm then someone is either not strong or not happy and vice versa.
If someone is either not curious or not old then someone is either not wise or tall.
Everyone who is both not funny and rich is both not old and brave.
Everyone who is both humble and curious is both not calm and brave and vice versa.
Everyone who is curious or quiet is humble and vice versa.
Everyone who is patient is not strong.
Everyone who is either not patient or curious is either patient or quiet.
If paul is tall then someone is both patient and not quiet and vice versa.
Everyone who is not quiet or rich is both not humble and not quiet.
Everyone who is creative or not generous is kind or tall.
If alice is kind or patient then someone is not brave.
Everyone who is either quiet or old is both not funny and brave.
If someone is not tall or quiet then someone is both not generous and not funny.
Everyone who is both not kind and old is either not patient or not happy and vice versa.
Everyone who is not rich is not humble or not strong.
If someone is either not rich or not strong then someone is both curious and happy and vice versa.
Alice is patient.
Someone is kind.
Fred is happy or patient.
Someone is both not old and not rich.
Someone is not patient.
Lucy is not curious or creative.
Alice is both brave and not quiet.
Someone is either not tall or not quiet. | Lucy is humble. | neutral | (((~humble(lucy)<~>calm(lucy)))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:((~wise(X)<~>tall(X)))))&
(![X]:((~funny(X)&rich(X))=>(~old(X)&brave(X))))&
(![X]:((humble(X)&curious(X))<=>(~calm(X)&brave(X))))&
(![X]:((curious(X)|quiet(X))<=>humble(X)))&
(![X]:(patient(X)=>~strong(X)))&
(![X]:((~patient(X)<~>curious(X))=>(patient(X)<~>quiet(X))))&
((tall(paul))<=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((~quiet(X)|rich(X))=>(~humble(X)&~quiet(X))))&
(![X]:((creative(X)|~generous(X))=>(kind(X)|tall(X))))&
(((kind(alice)|patient(alice)))=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)<~>old(X))=>(~funny(X)&brave(X))))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((~kind(X)&old(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:(~rich(X)=>(~humble(X)|~strong(X))))&
((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:((curious(X)&happy(X)))))&
(patient(alice))&
(?[X]:(kind(X)))&
((happy(fred)|patient(fred)))&
(?[X]:((~old(X)&~rich(X))))&
(?[X]:(~patient(X)))&
((~curious(lucy)|creative(lucy)))&
((brave(alice)&~quiet(alice)))&
(?[X]:((~tall(X)<~>~quiet(X)))) | humble(lucy) | [] | null | 0 |
Everyone who is either not tall or strong is both strong and not kind and vice versa.
If mary is creative then mary is both brave and strong.
Everyone who is not old or humble is quiet and vice versa.
Everyone who is funny or tall is both not tall and kind.
If someone is both not rich and not wise then alice is curious or not generous and vice versa.
Everyone who is both creative and patient is both patient and not curious.
Everyone who is both happy and creative is curious and vice versa.
If paul is funny or not brave then someone is both creative and not wise.
Everyone who is not funny is either not creative or humble and vice versa.
If susan is rich or not curious then someone is both not tall and not rich.
If mary is either not brave or humble then alice is old and vice versa.
If alice is either old or creative then someone is not quiet and vice versa.
Everyone who is not funny or patient is not calm and vice versa.
Everyone who is both not old and not creative is not tall and vice versa.
Everyone who is not rich is either old or humble.
Someone is not happy.
Paul is not humble or quiet.
Someone is not patient or quiet.
Alice is curious or not calm.
Someone is happy.
Mary is both brave and not patient.
Someone is patient.
Someone is not patient. | Mary is not rich. | contradiction | (![X]:((~tall(X)<~>strong(X))<=>(strong(X)&~kind(X))))&
((creative(mary))=>((brave(mary)&strong(mary))))&
(![X]:((~old(X)|humble(X))<=>quiet(X)))&
(![X]:((funny(X)|tall(X))=>(~tall(X)&kind(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>((curious(alice)|~generous(alice))))&
(![X]:((creative(X)&patient(X))=>(patient(X)&~curious(X))))&
(![X]:((happy(X)&creative(X))<=>curious(X)))&
(((funny(paul)|~brave(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:(~funny(X)<=>(~creative(X)<~>humble(X))))&
(((rich(susan)|~curious(susan)))=>(?[X]:((~tall(X)&~rich(X)))))&
(((~brave(mary)<~>humble(mary)))<=>(old(alice)))&
(((old(alice)<~>creative(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((~funny(X)|patient(X))<=>~calm(X)))&
(![X]:((~old(X)&~creative(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(old(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((~humble(paul)|quiet(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
((curious(alice)|~calm(alice)))&
(?[X]:(happy(X)))&
((brave(mary)&~patient(mary)))&
(?[X]:(patient(X)))&
(?[X]:(~patient(X))) | ~rich(mary) | [
"p3",
"p10",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5630491755885624098759632
% SZS output start Proof for 5630491755885624098759632
4. ! [X0] : ((tall(X0) | funny(X0)) => (kind(X0) & ~tall(X0))) [input p3]
11. (~brave(mary) <~> humble(mary)) <=> old(alice) [input p10]
14. ! [X0] : ((~creative(X0) & ~old(X0)) <=> ~tall(X0)) [input p13]
15. ! [X0] : (~rich(X0) => (old(X0) <~> humble(X0))) [input p14]
21. ~patient(mary) & brave(mary) [input p20]
24. ~rich(mary) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~tall(X0)) | (~tall(X0) & ~funny(X0))) [ennf transformation 4]
36. ! [X0] : ((old(X0) <~> humble(X0)) | rich(X0)) [ennf transformation 15]
53. (((~humble(mary) | brave(mary)) & (humble(mary) | ~brave(mary))) | ~old(alice)) & (old(alice) | ((~brave(mary) | ~humble(mary)) & (humble(mary) | brave(mary)))) [nnf transformation 11]
58. ! [X0] : (((~creative(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) | old(X0)))) [nnf transformation 14]
59. ! [X0] : (((~creative(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | creative(X0) | old(X0))) [flattening 58]
60. ! [X0] : (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | rich(X0)) [nnf transformation 36]
83. ~tall(X0) | ~tall(X0) [cnf transformation 28]
107. old(alice) | ~brave(mary) | ~humble(mary) [cnf transformation 53]
116. ~old(X0) | tall(X0) [cnf transformation 59]
118. humble(X0) | old(X0) | rich(X0) [cnf transformation 60]
125. brave(mary) [cnf transformation 21]
129. ~rich(mary) [cnf transformation 24]
130. ~tall(X0) [duplicate literal removal 83]
143. 3 <=> brave(mary) [avatar definition]
206. 16 <=> old(alice) [avatar definition]
207. old(alice) <- (16) [avatar component clause 206]
210. 17 <=> humble(mary) [avatar definition]
212. ~humble(mary) <- (~17) [avatar component clause 210]
215. ~17 | ~3 | 16 [avatar split clause 107,206,143,210]
233. ~old(X0) [subsumption resolution 116,130]
234. rich(X0) | humble(X0) [subsumption resolution 118,233]
249. 3 [avatar split clause 125,143]
250. $false <- (16) [subsumption resolution 207,233]
251. ~16 [avatar contradiction clause 250]
256. humble(mary) [resolution 234,129]
259. $false <- (~17) [subsumption resolution 256,212]
260. 17 [avatar contradiction clause 259]
261. $false [avatar sat refutation 215,249,251,260]
% SZS output end Proof for 5630491755885624098759632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not creative or curious then paul is either not kind or not curious.
Everyone who is not quiet or generous is both not creative and not wise and vice versa.
Everyone who is not quiet is calm.
Everyone who is either not patient or funny is both not old and humble and vice versa.
If alice is not kind or funny then susan is creative.
Everyone who is both generous and not wise is both not tall and brave and vice versa.
Everyone who is either not creative or not kind is not calm or patient.
If someone is not generous or wise then paul is old and vice versa.
If someone is both not rich and not calm then someone is both not rich and happy.
If someone is both kind and not humble then someone is brave or calm.
Everyone who is generous is both not patient and funny and vice versa.
Everyone who is either not rich or curious is curious or not generous.
Everyone who is not curious or not generous is both not tall and not kind.
Everyone who is both not strong and not humble is not kind.
Everyone who is not old or brave is curious.
Everyone who is both not calm and brave is patient and vice versa.
Alice is not wise or not funny.
Someone is not generous or not brave.
Alice is old.
Someone is not old or not humble.
Alice is either kind or old.
Someone is not kind.
John is either wise or creative. | Susan is not kind. | entailment | (((~creative(mary)|curious(mary)))=>((~kind(paul)<~>~curious(paul))))&
(![X]:((~quiet(X)|generous(X))<=>(~creative(X)&~wise(X))))&
(![X]:(~quiet(X)=>calm(X)))&
(![X]:((~patient(X)<~>funny(X))<=>(~old(X)&humble(X))))&
(((~kind(alice)|funny(alice)))=>(creative(susan)))&
(![X]:((generous(X)&~wise(X))<=>(~tall(X)&brave(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(~calm(X)|patient(X))))&
((?[X]:((~generous(X)|wise(X))))<=>(old(paul)))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((~rich(X)&happy(X)))))&
((?[X]:((kind(X)&~humble(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:(generous(X)<=>(~patient(X)&funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>(curious(X)|~generous(X))))&
(![X]:((~curious(X)|~generous(X))=>(~tall(X)&~kind(X))))&
(![X]:((~strong(X)&~humble(X))=>~kind(X)))&
(![X]:((~old(X)|brave(X))=>curious(X)))&
(![X]:((~calm(X)&brave(X))<=>patient(X)))&
((~wise(alice)|~funny(alice)))&
(?[X]:((~generous(X)|~brave(X))))&
(old(alice))&
(?[X]:((~old(X)|~humble(X))))&
((kind(alice)<~>old(alice)))&
(?[X]:(~kind(X)))&
((wise(john)<~>creative(john))) | ~kind(susan) | [
"p1",
"p4",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2119614327321587044392387
% SZS output start Proof for 2119614327321587044392387
2. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (~wise(X0) & ~creative(X0))) [input p1]
5. (funny(alice) | ~kind(alice)) => creative(susan) [input p4]
13. ! [X0] : ((~generous(X0) | ~curious(X0)) => (~kind(X0) & ~tall(X0))) [input p12]
19. old(alice) [input p18]
21. kind(alice) <~> old(alice) [input p20]
24. kind(susan) [input hypothesis]
31. creative(susan) | (~funny(alice) & kind(alice)) [ennf transformation 5]
38. ! [X0] : ((~kind(X0) & ~tall(X0)) | (generous(X0) & curious(X0))) [ennf transformation 13]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | (wise(X0) | creative(X0))) & ((~wise(X0) & ~creative(X0)) | (~generous(X0) & quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | wise(X0) | creative(X0)) & ((~wise(X0) & ~creative(X0)) | (~generous(X0) & quiet(X0)))) [flattening 41]
67. (~old(alice) | ~kind(alice)) & (old(alice) | kind(alice)) [nnf transformation 21]
76. ~generous(X0) | ~creative(X0) [cnf transformation 42]
87. creative(susan) | kind(alice) [cnf transformation 31]
108. ~kind(X0) | generous(X0) [cnf transformation 38]
116. old(alice) [cnf transformation 19]
119. ~old(alice) | ~kind(alice) [cnf transformation 67]
123. kind(susan) [cnf transformation 24]
150. 6 <=> creative(susan) [avatar definition]
152. creative(susan) <- (6) [avatar component clause 150]
155. 7 <=> kind(alice) [avatar definition]
158. 7 | 6 [avatar split clause 87,150,155]
215. ~kind(alice) [subsumption resolution 119,116]
216. ~7 [avatar split clause 215,155]
236. generous(susan) [resolution 108,123]
239. ~creative(susan) [resolution 236,76]
240. $false <- (6) [subsumption resolution 239,152]
241. ~6 [avatar contradiction clause 240]
242. $false [avatar sat refutation 158,216,241]
% SZS output end Proof for 2119614327321587044392387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is wise or quiet then someone is either generous or kind.
If fred is either not brave or strong then john is not happy or curious.
Everyone who is both funny and not strong is not strong or happy and vice versa.
If paul is either tall or not patient then susan is both not funny and creative.
Everyone who is not rich or calm is both happy and humble.
If paul is both funny and not rich then someone is not creative and vice versa.
Everyone who is either not quiet or not calm is either rich or strong and vice versa.
Everyone who is not strong or not generous is not quiet and vice versa.
Everyone who is not patient or brave is happy or funny.
Everyone who is not rich or brave is either not calm or humble.
If someone is funny or not generous then susan is both brave and not wise.
If lucy is calm or not patient then someone is humble.
If someone is both rich and old then john is either not quiet or curious.
Everyone who is both quiet and not brave is either not rich or not happy and vice versa.
Everyone who is both not rich and strong is not rich or not brave and vice versa.
If someone is happy then paul is either not creative or happy.
Someone is creative or happy.
Someone is not quiet or generous.
Someone is not tall.
Susan is rich.
John is generous.
Fred is not patient.
Someone is either not strong or quiet.
Lucy is not strong or generous. | Paul is rich. | entailment | (((wise(mary)|quiet(mary)))=>(?[X]:((generous(X)<~>kind(X)))))&
(((~brave(fred)<~>strong(fred)))=>((~happy(john)|curious(john))))&
(![X]:((funny(X)&~strong(X))<=>(~strong(X)|happy(X))))&
(((tall(paul)<~>~patient(paul)))=>((~funny(susan)&creative(susan))))&
(![X]:((~rich(X)|calm(X))=>(happy(X)&humble(X))))&
(((funny(paul)&~rich(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(rich(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~patient(X)|brave(X))=>(happy(X)|funny(X))))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((funny(X)|~generous(X))))=>((brave(susan)&~wise(susan))))&
(((calm(lucy)|~patient(lucy)))=>(?[X]:(humble(X))))&
((?[X]:((rich(X)&old(X))))=>((~quiet(john)<~>curious(john))))&
(![X]:((quiet(X)&~brave(X))<=>(~rich(X)<~>~happy(X))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(happy(X)))=>((~creative(paul)<~>happy(paul))))&
(?[X]:((creative(X)|happy(X))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:(~tall(X)))&
(rich(susan))&
(generous(john))&
(~patient(fred))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~strong(lucy)|generous(lucy))) | rich(paul) | [
"p2",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5263250701366730379152092
% SZS output start Proof for 5263250701366730379152092
3. ! [X0] : ((~strong(X0) & funny(X0)) <=> (happy(X0) | ~strong(X0))) [input p2]
5. ! [X0] : ((calm(X0) | ~rich(X0)) => (humble(X0) & happy(X0))) [input p4]
15. ! [X0] : ((strong(X0) & ~rich(X0)) <=> (~brave(X0) | ~rich(X0))) [input p14]
25. ~rich(paul) [input hypothesis]
32. ! [X0] : ((humble(X0) & happy(X0)) | (~calm(X0) & rich(X0))) [ennf transformation 5]
42. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 3]
43. ! [X0] : (((~strong(X0) & funny(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | strong(X0) | ~funny(X0))) [flattening 42]
58. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~strong(X0) | rich(X0)))) [nnf transformation 15]
59. ! [X0] : (((strong(X0) & ~rich(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~strong(X0) | rich(X0))) [flattening 58]
76. ~happy(X0) | ~strong(X0) [cnf transformation 43]
81. rich(X0) | happy(X0) [cnf transformation 32]
118. rich(X0) | strong(X0) [cnf transformation 59]
131. ~rich(paul) [cnf transformation 25]
170. 9 <=> rich(paul) [avatar definition]
172. ~rich(paul) <- (~9) [avatar component clause 170]
225. 20 <=> happy(paul) [avatar definition]
226. happy(paul) <- (20) [avatar component clause 225]
257. ~9 [avatar split clause 131,170]
260. happy(paul) <- (~9) [resolution 81,172]
263. 20 | 9 [avatar split clause 260,170,225]
265. ~strong(paul) <- (20) [resolution 226,76]
273. strong(paul) <- (~9) [resolution 118,172]
275. $false <- (~9, 20) [subsumption resolution 273,265]
276. 9 | ~20 [avatar contradiction clause 275]
277. $false [avatar sat refutation 257,263,276]
% SZS output end Proof for 5263250701366730379152092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not quiet is both kind and generous and vice versa.
If mary is not creative then fred is both humble and strong and vice versa.
If someone is both not strong and curious then someone is either not generous or not strong.
If someone is not tall or not strong then fred is not generous.
Everyone who is generous or old is both brave and curious and vice versa.
Everyone who is not old is not strong or not creative and vice versa.
Everyone who is either humble or not humble is brave or old.
Everyone who is both not creative and not humble is both not humble and wise and vice versa.
Everyone who is creative or funny is not generous.
Everyone who is creative is not strong or kind and vice versa.
If mary is not patient then someone is both not funny and not old and vice versa.
If someone is not old or tall then fred is either happy or not humble.
If someone is both not creative and quiet then someone is both happy and generous.
If someone is not kind or not creative then someone is not calm and vice versa.
Everyone who is wise or curious is creative or patient and vice versa.
If mary is either brave or not old then someone is both not wise and kind and vice versa.
Someone is not rich or happy.
Alice is funny or kind.
Someone is either patient or funny.
John is both not humble and kind.
Someone is patient.
Someone is not happy. | John is strong. | entailment | (![X]:((generous(X)|~quiet(X))<=>(kind(X)&generous(X))))&
((~creative(mary))<=>((humble(fred)&strong(fred))))&
((?[X]:((~strong(X)&curious(X))))=>(?[X]:((~generous(X)<~>~strong(X)))))&
((?[X]:((~tall(X)|~strong(X))))=>(~generous(fred)))&
(![X]:((generous(X)|old(X))<=>(brave(X)&curious(X))))&
(![X]:(~old(X)<=>(~strong(X)|~creative(X))))&
(![X]:((humble(X)<~>~humble(X))=>(brave(X)|old(X))))&
(![X]:((~creative(X)&~humble(X))<=>(~humble(X)&wise(X))))&
(![X]:((creative(X)|funny(X))=>~generous(X)))&
(![X]:(creative(X)<=>(~strong(X)|kind(X))))&
((~patient(mary))<=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((~old(X)|tall(X))))=>((happy(fred)<~>~humble(fred))))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((happy(X)&generous(X)))))&
((?[X]:((~kind(X)|~creative(X))))<=>(?[X]:(~calm(X))))&
(![X]:((wise(X)|curious(X))<=>(creative(X)|patient(X))))&
(((brave(mary)<~>~old(mary)))<=>(?[X]:((~wise(X)&kind(X)))))&
(?[X]:((~rich(X)|happy(X))))&
((funny(alice)|kind(alice)))&
(?[X]:((patient(X)<~>funny(X))))&
((~humble(john)&kind(john)))&
(?[X]:(patient(X)))&
(?[X]:(~happy(X))) | strong(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 890757112100759200109949
% SZS output start Proof for 890757112100759200109949
1. ! [X0] : ((~quiet(X0) | generous(X0)) <=> (generous(X0) & kind(X0))) [input p0]
5. ! [X0] : ((old(X0) | generous(X0)) <=> (curious(X0) & brave(X0))) [input p4]
6. ! [X0] : (~old(X0) <=> (~creative(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (old(X0) | brave(X0))) [input p6]
8. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> (wise(X0) & ~humble(X0))) [input p7]
9. ! [X0] : ((funny(X0) | creative(X0)) => ~generous(X0)) [input p8]
10. ! [X0] : (creative(X0) <=> (kind(X0) | ~strong(X0))) [input p9]
13. ? [X0] : (quiet(X0) & ~creative(X0)) => ? [X0] : (generous(X0) & happy(X0)) [input p12]
15. ! [X0] : ((curious(X0) | wise(X0)) <=> (patient(X0) | creative(X0))) [input p14]
20. kind(john) & ~humble(john) [input p19]
23. ~strong(john) [input hypothesis]
25. ? [X0] : (quiet(X0) & ~creative(X0)) => ? [X1] : (generous(X1) & happy(X1)) [rectify 13]
30. ! [X0] : ((old(X0) | brave(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 7]
31. ! [X0] : (old(X0) | brave(X0) | (humble(X0) <=> ~humble(X0))) [flattening 30]
32. ! [X0] : (~generous(X0) | (~funny(X0) & ~creative(X0))) [ennf transformation 9]
34. ? [X1] : (generous(X1) & happy(X1)) | ! [X0] : (~quiet(X0) | creative(X0)) [ennf transformation 25]
35. ! [X0] : (((~quiet(X0) | generous(X0)) | (~generous(X0) | ~kind(X0))) & ((generous(X0) & kind(X0)) | (quiet(X0) & ~generous(X0)))) [nnf transformation 1]
36. ! [X0] : ((~quiet(X0) | generous(X0) | ~generous(X0) | ~kind(X0)) & ((generous(X0) & kind(X0)) | (quiet(X0) & ~generous(X0)))) [flattening 35]
43. ! [X0] : (((old(X0) | generous(X0)) | (~curious(X0) | ~brave(X0))) & ((curious(X0) & brave(X0)) | (~old(X0) & ~generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((old(X0) | generous(X0) | ~curious(X0) | ~brave(X0)) & ((curious(X0) & brave(X0)) | (~old(X0) & ~generous(X0)))) [flattening 43]
45. ! [X0] : ((~old(X0) | (creative(X0) & strong(X0))) & ((~creative(X0) | ~strong(X0)) | old(X0))) [nnf transformation 6]
46. ! [X0] : ((~old(X0) | (creative(X0) & strong(X0))) & (~creative(X0) | ~strong(X0) | old(X0))) [flattening 45]
47. ! [X0] : (old(X0) | brave(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 31]
48. ! [X0] : (((~humble(X0) & ~creative(X0)) | (~wise(X0) | humble(X0))) & ((wise(X0) & ~humble(X0)) | (humble(X0) | creative(X0)))) [nnf transformation 8]
49. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~wise(X0) | humble(X0)) & ((wise(X0) & ~humble(X0)) | humble(X0) | creative(X0))) [flattening 48]
50. ! [X0] : ((creative(X0) | (~kind(X0) & strong(X0))) & ((kind(X0) | ~strong(X0)) | ~creative(X0))) [nnf transformation 10]
51. ! [X0] : ((creative(X0) | (~kind(X0) & strong(X0))) & (kind(X0) | ~strong(X0) | ~creative(X0))) [flattening 50]
57. ? [X0] : (generous(X0) & happy(X0)) | ! [X1] : (~quiet(X1) | creative(X1)) [rectify 34]
58. ? [X0] : (generous(X0) & happy(X0)) => (generous(sK2) & happy(sK2)) [choice axiom]
59. (generous(sK2) & happy(sK2)) | ! [X1] : (~quiet(X1) | creative(X1)) [skolemisation 57,58]
65. ! [X0] : (((curious(X0) | wise(X0)) | (~patient(X0) & ~creative(X0))) & ((patient(X0) | creative(X0)) | (~curious(X0) & ~wise(X0)))) [nnf transformation 15]
66. ! [X0] : ((curious(X0) | wise(X0) | (~patient(X0) & ~creative(X0))) & (patient(X0) | creative(X0) | (~curious(X0) & ~wise(X0)))) [flattening 65]
78. ~generous(X0) | kind(X0) [cnf transformation 36]
79. kind(X0) | quiet(X0) [cnf transformation 36]
91. ~old(X0) | brave(X0) [cnf transformation 44]
94. ~brave(X0) | generous(X0) | ~curious(X0) | old(X0) [cnf transformation 44]
96. ~old(X0) | strong(X0) [cnf transformation 46]
98. old(X0) | brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
99. old(X0) | brave(X0) | humble(X0) | humble(X0) [cnf transformation 47]
102. ~wise(X0) | ~creative(X0) | humble(X0) [cnf transformation 49]
104. ~creative(X0) | ~generous(X0) [cnf transformation 32]
107. strong(X0) | creative(X0) [cnf transformation 51]
108. ~kind(X0) | creative(X0) [cnf transformation 51]
117. generous(sK2) | ~quiet(X1) | creative(X1) [cnf transformation 59]
123. ~creative(X0) | wise(X0) | curious(X0) [cnf transformation 66]
134. ~humble(john) [cnf transformation 20]
138. ~strong(john) [cnf transformation 23]
139. old(X0) | brave(X0) | ~humble(X0) [duplicate literal removal 98]
140. old(X0) | brave(X0) | humble(X0) [duplicate literal removal 99]
181. brave(X0) | humble(X0) [subsumption resolution 140,91]
182. brave(X0) | ~humble(X0) [subsumption resolution 139,91]
183. brave(X0) [subsumption resolution 182,181]
217. 17 <=> ! [X1] : (~quiet(X1) | creative(X1)) [avatar definition]
218. ~quiet(X1) | creative(X1) <- (17) [avatar component clause 217]
220. 18 <=> generous(sK2) [avatar definition]
222. generous(sK2) <- (18) [avatar component clause 220]
223. 17 | 18 [avatar split clause 117,220,217]
239. 22 <=> ! [X3] : creative(X3) [avatar definition]
240. creative(X3) <- (22) [avatar component clause 239]
293. creative(john) [resolution 107,138]
296. creative(X0) | quiet(X0) [resolution 108,79]
297. creative(X0) <- (17) [subsumption resolution 296,218]
298. 22 | ~17 [avatar split clause 297,217,239]
301. kind(sK2) <- (18) [resolution 222,78]
303. creative(sK2) <- (18) [resolution 301,108]
310. ~generous(sK2) <- (18) [resolution 303,104]
311. $false <- (18) [subsumption resolution 310,222]
312. ~18 [avatar contradiction clause 311]
313. ~generous(X0) <- (22) [resolution 240,104]
335. wise(john) | curious(john) [resolution 123,293]
338. 33 <=> curious(john) [avatar definition]
340. curious(john) <- (33) [avatar component clause 338]
342. 34 <=> wise(john) [avatar definition]
344. wise(john) <- (34) [avatar component clause 342]
345. 33 | 34 [avatar split clause 335,342,338]
361. generous(X1) | ~curious(X1) | old(X1) [resolution 94,183]
363. ~curious(X1) | old(X1) <- (22) [subsumption resolution 361,313]
377. old(john) <- (22, 33) [resolution 363,340]
381. strong(john) <- (22, 33) [resolution 377,96]
384. $false <- (22, 33) [subsumption resolution 381,138]
385. ~22 | ~33 [avatar contradiction clause 384]
390. ~creative(john) | humble(john) <- (34) [resolution 344,102]
391. humble(john) <- (34) [subsumption resolution 390,293]
392. $false <- (34) [subsumption resolution 391,134]
393. ~34 [avatar contradiction clause 392]
394. $false [avatar sat refutation 223,298,312,345,385,393]
% SZS output end Proof for 890757112100759200109949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or humble is either not creative or not brave.
Everyone who is not happy or strong is both patient and generous.
If paul is both strong and not happy then john is both wise and strong.
Everyone who is happy is calm or not wise.
If someone is not calm then susan is either not tall or not wise and vice versa.
Everyone who is creative is brave and vice versa.
Everyone who is old is not funny and vice versa.
If fred is either curious or strong then someone is both brave and not kind.
Everyone who is not calm or calm is either not rich or not humble.
If someone is not calm then paul is not funny or quiet.
Everyone who is either tall or not rich is either not wise or not creative.
Everyone who is both curious and calm is either not funny or humble.
If fred is not strong then someone is either not funny or tall.
Everyone who is not strong is strong or quiet and vice versa.
Everyone who is creative is not wise or not old.
Everyone who is creative is both quiet and kind.
Someone is not strong.
Someone is either not kind or happy.
Someone is both not funny and quiet.
Someone is creative.
Alice is rich or not old.
Paul is either not generous or not rich.
Paul is both not wise and not kind.
Susan is both not curious and not rich. | Alice is old. | contradiction | (![X]:((~funny(X)<~>humble(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~happy(X)|strong(X))=>(patient(X)&generous(X))))&
(((strong(paul)&~happy(paul)))=>((wise(john)&strong(john))))&
(![X]:(happy(X)=>(calm(X)|~wise(X))))&
((?[X]:(~calm(X)))<=>((~tall(susan)<~>~wise(susan))))&
(![X]:(creative(X)<=>brave(X)))&
(![X]:(old(X)<=>~funny(X)))&
(((curious(fred)<~>strong(fred)))=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~calm(X)|calm(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:(~calm(X)))=>((~funny(paul)|quiet(paul))))&
(![X]:((tall(X)<~>~rich(X))=>(~wise(X)<~>~creative(X))))&
(![X]:((curious(X)&calm(X))=>(~funny(X)<~>humble(X))))&
((~strong(fred))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:(~strong(X)<=>(strong(X)|quiet(X))))&
(![X]:(creative(X)=>(~wise(X)|~old(X))))&
(![X]:(creative(X)=>(quiet(X)&kind(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~funny(X)&quiet(X))))&
(?[X]:(creative(X)))&
((rich(alice)|~old(alice)))&
((~generous(paul)<~>~rich(paul)))&
((~wise(paul)&~kind(paul)))&
((~curious(susan)&~rich(susan))) | old(alice) | [
"p0",
"p5",
"p6",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7821512781075005629734924
% SZS output start Proof for 7821512781075005629734924
1. ! [X0] : ((~funny(X0) <~> humble(X0)) => (~creative(X0) <~> ~brave(X0))) [input p0]
6. ! [X0] : (creative(X0) <=> brave(X0)) [input p5]
7. ! [X0] : (old(X0) <=> ~funny(X0)) [input p6]
9. ! [X0] : ((calm(X0) | ~calm(X0)) => (~rich(X0) <~> ~humble(X0))) [input p8]
21. ~old(alice) | rich(alice) [input p20]
25. old(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) <~> ~brave(X0)) | (~funny(X0) <=> humble(X0))) [ennf transformation 1]
34. ! [X0] : ((~rich(X0) <~> ~humble(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 9]
44. ! [X0] : (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0)))) [nnf transformation 27]
49. ! [X0] : ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))) [nnf transformation 6]
50. ! [X0] : ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))) [nnf transformation 7]
54. ! [X0] : (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (~calm(X0) & calm(X0))) [nnf transformation 34]
72. ~brave(X0) | ~creative(X0) | humble(X0) | funny(X0) [cnf transformation 44]
74. brave(X0) | creative(X0) | humble(X0) | funny(X0) [cnf transformation 44]
85. ~creative(X0) | brave(X0) [cnf transformation 49]
86. ~brave(X0) | creative(X0) [cnf transformation 49]
87. ~old(X0) | ~funny(X0) [cnf transformation 50]
93. ~humble(X0) | ~rich(X0) | calm(X0) [cnf transformation 54]
94. ~rich(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 54]
118. ~old(alice) | rich(alice) [cnf transformation 21]
125. old(alice) [cnf transformation 25]
186. ~rich(X0) | ~humble(X0) [subsumption resolution 93,94]
218. 19 <=> rich(alice) [avatar definition]
220. rich(alice) <- (19) [avatar component clause 218]
222. 20 <=> old(alice) [avatar definition]
223. old(alice) <- (20) [avatar component clause 222]
225. 19 | ~20 [avatar split clause 118,222,218]
236. 20 [avatar split clause 125,222]
239. ~funny(alice) <- (20) [resolution 87,223]
245. ~humble(alice) <- (19) [resolution 186,220]
262. 25 <=> creative(alice) [avatar definition]
263. creative(alice) <- (25) [avatar component clause 262]
264. ~creative(alice) <- (~25) [avatar component clause 262]
287. creative(X2) | humble(X2) | funny(X2) | creative(X2) [resolution 74,86]
288. creative(X2) | humble(X2) | funny(X2) [duplicate literal removal 287]
313. humble(alice) | funny(alice) <- (~25) [resolution 288,264]
315. funny(alice) <- (19, ~25) [subsumption resolution 313,245]
316. $false <- (19, 20, ~25) [subsumption resolution 315,239]
317. ~19 | ~20 | 25 [avatar contradiction clause 316]
326. brave(alice) <- (25) [resolution 263,85]
363. ~creative(alice) | humble(alice) | funny(alice) <- (25) [resolution 326,72]
365. humble(alice) | funny(alice) <- (25) [subsumption resolution 363,263]
366. funny(alice) <- (19, 25) [subsumption resolution 365,245]
367. $false <- (19, 20, 25) [subsumption resolution 366,239]
368. ~19 | ~20 | ~25 [avatar contradiction clause 367]
369. $false [avatar sat refutation 225,236,317,368]
% SZS output end Proof for 7821512781075005629734924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either kind or not tall then alice is not wise or strong and vice versa.
If mary is not generous or creative then someone is not old.
If fred is curious or kind then someone is either not generous or not creative.
Everyone who is both kind and not wise is tall.
Everyone who is either calm or happy is both not wise and not curious and vice versa.
Everyone who is both tall and not old is either not kind or funny and vice versa.
If someone is either not patient or not funny then fred is both wise and strong.
Everyone who is wise or not humble is not happy and vice versa.
Everyone who is funny or not old is either generous or not patient and vice versa.
If someone is funny then paul is wise and vice versa.
If alice is both rich and tall then paul is either not calm or brave and vice versa.
Everyone who is brave or not calm is both funny and not funny.
If fred is both wise and not curious then someone is humble or not strong.
Everyone who is either patient or not happy is not creative or generous and vice versa.
If someone is not quiet then john is curious and vice versa.
Everyone who is humble or patient is calm or not patient.
Someone is not rich.
Someone is generous.
Someone is both happy and not kind. | John is happy. | contradiction | (((kind(john)<~>~tall(john)))<=>((~wise(alice)|strong(alice))))&
(((~generous(mary)|creative(mary)))=>(?[X]:(~old(X))))&
(((curious(fred)|kind(fred)))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((kind(X)&~wise(X))=>tall(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~wise(X)&~curious(X))))&
(![X]:((tall(X)&~old(X))<=>(~kind(X)<~>funny(X))))&
((?[X]:((~patient(X)<~>~funny(X))))=>((wise(fred)&strong(fred))))&
(![X]:((wise(X)|~humble(X))<=>~happy(X)))&
(![X]:((funny(X)|~old(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:(funny(X)))<=>(wise(paul)))&
(((rich(alice)&tall(alice)))<=>((~calm(paul)<~>brave(paul))))&
(![X]:((brave(X)|~calm(X))=>(funny(X)&~funny(X))))&
(((wise(fred)&~curious(fred)))=>(?[X]:((humble(X)|~strong(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>(~creative(X)|generous(X))))&
((?[X]:(~quiet(X)))<=>(curious(john)))&
(![X]:((humble(X)|patient(X))=>(calm(X)|~patient(X))))&
(?[X]:(~rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((happy(X)&~kind(X)))) | happy(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1059097567572700916141498
% SZS output start Proof for 1059097567572700916141498
1. (kind(john) <~> ~tall(john)) <=> (strong(alice) | ~wise(alice)) [input p0]
5. ! [X0] : ((calm(X0) <~> happy(X0)) <=> (~curious(X0) & ~wise(X0))) [input p4]
6. ! [X0] : ((~old(X0) & tall(X0)) <=> (~kind(X0) <~> funny(X0))) [input p5]
7. ? [X0] : (~patient(X0) <~> ~funny(X0)) => (strong(fred) & wise(fred)) [input p6]
8. ! [X0] : ((~humble(X0) | wise(X0)) <=> ~happy(X0)) [input p7]
9. ! [X0] : ((~old(X0) | funny(X0)) <=> (generous(X0) <~> ~patient(X0))) [input p8]
10. ? [X0] : funny(X0) <=> wise(paul) [input p9]
12. ! [X0] : ((~calm(X0) | brave(X0)) => (~funny(X0) & funny(X0))) [input p11]
14. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (generous(X0) | ~creative(X0))) [input p13]
20. happy(john) [input hypothesis]
25. (strong(fred) & wise(fred)) | ! [X0] : (~patient(X0) <=> ~funny(X0)) [ennf transformation 7]
26. ! [X0] : ((~funny(X0) & funny(X0)) | (calm(X0) & ~brave(X0))) [ennf transformation 12]
31. (((tall(john) | ~kind(john)) & (~tall(john) | kind(john))) | (~strong(alice) & wise(alice))) & ((strong(alice) | ~wise(alice)) | ((kind(john) | tall(john)) & (~tall(john) | ~kind(john)))) [nnf transformation 1]
32. (((tall(john) | ~kind(john)) & (~tall(john) | kind(john))) | (~strong(alice) & wise(alice))) & (strong(alice) | ~wise(alice) | ((kind(john) | tall(john)) & (~tall(john) | ~kind(john)))) [flattening 31]
38. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [flattening 38]
40. ! [X0] : (((~old(X0) & tall(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | (old(X0) | ~tall(X0)))) [nnf transformation 6]
41. ! [X0] : (((~old(X0) & tall(X0)) | ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0)))) & (((~funny(X0) | kind(X0)) & (funny(X0) | ~kind(X0))) | old(X0) | ~tall(X0))) [flattening 40]
42. (strong(fred) & wise(fred)) | ! [X0] : ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))) [nnf transformation 25]
43. ! [X0] : (((~humble(X0) | wise(X0)) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [nnf transformation 8]
44. ! [X0] : ((~humble(X0) | wise(X0) | happy(X0)) & (~happy(X0) | (humble(X0) & ~wise(X0)))) [flattening 43]
45. ! [X0] : (((~old(X0) | funny(X0)) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0)))) & (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (old(X0) & ~funny(X0)))) [nnf transformation 9]
46. ! [X0] : ((~old(X0) | funny(X0) | ((generous(X0) | patient(X0)) & (~patient(X0) | ~generous(X0)))) & (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | (old(X0) & ~funny(X0)))) [flattening 45]
47. (? [X0] : funny(X0) | ~wise(paul)) & (wise(paul) | ! [X0] : ~funny(X0)) [nnf transformation 10]
48. (? [X0] : funny(X0) | ~wise(paul)) & (wise(paul) | ! [X1] : ~funny(X1)) [rectify 47]
49. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
50. (funny(sK2) | ~wise(paul)) & (wise(paul) | ! [X1] : ~funny(X1)) [skolemisation 48,49]
55. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 14]
56. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [flattening 55]
69. ~tall(john) | kind(john) | wise(alice) [cnf transformation 32]
71. tall(john) | ~kind(john) | wise(alice) [cnf transformation 32]
80. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 39]
86. ~tall(X0) | ~kind(X0) | old(X0) | funny(X0) [cnf transformation 41]
88. funny(X0) | tall(X0) | kind(X0) [cnf transformation 41]
93. wise(fred) | ~patient(X0) | funny(X0) [cnf transformation 42]
96. ~happy(X0) | ~wise(X0) [cnf transformation 44]
104. ~old(X0) | funny(X0) | generous(X0) | patient(X0) [cnf transformation 46]
105. wise(paul) | ~funny(X1) [cnf transformation 50]
114. funny(X0) | calm(X0) [cnf transformation 26]
116. ~funny(X0) | calm(X0) [cnf transformation 26]
121. ~happy(X0) | patient(X0) | ~generous(X0) [cnf transformation 56]
132. happy(john) [cnf transformation 20]
139. 2 <=> kind(john) [avatar definition]
140. kind(john) <- (2) [avatar component clause 139]
141. ~kind(john) <- (~2) [avatar component clause 139]
143. 3 <=> tall(john) [avatar definition]
144. ~tall(john) <- (~3) [avatar component clause 143]
145. tall(john) <- (3) [avatar component clause 143]
148. 4 <=> wise(alice) [avatar definition]
150. wise(alice) <- (4) [avatar component clause 148]
151. 4 | ~2 | 3 [avatar split clause 71,143,139,148]
153. 4 | 2 | ~3 [avatar split clause 69,143,139,148]
191. 12 <=> ! [X0] : (~patient(X0) | funny(X0)) [avatar definition]
192. ~patient(X0) | funny(X0) <- (12) [avatar component clause 191]
203. 15 <=> wise(fred) [avatar definition]
205. wise(fred) <- (15) [avatar component clause 203]
206. 12 | 15 [avatar split clause 93,203,191]
209. 16 <=> wise(paul) [avatar definition]
210. wise(paul) <- (16) [avatar component clause 209]
218. 18 <=> ! [X1] : ~funny(X1) [avatar definition]
219. ~funny(X1) <- (18) [avatar component clause 218]
220. 18 | 16 [avatar split clause 105,209,218]
243. calm(X0) [subsumption resolution 114,116]
278. happy(X0) | ~wise(X0) [resolution 80,243]
279. ~wise(X0) [subsumption resolution 278,96]
282. $false <- (16) [resolution 279,210]
283. ~16 [avatar contradiction clause 282]
290. tall(X0) | kind(X0) <- (18) [resolution 88,219]
293. kind(john) <- (~3, 18) [resolution 290,144]
295. $false <- (~2, ~3, 18) [subsumption resolution 293,141]
296. 2 | 3 | ~18 [avatar contradiction clause 295]
297. $false <- (4) [subsumption resolution 150,279]
298. ~4 [avatar contradiction clause 297]
336. 33 <=> patient(john) [avatar definition]
338. patient(john) <- (33) [avatar component clause 336]
343. patient(john) | ~generous(john) [resolution 121,132]
350. 35 <=> generous(john) [avatar definition]
352. ~generous(john) <- (~35) [avatar component clause 350]
353. ~35 | 33 [avatar split clause 343,336,350]
370. ~kind(john) | old(john) | funny(john) <- (3) [resolution 86,145]
372. old(john) | funny(john) <- (2, 3) [subsumption resolution 370,140]
373. old(john) <- (2, 3, 18) [subsumption resolution 372,219]
390. funny(john) | generous(john) | patient(john) <- (2, 3, 18) [resolution 104,373]
391. generous(john) | patient(john) <- (2, 3, 18) [subsumption resolution 390,219]
392. patient(john) <- (2, 3, 18, ~35) [subsumption resolution 391,352]
393. 33 | ~2 | ~3 | ~18 | 35 [avatar split clause 392,350,218,143,139,336]
399. funny(john) <- (12, 33) [resolution 338,192]
400. $false <- (12, 18, 33) [subsumption resolution 399,219]
401. ~12 | ~18 | ~33 [avatar contradiction clause 400]
402. $false <- (15) [subsumption resolution 205,279]
403. ~15 [avatar contradiction clause 402]
404. $false [avatar sat refutation 151,153,206,220,283,296,298,353,393,401,403]
% SZS output end Proof for 1059097567572700916141498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is either rich or patient.
If someone is both not quiet and not brave then someone is both old and not generous and vice versa.
Everyone who is either not calm or happy is not patient and vice versa.
If someone is either quiet or not calm then someone is calm or not curious and vice versa.
Everyone who is either not kind or brave is calm.
If lucy is both generous and not funny then susan is both tall and funny and vice versa.
Everyone who is either not generous or humble is not wise.
Everyone who is not funny or brave is generous.
If alice is either rich or not quiet then someone is not tall or curious.
If paul is strong then someone is curious or rich.
If susan is not wise or humble then mary is not generous or kind and vice versa.
If someone is patient or not strong then someone is either rich or not calm.
If paul is both not creative and old then someone is both not generous and not creative and vice versa.
If alice is either not patient or humble then susan is both not patient and wise.
Everyone who is not brave or tall is both brave and not generous.
If someone is not patient or not wise then someone is both not generous and wise.
Someone is curious or not strong.
Fred is either happy or not patient.
John is either not quiet or old.
Lucy is not curious.
Someone is either wise or tall.
Paul is either not quiet or patient.
John is curious. | Susan is humble. | contradiction | ((?[X]:(~creative(X)))=>(?[X]:((rich(X)<~>patient(X)))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((old(X)&~generous(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>~patient(X)))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((~kind(X)<~>brave(X))=>calm(X)))&
(((generous(lucy)&~funny(lucy)))<=>((tall(susan)&funny(susan))))&
(![X]:((~generous(X)<~>humble(X))=>~wise(X)))&
(![X]:((~funny(X)|brave(X))=>generous(X)))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)|curious(X)))))&
((strong(paul))=>(?[X]:((curious(X)|rich(X)))))&
(((~wise(susan)|humble(susan)))<=>((~generous(mary)|kind(mary))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((~creative(paul)&old(paul)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~patient(alice)<~>humble(alice)))=>((~patient(susan)&wise(susan))))&
(![X]:((~brave(X)|tall(X))=>(brave(X)&~generous(X))))&
((?[X]:((~patient(X)|~wise(X))))=>(?[X]:((~generous(X)&wise(X)))))&
(?[X]:((curious(X)|~strong(X))))&
((happy(fred)<~>~patient(fred)))&
((~quiet(john)<~>old(john)))&
(~curious(lucy))&
(?[X]:((wise(X)<~>tall(X))))&
((~quiet(paul)<~>patient(paul)))&
(curious(john)) | humble(susan) | [
"p6",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 874080003675367954196084
% SZS output start Proof for 874080003675367954196084
7. ! [X0] : ((~generous(X0) <~> humble(X0)) => ~wise(X0)) [input p6]
8. ! [X0] : ((brave(X0) | ~funny(X0)) => generous(X0)) [input p7]
15. ! [X0] : ((tall(X0) | ~brave(X0)) => (~generous(X0) & brave(X0))) [input p14]
16. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X0] : (wise(X0) & ~generous(X0)) [input p15]
24. humble(susan) [input hypothesis]
29. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X1] : (wise(X1) & ~generous(X1)) [rectify 16]
32. ! [X0] : (~wise(X0) | (~generous(X0) <=> humble(X0))) [ennf transformation 7]
33. ! [X0] : (generous(X0) | (~brave(X0) & funny(X0))) [ennf transformation 8]
38. ! [X0] : ((~generous(X0) & brave(X0)) | (~tall(X0) & brave(X0))) [ennf transformation 15]
39. ? [X1] : (wise(X1) & ~generous(X1)) | ! [X0] : (wise(X0) & patient(X0)) [ennf transformation 29]
58. ! [X0] : (~wise(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) [nnf transformation 32]
76. ? [X0] : (wise(X0) & ~generous(X0)) | ! [X1] : (wise(X1) & patient(X1)) [rectify 39]
77. ? [X0] : (wise(X0) & ~generous(X0)) => (wise(sK9) & ~generous(sK9)) [choice axiom]
78. (wise(sK9) & ~generous(sK9)) | ! [X1] : (wise(X1) & patient(X1)) [skolemisation 76,77]
110. ~wise(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 58]
112. ~brave(X0) | generous(X0) [cnf transformation 33]
132. brave(X0) | brave(X0) [cnf transformation 38]
137. ~generous(sK9) | wise(X1) [cnf transformation 78]
151. humble(susan) [cnf transformation 24]
152. brave(X0) [duplicate literal removal 132]
286. 31 <=> humble(susan) [avatar definition]
288. humble(susan) <- (31) [avatar component clause 286]
355. 45 <=> ! [X1] : wise(X1) [avatar definition]
356. wise(X1) <- (45) [avatar component clause 355]
367. 48 <=> generous(sK9) [avatar definition]
369. ~generous(sK9) <- (~48) [avatar component clause 367]
370. 45 | ~48 [avatar split clause 137,367,355]
421. 31 [avatar split clause 151,286]
424. generous(X0) [resolution 112,152]
427. $false <- (~48) [resolution 424,369]
428. 48 [avatar contradiction clause 427]
464. ~generous(X0) | ~humble(X0) <- (45) [resolution 110,356]
468. ~humble(X0) <- (45) [subsumption resolution 464,424]
469. $false <- (31, 45) [resolution 468,288]
470. ~31 | ~45 [avatar contradiction clause 469]
471. $false [avatar sat refutation 370,421,428,470]
% SZS output end Proof for 874080003675367954196084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either patient or not generous then alice is not rich or wise and vice versa.
Everyone who is both not old and not tall is not tall or funny.
Everyone who is both patient and not rich is both happy and not happy.
Everyone who is not creative or calm is not humble or not funny.
Everyone who is calm is not wise.
Everyone who is both wise and not humble is not funny or creative.
Everyone who is brave or wise is both not curious and not old and vice versa.
Everyone who is both patient and not kind is creative and vice versa.
Everyone who is not strong is not brave or not tall and vice versa.
Everyone who is not kind or strong is either happy or creative.
If someone is both curious and not tall then john is both old and calm and vice versa.
Everyone who is patient or kind is both quiet and not patient.
Everyone who is either not old or old is curious.
Everyone who is not humble is both funny and curious.
If fred is not old then someone is rich and vice versa.
Everyone who is either patient or calm is either not curious or funny and vice versa.
Someone is generous or tall.
Mary is either humble or not rich.
Fred is both curious and not generous.
Someone is kind.
Someone is both not calm and not kind.
Someone is not tall or not rich.
Someone is not strong or not old.
Someone is not happy or tall. | Alice is not patient. | entailment | (((patient(paul)<~>~generous(paul)))<=>((~rich(alice)|wise(alice))))&
(![X]:((~old(X)&~tall(X))=>(~tall(X)|funny(X))))&
(![X]:((patient(X)&~rich(X))=>(happy(X)&~happy(X))))&
(![X]:((~creative(X)|calm(X))=>(~humble(X)|~funny(X))))&
(![X]:(calm(X)=>~wise(X)))&
(![X]:((wise(X)&~humble(X))=>(~funny(X)|creative(X))))&
(![X]:((brave(X)|wise(X))<=>(~curious(X)&~old(X))))&
(![X]:((patient(X)&~kind(X))<=>creative(X)))&
(![X]:(~strong(X)<=>(~brave(X)|~tall(X))))&
(![X]:((~kind(X)|strong(X))=>(happy(X)<~>creative(X))))&
((?[X]:((curious(X)&~tall(X))))<=>((old(john)&calm(john))))&
(![X]:((patient(X)|kind(X))=>(quiet(X)&~patient(X))))&
(![X]:((~old(X)<~>old(X))=>curious(X)))&
(![X]:(~humble(X)=>(funny(X)&curious(X))))&
((~old(fred))<=>(?[X]:(rich(X))))&
(![X]:((patient(X)<~>calm(X))<=>(~curious(X)<~>funny(X))))&
(?[X]:((generous(X)|tall(X))))&
((humble(mary)<~>~rich(mary)))&
((curious(fred)&~generous(fred)))&
(?[X]:(kind(X)))&
(?[X]:((~calm(X)&~kind(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((~strong(X)|~old(X))))&
(?[X]:((~happy(X)|tall(X)))) | ~patient(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 621114354130904648253521
% SZS output start Proof for 621114354130904648253521
12. ! [X0] : ((kind(X0) | patient(X0)) => (~patient(X0) & quiet(X0))) [input p11]
25. patient(alice) [input hypothesis]
27. ! [X0] : ((kind(X0) | patient(X0)) => ~patient(X0)) [pure predicate removal 12]
40. ! [X0] : (~patient(X0) | (~kind(X0) & ~patient(X0))) [ennf transformation 27]
104. ~patient(X0) | ~patient(X0) [cnf transformation 40]
131. patient(alice) [cnf transformation 25]
134. ~patient(X0) [duplicate literal removal 104]
247. $false [subsumption resolution 131,134]
% SZS output end Proof for 621114354130904648253521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both creative and not creative then someone is not strong and vice versa.
If someone is both not wise and not calm then someone is either not creative or strong and vice versa.
If mary is both tall and happy then susan is both strong and not funny.
Everyone who is both not kind and not wise is wise.
If someone is both humble and funny then alice is either not quiet or generous.
Everyone who is either creative or not happy is both strong and wise and vice versa.
Everyone who is either not brave or creative is either not quiet or curious and vice versa.
Everyone who is rich or not funny is either happy or curious.
If someone is not tall or not happy then susan is both not funny and not tall.
Everyone who is either not strong or rich is either not humble or not funny and vice versa.
If someone is wise or generous then john is generous and vice versa.
If someone is not kind then someone is creative and vice versa.
Everyone who is either wise or generous is kind or calm.
If susan is both generous and creative then someone is either generous or calm.
Someone is humble.
Susan is not wise or not humble.
Lucy is generous or creative.
Someone is not calm or rich.
Someone is quiet or humble. | John is generous. | entailment | ((?[X]:((creative(X)&~creative(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((~creative(X)<~>strong(X)))))&
(((tall(mary)&happy(mary)))=>((strong(susan)&~funny(susan))))&
(![X]:((~kind(X)&~wise(X))=>wise(X)))&
((?[X]:((humble(X)&funny(X))))=>((~quiet(alice)<~>generous(alice))))&
(![X]:((creative(X)<~>~happy(X))<=>(strong(X)&wise(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((rich(X)|~funny(X))=>(happy(X)<~>curious(X))))&
((?[X]:((~tall(X)|~happy(X))))=>((~funny(susan)&~tall(susan))))&
(![X]:((~strong(X)<~>rich(X))<=>(~humble(X)<~>~funny(X))))&
((?[X]:((wise(X)|generous(X))))<=>(generous(john)))&
((?[X]:(~kind(X)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)<~>generous(X))=>(kind(X)|calm(X))))&
(((generous(susan)&creative(susan)))=>(?[X]:((generous(X)<~>calm(X)))))&
(?[X]:(humble(X)))&
((~wise(susan)|~humble(susan)))&
((generous(lucy)|creative(lucy)))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((quiet(X)|humble(X)))) | generous(john) | [
"p3",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 956814106128140534627009
% SZS output start Proof for 956814106128140534627009
4. ! [X0] : ((~wise(X0) & ~kind(X0)) => wise(X0)) [input p3]
11. ? [X0] : (generous(X0) | wise(X0)) <=> generous(john) [input p10]
12. ? [X0] : ~kind(X0) <=> ? [X0] : creative(X0) [input p11]
17. creative(lucy) | generous(lucy) [input p16]
20. ~generous(john) [input hypothesis]
23. ? [X0] : ~kind(X0) <=> ? [X1] : creative(X1) [rectify 12]
26. ! [X0] : (wise(X0) | (wise(X0) | kind(X0))) [ennf transformation 4]
27. ! [X0] : (wise(X0) | wise(X0) | kind(X0)) [flattening 26]
51. (? [X0] : (generous(X0) | wise(X0)) | ~generous(john)) & (generous(john) | ! [X0] : (~generous(X0) & ~wise(X0))) [nnf transformation 11]
52. (? [X0] : (generous(X0) | wise(X0)) | ~generous(john)) & (generous(john) | ! [X1] : (~generous(X1) & ~wise(X1))) [rectify 51]
53. ? [X0] : (generous(X0) | wise(X0)) => (generous(sK4) | wise(sK4)) [choice axiom]
54. ((generous(sK4) | wise(sK4)) | ~generous(john)) & (generous(john) | ! [X1] : (~generous(X1) & ~wise(X1))) [skolemisation 52,53]
55. (? [X0] : ~kind(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : kind(X0)) [nnf transformation 23]
56. (? [X0] : ~kind(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : kind(X3)) [rectify 55]
57. ? [X0] : ~kind(X0) => ~kind(sK5) [choice axiom]
58. ? [X2] : creative(X2) => creative(sK6) [choice axiom]
59. (~kind(sK5) | ! [X1] : ~creative(X1)) & (creative(sK6) | ! [X3] : kind(X3)) [skolemisation 56,58,57]
81. wise(X0) | wise(X0) | kind(X0) [cnf transformation 27]
114. generous(john) | ~wise(X1) [cnf transformation 54]
115. generous(john) | ~generous(X1) [cnf transformation 54]
118. ~kind(sK5) | ~creative(X1) [cnf transformation 59]
125. creative(lucy) | generous(lucy) [cnf transformation 17]
128. ~generous(john) [cnf transformation 20]
129. kind(X0) | wise(X0) [duplicate literal removal 81]
216. 20 <=> generous(john) [avatar definition]
229. 23 <=> ! [X1] : ~generous(X1) [avatar definition]
230. ~generous(X1) <- (23) [avatar component clause 229]
231. 23 | 20 [avatar split clause 115,216,229]
233. 24 <=> ! [X1] : ~wise(X1) [avatar definition]
234. ~wise(X1) <- (24) [avatar component clause 233]
235. 24 | 20 [avatar split clause 114,216,233]
237. 25 <=> ! [X1] : ~creative(X1) [avatar definition]
238. ~creative(X1) <- (25) [avatar component clause 237]
240. 26 <=> kind(sK5) [avatar definition]
242. ~kind(sK5) <- (~26) [avatar component clause 240]
243. 25 | ~26 [avatar split clause 118,240,237]
281. 35 <=> generous(lucy) [avatar definition]
283. generous(lucy) <- (35) [avatar component clause 281]
285. 36 <=> creative(lucy) [avatar definition]
287. creative(lucy) <- (36) [avatar component clause 285]
288. 35 | 36 [avatar split clause 125,285,281]
307. ~20 [avatar split clause 128,216]
313. $false <- (23, 35) [resolution 283,230]
314. ~23 | ~35 [avatar contradiction clause 313]
315. $false <- (25, 36) [subsumption resolution 287,238]
316. ~25 | ~36 [avatar contradiction clause 315]
321. wise(sK5) <- (~26) [resolution 129,242]
322. $false <- (24, ~26) [subsumption resolution 321,234]
323. ~24 | 26 [avatar contradiction clause 322]
324. $false [avatar sat refutation 231,235,243,288,307,314,316,323]
% SZS output end Proof for 956814106128140534627009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and patient is not humble or kind and vice versa.
If john is not tall then john is either not quiet or wise.
If susan is tall or not happy then someone is both not curious and not old.
If someone is tall or not calm then someone is not quiet and vice versa.
Everyone who is either strong or not strong is both wise and happy and vice versa.
Everyone who is humble or generous is strong.
Everyone who is either happy or not creative is tall or brave.
If someone is either not wise or quiet then john is old and vice versa.
Everyone who is strong is curious and vice versa.
Everyone who is either not humble or not funny is not kind and vice versa.
If someone is both not creative and calm then fred is either tall or curious and vice versa.
If someone is not tall then fred is either rich or not calm and vice versa.
If someone is rich or not strong then someone is both not funny and not wise.
Everyone who is both not strong and not tall is calm or old and vice versa.
Everyone who is either funny or creative is not old or curious.
John is rich or wise.
John is either not old or patient.
Someone is not funny or not humble.
Someone is curious or not kind.
Someone is either not funny or happy.
John is both not kind and creative.
Someone is either kind or not kind. | Fred is not old. | entailment | (![X]:((strong(X)&patient(X))<=>(~humble(X)|kind(X))))&
((~tall(john))=>((~quiet(john)<~>wise(john))))&
(((tall(susan)|~happy(susan)))=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(wise(X)&happy(X))))&
(![X]:((humble(X)|generous(X))=>strong(X)))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)|brave(X))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(old(john)))&
(![X]:(strong(X)<=>curious(X)))&
(![X]:((~humble(X)<~>~funny(X))<=>~kind(X)))&
((?[X]:((~creative(X)&calm(X))))<=>((tall(fred)<~>curious(fred))))&
((?[X]:(~tall(X)))<=>((rich(fred)<~>~calm(fred))))&
((?[X]:((rich(X)|~strong(X))))=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(calm(X)|old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~old(X)|curious(X))))&
((rich(john)|wise(john)))&
((~old(john)<~>patient(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((~funny(X)<~>happy(X))))&
((~kind(john)&creative(john)))&
(?[X]:((kind(X)<~>~kind(X)))) | ~old(fred) | [
"p0",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2160705236137128156808505
% SZS output start Proof for 2160705236137128156808505
1. ! [X0] : ((patient(X0) & strong(X0)) <=> (kind(X0) | ~humble(X0))) [input p0]
6. ! [X0] : ((generous(X0) | humble(X0)) => strong(X0)) [input p5]
14. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (old(X0) | calm(X0))) [input p13]
23. old(fred) [input hypothesis]
27. ! [X0] : (humble(X0) => strong(X0)) [pure predicate removal 6]
30. ! [X0] : (strong(X0) | ~humble(X0)) [ennf transformation 27]
34. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~patient(X0) | ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~patient(X0) | ~strong(X0))) [flattening 34]
63. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~old(X0) & ~calm(X0))) & ((old(X0) | calm(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 14]
64. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~old(X0) & ~calm(X0))) & (old(X0) | calm(X0) | tall(X0) | strong(X0))) [flattening 63]
78. strong(X0) | humble(X0) [cnf transformation 35]
97. strong(X0) | ~humble(X0) [cnf transformation 30]
124. ~strong(X0) | ~old(X0) [cnf transformation 64]
140. old(fred) [cnf transformation 23]
205. strong(X0) [subsumption resolution 97,78]
263. ~old(X0) [subsumption resolution 124,205]
276. $false [subsumption resolution 140,263]
% SZS output end Proof for 2160705236137128156808505
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then lucy is not patient or strong and vice versa.
Everyone who is not wise is either not tall or tall and vice versa.
Everyone who is not funny or creative is either wise or happy.
If someone is either not brave or not funny then someone is either generous or not tall.
If someone is not calm or not tall then someone is either humble or not humble.
Everyone who is not rich or not curious is both not tall and not kind and vice versa.
Everyone who is either wise or funny is calm and vice versa.
If john is not humble or brave then someone is not quiet.
If someone is either quiet or funny then alice is not quiet.
Everyone who is not tall or not humble is not tall.
If someone is curious then john is either humble or not funny and vice versa.
Everyone who is tall or not quiet is both not strong and quiet and vice versa.
Everyone who is either not tall or not wise is both not calm and curious and vice versa.
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Everyone who is both not tall and quiet is kind and vice versa.
John is not kind or calm.
Someone is both not wise and not old.
Mary is calm.
Someone is old or humble.
Someone is both happy and quiet.
Fred is either not calm or funny. | Alice is kind. | entailment | ((?[X]:((~curious(X)<~>~old(X))))<=>((~patient(lucy)|strong(lucy))))&
(![X]:(~wise(X)<=>(~tall(X)<~>tall(X))))&
(![X]:((~funny(X)|creative(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>calm(X)))&
(((~humble(john)|brave(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>funny(X))))=>(~quiet(alice)))&
(![X]:((~tall(X)|~humble(X))=>~tall(X)))&
((?[X]:(curious(X)))<=>((humble(john)<~>~funny(john))))&
(![X]:((tall(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((~tall(X)&quiet(X))<=>kind(X)))&
((~kind(john)|calm(john)))&
(?[X]:((~wise(X)&~old(X))))&
(calm(mary))&
(?[X]:((old(X)|humble(X))))&
(?[X]:((happy(X)&quiet(X))))&
((~calm(fred)<~>funny(fred))) | kind(alice) | [
"p1",
"p6",
"p8",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7648810489000612081845955
% SZS output start Proof for 7648810489000612081845955
2. ! [X0] : (~wise(X0) <=> (~tall(X0) <~> tall(X0))) [input p1]
7. ! [X0] : ((wise(X0) <~> funny(X0)) <=> calm(X0)) [input p6]
9. ? [X0] : (quiet(X0) <~> funny(X0)) => ~quiet(alice) [input p8]
12. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (quiet(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (curious(X0) & ~calm(X0))) [input p12]
16. ! [X0] : ((quiet(X0) & ~tall(X0)) <=> kind(X0)) [input p15]
23. ~kind(alice) [input hypothesis]
32. ~quiet(alice) | ! [X0] : (quiet(X0) <=> funny(X0)) [ennf transformation 9]
39. ! [X0] : ((~wise(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | wise(X0))) [nnf transformation 2]
51. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~calm(X0)) & (calm(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 7]
54. ~quiet(alice) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0))) [nnf transformation 32]
59. ! [X0] : (((~quiet(X0) | tall(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~quiet(X0) | tall(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 59]
61. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (~curious(X0) | calm(X0))) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 13]
62. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ~curious(X0) | calm(X0)) & ((curious(X0) & ~calm(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [flattening 61]
72. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) | tall(X0)))) [nnf transformation 16]
73. ! [X0] : (((quiet(X0) & ~tall(X0)) | ~kind(X0)) & (kind(X0) | ~quiet(X0) | tall(X0))) [flattening 72]
89. ~wise(X0) | tall(X0) | tall(X0) [cnf transformation 39]
90. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 39]
107. calm(X0) | wise(X0) | ~funny(X0) [cnf transformation 51]
112. ~quiet(alice) | funny(X0) | ~quiet(X0) [cnf transformation 54]
123. quiet(X0) | quiet(X0) [cnf transformation 60]
126. ~calm(X0) | ~tall(X0) | wise(X0) [cnf transformation 62]
138. kind(X0) | ~quiet(X0) | tall(X0) [cnf transformation 73]
150. ~kind(alice) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 123]
153. ~wise(X0) | tall(X0) [duplicate literal removal 89]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 90]
183. ~wise(X0) [subsumption resolution 153,154]
204. ~funny(X0) | calm(X0) [subsumption resolution 107,183]
223. 15 <=> quiet(alice) [avatar definition]
225. ~quiet(alice) <- (~15) [avatar component clause 223]
228. 16 <=> ! [X0] : (funny(X0) | ~quiet(X0)) [avatar definition]
229. funny(X0) | ~quiet(X0) <- (16) [avatar component clause 228]
230. 16 | ~15 [avatar split clause 112,223,228]
247. ~calm(X0) | ~tall(X0) [subsumption resolution 126,183]
275. kind(X0) | tall(X0) [subsumption resolution 138,151]
294. $false <- (~15) [subsumption resolution 225,151]
295. 15 [avatar contradiction clause 294]
298. funny(X0) <- (16) [subsumption resolution 229,151]
302. calm(X0) <- (16) [resolution 204,298]
304. ~tall(X0) <- (16) [resolution 302,247]
306. tall(alice) [resolution 275,150]
311. $false <- (16) [subsumption resolution 306,304]
312. ~16 [avatar contradiction clause 311]
318. $false [avatar sat refutation 230,295,312]
% SZS output end Proof for 7648810489000612081845955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both calm and curious then someone is either not curious or patient.
Everyone who is both not old and patient is both humble and not calm and vice versa.
If lucy is either not patient or calm then someone is funny and vice versa.
Everyone who is creative or quiet is either old or tall and vice versa.
Everyone who is both not tall and not calm is generous and vice versa.
Everyone who is not calm is tall or wise and vice versa.
Everyone who is both not kind and quiet is not generous or kind and vice versa.
Everyone who is not funny or humble is either not tall or not quiet.
If someone is both not strong and not rich then john is both not funny and not curious and vice versa.
Everyone who is either tall or humble is not tall and vice versa.
If john is quiet or happy then fred is strong and vice versa.
If mary is not patient or curious then someone is either tall or calm.
Everyone who is both old and not strong is either not kind or creative.
If someone is not calm or not brave then john is either not wise or brave and vice versa.
Everyone who is either calm or tall is both not rich and not curious.
John is funny or not funny.
Someone is either not strong or wise.
Lucy is both not strong and humble. | Lucy is rich. | contradiction | (((calm(mary)&curious(mary)))=>(?[X]:((~curious(X)<~>patient(X)))))&
(![X]:((~old(X)&patient(X))<=>(humble(X)&~calm(X))))&
(((~patient(lucy)<~>calm(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(![X]:(~calm(X)<=>(tall(X)|wise(X))))&
(![X]:((~kind(X)&quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~funny(john)&~curious(john))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(((quiet(john)|happy(john)))<=>(strong(fred)))&
(((~patient(mary)|curious(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((old(X)&~strong(X))=>(~kind(X)<~>creative(X))))&
((?[X]:((~calm(X)|~brave(X))))<=>((~wise(john)<~>brave(john))))&
(![X]:((calm(X)<~>tall(X))=>(~rich(X)&~curious(X))))&
((funny(john)|~funny(john)))&
(?[X]:((~strong(X)<~>wise(X))))&
((~strong(lucy)&humble(lucy))) | rich(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4909179797966757283210375
% SZS output start Proof for 4909179797966757283210375
2. ! [X0] : ((patient(X0) & ~old(X0)) <=> (~calm(X0) & humble(X0))) [input p1]
3. (~patient(lucy) <~> calm(lucy)) <=> ? [X0] : funny(X0) [input p2]
4. ! [X0] : ((quiet(X0) | creative(X0)) <=> (old(X0) <~> tall(X0))) [input p3]
5. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> generous(X0)) [input p4]
6. ! [X0] : (~calm(X0) <=> (wise(X0) | tall(X0))) [input p5]
7. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> (kind(X0) | ~generous(X0))) [input p6]
8. ! [X0] : ((humble(X0) | ~funny(X0)) => (~tall(X0) <~> ~quiet(X0))) [input p7]
10. ! [X0] : ((tall(X0) <~> humble(X0)) <=> ~tall(X0)) [input p9]
15. ! [X0] : ((calm(X0) <~> tall(X0)) => (~curious(X0) & ~rich(X0))) [input p14]
19. rich(lucy) [input hypothesis]
22. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 8]
26. ! [X0] : ((~curious(X0) & ~rich(X0)) | (calm(X0) <=> tall(X0))) [ennf transformation 15]
30. ! [X0] : (((patient(X0) & ~old(X0)) | (calm(X0) | ~humble(X0))) & ((~calm(X0) & humble(X0)) | (~patient(X0) | old(X0)))) [nnf transformation 2]
31. ! [X0] : (((patient(X0) & ~old(X0)) | calm(X0) | ~humble(X0)) & ((~calm(X0) & humble(X0)) | ~patient(X0) | old(X0))) [flattening 30]
32. (((~calm(lucy) | patient(lucy)) & (calm(lucy) | ~patient(lucy))) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ((~patient(lucy) | ~calm(lucy)) & (calm(lucy) | patient(lucy)))) [nnf transformation 3]
33. (((~calm(lucy) | patient(lucy)) & (calm(lucy) | ~patient(lucy))) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ((~patient(lucy) | ~calm(lucy)) & (calm(lucy) | patient(lucy)))) [rectify 32]
34. ? [X1] : funny(X1) => funny(sK1) [choice axiom]
35. (((~calm(lucy) | patient(lucy)) & (calm(lucy) | ~patient(lucy))) | ! [X0] : ~funny(X0)) & (funny(sK1) | ((~patient(lucy) | ~calm(lucy)) & (calm(lucy) | patient(lucy)))) [skolemisation 33,34]
36. ! [X0] : (((quiet(X0) | creative(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [nnf transformation 4]
37. ! [X0] : ((quiet(X0) | creative(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [flattening 36]
38. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | (calm(X0) | tall(X0)))) [nnf transformation 5]
39. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | calm(X0) | tall(X0))) [flattening 38]
40. ! [X0] : ((~calm(X0) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | calm(X0))) [nnf transformation 6]
41. ! [X0] : ((~calm(X0) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | calm(X0))) [flattening 40]
42. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | (~quiet(X0) | kind(X0)))) [nnf transformation 7]
43. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | ~quiet(X0) | kind(X0))) [flattening 42]
44. ! [X0] : (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~humble(X0) & funny(X0))) [nnf transformation 22]
50. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | tall(X0)) & (~tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 10]
61. ! [X0] : ((~curious(X0) & ~rich(X0)) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0)))) [nnf transformation 26]
69. ~humble(X0) | calm(X0) | ~old(X0) [cnf transformation 31]
70. ~humble(X0) | calm(X0) | patient(X0) [cnf transformation 31]
73. calm(lucy) | ~patient(lucy) | ~funny(X0) [cnf transformation 35]
76. ~quiet(X0) | old(X0) | tall(X0) [cnf transformation 37]
82. ~generous(X0) | ~tall(X0) [cnf transformation 39]
85. ~tall(X0) | ~calm(X0) [cnf transformation 41]
90. generous(X0) | quiet(X0) [cnf transformation 43]
92. ~tall(X0) | ~quiet(X0) | funny(X0) [cnf transformation 44]
94. tall(X0) | quiet(X0) | funny(X0) [cnf transformation 44]
100. ~tall(X0) | humble(X0) | ~tall(X0) [cnf transformation 50]
102. humble(X0) | tall(X0) | tall(X0) [cnf transformation 50]
119. ~rich(X0) | tall(X0) | ~calm(X0) [cnf transformation 61]
120. ~rich(X0) | calm(X0) | ~tall(X0) [cnf transformation 61]
128. rich(lucy) [cnf transformation 19]
129. ~tall(X0) | humble(X0) [duplicate literal removal 100]
130. tall(X0) | humble(X0) [duplicate literal removal 102]
152. 5 <=> ! [X0] : ~funny(X0) [avatar definition]
153. ~funny(X0) <- (5) [avatar component clause 152]
155. 6 <=> patient(lucy) [avatar definition]
156. ~patient(lucy) <- (~6) [avatar component clause 155]
159. 7 <=> calm(lucy) [avatar definition]
161. ~calm(lucy) <- (~7) [avatar component clause 159]
163. 5 | ~6 | 7 [avatar split clause 73,159,155,152]
194. humble(X0) [subsumption resolution 129,130]
248. 25 <=> ! [X1] : calm(X1) [avatar definition]
249. calm(X1) <- (25) [avatar component clause 248]
255. ~rich(X0) | ~tall(X0) [subsumption resolution 120,85]
256. ~rich(X0) | ~calm(X0) [subsumption resolution 119,255]
270. ~tall(X1) | quiet(X1) [resolution 90,82]
277. ~calm(lucy) [resolution 256,128]
282. ~old(X0) | calm(X0) [resolution 69,194]
283. patient(X0) | calm(X0) [resolution 70,194]
344. quiet(X6) | funny(X6) | quiet(X6) [resolution 94,270]
347. quiet(X6) | funny(X6) [duplicate literal removal 344]
351. quiet(X6) <- (5) [subsumption resolution 347,153]
364. tall(X0) | old(X0) <- (5) [resolution 351,76]
370. old(X3) | ~quiet(X3) | funny(X3) <- (5) [resolution 364,92]
376. old(X3) | funny(X3) <- (5) [subsumption resolution 370,351]
377. old(X3) <- (5) [subsumption resolution 376,153]
378. calm(X0) <- (5) [resolution 377,282]
381. 25 | ~5 [avatar split clause 378,152,248]
393. $false <- (25) [subsumption resolution 277,249]
394. ~25 [avatar contradiction clause 393]
396. ~7 [avatar split clause 277,159]
398. calm(lucy) <- (~6) [resolution 156,283]
399. $false <- (~6, ~7) [subsumption resolution 398,161]
400. 6 | 7 [avatar contradiction clause 399]
401. $false [avatar sat refutation 163,381,394,396,400]
% SZS output end Proof for 4909179797966757283210375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Everyone who is humble is tall or curious.
Everyone who is either not old or not quiet is brave or not curious and vice versa.
Everyone who is not kind is either not generous or not brave and vice versa.
Everyone who is either funny or curious is not funny and vice versa.
Everyone who is curious is not humble and vice versa.
If someone is tall or not curious then alice is both quiet and not humble and vice versa.
Everyone who is both not calm and happy is either calm or not humble.
Mary is not creative.
Susan is not strong.
Someone is both not funny and not brave.
John is both wise and not happy.
Someone is funny.
Someone is either not kind or kind.
Someone is either generous or creative. | Mary is not quiet. | entailment | ((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:(humble(X)=>(tall(X)|curious(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(brave(X)|~curious(X))))&
(![X]:(~kind(X)<=>(~generous(X)<~>~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>~funny(X)))&
(![X]:(curious(X)<=>~humble(X)))&
((?[X]:((tall(X)|~curious(X))))<=>((quiet(alice)&~humble(alice))))&
(![X]:((~calm(X)&happy(X))=>(calm(X)<~>~humble(X))))&
(~creative(mary))&
(~strong(susan))&
(?[X]:((~funny(X)&~brave(X))))&
((wise(john)&~happy(john)))&
(?[X]:(funny(X)))&
(?[X]:((~kind(X)<~>kind(X))))&
(?[X]:((generous(X)<~>creative(X)))) | ~quiet(mary) | [
"p4",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2727429498658744084246017
% SZS output start Proof for 2727429498658744084246017
5. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (wise(X0) | ~creative(X0))) [input p4]
13. ! [X0] : ((funny(X0) <~> curious(X0)) <=> ~funny(X0)) [input p12]
17. ~creative(mary) [input p16]
24. quiet(mary) [input hypothesis]
47. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 5]
48. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 47]
59. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 13]
91. ~curious(X0) | ~quiet(X0) | creative(X0) [cnf transformation 48]
120. ~funny(X0) | curious(X0) | ~funny(X0) [cnf transformation 59]
122. curious(X0) | funny(X0) | funny(X0) [cnf transformation 59]
133. ~creative(mary) [cnf transformation 17]
144. quiet(mary) [cnf transformation 24]
146. ~funny(X0) | curious(X0) [duplicate literal removal 120]
147. curious(X0) | funny(X0) [duplicate literal removal 122]
218. curious(X0) [subsumption resolution 146,147]
261. ~quiet(X1) | creative(X1) [resolution 91,218]
264. creative(mary) [resolution 261,144]
266. $false [subsumption resolution 264,133]
% SZS output end Proof for 2727429498658744084246017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both happy and not curious then fred is patient or wise.
Everyone who is not wise or not kind is either not strong or curious.
If someone is not rich or happy then someone is both happy and not creative and vice versa.
Everyone who is not calm or creative is both not brave and strong.
If mary is either wise or not creative then someone is not old and vice versa.
Everyone who is either not tall or not generous is both quiet and not calm and vice versa.
Everyone who is either not generous or happy is not brave.
Everyone who is wise or not old is both not funny and wise.
If someone is both not strong and generous then susan is both happy and rich.
Everyone who is both old and not patient is not funny or not tall.
If alice is both creative and patient then fred is both not calm and rich.
Everyone who is either not rich or not patient is not humble or strong and vice versa.
If alice is not old or calm then alice is not funny and vice versa.
Everyone who is not tall or not creative is both not brave and quiet.
If someone is either rich or not tall then john is either not funny or old and vice versa.
If someone is either not humble or old then mary is humble or creative and vice versa.
Fred is either old or not kind.
Someone is not strong or generous.
John is not curious or curious.
Someone is both wise and not calm.
Mary is wise or not quiet.
Someone is both rich and old.
Lucy is either calm or not rich.
Alice is not strong. | Alice is funny. | contradiction | (((happy(fred)&~curious(fred)))=>((patient(fred)|wise(fred))))&
(![X]:((~wise(X)|~kind(X))=>(~strong(X)<~>curious(X))))&
((?[X]:((~rich(X)|happy(X))))<=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~calm(X)|creative(X))=>(~brave(X)&strong(X))))&
(((wise(mary)<~>~creative(mary)))<=>(?[X]:(~old(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(quiet(X)&~calm(X))))&
(![X]:((~generous(X)<~>happy(X))=>~brave(X)))&
(![X]:((wise(X)|~old(X))=>(~funny(X)&wise(X))))&
((?[X]:((~strong(X)&generous(X))))=>((happy(susan)&rich(susan))))&
(![X]:((old(X)&~patient(X))=>(~funny(X)|~tall(X))))&
(((creative(alice)&patient(alice)))=>((~calm(fred)&rich(fred))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~humble(X)|strong(X))))&
(((~old(alice)|calm(alice)))<=>(~funny(alice)))&
(![X]:((~tall(X)|~creative(X))=>(~brave(X)&quiet(X))))&
((?[X]:((rich(X)<~>~tall(X))))<=>((~funny(john)<~>old(john))))&
((?[X]:((~humble(X)<~>old(X))))<=>((humble(mary)|creative(mary))))&
((old(fred)<~>~kind(fred)))&
(?[X]:((~strong(X)|generous(X))))&
((~curious(john)|curious(john)))&
(?[X]:((wise(X)&~calm(X))))&
((wise(mary)|~quiet(mary)))&
(?[X]:((rich(X)&old(X))))&
((calm(lucy)<~>~rich(lucy)))&
(~strong(alice)) | funny(alice) | [
"p3",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1474151884234878152211781
% SZS output start Proof for 1474151884234878152211781
4. ! [X0] : ((creative(X0) | ~calm(X0)) => (strong(X0) & ~brave(X0))) [input p3]
13. (calm(alice) | ~old(alice)) <=> ~funny(alice) [input p12]
24. ~strong(alice) [input p23]
25. funny(alice) [input hypothesis]
29. ! [X0] : ((creative(X0) | ~calm(X0)) => strong(X0)) [pure predicate removal 4]
33. ! [X0] : (strong(X0) | (~creative(X0) & calm(X0))) [ennf transformation 29]
55. ((calm(alice) | ~old(alice)) | funny(alice)) & (~funny(alice) | (~calm(alice) & old(alice))) [nnf transformation 13]
56. (calm(alice) | ~old(alice) | funny(alice)) & (~funny(alice) | (~calm(alice) & old(alice))) [flattening 55]
84. calm(X0) | strong(X0) [cnf transformation 33]
112. ~funny(alice) | ~calm(alice) [cnf transformation 56]
141. ~strong(alice) [cnf transformation 24]
142. funny(alice) [cnf transformation 25]
242. 23 <=> funny(alice) [avatar definition]
250. 25 <=> calm(alice) [avatar definition]
251. ~calm(alice) <- (~25) [avatar component clause 250]
254. ~25 | ~23 [avatar split clause 112,242,250]
345. 23 [avatar split clause 142,242]
355. strong(alice) <- (~25) [resolution 84,251]
357. $false <- (~25) [subsumption resolution 355,141]
358. 25 [avatar contradiction clause 357]
359. $false [avatar sat refutation 254,345,358]
% SZS output end Proof for 1474151884234878152211781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not humble or not curious then someone is both wise and not calm and vice versa.
Everyone who is quiet or strong is either quiet or not kind and vice versa.
Everyone who is not quiet is not tall and vice versa.
Everyone who is both not wise and not patient is quiet or calm.
If someone is both patient and rich then someone is quiet and vice versa.
Everyone who is not tall or not humble is both not calm and humble and vice versa.
Everyone who is both happy and brave is funny or old and vice versa.
Everyone who is both not kind and kind is wise or quiet and vice versa.
If someone is both not strong and creative then someone is either old or quiet.
If someone is generous or not rich then someone is either not generous or wise.
Everyone who is both generous and quiet is strong.
If someone is either not funny or tall then john is both generous and kind.
Everyone who is happy or tall is tall and vice versa.
If paul is both not happy and strong then someone is not old.
Everyone who is brave is either not funny or brave.
Everyone who is either wise or rich is both not humble and calm and vice versa.
Mary is not generous.
Someone is either tall or kind.
Someone is not wise.
Alice is either strong or curious.
Someone is calm or kind.
Mary is calm or not curious.
Someone is not curious.
Someone is brave or not strong. | Mary is brave. | contradiction | (((~humble(paul)<~>~curious(paul)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((quiet(X)|strong(X))<=>(quiet(X)<~>~kind(X))))&
(![X]:(~quiet(X)<=>~tall(X)))&
(![X]:((~wise(X)&~patient(X))=>(quiet(X)|calm(X))))&
((?[X]:((patient(X)&rich(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~tall(X)|~humble(X))<=>(~calm(X)&humble(X))))&
(![X]:((happy(X)&brave(X))<=>(funny(X)|old(X))))&
(![X]:((~kind(X)&kind(X))<=>(wise(X)|quiet(X))))&
((?[X]:((~strong(X)&creative(X))))=>(?[X]:((old(X)<~>quiet(X)))))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((generous(X)&quiet(X))=>strong(X)))&
((?[X]:((~funny(X)<~>tall(X))))=>((generous(john)&kind(john))))&
(![X]:((happy(X)|tall(X))<=>tall(X)))&
(((~happy(paul)&strong(paul)))=>(?[X]:(~old(X))))&
(![X]:(brave(X)=>(~funny(X)<~>brave(X))))&
(![X]:((wise(X)<~>rich(X))<=>(~humble(X)&calm(X))))&
(~generous(mary))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:(~wise(X)))&
((strong(alice)<~>curious(alice)))&
(?[X]:((calm(X)|kind(X))))&
((calm(mary)|~curious(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)|~strong(X)))) | brave(mary) | [
"p1",
"p2",
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 377308024364598933885215
% SZS output start Proof for 377308024364598933885215
2. ! [X0] : ((strong(X0) | quiet(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p1]
3. ! [X0] : (~quiet(X0) <=> ~tall(X0)) [input p2]
7. ! [X0] : ((brave(X0) & happy(X0)) <=> (old(X0) | funny(X0))) [input p6]
8. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (quiet(X0) | wise(X0))) [input p7]
13. ! [X0] : ((tall(X0) | happy(X0)) <=> tall(X0)) [input p12]
15. ! [X0] : (brave(X0) => (~funny(X0) <~> brave(X0))) [input p14]
25. brave(mary) [input hypothesis]
38. ! [X0] : ((~funny(X0) <~> brave(X0)) | ~brave(X0)) [ennf transformation 15]
43. ! [X0] : (((strong(X0) | quiet(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~strong(X0) & ~quiet(X0)))) [nnf transformation 2]
44. ! [X0] : ((strong(X0) | quiet(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (~strong(X0) & ~quiet(X0)))) [flattening 43]
45. ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 3]
53. ! [X0] : (((brave(X0) & happy(X0)) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | (~brave(X0) | ~happy(X0)))) [nnf transformation 7]
54. ! [X0] : (((brave(X0) & happy(X0)) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ~brave(X0) | ~happy(X0))) [flattening 53]
55. ! [X0] : (((kind(X0) & ~kind(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~kind(X0) | kind(X0)))) [nnf transformation 8]
56. ! [X0] : (((kind(X0) & ~kind(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~kind(X0) | kind(X0))) [flattening 55]
62. ! [X0] : (((tall(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~happy(X0)))) [nnf transformation 13]
63. ! [X0] : ((tall(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~happy(X0)))) [flattening 62]
66. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | ~brave(X0)) [nnf transformation 38]
89. kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 44]
93. ~tall(X0) | quiet(X0) [cnf transformation 45]
105. ~funny(X0) | happy(X0) [cnf transformation 54]
111. ~kind(X0) | ~quiet(X0) [cnf transformation 56]
123. ~happy(X0) | tall(X0) [cnf transformation 63]
128. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 66]
145. brave(mary) [cnf transformation 25]
146. ~brave(X0) | funny(X0) [duplicate literal removal 128]
149. ~quiet(X0) | kind(X0) [duplicate literal removal 89]
177. 6 <=> ! [X1] : ~quiet(X1) [avatar definition]
178. ~quiet(X1) <- (6) [avatar component clause 177]
197. ~quiet(X0) [subsumption resolution 111,149]
198. 6 [avatar split clause 197,177]
304. funny(mary) [resolution 146,145]
306. happy(mary) [resolution 304,105]
308. tall(mary) [resolution 306,123]
319. quiet(mary) [resolution 308,93]
320. $false <- (6) [subsumption resolution 319,178]
321. ~6 [avatar contradiction clause 320]
322. $false [avatar sat refutation 198,321]
% SZS output end Proof for 377308024364598933885215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or brave is either not kind or not strong and vice versa. If someone is not humble then someone is not tall. If susan is both not calm and rich then someone is calm or not patient. If paul is brave then someone is not rich or humble. Everyone who is either curious or generous is not generous or not funny. If paul is not generous then susan is not rich and vice versa. Everyone who is both brave and humble is either not quiet or tall and vice versa. If mary is both not tall and not creative then lucy is both not strong and wise and vice versa. Everyone who is both humble and not creative is either not calm or rich and vice versa. Everyone who is not kind is either not kind or creative and vice versa. Everyone who is quiet or not tall is kind or curious. If someone is happy then someone is both wise and rich. If someone is patient then someone is not generous or not rich and vice versa. Everyone who is quiet or brave is both not tall and not brave. Everyone who is generous or kind is tall and vice versa. Everyone who is either not calm or creative is either not happy or strong and vice versa. Someone is both not strong and quiet. Lucy is strong. Someone is not curious. Someone is not creative or not happy. Lucy is either old or not funny. Paul is not calm or not strong. Someone is generous or not curious. | Paul is not calm. | neutral | (![X]:((~happy(X)<~>brave(X))<=>(~kind(X)<~>~strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~tall(X))))&
(((~calm(susan)&rich(susan)))=>(?[X]:((calm(X)|~patient(X)))))&
((brave(paul))=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((curious(X)<~>generous(X))=>(~generous(X)|~funny(X))))&
((~generous(paul))<=>(~rich(susan)))&
(![X]:((brave(X)&humble(X))<=>(~quiet(X)<~>tall(X))))&
(((~tall(mary)&~creative(mary)))<=>((~strong(lucy)&wise(lucy))))&
(![X]:((humble(X)&~creative(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~kind(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((quiet(X)|~tall(X))=>(kind(X)|curious(X))))&
((?[X]:(happy(X)))=>(?[X]:((wise(X)&rich(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((quiet(X)|brave(X))=>(~tall(X)&~brave(X))))&
(![X]:((generous(X)|kind(X))<=>tall(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~happy(X)<~>strong(X))))&
(?[X]:((~strong(X)&quiet(X))))&
(strong(lucy))&
(?[X]:(~curious(X)))&
(?[X]:((~creative(X)|~happy(X))))&
((old(lucy)<~>~funny(lucy)))&
((~calm(paul)|~strong(paul)))&
(?[X]:((generous(X)|~curious(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is not rich is not calm or brave.
If someone is either not patient or not strong then someone is generous.
If someone is quiet then someone is generous and vice versa.
If paul is both creative and calm then someone is not generous.
Everyone who is not curious or not brave is not brave or quiet and vice versa.
Everyone who is not tall or not generous is either rich or old.
Everyone who is not kind is not curious and vice versa.
Everyone who is both brave and wise is not kind and vice versa.
Everyone who is both rich and creative is both not patient and curious and vice versa.
If john is happy then someone is rich or patient.
If someone is not strong then someone is both not happy and not calm and vice versa.
Everyone who is both calm and not happy is tall and vice versa.
Everyone who is both not calm and humble is both not tall and not kind and vice versa.
Everyone who is not old or tall is funny.
If mary is curious then susan is calm.
Everyone who is either not rich or calm is not funny or not generous.
Fred is funny.
Someone is not calm or calm.
Lucy is both rich and not kind.
John is quiet or curious.
Susan is either not rich or not creative.
Mary is curious.
Paul is both not kind and not old.
Susan is both not generous and patient. | Lucy is not old. | entailment | (![X]:(~rich(X)=>(~calm(X)|brave(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:(generous(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(generous(X))))&
(((creative(paul)&calm(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)|~brave(X))<=>(~brave(X)|quiet(X))))&
(![X]:((~tall(X)|~generous(X))=>(rich(X)<~>old(X))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:((brave(X)&wise(X))<=>~kind(X)))&
(![X]:((rich(X)&creative(X))<=>(~patient(X)&curious(X))))&
((happy(john))=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((calm(X)&~happy(X))<=>tall(X)))&
(![X]:((~calm(X)&humble(X))<=>(~tall(X)&~kind(X))))&
(![X]:((~old(X)|tall(X))=>funny(X)))&
((curious(mary))=>(calm(susan)))&
(![X]:((~rich(X)<~>calm(X))=>(~funny(X)|~generous(X))))&
(funny(fred))&
(?[X]:((~calm(X)|calm(X))))&
((rich(lucy)&~kind(lucy)))&
((quiet(john)|curious(john)))&
((~rich(susan)<~>~creative(susan)))&
(curious(mary))&
((~kind(paul)&~old(paul)))&
((~generous(susan)&patient(susan))) | ~old(lucy) | [
"p5",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1058698117036743371274773
% SZS output start Proof for 1058698117036743371274773
6. ! [X0] : ((~generous(X0) | ~tall(X0)) => (rich(X0) <~> old(X0))) [input p5]
12. ! [X0] : ((~happy(X0) & calm(X0)) <=> tall(X0)) [input p11]
14. ! [X0] : ((tall(X0) | ~old(X0)) => funny(X0)) [input p13]
16. ! [X0] : ((~rich(X0) <~> calm(X0)) => (~generous(X0) | ~funny(X0))) [input p15]
19. ~kind(lucy) & rich(lucy) [input p18]
25. old(lucy) [input hypothesis]
34. ! [X0] : ((rich(X0) <~> old(X0)) | (generous(X0) & tall(X0))) [ennf transformation 6]
36. ! [X0] : (funny(X0) | (~tall(X0) & old(X0))) [ennf transformation 14]
38. ! [X0] : ((~generous(X0) | ~funny(X0)) | (~rich(X0) <=> calm(X0))) [ennf transformation 16]
39. ! [X0] : (~generous(X0) | ~funny(X0) | (~rich(X0) <=> calm(X0))) [flattening 38]
53. ! [X0] : (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (generous(X0) & tall(X0))) [nnf transformation 34]
66. ! [X0] : (((~happy(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 12]
67. ! [X0] : (((~happy(X0) & calm(X0)) | ~tall(X0)) & (tall(X0) | happy(X0) | ~calm(X0))) [flattening 66]
70. ! [X0] : (~generous(X0) | ~funny(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0)))) [nnf transformation 39]
86. ~old(X0) | ~rich(X0) | tall(X0) [cnf transformation 53]
87. ~old(X0) | ~rich(X0) | generous(X0) [cnf transformation 53]
102. ~tall(X0) | calm(X0) [cnf transformation 67]
109. ~tall(X0) | funny(X0) [cnf transformation 36]
112. ~funny(X0) | ~generous(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 70]
115. rich(lucy) [cnf transformation 19]
125. old(lucy) [cnf transformation 25]
312. ~rich(lucy) | tall(lucy) [resolution 86,125]
316. tall(lucy) [subsumption resolution 312,115]
317. funny(lucy) [resolution 316,109]
318. calm(lucy) [resolution 316,102]
319. ~rich(lucy) | generous(lucy) [resolution 87,125]
323. generous(lucy) [subsumption resolution 319,115]
416. ~generous(lucy) | ~rich(lucy) | ~calm(lucy) [resolution 317,112]
418. ~rich(lucy) | ~calm(lucy) [subsumption resolution 416,323]
419. ~calm(lucy) [subsumption resolution 418,115]
420. $false [subsumption resolution 419,318]
% SZS output end Proof for 1058698117036743371274773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If susan is quiet or not old then someone is either not wise or humble and vice versa.
Everyone who is strong is generous or not brave.
Everyone who is funny or brave is not strong.
Everyone who is not wise is not strong or happy.
If someone is either not kind or brave then someone is not strong or not old and vice versa.
Everyone who is both rich and tall is old or strong.
Everyone who is rich or happy is both quiet and not strong.
Everyone who is not quiet is both not tall and not strong and vice versa.
Everyone who is not creative or not quiet is either old or not rich and vice versa.
Everyone who is either humble or not tall is both wise and not patient and vice versa.
If mary is quiet then lucy is not old or not quiet and vice versa.
If john is either tall or rich then someone is strong.
If someone is rich then lucy is both not quiet and not humble and vice versa.
Everyone who is wise is not wise or not patient and vice versa.
Everyone who is not creative is patient or wise and vice versa.
Everyone who is both calm and funny is not curious and vice versa.
Someone is not kind.
Fred is rich or not brave.
Alice is either rich or curious.
Lucy is both wise and not brave.
Susan is either not patient or not brave.
John is not curious or calm.
Someone is not generous. | Susan is not rich. | neutral | (((quiet(susan)|~old(susan)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(strong(X)=>(generous(X)|~brave(X))))&
(![X]:((funny(X)|brave(X))=>~strong(X)))&
(![X]:(~wise(X)=>(~strong(X)|happy(X))))&
((?[X]:((~kind(X)<~>brave(X))))<=>(?[X]:((~strong(X)|~old(X)))))&
(![X]:((rich(X)&tall(X))=>(old(X)|strong(X))))&
(![X]:((rich(X)|happy(X))=>(quiet(X)&~strong(X))))&
(![X]:(~quiet(X)<=>(~tall(X)&~strong(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(old(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~tall(X))<=>(wise(X)&~patient(X))))&
((quiet(mary))<=>((~old(lucy)|~quiet(lucy))))&
(((tall(john)<~>rich(john)))=>(?[X]:(strong(X))))&
((?[X]:(rich(X)))<=>((~quiet(lucy)&~humble(lucy))))&
(![X]:(wise(X)<=>(~wise(X)|~patient(X))))&
(![X]:(~creative(X)<=>(patient(X)|wise(X))))&
(![X]:((calm(X)&funny(X))<=>~curious(X)))&
(?[X]:(~kind(X)))&
((rich(fred)|~brave(fred)))&
((rich(alice)<~>curious(alice)))&
((wise(lucy)&~brave(lucy)))&
((~patient(susan)<~>~brave(susan)))&
((~curious(john)|calm(john)))&
(?[X]:(~generous(X))) | ~rich(susan) | [] | null | 0 |
Everyone who is either not happy or curious is calm and vice versa.
Everyone who is generous is not brave and vice versa.
Everyone who is both calm and tall is both wise and not curious and vice versa.
Everyone who is not strong or not funny is not quiet and vice versa.
If someone is both calm and creative then paul is humble or not quiet and vice versa.
If someone is both not strong and not patient then susan is either funny or patient.
If someone is strong then someone is both creative and funny.
Everyone who is either not tall or not humble is either quiet or not generous and vice versa.
Everyone who is not strong or not brave is old or curious and vice versa.
If someone is both humble and not funny then alice is not wise or not generous and vice versa.
Everyone who is both brave and not humble is both calm and happy and vice versa.
Everyone who is either patient or not generous is either creative or not kind and vice versa.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
John is strong.
Someone is either not curious or not happy.
Someone is rich or not happy.
Lucy is not calm.
Paul is both happy and not kind.
Someone is either generous or not curious.
John is both not creative and not wise. | Paul is not curious. | entailment | (![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:(generous(X)<=>~brave(X)))&
(![X]:((calm(X)&tall(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)|~funny(X))<=>~quiet(X)))&
((?[X]:((calm(X)&creative(X))))<=>((humble(paul)|~quiet(paul))))&
((?[X]:((~strong(X)&~patient(X))))=>((funny(susan)<~>patient(susan))))&
((?[X]:(strong(X)))=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~strong(X)|~brave(X))<=>(old(X)|curious(X))))&
((?[X]:((humble(X)&~funny(X))))<=>((~wise(alice)|~generous(alice))))&
(![X]:((brave(X)&~humble(X))<=>(calm(X)&happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(strong(john))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((rich(X)|~happy(X))))&
(~calm(lucy))&
((happy(paul)&~kind(paul)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~creative(john)&~wise(john))) | ~curious(paul) | [
"p0",
"p1",
"p2",
"p3",
"p7",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 436082024274668033498330
% SZS output start Proof for 436082024274668033498330
1. ! [X0] : ((~happy(X0) <~> curious(X0)) <=> calm(X0)) [input p0]
2. ! [X0] : (generous(X0) <=> ~brave(X0)) [input p1]
3. ! [X0] : ((tall(X0) & calm(X0)) <=> (~curious(X0) & wise(X0))) [input p2]
4. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> ~quiet(X0)) [input p3]
8. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (quiet(X0) <~> ~generous(X0))) [input p7]
9. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> (curious(X0) | old(X0))) [input p8]
11. ! [X0] : ((~humble(X0) & brave(X0)) <=> (happy(X0) & calm(X0))) [input p10]
20. ~kind(paul) & happy(paul) [input p19]
23. curious(paul) [input hypothesis]
34. ! [X0] : ((((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))))) [nnf transformation 1]
35. ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))) [nnf transformation 2]
36. ! [X0] : (((tall(X0) & calm(X0)) | (curious(X0) | ~wise(X0))) & ((~curious(X0) & wise(X0)) | (~tall(X0) | ~calm(X0)))) [nnf transformation 3]
37. ! [X0] : (((tall(X0) & calm(X0)) | curious(X0) | ~wise(X0)) & ((~curious(X0) & wise(X0)) | ~tall(X0) | ~calm(X0))) [flattening 36]
38. ! [X0] : (((~funny(X0) | ~strong(X0)) | quiet(X0)) & (~quiet(X0) | (funny(X0) & strong(X0)))) [nnf transformation 4]
39. ! [X0] : ((~funny(X0) | ~strong(X0) | quiet(X0)) & (~quiet(X0) | (funny(X0) & strong(X0)))) [flattening 38]
49. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 8]
50. ! [X0] : (((~brave(X0) | ~strong(X0)) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | (brave(X0) & strong(X0)))) [nnf transformation 9]
51. ! [X0] : ((~brave(X0) | ~strong(X0) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | (brave(X0) & strong(X0)))) [flattening 50]
57. ! [X0] : (((~humble(X0) & brave(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (humble(X0) | ~brave(X0)))) [nnf transformation 11]
58. ! [X0] : (((~humble(X0) & brave(X0)) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | humble(X0) | ~brave(X0))) [flattening 57]
71. ~curious(X0) | ~happy(X0) | calm(X0) [cnf transformation 34]
74. ~brave(X0) | ~generous(X0) [cnf transformation 35]
77. ~tall(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 37]
80. ~quiet(X0) | strong(X0) [cnf transformation 39]
99. humble(X0) | tall(X0) | quiet(X0) | generous(X0) [cnf transformation 49]
103. ~strong(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 51]
111. ~calm(X0) | ~happy(X0) | brave(X0) [cnf transformation 58]
112. ~humble(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 58]
132. happy(paul) [cnf transformation 20]
138. curious(paul) [cnf transformation 23]
140. 1 <=> quiet(paul) [avatar definition]
142. quiet(paul) <- (1) [avatar component clause 140]
149. 3 <=> humble(paul) [avatar definition]
150. humble(paul) <- (3) [avatar component clause 149]
151. ~humble(paul) <- (~3) [avatar component clause 149]
265. ~happy(paul) | calm(paul) [resolution 71,138]
268. calm(paul) [subsumption resolution 265,132]
344. ~happy(paul) | brave(paul) [resolution 111,268]
347. brave(paul) [subsumption resolution 344,132]
367. ~generous(paul) [resolution 347,74]
443. strong(paul) <- (1) [resolution 142,80]
446. tall(paul) | quiet(paul) | generous(paul) <- (~3) [resolution 151,99]
452. ~brave(paul) | ~curious(paul) <- (1) [resolution 443,103]
453. ~curious(paul) <- (1) [subsumption resolution 452,347]
454. $false <- (1) [subsumption resolution 453,138]
455. ~1 [avatar contradiction clause 454]
456. tall(paul) | quiet(paul) <- (~3) [subsumption resolution 446,367]
458. 50 <=> tall(paul) [avatar definition]
460. tall(paul) <- (50) [avatar component clause 458]
461. 1 | 50 | 3 [avatar split clause 456,149,458,140]
470. ~happy(paul) | ~calm(paul) <- (3) [resolution 150,112]
474. ~calm(paul) <- (3) [subsumption resolution 470,132]
475. $false <- (3) [subsumption resolution 474,268]
476. ~3 [avatar contradiction clause 475]
494. ~curious(paul) | ~calm(paul) <- (50) [resolution 460,77]
505. ~calm(paul) <- (50) [subsumption resolution 494,138]
506. $false <- (50) [subsumption resolution 505,268]
507. ~50 [avatar contradiction clause 506]
509. $false [avatar sat refutation 455,461,476,507]
% SZS output end Proof for 436082024274668033498330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is either not generous or not kind. Everyone who is either not humble or calm is not tall or not patient. If fred is creative or patient then someone is not funny or generous. If alice is strong then someone is not calm. If someone is not happy then paul is either wise or kind. If fred is both curious and happy then susan is funny and vice versa. Everyone who is curious or creative is both not kind and generous. Everyone who is happy or not kind is not curious. Everyone who is not brave is both not happy and not brave. Everyone who is both happy and not tall is generous and vice versa. If someone is not calm or not humble then mary is not strong or calm and vice versa. If someone is not creative then someone is not strong or not creative and vice versa. Everyone who is not humble is both not kind and not brave. If john is either old or tall then someone is not happy. If someone is both not kind and patient then susan is tall or humble and vice versa. If someone is either wise or not happy then someone is either not calm or strong. Someone is either strong or generous. Someone is not quiet or not happy. Someone is kind or happy. Paul is either not old or tall. Alice is both rich and not happy. Someone is either generous or not funny. Someone is both funny and not wise. | Alice is kind. | entailment | (![X]:((happy(X)|~curious(X))=>(~generous(X)<~>~kind(X))))&
(![X]:((~humble(X)<~>calm(X))=>(~tall(X)|~patient(X))))&
(((creative(fred)|patient(fred)))=>(?[X]:((~funny(X)|generous(X)))))&
((strong(alice))=>(?[X]:(~calm(X))))&
((?[X]:(~happy(X)))=>((wise(paul)<~>kind(paul))))&
(((curious(fred)&happy(fred)))<=>(funny(susan)))&
(![X]:((curious(X)|creative(X))=>(~kind(X)&generous(X))))&
(![X]:((happy(X)|~kind(X))=>~curious(X)))&
(![X]:(~brave(X)=>(~happy(X)&~brave(X))))&
(![X]:((happy(X)&~tall(X))<=>generous(X)))&
((?[X]:((~calm(X)|~humble(X))))<=>((~strong(mary)|calm(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)|~creative(X)))))&
(![X]:(~humble(X)=>(~kind(X)&~brave(X))))&
(((old(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
((?[X]:((~kind(X)&patient(X))))<=>((tall(susan)|humble(susan))))&
((?[X]:((wise(X)<~>~happy(X))))=>(?[X]:((~calm(X)<~>strong(X)))))&
(?[X]:((strong(X)<~>generous(X))))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((kind(X)|happy(X))))&
((~old(paul)<~>tall(paul)))&
((rich(alice)&~happy(alice)))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:((funny(X)&~wise(X)))) | kind(alice) | [
"p0",
"p6",
"p7",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9080562322809239652380598
% SZS output start Proof for 9080562322809239652380598
1. ! [X0] : ((~curious(X0) | happy(X0)) => (~generous(X0) <~> ~kind(X0))) [input p0]
7. ! [X0] : ((creative(X0) | curious(X0)) => (generous(X0) & ~kind(X0))) [input p6]
8. ! [X0] : ((~kind(X0) | happy(X0)) => ~curious(X0)) [input p7]
10. ! [X0] : ((~tall(X0) & happy(X0)) <=> generous(X0)) [input p9]
21. ~happy(alice) & rich(alice) [input p20]
24. ~kind(alice) [input hypothesis]
27. ~happy(alice) [pure predicate removal 21]
29. ! [X0] : ((~generous(X0) <~> ~kind(X0)) | (curious(X0) & ~happy(X0))) [ennf transformation 1]
35. ! [X0] : ((generous(X0) & ~kind(X0)) | (~creative(X0) & ~curious(X0))) [ennf transformation 7]
36. ! [X0] : (~curious(X0) | (kind(X0) & ~happy(X0))) [ennf transformation 8]
41. ! [X0] : (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (curious(X0) & ~happy(X0))) [nnf transformation 29]
50. ! [X0] : (((~tall(X0) & happy(X0)) | ~generous(X0)) & (generous(X0) | (tall(X0) | ~happy(X0)))) [nnf transformation 10]
51. ! [X0] : (((~tall(X0) & happy(X0)) | ~generous(X0)) & (generous(X0) | tall(X0) | ~happy(X0))) [flattening 50]
88. kind(X0) | generous(X0) | curious(X0) [cnf transformation 41]
99. ~kind(X0) | ~curious(X0) [cnf transformation 35]
104. ~curious(X0) | kind(X0) [cnf transformation 36]
108. ~generous(X0) | happy(X0) [cnf transformation 51]
135. ~happy(alice) [cnf transformation 27]
140. ~kind(alice) [cnf transformation 24]
196. ~curious(X0) [subsumption resolution 104,99]
350. generous(alice) | curious(alice) [resolution 88,140]
355. generous(alice) [subsumption resolution 350,196]
358. happy(alice) [resolution 355,108]
359. $false [subsumption resolution 358,135]
% SZS output end Proof for 9080562322809239652380598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not old or tall then lucy is both brave and not calm and vice versa.
Everyone who is funny is both not generous and not happy.
Everyone who is kind is humble or curious and vice versa.
If lucy is both not curious and not happy then fred is funny or not old and vice versa.
If someone is kind or not tall then lucy is not rich.
If lucy is not quiet or wise then alice is not quiet or old and vice versa.
If someone is not wise or patient then alice is wise or tall.
If someone is not rich or not curious then someone is either rich or not quiet and vice versa.
Everyone who is either generous or happy is old and vice versa.
If mary is happy or strong then mary is rich.
Everyone who is funny or happy is both not funny and generous.
Everyone who is either not rich or not brave is either not wise or not brave and vice versa.
If someone is not patient then someone is either creative or rich and vice versa.
Everyone who is not humble is either generous or quiet and vice versa.
Everyone who is not old is either not calm or funny.
Everyone who is either calm or kind is not calm or calm.
Paul is either not wise or patient.
John is brave.
Someone is brave.
Paul is both not old and not happy.
Lucy is not funny.
Lucy is not kind.
John is either old or not strong.
Someone is either old or not brave. | Mary is not funny. | entailment | (((~old(paul)|tall(paul)))<=>((brave(lucy)&~calm(lucy))))&
(![X]:(funny(X)=>(~generous(X)&~happy(X))))&
(![X]:(kind(X)<=>(humble(X)|curious(X))))&
(((~curious(lucy)&~happy(lucy)))<=>((funny(fred)|~old(fred))))&
((?[X]:((kind(X)|~tall(X))))=>(~rich(lucy)))&
(((~quiet(lucy)|wise(lucy)))<=>((~quiet(alice)|old(alice))))&
((?[X]:((~wise(X)|patient(X))))=>((wise(alice)|tall(alice))))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>happy(X))<=>old(X)))&
(((happy(mary)|strong(mary)))=>(rich(mary)))&
(![X]:((funny(X)|happy(X))=>(~funny(X)&generous(X))))&
(![X]:((~rich(X)<~>~brave(X))<=>(~wise(X)<~>~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((creative(X)<~>rich(X)))))&
(![X]:(~humble(X)<=>(generous(X)<~>quiet(X))))&
(![X]:(~old(X)=>(~calm(X)<~>funny(X))))&
(![X]:((calm(X)<~>kind(X))=>(~calm(X)|calm(X))))&
((~wise(paul)<~>patient(paul)))&
(brave(john))&
(?[X]:(brave(X)))&
((~old(paul)&~happy(paul)))&
(~funny(lucy))&
(~kind(lucy))&
((old(john)<~>~strong(john)))&
(?[X]:((old(X)<~>~brave(X)))) | ~funny(mary) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1853977921524906255256320
% SZS output start Proof for 1853977921524906255256320
2. ! [X0] : (funny(X0) => (~happy(X0) & ~generous(X0))) [input p1]
11. ! [X0] : ((happy(X0) | funny(X0)) => (generous(X0) & ~funny(X0))) [input p10]
25. funny(mary) [input hypothesis]
28. ! [X0] : ((~happy(X0) & ~generous(X0)) | ~funny(X0)) [ennf transformation 2]
33. ! [X0] : ((generous(X0) & ~funny(X0)) | (~happy(X0) & ~funny(X0))) [ennf transformation 11]
72. ~generous(X0) | ~funny(X0) [cnf transformation 28]
104. generous(X0) | ~funny(X0) [cnf transformation 33]
138. funny(mary) [cnf transformation 25]
284. ~funny(X0) [subsumption resolution 104,72]
344. $false [subsumption resolution 138,284]
% SZS output end Proof for 1853977921524906255256320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not brave or happy and vice versa.
Everyone who is not strong is either calm or kind.
If alice is not curious or rich then someone is either generous or not brave and vice versa.
If someone is both not brave and not funny then someone is not kind and vice versa.
Everyone who is not wise or brave is quiet or not funny.
Everyone who is both not curious and brave is not patient or not calm and vice versa.
If alice is both funny and curious then alice is either not calm or funny.
Everyone who is not happy or not strong is quiet or not calm.
Everyone who is strong or calm is both humble and funny.
If someone is both not curious and calm then alice is not tall or rich and vice versa.
If someone is either wise or not strong then someone is kind or curious and vice versa.
Everyone who is both humble and quiet is both not old and not humble and vice versa.
Everyone who is either not brave or rich is both not curious and not generous.
Everyone who is wise or curious is both not tall and not funny.
If someone is either not kind or not wise then someone is both brave and not curious and vice versa.
Lucy is either happy or not patient.
Someone is either not happy or not wise.
Someone is rich.
Susan is not creative.
Someone is both not strong and not rich.
Someone is not strong or strong.
Alice is either old or not humble. | Susan is curious. | contradiction | (![X]:(humble(X)<=>(~brave(X)|happy(X))))&
(![X]:(~strong(X)=>(calm(X)<~>kind(X))))&
(((~curious(alice)|rich(alice)))<=>(?[X]:((generous(X)<~>~brave(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)|~funny(X))))&
(![X]:((~curious(X)&brave(X))<=>(~patient(X)|~calm(X))))&
(((funny(alice)&curious(alice)))=>((~calm(alice)<~>funny(alice))))&
(![X]:((~happy(X)|~strong(X))=>(quiet(X)|~calm(X))))&
(![X]:((strong(X)|calm(X))=>(humble(X)&funny(X))))&
((?[X]:((~curious(X)&calm(X))))<=>((~tall(alice)|rich(alice))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((humble(X)&quiet(X))<=>(~old(X)&~humble(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~curious(X)&~generous(X))))&
(![X]:((wise(X)|curious(X))=>(~tall(X)&~funny(X))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:((brave(X)&~curious(X)))))&
((happy(lucy)<~>~patient(lucy)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:(rich(X)))&
(~creative(susan))&
(?[X]:((~strong(X)&~rich(X))))&
(?[X]:((~strong(X)|strong(X))))&
((old(alice)<~>~humble(alice))) | curious(susan) | [
"p5",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 458617897623587170251125
% SZS output start Proof for 458617897623587170251125
6. ! [X0] : ((brave(X0) & ~curious(X0)) <=> (~calm(X0) | ~patient(X0))) [input p5]
9. ! [X0] : ((calm(X0) | strong(X0)) => (funny(X0) & humble(X0))) [input p8]
14. ! [X0] : ((curious(X0) | wise(X0)) => (~funny(X0) & ~tall(X0))) [input p13]
23. curious(susan) [input hypothesis]
35. ! [X0] : ((funny(X0) & humble(X0)) | (~calm(X0) & ~strong(X0))) [ennf transformation 9]
37. ! [X0] : ((~funny(X0) & ~tall(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 14]
51. ! [X0] : (((brave(X0) & ~curious(X0)) | (calm(X0) & patient(X0))) & ((~calm(X0) | ~patient(X0)) | (~brave(X0) | curious(X0)))) [nnf transformation 6]
52. ! [X0] : (((brave(X0) & ~curious(X0)) | (calm(X0) & patient(X0))) & (~calm(X0) | ~patient(X0) | ~brave(X0) | curious(X0))) [flattening 51]
101. ~curious(X0) | calm(X0) [cnf transformation 52]
111. ~calm(X0) | funny(X0) [cnf transformation 35]
134. ~funny(X0) | ~curious(X0) [cnf transformation 37]
151. curious(susan) [cnf transformation 23]
315. calm(susan) [resolution 101,151]
321. funny(susan) [resolution 111,315]
325. ~curious(susan) [resolution 134,321]
326. $false [subsumption resolution 325,151]
% SZS output end Proof for 458617897623587170251125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not old or not kind and vice versa. Everyone who is either strong or not old is humble or wise and vice versa. If susan is rich or not brave then someone is both wise and creative and vice versa. If paul is quiet then alice is both not strong and curious. Everyone who is brave or generous is either curious or not brave. Everyone who is both not wise and not patient is both not tall and not funny. Everyone who is tall or rich is generous and vice versa. Everyone who is either brave or funny is not happy and vice versa. If mary is both not brave and not generous then susan is not humble and vice versa. If paul is not generous or calm then john is patient or strong and vice versa. If susan is not quiet or not curious then someone is generous or happy and vice versa. If susan is both generous and brave then someone is either not quiet or funny. If someone is not wise or not happy then someone is not kind and vice versa. If lucy is either not generous or old then someone is both not old and not kind. Everyone who is either not generous or not calm is patient. Everyone who is both creative and strong is both wise and not calm and vice versa. Someone is not curious. Someone is funny. Susan is not funny. John is both strong and wise. Someone is both rich and not funny. Lucy is tall or not tall. Someone is either not patient or funny. | Paul is quiet. | neutral | (![X]:(happy(X)<=>(~old(X)|~kind(X))))&
(![X]:((strong(X)<~>~old(X))<=>(humble(X)|wise(X))))&
(((rich(susan)|~brave(susan)))<=>(?[X]:((wise(X)&creative(X)))))&
((quiet(paul))=>((~strong(alice)&curious(alice))))&
(![X]:((brave(X)|generous(X))=>(curious(X)<~>~brave(X))))&
(![X]:((~wise(X)&~patient(X))=>(~tall(X)&~funny(X))))&
(![X]:((tall(X)|rich(X))<=>generous(X)))&
(![X]:((brave(X)<~>funny(X))<=>~happy(X)))&
(((~brave(mary)&~generous(mary)))<=>(~humble(susan)))&
(((~generous(paul)|calm(paul)))<=>((patient(john)|strong(john))))&
(((~quiet(susan)|~curious(susan)))<=>(?[X]:((generous(X)|happy(X)))))&
(((generous(susan)&brave(susan)))=>(?[X]:((~quiet(X)<~>funny(X)))))&
((?[X]:((~wise(X)|~happy(X))))<=>(?[X]:(~kind(X))))&
(((~generous(lucy)<~>old(lucy)))=>(?[X]:((~old(X)&~kind(X)))))&
(![X]:((~generous(X)<~>~calm(X))=>patient(X)))&
(![X]:((creative(X)&strong(X))<=>(wise(X)&~calm(X))))&
(?[X]:(~curious(X)))&
(?[X]:(funny(X)))&
(~funny(susan))&
((strong(john)&wise(john)))&
(?[X]:((rich(X)&~funny(X))))&
((tall(lucy)|~tall(lucy)))&
(?[X]:((~patient(X)<~>funny(X)))) | quiet(paul) | [] | null | 0 |
Everyone who is either not generous or humble is either patient or not brave. If fred is both not tall and funny then someone is not brave. If paul is both old and not brave then someone is either not creative or funny and vice versa. Everyone who is not quiet or kind is quiet or not funny. Everyone who is both not tall and brave is not rich or wise and vice versa. Everyone who is not kind is both generous and not strong. Everyone who is both generous and not kind is either not funny or strong and vice versa. If someone is either calm or happy then lucy is brave. If someone is both calm and funny then fred is both not generous and not strong. If someone is both not funny and rich then lucy is either not generous or rich. If susan is both not old and generous then fred is rich and vice versa. Everyone who is both rich and patient is not brave and vice versa. Everyone who is either quiet or brave is both not patient and kind and vice versa. If someone is not patient then someone is both not rich and not wise. Everyone who is either not tall or not quiet is happy or wise. Everyone who is both rich and not patient is either old or not happy and vice versa. Someone is either not kind or not old. Someone is both not kind and old. Someone is both funny and not tall. Someone is either not happy or not creative. Someone is both not wise and patient. Someone is happy. Lucy is both not creative and kind. | Paul is not creative. | neutral | (![X]:((~generous(X)<~>humble(X))=>(patient(X)<~>~brave(X))))&
(((~tall(fred)&funny(fred)))=>(?[X]:(~brave(X))))&
(((old(paul)&~brave(paul)))<=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:((~quiet(X)|kind(X))=>(quiet(X)|~funny(X))))&
(![X]:((~tall(X)&brave(X))<=>(~rich(X)|wise(X))))&
(![X]:(~kind(X)=>(generous(X)&~strong(X))))&
(![X]:((generous(X)&~kind(X))<=>(~funny(X)<~>strong(X))))&
((?[X]:((calm(X)<~>happy(X))))=>(brave(lucy)))&
((?[X]:((calm(X)&funny(X))))=>((~generous(fred)&~strong(fred))))&
((?[X]:((~funny(X)&rich(X))))=>((~generous(lucy)<~>rich(lucy))))&
(((~old(susan)&generous(susan)))<=>(rich(fred)))&
(![X]:((rich(X)&patient(X))<=>~brave(X)))&
(![X]:((quiet(X)<~>brave(X))<=>(~patient(X)&kind(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((~tall(X)<~>~quiet(X))=>(happy(X)|wise(X))))&
(![X]:((rich(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
(?[X]:((~kind(X)&old(X))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:((~wise(X)&patient(X))))&
(?[X]:(happy(X)))&
((~creative(lucy)&kind(lucy))) | ~creative(paul) | [] | null | 0 |
If someone is either patient or not kind then paul is either not tall or not funny and vice versa. Everyone who is not strong or happy is wise. If someone is not creative then someone is not rich or not strong and vice versa. If susan is both quiet and generous then alice is quiet or not curious and vice versa. Everyone who is both not brave and not happy is not kind or not tall and vice versa. Everyone who is either not creative or not rich is both not generous and not tall. Everyone who is tall or brave is either not generous or tall and vice versa. Everyone who is rich is either curious or not tall. Everyone who is both curious and funny is both not tall and creative. If lucy is either not humble or brave then mary is quiet or old and vice versa. If someone is tall then mary is both not rich and quiet. Everyone who is either not quiet or not strong is not rich and vice versa. Everyone who is not kind is both tall and humble. If someone is rich then someone is tall or funny. Everyone who is happy is humble or wise. If someone is both wise and funny then john is not kind or not humble. Fred is not quiet. John is both not wise and not curious. Someone is either brave or not calm. Someone is either not curious or wise. Fred is not generous or not rich. Someone is not funny. Mary is both wise and not patient. | Fred is not strong. | contradiction | ((?[X]:((patient(X)<~>~kind(X))))<=>((~tall(paul)<~>~funny(paul))))&
(![X]:((~strong(X)|happy(X))=>wise(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~rich(X)|~strong(X)))))&
(((quiet(susan)&generous(susan)))<=>((quiet(alice)|~curious(alice))))&
(![X]:((~brave(X)&~happy(X))<=>(~kind(X)|~tall(X))))&
(![X]:((~creative(X)<~>~rich(X))=>(~generous(X)&~tall(X))))&
(![X]:((tall(X)|brave(X))<=>(~generous(X)<~>tall(X))))&
(![X]:(rich(X)=>(curious(X)<~>~tall(X))))&
(![X]:((curious(X)&funny(X))=>(~tall(X)&creative(X))))&
(((~humble(lucy)<~>brave(lucy)))<=>((quiet(mary)|old(mary))))&
((?[X]:(tall(X)))=>((~rich(mary)&quiet(mary))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~rich(X)))&
(![X]:(~kind(X)=>(tall(X)&humble(X))))&
((?[X]:(rich(X)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:(happy(X)=>(humble(X)|wise(X))))&
((?[X]:((wise(X)&funny(X))))=>((~kind(john)|~humble(john))))&
(~quiet(fred))&
((~wise(john)&~curious(john)))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((~generous(fred)|~rich(fred)))&
(?[X]:(~funny(X)))&
((wise(mary)&~patient(mary))) | ~strong(fred) | [
"p4",
"p6",
"p11",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5638753641483322191703194
% SZS output start Proof for 5638753641483322191703194
5. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (~tall(X0) | ~kind(X0))) [input p4]
7. ! [X0] : ((brave(X0) | tall(X0)) <=> (~generous(X0) <~> tall(X0))) [input p6]
12. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) <=> ~rich(X0)) [input p11]
17. ~quiet(fred) [input p16]
21. ~rich(fred) | ~generous(fred) [input p20]
24. ~strong(fred) [input hypothesis]
50. ! [X0] : (((~happy(X0) & ~brave(X0)) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 5]
51. ! [X0] : (((~happy(X0) & ~brave(X0)) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | happy(X0) | brave(X0))) [flattening 50]
53. ! [X0] : (((brave(X0) | tall(X0)) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 7]
54. ! [X0] : ((brave(X0) | tall(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 53]
58. ! [X0] : ((((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | rich(X0)) & (~rich(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0))))) [nnf transformation 12]
90. ~brave(X0) | tall(X0) [cnf transformation 51]
99. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 54]
101. brave(X0) | tall(X0) | tall(X0) | generous(X0) [cnf transformation 54]
118. quiet(X0) | strong(X0) | rich(X0) [cnf transformation 58]
124. ~quiet(fred) [cnf transformation 17]
131. ~rich(fred) | ~generous(fred) [cnf transformation 21]
135. ~strong(fred) [cnf transformation 24]
136. ~tall(X0) | generous(X0) [duplicate literal removal 99]
137. brave(X0) | tall(X0) | generous(X0) [duplicate literal removal 101]
213. generous(X0) | tall(X0) [subsumption resolution 137,90]
215. generous(X0) [subsumption resolution 136,213]
291. ~rich(fred) [subsumption resolution 131,215]
325. strong(fred) | rich(fred) [resolution 118,124]
330. rich(fred) [subsumption resolution 325,135]
331. $false [subsumption resolution 330,291]
% SZS output end Proof for 5638753641483322191703194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not generous and vice versa.
If paul is either not wise or brave then alice is both curious and not calm.
If someone is not tall then alice is either not kind or brave.
Everyone who is not rich is both rich and happy and vice versa.
Everyone who is both not generous and wise is patient.
If lucy is not tall or quiet then someone is either not humble or brave and vice versa.
Everyone who is either calm or strong is both not wise and not rich.
If someone is not rich or generous then alice is old.
Everyone who is not rich or kind is kind or wise and vice versa.
If someone is strong or wise then someone is curious and vice versa.
Everyone who is rich or strong is curious.
If fred is curious then someone is both kind and not quiet.
If paul is either brave or not humble then someone is not curious and vice versa.
Everyone who is patient is happy or generous and vice versa.
Everyone who is both not kind and not old is both not funny and not quiet.
If someone is not old then someone is not funny and vice versa.
Fred is not brave.
Fred is either curious or happy.
Mary is not wise.
Someone is either funny or calm.
Lucy is rich or not tall.
Someone is both curious and not happy. | Paul is kind. | neutral | (![X]:(brave(X)<=>~generous(X)))&
(((~wise(paul)<~>brave(paul)))=>((curious(alice)&~calm(alice))))&
((?[X]:(~tall(X)))=>((~kind(alice)<~>brave(alice))))&
(![X]:(~rich(X)<=>(rich(X)&happy(X))))&
(![X]:((~generous(X)&wise(X))=>patient(X)))&
(((~tall(lucy)|quiet(lucy)))<=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((calm(X)<~>strong(X))=>(~wise(X)&~rich(X))))&
((?[X]:((~rich(X)|generous(X))))=>(old(alice)))&
(![X]:((~rich(X)|kind(X))<=>(kind(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:(curious(X))))&
(![X]:((rich(X)|strong(X))=>curious(X)))&
((curious(fred))=>(?[X]:((kind(X)&~quiet(X)))))&
(((brave(paul)<~>~humble(paul)))<=>(?[X]:(~curious(X))))&
(![X]:(patient(X)<=>(happy(X)|generous(X))))&
(![X]:((~kind(X)&~old(X))=>(~funny(X)&~quiet(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~funny(X))))&
(~brave(fred))&
((curious(fred)<~>happy(fred)))&
(~wise(mary))&
(?[X]:((funny(X)<~>calm(X))))&
((rich(lucy)|~tall(lucy)))&
(?[X]:((curious(X)&~happy(X)))) | kind(paul) | [] | null | 0 |
Everyone who is not creative is either not humble or not quiet and vice versa. Everyone who is both not creative and funny is either generous or old. If someone is both strong and happy then someone is both strong and rich and vice versa. If someone is not calm then someone is not happy or tall and vice versa. Everyone who is strong or happy is both not wise and not brave and vice versa. Everyone who is both wise and not wise is calm or not quiet. Everyone who is patient is both happy and quiet and vice versa. Everyone who is not wise or funny is either kind or creative and vice versa. If someone is either rich or curious then john is both kind and happy and vice versa. Everyone who is not old or generous is not strong or patient and vice versa. If someone is strong then someone is either not quiet or not patient and vice versa. Everyone who is happy is curious and vice versa. Everyone who is not generous is old or curious and vice versa. Everyone who is either generous or not creative is both not old and not strong. If mary is either wise or not brave then someone is not happy or not humble and vice versa. If paul is not tall or generous then someone is rich or generous and vice versa. Lucy is not quiet or not humble. Someone is either calm or not patient. Susan is not funny. Alice is both not happy and not quiet. Fred is both tall and calm. Someone is brave. Susan is patient. Someone is either old or curious. | Susan is generous. | contradiction | (![X]:(~creative(X)<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~creative(X)&funny(X))=>(generous(X)<~>old(X))))&
((?[X]:((strong(X)&happy(X))))<=>(?[X]:((strong(X)&rich(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((strong(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((wise(X)&~wise(X))=>(calm(X)|~quiet(X))))&
(![X]:(patient(X)<=>(happy(X)&quiet(X))))&
(![X]:((~wise(X)|funny(X))<=>(kind(X)<~>creative(X))))&
((?[X]:((rich(X)<~>curious(X))))<=>((kind(john)&happy(john))))&
(![X]:((~old(X)|generous(X))<=>(~strong(X)|patient(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:(happy(X)<=>curious(X)))&
(![X]:(~generous(X)<=>(old(X)|curious(X))))&
(![X]:((generous(X)<~>~creative(X))=>(~old(X)&~strong(X))))&
(((wise(mary)<~>~brave(mary)))<=>(?[X]:((~happy(X)|~humble(X)))))&
(((~tall(paul)|generous(paul)))<=>(?[X]:((rich(X)|generous(X)))))&
((~quiet(lucy)|~humble(lucy)))&
(?[X]:((calm(X)<~>~patient(X))))&
(~funny(susan))&
((~happy(alice)&~quiet(alice)))&
((tall(fred)&calm(fred)))&
(?[X]:(brave(X)))&
(patient(susan))&
(?[X]:((old(X)<~>curious(X)))) | generous(susan) | [
"p6",
"p11",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1621836988280352505567389
% SZS output start Proof for 1621836988280352505567389
7. ! [X0] : (patient(X0) <=> (quiet(X0) & happy(X0))) [input p6]
12. ! [X0] : (happy(X0) <=> curious(X0)) [input p11]
13. ! [X0] : (~generous(X0) <=> (curious(X0) | old(X0))) [input p12]
23. patient(susan) [input p22]
25. generous(susan) [input hypothesis]
48. ! [X0] : ((patient(X0) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | ~patient(X0))) [nnf transformation 7]
49. ! [X0] : ((patient(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | ~patient(X0))) [flattening 48]
64. ! [X0] : ((happy(X0) | ~curious(X0)) & (curious(X0) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((~generous(X0) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | generous(X0))) [nnf transformation 13]
66. ! [X0] : ((~generous(X0) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | generous(X0))) [flattening 65]
104. ~patient(X0) | happy(X0) [cnf transformation 49]
127. ~happy(X0) | curious(X0) [cnf transformation 64]
131. ~curious(X0) | ~generous(X0) [cnf transformation 66]
155. patient(susan) [cnf transformation 23]
158. generous(susan) [cnf transformation 25]
351. happy(susan) [resolution 104,155]
355. curious(susan) [resolution 127,351]
455. ~generous(susan) [resolution 355,131]
457. $false [subsumption resolution 455,158]
% SZS output end Proof for 1621836988280352505567389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is not brave or happy. If someone is both not happy and generous then someone is not wise. If someone is both patient and old then mary is not generous. If someone is either kind or not tall then someone is either kind or not patient and vice versa. If someone is not strong then susan is not curious and vice versa. Everyone who is either humble or not curious is rich and vice versa. If alice is both not calm and rich then someone is either not humble or not brave. Everyone who is both strong and not generous is not tall or quiet and vice versa. If someone is both not brave and not humble then paul is both brave and generous and vice versa. Everyone who is both generous and tall is both not curious and not quiet. Everyone who is either not humble or not quiet is funny and vice versa. Everyone who is both generous and not humble is both creative and rich. Everyone who is curious is both kind and curious. Everyone who is not patient is either not tall or not generous and vice versa. Everyone who is either creative or humble is either funny or tall and vice versa. If someone is either not quiet or not humble then someone is either not strong or calm. Someone is either patient or not kind. Alice is not quiet or not brave. Someone is both happy and not quiet. Mary is both not curious and calm. Lucy is both generous and brave. Someone is brave. Someone is not humble or not kind. Fred is either quiet or kind. | Alice is not curious. | neutral | (![X]:(quiet(X)=>(~brave(X)|happy(X))))&
((?[X]:((~happy(X)&generous(X))))=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&old(X))))=>(~generous(mary)))&
((?[X]:((kind(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:(~strong(X)))<=>(~curious(susan)))&
(![X]:((humble(X)<~>~curious(X))<=>rich(X)))&
(((~calm(alice)&rich(alice)))=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((strong(X)&~generous(X))<=>(~tall(X)|quiet(X))))&
((?[X]:((~brave(X)&~humble(X))))<=>((brave(paul)&generous(paul))))&
(![X]:((generous(X)&tall(X))=>(~curious(X)&~quiet(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>funny(X)))&
(![X]:((generous(X)&~humble(X))=>(creative(X)&rich(X))))&
(![X]:(curious(X)=>(kind(X)&curious(X))))&
(![X]:(~patient(X)<=>(~tall(X)<~>~generous(X))))&
(![X]:((creative(X)<~>humble(X))<=>(funny(X)<~>tall(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
(?[X]:((patient(X)<~>~kind(X))))&
((~quiet(alice)|~brave(alice)))&
(?[X]:((happy(X)&~quiet(X))))&
((~curious(mary)&calm(mary)))&
((generous(lucy)&brave(lucy)))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)|~kind(X))))&
((quiet(fred)<~>kind(fred))) | ~curious(alice) | [] | null | 0 |
Everyone who is both happy and not rich is generous or not kind.
Everyone who is either calm or brave is not funny or not strong.
Everyone who is not happy or not kind is not calm.
Everyone who is either not funny or wise is both wise and not rich and vice versa.
Everyone who is not creative or not humble is rich and vice versa.
If susan is both generous and not rich then fred is either humble or happy.
If someone is either not kind or not wise then someone is not patient and vice versa.
If someone is not creative then someone is both funny and not quiet.
If alice is both not brave and not wise then someone is both not creative and quiet and vice versa.
If someone is not wise or wise then someone is not rich and vice versa.
Everyone who is not curious is quiet and vice versa.
Everyone who is both not quiet and happy is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Mary is either tall or not quiet.
Mary is creative or brave.
Alice is happy or tall.
Someone is patient or not brave.
Someone is brave or patient. | Fred is brave. | entailment | (![X]:((happy(X)&~rich(X))=>(generous(X)|~kind(X))))&
(![X]:((calm(X)<~>brave(X))=>(~funny(X)|~strong(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((~funny(X)<~>wise(X))<=>(wise(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>rich(X)))&
(((generous(susan)&~rich(susan)))=>((humble(fred)<~>happy(fred))))&
((?[X]:((~kind(X)<~>~wise(X))))<=>(?[X]:(~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((funny(X)&~quiet(X)))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:((~quiet(X)&happy(X))<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
((tall(mary)<~>~quiet(mary)))&
((creative(mary)|brave(mary)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((brave(X)|patient(X)))) | brave(fred) | [
"p3",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3777442238106980003510757
% SZS output start Proof for 3777442238106980003510757
4. ! [X0] : ((~funny(X0) <~> wise(X0)) <=> (~rich(X0) & wise(X0))) [input p3]
11. ! [X0] : (~curious(X0) <=> quiet(X0)) [input p10]
14. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p13]
15. ! [X0] : (brave(X0) <=> (~generous(X0) | funny(X0))) [input p14]
22. ~brave(fred) [input hypothesis]
34. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [nnf transformation 4]
35. ! [X0] : ((((~wise(X0) | funny(X0)) & (wise(X0) | ~funny(X0))) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ((~funny(X0) | ~wise(X0)) & (wise(X0) | funny(X0))))) [flattening 34]
57. ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))) [nnf transformation 11]
62. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 14]
63. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 62]
64. ! [X0] : ((brave(X0) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | ~brave(X0))) [nnf transformation 15]
65. ! [X0] : ((brave(X0) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ~brave(X0))) [flattening 64]
73. wise(X0) | wise(X0) | funny(X0) [cnf transformation 35]
78. ~wise(X0) | funny(X0) | rich(X0) | ~wise(X0) [cnf transformation 35]
97. curious(X0) | quiet(X0) [cnf transformation 57]
109. ~quiet(X0) | ~rich(X0) [cnf transformation 63]
110. ~curious(X0) | ~rich(X0) [cnf transformation 63]
112. ~funny(X0) | brave(X0) [cnf transformation 65]
124. ~brave(fred) [cnf transformation 22]
125. wise(X0) | funny(X0) [duplicate literal removal 73]
126. ~wise(X0) | funny(X0) | rich(X0) [duplicate literal removal 78]
292. ~rich(X0) | quiet(X0) [resolution 110,97]
293. ~rich(X0) [subsumption resolution 292,109]
336. funny(X0) | rich(X0) | funny(X0) [resolution 126,125]
337. funny(X0) | rich(X0) [duplicate literal removal 336]
341. funny(X0) [subsumption resolution 337,293]
346. brave(X0) [resolution 341,112]
350. $false [resolution 346,124]
% SZS output end Proof for 3777442238106980003510757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or tall then paul is either strong or not generous and vice versa.
Everyone who is curious or patient is both not kind and not happy.
If mary is not wise then someone is both quiet and not patient and vice versa.
Everyone who is not generous is not patient and vice versa.
Everyone who is tall or not curious is both strong and not strong.
Everyone who is old is both not kind and not calm and vice versa.
Everyone who is patient is old or not quiet.
If someone is both tall and brave then someone is both not wise and funny and vice versa.
Everyone who is either not strong or not brave is both not happy and not creative and vice versa.
Everyone who is generous or funny is brave.
Everyone who is not creative is not quiet or wise.
If alice is not generous then paul is brave or not strong and vice versa.
Everyone who is either not brave or not rich is not old or patient.
Everyone who is strong or tall is not patient and vice versa.
If someone is tall then john is creative or not calm and vice versa.
Everyone who is creative or calm is not tall or quiet.
Fred is either not funny or not quiet.
Someone is not funny or strong.
Someone is both not patient and old.
Someone is not funny or not happy.
Alice is both not tall and patient.
John is not old. | Paul is generous. | contradiction | ((?[X]:((kind(X)|tall(X))))<=>((strong(paul)<~>~generous(paul))))&
(![X]:((curious(X)|patient(X))=>(~kind(X)&~happy(X))))&
((~wise(mary))<=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((tall(X)|~curious(X))=>(strong(X)&~strong(X))))&
(![X]:(old(X)<=>(~kind(X)&~calm(X))))&
(![X]:(patient(X)=>(old(X)|~quiet(X))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~happy(X)&~creative(X))))&
(![X]:((generous(X)|funny(X))=>brave(X)))&
(![X]:(~creative(X)=>(~quiet(X)|wise(X))))&
((~generous(alice))<=>((brave(paul)|~strong(paul))))&
(![X]:((~brave(X)<~>~rich(X))=>(~old(X)|patient(X))))&
(![X]:((strong(X)|tall(X))<=>~patient(X)))&
((?[X]:(tall(X)))<=>((creative(john)|~calm(john))))&
(![X]:((creative(X)|calm(X))=>(~tall(X)|quiet(X))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((~tall(alice)&patient(alice)))&
(~old(john)) | generous(paul) | [
"p0",
"p1",
"p3",
"p4",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8375408355128444464510783
% SZS output start Proof for 8375408355128444464510783
1. ? [X0] : (tall(X0) | kind(X0)) <=> (strong(paul) <~> ~generous(paul)) [input p0]
2. ! [X0] : ((patient(X0) | curious(X0)) => (~happy(X0) & ~kind(X0))) [input p1]
4. ! [X0] : (~generous(X0) <=> ~patient(X0)) [input p3]
5. ! [X0] : ((~curious(X0) | tall(X0)) => (~strong(X0) & strong(X0))) [input p4]
12. ~generous(alice) <=> (~strong(paul) | brave(paul)) [input p11]
21. patient(alice) & ~tall(alice) [input p20]
23. generous(paul) [input hypothesis]
25. ! [X0] : ((~happy(X0) & ~kind(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 2]
26. ! [X0] : ((~strong(X0) & strong(X0)) | (curious(X0) & ~tall(X0))) [ennf transformation 5]
36. (? [X0] : (tall(X0) | kind(X0)) | ((strong(paul) | generous(paul)) & (~generous(paul) | ~strong(paul)))) & (((generous(paul) | ~strong(paul)) & (~generous(paul) | strong(paul))) | ! [X0] : (~tall(X0) & ~kind(X0))) [nnf transformation 1]
37. (? [X0] : (tall(X0) | kind(X0)) | ((strong(paul) | generous(paul)) & (~generous(paul) | ~strong(paul)))) & (((generous(paul) | ~strong(paul)) & (~generous(paul) | strong(paul))) | ! [X1] : (~tall(X1) & ~kind(X1))) [rectify 36]
38. ? [X0] : (tall(X0) | kind(X0)) => (tall(sK0) | kind(sK0)) [choice axiom]
39. ((tall(sK0) | kind(sK0)) | ((strong(paul) | generous(paul)) & (~generous(paul) | ~strong(paul)))) & (((generous(paul) | ~strong(paul)) & (~generous(paul) | strong(paul))) | ! [X1] : (~tall(X1) & ~kind(X1))) [skolemisation 37,38]
44. ! [X0] : ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0))) [nnf transformation 4]
54. (~generous(alice) | (strong(paul) & ~brave(paul))) & ((~strong(paul) | brave(paul)) | generous(alice)) [nnf transformation 12]
55. (~generous(alice) | (strong(paul) & ~brave(paul))) & (~strong(paul) | brave(paul) | generous(alice)) [flattening 54]
75. tall(sK0) | kind(sK0) | ~generous(paul) | ~strong(paul) [cnf transformation 39]
77. ~curious(X0) | ~kind(X0) [cnf transformation 25]
84. ~patient(X0) | generous(X0) [cnf transformation 44]
86. strong(X0) | ~tall(X0) [cnf transformation 26]
87. strong(X0) | curious(X0) [cnf transformation 26]
88. ~strong(X0) | ~tall(X0) [cnf transformation 26]
89. ~strong(X0) | curious(X0) [cnf transformation 26]
109. ~generous(alice) | strong(paul) [cnf transformation 55]
127. patient(alice) [cnf transformation 21]
129. generous(paul) [cnf transformation 23]
131. 1 <=> generous(paul) [avatar definition]
135. 2 <=> strong(paul) [avatar definition]
139. 3 <=> kind(sK0) [avatar definition]
141. kind(sK0) <- (3) [avatar component clause 139]
143. 4 <=> tall(sK0) [avatar definition]
145. tall(sK0) <- (4) [avatar component clause 143]
147. ~2 | ~1 | 3 | 4 [avatar split clause 75,143,139,131,135]
149. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
150. ~tall(X1) <- (5) [avatar component clause 149]
153. 6 <=> ! [X1] : ~kind(X1) [avatar definition]
154. ~kind(X1) <- (6) [avatar component clause 153]
176. curious(X0) [subsumption resolution 87,89]
177. ~tall(X0) [subsumption resolution 86,88]
178. 5 [avatar split clause 177,149]
206. 17 <=> generous(alice) [avatar definition]
209. 2 | ~17 [avatar split clause 109,206,135]
259. 1 [avatar split clause 129,131]
260. ~kind(X0) [resolution 77,176]
262. generous(alice) [resolution 84,127]
265. 17 [avatar split clause 262,206]
266. $false <- (4, 5) [subsumption resolution 145,150]
267. ~4 | ~5 [avatar contradiction clause 266]
268. $false <- (3, 6) [subsumption resolution 141,154]
269. ~3 | ~6 [avatar contradiction clause 268]
270. 6 [avatar split clause 260,153]
271. $false [avatar sat refutation 147,178,209,259,265,267,269,270]
% SZS output end Proof for 8375408355128444464510783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not patient is both humble and not wise.
Everyone who is creative or not funny is either old or not strong.
If someone is not rich or not curious then fred is either happy or creative.
Everyone who is not calm is either not old or tall and vice versa.
Everyone who is not rich or not humble is either not rich or not curious and vice versa.
If susan is both not tall and not wise then susan is both not humble and not curious and vice versa.
Everyone who is both not calm and not happy is not rich or not patient and vice versa.
Everyone who is either not wise or not creative is both funny and kind and vice versa.
Everyone who is calm or not kind is both rich and kind and vice versa.
If someone is both not curious and old then someone is both not patient and quiet and vice versa.
If mary is either not wise or not creative then john is either not kind or not curious.
If someone is not creative or not tall then susan is not quiet or not tall and vice versa.
If alice is either brave or not kind then someone is not humble or not old.
If susan is both not patient and not wise then susan is not funny.
Everyone who is not curious or funny is wise.
If someone is both not curious and old then fred is both not kind and humble.
Someone is strong or patient.
John is not quiet.
Alice is either not curious or not quiet.
Fred is both funny and wise.
Someone is not humble.
Alice is creative or not wise.
Someone is humble or happy. | Susan is happy. | neutral | (![X]:((strong(X)<~>~patient(X))=>(humble(X)&~wise(X))))&
(![X]:((creative(X)|~funny(X))=>(old(X)<~>~strong(X))))&
((?[X]:((~rich(X)|~curious(X))))=>((happy(fred)<~>creative(fred))))&
(![X]:(~calm(X)<=>(~old(X)<~>tall(X))))&
(![X]:((~rich(X)|~humble(X))<=>(~rich(X)<~>~curious(X))))&
(((~tall(susan)&~wise(susan)))<=>((~humble(susan)&~curious(susan))))&
(![X]:((~calm(X)&~happy(X))<=>(~rich(X)|~patient(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(funny(X)&kind(X))))&
(![X]:((calm(X)|~kind(X))<=>(rich(X)&kind(X))))&
((?[X]:((~curious(X)&old(X))))<=>(?[X]:((~patient(X)&quiet(X)))))&
(((~wise(mary)<~>~creative(mary)))=>((~kind(john)<~>~curious(john))))&
((?[X]:((~creative(X)|~tall(X))))<=>((~quiet(susan)|~tall(susan))))&
(((brave(alice)<~>~kind(alice)))=>(?[X]:((~humble(X)|~old(X)))))&
(((~patient(susan)&~wise(susan)))=>(~funny(susan)))&
(![X]:((~curious(X)|funny(X))=>wise(X)))&
((?[X]:((~curious(X)&old(X))))=>((~kind(fred)&humble(fred))))&
(?[X]:((strong(X)|patient(X))))&
(~quiet(john))&
((~curious(alice)<~>~quiet(alice)))&
((funny(fred)&wise(fred)))&
(?[X]:(~humble(X)))&
((creative(alice)|~wise(alice)))&
(?[X]:((humble(X)|happy(X)))) | happy(susan) | [] | null | 0 |
Everyone who is creative is not tall and vice versa. Everyone who is not wise or humble is not kind. If alice is both wise and not patient then someone is not rich and vice versa. If alice is either wise or calm then lucy is both not calm and patient. Everyone who is both rich and calm is not tall and vice versa. Everyone who is either creative or curious is either generous or wise. Everyone who is either generous or not patient is not generous. If someone is brave or not brave then susan is both not wise and strong. Everyone who is either humble or rich is both quiet and not quiet and vice versa. If someone is either wise or humble then susan is creative and vice versa. If fred is tall then alice is not humble and vice versa. If john is not strong then someone is either not calm or patient and vice versa. If someone is both calm and not old then mary is not kind and vice versa. If susan is both quiet and not happy then mary is either creative or not generous and vice versa. Everyone who is either not kind or quiet is not generous. Everyone who is not strong or generous is both not kind and funny and vice versa. Someone is both brave and happy. Someone is not rich. Mary is either not generous or kind. Someone is either not quiet or generous. Fred is humble. Someone is patient or old. Someone is both not kind and humble. | John is patient. | neutral | (![X]:(creative(X)<=>~tall(X)))&
(![X]:((~wise(X)|humble(X))=>~kind(X)))&
(((wise(alice)&~patient(alice)))<=>(?[X]:(~rich(X))))&
(((wise(alice)<~>calm(alice)))=>((~calm(lucy)&patient(lucy))))&
(![X]:((rich(X)&calm(X))<=>~tall(X)))&
(![X]:((creative(X)<~>curious(X))=>(generous(X)<~>wise(X))))&
(![X]:((generous(X)<~>~patient(X))=>~generous(X)))&
((?[X]:((brave(X)|~brave(X))))=>((~wise(susan)&strong(susan))))&
(![X]:((humble(X)<~>rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(creative(susan)))&
((tall(fred))<=>(~humble(alice)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(~kind(mary)))&
(((quiet(susan)&~happy(susan)))<=>((creative(mary)<~>~generous(mary))))&
(![X]:((~kind(X)<~>quiet(X))=>~generous(X)))&
(![X]:((~strong(X)|generous(X))<=>(~kind(X)&funny(X))))&
(?[X]:((brave(X)&happy(X))))&
(?[X]:(~rich(X)))&
((~generous(mary)<~>kind(mary)))&
(?[X]:((~quiet(X)<~>generous(X))))&
(humble(fred))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~kind(X)&humble(X)))) | patient(john) | [] | null | 0 |
If lucy is not brave then someone is humble and vice versa.
If someone is either wise or not strong then someone is calm or rich.
Everyone who is not rich is not rich or happy and vice versa.
Everyone who is not generous is either curious or not curious and vice versa.
Everyone who is either rich or not calm is not old or happy and vice versa.
Everyone who is humble or not happy is not humble.
If alice is not curious then someone is both creative and not old.
Everyone who is not happy or not tall is not wise or wise and vice versa.
Everyone who is either not funny or patient is either not calm or not rich.
If susan is either not happy or not brave then fred is either humble or not tall and vice versa.
Everyone who is either not rich or tall is both not brave and generous.
Everyone who is either humble or rich is humble and vice versa.
If someone is both not creative and rich then someone is both happy and rich.
Everyone who is strong or kind is not curious.
If someone is either patient or not wise then someone is not quiet and vice versa.
Everyone who is quiet is not calm or not humble.
Someone is both not generous and tall.
Someone is either generous or not humble.
Someone is both not brave and not strong.
Fred is tall or brave.
Someone is not patient.
Someone is tall or strong. | Lucy is happy. | contradiction | ((~brave(lucy))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~rich(X)|happy(X))))&
(![X]:(~generous(X)<=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~old(X)|happy(X))))&
(![X]:((humble(X)|~happy(X))=>~humble(X)))&
((~curious(alice))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|wise(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~calm(X)<~>~rich(X))))&
(((~happy(susan)<~>~brave(susan)))<=>((humble(fred)<~>~tall(fred))))&
(![X]:((~rich(X)<~>tall(X))=>(~brave(X)&generous(X))))&
(![X]:((humble(X)<~>rich(X))<=>humble(X)))&
((?[X]:((~creative(X)&rich(X))))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((strong(X)|kind(X))=>~curious(X)))&
((?[X]:((patient(X)<~>~wise(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(~calm(X)|~humble(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:((~brave(X)&~strong(X))))&
((tall(fred)|brave(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|strong(X)))) | happy(lucy) | [
"p3",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6425042222610319923173972
% SZS output start Proof for 6425042222610319923173972
4. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~curious(X0))) [input p3]
8. ! [X0] : ((~tall(X0) | ~happy(X0)) <=> (wise(X0) | ~wise(X0))) [input p7]
11. ! [X0] : ((~rich(X0) <~> tall(X0)) => (generous(X0) & ~brave(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> rich(X0)) <=> humble(X0)) [input p11]
23. happy(lucy) [input hypothesis]
34. ! [X0] : ((generous(X0) & ~brave(X0)) | (~rich(X0) <=> tall(X0))) [ennf transformation 11]
48. ! [X0] : ((~generous(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0))) [nnf transformation 4]
53. ! [X0] : (((~tall(X0) | ~happy(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (tall(X0) & happy(X0)))) [nnf transformation 8]
54. ! [X0] : ((~tall(X0) | ~happy(X0) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | (tall(X0) & happy(X0)))) [flattening 53]
57. ! [X0] : ((generous(X0) & ~brave(X0)) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) [nnf transformation 34]
58. ! [X0] : ((((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ~humble(X0)) & (humble(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0))))) [nnf transformation 12]
84. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48]
85. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 48]
97. ~tall(X0) | ~happy(X0) | wise(X0) [cnf transformation 54]
98. ~tall(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 54]
113. generous(X0) | tall(X0) | rich(X0) [cnf transformation 57]
116. humble(X0) | humble(X0) | ~rich(X0) [cnf transformation 58]
118. ~rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 58]
134. happy(lucy) [cnf transformation 23]
135. humble(X0) | ~rich(X0) [duplicate literal removal 116]
136. ~rich(X0) | ~humble(X0) [duplicate literal removal 118]
138. ~generous(X0) | ~curious(X0) [duplicate literal removal 84]
139. ~generous(X0) | curious(X0) [duplicate literal removal 85]
169. ~generous(X0) [subsumption resolution 138,139]
182. ~tall(X0) | ~happy(X0) [subsumption resolution 97,98]
208. tall(X0) | rich(X0) [subsumption resolution 113,169]
209. ~rich(X0) [subsumption resolution 135,136]
261. rich(X1) | ~happy(X1) [resolution 208,182]
262. ~happy(X1) [subsumption resolution 261,209]
265. $false [resolution 262,134]
% SZS output end Proof for 6425042222610319923173972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is brave then susan is not kind or not old and vice versa.
Everyone who is both funny and happy is not strong or not creative.
If john is not curious then fred is happy and vice versa.
Everyone who is tall or not curious is either creative or not calm.
Everyone who is both calm and not curious is both not happy and not kind.
If someone is either not curious or not creative then susan is both not old and not tall and vice versa.
Everyone who is both rich and funny is both not old and calm and vice versa.
Everyone who is both not wise and not quiet is creative.
If fred is either not patient or not humble then someone is either not strong or not tall and vice versa.
Everyone who is both strong and tall is not brave or brave and vice versa.
Everyone who is not tall is funny or not humble and vice versa.
Everyone who is either not old or not quiet is either funny or not patient and vice versa.
If mary is either generous or happy then someone is either generous or happy and vice versa.
Everyone who is both not wise and rich is either not rich or not strong and vice versa.
If paul is either quiet or tall then paul is not patient and vice versa.
Everyone who is either not kind or not creative is not patient or quiet and vice versa.
Someone is either not calm or not tall.
Someone is funny or not quiet.
Paul is not creative or not funny.
Mary is both generous and kind.
Someone is either not strong or old.
Mary is not creative or not generous.
John is either not curious or kind. | Susan is not generous. | neutral | ((brave(john))<=>((~kind(susan)|~old(susan))))&
(![X]:((funny(X)&happy(X))=>(~strong(X)|~creative(X))))&
((~curious(john))<=>(happy(fred)))&
(![X]:((tall(X)|~curious(X))=>(creative(X)<~>~calm(X))))&
(![X]:((calm(X)&~curious(X))=>(~happy(X)&~kind(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>((~old(susan)&~tall(susan))))&
(![X]:((rich(X)&funny(X))<=>(~old(X)&calm(X))))&
(![X]:((~wise(X)&~quiet(X))=>creative(X)))&
(((~patient(fred)<~>~humble(fred)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:((strong(X)&tall(X))<=>(~brave(X)|brave(X))))&
(![X]:(~tall(X)<=>(funny(X)|~humble(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(funny(X)<~>~patient(X))))&
(((generous(mary)<~>happy(mary)))<=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((~wise(X)&rich(X))<=>(~rich(X)<~>~strong(X))))&
(((quiet(paul)<~>tall(paul)))<=>(~patient(paul)))&
(![X]:((~kind(X)<~>~creative(X))<=>(~patient(X)|quiet(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((funny(X)|~quiet(X))))&
((~creative(paul)|~funny(paul)))&
((generous(mary)&kind(mary)))&
(?[X]:((~strong(X)<~>old(X))))&
((~creative(mary)|~generous(mary)))&
((~curious(john)<~>kind(john))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not brave or not happy is not funny.
Everyone who is either brave or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Someone is both patient and not quiet.
John is not rich or not creative.
Paul is either not brave or happy.
Susan is either happy or not generous.
Someone is both tall and kind.
Susan is not creative. | Paul is not calm. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((brave(X)<~>~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X))))&
(~creative(susan)) | ~calm(paul) | [] | null | 0 |
If mary is either kind or not calm then susan is either strong or not curious and vice versa. Everyone who is either old or creative is both not old and not funny and vice versa. Everyone who is either not patient or happy is not patient or not brave and vice versa. Everyone who is creative is not wise or rich. If someone is not brave or happy then someone is strong and vice versa. If someone is either not old or not funny then someone is either quiet or brave and vice versa. If someone is funny then someone is not old. Everyone who is both not patient and not funny is both not patient and happy. If lucy is strong or not curious then someone is both not kind and creative and vice versa. If alice is both not generous and not funny then susan is either old or brave and vice versa. If susan is both funny and not generous then someone is patient or not generous. Everyone who is both happy and not quiet is both happy and not patient and vice versa. If john is not kind or old then susan is not humble and vice versa. Everyone who is either not happy or not quiet is brave. Everyone who is either not curious or not creative is either not wise or not kind. Everyone who is not old or not quiet is both old and not tall. Someone is both not calm and kind. Someone is not tall or rich. Fred is old or kind. Mary is creative or not curious. Alice is either not brave or funny. Someone is not kind. Paul is not tall. Someone is both not wise and not happy. | Alice is not old. | contradiction | (((kind(mary)<~>~calm(mary)))<=>((strong(susan)<~>~curious(susan))))&
(![X]:((old(X)<~>creative(X))<=>(~old(X)&~funny(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~patient(X)|~brave(X))))&
(![X]:(creative(X)=>(~wise(X)|rich(X))))&
((?[X]:((~brave(X)|happy(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~old(X)<~>~funny(X))))<=>(?[X]:((quiet(X)<~>brave(X)))))&
((?[X]:(funny(X)))=>(?[X]:(~old(X))))&
(![X]:((~patient(X)&~funny(X))=>(~patient(X)&happy(X))))&
(((strong(lucy)|~curious(lucy)))<=>(?[X]:((~kind(X)&creative(X)))))&
(((~generous(alice)&~funny(alice)))<=>((old(susan)<~>brave(susan))))&
(((funny(susan)&~generous(susan)))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(happy(X)&~patient(X))))&
(((~kind(john)|old(john)))<=>(~humble(susan)))&
(![X]:((~happy(X)<~>~quiet(X))=>brave(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((~old(X)|~quiet(X))=>(old(X)&~tall(X))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((~tall(X)|rich(X))))&
((old(fred)|kind(fred)))&
((creative(mary)|~curious(mary)))&
((~brave(alice)<~>funny(alice)))&
(?[X]:(~kind(X)))&
(~tall(paul))&
(?[X]:((~wise(X)&~happy(X)))) | ~old(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5037501846923995451417369
% SZS output start Proof for 5037501846923995451417369
16. ! [X0] : ((~quiet(X0) | ~old(X0)) => (~tall(X0) & old(X0))) [input p15]
25. ~old(alice) [input hypothesis]
30. ! [X0] : ((~quiet(X0) | ~old(X0)) => old(X0)) [pure predicate removal 16]
40. ! [X0] : (old(X0) | (quiet(X0) & old(X0))) [ennf transformation 30]
140. old(X0) | old(X0) [cnf transformation 40]
151. ~old(alice) [cnf transformation 25]
152. old(X0) [duplicate literal removal 140]
342. $false [subsumption resolution 151,152]
% SZS output end Proof for 5037501846923995451417369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not humble then someone is calm or not patient.
Everyone who is either not funny or not happy is either not brave or not funny and vice versa.
Everyone who is old is not kind and vice versa.
Everyone who is quiet or funny is creative or brave and vice versa.
Everyone who is either kind or not happy is both not tall and not funny and vice versa.
Everyone who is creative is either not wise or not strong and vice versa.
Everyone who is both funny and not old is both not old and humble.
Everyone who is creative or not humble is not quiet or quiet and vice versa.
If someone is rich or quiet then someone is both not quiet and strong and vice versa.
Everyone who is old is either not wise or not strong and vice versa.
If someone is both creative and strong then someone is not brave.
If fred is wise or not funny then someone is not old or rich and vice versa.
If someone is either kind or curious then john is wise or not creative.
Everyone who is not brave is both not patient and not calm.
If someone is either not humble or brave then someone is both not funny and generous and vice versa.
Everyone who is not kind is both not happy and calm and vice versa.
Lucy is patient.
Susan is humble or strong.
Mary is both not happy and not strong.
John is not creative.
Someone is not funny or not old. | Fred is not humble. | entailment | ((~humble(lucy))=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:(old(X)<=>~kind(X)))&
(![X]:((quiet(X)|funny(X))<=>(creative(X)|brave(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~tall(X)&~funny(X))))&
(![X]:(creative(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((funny(X)&~old(X))=>(~old(X)&humble(X))))&
(![X]:((creative(X)|~humble(X))<=>(~quiet(X)|quiet(X))))&
((?[X]:((rich(X)|quiet(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~strong(X))))&
((?[X]:((creative(X)&strong(X))))=>(?[X]:(~brave(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((kind(X)<~>curious(X))))=>((wise(john)|~creative(john))))&
(![X]:(~brave(X)=>(~patient(X)&~calm(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:(~kind(X)<=>(~happy(X)&calm(X))))&
(patient(lucy))&
((humble(susan)|strong(susan)))&
((~happy(mary)&~strong(mary)))&
(~creative(john))&
(?[X]:((~funny(X)|~old(X)))) | ~humble(fred) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7350364620108436646520955
% SZS output start Proof for 7350364620108436646520955
2. ! [X0] : ((~funny(X0) <~> ~happy(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p1]
3. ! [X0] : (old(X0) <=> ~kind(X0)) [input p2]
5. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (~funny(X0) & ~tall(X0))) [input p4]
6. ! [X0] : (creative(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p5]
8. ! [X0] : ((~humble(X0) | creative(X0)) <=> (quiet(X0) | ~quiet(X0))) [input p7]
10. ! [X0] : (old(X0) <=> (~wise(X0) <~> ~strong(X0))) [input p9]
14. ! [X0] : (~brave(X0) => (~calm(X0) & ~patient(X0))) [input p13]
16. ! [X0] : (~kind(X0) <=> (calm(X0) & ~happy(X0))) [input p15]
22. humble(fred) [input hypothesis]
32. ! [X0] : ((~calm(X0) & ~patient(X0)) | brave(X0)) [ennf transformation 14]
35. ! [X0] : ((((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0))))) [nnf transformation 2]
36. ! [X0] : ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))) [nnf transformation 3]
39. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (funny(X0) | tall(X0))) & ((~funny(X0) & ~tall(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 5]
40. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | funny(X0) | tall(X0)) & ((~funny(X0) & ~tall(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 39]
41. ! [X0] : ((creative(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~creative(X0))) [nnf transformation 6]
42. ! [X0] : (((~humble(X0) | creative(X0)) | (~quiet(X0) & quiet(X0))) & ((quiet(X0) | ~quiet(X0)) | (humble(X0) & ~creative(X0)))) [nnf transformation 8]
43. ! [X0] : ((~humble(X0) | creative(X0) | (~quiet(X0) & quiet(X0))) & (quiet(X0) | ~quiet(X0) | (humble(X0) & ~creative(X0)))) [flattening 42]
49. ! [X0] : ((old(X0) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ~old(X0))) [nnf transformation 10]
64. ! [X0] : ((~kind(X0) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | kind(X0))) [nnf transformation 16]
65. ! [X0] : ((~kind(X0) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | kind(X0))) [flattening 64]
76. happy(X0) | funny(X0) | ~brave(X0) | funny(X0) [cnf transformation 35]
77. ~kind(X0) | ~old(X0) [cnf transformation 36]
86. ~funny(X0) | kind(X0) | happy(X0) [cnf transformation 40]
89. ~strong(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 41]
90. ~creative(X0) | wise(X0) | strong(X0) [cnf transformation 41]
97. ~humble(X0) | creative(X0) | quiet(X0) [cnf transformation 43]
98. ~quiet(X0) | creative(X0) | ~humble(X0) [cnf transformation 43]
106. ~strong(X0) | old(X0) | wise(X0) [cnf transformation 49]
107. ~wise(X0) | old(X0) | strong(X0) [cnf transformation 49]
116. ~calm(X0) | brave(X0) [cnf transformation 32]
123. ~happy(X0) | kind(X0) [cnf transformation 65]
124. kind(X0) | calm(X0) [cnf transformation 65]
132. humble(fred) [cnf transformation 22]
136. ~brave(X0) | funny(X0) | happy(X0) [duplicate literal removal 76]
152. ~humble(X0) | creative(X0) [subsumption resolution 97,98]
192. 13 <=> wise(fred) [avatar definition]
193. ~wise(fred) <- (~13) [avatar component clause 192]
194. wise(fred) <- (13) [avatar component clause 192]
196. 14 <=> funny(fred) [avatar definition]
197. funny(fred) <- (14) [avatar component clause 196]
198. ~funny(fred) <- (~14) [avatar component clause 196]
282. ~old(X0) | calm(X0) [resolution 124,77]
286. creative(fred) [resolution 152,132]
344. wise(fred) | strong(fred) [resolution 90,286]
346. 41 <=> strong(fred) [avatar definition]
348. strong(fred) <- (41) [avatar component clause 346]
349. 41 | 13 [avatar split clause 344,192,346]
399. old(fred) | strong(fred) <- (13) [resolution 107,194]
401. 45 <=> old(fred) [avatar definition]
403. old(fred) <- (45) [avatar component clause 401]
404. 41 | 45 | ~13 [avatar split clause 399,192,401,346]
406. calm(fred) <- (45) [resolution 403,282]
410. brave(fred) <- (45) [resolution 406,116]
516. funny(fred) | happy(fred) <- (45) [resolution 410,136]
519. happy(fred) <- (~14, 45) [subsumption resolution 516,198]
531. kind(fred) <- (~14, 45) [resolution 519,123]
538. 55 <=> kind(fred) [avatar definition]
539. ~kind(fred) <- (~55) [avatar component clause 538]
540. kind(fred) <- (55) [avatar component clause 538]
542. 55 | 14 | ~45 [avatar split clause 531,401,196,538]
550. ~old(fred) <- (55) [resolution 540,77]
553. ~45 | ~55 [avatar split clause 550,538,401]
555. 56 <=> happy(fred) [avatar definition]
557. happy(fred) <- (56) [avatar component clause 555]
565. old(fred) | wise(fred) <- (41) [resolution 348,106]
568. ~wise(fred) | ~creative(fred) <- (41) [resolution 348,89]
572. ~wise(fred) <- (41) [subsumption resolution 568,286]
573. ~13 | ~41 [avatar split clause 572,346,192]
581. old(fred) <- (~13, 41) [subsumption resolution 565,193]
582. 45 | 13 | ~41 [avatar split clause 581,346,192,401]
584. kind(fred) | happy(fred) <- (14) [resolution 197,86]
625. kind(fred) <- (56) [resolution 557,123]
627. $false <- (~55, 56) [subsumption resolution 625,539]
628. 55 | ~56 [avatar contradiction clause 627]
629. happy(fred) <- (14, ~55) [subsumption resolution 584,539]
630. 56 | ~14 | 55 [avatar split clause 629,538,196,555]
631. $false [avatar sat refutation 349,404,542,553,573,582,628,630]
% SZS output end Proof for 7350364620108436646520955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or funny is both calm and wise and vice versa.
Everyone who is not patient is not strong.
If someone is not kind then someone is calm or old and vice versa.
Everyone who is not rich is generous or patient and vice versa.
Everyone who is not patient is not happy.
Everyone who is not generous is both rich and humble.
Everyone who is both not kind and old is rich or brave and vice versa.
Everyone who is not old is wise and vice versa.
If someone is generous or not strong then alice is both humble and not funny and vice versa.
Everyone who is curious is either not happy or happy and vice versa.
If paul is not brave then lucy is both brave and not generous.
Everyone who is both not humble and patient is both funny and brave and vice versa.
Everyone who is both not happy and old is old or not funny and vice versa.
If fred is humble or creative then someone is either not patient or not calm and vice versa.
If someone is not brave then lucy is old.
Everyone who is both not calm and patient is either creative or calm.
Someone is either humble or calm.
Someone is either calm or not funny.
Someone is not patient or not wise.
Alice is humble.
Susan is either funny or not kind.
Someone is both kind and humble.
Someone is not generous. | Susan is not funny. | neutral | (![X]:((~tall(X)|funny(X))<=>(calm(X)&wise(X))))&
(![X]:(~patient(X)=>~strong(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((calm(X)|old(X)))))&
(![X]:(~rich(X)<=>(generous(X)|patient(X))))&
(![X]:(~patient(X)=>~happy(X)))&
(![X]:(~generous(X)=>(rich(X)&humble(X))))&
(![X]:((~kind(X)&old(X))<=>(rich(X)|brave(X))))&
(![X]:(~old(X)<=>wise(X)))&
((?[X]:((generous(X)|~strong(X))))<=>((humble(alice)&~funny(alice))))&
(![X]:(curious(X)<=>(~happy(X)<~>happy(X))))&
((~brave(paul))=>((brave(lucy)&~generous(lucy))))&
(![X]:((~humble(X)&patient(X))<=>(funny(X)&brave(X))))&
(![X]:((~happy(X)&old(X))<=>(old(X)|~funny(X))))&
(((humble(fred)|creative(fred)))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
((?[X]:(~brave(X)))=>(old(lucy)))&
(![X]:((~calm(X)&patient(X))=>(creative(X)<~>calm(X))))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:((calm(X)<~>~funny(X))))&
(?[X]:((~patient(X)|~wise(X))))&
(humble(alice))&
((funny(susan)<~>~kind(susan)))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:(~generous(X))) | ~funny(susan) | [] | null | 0 |
Everyone who is not strong or happy is either calm or not strong and vice versa.
Everyone who is generous is either quiet or not generous and vice versa.
Everyone who is both creative and not tall is either not funny or not strong.
Everyone who is either wise or patient is patient and vice versa.
Everyone who is happy or not quiet is both generous and not old and vice versa.
If susan is both wise and rich then lucy is either tall or not brave and vice versa.
If someone is generous or wise then someone is not calm and vice versa.
Everyone who is either strong or not kind is both not curious and strong.
If fred is either patient or not wise then susan is either not curious or tall.
If paul is strong or not rich then someone is not patient.
Everyone who is either not calm or quiet is both curious and kind and vice versa.
Everyone who is not quiet is kind and vice versa.
Everyone who is both rich and creative is both curious and not old and vice versa.
If susan is not quiet or calm then someone is both old and tall and vice versa.
If someone is both not funny and not calm then someone is funny.
Someone is old or curious.
Mary is not generous.
Paul is either not quiet or not wise.
Someone is either quiet or not brave.
Someone is curious or wise.
Fred is funny or not calm.
Someone is both rich and not patient. | Lucy is strong. | entailment | (![X]:((~strong(X)|happy(X))<=>(calm(X)<~>~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(funny(X))))&
(?[X]:((old(X)|curious(X))))&
(~generous(mary))&
((~quiet(paul)<~>~wise(paul)))&
(?[X]:((quiet(X)<~>~brave(X))))&
(?[X]:((curious(X)|wise(X))))&
((funny(fred)|~calm(fred)))&
(?[X]:((rich(X)&~patient(X)))) | strong(lucy) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7591022427299803189391569
% SZS output start Proof for 7591022427299803189391569
2. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p1]
8. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (strong(X0) & ~curious(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> kind(X0)) [input p11]
23. ~strong(lucy) [input hypothesis]
28. ! [X0] : ((strong(X0) & ~curious(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 8]
34. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 2]
46. ! [X0] : ((strong(X0) & ~curious(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 28]
52. ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 12]
79. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 34]
82. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 34]
106. strong(X0) | strong(X0) | kind(X0) [cnf transformation 46]
120. ~quiet(X0) | ~kind(X0) [cnf transformation 52]
141. ~strong(lucy) [cnf transformation 23]
142. kind(X0) | strong(X0) [duplicate literal removal 106]
145. ~generous(X0) | quiet(X0) [duplicate literal removal 79]
146. generous(X0) | quiet(X0) [duplicate literal removal 82]
149. quiet(X0) [subsumption resolution 145,146]
220. ~kind(X0) [subsumption resolution 120,149]
271. strong(X0) [resolution 142,220]
272. $false [resolution 271,141]
% SZS output end Proof for 7591022427299803189391569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not kind is not wise.
Everyone who is not quiet or not humble is either not old or quiet.
Everyone who is either not rich or old is brave and vice versa.
Everyone who is either funny or creative is either not happy or not generous.
If someone is not funny or curious then lucy is either creative or patient.
Everyone who is either tall or quiet is both not tall and quiet.
Everyone who is not generous or not funny is both not patient and old.
Everyone who is either old or not patient is both not brave and not happy and vice versa.
Everyone who is old is either wise or funny.
Everyone who is rich is both generous and brave and vice versa.
Everyone who is tall or not brave is not creative.
If lucy is happy then someone is either not brave or not strong and vice versa.
If someone is either old or not kind then someone is both not humble and not happy.
If susan is patient or not tall then lucy is not curious.
If someone is both humble and brave then lucy is both calm and generous.
If lucy is either not humble or brave then someone is both generous and tall.
Paul is not brave.
Alice is both not humble and not patient.
Fred is not calm or not creative.
Lucy is both not tall and not brave. | Lucy is not wise. | entailment | (![X]:((~quiet(X)&~kind(X))=>~wise(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~old(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>old(X))<=>brave(X)))&
(![X]:((funny(X)<~>creative(X))=>(~happy(X)<~>~generous(X))))&
((?[X]:((~funny(X)|curious(X))))=>((creative(lucy)<~>patient(lucy))))&
(![X]:((tall(X)<~>quiet(X))=>(~tall(X)&quiet(X))))&
(![X]:((~generous(X)|~funny(X))=>(~patient(X)&old(X))))&
(![X]:((old(X)<~>~patient(X))<=>(~brave(X)&~happy(X))))&
(![X]:(old(X)=>(wise(X)<~>funny(X))))&
(![X]:(rich(X)<=>(generous(X)&brave(X))))&
(![X]:((tall(X)|~brave(X))=>~creative(X)))&
((happy(lucy))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((old(X)<~>~kind(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(((patient(susan)|~tall(susan)))=>(~curious(lucy)))&
((?[X]:((humble(X)&brave(X))))=>((calm(lucy)&generous(lucy))))&
(((~humble(lucy)<~>brave(lucy)))=>(?[X]:((generous(X)&tall(X)))))&
(~brave(paul))&
((~humble(alice)&~patient(alice)))&
((~calm(fred)|~creative(fred)))&
((~tall(lucy)&~brave(lucy))) | ~wise(lucy) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1374880189841544376190831
% SZS output start Proof for 1374880189841544376190831
3. ! [X0] : ((~rich(X0) <~> old(X0)) <=> brave(X0)) [input p2]
5. ? [X0] : (curious(X0) | ~funny(X0)) => (creative(lucy) <~> patient(lucy)) [input p4]
7. ! [X0] : ((~funny(X0) | ~generous(X0)) => (old(X0) & ~patient(X0))) [input p6]
9. ! [X0] : (old(X0) => (wise(X0) <~> funny(X0))) [input p8]
10. ! [X0] : (rich(X0) <=> (brave(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~brave(X0) | tall(X0)) => ~creative(X0)) [input p10]
20. ~brave(lucy) & ~tall(lucy) [input p19]
21. wise(lucy) [input hypothesis]
24. ? [X0] : ~funny(X0) => (creative(lucy) <~> patient(lucy)) [pure predicate removal 5]
29. (creative(lucy) <~> patient(lucy)) | ! [X0] : funny(X0) [ennf transformation 24]
31. ! [X0] : ((old(X0) & ~patient(X0)) | (funny(X0) & generous(X0))) [ennf transformation 7]
32. ! [X0] : ((wise(X0) <~> funny(X0)) | ~old(X0)) [ennf transformation 9]
33. ! [X0] : (~creative(X0) | (brave(X0) & ~tall(X0))) [ennf transformation 11]
38. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | ~brave(X0)) & (brave(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [nnf transformation 3]
40. ((~patient(lucy) | ~creative(lucy)) & (patient(lucy) | creative(lucy))) | ! [X0] : funny(X0) [nnf transformation 29]
44. ! [X0] : (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~old(X0)) [nnf transformation 32]
45. ! [X0] : ((rich(X0) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | ~rich(X0))) [nnf transformation 10]
46. ! [X0] : ((rich(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | ~rich(X0))) [flattening 45]
63. brave(X0) | old(X0) | rich(X0) [cnf transformation 38]
71. patient(lucy) | creative(lucy) | funny(X0) [cnf transformation 40]
78. ~patient(X0) | funny(X0) [cnf transformation 31]
88. ~funny(X0) | ~wise(X0) | ~old(X0) [cnf transformation 44]
90. ~rich(X0) | brave(X0) [cnf transformation 46]
93. ~creative(X0) | brave(X0) [cnf transformation 33]
113. ~brave(lucy) [cnf transformation 20]
114. wise(lucy) [cnf transformation 21]
119. 1 <=> ! [X0] : funny(X0) [avatar definition]
120. funny(X0) <- (1) [avatar component clause 119]
122. 2 <=> creative(lucy) [avatar definition]
123. creative(lucy) <- (2) [avatar component clause 122]
126. 3 <=> patient(lucy) [avatar definition]
127. patient(lucy) <- (3) [avatar component clause 126]
130. 1 | 2 | 3 [avatar split clause 71,126,122,119]
186. 16 <=> brave(lucy) [avatar definition]
188. ~brave(lucy) <- (~16) [avatar component clause 186]
214. ~16 [avatar split clause 113,186]
215. brave(lucy) <- (2) [resolution 93,123]
216. $false <- (2, ~16) [subsumption resolution 215,188]
217. ~2 | 16 [avatar contradiction clause 216]
218. funny(lucy) <- (3) [resolution 127,78]
233. old(lucy) | rich(lucy) <- (~16) [resolution 63,188]
246. 26 <=> rich(lucy) [avatar definition]
248. rich(lucy) <- (26) [avatar component clause 246]
250. 27 <=> old(lucy) [avatar definition]
252. old(lucy) <- (27) [avatar component clause 250]
253. 26 | 27 | 16 [avatar split clause 233,186,250,246]
275. brave(lucy) <- (26) [resolution 248,90]
279. $false <- (~16, 26) [subsumption resolution 275,188]
280. 16 | ~26 [avatar contradiction clause 279]
290. ~wise(lucy) | ~old(lucy) <- (3) [resolution 88,218]
291. ~old(lucy) <- (3) [subsumption resolution 290,114]
292. $false <- (3, 27) [subsumption resolution 291,252]
293. ~3 | ~27 [avatar contradiction clause 292]
294. ~old(X0) | ~wise(X0) <- (1) [resolution 120,88]
299. ~wise(lucy) <- (1, 27) [resolution 294,252]
300. $false <- (1, 27) [subsumption resolution 299,114]
301. ~1 | ~27 [avatar contradiction clause 300]
302. $false [avatar sat refutation 130,214,217,253,280,293,301]
% SZS output end Proof for 1374880189841544376190831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not quiet is either not brave or kind.
If mary is either wise or not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Everyone who is either not wise or not calm is either not curious or wise.
Everyone who is tall is both strong and not happy.
Everyone who is not humble or old is not rich and vice versa.
Everyone who is both strong and not rich is either not generous or creative and vice versa.
Everyone who is either not brave or patient is both rich and not kind and vice versa.
If someone is either humble or rich then lucy is quiet or not funny.
If someone is either kind or not kind then alice is quiet or not happy.
Everyone who is kind is either not quiet or happy.
If alice is quiet then john is either not old or not generous and vice versa.
Everyone who is not generous is quiet or wise and vice versa.
If lucy is either not kind or not happy then someone is not wise.
Everyone who is both not generous and not strong is calm or kind and vice versa.
Everyone who is not rich is either generous or quiet and vice versa.
Someone is either brave or not strong.
Susan is both not funny and not kind.
Susan is not old.
Someone is either not generous or generous.
Someone is either happy or humble.
Fred is either tall or not old.
Someone is wise or not brave.
Paul is either not happy or not tall. | Lucy is not generous. | neutral | (![X]:((~tall(X)|~quiet(X))=>(~brave(X)<~>kind(X))))&
(((wise(mary)<~>~old(mary)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(![X]:((~wise(X)<~>~calm(X))=>(~curious(X)<~>wise(X))))&
(![X]:(tall(X)=>(strong(X)&~happy(X))))&
(![X]:((~humble(X)|old(X))<=>~rich(X)))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(rich(X)&~kind(X))))&
((?[X]:((humble(X)<~>rich(X))))=>((quiet(lucy)|~funny(lucy))))&
((?[X]:((kind(X)<~>~kind(X))))=>((quiet(alice)|~happy(alice))))&
(![X]:(kind(X)=>(~quiet(X)<~>happy(X))))&
((quiet(alice))<=>((~old(john)<~>~generous(john))))&
(![X]:(~generous(X)<=>(quiet(X)|wise(X))))&
(((~kind(lucy)<~>~happy(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~generous(X)&~strong(X))<=>(calm(X)|kind(X))))&
(![X]:(~rich(X)<=>(generous(X)<~>quiet(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
((~funny(susan)&~kind(susan)))&
(~old(susan))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((tall(fred)<~>~old(fred)))&
(?[X]:((wise(X)|~brave(X))))&
((~happy(paul)<~>~tall(paul))) | ~generous(lucy) | [] | null | 0 |
Everyone who is not brave is not wise or generous and vice versa. Everyone who is curious is either not patient or tall. Everyone who is not strong is either rich or not old and vice versa. If john is both not curious and not humble then someone is not humble and vice versa. Everyone who is not patient or not creative is either not calm or not happy. If someone is patient then someone is either not happy or not calm and vice versa. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Fred is both not funny and tall. Someone is not patient. John is either not patient or not curious. Someone is either humble or not happy. Someone is not strong. Someone is not tall or kind. | Fred is curious. | neutral | (![X]:(~brave(X)<=>(~wise(X)|generous(X))))&
(![X]:(curious(X)=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
((~funny(fred)&tall(fred)))&
(?[X]:(~patient(X)))&
((~patient(john)<~>~curious(john)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|kind(X)))) | curious(fred) | [] | null | 0 |
If someone is funny then someone is either strong or funny.
If someone is not funny or kind then someone is either not creative or not quiet.
Everyone who is either not patient or tall is not creative.
If fred is not happy then alice is either wise or old.
Everyone who is funny or not old is both not kind and calm.
Everyone who is quiet or kind is not creative and vice versa.
Everyone who is kind is funny.
If someone is either not curious or brave then mary is rich.
If lucy is strong then john is either not kind or not humble and vice versa.
If someone is either not calm or not funny then someone is either wise or humble.
If someone is not brave or not old then someone is either not rich or tall and vice versa.
Everyone who is not patient is quiet.
If someone is either brave or not happy then mary is not strong or calm and vice versa.
If john is either not old or tall then mary is both not wise and calm and vice versa.
Everyone who is both not strong and not curious is either humble or generous and vice versa.
If someone is not strong or calm then alice is either not generous or tall and vice versa.
Someone is not creative or humble.
Susan is either not happy or patient.
John is both tall and curious.
Someone is funny.
Someone is tall.
Lucy is not quiet or not happy.
Someone is both not calm and not curious. | John is quiet. | entailment | ((?[X]:(funny(X)))=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~funny(X)|kind(X))))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((~patient(X)<~>tall(X))=>~creative(X)))&
((~happy(fred))=>((wise(alice)<~>old(alice))))&
(![X]:((funny(X)|~old(X))=>(~kind(X)&calm(X))))&
(![X]:((quiet(X)|kind(X))<=>~creative(X)))&
(![X]:(kind(X)=>funny(X)))&
((?[X]:((~curious(X)<~>brave(X))))=>(rich(mary)))&
((strong(lucy))<=>((~kind(john)<~>~humble(john))))&
((?[X]:((~calm(X)<~>~funny(X))))=>(?[X]:((wise(X)<~>humble(X)))))&
((?[X]:((~brave(X)|~old(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~strong(mary)|calm(mary))))&
(((~old(john)<~>tall(john)))<=>((~wise(mary)&calm(mary))))&
(![X]:((~strong(X)&~curious(X))<=>(humble(X)<~>generous(X))))&
((?[X]:((~strong(X)|calm(X))))<=>((~generous(alice)<~>tall(alice))))&
(?[X]:((~creative(X)|humble(X))))&
((~happy(susan)<~>patient(susan)))&
((tall(john)&curious(john)))&
(?[X]:(funny(X)))&
(?[X]:(tall(X)))&
((~quiet(lucy)|~happy(lucy)))&
(?[X]:((~calm(X)&~curious(X)))) | quiet(john) | [
"p2",
"p4",
"p5",
"p6",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 876143403661088836556053
% SZS output start Proof for 876143403661088836556053
3. ! [X0] : ((~patient(X0) <~> tall(X0)) => ~creative(X0)) [input p2]
5. ! [X0] : ((~old(X0) | funny(X0)) => (calm(X0) & ~kind(X0))) [input p4]
6. ! [X0] : ((kind(X0) | quiet(X0)) <=> ~creative(X0)) [input p5]
7. ! [X0] : (kind(X0) => funny(X0)) [input p6]
12. ! [X0] : (~patient(X0) => quiet(X0)) [input p11]
19. curious(john) & tall(john) [input p18]
24. ~quiet(john) [input hypothesis]
31. ! [X0] : (~creative(X0) | (~patient(X0) <=> tall(X0))) [ennf transformation 3]
33. ! [X0] : ((calm(X0) & ~kind(X0)) | (old(X0) & ~funny(X0))) [ennf transformation 5]
34. ! [X0] : (funny(X0) | ~kind(X0)) [ennf transformation 7]
37. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 12]
46. ! [X0] : (~creative(X0) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 31]
48. ! [X0] : (((kind(X0) | quiet(X0)) | creative(X0)) & (~creative(X0) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 6]
49. ! [X0] : ((kind(X0) | quiet(X0) | creative(X0)) & (~creative(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 48]
90. ~tall(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 46]
93. ~kind(X0) | ~funny(X0) [cnf transformation 33]
99. quiet(X0) | kind(X0) | creative(X0) [cnf transformation 49]
100. funny(X0) | ~kind(X0) [cnf transformation 34]
117. patient(X0) | quiet(X0) [cnf transformation 37]
145. tall(john) [cnf transformation 19]
152. ~quiet(john) [cnf transformation 24]
167. 4 <=> ! [X1] : ~kind(X1) [avatar definition]
168. ~kind(X1) <- (4) [avatar component clause 167]
198. ~kind(X0) [subsumption resolution 100,93]
199. 4 [avatar split clause 198,167]
312. 36 <=> tall(john) [avatar definition]
313. tall(john) <- (36) [avatar component clause 312]
368. 36 [avatar split clause 145,312]
400. ~patient(john) | ~creative(john) <- (36) [resolution 90,313]
411. 53 <=> creative(john) [avatar definition]
415. 54 <=> patient(john) [avatar definition]
417. ~patient(john) <- (~54) [avatar component clause 415]
418. ~53 | ~54 | ~36 [avatar split clause 400,312,415,411]
419. kind(john) | creative(john) [resolution 99,152]
423. creative(john) <- (4) [subsumption resolution 419,168]
424. 53 | ~4 [avatar split clause 423,167,411]
429. quiet(john) <- (~54) [resolution 417,117]
430. $false <- (~54) [subsumption resolution 429,152]
431. 54 [avatar contradiction clause 430]
432. $false [avatar sat refutation 199,368,418,424,431]
% SZS output end Proof for 876143403661088836556053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not calm and not rich is not funny or not brave.
Everyone who is either not happy or kind is both not calm and not strong.
Everyone who is either not funny or not rich is not rich or calm.
If someone is either not brave or curious then someone is calm or not happy and vice versa.
If paul is quiet then someone is quiet or not old and vice versa.
If someone is either patient or not generous then fred is generous or not brave.
Everyone who is not curious or happy is wise.
If lucy is either calm or tall then someone is either not wise or rich.
Everyone who is either strong or not rich is old or not wise and vice versa.
If someone is kind or old then someone is not creative or not tall.
Everyone who is either happy or not calm is both wise and funny and vice versa.
If someone is wise then fred is funny or old.
Everyone who is calm is both not rich and not calm and vice versa.
Everyone who is either creative or curious is not strong or not curious.
Everyone who is both generous and not humble is either humble or not strong and vice versa.
If someone is both not wise and funny then someone is curious and vice versa.
Lucy is either brave or not generous.
Paul is kind.
Someone is either rich or not quiet.
Someone is both not curious and not brave.
Lucy is patient.
Alice is quiet.
Fred is not strong. | Alice is curious. | contradiction | (![X]:((~calm(X)&~rich(X))=>(~funny(X)|~brave(X))))&
(![X]:((~happy(X)<~>kind(X))=>(~calm(X)&~strong(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~rich(X)|calm(X))))&
((?[X]:((~brave(X)<~>curious(X))))<=>(?[X]:((calm(X)|~happy(X)))))&
((quiet(paul))<=>(?[X]:((quiet(X)|~old(X)))))&
((?[X]:((patient(X)<~>~generous(X))))=>((generous(fred)|~brave(fred))))&
(![X]:((~curious(X)|happy(X))=>wise(X)))&
(((calm(lucy)<~>tall(lucy)))=>(?[X]:((~wise(X)<~>rich(X)))))&
(![X]:((strong(X)<~>~rich(X))<=>(old(X)|~wise(X))))&
((?[X]:((kind(X)|old(X))))=>(?[X]:((~creative(X)|~tall(X)))))&
(![X]:((happy(X)<~>~calm(X))<=>(wise(X)&funny(X))))&
((?[X]:(wise(X)))=>((funny(fred)|old(fred))))&
(![X]:(calm(X)<=>(~rich(X)&~calm(X))))&
(![X]:((creative(X)<~>curious(X))=>(~strong(X)|~curious(X))))&
(![X]:((generous(X)&~humble(X))<=>(humble(X)<~>~strong(X))))&
((?[X]:((~wise(X)&funny(X))))<=>(?[X]:(curious(X))))&
((brave(lucy)<~>~generous(lucy)))&
(kind(paul))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:((~curious(X)&~brave(X))))&
(patient(lucy))&
(quiet(alice))&
(~strong(fred)) | curious(alice) | [
"p6",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2958067909400441136365537
% SZS output start Proof for 2958067909400441136365537
7. ! [X0] : ((happy(X0) | ~curious(X0)) => wise(X0)) [input p6]
11. ! [X0] : ((happy(X0) <~> ~calm(X0)) <=> (funny(X0) & wise(X0))) [input p10]
13. ! [X0] : (calm(X0) <=> (~calm(X0) & ~rich(X0))) [input p12]
16. ? [X0] : (funny(X0) & ~wise(X0)) <=> ? [X0] : curious(X0) [input p15]
24. curious(alice) [input hypothesis]
27. ? [X0] : (funny(X0) & ~wise(X0)) <=> ? [X1] : curious(X1) [rectify 16]
35. ! [X0] : (wise(X0) | (~happy(X0) & curious(X0))) [ennf transformation 7]
62. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (~funny(X0) | ~wise(X0))) & ((funny(X0) & wise(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [nnf transformation 11]
63. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | ~funny(X0) | ~wise(X0)) & ((funny(X0) & wise(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [flattening 62]
64. ! [X0] : ((calm(X0) | (calm(X0) | rich(X0))) & ((~calm(X0) & ~rich(X0)) | ~calm(X0))) [nnf transformation 13]
65. ! [X0] : ((calm(X0) | calm(X0) | rich(X0)) & ((~calm(X0) & ~rich(X0)) | ~calm(X0))) [flattening 64]
69. (? [X0] : (funny(X0) & ~wise(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~funny(X0) | wise(X0))) [nnf transformation 27]
70. (? [X0] : (funny(X0) & ~wise(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~funny(X3) | wise(X3))) [rectify 69]
71. ? [X0] : (funny(X0) & ~wise(X0)) => (funny(sK5) & ~wise(sK5)) [choice axiom]
72. ? [X2] : curious(X2) => curious(sK6) [choice axiom]
73. ((funny(sK5) & ~wise(sK5)) | ! [X1] : ~curious(X1)) & (curious(sK6) | ! [X3] : (~funny(X3) | wise(X3))) [skolemisation 70,72,71]
99. ~happy(X0) | wise(X0) [cnf transformation 35]
113. wise(X0) | happy(X0) | calm(X0) [cnf transformation 63]
120. ~calm(X0) | ~calm(X0) [cnf transformation 65]
131. ~wise(sK5) | ~curious(X1) [cnf transformation 73]
143. curious(alice) [cnf transformation 24]
147. ~calm(X0) [duplicate literal removal 120]
163. 4 <=> ! [X1] : ~calm(X1) [avatar definition]
164. ~calm(X1) <- (4) [avatar component clause 163]
258. wise(X0) | calm(X0) [subsumption resolution 113,99]
271. 4 [avatar split clause 147,163]
274. 29 <=> ! [X1] : ~curious(X1) [avatar definition]
275. ~curious(X1) <- (29) [avatar component clause 274]
282. 31 <=> wise(sK5) [avatar definition]
284. ~wise(sK5) <- (~31) [avatar component clause 282]
285. 29 | ~31 [avatar split clause 131,282,274]
314. $false <- (29) [resolution 275,143]
315. ~29 [avatar contradiction clause 314]
327. calm(sK5) <- (~31) [resolution 258,284]
328. $false <- (4, ~31) [subsumption resolution 327,164]
329. ~4 | 31 [avatar contradiction clause 328]
330. $false [avatar sat refutation 271,285,315,329]
% SZS output end Proof for 2958067909400441136365537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then paul is both not funny and not rich and vice versa.
Everyone who is either not tall or patient is happy and vice versa.
Everyone who is both brave and strong is either funny or strong.
Everyone who is both not brave and not quiet is both not curious and not happy and vice versa.
If alice is old then someone is both tall and strong.
If alice is humble or patient then someone is not patient or creative and vice versa.
If someone is kind or not generous then someone is generous.
Everyone who is brave or wise is wise and vice versa.
Everyone who is both quiet and not humble is both tall and quiet.
Everyone who is both brave and not creative is calm.
If someone is either not kind or not patient then paul is either strong or not calm and vice versa.
Everyone who is both not creative and funny is not kind.
If lucy is both calm and funny then someone is both not tall and tall.
Everyone who is not brave or not calm is both not curious and calm and vice versa.
Everyone who is not humble is either not patient or not kind.
If someone is patient or not wise then someone is either not tall or old and vice versa.
Fred is old.
John is both not rich and old.
Someone is strong or calm.
Someone is both not patient and creative.
Alice is calm or not tall.
Lucy is both tall and happy.
Someone is either curious or not brave.
Someone is both not quiet and not old. | Paul is not rich. | entailment | ((?[X]:(calm(X)))<=>((~funny(paul)&~rich(paul))))&
(![X]:((~tall(X)<~>patient(X))<=>happy(X)))&
(![X]:((brave(X)&strong(X))=>(funny(X)<~>strong(X))))&
(![X]:((~brave(X)&~quiet(X))<=>(~curious(X)&~happy(X))))&
((old(alice))=>(?[X]:((tall(X)&strong(X)))))&
(((humble(alice)|patient(alice)))<=>(?[X]:((~patient(X)|creative(X)))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|wise(X))<=>wise(X)))&
(![X]:((quiet(X)&~humble(X))=>(tall(X)&quiet(X))))&
(![X]:((brave(X)&~creative(X))=>calm(X)))&
((?[X]:((~kind(X)<~>~patient(X))))<=>((strong(paul)<~>~calm(paul))))&
(![X]:((~creative(X)&funny(X))=>~kind(X)))&
(((calm(lucy)&funny(lucy)))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~brave(X)|~calm(X))<=>(~curious(X)&calm(X))))&
(![X]:(~humble(X)=>(~patient(X)<~>~kind(X))))&
((?[X]:((patient(X)|~wise(X))))<=>(?[X]:((~tall(X)<~>old(X)))))&
(old(fred))&
((~rich(john)&old(john)))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((~patient(X)&creative(X))))&
((calm(alice)|~tall(alice)))&
((tall(lucy)&happy(lucy)))&
(?[X]:((curious(X)<~>~brave(X))))&
(?[X]:((~quiet(X)&~old(X)))) | ~rich(paul) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8695631866240848690725438
% SZS output start Proof for 8695631866240848690725438
1. ? [X0] : calm(X0) <=> (~rich(paul) & ~funny(paul)) [input p0]
14. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (calm(X0) & ~curious(X0))) [input p13]
25. rich(paul) [input hypothesis]
41. (? [X0] : calm(X0) | (rich(paul) | funny(paul))) & ((~rich(paul) & ~funny(paul)) | ! [X0] : ~calm(X0)) [nnf transformation 1]
42. (? [X0] : calm(X0) | rich(paul) | funny(paul)) & ((~rich(paul) & ~funny(paul)) | ! [X0] : ~calm(X0)) [flattening 41]
43. (? [X0] : calm(X0) | rich(paul) | funny(paul)) & ((~rich(paul) & ~funny(paul)) | ! [X1] : ~calm(X1)) [rectify 42]
44. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
45. (calm(sK0) | rich(paul) | funny(paul)) & ((~rich(paul) & ~funny(paul)) | ! [X1] : ~calm(X1)) [skolemisation 43,44]
65. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~calm(X0) | curious(X0))) & ((calm(X0) & ~curious(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 14]
66. ! [X0] : ((~calm(X0) | ~brave(X0) | ~calm(X0) | curious(X0)) & ((calm(X0) & ~curious(X0)) | (calm(X0) & brave(X0)))) [flattening 65]
83. ~rich(paul) | ~calm(X1) [cnf transformation 45]
121. calm(X0) | calm(X0) [cnf transformation 66]
144. rich(paul) [cnf transformation 25]
145. calm(X0) [duplicate literal removal 121]
153. 2 <=> rich(paul) [avatar definition]
162. 4 <=> ! [X1] : ~calm(X1) [avatar definition]
163. ~calm(X1) <- (4) [avatar component clause 162]
164. 4 | ~2 [avatar split clause 83,153,162]
293. 2 [avatar split clause 144,153]
298. $false <- (4) [subsumption resolution 163,145]
299. ~4 [avatar contradiction clause 298]
300. $false [avatar sat refutation 164,293,299]
% SZS output end Proof for 8695631866240848690725438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not creative or not quiet. If alice is not humble then someone is both rich and happy. Everyone who is not patient is not strong or rich. Everyone who is both not generous and not patient is either strong or not quiet. Everyone who is kind is both quiet and funny. Everyone who is both old and strong is not calm and vice versa. Everyone who is not strong or not kind is either curious or happy and vice versa. Everyone who is kind is curious or rich and vice versa. Everyone who is wise is either not brave or kind. If susan is patient then someone is either not brave or not quiet. Everyone who is rich or curious is not wise. Everyone who is not tall or not funny is either happy or not humble and vice versa. Everyone who is both kind and strong is rich. If john is not rich or quiet then someone is tall or generous and vice versa. Everyone who is not kind is both quiet and generous and vice versa. If someone is not strong then someone is quiet or patient. Someone is not tall or not happy. Someone is not generous or not rich. Fred is both not creative and not happy. Someone is funny or creative. Someone is funny. Someone is both not rich and old. Someone is either old or not happy. Paul is not calm. | Fred is not wise. | entailment | (![X]:(~creative(X)=>(~creative(X)|~quiet(X))))&
((~humble(alice))=>(?[X]:((rich(X)&happy(X)))))&
(![X]:(~patient(X)=>(~strong(X)|rich(X))))&
(![X]:((~generous(X)&~patient(X))=>(strong(X)<~>~quiet(X))))&
(![X]:(kind(X)=>(quiet(X)&funny(X))))&
(![X]:((old(X)&strong(X))<=>~calm(X)))&
(![X]:((~strong(X)|~kind(X))<=>(curious(X)<~>happy(X))))&
(![X]:(kind(X)<=>(curious(X)|rich(X))))&
(![X]:(wise(X)=>(~brave(X)<~>kind(X))))&
((patient(susan))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((rich(X)|curious(X))=>~wise(X)))&
(![X]:((~tall(X)|~funny(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((kind(X)&strong(X))=>rich(X)))&
(((~rich(john)|quiet(john)))<=>(?[X]:((tall(X)|generous(X)))))&
(![X]:(~kind(X)<=>(quiet(X)&generous(X))))&
((?[X]:(~strong(X)))=>(?[X]:((quiet(X)|patient(X)))))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((~generous(X)|~rich(X))))&
((~creative(fred)&~happy(fred)))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:((old(X)<~>~happy(X))))&
(~calm(paul)) | ~wise(fred) | [
"p6",
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8132557527314437361757110
% SZS output start Proof for 8132557527314437361757110
7. ! [X0] : ((~kind(X0) | ~strong(X0)) <=> (curious(X0) <~> happy(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> (rich(X0) | curious(X0))) [input p7]
11. ! [X0] : ((curious(X0) | rich(X0)) => ~wise(X0)) [input p10]
19. ~happy(fred) & ~creative(fred) [input p18]
25. wise(fred) [input hypothesis]
39. ! [X0] : (~wise(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 11]
46. ! [X0] : (((~kind(X0) | ~strong(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (kind(X0) & strong(X0)))) [nnf transformation 7]
47. ! [X0] : ((~kind(X0) | ~strong(X0) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (kind(X0) & strong(X0)))) [flattening 46]
48. ! [X0] : ((kind(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ~kind(X0))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~kind(X0))) [flattening 48]
90. curious(X0) | happy(X0) | kind(X0) [cnf transformation 47]
95. ~kind(X0) | curious(X0) | rich(X0) [cnf transformation 49]
96. ~curious(X0) | kind(X0) [cnf transformation 49]
102. ~wise(X0) | ~rich(X0) [cnf transformation 39]
103. ~wise(X0) | ~curious(X0) [cnf transformation 39]
122. ~happy(fred) [cnf transformation 19]
130. wise(fred) [cnf transformation 25]
232. ~rich(fred) [resolution 102,130]
235. ~curious(fred) [resolution 103,130]
257. happy(X0) | kind(X0) | kind(X0) [resolution 90,96]
259. kind(X0) | happy(X0) [duplicate literal removal 257]
278. 23 <=> kind(fred) [avatar definition]
279. kind(fred) <- (23) [avatar component clause 278]
280. ~kind(fred) <- (~23) [avatar component clause 278]
286. happy(fred) <- (~23) [resolution 280,259]
288. $false <- (~23) [subsumption resolution 286,122]
289. 23 [avatar contradiction clause 288]
292. curious(fred) | rich(fred) <- (23) [resolution 279,95]
338. rich(fred) <- (23) [subsumption resolution 292,235]
339. $false <- (23) [subsumption resolution 338,232]
340. ~23 [avatar contradiction clause 339]
341. $false [avatar sat refutation 289,340]
% SZS output end Proof for 8132557527314437361757110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny then someone is not generous and vice versa.
Everyone who is brave is not generous.
If alice is both not patient and not strong then someone is quiet and vice versa.
Everyone who is kind is not creative and vice versa.
If someone is both not old and not patient then mary is old.
If someone is not funny or creative then someone is calm and vice versa.
Everyone who is not funny or not patient is both creative and not tall.
Everyone who is not generous is either rich or not wise and vice versa.
Everyone who is not quiet or happy is not funny or generous and vice versa.
Everyone who is both rich and not patient is both not tall and rich.
Everyone who is not kind is not old.
Everyone who is either not creative or not kind is both curious and not funny.
If someone is both rich and old then alice is either not happy or curious.
If someone is both not creative and funny then someone is rich or old.
Everyone who is either tall or humble is funny or not generous and vice versa.
If lucy is both not creative and not quiet then paul is either not old or not tall and vice versa.
Someone is wise.
Someone is not quiet or not patient.
Susan is not funny or not strong.
Lucy is not creative or not funny.
Fred is both not tall and not humble.
Susan is either not brave or tall. | Lucy is quiet. | contradiction | ((funny(alice))<=>(?[X]:(~generous(X))))&
(![X]:(brave(X)=>~generous(X)))&
(((~patient(alice)&~strong(alice)))<=>(?[X]:(quiet(X))))&
(![X]:(kind(X)<=>~creative(X)))&
((?[X]:((~old(X)&~patient(X))))=>(old(mary)))&
((?[X]:((~funny(X)|creative(X))))<=>(?[X]:(calm(X))))&
(![X]:((~funny(X)|~patient(X))=>(creative(X)&~tall(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>~wise(X))))&
(![X]:((~quiet(X)|happy(X))<=>(~funny(X)|generous(X))))&
(![X]:((rich(X)&~patient(X))=>(~tall(X)&rich(X))))&
(![X]:(~kind(X)=>~old(X)))&
(![X]:((~creative(X)<~>~kind(X))=>(curious(X)&~funny(X))))&
((?[X]:((rich(X)&old(X))))=>((~happy(alice)<~>curious(alice))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:((rich(X)|old(X)))))&
(![X]:((tall(X)<~>humble(X))<=>(funny(X)|~generous(X))))&
(((~creative(lucy)&~quiet(lucy)))<=>((~old(paul)<~>~tall(paul))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|~patient(X))))&
((~funny(susan)|~strong(susan)))&
((~creative(lucy)|~funny(lucy)))&
((~tall(fred)&~humble(fred)))&
((~brave(susan)<~>tall(susan))) | quiet(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8751983003235394188522938
% SZS output start Proof for 8751983003235394188522938
3. (~strong(alice) & ~patient(alice)) <=> ? [X0] : quiet(X0) [input p2]
4. ! [X0] : (kind(X0) <=> ~creative(X0)) [input p3]
5. ? [X0] : (~patient(X0) & ~old(X0)) => old(mary) [input p4]
7. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~tall(X0) & creative(X0))) [input p6]
11. ! [X0] : (~kind(X0) => ~old(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> ~kind(X0)) => (~funny(X0) & curious(X0))) [input p11]
23. quiet(lucy) [input hypothesis]
27. old(mary) | ! [X0] : (patient(X0) | old(X0)) [ennf transformation 5]
28. ! [X0] : ((~tall(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 7]
31. ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 11]
32. ! [X0] : ((~funny(X0) & curious(X0)) | (~creative(X0) <=> ~kind(X0))) [ennf transformation 12]
39. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (strong(alice) | patient(alice))) [nnf transformation 3]
40. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | strong(alice) | patient(alice)) [flattening 39]
41. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | strong(alice) | patient(alice)) [rectify 40]
42. ? [X1] : quiet(X1) => quiet(sK1) [choice axiom]
43. ((~strong(alice) & ~patient(alice)) | ! [X0] : ~quiet(X0)) & (quiet(sK1) | strong(alice) | patient(alice)) [skolemisation 41,42]
44. ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 4]
53. ! [X0] : ((~funny(X0) & curious(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) [nnf transformation 32]
71. ~patient(alice) | ~quiet(X0) [cnf transformation 43]
73. ~creative(X0) | ~kind(X0) [cnf transformation 44]
74. creative(X0) | kind(X0) [cnf transformation 44]
75. old(mary) | patient(X0) | old(X0) [cnf transformation 27]
79. creative(X0) | funny(X0) [cnf transformation 28]
93. ~old(X0) | kind(X0) [cnf transformation 31]
96. ~funny(X0) | ~kind(X0) | creative(X0) [cnf transformation 53]
121. quiet(lucy) [cnf transformation 23]
136. 4 <=> ! [X0] : ~quiet(X0) [avatar definition]
137. ~quiet(X0) <- (4) [avatar component clause 136]
144. 6 <=> patient(alice) [avatar definition]
146. ~patient(alice) <- (~6) [avatar component clause 144]
147. 4 | ~6 [avatar split clause 71,144,136]
154. 8 <=> ! [X0] : (patient(X0) | old(X0)) [avatar definition]
155. old(X0) | patient(X0) <- (8) [avatar component clause 154]
157. 9 <=> old(mary) [avatar definition]
159. old(mary) <- (9) [avatar component clause 157]
160. 8 | 9 [avatar split clause 75,157,154]
186. ~funny(X0) | creative(X0) [subsumption resolution 96,74]
187. creative(X0) [subsumption resolution 186,79]
213. 21 <=> quiet(lucy) [avatar definition]
214. quiet(lucy) <- (21) [avatar component clause 213]
251. 21 [avatar split clause 121,213]
252. $false <- (4, 21) [resolution 214,137]
253. ~4 | ~21 [avatar contradiction clause 252]
254. ~kind(X0) [resolution 73,187]
259. patient(X0) | kind(X0) <- (8) [resolution 155,93]
260. patient(X0) <- (8) [subsumption resolution 259,254]
269. $false <- (~6, 8) [resolution 260,146]
272. 6 | ~8 [avatar contradiction clause 269]
273. kind(mary) <- (9) [resolution 159,93]
274. $false <- (9) [subsumption resolution 273,254]
275. ~9 [avatar contradiction clause 274]
276. $false [avatar sat refutation 147,160,251,253,272,275]
% SZS output end Proof for 8751983003235394188522938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not happy is funny or not wise and vice versa.
Everyone who is either not curious or humble is kind.
Everyone who is curious or old is not strong or not humble.
If lucy is either not happy or quiet then susan is both not quiet and old.
If someone is both not old and not quiet then paul is generous.
Everyone who is not rich is both not kind and not rich.
Everyone who is either quiet or not brave is happy.
Everyone who is either funny or not kind is wise or quiet.
If someone is not kind then paul is both brave and generous.
Everyone who is both patient and not rich is tall or not brave and vice versa.
If susan is both brave and not tall then someone is brave.
If someone is calm then fred is creative.
Everyone who is not wise is brave or quiet.
Everyone who is not strong or wise is curious and vice versa.
If someone is strong then someone is both wise and humble and vice versa.
If paul is not tall or creative then fred is either calm or not kind and vice versa.
Someone is either curious or strong.
John is generous or not humble.
Fred is funny or not funny.
John is both curious and calm.
Someone is not quiet.
Lucy is not kind or rich.
Someone is both not happy and strong.
Paul is wise or not kind. | Paul is brave. | entailment | (![X]:((curious(X)|~happy(X))<=>(funny(X)|~wise(X))))&
(![X]:((~curious(X)<~>humble(X))=>kind(X)))&
(![X]:((curious(X)|old(X))=>(~strong(X)|~humble(X))))&
(((~happy(lucy)<~>quiet(lucy)))=>((~quiet(susan)&old(susan))))&
((?[X]:((~old(X)&~quiet(X))))=>(generous(paul)))&
(![X]:(~rich(X)=>(~kind(X)&~rich(X))))&
(![X]:((quiet(X)<~>~brave(X))=>happy(X)))&
(![X]:((funny(X)<~>~kind(X))=>(wise(X)|quiet(X))))&
((?[X]:(~kind(X)))=>((brave(paul)&generous(paul))))&
(![X]:((patient(X)&~rich(X))<=>(tall(X)|~brave(X))))&
(((brave(susan)&~tall(susan)))=>(?[X]:(brave(X))))&
((?[X]:(calm(X)))=>(creative(fred)))&
(![X]:(~wise(X)=>(brave(X)|quiet(X))))&
(![X]:((~strong(X)|wise(X))<=>curious(X)))&
((?[X]:(strong(X)))<=>(?[X]:((wise(X)&humble(X)))))&
(((~tall(paul)|creative(paul)))<=>((calm(fred)<~>~kind(fred))))&
(?[X]:((curious(X)<~>strong(X))))&
((generous(john)|~humble(john)))&
((funny(fred)|~funny(fred)))&
((curious(john)&calm(john)))&
(?[X]:(~quiet(X)))&
((~kind(lucy)|rich(lucy)))&
(?[X]:((~happy(X)&strong(X))))&
((wise(paul)|~kind(paul))) | brave(paul) | [
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 491911800370941906054265
% SZS output start Proof for 491911800370941906054265
6. ! [X0] : (~rich(X0) => (~rich(X0) & ~kind(X0))) [input p5]
9. ? [X0] : ~kind(X0) => (generous(paul) & brave(paul)) [input p8]
10. ! [X0] : ((~rich(X0) & patient(X0)) <=> (~brave(X0) | tall(X0))) [input p9]
25. ~brave(paul) [input hypothesis]
28. ? [X0] : ~kind(X0) => brave(paul) [pure predicate removal 9]
34. ! [X0] : ((~rich(X0) & ~kind(X0)) | rich(X0)) [ennf transformation 6]
38. brave(paul) | ! [X0] : kind(X0) [ennf transformation 28]
50. ! [X0] : (((~rich(X0) & patient(X0)) | (brave(X0) & ~tall(X0))) & ((~brave(X0) | tall(X0)) | (rich(X0) | ~patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~rich(X0) & patient(X0)) | (brave(X0) & ~tall(X0))) & (~brave(X0) | tall(X0) | rich(X0) | ~patient(X0))) [flattening 50]
82. ~kind(X0) | rich(X0) [cnf transformation 34]
88. brave(paul) | kind(X0) [cnf transformation 38]
93. ~rich(X0) | brave(X0) [cnf transformation 51]
119. ~brave(paul) [cnf transformation 25]
141. 5 <=> ! [X0] : kind(X0) [avatar definition]
142. kind(X0) <- (5) [avatar component clause 141]
144. 6 <=> brave(paul) [avatar definition]
145. ~brave(paul) <- (~6) [avatar component clause 144]
147. 5 | 6 [avatar split clause 88,144,141]
230. ~6 [avatar split clause 119,144]
239. rich(X0) <- (5) [resolution 82,142]
240. brave(X0) <- (5) [resolution 93,239]
241. $false <- (5, ~6) [resolution 240,145]
244. ~5 | 6 [avatar contradiction clause 241]
245. $false [avatar sat refutation 147,230,244]
% SZS output end Proof for 491911800370941906054265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is wise.
Everyone who is not happy or not curious is both funny and rich.
If fred is either not happy or not wise then someone is generous or humble.
If someone is either not quiet or not wise then lucy is either creative or not creative and vice versa.
If someone is not brave then paul is calm or not tall.
If someone is patient then someone is either not wise or not creative and vice versa.
Everyone who is not kind is either generous or humble.
Everyone who is not funny is either not generous or quiet.
If alice is either strong or not brave then someone is not calm.
Everyone who is either not happy or not generous is either strong or creative and vice versa.
Everyone who is strong or not creative is old and vice versa.
If someone is both rich and calm then someone is not patient or funny and vice versa.
If someone is either rich or wise then someone is not curious.
Everyone who is not patient is both calm and funny and vice versa.
Everyone who is old or not strong is not calm or not patient and vice versa.
Everyone who is curious is not humble.
Someone is not calm.
Alice is wise.
Someone is either strong or calm.
Lucy is both quiet and strong.
Lucy is both brave and creative.
Someone is not calm or wise.
Alice is not funny. | Alice is not brave. | neutral | (![X]:((calm(X)|kind(X))=>wise(X)))&
(![X]:((~happy(X)|~curious(X))=>(funny(X)&rich(X))))&
(((~happy(fred)<~>~wise(fred)))=>(?[X]:((generous(X)|humble(X)))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>((creative(lucy)<~>~creative(lucy))))&
((?[X]:(~brave(X)))=>((calm(paul)|~tall(paul))))&
((?[X]:(patient(X)))<=>(?[X]:((~wise(X)<~>~creative(X)))))&
(![X]:(~kind(X)=>(generous(X)<~>humble(X))))&
(![X]:(~funny(X)=>(~generous(X)<~>quiet(X))))&
(((strong(alice)<~>~brave(alice)))=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(strong(X)<~>creative(X))))&
(![X]:((strong(X)|~creative(X))<=>old(X)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((~patient(X)|funny(X)))))&
((?[X]:((rich(X)<~>wise(X))))=>(?[X]:(~curious(X))))&
(![X]:(~patient(X)<=>(calm(X)&funny(X))))&
(![X]:((old(X)|~strong(X))<=>(~calm(X)|~patient(X))))&
(![X]:(curious(X)=>~humble(X)))&
(?[X]:(~calm(X)))&
(wise(alice))&
(?[X]:((strong(X)<~>calm(X))))&
((quiet(lucy)&strong(lucy)))&
((brave(lucy)&creative(lucy)))&
(?[X]:((~calm(X)|wise(X))))&
(~funny(alice)) | ~brave(alice) | [] | null | 0 |
If someone is not curious or calm then someone is both not humble and not strong and vice versa.
Everyone who is patient or not creative is not wise and vice versa.
If paul is not tall or not calm then someone is either calm or not curious and vice versa.
If paul is not brave then someone is not calm.
Everyone who is not curious or not humble is both not rich and not curious.
Everyone who is either not creative or brave is not curious or not generous and vice versa.
If someone is either quiet or not generous then alice is not calm or tall.
Everyone who is funny is kind or not kind and vice versa.
If john is strong or not tall then someone is either tall or funny.
Everyone who is not curious is either not funny or happy and vice versa.
If mary is not funny then someone is not old or creative and vice versa.
If john is not humble or patient then someone is not wise.
If someone is either curious or quiet then mary is either brave or generous and vice versa.
If fred is not quiet or curious then lucy is kind and vice versa.
Everyone who is not tall is either not funny or not rich and vice versa.
Someone is either not strong or brave.
Someone is not quiet or not calm.
Someone is funny.
Lucy is kind. | John is not brave. | neutral | ((?[X]:((~curious(X)|calm(X))))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((patient(X)|~creative(X))<=>~wise(X)))&
(((~tall(paul)|~calm(paul)))<=>(?[X]:((calm(X)<~>~curious(X)))))&
((~brave(paul))=>(?[X]:(~calm(X))))&
(![X]:((~curious(X)|~humble(X))=>(~rich(X)&~curious(X))))&
(![X]:((~creative(X)<~>brave(X))<=>(~curious(X)|~generous(X))))&
((?[X]:((quiet(X)<~>~generous(X))))=>((~calm(alice)|tall(alice))))&
(![X]:(funny(X)<=>(kind(X)|~kind(X))))&
(((strong(john)|~tall(john)))=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:(~curious(X)<=>(~funny(X)<~>happy(X))))&
((~funny(mary))<=>(?[X]:((~old(X)|creative(X)))))&
(((~humble(john)|patient(john)))=>(?[X]:(~wise(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>((brave(mary)<~>generous(mary))))&
(((~quiet(fred)|curious(fred)))<=>(kind(lucy)))&
(![X]:(~tall(X)<=>(~funny(X)<~>~rich(X))))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:(funny(X)))&
(kind(lucy)) | ~brave(john) | [] | null | 0 |
Everyone who is both patient and humble is tall or brave. Everyone who is wise or not curious is either curious or wise and vice versa. If john is patient then someone is both not happy and generous. Everyone who is old is either not wise or not tall and vice versa. If john is both wise and generous then someone is not rich and vice versa. If someone is not brave or not strong then someone is either not happy or not funny and vice versa. If susan is not patient then alice is strong or curious and vice versa. Everyone who is not rich or not creative is rich or not calm. Everyone who is happy is not brave and vice versa. Everyone who is both not humble and rich is either not quiet or not creative and vice versa. Everyone who is either not calm or happy is either curious or happy. If susan is both creative and happy then someone is either not brave or humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. John is not generous or generous. Lucy is either wise or generous. Someone is either not wise or not rich. Someone is funny. Paul is both patient and rich. Someone is not tall. Lucy is not strong or creative. | Lucy is rich. | neutral | (![X]:((patient(X)&humble(X))=>(tall(X)|brave(X))))&
(![X]:((wise(X)|~curious(X))<=>(curious(X)<~>wise(X))))&
((patient(john))=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:(old(X)<=>(~wise(X)<~>~tall(X))))&
(((wise(john)&generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~brave(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>~funny(X)))))&
((~patient(susan))<=>((strong(alice)|curious(alice))))&
(![X]:((~rich(X)|~creative(X))=>(rich(X)|~calm(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((~humble(X)&rich(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)<~>happy(X))=>(curious(X)<~>happy(X))))&
(((creative(susan)&happy(susan)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
((~generous(john)|generous(john)))&
((wise(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(?[X]:(funny(X)))&
((patient(paul)&rich(paul)))&
(?[X]:(~tall(X)))&
((~strong(lucy)|creative(lucy))) | rich(lucy) | [] | null | 0 |
If alice is humble then someone is old or not creative.
Everyone who is not strong or not funny is both not humble and generous and vice versa.
If someone is not tall or not curious then someone is either brave or not wise and vice versa.
If fred is both old and not tall then lucy is humble and vice versa.
Everyone who is either not strong or not creative is not creative and vice versa.
If paul is not strong then someone is quiet.
Everyone who is not curious is not strong and vice versa.
Everyone who is strong is both creative and not quiet and vice versa.
Everyone who is both not curious and strong is either strong or rich.
Everyone who is both quiet and not calm is both curious and not strong.
If susan is either not quiet or tall then someone is either brave or not strong.
Everyone who is not patient is quiet.
If someone is either not strong or brave then someone is either not strong or calm and vice versa.
If someone is either wise or quiet then someone is not happy or not creative and vice versa.
Everyone who is not humble or not kind is rich or not tall and vice versa.
Alice is either not strong or patient.
Someone is funny or humble.
Paul is generous or not rich.
Alice is strong or humble.
Paul is both not humble and creative.
Paul is either curious or not calm.
John is calm. | John is strong. | entailment | ((humble(alice))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~humble(X)&generous(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((old(fred)&~tall(fred)))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(((~quiet(susan)<~>tall(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(rich(X)|~tall(X))))&
((~strong(alice)<~>patient(alice)))&
(?[X]:((funny(X)|humble(X))))&
((generous(paul)|~rich(paul)))&
((strong(alice)|humble(alice)))&
((~humble(paul)&creative(paul)))&
((curious(paul)<~>~calm(paul)))&
(calm(john)) | strong(john) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7998682815587575243202985
% SZS output start Proof for 7998682815587575243202985
5. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p4]
23. ~strong(john) [input hypothesis]
46. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | creative(X0)) & (~creative(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 5]
87. ~creative(X0) | ~creative(X0) | strong(X0) [cnf transformation 46]
90. creative(X0) | strong(X0) | creative(X0) [cnf transformation 46]
134. ~strong(john) [cnf transformation 23]
136. ~creative(X0) | strong(X0) [duplicate literal removal 87]
137. creative(X0) | strong(X0) [duplicate literal removal 90]
200. strong(X0) [subsumption resolution 136,137]
277. $false [subsumption resolution 134,200]
% SZS output end Proof for 7998682815587575243202985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then lucy is brave or not patient.
Everyone who is both old and not quiet is either brave or not old.
Everyone who is not kind is not curious.
Everyone who is either not curious or brave is creative.
If someone is both not rich and not generous then someone is not calm.
If john is both creative and curious then lucy is both kind and wise and vice versa.
Everyone who is both old and not strong is brave or funny and vice versa.
Everyone who is happy or creative is not generous and vice versa.
Everyone who is generous is not humble and vice versa.
Everyone who is brave or not calm is strong and vice versa.
Everyone who is both happy and patient is either strong or patient and vice versa.
If someone is both rich and not curious then fred is not brave.
Everyone who is both funny and wise is not tall or not happy and vice versa.
Everyone who is either humble or not rich is both not strong and not funny and vice versa.
Everyone who is both not creative and not strong is not patient.
If someone is not happy or not old then john is either strong or not tall.
Alice is both creative and not generous.
Someone is wise.
Someone is both curious and creative.
John is both not strong and not tall.
Mary is either wise or not generous.
Fred is not wise.
Someone is not creative. | John is rich. | entailment | ((creative(alice))=>((brave(lucy)|~patient(lucy))))&
(![X]:((old(X)&~quiet(X))=>(brave(X)<~>~old(X))))&
(![X]:(~kind(X)=>~curious(X)))&
(![X]:((~curious(X)<~>brave(X))=>creative(X)))&
((?[X]:((~rich(X)&~generous(X))))=>(?[X]:(~calm(X))))&
(((creative(john)&curious(john)))<=>((kind(lucy)&wise(lucy))))&
(![X]:((old(X)&~strong(X))<=>(brave(X)|funny(X))))&
(![X]:((happy(X)|creative(X))<=>~generous(X)))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((brave(X)|~calm(X))<=>strong(X)))&
(![X]:((happy(X)&patient(X))<=>(strong(X)<~>patient(X))))&
((?[X]:((rich(X)&~curious(X))))=>(~brave(fred)))&
(![X]:((funny(X)&wise(X))<=>(~tall(X)|~happy(X))))&
(![X]:((humble(X)<~>~rich(X))<=>(~strong(X)&~funny(X))))&
(![X]:((~creative(X)&~strong(X))=>~patient(X)))&
((?[X]:((~happy(X)|~old(X))))=>((strong(john)<~>~tall(john))))&
((creative(alice)&~generous(alice)))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&creative(X))))&
((~strong(john)&~tall(john)))&
((wise(mary)<~>~generous(mary)))&
(~wise(fred))&
(?[X]:(~creative(X))) | rich(john) | [
"p4",
"p6",
"p8",
"p9",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9023479027076503050449393
% SZS output start Proof for 9023479027076503050449393
5. ? [X0] : (~generous(X0) & ~rich(X0)) => ? [X0] : ~calm(X0) [input p4]
7. ! [X0] : ((~strong(X0) & old(X0)) <=> (funny(X0) | brave(X0))) [input p6]
9. ! [X0] : (generous(X0) <=> ~humble(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | brave(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : ((patient(X0) & happy(X0)) <=> (strong(X0) <~> patient(X0))) [input p10]
13. ! [X0] : ((wise(X0) & funny(X0)) <=> (~happy(X0) | ~tall(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~rich(X0)) <=> (~funny(X0) & ~strong(X0))) [input p13]
20. ~tall(john) & ~strong(john) [input p19]
24. ~rich(john) [input hypothesis]
25. ? [X0] : (~generous(X0) & ~rich(X0)) => ? [X1] : ~calm(X1) [rectify 5]
31. ? [X1] : ~calm(X1) | ! [X0] : (generous(X0) | rich(X0)) [ennf transformation 25]
37. ? [X0] : ~calm(X0) | ! [X1] : (generous(X1) | rich(X1)) [rectify 31]
38. ? [X0] : ~calm(X0) => ~calm(sK0) [choice axiom]
39. ~calm(sK0) | ! [X1] : (generous(X1) | rich(X1)) [skolemisation 37,38]
42. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 7]
43. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | strong(X0) | ~old(X0))) [flattening 42]
46. ! [X0] : ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))) [nnf transformation 9]
47. ! [X0] : (((~calm(X0) | brave(X0)) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | brave(X0) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [flattening 47]
49. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ~patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (~wise(X0) | ~funny(X0)))) [nnf transformation 13]
52. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ~wise(X0) | ~funny(X0))) [flattening 51]
53. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (funny(X0) | strong(X0))) & ((~funny(X0) & ~strong(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [nnf transformation 14]
54. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | funny(X0) | strong(X0)) & ((~funny(X0) & ~strong(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [flattening 53]
67. ~calm(sK0) | generous(X1) | rich(X1) [cnf transformation 39]
76. ~funny(X0) | ~strong(X0) [cnf transformation 43]
80. ~humble(X0) | ~generous(X0) [cnf transformation 46]
83. strong(X0) | calm(X0) [cnf transformation 48]
86. ~patient(X0) | ~strong(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 50]
89. patient(X0) | patient(X0) | ~strong(X0) [cnf transformation 50]
93. tall(X0) | funny(X0) [cnf transformation 52]
94. happy(X0) | funny(X0) [cnf transformation 52]
100. ~funny(X0) | humble(X0) | rich(X0) [cnf transformation 54]
114. ~tall(john) [cnf transformation 20]
119. ~rich(john) [cnf transformation 24]
120. ~patient(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 86]
121. ~strong(X0) | patient(X0) [duplicate literal removal 89]
136. 4 <=> ! [X1] : (generous(X1) | rich(X1)) [avatar definition]
137. generous(X1) | rich(X1) <- (4) [avatar component clause 136]
139. 5 <=> calm(sK0) [avatar definition]
141. ~calm(sK0) <- (~5) [avatar component clause 139]
142. 4 | ~5 [avatar split clause 67,139,136]
165. ~happy(X0) | ~strong(X0) [subsumption resolution 120,121]
174. 12 <=> tall(john) [avatar definition]
175. ~tall(john) <- (~12) [avatar component clause 174]
185. ~12 [avatar split clause 114,174]
201. funny(john) <- (~12) [resolution 93,175]
210. ~strong(X1) | funny(X1) [resolution 165,94]
211. ~strong(X1) [subsumption resolution 210,76]
218. calm(X0) [resolution 211,83]
225. $false <- (~5) [resolution 218,141]
226. 5 [avatar contradiction clause 225]
236. humble(john) | rich(john) <- (~12) [resolution 100,201]
237. humble(john) <- (~12) [subsumption resolution 236,119]
240. ~generous(john) <- (~12) [resolution 237,80]
241. rich(john) <- (4, ~12) [resolution 240,137]
242. $false <- (4, ~12) [subsumption resolution 241,119]
243. ~4 | 12 [avatar contradiction clause 242]
244. $false [avatar sat refutation 142,185,226,243]
% SZS output end Proof for 9023479027076503050449393
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or strong is not rich.
If someone is both curious and not generous then someone is either not strong or calm.
If someone is both strong and wise then someone is both curious and not funny.
Everyone who is either not kind or happy is creative or not wise and vice versa.
If susan is quiet then someone is both not funny and not patient.
If someone is not strong then alice is either not calm or wise and vice versa.
If someone is both not calm and happy then someone is either strong or quiet and vice versa.
Everyone who is not generous is not calm or not strong and vice versa.
If someone is generous then someone is not funny or not happy and vice versa.
If paul is old or not brave then susan is calm and vice versa.
If lucy is quiet or not humble then paul is either not wise or not quiet.
If mary is funny or tall then someone is not funny and vice versa.
Everyone who is either not wise or wise is not calm or rich and vice versa.
Everyone who is both patient and generous is generous or humble.
Everyone who is either not calm or wise is wise and vice versa.
If fred is both not patient and patient then alice is either creative or not wise and vice versa.
Mary is old.
Fred is quiet or not calm.
Paul is generous or rich.
Paul is not rich or not curious.
Someone is either not kind or creative. | Susan is not quiet. | contradiction | (![X]:((calm(X)<~>strong(X))=>~rich(X)))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:((~kind(X)<~>happy(X))<=>(creative(X)|~wise(X))))&
((quiet(susan))=>(?[X]:((~funny(X)&~patient(X)))))&
((?[X]:(~strong(X)))<=>((~calm(alice)<~>wise(alice))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(((old(paul)|~brave(paul)))<=>(calm(susan)))&
(((quiet(lucy)|~humble(lucy)))=>((~wise(paul)<~>~quiet(paul))))&
(((funny(mary)|tall(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)<~>wise(X))<=>(~calm(X)|rich(X))))&
(![X]:((patient(X)&generous(X))=>(generous(X)|humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>wise(X)))&
(((~patient(fred)&patient(fred)))<=>((creative(alice)<~>~wise(alice))))&
(old(mary))&
((quiet(fred)|~calm(fred)))&
((generous(paul)|rich(paul)))&
((~rich(paul)|~curious(paul)))&
(?[X]:((~kind(X)<~>creative(X)))) | ~quiet(susan) | [
"p0",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2910807510000607774341755
% SZS output start Proof for 2910807510000607774341755
1. ! [X0] : ((calm(X0) <~> strong(X0)) => ~rich(X0)) [input p0]
7. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X0] : (strong(X0) <~> quiet(X0)) [input p6]
13. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (rich(X0) | ~calm(X0))) [input p12]
15. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> wise(X0)) [input p14]
22. ~quiet(susan) [input hypothesis]
25. ? [X0] : (happy(X0) & ~calm(X0)) <=> ? [X1] : (strong(X1) <~> quiet(X1)) [rectify 7]
29. ! [X0] : (~rich(X0) | (calm(X0) <=> strong(X0))) [ennf transformation 1]
34. ! [X0] : (~rich(X0) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) [nnf transformation 29]
50. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : ((strong(X1) | ~quiet(X1)) & (quiet(X1) | ~strong(X1)))) & (? [X1] : ((~quiet(X1) | ~strong(X1)) & (quiet(X1) | strong(X1))) | ! [X0] : (~happy(X0) | calm(X0))) [nnf transformation 25]
51. (? [X0] : (happy(X0) & ~calm(X0)) | ! [X1] : ((strong(X1) | ~quiet(X1)) & (quiet(X1) | ~strong(X1)))) & (? [X2] : ((~quiet(X2) | ~strong(X2)) & (quiet(X2) | strong(X2))) | ! [X3] : (~happy(X3) | calm(X3))) [rectify 50]
52. ? [X0] : (happy(X0) & ~calm(X0)) => (happy(sK4) & ~calm(sK4)) [choice axiom]
53. ? [X2] : ((~quiet(X2) | ~strong(X2)) & (quiet(X2) | strong(X2))) => ((~quiet(sK5) | ~strong(sK5)) & (quiet(sK5) | strong(sK5))) [choice axiom]
54. ((happy(sK4) & ~calm(sK4)) | ! [X1] : ((strong(X1) | ~quiet(X1)) & (quiet(X1) | ~strong(X1)))) & (((~quiet(sK5) | ~strong(sK5)) & (quiet(sK5) | strong(sK5))) | ! [X3] : (~happy(X3) | calm(X3))) [skolemisation 51,53,52]
70. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 13]
71. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 70]
72. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~wise(X0)) & (wise(X0) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 15]
78. ~rich(X0) | strong(X0) | ~calm(X0) [cnf transformation 34]
98. ~calm(sK4) | quiet(X1) | ~strong(X1) [cnf transformation 54]
116. rich(X0) | ~calm(X0) | wise(X0) | wise(X0) [cnf transformation 71]
117. rich(X0) | ~calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 71]
122. wise(X0) | wise(X0) | calm(X0) [cnf transformation 72]
125. ~wise(X0) | calm(X0) | ~wise(X0) [cnf transformation 72]
138. ~quiet(susan) [cnf transformation 22]
139. wise(X0) | calm(X0) [duplicate literal removal 122]
140. ~wise(X0) | calm(X0) [duplicate literal removal 125]
141. rich(X0) | ~calm(X0) | wise(X0) [duplicate literal removal 116]
142. rich(X0) | ~calm(X0) | ~wise(X0) [duplicate literal removal 117]
170. 7 <=> quiet(susan) [avatar definition]
172. ~quiet(susan) <- (~7) [avatar component clause 170]
198. 13 <=> ! [X1] : strong(X1) [avatar definition]
199. strong(X1) <- (13) [avatar component clause 198]
211. 16 <=> ! [X1] : (quiet(X1) | ~strong(X1)) [avatar definition]
212. ~strong(X1) | quiet(X1) <- (16) [avatar component clause 211]
215. 17 <=> calm(sK4) [avatar definition]
217. ~calm(sK4) <- (~17) [avatar component clause 215]
219. 16 | ~17 [avatar split clause 98,215,211]
301. ~calm(X0) | rich(X0) [subsumption resolution 141,142]
302. calm(X0) [subsumption resolution 139,140]
340. ~7 [avatar split clause 138,170]
341. $false <- (~17) [subsumption resolution 217,302]
342. 17 [avatar contradiction clause 341]
361. rich(X0) [resolution 301,302]
365. strong(X0) | ~calm(X0) [resolution 78,361]
366. strong(X0) [subsumption resolution 365,302]
367. 13 [avatar split clause 366,198]
368. quiet(X0) <- (13, 16) [resolution 199,212]
379. $false <- (~7, 13, 16) [resolution 368,172]
383. 7 | ~13 | ~16 [avatar contradiction clause 379]
384. $false [avatar sat refutation 219,340,342,367,383]
% SZS output end Proof for 2910807510000607774341755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or quiet then paul is not wise or not curious.
Everyone who is both not happy and quiet is not brave or not old and vice versa.
If someone is calm then someone is not rich or not happy and vice versa.
Everyone who is not generous or not funny is both old and curious.
If someone is not curious then someone is both old and not calm.
Everyone who is both curious and not kind is creative.
Everyone who is both not humble and not brave is humble and vice versa.
If alice is tall then someone is both kind and patient and vice versa.
If lucy is either wise or tall then mary is both curious and not funny.
If someone is both quiet and not generous then someone is either calm or not humble.
If someone is both not funny and humble then someone is either not rich or curious.
Everyone who is either not kind or rich is either rich or kind.
If someone is tall or patient then lucy is curious and vice versa.
Everyone who is both curious and not strong is both calm and creative.
If paul is either calm or not tall then lucy is rich or not humble and vice versa.
Everyone who is not wise is either not quiet or funny.
Alice is both not strong and rich.
Someone is old.
Someone is either not happy or brave.
Someone is calm.
Someone is both happy and not kind.
Paul is kind.
Someone is kind or not calm.
Fred is either strong or humble. | Fred is not brave. | contradiction | ((?[X]:((~happy(X)|quiet(X))))=>((~wise(paul)|~curious(paul))))&
(![X]:((~happy(X)&quiet(X))<=>(~brave(X)|~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((~generous(X)|~funny(X))=>(old(X)&curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((curious(X)&~kind(X))=>creative(X)))&
(![X]:((~humble(X)&~brave(X))<=>humble(X)))&
((tall(alice))<=>(?[X]:((kind(X)&patient(X)))))&
(((wise(lucy)<~>tall(lucy)))=>((curious(mary)&~funny(mary))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((~funny(X)&humble(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(rich(X)<~>kind(X))))&
((?[X]:((tall(X)|patient(X))))<=>(curious(lucy)))&
(![X]:((curious(X)&~strong(X))=>(calm(X)&creative(X))))&
(((calm(paul)<~>~tall(paul)))<=>((rich(lucy)|~humble(lucy))))&
(![X]:(~wise(X)=>(~quiet(X)<~>funny(X))))&
((~strong(alice)&rich(alice)))&
(?[X]:(old(X)))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((happy(X)&~kind(X))))&
(kind(paul))&
(?[X]:((kind(X)|~calm(X))))&
((strong(fred)<~>humble(fred))) | ~brave(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6392597695022177227315204
% SZS output start Proof for 6392597695022177227315204
7. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> humble(X0)) [input p6]
25. ~brave(fred) [input hypothesis]
54. ! [X0] : (((~brave(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) | humble(X0)))) [nnf transformation 7]
55. ! [X0] : (((~brave(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | brave(X0) | humble(X0))) [flattening 54]
99. humble(X0) | brave(X0) | humble(X0) [cnf transformation 55]
100. ~humble(X0) | ~humble(X0) [cnf transformation 55]
139. ~brave(fred) [cnf transformation 25]
142. humble(X0) | brave(X0) [duplicate literal removal 99]
143. ~humble(X0) [duplicate literal removal 100]
194. brave(X0) [subsumption resolution 142,143]
283. $false [subsumption resolution 139,194]
% SZS output end Proof for 6392597695022177227315204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both happy and tall and vice versa.
Everyone who is both creative and patient is not creative or not calm and vice versa.
Everyone who is patient or not brave is both not curious and not quiet and vice versa.
If someone is curious or calm then someone is not funny or not tall and vice versa.
Everyone who is not tall or not wise is both not wise and wise.
If someone is both wise and creative then lucy is strong and vice versa.
Everyone who is both quiet and not funny is either not wise or tall.
Everyone who is either strong or tall is either strong or not kind.
Everyone who is both not funny and happy is either curious or creative and vice versa.
If someone is either not happy or not kind then fred is not funny or not curious.
Everyone who is not rich or not curious is either creative or not rich.
If mary is not kind then susan is not humble or not brave and vice versa.
If someone is creative then susan is wise or brave and vice versa.
If alice is either happy or not quiet then someone is both not happy and not humble and vice versa.
Everyone who is either not brave or old is both not generous and quiet.
Alice is both not strong and old.
Someone is quiet.
Someone is not brave or old.
Someone is funny. | Fred is funny. | contradiction | (![X]:(~creative(X)<=>(happy(X)&tall(X))))&
(![X]:((creative(X)&patient(X))<=>(~creative(X)|~calm(X))))&
(![X]:((patient(X)|~brave(X))<=>(~curious(X)&~quiet(X))))&
((?[X]:((curious(X)|calm(X))))<=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((~tall(X)|~wise(X))=>(~wise(X)&wise(X))))&
((?[X]:((wise(X)&creative(X))))<=>(strong(lucy)))&
(![X]:((quiet(X)&~funny(X))=>(~wise(X)<~>tall(X))))&
(![X]:((strong(X)<~>tall(X))=>(strong(X)<~>~kind(X))))&
(![X]:((~funny(X)&happy(X))<=>(curious(X)<~>creative(X))))&
((?[X]:((~happy(X)<~>~kind(X))))=>((~funny(fred)|~curious(fred))))&
(![X]:((~rich(X)|~curious(X))=>(creative(X)<~>~rich(X))))&
((~kind(mary))<=>((~humble(susan)|~brave(susan))))&
((?[X]:(creative(X)))<=>((wise(susan)|brave(susan))))&
(((happy(alice)<~>~quiet(alice)))<=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((~brave(X)<~>old(X))=>(~generous(X)&quiet(X))))&
((~strong(alice)&old(alice)))&
(?[X]:(quiet(X)))&
(?[X]:((~brave(X)|old(X))))&
(?[X]:(funny(X))) | funny(fred) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p9",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1783326793187405126106006
% SZS output start Proof for 1783326793187405126106006
1. ! [X0] : (~creative(X0) <=> (tall(X0) & happy(X0))) [input p0]
2. ! [X0] : ((patient(X0) & creative(X0)) <=> (~calm(X0) | ~creative(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | patient(X0)) <=> (~quiet(X0) & ~curious(X0))) [input p2]
5. ! [X0] : ((~wise(X0) | ~tall(X0)) => (wise(X0) & ~wise(X0))) [input p4]
9. ! [X0] : ((happy(X0) & ~funny(X0)) <=> (curious(X0) <~> creative(X0))) [input p8]
10. ? [X0] : (~happy(X0) <~> ~kind(X0)) => (~curious(fred) | ~funny(fred)) [input p9]
12. ~kind(mary) <=> (~brave(susan) | ~humble(susan)) [input p11]
14. (happy(alice) <~> ~quiet(alice)) <=> ? [X0] : (~humble(X0) & ~happy(X0)) [input p13]
15. ! [X0] : ((~brave(X0) <~> old(X0)) => (quiet(X0) & ~generous(X0))) [input p14]
16. old(alice) & ~strong(alice) [input p15]
20. funny(fred) [input hypothesis]
22. ! [X0] : ((~brave(X0) <~> old(X0)) => quiet(X0)) [pure predicate removal 15]
23. ! [X0] : ((wise(X0) & ~wise(X0)) | (wise(X0) & tall(X0))) [ennf transformation 5]
27. (~curious(fred) | ~funny(fred)) | ! [X0] : (~happy(X0) <=> ~kind(X0)) [ennf transformation 10]
28. ~curious(fred) | ~funny(fred) | ! [X0] : (~happy(X0) <=> ~kind(X0)) [flattening 27]
30. ! [X0] : (quiet(X0) | (~brave(X0) <=> old(X0))) [ennf transformation 22]
31. ! [X0] : ((~creative(X0) | (~tall(X0) | ~happy(X0))) & ((tall(X0) & happy(X0)) | creative(X0))) [nnf transformation 1]
32. ! [X0] : ((~creative(X0) | ~tall(X0) | ~happy(X0)) & ((tall(X0) & happy(X0)) | creative(X0))) [flattening 31]
33. ! [X0] : (((patient(X0) & creative(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (~patient(X0) | ~creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((patient(X0) & creative(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | ~patient(X0) | ~creative(X0))) [flattening 33]
35. ! [X0] : (((~brave(X0) | patient(X0)) | (quiet(X0) | curious(X0))) & ((~quiet(X0) & ~curious(X0)) | (brave(X0) & ~patient(X0)))) [nnf transformation 3]
36. ! [X0] : ((~brave(X0) | patient(X0) | quiet(X0) | curious(X0)) & ((~quiet(X0) & ~curious(X0)) | (brave(X0) & ~patient(X0)))) [flattening 35]
48. ! [X0] : (((happy(X0) & ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~happy(X0) | funny(X0)))) [nnf transformation 9]
49. ! [X0] : (((happy(X0) & ~funny(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~happy(X0) | funny(X0))) [flattening 48]
50. ~curious(fred) | ~funny(fred) | ! [X0] : ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0))) [nnf transformation 28]
52. (~kind(mary) | (brave(susan) & humble(susan))) & ((~brave(susan) | ~humble(susan)) | kind(mary)) [nnf transformation 12]
53. (~kind(mary) | (brave(susan) & humble(susan))) & (~brave(susan) | ~humble(susan) | kind(mary)) [flattening 52]
59. (((quiet(alice) | ~happy(alice)) & (~quiet(alice) | happy(alice))) | ! [X0] : (humble(X0) | happy(X0))) & (? [X0] : (~humble(X0) & ~happy(X0)) | ((happy(alice) | quiet(alice)) & (~quiet(alice) | ~happy(alice)))) [nnf transformation 14]
60. (((quiet(alice) | ~happy(alice)) & (~quiet(alice) | happy(alice))) | ! [X0] : (humble(X0) | happy(X0))) & (? [X1] : (~humble(X1) & ~happy(X1)) | ((happy(alice) | quiet(alice)) & (~quiet(alice) | ~happy(alice)))) [rectify 59]
61. ? [X1] : (~humble(X1) & ~happy(X1)) => (~humble(sK4) & ~happy(sK4)) [choice axiom]
62. (((quiet(alice) | ~happy(alice)) & (~quiet(alice) | happy(alice))) | ! [X0] : (humble(X0) | happy(X0))) & ((~humble(sK4) & ~happy(sK4)) | ((happy(alice) | quiet(alice)) & (~quiet(alice) | ~happy(alice)))) [skolemisation 60,61]
63. ! [X0] : (quiet(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) [nnf transformation 30]
72. ~tall(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 32]
74. creative(X0) | creative(X0) [cnf transformation 34]
79. ~curious(X0) | brave(X0) [cnf transformation 36]
87. ~wise(X0) | tall(X0) [cnf transformation 23]
90. wise(X0) | wise(X0) [cnf transformation 23]
103. ~funny(X0) | curious(X0) | ~creative(X0) [cnf transformation 49]
105. happy(X0) | curious(X0) | ~creative(X0) [cnf transformation 49]
106. ~curious(fred) | ~funny(fred) | ~kind(X0) | happy(X0) [cnf transformation 50]
112. ~brave(susan) | ~humble(susan) | kind(mary) [cnf transformation 53]
122. ~quiet(alice) | happy(alice) | humble(X0) | happy(X0) [cnf transformation 62]
125. ~old(X0) | ~brave(X0) | quiet(X0) [cnf transformation 63]
127. old(alice) [cnf transformation 16]
131. funny(fred) [cnf transformation 20]
135. wise(X0) [duplicate literal removal 90]
137. creative(X0) [duplicate literal removal 74]
140. 1 <=> ! [X1] : tall(X1) [avatar definition]
141. tall(X1) <- (1) [avatar component clause 140]
171. tall(X0) [subsumption resolution 87,135]
172. 1 [avatar split clause 171,140]
176. curious(X0) | happy(X0) [subsumption resolution 105,137]
177. ~funny(X0) | curious(X0) [subsumption resolution 103,137]
184. 10 <=> funny(fred) [avatar definition]
188. ~funny(fred) | ~kind(X0) | happy(X0) [subsumption resolution 106,177]
190. 11 <=> ! [X0] : (~kind(X0) | happy(X0)) [avatar definition]
191. ~kind(X0) | happy(X0) <- (11) [avatar component clause 190]
192. 11 | ~10 [avatar split clause 188,184,190]
196. 12 <=> brave(susan) [avatar definition]
197. ~brave(susan) <- (~12) [avatar component clause 196]
200. 13 <=> kind(mary) [avatar definition]
201. kind(mary) <- (13) [avatar component clause 200]
205. 14 <=> humble(susan) [avatar definition]
206. ~humble(susan) <- (~14) [avatar component clause 205]
209. 13 | ~14 | ~12 [avatar split clause 112,196,205,200]
211. 15 <=> ! [X0] : (humble(X0) | happy(X0)) [avatar definition]
212. humble(X0) | happy(X0) <- (15) [avatar component clause 211]
214. 16 <=> happy(alice) [avatar definition]
215. happy(alice) <- (16) [avatar component clause 214]
218. 17 <=> quiet(alice) [avatar definition]
219. ~quiet(alice) <- (~17) [avatar component clause 218]
222. 15 | 16 | ~17 [avatar split clause 122,218,214,211]
237. 10 [avatar split clause 131,184]
246. brave(X0) | happy(X0) [resolution 176,79]
258. ~creative(X1) | ~happy(X1) <- (1) [resolution 72,141]
259. ~happy(X1) <- (1) [subsumption resolution 258,137]
261. ~brave(alice) | quiet(alice) [resolution 125,127]
264. ~brave(alice) <- (~17) [subsumption resolution 261,219]
277. happy(susan) <- (~12) [resolution 246,197]
278. happy(alice) <- (~17) [resolution 246,264]
280. $false <- (1, ~12) [subsumption resolution 277,259]
281. ~1 | 12 [avatar contradiction clause 280]
286. $false <- (1, ~17) [subsumption resolution 278,259]
287. ~1 | 17 [avatar contradiction clause 286]
288. $false <- (1, 16) [subsumption resolution 215,259]
289. ~1 | ~16 [avatar contradiction clause 288]
290. humble(X0) <- (1, 15) [subsumption resolution 212,259]
291. $false <- (1, ~14, 15) [subsumption resolution 206,290]
292. ~1 | 14 | ~15 [avatar contradiction clause 291]
299. happy(mary) <- (11, 13) [resolution 201,191]
301. $false <- (1, 11, 13) [subsumption resolution 299,259]
302. ~1 | ~11 | ~13 [avatar contradiction clause 301]
303. $false [avatar sat refutation 172,192,209,222,237,281,287,289,292,302]
% SZS output end Proof for 1783326793187405126106006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is both not kind and not strong and vice versa.
If someone is not creative then someone is both creative and strong and vice versa.
If paul is not kind or brave then fred is not quiet or kind and vice versa.
If alice is either strong or funny then someone is both not rich and tall.
Everyone who is either happy or not calm is either rich or not calm.
Everyone who is not quiet or humble is calm and vice versa.
If someone is both not tall and creative then someone is either funny or calm and vice versa.
Everyone who is both not brave and quiet is either patient or not creative and vice versa.
If someone is not happy then susan is either not curious or not kind and vice versa.
Everyone who is strong is not calm or not strong and vice versa.
Everyone who is brave is not quiet and vice versa.
If someone is either not tall or not creative then susan is both not quiet and strong.
If paul is funny or calm then someone is not kind.
If alice is both not tall and creative then someone is not curious and vice versa.
Everyone who is either quiet or generous is humble.
Paul is rich or not creative.
Someone is tall or not wise.
Someone is either quiet or humble.
Mary is both not funny and not patient.
Someone is both strong and wise.
Susan is either not tall or brave.
Someone is either rich or not humble.
Alice is either quiet or not strong. | Mary is not tall. | entailment | (![X]:(old(X)<=>(~kind(X)&~strong(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((creative(X)&strong(X)))))&
(((~kind(paul)|brave(paul)))<=>((~quiet(fred)|kind(fred))))&
(((strong(alice)<~>funny(alice)))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(rich(X)<~>~calm(X))))&
(![X]:((~quiet(X)|humble(X))<=>calm(X)))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(patient(X)<~>~creative(X))))&
((?[X]:(~happy(X)))<=>((~curious(susan)<~>~kind(susan))))&
(![X]:(strong(X)<=>(~calm(X)|~strong(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~quiet(susan)&strong(susan))))&
(((funny(paul)|calm(paul)))=>(?[X]:(~kind(X))))&
(((~tall(alice)&creative(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>generous(X))=>humble(X)))&
((rich(paul)|~creative(paul)))&
(?[X]:((tall(X)|~wise(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
((~funny(mary)&~patient(mary)))&
(?[X]:((strong(X)&wise(X))))&
((~tall(susan)<~>brave(susan)))&
(?[X]:((rich(X)<~>~humble(X))))&
((quiet(alice)<~>~strong(alice))) | ~tall(mary) | [
"p5",
"p7",
"p9",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5057467992148374245416849
% SZS output start Proof for 5057467992148374245416849
6. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> calm(X0)) [input p5]
8. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> (patient(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : (strong(X0) <=> (~strong(X0) | ~calm(X0))) [input p9]
11. ! [X0] : (brave(X0) <=> ~quiet(X0)) [input p10]
12. ? [X0] : (~tall(X0) <~> ~creative(X0)) => (strong(susan) & ~quiet(susan)) [input p11]
19. ~patient(mary) & ~funny(mary) [input p18]
24. tall(mary) [input hypothesis]
29. (strong(susan) & ~quiet(susan)) | ! [X0] : (~tall(X0) <=> ~creative(X0)) [ennf transformation 12]
43. ! [X0] : (((humble(X0) | ~quiet(X0)) | ~calm(X0)) & (calm(X0) | (~humble(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | ~quiet(X0) | ~calm(X0)) & (calm(X0) | (~humble(X0) & quiet(X0)))) [flattening 43]
50. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~quiet(X0) | brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ~quiet(X0) | brave(X0))) [flattening 50]
56. ! [X0] : ((strong(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~strong(X0))) [nnf transformation 10]
57. ! [X0] : ((strong(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~strong(X0))) [flattening 56]
58. ! [X0] : ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))) [nnf transformation 11]
59. (strong(susan) & ~quiet(susan)) | ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 29]
95. calm(X0) | quiet(X0) [cnf transformation 44]
104. ~quiet(X0) | patient(X0) | ~creative(X0) | brave(X0) [cnf transformation 51]
114. ~strong(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 57]
116. strong(X0) | strong(X0) [cnf transformation 57]
117. ~quiet(X0) | ~brave(X0) [cnf transformation 58]
118. quiet(X0) | brave(X0) [cnf transformation 58]
120. ~quiet(susan) | ~tall(X0) | creative(X0) [cnf transformation 59]
135. ~patient(mary) [cnf transformation 19]
144. tall(mary) [cnf transformation 24]
145. ~strong(X0) | ~calm(X0) [duplicate literal removal 114]
146. strong(X0) [duplicate literal removal 116]
260. ~calm(X0) [subsumption resolution 145,146]
262. 25 <=> ! [X0] : (~tall(X0) | creative(X0)) [avatar definition]
263. ~tall(X0) | creative(X0) <- (25) [avatar component clause 262]
265. 26 <=> quiet(susan) [avatar definition]
267. ~quiet(susan) <- (~26) [avatar component clause 265]
268. 25 | ~26 [avatar split clause 120,265,262]
355. quiet(X0) [resolution 95,260]
357. $false <- (~26) [resolution 355,267]
358. 26 [avatar contradiction clause 357]
362. ~brave(X0) [resolution 117,355]
372. creative(mary) <- (25) [resolution 263,144]
406. patient(X0) | ~creative(X0) | brave(X0) | brave(X0) [resolution 104,118]
408. patient(X0) | ~creative(X0) | brave(X0) [duplicate literal removal 406]
419. ~creative(X0) | patient(X0) [subsumption resolution 408,362]
424. patient(mary) <- (25) [resolution 419,372]
428. $false <- (25) [subsumption resolution 424,135]
429. ~25 [avatar contradiction clause 428]
430. $false [avatar sat refutation 268,358,429]
% SZS output end Proof for 5057467992148374245416849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not generous is both not kind and humble and vice versa. Everyone who is happy is happy or not curious. If someone is funny then someone is not strong and vice versa. Everyone who is both not happy and funny is both tall and wise and vice versa. If someone is patient then lucy is old or humble and vice versa. If paul is tall then paul is either curious or tall. Everyone who is either not strong or not tall is not humble. Everyone who is either not creative or calm is not funny or not tall. If paul is curious or not curious then someone is patient or kind. Everyone who is not humble or not curious is both not tall and strong. Everyone who is generous is not tall and vice versa. Everyone who is both not wise and generous is not quiet and vice versa. Everyone who is both kind and creative is not curious and vice versa. Everyone who is not kind or not brave is either generous or not generous. Everyone who is both brave and not rich is both old and funny. John is happy or not curious. Someone is both generous and strong. Someone is both not generous and old. Alice is either not old or not humble. Someone is patient or kind. Fred is brave. | Alice is not happy. | neutral | (![X]:((humble(X)|~generous(X))<=>(~kind(X)&humble(X))))&
(![X]:(happy(X)=>(happy(X)|~curious(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~happy(X)&funny(X))<=>(tall(X)&wise(X))))&
((?[X]:(patient(X)))<=>((old(lucy)|humble(lucy))))&
((tall(paul))=>((curious(paul)<~>tall(paul))))&
(![X]:((~strong(X)<~>~tall(X))=>~humble(X)))&
(![X]:((~creative(X)<~>calm(X))=>(~funny(X)|~tall(X))))&
(((curious(paul)|~curious(paul)))=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~tall(X)&strong(X))))&
(![X]:(generous(X)<=>~tall(X)))&
(![X]:((~wise(X)&generous(X))<=>~quiet(X)))&
(![X]:((kind(X)&creative(X))<=>~curious(X)))&
(![X]:((~kind(X)|~brave(X))=>(generous(X)<~>~generous(X))))&
(![X]:((brave(X)&~rich(X))=>(old(X)&funny(X))))&
((happy(john)|~curious(john)))&
(?[X]:((generous(X)&strong(X))))&
(?[X]:((~generous(X)&old(X))))&
((~old(alice)<~>~humble(alice)))&
(?[X]:((patient(X)|kind(X))))&
(brave(fred)) | ~happy(alice) | [] | null | 0 |
Everyone who is either not brave or calm is either not quiet or not calm. If someone is both not quiet and not creative then someone is not kind. If someone is both curious and not funny then someone is either brave or not generous. If someone is not old then someone is creative and vice versa. If someone is not patient then someone is both not happy and not tall and vice versa. If someone is not rich or not generous then someone is either humble or not brave. Everyone who is humble or not humble is kind or old. If someone is tall then someone is calm. If mary is wise then paul is both brave and tall and vice versa. If john is both generous and not humble then alice is both strong and funny and vice versa. Everyone who is not happy is both not happy and tall. Everyone who is both not funny and kind is either not patient or not rich and vice versa. Everyone who is funny or not funny is not creative. Everyone who is both not tall and not kind is not funny or rich and vice versa. If paul is not strong or not rich then susan is both old and rich and vice versa. If someone is either not humble or kind then alice is not happy or not humble. Someone is either not old or not wise. Someone is either generous or not strong. Paul is either funny or not calm. Someone is not curious or brave. Someone is both generous and not creative. John is either not happy or not wise. | Alice is not old. | contradiction | (![X]:((~brave(X)<~>calm(X))=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:((brave(X)<~>~generous(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(creative(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:((~rich(X)|~generous(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((humble(X)|~humble(X))=>(kind(X)|old(X))))&
((?[X]:(tall(X)))=>(?[X]:(calm(X))))&
((wise(mary))<=>((brave(paul)&tall(paul))))&
(((generous(john)&~humble(john)))<=>((strong(alice)&funny(alice))))&
(![X]:(~happy(X)=>(~happy(X)&tall(X))))&
(![X]:((~funny(X)&kind(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((funny(X)|~funny(X))=>~creative(X)))&
(![X]:((~tall(X)&~kind(X))<=>(~funny(X)|rich(X))))&
(((~strong(paul)|~rich(paul)))<=>((old(susan)&rich(susan))))&
((?[X]:((~humble(X)<~>kind(X))))=>((~happy(alice)|~humble(alice))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
((funny(paul)<~>~calm(paul)))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:((generous(X)&~creative(X))))&
((~happy(john)<~>~wise(john))) | ~old(alice) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8391127730125570310173212
% SZS output start Proof for 8391127730125570310173212
4. ? [X0] : ~old(X0) <=> ? [X0] : creative(X0) [input p3]
13. ! [X0] : ((~funny(X0) | funny(X0)) => ~creative(X0)) [input p12]
23. ~old(alice) [input hypothesis]
26. ? [X0] : ~old(X0) <=> ? [X1] : creative(X1) [rectify 4]
39. ! [X0] : (~creative(X0) | (funny(X0) & ~funny(X0))) [ennf transformation 13]
46. (? [X0] : ~old(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : old(X0)) [nnf transformation 26]
47. (? [X0] : ~old(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : old(X3)) [rectify 46]
48. ? [X0] : ~old(X0) => ~old(sK1) [choice axiom]
49. ? [X2] : creative(X2) => creative(sK2) [choice axiom]
50. (~old(sK1) | ! [X1] : ~creative(X1)) & (creative(sK2) | ! [X3] : old(X3)) [skolemisation 47,49,48]
89. creative(sK2) | old(X3) [cnf transformation 50]
116. ~creative(X0) | ~funny(X0) [cnf transformation 39]
117. ~creative(X0) | funny(X0) [cnf transformation 39]
140. ~old(alice) [cnf transformation 23]
152. 3 <=> ! [X1] : ~creative(X1) [avatar definition]
153. ~creative(X1) <- (3) [avatar component clause 152]
160. 5 <=> ! [X3] : old(X3) [avatar definition]
161. old(X3) <- (5) [avatar component clause 160]
163. 6 <=> creative(sK2) [avatar definition]
165. creative(sK2) <- (6) [avatar component clause 163]
166. 5 | 6 [avatar split clause 89,163,160]
251. ~creative(X0) [subsumption resolution 116,117]
252. 3 [avatar split clause 251,152]
331. $false <- (5) [resolution 161,140]
332. ~5 [avatar contradiction clause 331]
333. $false <- (3, 6) [subsumption resolution 165,153]
334. ~3 | ~6 [avatar contradiction clause 333]
335. $false [avatar sat refutation 166,252,332,334]
% SZS output end Proof for 8391127730125570310173212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or curious then paul is either not wise or not humble and vice versa. Everyone who is generous or not humble is wise or kind and vice versa. Everyone who is not generous or not rich is both wise and funny. Everyone who is both not old and curious is either not happy or old. Everyone who is either strong or not humble is generous or not rich. Everyone who is not patient is not curious. Everyone who is not strong is both rich and not happy and vice versa. Everyone who is both not old and not funny is calm. If someone is either strong or old then someone is either humble or patient and vice versa. Everyone who is not old is happy or rich and vice versa. If john is calm then someone is old and vice versa. Everyone who is not kind or not strong is not wise and vice versa. Everyone who is either patient or not calm is kind or not tall and vice versa. If someone is both not strong and happy then someone is not calm or not quiet and vice versa. Everyone who is happy is either not patient or not wise. If paul is either not brave or not patient then someone is calm or old and vice versa. Lucy is either generous or not quiet. Susan is creative. Someone is either not patient or funny. Someone is either not curious or old. | Susan is not kind. | contradiction | ((?[X]:((generous(X)|curious(X))))<=>((~wise(paul)<~>~humble(paul))))&
(![X]:((generous(X)|~humble(X))<=>(wise(X)|kind(X))))&
(![X]:((~generous(X)|~rich(X))=>(wise(X)&funny(X))))&
(![X]:((~old(X)&curious(X))=>(~happy(X)<~>old(X))))&
(![X]:((strong(X)<~>~humble(X))=>(generous(X)|~rich(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:(~strong(X)<=>(rich(X)&~happy(X))))&
(![X]:((~old(X)&~funny(X))=>calm(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:((humble(X)<~>patient(X)))))&
(![X]:(~old(X)<=>(happy(X)|rich(X))))&
((calm(john))<=>(?[X]:(old(X))))&
(![X]:((~kind(X)|~strong(X))<=>~wise(X)))&
(![X]:((patient(X)<~>~calm(X))<=>(kind(X)|~tall(X))))&
((?[X]:((~strong(X)&happy(X))))<=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:(happy(X)=>(~patient(X)<~>~wise(X))))&
(((~brave(paul)<~>~patient(paul)))<=>(?[X]:((calm(X)|old(X)))))&
((generous(lucy)<~>~quiet(lucy)))&
(creative(susan))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~curious(X)<~>old(X)))) | ~kind(susan) | [
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7118408133841713268839617
% SZS output start Proof for 7118408133841713268839617
2. ! [X0] : ((~humble(X0) | generous(X0)) <=> (kind(X0) | wise(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | ~generous(X0)) => (funny(X0) & wise(X0))) [input p2]
12. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> ~wise(X0)) [input p11]
21. ~kind(susan) [input hypothesis]
25. ! [X0] : ((funny(X0) & wise(X0)) | (rich(X0) & generous(X0))) [ennf transformation 3]
38. ! [X0] : (((~humble(X0) | generous(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (humble(X0) & ~generous(X0)))) [nnf transformation 2]
39. ! [X0] : ((~humble(X0) | generous(X0) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | (humble(X0) & ~generous(X0)))) [flattening 38]
55. ! [X0] : (((~strong(X0) | ~kind(X0)) | wise(X0)) & (~wise(X0) | (strong(X0) & kind(X0)))) [nnf transformation 12]
56. ! [X0] : ((~strong(X0) | ~kind(X0) | wise(X0)) & (~wise(X0) | (strong(X0) & kind(X0)))) [flattening 55]
82. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 39]
83. kind(X0) | wise(X0) | humble(X0) [cnf transformation 39]
84. ~humble(X0) | generous(X0) | ~wise(X0) [cnf transformation 39]
86. wise(X0) | generous(X0) [cnf transformation 25]
112. ~wise(X0) | kind(X0) [cnf transformation 56]
140. ~kind(susan) [cnf transformation 21]
326. wise(susan) | humble(susan) [resolution 83,140]
328. 33 <=> humble(susan) [avatar definition]
330. humble(susan) <- (33) [avatar component clause 328]
332. 34 <=> wise(susan) [avatar definition]
334. wise(susan) <- (34) [avatar component clause 332]
335. 33 | 34 [avatar split clause 326,332,328]
338. generous(susan) | ~wise(susan) <- (33) [resolution 84,330]
340. generous(susan) <- (33) [subsumption resolution 338,86]
395. wise(susan) | kind(susan) <- (33) [resolution 340,82]
396. wise(susan) <- (33) [subsumption resolution 395,140]
397. 34 | ~33 [avatar split clause 396,328,332]
401. kind(susan) <- (34) [resolution 334,112]
402. $false <- (34) [subsumption resolution 401,140]
403. ~34 [avatar contradiction clause 402]
404. $false [avatar sat refutation 335,397,403]
% SZS output end Proof for 7118408133841713268839617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not curious then someone is strong or not curious. If john is quiet or curious then mary is not quiet. If paul is humble or strong then susan is either not quiet or tall and vice versa. Everyone who is both wise and not patient is not funny or strong and vice versa. Everyone who is either not tall or curious is not tall. If susan is generous then mary is quiet or not funny and vice versa. Everyone who is patient is strong and vice versa. Everyone who is either rich or calm is not quiet. Everyone who is both not creative and patient is not brave and vice versa. Everyone who is quiet is kind or strong and vice versa. If someone is either quiet or not tall then someone is both not creative and not curious and vice versa. If someone is either wise or not old then someone is either not tall or not happy and vice versa. Everyone who is not brave or not old is both kind and not generous. Everyone who is both not generous and tall is both not patient and brave. If someone is either quiet or not tall then fred is not old and vice versa. Susan is both not quiet and happy. Someone is kind or brave. Someone is both not curious and not strong. Someone is not happy or not brave. Someone is funny. Someone is either not brave or kind. Someone is both not quiet and not tall. Paul is either not curious or tall. | Mary is quiet. | neutral | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|~curious(X)))))&
(((quiet(john)|curious(john)))=>(~quiet(mary)))&
(((humble(paul)|strong(paul)))<=>((~quiet(susan)<~>tall(susan))))&
(![X]:((wise(X)&~patient(X))<=>(~funny(X)|strong(X))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
((~quiet(susan)&happy(susan)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
(?[X]:((~quiet(X)&~tall(X))))&
((~curious(paul)<~>tall(paul))) | quiet(mary) | [] | null | 0 |
Everyone who is brave or not strong is both not tall and not wise and vice versa. Everyone who is both tall and not generous is tall or curious. If someone is not happy then someone is either humble or not kind. Everyone who is both brave and not rich is not creative or rich and vice versa. If john is humble then mary is both not kind and patient. If someone is either not strong or not old then mary is generous or not humble. If someone is not creative or not funny then someone is either brave or not patient and vice versa. If mary is either not humble or not strong then someone is either rich or not humble and vice versa. Everyone who is both not brave and not generous is either not kind or tall. Everyone who is either not humble or not quiet is creative or not calm and vice versa. If someone is both not old and happy then mary is kind or not brave. Everyone who is both not happy and not patient is either generous or calm and vice versa. If susan is both not patient and not generous then lucy is either not patient or not wise. If john is tall then someone is either brave or not rich and vice versa. Everyone who is not creative is either not humble or tall. If someone is not brave then mary is either not rich or not creative and vice versa. Someone is either old or curious. John is not tall or old. Alice is not generous. Susan is strong or not creative. Susan is either not quiet or not creative. Fred is creative or patient. | Fred is calm. | neutral | (![X]:((brave(X)|~strong(X))<=>(~tall(X)&~wise(X))))&
(![X]:((tall(X)&~generous(X))=>(tall(X)|curious(X))))&
((?[X]:(~happy(X)))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((brave(X)&~rich(X))<=>(~creative(X)|rich(X))))&
((humble(john))=>((~kind(mary)&patient(mary))))&
((?[X]:((~strong(X)<~>~old(X))))=>((generous(mary)|~humble(mary))))&
((?[X]:((~creative(X)|~funny(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
(((~humble(mary)<~>~strong(mary)))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((~brave(X)&~generous(X))=>(~kind(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(creative(X)|~calm(X))))&
((?[X]:((~old(X)&happy(X))))=>((kind(mary)|~brave(mary))))&
(![X]:((~happy(X)&~patient(X))<=>(generous(X)<~>calm(X))))&
(((~patient(susan)&~generous(susan)))=>((~patient(lucy)<~>~wise(lucy))))&
((tall(john))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~creative(X)=>(~humble(X)<~>tall(X))))&
((?[X]:(~brave(X)))<=>((~rich(mary)<~>~creative(mary))))&
(?[X]:((old(X)<~>curious(X))))&
((~tall(john)|old(john)))&
(~generous(alice))&
((strong(susan)|~creative(susan)))&
((~quiet(susan)<~>~creative(susan)))&
((creative(fred)|patient(fred))) | calm(fred) | [] | null | 0 |
Everyone who is generous is not happy or not creative and vice versa.
If john is both creative and not curious then mary is kind or patient and vice versa.
If mary is not wise then alice is either tall or kind and vice versa.
Everyone who is creative or not creative is wise or curious and vice versa.
Everyone who is quiet or patient is both not quiet and not brave.
Everyone who is both not generous and curious is both not curious and creative and vice versa.
Everyone who is either not happy or brave is both not happy and wise and vice versa.
Everyone who is rich is either quiet or not quiet and vice versa.
If mary is either not quiet or happy then someone is either not happy or not patient.
If someone is humble or curious then john is both patient and strong.
If susan is not wise then someone is both curious and tall and vice versa.
If someone is old or strong then susan is not strong and vice versa.
Everyone who is not humble is not old.
If someone is both creative and curious then mary is either not tall or not old and vice versa.
If someone is both humble and not kind then someone is not strong or not rich.
Mary is generous or kind.
Lucy is strong or wise.
Someone is strong or not curious.
Alice is both generous and patient.
Someone is brave. | John is strong. | entailment | (![X]:(generous(X)<=>(~happy(X)|~creative(X))))&
(((creative(john)&~curious(john)))<=>((kind(mary)|patient(mary))))&
((~wise(mary))<=>((tall(alice)<~>kind(alice))))&
(![X]:((creative(X)|~creative(X))<=>(wise(X)|curious(X))))&
(![X]:((quiet(X)|patient(X))=>(~quiet(X)&~brave(X))))&
(![X]:((~generous(X)&curious(X))<=>(~curious(X)&creative(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~happy(X)&wise(X))))&
(![X]:(rich(X)<=>(quiet(X)<~>~quiet(X))))&
(((~quiet(mary)<~>happy(mary)))=>(?[X]:((~happy(X)<~>~patient(X)))))&
((?[X]:((humble(X)|curious(X))))=>((patient(john)&strong(john))))&
((~wise(susan))<=>(?[X]:((curious(X)&tall(X)))))&
((?[X]:((old(X)|strong(X))))<=>(~strong(susan)))&
(![X]:(~humble(X)=>~old(X)))&
((?[X]:((creative(X)&curious(X))))<=>((~tall(mary)<~>~old(mary))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((~strong(X)|~rich(X)))))&
((generous(mary)|kind(mary)))&
((strong(lucy)|wise(lucy)))&
(?[X]:((strong(X)|~curious(X))))&
((generous(alice)&patient(alice)))&
(?[X]:(brave(X))) | strong(john) | [
"p3",
"p6",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1466073765516913889434346
% SZS output start Proof for 1466073765516913889434346
4. ! [X0] : ((~creative(X0) | creative(X0)) <=> (curious(X0) | wise(X0))) [input p3]
7. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (wise(X0) & ~happy(X0))) [input p6]
10. ? [X0] : (curious(X0) | humble(X0)) => (strong(john) & patient(john)) [input p9]
20. ? [X0] : brave(X0) [input p19]
21. ~strong(john) [input hypothesis]
27. (strong(john) & patient(john)) | ! [X0] : (~curious(X0) & ~humble(X0)) [ennf transformation 10]
35. ! [X0] : (((~creative(X0) | creative(X0)) | (~curious(X0) & ~wise(X0))) & ((curious(X0) | wise(X0)) | (creative(X0) & ~creative(X0)))) [nnf transformation 4]
36. ! [X0] : ((~creative(X0) | creative(X0) | (~curious(X0) & ~wise(X0))) & (curious(X0) | wise(X0) | (creative(X0) & ~creative(X0)))) [flattening 35]
39. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~wise(X0) | happy(X0))) & ((wise(X0) & ~happy(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 7]
40. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~wise(X0) | happy(X0)) & ((wise(X0) & ~happy(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 39]
62. ? [X0] : brave(X0) => brave(sK6) [choice axiom]
63. brave(sK6) [skolemisation 20,62]
76. curious(X0) | wise(X0) | ~creative(X0) [cnf transformation 36]
77. wise(X0) | curious(X0) | creative(X0) [cnf transformation 36]
89. ~happy(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 40]
93. ~brave(X0) | happy(X0) | ~wise(X0) | happy(X0) [cnf transformation 40]
103. strong(john) | ~curious(X0) [cnf transformation 27]
123. brave(sK6) [cnf transformation 63]
124. ~strong(john) [cnf transformation 21]
127. ~brave(X0) | ~happy(X0) [duplicate literal removal 89]
128. ~brave(X0) | happy(X0) | ~wise(X0) [duplicate literal removal 93]
169. wise(X0) | curious(X0) [subsumption resolution 76,77]
188. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
189. ~curious(X0) <- (11) [avatar component clause 188]
191. 12 <=> strong(john) [avatar definition]
194. 11 | 12 [avatar split clause 103,191,188]
303. ~12 [avatar split clause 124,191]
320. ~happy(sK6) [resolution 127,123]
334. happy(sK6) | ~wise(sK6) [resolution 128,123]
337. ~wise(sK6) [subsumption resolution 334,320]
339. curious(sK6) [resolution 337,169]
343. $false <- (11) [subsumption resolution 339,189]
344. ~11 [avatar contradiction clause 343]
345. $false [avatar sat refutation 194,303,344]
% SZS output end Proof for 1466073765516913889434346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and creative then mary is both not brave and strong.
Everyone who is both not wise and not tall is happy or not tall.
If paul is not kind then paul is not generous or not kind and vice versa.
Everyone who is either quiet or not humble is humble.
Everyone who is creative or not strong is not strong or creative and vice versa.
Everyone who is not tall or tall is both tall and not rich and vice versa.
If susan is either humble or calm then someone is both not brave and not curious and vice versa.
If paul is not old or not kind then susan is not funny or rich and vice versa.
Everyone who is funny is both not creative and creative and vice versa.
If lucy is not strong then someone is strong and vice versa.
Everyone who is strong or not rich is either rich or not patient and vice versa.
Everyone who is not old is either rich or wise.
Everyone who is not rich or quiet is either old or not calm.
If fred is funny then susan is both generous and happy and vice versa.
Everyone who is wise or quiet is both not kind and not brave and vice versa.
Everyone who is not strong or not old is either not happy or curious and vice versa.
Susan is not calm.
Someone is not wise.
Paul is either calm or not patient.
Someone is not kind.
Fred is calm or quiet.
Someone is both not curious and humble.
Someone is funny or not humble.
Fred is curious. | Fred is rich. | contradiction | ((?[X]:((~patient(X)&creative(X))))=>((~brave(mary)&strong(mary))))&
(![X]:((~wise(X)&~tall(X))=>(happy(X)|~tall(X))))&
((~kind(paul))<=>((~generous(paul)|~kind(paul))))&
(![X]:((quiet(X)<~>~humble(X))=>humble(X)))&
(![X]:((creative(X)|~strong(X))<=>(~strong(X)|creative(X))))&
(![X]:((~tall(X)|tall(X))<=>(tall(X)&~rich(X))))&
(((humble(susan)<~>calm(susan)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(((~old(paul)|~kind(paul)))<=>((~funny(susan)|rich(susan))))&
(![X]:(funny(X)<=>(~creative(X)&creative(X))))&
((~strong(lucy))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)|~rich(X))<=>(rich(X)<~>~patient(X))))&
(![X]:(~old(X)=>(rich(X)<~>wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(old(X)<~>~calm(X))))&
((funny(fred))<=>((generous(susan)&happy(susan))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~strong(X)|~old(X))<=>(~happy(X)<~>curious(X))))&
(~calm(susan))&
(?[X]:(~wise(X)))&
((calm(paul)<~>~patient(paul)))&
(?[X]:(~kind(X)))&
((calm(fred)|quiet(fred)))&
(?[X]:((~curious(X)&humble(X))))&
(?[X]:((funny(X)|~humble(X))))&
(curious(fred)) | rich(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1401673866509440765626867
% SZS output start Proof for 1401673866509440765626867
6. ! [X0] : ((tall(X0) | ~tall(X0)) <=> (~rich(X0) & tall(X0))) [input p5]
25. rich(fred) [input hypothesis]
37. ! [X0] : (((tall(X0) | ~tall(X0)) | (rich(X0) | ~tall(X0))) & ((~rich(X0) & tall(X0)) | (~tall(X0) & tall(X0)))) [nnf transformation 6]
38. ! [X0] : ((tall(X0) | ~tall(X0) | rich(X0) | ~tall(X0)) & ((~rich(X0) & tall(X0)) | (~tall(X0) & tall(X0)))) [flattening 37]
84. ~rich(X0) | tall(X0) [cnf transformation 38]
85. ~rich(X0) | ~tall(X0) [cnf transformation 38]
138. rich(fred) [cnf transformation 25]
166. ~rich(X0) [subsumption resolution 84,85]
245. $false [subsumption resolution 138,166]
% SZS output end Proof for 1401673866509440765626867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is not generous or not curious and vice versa.
Everyone who is kind or calm is both happy and wise and vice versa.
If someone is both not patient and funny then someone is both not generous and rich.
If someone is not tall or brave then susan is both not old and funny and vice versa.
If lucy is either not creative or calm then susan is not creative or not generous.
Everyone who is wise is not funny and vice versa.
If john is generous or not happy then fred is not quiet and vice versa.
If someone is both not kind and not tall then alice is not calm or not humble and vice versa.
Everyone who is either tall or generous is either wise or kind and vice versa.
Everyone who is not kind or creative is not patient or funny.
If someone is generous or curious then mary is wise.
If lucy is not tall then someone is either not happy or not curious.
If someone is not calm or not funny then someone is either not quiet or creative and vice versa.
If alice is both brave and humble then someone is not happy or not patient and vice versa.
Everyone who is both not calm and kind is wise.
Everyone who is calm or humble is not funny and vice versa.
Someone is both not calm and quiet.
Someone is both creative and brave.
Lucy is both not strong and not creative.
Someone is curious or funny.
Susan is either funny or not strong.
Paul is rich or tall.
John is not wise.
Lucy is either humble or not creative. | Paul is rich. | neutral | (![X]:(humble(X)<=>(~generous(X)|~curious(X))))&
(![X]:((kind(X)|calm(X))<=>(happy(X)&wise(X))))&
((?[X]:((~patient(X)&funny(X))))=>(?[X]:((~generous(X)&rich(X)))))&
((?[X]:((~tall(X)|brave(X))))<=>((~old(susan)&funny(susan))))&
(((~creative(lucy)<~>calm(lucy)))=>((~creative(susan)|~generous(susan))))&
(![X]:(wise(X)<=>~funny(X)))&
(((generous(john)|~happy(john)))<=>(~quiet(fred)))&
((?[X]:((~kind(X)&~tall(X))))<=>((~calm(alice)|~humble(alice))))&
(![X]:((tall(X)<~>generous(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~kind(X)|creative(X))=>(~patient(X)|funny(X))))&
((?[X]:((generous(X)|curious(X))))=>(wise(mary)))&
((~tall(lucy))=>(?[X]:((~happy(X)<~>~curious(X)))))&
((?[X]:((~calm(X)|~funny(X))))<=>(?[X]:((~quiet(X)<~>creative(X)))))&
(((brave(alice)&humble(alice)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((~calm(X)&kind(X))=>wise(X)))&
(![X]:((calm(X)|humble(X))<=>~funny(X)))&
(?[X]:((~calm(X)&quiet(X))))&
(?[X]:((creative(X)&brave(X))))&
((~strong(lucy)&~creative(lucy)))&
(?[X]:((curious(X)|funny(X))))&
((funny(susan)<~>~strong(susan)))&
((rich(paul)|tall(paul)))&
(~wise(john))&
((humble(lucy)<~>~creative(lucy))) | rich(paul) | [] | null | 0 |
If mary is both strong and happy then susan is not creative or wise. Everyone who is both strong and not brave is happy and vice versa. If someone is either not strong or funny then someone is not strong or not curious. If someone is curious then someone is wise or not quiet and vice versa. Everyone who is calm or not creative is both funny and not happy and vice versa. Everyone who is both generous and not tall is wise or not tall and vice versa. If alice is either not funny or patient then someone is either happy or wise and vice versa. If paul is not happy or patient then someone is humble. If someone is not kind then someone is not funny or generous and vice versa. Everyone who is happy is not strong and vice versa. Everyone who is not funny or not quiet is both not creative and brave and vice versa. Everyone who is either funny or not humble is either old or not humble. Everyone who is not happy is both not generous and not wise and vice versa. If john is quiet or tall then someone is rich. Everyone who is either strong or humble is either funny or old and vice versa. If someone is curious then someone is either not calm or not patient and vice versa. Mary is both not happy and not wise. John is rich or not rich. Someone is not tall or brave. Susan is not brave or not patient. Someone is funny. Alice is either not tall or old. Susan is either generous or not patient. Someone is not kind or brave. | Paul is not kind. | contradiction | (((strong(mary)&happy(mary)))=>((~creative(susan)|wise(susan))))&
(![X]:((strong(X)&~brave(X))<=>happy(X)))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:((~strong(X)|~curious(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((calm(X)|~creative(X))<=>(funny(X)&~happy(X))))&
(![X]:((generous(X)&~tall(X))<=>(wise(X)|~tall(X))))&
(((~funny(alice)<~>patient(alice)))<=>(?[X]:((happy(X)<~>wise(X)))))&
(((~happy(paul)|patient(paul)))=>(?[X]:(humble(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(happy(X)<=>~strong(X)))&
(![X]:((~funny(X)|~quiet(X))<=>(~creative(X)&brave(X))))&
(![X]:((funny(X)<~>~humble(X))=>(old(X)<~>~humble(X))))&
(![X]:(~happy(X)<=>(~generous(X)&~wise(X))))&
(((quiet(john)|tall(john)))=>(?[X]:(rich(X))))&
(![X]:((strong(X)<~>humble(X))<=>(funny(X)<~>old(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((~happy(mary)&~wise(mary)))&
((rich(john)|~rich(john)))&
(?[X]:((~tall(X)|brave(X))))&
((~brave(susan)|~patient(susan)))&
(?[X]:(funny(X)))&
((~tall(alice)<~>old(alice)))&
((generous(susan)<~>~patient(susan)))&
(?[X]:((~kind(X)|brave(X)))) | ~kind(paul) | [
"p1",
"p4",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7376459669977048328741340
% SZS output start Proof for 7376459669977048328741340
2. ! [X0] : ((~brave(X0) & strong(X0)) <=> happy(X0)) [input p1]
5. ! [X0] : ((~creative(X0) | calm(X0)) <=> (~happy(X0) & funny(X0))) [input p4]
9. ? [X0] : ~kind(X0) <=> ? [X0] : (generous(X0) | ~funny(X0)) [input p8]
10. ! [X0] : (happy(X0) <=> ~strong(X0)) [input p9]
11. ! [X0] : ((~quiet(X0) | ~funny(X0)) <=> (brave(X0) & ~creative(X0))) [input p10]
13. ! [X0] : (~happy(X0) <=> (~wise(X0) & ~generous(X0))) [input p12]
25. ~kind(paul) [input hypothesis]
28. ? [X0] : ~kind(X0) <=> ? [X1] : (generous(X1) | ~funny(X1)) [rectify 9]
36. ! [X0] : (((~brave(X0) & strong(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) | ~strong(X0)))) [nnf transformation 2]
37. ! [X0] : (((~brave(X0) & strong(X0)) | ~happy(X0)) & (happy(X0) | brave(X0) | ~strong(X0))) [flattening 36]
47. ! [X0] : (((~creative(X0) | calm(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (creative(X0) & ~calm(X0)))) [nnf transformation 5]
48. ! [X0] : ((~creative(X0) | calm(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (creative(X0) & ~calm(X0)))) [flattening 47]
57. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) & funny(X1))) & (? [X1] : (generous(X1) | ~funny(X1)) | ! [X0] : kind(X0)) [nnf transformation 28]
58. (? [X0] : ~kind(X0) | ! [X1] : (~generous(X1) & funny(X1))) & (? [X2] : (generous(X2) | ~funny(X2)) | ! [X3] : kind(X3)) [rectify 57]
59. ? [X0] : ~kind(X0) => ~kind(sK5) [choice axiom]
60. ? [X2] : (generous(X2) | ~funny(X2)) => (generous(sK6) | ~funny(sK6)) [choice axiom]
61. (~kind(sK5) | ! [X1] : (~generous(X1) & funny(X1))) & ((generous(sK6) | ~funny(sK6)) | ! [X3] : kind(X3)) [skolemisation 58,60,59]
62. ! [X0] : ((happy(X0) | strong(X0)) & (~strong(X0) | ~happy(X0))) [nnf transformation 10]
63. ! [X0] : (((~quiet(X0) | ~funny(X0)) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | (quiet(X0) & funny(X0)))) [nnf transformation 11]
64. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | (quiet(X0) & funny(X0)))) [flattening 63]
66. ! [X0] : ((~happy(X0) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | happy(X0))) [nnf transformation 13]
67. ! [X0] : ((~happy(X0) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | happy(X0))) [flattening 66]
86. strong(X0) | ~happy(X0) [cnf transformation 37]
94. funny(X0) | creative(X0) [cnf transformation 48]
113. generous(sK6) | ~funny(sK6) | kind(X3) [cnf transformation 61]
116. ~strong(X0) | ~happy(X0) [cnf transformation 62]
117. happy(X0) | strong(X0) [cnf transformation 62]
118. ~creative(X0) | funny(X0) [cnf transformation 64]
127. ~generous(X0) | happy(X0) [cnf transformation 67]
155. ~kind(paul) [cnf transformation 25]
260. 24 <=> ! [X1] : ~generous(X1) [avatar definition]
261. ~generous(X1) <- (24) [avatar component clause 260]
268. 26 <=> ! [X1] : funny(X1) [avatar definition]
269. funny(X1) <- (26) [avatar component clause 268]
272. 27 <=> ! [X3] : kind(X3) [avatar definition]
273. kind(X3) <- (27) [avatar component clause 272]
275. 28 <=> funny(sK6) [avatar definition]
277. ~funny(sK6) <- (~28) [avatar component clause 275]
279. 29 <=> generous(sK6) [avatar definition]
281. generous(sK6) <- (29) [avatar component clause 279]
282. 27 | ~28 | 29 [avatar split clause 113,279,275,272]
283. strong(X0) [subsumption resolution 117,86]
284. ~happy(X0) [subsumption resolution 116,283]
286. funny(X0) [subsumption resolution 118,94]
287. 26 [avatar split clause 286,268]
290. ~generous(X0) [subsumption resolution 127,284]
291. 24 [avatar split clause 290,260]
383. $false <- (26, ~28) [resolution 277,269]
384. ~26 | 28 [avatar contradiction clause 383]
385. $false <- (27) [resolution 273,155]
386. ~27 [avatar contradiction clause 385]
387. $false <- (24, 29) [subsumption resolution 281,261]
388. ~24 | ~29 [avatar contradiction clause 387]
389. $false [avatar sat refutation 282,287,291,384,386,388]
% SZS output end Proof for 7376459669977048328741340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is humble or not funny then someone is curious or not strong and vice versa.
If someone is not creative or not old then paul is not funny.
If lucy is brave then someone is not brave and vice versa.
Everyone who is both not curious and happy is both not kind and calm.
If fred is both not happy and not tall then someone is tall.
If someone is not funny or not old then lucy is not humble.
Everyone who is both not tall and not quiet is both curious and quiet.
Everyone who is rich or humble is not rich or curious and vice versa.
If someone is both not tall and kind then paul is not brave and vice versa.
If alice is not strong or not calm then lucy is funny or not rich.
If paul is not humble then john is not generous or not calm and vice versa.
Everyone who is not calm is strong and vice versa.
If someone is both not wise and wise then someone is curious or kind.
Everyone who is either curious or happy is funny and vice versa.
If someone is funny or calm then someone is brave.
Everyone who is both creative and funny is wise.
Alice is funny.
Someone is either tall or strong.
Someone is not creative.
Susan is not tall.
Someone is either not happy or quiet.
Someone is either not calm or not tall.
Paul is both kind and patient.
Lucy is not generous. | Lucy is rich. | entailment | (((humble(john)|~funny(john)))<=>(?[X]:((curious(X)|~strong(X)))))&
((?[X]:((~creative(X)|~old(X))))=>(~funny(paul)))&
((brave(lucy))<=>(?[X]:(~brave(X))))&
(![X]:((~curious(X)&happy(X))=>(~kind(X)&calm(X))))&
(((~happy(fred)&~tall(fred)))=>(?[X]:(tall(X))))&
((?[X]:((~funny(X)|~old(X))))=>(~humble(lucy)))&
(![X]:((~tall(X)&~quiet(X))=>(curious(X)&quiet(X))))&
(![X]:((rich(X)|humble(X))<=>(~rich(X)|curious(X))))&
((?[X]:((~tall(X)&kind(X))))<=>(~brave(paul)))&
(((~strong(alice)|~calm(alice)))=>((funny(lucy)|~rich(lucy))))&
((~humble(paul))<=>((~generous(john)|~calm(john))))&
(![X]:(~calm(X)<=>strong(X)))&
((?[X]:((~wise(X)&wise(X))))=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((curious(X)<~>happy(X))<=>funny(X)))&
((?[X]:((funny(X)|calm(X))))=>(?[X]:(brave(X))))&
(![X]:((creative(X)&funny(X))=>wise(X)))&
(funny(alice))&
(?[X]:((tall(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(~tall(susan))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
((kind(paul)&patient(paul)))&
(~generous(lucy)) | rich(lucy) | [
"p1",
"p5",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 559119624054275020961567
% SZS output start Proof for 559119624054275020961567
2. ? [X0] : (~old(X0) | ~creative(X0)) => ~funny(paul) [input p1]
6. ? [X0] : (~old(X0) | ~funny(X0)) => ~humble(lucy) [input p5]
8. ! [X0] : ((humble(X0) | rich(X0)) <=> (curious(X0) | ~rich(X0))) [input p7]
19. ? [X0] : ~creative(X0) [input p18]
25. ~rich(lucy) [input hypothesis]
29. ? [X0] : ~creative(X0) => ~funny(paul) [pure predicate removal 2]
30. ? [X0] : ~funny(X0) => ~humble(lucy) [pure predicate removal 6]
31. ~funny(paul) | ! [X0] : creative(X0) [ennf transformation 29]
36. ~humble(lucy) | ! [X0] : funny(X0) [ennf transformation 30]
56. ! [X0] : (((humble(X0) | rich(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (~humble(X0) & ~rich(X0)))) [nnf transformation 8]
57. ! [X0] : ((humble(X0) | rich(X0) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | (~humble(X0) & ~rich(X0)))) [flattening 56]
75. ? [X0] : ~creative(X0) => ~creative(sK7) [choice axiom]
76. ~creative(sK7) [skolemisation 19,75]
87. ~funny(paul) | creative(X0) [cnf transformation 31]
93. ~humble(lucy) | funny(X0) [cnf transformation 36]
98. humble(X0) | rich(X0) | rich(X0) [cnf transformation 57]
121. ~creative(sK7) [cnf transformation 76]
129. ~rich(lucy) [cnf transformation 25]
131. rich(X0) | humble(X0) [duplicate literal removal 98]
160. 7 <=> ! [X0] : creative(X0) [avatar definition]
161. creative(X0) <- (7) [avatar component clause 160]
163. 8 <=> funny(paul) [avatar definition]
165. ~funny(paul) <- (~8) [avatar component clause 163]
166. 7 | ~8 [avatar split clause 87,163,160]
194. 15 <=> ! [X0] : funny(X0) [avatar definition]
195. funny(X0) <- (15) [avatar component clause 194]
197. 16 <=> humble(lucy) [avatar definition]
200. 15 | ~16 [avatar split clause 93,197,194]
228. 23 <=> rich(lucy) [avatar definition]
230. ~rich(lucy) <- (~23) [avatar component clause 228]
294. ~23 [avatar split clause 129,228]
299. humble(lucy) <- (~23) [resolution 131,230]
303. 16 | 23 [avatar split clause 299,228,197]
305. $false <- (~8, 15) [resolution 195,165]
306. 8 | ~15 [avatar contradiction clause 305]
308. $false <- (7) [resolution 161,121]
309. ~7 [avatar contradiction clause 308]
310. $false [avatar sat refutation 166,200,294,303,306,309]
% SZS output end Proof for 559119624054275020961567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not generous then someone is either not funny or not old and vice versa. Everyone who is not wise or happy is not rich and vice versa. Everyone who is both humble and brave is not tall. Everyone who is not curious is both generous and not kind and vice versa. Everyone who is not brave is both quiet and humble. Everyone who is both not quiet and quiet is not humble or kind and vice versa. If someone is not quiet or funny then someone is not creative or old and vice versa. If susan is both humble and calm then someone is not curious or not strong. Everyone who is either creative or quiet is both not patient and not generous. Everyone who is either rich or not humble is old and vice versa. Everyone who is either not happy or patient is both funny and not creative and vice versa. Everyone who is either old or creative is either not calm or not tall. Everyone who is rich is tall or old and vice versa. If someone is tall or not rich then someone is either quiet or creative and vice versa. Everyone who is kind or not generous is either strong or not quiet and vice versa. If someone is either calm or not wise then someone is not tall. Susan is tall or not strong. Lucy is not calm or not humble. Someone is generous or patient. Alice is both generous and not rich. Susan is not curious. Lucy is humble or quiet. Mary is either quiet or not creative. Someone is not patient. | Lucy is tall. | neutral | ((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~wise(X)|happy(X))<=>~rich(X)))&
(![X]:((humble(X)&brave(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
((tall(susan)|~strong(susan)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy)))&
((quiet(mary)<~>~creative(mary)))&
(?[X]:(~patient(X))) | tall(lucy) | [] | null | 0 |
Everyone who is not patient or not calm is both not curious and not happy and vice versa.
Everyone who is either not kind or creative is not creative.
If someone is not quiet or not brave then someone is creative or not curious and vice versa.
If someone is both happy and funny then someone is both tall and rich.
If someone is patient then lucy is happy and vice versa.
Everyone who is either not creative or not brave is either happy or patient.
Everyone who is not funny is wise and vice versa.
If someone is strong or generous then lucy is not rich and vice versa.
Everyone who is either happy or not brave is not generous or creative and vice versa.
Everyone who is both not patient and not happy is patient or calm and vice versa.
Everyone who is strong or not creative is old or creative and vice versa.
If someone is both tall and creative then alice is not generous or creative.
If john is either tall or patient then john is not creative and vice versa.
Everyone who is not brave or kind is humble.
Everyone who is either generous or creative is either rich or generous and vice versa.
Someone is both not curious and funny.
Mary is curious or old.
Someone is both not brave and not happy.
Someone is not strong. | Lucy is brave. | contradiction | (![X]:((~patient(X)|~calm(X))<=>(~curious(X)&~happy(X))))&
(![X]:((~kind(X)<~>creative(X))=>~creative(X)))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:((creative(X)|~curious(X)))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:(patient(X)))<=>(happy(lucy)))&
(![X]:((~creative(X)<~>~brave(X))=>(happy(X)<~>patient(X))))&
(![X]:(~funny(X)<=>wise(X)))&
((?[X]:((strong(X)|generous(X))))<=>(~rich(lucy)))&
(![X]:((happy(X)<~>~brave(X))<=>(~generous(X)|creative(X))))&
(![X]:((~patient(X)&~happy(X))<=>(patient(X)|calm(X))))&
(![X]:((strong(X)|~creative(X))<=>(old(X)|creative(X))))&
((?[X]:((tall(X)&creative(X))))=>((~generous(alice)|creative(alice))))&
(((tall(john)<~>patient(john)))<=>(~creative(john)))&
(![X]:((~brave(X)|kind(X))=>humble(X)))&
(![X]:((generous(X)<~>creative(X))<=>(rich(X)<~>generous(X))))&
(?[X]:((~curious(X)&funny(X))))&
((curious(mary)|old(mary)))&
(?[X]:((~brave(X)&~happy(X))))&
(?[X]:(~strong(X))) | brave(lucy) | [
"p0",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7257907065494015069300858
% SZS output start Proof for 7257907065494015069300858
1. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> (~happy(X0) & ~curious(X0))) [input p0]
6. ! [X0] : ((~creative(X0) <~> ~brave(X0)) => (happy(X0) <~> patient(X0))) [input p5]
9. ! [X0] : ((happy(X0) <~> ~brave(X0)) <=> (creative(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (calm(X0) | patient(X0))) [input p9]
20. brave(lucy) [input hypothesis]
26. ! [X0] : ((happy(X0) <~> patient(X0)) | (~creative(X0) <=> ~brave(X0))) [ennf transformation 6]
29. ! [X0] : (((~calm(X0) | ~patient(X0)) | (happy(X0) | curious(X0))) & ((~happy(X0) & ~curious(X0)) | (calm(X0) & patient(X0)))) [nnf transformation 1]
30. ! [X0] : ((~calm(X0) | ~patient(X0) | happy(X0) | curious(X0)) & ((~happy(X0) & ~curious(X0)) | (calm(X0) & patient(X0)))) [flattening 29]
44. ! [X0] : (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) [nnf transformation 26]
50. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [nnf transformation 9]
51. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [flattening 50]
52. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 10]
53. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | happy(X0) | patient(X0))) [flattening 52]
66. ~happy(X0) | patient(X0) [cnf transformation 30]
67. ~happy(X0) | calm(X0) [cnf transformation 30]
79. patient(X0) | happy(X0) | ~brave(X0) | creative(X0) [cnf transformation 44]
81. ~patient(X0) | ~happy(X0) | ~brave(X0) | creative(X0) [cnf transformation 44]
91. ~brave(X0) | happy(X0) | ~creative(X0) [cnf transformation 51]
95. ~patient(X0) | ~patient(X0) [cnf transformation 53]
98. ~happy(X0) | ~calm(X0) [cnf transformation 53]
122. brave(lucy) [cnf transformation 20]
130. ~patient(X0) [duplicate literal removal 95]
187. 14 <=> ! [X1] : ~patient(X1) [avatar definition]
188. ~patient(X1) <- (14) [avatar component clause 187]
191. ~brave(X0) | ~happy(X0) | creative(X0) [subsumption resolution 81,66]
193. ~brave(X0) | patient(X0) | creative(X0) [subsumption resolution 79,191]
215. ~happy(X0) [subsumption resolution 98,67]
216. 14 [avatar split clause 130,187]
268. happy(lucy) | ~creative(lucy) [resolution 91,122]
269. ~creative(lucy) [subsumption resolution 268,215]
283. patient(lucy) | creative(lucy) [resolution 193,122]
284. creative(lucy) <- (14) [subsumption resolution 283,188]
285. $false <- (14) [subsumption resolution 284,269]
286. ~14 [avatar contradiction clause 285]
287. $false [avatar sat refutation 216,286]
% SZS output end Proof for 7257907065494015069300858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not old then lucy is kind and vice versa.
Everyone who is both tall and patient is either curious or not happy.
If someone is strong or happy then alice is both curious and tall and vice versa.
Everyone who is not funny or creative is either wise or happy.
If someone is either not brave or not funny then someone is either generous or not tall.
If someone is not calm or not tall then someone is either humble or not humble.
Everyone who is not rich or not curious is both not tall and not kind and vice versa.
Everyone who is either wise or funny is calm and vice versa.
If john is not humble or brave then someone is not quiet.
If someone is either quiet or funny then alice is not quiet.
Everyone who is not tall or not humble is not tall.
If someone is curious then john is either humble or not funny and vice versa.
Everyone who is tall or not quiet is both not strong and quiet and vice versa.
If someone is not old or calm then someone is not rich or rich and vice versa.
If john is old then someone is both wise and not rich and vice versa.
Someone is not tall or not happy.
Alice is creative or not patient.
Someone is not brave.
Paul is both patient and generous.
Someone is either calm or not strong. | Alice is wise. | neutral | ((?[X]:((~curious(X)<~>~old(X))))<=>(kind(lucy)))&
(![X]:((tall(X)&patient(X))=>(curious(X)<~>~happy(X))))&
((?[X]:((strong(X)|happy(X))))<=>((curious(alice)&tall(alice))))&
(![X]:((~funny(X)|creative(X))=>(wise(X)<~>happy(X))))&
((?[X]:((~brave(X)<~>~funny(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((~calm(X)|~tall(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~rich(X)|~curious(X))<=>(~tall(X)&~kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>calm(X)))&
(((~humble(john)|brave(john)))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>funny(X))))=>(~quiet(alice)))&
(![X]:((~tall(X)|~humble(X))=>~tall(X)))&
((?[X]:(curious(X)))<=>((humble(john)<~>~funny(john))))&
(![X]:((tall(X)|~quiet(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~old(X)|calm(X))))<=>(?[X]:((~rich(X)|rich(X)))))&
((old(john))<=>(?[X]:((wise(X)&~rich(X)))))&
(?[X]:((~tall(X)|~happy(X))))&
((creative(alice)|~patient(alice)))&
(?[X]:(~brave(X)))&
((patient(paul)&generous(paul)))&
(?[X]:((calm(X)<~>~strong(X)))) | wise(alice) | [] | null | 0 |
Everyone who is old is not tall or brave. If mary is either not funny or wise then lucy is either not kind or not curious. Everyone who is wise is either tall or not tall and vice versa. Everyone who is either not old or not rich is both not curious and calm and vice versa. Everyone who is either not strong or curious is either calm or happy and vice versa. Everyone who is calm is not tall. Everyone who is either not calm or curious is not happy or not humble. If john is curious then someone is kind and vice versa. Everyone who is wise or kind is patient or not funny. Everyone who is both not old and not funny is not kind and vice versa. Everyone who is either calm or strong is not quiet or patient. If someone is happy then someone is not patient or strong. Everyone who is either not wise or not calm is both patient and strong and vice versa. If someone is either not funny or not calm then john is not strong or humble and vice versa. If someone is not curious then someone is either humble or brave and vice versa. Everyone who is not brave is either not kind or not curious and vice versa. Someone is not old or wise. Fred is quiet or not calm. Someone is either not old or funny. Someone is not wise or not tall. Fred is either old or creative. Fred is old. Someone is either not strong or not quiet. Someone is not generous. | Mary is old. | neutral | (![X]:(old(X)=>(~tall(X)|brave(X))))&
(((~funny(mary)<~>wise(mary)))=>((~kind(lucy)<~>~curious(lucy))))&
(![X]:(wise(X)<=>(tall(X)<~>~tall(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>curious(X))<=>(calm(X)<~>happy(X))))&
(![X]:(calm(X)=>~tall(X)))&
(![X]:((~calm(X)<~>curious(X))=>(~happy(X)|~humble(X))))&
((curious(john))<=>(?[X]:(kind(X))))&
(![X]:((wise(X)|kind(X))=>(patient(X)|~funny(X))))&
(![X]:((~old(X)&~funny(X))<=>~kind(X)))&
(![X]:((calm(X)<~>strong(X))=>(~quiet(X)|patient(X))))&
((?[X]:(happy(X)))=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(patient(X)&strong(X))))&
((?[X]:((~funny(X)<~>~calm(X))))<=>((~strong(john)|humble(john))))&
((?[X]:(~curious(X)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~brave(X)<=>(~kind(X)<~>~curious(X))))&
(?[X]:((~old(X)|wise(X))))&
((quiet(fred)|~calm(fred)))&
(?[X]:((~old(X)<~>funny(X))))&
(?[X]:((~wise(X)|~tall(X))))&
((old(fred)<~>creative(fred)))&
(old(fred))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:(~generous(X))) | old(mary) | [] | null | 0 |
If someone is both kind and not curious then someone is either happy or not happy and vice versa.
Everyone who is both not funny and creative is generous and vice versa.
If fred is creative or funny then john is not brave or tall and vice versa.
If someone is both not brave and brave then someone is either patient or curious and vice versa.
If john is both curious and calm then someone is both not strong and not curious and vice versa.
If someone is both generous and brave then someone is curious or not curious.
Everyone who is both humble and not rich is not happy and vice versa.
Everyone who is humble is not kind and vice versa.
If someone is both old and not humble then lucy is either not brave or patient.
Everyone who is not calm or not patient is either creative or generous and vice versa.
Everyone who is rich or patient is either strong or not wise.
If john is not tall then someone is either strong or tall and vice versa.
Everyone who is wise is calm.
If fred is patient or not funny then paul is not quiet or humble and vice versa.
Everyone who is not happy or rich is either not patient or old.
Someone is both not humble and creative.
Paul is both rich and not generous.
Someone is both quiet and not creative.
Fred is both strong and old.
Someone is either not calm or patient.
Someone is generous.
Lucy is not patient or quiet.
Someone is wise. | Fred is creative. | neutral | ((?[X]:((kind(X)&~curious(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((~funny(X)&creative(X))<=>generous(X)))&
(((creative(fred)|funny(fred)))<=>((~brave(john)|tall(john))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((patient(X)<~>curious(X)))))&
(((curious(john)&calm(john)))<=>(?[X]:((~strong(X)&~curious(X)))))&
((?[X]:((generous(X)&brave(X))))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((humble(X)&~rich(X))<=>~happy(X)))&
(![X]:(humble(X)<=>~kind(X)))&
((?[X]:((old(X)&~humble(X))))=>((~brave(lucy)<~>patient(lucy))))&
(![X]:((~calm(X)|~patient(X))<=>(creative(X)<~>generous(X))))&
(![X]:((rich(X)|patient(X))=>(strong(X)<~>~wise(X))))&
((~tall(john))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:(wise(X)=>calm(X)))&
(((patient(fred)|~funny(fred)))<=>((~quiet(paul)|humble(paul))))&
(![X]:((~happy(X)|rich(X))=>(~patient(X)<~>old(X))))&
(?[X]:((~humble(X)&creative(X))))&
((rich(paul)&~generous(paul)))&
(?[X]:((quiet(X)&~creative(X))))&
((strong(fred)&old(fred)))&
(?[X]:((~calm(X)<~>patient(X))))&
(?[X]:(generous(X)))&
((~patient(lucy)|quiet(lucy)))&
(?[X]:(wise(X))) | creative(fred) | [] | null | 0 |
If someone is creative or not curious then lucy is not brave and vice versa.
If paul is either brave or happy then someone is both not creative and curious and vice versa.
Everyone who is either patient or not humble is not curious.
Everyone who is not strong is both quiet and not happy.
If someone is either not generous or humble then mary is happy or quiet.
If paul is both not humble and humble then someone is not happy.
Everyone who is not quiet is tall or funny and vice versa.
If someone is not calm or not wise then someone is creative or generous and vice versa.
If someone is curious then someone is either curious or not old.
Everyone who is both old and kind is tall or calm.
Everyone who is not humble is not humble or not brave and vice versa.
If john is both not calm and wise then someone is either tall or old.
Everyone who is either funny or brave is generous or not happy and vice versa.
If mary is either not humble or not rich then mary is either old or brave.
Everyone who is curious is generous or humble.
Someone is both not kind and not rich.
Someone is either quiet or tall.
Someone is both not kind and calm.
Someone is either not tall or not creative.
John is humble or not calm.
John is both happy and calm.
Someone is patient.
Mary is either tall or not curious. | Lucy is not brave. | neutral | ((?[X]:((creative(X)|~curious(X))))<=>(~brave(lucy)))&
(((brave(paul)<~>happy(paul)))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:((patient(X)<~>~humble(X))=>~curious(X)))&
(![X]:(~strong(X)=>(quiet(X)&~happy(X))))&
((?[X]:((~generous(X)<~>humble(X))))=>((happy(mary)|quiet(mary))))&
(((~humble(paul)&humble(paul)))=>(?[X]:(~happy(X))))&
(![X]:(~quiet(X)<=>(tall(X)|funny(X))))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:(curious(X)))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((old(X)&kind(X))=>(tall(X)|calm(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~brave(X))))&
(((~calm(john)&wise(john)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((funny(X)<~>brave(X))<=>(generous(X)|~happy(X))))&
(((~humble(mary)<~>~rich(mary)))=>((old(mary)<~>brave(mary))))&
(![X]:(curious(X)=>(generous(X)|humble(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
((humble(john)|~calm(john)))&
((happy(john)&calm(john)))&
(?[X]:(patient(X)))&
((tall(mary)<~>~curious(mary))) | ~brave(lucy) | [] | null | 0 |
If someone is patient then someone is either happy or not tall and vice versa.
If someone is not humble then mary is either strong or patient and vice versa.
Everyone who is both not brave and not old is creative.
If someone is not humble or funny then someone is both tall and not wise and vice versa.
If someone is both not brave and not wise then alice is either not quiet or calm.
Everyone who is quiet or humble is either not old or kind and vice versa.
If alice is happy or not quiet then someone is either quiet or not quiet and vice versa.
Everyone who is both strong and not calm is not quiet and vice versa.
Everyone who is not brave or calm is not patient or humble.
Everyone who is not kind or tall is both kind and not quiet.
If someone is both not tall and patient then alice is rich and vice versa.
Everyone who is both not generous and not brave is not calm and vice versa.
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.
If someone is strong or not funny then someone is not happy or not brave and vice versa.
Someone is creative or not old.
Someone is both not strong and old.
Paul is either humble or curious.
Someone is old. | Paul is not old. | contradiction | ((?[X]:(patient(X)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:(~humble(X)))<=>((strong(mary)<~>patient(mary))))&
(![X]:((~brave(X)&~old(X))=>creative(X)))&
((?[X]:((~humble(X)|funny(X))))<=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~brave(X)&~wise(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((quiet(X)|humble(X))<=>(~old(X)<~>kind(X))))&
(((happy(alice)|~quiet(alice)))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:((~brave(X)|calm(X))=>(~patient(X)|humble(X))))&
(![X]:((~kind(X)|tall(X))=>(kind(X)&~quiet(X))))&
((?[X]:((~tall(X)&patient(X))))<=>(rich(alice)))&
(![X]:((~generous(X)&~brave(X))<=>~calm(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]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~strong(X)&old(X))))&
((humble(paul)<~>curious(paul)))&
(?[X]:(old(X))) | ~old(paul) | [
"p3",
"p5",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7692724677099507164711021
% SZS output start Proof for 7692724677099507164711021
4. ? [X0] : (funny(X0) | ~humble(X0)) <=> ? [X0] : (~wise(X0) & tall(X0)) [input p3]
6. ! [X0] : ((humble(X0) | quiet(X0)) <=> (~old(X0) <~> kind(X0))) [input p5]
8. ! [X0] : ((~calm(X0) & strong(X0)) <=> ~quiet(X0)) [input p7]
10. ! [X0] : ((tall(X0) | ~kind(X0)) => (~quiet(X0) & kind(X0))) [input p9]
14. ! [X0] : ((strong(X0) | ~curious(X0)) <=> wise(X0)) [input p13]
21. ~old(paul) [input hypothesis]
23. ? [X0] : (funny(X0) | ~humble(X0)) <=> ? [X1] : (~wise(X1) & tall(X1)) [rectify 4]
30. ! [X0] : ((~quiet(X0) & kind(X0)) | (~tall(X0) & kind(X0))) [ennf transformation 10]
41. (? [X0] : (funny(X0) | ~humble(X0)) | ! [X1] : (wise(X1) | ~tall(X1))) & (? [X1] : (~wise(X1) & tall(X1)) | ! [X0] : (~funny(X0) & humble(X0))) [nnf transformation 23]
42. (? [X0] : (funny(X0) | ~humble(X0)) | ! [X1] : (wise(X1) | ~tall(X1))) & (? [X2] : (~wise(X2) & tall(X2)) | ! [X3] : (~funny(X3) & humble(X3))) [rectify 41]
43. ? [X0] : (funny(X0) | ~humble(X0)) => (funny(sK3) | ~humble(sK3)) [choice axiom]
44. ? [X2] : (~wise(X2) & tall(X2)) => (~wise(sK4) & tall(sK4)) [choice axiom]
45. ((funny(sK3) | ~humble(sK3)) | ! [X1] : (wise(X1) | ~tall(X1))) & ((~wise(sK4) & tall(sK4)) | ! [X3] : (~funny(X3) & humble(X3))) [skolemisation 42,44,43]
47. ! [X0] : (((humble(X0) | quiet(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 6]
48. ! [X0] : ((humble(X0) | quiet(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~humble(X0) & ~quiet(X0)))) [flattening 47]
54. ! [X0] : (((~calm(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (calm(X0) | ~strong(X0)))) [nnf transformation 8]
55. ! [X0] : (((~calm(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | calm(X0) | ~strong(X0))) [flattening 54]
62. ! [X0] : (((strong(X0) | ~curious(X0)) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [nnf transformation 14]
63. ! [X0] : ((strong(X0) | ~curious(X0) | ~wise(X0)) & (wise(X0) | (~strong(X0) & curious(X0)))) [flattening 62]
84. tall(sK4) | humble(X3) [cnf transformation 45]
86. ~wise(sK4) | humble(X3) [cnf transformation 45]
94. ~kind(X0) | old(X0) | ~humble(X0) [cnf transformation 48]
104. quiet(X0) | strong(X0) [cnf transformation 55]
108. kind(X0) | kind(X0) [cnf transformation 30]
111. ~quiet(X0) | ~tall(X0) [cnf transformation 30]
123. ~strong(X0) | wise(X0) [cnf transformation 63]
139. ~old(paul) [cnf transformation 21]
142. kind(X0) [duplicate literal removal 108]
185. 10 <=> ! [X1] : humble(X1) [avatar definition]
186. humble(X1) <- (10) [avatar component clause 185]
205. 15 <=> wise(sK4) [avatar definition]
207. ~wise(sK4) <- (~15) [avatar component clause 205]
209. 10 | ~15 [avatar split clause 86,205,185]
211. 16 <=> tall(sK4) [avatar definition]
213. tall(sK4) <- (16) [avatar component clause 211]
215. 10 | 16 [avatar split clause 84,211,185]
290. ~tall(X0) | strong(X0) [resolution 111,104]
314. ~humble(X0) | old(X0) [resolution 94,142]
315. strong(sK4) <- (16) [resolution 290,213]
317. wise(sK4) <- (16) [resolution 315,123]
318. $false <- (~15, 16) [subsumption resolution 317,207]
319. 15 | ~16 [avatar contradiction clause 318]
359. old(X0) <- (10) [resolution 314,186]
367. $false <- (10) [resolution 359,139]
369. ~10 [avatar contradiction clause 367]
370. $false [avatar sat refutation 209,215,319,369]
% SZS output end Proof for 7692724677099507164711021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or funny is curious and vice versa.
Everyone who is both not quiet and calm is either humble or calm and vice versa.
Everyone who is either not kind or not wise is either not funny or rich and vice versa.
If someone is either funny or rich then someone is not calm or kind and vice versa.
If alice is both quiet and not happy then someone is both not funny and rich and vice versa.
If someone is happy or not wise then john is both wise and not creative.
Everyone who is not rich or not patient is brave or not generous.
Everyone who is not calm or generous is not generous.
If someone is funny then paul is both strong and not creative.
Everyone who is both curious and kind is either kind or tall.
If mary is both patient and not old then john is tall or happy.
Everyone who is either quiet or not rich is funny.
Everyone who is both quiet and not brave is not humble and vice versa.
Everyone who is either old or not tall is both not kind and not brave and vice versa.
Everyone who is either not rich or quiet is both funny and not generous.
If someone is not brave then paul is both patient and funny and vice versa.
Someone is either not wise or happy.
Someone is rich or curious.
Someone is both not happy and not creative.
Someone is both not happy and old.
Someone is either kind or not calm.
Susan is not calm.
Lucy is both happy and wise.
Someone is either not strong or not happy. | John is not patient. | neutral | (![X]:((~generous(X)<~>funny(X))<=>curious(X)))&
(![X]:((~quiet(X)&calm(X))<=>(humble(X)<~>calm(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(?[X]:((~calm(X)|kind(X)))))&
(((quiet(alice)&~happy(alice)))<=>(?[X]:((~funny(X)&rich(X)))))&
((?[X]:((happy(X)|~wise(X))))=>((wise(john)&~creative(john))))&
(![X]:((~rich(X)|~patient(X))=>(brave(X)|~generous(X))))&
(![X]:((~calm(X)|generous(X))=>~generous(X)))&
((?[X]:(funny(X)))=>((strong(paul)&~creative(paul))))&
(![X]:((curious(X)&kind(X))=>(kind(X)<~>tall(X))))&
(((patient(mary)&~old(mary)))=>((tall(john)|happy(john))))&
(![X]:((quiet(X)<~>~rich(X))=>funny(X)))&
(![X]:((quiet(X)&~brave(X))<=>~humble(X)))&
(![X]:((old(X)<~>~tall(X))<=>(~kind(X)&~brave(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(funny(X)&~generous(X))))&
((?[X]:(~brave(X)))<=>((patient(paul)&funny(paul))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:((~happy(X)&old(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
(~calm(susan))&
((happy(lucy)&wise(lucy)))&
(?[X]:((~strong(X)<~>~happy(X)))) | ~patient(john) | [] | null | 0 |
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