premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Everyone who is either not brave or patient is either not rich or curious.
Someone is both calm and wise.
Lucy is rich or not tall.
Mary is wise or happy.
Someone is curious or old. | Fred is not creative. | neutral | (![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((rich(lucy)|~tall(lucy)))&
((wise(mary)|happy(mary)))&
(?[X]:((curious(X)|old(X)))) | ~creative(fred) | [] | null | 0 |
If someone is not happy then fred is tall. If someone is both not tall and patient then someone is both not humble and creative. Everyone who is not quiet or kind is creative and vice versa. If john is both wise and humble then susan is both wise and not quiet. Everyone who is not patient or funny is funny or tall. Everyone who is both calm and not creative is either curious or not quiet. Everyone who is happy is not quiet or tall. If someone is old or calm then lucy is both brave and not calm. If someone is calm or quiet then mary is old or strong and vice versa. Everyone who is both old and not happy is both quiet and not brave. If someone is strong or not strong then alice is creative and vice versa. If paul is both old and not patient then someone is either generous or creative. Everyone who is not brave is both not calm and generous and vice versa. Everyone who is either strong or patient is both not calm and not funny. Everyone who is either funny or patient is happy and vice versa. If fred is either curious or not kind then john is both quiet and not old. Someone is happy. John is both not strong and not wise. Someone is both not humble and not tall. Someone is calm. Lucy is not happy. Lucy is both not calm and strong. Someone is quiet or humble. Mary is both curious and not quiet. | Paul is patient. | neutral | ((?[X]:(~happy(X)))=>(tall(fred)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~quiet(X)|kind(X))<=>creative(X)))&
(((wise(john)&humble(john)))=>((wise(susan)&~quiet(susan))))&
(![X]:((~patient(X)|funny(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&~creative(X))=>(curious(X)<~>~quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)|tall(X))))&
((?[X]:((old(X)|calm(X))))=>((brave(lucy)&~calm(lucy))))&
((?[X]:((calm(X)|quiet(X))))<=>((old(mary)|strong(mary))))&
(![X]:((old(X)&~happy(X))=>(quiet(X)&~brave(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(creative(alice)))&
(((old(paul)&~patient(paul)))=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~brave(X)<=>(~calm(X)&generous(X))))&
(![X]:((strong(X)<~>patient(X))=>(~calm(X)&~funny(X))))&
(![X]:((funny(X)<~>patient(X))<=>happy(X)))&
(((curious(fred)<~>~kind(fred)))=>((quiet(john)&~old(john))))&
(?[X]:(happy(X)))&
((~strong(john)&~wise(john)))&
(?[X]:((~humble(X)&~tall(X))))&
(?[X]:(calm(X)))&
(~happy(lucy))&
((~calm(lucy)&strong(lucy)))&
(?[X]:((quiet(X)|humble(X))))&
((curious(mary)&~quiet(mary))) | patient(paul) | [] | null | 0 |
If mary is not funny then paul is tall or not patient. Everyone who is either not brave or wise is both generous and not quiet and vice versa. If someone is either happy or creative then paul is both calm and not tall. If someone is not rich then john is both not quiet and not strong. Everyone who is not curious or brave is not kind or not brave. Everyone who is either humble or wise is old and vice versa. Everyone who is either rich or not happy is both not brave and quiet and vice versa. If paul is both not generous and not wise then someone is not quiet and vice versa. Everyone who is brave is funny. Everyone who is brave is both not tall and generous and vice versa. Everyone who is both strong and not generous is both not kind and not quiet. If someone is not quiet or funny then someone is calm or not quiet. Everyone who is not kind is rich and vice versa. If someone is calm or not humble then someone is either not calm or not patient and vice versa. Everyone who is either not patient or not rich is happy. If someone is either not quiet or not generous then someone is both not curious and not calm. Someone is not patient or funny. Someone is both tall and generous. Someone is both curious and not humble. John is either not calm or creative. Susan is wise. Someone is either not humble or not curious. | Mary is kind. | contradiction | ((~funny(mary))=>((tall(paul)|~patient(paul))))&
(![X]:((~brave(X)<~>wise(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((calm(paul)&~tall(paul))))&
((?[X]:(~rich(X)))=>((~quiet(john)&~strong(john))))&
(![X]:((~curious(X)|brave(X))=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)<~>wise(X))<=>old(X)))&
(![X]:((rich(X)<~>~happy(X))<=>(~brave(X)&quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>funny(X)))&
(![X]:(brave(X)<=>(~tall(X)&generous(X))))&
(![X]:((strong(X)&~generous(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>happy(X)))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((curious(X)&~humble(X))))&
((~calm(john)<~>creative(john)))&
(wise(susan))&
(?[X]:((~humble(X)<~>~curious(X)))) | kind(mary) | [
"p1",
"p3",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8103682529260212160809295
% SZS output start Proof for 8103682529260212160809295
2. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~quiet(X0) & generous(X0))) [input p1]
4. ? [X0] : ~rich(X0) => (~strong(john) & ~quiet(john)) [input p3]
8. (~wise(paul) & ~generous(paul)) <=> ? [X0] : ~quiet(X0) [input p7]
10. ! [X0] : (brave(X0) <=> (generous(X0) & ~tall(X0))) [input p9]
13. ! [X0] : (~kind(X0) <=> rich(X0)) [input p12]
23. kind(mary) [input hypothesis]
28. ? [X0] : ~rich(X0) => ~quiet(john) [pure predicate removal 4]
32. ~quiet(john) | ! [X0] : rich(X0) [ennf transformation 28]
39. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 39]
44. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (wise(paul) | generous(paul))) [nnf transformation 8]
45. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | wise(paul) | generous(paul)) [flattening 44]
46. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | wise(paul) | generous(paul)) [rectify 45]
47. ? [X1] : ~quiet(X1) => ~quiet(sK0) [choice axiom]
48. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (~quiet(sK0) | wise(paul) | generous(paul)) [skolemisation 46,47]
49. ! [X0] : ((brave(X0) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ~brave(X0))) [nnf transformation 10]
50. ! [X0] : ((brave(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~brave(X0))) [flattening 49]
54. ! [X0] : ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))) [nnf transformation 13]
76. generous(X0) | wise(X0) | brave(X0) [cnf transformation 40]
86. ~quiet(john) | rich(X0) [cnf transformation 32]
96. ~generous(paul) | quiet(X0) [cnf transformation 48]
97. ~wise(paul) | quiet(X0) [cnf transformation 48]
100. ~brave(X0) | generous(X0) [cnf transformation 50]
105. ~kind(X0) | ~rich(X0) [cnf transformation 54]
128. kind(mary) [cnf transformation 23]
158. 7 <=> ! [X0] : rich(X0) [avatar definition]
159. rich(X0) <- (7) [avatar component clause 158]
161. 8 <=> quiet(john) [avatar definition]
163. ~quiet(john) <- (~8) [avatar component clause 161]
164. 7 | ~8 [avatar split clause 86,161,158]
166. 9 <=> ! [X0] : quiet(X0) [avatar definition]
167. quiet(X0) <- (9) [avatar component clause 166]
169. 10 <=> wise(paul) [avatar definition]
171. ~wise(paul) <- (~10) [avatar component clause 169]
172. 9 | ~10 [avatar split clause 97,169,166]
174. 11 <=> generous(paul) [avatar definition]
176. ~generous(paul) <- (~11) [avatar component clause 174]
177. 9 | ~11 [avatar split clause 96,174,166]
277. ~rich(mary) [resolution 105,128]
281. wise(paul) | brave(paul) <- (~11) [resolution 76,176]
282. brave(paul) <- (~10, ~11) [subsumption resolution 281,171]
283. generous(paul) <- (~10, ~11) [resolution 282,100]
286. $false <- (~10, ~11) [subsumption resolution 283,176]
287. 10 | 11 [avatar contradiction clause 286]
293. $false <- (~8, 9) [resolution 167,163]
298. 8 | ~9 [avatar contradiction clause 293]
299. $false <- (7) [resolution 159,277]
300. ~7 [avatar contradiction clause 299]
301. $false [avatar sat refutation 164,172,177,287,298,300]
% SZS output end Proof for 8103682529260212160809295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not wise then alice is generous or humble.
Everyone who is not funny is not happy or humble and vice versa.
If someone is either not quiet or not tall then fred is both not quiet and not old and vice versa.
If someone is both strong and humble then someone is either not rich or wise.
Everyone who is generous or humble is either wise or not rich.
If alice is strong then someone is not kind or kind and vice versa.
If john is humble then someone is funny.
If john is tall then someone is both not calm and kind and vice versa.
Everyone who is not funny or not brave is either not brave or not strong.
Everyone who is quiet is both not old and not generous and vice versa.
If someone is not brave then someone is happy or not wise.
Everyone who is not happy or humble is both wise and calm.
Everyone who is happy is kind and vice versa.
Everyone who is either tall or kind is humble.
If someone is not kind then lucy is either calm or happy and vice versa.
If mary is either not funny or generous then someone is both not curious and not kind.
Alice is both tall and strong.
Someone is generous.
Paul is brave.
John is both not brave and patient.
John is old.
Paul is both old and not happy.
Susan is both not old and not kind.
Fred is calm. | Paul is strong. | contradiction | ((?[X]:((calm(X)|~wise(X))))=>((generous(alice)|humble(alice))))&
(![X]:(~funny(X)<=>(~happy(X)|humble(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>((~quiet(fred)&~old(fred))))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((generous(X)|humble(X))=>(wise(X)<~>~rich(X))))&
((strong(alice))<=>(?[X]:((~kind(X)|kind(X)))))&
((humble(john))=>(?[X]:(funny(X))))&
((tall(john))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((~funny(X)|~brave(X))=>(~brave(X)<~>~strong(X))))&
(![X]:(quiet(X)<=>(~old(X)&~generous(X))))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:((~happy(X)|humble(X))=>(wise(X)&calm(X))))&
(![X]:(happy(X)<=>kind(X)))&
(![X]:((tall(X)<~>kind(X))=>humble(X)))&
((?[X]:(~kind(X)))<=>((calm(lucy)<~>happy(lucy))))&
(((~funny(mary)<~>generous(mary)))=>(?[X]:((~curious(X)&~kind(X)))))&
((tall(alice)&strong(alice)))&
(?[X]:(generous(X)))&
(brave(paul))&
((~brave(john)&patient(john)))&
(old(john))&
((old(paul)&~happy(paul)))&
((~old(susan)&~kind(susan)))&
(calm(fred)) | strong(paul) | [
"p1",
"p8",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4056556164393859639419360
% SZS output start Proof for 4056556164393859639419360
2. ! [X0] : (~funny(X0) <=> (humble(X0) | ~happy(X0))) [input p1]
9. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~brave(X0) <~> ~strong(X0))) [input p8]
19. brave(paul) [input p18]
22. ~happy(paul) & old(paul) [input p21]
25. strong(paul) [input hypothesis]
35. ! [X0] : ((~brave(X0) <~> ~strong(X0)) | (brave(X0) & funny(X0))) [ennf transformation 9]
40. ! [X0] : ((~funny(X0) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | funny(X0))) [nnf transformation 2]
41. ! [X0] : ((~funny(X0) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | funny(X0))) [flattening 40]
62. ! [X0] : (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | (brave(X0) & funny(X0))) [nnf transformation 35]
82. ~funny(X0) | happy(X0) [cnf transformation 41]
103. ~brave(X0) | ~strong(X0) | funny(X0) [cnf transformation 62]
128. brave(paul) [cnf transformation 19]
132. ~happy(paul) [cnf transformation 22]
136. strong(paul) [cnf transformation 25]
335. ~strong(paul) | funny(paul) [resolution 103,128]
337. funny(paul) [subsumption resolution 335,136]
339. happy(paul) [resolution 337,82]
340. $false [subsumption resolution 339,132]
% SZS output end Proof for 4056556164393859639419360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not rich is calm or not patient and vice versa. If someone is either not calm or quiet then susan is rich or not quiet and vice versa. Everyone who is either not brave or not patient is not quiet or not kind. If someone is not calm then john is both not creative and not quiet and vice versa. Everyone who is both humble and not strong is either tall or rich and vice versa. If someone is either creative or not brave then someone is either kind or not happy and vice versa. If lucy is calm or tall then susan is both not tall and not wise. If someone is either wise or generous then lucy is both patient and wise and vice versa. Everyone who is either strong or not curious is not calm or not wise and vice versa. If john is rich or not old then someone is both strong and not creative and vice versa. Everyone who is either not calm or not quiet is either not wise or not old. If lucy is either old or not rich then someone is tall. Everyone who is either kind or wise is not humble or not generous. Everyone who is humble or funny is both quiet and humble and vice versa. Everyone who is humble is both not rich and not funny and vice versa. Alice is both not brave and creative. Someone is not funny. Fred is rich. Someone is both not calm and not wise. Alice is patient. Someone is either not curious or quiet. | Susan is not strong. | neutral | (![X]:((curious(X)|~rich(X))<=>(calm(X)|~patient(X))))&
((?[X]:((~calm(X)<~>quiet(X))))<=>((rich(susan)|~quiet(susan))))&
(![X]:((~brave(X)<~>~patient(X))=>(~quiet(X)|~kind(X))))&
((?[X]:(~calm(X)))<=>((~creative(john)&~quiet(john))))&
(![X]:((humble(X)&~strong(X))<=>(tall(X)<~>rich(X))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(((calm(lucy)|tall(lucy)))=>((~tall(susan)&~wise(susan))))&
((?[X]:((wise(X)<~>generous(X))))<=>((patient(lucy)&wise(lucy))))&
(![X]:((strong(X)<~>~curious(X))<=>(~calm(X)|~wise(X))))&
(((rich(john)|~old(john)))<=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~wise(X)<~>~old(X))))&
(((old(lucy)<~>~rich(lucy)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)<~>wise(X))=>(~humble(X)|~generous(X))))&
(![X]:((humble(X)|funny(X))<=>(quiet(X)&humble(X))))&
(![X]:(humble(X)<=>(~rich(X)&~funny(X))))&
((~brave(alice)&creative(alice)))&
(?[X]:(~funny(X)))&
(rich(fred))&
(?[X]:((~calm(X)&~wise(X))))&
(patient(alice))&
(?[X]:((~curious(X)<~>quiet(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is not funny or funny is either curious or rich and vice versa. If someone is either not rich or creative then paul is both strong and not brave and vice versa. Everyone who is not wise is not humble and vice versa. Everyone who is either rich or curious is strong. Everyone who is wise or not tall is not curious or strong. Everyone who is generous is tall or not rich and vice versa. Everyone who is patient or not kind is both not kind and kind and vice versa. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Paul is not old or old. Someone is kind or rich. Someone is generous. Alice is not wise or quiet. Someone is old or brave. Mary is old or tall. | Mary is quiet. | neutral | (![X]:((~funny(X)|funny(X))<=>(curious(X)<~>rich(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((strong(paul)&~brave(paul))))&
(![X]:(~wise(X)<=>~humble(X)))&
(![X]:((rich(X)<~>curious(X))=>strong(X)))&
(![X]:((wise(X)|~tall(X))=>(~curious(X)|strong(X))))&
(![X]:(generous(X)<=>(tall(X)|~rich(X))))&
(![X]:((patient(X)|~kind(X))<=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
((~old(paul)|old(paul)))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:(generous(X)))&
((~wise(alice)|quiet(alice)))&
(?[X]:((old(X)|brave(X))))&
((old(mary)|tall(mary))) | quiet(mary) | [] | null | 0 |
Everyone who is either brave or not kind is either happy or not kind and vice versa.
Everyone who is both happy and not quiet is not old or not tall.
If john is either rich or not brave then mary is not brave.
Everyone who is tall is both not happy and generous and vice versa.
If someone is not kind then fred is wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
If someone is either tall or not quiet then susan is creative and vice versa.
Everyone who is not patient or creative is not quiet and vice versa.
Everyone who is not kind or tall is quiet.
If someone is funny then someone is creative.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
If john is patient or old then someone is both not tall and not rich and vice versa.
Someone is either not quiet or kind.
Someone is either curious or kind.
Someone is not curious.
Someone is not generous or rich.
Fred is generous or not brave.
John is both happy and generous. | Mary is not generous. | neutral | (![X]:((brave(X)<~>~kind(X))<=>(happy(X)<~>~kind(X))))&
(![X]:((happy(X)&~quiet(X))=>(~old(X)|~tall(X))))&
(((rich(john)<~>~brave(john)))=>(~brave(mary)))&
(![X]:(tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:(~kind(X)))=>((wise(fred)|~creative(fred))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(creative(susan)))&
(![X]:((~patient(X)|creative(X))<=>~quiet(X)))&
(![X]:((~kind(X)|tall(X))=>quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((curious(X)<~>kind(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~generous(X)|rich(X))))&
((generous(fred)|~brave(fred)))&
((happy(john)&generous(john))) | ~generous(mary) | [] | null | 0 |
Everyone who is humble or not humble is not strong and vice versa.
Everyone who is either not calm or not kind is not humble.
Everyone who is curious is not quiet or strong.
If someone is both old and not kind then fred is both funny and not funny.
If john is either not tall or not curious then someone is not happy and vice versa.
Everyone who is either creative or not tall is both tall and not calm.
Everyone who is either generous or calm is rich and vice versa.
If someone is either creative or strong then mary is not brave.
Everyone who is both humble and happy is either not kind or funny and vice versa.
Everyone who is not quiet is not brave or not rich and vice versa.
Everyone who is old is generous or not old and vice versa.
Everyone who is not rich is both strong and quiet.
Everyone who is both not rich and not tall is both patient and happy.
Everyone who is quiet or not funny is curious or generous.
If someone is humble or not kind then someone is not brave or not old and vice versa.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
John is either not funny or patient.
Someone is not humble.
Alice is quiet.
Alice is not happy or happy.
Someone is not rich or not curious. | Susan is humble. | contradiction | (![X]:((humble(X)|~humble(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~kind(X))=>~humble(X)))&
(![X]:(curious(X)=>(~quiet(X)|strong(X))))&
((?[X]:((old(X)&~kind(X))))=>((funny(fred)&~funny(fred))))&
(((~tall(john)<~>~curious(john)))<=>(?[X]:(~happy(X))))&
(![X]:((creative(X)<~>~tall(X))=>(tall(X)&~calm(X))))&
(![X]:((generous(X)<~>calm(X))<=>rich(X)))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((~funny(john)<~>patient(john)))&
(?[X]:(~humble(X)))&
(quiet(alice))&
((~happy(alice)|happy(alice)))&
(?[X]:((~rich(X)|~curious(X)))) | humble(susan) | [
"p1",
"p3",
"p6",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8939457266940844538159134
% SZS output start Proof for 8939457266940844538159134
2. ! [X0] : ((~calm(X0) <~> ~kind(X0)) => ~humble(X0)) [input p1]
4. ? [X0] : (~kind(X0) & old(X0)) => (~funny(fred) & funny(fred)) [input p3]
7. ! [X0] : ((generous(X0) <~> calm(X0)) <=> rich(X0)) [input p6]
10. ! [X0] : (~quiet(X0) <=> (~rich(X0) | ~brave(X0))) [input p9]
11. ! [X0] : (old(X0) <=> (~old(X0) | generous(X0))) [input p10]
12. ! [X0] : (~rich(X0) => (quiet(X0) & strong(X0))) [input p11]
22. humble(susan) [input hypothesis]
24. ! [X0] : (~humble(X0) | (~calm(X0) <=> ~kind(X0))) [ennf transformation 2]
27. (~funny(fred) & funny(fred)) | ! [X0] : (kind(X0) | ~old(X0)) [ennf transformation 4]
30. ! [X0] : ((quiet(X0) & strong(X0)) | rich(X0)) [ennf transformation 12]
37. ! [X0] : (~humble(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0)))) [nnf transformation 24]
43. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | ~rich(X0)) & (rich(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 7]
47. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & ((~rich(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 10]
48. ! [X0] : ((~quiet(X0) | (rich(X0) & brave(X0))) & (~rich(X0) | ~brave(X0) | quiet(X0))) [flattening 47]
49. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | ~old(X0))) [nnf transformation 11]
50. ! [X0] : ((old(X0) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~old(X0))) [flattening 49]
69. ~kind(X0) | ~humble(X0) | calm(X0) [cnf transformation 37]
72. funny(fred) | kind(X0) | ~old(X0) [cnf transformation 27]
73. ~funny(fred) | kind(X0) | ~old(X0) [cnf transformation 27]
85. ~rich(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 43]
96. ~quiet(X0) | rich(X0) [cnf transformation 48]
97. ~old(X0) | generous(X0) | ~old(X0) [cnf transformation 50]
99. old(X0) | old(X0) [cnf transformation 50]
101. quiet(X0) | rich(X0) [cnf transformation 30]
122. humble(susan) [cnf transformation 22]
123. ~old(X0) | generous(X0) [duplicate literal removal 97]
124. old(X0) [duplicate literal removal 99]
129. 1 <=> ! [X0] : (kind(X0) | ~old(X0)) [avatar definition]
130. kind(X0) | ~old(X0) <- (1) [avatar component clause 129]
132. 2 <=> funny(fred) [avatar definition]
135. 1 | ~2 [avatar split clause 73,132,129]
136. 1 | 2 [avatar split clause 72,132,129]
165. generous(X0) [subsumption resolution 123,124]
166. rich(X0) [subsumption resolution 101,96]
181. 12 <=> ! [X3] : kind(X3) [avatar definition]
182. kind(X3) <- (12) [avatar component clause 181]
228. kind(X0) <- (1) [subsumption resolution 130,124]
229. 12 | ~1 [avatar split clause 228,129,181]
244. ~humble(X0) | calm(X0) <- (12) [resolution 69,182]
245. calm(susan) <- (12) [resolution 244,122]
256. ~generous(X0) | ~calm(X0) [resolution 85,166]
257. ~calm(X0) [subsumption resolution 256,165]
259. $false <- (12) [resolution 257,245]
262. ~12 [avatar contradiction clause 259]
263. $false [avatar sat refutation 135,136,229,262]
% SZS output end Proof for 8939457266940844538159134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and quiet is both not tall and not funny. Everyone who is either not rich or creative is not kind or patient and vice versa. Everyone who is not curious is not generous and vice versa. Everyone who is either creative or not humble is both not tall and humble. If someone is either not brave or not quiet then mary is strong or quiet. Everyone who is tall is both not curious and old. If someone is both not tall and generous then someone is both not humble and happy. If fred is either not strong or rich then someone is either curious or tall. Everyone who is both humble and not old is both not generous and curious and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not generous and not brave is both patient and not old and vice versa. Everyone who is either old or not creative is either tall or not wise. Everyone who is either quiet or not calm is wise or not strong. If mary is either not wise or not tall then someone is creative. Everyone who is both not tall and tall is old and vice versa. Everyone who is both not generous and creative is not quiet and vice versa. Alice is not wise or calm. Someone is either funny or not funny. Someone is either happy or not kind. Someone is wise or happy. John is not tall. | Mary is not curious. | neutral | (![X]:((humble(X)&quiet(X))=>(~tall(X)&~funny(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(~kind(X)|patient(X))))&
(![X]:(~curious(X)<=>~generous(X)))&
(![X]:((creative(X)<~>~humble(X))=>(~tall(X)&humble(X))))&
((?[X]:((~brave(X)<~>~quiet(X))))=>((strong(mary)|quiet(mary))))&
(![X]:(tall(X)=>(~curious(X)&old(X))))&
((?[X]:((~tall(X)&generous(X))))=>(?[X]:((~humble(X)&happy(X)))))&
(((~strong(fred)<~>rich(fred)))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((humble(X)&~old(X))<=>(~generous(X)&curious(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~generous(X)&~brave(X))<=>(patient(X)&~old(X))))&
(![X]:((old(X)<~>~creative(X))=>(tall(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(wise(X)|~strong(X))))&
(((~wise(mary)<~>~tall(mary)))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)&tall(X))<=>old(X)))&
(![X]:((~generous(X)&creative(X))<=>~quiet(X)))&
((~wise(alice)|calm(alice)))&
(?[X]:((funny(X)<~>~funny(X))))&
(?[X]:((happy(X)<~>~kind(X))))&
(?[X]:((wise(X)|happy(X))))&
(~tall(john)) | ~curious(mary) | [] | null | 0 |
If paul is either brave or not strong then someone is both brave and not kind and vice versa.
Everyone who is both not old and wise is both funny and not happy and vice versa.
Everyone who is not tall or not humble is both not creative and wise.
Everyone who is both not brave and not generous is not happy or calm.
Everyone who is wise or patient is not quiet and vice versa.
If someone is both not kind and happy then someone is not strong.
Everyone who is creative or not quiet is both not quiet and funny and vice versa.
Everyone who is either patient or quiet is not old and vice versa.
Everyone who is both happy and not creative is calm or brave and vice versa.
Everyone who is not creative is brave or not strong.
If john is either not creative or not quiet then fred is either calm or curious.
Everyone who is both not brave and not quiet is tall or patient and vice versa.
If someone is calm then lucy is tall or not old.
If paul is both not curious and kind then someone is both not wise and brave.
Everyone who is tall is either not creative or not humble and vice versa.
Everyone who is either not rich or happy is strong or not brave.
Paul is calm or old.
Someone is kind.
Someone is not brave or not wise.
Fred is generous or not calm.
Someone is not brave or not strong.
Susan is not patient or not curious.
Fred is both generous and kind.
Someone is either generous or kind. | Fred is not creative. | entailment | (((brave(paul)<~>~strong(paul)))<=>(?[X]:((brave(X)&~kind(X)))))&
(![X]:((~old(X)&wise(X))<=>(funny(X)&~happy(X))))&
(![X]:((~tall(X)|~humble(X))=>(~creative(X)&wise(X))))&
(![X]:((~brave(X)&~generous(X))=>(~happy(X)|calm(X))))&
(![X]:((wise(X)|patient(X))<=>~quiet(X)))&
((?[X]:((~kind(X)&happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((creative(X)|~quiet(X))<=>(~quiet(X)&funny(X))))&
(![X]:((patient(X)<~>quiet(X))<=>~old(X)))&
(![X]:((happy(X)&~creative(X))<=>(calm(X)|brave(X))))&
(![X]:(~creative(X)=>(brave(X)|~strong(X))))&
(((~creative(john)<~>~quiet(john)))=>((calm(fred)<~>curious(fred))))&
(![X]:((~brave(X)&~quiet(X))<=>(tall(X)|patient(X))))&
((?[X]:(calm(X)))=>((tall(lucy)|~old(lucy))))&
(((~curious(paul)&kind(paul)))=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:(tall(X)<=>(~creative(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>happy(X))=>(strong(X)|~brave(X))))&
((calm(paul)|old(paul)))&
(?[X]:(kind(X)))&
(?[X]:((~brave(X)|~wise(X))))&
((generous(fred)|~calm(fred)))&
(?[X]:((~brave(X)|~strong(X))))&
((~patient(susan)|~curious(susan)))&
((generous(fred)&kind(fred)))&
(?[X]:((generous(X)<~>kind(X)))) | ~creative(fred) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7695617765698050818519659
% SZS output start Proof for 7695617765698050818519659
3. ! [X0] : ((~humble(X0) | ~tall(X0)) => (wise(X0) & ~creative(X0))) [input p2]
15. ! [X0] : (tall(X0) <=> (~creative(X0) <~> ~humble(X0))) [input p14]
25. creative(fred) [input hypothesis]
27. ! [X0] : ((wise(X0) & ~creative(X0)) | (humble(X0) & tall(X0))) [ennf transformation 3]
61. ! [X0] : ((tall(X0) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0)))) & (((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ~tall(X0))) [nnf transformation 15]
82. ~creative(X0) | tall(X0) [cnf transformation 27]
83. ~creative(X0) | humble(X0) [cnf transformation 27]
118. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 61]
134. creative(fred) [cnf transformation 25]
226. ~creative(X0) | ~tall(X0) [subsumption resolution 118,83]
227. ~creative(X0) [subsumption resolution 226,82]
281. $false [subsumption resolution 134,227]
% SZS output end Proof for 7695617765698050818519659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is generous then alice is creative.
Everyone who is old is either patient or happy.
Everyone who is both not patient and not tall is wise or not curious and vice versa.
Everyone who is not humble is both not patient and not curious and vice versa.
Everyone who is strong or not old is both not humble and tall and vice versa.
If john is patient then someone is curious.
If someone is either not rich or not patient then someone is not rich or not brave and vice versa.
Everyone who is either not wise or not patient is not old and vice versa.
Everyone who is not quiet is both not patient and not curious.
Everyone who is not happy or not rich is curious and vice versa.
If someone is strong or not brave then alice is not funny or not humble.
If alice is generous then paul is both strong and old and vice versa.
Everyone who is not funny is not old and vice versa.
Everyone who is both not strong and not patient is strong or not patient and vice versa.
Everyone who is both not kind and brave is either curious or not old and vice versa.
Paul is either not creative or calm.
Someone is either quiet or not strong.
Someone is either generous or curious.
Someone is brave or calm. | Alice is rich. | neutral | ((generous(lucy))=>(creative(alice)))&
(![X]:(old(X)=>(patient(X)<~>happy(X))))&
(![X]:((~patient(X)&~tall(X))<=>(wise(X)|~curious(X))))&
(![X]:(~humble(X)<=>(~patient(X)&~curious(X))))&
(![X]:((strong(X)|~old(X))<=>(~humble(X)&tall(X))))&
((patient(john))=>(?[X]:(curious(X))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
(![X]:((~wise(X)<~>~patient(X))<=>~old(X)))&
(![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((~happy(X)|~rich(X))<=>curious(X)))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(![X]:(~funny(X)<=>~old(X)))&
(![X]:((~strong(X)&~patient(X))<=>(strong(X)|~patient(X))))&
(![X]:((~kind(X)&brave(X))<=>(curious(X)<~>~old(X))))&
((~creative(paul)<~>calm(paul)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((brave(X)|calm(X)))) | rich(alice) | [] | null | 0 |
Everyone who is either humble or not strong is either not quiet or not rich.
Everyone who is not old is both old and calm.
Everyone who is patient is either not patient or not strong and vice versa.
Everyone who is both not generous and curious is not funny or old.
Everyone who is creative is both happy and not old.
If someone is both humble and creative then paul is both not funny and quiet and vice versa.
Everyone who is not generous is kind.
If someone is old or rich then john is not creative.
If someone is either not creative or not old then paul is either old or not quiet and vice versa.
If someone is not curious or not wise then someone is either not generous or not humble.
Everyone who is either calm or not quiet is both wise and not happy and vice versa.
If someone is either humble or not tall then someone is both not generous and not kind.
If someone is both not calm and wise then mary is not tall and vice versa.
Everyone who is not quiet or happy is either kind or wise.
Everyone who is either brave or not creative is not brave and vice versa.
Someone is either not tall or not quiet.
Someone is either humble or generous.
Someone is not rich.
John is both not wise and generous.
Lucy is not brave.
Someone is both quiet and humble.
Someone is rich or not wise. | Lucy is strong. | contradiction | (![X]:((humble(X)<~>~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(~old(X)=>(old(X)&calm(X))))&
(![X]:(patient(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:((~generous(X)&curious(X))=>(~funny(X)|old(X))))&
(![X]:(creative(X)=>(happy(X)&~old(X))))&
((?[X]:((humble(X)&creative(X))))<=>((~funny(paul)&quiet(paul))))&
(![X]:(~generous(X)=>kind(X)))&
((?[X]:((old(X)|rich(X))))=>(~creative(john)))&
((?[X]:((~creative(X)<~>~old(X))))<=>((old(paul)<~>~quiet(paul))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:((calm(X)<~>~quiet(X))<=>(wise(X)&~happy(X))))&
((?[X]:((humble(X)<~>~tall(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~calm(X)&wise(X))))<=>(~tall(mary)))&
(![X]:((~quiet(X)|happy(X))=>(kind(X)<~>wise(X))))&
(![X]:((brave(X)<~>~creative(X))<=>~brave(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
((~wise(john)&generous(john)))&
(~brave(lucy))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((rich(X)|~wise(X)))) | strong(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 626454107427292037362829
% SZS output start Proof for 626454107427292037362829
3. ! [X0] : (patient(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p2]
23. strong(lucy) [input hypothesis]
37. ! [X0] : ((patient(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ~patient(X0))) [nnf transformation 3]
81. ~strong(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 37]
83. patient(X0) | ~strong(X0) | patient(X0) [cnf transformation 37]
139. strong(lucy) [cnf transformation 23]
142. ~strong(X0) | ~patient(X0) [duplicate literal removal 81]
143. patient(X0) | ~strong(X0) [duplicate literal removal 83]
145. ~strong(X0) [subsumption resolution 142,143]
249. $false [subsumption resolution 139,145]
% SZS output end Proof for 626454107427292037362829
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either not humble or funny and vice versa.
Everyone who is wise is both not tall and not brave and vice versa.
Everyone who is not brave is either brave or not calm and vice versa.
Everyone who is not generous is generous.
If someone is quiet then someone is curious and vice versa.
Everyone who is both not humble and strong is both not funny and funny and vice versa.
If mary is either not quiet or not generous then susan is not funny or not curious and vice versa.
Everyone who is not calm is both not humble and tall.
Everyone who is tall or not creative is both creative and curious.
Everyone who is creative or not happy is either not patient or not brave and vice versa.
If paul is both not wise and not kind then susan is not quiet or happy and vice versa.
Everyone who is not generous is calm or not brave and vice versa.
If fred is either strong or curious then someone is not generous or not old and vice versa.
Everyone who is not happy is either not strong or not humble and vice versa.
Paul is generous.
Someone is strong or rich.
Alice is tall.
Paul is not quiet or not tall.
Alice is not funny or not humble.
Someone is not wise or not tall. | Alice is funny. | contradiction | (![X]:(~patient(X)<=>(~humble(X)<~>funny(X))))&
(![X]:(wise(X)<=>(~tall(X)&~brave(X))))&
(![X]:(~brave(X)<=>(brave(X)<~>~calm(X))))&
(![X]:(~generous(X)=>generous(X)))&
((?[X]:(quiet(X)))<=>(?[X]:(curious(X))))&
(![X]:((~humble(X)&strong(X))<=>(~funny(X)&funny(X))))&
(((~quiet(mary)<~>~generous(mary)))<=>((~funny(susan)|~curious(susan))))&
(![X]:(~calm(X)=>(~humble(X)&tall(X))))&
(![X]:((tall(X)|~creative(X))=>(creative(X)&curious(X))))&
(![X]:((creative(X)|~happy(X))<=>(~patient(X)<~>~brave(X))))&
(((~wise(paul)&~kind(paul)))<=>((~quiet(susan)|happy(susan))))&
(![X]:(~generous(X)<=>(calm(X)|~brave(X))))&
(((strong(fred)<~>curious(fred)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:(~happy(X)<=>(~strong(X)<~>~humble(X))))&
(generous(paul))&
(?[X]:((strong(X)|rich(X))))&
(tall(alice))&
((~quiet(paul)|~tall(paul)))&
((~funny(alice)|~humble(alice)))&
(?[X]:((~wise(X)|~tall(X)))) | funny(alice) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6477277746785843602506730
% SZS output start Proof for 6477277746785843602506730
1. ! [X0] : (~patient(X0) <=> (~humble(X0) <~> funny(X0))) [input p0]
3. ! [X0] : (~brave(X0) <=> (brave(X0) <~> ~calm(X0))) [input p2]
4. ! [X0] : (~generous(X0) => generous(X0)) [input p3]
8. ! [X0] : (~calm(X0) => (tall(X0) & ~humble(X0))) [input p7]
9. ! [X0] : ((~creative(X0) | tall(X0)) => (curious(X0) & creative(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | creative(X0)) <=> (~patient(X0) <~> ~brave(X0))) [input p9]
12. ! [X0] : (~generous(X0) <=> (~brave(X0) | calm(X0))) [input p11]
21. funny(alice) [input hypothesis]
24. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 4]
25. ! [X0] : ((tall(X0) & ~humble(X0)) | calm(X0)) [ennf transformation 8]
26. ! [X0] : ((curious(X0) & creative(X0)) | (creative(X0) & ~tall(X0))) [ennf transformation 9]
27. ! [X0] : ((~patient(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) & (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | patient(X0))) [nnf transformation 1]
30. ! [X0] : ((~brave(X0) | ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0)))) & (((calm(X0) | ~brave(X0)) & (~calm(X0) | brave(X0))) | brave(X0))) [nnf transformation 3]
40. ! [X0] : (((~happy(X0) | creative(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (happy(X0) & ~creative(X0)))) [nnf transformation 10]
41. ! [X0] : ((~happy(X0) | creative(X0) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) & (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (happy(X0) & ~creative(X0)))) [flattening 40]
44. ! [X0] : ((~generous(X0) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | generous(X0))) [nnf transformation 12]
45. ! [X0] : ((~generous(X0) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | generous(X0))) [flattening 44]
54. ~funny(X0) | humble(X0) | patient(X0) [cnf transformation 27]
60. ~calm(X0) | brave(X0) | brave(X0) [cnf transformation 30]
62. ~brave(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 30]
64. generous(X0) | generous(X0) [cnf transformation 24]
77. ~humble(X0) | calm(X0) [cnf transformation 25]
80. creative(X0) | creative(X0) [cnf transformation 26]
83. ~brave(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 41]
96. ~generous(X0) | brave(X0) [cnf transformation 45]
112. funny(alice) [cnf transformation 21]
113. creative(X0) [duplicate literal removal 80]
114. generous(X0) [duplicate literal removal 64]
115. ~calm(X0) | brave(X0) [duplicate literal removal 60]
116. ~calm(X0) | ~brave(X0) [duplicate literal removal 62]
117. ~calm(X0) [subsumption resolution 115,116]
154. ~humble(X0) [subsumption resolution 77,117]
157. ~brave(X0) | ~patient(X0) [subsumption resolution 83,113]
179. brave(X0) [subsumption resolution 96,114]
206. ~patient(X1) [resolution 157,179]
207. humble(alice) | patient(alice) [resolution 54,112]
208. patient(alice) [subsumption resolution 207,154]
209. $false [subsumption resolution 208,206]
% SZS output end Proof for 6477277746785843602506730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is happy. Everyone who is not quiet or not kind is not rich or quiet and vice versa. Everyone who is generous or tall is patient or creative and vice versa. If someone is both old and quiet then alice is both not old and humble and vice versa. Everyone who is happy is not brave and vice versa. If alice is both brave and not kind then john is both not tall and not strong. Everyone who is not funny is not rich or curious. If someone is generous or calm then susan is both not calm and curious and vice versa. Everyone who is not brave or tall is not quiet or generous and vice versa. Everyone who is not wise or not rich is not creative. If lucy is not happy or strong then lucy is not quiet or not generous and vice versa. If someone is either creative or tall then someone is calm or quiet and vice versa. If someone is both rich and not brave then paul is happy or strong. If john is not tall or strong then paul is both not patient and old and vice versa. Everyone who is either old or rich is both not brave and brave. If john is both not brave and tall then someone is patient or strong and vice versa. Someone is old. John is rich. Susan is not rich or not creative. Mary is both calm and creative. Someone is not old. Susan is not creative or not patient. Alice is either generous or brave. Someone is brave. | Mary is happy. | entailment | (![X]:(generous(X)=>happy(X)))&
(![X]:((~quiet(X)|~kind(X))<=>(~rich(X)|quiet(X))))&
(![X]:((generous(X)|tall(X))<=>(patient(X)|creative(X))))&
((?[X]:((old(X)&quiet(X))))<=>((~old(alice)&humble(alice))))&
(![X]:(happy(X)<=>~brave(X)))&
(((brave(alice)&~kind(alice)))=>((~tall(john)&~strong(john))))&
(![X]:(~funny(X)=>(~rich(X)|curious(X))))&
((?[X]:((generous(X)|calm(X))))<=>((~calm(susan)&curious(susan))))&
(![X]:((~brave(X)|tall(X))<=>(~quiet(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>~creative(X)))&
(((~happy(lucy)|strong(lucy)))<=>((~quiet(lucy)|~generous(lucy))))&
((?[X]:((creative(X)<~>tall(X))))<=>(?[X]:((calm(X)|quiet(X)))))&
((?[X]:((rich(X)&~brave(X))))=>((happy(paul)|strong(paul))))&
(((~tall(john)|strong(john)))<=>((~patient(paul)&old(paul))))&
(![X]:((old(X)<~>rich(X))=>(~brave(X)&brave(X))))&
(((~brave(john)&tall(john)))<=>(?[X]:((patient(X)|strong(X)))))&
(?[X]:(old(X)))&
(rich(john))&
((~rich(susan)|~creative(susan)))&
((calm(mary)&creative(mary)))&
(?[X]:(~old(X)))&
((~creative(susan)|~patient(susan)))&
((generous(alice)<~>brave(alice)))&
(?[X]:(brave(X))) | happy(mary) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6743747962348971153348992
% SZS output start Proof for 6743747962348971153348992
1. ! [X0] : (generous(X0) => happy(X0)) [input p0]
2. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> (quiet(X0) | ~rich(X0))) [input p1]
3. ! [X0] : ((tall(X0) | generous(X0)) <=> (creative(X0) | patient(X0))) [input p2]
9. ! [X0] : ((tall(X0) | ~brave(X0)) <=> (generous(X0) | ~quiet(X0))) [input p8]
10. ! [X0] : ((~rich(X0) | ~wise(X0)) => ~creative(X0)) [input p9]
20. creative(mary) & calm(mary) [input p19]
25. ~happy(mary) [input hypothesis]
27. ! [X0] : (~rich(X0) => ~creative(X0)) [pure predicate removal 10]
29. ! [X0] : (happy(X0) | ~generous(X0)) [ennf transformation 1]
32. ! [X0] : (~creative(X0) | rich(X0)) [ennf transformation 27]
36. ! [X0] : (((~kind(X0) | ~quiet(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (kind(X0) & quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | ~quiet(X0) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | (kind(X0) & quiet(X0)))) [flattening 36]
38. ! [X0] : (((tall(X0) | generous(X0)) | (~creative(X0) & ~patient(X0))) & ((creative(X0) | patient(X0)) | (~tall(X0) & ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : ((tall(X0) | generous(X0) | (~creative(X0) & ~patient(X0))) & (creative(X0) | patient(X0) | (~tall(X0) & ~generous(X0)))) [flattening 38]
51. ! [X0] : (((tall(X0) | ~brave(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~tall(X0) & brave(X0)))) [nnf transformation 9]
52. ! [X0] : ((tall(X0) | ~brave(X0) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | (~tall(X0) & brave(X0)))) [flattening 51]
75. ~generous(X0) | happy(X0) [cnf transformation 29]
76. quiet(X0) | ~rich(X0) | quiet(X0) [cnf transformation 37]
83. ~creative(X0) | generous(X0) | tall(X0) [cnf transformation 39]
98. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 52]
101. ~creative(X0) | rich(X0) [cnf transformation 32]
131. creative(mary) [cnf transformation 20]
137. ~happy(mary) [cnf transformation 25]
138. ~rich(X0) | quiet(X0) [duplicate literal removal 76]
323. rich(mary) [resolution 101,131]
326. quiet(mary) [resolution 138,323]
391. generous(mary) | tall(mary) [resolution 83,131]
395. 42 <=> tall(mary) [avatar definition]
397. tall(mary) <- (42) [avatar component clause 395]
399. 43 <=> generous(mary) [avatar definition]
401. generous(mary) <- (43) [avatar component clause 399]
402. 42 | 43 [avatar split clause 391,399,395]
441. ~quiet(mary) | generous(mary) <- (42) [resolution 397,98]
443. generous(mary) <- (42) [subsumption resolution 441,326]
444. 43 | ~42 [avatar split clause 443,395,399]
449. happy(mary) <- (43) [resolution 401,75]
450. $false <- (43) [subsumption resolution 449,137]
451. ~43 [avatar contradiction clause 450]
452. $false [avatar sat refutation 402,444,451]
% SZS output end Proof for 6743747962348971153348992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not kind is either humble or not old and vice versa.
If fred is calm or wise then fred is both brave and not humble and vice versa.
Everyone who is either not old or not patient is either funny or patient.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
If someone is both not generous and not funny then someone is either generous or not funny.
If john is not calm then someone is either generous or happy.
Everyone who is both patient and not humble is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Alice is both not old and not quiet.
Paul is both kind and not curious.
Someone is both creative and not wise.
Someone is both old and not brave. | Mary is not curious. | neutral | (![X]:((~old(X)<~>~kind(X))<=>(humble(X)<~>~old(X))))&
(((calm(fred)|wise(fred)))<=>((brave(fred)&~humble(fred))))&
(![X]:((~old(X)<~>~patient(X))=>(funny(X)<~>patient(X))))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
((~calm(john))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
((~old(alice)&~quiet(alice)))&
((kind(paul)&~curious(paul)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((old(X)&~brave(X)))) | ~curious(mary) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
If someone is kind or not strong then lucy is either creative or brave.
If susan is either creative or tall then fred is not strong.
If fred is quiet or not rich then susan is not happy or not old.
Everyone who is rich or not wise is not brave.
Everyone who is not strong or not generous is strong.
If fred is either not old or kind then someone is strong and vice versa.
Everyone who is not brave is both happy and not wise and vice versa.
Everyone who is both not wise and rich is either generous or brave and vice versa.
If susan is either strong or happy then paul is either patient or not tall and vice versa.
Everyone who is brave is either tall or not brave and vice versa.
Everyone who is either not humble or not old is both tall and old and vice versa.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind.
Paul is either wise or funny.
Lucy is both not creative and not generous.
Alice is not funny.
Someone is not humble. | Lucy is funny. | entailment | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((creative(lucy)<~>brave(lucy))))&
(((creative(susan)<~>tall(susan)))=>(~strong(fred)))&
(((quiet(fred)|~rich(fred)))=>((~happy(susan)|~old(susan))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(![X]:((~strong(X)|~generous(X))=>strong(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(strong(X))))&
(![X]:(~brave(X)<=>(happy(X)&~wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | funny(lucy) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"p11",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1118732275248484390910013
% SZS output start Proof for 1118732275248484390910013
1. ! [X0] : (funny(X0) <=> (~wise(X0) <~> calm(X0))) [input p0]
5. ! [X0] : ((~wise(X0) | rich(X0)) => ~brave(X0)) [input p4]
8. ! [X0] : (~brave(X0) <=> (~wise(X0) & happy(X0))) [input p7]
9. ! [X0] : ((rich(X0) & ~wise(X0)) <=> (generous(X0) <~> brave(X0))) [input p8]
11. ! [X0] : (brave(X0) <=> (tall(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (old(X0) & tall(X0))) [input p11]
13. ! [X0] : ((calm(X0) & patient(X0)) => (~happy(X0) | humble(X0))) [input p12]
15. ! [X0] : ((patient(X0) <~> ~wise(X0)) => rich(X0)) [input p14]
22. ~generous(lucy) & ~creative(lucy) [input p21]
25. ~funny(lucy) [input hypothesis]
31. ! [X0] : (~brave(X0) | (wise(X0) & ~rich(X0))) [ennf transformation 5]
33. ! [X0] : ((~happy(X0) | humble(X0)) | (~calm(X0) | ~patient(X0))) [ennf transformation 13]
34. ! [X0] : (~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0)) [flattening 33]
37. ! [X0] : (rich(X0) | (patient(X0) <=> ~wise(X0))) [ennf transformation 15]
38. ! [X0] : ((funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ~funny(X0))) [nnf transformation 1]
45. ! [X0] : ((~brave(X0) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | brave(X0))) [nnf transformation 8]
46. ! [X0] : ((~brave(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | brave(X0))) [flattening 45]
47. ! [X0] : (((rich(X0) & ~wise(X0)) | ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0)))) & (((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | (~rich(X0) | wise(X0)))) [nnf transformation 9]
48. ! [X0] : (((rich(X0) & ~wise(X0)) | ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0)))) & (((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | ~rich(X0) | wise(X0))) [flattening 47]
50. ! [X0] : ((brave(X0) | ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) & (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ~brave(X0))) [nnf transformation 11]
51. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 12]
52. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [flattening 51]
53. ! [X0] : (rich(X0) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) [nnf transformation 37]
71. calm(X0) | funny(X0) | wise(X0) [cnf transformation 38]
81. ~rich(X0) | ~brave(X0) [cnf transformation 31]
89. happy(X0) | brave(X0) [cnf transformation 46]
90. ~wise(X0) | brave(X0) [cnf transformation 46]
92. brave(X0) | generous(X0) | ~rich(X0) | wise(X0) [cnf transformation 48]
97. rich(X0) | generous(X0) | ~brave(X0) [cnf transformation 48]
106. ~brave(X0) | tall(X0) | ~brave(X0) [cnf transformation 50]
109. brave(X0) | tall(X0) | brave(X0) [cnf transformation 50]
113. old(X0) | ~humble(X0) | old(X0) [cnf transformation 52]
114. ~old(X0) | ~humble(X0) | ~old(X0) | ~tall(X0) [cnf transformation 52]
116. ~happy(X0) | humble(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 34]
119. patient(X0) | rich(X0) | wise(X0) [cnf transformation 53]
132. ~generous(lucy) [cnf transformation 22]
135. ~funny(lucy) [cnf transformation 25]
136. old(X0) | ~humble(X0) [duplicate literal removal 113]
137. ~old(X0) | ~humble(X0) | ~tall(X0) [duplicate literal removal 114]
138. ~brave(X0) | tall(X0) [duplicate literal removal 106]
139. tall(X0) | brave(X0) [duplicate literal removal 109]
149. 3 <=> brave(lucy) [avatar definition]
150. brave(lucy) <- (3) [avatar component clause 149]
151. ~brave(lucy) <- (~3) [avatar component clause 149]
211. ~brave(X0) | generous(X0) [subsumption resolution 97,81]
212. ~rich(X0) | generous(X0) | wise(X0) [subsumption resolution 92,81]
233. tall(X0) [subsumption resolution 138,139]
234. ~humble(X0) | ~old(X0) [subsumption resolution 137,233]
235. ~humble(X0) [subsumption resolution 136,234]
236. ~patient(X0) | ~calm(X0) | ~happy(X0) [subsumption resolution 116,235]
313. generous(lucy) <- (3) [resolution 150,211]
315. $false <- (3) [subsumption resolution 313,132]
316. ~3 [avatar contradiction clause 315]
344. ~happy(X0) | ~calm(X0) | rich(X0) | wise(X0) [resolution 236,119]
376. ~calm(X0) | rich(X0) | wise(X0) | brave(X0) [resolution 344,89]
378. ~calm(X0) | rich(X0) | brave(X0) [subsumption resolution 376,90]
396. rich(X0) | brave(X0) | funny(X0) | wise(X0) [resolution 378,71]
397. rich(X0) | brave(X0) | funny(X0) [subsumption resolution 396,90]
399. brave(X0) | funny(X0) | generous(X0) | wise(X0) [resolution 397,212]
401. generous(X0) | funny(X0) | wise(X0) [subsumption resolution 399,211]
402. funny(lucy) | wise(lucy) [resolution 401,132]
405. wise(lucy) [subsumption resolution 402,135]
416. brave(lucy) [resolution 405,90]
417. $false <- (~3) [subsumption resolution 416,151]
418. 3 [avatar contradiction clause 417]
419. $false [avatar sat refutation 316,418]
% SZS output end Proof for 1118732275248484390910013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not humble or not generous is either not quiet or tall.
Everyone who is strong is both rich and kind.
If john is both brave and not tall then someone is creative or not rich and vice versa.
If susan is brave or quiet then paul is not patient or kind.
If someone is either not rich or not generous then mary is happy.
Everyone who is funny is either not rich or kind and vice versa.
Everyone who is both funny and curious is both wise and not tall and vice versa.
Everyone who is calm is not calm or not generous and vice versa.
If someone is either not kind or not generous then fred is either not wise or not quiet and vice versa.
Everyone who is both rich and not humble is both not creative and not brave.
Everyone who is either curious or not tall is old.
If john is happy or humble then paul is both happy and rich and vice versa.
Everyone who is rich is old or wise.
If fred is both not humble and strong then paul is both generous and funny and vice versa.
If someone is either not wise or kind then mary is calm and vice versa.
Everyone who is not calm or old is either patient or not tall.
John is both not tall and curious.
Paul is both not funny and not creative.
Lucy is not rich or not quiet.
Someone is strong or old.
Someone is either not kind or not funny.
Susan is both not tall and not quiet.
Someone is strong.
Paul is wise. | Mary is happy. | entailment | (![X]:((~humble(X)|~generous(X))=>(~quiet(X)<~>tall(X))))&
(![X]:(strong(X)=>(rich(X)&kind(X))))&
(((brave(john)&~tall(john)))<=>(?[X]:((creative(X)|~rich(X)))))&
(((brave(susan)|quiet(susan)))=>((~patient(paul)|kind(paul))))&
((?[X]:((~rich(X)<~>~generous(X))))=>(happy(mary)))&
(![X]:(funny(X)<=>(~rich(X)<~>kind(X))))&
(![X]:((funny(X)&curious(X))<=>(wise(X)&~tall(X))))&
(![X]:(calm(X)<=>(~calm(X)|~generous(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((rich(X)&~humble(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~tall(X))=>old(X)))&
(((happy(john)|humble(john)))<=>((happy(paul)&rich(paul))))&
(![X]:(rich(X)=>(old(X)|wise(X))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
((~tall(john)&curious(john)))&
((~funny(paul)&~creative(paul)))&
((~rich(lucy)|~quiet(lucy)))&
(?[X]:((strong(X)|old(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
((~tall(susan)&~quiet(susan)))&
(?[X]:(strong(X)))&
(wise(paul)) | happy(mary) | [
"p1",
"p4",
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6198974269321747869698363
% SZS output start Proof for 6198974269321747869698363
2. ! [X0] : (strong(X0) => (kind(X0) & rich(X0))) [input p1]
5. ? [X0] : (~rich(X0) <~> ~generous(X0)) => happy(mary) [input p4]
8. ! [X0] : (calm(X0) <=> (~generous(X0) | ~calm(X0))) [input p7]
23. ? [X0] : strong(X0) [input p22]
25. ~happy(mary) [input hypothesis]
27. ! [X0] : ((kind(X0) & rich(X0)) | ~strong(X0)) [ennf transformation 2]
30. happy(mary) | ! [X0] : (~rich(X0) <=> ~generous(X0)) [ennf transformation 5]
43. happy(mary) | ! [X0] : ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))) [nnf transformation 30]
47. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 8]
48. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ~calm(X0))) [flattening 47]
68. ? [X0] : strong(X0) => strong(sK5) [choice axiom]
69. strong(sK5) [skolemisation 23,68]
74. ~strong(X0) | rich(X0) [cnf transformation 27]
84. happy(mary) | ~rich(X0) | generous(X0) [cnf transformation 43]
93. ~generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 48]
94. calm(X0) | calm(X0) [cnf transformation 48]
136. strong(sK5) [cnf transformation 69]
138. ~happy(mary) [cnf transformation 25]
139. ~generous(X0) | ~calm(X0) [duplicate literal removal 93]
140. calm(X0) [duplicate literal removal 94]
187. 11 <=> ! [X0] : (~rich(X0) | generous(X0)) [avatar definition]
188. ~rich(X0) | generous(X0) <- (11) [avatar component clause 187]
190. 12 <=> happy(mary) [avatar definition]
193. 11 | 12 [avatar split clause 84,190,187]
198. ~generous(X0) [subsumption resolution 139,140]
301. ~12 [avatar split clause 138,190]
302. ~rich(X0) <- (11) [subsumption resolution 188,198]
303. rich(sK5) [resolution 74,136]
305. $false <- (11) [subsumption resolution 303,302]
306. ~11 [avatar contradiction clause 305]
309. $false [avatar sat refutation 193,301,306]
% SZS output end Proof for 6198974269321747869698363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not humble is tall and vice versa.
Everyone who is both rich and not curious is both not happy and patient.
If someone is not calm or not quiet then lucy is creative or calm and vice versa.
Everyone who is not creative is both not curious and rich.
Everyone who is strong is either not quiet or kind and vice versa.
If alice is not calm then john is either humble or not tall and vice versa.
If fred is not curious or not wise then lucy is funny and vice versa.
Everyone who is strong or not kind is either not generous or not creative and vice versa.
If someone is either brave or humble then alice is either tall or not kind.
Everyone who is both old and humble is not curious or not happy and vice versa.
Everyone who is not brave is either not kind or humble.
If lucy is either strong or calm then john is either rich or not brave and vice versa.
Everyone who is not happy is both tall and kind.
Everyone who is not funny or patient is either not humble or not patient.
Everyone who is both humble and not happy is either generous or calm and vice versa.
If someone is either not happy or curious then someone is both not curious and funny.
Lucy is both not brave and not quiet.
Someone is both brave and creative.
Fred is happy.
Lucy is tall or creative.
Someone is funny.
Someone is not generous or brave.
Paul is not calm. | Fred is not calm. | neutral | (![X]:((funny(X)|~humble(X))<=>tall(X)))&
(![X]:((rich(X)&~curious(X))=>(~happy(X)&patient(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((creative(lucy)|calm(lucy))))&
(![X]:(~creative(X)=>(~curious(X)&rich(X))))&
(![X]:(strong(X)<=>(~quiet(X)<~>kind(X))))&
((~calm(alice))<=>((humble(john)<~>~tall(john))))&
(((~curious(fred)|~wise(fred)))<=>(funny(lucy)))&
(![X]:((strong(X)|~kind(X))<=>(~generous(X)<~>~creative(X))))&
((?[X]:((brave(X)<~>humble(X))))=>((tall(alice)<~>~kind(alice))))&
(![X]:((old(X)&humble(X))<=>(~curious(X)|~happy(X))))&
(![X]:(~brave(X)=>(~kind(X)<~>humble(X))))&
(((strong(lucy)<~>calm(lucy)))<=>((rich(john)<~>~brave(john))))&
(![X]:(~happy(X)=>(tall(X)&kind(X))))&
(![X]:((~funny(X)|patient(X))=>(~humble(X)<~>~patient(X))))&
(![X]:((humble(X)&~happy(X))<=>(generous(X)<~>calm(X))))&
((?[X]:((~happy(X)<~>curious(X))))=>(?[X]:((~curious(X)&funny(X)))))&
((~brave(lucy)&~quiet(lucy)))&
(?[X]:((brave(X)&creative(X))))&
(happy(fred))&
((tall(lucy)|creative(lucy)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|brave(X))))&
(~calm(paul)) | ~calm(fred) | [] | null | 0 |
If fred is both wise and curious then susan is both not wise and curious.
Everyone who is not tall or rich is both not old and humble and vice versa.
If susan is both not wise and not funny then lucy is not wise and vice versa.
If susan is both generous and patient then someone is not brave or not tall.
If fred is humble or not old then mary is calm or not tall and vice versa.
If someone is not generous then someone is not kind and vice versa.
Everyone who is not calm is not tall.
Everyone who is not tall is not tall or strong and vice versa.
Everyone who is not wise or tall is calm or not brave and vice versa.
Everyone who is not strong or curious is both creative and brave and vice versa.
Everyone who is patient is not strong or not brave.
Everyone who is humble is both wise and not humble and vice versa.
If someone is either not happy or not calm then john is either generous or not humble.
If alice is both kind and quiet then someone is creative or not patient.
If paul is either curious or not brave then someone is both not kind and not funny and vice versa.
Someone is patient or humble.
Paul is both old and not wise.
Someone is kind.
John is old.
Susan is patient or wise.
Someone is not wise.
Someone is either creative or generous. | Lucy is old. | neutral | (((wise(fred)&curious(fred)))=>((~wise(susan)&curious(susan))))&
(![X]:((~tall(X)|rich(X))<=>(~old(X)&humble(X))))&
(((~wise(susan)&~funny(susan)))<=>(~wise(lucy)))&
(((generous(susan)&patient(susan)))=>(?[X]:((~brave(X)|~tall(X)))))&
(((humble(fred)|~old(fred)))<=>((calm(mary)|~tall(mary))))&
((?[X]:(~generous(X)))<=>(?[X]:(~kind(X))))&
(![X]:(~calm(X)=>~tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)|strong(X))))&
(![X]:((~wise(X)|tall(X))<=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|curious(X))<=>(creative(X)&brave(X))))&
(![X]:(patient(X)=>(~strong(X)|~brave(X))))&
(![X]:(humble(X)<=>(wise(X)&~humble(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>((generous(john)<~>~humble(john))))&
(((kind(alice)&quiet(alice)))=>(?[X]:((creative(X)|~patient(X)))))&
(((curious(paul)<~>~brave(paul)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(?[X]:((patient(X)|humble(X))))&
((old(paul)&~wise(paul)))&
(?[X]:(kind(X)))&
(old(john))&
((patient(susan)|wise(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((creative(X)<~>generous(X)))) | old(lucy) | [] | null | 0 |
Everyone who is either not strong or not patient is not calm or not quiet and vice versa.
If paul is both strong and generous then someone is patient and vice versa.
Everyone who is creative is either not rich or tall and vice versa.
If someone is wise or calm then fred is old or not tall.
If someone is creative or not quiet then someone is both quiet and rich.
If paul is both curious and generous then someone is humble or funny.
If someone is curious or not patient then someone is both not tall and not wise.
If john is not curious or happy then susan is tall or curious and vice versa.
Everyone who is creative is both humble and not creative.
Everyone who is either creative or not generous is not funny.
Everyone who is not calm is either tall or not quiet and vice versa.
Everyone who is both kind and rich is not calm and vice versa.
If someone is either rich or calm then susan is not curious and vice versa.
If alice is not funny then paul is humble and vice versa.
Everyone who is either creative or rich is patient and vice versa.
Everyone who is both wise and not patient is both generous and not tall.
Paul is either creative or not rich.
Fred is not tall.
Fred is not kind or not rich.
Someone is either not brave or not humble.
Someone is not strong or not humble.
Susan is brave or not strong.
Someone is either not wise or not kind. | Paul is not strong. | contradiction | (![X]:((~strong(X)<~>~patient(X))<=>(~calm(X)|~quiet(X))))&
(((strong(paul)&generous(paul)))<=>(?[X]:(patient(X))))&
(![X]:(creative(X)<=>(~rich(X)<~>tall(X))))&
((?[X]:((wise(X)|calm(X))))=>((old(fred)|~tall(fred))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(((curious(paul)&generous(paul)))=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((curious(X)|~patient(X))))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~curious(john)|happy(john)))<=>((tall(susan)|curious(susan))))&
(![X]:(creative(X)=>(humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((kind(X)&rich(X))<=>~calm(X)))&
((?[X]:((rich(X)<~>calm(X))))<=>(~curious(susan)))&
((~funny(alice))<=>(humble(paul)))&
(![X]:((creative(X)<~>rich(X))<=>patient(X)))&
(![X]:((wise(X)&~patient(X))=>(generous(X)&~tall(X))))&
((creative(paul)<~>~rich(paul)))&
(~tall(fred))&
((~kind(fred)|~rich(fred)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((brave(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~kind(X)))) | ~strong(paul) | [
"p1",
"p2",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5249900065349049170802744
% SZS output start Proof for 5249900065349049170802744
2. (generous(paul) & strong(paul)) <=> ? [X0] : patient(X0) [input p1]
3. ! [X0] : (creative(X0) <=> (~rich(X0) <~> tall(X0))) [input p2]
9. ! [X0] : (creative(X0) => (~creative(X0) & humble(X0))) [input p8]
15. ! [X0] : ((creative(X0) <~> rich(X0)) <=> patient(X0)) [input p14]
18. ~tall(fred) [input p17]
24. ~strong(paul) [input hypothesis]
32. ! [X0] : ((~creative(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 9]
38. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (~generous(paul) | ~strong(paul))) [nnf transformation 2]
39. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | ~generous(paul) | ~strong(paul)) [flattening 38]
40. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | ~generous(paul) | ~strong(paul)) [rectify 39]
41. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
42. ((generous(paul) & strong(paul)) | ! [X0] : ~patient(X0)) & (patient(sK0) | ~generous(paul) | ~strong(paul)) [skolemisation 40,41]
43. ! [X0] : ((creative(X0) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0)))) & (((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | ~creative(X0))) [nnf transformation 3]
63. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ~patient(X0)) & (patient(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 15]
80. strong(paul) | ~patient(X0) [cnf transformation 42]
84. tall(X0) | creative(X0) | rich(X0) [cnf transformation 43]
100. ~creative(X0) | ~creative(X0) [cnf transformation 32]
117. ~rich(X0) | creative(X0) | patient(X0) [cnf transformation 63]
124. ~tall(fred) [cnf transformation 18]
132. ~strong(paul) [cnf transformation 24]
133. ~creative(X0) [duplicate literal removal 100]
135. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
136. ~patient(X0) <- (1) [avatar component clause 135]
143. 3 <=> strong(paul) [avatar definition]
146. 1 | 3 [avatar split clause 80,143,135]
161. 7 <=> ! [X1] : ~creative(X1) [avatar definition]
162. ~creative(X1) <- (7) [avatar component clause 161]
221. 7 [avatar split clause 133,161]
266. 29 <=> rich(fred) [avatar definition]
267. rich(fred) <- (29) [avatar component clause 266]
308. ~3 [avatar split clause 132,143]
316. creative(fred) | rich(fred) [resolution 84,124]
320. rich(fred) <- (7) [subsumption resolution 316,162]
325. 29 | ~7 [avatar split clause 320,161,266]
403. creative(fred) | patient(fred) <- (29) [resolution 117,267]
407. patient(fred) <- (7, 29) [subsumption resolution 403,162]
408. $false <- (1, 7, 29) [subsumption resolution 407,136]
409. ~1 | ~7 | ~29 [avatar contradiction clause 408]
419. $false [avatar sat refutation 146,221,308,325,409]
% SZS output end Proof for 5249900065349049170802744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or generous then alice is funny.
If someone is either humble or kind then someone is both not brave and not patient.
Everyone who is strong is generous or happy and vice versa.
Everyone who is not patient is creative and vice versa.
If someone is happy or not tall then someone is both not kind and humble and vice versa.
Everyone who is not creative is both old and wise and vice versa.
Everyone who is both not strong and not creative is wise or humble and vice versa.
Everyone who is not patient or wise is not quiet and vice versa.
Everyone who is either brave or old is both quiet and not patient.
Everyone who is brave is quiet or old and vice versa.
Everyone who is old or tall is wise.
Everyone who is happy or not brave is not tall and vice versa.
Everyone who is either old or wise is both kind and not curious and vice versa.
If someone is both tall and not quiet then someone is humble.
Everyone who is old or strong is not brave or not funny and vice versa.
Someone is both not happy and kind.
Lucy is not brave or not patient.
Someone is either quiet or not wise.
Someone is both not calm and not funny.
Susan is not rich.
Paul is both not strong and brave.
Someone is quiet or not calm. | Alice is not patient. | entailment | ((?[X]:((~happy(X)<~>generous(X))))=>(funny(alice)))&
((?[X]:((humble(X)<~>kind(X))))=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:(strong(X)<=>(generous(X)|happy(X))))&
(![X]:(~patient(X)<=>creative(X)))&
((?[X]:((happy(X)|~tall(X))))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:(~creative(X)<=>(old(X)&wise(X))))&
(![X]:((~strong(X)&~creative(X))<=>(wise(X)|humble(X))))&
(![X]:((~patient(X)|wise(X))<=>~quiet(X)))&
(![X]:((brave(X)<~>old(X))=>(quiet(X)&~patient(X))))&
(![X]:(brave(X)<=>(quiet(X)|old(X))))&
(![X]:((old(X)|tall(X))=>wise(X)))&
(![X]:((happy(X)|~brave(X))<=>~tall(X)))&
(![X]:((old(X)<~>wise(X))<=>(kind(X)&~curious(X))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:(humble(X))))&
(![X]:((old(X)|strong(X))<=>(~brave(X)|~funny(X))))&
(?[X]:((~happy(X)&kind(X))))&
((~brave(lucy)|~patient(lucy)))&
(?[X]:((quiet(X)<~>~wise(X))))&
(?[X]:((~calm(X)&~funny(X))))&
(~rich(susan))&
((~strong(paul)&brave(paul)))&
(?[X]:((quiet(X)|~calm(X)))) | ~patient(alice) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5882370464891568079686732
% SZS output start Proof for 5882370464891568079686732
1. ? [X0] : (~happy(X0) <~> generous(X0)) => funny(alice) [input p0]
3. ! [X0] : (strong(X0) <=> (happy(X0) | generous(X0))) [input p2]
6. ! [X0] : (~creative(X0) <=> (wise(X0) & old(X0))) [input p5]
7. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (humble(X0) | wise(X0))) [input p6]
8. ! [X0] : ((wise(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p7]
9. ! [X0] : ((brave(X0) <~> old(X0)) => (~patient(X0) & quiet(X0))) [input p8]
10. ! [X0] : (brave(X0) <=> (old(X0) | quiet(X0))) [input p9]
15. ! [X0] : ((strong(X0) | old(X0)) <=> (~funny(X0) | ~brave(X0))) [input p14]
21. brave(paul) & ~strong(paul) [input p20]
23. patient(alice) [input hypothesis]
30. funny(alice) | ! [X0] : (~happy(X0) <=> generous(X0)) [ennf transformation 1]
32. ! [X0] : ((~patient(X0) & quiet(X0)) | (brave(X0) <=> old(X0))) [ennf transformation 9]
35. funny(alice) | ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))) [nnf transformation 30]
40. ! [X0] : ((strong(X0) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 3]
41. ! [X0] : ((strong(X0) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | ~strong(X0))) [flattening 40]
48. ! [X0] : ((~creative(X0) | (~wise(X0) | ~old(X0))) & ((wise(X0) & old(X0)) | creative(X0))) [nnf transformation 6]
49. ! [X0] : ((~creative(X0) | ~wise(X0) | ~old(X0)) & ((wise(X0) & old(X0)) | creative(X0))) [flattening 48]
50. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~humble(X0) & ~wise(X0))) & ((humble(X0) | wise(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 7]
51. ! [X0] : (((~creative(X0) & ~strong(X0)) | (~humble(X0) & ~wise(X0))) & (humble(X0) | wise(X0) | creative(X0) | strong(X0))) [flattening 50]
52. ! [X0] : (((wise(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~wise(X0) & patient(X0)))) [nnf transformation 8]
53. ! [X0] : ((wise(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~wise(X0) & patient(X0)))) [flattening 52]
54. ! [X0] : ((~patient(X0) & quiet(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) [nnf transformation 32]
55. ! [X0] : ((brave(X0) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | ~brave(X0))) [nnf transformation 10]
56. ! [X0] : ((brave(X0) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | ~brave(X0))) [flattening 55]
64. ! [X0] : (((strong(X0) | old(X0)) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | (~strong(X0) & ~old(X0)))) [nnf transformation 15]
65. ! [X0] : ((strong(X0) | old(X0) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | (~strong(X0) & ~old(X0)))) [flattening 64]
73. funny(alice) | generous(X0) | happy(X0) [cnf transformation 35]
80. ~generous(X0) | strong(X0) [cnf transformation 41]
81. ~happy(X0) | strong(X0) [cnf transformation 41]
89. old(X0) | creative(X0) [cnf transformation 49]
95. ~wise(X0) | ~creative(X0) [cnf transformation 51]
99. ~patient(X0) | wise(X0) | quiet(X0) [cnf transformation 53]
102. ~patient(X0) | old(X0) | ~brave(X0) [cnf transformation 54]
105. ~quiet(X0) | brave(X0) [cnf transformation 56]
106. ~old(X0) | brave(X0) [cnf transformation 56]
119. ~funny(X0) | ~brave(X0) | ~old(X0) [cnf transformation 65]
129. ~strong(paul) [cnf transformation 21]
131. patient(alice) [cnf transformation 23]
136. 2 <=> funny(alice) [avatar definition]
138. funny(alice) <- (2) [avatar component clause 136]
141. 3 <=> ! [X0] : (generous(X0) | happy(X0)) [avatar definition]
142. generous(X0) | happy(X0) <- (3) [avatar component clause 141]
143. 3 | 2 [avatar split clause 73,136,141]
200. ~old(X0) | ~funny(X0) [subsumption resolution 119,106]
228. wise(alice) | quiet(alice) [resolution 99,131]
230. 18 <=> quiet(alice) [avatar definition]
232. quiet(alice) <- (18) [avatar component clause 230]
234. 19 <=> wise(alice) [avatar definition]
236. wise(alice) <- (19) [avatar component clause 234]
237. 18 | 19 [avatar split clause 228,234,230]
238. brave(alice) <- (18) [resolution 232,105]
257. old(alice) | ~brave(alice) [resolution 102,131]
258. old(alice) <- (18) [subsumption resolution 257,238]
260. ~funny(alice) <- (18) [resolution 258,200]
263. $false <- (2, 18) [subsumption resolution 260,138]
264. ~2 | ~18 [avatar contradiction clause 263]
272. 23 <=> old(alice) [avatar definition]
273. ~old(alice) <- (~23) [avatar component clause 272]
274. old(alice) <- (23) [avatar component clause 272]
288. ~creative(alice) <- (19) [resolution 236,95]
291. 26 <=> creative(alice) [avatar definition]
293. ~creative(alice) <- (~26) [avatar component clause 291]
295. ~26 | ~19 [avatar split clause 288,234,291]
305. ~funny(alice) <- (23) [resolution 274,200]
314. $false <- (2, 23) [subsumption resolution 305,138]
315. ~2 | ~23 [avatar contradiction clause 314]
319. creative(alice) <- (~23) [resolution 273,89]
320. $false <- (~23, ~26) [subsumption resolution 319,293]
321. 23 | 26 [avatar contradiction clause 320]
339. happy(X1) | strong(X1) <- (3) [resolution 142,80]
340. strong(X1) <- (3) [subsumption resolution 339,81]
384. $false <- (3) [resolution 340,129]
389. ~3 [avatar contradiction clause 384]
390. $false [avatar sat refutation 143,237,264,295,315,321,389]
% SZS output end Proof for 5882370464891568079686732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and kind is not generous and vice versa.
If john is both not curious and tall then someone is either not tall or kind and vice versa.
Everyone who is not brave is both kind and creative and vice versa.
If someone is either strong or humble then someone is both strong and wise and vice versa.
Everyone who is quiet is not patient or not generous.
If fred is either patient or not strong then susan is not rich and vice versa.
Everyone who is not wise is both not curious and old.
If fred is not humble then alice is not funny or not curious and vice versa.
Everyone who is either not rich or not happy is not creative and vice versa.
Everyone who is happy or patient is either patient or not rich and vice versa.
If paul is happy then lucy is strong or not kind.
If someone is not patient or not quiet then alice is both not kind and not creative.
If paul is not happy then someone is humble or not creative and vice versa.
Everyone who is both patient and not happy is funny and vice versa.
If someone is either not calm or not kind then someone is not generous and vice versa.
Everyone who is not quiet or not funny is either not happy or not quiet.
Lucy is not happy or kind.
Fred is either quiet or kind.
John is rich or not tall.
Fred is both not brave and not calm.
Fred is generous.
Someone is not patient or strong.
Fred is rich or not humble.
John is not kind. | Fred is not funny. | entailment | (![X]:((funny(X)&kind(X))<=>~generous(X)))&
(((~curious(john)&tall(john)))<=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:(~brave(X)<=>(kind(X)&creative(X))))&
((?[X]:((strong(X)<~>humble(X))))<=>(?[X]:((strong(X)&wise(X)))))&
(![X]:(quiet(X)=>(~patient(X)|~generous(X))))&
(((patient(fred)<~>~strong(fred)))<=>(~rich(susan)))&
(![X]:(~wise(X)=>(~curious(X)&old(X))))&
((~humble(fred))<=>((~funny(alice)|~curious(alice))))&
(![X]:((~rich(X)<~>~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|patient(X))<=>(patient(X)<~>~rich(X))))&
((happy(paul))=>((strong(lucy)|~kind(lucy))))&
((?[X]:((~patient(X)|~quiet(X))))=>((~kind(alice)&~creative(alice))))&
((~happy(paul))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((patient(X)&~happy(X))<=>funny(X)))&
((?[X]:((~calm(X)<~>~kind(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~happy(X)<~>~quiet(X))))&
((~happy(lucy)|kind(lucy)))&
((quiet(fred)<~>kind(fred)))&
((rich(john)|~tall(john)))&
((~brave(fred)&~calm(fred)))&
(generous(fred))&
(?[X]:((~patient(X)|strong(X))))&
((rich(fred)|~humble(fred)))&
(~kind(john)) | ~funny(fred) | [
"p0",
"p2",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1665494863988714278646439
% SZS output start Proof for 1665494863988714278646439
1. ! [X0] : ((kind(X0) & funny(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : (~brave(X0) <=> (creative(X0) & kind(X0))) [input p2]
20. ~calm(fred) & ~brave(fred) [input p19]
21. generous(fred) [input p20]
25. funny(fred) [input hypothesis]
28. ! [X0] : (~brave(X0) => (creative(X0) & kind(X0))) [unused predicate definition removal 3]
30. ! [X0] : ((creative(X0) & kind(X0)) | brave(X0)) [ennf transformation 28]
38. ! [X0] : (((kind(X0) & funny(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 1]
39. ! [X0] : (((kind(X0) & funny(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | ~funny(X0))) [flattening 38]
71. ~generous(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 39]
80. brave(X0) | kind(X0) [cnf transformation 30]
130. ~brave(fred) [cnf transformation 20]
132. generous(fred) [cnf transformation 21]
136. funny(fred) [cnf transformation 25]
314. 39 <=> kind(fred) [avatar definition]
315. kind(fred) <- (39) [avatar component clause 314]
342. kind(fred) [resolution 80,130]
345. 39 [avatar split clause 342,314]
360. ~kind(fred) | ~funny(fred) [resolution 71,132]
363. ~funny(fred) <- (39) [subsumption resolution 360,315]
364. $false <- (39) [subsumption resolution 363,136]
365. ~39 [avatar contradiction clause 364]
366. $false [avatar sat refutation 345,365]
% SZS output end Proof for 1665494863988714278646439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not quiet is both not wise and not patient.
If someone is either not quiet or not curious then someone is both wise and quiet and vice versa.
Everyone who is both not kind and tall is both not old and brave.
Everyone who is both not patient and curious is kind.
If alice is not calm then mary is not patient or not happy and vice versa.
If mary is generous then lucy is both funny and happy.
Everyone who is either patient or not old is not calm and vice versa.
If someone is either humble or happy then fred is not quiet or not kind.
If someone is either brave or calm then someone is both not humble and not creative and vice versa.
Everyone who is either not kind or curious is quiet and vice versa.
If lucy is either not tall or not generous then john is not humble.
Everyone who is rich or quiet is kind and vice versa.
Everyone who is both tall and calm is either not strong or not tall.
If susan is not curious or patient then mary is wise and vice versa.
Everyone who is not quiet is not old or old and vice versa.
If mary is not tall then someone is both kind and strong and vice versa.
Someone is not creative or not humble.
Someone is both not calm and generous.
Susan is either not brave or quiet.
Fred is patient.
Someone is not rich or old. | Susan is old. | neutral | (![X]:((~tall(X)&~quiet(X))=>(~wise(X)&~patient(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((wise(X)&quiet(X)))))&
(![X]:((~kind(X)&tall(X))=>(~old(X)&brave(X))))&
(![X]:((~patient(X)&curious(X))=>kind(X)))&
((~calm(alice))<=>((~patient(mary)|~happy(mary))))&
((generous(mary))=>((funny(lucy)&happy(lucy))))&
(![X]:((patient(X)<~>~old(X))<=>~calm(X)))&
((?[X]:((humble(X)<~>happy(X))))=>((~quiet(fred)|~kind(fred))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:((~kind(X)<~>curious(X))<=>quiet(X)))&
(((~tall(lucy)<~>~generous(lucy)))=>(~humble(john)))&
(![X]:((rich(X)|quiet(X))<=>kind(X)))&
(![X]:((tall(X)&calm(X))=>(~strong(X)<~>~tall(X))))&
(((~curious(susan)|patient(susan)))<=>(wise(mary)))&
(![X]:(~quiet(X)<=>(~old(X)|old(X))))&
((~tall(mary))<=>(?[X]:((kind(X)&strong(X)))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:((~calm(X)&generous(X))))&
((~brave(susan)<~>quiet(susan)))&
(patient(fred))&
(?[X]:((~rich(X)|old(X)))) | old(susan) | [] | null | 0 |
Everyone who is humble or not old is both wise and generous. Everyone who is both not quiet and not happy is kind or wise and vice versa. Everyone who is creative or not curious is not curious or not kind and vice versa. If alice is either happy or generous then alice is not happy or not wise. Everyone who is not creative or not patient is not quiet. If someone is not curious or not quiet then susan is rich and vice versa. Everyone who is both not humble and creative is either rich or old and vice versa. If someone is not brave or not creative then alice is either patient or funny and vice versa. Everyone who is generous is either kind or not funny and vice versa. Everyone who is generous is calm and vice versa. Everyone who is either tall or not tall is both curious and creative and vice versa. Everyone who is calm or not funny is not funny or not generous. If someone is either curious or not happy then fred is either not funny or brave and vice versa. Everyone who is both not rich and generous is both not quiet and not old. If someone is not brave then lucy is both curious and not old. Everyone who is not kind or creative is not tall or calm and vice versa. Lucy is both tall and not funny. Someone is strong. Susan is not quiet. Someone is not happy. Someone is not wise or not curious. Someone is not tall. Someone is both not old and rich. Someone is both patient and not tall. | Lucy is rich. | neutral | (![X]:((humble(X)|~old(X))=>(wise(X)&generous(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(kind(X)|wise(X))))&
(![X]:((creative(X)|~curious(X))<=>(~curious(X)|~kind(X))))&
(((happy(alice)<~>generous(alice)))=>((~happy(alice)|~wise(alice))))&
(![X]:((~creative(X)|~patient(X))=>~quiet(X)))&
((?[X]:((~curious(X)|~quiet(X))))<=>(rich(susan)))&
(![X]:((~humble(X)&creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~brave(X)|~creative(X))))<=>((patient(alice)<~>funny(alice))))&
(![X]:(generous(X)<=>(kind(X)<~>~funny(X))))&
(![X]:(generous(X)<=>calm(X)))&
(![X]:((tall(X)<~>~tall(X))<=>(curious(X)&creative(X))))&
(![X]:((calm(X)|~funny(X))=>(~funny(X)|~generous(X))))&
((?[X]:((curious(X)<~>~happy(X))))<=>((~funny(fred)<~>brave(fred))))&
(![X]:((~rich(X)&generous(X))=>(~quiet(X)&~old(X))))&
((?[X]:(~brave(X)))=>((curious(lucy)&~old(lucy))))&
(![X]:((~kind(X)|creative(X))<=>(~tall(X)|calm(X))))&
((tall(lucy)&~funny(lucy)))&
(?[X]:(strong(X)))&
(~quiet(susan))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~old(X)&rich(X))))&
(?[X]:((patient(X)&~tall(X)))) | rich(lucy) | [] | null | 0 |
If someone is both not happy and funny then someone is patient or calm.
If mary is calm or not brave then john is old or not strong.
Everyone who is not quiet or humble is not strong or not old.
If someone is both rich and not humble then someone is either happy or creative.
Everyone who is both strong and not brave is not kind and vice versa.
If john is both wise and tall then fred is brave and vice versa.
Everyone who is either calm or wise is both not kind and kind.
If alice is either curious or not calm then someone is patient.
Everyone who is both old and not curious is not quiet or not humble and vice versa.
If someone is brave then someone is both not patient and curious.
Everyone who is not humble or generous is creative.
If john is not strong or rich then paul is not happy or strong and vice versa.
If lucy is both not tall and not rich then mary is both strong and not generous and vice versa.
Everyone who is not wise or generous is not curious and vice versa.
Everyone who is both funny and not brave is either calm or happy and vice versa.
If someone is not patient then fred is both not old and not calm.
Alice is both not tall and generous.
Someone is not strong.
Someone is either happy or strong.
Someone is tall or humble.
Paul is either not patient or kind.
John is not wise or humble.
Someone is not tall or not quiet.
John is either brave or rich. | Alice is happy. | neutral | ((?[X]:((~happy(X)&funny(X))))=>(?[X]:((patient(X)|calm(X)))))&
(((calm(mary)|~brave(mary)))=>((old(john)|~strong(john))))&
(![X]:((~quiet(X)|humble(X))=>(~strong(X)|~old(X))))&
((?[X]:((rich(X)&~humble(X))))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:((strong(X)&~brave(X))<=>~kind(X)))&
(((wise(john)&tall(john)))<=>(brave(fred)))&
(![X]:((calm(X)<~>wise(X))=>(~kind(X)&kind(X))))&
(((curious(alice)<~>~calm(alice)))=>(?[X]:(patient(X))))&
(![X]:((old(X)&~curious(X))<=>(~quiet(X)|~humble(X))))&
((?[X]:(brave(X)))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~humble(X)|generous(X))=>creative(X)))&
(((~strong(john)|rich(john)))<=>((~happy(paul)|strong(paul))))&
(((~tall(lucy)&~rich(lucy)))<=>((strong(mary)&~generous(mary))))&
(![X]:((~wise(X)|generous(X))<=>~curious(X)))&
(![X]:((funny(X)&~brave(X))<=>(calm(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~old(fred)&~calm(fred))))&
((~tall(alice)&generous(alice)))&
(?[X]:(~strong(X)))&
(?[X]:((happy(X)<~>strong(X))))&
(?[X]:((tall(X)|humble(X))))&
((~patient(paul)<~>kind(paul)))&
((~wise(john)|humble(john)))&
(?[X]:((~tall(X)|~quiet(X))))&
((brave(john)<~>rich(john))) | happy(alice) | [] | null | 0 |
Everyone who is either wise or not humble is kind and vice versa. Everyone who is either not strong or not generous is both humble and kind. Everyone who is patient or rich is not generous. Everyone who is either not calm or funny is tall or not rich. If someone is not happy or not patient then someone is old and vice versa. If john is happy or calm then someone is either not creative or not strong and vice versa. Everyone who is patient is not quiet. If someone is not humble or not curious then alice is both rich and not creative. Everyone who is both not generous and funny is either curious or not brave and vice versa. Everyone who is either generous or quiet is not happy and vice versa. Everyone who is brave is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. Everyone who is quiet is not quiet or not humble and vice versa. Everyone who is brave or patient is not tall and vice versa. If someone is both not old and not strong then susan is tall and vice versa. Alice is creative or quiet. Someone is either not tall or strong. Alice is both not creative and not strong. Susan is either not generous or not curious. | Alice is kind. | entailment | (![X]:((wise(X)<~>~humble(X))<=>kind(X)))&
(![X]:((~strong(X)<~>~generous(X))=>(humble(X)&kind(X))))&
(![X]:((patient(X)|rich(X))=>~generous(X)))&
(![X]:((~calm(X)<~>funny(X))=>(tall(X)|~rich(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:(old(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:((~humble(X)|~curious(X))))=>((rich(alice)&~creative(alice))))&
(![X]:((~generous(X)&funny(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((generous(X)<~>quiet(X))<=>~happy(X)))&
(![X]:(brave(X)<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(quiet(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|patient(X))<=>~tall(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
((creative(alice)|quiet(alice)))&
(?[X]:((~tall(X)<~>strong(X))))&
((~creative(alice)&~strong(alice)))&
((~generous(susan)<~>~curious(susan))) | kind(alice) | [
"p0",
"p3",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2447451306037168205488316
% SZS output start Proof for 2447451306037168205488316
1. ! [X0] : ((wise(X0) <~> ~humble(X0)) <=> kind(X0)) [input p0]
4. ! [X0] : ((~calm(X0) <~> funny(X0)) => (~rich(X0) | tall(X0))) [input p3]
7. ! [X0] : (patient(X0) => ~quiet(X0)) [input p6]
8. ? [X0] : (~curious(X0) | ~humble(X0)) => (~creative(alice) & rich(alice)) [input p7]
9. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p8]
11. ! [X0] : (brave(X0) <=> (wise(X0) | ~curious(X0))) [input p10]
13. (~rich(alice) | patient(alice)) <=> ? [X0] : (~calm(X0) | ~curious(X0)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~humble(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((patient(X0) | brave(X0)) <=> ~tall(X0)) [input p14]
21. ~kind(alice) [input hypothesis]
25. ! [X0] : ((~rich(X0) | tall(X0)) | (~calm(X0) <=> funny(X0))) [ennf transformation 4]
26. ! [X0] : (~rich(X0) | tall(X0) | (~calm(X0) <=> funny(X0))) [flattening 25]
27. ! [X0] : (~quiet(X0) | ~patient(X0)) [ennf transformation 7]
28. (~creative(alice) & rich(alice)) | ! [X0] : (curious(X0) & humble(X0)) [ennf transformation 8]
30. ! [X0] : ((((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | ~kind(X0)) & (kind(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0))))) [nnf transformation 1]
32. ! [X0] : (~rich(X0) | tall(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [nnf transformation 26]
43. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~funny(X0) | generous(X0)))) [nnf transformation 9]
44. ! [X0] : (((funny(X0) & ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~funny(X0) | generous(X0))) [flattening 43]
46. ! [X0] : ((brave(X0) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | ~brave(X0))) [nnf transformation 11]
47. ! [X0] : ((brave(X0) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | ~brave(X0))) [flattening 46]
48. ((~rich(alice) | patient(alice)) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [nnf transformation 13]
49. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X0] : (~calm(X0) | ~curious(X0)) | (rich(alice) & ~patient(alice))) [flattening 48]
50. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & (? [X1] : (~calm(X1) | ~curious(X1)) | (rich(alice) & ~patient(alice))) [rectify 49]
51. ? [X1] : (~calm(X1) | ~curious(X1)) => (~calm(sK3) | ~curious(sK3)) [choice axiom]
52. (~rich(alice) | patient(alice) | ! [X0] : (calm(X0) & curious(X0))) & ((~calm(sK3) | ~curious(sK3)) | (rich(alice) & ~patient(alice))) [skolemisation 50,51]
53. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ~quiet(X0))) [nnf transformation 14]
54. ! [X0] : ((quiet(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ~quiet(X0))) [flattening 53]
55. ! [X0] : (((patient(X0) | brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [nnf transformation 15]
56. ! [X0] : ((patient(X0) | brave(X0) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~brave(X0)))) [flattening 55]
66. kind(X0) | wise(X0) | humble(X0) [cnf transformation 30]
76. ~funny(X0) | tall(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 32]
86. ~quiet(X0) | ~patient(X0) [cnf transformation 27]
87. rich(alice) | humble(X0) [cnf transformation 28]
95. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
103. ~wise(X0) | brave(X0) [cnf transformation 47]
108. ~rich(alice) | patient(alice) | curious(X0) [cnf transformation 52]
109. ~rich(alice) | patient(alice) | calm(X0) [cnf transformation 52]
110. ~humble(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
111. quiet(X0) | quiet(X0) [cnf transformation 54]
113. ~brave(X0) | ~tall(X0) [cnf transformation 56]
126. ~kind(alice) [cnf transformation 21]
127. ~humble(X0) | ~quiet(X0) [duplicate literal removal 110]
128. quiet(X0) [duplicate literal removal 111]
182. 13 <=> ! [X0] : curious(X0) [avatar definition]
183. curious(X0) <- (13) [avatar component clause 182]
190. 15 <=> ! [X0] : humble(X0) [avatar definition]
191. humble(X0) <- (15) [avatar component clause 190]
194. 16 <=> rich(alice) [avatar definition]
196. rich(alice) <- (16) [avatar component clause 194]
198. 15 | 16 [avatar split clause 87,194,190]
200. 17 <=> ! [X0] : calm(X0) [avatar definition]
201. calm(X0) <- (17) [avatar component clause 200]
203. 18 <=> patient(alice) [avatar definition]
205. patient(alice) <- (18) [avatar component clause 203]
206. 17 | 18 | ~16 [avatar split clause 109,194,203,200]
207. 13 | 18 | ~16 [avatar split clause 108,194,203,182]
218. ~humble(X0) [subsumption resolution 127,128]
258. $false <- (15) [subsumption resolution 191,218]
259. ~15 [avatar contradiction clause 258]
266. ~patient(X0) [resolution 86,128]
267. $false <- (18) [resolution 266,205]
268. ~18 [avatar contradiction clause 267]
279. wise(alice) | humble(alice) [resolution 66,126]
280. wise(alice) [subsumption resolution 279,218]
281. brave(alice) [resolution 280,103]
284. ~tall(alice) [resolution 281,113]
290. funny(alice) | ~curious(alice) [resolution 95,281]
291. funny(alice) <- (13) [subsumption resolution 290,183]
326. tall(alice) | ~calm(alice) | ~rich(alice) <- (13) [resolution 76,291]
327. ~calm(alice) | ~rich(alice) <- (13) [subsumption resolution 326,284]
328. ~rich(alice) <- (13, 17) [subsumption resolution 327,201]
329. $false <- (13, 16, 17) [subsumption resolution 328,196]
330. ~13 | ~16 | ~17 [avatar contradiction clause 329]
331. $false [avatar sat refutation 198,206,207,259,268,330]
% SZS output end Proof for 2447451306037168205488316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm then alice is not funny and vice versa.
If mary is not strong then mary is either not curious or tall.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
If fred is both not old and calm then susan is either not happy or not humble and vice versa.
If someone is either strong or funny then someone is either patient or rich and vice versa.
Everyone who is either not rich or not creative is rich and vice versa.
If someone is both not funny and not happy then paul is either not generous or not creative and vice versa.
Everyone who is both tall and generous is both happy and calm and vice versa.
If lucy is not generous then mary is not quiet or happy.
If lucy is both creative and funny then mary is both not generous and not rich.
If fred is either funny or curious then paul is both rich and not strong and vice versa.
If someone is either not creative or not strong then paul is either curious or calm and vice versa.
If alice is not old then fred is either not old or not funny and vice versa.
Everyone who is not brave or not creative is both not quiet and not funny.
If fred is tall or not creative then lucy is both not kind and happy.
Mary is not funny or not generous.
Someone is quiet or not quiet.
Someone is happy or not old.
Someone is either not old or not humble.
Fred is both old and humble.
Someone is either rich or wise. | Paul is rich. | neutral | ((~calm(mary))<=>(~funny(alice)))&
((~strong(mary))=>((~curious(mary)<~>tall(mary))))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
(((~old(fred)&calm(fred)))<=>((~happy(susan)<~>~humble(susan))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((~rich(X)<~>~creative(X))<=>rich(X)))&
((?[X]:((~funny(X)&~happy(X))))<=>((~generous(paul)<~>~creative(paul))))&
(![X]:((tall(X)&generous(X))<=>(happy(X)&calm(X))))&
((~generous(lucy))=>((~quiet(mary)|happy(mary))))&
(((creative(lucy)&funny(lucy)))=>((~generous(mary)&~rich(mary))))&
(((funny(fred)<~>curious(fred)))<=>((rich(paul)&~strong(paul))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((curious(paul)<~>calm(paul))))&
((~old(alice))<=>((~old(fred)<~>~funny(fred))))&
(![X]:((~brave(X)|~creative(X))=>(~quiet(X)&~funny(X))))&
(((tall(fred)|~creative(fred)))=>((~kind(lucy)&happy(lucy))))&
((~funny(mary)|~generous(mary)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
((old(fred)&humble(fred)))&
(?[X]:((rich(X)<~>wise(X)))) | rich(paul) | [] | null | 0 |
If fred is both not funny and patient then mary is brave or not calm.
If susan is strong or humble then lucy is old or creative.
If someone is tall then john is happy or not brave.
Everyone who is generous is not tall.
If someone is curious or not quiet then susan is either not funny or not wise.
Everyone who is both not old and not tall is not generous and vice versa.
If someone is both curious and quiet then someone is humble or not kind.
If mary is both strong and old then someone is not quiet or not strong.
If fred is quiet then someone is either not patient or happy.
Everyone who is both not old and not tall is both not tall and wise.
If fred is both not curious and happy then lucy is quiet or wise and vice versa.
Everyone who is both not tall and strong is not kind.
Everyone who is not quiet or funny is either wise or creative.
Everyone who is brave is either not humble or not strong.
If someone is curious or calm then someone is strong or not brave.
Everyone who is not wise is both not quiet and strong and vice versa.
Someone is either not wise or strong.
Fred is either old or not quiet.
John is humble or happy.
Someone is not tall.
Someone is not creative.
Someone is calm or not calm.
Someone is kind.
Someone is strong or generous. | Lucy is old. | neutral | (((~funny(fred)&patient(fred)))=>((brave(mary)|~calm(mary))))&
(((strong(susan)|humble(susan)))=>((old(lucy)|creative(lucy))))&
((?[X]:(tall(X)))=>((happy(john)|~brave(john))))&
(![X]:(generous(X)=>~tall(X)))&
((?[X]:((curious(X)|~quiet(X))))=>((~funny(susan)<~>~wise(susan))))&
(![X]:((~old(X)&~tall(X))<=>~generous(X)))&
((?[X]:((curious(X)&quiet(X))))=>(?[X]:((humble(X)|~kind(X)))))&
(((strong(mary)&old(mary)))=>(?[X]:((~quiet(X)|~strong(X)))))&
((quiet(fred))=>(?[X]:((~patient(X)<~>happy(X)))))&
(![X]:((~old(X)&~tall(X))=>(~tall(X)&wise(X))))&
(((~curious(fred)&happy(fred)))<=>((quiet(lucy)|wise(lucy))))&
(![X]:((~tall(X)&strong(X))=>~kind(X)))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)<~>creative(X))))&
(![X]:(brave(X)=>(~humble(X)<~>~strong(X))))&
((?[X]:((curious(X)|calm(X))))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:(~wise(X)<=>(~quiet(X)&strong(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
((old(fred)<~>~quiet(fred)))&
((humble(john)|happy(john)))&
(?[X]:(~tall(X)))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)|generous(X)))) | old(lucy) | [] | null | 0 |
If someone is rich or not calm then someone is either not brave or not quiet and vice versa.
If alice is either tall or not funny then john is either wise or not rich.
Everyone who is not happy or not wise is funny and vice versa.
Everyone who is strong or tall is curious or not tall and vice versa.
If susan is either quiet or happy then paul is calm or happy and vice versa.
If someone is both not generous and not rich then someone is either not generous or strong.
Everyone who is both not kind and not creative is not wise or rich.
Everyone who is both not kind and humble is brave and vice versa.
Everyone who is patient is both funny and not funny.
If john is curious or not generous then alice is either not happy or not strong and vice versa.
Everyone who is both not strong and not calm is either strong or not creative.
If someone is either patient or not creative then someone is either not calm or not patient and vice versa.
Everyone who is both not tall and not patient is both not curious and rich and vice versa.
Everyone who is happy is both happy and not strong.
Everyone who is not strong is either wise or patient.
If lucy is not funny then someone is both patient and strong and vice versa.
Susan is not creative or brave.
John is both happy and calm.
Someone is funny.
Alice is funny.
Someone is both not brave and not rich.
Fred is not rich.
Lucy is happy or strong.
Susan is generous. | Fred is not tall. | contradiction | ((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((tall(alice)<~>~funny(alice)))=>((wise(john)<~>~rich(john))))&
(![X]:((~happy(X)|~wise(X))<=>funny(X)))&
(![X]:((strong(X)|tall(X))<=>(curious(X)|~tall(X))))&
(((quiet(susan)<~>happy(susan)))<=>((calm(paul)|happy(paul))))&
((?[X]:((~generous(X)&~rich(X))))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:((~kind(X)&~creative(X))=>(~wise(X)|rich(X))))&
(![X]:((~kind(X)&humble(X))<=>brave(X)))&
(![X]:(patient(X)=>(funny(X)&~funny(X))))&
(((curious(john)|~generous(john)))<=>((~happy(alice)<~>~strong(alice))))&
(![X]:((~strong(X)&~calm(X))=>(strong(X)<~>~creative(X))))&
((?[X]:((patient(X)<~>~creative(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~tall(X)&~patient(X))<=>(~curious(X)&rich(X))))&
(![X]:(happy(X)=>(happy(X)&~strong(X))))&
(![X]:(~strong(X)=>(wise(X)<~>patient(X))))&
((~funny(lucy))<=>(?[X]:((patient(X)&strong(X)))))&
((~creative(susan)|brave(susan)))&
((happy(john)&calm(john)))&
(?[X]:(funny(X)))&
(funny(alice))&
(?[X]:((~brave(X)&~rich(X))))&
(~rich(fred))&
((happy(lucy)|strong(lucy)))&
(generous(susan)) | ~tall(fred) | [
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 404695612009307728931194
% SZS output start Proof for 404695612009307728931194
9. ! [X0] : (patient(X0) => (~funny(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (rich(X0) & ~curious(X0))) [input p12]
22. ~rich(fred) [input p21]
25. ~tall(fred) [input hypothesis]
33. ! [X0] : ((~funny(X0) & funny(X0)) | ~patient(X0)) [ennf transformation 9]
64. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~rich(X0) | curious(X0))) & ((rich(X0) & ~curious(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 13]
65. ! [X0] : (((~patient(X0) & ~tall(X0)) | ~rich(X0) | curious(X0)) & ((rich(X0) & ~curious(X0)) | patient(X0) | tall(X0))) [flattening 64]
104. funny(X0) | ~patient(X0) [cnf transformation 33]
105. ~patient(X0) | ~funny(X0) [cnf transformation 33]
123. rich(X0) | patient(X0) | tall(X0) [cnf transformation 65]
140. ~rich(fred) [cnf transformation 22]
143. ~tall(fred) [cnf transformation 25]
236. ~patient(X0) [subsumption resolution 104,105]
279. tall(X0) | rich(X0) [subsumption resolution 123,236]
324. rich(fred) [resolution 279,143]
327. $false [subsumption resolution 324,140]
% SZS output end Proof for 404695612009307728931194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then paul is not kind or generous and vice versa.
Everyone who is humble or not rich is rich or funny and vice versa.
Everyone who is both not curious and brave is not curious or strong.
If someone is generous then susan is either not happy or not patient.
If susan is both not brave and not kind then alice is both humble and brave.
If someone is either not generous or creative then someone is not happy.
Everyone who is rich or not kind is not curious or curious.
Everyone who is either not creative or patient is kind or not generous.
Everyone who is both old and not rich is both happy and patient and vice versa.
Everyone who is not patient is tall or strong.
Everyone who is not funny or not curious is not patient or tall.
Everyone who is not wise is not humble or kind and vice versa.
If susan is not funny or tall then someone is humble or not tall.
Everyone who is both not happy and not funny is tall.
Everyone who is not calm is both curious and not kind and vice versa.
Everyone who is either not strong or not wise is not brave or not tall.
Someone is not strong.
Alice is both not brave and not funny.
Someone is both not brave and humble.
Someone is both old and not quiet.
Paul is calm.
Someone is humble.
Alice is patient.
Someone is either funny or rich. | Paul is funny. | neutral | ((?[X]:(~tall(X)))<=>((~kind(paul)|generous(paul))))&
(![X]:((humble(X)|~rich(X))<=>(rich(X)|funny(X))))&
(![X]:((~curious(X)&brave(X))=>(~curious(X)|strong(X))))&
((?[X]:(generous(X)))=>((~happy(susan)<~>~patient(susan))))&
(((~brave(susan)&~kind(susan)))=>((humble(alice)&brave(alice))))&
((?[X]:((~generous(X)<~>creative(X))))=>(?[X]:(~happy(X))))&
(![X]:((rich(X)|~kind(X))=>(~curious(X)|curious(X))))&
(![X]:((~creative(X)<~>patient(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)&~rich(X))<=>(happy(X)&patient(X))))&
(![X]:(~patient(X)=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~curious(X))=>(~patient(X)|tall(X))))&
(![X]:(~wise(X)<=>(~humble(X)|kind(X))))&
(((~funny(susan)|tall(susan)))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~happy(X)&~funny(X))=>tall(X)))&
(![X]:(~calm(X)<=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(~brave(X)|~tall(X))))&
(?[X]:(~strong(X)))&
((~brave(alice)&~funny(alice)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((old(X)&~quiet(X))))&
(calm(paul))&
(?[X]:(humble(X)))&
(patient(alice))&
(?[X]:((funny(X)<~>rich(X)))) | funny(paul) | [] | null | 0 |
If someone is both not calm and curious then someone is either not quiet or rich and vice versa.
Everyone who is not kind or not strong is quiet and vice versa.
Everyone who is either not generous or humble is not rich and vice versa.
If susan is both tall and not brave then someone is both rich and not funny.
Everyone who is tall or not happy is both generous and not brave and vice versa.
Everyone who is not strong is not rich or not patient and vice versa.
If mary is humble then someone is old.
If alice is either not wise or not tall then someone is not calm.
If someone is both not brave and happy then lucy is either rich or not curious and vice versa.
If someone is either not generous or quiet then fred is not wise and vice versa.
Everyone who is both not wise and not kind is not old and vice versa.
If someone is brave then alice is rich or not rich and vice versa.
If someone is either not happy or happy then paul is both not rich and funny.
If mary is either quiet or wise then lucy is not curious and vice versa.
Everyone who is wise is not quiet or happy and vice versa.
Everyone who is not happy or quiet is both brave and not curious.
Paul is humble or patient.
Someone is either not creative or patient.
Someone is either not tall or not wise.
Susan is strong or kind.
Paul is old.
John is generous.
Susan is both not generous and not tall.
Someone is brave or funny. | Paul is not curious. | entailment | ((?[X]:((~calm(X)&curious(X))))<=>(?[X]:((~quiet(X)<~>rich(X)))))&
(![X]:((~kind(X)|~strong(X))<=>quiet(X)))&
(![X]:((~generous(X)<~>humble(X))<=>~rich(X)))&
(((tall(susan)&~brave(susan)))=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((tall(X)|~happy(X))<=>(generous(X)&~brave(X))))&
(![X]:(~strong(X)<=>(~rich(X)|~patient(X))))&
((humble(mary))=>(?[X]:(old(X))))&
(((~wise(alice)<~>~tall(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((~brave(X)&happy(X))))<=>((rich(lucy)<~>~curious(lucy))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>(~wise(fred)))&
(![X]:((~wise(X)&~kind(X))<=>~old(X)))&
((?[X]:(brave(X)))<=>((rich(alice)|~rich(alice))))&
((?[X]:((~happy(X)<~>happy(X))))=>((~rich(paul)&funny(paul))))&
(((quiet(mary)<~>wise(mary)))<=>(~curious(lucy)))&
(![X]:(wise(X)<=>(~quiet(X)|happy(X))))&
(![X]:((~happy(X)|quiet(X))=>(brave(X)&~curious(X))))&
((humble(paul)|patient(paul)))&
(?[X]:((~creative(X)<~>patient(X))))&
(?[X]:((~tall(X)<~>~wise(X))))&
((strong(susan)|kind(susan)))&
(old(paul))&
(generous(john))&
((~generous(susan)&~tall(susan)))&
(?[X]:((brave(X)|funny(X)))) | ~curious(paul) | [
"p1",
"p4",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5984199197872024425653298
% SZS output start Proof for 5984199197872024425653298
2. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> quiet(X0)) [input p1]
5. ! [X0] : ((~happy(X0) | tall(X0)) <=> (~brave(X0) & generous(X0))) [input p4]
6. ! [X0] : (~strong(X0) <=> (~patient(X0) | ~rich(X0))) [input p5]
13. ? [X0] : (~happy(X0) <~> happy(X0)) => (funny(paul) & ~rich(paul)) [input p12]
16. ! [X0] : ((quiet(X0) | ~happy(X0)) => (~curious(X0) & brave(X0))) [input p15]
25. curious(paul) [input hypothesis]
34. (funny(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) <=> happy(X0)) [ennf transformation 13]
35. ! [X0] : ((~curious(X0) & brave(X0)) | (~quiet(X0) & happy(X0))) [ennf transformation 16]
41. ! [X0] : (((~strong(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & kind(X0)))) [nnf transformation 2]
42. ! [X0] : ((~strong(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & kind(X0)))) [flattening 41]
46. ! [X0] : (((~happy(X0) | tall(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (happy(X0) & ~tall(X0)))) [nnf transformation 5]
47. ! [X0] : ((~happy(X0) | tall(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | (happy(X0) & ~tall(X0)))) [flattening 46]
48. ! [X0] : ((~strong(X0) | (patient(X0) & rich(X0))) & ((~patient(X0) | ~rich(X0)) | strong(X0))) [nnf transformation 6]
49. ! [X0] : ((~strong(X0) | (patient(X0) & rich(X0))) & (~patient(X0) | ~rich(X0) | strong(X0))) [flattening 48]
68. (funny(paul) & ~rich(paul)) | ! [X0] : ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))) [nnf transformation 34]
87. strong(X0) | quiet(X0) [cnf transformation 42]
98. ~brave(X0) | happy(X0) [cnf transformation 47]
101. ~strong(X0) | rich(X0) [cnf transformation 49]
121. ~rich(paul) | ~happy(X0) | ~happy(X0) [cnf transformation 68]
131. brave(X0) | happy(X0) [cnf transformation 35]
134. ~quiet(X0) | ~curious(X0) [cnf transformation 35]
146. curious(paul) [cnf transformation 25]
148. ~rich(paul) | ~happy(X0) [duplicate literal removal 121]
160. 3 <=> ! [X1] : (rich(X1) | quiet(X1)) [avatar definition]
161. rich(X1) | quiet(X1) <- (3) [avatar component clause 160]
281. 29 <=> ! [X0] : ~happy(X0) [avatar definition]
282. ~happy(X0) <- (29) [avatar component clause 281]
289. 31 <=> ! [X0] : happy(X0) [avatar definition]
290. happy(X0) <- (31) [avatar component clause 289]
293. 32 <=> rich(paul) [avatar definition]
295. ~rich(paul) <- (~32) [avatar component clause 293]
296. 29 | ~32 [avatar split clause 148,293,281]
310. happy(X0) [subsumption resolution 131,98]
311. 31 [avatar split clause 310,289]
360. $false <- (29, 31) [subsumption resolution 282,290]
361. ~29 | ~31 [avatar contradiction clause 360]
368. rich(X0) | quiet(X0) [resolution 101,87]
369. 3 [avatar split clause 368,160]
396. quiet(paul) <- (3, ~32) [resolution 161,295]
409. ~curious(paul) <- (3, ~32) [resolution 396,134]
411. $false <- (3, ~32) [subsumption resolution 409,146]
412. ~3 | 32 [avatar contradiction clause 411]
413. $false [avatar sat refutation 296,311,361,369,412]
% SZS output end Proof for 5984199197872024425653298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not humble or not brave then someone is both curious and not old. Everyone who is both generous and not creative is not wise and vice versa. Everyone who is both not wise and not brave is either calm or not generous. Everyone who is not brave is both humble and kind and vice versa. Everyone who is funny or humble is either quiet or not generous. If mary is both kind and strong then someone is both quiet and not quiet and vice versa. Everyone who is both tall and calm is either not happy or not creative and vice versa. If susan is either strong or old then someone is not curious or brave and vice versa. Everyone who is not old is not wise and vice versa. Everyone who is either not humble or patient is not kind or not curious. Everyone who is both not old and not rich is not strong and vice versa. If paul is creative or not funny then someone is not rich or rich and vice versa. If someone is either not funny or not generous then mary is calm or not brave and vice versa. Everyone who is brave is not calm or brave and vice versa. Everyone who is both brave and patient is rich and vice versa. Everyone who is not rich or rich is either patient or tall and vice versa. Someone is both not humble and not quiet. Someone is not generous. Paul is both not happy and funny. Someone is either rich or happy. John is not creative. Someone is both old and not patient. Someone is either curious or generous. Paul is strong or not strong. | Mary is calm. | neutral | (((~humble(mary)<~>~brave(mary)))=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((generous(X)&~creative(X))<=>~wise(X)))&
(![X]:((~wise(X)&~brave(X))=>(calm(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(![X]:((funny(X)|humble(X))=>(quiet(X)<~>~generous(X))))&
(((kind(mary)&strong(mary)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:((tall(X)&calm(X))<=>(~happy(X)<~>~creative(X))))&
(((strong(susan)<~>old(susan)))<=>(?[X]:((~curious(X)|brave(X)))))&
(![X]:(~old(X)<=>~wise(X)))&
(![X]:((~humble(X)<~>patient(X))=>(~kind(X)|~curious(X))))&
(![X]:((~old(X)&~rich(X))<=>~strong(X)))&
(((creative(paul)|~funny(paul)))<=>(?[X]:((~rich(X)|rich(X)))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>((calm(mary)|~brave(mary))))&
(![X]:(brave(X)<=>(~calm(X)|brave(X))))&
(![X]:((brave(X)&patient(X))<=>rich(X)))&
(![X]:((~rich(X)|rich(X))<=>(patient(X)<~>tall(X))))&
(?[X]:((~humble(X)&~quiet(X))))&
(?[X]:(~generous(X)))&
((~happy(paul)&funny(paul)))&
(?[X]:((rich(X)<~>happy(X))))&
(~creative(john))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:((curious(X)<~>generous(X))))&
((strong(paul)|~strong(paul))) | calm(mary) | [] | null | 0 |
Everyone who is either not kind or not humble is quiet and vice versa. If someone is brave or not patient then susan is either patient or not strong. Everyone who is humble is either not creative or tall and vice versa. If someone is funny then susan is not happy or not kind. If alice is either not tall or not strong then someone is not old and vice versa. Everyone who is both not tall and rich is both strong and not curious and vice versa. Everyone who is both patient and not wise is kind. Everyone who is either not strong or generous is either not creative or not happy and vice versa. If someone is strong or not tall then fred is not quiet or tall and vice versa. If someone is both not funny and generous then fred is both funny and humble and vice versa. If someone is both tall and not strong then susan is either not wise or not curious. If someone is either not calm or not curious then susan is both not calm and not old and vice versa. Everyone who is old or tall is not humble. Everyone who is both kind and not patient is not humble and vice versa. If susan is not calm then paul is strong or calm. Everyone who is strong or quiet is not humble or old. Someone is both curious and rich. Someone is quiet. Someone is not calm. Someone is both not calm and creative. Lucy is either not strong or not generous. Someone is funny or not brave. Someone is not creative or creative. Someone is not patient or not funny. | Fred is kind. | entailment | (![X]:((~kind(X)<~>~humble(X))<=>quiet(X)))&
((?[X]:((brave(X)|~patient(X))))=>((patient(susan)<~>~strong(susan))))&
(![X]:(humble(X)<=>(~creative(X)<~>tall(X))))&
((?[X]:(funny(X)))=>((~happy(susan)|~kind(susan))))&
(((~tall(alice)<~>~strong(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~tall(X)&rich(X))<=>(strong(X)&~curious(X))))&
(![X]:((patient(X)&~wise(X))=>kind(X)))&
(![X]:((~strong(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~quiet(fred)|tall(fred))))&
((?[X]:((~funny(X)&generous(X))))<=>((funny(fred)&humble(fred))))&
((?[X]:((tall(X)&~strong(X))))=>((~wise(susan)<~>~curious(susan))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~calm(susan)&~old(susan))))&
(![X]:((old(X)|tall(X))=>~humble(X)))&
(![X]:((kind(X)&~patient(X))<=>~humble(X)))&
((~calm(susan))=>((strong(paul)|calm(paul))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)|old(X))))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(quiet(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~calm(X)&creative(X))))&
((~strong(lucy)<~>~generous(lucy)))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((~patient(X)|~funny(X)))) | kind(fred) | [
"p0",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8061853165046484941994856
% SZS output start Proof for 8061853165046484941994856
1. ! [X0] : ((~kind(X0) <~> ~humble(X0)) <=> quiet(X0)) [input p0]
9. ? [X0] : (~tall(X0) | strong(X0)) <=> (tall(fred) | ~quiet(fred)) [input p8]
13. ! [X0] : ((tall(X0) | old(X0)) => ~humble(X0)) [input p12]
14. ! [X0] : ((~patient(X0) & kind(X0)) <=> ~humble(X0)) [input p13]
25. ~kind(fred) [input hypothesis]
34. ! [X0] : (~humble(X0) | (~tall(X0) & ~old(X0))) [ennf transformation 13]
39. ! [X0] : ((((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | ~quiet(X0)) & (quiet(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))))) [nnf transformation 1]
49. (? [X0] : (~tall(X0) | strong(X0)) | (~tall(fred) & quiet(fred))) & ((tall(fred) | ~quiet(fred)) | ! [X0] : (tall(X0) & ~strong(X0))) [nnf transformation 9]
50. (? [X0] : (~tall(X0) | strong(X0)) | (~tall(fred) & quiet(fred))) & (tall(fred) | ~quiet(fred) | ! [X0] : (tall(X0) & ~strong(X0))) [flattening 49]
51. (? [X0] : (~tall(X0) | strong(X0)) | (~tall(fred) & quiet(fred))) & (tall(fred) | ~quiet(fred) | ! [X1] : (tall(X1) & ~strong(X1))) [rectify 50]
52. ? [X0] : (~tall(X0) | strong(X0)) => (~tall(sK1) | strong(sK1)) [choice axiom]
53. ((~tall(sK1) | strong(sK1)) | (~tall(fred) & quiet(fred))) & (tall(fred) | ~quiet(fred) | ! [X1] : (tall(X1) & ~strong(X1))) [skolemisation 51,52]
65. ! [X0] : (((~patient(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | (patient(X0) | ~kind(X0)))) [nnf transformation 14]
66. ! [X0] : (((~patient(X0) & kind(X0)) | humble(X0)) & (~humble(X0) | patient(X0) | ~kind(X0))) [flattening 65]
80. ~humble(X0) | quiet(X0) | kind(X0) [cnf transformation 39]
109. tall(fred) | ~quiet(fred) | tall(X1) [cnf transformation 53]
125. ~tall(X0) | ~humble(X0) [cnf transformation 34]
127. humble(X0) | kind(X0) [cnf transformation 66]
142. ~kind(fred) [cnf transformation 25]
188. 11 <=> tall(fred) [avatar definition]
189. tall(fred) <- (11) [avatar component clause 188]
190. ~tall(fred) <- (~11) [avatar component clause 188]
201. 14 <=> quiet(fred) [avatar definition]
202. ~quiet(fred) <- (~14) [avatar component clause 201]
206. 15 <=> ! [X1] : tall(X1) [avatar definition]
207. tall(X1) <- (15) [avatar component clause 206]
208. 15 | ~14 | 11 [avatar split clause 109,188,201,206]
218. 18 <=> humble(fred) [avatar definition]
219. humble(fred) <- (18) [avatar component clause 218]
220. ~humble(fred) <- (~18) [avatar component clause 218]
323. quiet(fred) | kind(fred) <- (18) [resolution 80,219]
326. kind(fred) <- (~14, 18) [subsumption resolution 323,202]
327. $false <- (~14, 18) [subsumption resolution 326,142]
328. 14 | ~18 [avatar contradiction clause 327]
329. kind(fred) <- (~18) [resolution 220,127]
330. $false <- (~18) [subsumption resolution 329,142]
331. 18 [avatar contradiction clause 330]
333. ~humble(fred) <- (11) [resolution 189,125]
334. $false <- (11, 18) [subsumption resolution 333,219]
335. ~11 | ~18 [avatar contradiction clause 334]
336. $false <- (~11, 15) [subsumption resolution 190,207]
337. 11 | ~15 [avatar contradiction clause 336]
338. $false [avatar sat refutation 208,328,331,335,337]
% SZS output end Proof for 8061853165046484941994856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is brave then susan is not calm. If paul is both not generous and not strong then someone is humble or strong. If someone is rich then someone is both curious and wise. Everyone who is both old and curious is not generous or quiet and vice versa. If someone is both not calm and curious then fred is both not wise and happy and vice versa. Everyone who is both not quiet and not strong is both kind and rich. If someone is not brave or creative then someone is both not tall and generous. If alice is either not patient or not curious then lucy is both not brave and kind and vice versa. If lucy is quiet then someone is either creative or not tall and vice versa. Everyone who is quiet or rich is not generous. Everyone who is not humble or not curious is both rich and not calm and vice versa. If someone is both tall and brave then someone is both curious and rich and vice versa. Everyone who is both not happy and creative is not brave. Everyone who is not humble or not patient is both generous and kind and vice versa. Everyone who is strong is both quiet and not calm. Fred is not tall or not strong. Someone is not tall. Someone is calm. Fred is either wise or not creative. Lucy is happy or curious. Lucy is quiet. | Lucy is not old. | contradiction | ((brave(susan))=>(~calm(susan)))&
(((~generous(paul)&~strong(paul)))=>(?[X]:((humble(X)|strong(X)))))&
((?[X]:(rich(X)))=>(?[X]:((curious(X)&wise(X)))))&
(![X]:((old(X)&curious(X))<=>(~generous(X)|quiet(X))))&
((?[X]:((~calm(X)&curious(X))))<=>((~wise(fred)&happy(fred))))&
(![X]:((~quiet(X)&~strong(X))=>(kind(X)&rich(X))))&
((?[X]:((~brave(X)|creative(X))))=>(?[X]:((~tall(X)&generous(X)))))&
(((~patient(alice)<~>~curious(alice)))<=>((~brave(lucy)&kind(lucy))))&
((quiet(lucy))<=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((quiet(X)|rich(X))=>~generous(X)))&
(![X]:((~humble(X)|~curious(X))<=>(rich(X)&~calm(X))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((curious(X)&rich(X)))))&
(![X]:((~happy(X)&creative(X))=>~brave(X)))&
(![X]:((~humble(X)|~patient(X))<=>(generous(X)&kind(X))))&
(![X]:(strong(X)=>(quiet(X)&~calm(X))))&
((~tall(fred)|~strong(fred)))&
(?[X]:(~tall(X)))&
(?[X]:(calm(X)))&
((wise(fred)<~>~creative(fred)))&
((happy(lucy)|curious(lucy)))&
(quiet(lucy)) | ~old(lucy) | [
"p3",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3386085694562451910116111
% SZS output start Proof for 3386085694562451910116111
4. ! [X0] : ((curious(X0) & old(X0)) <=> (quiet(X0) | ~generous(X0))) [input p3]
21. quiet(lucy) [input p20]
22. ~old(lucy) [input hypothesis]
42. ! [X0] : (((curious(X0) & old(X0)) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 4]
43. ! [X0] : (((curious(X0) & old(X0)) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | ~curious(X0) | ~old(X0))) [flattening 42]
78. ~quiet(X0) | old(X0) [cnf transformation 43]
126. quiet(lucy) [cnf transformation 21]
127. ~old(lucy) [cnf transformation 22]
234. 24 <=> quiet(lucy) [avatar definition]
236. quiet(lucy) <- (24) [avatar component clause 234]
302. 24 [avatar split clause 126,234]
304. old(lucy) <- (24) [resolution 78,236]
305. $false <- (24) [subsumption resolution 304,127]
306. ~24 [avatar contradiction clause 305]
307. $false [avatar sat refutation 302,306]
% SZS output end Proof for 3386085694562451910116111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or kind is either happy or curious and vice versa.
Everyone who is not quiet is humble and vice versa.
Everyone who is both not tall and strong is either calm or kind.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Everyone who is old is tall or curious.
If someone is wise then mary is not rich or not humble.
Someone is both not kind and tall.
Someone is either curious or rich.
Someone is not quiet or brave.
John is either not strong or not generous. | Paul is patient. | neutral | (![X]:((~funny(X)<~>kind(X))<=>(happy(X)<~>curious(X))))&
(![X]:(~quiet(X)<=>humble(X)))&
(![X]:((~tall(X)&strong(X))=>(calm(X)<~>kind(X))))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(![X]:(old(X)=>(tall(X)|curious(X))))&
((?[X]:(wise(X)))=>((~rich(mary)|~humble(mary))))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~quiet(X)|brave(X))))&
((~strong(john)<~>~generous(john))) | patient(paul) | [] | null | 0 |
Everyone who is calm or not wise is strong and vice versa.
Everyone who is not kind or strong is either happy or tall.
Everyone who is not wise is either wise or creative.
Everyone who is either happy or not old is both creative and rich.
If someone is not brave or calm then someone is not rich or patient.
Everyone who is curious or calm is not creative or not wise.
Everyone who is either quiet or wise is quiet or not brave and vice versa.
If mary is either tall or not old then john is both not kind and funny.
Everyone who is not kind or not curious is both old and rich and vice versa.
Everyone who is not generous or not wise is not wise.
Everyone who is either curious or not creative is either not creative or not strong and vice versa.
If someone is either wise or not curious then alice is curious and vice versa.
If someone is both not generous and not curious then someone is both strong and not curious and vice versa.
If lucy is either old or not old then someone is not curious.
If someone is tall or funny then fred is both not happy and not old.
Everyone who is either old or not strong is both quiet and not curious and vice versa.
Someone is not creative or not brave.
Susan is both curious and generous.
Someone is either patient or not generous.
Fred is either not kind or not wise.
Alice is either patient or not calm.
Alice is either not kind or not rich. | Susan is not funny. | entailment | (![X]:((calm(X)|~wise(X))<=>strong(X)))&
(![X]:((~kind(X)|strong(X))=>(happy(X)<~>tall(X))))&
(![X]:(~wise(X)=>(wise(X)<~>creative(X))))&
(![X]:((happy(X)<~>~old(X))=>(creative(X)&rich(X))))&
((?[X]:((~brave(X)|calm(X))))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((curious(X)|calm(X))=>(~creative(X)|~wise(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(quiet(X)|~brave(X))))&
(((tall(mary)<~>~old(mary)))=>((~kind(john)&funny(john))))&
(![X]:((~kind(X)|~curious(X))<=>(old(X)&rich(X))))&
(![X]:((~generous(X)|~wise(X))=>~wise(X)))&
(![X]:((curious(X)<~>~creative(X))<=>(~creative(X)<~>~strong(X))))&
((?[X]:((wise(X)<~>~curious(X))))<=>(curious(alice)))&
((?[X]:((~generous(X)&~curious(X))))<=>(?[X]:((strong(X)&~curious(X)))))&
(((old(lucy)<~>~old(lucy)))=>(?[X]:(~curious(X))))&
((?[X]:((tall(X)|funny(X))))=>((~happy(fred)&~old(fred))))&
(![X]:((old(X)<~>~strong(X))<=>(quiet(X)&~curious(X))))&
(?[X]:((~creative(X)|~brave(X))))&
((curious(susan)&generous(susan)))&
(?[X]:((patient(X)<~>~generous(X))))&
((~kind(fred)<~>~wise(fred)))&
((patient(alice)<~>~calm(alice)))&
((~kind(alice)<~>~rich(alice))) | ~funny(susan) | [
"p8",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2121988628279199202146104
% SZS output start Proof for 2121988628279199202146104
9. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (rich(X0) & old(X0))) [input p8]
11. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> (~creative(X0) <~> ~strong(X0))) [input p10]
15. ? [X0] : (funny(X0) | tall(X0)) => (~old(fred) & ~happy(fred)) [input p14]
16. ! [X0] : ((old(X0) <~> ~strong(X0)) <=> (~curious(X0) & quiet(X0))) [input p15]
23. funny(susan) [input hypothesis]
35. (~old(fred) & ~happy(fred)) | ! [X0] : (~funny(X0) & ~tall(X0)) [ennf transformation 15]
47. ! [X0] : (((~curious(X0) | ~kind(X0)) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 9]
48. ! [X0] : ((~curious(X0) | ~kind(X0) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | (curious(X0) & kind(X0)))) [flattening 47]
49. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0)))) & (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 11]
62. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [nnf transformation 16]
63. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [flattening 62]
100. curious(X0) | old(X0) [cnf transformation 48]
106. ~strong(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 49]
109. strong(X0) | creative(X0) | curious(X0) | creative(X0) [cnf transformation 49]
111. ~creative(X0) | curious(X0) | ~creative(X0) | strong(X0) [cnf transformation 49]
112. creative(X0) | ~curious(X0) | ~strong(X0) | creative(X0) [cnf transformation 49]
127. ~old(fred) | ~funny(X0) [cnf transformation 35]
131. ~curious(X0) | old(X0) | strong(X0) [cnf transformation 63]
145. funny(susan) [cnf transformation 23]
148. ~strong(X0) | ~creative(X0) | ~curious(X0) [duplicate literal removal 106]
149. strong(X0) | creative(X0) | curious(X0) [duplicate literal removal 109]
150. ~creative(X0) | curious(X0) | strong(X0) [duplicate literal removal 111]
151. creative(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 112]
192. curious(X0) | strong(X0) [subsumption resolution 149,150]
193. ~curious(X0) | ~strong(X0) [subsumption resolution 148,151]
255. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
256. ~funny(X0) <- (22) [avatar component clause 255]
258. 23 <=> old(fred) [avatar definition]
260. ~old(fred) <- (~23) [avatar component clause 258]
261. 22 | ~23 [avatar split clause 127,258,255]
272. old(X0) | strong(X0) [subsumption resolution 131,192]
338. ~strong(X2) | old(X2) [resolution 193,100]
339. old(X2) [subsumption resolution 338,272]
420. $false <- (~23) [resolution 339,260]
421. 23 [avatar contradiction clause 420]
422. $false <- (22) [resolution 256,145]
425. ~22 [avatar contradiction clause 422]
426. $false [avatar sat refutation 261,421,425]
% SZS output end Proof for 2121988628279199202146104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not strong or not rich then alice is both generous and happy and vice versa. Everyone who is not brave or funny is both not patient and wise and vice versa. Everyone who is either quiet or not creative is quiet and vice versa. If someone is curious then mary is old. If someone is either quiet or rich then fred is not quiet or not rich. If susan is both not strong and not humble then mary is either not humble or kind and vice versa. If someone is quiet then fred is either not tall or not generous. Everyone who is either calm or funny is both strong and not brave. If someone is kind then someone is either patient or happy. If someone is both not happy and funny then mary is brave or not generous and vice versa. Everyone who is not rich or generous is either humble or not quiet and vice versa. Everyone who is not quiet or creative is both brave and quiet. Everyone who is not brave is both not quiet and not patient and vice versa. Everyone who is old or wise is old and vice versa. If john is both old and not quiet then someone is either not creative or not rich and vice versa. If mary is either quiet or strong then alice is happy or not creative and vice versa. Mary is wise or not creative. John is not calm or strong. Lucy is not funny. Paul is either funny or old. Lucy is either funny or tall. Susan is both old and wise. | John is not strong. | neutral | (((~strong(fred)|~rich(fred)))<=>((generous(alice)&happy(alice))))&
(![X]:((~brave(X)|funny(X))<=>(~patient(X)&wise(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>quiet(X)))&
((?[X]:(curious(X)))=>(old(mary)))&
((?[X]:((quiet(X)<~>rich(X))))=>((~quiet(fred)|~rich(fred))))&
(((~strong(susan)&~humble(susan)))<=>((~humble(mary)<~>kind(mary))))&
((?[X]:(quiet(X)))=>((~tall(fred)<~>~generous(fred))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((brave(mary)|~generous(mary))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|creative(X))=>(brave(X)&quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)&~patient(X))))&
(![X]:((old(X)|wise(X))<=>old(X)))&
(((old(john)&~quiet(john)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(((quiet(mary)<~>strong(mary)))<=>((happy(alice)|~creative(alice))))&
((wise(mary)|~creative(mary)))&
((~calm(john)|strong(john)))&
(~funny(lucy))&
((funny(paul)<~>old(paul)))&
((funny(lucy)<~>tall(lucy)))&
((old(susan)&wise(susan))) | ~strong(john) | [] | null | 0 |
Everyone who is calm is either not funny or calm. Everyone who is tall or rich is either wise or not brave and vice versa. Everyone who is creative is not funny or generous. Everyone who is either patient or rich is tall. Everyone who is not brave or not curious is tall. Everyone who is both not calm and strong is either not generous or not patient. If someone is either not tall or not old then mary is either wise or calm and vice versa. Everyone who is happy is funny or humble. Everyone who is old or not old is either wise or not curious and vice versa. Everyone who is not rich or patient is both not humble and old and vice versa. Everyone who is either quiet or not calm is either funny or not funny. If someone is curious or not kind then susan is generous or not generous and vice versa. Everyone who is old or funny is rich or not kind and vice versa. If someone is not tall then mary is not old or not calm. Everyone who is not rich is either not wise or not creative. Everyone who is patient or happy is both creative and not brave. Alice is either old or not kind. Alice is wise or tall. Lucy is either patient or happy. Someone is both not funny and not curious. Someone is creative. Mary is rich or not rich. Paul is either not brave or generous. | Alice is tall. | entailment | (![X]:(calm(X)=>(~funny(X)<~>calm(X))))&
(![X]:((tall(X)|rich(X))<=>(wise(X)<~>~brave(X))))&
(![X]:(creative(X)=>(~funny(X)|generous(X))))&
(![X]:((patient(X)<~>rich(X))=>tall(X)))&
(![X]:((~brave(X)|~curious(X))=>tall(X)))&
(![X]:((~calm(X)&strong(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>((wise(mary)<~>calm(mary))))&
(![X]:(happy(X)=>(funny(X)|humble(X))))&
(![X]:((old(X)|~old(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((~rich(X)|patient(X))<=>(~humble(X)&old(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(funny(X)<~>~funny(X))))&
((?[X]:((curious(X)|~kind(X))))<=>((generous(susan)|~generous(susan))))&
(![X]:((old(X)|funny(X))<=>(rich(X)|~kind(X))))&
((?[X]:(~tall(X)))=>((~old(mary)|~calm(mary))))&
(![X]:(~rich(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((patient(X)|happy(X))=>(creative(X)&~brave(X))))&
((old(alice)<~>~kind(alice)))&
((wise(alice)|tall(alice)))&
((patient(lucy)<~>happy(lucy)))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:(creative(X)))&
((rich(mary)|~rich(mary)))&
((~brave(paul)<~>generous(paul))) | tall(alice) | [
"p1",
"p3",
"p9",
"p12",
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6557630171505506912515136
% SZS output start Proof for 6557630171505506912515136
2. ! [X0] : ((rich(X0) | tall(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p1]
4. ! [X0] : ((patient(X0) <~> rich(X0)) => tall(X0)) [input p3]
10. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (old(X0) & ~humble(X0))) [input p9]
13. ! [X0] : ((funny(X0) | old(X0)) <=> (~kind(X0) | rich(X0))) [input p12]
16. ! [X0] : ((happy(X0) | patient(X0)) => (~brave(X0) & creative(X0))) [input p15]
17. old(alice) <~> ~kind(alice) [input p16]
18. tall(alice) | wise(alice) [input p17]
24. ~tall(alice) [input hypothesis]
29. ! [X0] : (tall(X0) | (patient(X0) <=> rich(X0))) [ennf transformation 4]
37. ! [X0] : ((~brave(X0) & creative(X0)) | (~happy(X0) & ~patient(X0))) [ennf transformation 16]
39. ! [X0] : (((rich(X0) | tall(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~rich(X0) & ~tall(X0)))) [nnf transformation 2]
40. ! [X0] : ((rich(X0) | tall(X0) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~rich(X0) & ~tall(X0)))) [flattening 39]
41. ! [X0] : (tall(X0) | ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0)))) [nnf transformation 29]
48. ! [X0] : (((patient(X0) | ~rich(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 10]
49. ! [X0] : ((patient(X0) | ~rich(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 48]
56. ! [X0] : (((funny(X0) | old(X0)) | (kind(X0) & ~rich(X0))) & ((~kind(X0) | rich(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 13]
57. ! [X0] : ((funny(X0) | old(X0) | (kind(X0) & ~rich(X0))) & (~kind(X0) | rich(X0) | (~funny(X0) & ~old(X0)))) [flattening 56]
59. (kind(alice) | ~old(alice)) & (~kind(alice) | old(alice)) [nnf transformation 17]
71. ~wise(X0) | brave(X0) | ~rich(X0) [cnf transformation 40]
76. ~rich(X0) | patient(X0) | tall(X0) [cnf transformation 41]
96. old(X0) | rich(X0) [cnf transformation 49]
97. ~patient(X0) | old(X0) [cnf transformation 49]
107. ~kind(X0) | rich(X0) | ~old(X0) [cnf transformation 57]
116. ~patient(X0) | ~brave(X0) [cnf transformation 37]
119. kind(alice) | ~old(alice) [cnf transformation 59]
120. tall(alice) | wise(alice) [cnf transformation 18]
129. ~tall(alice) [cnf transformation 24]
178. ~kind(X0) | rich(X0) [subsumption resolution 107,96]
188. 12 <=> old(alice) [avatar definition]
190. ~old(alice) <- (~12) [avatar component clause 188]
192. 13 <=> kind(alice) [avatar definition]
194. kind(alice) <- (13) [avatar component clause 192]
195. ~12 | 13 [avatar split clause 119,192,188]
198. 14 <=> wise(alice) [avatar definition]
200. wise(alice) <- (14) [avatar component clause 198]
202. 15 <=> tall(alice) [avatar definition]
203. ~tall(alice) <- (~15) [avatar component clause 202]
205. 14 | 15 [avatar split clause 120,202,198]
226. ~15 [avatar split clause 129,202]
230. rich(alice) <- (~12) [resolution 96,190]
250. brave(alice) | ~rich(alice) <- (14) [resolution 71,200]
279. patient(alice) | tall(alice) <- (~12) [resolution 76,230]
280. patient(alice) <- (~12, ~15) [subsumption resolution 279,203]
284. old(alice) <- (~12, ~15) [resolution 280,97]
287. $false <- (~12, ~15) [subsumption resolution 284,190]
288. 12 | 15 [avatar contradiction clause 287]
290. 24 <=> rich(alice) [avatar definition]
291. rich(alice) <- (24) [avatar component clause 290]
294. 25 <=> brave(alice) [avatar definition]
296. brave(alice) <- (25) [avatar component clause 294]
297. ~24 | 25 | ~14 [avatar split clause 250,198,294,290]
298. rich(alice) <- (13) [resolution 194,178]
301. 24 | ~13 [avatar split clause 298,192,290]
305. patient(alice) | tall(alice) <- (24) [resolution 291,76]
306. patient(alice) <- (~15, 24) [subsumption resolution 305,203]
314. ~brave(alice) <- (~15, 24) [resolution 306,116]
317. $false <- (~15, 24, 25) [subsumption resolution 314,296]
318. 15 | ~24 | ~25 [avatar contradiction clause 317]
319. $false [avatar sat refutation 195,205,226,288,297,301,318]
% SZS output end Proof for 6557630171505506912515136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or patient then fred is calm or not tall and vice versa.
If someone is both not curious and not brave then someone is either not wise or happy and vice versa.
Everyone who is both rich and not calm is patient or not wise.
Everyone who is not creative or not rich is rich or wise.
If susan is either not brave or not patient then someone is both patient and old and vice versa.
Everyone who is wise or brave is not funny and vice versa.
Everyone who is either not funny or not kind is tall and vice versa.
If mary is either tall or curious then alice is curious.
Everyone who is both not patient and not calm is both not calm and not creative.
Everyone who is creative is quiet.
Everyone who is either not humble or not generous is old or happy and vice versa.
If mary is either not rich or not tall then lucy is creative or not brave and vice versa.
Everyone who is not strong or calm is both not kind and not curious.
Everyone who is both old and not patient is old or brave and vice versa.
Everyone who is either not rich or not old is not brave or not patient.
If lucy is either happy or not quiet then john is strong and vice versa.
Paul is either not patient or not old.
Someone is both not generous and not patient.
Someone is tall or not rich.
Someone is not creative or not strong.
Lucy is not rich.
Someone is both not kind and creative.
Someone is creative or generous. | Paul is funny. | neutral | (((funny(alice)|patient(alice)))<=>((calm(fred)|~tall(fred))))&
((?[X]:((~curious(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
(![X]:((rich(X)&~calm(X))=>(patient(X)|~wise(X))))&
(![X]:((~creative(X)|~rich(X))=>(rich(X)|wise(X))))&
(((~brave(susan)<~>~patient(susan)))<=>(?[X]:((patient(X)&old(X)))))&
(![X]:((wise(X)|brave(X))<=>~funny(X)))&
(![X]:((~funny(X)<~>~kind(X))<=>tall(X)))&
(((tall(mary)<~>curious(mary)))=>(curious(alice)))&
(![X]:((~patient(X)&~calm(X))=>(~calm(X)&~creative(X))))&
(![X]:(creative(X)=>quiet(X)))&
(![X]:((~humble(X)<~>~generous(X))<=>(old(X)|happy(X))))&
(((~rich(mary)<~>~tall(mary)))<=>((creative(lucy)|~brave(lucy))))&
(![X]:((~strong(X)|calm(X))=>(~kind(X)&~curious(X))))&
(![X]:((old(X)&~patient(X))<=>(old(X)|brave(X))))&
(![X]:((~rich(X)<~>~old(X))=>(~brave(X)|~patient(X))))&
(((happy(lucy)<~>~quiet(lucy)))<=>(strong(john)))&
((~patient(paul)<~>~old(paul)))&
(?[X]:((~generous(X)&~patient(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~creative(X)|~strong(X))))&
(~rich(lucy))&
(?[X]:((~kind(X)&creative(X))))&
(?[X]:((creative(X)|generous(X)))) | funny(paul) | [] | null | 0 |
If someone is both generous and not curious then paul is not tall or creative.
If someone is either kind or strong then susan is both old and happy and vice versa.
Everyone who is not old is either not rich or rich and vice versa.
If mary is both patient and not quiet then someone is both kind and happy and vice versa.
Everyone who is not patient or not kind is humble or rich.
If someone is not patient then someone is not kind or not brave and vice versa.
Everyone who is either not creative or not kind is either quiet or generous and vice versa.
Everyone who is patient or strong is both brave and not strong.
Everyone who is both not wise and not tall is funny or not rich and vice versa.
If someone is not calm then someone is both not kind and strong.
Everyone who is quiet is not patient or strong and vice versa.
Everyone who is either patient or not curious is not old or not brave and vice versa.
Everyone who is either brave or not humble is both wise and humble and vice versa.
If someone is either brave or not kind then someone is both generous and not quiet and vice versa.
If paul is either generous or not humble then susan is either strong or not wise and vice versa.
If someone is both not strong and not humble then paul is not old or patient.
Paul is either not old or patient.
Alice is both tall and creative.
Someone is either not brave or old.
Someone is not quiet.
Susan is generous.
Lucy is either not old or kind.
Someone is either not humble or brave.
Someone is either humble or not funny. | Paul is calm. | entailment | ((?[X]:((generous(X)&~curious(X))))=>((~tall(paul)|creative(paul))))&
((?[X]:((kind(X)<~>strong(X))))<=>((old(susan)&happy(susan))))&
(![X]:(~old(X)<=>(~rich(X)<~>rich(X))))&
(((patient(mary)&~quiet(mary)))<=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~patient(X)|~kind(X))=>(humble(X)|rich(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:((~creative(X)<~>~kind(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((patient(X)|strong(X))=>(brave(X)&~strong(X))))&
(![X]:((~wise(X)&~tall(X))<=>(funny(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~kind(X)&strong(X)))))&
(![X]:(quiet(X)<=>(~patient(X)|strong(X))))&
(![X]:((patient(X)<~>~curious(X))<=>(~old(X)|~brave(X))))&
(![X]:((brave(X)<~>~humble(X))<=>(wise(X)&humble(X))))&
((?[X]:((brave(X)<~>~kind(X))))<=>(?[X]:((generous(X)&~quiet(X)))))&
(((generous(paul)<~>~humble(paul)))<=>((strong(susan)<~>~wise(susan))))&
((?[X]:((~strong(X)&~humble(X))))=>((~old(paul)|patient(paul))))&
((~old(paul)<~>patient(paul)))&
((tall(alice)&creative(alice)))&
(?[X]:((~brave(X)<~>old(X))))&
(?[X]:(~quiet(X)))&
(generous(susan))&
((~old(lucy)<~>kind(lucy)))&
(?[X]:((~humble(X)<~>brave(X))))&
(?[X]:((humble(X)<~>~funny(X)))) | calm(paul) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6374083092447953991182834
% SZS output start Proof for 6374083092447953991182834
8. ! [X0] : ((strong(X0) | patient(X0)) => (~strong(X0) & brave(X0))) [input p7]
10. ? [X0] : ~calm(X0) => ? [X0] : (strong(X0) & ~kind(X0)) [input p9]
25. ~calm(paul) [input hypothesis]
27. ? [X0] : ~calm(X0) => ? [X1] : (strong(X1) & ~kind(X1)) [rectify 10]
33. ! [X0] : ((~strong(X0) & brave(X0)) | (~strong(X0) & ~patient(X0))) [ennf transformation 8]
34. ? [X1] : (strong(X1) & ~kind(X1)) | ! [X0] : calm(X0) [ennf transformation 27]
56. ? [X0] : (strong(X0) & ~kind(X0)) | ! [X1] : calm(X1) [rectify 34]
57. ? [X0] : (strong(X0) & ~kind(X0)) => (strong(sK4) & ~kind(sK4)) [choice axiom]
58. (strong(sK4) & ~kind(sK4)) | ! [X1] : calm(X1) [skolemisation 56,57]
115. ~strong(X0) | ~strong(X0) [cnf transformation 33]
122. strong(sK4) | calm(X1) [cnf transformation 58]
167. ~calm(paul) [cnf transformation 25]
170. ~strong(X0) [duplicate literal removal 115]
261. calm(X1) [subsumption resolution 122,170]
332. $false [subsumption resolution 167,261]
% SZS output end Proof for 6374083092447953991182834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not funny and wise then paul is not calm. Everyone who is quiet or not curious is both not brave and kind and vice versa. If john is both not quiet and wise then someone is humble and vice versa. If susan is not rich then mary is either not funny or not tall. If someone is either rich or not tall then someone is either not kind or creative and vice versa. If paul is both generous and not kind then someone is funny or not old and vice versa. Everyone who is not curious or not humble is both funny and humble. If someone is both not quiet and not curious then someone is not humble and vice versa. If john is tall or not humble then someone is not funny or not quiet and vice versa. If someone is either not creative or not calm then someone is either tall or old. Everyone who is not kind or curious is either not strong or not humble. Everyone who is not creative or happy is either not patient or calm and vice versa. If someone is not humble or creative then someone is both not funny and not brave. Everyone who is not funny or not creative is old or quiet. Everyone who is both not calm and old is either calm or not patient and vice versa. Someone is strong. Mary is not creative. Someone is both funny and quiet. Paul is old or not humble. Paul is either not old or creative. Susan is both calm and funny. Someone is not rich or creative. Someone is both quiet and rich. | Paul is not strong. | entailment | (((~funny(paul)&wise(paul)))=>(~calm(paul)))&
(![X]:((quiet(X)|~curious(X))<=>(~brave(X)&kind(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:(humble(X))))&
((~rich(susan))=>((~funny(mary)<~>~tall(mary))))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(((generous(paul)&~kind(paul)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((~curious(X)|~humble(X))=>(funny(X)&humble(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~creative(X)<~>~calm(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~kind(X)|curious(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~creative(X)|happy(X))<=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(![X]:((~calm(X)&old(X))<=>(calm(X)<~>~patient(X))))&
(?[X]:(strong(X)))&
(~creative(mary))&
(?[X]:((funny(X)&quiet(X))))&
((old(paul)|~humble(paul)))&
((~old(paul)<~>creative(paul)))&
((calm(susan)&funny(susan)))&
(?[X]:((~rich(X)|creative(X))))&
(?[X]:((quiet(X)&rich(X)))) | ~strong(paul) | [
"p1",
"p5",
"p6",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4851608172543158853238123
% SZS output start Proof for 4851608172543158853238123
2. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p1]
6. (~kind(paul) & generous(paul)) <=> ? [X0] : (~old(X0) | funny(X0)) [input p5]
7. ! [X0] : ((~humble(X0) | ~curious(X0)) => (humble(X0) & funny(X0))) [input p6]
11. ! [X0] : ((curious(X0) | ~kind(X0)) => (~strong(X0) <~> ~humble(X0))) [input p10]
18. ? [X0] : (quiet(X0) & funny(X0)) [input p17]
24. strong(paul) [input hypothesis]
32. ! [X0] : ((humble(X0) & funny(X0)) | (humble(X0) & curious(X0))) [ennf transformation 7]
34. ! [X0] : ((~strong(X0) <~> ~humble(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 11]
38. ! [X0] : (((~curious(X0) | quiet(X0)) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : ((~curious(X0) | quiet(X0) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 38]
51. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | (kind(paul) | ~generous(paul))) [nnf transformation 6]
52. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | kind(paul) | ~generous(paul)) [flattening 51]
53. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X1] : (~old(X1) | funny(X1)) | kind(paul) | ~generous(paul)) [rectify 52]
54. ? [X1] : (~old(X1) | funny(X1)) => (~old(sK3) | funny(sK3)) [choice axiom]
55. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & ((~old(sK3) | funny(sK3)) | kind(paul) | ~generous(paul)) [skolemisation 53,54]
70. ! [X0] : (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~curious(X0) & kind(X0))) [nnf transformation 34]
80. ? [X0] : (quiet(X0) & funny(X0)) => (quiet(sK10) & funny(sK10)) [choice axiom]
81. quiet(sK10) & funny(sK10) [skolemisation 18,80]
91. kind(X0) | curious(X0) [cnf transformation 39]
109. ~kind(paul) | ~funny(X0) [cnf transformation 55]
114. humble(X0) | humble(X0) [cnf transformation 32]
127. ~humble(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 70]
150. funny(sK10) [cnf transformation 81]
160. strong(paul) [cnf transformation 24]
163. humble(X0) [duplicate literal removal 114]
249. 20 <=> kind(paul) [avatar definition]
251. ~kind(paul) <- (~20) [avatar component clause 249]
254. 21 <=> ! [X0] : ~funny(X0) [avatar definition]
255. ~funny(X0) <- (21) [avatar component clause 254]
256. 21 | ~20 [avatar split clause 109,249,254]
314. ~strong(X0) | ~curious(X0) [subsumption resolution 127,163]
343. $false <- (21) [resolution 255,150]
346. ~21 [avatar contradiction clause 343]
352. curious(paul) <- (~20) [resolution 91,251]
354. ~curious(paul) [resolution 314,160]
355. $false <- (~20) [subsumption resolution 354,352]
356. 20 [avatar contradiction clause 355]
357. $false [avatar sat refutation 256,346,356]
% SZS output end Proof for 4851608172543158853238123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall then someone is both not patient and kind.
Everyone who is humble is generous or not rich and vice versa.
If fred is not curious then someone is creative or tall and vice versa.
Everyone who is either not calm or patient is either kind or not generous.
If fred is either not curious or not old then someone is not rich or calm and vice versa.
Everyone who is both tall and funny is generous and vice versa.
If someone is both not wise and not happy then paul is both not curious and not quiet and vice versa.
If alice is either not rich or not creative then fred is both not brave and funny and vice versa.
If alice is quiet or not tall then fred is both rich and not humble and vice versa.
Everyone who is both not wise and funny is tall or brave and vice versa.
Everyone who is quiet or not strong is wise or not kind.
Everyone who is either strong or not rich is wise.
If lucy is curious then alice is not generous.
Everyone who is both wise and tall is both curious and not funny and vice versa.
If susan is not happy or patient then paul is not brave or tall and vice versa.
Everyone who is either patient or not quiet is either not strong or brave.
Paul is either brave or not tall.
Paul is quiet.
Someone is not tall or not humble.
Someone is creative.
Lucy is not creative or old.
Susan is not tall.
Paul is either quiet or kind.
Susan is both quiet and not old. | Lucy is not calm. | neutral | ((~tall(susan))=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:(humble(X)<=>(generous(X)|~rich(X))))&
((~curious(fred))<=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((~calm(X)<~>patient(X))=>(kind(X)<~>~generous(X))))&
(((~curious(fred)<~>~old(fred)))<=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((tall(X)&funny(X))<=>generous(X)))&
((?[X]:((~wise(X)&~happy(X))))<=>((~curious(paul)&~quiet(paul))))&
(((~rich(alice)<~>~creative(alice)))<=>((~brave(fred)&funny(fred))))&
(((quiet(alice)|~tall(alice)))<=>((rich(fred)&~humble(fred))))&
(![X]:((~wise(X)&funny(X))<=>(tall(X)|brave(X))))&
(![X]:((quiet(X)|~strong(X))=>(wise(X)|~kind(X))))&
(![X]:((strong(X)<~>~rich(X))=>wise(X)))&
((curious(lucy))=>(~generous(alice)))&
(![X]:((wise(X)&tall(X))<=>(curious(X)&~funny(X))))&
(((~happy(susan)|patient(susan)))<=>((~brave(paul)|tall(paul))))&
(![X]:((patient(X)<~>~quiet(X))=>(~strong(X)<~>brave(X))))&
((brave(paul)<~>~tall(paul)))&
(quiet(paul))&
(?[X]:((~tall(X)|~humble(X))))&
(?[X]:(creative(X)))&
((~creative(lucy)|old(lucy)))&
(~tall(susan))&
((quiet(paul)<~>kind(paul)))&
((quiet(susan)&~old(susan))) | ~calm(lucy) | [] | null | 0 |
If mary is both generous and calm then susan is both wise and not calm.
Everyone who is calm or not generous is wise or creative and vice versa.
Everyone who is rich is not brave and vice versa.
Everyone who is funny or brave is tall or not generous.
If lucy is either generous or rich then fred is either not wise or not rich and vice versa.
Everyone who is rich is not kind.
Everyone who is not funny is both kind and calm and vice versa.
If someone is not creative then lucy is not humble or not kind.
If someone is both patient and curious then lucy is calm or humble.
If alice is both not old and not wise then paul is either curious or humble.
If alice is not quiet then someone is not calm.
Everyone who is either brave or not kind is calm or tall.
Everyone who is not quiet or quiet is not happy or not calm and vice versa.
Everyone who is creative or calm is wise or not kind and vice versa.
Everyone who is old is both generous and calm.
If someone is both funny and not old then someone is both rich and not rich and vice versa.
Susan is not creative or old.
Someone is both not humble and not funny.
Someone is either not rich or not creative.
Susan is both not old and not creative.
Someone is either not patient or not brave.
Someone is not wise or not rich.
Someone is either quiet or not humble.
Someone is both old and not quiet. | Mary is not old. | entailment | (((generous(mary)&calm(mary)))=>((wise(susan)&~calm(susan))))&
(![X]:((calm(X)|~generous(X))<=>(wise(X)|creative(X))))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((funny(X)|brave(X))=>(tall(X)|~generous(X))))&
(((generous(lucy)<~>rich(lucy)))<=>((~wise(fred)<~>~rich(fred))))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:(~funny(X)<=>(kind(X)&calm(X))))&
((?[X]:(~creative(X)))=>((~humble(lucy)|~kind(lucy))))&
((?[X]:((patient(X)&curious(X))))=>((calm(lucy)|humble(lucy))))&
(((~old(alice)&~wise(alice)))=>((curious(paul)<~>humble(paul))))&
((~quiet(alice))=>(?[X]:(~calm(X))))&
(![X]:((brave(X)<~>~kind(X))=>(calm(X)|tall(X))))&
(![X]:((~quiet(X)|quiet(X))<=>(~happy(X)|~calm(X))))&
(![X]:((creative(X)|calm(X))<=>(wise(X)|~kind(X))))&
(![X]:(old(X)=>(generous(X)&calm(X))))&
((?[X]:((funny(X)&~old(X))))<=>(?[X]:((rich(X)&~rich(X)))))&
((~creative(susan)|old(susan)))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
((~old(susan)&~creative(susan)))&
(?[X]:((~patient(X)<~>~brave(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(?[X]:((old(X)&~quiet(X)))) | ~old(mary) | [
"p0",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9121839916470815945686021
% SZS output start Proof for 9121839916470815945686021
1. (calm(mary) & generous(mary)) => (~calm(susan) & wise(susan)) [input p0]
7. ! [X0] : (~funny(X0) <=> (calm(X0) & kind(X0))) [input p6]
15. ! [X0] : (old(X0) => (calm(X0) & generous(X0))) [input p14]
16. ? [X0] : (~old(X0) & funny(X0)) <=> ? [X0] : (~rich(X0) & rich(X0)) [input p15]
25. old(mary) [input hypothesis]
26. ? [X0] : (~old(X0) & funny(X0)) <=> ? [X1] : (~rich(X1) & rich(X1)) [rectify 16]
29. (~calm(susan) & wise(susan)) | (~calm(mary) | ~generous(mary)) [ennf transformation 1]
30. (~calm(susan) & wise(susan)) | ~calm(mary) | ~generous(mary) [flattening 29]
39. ! [X0] : ((calm(X0) & generous(X0)) | ~old(X0)) [ennf transformation 15]
44. ! [X0] : ((~funny(X0) | (~calm(X0) | ~kind(X0))) & ((calm(X0) & kind(X0)) | funny(X0))) [nnf transformation 7]
45. ! [X0] : ((~funny(X0) | ~calm(X0) | ~kind(X0)) & ((calm(X0) & kind(X0)) | funny(X0))) [flattening 44]
53. (? [X0] : (~old(X0) & funny(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X1] : (~rich(X1) & rich(X1)) | ! [X0] : (old(X0) | ~funny(X0))) [nnf transformation 26]
54. (? [X0] : (~old(X0) & funny(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X2] : (~rich(X2) & rich(X2)) | ! [X3] : (old(X3) | ~funny(X3))) [rectify 53]
55. ? [X0] : (~old(X0) & funny(X0)) => (~old(sK1) & funny(sK1)) [choice axiom]
56. ? [X2] : (~rich(X2) & rich(X2)) => (~rich(sK2) & rich(sK2)) [choice axiom]
57. ((~old(sK1) & funny(sK1)) | ! [X1] : (rich(X1) | ~rich(X1))) & ((~rich(sK2) & rich(sK2)) | ! [X3] : (old(X3) | ~funny(X3))) [skolemisation 54,56,55]
74. ~calm(susan) | ~calm(mary) | ~generous(mary) [cnf transformation 30]
91. funny(X0) | calm(X0) [cnf transformation 45]
106. ~old(X0) | generous(X0) [cnf transformation 39]
107. ~old(X0) | calm(X0) [cnf transformation 39]
108. rich(sK2) | old(X3) | ~funny(X3) [cnf transformation 57]
109. ~rich(sK2) | old(X3) | ~funny(X3) [cnf transformation 57]
126. old(mary) [cnf transformation 25]
128. 1 <=> generous(mary) [avatar definition]
132. 2 <=> calm(mary) [avatar definition]
136. 3 <=> calm(susan) [avatar definition]
138. ~calm(susan) <- (~3) [avatar component clause 136]
139. ~1 | ~2 | ~3 [avatar split clause 74,136,132,128]
218. 20 <=> ! [X3] : (old(X3) | ~funny(X3)) [avatar definition]
219. ~funny(X3) | old(X3) <- (20) [avatar component clause 218]
221. 21 <=> rich(sK2) [avatar definition]
224. 20 | ~21 [avatar split clause 109,221,218]
225. 20 | 21 [avatar split clause 108,221,218]
282. generous(mary) [resolution 106,126]
284. 1 [avatar split clause 282,128]
286. calm(mary) [resolution 107,126]
290. 2 [avatar split clause 286,132]
292. old(X0) | calm(X0) <- (20) [resolution 219,91]
293. calm(X0) <- (20) [subsumption resolution 292,107]
342. $false <- (~3, 20) [resolution 293,138]
344. 3 | ~20 [avatar contradiction clause 342]
346. $false [avatar sat refutation 139,224,225,284,290,344]
% SZS output end Proof for 9121839916470815945686021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both creative and wise then someone is both curious and not brave. Everyone who is brave is not generous or happy. Everyone who is not old or old is both creative and strong and vice versa. If alice is old or not calm then someone is both not tall and not brave and vice versa. Everyone who is either not strong or not quiet is funny and vice versa. Everyone who is not generous is either quiet or not quiet. Everyone who is not strong or rich is both not curious and not kind and vice versa. If susan is both wise and kind then susan is not strong or curious. Everyone who is not wise or not quiet is either wise or not brave and vice versa. Everyone who is either brave or not creative is not kind. If someone is either not tall or not kind then someone is either not wise or strong and vice versa. If someone is either quiet or creative then someone is not tall. If someone is not strong then someone is both not tall and not wise and vice versa. Everyone who is either not brave or not tall is either rich or not brave and vice versa. Everyone who is not wise is either not generous or not strong. Everyone who is not funny or not old is both strong and tall. Someone is either not brave or not happy. Susan is both kind and not rich. Someone is patient or not happy. Someone is not brave or not quiet. Someone is strong or humble. Fred is rich or humble. Someone is either calm or not patient. John is old. | Alice is old. | contradiction | (((creative(lucy)&wise(lucy)))=>(?[X]:((curious(X)&~brave(X)))))&
(![X]:(brave(X)=>(~generous(X)|happy(X))))&
(![X]:((~old(X)|old(X))<=>(creative(X)&strong(X))))&
(((old(alice)|~calm(alice)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~strong(X)<~>~quiet(X))<=>funny(X)))&
(![X]:(~generous(X)=>(quiet(X)<~>~quiet(X))))&
(![X]:((~strong(X)|rich(X))<=>(~curious(X)&~kind(X))))&
(((wise(susan)&kind(susan)))=>((~strong(susan)|curious(susan))))&
(![X]:((~wise(X)|~quiet(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((brave(X)<~>~creative(X))=>~kind(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:(~tall(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((~brave(X)<~>~tall(X))<=>(rich(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(~generous(X)<~>~strong(X))))&
(![X]:((~funny(X)|~old(X))=>(strong(X)&tall(X))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((kind(susan)&~rich(susan)))&
(?[X]:((patient(X)|~happy(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
(?[X]:((strong(X)|humble(X))))&
((rich(fred)|humble(fred)))&
(?[X]:((calm(X)<~>~patient(X))))&
(old(john)) | old(alice) | [
"p2",
"p3",
"p4",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 514733775198904238184900
% SZS output start Proof for 514733775198904238184900
3. ! [X0] : ((old(X0) | ~old(X0)) <=> (strong(X0) & creative(X0))) [input p2]
4. (~calm(alice) | old(alice)) <=> ? [X0] : (~brave(X0) & ~tall(X0)) [input p3]
5. ! [X0] : ((~strong(X0) <~> ~quiet(X0)) <=> funny(X0)) [input p4]
9. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p8]
13. ? [X0] : ~strong(X0) <=> ? [X0] : (~wise(X0) & ~tall(X0)) [input p12]
16. ! [X0] : ((~old(X0) | ~funny(X0)) => (tall(X0) & strong(X0))) [input p15]
25. old(alice) [input hypothesis]
28. ? [X0] : ~strong(X0) <=> ? [X1] : (~wise(X1) & ~tall(X1)) [rectify 13]
29. ! [X0] : (funny(X0) => (~strong(X0) <~> ~quiet(X0))) [unused predicate definition removal 5]
36. ! [X0] : ((~strong(X0) <~> ~quiet(X0)) | ~funny(X0)) [ennf transformation 29]
43. ! [X0] : ((tall(X0) & strong(X0)) | (old(X0) & funny(X0))) [ennf transformation 16]
46. ! [X0] : (((old(X0) | ~old(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (~old(X0) & old(X0)))) [nnf transformation 3]
47. ! [X0] : ((old(X0) | ~old(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (~old(X0) & old(X0)))) [flattening 46]
48. ((~calm(alice) | old(alice)) | ! [X0] : (brave(X0) | tall(X0))) & (? [X0] : (~brave(X0) & ~tall(X0)) | (calm(alice) & ~old(alice))) [nnf transformation 4]
49. (~calm(alice) | old(alice) | ! [X0] : (brave(X0) | tall(X0))) & (? [X0] : (~brave(X0) & ~tall(X0)) | (calm(alice) & ~old(alice))) [flattening 48]
50. (~calm(alice) | old(alice) | ! [X0] : (brave(X0) | tall(X0))) & (? [X1] : (~brave(X1) & ~tall(X1)) | (calm(alice) & ~old(alice))) [rectify 49]
51. ? [X1] : (~brave(X1) & ~tall(X1)) => (~brave(sK1) & ~tall(sK1)) [choice axiom]
52. (~calm(alice) | old(alice) | ! [X0] : (brave(X0) | tall(X0))) & ((~brave(sK1) & ~tall(sK1)) | (calm(alice) & ~old(alice))) [skolemisation 50,51]
53. ! [X0] : (((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) | ~funny(X0)) [nnf transformation 36]
57. ! [X0] : (((~quiet(X0) | ~wise(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (quiet(X0) & wise(X0)))) [nnf transformation 9]
58. ! [X0] : ((~quiet(X0) | ~wise(X0) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (quiet(X0) & wise(X0)))) [flattening 57]
69. (? [X0] : ~strong(X0) | ! [X1] : (wise(X1) | tall(X1))) & (? [X1] : (~wise(X1) & ~tall(X1)) | ! [X0] : strong(X0)) [nnf transformation 28]
70. (? [X0] : ~strong(X0) | ! [X1] : (wise(X1) | tall(X1))) & (? [X2] : (~wise(X2) & ~tall(X2)) | ! [X3] : strong(X3)) [rectify 69]
71. ? [X0] : ~strong(X0) => ~strong(sK5) [choice axiom]
72. ? [X2] : (~wise(X2) & ~tall(X2)) => (~wise(sK6) & ~tall(sK6)) [choice axiom]
73. (~strong(sK5) | ! [X1] : (wise(X1) | tall(X1))) & ((~wise(sK6) & ~tall(sK6)) | ! [X3] : strong(X3)) [skolemisation 70,72,71]
91. strong(X0) | old(X0) [cnf transformation 47]
92. ~old(X0) | strong(X0) [cnf transformation 47]
94. ~tall(sK1) | ~old(alice) [cnf transformation 52]
96. ~brave(sK1) | ~old(alice) [cnf transformation 52]
99. ~quiet(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 53]
112. ~wise(X0) | brave(X0) | quiet(X0) [cnf transformation 58]
129. ~strong(sK5) | wise(X1) | tall(X1) [cnf transformation 73]
142. funny(X0) | tall(X0) [cnf transformation 43]
153. old(alice) [cnf transformation 25]
178. strong(X0) [subsumption resolution 91,92]
184. 6 <=> old(alice) [avatar definition]
193. 8 <=> brave(sK1) [avatar definition]
195. ~brave(sK1) <- (~8) [avatar component clause 193]
197. ~6 | ~8 [avatar split clause 96,193,184]
199. 9 <=> tall(sK1) [avatar definition]
201. ~tall(sK1) <- (~9) [avatar component clause 199]
203. ~6 | ~9 [avatar split clause 94,199,184]
204. ~funny(X0) | ~quiet(X0) [subsumption resolution 99,178]
259. tall(X1) | wise(X1) [subsumption resolution 129,178]
302. 6 [avatar split clause 153,184]
317. ~quiet(X0) | tall(X0) [resolution 204,142]
321. wise(sK1) <- (~9) [resolution 259,201]
327. brave(sK1) | quiet(sK1) <- (~9) [resolution 112,321]
331. quiet(sK1) <- (~8, ~9) [subsumption resolution 327,195]
353. tall(sK1) <- (~8, ~9) [resolution 331,317]
363. $false <- (~8, ~9) [subsumption resolution 353,201]
364. 8 | 9 [avatar contradiction clause 363]
365. $false [avatar sat refutation 197,203,302,364]
% SZS output end Proof for 514733775198904238184900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and quiet is not curious or not creative and vice versa.
If someone is both tall and not kind then alice is strong and vice versa.
If someone is not rich then someone is both not curious and quiet.
Everyone who is not kind is both kind and tall and vice versa.
Everyone who is humble or quiet is either not rich or not strong.
Everyone who is not humble is either curious or quiet.
If fred is not kind then alice is either generous or wise and vice versa.
If someone is both funny and not curious then fred is creative or not curious.
Everyone who is either not old or brave is patient.
Everyone who is funny is both tall and not humble and vice versa.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is both tall and old then fred is not brave or creative.
Everyone who is tall is wise and vice versa.
Everyone who is happy is both humble and wise and vice versa.
Everyone who is either not creative or not quiet is not strong and vice versa.
John is both not calm and not old.
Someone is not kind or strong.
Someone is not old or not quiet.
Susan is both not patient and quiet.
Someone is either not patient or not old.
Someone is either brave or not quiet. | Fred is kind. | entailment | (![X]:((strong(X)&quiet(X))<=>(~curious(X)|~creative(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(strong(alice)))&
((?[X]:(~rich(X)))=>(?[X]:((~curious(X)&quiet(X)))))&
(![X]:(~kind(X)<=>(kind(X)&tall(X))))&
(![X]:((humble(X)|quiet(X))=>(~rich(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(curious(X)<~>quiet(X))))&
((~kind(fred))<=>((generous(alice)<~>wise(alice))))&
((?[X]:((funny(X)&~curious(X))))=>((creative(fred)|~curious(fred))))&
(![X]:((~old(X)<~>brave(X))=>patient(X)))&
(![X]:(funny(X)<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((tall(X)&old(X))))=>((~brave(fred)|creative(fred))))&
(![X]:(tall(X)<=>wise(X)))&
(![X]:(happy(X)<=>(humble(X)&wise(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>~strong(X)))&
((~calm(john)&~old(john)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~old(X)|~quiet(X))))&
((~patient(susan)&quiet(susan)))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((brave(X)<~>~quiet(X)))) | kind(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2268551481302760387381315
% SZS output start Proof for 2268551481302760387381315
4. ! [X0] : (~kind(X0) <=> (tall(X0) & kind(X0))) [input p3]
22. ~kind(fred) [input hypothesis]
45. ! [X0] : ((~kind(X0) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | kind(X0))) [nnf transformation 4]
46. ! [X0] : ((~kind(X0) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | kind(X0))) [flattening 45]
77. kind(X0) | kind(X0) [cnf transformation 46]
118. ~kind(fred) [cnf transformation 22]
119. kind(X0) [duplicate literal removal 77]
218. $false [subsumption resolution 118,119]
% SZS output end Proof for 2268551481302760387381315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not rich then susan is not kind or kind and vice versa. Everyone who is happy is either not humble or humble and vice versa. If someone is not rich then someone is not curious and vice versa. Everyone who is either generous or not wise is both not wise and not patient. If someone is both funny and not strong then someone is both quiet and patient and vice versa. Everyone who is both not curious and tall is not strong and vice versa. Everyone who is quiet is both quiet and funny. Everyone who is not creative is either happy or generous. If someone is not wise or curious then someone is either not brave or calm and vice versa. Everyone who is both creative and not rich is happy and vice versa. If alice is wise or not funny then someone is both not happy and not calm and vice versa. Everyone who is not brave or not patient is not curious or not funny and vice versa. If someone is not strong then lucy is generous or wise. If someone is both not tall and rich then someone is not humble and vice versa. Everyone who is not brave is either not happy or funny and vice versa. If paul is not tall then mary is both curious and not patient. Someone is not humble or strong. Fred is not strong or quiet. Fred is rich or not curious. Paul is either kind or not tall. Someone is patient or happy. Alice is either strong or old. Someone is either wise or old. | Susan is not kind. | neutral | ((?[X]:((calm(X)<~>~rich(X))))<=>((~kind(susan)|kind(susan))))&
(![X]:(happy(X)<=>(~humble(X)<~>humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)<~>~wise(X))=>(~wise(X)&~patient(X))))&
((?[X]:((funny(X)&~strong(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((~curious(X)&tall(X))<=>~strong(X)))&
(![X]:(quiet(X)=>(quiet(X)&funny(X))))&
(![X]:(~creative(X)=>(happy(X)<~>generous(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:((creative(X)&~rich(X))<=>happy(X)))&
(((wise(alice)|~funny(alice)))<=>(?[X]:((~happy(X)&~calm(X)))))&
(![X]:((~brave(X)|~patient(X))<=>(~curious(X)|~funny(X))))&
((?[X]:(~strong(X)))=>((generous(lucy)|wise(lucy))))&
((?[X]:((~tall(X)&rich(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>funny(X))))&
((~tall(paul))=>((curious(mary)&~patient(mary))))&
(?[X]:((~humble(X)|strong(X))))&
((~strong(fred)|quiet(fred)))&
((rich(fred)|~curious(fred)))&
((kind(paul)<~>~tall(paul)))&
(?[X]:((patient(X)|happy(X))))&
((strong(alice)<~>old(alice)))&
(?[X]:((wise(X)<~>old(X)))) | ~kind(susan) | [] | null | 0 |
Everyone who is either not happy or not curious is curious.
If someone is either rich or funny then someone is both humble and creative and vice versa.
If john is both not generous and generous then someone is either humble or tall.
Everyone who is not kind or creative is not calm or old and vice versa.
If alice is funny or kind then alice is not quiet or quiet and vice versa.
Everyone who is both quiet and rich is both curious and kind.
Everyone who is not tall or creative is creative and vice versa.
If paul is either happy or not wise then someone is humble and vice versa.
If lucy is either not funny or not strong then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
Fred is either curious or not calm.
Someone is calm or tall.
Fred is either quiet or not patient.
Someone is either not brave or not calm.
Someone is brave or creative. | Susan is humble. | contradiction | (![X]:((~happy(X)<~>~curious(X))=>curious(X)))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)|old(X))))&
(((funny(alice)|kind(alice)))<=>((~quiet(alice)|quiet(alice))))&
(![X]:((quiet(X)&rich(X))=>(curious(X)&kind(X))))&
(![X]:((~tall(X)|creative(X))<=>creative(X)))&
(((happy(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((~funny(lucy)<~>~strong(lucy)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
((curious(fred)<~>~calm(fred)))&
(?[X]:((calm(X)|tall(X))))&
((quiet(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X)))) | humble(susan) | [
"p0",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7017010320650258864417980
% SZS output start Proof for 7017010320650258864417980
1. ! [X0] : ((~happy(X0) <~> ~curious(X0)) => curious(X0)) [input p0]
8. (happy(paul) <~> ~wise(paul)) <=> ? [X0] : humble(X0) [input p7]
10. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p9]
12. ! [X0] : ((~funny(X0) & wise(X0)) <=> (~happy(X0) | rich(X0))) [input p11]
21. humble(susan) [input hypothesis]
24. ! [X0] : (curious(X0) | (~happy(X0) <=> ~curious(X0))) [ennf transformation 1]
29. ! [X0] : (curious(X0) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) [nnf transformation 24]
44. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [nnf transformation 8]
45. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [rectify 44]
46. ? [X1] : humble(X1) => humble(sK3) [choice axiom]
47. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (humble(sK3) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [skolemisation 45,46]
52. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 10]
53. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 52]
59. ! [X0] : (((~funny(X0) & wise(X0)) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | (funny(X0) | ~wise(X0)))) [nnf transformation 12]
60. ! [X0] : (((~funny(X0) & wise(X0)) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | funny(X0) | ~wise(X0))) [flattening 59]
82. curious(X0) | ~happy(X0) | curious(X0) [cnf transformation 29]
106. ~wise(paul) | happy(paul) | ~humble(X0) [cnf transformation 47]
117. ~curious(X0) | ~curious(X0) [cnf transformation 53]
124. wise(X0) | happy(X0) [cnf transformation 60]
152. humble(susan) [cnf transformation 21]
157. ~curious(X0) [duplicate literal removal 117]
159. ~happy(X0) | curious(X0) [duplicate literal removal 82]
206. 11 <=> ! [X0] : ~humble(X0) [avatar definition]
207. ~humble(X0) <- (11) [avatar component clause 206]
209. 12 <=> happy(paul) [avatar definition]
210. happy(paul) <- (12) [avatar component clause 209]
211. ~happy(paul) <- (~12) [avatar component clause 209]
213. 13 <=> wise(paul) [avatar definition]
214. ~wise(paul) <- (~13) [avatar component clause 213]
217. 11 | 12 | ~13 [avatar split clause 106,213,209,206]
279. 27 <=> humble(susan) [avatar definition]
280. humble(susan) <- (27) [avatar component clause 279]
364. 27 [avatar split clause 152,279]
392. happy(paul) <- (~13) [resolution 214,124]
393. $false <- (~12, ~13) [subsumption resolution 392,211]
394. 12 | 13 [avatar contradiction clause 393]
401. curious(paul) <- (12) [resolution 159,210]
404. $false <- (12) [subsumption resolution 401,157]
405. ~12 [avatar contradiction clause 404]
411. $false <- (11, 27) [resolution 207,280]
412. ~11 | ~27 [avatar contradiction clause 411]
413. $false [avatar sat refutation 217,364,394,405,412]
% SZS output end Proof for 7017010320650258864417980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not funny is kind.
If someone is either not patient or not rich then someone is not brave or not quiet and vice versa.
If fred is not strong then john is both not creative and not generous and vice versa.
Everyone who is creative or not generous is not rich or not calm and vice versa.
If someone is either not old or not rich then mary is both creative and not generous and vice versa.
If john is both not calm and wise then lucy is not strong or not curious and vice versa.
If someone is not curious then susan is either not wise or creative and vice versa.
If mary is either not patient or rich then someone is either not quiet or not calm and vice versa.
Everyone who is either kind or not creative is both patient and not strong and vice versa.
If lucy is both not generous and not humble then someone is either generous or kind and vice versa.
Everyone who is humble or not happy is old.
Everyone who is either creative or not funny is not happy or not wise and vice versa.
Everyone who is both funny and happy is either curious or brave and vice versa.
If paul is brave then someone is both happy and old.
If lucy is not calm or curious then someone is either rich or humble.
Everyone who is both generous and not generous is tall or creative and vice versa.
John is not generous.
Someone is not rich or not curious.
Someone is both not humble and not creative.
Someone is either wise or humble.
Someone is both strong and not calm.
Someone is brave or not wise.
Alice is both not brave and funny. | Lucy is not humble. | entailment | (![X]:((~strong(X)&~funny(X))=>kind(X)))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
((~strong(fred))<=>((~creative(john)&~generous(john))))&
(![X]:((creative(X)|~generous(X))<=>(~rich(X)|~calm(X))))&
((?[X]:((~old(X)<~>~rich(X))))<=>((creative(mary)&~generous(mary))))&
(((~calm(john)&wise(john)))<=>((~strong(lucy)|~curious(lucy))))&
((?[X]:(~curious(X)))<=>((~wise(susan)<~>creative(susan))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:((~quiet(X)<~>~calm(X)))))&
(![X]:((kind(X)<~>~creative(X))<=>(patient(X)&~strong(X))))&
(((~generous(lucy)&~humble(lucy)))<=>(?[X]:((generous(X)<~>kind(X)))))&
(![X]:((humble(X)|~happy(X))=>old(X)))&
(![X]:((creative(X)<~>~funny(X))<=>(~happy(X)|~wise(X))))&
(![X]:((funny(X)&happy(X))<=>(curious(X)<~>brave(X))))&
((brave(paul))=>(?[X]:((happy(X)&old(X)))))&
(((~calm(lucy)|curious(lucy)))=>(?[X]:((rich(X)<~>humble(X)))))&
(![X]:((generous(X)&~generous(X))<=>(tall(X)|creative(X))))&
(~generous(john))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((wise(X)<~>humble(X))))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:((brave(X)|~wise(X))))&
((~brave(alice)&funny(alice))) | ~humble(lucy) | [
"p3",
"p8",
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 75549174326588520769206
% SZS output start Proof for 75549174326588520769206
4. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~calm(X0) | ~rich(X0))) [input p3]
9. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (~strong(X0) & patient(X0))) [input p8]
10. (~humble(lucy) & ~generous(lucy)) <=> ? [X0] : (generous(X0) <~> kind(X0)) [input p9]
16. ! [X0] : ((~generous(X0) & generous(X0)) <=> (creative(X0) | tall(X0))) [input p15]
21. ? [X0] : (~calm(X0) & strong(X0)) [input p20]
24. humble(lucy) [input hypothesis]
38. ! [X0] : (((~generous(X0) | creative(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 4]
39. ! [X0] : ((~generous(X0) | creative(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (generous(X0) & ~creative(X0)))) [flattening 38]
55. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 9]
56. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [flattening 55]
57. ((~humble(lucy) & ~generous(lucy)) | ! [X0] : ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (? [X0] : ((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | (humble(lucy) | generous(lucy))) [nnf transformation 10]
58. ((~humble(lucy) & ~generous(lucy)) | ! [X0] : ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (? [X0] : ((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | humble(lucy) | generous(lucy)) [flattening 57]
59. ((~humble(lucy) & ~generous(lucy)) | ! [X0] : ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (? [X1] : ((~kind(X1) | ~generous(X1)) & (kind(X1) | generous(X1))) | humble(lucy) | generous(lucy)) [rectify 58]
60. ? [X1] : ((~kind(X1) | ~generous(X1)) & (kind(X1) | generous(X1))) => ((~kind(sK5) | ~generous(sK5)) & (kind(sK5) | generous(sK5))) [choice axiom]
61. ((~humble(lucy) & ~generous(lucy)) | ! [X0] : ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(sK5) | ~generous(sK5)) & (kind(sK5) | generous(sK5))) | humble(lucy) | generous(lucy)) [skolemisation 59,60]
71. ! [X0] : (((~generous(X0) & generous(X0)) | (~creative(X0) & ~tall(X0))) & ((creative(X0) | tall(X0)) | (generous(X0) | ~generous(X0)))) [nnf transformation 16]
72. ! [X0] : (((~generous(X0) & generous(X0)) | (~creative(X0) & ~tall(X0))) & (creative(X0) | tall(X0) | generous(X0) | ~generous(X0))) [flattening 71]
80. ? [X0] : (~calm(X0) & strong(X0)) => (~calm(sK11) & strong(sK11)) [choice axiom]
81. ~calm(sK11) & strong(sK11) [skolemisation 21,80]
97. ~generous(X0) | creative(X0) | calm(X0) [cnf transformation 39]
124. ~strong(X0) | kind(X0) | creative(X0) [cnf transformation 56]
132. ~humble(lucy) | generous(X0) | ~kind(X0) [cnf transformation 61]
155. generous(X0) | ~creative(X0) [cnf transformation 72]
157. ~generous(X0) | ~creative(X0) [cnf transformation 72]
164. strong(sK11) [cnf transformation 81]
165. ~calm(sK11) [cnf transformation 81]
169. humble(lucy) [cnf transformation 24]
318. 32 <=> ! [X0] : (generous(X0) | ~kind(X0)) [avatar definition]
319. ~kind(X0) | generous(X0) <- (32) [avatar component clause 318]
321. 33 <=> humble(lucy) [avatar definition]
324. 32 | ~33 [avatar split clause 132,321,318]
375. ~creative(X0) [subsumption resolution 155,157]
406. 33 [avatar split clause 169,321]
422. kind(sK11) | creative(sK11) [resolution 124,164]
423. kind(sK11) [subsumption resolution 422,375]
424. generous(sK11) <- (32) [resolution 423,319]
430. creative(sK11) | calm(sK11) <- (32) [resolution 424,97]
434. calm(sK11) <- (32) [subsumption resolution 430,375]
435. $false <- (32) [subsumption resolution 434,165]
436. ~32 [avatar contradiction clause 435]
438. $false [avatar sat refutation 324,406,436]
% SZS output end Proof for 75549174326588520769206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not creative then lucy is not rich and vice versa.
If fred is happy then someone is both not curious and kind and vice versa.
Everyone who is both not rich and not wise is not rich or humble and vice versa.
If paul is not curious then john is both wise and rich and vice versa.
If someone is not patient then someone is not quiet and vice versa.
Everyone who is creative or generous is both quiet and not calm.
Everyone who is creative is old or not patient.
Everyone who is both strong and kind is not wise.
If mary is rich then fred is wise and vice versa.
If someone is not calm or funny then susan is either generous or not quiet.
If alice is both kind and not patient then someone is not generous or not rich.
Everyone who is both not happy and brave is either not humble or rich and vice versa.
Everyone who is both not curious and not rich is curious or not generous and vice versa.
If susan is not calm then john is both not curious and wise and vice versa.
Everyone who is not tall or not happy is either patient or not generous and vice versa.
Everyone who is both not tall and not calm is not quiet or funny.
Someone is both not funny and not wise.
Alice is not patient or strong.
Someone is not generous or patient.
Susan is either quiet or not strong.
Lucy is wise.
Someone is either tall or old.
John is patient or not quiet.
Someone is not wise or quiet. | Fred is calm. | contradiction | ((?[X]:((~kind(X)|~creative(X))))<=>(~rich(lucy)))&
((happy(fred))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((~rich(X)&~wise(X))<=>(~rich(X)|humble(X))))&
((~curious(paul))<=>((wise(john)&rich(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|generous(X))=>(quiet(X)&~calm(X))))&
(![X]:(creative(X)=>(old(X)|~patient(X))))&
(![X]:((strong(X)&kind(X))=>~wise(X)))&
((rich(mary))<=>(wise(fred)))&
((?[X]:((~calm(X)|funny(X))))=>((generous(susan)<~>~quiet(susan))))&
(((kind(alice)&~patient(alice)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~happy(X)&brave(X))<=>(~humble(X)<~>rich(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|~generous(X))))&
((~calm(susan))<=>((~curious(john)&wise(john))))&
(![X]:((~tall(X)|~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((~tall(X)&~calm(X))=>(~quiet(X)|funny(X))))&
(?[X]:((~funny(X)&~wise(X))))&
((~patient(alice)|strong(alice)))&
(?[X]:((~generous(X)|patient(X))))&
((quiet(susan)<~>~strong(susan)))&
(wise(lucy))&
(?[X]:((tall(X)<~>old(X))))&
((patient(john)|~quiet(john)))&
(?[X]:((~wise(X)|quiet(X)))) | calm(fred) | [
"p0",
"p2",
"p5",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2667633935341078894801302
% SZS output start Proof for 2667633935341078894801302
1. ? [X0] : (~creative(X0) | ~kind(X0)) <=> ~rich(lucy) [input p0]
3. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (humble(X0) | ~rich(X0))) [input p2]
6. ! [X0] : ((generous(X0) | creative(X0)) => (~calm(X0) & quiet(X0))) [input p5]
21. wise(lucy) [input p20]
25. calm(fred) [input hypothesis]
27. ! [X0] : ((~calm(X0) & quiet(X0)) | (~generous(X0) & ~creative(X0))) [ennf transformation 6]
37. (? [X0] : (~creative(X0) | ~kind(X0)) | rich(lucy)) & (~rich(lucy) | ! [X0] : (creative(X0) & kind(X0))) [nnf transformation 1]
38. (? [X0] : (~creative(X0) | ~kind(X0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (creative(X1) & kind(X1))) [rectify 37]
39. ? [X0] : (~creative(X0) | ~kind(X0)) => (~creative(sK0) | ~kind(sK0)) [choice axiom]
40. ((~creative(sK0) | ~kind(sK0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (creative(X1) & kind(X1))) [skolemisation 38,39]
45. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~humble(X0) & rich(X0))) & ((humble(X0) | ~rich(X0)) | (wise(X0) | rich(X0)))) [nnf transformation 3]
46. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~humble(X0) & rich(X0))) & (humble(X0) | ~rich(X0) | wise(X0) | rich(X0))) [flattening 45]
77. ~rich(lucy) | creative(X1) [cnf transformation 40]
85. ~wise(X0) | rich(X0) [cnf transformation 46]
94. ~calm(X0) | ~creative(X0) [cnf transformation 27]
132. wise(lucy) [cnf transformation 21]
137. calm(fred) [cnf transformation 25]
141. 1 <=> rich(lucy) [avatar definition]
154. 4 <=> ! [X1] : creative(X1) [avatar definition]
155. creative(X1) <- (4) [avatar component clause 154]
156. 4 | ~1 [avatar split clause 77,141,154]
313. rich(lucy) [resolution 85,132]
317. 1 [avatar split clause 313,141]
335. ~creative(fred) [resolution 94,137]
336. $false <- (4) [subsumption resolution 335,155]
337. ~4 [avatar contradiction clause 336]
338. $false [avatar sat refutation 156,317,337]
% SZS output end Proof for 2667633935341078894801302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and brave is not brave and vice versa.
If paul is both not curious and wise then someone is quiet or not tall.
Everyone who is either calm or not kind is generous and vice versa.
Everyone who is not quiet or strong is both tall and not brave and vice versa.
Everyone who is happy or not strong is old or not patient.
If fred is both not humble and not happy then someone is rich or not rich.
Everyone who is brave is both old and not calm and vice versa.
Everyone who is patient or not calm is rich or not wise and vice versa.
Everyone who is both not happy and not humble is tall or not tall.
If someone is quiet or old then lucy is not strong and vice versa.
If mary is both not strong and humble then mary is either not generous or not calm and vice versa.
Everyone who is not patient is generous and vice versa.
Everyone who is happy is not strong.
If someone is either not calm or kind then susan is both generous and not brave and vice versa.
If someone is tall or not creative then john is either not humble or not happy.
Mary is not curious.
Someone is not creative.
Mary is wise.
Someone is not calm or not happy.
Someone is either not old or happy.
Fred is either not old or funny.
Alice is tall. | Mary is kind. | entailment | (![X]:((curious(X)&brave(X))<=>~brave(X)))&
(((~curious(paul)&wise(paul)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((calm(X)<~>~kind(X))<=>generous(X)))&
(![X]:((~quiet(X)|strong(X))<=>(tall(X)&~brave(X))))&
(![X]:((happy(X)|~strong(X))=>(old(X)|~patient(X))))&
(((~humble(fred)&~happy(fred)))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(brave(X)<=>(old(X)&~calm(X))))&
(![X]:((patient(X)|~calm(X))<=>(rich(X)|~wise(X))))&
(![X]:((~happy(X)&~humble(X))=>(tall(X)|~tall(X))))&
((?[X]:((quiet(X)|old(X))))<=>(~strong(lucy)))&
(((~strong(mary)&humble(mary)))<=>((~generous(mary)<~>~calm(mary))))&
(![X]:(~patient(X)<=>generous(X)))&
(![X]:(happy(X)=>~strong(X)))&
((?[X]:((~calm(X)<~>kind(X))))<=>((generous(susan)&~brave(susan))))&
((?[X]:((tall(X)|~creative(X))))=>((~humble(john)<~>~happy(john))))&
(~curious(mary))&
(?[X]:(~creative(X)))&
(wise(mary))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:((~old(X)<~>happy(X))))&
((~old(fred)<~>funny(fred)))&
(tall(alice)) | kind(mary) | [
"p0",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6568132407567779681678411
% SZS output start Proof for 6568132407567779681678411
1. ! [X0] : ((brave(X0) & curious(X0)) <=> ~brave(X0)) [input p0]
7. ! [X0] : (brave(X0) <=> (~calm(X0) & old(X0))) [input p6]
14. ? [X0] : (~calm(X0) <~> kind(X0)) <=> (~brave(susan) & generous(susan)) [input p13]
23. ~kind(mary) [input hypothesis]
34. ! [X0] : (((brave(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) | ~curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((brave(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | ~brave(X0) | ~curious(X0))) [flattening 34]
43. ! [X0] : ((brave(X0) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | ~brave(X0))) [nnf transformation 7]
44. ! [X0] : ((brave(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | ~brave(X0))) [flattening 43]
54. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (brave(susan) | ~generous(susan))) & ((~brave(susan) & generous(susan)) | ! [X0] : ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0)))) [nnf transformation 14]
55. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X0] : ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0)))) [flattening 54]
56. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1)))) [rectify 55]
57. ? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) => ((~kind(sK3) | calm(sK3)) & (kind(sK3) | ~calm(sK3))) [choice axiom]
58. (((~kind(sK3) | calm(sK3)) & (kind(sK3) | ~calm(sK3))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1)))) [skolemisation 56,57]
70. brave(X0) | brave(X0) [cnf transformation 35]
85. ~calm(X0) | ~brave(X0) [cnf transformation 44]
106. ~brave(susan) | kind(X1) | calm(X1) [cnf transformation 58]
123. ~kind(mary) [cnf transformation 23]
125. brave(X0) [duplicate literal removal 70]
144. ~calm(X0) [subsumption resolution 85,125]
160. kind(X1) | calm(X1) [subsumption resolution 106,125]
161. kind(X1) [subsumption resolution 160,144]
182. $false [subsumption resolution 123,161]
% SZS output end Proof for 6568132407567779681678411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both patient and strong then someone is not calm and vice versa.
If alice is either brave or not rich then susan is both not tall and not funny.
If someone is not humble or wise then paul is both tall and creative.
Everyone who is either happy or not old is creative.
If paul is either not calm or not humble then someone is not quiet.
Everyone who is not patient or not strong is not quiet.
Everyone who is not happy is not strong or not happy and vice versa.
If someone is happy then someone is funny.
If someone is either calm or generous then someone is quiet.
If fred is rich then alice is not wise.
Everyone who is calm or not happy is happy or quiet and vice versa.
Everyone who is not kind or not generous is both not tall and not old and vice versa.
If someone is both funny and patient then lucy is not rich and vice versa.
Everyone who is creative is quiet or tall and vice versa.
Everyone who is wise or humble is not kind or not happy.
Everyone who is not happy is generous or patient and vice versa.
Someone is either quiet or not kind.
Paul is happy.
Susan is either humble or not humble.
Someone is not calm.
Fred is both not tall and kind. | Alice is not tall. | neutral | (((patient(mary)&strong(mary)))<=>(?[X]:(~calm(X))))&
(((brave(alice)<~>~rich(alice)))=>((~tall(susan)&~funny(susan))))&
((?[X]:((~humble(X)|wise(X))))=>((tall(paul)&creative(paul))))&
(![X]:((happy(X)<~>~old(X))=>creative(X)))&
(((~calm(paul)<~>~humble(paul)))=>(?[X]:(~quiet(X))))&
(![X]:((~patient(X)|~strong(X))=>~quiet(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~happy(X))))&
((?[X]:(happy(X)))=>(?[X]:(funny(X))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:(quiet(X))))&
((rich(fred))=>(~wise(alice)))&
(![X]:((calm(X)|~happy(X))<=>(happy(X)|quiet(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~tall(X)&~old(X))))&
((?[X]:((funny(X)&patient(X))))<=>(~rich(lucy)))&
(![X]:(creative(X)<=>(quiet(X)|tall(X))))&
(![X]:((wise(X)|humble(X))=>(~kind(X)|~happy(X))))&
(![X]:(~happy(X)<=>(generous(X)|patient(X))))&
(?[X]:((quiet(X)<~>~kind(X))))&
(happy(paul))&
((humble(susan)<~>~humble(susan)))&
(?[X]:(~calm(X)))&
((~tall(fred)&kind(fred))) | ~tall(alice) | [] | null | 0 |
If paul is not happy then lucy is either calm or wise and vice versa.
If john is either old or not old then someone is both funny and rich.
Everyone who is not tall or humble is both patient and not creative.
If someone is both kind and not old then john is either tall or not rich and vice versa.
If mary is either kind or not curious then fred is creative.
If someone is old or not humble then mary is both not wise and humble.
If someone is patient then someone is happy or strong and vice versa.
Everyone who is both not brave and not tall is either patient or not wise and vice versa.
If someone is kind then someone is either not patient or not funny.
If john is either funny or creative then someone is either not wise or quiet and vice versa.
Everyone who is both quiet and not tall is both wise and quiet and vice versa.
If someone is not strong or not patient then john is both generous and old.
If someone is not wise or not rich then alice is quiet and vice versa.
Everyone who is not happy is either not rich or curious.
If someone is either humble or quiet then someone is either curious or humble and vice versa.
Lucy is not patient.
Someone is both not generous and kind.
Paul is not humble or not happy.
Paul is not brave.
Alice is wise.
Susan is both not humble and not patient.
Someone is not old.
Someone is both brave and patient. | Lucy is tall. | entailment | ((~happy(paul))<=>((calm(lucy)<~>wise(lucy))))&
(((old(john)<~>~old(john)))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~tall(X)|humble(X))=>(patient(X)&~creative(X))))&
((?[X]:((kind(X)&~old(X))))<=>((tall(john)<~>~rich(john))))&
(((kind(mary)<~>~curious(mary)))=>(creative(fred)))&
((?[X]:((old(X)|~humble(X))))=>((~wise(mary)&humble(mary))))&
((?[X]:(patient(X)))<=>(?[X]:((happy(X)|strong(X)))))&
(![X]:((~brave(X)&~tall(X))<=>(patient(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:((~patient(X)<~>~funny(X)))))&
(((funny(john)<~>creative(john)))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((quiet(X)&~tall(X))<=>(wise(X)&quiet(X))))&
((?[X]:((~strong(X)|~patient(X))))=>((generous(john)&old(john))))&
((?[X]:((~wise(X)|~rich(X))))<=>(quiet(alice)))&
(![X]:(~happy(X)=>(~rich(X)<~>curious(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(~patient(lucy))&
(?[X]:((~generous(X)&kind(X))))&
((~humble(paul)|~happy(paul)))&
(~brave(paul))&
(wise(alice))&
((~humble(susan)&~patient(susan)))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)&patient(X)))) | tall(lucy) | [
"p2",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 486498408485846921139075
% SZS output start Proof for 486498408485846921139075
3. ! [X0] : ((humble(X0) | ~tall(X0)) => (~creative(X0) & patient(X0))) [input p2]
16. ~patient(lucy) [input p15]
24. ~tall(lucy) [input hypothesis]
29. ! [X0] : ((~creative(X0) & patient(X0)) | (~humble(X0) & tall(X0))) [ennf transformation 3]
85. patient(X0) | tall(X0) [cnf transformation 29]
141. ~patient(lucy) [cnf transformation 16]
152. ~tall(lucy) [cnf transformation 24]
401. tall(lucy) [resolution 85,141]
403. $false [subsumption resolution 401,152]
% SZS output end Proof for 486498408485846921139075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not curious or strong then fred is not wise or not patient and vice versa.
Everyone who is calm or not happy is brave.
Everyone who is old is both not calm and tall.
Everyone who is old or not old is both patient and old and vice versa.
If susan is either wise or curious then someone is either not funny or not old and vice versa.
Everyone who is both humble and not humble is not kind or patient.
If someone is happy then lucy is both tall and not kind.
Everyone who is not tall is either strong or patient.
If someone is not tall then mary is both not generous and creative and vice versa.
Everyone who is both brave and not strong is either curious or tall and vice versa.
If someone is not humble or not creative then fred is either patient or generous and vice versa.
Everyone who is both not kind and not strong is either generous or not funny and vice versa.
If someone is not tall or old then susan is both not happy and curious.
If fred is either not brave or not creative then someone is curious and vice versa.
Everyone who is both quiet and old is kind.
If fred is either not calm or not tall then fred is kind or happy.
Paul is not kind or generous.
Someone is both not wise and not happy.
Lucy is not calm.
Someone is both curious and not kind. | Mary is not happy. | neutral | (((~curious(mary)<~>strong(mary)))<=>((~wise(fred)|~patient(fred))))&
(![X]:((calm(X)|~happy(X))=>brave(X)))&
(![X]:(old(X)=>(~calm(X)&tall(X))))&
(![X]:((old(X)|~old(X))<=>(patient(X)&old(X))))&
(((wise(susan)<~>curious(susan)))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((humble(X)&~humble(X))=>(~kind(X)|patient(X))))&
((?[X]:(happy(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:(~tall(X)=>(strong(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>((~generous(mary)&creative(mary))))&
(![X]:((brave(X)&~strong(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((patient(fred)<~>generous(fred))))&
(![X]:((~kind(X)&~strong(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~tall(X)|old(X))))=>((~happy(susan)&curious(susan))))&
(((~brave(fred)<~>~creative(fred)))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&old(X))=>kind(X)))&
(((~calm(fred)<~>~tall(fred)))=>((kind(fred)|happy(fred))))&
((~kind(paul)|generous(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(~calm(lucy))&
(?[X]:((curious(X)&~kind(X)))) | ~happy(mary) | [] | null | 0 |
If someone is not tall then someone is strong or patient and vice versa. Everyone who is generous or strong is not curious or kind. If someone is both happy and calm then mary is not brave or not generous. If fred is either quiet or not quiet then someone is rich and vice versa. Everyone who is either not happy or humble is not calm and vice versa. Everyone who is both not quiet and not tall is not patient and vice versa. Everyone who is either strong or not humble is calm or brave. If lucy is either curious or not generous then susan is both brave and not brave. Everyone who is not brave is both not curious and happy. If someone is not patient then someone is strong and vice versa. Everyone who is both not strong and not humble is strong or quiet and vice versa. If mary is both funny and not calm then susan is calm. Everyone who is either not wise or kind is either calm or rich. If lucy is not patient or not wise then alice is not brave. Everyone who is humble or strong is both not wise and not tall. Everyone who is not old is either not quiet or not tall. Someone is quiet or not strong. Someone is not kind or generous. Someone is both creative and not humble. Susan is either not old or funny. Someone is either curious or brave. Fred is either not patient or not kind. Mary is generous or not tall. | Lucy is patient. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:((strong(X)|patient(X)))))&
(![X]:((generous(X)|strong(X))=>(~curious(X)|kind(X))))&
((?[X]:((happy(X)&calm(X))))=>((~brave(mary)|~generous(mary))))&
(((quiet(fred)<~>~quiet(fred)))<=>(?[X]:(rich(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~tall(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~humble(X))=>(calm(X)|brave(X))))&
(((curious(lucy)<~>~generous(lucy)))=>((brave(susan)&~brave(susan))))&
(![X]:(~brave(X)=>(~curious(X)&happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~humble(X))<=>(strong(X)|quiet(X))))&
(((funny(mary)&~calm(mary)))=>(calm(susan)))&
(![X]:((~wise(X)<~>kind(X))=>(calm(X)<~>rich(X))))&
(((~patient(lucy)|~wise(lucy)))=>(~brave(alice)))&
(![X]:((humble(X)|strong(X))=>(~wise(X)&~tall(X))))&
(![X]:(~old(X)=>(~quiet(X)<~>~tall(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((~kind(X)|generous(X))))&
(?[X]:((creative(X)&~humble(X))))&
((~old(susan)<~>funny(susan)))&
(?[X]:((curious(X)<~>brave(X))))&
((~patient(fred)<~>~kind(fred)))&
((generous(mary)|~tall(mary))) | patient(lucy) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7892149272625960765368645
% SZS output start Proof for 7892149272625960765368645
10. ? [X0] : ~patient(X0) <=> ? [X0] : strong(X0) [input p9]
11. ! [X0] : ((~humble(X0) & ~strong(X0)) <=> (quiet(X0) | strong(X0))) [input p10]
24. ~patient(lucy) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : strong(X1) [rectify 10]
56. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X1] : strong(X1) | ! [X0] : patient(X0)) [nnf transformation 26]
57. (? [X0] : ~patient(X0) | ! [X1] : ~strong(X1)) & (? [X2] : strong(X2) | ! [X3] : patient(X3)) [rectify 56]
58. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
59. ? [X2] : strong(X2) => strong(sK4) [choice axiom]
60. (~patient(sK3) | ! [X1] : ~strong(X1)) & (strong(sK4) | ! [X3] : patient(X3)) [skolemisation 57,59,58]
61. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (humble(X0) | strong(X0)))) [nnf transformation 11]
62. ! [X0] : (((~humble(X0) & ~strong(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | humble(X0) | strong(X0))) [flattening 61]
101. strong(sK4) | patient(X3) [cnf transformation 60]
104. ~strong(X0) | ~strong(X0) [cnf transformation 62]
131. ~patient(lucy) [cnf transformation 24]
133. ~strong(X0) [duplicate literal removal 104]
145. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
146. ~strong(X1) <- (3) [avatar component clause 145]
204. 16 <=> ! [X3] : patient(X3) [avatar definition]
205. patient(X3) <- (16) [avatar component clause 204]
207. 17 <=> strong(sK4) [avatar definition]
209. strong(sK4) <- (17) [avatar component clause 207]
210. 16 | 17 [avatar split clause 101,207,204]
211. 3 [avatar split clause 133,145]
235. 23 <=> patient(lucy) [avatar definition]
236. ~patient(lucy) <- (~23) [avatar component clause 235]
276. ~23 [avatar split clause 131,235]
281. $false <- (16, ~23) [resolution 236,205]
282. ~16 | 23 [avatar contradiction clause 281]
283. $false <- (3, 17) [subsumption resolution 209,146]
284. ~3 | ~17 [avatar contradiction clause 283]
285. $false [avatar sat refutation 210,211,276,282,284]
% SZS output end Proof for 7892149272625960765368645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then mary is quiet or happy and vice versa.
Everyone who is either not wise or wise is both not curious and kind.
Everyone who is brave is both brave and happy and vice versa.
If lucy is both old and not humble then someone is either creative or not strong.
If someone is not humble then fred is not quiet or not happy and vice versa.
Everyone who is not funny or curious is rich or patient.
Everyone who is quiet is not old and vice versa.
If someone is either not kind or not happy then lucy is not wise and vice versa.
If someone is not curious then someone is both humble and not strong.
Everyone who is not strong is wise.
Everyone who is not quiet or not humble is both kind and patient.
If fred is not old then someone is calm or funny.
Everyone who is happy is funny and vice versa.
If someone is generous then john is both quiet and not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
Someone is either tall or calm.
Lucy is funny or happy.
Someone is either rich or not happy.
Someone is either old or not patient.
Someone is tall.
Fred is both not generous and not funny. | Paul is humble. | neutral | ((tall(john))<=>((quiet(mary)|happy(mary))))&
(![X]:((~wise(X)<~>wise(X))=>(~curious(X)&kind(X))))&
(![X]:(brave(X)<=>(brave(X)&happy(X))))&
(((old(lucy)&~humble(lucy)))=>(?[X]:((creative(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))<=>((~quiet(fred)|~happy(fred))))&
(![X]:((~funny(X)|curious(X))=>(rich(X)|patient(X))))&
(![X]:(quiet(X)<=>~old(X)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(~wise(lucy)))&
((?[X]:(~curious(X)))=>(?[X]:((humble(X)&~strong(X)))))&
(![X]:(~strong(X)=>wise(X)))&
(![X]:((~quiet(X)|~humble(X))=>(kind(X)&patient(X))))&
((~old(fred))=>(?[X]:((calm(X)|funny(X)))))&
(![X]:(happy(X)<=>funny(X)))&
((?[X]:(generous(X)))<=>((quiet(john)&~rich(john))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((funny(lucy)|happy(lucy)))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:(tall(X)))&
((~generous(fred)&~funny(fred))) | humble(paul) | [] | null | 0 |
Everyone who is both not calm and creative is either kind or wise.
If someone is either not curious or strong then someone is both rich and not patient.
Everyone who is humble or not calm is not tall or strong.
If paul is both wise and not generous then someone is both funny and not patient.
Everyone who is both creative and curious is either happy or not old and vice versa.
If someone is either not creative or rich then someone is either not humble or strong and vice versa.
Everyone who is both creative and not kind is both strong and not happy and vice versa.
Everyone who is both not kind and strong is happy and vice versa.
Everyone who is both not happy and brave is creative and vice versa.
Everyone who is brave is both happy and not generous.
Everyone who is either not rich or tall is rich.
Everyone who is not tall or strong is both not wise and wise and vice versa.
Everyone who is either quiet or not curious is either not wise or not curious.
If someone is not calm then paul is creative.
Everyone who is either not calm or not creative is both not funny and not humble and vice versa.
Susan is either generous or not happy.
Someone is not brave.
Someone is either patient or not creative.
John is humble or not patient.
Fred is not kind.
Alice is either not humble or generous. | Fred is not funny. | entailment | (![X]:((~calm(X)&creative(X))=>(kind(X)<~>wise(X))))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((humble(X)|~calm(X))=>(~tall(X)|strong(X))))&
(((wise(paul)&~generous(paul)))=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:((creative(X)&curious(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((~creative(X)<~>rich(X))))<=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((creative(X)&~kind(X))<=>(strong(X)&~happy(X))))&
(![X]:((~kind(X)&strong(X))<=>happy(X)))&
(![X]:((~happy(X)&brave(X))<=>creative(X)))&
(![X]:(brave(X)=>(happy(X)&~generous(X))))&
(![X]:((~rich(X)<~>tall(X))=>rich(X)))&
(![X]:((~tall(X)|strong(X))<=>(~wise(X)&wise(X))))&
(![X]:((quiet(X)<~>~curious(X))=>(~wise(X)<~>~curious(X))))&
((?[X]:(~calm(X)))=>(creative(paul)))&
(![X]:((~calm(X)<~>~creative(X))<=>(~funny(X)&~humble(X))))&
((generous(susan)<~>~happy(susan)))&
(?[X]:(~brave(X)))&
(?[X]:((patient(X)<~>~creative(X))))&
((humble(john)|~patient(john)))&
(~kind(fred))&
((~humble(alice)<~>generous(alice))) | ~funny(fred) | [
"p2",
"p6",
"p11",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5274141300553978042967391
% SZS output start Proof for 5274141300553978042967391
3. ! [X0] : ((~calm(X0) | humble(X0)) => (strong(X0) | ~tall(X0))) [input p2]
7. ! [X0] : ((~kind(X0) & creative(X0)) <=> (~happy(X0) & strong(X0))) [input p6]
12. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (wise(X0) & ~wise(X0))) [input p11]
15. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (~humble(X0) & ~funny(X0))) [input p14]
20. ~kind(fred) [input p19]
22. funny(fred) [input hypothesis]
28. ! [X0] : ((strong(X0) | ~tall(X0)) | (calm(X0) & ~humble(X0))) [ennf transformation 3]
29. ! [X0] : (strong(X0) | ~tall(X0) | (calm(X0) & ~humble(X0))) [flattening 28]
50. ! [X0] : (((~kind(X0) & creative(X0)) | (happy(X0) | ~strong(X0))) & ((~happy(X0) & strong(X0)) | (kind(X0) | ~creative(X0)))) [nnf transformation 7]
51. ! [X0] : (((~kind(X0) & creative(X0)) | happy(X0) | ~strong(X0)) & ((~happy(X0) & strong(X0)) | kind(X0) | ~creative(X0))) [flattening 50]
57. ! [X0] : (((strong(X0) | ~tall(X0)) | (~wise(X0) | wise(X0))) & ((wise(X0) & ~wise(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 12]
58. ! [X0] : ((strong(X0) | ~tall(X0) | ~wise(X0) | wise(X0)) & ((wise(X0) & ~wise(X0)) | (~strong(X0) & tall(X0)))) [flattening 57]
60. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 15]
61. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 60]
76. ~tall(X0) | strong(X0) | calm(X0) [cnf transformation 29]
93. ~creative(X0) | kind(X0) | strong(X0) [cnf transformation 51]
107. ~wise(X0) | tall(X0) [cnf transformation 58]
108. ~wise(X0) | ~strong(X0) [cnf transformation 58]
109. tall(X0) | wise(X0) [cnf transformation 58]
110. ~strong(X0) | wise(X0) [cnf transformation 58]
118. ~funny(X0) | ~calm(X0) | creative(X0) [cnf transformation 61]
129. ~kind(fred) [cnf transformation 20]
132. funny(fred) [cnf transformation 22]
209. ~strong(X0) [subsumption resolution 108,110]
210. tall(X0) [subsumption resolution 107,109]
212. 17 <=> ! [X0] : calm(X0) [avatar definition]
213. calm(X0) <- (17) [avatar component clause 212]
266. strong(X2) | calm(X2) [resolution 76,210]
274. ~calm(fred) | creative(fred) [resolution 118,132]
275. creative(fred) <- (17) [subsumption resolution 274,213]
276. kind(fred) | strong(fred) <- (17) [resolution 275,93]
278. strong(fred) <- (17) [subsumption resolution 276,129]
279. $false <- (17) [subsumption resolution 278,209]
280. ~17 [avatar contradiction clause 279]
291. calm(X2) [subsumption resolution 266,209]
292. 17 [avatar split clause 291,212]
295. $false [avatar sat refutation 280,292]
% SZS output end Proof for 5274141300553978042967391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or old is not creative or creative.
If someone is wise then paul is not creative and vice versa.
If susan is not tall or humble then lucy is both humble and strong and vice versa.
Everyone who is either calm or not curious is not quiet or not rich and vice versa.
If susan is strong or not funny then someone is either not curious or quiet and vice versa.
If someone is not generous then someone is both not creative and not calm.
If lucy is either patient or not patient then someone is either patient or not humble and vice versa.
Everyone who is not brave is either not rich or not quiet and vice versa.
If someone is happy or not calm then susan is either not quiet or not brave and vice versa.
If someone is not patient or not kind then someone is curious.
If susan is either brave or not tall then susan is strong.
If someone is both not curious and not creative then someone is either not brave or strong.
Everyone who is both not rich and not funny is not quiet.
Everyone who is both creative and strong is not quiet and vice versa.
If someone is either creative or not old then someone is rich and vice versa.
Everyone who is quiet or old is both generous and not funny.
Someone is both not calm and not quiet.
Paul is patient or not curious.
Someone is not calm.
Someone is both not funny and not calm.
Someone is not kind.
Someone is not quiet.
Alice is either creative or curious.
John is brave. | Susan is not strong. | contradiction | (![X]:((happy(X)<~>old(X))=>(~creative(X)|creative(X))))&
((?[X]:(wise(X)))<=>(~creative(paul)))&
(((~tall(susan)|humble(susan)))<=>((humble(lucy)&strong(lucy))))&
(![X]:((calm(X)<~>~curious(X))<=>(~quiet(X)|~rich(X))))&
(((strong(susan)|~funny(susan)))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~creative(X)&~calm(X)))))&
(((patient(lucy)<~>~patient(lucy)))<=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:(~brave(X)<=>(~rich(X)<~>~quiet(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((~quiet(susan)<~>~brave(susan))))&
((?[X]:((~patient(X)|~kind(X))))=>(?[X]:(curious(X))))&
(((brave(susan)<~>~tall(susan)))=>(strong(susan)))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:((~rich(X)&~funny(X))=>~quiet(X)))&
(![X]:((creative(X)&strong(X))<=>~quiet(X)))&
((?[X]:((creative(X)<~>~old(X))))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)|old(X))=>(generous(X)&~funny(X))))&
(?[X]:((~calm(X)&~quiet(X))))&
((patient(paul)|~curious(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~quiet(X)))&
((creative(alice)<~>curious(alice)))&
(brave(john)) | ~strong(susan) | [
"p7",
"p8",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7615185797373010671548112
% SZS output start Proof for 7615185797373010671548112
8. ! [X0] : (~brave(X0) <=> (~rich(X0) <~> ~quiet(X0))) [input p7]
9. ? [X0] : (~calm(X0) | happy(X0)) <=> (~quiet(susan) <~> ~brave(susan)) [input p8]
13. ! [X0] : ((~funny(X0) & ~rich(X0)) => ~quiet(X0)) [input p12]
14. ! [X0] : ((strong(X0) & creative(X0)) <=> ~quiet(X0)) [input p13]
16. ! [X0] : ((old(X0) | quiet(X0)) => (~funny(X0) & generous(X0))) [input p15]
17. ? [X0] : (~quiet(X0) & ~calm(X0)) [input p16]
25. ~strong(susan) [input hypothesis]
31. ! [X0] : ((old(X0) | quiet(X0)) => ~funny(X0)) [pure predicate removal 16]
37. ! [X0] : (~quiet(X0) | (funny(X0) | rich(X0))) [ennf transformation 13]
38. ! [X0] : (~quiet(X0) | funny(X0) | rich(X0)) [flattening 37]
39. ! [X0] : (~funny(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 31]
58. ! [X0] : ((~brave(X0) | ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0)))) & (((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | brave(X0))) [nnf transformation 8]
59. (? [X0] : (~calm(X0) | happy(X0)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X0] : (calm(X0) & ~happy(X0))) [nnf transformation 9]
60. (? [X0] : (~calm(X0) | happy(X0)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X1] : (calm(X1) & ~happy(X1))) [rectify 59]
61. ? [X0] : (~calm(X0) | happy(X0)) => (~calm(sK3) | happy(sK3)) [choice axiom]
62. ((~calm(sK3) | happy(sK3)) | ((~quiet(susan) | brave(susan)) & (~brave(susan) | quiet(susan)))) & (((brave(susan) | quiet(susan)) & (~brave(susan) | ~quiet(susan))) | ! [X1] : (calm(X1) & ~happy(X1))) [skolemisation 60,61]
71. ! [X0] : (((strong(X0) & creative(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) | ~creative(X0)))) [nnf transformation 14]
72. ! [X0] : (((strong(X0) & creative(X0)) | quiet(X0)) & (~quiet(X0) | ~strong(X0) | ~creative(X0))) [flattening 71]
78. ? [X0] : (~quiet(X0) & ~calm(X0)) => (~quiet(sK8) & ~calm(sK8)) [choice axiom]
79. ~quiet(sK8) & ~calm(sK8) [skolemisation 17,78]
118. ~rich(X0) | ~quiet(X0) | brave(X0) [cnf transformation 58]
123. ~brave(susan) | ~quiet(susan) | calm(X1) [cnf transformation 62]
134. ~quiet(X0) | funny(X0) | rich(X0) [cnf transformation 38]
137. quiet(X0) | strong(X0) [cnf transformation 72]
142. ~funny(X0) | ~quiet(X0) [cnf transformation 39]
144. ~calm(sK8) [cnf transformation 79]
155. ~strong(susan) [cnf transformation 25]
198. 9 <=> strong(susan) [avatar definition]
199. ~strong(susan) <- (~9) [avatar component clause 198]
202. 10 <=> funny(susan) [avatar definition]
203. funny(susan) <- (10) [avatar component clause 202]
204. ~funny(susan) <- (~10) [avatar component clause 202]
239. 17 <=> brave(susan) [avatar definition]
240. ~brave(susan) <- (~17) [avatar component clause 239]
243. 18 <=> quiet(susan) [avatar definition]
244. quiet(susan) <- (18) [avatar component clause 243]
245. ~quiet(susan) <- (~18) [avatar component clause 243]
257. 21 <=> ! [X1] : calm(X1) [avatar definition]
258. calm(X1) <- (21) [avatar component clause 257]
264. 21 | ~18 | ~17 [avatar split clause 123,239,243,257]
337. ~9 [avatar split clause 155,198]
342. strong(susan) <- (~18) [resolution 137,245]
346. $false <- (~9, ~18) [subsumption resolution 342,199]
347. 9 | 18 [avatar contradiction clause 346]
429. funny(susan) | rich(susan) <- (18) [resolution 134,244]
431. rich(susan) <- (~10, 18) [subsumption resolution 429,204]
448. ~quiet(susan) | brave(susan) <- (~10, 18) [resolution 431,118]
461. brave(susan) <- (~10, 18) [subsumption resolution 448,244]
462. $false <- (~10, ~17, 18) [subsumption resolution 461,240]
463. 10 | 17 | ~18 [avatar contradiction clause 462]
470. ~quiet(susan) <- (10) [resolution 203,142]
471. $false <- (10, 18) [subsumption resolution 470,244]
472. ~10 | ~18 [avatar contradiction clause 471]
478. $false <- (21) [resolution 258,144]
483. ~21 [avatar contradiction clause 478]
485. $false [avatar sat refutation 264,337,347,463,472,483]
% SZS output end Proof for 7615185797373010671548112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is either not strong or kind and vice versa.
If lucy is both not tall and funny then fred is both strong and old and vice versa.
Everyone who is funny or curious is not happy and vice versa.
If alice is both creative and kind then mary is quiet.
If someone is not old then fred is both not curious and generous.
If someone is not funny then someone is not happy.
Everyone who is either happy or generous is not calm and vice versa.
Everyone who is not generous or not funny is funny and vice versa.
Everyone who is not kind is curious and vice versa.
If paul is not rich or generous then someone is both not funny and happy and vice versa.
If someone is not rich or not humble then someone is not calm and vice versa.
If someone is either not tall or not humble then mary is both not humble and not tall.
Everyone who is generous or not rich is not brave.
If lucy is both calm and not calm then mary is not quiet.
If someone is brave then paul is quiet or not strong and vice versa.
If someone is not rich or not quiet then someone is either strong or not creative and vice versa.
Someone is either curious or not brave.
John is both curious and quiet.
Someone is either curious or kind.
Mary is funny.
Susan is either not calm or strong.
Fred is patient or not creative. | Fred is tall. | entailment | (![X]:(~strong(X)<=>(~strong(X)<~>kind(X))))&
(((~tall(lucy)&funny(lucy)))<=>((strong(fred)&old(fred))))&
(![X]:((funny(X)|curious(X))<=>~happy(X)))&
(((creative(alice)&kind(alice)))=>(quiet(mary)))&
((?[X]:(~old(X)))=>((~curious(fred)&generous(fred))))&
((?[X]:(~funny(X)))=>(?[X]:(~happy(X))))&
(![X]:((happy(X)<~>generous(X))<=>~calm(X)))&
(![X]:((~generous(X)|~funny(X))<=>funny(X)))&
(![X]:(~kind(X)<=>curious(X)))&
(((~rich(paul)|generous(paul)))<=>(?[X]:((~funny(X)&happy(X)))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((~tall(X)<~>~humble(X))))=>((~humble(mary)&~tall(mary))))&
(![X]:((generous(X)|~rich(X))=>~brave(X)))&
(((calm(lucy)&~calm(lucy)))=>(~quiet(mary)))&
((?[X]:(brave(X)))<=>((quiet(paul)|~strong(paul))))&
((?[X]:((~rich(X)|~quiet(X))))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(?[X]:((curious(X)<~>~brave(X))))&
((curious(john)&quiet(john)))&
(?[X]:((curious(X)<~>kind(X))))&
(funny(mary))&
((~calm(susan)<~>strong(susan)))&
((patient(fred)|~creative(fred))) | tall(fred) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2640186453713334145701986
% SZS output start Proof for 2640186453713334145701986
1. ! [X0] : (~strong(X0) <=> (~strong(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((curious(X0) | funny(X0)) <=> ~happy(X0)) [input p2]
7. ! [X0] : ((happy(X0) <~> generous(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | ~generous(X0)) <=> funny(X0)) [input p7]
9. ! [X0] : (~kind(X0) <=> curious(X0)) [input p8]
10. (generous(paul) | ~rich(paul)) <=> ? [X0] : (happy(X0) & ~funny(X0)) [input p9]
11. ? [X0] : (~humble(X0) | ~rich(X0)) <=> ? [X0] : ~calm(X0) [input p10]
12. ? [X0] : (~tall(X0) <~> ~humble(X0)) => (~tall(mary) & ~humble(mary)) [input p11]
23. ~tall(fred) [input hypothesis]
25. ? [X0] : (~humble(X0) | ~rich(X0)) <=> ? [X1] : ~calm(X1) [rectify 11]
32. (~tall(mary) & ~humble(mary)) | ! [X0] : (~tall(X0) <=> ~humble(X0)) [ennf transformation 12]
36. ! [X0] : ((~strong(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0)))) & (((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | strong(X0))) [nnf transformation 1]
39. ! [X0] : (((curious(X0) | funny(X0)) | happy(X0)) & (~happy(X0) | (~curious(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((curious(X0) | funny(X0) | happy(X0)) & (~happy(X0) | (~curious(X0) & ~funny(X0)))) [flattening 39]
44. ! [X0] : ((((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | calm(X0)) & (~calm(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))))) [nnf transformation 7]
45. ! [X0] : (((~funny(X0) | ~generous(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) & generous(X0)))) [nnf transformation 8]
46. ! [X0] : ((~funny(X0) | ~generous(X0) | ~funny(X0)) & (funny(X0) | (funny(X0) & generous(X0)))) [flattening 45]
47. ! [X0] : ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0))) [nnf transformation 9]
48. ((generous(paul) | ~rich(paul)) | ! [X0] : (~happy(X0) | funny(X0))) & (? [X0] : (happy(X0) & ~funny(X0)) | (~generous(paul) & rich(paul))) [nnf transformation 10]
49. (generous(paul) | ~rich(paul) | ! [X0] : (~happy(X0) | funny(X0))) & (? [X0] : (happy(X0) & ~funny(X0)) | (~generous(paul) & rich(paul))) [flattening 48]
50. (generous(paul) | ~rich(paul) | ! [X0] : (~happy(X0) | funny(X0))) & (? [X1] : (happy(X1) & ~funny(X1)) | (~generous(paul) & rich(paul))) [rectify 49]
51. ? [X1] : (happy(X1) & ~funny(X1)) => (happy(sK1) & ~funny(sK1)) [choice axiom]
52. (generous(paul) | ~rich(paul) | ! [X0] : (~happy(X0) | funny(X0))) & ((happy(sK1) & ~funny(sK1)) | (~generous(paul) & rich(paul))) [skolemisation 50,51]
53. (? [X0] : (~humble(X0) | ~rich(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (humble(X0) & rich(X0))) [nnf transformation 25]
54. (? [X0] : (~humble(X0) | ~rich(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (humble(X3) & rich(X3))) [rectify 53]
55. ? [X0] : (~humble(X0) | ~rich(X0)) => (~humble(sK2) | ~rich(sK2)) [choice axiom]
56. ? [X2] : ~calm(X2) => ~calm(sK3) [choice axiom]
57. ((~humble(sK2) | ~rich(sK2)) | ! [X1] : calm(X1)) & (~calm(sK3) | ! [X3] : (humble(X3) & rich(X3))) [skolemisation 54,56,55]
58. (~tall(mary) & ~humble(mary)) | ! [X0] : ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))) [nnf transformation 32]
77. ~kind(X0) | strong(X0) | strong(X0) [cnf transformation 36]
79. ~strong(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 36]
84. ~happy(X0) | ~funny(X0) [cnf transformation 40]
85. ~happy(X0) | ~curious(X0) [cnf transformation 40]
93. calm(X0) | happy(X0) | generous(X0) [cnf transformation 44]
96. funny(X0) | funny(X0) [cnf transformation 46]
97. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 46]
98. curious(X0) | kind(X0) [cnf transformation 47]
102. happy(sK1) | rich(paul) [cnf transformation 52]
103. happy(sK1) | ~generous(paul) [cnf transformation 52]
104. generous(paul) | ~rich(paul) | ~happy(X0) | funny(X0) [cnf transformation 52]
106. ~calm(sK3) | humble(X3) [cnf transformation 57]
108. ~humble(mary) | ~humble(X0) | tall(X0) [cnf transformation 58]
133. ~tall(fred) [cnf transformation 23]
134. funny(X0) [duplicate literal removal 96]
135. ~generous(X0) | ~funny(X0) [duplicate literal removal 97]
136. ~kind(X0) | strong(X0) [duplicate literal removal 77]
137. ~kind(X0) | ~strong(X0) [duplicate literal removal 79]
138. ~kind(X0) [subsumption resolution 136,137]
173. 8 <=> ! [X1] : funny(X1) [avatar definition]
174. funny(X1) <- (8) [avatar component clause 173]
180. 8 [avatar split clause 134,173]
181. curious(X0) [subsumption resolution 98,138]
182. generous(paul) | ~rich(paul) | ~happy(X0) [subsumption resolution 104,84]
184. 10 <=> ! [X0] : ~happy(X0) [avatar definition]
185. ~happy(X0) <- (10) [avatar component clause 184]
187. 11 <=> rich(paul) [avatar definition]
191. 12 <=> generous(paul) [avatar definition]
194. 10 | ~11 | 12 [avatar split clause 182,191,187,184]
196. 13 <=> happy(sK1) [avatar definition]
198. happy(sK1) <- (13) [avatar component clause 196]
199. ~12 | 13 [avatar split clause 103,196,191]
200. 11 | 13 [avatar split clause 102,196,187]
220. 18 <=> ! [X3] : humble(X3) [avatar definition]
221. humble(X3) <- (18) [avatar component clause 220]
223. 19 <=> calm(sK3) [avatar definition]
225. ~calm(sK3) <- (~19) [avatar component clause 223]
226. 18 | ~19 [avatar split clause 106,223,220]
240. 23 <=> ! [X0] : (~humble(X0) | tall(X0)) [avatar definition]
241. ~humble(X0) | tall(X0) <- (23) [avatar component clause 240]
244. 24 <=> humble(mary) [avatar definition]
246. ~humble(mary) <- (~24) [avatar component clause 244]
248. 23 | ~24 [avatar split clause 108,244,240]
322. happy(sK3) | generous(sK3) <- (~19) [resolution 93,225]
328. generous(sK3) <- (10, ~19) [subsumption resolution 322,185]
332. ~funny(sK3) <- (10, ~19) [resolution 328,135]
333. $false <- (8, 10, ~19) [subsumption resolution 332,174]
334. ~8 | ~10 | 19 [avatar contradiction clause 333]
358. ~curious(sK1) <- (13) [resolution 198,85]
361. $false <- (13) [subsumption resolution 358,181]
362. ~13 [avatar contradiction clause 361]
365. $false <- (18, ~24) [resolution 221,246]
366. ~18 | 24 [avatar contradiction clause 365]
367. tall(X0) <- (18, 23) [subsumption resolution 241,221]
383. $false <- (18, 23) [resolution 367,133]
386. ~18 | ~23 [avatar contradiction clause 383]
387. $false [avatar sat refutation 180,194,199,200,226,248,334,362,366,386]
% SZS output end Proof for 2640186453713334145701986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not generous is either not happy or happy and vice versa.
Everyone who is both generous and creative is either humble or not generous and vice versa.
Everyone who is patient is either not creative or kind.
If someone is not quiet then paul is both quiet and not old.
If someone is not old then someone is tall or happy.
Everyone who is both rich and not curious is either not kind or not rich and vice versa.
Everyone who is both not quiet and wise is not calm or creative.
Everyone who is not curious or funny is not calm or calm.
If someone is patient or happy then someone is both strong and creative.
If someone is either not strong or generous then someone is old or calm and vice versa.
Everyone who is both not generous and not patient is both not strong and strong and vice versa.
Everyone who is both not generous and not strong is not kind.
Everyone who is either tall or quiet is both patient and brave.
If someone is wise then john is not kind or calm.
Everyone who is humble or not creative is both calm and not funny and vice versa.
Everyone who is curious is not brave or old and vice versa.
Mary is wise or not strong.
Someone is either creative or not creative.
Paul is wise.
Someone is both curious and not wise.
Someone is either not curious or not quiet.
Paul is not rich or tall.
Someone is either not generous or creative.
Susan is creative. | Susan is not rich. | contradiction | (![X]:((~calm(X)|~generous(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((generous(X)&creative(X))<=>(humble(X)<~>~generous(X))))&
(![X]:(patient(X)=>(~creative(X)<~>kind(X))))&
((?[X]:(~quiet(X)))=>((quiet(paul)&~old(paul))))&
((?[X]:(~old(X)))=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((rich(X)&~curious(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((~quiet(X)&wise(X))=>(~calm(X)|creative(X))))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)|calm(X))))&
((?[X]:((patient(X)|happy(X))))=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
(![X]:((tall(X)<~>quiet(X))=>(patient(X)&brave(X))))&
((?[X]:(wise(X)))=>((~kind(john)|calm(john))))&
(![X]:((humble(X)|~creative(X))<=>(calm(X)&~funny(X))))&
(![X]:(curious(X)<=>(~brave(X)|old(X))))&
((wise(mary)|~strong(mary)))&
(?[X]:((creative(X)<~>~creative(X))))&
(wise(paul))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((~rich(paul)|tall(paul)))&
(?[X]:((~generous(X)<~>creative(X))))&
(creative(susan)) | ~rich(susan) | [
"p0",
"p1",
"p2",
"p5",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 388611035735080350381964
% SZS output start Proof for 388611035735080350381964
1. ! [X0] : ((~generous(X0) | ~calm(X0)) <=> (~happy(X0) <~> happy(X0))) [input p0]
2. ! [X0] : ((creative(X0) & generous(X0)) <=> (humble(X0) <~> ~generous(X0))) [input p1]
3. ! [X0] : (patient(X0) => (~creative(X0) <~> kind(X0))) [input p2]
6. ! [X0] : ((~curious(X0) & rich(X0)) <=> (~kind(X0) <~> ~rich(X0))) [input p5]
11. ! [X0] : ((~patient(X0) & ~generous(X0)) <=> (strong(X0) & ~strong(X0))) [input p10]
15. ! [X0] : ((~creative(X0) | humble(X0)) <=> (~funny(X0) & calm(X0))) [input p14]
24. creative(susan) [input p23]
25. ~rich(susan) [input hypothesis]
29. ! [X0] : ((~creative(X0) <~> kind(X0)) | ~patient(X0)) [ennf transformation 3]
42. ! [X0] : (((~generous(X0) | ~calm(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (generous(X0) & calm(X0)))) [nnf transformation 1]
43. ! [X0] : ((~generous(X0) | ~calm(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (generous(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (~creative(X0) | ~generous(X0)))) [nnf transformation 2]
45. ! [X0] : (((creative(X0) & generous(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ~creative(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~patient(X0)) [nnf transformation 29]
50. ! [X0] : (((~curious(X0) & rich(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | (curious(X0) | ~rich(X0)))) [nnf transformation 6]
51. ! [X0] : (((~curious(X0) & rich(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | curious(X0) | ~rich(X0))) [flattening 50]
60. ! [X0] : (((~patient(X0) & ~generous(X0)) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | (patient(X0) | generous(X0)))) [nnf transformation 11]
61. ! [X0] : (((~patient(X0) & ~generous(X0)) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | patient(X0) | generous(X0))) [flattening 60]
63. ! [X0] : (((~creative(X0) | humble(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 15]
64. ! [X0] : ((~creative(X0) | humble(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [flattening 63]
82. ~generous(X0) | ~calm(X0) | happy(X0) | happy(X0) [cnf transformation 43]
83. ~generous(X0) | ~calm(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 43]
84. ~generous(X0) | humble(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 45]
87. generous(X0) | humble(X0) | generous(X0) [cnf transformation 45]
90. ~patient(X0) | ~creative(X0) | kind(X0) [cnf transformation 46]
98. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 51]
114. ~strong(X0) | patient(X0) | generous(X0) [cnf transformation 61]
115. strong(X0) | patient(X0) | generous(X0) [cnf transformation 61]
124. ~humble(X0) | calm(X0) [cnf transformation 64]
125. creative(X0) | calm(X0) [cnf transformation 64]
143. creative(susan) [cnf transformation 24]
144. ~rich(susan) [cnf transformation 25]
146. ~kind(X0) | rich(X0) [duplicate literal removal 98]
147. ~generous(X0) | humble(X0) | ~creative(X0) [duplicate literal removal 84]
148. humble(X0) | generous(X0) [duplicate literal removal 87]
149. ~generous(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 82]
150. ~happy(X0) | ~calm(X0) | ~generous(X0) [duplicate literal removal 83]
151. ~generous(X0) | ~calm(X0) [subsumption resolution 149,150]
152. ~creative(X0) | humble(X0) [subsumption resolution 147,148]
231. patient(X0) | generous(X0) [subsumption resolution 114,115]
294. humble(X0) | calm(X0) [resolution 152,125]
295. calm(X0) [subsumption resolution 294,124]
313. ~creative(X0) | kind(X0) | generous(X0) [resolution 90,231]
354. kind(susan) | generous(susan) [resolution 313,143]
358. 34 <=> generous(susan) [avatar definition]
360. generous(susan) <- (34) [avatar component clause 358]
362. 35 <=> kind(susan) [avatar definition]
364. kind(susan) <- (35) [avatar component clause 362]
365. 34 | 35 [avatar split clause 354,362,358]
379. rich(susan) <- (35) [resolution 364,146]
385. $false <- (35) [subsumption resolution 379,144]
386. ~35 [avatar contradiction clause 385]
387. ~calm(susan) <- (34) [resolution 360,151]
388. $false <- (34) [subsumption resolution 387,295]
389. ~34 [avatar contradiction clause 388]
390. $false [avatar sat refutation 365,386,389]
% SZS output end Proof for 388611035735080350381964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not brave is both kind and old and vice versa.
Everyone who is both not curious and not old is either brave or not calm and vice versa.
If someone is either not creative or generous then someone is either funny or wise.
If john is calm then fred is both old and creative and vice versa.
If someone is not brave then someone is either not tall or not happy.
Everyone who is not happy or kind is either creative or happy.
Everyone who is either curious or brave is not old or not generous and vice versa.
Everyone who is kind or humble is not curious and vice versa.
If someone is not curious then mary is both creative and kind and vice versa.
If paul is patient then john is humble and vice versa.
Everyone who is either not funny or not brave is quiet.
If someone is both not patient and not calm then alice is either not happy or not wise.
If john is not old then mary is either not patient or kind and vice versa.
Everyone who is not happy or patient is either brave or rich.
Everyone who is old or not tall is tall or patient and vice versa.
If mary is both not patient and not curious then someone is wise or not old and vice versa.
Someone is either not patient or strong.
Someone is either curious or not wise.
Someone is either rich or not rich.
Paul is both tall and not brave.
Someone is generous or patient. | Fred is rich. | neutral | (![X]:((~humble(X)|~brave(X))<=>(kind(X)&old(X))))&
(![X]:((~curious(X)&~old(X))<=>(brave(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>generous(X))))=>(?[X]:((funny(X)<~>wise(X)))))&
((calm(john))<=>((old(fred)&creative(fred))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~happy(X)|kind(X))=>(creative(X)<~>happy(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~old(X)|~generous(X))))&
(![X]:((kind(X)|humble(X))<=>~curious(X)))&
((?[X]:(~curious(X)))<=>((creative(mary)&kind(mary))))&
((patient(paul))<=>(humble(john)))&
(![X]:((~funny(X)<~>~brave(X))=>quiet(X)))&
((?[X]:((~patient(X)&~calm(X))))=>((~happy(alice)<~>~wise(alice))))&
((~old(john))<=>((~patient(mary)<~>kind(mary))))&
(![X]:((~happy(X)|patient(X))=>(brave(X)<~>rich(X))))&
(![X]:((old(X)|~tall(X))<=>(tall(X)|patient(X))))&
(((~patient(mary)&~curious(mary)))<=>(?[X]:((wise(X)|~old(X)))))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
(?[X]:((rich(X)<~>~rich(X))))&
((tall(paul)&~brave(paul)))&
(?[X]:((generous(X)|patient(X)))) | rich(fred) | [] | null | 0 |
If someone is either happy or not old then someone is not quiet and vice versa. If lucy is not old or brave then paul is both brave and not humble. If someone is both not curious and strong then lucy is not tall or not rich. Everyone who is strong or brave is old or strong. Everyone who is either humble or kind is either not rich or old and vice versa. If someone is not brave or not humble then someone is not creative or rich and vice versa. Everyone who is either not patient or humble is either old or curious and vice versa. If john is both not brave and not funny then alice is either funny or patient and vice versa. If someone is calm or wise then someone is not strong or calm. Everyone who is both not happy and creative is wise or brave and vice versa. Everyone who is either brave or not patient is either brave or wise. Everyone who is happy or not wise is both brave and not brave and vice versa. Everyone who is either funny or not kind is kind and vice versa. Everyone who is not generous or quiet is both strong and not tall. Everyone who is not rich or not tall is quiet or patient and vice versa. If john is not generous then paul is both quiet and old and vice versa. Someone is not calm or not rich. Someone is not patient. Mary is calm. Alice is generous or not quiet. Someone is either tall or not funny. Someone is calm or humble. Paul is both not old and curious. Someone is either wise or not brave. | Alice is not happy. | entailment | ((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:(~quiet(X))))&
(((~old(lucy)|brave(lucy)))=>((brave(paul)&~humble(paul))))&
((?[X]:((~curious(X)&strong(X))))=>((~tall(lucy)|~rich(lucy))))&
(![X]:((strong(X)|brave(X))=>(old(X)|strong(X))))&
(![X]:((humble(X)<~>kind(X))<=>(~rich(X)<~>old(X))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
(?[X]:((~calm(X)|~rich(X))))&
(?[X]:(~patient(X)))&
(calm(mary))&
((generous(alice)|~quiet(alice)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((calm(X)|humble(X))))&
((~old(paul)&curious(paul)))&
(?[X]:((wise(X)<~>~brave(X)))) | ~happy(alice) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5529572243141570368928875
% SZS output start Proof for 5529572243141570368928875
10. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (brave(X0) | wise(X0))) [input p9]
12. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p11]
25. happy(alice) [input hypothesis]
54. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 10]
55. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~creative(X0) | happy(X0))) [flattening 54]
57. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 57]
117. ~happy(X0) | ~brave(X0) [cnf transformation 55]
124. brave(X0) | ~happy(X0) [cnf transformation 58]
155. happy(alice) [cnf transformation 25]
288. ~happy(X0) [subsumption resolution 124,117]
335. $false [subsumption resolution 155,288]
% SZS output end Proof for 5529572243141570368928875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and kind is either not creative or calm and vice versa.
Everyone who is both not strong and not quiet is brave and vice versa.
Everyone who is rich is curious or not happy and vice versa.
Everyone who is either tall or humble is either not happy or tall.
Everyone who is not happy is either quiet or humble and vice versa.
If someone is generous or old then someone is kind or not old and vice versa.
Everyone who is strong or humble is rich or strong and vice versa.
Everyone who is both quiet and strong is not wise.
If alice is both happy and generous then john is not calm or calm.
If someone is both not strong and not curious then fred is both not kind and not brave.
Everyone who is either happy or not wise is not brave or quiet and vice versa.
If someone is not brave or kind then lucy is both tall and wise and vice versa.
If someone is both calm and not brave then susan is humble and vice versa.
If someone is tall then alice is creative or not curious and vice versa.
If someone is not curious or not creative then someone is not humble and vice versa.
If lucy is either not creative or not happy then susan is both happy and not patient and vice versa.
Fred is not patient.
Someone is not curious or humble.
Lucy is either not kind or creative.
Someone is both not patient and brave.
Alice is not creative.
Someone is not brave or tall.
Someone is either not rich or not humble.
Someone is both not patient and not happy. | Susan is humble. | neutral | (![X]:((brave(X)&kind(X))<=>(~creative(X)<~>calm(X))))&
(![X]:((~strong(X)&~quiet(X))<=>brave(X)))&
(![X]:(rich(X)<=>(curious(X)|~happy(X))))&
(![X]:((tall(X)<~>humble(X))=>(~happy(X)<~>tall(X))))&
(![X]:(~happy(X)<=>(quiet(X)<~>humble(X))))&
((?[X]:((generous(X)|old(X))))<=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((strong(X)|humble(X))<=>(rich(X)|strong(X))))&
(![X]:((quiet(X)&strong(X))=>~wise(X)))&
(((happy(alice)&generous(alice)))=>((~calm(john)|calm(john))))&
((?[X]:((~strong(X)&~curious(X))))=>((~kind(fred)&~brave(fred))))&
(![X]:((happy(X)<~>~wise(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((~brave(X)|kind(X))))<=>((tall(lucy)&wise(lucy))))&
((?[X]:((calm(X)&~brave(X))))<=>(humble(susan)))&
((?[X]:(tall(X)))<=>((creative(alice)|~curious(alice))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:(~humble(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>((happy(susan)&~patient(susan))))&
(~patient(fred))&
(?[X]:((~curious(X)|humble(X))))&
((~kind(lucy)<~>creative(lucy)))&
(?[X]:((~patient(X)&brave(X))))&
(~creative(alice))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((~patient(X)&~happy(X)))) | humble(susan) | [] | null | 0 |
If someone is either not strong or curious then fred is either not strong or not old. Everyone who is not rich or not calm is both not patient and tall. Everyone who is both not old and funny is both not old and not brave and vice versa. If someone is not kind or wise then someone is either calm or funny. Everyone who is both tall and generous is both quiet and generous. If someone is both brave and wise then lucy is both curious and not rich. Everyone who is brave is wise or quiet and vice versa. If mary is both happy and not quiet then fred is calm or patient. Everyone who is both not happy and not generous is either creative or not kind. If paul is old or generous then someone is both kind and not generous and vice versa. Everyone who is either patient or kind is humble or quiet and vice versa. Everyone who is old is both not old and not curious and vice versa. Everyone who is both not tall and not rich is either kind or not old. Everyone who is either not calm or not quiet is kind or not funny and vice versa. Everyone who is strong or not tall is either creative or tall and vice versa. Someone is either not patient or funny. Mary is either not creative or not wise. Someone is wise. Mary is strong or not calm. Someone is not tall or not rich. Someone is not patient or not humble. Someone is both not brave and humble. | Paul is curious. | entailment | ((?[X]:((~strong(X)<~>curious(X))))=>((~strong(fred)<~>~old(fred))))&
(![X]:((~rich(X)|~calm(X))=>(~patient(X)&tall(X))))&
(![X]:((~old(X)&funny(X))<=>(~old(X)&~brave(X))))&
((?[X]:((~kind(X)|wise(X))))=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((tall(X)&generous(X))=>(quiet(X)&generous(X))))&
((?[X]:((brave(X)&wise(X))))=>((curious(lucy)&~rich(lucy))))&
(![X]:(brave(X)<=>(wise(X)|quiet(X))))&
(((happy(mary)&~quiet(mary)))=>((calm(fred)|patient(fred))))&
(![X]:((~happy(X)&~generous(X))=>(creative(X)<~>~kind(X))))&
(((old(paul)|generous(paul)))<=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((patient(X)<~>kind(X))<=>(humble(X)|quiet(X))))&
(![X]:(old(X)<=>(~old(X)&~curious(X))))&
(![X]:((~tall(X)&~rich(X))=>(kind(X)<~>~old(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(kind(X)|~funny(X))))&
(![X]:((strong(X)|~tall(X))<=>(creative(X)<~>tall(X))))&
(?[X]:((~patient(X)<~>funny(X))))&
((~creative(mary)<~>~wise(mary)))&
(?[X]:(wise(X)))&
((strong(mary)|~calm(mary)))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((~brave(X)&humble(X)))) | curious(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1466178467104246279936422
% SZS output start Proof for 1466178467104246279936422
12. ! [X0] : (old(X0) <=> (~curious(X0) & ~old(X0))) [input p11]
23. ~curious(paul) [input hypothesis]
54. ! [X0] : ((old(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | ~old(X0))) [nnf transformation 12]
55. ! [X0] : ((old(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | ~old(X0))) [flattening 54]
110. ~old(X0) | ~old(X0) [cnf transformation 55]
112. old(X0) | curious(X0) | old(X0) [cnf transformation 55]
137. ~curious(paul) [cnf transformation 23]
140. ~old(X0) [duplicate literal removal 110]
141. old(X0) | curious(X0) [duplicate literal removal 112]
284. curious(X1) [resolution 141,140]
285. $false [resolution 284,137]
% SZS output end Proof for 1466178467104246279936422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then lucy is either not strong or not rich.
If someone is either not patient or not quiet then someone is curious.
Everyone who is patient is both not tall and happy.
Everyone who is not rich is not brave or not creative and vice versa.
If someone is either tall or patient then someone is either happy or curious and vice versa.
Everyone who is creative or not creative is kind or not quiet and vice versa.
If paul is not calm or creative then someone is both wise and rich and vice versa.
If alice is not funny then john is humble and vice versa.
If someone is not strong then someone is either not kind or not old.
If fred is curious then someone is both not strong and not brave and vice versa.
Everyone who is kind or not calm is not old.
Everyone who is not old is both not creative and not strong and vice versa.
Everyone who is brave is either humble or not funny and vice versa.
Everyone who is rich is creative and vice versa.
If mary is happy or creative then someone is not funny and vice versa.
Everyone who is either not old or not kind is kind.
Someone is either generous or kind.
Mary is rich or calm.
Lucy is not calm or brave.
Someone is both not wise and curious.
Someone is not quiet.
Someone is either not generous or not patient.
Susan is not patient. | Paul is not old. | entailment | ((?[X]:(quiet(X)))=>((~strong(lucy)<~>~rich(lucy))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:(curious(X))))&
(![X]:(patient(X)=>(~tall(X)&happy(X))))&
(![X]:(~rich(X)<=>(~brave(X)|~creative(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((creative(X)|~creative(X))<=>(kind(X)|~quiet(X))))&
(((~calm(paul)|creative(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
((~funny(alice))<=>(humble(john)))&
((?[X]:(~strong(X)))=>(?[X]:((~kind(X)<~>~old(X)))))&
((curious(fred))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((kind(X)|~calm(X))=>~old(X)))&
(![X]:(~old(X)<=>(~creative(X)&~strong(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(rich(X)<=>creative(X)))&
(((happy(mary)|creative(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>kind(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((rich(mary)|calm(mary)))&
((~calm(lucy)|brave(lucy)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~patient(susan)) | ~old(paul) | [
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9114072390194959639185363
% SZS output start Proof for 9114072390194959639185363
11. ! [X0] : ((~calm(X0) | kind(X0)) => ~old(X0)) [input p10]
16. ! [X0] : ((~old(X0) <~> ~kind(X0)) => kind(X0)) [input p15]
24. old(paul) [input hypothesis]
32. ! [X0] : (~old(X0) | (calm(X0) & ~kind(X0))) [ennf transformation 11]
33. ! [X0] : (kind(X0) | (~old(X0) <=> ~kind(X0))) [ennf transformation 16]
71. ! [X0] : (kind(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 33]
115. ~old(X0) | ~kind(X0) [cnf transformation 32]
130. kind(X0) | ~old(X0) | kind(X0) [cnf transformation 71]
141. old(paul) [cnf transformation 24]
142. kind(X0) | ~old(X0) [duplicate literal removal 130]
290. ~old(X0) [subsumption resolution 142,115]
329. $false [subsumption resolution 141,290]
% SZS output end Proof for 9114072390194959639185363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous is not kind or not old and vice versa.
If someone is not creative then fred is not curious.
If paul is rich or not creative then someone is either not tall or not creative.
If alice is not strong or not humble then alice is rich or not curious.
If someone is wise or generous then john is either not humble or rich and vice versa.
Everyone who is creative or not wise is rich and vice versa.
Everyone who is curious or not happy is not tall or not happy and vice versa.
Everyone who is either not curious or brave is both funny and tall and vice versa.
Everyone who is not curious is not kind or humble and vice versa.
Everyone who is old is humble or rich.
Everyone who is creative is either humble or not wise and vice versa.
Everyone who is either not tall or not generous is not happy or strong and vice versa.
If someone is both not strong and not humble then susan is either not generous or not quiet.
If john is both tall and not generous then someone is either brave or not wise and vice versa.
Everyone who is both not rich and not humble is both brave and not old and vice versa.
Everyone who is wise or not generous is either not curious or rich.
Someone is either calm or tall.
Fred is not tall.
Someone is old or not brave.
John is both not old and not calm.
Someone is not tall or generous. | Susan is not creative. | contradiction | (![X]:((kind(X)|~generous(X))<=>(~kind(X)|~old(X))))&
((?[X]:(~creative(X)))=>(~curious(fred)))&
(((rich(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(((~strong(alice)|~humble(alice)))=>((rich(alice)|~curious(alice))))&
((?[X]:((wise(X)|generous(X))))<=>((~humble(john)<~>rich(john))))&
(![X]:((creative(X)|~wise(X))<=>rich(X)))&
(![X]:((curious(X)|~happy(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(funny(X)&tall(X))))&
(![X]:(~curious(X)<=>(~kind(X)|humble(X))))&
(![X]:(old(X)=>(humble(X)|rich(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~strong(X)&~humble(X))))=>((~generous(susan)<~>~quiet(susan))))&
(((tall(john)&~generous(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)&~old(X))))&
(![X]:((wise(X)|~generous(X))=>(~curious(X)<~>rich(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(~tall(fred))&
(?[X]:((old(X)|~brave(X))))&
((~old(john)&~calm(john)))&
(?[X]:((~tall(X)|generous(X)))) | ~creative(susan) | [
"p0",
"p1",
"p6",
"p7",
"p8",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 175065961653530503689085
% SZS output start Proof for 175065961653530503689085
1. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~old(X0) | ~kind(X0))) [input p0]
2. ? [X0] : ~creative(X0) => ~curious(fred) [input p1]
7. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~happy(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~curious(X0) <~> brave(X0)) <=> (tall(X0) & funny(X0))) [input p7]
9. ! [X0] : (~curious(X0) <=> (humble(X0) | ~kind(X0))) [input p8]
12. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
15. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (~old(X0) & brave(X0))) [input p14]
18. ~tall(fred) [input p17]
22. ~creative(susan) [input hypothesis]
23. ~curious(fred) | ! [X0] : creative(X0) [ennf transformation 2]
31. ! [X0] : (((~generous(X0) | kind(X0)) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~generous(X0) | kind(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | (generous(X0) & ~kind(X0)))) [flattening 31]
42. ! [X0] : (((~happy(X0) | curious(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : ((~happy(X0) | curious(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | (happy(X0) & ~curious(X0)))) [flattening 42]
44. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (~tall(X0) | ~funny(X0))) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | ~tall(X0) | ~funny(X0)) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [flattening 44]
46. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | curious(X0))) [flattening 46]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 12]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
57. ! [X0] : (((~humble(X0) & ~rich(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 15]
58. ! [X0] : (((~humble(X0) & ~rich(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | humble(X0) | rich(X0))) [flattening 57]
67. ~old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 32]
69. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 32]
71. ~curious(fred) | creative(X0) [cnf transformation 23]
89. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 43]
93. brave(X0) | tall(X0) | curious(X0) [cnf transformation 45]
97. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 47]
99. ~humble(X0) | ~curious(X0) [cnf transformation 47]
109. happy(X0) | tall(X0) | generous(X0) [cnf transformation 50]
122. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 58]
129. ~tall(fred) [cnf transformation 18]
134. ~creative(susan) [cnf transformation 22]
135. ~old(X0) | ~kind(X0) [duplicate literal removal 67]
136. ~generous(X0) | kind(X0) [duplicate literal removal 69]
138. 1 <=> ! [X0] : creative(X0) [avatar definition]
139. creative(X0) <- (1) [avatar component clause 138]
141. 2 <=> curious(fred) [avatar definition]
143. ~curious(fred) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 71,141,138]
375. tall(X0) | generous(X0) | curious(X0) | tall(X0) [resolution 109,89]
377. tall(X0) | generous(X0) | curious(X0) [duplicate literal removal 375]
454. old(X1) | ~humble(X1) | tall(X1) | curious(X1) [resolution 122,93]
478. ~humble(X1) | old(X1) | tall(X1) [subsumption resolution 454,99]
551. generous(fred) | curious(fred) [resolution 377,129]
555. generous(fred) <- (~2) [subsumption resolution 551,143]
618. kind(fred) <- (~2) [resolution 555,136]
620. 62 <=> old(fred) [avatar definition]
622. old(fred) <- (62) [avatar component clause 620]
624. 63 <=> kind(fred) [avatar definition]
626. kind(fred) <- (63) [avatar component clause 624]
628. 63 | 2 [avatar split clause 618,141,624]
667. humble(fred) | curious(fred) <- (63) [resolution 626,97]
668. humble(fred) <- (~2, 63) [subsumption resolution 667,143]
713. old(fred) | tall(fred) <- (~2, 63) [resolution 668,478]
717. old(fred) <- (~2, 63) [subsumption resolution 713,129]
718. 62 | 2 | ~63 [avatar split clause 717,624,141,620]
730. ~kind(fred) <- (62) [resolution 622,135]
740. ~63 | ~62 [avatar split clause 730,620,624]
744. $false <- (1) [resolution 139,134]
749. ~1 [avatar contradiction clause 744]
751. $false [avatar sat refutation 144,628,718,740,749]
% SZS output end Proof for 175065961653530503689085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not happy or wise then someone is either not old or kind.
If mary is either not happy or quiet then mary is kind.
If someone is generous then someone is either not creative or wise.
If paul is both rich and not strong then mary is both tall and not calm.
If someone is both calm and generous then mary is either curious or creative.
Everyone who is kind or rich is not kind and vice versa.
Everyone who is old or quiet is either not curious or curious.
Everyone who is not patient or old is either not patient or not brave and vice versa.
Everyone who is both not rich and quiet is not wise and vice versa.
Everyone who is not brave is not brave or not happy.
If fred is calm then someone is patient or not quiet and vice versa.
Everyone who is both quiet and funny is not strong or calm and vice versa.
If alice is both not humble and not old then susan is either tall or not strong.
Everyone who is both not kind and old is not curious and vice versa.
If someone is either not wise or rich then alice is wise.
Everyone who is rich or funny is not strong and vice versa.
Someone is not brave or patient.
Someone is either happy or calm.
John is either calm or quiet.
Lucy is brave.
Someone is either not rich or funny.
Susan is either not rich or rich. | Alice is not strong. | entailment | (((~happy(alice)<~>wise(alice)))=>(?[X]:((~old(X)<~>kind(X)))))&
(((~happy(mary)<~>quiet(mary)))=>(kind(mary)))&
((?[X]:(generous(X)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(((rich(paul)&~strong(paul)))=>((tall(mary)&~calm(mary))))&
((?[X]:((calm(X)&generous(X))))=>((curious(mary)<~>creative(mary))))&
(![X]:((kind(X)|rich(X))<=>~kind(X)))&
(![X]:((old(X)|quiet(X))=>(~curious(X)<~>curious(X))))&
(![X]:((~patient(X)|old(X))<=>(~patient(X)<~>~brave(X))))&
(![X]:((~rich(X)&quiet(X))<=>~wise(X)))&
(![X]:(~brave(X)=>(~brave(X)|~happy(X))))&
((calm(fred))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((quiet(X)&funny(X))<=>(~strong(X)|calm(X))))&
(((~humble(alice)&~old(alice)))=>((tall(susan)<~>~strong(susan))))&
(![X]:((~kind(X)&old(X))<=>~curious(X)))&
((?[X]:((~wise(X)<~>rich(X))))=>(wise(alice)))&
(![X]:((rich(X)|funny(X))<=>~strong(X)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((happy(X)<~>calm(X))))&
((calm(john)<~>quiet(john)))&
(brave(lucy))&
(?[X]:((~rich(X)<~>funny(X))))&
((~rich(susan)<~>rich(susan))) | ~strong(alice) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2642912775397992333151242
% SZS output start Proof for 2642912775397992333151242
6. ! [X0] : ((rich(X0) | kind(X0)) <=> ~kind(X0)) [input p5]
16. ! [X0] : ((funny(X0) | rich(X0)) <=> ~strong(X0)) [input p15]
23. strong(alice) [input hypothesis]
41. ! [X0] : (((rich(X0) | kind(X0)) | kind(X0)) & (~kind(X0) | (~rich(X0) & ~kind(X0)))) [nnf transformation 6]
42. ! [X0] : ((rich(X0) | kind(X0) | kind(X0)) & (~kind(X0) | (~rich(X0) & ~kind(X0)))) [flattening 41]
57. ! [X0] : (((funny(X0) | rich(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) & ~rich(X0)))) [nnf transformation 16]
58. ! [X0] : ((funny(X0) | rich(X0) | strong(X0)) & (~strong(X0) | (~funny(X0) & ~rich(X0)))) [flattening 57]
76. ~kind(X0) | ~kind(X0) [cnf transformation 42]
78. rich(X0) | kind(X0) | kind(X0) [cnf transformation 42]
106. ~strong(X0) | ~rich(X0) [cnf transformation 58]
119. strong(alice) [cnf transformation 23]
122. ~kind(X0) [duplicate literal removal 76]
123. rich(X0) | kind(X0) [duplicate literal removal 78]
232. ~rich(alice) [resolution 106,119]
254. kind(alice) [resolution 232,123]
255. $false [subsumption resolution 254,122]
% SZS output end Proof for 2642912775397992333151242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not kind or not tall. If alice is both not wise and not generous then fred is both happy and not funny and vice versa. Everyone who is either generous or tall is not tall and vice versa. Everyone who is both not quiet and not patient is either not funny or old and vice versa. Everyone who is both not rich and curious is not calm or humble. Everyone who is both strong and brave is both patient and not tall. If fred is not tall then lucy is either not brave or humble. If susan is either happy or not tall then someone is both not wise and not creative and vice versa. If fred is both calm and not strong then someone is either strong or not patient. If fred is funny or not strong then alice is both not old and not funny. Everyone who is either not funny or creative is not creative and vice versa. If someone is generous or old then paul is either not calm or calm and vice versa. Everyone who is both brave and not tall is either not curious or funny and vice versa. Everyone who is both not calm and not happy is quiet or not kind and vice versa. Everyone who is not brave is either not happy or not tall and vice versa. Everyone who is funny or not patient is both wise and creative and vice versa. Susan is not brave or humble. Paul is both not brave and not quiet. John is both patient and not calm. Susan is both not calm and strong. Someone is either not strong or not quiet. Alice is wise or patient. Alice is not old. | Paul is not generous. | contradiction | (![X]:(brave(X)=>(~kind(X)|~tall(X))))&
(((~wise(alice)&~generous(alice)))<=>((happy(fred)&~funny(fred))))&
(![X]:((generous(X)<~>tall(X))<=>~tall(X)))&
(![X]:((~quiet(X)&~patient(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~rich(X)&curious(X))=>(~calm(X)|humble(X))))&
(![X]:((strong(X)&brave(X))=>(patient(X)&~tall(X))))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~calm(X)&~happy(X))<=>(quiet(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~happy(X)<~>~tall(X))))&
(![X]:((funny(X)|~patient(X))<=>(wise(X)&creative(X))))&
((~brave(susan)|humble(susan)))&
((~brave(paul)&~quiet(paul)))&
((patient(john)&~calm(john)))&
((~calm(susan)&strong(susan)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((wise(alice)|patient(alice)))&
(~old(alice)) | ~generous(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3013990180466072333328306
% SZS output start Proof for 3013990180466072333328306
3. ! [X0] : ((generous(X0) <~> tall(X0)) <=> ~tall(X0)) [input p2]
24. ~generous(paul) [input hypothesis]
36. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 3]
68. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 36]
69. tall(X0) | generous(X0) | tall(X0) [cnf transformation 36]
134. ~generous(paul) [cnf transformation 24]
139. ~tall(X0) | generous(X0) [duplicate literal removal 68]
140. tall(X0) | generous(X0) [duplicate literal removal 69]
161. generous(X0) [subsumption resolution 139,140]
256. $false [subsumption resolution 134,161]
% SZS output end Proof for 3013990180466072333328306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not humble is either quiet or wise.
If susan is either tall or not rich then someone is either not happy or creative.
If alice is both not funny and not kind then someone is not old and vice versa.
Everyone who is brave is not kind and vice versa.
Everyone who is both curious and not funny is curious or happy.
Everyone who is brave or calm is both not brave and not quiet and vice versa.
If someone is either not calm or not curious then susan is not creative or not old and vice versa.
Everyone who is both kind and not calm is rich or kind.
Everyone who is rich or not wise is generous.
Everyone who is not strong is not tall or patient.
Everyone who is both not creative and not generous is not calm and vice versa.
If mary is both kind and happy then susan is either not kind or quiet and vice versa.
Everyone who is not tall or not quiet is funny or rich and vice versa.
Everyone who is not creative is old or tall and vice versa.
If mary is either wise or not patient then john is either old or not old and vice versa.
Everyone who is not funny or not wise is curious or not wise and vice versa.
Someone is either not rich or tall.
Someone is quiet.
Someone is either not creative or not wise.
Someone is both patient and not generous.
Mary is funny.
Someone is both happy and funny.
Someone is either not wise or not calm. | Alice is not kind. | contradiction | (![X]:((~tall(X)<~>~humble(X))=>(quiet(X)<~>wise(X))))&
(((tall(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~funny(alice)&~kind(alice)))<=>(?[X]:(~old(X))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:((curious(X)&~funny(X))=>(curious(X)|happy(X))))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~creative(susan)|~old(susan))))&
(![X]:((kind(X)&~calm(X))=>(rich(X)|kind(X))))&
(![X]:((rich(X)|~wise(X))=>generous(X)))&
(![X]:(~strong(X)=>(~tall(X)|patient(X))))&
(![X]:((~creative(X)&~generous(X))<=>~calm(X)))&
(((kind(mary)&happy(mary)))<=>((~kind(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(funny(X)|rich(X))))&
(![X]:(~creative(X)<=>(old(X)|tall(X))))&
(((wise(mary)<~>~patient(mary)))<=>((old(john)<~>~old(john))))&
(![X]:((~funny(X)|~wise(X))<=>(curious(X)|~wise(X))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((patient(X)&~generous(X))))&
(funny(mary))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((~wise(X)<~>~calm(X)))) | ~kind(alice) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 338824001322385477110917
% SZS output start Proof for 338824001322385477110917
4. ! [X0] : (brave(X0) <=> ~kind(X0)) [input p3]
6. ! [X0] : ((calm(X0) | brave(X0)) <=> (~quiet(X0) & ~brave(X0))) [input p5]
24. ~kind(alice) [input hypothesis]
42. ! [X0] : ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0))) [nnf transformation 4]
43. ! [X0] : (((calm(X0) | brave(X0)) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | (~calm(X0) & ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((calm(X0) | brave(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | (~calm(X0) & ~brave(X0)))) [flattening 43]
88. brave(X0) | kind(X0) [cnf transformation 42]
90. ~brave(X0) | ~brave(X0) [cnf transformation 44]
144. ~kind(alice) [cnf transformation 24]
149. ~brave(X0) [duplicate literal removal 90]
175. 6 <=> kind(alice) [avatar definition]
177. ~kind(alice) <- (~6) [avatar component clause 175]
285. ~6 [avatar split clause 144,175]
287. kind(X1) [resolution 88,149]
289. $false <- (~6) [resolution 287,177]
294. 6 [avatar contradiction clause 289]
295. $false [avatar sat refutation 285,294]
% SZS output end Proof for 338824001322385477110917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not tall.
If mary is both not rich and not calm then lucy is either not rich or not kind and vice versa.
If john is kind or patient then someone is brave or strong and vice versa.
Everyone who is both not strong and rich is kind.
Everyone who is not quiet or old is both not tall and quiet and vice versa.
If someone is either strong or not brave then someone is both not old and brave and vice versa.
Everyone who is either not curious or not tall is both not strong and generous and vice versa.
Everyone who is either calm or quiet is happy or not brave.
Everyone who is old is not humble or not tall.
If lucy is not humble then susan is not brave or not quiet.
If paul is not funny or not quiet then someone is not old or generous.
Everyone who is either creative or not funny is either not generous or tall.
If someone is not old or not calm then someone is both not tall and tall.
If lucy is either not patient or not funny then someone is wise.
If someone is both curious and not curious then lucy is not wise or funny and vice versa.
Everyone who is humble is creative or calm and vice versa.
Paul is strong or not brave.
Susan is quiet or not quiet.
Susan is either funny or not kind.
Someone is either not tall or happy.
Fred is either calm or not happy.
Someone is strong.
Lucy is either generous or patient. | Mary is rich. | neutral | (![X]:(~quiet(X)=>~tall(X)))&
(((~rich(mary)&~calm(mary)))<=>((~rich(lucy)<~>~kind(lucy))))&
(((kind(john)|patient(john)))<=>(?[X]:((brave(X)|strong(X)))))&
(![X]:((~strong(X)&rich(X))=>kind(X)))&
(![X]:((~quiet(X)|old(X))<=>(~tall(X)&quiet(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>(?[X]:((~old(X)&brave(X)))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~strong(X)&generous(X))))&
(![X]:((calm(X)<~>quiet(X))=>(happy(X)|~brave(X))))&
(![X]:(old(X)=>(~humble(X)|~tall(X))))&
((~humble(lucy))=>((~brave(susan)|~quiet(susan))))&
(((~funny(paul)|~quiet(paul)))=>(?[X]:((~old(X)|generous(X)))))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>tall(X))))&
((?[X]:((~old(X)|~calm(X))))=>(?[X]:((~tall(X)&tall(X)))))&
(((~patient(lucy)<~>~funny(lucy)))=>(?[X]:(wise(X))))&
((?[X]:((curious(X)&~curious(X))))<=>((~wise(lucy)|funny(lucy))))&
(![X]:(humble(X)<=>(creative(X)|calm(X))))&
((strong(paul)|~brave(paul)))&
((quiet(susan)|~quiet(susan)))&
((funny(susan)<~>~kind(susan)))&
(?[X]:((~tall(X)<~>happy(X))))&
((calm(fred)<~>~happy(fred)))&
(?[X]:(strong(X)))&
((generous(lucy)<~>patient(lucy))) | rich(mary) | [] | null | 0 |
Everyone who is wise or strong is either not kind or happy and vice versa. If susan is curious or tall then someone is creative or strong and vice versa. If john is both not calm and not strong then susan is not curious. Everyone who is both rich and creative is not wise. Everyone who is not generous or not kind is either wise or not strong and vice versa. Everyone who is tall or not strong is not kind or not strong. Everyone who is either not tall or strong is not creative or not brave and vice versa. Everyone who is not humble is both tall and calm and vice versa. If someone is brave or not old then someone is either wise or not brave and vice versa. Everyone who is either not patient or not brave is both not kind and not rich and vice versa. Everyone who is not wise or creative is both not calm and strong. If someone is either patient or funny then john is quiet or not generous. Everyone who is both not kind and generous is not strong or not old and vice versa. Everyone who is both curious and not kind is either not wise or not happy and vice versa. Everyone who is both generous and not curious is either brave or patient and vice versa. If fred is not tall then fred is not rich or old and vice versa. Someone is quiet. Someone is either not old or not patient. Lucy is both old and not kind. Lucy is either not kind or not calm. Susan is either not generous or not tall. Someone is kind. Someone is generous or not brave. | Susan is not creative. | entailment | (![X]:((wise(X)|strong(X))<=>(~kind(X)<~>happy(X))))&
(((curious(susan)|tall(susan)))<=>(?[X]:((creative(X)|strong(X)))))&
(((~calm(john)&~strong(john)))=>(~curious(susan)))&
(![X]:((rich(X)&creative(X))=>~wise(X)))&
(![X]:((~generous(X)|~kind(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~humble(X)<=>(tall(X)&calm(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((quiet(john)|~generous(john))))&
(![X]:((~kind(X)&generous(X))<=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&~kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((generous(X)&~curious(X))<=>(brave(X)<~>patient(X))))&
((~tall(fred))<=>((~rich(fred)|old(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~patient(X))))&
((old(lucy)&~kind(lucy)))&
((~kind(lucy)<~>~calm(lucy)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)|~brave(X)))) | ~creative(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2000873798564787103459445
% SZS output start Proof for 2000873798564787103459445
1. ! [X0] : ((strong(X0) | wise(X0)) <=> (~kind(X0) <~> happy(X0))) [input p0]
2. (tall(susan) | curious(susan)) <=> ? [X0] : (strong(X0) | creative(X0)) [input p1]
4. ! [X0] : ((creative(X0) & rich(X0)) => ~wise(X0)) [input p3]
5. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p4]
6. ! [X0] : ((~strong(X0) | tall(X0)) => (~strong(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~brave(X0) | ~creative(X0))) [input p6]
10. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~rich(X0) & ~kind(X0))) [input p9]
11. ! [X0] : ((creative(X0) | ~wise(X0)) => (strong(X0) & ~calm(X0))) [input p10]
13. ! [X0] : ((generous(X0) & ~kind(X0)) <=> (~old(X0) | ~strong(X0))) [input p12]
14. ! [X0] : ((~kind(X0) & curious(X0)) <=> (~wise(X0) <~> ~happy(X0))) [input p13]
15. ! [X0] : ((~curious(X0) & generous(X0)) <=> (brave(X0) <~> patient(X0))) [input p14]
21. ~generous(susan) <~> ~tall(susan) [input p20]
24. creative(susan) [input hypothesis]
30. ! [X0] : (~wise(X0) | (~creative(X0) | ~rich(X0))) [ennf transformation 4]
31. ! [X0] : (~wise(X0) | ~creative(X0) | ~rich(X0)) [flattening 30]
32. ! [X0] : ((~strong(X0) | ~kind(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 6]
33. ! [X0] : (~strong(X0) | ~kind(X0) | (strong(X0) & ~tall(X0))) [flattening 32]
34. ! [X0] : ((strong(X0) & ~calm(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 11]
35. ! [X0] : (((strong(X0) | wise(X0)) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | (~strong(X0) & ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((strong(X0) | wise(X0) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | (~strong(X0) & ~wise(X0)))) [flattening 35]
37. ((tall(susan) | curious(susan)) | ! [X0] : (~strong(X0) & ~creative(X0))) & (? [X0] : (strong(X0) | creative(X0)) | (~tall(susan) & ~curious(susan))) [nnf transformation 2]
38. (tall(susan) | curious(susan) | ! [X0] : (~strong(X0) & ~creative(X0))) & (? [X0] : (strong(X0) | creative(X0)) | (~tall(susan) & ~curious(susan))) [flattening 37]
39. (tall(susan) | curious(susan) | ! [X0] : (~strong(X0) & ~creative(X0))) & (? [X1] : (strong(X1) | creative(X1)) | (~tall(susan) & ~curious(susan))) [rectify 38]
40. ? [X1] : (strong(X1) | creative(X1)) => (strong(sK0) | creative(sK0)) [choice axiom]
41. (tall(susan) | curious(susan) | ! [X0] : (~strong(X0) & ~creative(X0))) & ((strong(sK0) | creative(sK0)) | (~tall(susan) & ~curious(susan))) [skolemisation 39,40]
42. ! [X0] : (((~kind(X0) | ~generous(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [nnf transformation 5]
43. ! [X0] : ((~kind(X0) | ~generous(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [flattening 42]
44. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & ((~brave(X0) | ~creative(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & (~brave(X0) | ~creative(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 44]
51. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 10]
52. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 51]
53. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | (~generous(X0) | kind(X0)))) [nnf transformation 13]
54. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ~generous(X0) | kind(X0))) [flattening 53]
55. ! [X0] : (((~kind(X0) & curious(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (kind(X0) | ~curious(X0)))) [nnf transformation 14]
56. ! [X0] : (((~kind(X0) & curious(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | kind(X0) | ~curious(X0))) [flattening 55]
57. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (curious(X0) | ~generous(X0)))) [nnf transformation 15]
58. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | curious(X0) | ~generous(X0))) [flattening 57]
65. (tall(susan) | generous(susan)) & (~tall(susan) | ~generous(susan)) [nnf transformation 21]
71. ~kind(X0) | happy(X0) | ~strong(X0) [cnf transformation 36]
72. ~happy(X0) | kind(X0) | ~wise(X0) [cnf transformation 36]
79. tall(susan) | curious(susan) | ~strong(X0) [cnf transformation 41]
81. ~rich(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 31]
82. ~strong(X0) | wise(X0) | generous(X0) [cnf transformation 43]
83. ~strong(X0) | wise(X0) | kind(X0) [cnf transformation 43]
85. ~wise(X0) | strong(X0) | kind(X0) [cnf transformation 43]
86. ~generous(X0) | ~kind(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 43]
88. ~tall(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 33]
91. ~brave(X0) | ~creative(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 45]
95. ~strong(X0) | tall(X0) | brave(X0) [cnf transformation 45]
106. ~patient(X0) | ~brave(X0) | rich(X0) | kind(X0) [cnf transformation 52]
107. patient(X0) | brave(X0) | rich(X0) | kind(X0) [cnf transformation 52]
110. strong(X0) | wise(X0) [cnf transformation 34]
111. ~creative(X0) | strong(X0) [cnf transformation 34]
113. ~kind(X0) | strong(X0) [cnf transformation 54]
120. ~wise(X0) | curious(X0) | happy(X0) [cnf transformation 56]
121. ~happy(X0) | ~kind(X0) | wise(X0) [cnf transformation 56]
127. ~brave(X0) | patient(X0) | ~curious(X0) [cnf transformation 58]
128. ~patient(X0) | brave(X0) | ~curious(X0) [cnf transformation 58]
138. ~tall(susan) | ~generous(susan) [cnf transformation 65]
139. tall(susan) | generous(susan) [cnf transformation 65]
142. creative(susan) [cnf transformation 24]
144. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
145. ~strong(X0) <- (1) [avatar component clause 144]
147. 2 <=> curious(susan) [avatar definition]
148. ~curious(susan) <- (~2) [avatar component clause 147]
149. curious(susan) <- (2) [avatar component clause 147]
151. 3 <=> tall(susan) [avatar definition]
152. ~tall(susan) <- (~3) [avatar component clause 151]
153. tall(susan) <- (3) [avatar component clause 151]
154. 1 | 2 | 3 [avatar split clause 79,151,147,144]
239. 22 <=> generous(susan) [avatar definition]
240. ~generous(susan) <- (~22) [avatar component clause 239]
241. generous(susan) <- (22) [avatar component clause 239]
242. 22 | 3 [avatar split clause 139,151,239]
243. ~22 | ~3 [avatar split clause 138,151,239]
255. strong(susan) [resolution 111,142]
277. wise(X0) | generous(X0) | wise(X0) [resolution 82,110]
281. generous(X0) | wise(X0) [duplicate literal removal 277]
282. wise(susan) <- (~22) [resolution 281,240]
283. wise(X0) | kind(X0) | wise(X0) [resolution 83,110]
287. kind(X0) | wise(X0) [duplicate literal removal 283]
291. wise(X0) | happy(X0) | ~strong(X0) [resolution 287,71]
295. happy(X0) | wise(X0) [subsumption resolution 291,110]
301. ~kind(susan) | ~strong(susan) <- (3) [resolution 88,153]
302. ~kind(susan) <- (3) [subsumption resolution 301,255]
327. tall(susan) | brave(susan) [resolution 95,255]
372. curious(susan) | happy(susan) <- (~22) [resolution 120,282]
383. happy(susan) <- (~2, ~22) [subsumption resolution 372,148]
452. kind(susan) | ~wise(susan) <- (~2, ~22) [resolution 383,72]
456. ~wise(susan) <- (~2, 3, ~22) [subsumption resolution 452,302]
457. $false <- (~2, 3, ~22) [subsumption resolution 456,282]
458. 2 | ~3 | 22 [avatar contradiction clause 457]
527. brave(X1) | rich(X1) | kind(X1) | brave(X1) | ~curious(X1) [resolution 107,128]
534. ~curious(X1) | rich(X1) | kind(X1) | brave(X1) [duplicate literal removal 527]
680. rich(susan) | kind(susan) | brave(susan) <- (2) [resolution 534,149]
692. rich(susan) | brave(susan) <- (2, 3) [subsumption resolution 680,302]
694. 63 <=> brave(susan) [avatar definition]
696. brave(susan) <- (63) [avatar component clause 694]
698. 64 <=> rich(susan) [avatar definition]
700. rich(susan) <- (64) [avatar component clause 698]
701. 63 | 64 | ~2 | ~3 [avatar split clause 692,151,147,698,694]
749. ~creative(susan) | ~tall(susan) | ~strong(susan) <- (63) [resolution 696,91]
755. ~tall(susan) | ~strong(susan) <- (63) [subsumption resolution 749,142]
756. ~strong(susan) <- (3, 63) [subsumption resolution 755,153]
757. $false <- (3, 63) [subsumption resolution 756,255]
758. ~3 | ~63 [avatar contradiction clause 757]
767. 70 <=> wise(susan) [avatar definition]
768. ~wise(susan) <- (~70) [avatar component clause 767]
773. 71 <=> kind(susan) [avatar definition]
780. brave(susan) <- (~3) [subsumption resolution 327,152]
781. 63 | 3 [avatar split clause 780,151,694]
785. ~kind(susan) | ~strong(susan) | ~wise(susan) <- (22) [resolution 241,86]
786. ~kind(susan) | ~wise(susan) <- (22) [subsumption resolution 785,255]
787. ~70 | ~71 | ~22 [avatar split clause 786,239,773,767]
790. patient(susan) | ~curious(susan) <- (63) [resolution 696,127]
794. patient(susan) <- (2, 63) [subsumption resolution 790,149]
796. wise(X1) | ~kind(X1) | wise(X1) [resolution 295,121]
803. wise(X1) | ~kind(X1) [duplicate literal removal 796]
805. wise(X1) [subsumption resolution 803,287]
949. ~brave(susan) | rich(susan) | kind(susan) <- (2, 63) [resolution 794,106]
954. rich(susan) | kind(susan) <- (2, 63) [subsumption resolution 949,696]
955. 71 | 64 | ~2 | ~63 [avatar split clause 954,694,147,698,773]
969. strong(X1) | kind(X1) [resolution 805,85]
971. $false <- (~70) [resolution 805,768]
972. 70 [avatar contradiction clause 971]
974. strong(X1) [subsumption resolution 969,113]
1084. ~creative(susan) | ~wise(susan) <- (64) [resolution 700,81]
1085. ~wise(susan) <- (64) [subsumption resolution 1084,142]
1086. $false <- (64) [subsumption resolution 1085,805]
1087. ~64 [avatar contradiction clause 1086]
1094. $false <- (1) [subsumption resolution 145,974]
1095. ~1 [avatar contradiction clause 1094]
1096. $false [avatar sat refutation 154,242,243,458,701,758,781,787,955,972,1087,1095]
% SZS output end Proof for 2000873798564787103459445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or not tall then someone is not calm and vice versa. If someone is generous or not patient then alice is either not happy or humble and vice versa. If fred is either not old or not tall then fred is not creative and vice versa. Everyone who is funny is both not generous and not happy. Everyone who is not quiet or not rich is not old and vice versa. Everyone who is not quiet is strong. Everyone who is either generous or not wise is happy. Everyone who is curious or quiet is both old and creative. If someone is both tall and strong then someone is not quiet or not strong and vice versa. Everyone who is calm is both not wise and not curious. Everyone who is both funny and not tall is not patient or humble and vice versa. Everyone who is both strong and not quiet is both not patient and not wise. Everyone who is both not quiet and not wise is wise and vice versa. If john is both not rich and generous then someone is either not quiet or quiet. Susan is calm. Lucy is not strong or patient. Paul is not humble or not kind. | Paul is generous. | neutral | ((?[X]:((~wise(X)|~tall(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)|~patient(X))))<=>((~happy(alice)<~>humble(alice))))&
(((~old(fred)<~>~tall(fred)))<=>(~creative(fred)))&
(![X]:(funny(X)=>(~generous(X)&~happy(X))))&
(![X]:((~quiet(X)|~rich(X))<=>~old(X)))&
(![X]:(~quiet(X)=>strong(X)))&
(![X]:((generous(X)<~>~wise(X))=>happy(X)))&
(![X]:((curious(X)|quiet(X))=>(old(X)&creative(X))))&
((?[X]:((tall(X)&strong(X))))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(![X]:(calm(X)=>(~wise(X)&~curious(X))))&
(![X]:((funny(X)&~tall(X))<=>(~patient(X)|humble(X))))&
(![X]:((strong(X)&~quiet(X))=>(~patient(X)&~wise(X))))&
(![X]:((~quiet(X)&~wise(X))<=>wise(X)))&
(((~rich(john)&generous(john)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(calm(susan))&
((~strong(lucy)|patient(lucy)))&
((~humble(paul)|~kind(paul))) | generous(paul) | [] | null | 0 |
If paul is either not kind or happy then mary is curious. Everyone who is either not creative or humble is either strong or not quiet and vice versa. If fred is not humble then alice is both not humble and kind and vice versa. If someone is either happy or not strong then someone is either not kind or old. Everyone who is not funny or not rich is not creative. Everyone who is patient or curious is both patient and not kind. Everyone who is not tall or not happy is not quiet or not wise and vice versa. Everyone who is both not creative and not kind is both brave and not creative and vice versa. If john is not quiet then someone is both creative and calm. If someone is tall or not patient then someone is not brave or kind. If someone is both not kind and funny then john is both not funny and kind and vice versa. Everyone who is tall or not humble is both humble and not curious and vice versa. Everyone who is either kind or humble is not brave. Everyone who is not calm is both not wise and not creative. If someone is not funny or not quiet then lucy is not humble or patient and vice versa. Everyone who is either not old or calm is both humble and not happy. Lucy is not generous. Paul is patient or creative. Someone is either calm or not rich. Alice is both generous and happy. Lucy is either not wise or rich. Someone is both not happy and curious. Susan is either humble or brave. Someone is not curious or tall. | Lucy is not funny. | contradiction | (((~kind(paul)<~>happy(paul)))=>(curious(mary)))&
(![X]:((~creative(X)<~>humble(X))<=>(strong(X)<~>~quiet(X))))&
((~humble(fred))<=>((~humble(alice)&kind(alice))))&
((?[X]:((happy(X)<~>~strong(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~funny(X)|~rich(X))=>~creative(X)))&
(![X]:((patient(X)|curious(X))=>(patient(X)&~kind(X))))&
(![X]:((~tall(X)|~happy(X))<=>(~quiet(X)|~wise(X))))&
(![X]:((~creative(X)&~kind(X))<=>(brave(X)&~creative(X))))&
((~quiet(john))=>(?[X]:((creative(X)&calm(X)))))&
((?[X]:((tall(X)|~patient(X))))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:((~kind(X)&funny(X))))<=>((~funny(john)&kind(john))))&
(![X]:((tall(X)|~humble(X))<=>(humble(X)&~curious(X))))&
(![X]:((kind(X)<~>humble(X))=>~brave(X)))&
(![X]:(~calm(X)=>(~wise(X)&~creative(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>((~humble(lucy)|patient(lucy))))&
(![X]:((~old(X)<~>calm(X))=>(humble(X)&~happy(X))))&
(~generous(lucy))&
((patient(paul)|creative(paul)))&
(?[X]:((calm(X)<~>~rich(X))))&
((generous(alice)&happy(alice)))&
((~wise(lucy)<~>rich(lucy)))&
(?[X]:((~happy(X)&curious(X))))&
((humble(susan)<~>brave(susan)))&
(?[X]:((~curious(X)|tall(X)))) | ~funny(lucy) | [
"p4",
"p5",
"p7",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7116375993490385904265620
% SZS output start Proof for 7116375993490385904265620
5. ! [X0] : ((~rich(X0) | ~funny(X0)) => ~creative(X0)) [input p4]
6. ! [X0] : ((curious(X0) | patient(X0)) => (~kind(X0) & patient(X0))) [input p5]
8. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (~creative(X0) & brave(X0))) [input p7]
12. ! [X0] : ((~humble(X0) | tall(X0)) <=> (~curious(X0) & humble(X0))) [input p11]
13. ! [X0] : ((kind(X0) <~> humble(X0)) => ~brave(X0)) [input p12]
15. ? [X0] : (~quiet(X0) | ~funny(X0)) <=> (patient(lucy) | ~humble(lucy)) [input p14]
25. ~funny(lucy) [input hypothesis]
30. ! [X0] : (~creative(X0) | (rich(X0) & funny(X0))) [ennf transformation 5]
31. ! [X0] : ((~kind(X0) & patient(X0)) | (~curious(X0) & ~patient(X0))) [ennf transformation 6]
34. ! [X0] : (~brave(X0) | (kind(X0) <=> humble(X0))) [ennf transformation 13]
47. ! [X0] : (((~kind(X0) & ~creative(X0)) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 8]
48. ! [X0] : (((~kind(X0) & ~creative(X0)) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | kind(X0) | creative(X0))) [flattening 47]
59. ! [X0] : (((~humble(X0) | tall(X0)) | (curious(X0) | ~humble(X0))) & ((~curious(X0) & humble(X0)) | (humble(X0) & ~tall(X0)))) [nnf transformation 12]
60. ! [X0] : ((~humble(X0) | tall(X0) | curious(X0) | ~humble(X0)) & ((~curious(X0) & humble(X0)) | (humble(X0) & ~tall(X0)))) [flattening 59]
61. ! [X0] : (~brave(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) [nnf transformation 34]
62. (? [X0] : (~quiet(X0) | ~funny(X0)) | (~patient(lucy) & humble(lucy))) & ((patient(lucy) | ~humble(lucy)) | ! [X0] : (quiet(X0) & funny(X0))) [nnf transformation 15]
63. (? [X0] : (~quiet(X0) | ~funny(X0)) | (~patient(lucy) & humble(lucy))) & (patient(lucy) | ~humble(lucy) | ! [X0] : (quiet(X0) & funny(X0))) [flattening 62]
64. (? [X0] : (~quiet(X0) | ~funny(X0)) | (~patient(lucy) & humble(lucy))) & (patient(lucy) | ~humble(lucy) | ! [X1] : (quiet(X1) & funny(X1))) [rectify 63]
65. ? [X0] : (~quiet(X0) | ~funny(X0)) => (~quiet(sK4) | ~funny(sK4)) [choice axiom]
66. ((~quiet(sK4) | ~funny(sK4)) | (~patient(lucy) & humble(lucy))) & (patient(lucy) | ~humble(lucy) | ! [X1] : (quiet(X1) & funny(X1))) [skolemisation 64,65]
94. ~creative(X0) | funny(X0) [cnf transformation 30]
98. ~patient(X0) | ~kind(X0) [cnf transformation 31]
104. brave(X0) | kind(X0) | creative(X0) [cnf transformation 48]
117. humble(X0) | humble(X0) [cnf transformation 60]
122. ~brave(X0) | kind(X0) | ~humble(X0) [cnf transformation 61]
125. patient(lucy) | ~humble(lucy) | funny(X1) [cnf transformation 66]
146. ~funny(lucy) [cnf transformation 25]
147. humble(X0) [duplicate literal removal 117]
249. ~brave(X0) | kind(X0) [subsumption resolution 122,147]
251. 23 <=> patient(lucy) [avatar definition]
252. patient(lucy) <- (23) [avatar component clause 251]
268. patient(lucy) | funny(X1) [subsumption resolution 125,147]
270. 27 <=> ! [X1] : funny(X1) [avatar definition]
271. funny(X1) <- (27) [avatar component clause 270]
272. 27 | 23 [avatar split clause 268,251,270]
309. ~kind(lucy) <- (23) [resolution 98,252]
323. kind(X0) | creative(X0) | kind(X0) [resolution 104,249]
324. creative(X0) | kind(X0) [duplicate literal removal 323]
379. funny(X2) | kind(X2) [resolution 324,94]
421. kind(lucy) [resolution 379,146]
423. $false <- (23) [subsumption resolution 421,309]
424. ~23 [avatar contradiction clause 423]
435. $false <- (27) [resolution 271,146]
438. ~27 [avatar contradiction clause 435]
439. $false [avatar sat refutation 272,424,438]
% SZS output end Proof for 7116375993490385904265620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not strong or not quiet then someone is both not old and not funny and vice versa.
If someone is either strong or humble then alice is not strong.
Everyone who is either kind or creative is both tall and funny and vice versa.
Everyone who is either curious or not calm is not brave.
If fred is kind or not creative then someone is kind or brave.
Everyone who is old is brave and vice versa.
Everyone who is not old or not curious is either not creative or not brave.
If someone is both not patient and not humble then mary is both happy and not quiet.
If someone is not humble then paul is both not patient and not creative and vice versa.
If someone is either not tall or generous then mary is both not brave and not happy and vice versa.
If someone is creative or not quiet then someone is both strong and not strong.
If mary is calm or not happy then paul is both not tall and old.
If mary is either not strong or kind then someone is either not quiet or not happy and vice versa.
If someone is both tall and calm then someone is either not generous or not curious and vice versa.
If someone is both calm and not rich then john is strong and vice versa.
Fred is old.
Someone is not creative.
Someone is tall or not strong.
Someone is either not curious or not creative.
Someone is either humble or kind. | John is creative. | contradiction | (((~strong(fred)|~quiet(fred)))<=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((strong(X)<~>humble(X))))=>(~strong(alice)))&
(![X]:((kind(X)<~>creative(X))<=>(tall(X)&funny(X))))&
(![X]:((curious(X)<~>~calm(X))=>~brave(X)))&
(((kind(fred)|~creative(fred)))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(old(X)<=>brave(X)))&
(![X]:((~old(X)|~curious(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:((~patient(X)&~humble(X))))=>((happy(mary)&~quiet(mary))))&
((?[X]:(~humble(X)))<=>((~patient(paul)&~creative(paul))))&
((?[X]:((~tall(X)<~>generous(X))))<=>((~brave(mary)&~happy(mary))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(((calm(mary)|~happy(mary)))=>((~tall(paul)&old(paul))))&
(((~strong(mary)<~>kind(mary)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
((?[X]:((tall(X)&calm(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((calm(X)&~rich(X))))<=>(strong(john)))&
(old(fred))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
(?[X]:((humble(X)<~>kind(X)))) | creative(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5456166101125509274338093
% SZS output start Proof for 5456166101125509274338093
11. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X0] : (~strong(X0) & strong(X0)) [input p10]
21. creative(john) [input hypothesis]
22. ? [X0] : (~quiet(X0) | creative(X0)) => ? [X1] : (~strong(X1) & strong(X1)) [rectify 11]
29. ? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : (quiet(X0) & ~creative(X0)) [ennf transformation 22]
54. ? [X0] : (~strong(X0) & strong(X0)) | ! [X1] : (quiet(X1) & ~creative(X1)) [rectify 29]
55. ? [X0] : (~strong(X0) & strong(X0)) => (~strong(sK4) & strong(sK4)) [choice axiom]
56. (~strong(sK4) & strong(sK4)) | ! [X1] : (quiet(X1) & ~creative(X1)) [skolemisation 54,55]
114. strong(sK4) | ~creative(X1) [cnf transformation 56]
116. ~strong(sK4) | ~creative(X1) [cnf transformation 56]
146. creative(john) [cnf transformation 21]
261. 26 <=> strong(sK4) [avatar definition]
266. 27 <=> ! [X1] : ~creative(X1) [avatar definition]
267. ~creative(X1) <- (27) [avatar component clause 266]
268. 27 | ~26 [avatar split clause 116,261,266]
270. 27 | 26 [avatar split clause 114,261,266]
401. $false <- (27) [resolution 267,146]
402. ~27 [avatar contradiction clause 401]
403. $false [avatar sat refutation 268,270,402]
% SZS output end Proof for 5456166101125509274338093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both creative and strong is both not kind and wise and vice versa.
Everyone who is not calm or wise is not happy.
Everyone who is either patient or not patient is both rich and tall.
If someone is tall or funny then someone is either happy or not curious.
Everyone who is humble is either old or strong.
Everyone who is both wise and funny is not curious and vice versa.
If susan is not tall then paul is either not strong or generous and vice versa.
If someone is happy then alice is both not calm and funny.
Everyone who is calm or quiet is happy.
Everyone who is either generous or not strong is either not funny or not wise and vice versa.
Everyone who is both not wise and not kind is not curious.
If someone is either not patient or not funny then paul is both old and not strong and vice versa.
Everyone who is not patient or strong is both not strong and brave.
If paul is either quiet or not happy then someone is rich or tall.
If john is tall or not kind then someone is either happy or old.
Susan is either calm or not wise.
Lucy is either tall or not humble.
Someone is both old and not generous.
Mary is calm.
Lucy is generous or not rich.
John is either happy or curious.
Someone is funny.
Someone is both not generous and not wise. | Alice is not calm. | entailment | (![X]:((creative(X)&strong(X))<=>(~kind(X)&wise(X))))&
(![X]:((~calm(X)|wise(X))=>~happy(X)))&
(![X]:((patient(X)<~>~patient(X))=>(rich(X)&tall(X))))&
((?[X]:((tall(X)|funny(X))))=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:(humble(X)=>(old(X)<~>strong(X))))&
(![X]:((wise(X)&funny(X))<=>~curious(X)))&
((~tall(susan))<=>((~strong(paul)<~>generous(paul))))&
((?[X]:(happy(X)))=>((~calm(alice)&funny(alice))))&
(![X]:((calm(X)|quiet(X))=>happy(X)))&
(![X]:((generous(X)<~>~strong(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~wise(X)&~kind(X))=>~curious(X)))&
((?[X]:((~patient(X)<~>~funny(X))))<=>((old(paul)&~strong(paul))))&
(![X]:((~patient(X)|strong(X))=>(~strong(X)&brave(X))))&
(((quiet(paul)<~>~happy(paul)))=>(?[X]:((rich(X)|tall(X)))))&
(((tall(john)|~kind(john)))=>(?[X]:((happy(X)<~>old(X)))))&
((calm(susan)<~>~wise(susan)))&
((tall(lucy)<~>~humble(lucy)))&
(?[X]:((old(X)&~generous(X))))&
(calm(mary))&
((generous(lucy)|~rich(lucy)))&
((happy(john)<~>curious(john)))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)&~wise(X)))) | ~calm(alice) | [
"p7",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4266934883729260620222146
% SZS output start Proof for 4266934883729260620222146
8. ? [X0] : happy(X0) => (funny(alice) & ~calm(alice)) [input p7]
9. ! [X0] : ((quiet(X0) | calm(X0)) => happy(X0)) [input p8]
19. calm(mary) [input p18]
24. calm(alice) [input hypothesis]
31. (funny(alice) & ~calm(alice)) | ! [X0] : ~happy(X0) [ennf transformation 8]
32. ! [X0] : (happy(X0) | (~quiet(X0) & ~calm(X0))) [ennf transformation 9]
93. ~calm(alice) | ~happy(X0) [cnf transformation 31]
95. ~calm(X0) | happy(X0) [cnf transformation 32]
126. calm(mary) [cnf transformation 19]
133. calm(alice) [cnf transformation 24]
171. 6 <=> ! [X0] : ~happy(X0) [avatar definition]
172. ~happy(X0) <- (6) [avatar component clause 171]
179. 8 <=> calm(alice) [avatar definition]
182. 6 | ~8 [avatar split clause 93,179,171]
248. 8 [avatar split clause 133,179]
255. happy(mary) [resolution 95,126]
257. $false <- (6) [subsumption resolution 255,172]
258. ~6 [avatar contradiction clause 257]
261. $false [avatar sat refutation 182,248,258]
% SZS output end Proof for 4266934883729260620222146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or quiet is both not tall and not funny and vice versa.
If someone is both not wise and not strong then paul is not humble or old.
If susan is either humble or not brave then paul is kind or tall and vice versa.
Everyone who is either not brave or tall is not happy or not tall.
Everyone who is patient or rich is either not brave or not rich.
Everyone who is not rich or generous is both not rich and not tall.
Everyone who is both calm and not tall is either patient or brave and vice versa.
If fred is wise or not funny then someone is either not quiet or not tall.
Everyone who is either not kind or not wise is both not tall and generous and vice versa.
If someone is either not wise or wise then alice is rich or not happy.
Everyone who is both not kind and curious is either curious or quiet.
If someone is rich or not old then john is both patient and not curious.
If paul is both not strong and calm then someone is strong or rich.
Everyone who is not rich or old is not old or not rich and vice versa.
Everyone who is happy or funny is both happy and wise and vice versa.
If fred is curious or tall then someone is not tall and vice versa.
Someone is generous or not tall.
Mary is both not happy and wise.
John is creative.
John is both kind and curious.
Someone is not curious.
John is either tall or humble.
Fred is both not humble and old. | Fred is funny. | neutral | (![X]:((tall(X)<~>quiet(X))<=>(~tall(X)&~funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~humble(paul)|old(paul))))&
(((humble(susan)<~>~brave(susan)))<=>((kind(paul)|tall(paul))))&
(![X]:((~brave(X)<~>tall(X))=>(~happy(X)|~tall(X))))&
(![X]:((patient(X)|rich(X))=>(~brave(X)<~>~rich(X))))&
(![X]:((~rich(X)|generous(X))=>(~rich(X)&~tall(X))))&
(![X]:((calm(X)&~tall(X))<=>(patient(X)<~>brave(X))))&
(((wise(fred)|~funny(fred)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~tall(X)&generous(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>((rich(alice)|~happy(alice))))&
(![X]:((~kind(X)&curious(X))=>(curious(X)<~>quiet(X))))&
((?[X]:((rich(X)|~old(X))))=>((patient(john)&~curious(john))))&
(((~strong(paul)&calm(paul)))=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((~rich(X)|old(X))<=>(~old(X)|~rich(X))))&
(![X]:((happy(X)|funny(X))<=>(happy(X)&wise(X))))&
(((curious(fred)|tall(fred)))<=>(?[X]:(~tall(X))))&
(?[X]:((generous(X)|~tall(X))))&
((~happy(mary)&wise(mary)))&
(creative(john))&
((kind(john)&curious(john)))&
(?[X]:(~curious(X)))&
((tall(john)<~>humble(john)))&
((~humble(fred)&old(fred))) | funny(fred) | [] | null | 0 |
Everyone who is either old or calm is creative or happy.
Everyone who is either old or not generous is not tall or not rich.
If paul is both brave and not generous then john is not curious and vice versa.
If someone is not funny then mary is not generous or not curious.
If someone is brave or not quiet then fred is both not patient and not happy and vice versa.
Everyone who is rich or not old is both not wise and not strong.
Everyone who is either not patient or kind is not creative or not generous and vice versa.
Everyone who is either not kind or kind is both not rich and not wise.
Everyone who is both not humble and kind is quiet or not patient.
If alice is both not brave and creative then alice is not calm and vice versa.
Everyone who is either patient or not kind is either calm or not wise.
If someone is strong then susan is generous or creative and vice versa.
Everyone who is either not happy or happy is not strong or patient and vice versa.
If mary is rich or not wise then someone is both not humble and curious and vice versa.
Everyone who is both funny and patient is not rich and vice versa.
Everyone who is wise or not patient is either kind or not strong and vice versa.
Fred is either generous or brave.
Someone is either not wise or not patient.
Someone is either not curious or not funny.
John is calm or strong. | Mary is not wise. | entailment | (![X]:((old(X)<~>calm(X))=>(creative(X)|happy(X))))&
(![X]:((old(X)<~>~generous(X))=>(~tall(X)|~rich(X))))&
(((brave(paul)&~generous(paul)))<=>(~curious(john)))&
((?[X]:(~funny(X)))=>((~generous(mary)|~curious(mary))))&
((?[X]:((brave(X)|~quiet(X))))<=>((~patient(fred)&~happy(fred))))&
(![X]:((rich(X)|~old(X))=>(~wise(X)&~strong(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~generous(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~rich(X)&~wise(X))))&
(![X]:((~humble(X)&kind(X))=>(quiet(X)|~patient(X))))&
(((~brave(alice)&creative(alice)))<=>(~calm(alice)))&
(![X]:((patient(X)<~>~kind(X))=>(calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>((generous(susan)|creative(susan))))&
(![X]:((~happy(X)<~>happy(X))<=>(~strong(X)|patient(X))))&
(((rich(mary)|~wise(mary)))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((funny(X)&patient(X))<=>~rich(X)))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>~strong(X))))&
((generous(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((calm(john)|strong(john))) | ~wise(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8762433074349456257185997
% SZS output start Proof for 8762433074349456257185997
8. ! [X0] : ((~kind(X0) <~> kind(X0)) => (~wise(X0) & ~rich(X0))) [input p7]
21. wise(mary) [input hypothesis]
28. ! [X0] : ((~wise(X0) & ~rich(X0)) | (~kind(X0) <=> kind(X0))) [ennf transformation 8]
42. ! [X0] : ((~wise(X0) & ~rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) [nnf transformation 28]
92. ~wise(X0) | kind(X0) | kind(X0) [cnf transformation 42]
93. ~wise(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 42]
132. wise(mary) [cnf transformation 21]
137. ~wise(X0) | kind(X0) [duplicate literal removal 92]
138. ~wise(X0) | ~kind(X0) [duplicate literal removal 93]
193. ~wise(X0) [subsumption resolution 137,138]
269. $false [subsumption resolution 132,193]
% SZS output end Proof for 8762433074349456257185997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and humble is not kind and vice versa. Everyone who is strong is not happy. If john is not strong then someone is calm and vice versa. If someone is either not quiet or quiet then john is both not generous and not creative and vice versa. Everyone who is either patient or not curious is not wise or generous and vice versa. Everyone who is not humble or not curious is not rich. Everyone who is both not brave and curious is either not calm or rich and vice versa. If lucy is either humble or not calm then someone is both quiet and old and vice versa. Everyone who is both brave and not quiet is not calm and vice versa. If mary is either not curious or not brave then someone is not happy or not old and vice versa. If someone is not curious then alice is rich. Everyone who is either not happy or not quiet is not humble and vice versa. Everyone who is calm or creative is quiet or not old. Everyone who is creative or happy is not creative or not quiet and vice versa. If fred is not tall or generous then susan is either not rich or not old and vice versa. If john is patient then someone is happy. Someone is not creative or not rich. Someone is not humble. Someone is either not brave or not creative. Someone is not brave. Someone is both not old and tall. Someone is both patient and not kind. Someone is either not tall or not wise. | Mary is calm. | entailment | (![X]:((patient(X)&humble(X))<=>~kind(X)))&
(![X]:(strong(X)=>~happy(X)))&
((~strong(john))<=>(?[X]:(calm(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>((~generous(john)&~creative(john))))&
(![X]:((patient(X)<~>~curious(X))<=>(~wise(X)|generous(X))))&
(![X]:((~humble(X)|~curious(X))=>~rich(X)))&
(![X]:((~brave(X)&curious(X))<=>(~calm(X)<~>rich(X))))&
(((humble(lucy)<~>~calm(lucy)))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((brave(X)&~quiet(X))<=>~calm(X)))&
(((~curious(mary)<~>~brave(mary)))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:(~curious(X)))=>(rich(alice)))&
(![X]:((~happy(X)<~>~quiet(X))<=>~humble(X)))&
(![X]:((calm(X)|creative(X))=>(quiet(X)|~old(X))))&
(![X]:((creative(X)|happy(X))<=>(~creative(X)|~quiet(X))))&
(((~tall(fred)|generous(fred)))<=>((~rich(susan)<~>~old(susan))))&
((patient(john))=>(?[X]:(happy(X))))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~old(X)&tall(X))))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((~tall(X)<~>~wise(X)))) | calm(mary) | [
"p5",
"p6",
"p8",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4777433274776536261406903
% SZS output start Proof for 4777433274776536261406903
6. ! [X0] : ((~curious(X0) | ~humble(X0)) => ~rich(X0)) [input p5]
7. ! [X0] : ((curious(X0) & ~brave(X0)) <=> (~calm(X0) <~> rich(X0))) [input p6]
9. ! [X0] : ((~quiet(X0) & brave(X0)) <=> ~calm(X0)) [input p8]
10. (~curious(mary) <~> ~brave(mary)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p9]
21. ? [X0] : (tall(X0) & ~old(X0)) [input p20]
24. ~calm(mary) [input hypothesis]
28. ! [X0] : (~rich(X0) | (curious(X0) & humble(X0))) [ennf transformation 6]
44. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~curious(X0) | brave(X0)))) [nnf transformation 7]
45. ! [X0] : (((curious(X0) & ~brave(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ~curious(X0) | brave(X0))) [flattening 44]
50. ! [X0] : (((~quiet(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | (quiet(X0) | ~brave(X0)))) [nnf transformation 9]
51. ! [X0] : (((~quiet(X0) & brave(X0)) | calm(X0)) & (~calm(X0) | quiet(X0) | ~brave(X0))) [flattening 50]
52. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [nnf transformation 10]
53. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & (? [X1] : (~old(X1) | ~happy(X1)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [rectify 52]
54. ? [X1] : (~old(X1) | ~happy(X1)) => (~old(sK3) | ~happy(sK3)) [choice axiom]
55. (((brave(mary) | curious(mary)) & (~brave(mary) | ~curious(mary))) | ! [X0] : (old(X0) & happy(X0))) & ((~old(sK3) | ~happy(sK3)) | ((~curious(mary) | brave(mary)) & (~brave(mary) | curious(mary)))) [skolemisation 53,54]
72. ? [X0] : (tall(X0) & ~old(X0)) => (tall(sK9) & ~old(sK9)) [choice axiom]
73. tall(sK9) & ~old(sK9) [skolemisation 21,72]
97. ~rich(X0) | curious(X0) [cnf transformation 28]
102. curious(X0) | rich(X0) | calm(X0) [cnf transformation 45]
111. brave(X0) | calm(X0) [cnf transformation 51]
116. ~brave(mary) | ~curious(mary) | old(X0) [cnf transformation 55]
142. ~old(sK9) [cnf transformation 73]
148. ~calm(mary) [cnf transformation 24]
186. curious(X0) | calm(X0) [subsumption resolution 102,97]
214. 13 <=> ! [X0] : old(X0) [avatar definition]
215. old(X0) <- (13) [avatar component clause 214]
217. 14 <=> curious(mary) [avatar definition]
218. ~curious(mary) <- (~14) [avatar component clause 217]
221. 15 <=> brave(mary) [avatar definition]
222. ~brave(mary) <- (~15) [avatar component clause 221]
229. 13 | ~14 | ~15 [avatar split clause 116,221,217,214]
312. calm(mary) <- (~15) [resolution 111,222]
313. $false <- (~15) [subsumption resolution 312,148]
314. 15 [avatar contradiction clause 313]
317. $false <- (13) [resolution 215,142]
320. ~13 [avatar contradiction clause 317]
328. calm(mary) <- (~14) [resolution 186,218]
329. $false <- (~14) [subsumption resolution 328,148]
330. 14 [avatar contradiction clause 329]
331. $false [avatar sat refutation 229,314,320,330]
% SZS output end Proof for 4777433274776536261406903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not generous or creative then someone is strong or brave and vice versa. Everyone who is either not patient or not funny is not humble. Everyone who is either kind or strong is either curious or not creative. If someone is both calm and tall then lucy is old or generous. If someone is not wise or not curious then someone is not funny or curious. Everyone who is not tall or quiet is not old or kind. If susan is tall or not wise then alice is both quiet and not wise and vice versa. Everyone who is wise or not brave is both funny and not strong. Everyone who is not brave is strong. If susan is not patient then someone is either calm or not kind. If john is either not humble or not creative then john is old. If alice is not creative then someone is funny or not patient. If lucy is both not happy and brave then alice is either not strong or not old. Everyone who is generous is happy and vice versa. If someone is either not tall or creative then someone is either strong or calm. If someone is both not creative and not strong then someone is either calm or not brave and vice versa. Someone is old. Someone is either old or not happy. John is not quiet. Someone is either not curious or patient. Someone is patient. John is not calm or not humble. Someone is either not strong or strong. Someone is humble or not humble. | Lucy is not brave. | contradiction | (((~generous(paul)<~>creative(paul)))<=>(?[X]:((strong(X)|brave(X)))))&
(![X]:((~patient(X)<~>~funny(X))=>~humble(X)))&
(![X]:((kind(X)<~>strong(X))=>(curious(X)<~>~creative(X))))&
((?[X]:((calm(X)&tall(X))))=>((old(lucy)|generous(lucy))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((~funny(X)|curious(X)))))&
(![X]:((~tall(X)|quiet(X))=>(~old(X)|kind(X))))&
(((tall(susan)|~wise(susan)))<=>((quiet(alice)&~wise(alice))))&
(![X]:((wise(X)|~brave(X))=>(funny(X)&~strong(X))))&
(![X]:(~brave(X)=>strong(X)))&
((~patient(susan))=>(?[X]:((calm(X)<~>~kind(X)))))&
(((~humble(john)<~>~creative(john)))=>(old(john)))&
((~creative(alice))=>(?[X]:((funny(X)|~patient(X)))))&
(((~happy(lucy)&brave(lucy)))=>((~strong(alice)<~>~old(alice))))&
(![X]:(generous(X)<=>happy(X)))&
((?[X]:((~tall(X)<~>creative(X))))=>(?[X]:((strong(X)<~>calm(X)))))&
((?[X]:((~creative(X)&~strong(X))))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(?[X]:(old(X)))&
(?[X]:((old(X)<~>~happy(X))))&
(~quiet(john))&
(?[X]:((~curious(X)<~>patient(X))))&
(?[X]:(patient(X)))&
((~calm(john)|~humble(john)))&
(?[X]:((~strong(X)<~>strong(X))))&
(?[X]:((humble(X)|~humble(X)))) | ~brave(lucy) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6453220327714919887487099
% SZS output start Proof for 6453220327714919887487099
8. ! [X0] : ((~brave(X0) | wise(X0)) => (~strong(X0) & funny(X0))) [input p7]
9. ! [X0] : (~brave(X0) => strong(X0)) [input p8]
25. ~brave(lucy) [input hypothesis]
36. ! [X0] : ((~strong(X0) & funny(X0)) | (brave(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : (strong(X0) | brave(X0)) [ennf transformation 9]
112. ~strong(X0) | brave(X0) [cnf transformation 36]
113. strong(X0) | brave(X0) [cnf transformation 37]
144. ~brave(lucy) [cnf transformation 25]
222. brave(X0) [subsumption resolution 113,112]
347. $false [subsumption resolution 144,222]
% SZS output end Proof for 6453220327714919887487099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and not generous then someone is both tall and calm and vice versa.
Everyone who is both not generous and calm is both not curious and not generous and vice versa.
Everyone who is kind or not brave is not wise or not brave.
If someone is both humble and old then mary is both not funny and not creative.
Everyone who is not tall or tall is either not kind or kind and vice versa.
Everyone who is either kind or rich is curious or kind and vice versa.
If lucy is both brave and not curious then someone is not wise and vice versa.
Everyone who is kind or patient is not calm and vice versa.
Everyone who is either kind or creative is not curious and vice versa.
Everyone who is both not quiet and humble is not creative and vice versa.
If someone is either old or happy then someone is either not generous or strong.
Everyone who is kind is creative or not old and vice versa.
Everyone who is both rich and humble is not brave and vice versa.
If alice is curious or strong then someone is not funny and vice versa.
Everyone who is not rich or not funny is not funny or not tall.
Everyone who is wise or not kind is both not quiet and humble.
Mary is both not patient and rich.
Someone is both kind and creative.
Someone is either not funny or old.
Someone is either not wise or not old.
Fred is calm.
Alice is both not kind and patient.
Someone is kind. | Lucy is curious. | contradiction | ((?[X]:((~old(X)&~generous(X))))<=>(?[X]:((tall(X)&calm(X)))))&
(![X]:((~generous(X)&calm(X))<=>(~curious(X)&~generous(X))))&
(![X]:((kind(X)|~brave(X))=>(~wise(X)|~brave(X))))&
((?[X]:((humble(X)&old(X))))=>((~funny(mary)&~creative(mary))))&
(![X]:((~tall(X)|tall(X))<=>(~kind(X)<~>kind(X))))&
(![X]:((kind(X)<~>rich(X))<=>(curious(X)|kind(X))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~wise(X))))&
(![X]:((kind(X)|patient(X))<=>~calm(X)))&
(![X]:((kind(X)<~>creative(X))<=>~curious(X)))&
(![X]:((~quiet(X)&humble(X))<=>~creative(X)))&
((?[X]:((old(X)<~>happy(X))))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(kind(X)<=>(creative(X)|~old(X))))&
(![X]:((rich(X)&humble(X))<=>~brave(X)))&
(((curious(alice)|strong(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)|~funny(X))=>(~funny(X)|~tall(X))))&
(![X]:((wise(X)|~kind(X))=>(~quiet(X)&humble(X))))&
((~patient(mary)&rich(mary)))&
(?[X]:((kind(X)&creative(X))))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((~wise(X)<~>~old(X))))&
(calm(fred))&
((~kind(alice)&patient(alice)))&
(?[X]:(kind(X))) | curious(lucy) | [
"p2",
"p5",
"p6",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3900947811195995624619898
% SZS output start Proof for 3900947811195995624619898
3. ! [X0] : ((~brave(X0) | kind(X0)) => (~brave(X0) | ~wise(X0))) [input p2]
6. ! [X0] : ((kind(X0) <~> rich(X0)) <=> (kind(X0) | curious(X0))) [input p5]
7. (~curious(lucy) & brave(lucy)) <=> ? [X0] : ~wise(X0) [input p6]
13. ! [X0] : ((humble(X0) & rich(X0)) <=> ~brave(X0)) [input p12]
18. ? [X0] : (creative(X0) & kind(X0)) [input p17]
24. curious(lucy) [input hypothesis]
27. ! [X0] : ((~brave(X0) | ~wise(X0)) | (brave(X0) & ~kind(X0))) [ennf transformation 3]
28. ! [X0] : (~brave(X0) | ~wise(X0) | (brave(X0) & ~kind(X0))) [flattening 27]
43. ! [X0] : ((((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))))) [nnf transformation 6]
44. ! [X0] : ((((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))))) [flattening 43]
45. ((~curious(lucy) & brave(lucy)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | (curious(lucy) | ~brave(lucy))) [nnf transformation 7]
46. ((~curious(lucy) & brave(lucy)) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | curious(lucy) | ~brave(lucy)) [flattening 45]
47. ((~curious(lucy) & brave(lucy)) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | curious(lucy) | ~brave(lucy)) [rectify 46]
48. ? [X1] : ~wise(X1) => ~wise(sK2) [choice axiom]
49. ((~curious(lucy) & brave(lucy)) | ! [X0] : wise(X0)) & (~wise(sK2) | curious(lucy) | ~brave(lucy)) [skolemisation 47,48]
61. ! [X0] : (((humble(X0) & rich(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) | ~rich(X0)))) [nnf transformation 13]
62. ! [X0] : (((humble(X0) & rich(X0)) | brave(X0)) & (~brave(X0) | ~humble(X0) | ~rich(X0))) [flattening 61]
68. ? [X0] : (creative(X0) & kind(X0)) => (creative(sK5) & kind(sK5)) [choice axiom]
69. creative(sK5) & kind(sK5) [skolemisation 18,68]
86. ~wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 28]
101. ~rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44]
104. ~curious(lucy) | wise(X0) [cnf transformation 49]
123. rich(X0) | brave(X0) [cnf transformation 62]
136. kind(sK5) [cnf transformation 69]
146. curious(lucy) [cnf transformation 24]
148. ~rich(X0) | ~kind(X0) [duplicate literal removal 101]
192. 10 <=> ! [X0] : wise(X0) [avatar definition]
193. wise(X0) <- (10) [avatar component clause 192]
195. 11 <=> curious(lucy) [avatar definition]
198. 10 | ~11 [avatar split clause 104,195,192]
265. 11 [avatar split clause 146,195]
281. ~kind(X0) | brave(X0) [resolution 148,123]
323. ~brave(X0) | ~kind(X0) <- (10) [resolution 86,193]
325. ~kind(X0) <- (10) [subsumption resolution 323,281]
326. $false <- (10) [resolution 325,136]
330. ~10 [avatar contradiction clause 326]
331. $false [avatar sat refutation 198,265,330]
% SZS output end Proof for 3900947811195995624619898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not strong. If someone is not creative then someone is both not old and happy and vice versa. If paul is quiet then someone is both curious and not happy and vice versa. Everyone who is rich or old is not calm. Everyone who is not humble or humble is either happy or not creative. Everyone who is both generous and patient is creative and vice versa. If someone is either kind or not generous then someone is both not brave and creative and vice versa. If susan is both strong and rich then someone is not tall. If someone is either not funny or brave then someone is either not quiet or not brave. If someone is either patient or not humble then someone is both not happy and tall. Everyone who is both brave and not quiet is both not generous and not happy and vice versa. If someone is not tall or quiet then paul is not funny or quiet. Everyone who is both not generous and humble is not old or brave and vice versa. Everyone who is not kind or not old is either calm or not tall and vice versa. If mary is either strong or kind then susan is not curious. Everyone who is either not rich or not humble is both kind and not brave. Someone is not brave or not humble. Someone is not rich or not humble. | Mary is not strong. | neutral | (![X]:(~curious(X)=>~strong(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&happy(X)))))&
((quiet(paul))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((rich(X)|old(X))=>~calm(X)))&
(![X]:((~humble(X)|humble(X))=>(happy(X)<~>~creative(X))))&
(![X]:((generous(X)&patient(X))<=>creative(X)))&
((?[X]:((kind(X)<~>~generous(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
(((strong(susan)&rich(susan)))=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)<~>brave(X))))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:((brave(X)&~quiet(X))<=>(~generous(X)&~happy(X))))&
((?[X]:((~tall(X)|quiet(X))))=>((~funny(paul)|quiet(paul))))&
(![X]:((~generous(X)&humble(X))<=>(~old(X)|brave(X))))&
(![X]:((~kind(X)|~old(X))<=>(calm(X)<~>~tall(X))))&
(((strong(mary)<~>kind(mary)))=>(~curious(susan)))&
(![X]:((~rich(X)<~>~humble(X))=>(kind(X)&~brave(X))))&
(?[X]:((~brave(X)|~humble(X))))&
(?[X]:((~rich(X)|~humble(X)))) | ~strong(mary) | [] | null | 0 |
If susan is either not creative or not strong then someone is not creative or not patient and vice versa. Everyone who is either not creative or not happy is not happy or generous. Everyone who is both old and funny is creative or quiet and vice versa. Everyone who is not curious is creative. Everyone who is curious is either happy or brave and vice versa. If someone is both funny and not rich then lucy is not patient. If someone is both curious and generous then lucy is generous. If someone is old or not curious then john is old or not generous. Everyone who is rich is happy or funny and vice versa. If alice is both not curious and not brave then someone is either not patient or not rich. If paul is curious or funny then someone is wise or not generous and vice versa. If someone is not happy then someone is both calm and not brave. Everyone who is not humble is both funny and not brave. Everyone who is both not calm and happy is both patient and funny. Everyone who is either not curious or generous is not wise and vice versa. If someone is both generous and not creative then alice is both not humble and calm and vice versa. Susan is either rich or not rich. Fred is not kind or creative. Alice is not old. Someone is humble or not creative. Someone is not quiet or not strong. Lucy is both not happy and quiet. Someone is not brave. Someone is either generous or not brave. | Alice is not curious. | contradiction | (((~creative(susan)<~>~strong(susan)))<=>(?[X]:((~creative(X)|~patient(X)))))&
(![X]:((~creative(X)<~>~happy(X))=>(~happy(X)|generous(X))))&
(![X]:((old(X)&funny(X))<=>(creative(X)|quiet(X))))&
(![X]:(~curious(X)=>creative(X)))&
(![X]:(curious(X)<=>(happy(X)<~>brave(X))))&
((?[X]:((funny(X)&~rich(X))))=>(~patient(lucy)))&
((?[X]:((curious(X)&generous(X))))=>(generous(lucy)))&
((?[X]:((old(X)|~curious(X))))=>((old(john)|~generous(john))))&
(![X]:(rich(X)<=>(happy(X)|funny(X))))&
(((~curious(alice)&~brave(alice)))=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((curious(paul)|funny(paul)))<=>(?[X]:((wise(X)|~generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:(~humble(X)=>(funny(X)&~brave(X))))&
(![X]:((~calm(X)&happy(X))=>(patient(X)&funny(X))))&
(![X]:((~curious(X)<~>generous(X))<=>~wise(X)))&
((?[X]:((generous(X)&~creative(X))))<=>((~humble(alice)&calm(alice))))&
((rich(susan)<~>~rich(susan)))&
((~kind(fred)|creative(fred)))&
(~old(alice))&
(?[X]:((humble(X)|~creative(X))))&
(?[X]:((~quiet(X)|~strong(X))))&
((~happy(lucy)&quiet(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((generous(X)<~>~brave(X)))) | ~curious(alice) | [
"p2",
"p3",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 637823368492556854852274
% SZS output start Proof for 637823368492556854852274
3. ! [X0] : ((funny(X0) & old(X0)) <=> (quiet(X0) | creative(X0))) [input p2]
4. ! [X0] : (~curious(X0) => creative(X0)) [input p3]
19. ~old(alice) [input p18]
25. ~curious(alice) [input hypothesis]
30. ! [X0] : (creative(X0) | curious(X0)) [ennf transformation 4]
46. ! [X0] : (((funny(X0) & old(X0)) | (~quiet(X0) & ~creative(X0))) & ((quiet(X0) | creative(X0)) | (~funny(X0) | ~old(X0)))) [nnf transformation 3]
47. ! [X0] : (((funny(X0) & old(X0)) | (~quiet(X0) & ~creative(X0))) & (quiet(X0) | creative(X0) | ~funny(X0) | ~old(X0))) [flattening 46]
87. ~creative(X0) | old(X0) [cnf transformation 47]
91. curious(X0) | creative(X0) [cnf transformation 30]
125. ~old(alice) [cnf transformation 19]
133. ~curious(alice) [cnf transformation 25]
197. 15 <=> curious(alice) [avatar definition]
198. ~curious(alice) <- (~15) [avatar component clause 197]
304. ~15 [avatar split clause 133,197]
311. creative(alice) <- (~15) [resolution 91,198]
313. old(alice) <- (~15) [resolution 311,87]
314. $false <- (~15) [subsumption resolution 313,125]
315. 15 [avatar contradiction clause 314]
316. $false [avatar sat refutation 304,315]
% SZS output end Proof for 637823368492556854852274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is both not wise and rich. If lucy is not creative or not strong then susan is either not tall or patient. If someone is not rich then someone is either not humble or kind. If someone is not quiet or not curious then fred is kind or humble and vice versa. Everyone who is either quiet or not rich is not strong or not quiet and vice versa. If susan is both not funny and humble then john is either wise or happy. Everyone who is both not generous and not humble is curious or kind and vice versa. Everyone who is either funny or curious is not creative or not wise and vice versa. If mary is not funny or not calm then someone is not wise or not brave and vice versa. If someone is calm or not quiet then someone is either not strong or wise. Everyone who is not funny or not strong is either happy or tall and vice versa. Everyone who is funny is strong or tall. Everyone who is generous or wise is either not creative or generous. If someone is not humble or not patient then someone is both not kind and kind. Everyone who is not quiet or creative is not rich. Someone is not happy. John is not curious. Someone is both tall and not old. Someone is not creative. Someone is both not brave and patient. | Susan is strong. | contradiction | (![X]:(strong(X)=>(~wise(X)&rich(X))))&
(((~creative(lucy)|~strong(lucy)))=>((~tall(susan)<~>patient(susan))))&
((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~quiet(X)|~curious(X))))<=>((kind(fred)|humble(fred))))&
(![X]:((quiet(X)<~>~rich(X))<=>(~strong(X)|~quiet(X))))&
(((~funny(susan)&humble(susan)))=>((wise(john)<~>happy(john))))&
(![X]:((~generous(X)&~humble(X))<=>(curious(X)|kind(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~creative(X)|~wise(X))))&
(((~funny(mary)|~calm(mary)))<=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~funny(X)|~strong(X))<=>(happy(X)<~>tall(X))))&
(![X]:(funny(X)=>(strong(X)|tall(X))))&
(![X]:((generous(X)|wise(X))=>(~creative(X)<~>generous(X))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((~quiet(X)|creative(X))=>~rich(X)))&
(?[X]:(~happy(X)))&
(~curious(john))&
(?[X]:((tall(X)&~old(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)&patient(X)))) | strong(susan) | [
"p0",
"p2",
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6213798006775297180675504
% SZS output start Proof for 6213798006775297180675504
1. ! [X0] : (strong(X0) => (rich(X0) & ~wise(X0))) [input p0]
3. ? [X0] : ~rich(X0) => ? [X0] : (~humble(X0) <~> kind(X0)) [input p2]
5. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p4]
7. ! [X0] : ((~humble(X0) & ~generous(X0)) <=> (kind(X0) | curious(X0))) [input p6]
14. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p13]
21. strong(susan) [input hypothesis]
22. ? [X0] : ~rich(X0) => ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 3]
24. ? [X0] : (~patient(X0) | ~humble(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 14]
26. ! [X0] : ((rich(X0) & ~wise(X0)) | ~strong(X0)) [ennf transformation 1]
28. ? [X1] : (~humble(X1) <~> kind(X1)) | ! [X0] : rich(X0) [ennf transformation 22]
35. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : (patient(X0) & humble(X0)) [ennf transformation 24]
38. ? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : rich(X0) [nnf transformation 28]
39. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ! [X1] : rich(X1) [rectify 38]
40. ? [X0] : ((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) => ((~kind(sK0) | humble(sK0)) & (kind(sK0) | ~humble(sK0))) [choice axiom]
41. ((~kind(sK0) | humble(sK0)) & (kind(sK0) | ~humble(sK0))) | ! [X1] : rich(X1) [skolemisation 39,40]
47. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 5]
48. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [flattening 47]
50. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | (humble(X0) | generous(X0)))) [nnf transformation 7]
51. ! [X0] : (((~humble(X0) & ~generous(X0)) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | humble(X0) | generous(X0))) [flattening 50]
66. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : (patient(X1) & humble(X1)) [rectify 35]
67. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK4) & ~kind(sK4)) [choice axiom]
68. (kind(sK4) & ~kind(sK4)) | ! [X1] : (patient(X1) & humble(X1)) [skolemisation 66,67]
78. ~strong(X0) | rich(X0) [cnf transformation 26]
83. kind(sK0) | ~humble(sK0) | rich(X1) [cnf transformation 41]
89. ~quiet(X0) | ~strong(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 48]
92. ~rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 48]
101. ~kind(X0) | ~humble(X0) [cnf transformation 51]
127. ~kind(sK4) | humble(X1) [cnf transformation 68]
129. kind(sK4) | humble(X1) [cnf transformation 68]
139. strong(susan) [cnf transformation 21]
141. ~quiet(X0) | ~strong(X0) | ~rich(X0) [duplicate literal removal 89]
142. ~rich(X0) | quiet(X0) [duplicate literal removal 92]
164. 5 <=> ! [X1] : rich(X1) [avatar definition]
165. rich(X1) <- (5) [avatar component clause 164]
167. 6 <=> humble(sK0) [avatar definition]
168. ~humble(sK0) <- (~6) [avatar component clause 167]
171. 7 <=> kind(sK0) [avatar definition]
172. kind(sK0) <- (7) [avatar component clause 171]
175. 5 | ~6 | 7 [avatar split clause 83,171,167,164]
199. 13 <=> ! [X1] : quiet(X1) [avatar definition]
200. quiet(X1) <- (13) [avatar component clause 199]
203. ~quiet(X0) | ~strong(X0) [subsumption resolution 141,78]
271. 28 <=> kind(sK4) [avatar definition]
276. 29 <=> ! [X1] : humble(X1) [avatar definition]
277. humble(X1) <- (29) [avatar component clause 276]
278. 29 | 28 [avatar split clause 129,271,276]
280. 29 | ~28 [avatar split clause 127,271,276]
283. $false <- (~6, 29) [subsumption resolution 168,277]
284. 6 | ~29 [avatar contradiction clause 283]
289. quiet(X0) <- (5) [resolution 142,165]
290. 13 | ~5 [avatar split clause 289,164,199]
294. ~strong(X0) <- (13) [resolution 203,200]
295. $false <- (13) [resolution 294,139]
296. ~13 [avatar contradiction clause 295]
297. ~humble(sK0) <- (7) [resolution 172,101]
298. $false <- (7, 29) [subsumption resolution 297,277]
299. ~7 | ~29 [avatar contradiction clause 298]
300. $false [avatar sat refutation 175,278,280,284,290,296,299]
% SZS output end Proof for 6213798006775297180675504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not quiet then alice is not patient and vice versa.
If someone is patient then fred is both not patient and generous and vice versa.
If fred is both happy and not quiet then mary is not curious or not old.
Everyone who is humble is strong or not humble and vice versa.
If someone is not tall then alice is both not kind and not generous.
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.
Someone is both quiet and not wise.
Someone is either calm or generous.
Someone is calm or old.
Lucy is both curious and not patient.
Someone is not funny or strong.
Lucy is both quiet and curious.
Someone is not kind. | Alice is not old. | contradiction | ((~quiet(john))<=>(~patient(alice)))&
((?[X]:(patient(X)))<=>((~patient(fred)&generous(fred))))&
(((happy(fred)&~quiet(fred)))=>((~curious(mary)|~old(mary))))&
(![X]:(humble(X)<=>(strong(X)|~humble(X))))&
((?[X]:(~tall(X)))=>((~kind(alice)&~generous(alice))))&
((?[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))))&
(?[X]:((quiet(X)&~wise(X))))&
(?[X]:((calm(X)<~>generous(X))))&
(?[X]:((calm(X)|old(X))))&
((curious(lucy)&~patient(lucy)))&
(?[X]:((~funny(X)|strong(X))))&
((quiet(lucy)&curious(lucy)))&
(?[X]:(~kind(X))) | ~old(alice) | [
"p3",
"p4",
"p9",
"p13",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1912267735256903374772528
% SZS output start Proof for 1912267735256903374772528
4. ! [X0] : (humble(X0) <=> (~humble(X0) | strong(X0))) [input p3]
5. ? [X0] : ~tall(X0) => (~generous(alice) & ~kind(alice)) [input p4]
10. ! [X0] : ((humble(X0) <~> generous(X0)) => old(X0)) [input p9]
14. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (~tall(X0) | ~humble(X0))) [input p13]
20. ~patient(lucy) & curious(lucy) [input p19]
22. curious(lucy) & quiet(lucy) [input p21]
24. ~old(alice) [input hypothesis]
28. (~generous(alice) & ~kind(alice)) | ! [X0] : tall(X0) [ennf transformation 5]
31. ! [X0] : (old(X0) | (humble(X0) <=> generous(X0))) [ennf transformation 10]
41. ! [X0] : ((humble(X0) | (humble(X0) & ~strong(X0))) & ((~humble(X0) | strong(X0)) | ~humble(X0))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | (humble(X0) & ~strong(X0))) & (~humble(X0) | strong(X0) | ~humble(X0))) [flattening 41]
53. ! [X0] : (old(X0) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) [nnf transformation 31]
58. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 58]
81. humble(X0) | humble(X0) [cnf transformation 42]
83. ~generous(alice) | tall(X0) [cnf transformation 28]
95. old(X0) | generous(X0) | ~humble(X0) [cnf transformation 53]
112. ~tall(X0) | ~humble(X0) | patient(X0) | ~quiet(X0) [cnf transformation 59]
131. ~patient(lucy) [cnf transformation 20]
133. quiet(lucy) [cnf transformation 22]
136. ~old(alice) [cnf transformation 24]
142. humble(X0) [duplicate literal removal 81]
190. 11 <=> ! [X0] : tall(X0) [avatar definition]
191. tall(X0) <- (11) [avatar component clause 190]
193. 12 <=> generous(alice) [avatar definition]
196. 11 | ~12 [avatar split clause 83,193,190]
251. old(X0) | generous(X0) [subsumption resolution 95,142]
277. ~tall(X0) | patient(X0) | ~quiet(X0) [subsumption resolution 112,142]
290. generous(alice) [resolution 251,136]
294. 12 [avatar split clause 290,193]
299. ~quiet(X1) | patient(X1) <- (11) [resolution 277,191]
302. patient(lucy) <- (11) [resolution 299,133]
303. $false <- (11) [subsumption resolution 302,131]
304. ~11 [avatar contradiction clause 303]
305. $false [avatar sat refutation 196,294,304]
% SZS output end Proof for 1912267735256903374772528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and not curious then fred is brave or funny and vice versa.
Everyone who is not calm is not quiet and vice versa.
Everyone who is both tall and not brave is not generous.
Everyone who is not funny or not curious is both curious and not tall.
If lucy is both creative and not creative then mary is both generous and patient and vice versa.
If someone is kind or not patient then someone is quiet or curious and vice versa.
Everyone who is both not old and patient is old or creative.
Everyone who is either humble or old is not patient or tall.
If someone is not brave or not funny then someone is both creative and not quiet and vice versa.
Everyone who is not tall or curious is strong or not kind.
Everyone who is both not quiet and not calm is either not funny or not creative and vice versa.
Everyone who is either quiet or tall is not wise or brave and vice versa.
If lucy is not strong then mary is either quiet or not tall.
If someone is rich then susan is generous or not strong.
If someone is both not quiet and not strong then someone is not curious.
If someone is strong or not happy then someone is calm.
Someone is tall or not brave.
Someone is old.
Someone is both not tall and not kind.
Someone is quiet or old.
Someone is not calm or rich.
Mary is curious.
Someone is either quiet or patient.
Someone is both old and not quiet. | Fred is curious. | entailment | ((?[X]:((~funny(X)&~curious(X))))<=>((brave(fred)|funny(fred))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(![X]:((tall(X)&~brave(X))=>~generous(X)))&
(![X]:((~funny(X)|~curious(X))=>(curious(X)&~tall(X))))&
(((creative(lucy)&~creative(lucy)))<=>((generous(mary)&patient(mary))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~old(X)&patient(X))=>(old(X)|creative(X))))&
(![X]:((humble(X)<~>old(X))=>(~patient(X)|tall(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:((~tall(X)|curious(X))=>(strong(X)|~kind(X))))&
(![X]:((~quiet(X)&~calm(X))<=>(~funny(X)<~>~creative(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~wise(X)|brave(X))))&
((~strong(lucy))=>((quiet(mary)<~>~tall(mary))))&
((?[X]:(rich(X)))=>((generous(susan)|~strong(susan))))&
((?[X]:((~quiet(X)&~strong(X))))=>(?[X]:(~curious(X))))&
((?[X]:((strong(X)|~happy(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((~calm(X)|rich(X))))&
(curious(mary))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((old(X)&~quiet(X)))) | curious(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5711322059184559864257723
% SZS output start Proof for 5711322059184559864257723
4. ! [X0] : ((~curious(X0) | ~funny(X0)) => (~tall(X0) & curious(X0))) [input p3]
25. ~curious(fred) [input hypothesis]
33. ! [X0] : ((~tall(X0) & curious(X0)) | (curious(X0) & funny(X0))) [ennf transformation 4]
99. curious(X0) | curious(X0) [cnf transformation 33]
148. ~curious(fred) [cnf transformation 25]
150. curious(X0) [duplicate literal removal 99]
308. $false [subsumption resolution 148,150]
% SZS output end Proof for 5711322059184559864257723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not creative then paul is not tall and vice versa.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Everyone who is either tall or not brave is both strong and not generous and vice versa.
If someone is humble then alice is wise and vice versa.
If someone is not calm or not creative then someone is patient.
Susan is either humble or not curious.
Fred is brave or not kind.
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 not creative. | neutral | (((brave(john)|~creative(john)))<=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(![X]:((tall(X)<~>~brave(X))<=>(strong(X)&~generous(X))))&
((?[X]:(humble(X)))<=>(wise(alice)))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:(patient(X))))&
((humble(susan)<~>~curious(susan)))&
((brave(fred)|~kind(fred)))&
(~funny(john))&
(quiet(mary))&
((~creative(paul)|kind(paul)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((~humble(X)<~>brave(X)))) | ~creative(lucy) | [] | null | 0 |
If mary is both not patient and old then susan is not tall and vice versa.
Everyone who is either not patient or creative is either not brave or not kind and vice versa.
If fred is both brave and creative then someone is both not quiet and not old and vice versa.
If someone is either not old or curious then fred is both not patient and humble.
Everyone who is happy or not rich is either not generous or not brave.
If alice is not old or humble then someone is funny and vice versa.
Everyone who is both rich and not quiet is rich or not strong and vice versa.
Everyone who is not funny or not patient is both rich and quiet and vice versa.
Everyone who is either not humble or not funny is either not old or curious.
Everyone who is funny or kind is both funny and quiet and vice versa.
Everyone who is either old or wise is both not old and not happy and vice versa.
Everyone who is both not quiet and not tall is generous and vice versa.
If someone is curious then alice is both not generous and strong.
Everyone who is either patient or not kind is either not brave or not happy.
If lucy is not rich or patient then someone is either quiet or calm.
Someone is not tall.
Someone is not rich.
John is not old.
Susan is wise.
Someone is not kind or calm.
Lucy is either brave or not kind.
John is brave or not tall. | Alice is quiet. | entailment | (((~patient(mary)&old(mary)))<=>(~tall(susan)))&
(![X]:((~patient(X)<~>creative(X))<=>(~brave(X)<~>~kind(X))))&
(((brave(fred)&creative(fred)))<=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:((~old(X)<~>curious(X))))=>((~patient(fred)&humble(fred))))&
(![X]:((happy(X)|~rich(X))=>(~generous(X)<~>~brave(X))))&
(((~old(alice)|humble(alice)))<=>(?[X]:(funny(X))))&
(![X]:((rich(X)&~quiet(X))<=>(rich(X)|~strong(X))))&
(![X]:((~funny(X)|~patient(X))<=>(rich(X)&quiet(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(~old(X)<~>curious(X))))&
(![X]:((funny(X)|kind(X))<=>(funny(X)&quiet(X))))&
(![X]:((old(X)<~>wise(X))<=>(~old(X)&~happy(X))))&
(![X]:((~quiet(X)&~tall(X))<=>generous(X)))&
((?[X]:(curious(X)))=>((~generous(alice)&strong(alice))))&
(![X]:((patient(X)<~>~kind(X))=>(~brave(X)<~>~happy(X))))&
(((~rich(lucy)|patient(lucy)))=>(?[X]:((quiet(X)<~>calm(X)))))&
(?[X]:(~tall(X)))&
(?[X]:(~rich(X)))&
(~old(john))&
(wise(susan))&
(?[X]:((~kind(X)|calm(X))))&
((brave(lucy)<~>~kind(lucy)))&
((brave(john)|~tall(john))) | quiet(alice) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8406129204070698134961759
% SZS output start Proof for 8406129204070698134961759
8. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (quiet(X0) & rich(X0))) [input p7]
10. ! [X0] : ((kind(X0) | funny(X0)) <=> (quiet(X0) & funny(X0))) [input p9]
23. ~quiet(alice) [input hypothesis]
47. ! [X0] : (((~patient(X0) | ~funny(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 8]
48. ! [X0] : ((~patient(X0) | ~funny(X0) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | (patient(X0) & funny(X0)))) [flattening 47]
50. ! [X0] : (((kind(X0) | funny(X0)) | (~quiet(X0) | ~funny(X0))) & ((quiet(X0) & funny(X0)) | (~kind(X0) & ~funny(X0)))) [nnf transformation 10]
51. ! [X0] : ((kind(X0) | funny(X0) | ~quiet(X0) | ~funny(X0)) & ((quiet(X0) & funny(X0)) | (~kind(X0) & ~funny(X0)))) [flattening 50]
100. quiet(X0) | funny(X0) [cnf transformation 48]
109. quiet(X0) | ~funny(X0) [cnf transformation 51]
139. ~quiet(alice) [cnf transformation 23]
216. quiet(X0) [subsumption resolution 109,100]
270. $false [subsumption resolution 139,216]
% SZS output end Proof for 8406129204070698134961759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not kind is not creative or not curious and vice versa.
Everyone who is both strong and old is not happy.
If someone is happy then mary is funny or not humble and vice versa.
If susan is either not calm or creative then someone is both not rich and rich and vice versa.
Everyone who is either not creative or not brave is not quiet.
If someone is not generous then fred is either not brave or not humble and vice versa.
If someone is strong or kind then someone is either generous or not humble and vice versa.
Everyone who is both not humble and tall is curious or quiet and vice versa.
Everyone who is either not patient or not brave is rich and vice versa.
If susan is curious then alice is humble.
If someone is humble then someone is either not old or calm and vice versa.
Everyone who is not creative is both old and generous.
Everyone who is not funny is either not creative or not humble and vice versa.
Everyone who is either happy or not tall is both not happy and quiet and vice versa.
If someone is quiet or calm then fred is both not curious and quiet and vice versa.
If someone is not curious then someone is not funny or not brave.
Someone is either generous or not calm.
Someone is humble or funny.
Alice is not happy.
Mary is funny.
Someone is not humble or not old.
Someone is either not creative or not humble. | Alice is creative. | entailment | (![X]:((~tall(X)&~kind(X))<=>(~creative(X)|~curious(X))))&
(![X]:((strong(X)&old(X))=>~happy(X)))&
((?[X]:(happy(X)))<=>((funny(mary)|~humble(mary))))&
(((~calm(susan)<~>creative(susan)))<=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((~creative(X)<~>~brave(X))=>~quiet(X)))&
((?[X]:(~generous(X)))<=>((~brave(fred)<~>~humble(fred))))&
((?[X]:((strong(X)|kind(X))))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~humble(X)&tall(X))<=>(curious(X)|quiet(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>rich(X)))&
((curious(susan))=>(humble(alice)))&
((?[X]:(humble(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:(~creative(X)=>(old(X)&generous(X))))&
(![X]:(~funny(X)<=>(~creative(X)<~>~humble(X))))&
(![X]:((happy(X)<~>~tall(X))<=>(~happy(X)&quiet(X))))&
((?[X]:((quiet(X)|calm(X))))<=>((~curious(fred)&quiet(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|~brave(X)))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((humble(X)|funny(X))))&
(~happy(alice))&
(funny(mary))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:((~creative(X)<~>~humble(X)))) | creative(alice) | [
"p0",
"p7",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3896462837506092429939263
% SZS output start Proof for 3896462837506092429939263
1. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (~curious(X0) | ~creative(X0))) [input p0]
8. ! [X0] : ((tall(X0) & ~humble(X0)) <=> (quiet(X0) | curious(X0))) [input p7]
14. ! [X0] : ((happy(X0) <~> ~tall(X0)) <=> (quiet(X0) & ~happy(X0))) [input p13]
19. ~happy(alice) [input p18]
23. ~creative(alice) [input hypothesis]
33. ! [X0] : (((~kind(X0) & ~tall(X0)) | (curious(X0) & creative(X0))) & ((~curious(X0) | ~creative(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 1]
34. ! [X0] : (((~kind(X0) & ~tall(X0)) | (curious(X0) & creative(X0))) & (~curious(X0) | ~creative(X0) | kind(X0) | tall(X0))) [flattening 33]
54. ! [X0] : (((tall(X0) & ~humble(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (~tall(X0) | humble(X0)))) [nnf transformation 8]
55. ! [X0] : (((tall(X0) & ~humble(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | ~tall(X0) | humble(X0))) [flattening 54]
63. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (~quiet(X0) | happy(X0))) & ((quiet(X0) & ~happy(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [nnf transformation 14]
64. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ~quiet(X0) | happy(X0)) & ((quiet(X0) & ~happy(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [flattening 63]
84. ~tall(X0) | creative(X0) [cnf transformation 34]
114. ~quiet(X0) | tall(X0) [cnf transformation 55]
133. quiet(X0) | happy(X0) | tall(X0) [cnf transformation 64]
134. ~tall(X0) | happy(X0) | ~quiet(X0) | happy(X0) [cnf transformation 64]
145. ~happy(alice) [cnf transformation 19]
150. ~creative(alice) [cnf transformation 23]
152. ~tall(X0) | happy(X0) | ~quiet(X0) [duplicate literal removal 134]
274. ~quiet(X0) | happy(X0) [subsumption resolution 152,114]
275. happy(X0) | tall(X0) [subsumption resolution 133,274]
376. tall(alice) [resolution 275,145]
390. creative(alice) [resolution 376,84]
391. $false [subsumption resolution 390,150]
% SZS output end Proof for 3896462837506092429939263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then lucy is not wise or not happy and vice versa. If someone is not tall then paul is not strong and vice versa. Everyone who is not generous or curious is not old and vice versa. If fred is humble or generous then fred is not happy and vice versa. Everyone who is not funny is tall or not rich and vice versa. Everyone who is both kind and not old is tall. If lucy is both tall and not kind then someone is either calm or not wise and vice versa. If john is both not kind and not curious then john is not curious or not rich. Everyone who is creative or not creative is rich or not generous and vice versa. Everyone who is not kind or kind is either not calm or happy and vice versa. Everyone who is not old is not rich or funny and vice versa. Everyone who is funny or happy is old and vice versa. If someone is either rich or not humble then someone is quiet or tall and vice versa. If john is humble then someone is either not quiet or not humble and vice versa. If someone is curious or not humble then mary is brave. If someone is either tall or not funny then lucy is both humble and funny and vice versa. Mary is either curious or not humble. Someone is quiet. Alice is either not brave or funny. Mary is either not patient or rich. Mary is either tall or not generous. Someone is either not curious or wise. Someone is either creative or kind. Paul is tall or wise. | Mary is tall. | entailment | ((?[X]:(~generous(X)))<=>((~wise(lucy)|~happy(lucy))))&
((?[X]:(~tall(X)))<=>(~strong(paul)))&
(![X]:((~generous(X)|curious(X))<=>~old(X)))&
(((humble(fred)|generous(fred)))<=>(~happy(fred)))&
(![X]:(~funny(X)<=>(tall(X)|~rich(X))))&
(![X]:((kind(X)&~old(X))=>tall(X)))&
(((tall(lucy)&~kind(lucy)))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(((~kind(john)&~curious(john)))=>((~curious(john)|~rich(john))))&
(![X]:((creative(X)|~creative(X))<=>(rich(X)|~generous(X))))&
(![X]:((~kind(X)|kind(X))<=>(~calm(X)<~>happy(X))))&
(![X]:(~old(X)<=>(~rich(X)|funny(X))))&
(![X]:((funny(X)|happy(X))<=>old(X)))&
((?[X]:((rich(X)<~>~humble(X))))<=>(?[X]:((quiet(X)|tall(X)))))&
((humble(john))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
((?[X]:((curious(X)|~humble(X))))=>(brave(mary)))&
((?[X]:((tall(X)<~>~funny(X))))<=>((humble(lucy)&funny(lucy))))&
((curious(mary)<~>~humble(mary)))&
(?[X]:(quiet(X)))&
((~brave(alice)<~>funny(alice)))&
((~patient(mary)<~>rich(mary)))&
((tall(mary)<~>~generous(mary)))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((tall(paul)|wise(paul))) | tall(mary) | [
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 734459076620271245258800
% SZS output start Proof for 734459076620271245258800
11. ! [X0] : (~old(X0) <=> (funny(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((happy(X0) | funny(X0)) <=> old(X0)) [input p11]
16. ? [X0] : (tall(X0) <~> ~funny(X0)) <=> (funny(lucy) & humble(lucy)) [input p15]
25. ~tall(mary) [input hypothesis]
56. ! [X0] : ((~old(X0) | (~funny(X0) & rich(X0))) & ((funny(X0) | ~rich(X0)) | old(X0))) [nnf transformation 11]
57. ! [X0] : ((~old(X0) | (~funny(X0) & rich(X0))) & (funny(X0) | ~rich(X0) | old(X0))) [flattening 56]
58. ! [X0] : (((happy(X0) | funny(X0)) | ~old(X0)) & (old(X0) | (~happy(X0) & ~funny(X0)))) [nnf transformation 12]
59. ! [X0] : ((happy(X0) | funny(X0) | ~old(X0)) & (old(X0) | (~happy(X0) & ~funny(X0)))) [flattening 58]
69. (? [X0] : ((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (~funny(lucy) | ~humble(lucy))) & ((funny(lucy) & humble(lucy)) | ! [X0] : ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0)))) [nnf transformation 16]
70. (? [X0] : ((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~funny(lucy) | ~humble(lucy)) & ((funny(lucy) & humble(lucy)) | ! [X0] : ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0)))) [flattening 69]
71. (? [X0] : ((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~funny(lucy) | ~humble(lucy)) & ((funny(lucy) & humble(lucy)) | ! [X1] : ((tall(X1) | funny(X1)) & (~funny(X1) | ~tall(X1)))) [rectify 70]
72. ? [X0] : ((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) => ((funny(sK6) | ~tall(sK6)) & (~funny(sK6) | tall(sK6))) [choice axiom]
73. (((funny(sK6) | ~tall(sK6)) & (~funny(sK6) | tall(sK6))) | ~funny(lucy) | ~humble(lucy)) & ((funny(lucy) & humble(lucy)) | ! [X1] : ((tall(X1) | funny(X1)) & (~funny(X1) | ~tall(X1)))) [skolemisation 71,72]
120. ~old(X0) | ~funny(X0) [cnf transformation 57]
121. old(X0) | ~funny(X0) [cnf transformation 59]
139. funny(lucy) | tall(X1) | funny(X1) [cnf transformation 73]
156. ~tall(mary) [cnf transformation 25]
185. 7 <=> ! [X1] : tall(X1) [avatar definition]
186. tall(X1) <- (7) [avatar component clause 185]
235. ~funny(X0) [subsumption resolution 121,120]
304. tall(X1) | funny(X1) [subsumption resolution 139,235]
305. tall(X1) [subsumption resolution 304,235]
306. 7 [avatar split clause 305,185]
335. 38 <=> tall(mary) [avatar definition]
337. ~tall(mary) <- (~38) [avatar component clause 335]
373. ~38 [avatar split clause 156,335]
378. $false <- (7, ~38) [resolution 337,186]
379. ~7 | 38 [avatar contradiction clause 378]
380. $false [avatar sat refutation 306,373,379]
% SZS output end Proof for 734459076620271245258800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or calm is not happy.
If someone is both not generous and brave then lucy is old and vice versa.
Everyone who is both not wise and not rich is both curious and quiet and vice versa.
Everyone who is both not tall and quiet is tall or creative and vice versa.
Everyone who is rich or not funny is either not wise or not funny and vice versa.
If someone is either wise or funny then someone is not kind or funny.
If someone is either calm or not humble then lucy is both funny and not calm and vice versa.
Everyone who is either happy or not strong is both wise and not rich and vice versa.
If someone is not funny then fred is either not quiet or kind and vice versa.
Everyone who is not creative is generous or strong and vice versa.
If susan is both not curious and not rich then alice is not old and vice versa.
Everyone who is not generous or not wise is both old and wise and vice versa.
If someone is old then fred is humble.
If someone is either calm or generous then mary is not generous or creative.
Everyone who is either not rich or patient is not generous.
Alice is funny or not funny.
Someone is both calm and curious.
Mary is either not old or humble.
Susan is both rich and not old.
Paul is both not kind and not creative.
Someone is either not calm or wise.
John is not rich or not curious.
John is not patient. | Mary is not calm. | neutral | (![X]:((~calm(X)<~>calm(X))=>~happy(X)))&
((?[X]:((~generous(X)&brave(X))))<=>(old(lucy)))&
(![X]:((~wise(X)&~rich(X))<=>(curious(X)&quiet(X))))&
(![X]:((~tall(X)&quiet(X))<=>(tall(X)|creative(X))))&
(![X]:((rich(X)|~funny(X))<=>(~wise(X)<~>~funny(X))))&
((?[X]:((wise(X)<~>funny(X))))=>(?[X]:((~kind(X)|funny(X)))))&
((?[X]:((calm(X)<~>~humble(X))))<=>((funny(lucy)&~calm(lucy))))&
(![X]:((happy(X)<~>~strong(X))<=>(wise(X)&~rich(X))))&
((?[X]:(~funny(X)))<=>((~quiet(fred)<~>kind(fred))))&
(![X]:(~creative(X)<=>(generous(X)|strong(X))))&
(((~curious(susan)&~rich(susan)))<=>(~old(alice)))&
(![X]:((~generous(X)|~wise(X))<=>(old(X)&wise(X))))&
((?[X]:(old(X)))=>(humble(fred)))&
((?[X]:((calm(X)<~>generous(X))))=>((~generous(mary)|creative(mary))))&
(![X]:((~rich(X)<~>patient(X))=>~generous(X)))&
((funny(alice)|~funny(alice)))&
(?[X]:((calm(X)&curious(X))))&
((~old(mary)<~>humble(mary)))&
((rich(susan)&~old(susan)))&
((~kind(paul)&~creative(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
((~rich(john)|~curious(john)))&
(~patient(john)) | ~calm(mary) | [] | null | 0 |
Everyone who is either happy or not curious is either curious or not creative.
If someone is both rich and funny then fred is both kind and generous and vice versa.
If lucy is kind or not creative then lucy is not rich and vice versa.
Everyone who is both not wise and rich is wise or not strong and vice versa.
Everyone who is not curious is not wise or old.
If susan is not generous then fred is either tall or not patient and vice versa.
Everyone who is funny or not patient is rich or not strong.
If someone is both not generous and not rich then fred is not rich and vice versa.
Everyone who is creative is both old and not brave.
If paul is not patient or not generous then alice is not wise or not humble.
Everyone who is both not brave and brave is both brave and not strong.
If someone is either generous or quiet then alice is calm or tall.
Everyone who is both not curious and not strong is both not happy and not humble and vice versa.
If someone is either not creative or calm then john is both humble and creative.
Everyone who is both not tall and creative is either strong or rich.
If someone is not humble then someone is creative.
Someone is both not strong and old.
Someone is both calm and creative.
Fred is funny or happy.
Someone is not old or old.
Lucy is kind.
Someone is either funny or rich.
Lucy is both not calm and creative.
Someone is not brave. | Lucy is not patient. | contradiction | (![X]:((happy(X)<~>~curious(X))=>(curious(X)<~>~creative(X))))&
((?[X]:((rich(X)&funny(X))))<=>((kind(fred)&generous(fred))))&
(((kind(lucy)|~creative(lucy)))<=>(~rich(lucy)))&
(![X]:((~wise(X)&rich(X))<=>(wise(X)|~strong(X))))&
(![X]:(~curious(X)=>(~wise(X)|old(X))))&
((~generous(susan))<=>((tall(fred)<~>~patient(fred))))&
(![X]:((funny(X)|~patient(X))=>(rich(X)|~strong(X))))&
((?[X]:((~generous(X)&~rich(X))))<=>(~rich(fred)))&
(![X]:(creative(X)=>(old(X)&~brave(X))))&
(((~patient(paul)|~generous(paul)))=>((~wise(alice)|~humble(alice))))&
(![X]:((~brave(X)&brave(X))=>(brave(X)&~strong(X))))&
((?[X]:((generous(X)<~>quiet(X))))=>((calm(alice)|tall(alice))))&
(![X]:((~curious(X)&~strong(X))<=>(~happy(X)&~humble(X))))&
((?[X]:((~creative(X)<~>calm(X))))=>((humble(john)&creative(john))))&
(![X]:((~tall(X)&creative(X))=>(strong(X)<~>rich(X))))&
((?[X]:(~humble(X)))=>(?[X]:(creative(X))))&
(?[X]:((~strong(X)&old(X))))&
(?[X]:((calm(X)&creative(X))))&
((funny(fred)|happy(fred)))&
(?[X]:((~old(X)|old(X))))&
(kind(lucy))&
(?[X]:((funny(X)<~>rich(X))))&
((~calm(lucy)&creative(lucy)))&
(?[X]:(~brave(X))) | ~patient(lucy) | [
"p2",
"p3",
"p6",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6715032492342112239123646
% SZS output start Proof for 6715032492342112239123646
3. (~creative(lucy) | kind(lucy)) <=> ~rich(lucy) [input p2]
4. ! [X0] : ((rich(X0) & ~wise(X0)) <=> (~strong(X0) | wise(X0))) [input p3]
7. ! [X0] : ((~patient(X0) | funny(X0)) => (~strong(X0) | rich(X0))) [input p6]
21. kind(lucy) [input p20]
25. ~patient(lucy) [input hypothesis]
30. ! [X0] : ((~strong(X0) | rich(X0)) | (patient(X0) & ~funny(X0))) [ennf transformation 7]
31. ! [X0] : (~strong(X0) | rich(X0) | (patient(X0) & ~funny(X0))) [flattening 30]
49. ((~creative(lucy) | kind(lucy)) | rich(lucy)) & (~rich(lucy) | (creative(lucy) & ~kind(lucy))) [nnf transformation 3]
50. (~creative(lucy) | kind(lucy) | rich(lucy)) & (~rich(lucy) | (creative(lucy) & ~kind(lucy))) [flattening 49]
51. ! [X0] : (((rich(X0) & ~wise(X0)) | (strong(X0) & ~wise(X0))) & ((~strong(X0) | wise(X0)) | (~rich(X0) | wise(X0)))) [nnf transformation 4]
52. ! [X0] : (((rich(X0) & ~wise(X0)) | (strong(X0) & ~wise(X0))) & (~strong(X0) | wise(X0) | ~rich(X0) | wise(X0))) [flattening 51]
85. ~rich(lucy) | ~kind(lucy) [cnf transformation 50]
92. strong(X0) | rich(X0) [cnf transformation 52]
99. ~strong(X0) | rich(X0) | patient(X0) [cnf transformation 31]
128. kind(lucy) [cnf transformation 21]
134. ~patient(lucy) [cnf transformation 25]
164. 6 <=> rich(lucy) [avatar definition]
165. ~rich(lucy) <- (~6) [avatar component clause 164]
168. 7 <=> kind(lucy) [avatar definition]
177. ~7 | ~6 [avatar split clause 85,164,168]
195. patient(X0) | rich(X0) [subsumption resolution 99,92]
266. 7 [avatar split clause 128,168]
277. rich(lucy) [resolution 195,134]
279. $false <- (~6) [subsumption resolution 277,165]
280. 6 [avatar contradiction clause 279]
283. $false [avatar sat refutation 177,266,280]
% SZS output end Proof for 6715032492342112239123646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not humble then someone is both not rich and not generous and vice versa.
Everyone who is tall or patient is not old.
Everyone who is both not curious and tall is curious or funny.
Everyone who is either not creative or not tall is either not old or creative and vice versa.
Everyone who is calm is both funny and humble.
If someone is not generous or not brave then someone is not old and vice versa.
If paul is generous then someone is happy and vice versa.
Everyone who is not creative or creative is quiet or calm and vice versa.
If john is not patient then fred is either old or creative.
Everyone who is both generous and not curious is not old and vice versa.
If someone is both not calm and not rich then someone is kind and vice versa.
Everyone who is old is not rich and vice versa.
If john is both not kind and kind then lucy is not funny or not quiet and vice versa.
If someone is both not kind and not creative then someone is either not tall or not rich and vice versa.
Everyone who is both not patient and creative is not funny.
Everyone who is generous or not humble is not curious.
Susan is both calm and happy.
Someone is both brave and tall.
Someone is quiet.
Fred is not happy.
John is either tall or not generous.
Someone is not funny or not quiet.
Fred is generous or not rich.
Someone is both not strong and not brave. | Fred is not generous. | contradiction | ((~humble(susan))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((tall(X)|patient(X))=>~old(X)))&
(![X]:((~curious(X)&tall(X))=>(curious(X)|funny(X))))&
(![X]:((~creative(X)<~>~tall(X))<=>(~old(X)<~>creative(X))))&
(![X]:(calm(X)=>(funny(X)&humble(X))))&
((?[X]:((~generous(X)|~brave(X))))<=>(?[X]:(~old(X))))&
((generous(paul))<=>(?[X]:(happy(X))))&
(![X]:((~creative(X)|creative(X))<=>(quiet(X)|calm(X))))&
((~patient(john))=>((old(fred)<~>creative(fred))))&
(![X]:((generous(X)&~curious(X))<=>~old(X)))&
((?[X]:((~calm(X)&~rich(X))))<=>(?[X]:(kind(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~kind(john)&kind(john)))<=>((~funny(lucy)|~quiet(lucy))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(![X]:((~patient(X)&creative(X))=>~funny(X)))&
(![X]:((generous(X)|~humble(X))=>~curious(X)))&
((calm(susan)&happy(susan)))&
(?[X]:((brave(X)&tall(X))))&
(?[X]:(quiet(X)))&
(~happy(fred))&
((tall(john)<~>~generous(john)))&
(?[X]:((~funny(X)|~quiet(X))))&
((generous(fred)|~rich(fred)))&
(?[X]:((~strong(X)&~brave(X)))) | ~generous(fred) | [
"p0",
"p4",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 274716428347174203740326
% SZS output start Proof for 274716428347174203740326
1. ~humble(susan) <=> ? [X0] : (~generous(X0) & ~rich(X0)) [input p0]
5. ! [X0] : (calm(X0) => (humble(X0) & funny(X0))) [input p4]
10. ! [X0] : ((~curious(X0) & generous(X0)) <=> ~old(X0)) [input p9]
12. ! [X0] : (old(X0) <=> ~rich(X0)) [input p11]
17. happy(susan) & calm(susan) [input p16]
25. ~generous(fred) [input hypothesis]
33. ! [X0] : ((humble(X0) & funny(X0)) | ~calm(X0)) [ennf transformation 5]
38. (~humble(susan) | ! [X0] : (generous(X0) | rich(X0))) & (? [X0] : (~generous(X0) & ~rich(X0)) | humble(susan)) [nnf transformation 1]
39. (~humble(susan) | ! [X0] : (generous(X0) | rich(X0))) & (? [X1] : (~generous(X1) & ~rich(X1)) | humble(susan)) [rectify 38]
40. ? [X1] : (~generous(X1) & ~rich(X1)) => (~generous(sK0) & ~rich(sK0)) [choice axiom]
41. (~humble(susan) | ! [X0] : (generous(X0) | rich(X0))) & ((~generous(sK0) & ~rich(sK0)) | humble(susan)) [skolemisation 39,40]
55. ! [X0] : (((~curious(X0) & generous(X0)) | old(X0)) & (~old(X0) | (curious(X0) | ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : (((~curious(X0) & generous(X0)) | old(X0)) & (~old(X0) | curious(X0) | ~generous(X0))) [flattening 55]
62. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 12]
81. ~humble(susan) | generous(X0) | rich(X0) [cnf transformation 41]
94. ~calm(X0) | humble(X0) [cnf transformation 33]
107. old(X0) | generous(X0) [cnf transformation 56]
112. ~old(X0) | ~rich(X0) [cnf transformation 62]
128. calm(susan) [cnf transformation 17]
139. ~generous(fred) [cnf transformation 25]
146. 1 <=> ! [X0] : (generous(X0) | rich(X0)) [avatar definition]
147. generous(X0) | rich(X0) <- (1) [avatar component clause 146]
149. 2 <=> humble(susan) [avatar definition]
152. 1 | ~2 [avatar split clause 81,149,146]
185. 10 <=> ! [X3] : generous(X3) [avatar definition]
186. generous(X3) <- (10) [avatar component clause 185]
304. 36 <=> generous(fred) [avatar definition]
305. ~generous(fred) <- (~36) [avatar component clause 304]
312. ~36 [avatar split clause 139,304]
314. humble(susan) [resolution 94,128]
317. 2 [avatar split clause 314,149]
321. ~rich(X0) | generous(X0) [resolution 112,107]
322. generous(X0) <- (1) [subsumption resolution 321,147]
323. 10 | ~1 [avatar split clause 322,146,185]
325. $false <- (10, ~36) [resolution 186,305]
330. ~10 | 36 [avatar contradiction clause 325]
332. $false [avatar sat refutation 152,312,317,323,330]
% SZS output end Proof for 274716428347174203740326
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then mary is not rich and vice versa.
If someone is both not patient and not humble then someone is both quiet and kind.
If someone is both not creative and not patient then someone is both not calm and not strong.
If fred is either happy or not old then someone is old.
Everyone who is both not wise and not creative is not strong or patient.
Everyone who is wise is happy and vice versa.
Everyone who is both not quiet and old is curious or creative and vice versa.
Everyone who is not generous is not rich and vice versa.
If someone is either not humble or generous then john is both not curious and not patient and vice versa.
If fred is both old and not funny then john is either humble or not calm and vice versa.
Everyone who is both not generous and calm is rich and vice versa.
If someone is both not wise and not strong then fred is both not creative and funny and vice versa.
If someone is tall or not patient then susan is not patient or not old and vice versa.
If fred is patient then someone is both happy and tall and vice versa.
If someone is either wise or generous then paul is not creative and vice versa.
If lucy is calm then lucy is both calm and not rich.
Someone is not creative.
Someone is rich or not strong.
Someone is both not strong and not tall.
Fred is either not brave or rich.
Someone is not creative or not brave.
Alice is both not wise and tall.
Fred is either not quiet or not curious.
Someone is not tall or old. | John is not calm. | entailment | ((?[X]:(~patient(X)))<=>(~rich(mary)))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((quiet(X)&kind(X)))))&
((?[X]:((~creative(X)&~patient(X))))=>(?[X]:((~calm(X)&~strong(X)))))&
(((happy(fred)<~>~old(fred)))=>(?[X]:(old(X))))&
(![X]:((~wise(X)&~creative(X))=>(~strong(X)|patient(X))))&
(![X]:(wise(X)<=>happy(X)))&
(![X]:((~quiet(X)&old(X))<=>(curious(X)|creative(X))))&
(![X]:(~generous(X)<=>~rich(X)))&
((?[X]:((~humble(X)<~>generous(X))))<=>((~curious(john)&~patient(john))))&
(((old(fred)&~funny(fred)))<=>((humble(john)<~>~calm(john))))&
(![X]:((~generous(X)&calm(X))<=>rich(X)))&
((?[X]:((~wise(X)&~strong(X))))<=>((~creative(fred)&funny(fred))))&
((?[X]:((tall(X)|~patient(X))))<=>((~patient(susan)|~old(susan))))&
((patient(fred))<=>(?[X]:((happy(X)&tall(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(~creative(paul)))&
((calm(lucy))=>((calm(lucy)&~rich(lucy))))&
(?[X]:(~creative(X)))&
(?[X]:((rich(X)|~strong(X))))&
(?[X]:((~strong(X)&~tall(X))))&
((~brave(fred)<~>rich(fred)))&
(?[X]:((~creative(X)|~brave(X))))&
((~wise(alice)&tall(alice)))&
((~quiet(fred)<~>~curious(fred)))&
(?[X]:((~tall(X)|old(X)))) | ~calm(john) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1233991065421338810662795
% SZS output start Proof for 1233991065421338810662795
8. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p7]
11. ! [X0] : ((calm(X0) & ~generous(X0)) <=> rich(X0)) [input p10]
25. calm(john) [input hypothesis]
51. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 8]
59. ! [X0] : (((calm(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | (~calm(X0) | generous(X0)))) [nnf transformation 11]
60. ! [X0] : (((calm(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | ~calm(X0) | generous(X0))) [flattening 59]
106. ~rich(X0) | generous(X0) [cnf transformation 51]
107. ~generous(X0) | rich(X0) [cnf transformation 51]
120. rich(X0) | ~calm(X0) | generous(X0) [cnf transformation 60]
121. ~generous(X0) | ~rich(X0) [cnf transformation 60]
152. calm(john) [cnf transformation 25]
230. 18 <=> calm(john) [avatar definition]
232. calm(john) <- (18) [avatar component clause 230]
247. ~rich(X0) [subsumption resolution 121,106]
248. ~calm(X0) | generous(X0) [subsumption resolution 120,247]
360. 18 [avatar split clause 152,230]
367. generous(john) <- (18) [resolution 248,232]
369. rich(john) <- (18) [resolution 367,107]
370. $false <- (18) [subsumption resolution 369,247]
371. ~18 [avatar contradiction clause 370]
372. $false [avatar sat refutation 360,371]
% SZS output end Proof for 1233991065421338810662795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is kind or not creative. Everyone who is either not patient or not creative is either happy or not quiet. If lucy is either not creative or quiet then someone is both strong and not quiet. Everyone who is not patient or not creative is both not brave and not wise and vice versa. Everyone who is both funny and wise is both strong and not rich. If john is not happy then someone is wise or not quiet. Everyone who is not strong is not old. If paul is both generous and humble then someone is funny or not old. If fred is both not creative and not curious then alice is both not humble and not calm. Everyone who is curious is patient and vice versa. If paul is both not kind and not tall then paul is both not funny and tall and vice versa. If someone is both not patient and not wise then paul is either brave or happy and vice versa. Everyone who is both not happy and creative is calm or happy and vice versa. Everyone who is both quiet and not patient is not curious or patient. Everyone who is either not tall or brave is both not patient and humble and vice versa. If someone is patient or brave then someone is both not quiet and brave. Someone is both not creative and tall. Someone is creative or not strong. Someone is either quiet or calm. Alice is curious. Someone is humble or not tall. Susan is either humble or not old. Fred is both not wise and brave. | Lucy is not calm. | neutral | (![X]:(~kind(X)=>(kind(X)|~creative(X))))&
(![X]:((~patient(X)<~>~creative(X))=>(happy(X)<~>~quiet(X))))&
(((~creative(lucy)<~>quiet(lucy)))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~brave(X)&~wise(X))))&
(![X]:((funny(X)&wise(X))=>(strong(X)&~rich(X))))&
((~happy(john))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:(~strong(X)=>~old(X)))&
(((generous(paul)&humble(paul)))=>(?[X]:((funny(X)|~old(X)))))&
(((~creative(fred)&~curious(fred)))=>((~humble(alice)&~calm(alice))))&
(![X]:(curious(X)<=>patient(X)))&
(((~kind(paul)&~tall(paul)))<=>((~funny(paul)&tall(paul))))&
((?[X]:((~patient(X)&~wise(X))))<=>((brave(paul)<~>happy(paul))))&
(![X]:((~happy(X)&creative(X))<=>(calm(X)|happy(X))))&
(![X]:((quiet(X)&~patient(X))=>(~curious(X)|patient(X))))&
(![X]:((~tall(X)<~>brave(X))<=>(~patient(X)&humble(X))))&
((?[X]:((patient(X)|brave(X))))=>(?[X]:((~quiet(X)&brave(X)))))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((quiet(X)<~>calm(X))))&
(curious(alice))&
(?[X]:((humble(X)|~tall(X))))&
((humble(susan)<~>~old(susan)))&
((~wise(fred)&brave(fred))) | ~calm(lucy) | [] | null | 0 |
If someone is either not strong or brave then someone is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Everyone who is funny is either not brave or wise and vice versa.
Everyone who is both patient and strong is strong and vice versa.
Lucy is not patient or not tall.
Fred is either humble or strong.
Susan is wise or quiet.
Lucy is either curious or not rich.
Fred is both not happy and not rich. | Lucy is quiet. | entailment | ((?[X]:((~strong(X)<~>brave(X))))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((~patient(lucy)|~tall(lucy)))&
((humble(fred)<~>strong(fred)))&
((wise(susan)|quiet(susan)))&
((curious(lucy)<~>~rich(lucy)))&
((~happy(fred)&~rich(fred))) | quiet(lucy) | [
"p1",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4192414132314952960882380
% SZS output start Proof for 4192414132314952960882380
2. ! [X0] : ((strong(X0) & ~funny(X0)) <=> (quiet(X0) | wise(X0))) [input p1]
4. ! [X0] : (~curious(X0) <=> patient(X0)) [input p3]
6. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p6]
9. ? [X0] : (funny(X0) | ~generous(X0)) <=> ? [X0] : funny(X0) [input p8]
11. ! [X0] : ((tall(X0) & curious(X0)) => (creative(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) <~> generous(X0)) <=> (creative(X0) | rich(X0))) [input p11]
14. ! [X0] : ((~brave(X0) <~> ~wise(X0)) => (~funny(X0) <~> curious(X0))) [input p13]
15. ! [X0] : (funny(X0) <=> (~brave(X0) <~> wise(X0))) [input p14]
16. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p15]
22. ~quiet(lucy) [input hypothesis]
24. ? [X0] : (funny(X0) | ~generous(X0)) <=> ? [X1] : funny(X1) [rectify 9]
27. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 6]
28. ! [X0] : ((creative(X0) & ~patient(X0)) | (~tall(X0) | ~curious(X0))) [ennf transformation 11]
29. ! [X0] : ((creative(X0) & ~patient(X0)) | ~tall(X0) | ~curious(X0)) [flattening 28]
31. ! [X0] : ((~funny(X0) <~> curious(X0)) | (~brave(X0) <=> ~wise(X0))) [ennf transformation 14]
36. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~strong(X0) | funny(X0)))) [nnf transformation 2]
37. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~strong(X0) | funny(X0))) [flattening 36]
40. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 4]
42. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 42]
46. (? [X0] : (funny(X0) | ~generous(X0)) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : (~funny(X0) & generous(X0))) [nnf transformation 24]
47. (? [X0] : (funny(X0) | ~generous(X0)) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : (~funny(X3) & generous(X3))) [rectify 46]
48. ? [X0] : (funny(X0) | ~generous(X0)) => (funny(sK2) | ~generous(sK2)) [choice axiom]
49. ? [X2] : funny(X2) => funny(sK3) [choice axiom]
50. ((funny(sK2) | ~generous(sK2)) | ! [X1] : ~funny(X1)) & (funny(sK3) | ! [X3] : (~funny(X3) & generous(X3))) [skolemisation 47,49,48]
53. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | ((~quiet(X0) | ~generous(X0)) & (generous(X0) | quiet(X0))))) [flattening 53]
56. ! [X0] : (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) [nnf transformation 31]
57. ! [X0] : ((funny(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 15]
58. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 16]
59. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 58]
67. ~funny(X0) | ~wise(X0) [cnf transformation 37]
74. ~patient(X0) | ~curious(X0) [cnf transformation 40]
77. funny(X0) | strong(X0) [cnf transformation 27]
79. ~tall(X0) | strong(X0) [cnf transformation 27]
81. creative(X0) | tall(X0) [cnf transformation 43]
82. tall(X0) | brave(X0) [cnf transformation 43]
83. creative(X0) | curious(X0) [cnf transformation 43]
84. curious(X0) | brave(X0) [cnf transformation 43]
92. funny(sK3) | generous(X3) [cnf transformation 50]
102. creative(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 29]
108. ~generous(X0) | quiet(X0) | ~creative(X0) [cnf transformation 54]
114. curious(X0) | ~funny(X0) | ~brave(X0) | wise(X0) [cnf transformation 56]
115. ~curious(X0) | funny(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
117. wise(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 57]
122. ~strong(X0) | patient(X0) [cnf transformation 59]
132. ~quiet(lucy) [cnf transformation 22]
142. 3 <=> ! [X1] : (brave(X1) | strong(X1)) [avatar definition]
143. brave(X1) | strong(X1) <- (3) [avatar component clause 142]
182. 12 <=> funny(sK3) [avatar definition]
184. funny(sK3) <- (12) [avatar component clause 182]
187. 13 <=> ! [X3] : generous(X3) [avatar definition]
188. generous(X3) <- (13) [avatar component clause 187]
189. 13 | 12 [avatar split clause 92,182,187]
192. creative(X0) | ~tall(X0) [subsumption resolution 102,83]
193. creative(X0) [subsumption resolution 192,81]
194. ~generous(X0) | quiet(X0) [subsumption resolution 108,193]
196. funny(X0) | ~wise(X0) | brave(X0) [subsumption resolution 115,84]
197. ~wise(X0) | brave(X0) [subsumption resolution 196,67]
198. curious(X0) | ~funny(X0) | ~brave(X0) [subsumption resolution 114,67]
199. ~funny(X0) | curious(X0) [subsumption resolution 198,84]
200. funny(X0) | ~wise(X0) [subsumption resolution 120,197]
201. ~wise(X0) [subsumption resolution 200,67]
203. ~funny(X0) | ~brave(X0) [subsumption resolution 117,201]
244. brave(X0) | strong(X0) [resolution 82,79]
245. 3 [avatar split clause 244,142]
265. curious(sK3) <- (12) [resolution 199,184]
272. ~brave(X1) | strong(X1) [resolution 203,77]
273. strong(X1) <- (3) [subsumption resolution 272,143]
281. patient(X0) <- (3) [resolution 273,122]
283. ~curious(X0) <- (3) [resolution 281,74]
289. $false <- (3, 12) [resolution 283,265]
290. ~3 | ~12 [avatar contradiction clause 289]
296. quiet(X0) <- (13) [resolution 188,194]
298. $false <- (13) [resolution 296,132]
302. ~13 [avatar contradiction clause 298]
303. $false [avatar sat refutation 189,245,290,302]
% SZS output end Proof for 4192414132314952960882380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then someone is both old and strong.
If lucy is either tall or wise then alice is either not kind or not creative and vice versa.
If someone is both not kind and strong then lucy is humble.
If someone is either not tall or not calm then someone is brave.
Everyone who is calm is curious or brave and vice versa.
Everyone who is tall is rich.
If paul is either kind or not creative then john is not tall and vice versa.
Everyone who is not tall or humble is old or strong.
Everyone who is both kind and calm is both not old and tall.
Everyone who is creative is both not rich and strong and vice versa.
Everyone who is not tall or kind is both happy and not old.
If fred is curious or tall then someone is either not creative or humble and vice versa.
If susan is both not old and not curious then alice is kind or not humble and vice versa.
If lucy is either rich or not strong then someone is both not wise and not brave.
Everyone who is either quiet or humble is creative or tall.
Someone is both humble and generous.
Someone is both generous and not kind.
Someone is either kind or not calm.
Someone is either old or patient.
John is not wise.
John is either not kind or not creative.
Susan is not tall or curious.
Susan is creative. | John is not happy. | contradiction | ((~old(alice))=>(?[X]:((old(X)&strong(X)))))&
(((tall(lucy)<~>wise(lucy)))<=>((~kind(alice)<~>~creative(alice))))&
((?[X]:((~kind(X)&strong(X))))=>(humble(lucy)))&
((?[X]:((~tall(X)<~>~calm(X))))=>(?[X]:(brave(X))))&
(![X]:(calm(X)<=>(curious(X)|brave(X))))&
(![X]:(tall(X)=>rich(X)))&
(((kind(paul)<~>~creative(paul)))<=>(~tall(john)))&
(![X]:((~tall(X)|humble(X))=>(old(X)|strong(X))))&
(![X]:((kind(X)&calm(X))=>(~old(X)&tall(X))))&
(![X]:(creative(X)<=>(~rich(X)&strong(X))))&
(![X]:((~tall(X)|kind(X))=>(happy(X)&~old(X))))&
(((curious(fred)|tall(fred)))<=>(?[X]:((~creative(X)<~>humble(X)))))&
(((~old(susan)&~curious(susan)))<=>((kind(alice)|~humble(alice))))&
(((rich(lucy)<~>~strong(lucy)))=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((quiet(X)<~>humble(X))=>(creative(X)|tall(X))))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:((generous(X)&~kind(X))))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:((old(X)<~>patient(X))))&
(~wise(john))&
((~kind(john)<~>~creative(john)))&
((~tall(susan)|curious(susan)))&
(creative(susan)) | ~happy(john) | [
"p5",
"p9",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6769310228182119212943304
% SZS output start Proof for 6769310228182119212943304
6. ! [X0] : (tall(X0) => rich(X0)) [input p5]
10. ! [X0] : (creative(X0) <=> (strong(X0) & ~rich(X0))) [input p9]
11. ! [X0] : ((kind(X0) | ~tall(X0)) => (~old(X0) & happy(X0))) [input p10]
21. ~kind(john) <~> ~creative(john) [input p20]
24. ~happy(john) [input hypothesis]
31. ! [X0] : (rich(X0) | ~tall(X0)) [ennf transformation 6]
36. ! [X0] : ((~old(X0) & happy(X0)) | (~kind(X0) & tall(X0))) [ennf transformation 11]
50. ! [X0] : ((creative(X0) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | ~creative(X0))) [nnf transformation 10]
51. ! [X0] : ((creative(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | ~creative(X0))) [flattening 50]
73. (creative(john) | kind(john)) & (~creative(john) | ~kind(john)) [nnf transformation 21]
90. ~tall(X0) | rich(X0) [cnf transformation 31]
99. ~rich(X0) | ~creative(X0) [cnf transformation 51]
102. happy(X0) | tall(X0) [cnf transformation 36]
103. ~kind(X0) | happy(X0) [cnf transformation 36]
131. creative(john) | kind(john) [cnf transformation 73]
134. ~happy(john) [cnf transformation 24]
194. 13 <=> tall(john) [avatar definition]
196. tall(john) <- (13) [avatar component clause 194]
295. 33 <=> kind(john) [avatar definition]
297. kind(john) <- (33) [avatar component clause 295]
299. 34 <=> creative(john) [avatar definition]
301. creative(john) <- (34) [avatar component clause 299]
302. 33 | 34 [avatar split clause 131,299,295]
312. tall(john) [resolution 102,134]
315. 13 [avatar split clause 312,194]
316. rich(john) <- (13) [resolution 196,90]
317. happy(john) <- (33) [resolution 103,297]
319. $false <- (33) [subsumption resolution 317,134]
320. ~33 [avatar contradiction clause 319]
322. ~creative(john) <- (13) [resolution 316,99]
323. $false <- (13, 34) [subsumption resolution 322,301]
324. ~13 | ~34 [avatar contradiction clause 323]
325. $false [avatar sat refutation 302,315,320,324]
% SZS output end Proof for 6769310228182119212943304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either not calm or kind and vice versa.
Everyone who is either not generous or wise is both creative and quiet.
If someone is kind then paul is either generous or not old and vice versa.
Everyone who is either not wise or curious is calm.
If lucy is patient or strong then someone is not calm or not creative.
Everyone who is both not tall and calm is either not brave or creative.
If someone is either not patient or not quiet then someone is both humble and creative.
Everyone who is happy is either not kind or not creative.
Everyone who is not wise is either tall or not generous and vice versa.
If paul is both curious and creative then someone is both not rich and curious.
If someone is both not curious and not quiet then mary is either not old or patient and vice versa.
Everyone who is both not happy and not old is either not funny or not creative.
If someone is happy or not calm then someone is either curious or wise.
Everyone who is not humble is not curious or not patient and vice versa.
Everyone who is both funny and tall is quiet or not curious and vice versa.
Everyone who is either not old or not rich is both not creative and not curious and vice versa.
Paul is not funny or kind.
Paul is both calm and old.
Someone is wise.
Fred is both old and kind.
Fred is both calm and not wise.
Someone is either rich or kind.
Lucy is either brave or not calm. | Fred is patient. | contradiction | (![X]:(~patient(X)<=>(~calm(X)<~>kind(X))))&
(![X]:((~generous(X)<~>wise(X))=>(creative(X)&quiet(X))))&
((?[X]:(kind(X)))<=>((generous(paul)<~>~old(paul))))&
(![X]:((~wise(X)<~>curious(X))=>calm(X)))&
(((patient(lucy)|strong(lucy)))=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((~tall(X)&calm(X))=>(~brave(X)<~>creative(X))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((humble(X)&creative(X)))))&
(![X]:(happy(X)=>(~kind(X)<~>~creative(X))))&
(![X]:(~wise(X)<=>(tall(X)<~>~generous(X))))&
(((curious(paul)&creative(paul)))=>(?[X]:((~rich(X)&curious(X)))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((~old(mary)<~>patient(mary))))&
(![X]:((~happy(X)&~old(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((happy(X)|~calm(X))))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:(~humble(X)<=>(~curious(X)|~patient(X))))&
(![X]:((funny(X)&tall(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)&~curious(X))))&
((~funny(paul)|kind(paul)))&
((calm(paul)&old(paul)))&
(?[X]:(wise(X)))&
((old(fred)&kind(fred)))&
((calm(fred)&~wise(fred)))&
(?[X]:((rich(X)<~>kind(X))))&
((brave(lucy)<~>~calm(lucy))) | patient(fred) | [
"p0",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4309491946890906259721150
% SZS output start Proof for 4309491946890906259721150
1. ! [X0] : (~patient(X0) <=> (~calm(X0) <~> kind(X0))) [input p0]
20. kind(fred) & old(fred) [input p19]
21. ~wise(fred) & calm(fred) [input p20]
24. patient(fred) [input hypothesis]
42. ! [X0] : ((~patient(X0) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0)))) & (((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | patient(X0))) [nnf transformation 1]
82. ~kind(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 42]
138. kind(fred) [cnf transformation 20]
139. calm(fred) [cnf transformation 21]
145. patient(fred) [cnf transformation 24]
319. ~calm(fred) | ~patient(fred) [resolution 82,138]
322. ~patient(fred) [subsumption resolution 319,139]
323. $false [subsumption resolution 322,145]
% SZS output end Proof for 4309491946890906259721150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or kind is either patient or not kind and vice versa. If someone is either rich or happy then someone is either brave or not patient and vice versa. If someone is not happy then someone is both generous and not brave and vice versa. If someone is either brave or curious then someone is not tall. If mary is not brave or wise then paul is both kind and not wise. If lucy is funny or humble then someone is either strong or not brave and vice versa. Everyone who is both generous and not calm is both quiet and old. Everyone who is calm is both not calm and not funny. Everyone who is either brave or not funny is either not creative or not wise. Everyone who is curious or patient is both calm and not wise and vice versa. Everyone who is either not calm or not generous is not happy or not old. If lucy is funny or not tall then mary is old and vice versa. If someone is both humble and rich then paul is both kind and not brave and vice versa. Everyone who is humble is not creative. Everyone who is tall is either strong or patient. Fred is both not generous and old. Susan is not strong. Lucy is not creative. Lucy is either old or not funny. | Susan is humble. | neutral | (![X]:((~rich(X)|kind(X))<=>(patient(X)<~>~kind(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
(![X]:(tall(X)=>(strong(X)<~>patient(X))))&
((~generous(fred)&old(fred)))&
(~strong(susan))&
(~creative(lucy))&
((old(lucy)<~>~funny(lucy))) | humble(susan) | [] | null | 0 |
If someone is generous then paul is not generous or not kind and vice versa. Everyone who is wise is both not kind and kind and vice versa. If fred is calm then john is wise or generous. Everyone who is either not generous or patient is both not creative and not patient. Everyone who is brave is both not wise and not old and vice versa. If someone is both funny and not patient then mary is curious or not quiet and vice versa. If someone is not brave then alice is both not tall and not kind and vice versa. If john is both tall and generous then paul is curious or not tall. Everyone who is either not kind or not old is not strong or not quiet. If someone is quiet or not quiet then lucy is patient. Everyone who is not funny or not kind is calm or not funny. If someone is not patient then someone is not quiet. If lucy is tall or not happy then someone is not rich. Everyone who is old is not old. If john is patient or not humble then mary is both not quiet and not wise and vice versa. Everyone who is kind or old is not calm. Someone is either old or quiet. Someone is happy. Someone is not creative or old. Someone is either not tall or generous. John is both not humble and not generous. | Mary is not brave. | contradiction | ((?[X]:(generous(X)))<=>((~generous(paul)|~kind(paul))))&
(![X]:(wise(X)<=>(~kind(X)&kind(X))))&
((calm(fred))=>((wise(john)|generous(john))))&
(![X]:((~generous(X)<~>patient(X))=>(~creative(X)&~patient(X))))&
(![X]:(brave(X)<=>(~wise(X)&~old(X))))&
((?[X]:((funny(X)&~patient(X))))<=>((curious(mary)|~quiet(mary))))&
((?[X]:(~brave(X)))<=>((~tall(alice)&~kind(alice))))&
(((tall(john)&generous(john)))=>((curious(paul)|~tall(paul))))&
(![X]:((~kind(X)<~>~old(X))=>(~strong(X)|~quiet(X))))&
((?[X]:((quiet(X)|~quiet(X))))=>(patient(lucy)))&
(![X]:((~funny(X)|~kind(X))=>(calm(X)|~funny(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~quiet(X))))&
(((tall(lucy)|~happy(lucy)))=>(?[X]:(~rich(X))))&
(![X]:(old(X)=>~old(X)))&
(((patient(john)|~humble(john)))<=>((~quiet(mary)&~wise(mary))))&
(![X]:((kind(X)|old(X))=>~calm(X)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
((~humble(john)&~generous(john))) | ~brave(mary) | [
"p1",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8409566138652791027300742
% SZS output start Proof for 8409566138652791027300742
2. ! [X0] : (wise(X0) <=> (kind(X0) & ~kind(X0))) [input p1]
5. ! [X0] : (brave(X0) <=> (~old(X0) & ~wise(X0))) [input p4]
14. ! [X0] : (old(X0) => ~old(X0)) [input p13]
22. ~brave(mary) [input hypothesis]
38. ! [X0] : (~old(X0) | ~old(X0)) [ennf transformation 14]
45. ! [X0] : ((wise(X0) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | ~wise(X0))) [nnf transformation 2]
46. ! [X0] : ((wise(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | ~wise(X0))) [flattening 45]
48. ! [X0] : ((brave(X0) | (old(X0) | wise(X0))) & ((~old(X0) & ~wise(X0)) | ~brave(X0))) [nnf transformation 5]
49. ! [X0] : ((brave(X0) | old(X0) | wise(X0)) & ((~old(X0) & ~wise(X0)) | ~brave(X0))) [flattening 48]
74. ~kind(X0) | ~wise(X0) [cnf transformation 46]
75. ~wise(X0) | kind(X0) [cnf transformation 46]
82. brave(X0) | old(X0) | wise(X0) [cnf transformation 49]
97. ~old(X0) | ~old(X0) [cnf transformation 38]
111. ~brave(mary) [cnf transformation 22]
112. ~old(X0) [duplicate literal removal 97]
132. ~wise(X0) [subsumption resolution 74,75]
143. old(X0) | brave(X0) [subsumption resolution 82,132]
182. 15 <=> ! [X1] : brave(X1) [avatar definition]
183. brave(X1) <- (15) [avatar component clause 182]
246. brave(X1) [resolution 143,112]
247. 15 [avatar split clause 246,182]
248. $false <- (15) [resolution 183,111]
251. ~15 [avatar contradiction clause 248]
252. $false [avatar sat refutation 247,251]
% SZS output end Proof for 8409566138652791027300742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not funny then someone is strong or not brave.
Everyone who is not brave is both not kind and not calm.
If john is both humble and not kind then alice is creative.
If lucy is curious then lucy is either not generous or not patient and vice versa.
Everyone who is not brave is quiet or not old.
If someone is both not calm and not wise then someone is either happy or brave.
Everyone who is both not creative and not kind is both not curious and not kind.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
If paul is not happy or brave then alice is either creative or brave.
If paul is strong or not strong then john is old and vice versa.
Alice is strong or wise.
Someone is wise.
Someone is either creative or not humble.
Someone is either happy or not creative.
Someone is quiet or not patient.
Fred is not patient or rich. | Paul is not calm. | entailment | ((?[X]:((~calm(X)<~>~funny(X))))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:(~brave(X)=>(~kind(X)&~calm(X))))&
(((humble(john)&~kind(john)))=>(creative(alice)))&
((curious(lucy))<=>((~generous(lucy)<~>~patient(lucy))))&
(![X]:(~brave(X)=>(quiet(X)|~old(X))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~creative(X)&~kind(X))=>(~curious(X)&~kind(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
(((~happy(paul)|brave(paul)))=>((creative(alice)<~>brave(alice))))&
(((strong(paul)|~strong(paul)))<=>(old(john)))&
((strong(alice)|wise(alice)))&
(?[X]:(wise(X)))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((quiet(X)|~patient(X))))&
((~patient(fred)|rich(fred))) | ~calm(paul) | [
"p1",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 575869810939870526436086
% SZS output start Proof for 575869810939870526436086
2. ! [X0] : (~brave(X0) => (~calm(X0) & ~kind(X0))) [input p1]
9. ! [X0] : ((~creative(X0) <~> ~brave(X0)) <=> (~strong(X0) <~> strong(X0))) [input p8]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (~tall(X0) & creative(X0))) [input p9]
23. calm(paul) [input hypothesis]
30. ! [X0] : ((~calm(X0) & ~kind(X0)) | brave(X0)) [ennf transformation 2]
53. ! [X0] : ((((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))))) [nnf transformation 9]
54. ! [X0] : (((calm(X0) | patient(X0)) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
55. ! [X0] : ((calm(X0) | patient(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | (~calm(X0) & ~patient(X0)))) [flattening 54]
76. ~calm(X0) | brave(X0) [cnf transformation 30]
94. ~brave(X0) | ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 53]
95. ~brave(X0) | ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
99. ~calm(X0) | creative(X0) [cnf transformation 55]
123. calm(paul) [cnf transformation 23]
124. ~brave(X0) | ~creative(X0) | strong(X0) [duplicate literal removal 94]
125. ~brave(X0) | ~creative(X0) | ~strong(X0) [duplicate literal removal 95]
187. ~creative(X0) | ~brave(X0) [subsumption resolution 124,125]
263. brave(paul) [resolution 76,123]
266. creative(paul) [resolution 99,123]
277. ~brave(paul) [resolution 187,266]
280. $false [subsumption resolution 277,263]
% SZS output end Proof for 575869810939870526436086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise is creative.
Everyone who is not kind or patient is not quiet or brave.
Everyone who is either not patient or not wise is both brave and quiet.
Everyone who is not quiet is old.
If lucy is either not wise or quiet then alice is rich and vice versa.
If john is either not tall or funny then someone is not strong or strong.
If someone is both brave and humble then alice is both calm and strong and vice versa.
Everyone who is both not wise and not old is both strong and generous and vice versa.
If someone is wise then someone is either calm or old.
Everyone who is either kind or funny is both not funny and not patient.
Everyone who is either strong or patient is either not generous or old.
If someone is not old or not quiet then paul is either not creative or not generous and vice versa.
If alice is either strong or old then fred is both not rich and rich.
Everyone who is patient is both quiet and not generous.
If someone is both funny and tall then someone is not old and vice versa.
Everyone who is old is both quiet and happy and vice versa.
Alice is both curious and rich.
Someone is either not wise or not happy.
Someone is both generous and wise.
Someone is both not generous and not calm.
Fred is both funny and not brave.
Someone is either not kind or wise.
Mary is either not humble or not brave. | Fred is wise. | contradiction | (![X]:((creative(X)<~>~wise(X))=>creative(X)))&
(![X]:((~kind(X)|patient(X))=>(~quiet(X)|brave(X))))&
(![X]:((~patient(X)<~>~wise(X))=>(brave(X)&quiet(X))))&
(![X]:(~quiet(X)=>old(X)))&
(((~wise(lucy)<~>quiet(lucy)))<=>(rich(alice)))&
(((~tall(john)<~>funny(john)))=>(?[X]:((~strong(X)|strong(X)))))&
((?[X]:((brave(X)&humble(X))))<=>((calm(alice)&strong(alice))))&
(![X]:((~wise(X)&~old(X))<=>(strong(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((calm(X)<~>old(X)))))&
(![X]:((kind(X)<~>funny(X))=>(~funny(X)&~patient(X))))&
(![X]:((strong(X)<~>patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~creative(paul)<~>~generous(paul))))&
(((strong(alice)<~>old(alice)))=>((~rich(fred)&rich(fred))))&
(![X]:(patient(X)=>(quiet(X)&~generous(X))))&
((?[X]:((funny(X)&tall(X))))<=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>(quiet(X)&happy(X))))&
((curious(alice)&rich(alice)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:((generous(X)&wise(X))))&
(?[X]:((~generous(X)&~calm(X))))&
((funny(fred)&~brave(fred)))&
(?[X]:((~kind(X)<~>wise(X))))&
((~humble(mary)<~>~brave(mary))) | wise(fred) | [
"p1",
"p2",
"p3",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5251875266473799121405857
% SZS output start Proof for 5251875266473799121405857
2. ! [X0] : ((patient(X0) | ~kind(X0)) => (brave(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((~patient(X0) <~> ~wise(X0)) => (quiet(X0) & brave(X0))) [input p2]
4. ! [X0] : (~quiet(X0) => old(X0)) [input p3]
16. ! [X0] : (old(X0) <=> (happy(X0) & quiet(X0))) [input p15]
21. ~brave(fred) & funny(fred) [input p20]
24. wise(fred) [input hypothesis]
29. ! [X0] : ((brave(X0) | ~quiet(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 2]
30. ! [X0] : (brave(X0) | ~quiet(X0) | (~patient(X0) & kind(X0))) [flattening 29]
31. ! [X0] : ((quiet(X0) & brave(X0)) | (~patient(X0) <=> ~wise(X0))) [ennf transformation 3]
32. ! [X0] : (old(X0) | quiet(X0)) [ennf transformation 4]
40. ! [X0] : ((quiet(X0) & brave(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) [nnf transformation 31]
68. ! [X0] : ((old(X0) | (~happy(X0) | ~quiet(X0))) & ((happy(X0) & quiet(X0)) | ~old(X0))) [nnf transformation 16]
69. ! [X0] : ((old(X0) | ~happy(X0) | ~quiet(X0)) & ((happy(X0) & quiet(X0)) | ~old(X0))) [flattening 68]
84. ~quiet(X0) | brave(X0) | ~patient(X0) [cnf transformation 30]
85. ~wise(X0) | brave(X0) | patient(X0) [cnf transformation 40]
89. old(X0) | quiet(X0) [cnf transformation 32]
129. quiet(X0) | ~old(X0) [cnf transformation 69]
140. ~brave(fred) [cnf transformation 21]
145. wise(fred) [cnf transformation 24]
221. 16 <=> ! [X1] : quiet(X1) [avatar definition]
222. quiet(X1) <- (16) [avatar component clause 221]
261. quiet(X0) [subsumption resolution 129,89]
262. 16 [avatar split clause 261,221]
322. ~patient(X0) | brave(X0) <- (16) [resolution 84,222]
327. brave(fred) | patient(fred) [resolution 85,145]
332. patient(fred) [subsumption resolution 327,140]
432. brave(fred) <- (16) [resolution 322,332]
434. $false <- (16) [subsumption resolution 432,140]
435. ~16 [avatar contradiction clause 434]
436. $false [avatar sat refutation 262,435]
% SZS output end Proof for 5251875266473799121405857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits