premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
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| hypothesis_tptp
stringclasses 224
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sequencelengths 0
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stringlengths 684
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If someone is either not funny or not generous then alice is not brave or happy. If someone is either not calm or not brave then someone is curious or humble. Everyone who is rich or patient is not generous or not calm and vice versa. Everyone who is not funny or brave is both not calm and quiet and vice versa. If mary is either not wise or not curious then mary is either strong or funny and vice versa. Everyone who is not funny or not patient is both quiet and not humble and vice versa. If john is either creative or happy then someone is either patient or wise and vice versa. Everyone who is calm is wise. Everyone who is not humble is not tall. Everyone who is not generous is not calm and vice versa. If someone is not old then lucy is not wise. If fred is both creative and brave then john is not generous or not happy. If someone is kind then fred is either strong or not wise and vice versa. If someone is both creative and wise then someone is not curious or not creative and vice versa. If someone is not humble then alice is not tall or not patient. If someone is happy then someone is both patient and tall. Someone is curious. Lucy is both not quiet and not happy. Someone is both not wise and not quiet. Someone is not creative. Someone is both quiet and not tall. Someone is either humble or funny. Someone is not calm or not tall. Fred is not creative. | Lucy is patient. | entailment | ((?[X]:((~funny(X)<~>~generous(X))))=>((~brave(alice)|happy(alice))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(?[X]:((curious(X)|humble(X)))))&
(![X]:((rich(X)|patient(X))<=>(~generous(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))<=>(~calm(X)&quiet(X))))&
(((~wise(mary)<~>~curious(mary)))<=>((strong(mary)<~>funny(mary))))&
(![X]:((~funny(X)|~patient(X))<=>(quiet(X)&~humble(X))))&
(((creative(john)<~>happy(john)))<=>(?[X]:((patient(X)<~>wise(X)))))&
(![X]:(calm(X)=>wise(X)))&
(![X]:(~humble(X)=>~tall(X)))&
(![X]:(~generous(X)<=>~calm(X)))&
((?[X]:(~old(X)))=>(~wise(lucy)))&
(((creative(fred)&brave(fred)))=>((~generous(john)|~happy(john))))&
((?[X]:(kind(X)))<=>((strong(fred)<~>~wise(fred))))&
((?[X]:((creative(X)&wise(X))))<=>(?[X]:((~curious(X)|~creative(X)))))&
((?[X]:(~humble(X)))=>((~tall(alice)|~patient(alice))))&
((?[X]:(happy(X)))=>(?[X]:((patient(X)&tall(X)))))&
(?[X]:(curious(X)))&
((~quiet(lucy)&~happy(lucy)))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:(~creative(X)))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((humble(X)<~>funny(X))))&
(?[X]:((~calm(X)|~tall(X))))&
(~creative(fred)) | patient(lucy) | [
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4546695305091396371320384
% SZS output start Proof for 4546695305091396371320384
6. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (~humble(X0) & quiet(X0))) [input p5]
18. ~happy(lucy) & ~quiet(lucy) [input p17]
25. ~patient(lucy) [input hypothesis]
50. ! [X0] : (((~patient(X0) | ~funny(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 6]
51. ! [X0] : ((~patient(X0) | ~funny(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (patient(X0) & funny(X0)))) [flattening 50]
104. quiet(X0) | patient(X0) [cnf transformation 51]
134. ~quiet(lucy) [cnf transformation 18]
145. ~patient(lucy) [cnf transformation 25]
339. patient(lucy) [resolution 104,134]
341. $false [subsumption resolution 339,145]
% SZS output end Proof for 4546695305091396371320384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not generous. If susan is not strong then alice is either not curious or not patient. If someone is both not quiet and not happy then someone is not wise and vice versa. If someone is brave then someone is not quiet and vice versa. Everyone who is either not strong or not funny is either not old or patient and vice versa. Everyone who is strong is not rich and vice versa. If susan is either not wise or not generous then someone is not tall or happy. Everyone who is both not calm and strong is strong or not quiet and vice versa. Everyone who is both not humble and not happy is patient and vice versa. Everyone who is both strong and brave is either not humble or generous and vice versa. If someone is both strong and curious then someone is not funny or rich. Everyone who is not creative or not generous is not brave and vice versa. Everyone who is both not brave and not creative is curious. If fred is not old then someone is not patient. Everyone who is both patient and calm is brave or not quiet and vice versa. Everyone who is either humble or patient is creative and vice versa. Someone is either not happy or not wise. Someone is either not curious or not generous. Alice is old. Fred is not brave. Mary is either not generous or wise. Someone is either not happy or not quiet. Paul is quiet or not quiet. Fred is both not happy and curious. | Fred is patient. | contradiction | (![X]:(brave(X)=>~generous(X)))&
((~strong(susan))=>((~curious(alice)<~>~patient(alice))))&
((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:(~wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(~old(X)<~>patient(X))))&
(![X]:(strong(X)<=>~rich(X)))&
(((~wise(susan)<~>~generous(susan)))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((~calm(X)&strong(X))<=>(strong(X)|~quiet(X))))&
(![X]:((~humble(X)&~happy(X))<=>patient(X)))&
(![X]:((strong(X)&brave(X))<=>(~humble(X)<~>generous(X))))&
((?[X]:((strong(X)&curious(X))))=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~creative(X)|~generous(X))<=>~brave(X)))&
(![X]:((~brave(X)&~creative(X))=>curious(X)))&
((~old(fred))=>(?[X]:(~patient(X))))&
(![X]:((patient(X)&calm(X))<=>(brave(X)|~quiet(X))))&
(![X]:((humble(X)<~>patient(X))<=>creative(X)))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(old(alice))&
(~brave(fred))&
((~generous(mary)<~>wise(mary)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((quiet(paul)|~quiet(paul)))&
((~happy(fred)&curious(fred))) | patient(fred) | [
"p0",
"p8",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 148360152508991249758102
% SZS output start Proof for 148360152508991249758102
1. ! [X0] : (brave(X0) => ~generous(X0)) [input p0]
9. ! [X0] : ((~happy(X0) & ~humble(X0)) <=> patient(X0)) [input p8]
10. ! [X0] : ((brave(X0) & strong(X0)) <=> (~humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : ((~generous(X0) | ~creative(X0)) <=> ~brave(X0)) [input p11]
16. ! [X0] : ((humble(X0) <~> patient(X0)) <=> creative(X0)) [input p15]
25. patient(fred) [input hypothesis]
30. ! [X0] : (~generous(X0) | ~brave(X0)) [ennf transformation 1]
51. ! [X0] : (((~happy(X0) & ~humble(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) | humble(X0)))) [nnf transformation 9]
52. ! [X0] : (((~happy(X0) & ~humble(X0)) | ~patient(X0)) & (patient(X0) | happy(X0) | humble(X0))) [flattening 51]
53. ! [X0] : (((brave(X0) & strong(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~brave(X0) | ~strong(X0)))) [nnf transformation 10]
54. ! [X0] : (((brave(X0) & strong(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | ~brave(X0) | ~strong(X0))) [flattening 53]
58. ! [X0] : (((~generous(X0) | ~creative(X0)) | brave(X0)) & (~brave(X0) | (generous(X0) & creative(X0)))) [nnf transformation 12]
59. ! [X0] : ((~generous(X0) | ~creative(X0) | brave(X0)) & (~brave(X0) | (generous(X0) & creative(X0)))) [flattening 58]
64. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | ~creative(X0)) & (creative(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [nnf transformation 16]
75. ~generous(X0) | ~brave(X0) [cnf transformation 30]
99. ~humble(X0) | ~patient(X0) [cnf transformation 52]
105. humble(X0) | generous(X0) | brave(X0) [cnf transformation 54]
109. ~brave(X0) | generous(X0) [cnf transformation 59]
110. ~generous(X0) | ~creative(X0) | brave(X0) [cnf transformation 59]
119. creative(X0) | humble(X0) | ~patient(X0) [cnf transformation 64]
135. patient(fred) [cnf transformation 25]
180. 11 <=> ! [X3] : ~brave(X3) [avatar definition]
181. ~brave(X3) <- (11) [avatar component clause 180]
201. ~creative(X0) | ~generous(X0) [subsumption resolution 110,75]
202. ~brave(X0) [subsumption resolution 109,75]
203. 11 [avatar split clause 202,180]
217. ~patient(X0) | creative(X0) [subsumption resolution 119,99]
272. creative(fred) [resolution 217,135]
273. ~generous(fred) [resolution 272,201]
284. generous(X2) | brave(X2) | ~patient(X2) [resolution 105,99]
286. ~patient(X2) | generous(X2) <- (11) [subsumption resolution 284,181]
297. generous(fred) <- (11) [resolution 286,135]
298. $false <- (11) [subsumption resolution 297,273]
299. ~11 [avatar contradiction clause 298]
300. $false [avatar sat refutation 203,299]
% SZS output end Proof for 148360152508991249758102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise then alice is either not patient or strong and vice versa. Everyone who is tall or not tall is not patient and vice versa. If someone is not strong or not generous then someone is either patient or humble and vice versa. Everyone who is either not rich or kind is funny and vice versa. If someone is either not curious or strong then someone is quiet or not funny. If someone is not calm or not curious then susan is either happy or curious and vice versa. Everyone who is both generous and old is not quiet and vice versa. Everyone who is either not strong or tall is either generous or humble and vice versa. Everyone who is either not rich or not generous is kind. If paul is wise or generous then lucy is both quiet and not patient and vice versa. Everyone who is not happy is either not rich or quiet. Everyone who is both not rich and quiet is not strong and vice versa. Everyone who is either not kind or not rich is both not rich and quiet and vice versa. Everyone who is not rich or kind is either creative or not tall and vice versa. Everyone who is happy is both funny and strong. Everyone who is wise or not creative is either curious or not old and vice versa. Someone is funny or not wise. Someone is both not happy and not wise. Susan is either curious or patient. Someone is either strong or old. Paul is either calm or not happy. Mary is happy. Alice is humble. | Alice is strong. | entailment | ((?[X]:(wise(X)))<=>((~patient(alice)<~>strong(alice))))&
(![X]:((tall(X)|~tall(X))<=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>funny(X)))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((quiet(X)|~funny(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>((happy(susan)<~>curious(susan))))&
(![X]:((generous(X)&old(X))<=>~quiet(X)))&
(![X]:((~strong(X)<~>tall(X))<=>(generous(X)<~>humble(X))))&
(![X]:((~rich(X)<~>~generous(X))=>kind(X)))&
(((wise(paul)|generous(paul)))<=>((quiet(lucy)&~patient(lucy))))&
(![X]:(~happy(X)=>(~rich(X)<~>quiet(X))))&
(![X]:((~rich(X)&quiet(X))<=>~strong(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~rich(X)|kind(X))<=>(creative(X)<~>~tall(X))))&
(![X]:(happy(X)=>(funny(X)&strong(X))))&
(![X]:((wise(X)|~creative(X))<=>(curious(X)<~>~old(X))))&
(?[X]:((funny(X)|~wise(X))))&
(?[X]:((~happy(X)&~wise(X))))&
((curious(susan)<~>patient(susan)))&
(?[X]:((strong(X)<~>old(X))))&
((calm(paul)<~>~happy(paul)))&
(happy(mary))&
(humble(alice)) | strong(alice) | [
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8312891820174146708373243
% SZS output start Proof for 8312891820174146708373243
11. ! [X0] : (~happy(X0) => (~rich(X0) <~> quiet(X0))) [input p10]
12. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> ~strong(X0)) [input p11]
15. ! [X0] : (happy(X0) => (strong(X0) & funny(X0))) [input p14]
24. ~strong(alice) [input hypothesis]
29. ! [X0] : ((~rich(X0) <~> quiet(X0)) | happy(X0)) [ennf transformation 11]
30. ! [X0] : ((strong(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 15]
57. ! [X0] : (((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | happy(X0)) [nnf transformation 29]
58. ! [X0] : (((quiet(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | (~quiet(X0) | rich(X0)))) [nnf transformation 12]
59. ! [X0] : (((quiet(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | ~quiet(X0) | rich(X0))) [flattening 58]
119. ~quiet(X0) | rich(X0) | happy(X0) [cnf transformation 57]
121. ~rich(X0) | strong(X0) [cnf transformation 59]
122. quiet(X0) | strong(X0) [cnf transformation 59]
136. ~happy(X0) | strong(X0) [cnf transformation 30]
154. ~strong(alice) [cnf transformation 24]
158. 1 <=> strong(alice) [avatar definition]
160. ~strong(alice) <- (~1) [avatar component clause 158]
201. 10 <=> ! [X3] : strong(X3) [avatar definition]
202. strong(X3) <- (10) [avatar component clause 201]
295. ~1 [avatar split clause 154,158]
333. rich(X0) | happy(X0) | strong(X0) [resolution 119,122]
336. happy(X0) | strong(X0) [subsumption resolution 333,121]
337. strong(X0) [subsumption resolution 336,136]
338. 10 [avatar split clause 337,201]
348. $false <- (~1, 10) [resolution 202,160]
351. 1 | ~10 [avatar contradiction clause 348]
352. $false [avatar sat refutation 295,338,351]
% SZS output end Proof for 8312891820174146708373243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is either quiet or not tall and vice versa.
If someone is both not funny and curious then someone is both quiet and not humble and vice versa.
If fred is either strong or not creative then someone is patient or creative.
If susan is both not brave and wise then someone is calm.
Everyone who is both wise and generous is both not quiet and curious and vice versa.
If fred is not quiet or not kind then someone is both happy and creative and vice versa.
If susan is both strong and not patient then someone is either curious or quiet.
Everyone who is creative is funny.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
If someone is strong or not quiet then someone is curious or not tall.
If paul is either brave or not calm then mary is not kind or not humble and vice versa.
Everyone who is both not rich and brave is both brave and not calm and vice versa.
Susan is both not curious and old.
Someone is curious.
Fred is either not calm or not rich.
Someone is generous.
Someone is both quiet and not happy.
Someone is either curious or humble. | Fred is strong. | neutral | (![X]:((~rich(X)&~generous(X))<=>(quiet(X)<~>~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:(creative(X)=>funny(X)))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((strong(X)|~quiet(X))))=>(?[X]:((curious(X)|~tall(X)))))&
(((brave(paul)<~>~calm(paul)))<=>((~kind(mary)|~humble(mary))))&
(![X]:((~rich(X)&brave(X))<=>(brave(X)&~calm(X))))&
((~curious(susan)&old(susan)))&
(?[X]:(curious(X)))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:(generous(X)))&
(?[X]:((quiet(X)&~happy(X))))&
(?[X]:((curious(X)<~>humble(X)))) | strong(fred) | [] | null | 0 |
Everyone who is either not quiet or calm is either quiet or not humble.
If someone is brave or not calm then lucy is both not curious and not funny.
Everyone who is both curious and patient is strong or not creative and vice versa.
Everyone who is not strong is not kind or rich and vice versa.
If someone is not rich then someone is both not kind and not creative and vice versa.
If alice is old or not humble then susan is either not tall or not brave and vice versa.
If someone is not generous then someone is both kind and not old and vice versa.
Everyone who is either not rich or patient is both not happy and not calm and vice versa.
If fred is strong or quiet then someone is not kind or tall.
If someone is both tall and not generous then susan is either not calm or tall and vice versa.
If fred is not old then someone is both old and not brave and vice versa.
Everyone who is both patient and not tall is both creative and not funny and vice versa.
If lucy is humble then mary is both humble and brave.
If someone is not rich then someone is calm or not wise and vice versa.
Everyone who is not curious or not rich is either wise or brave.
Everyone who is not humble is not kind or strong.
Fred is creative.
Fred is wise or generous.
John is humble or brave.
Someone is not strong or not patient.
Susan is both not kind and rich.
Someone is either strong or not patient.
Fred is either curious or kind.
Susan is strong or not kind. | Fred is not wise. | neutral | (![X]:((~quiet(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|~creative(X))))&
(![X]:(~strong(X)<=>(~kind(X)|rich(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)&~creative(X)))))&
(((old(alice)|~humble(alice)))<=>((~tall(susan)<~>~brave(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~happy(X)&~calm(X))))&
(((strong(fred)|quiet(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((tall(X)&~generous(X))))<=>((~calm(susan)<~>tall(susan))))&
((~old(fred))<=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~funny(X))))&
((humble(lucy))=>((humble(mary)&brave(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~curious(X)|~rich(X))=>(wise(X)<~>brave(X))))&
(![X]:(~humble(X)=>(~kind(X)|strong(X))))&
(creative(fred))&
((wise(fred)|generous(fred)))&
((humble(john)|brave(john)))&
(?[X]:((~strong(X)|~patient(X))))&
((~kind(susan)&rich(susan)))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(fred)<~>kind(fred)))&
((strong(susan)|~kind(susan))) | ~wise(fred) | [] | null | 0 |
If mary is not generous then lucy is either not brave or not generous.
If someone is either quiet or patient then alice is quiet or generous and vice versa.
Everyone who is not funny is either not strong or tall and vice versa.
Everyone who is both not wise and strong is both rich and kind and vice versa.
Everyone who is not happy or not rich is humble or not quiet and vice versa.
If someone is both not strong and not patient then susan is either funny or patient.
If someone is strong then someone is both creative and funny.
Everyone who is either not tall or not humble is either quiet or not generous and vice versa.
Everyone who is not strong or not brave is old or curious and vice versa.
If someone is both humble and not funny then alice is not wise or not generous and vice versa.
Everyone who is both brave and not humble is both calm and happy and vice versa.
Everyone who is either patient or not generous is either creative or not kind and vice versa.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Everyone who is both not tall and tall is not quiet or not happy and vice versa.
John is strong.
Someone is either not curious or not happy.
Someone is rich or not happy.
Someone is not strong.
Lucy is not calm.
Paul is both happy and not kind.
Someone is either generous or not curious.
John is both not creative and not wise. | John is kind. | entailment | ((~generous(mary))=>((~brave(lucy)<~>~generous(lucy))))&
((?[X]:((quiet(X)<~>patient(X))))<=>((quiet(alice)|generous(alice))))&
(![X]:(~funny(X)<=>(~strong(X)<~>tall(X))))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)&kind(X))))&
(![X]:((~happy(X)|~rich(X))<=>(humble(X)|~quiet(X))))&
((?[X]:((~strong(X)&~patient(X))))=>((funny(susan)<~>patient(susan))))&
((?[X]:(strong(X)))=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~strong(X)|~brave(X))<=>(old(X)|curious(X))))&
((?[X]:((humble(X)&~funny(X))))<=>((~wise(alice)|~generous(alice))))&
(![X]:((brave(X)&~humble(X))<=>(calm(X)&happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((~tall(X)&tall(X))<=>(~quiet(X)|~happy(X))))&
(strong(john))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~strong(X)))&
(~calm(lucy))&
((happy(paul)&~kind(paul)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~creative(john)&~wise(john))) | kind(john) | [
"p3",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5558759605534048900458861
% SZS output start Proof for 5558759605534048900458861
4. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (kind(X0) & rich(X0))) [input p3]
17. strong(john) [input p16]
24. ~wise(john) & ~creative(john) [input p23]
25. ~kind(john) [input hypothesis]
43. ! [X0] : (((strong(X0) & ~wise(X0)) | (~kind(X0) | ~rich(X0))) & ((kind(X0) & rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 4]
44. ! [X0] : (((strong(X0) & ~wise(X0)) | ~kind(X0) | ~rich(X0)) & ((kind(X0) & rich(X0)) | ~strong(X0) | wise(X0))) [flattening 43]
91. ~strong(X0) | kind(X0) | wise(X0) [cnf transformation 44]
143. strong(john) [cnf transformation 17]
154. ~wise(john) [cnf transformation 24]
155. ~kind(john) [cnf transformation 25]
327. kind(john) | wise(john) [resolution 91,143]
330. wise(john) [subsumption resolution 327,155]
331. $false [subsumption resolution 330,154]
% SZS output end Proof for 5558759605534048900458861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is either not generous or not old.
Everyone who is happy is either tall or not quiet.
Everyone who is either not brave or not creative is either not humble or kind.
If someone is not curious then someone is both funny and creative.
Everyone who is not creative or not kind is not patient and vice versa.
Everyone who is not rich or rich is not strong.
If fred is happy or quiet then susan is both not quiet and not old.
Everyone who is not happy is not quiet or funny.
Everyone who is funny or humble is not calm or kind and vice versa.
Everyone who is both not generous and generous is both not calm and not strong and vice versa.
Everyone who is patient is either not kind or not patient.
If someone is kind or not funny then someone is not brave.
Everyone who is old is not kind or not humble and vice versa.
If mary is either not strong or not quiet then someone is not strong or funny.
Everyone who is either not rich or patient is funny or strong.
Everyone who is not strong or strong is not old and vice versa.
Someone is wise.
Lucy is either not old or rich.
Someone is humble or patient.
Someone is both humble and calm.
Fred is either not kind or funny. | Susan is curious. | entailment | (![X]:((~generous(X)&~rich(X))=>(~generous(X)<~>~old(X))))&
(![X]:(happy(X)=>(tall(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~humble(X)<~>kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~creative(X)|~kind(X))<=>~patient(X)))&
(![X]:((~rich(X)|rich(X))=>~strong(X)))&
(((happy(fred)|quiet(fred)))=>((~quiet(susan)&~old(susan))))&
(![X]:(~happy(X)=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)|kind(X))))&
(![X]:((~generous(X)&generous(X))<=>(~calm(X)&~strong(X))))&
(![X]:(patient(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(?[X]:(wise(X)))&
((~old(lucy)<~>rich(lucy)))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((humble(X)&calm(X))))&
((~kind(fred)<~>funny(fred))) | curious(susan) | [
"p3",
"p4",
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1440827341092774226961204
% SZS output start Proof for 1440827341092774226961204
4. ? [X0] : ~curious(X0) => ? [X0] : (creative(X0) & funny(X0)) [input p3]
5. ! [X0] : ((~kind(X0) | ~creative(X0)) <=> ~patient(X0)) [input p4]
6. ! [X0] : ((rich(X0) | ~rich(X0)) => ~strong(X0)) [input p5]
11. ! [X0] : (patient(X0) => (~kind(X0) <~> ~patient(X0))) [input p10]
13. ! [X0] : (old(X0) <=> (~humble(X0) | ~kind(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~strong(X0)) <=> ~old(X0)) [input p15]
22. ~curious(susan) [input hypothesis]
23. ? [X0] : ~curious(X0) => ? [X1] : (creative(X1) & funny(X1)) [rectify 4]
30. ? [X1] : (creative(X1) & funny(X1)) | ! [X0] : curious(X0) [ennf transformation 23]
31. ! [X0] : (~strong(X0) | (~rich(X0) & rich(X0))) [ennf transformation 6]
35. ! [X0] : ((~kind(X0) <~> ~patient(X0)) | ~patient(X0)) [ennf transformation 11]
43. ? [X0] : (creative(X0) & funny(X0)) | ! [X1] : curious(X1) [rectify 30]
44. ? [X0] : (creative(X0) & funny(X0)) => (creative(sK0) & funny(sK0)) [choice axiom]
45. (creative(sK0) & funny(sK0)) | ! [X1] : curious(X1) [skolemisation 43,44]
46. ! [X0] : (((~kind(X0) | ~creative(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & creative(X0)))) [nnf transformation 5]
47. ! [X0] : ((~kind(X0) | ~creative(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & creative(X0)))) [flattening 46]
52. ! [X0] : (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~patient(X0)) [nnf transformation 35]
56. ! [X0] : ((old(X0) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | ~old(X0))) [nnf transformation 13]
57. ! [X0] : ((old(X0) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | ~old(X0))) [flattening 56]
62. ! [X0] : (((strong(X0) | ~strong(X0)) | old(X0)) & (~old(X0) | (~strong(X0) & strong(X0)))) [nnf transformation 16]
63. ! [X0] : ((strong(X0) | ~strong(X0) | old(X0)) & (~old(X0) | (~strong(X0) & strong(X0)))) [flattening 62]
79. creative(sK0) | curious(X1) [cnf transformation 45]
81. ~patient(X0) | kind(X0) [cnf transformation 47]
82. ~kind(X0) | ~creative(X0) | patient(X0) [cnf transformation 47]
83. ~strong(X0) | rich(X0) [cnf transformation 31]
84. ~strong(X0) | ~rich(X0) [cnf transformation 31]
98. ~patient(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 52]
103. kind(X0) | old(X0) [cnf transformation 57]
109. ~old(X0) | strong(X0) [cnf transformation 63]
119. ~curious(susan) [cnf transformation 22]
120. ~patient(X0) | ~kind(X0) [duplicate literal removal 98]
123. 1 <=> ! [X1] : curious(X1) [avatar definition]
124. curious(X1) <- (1) [avatar component clause 123]
126. 2 <=> creative(sK0) [avatar definition]
128. creative(sK0) <- (2) [avatar component clause 126]
129. 1 | 2 [avatar split clause 79,126,123]
135. ~strong(X0) [subsumption resolution 83,84]
159. ~patient(X0) [subsumption resolution 120,81]
174. ~old(X0) [subsumption resolution 109,135]
190. ~creative(X0) | patient(X0) | old(X0) [resolution 82,103]
192. ~creative(X0) | old(X0) [subsumption resolution 190,159]
193. ~creative(X0) [subsumption resolution 192,174]
194. $false <- (2) [resolution 193,128]
195. ~2 [avatar contradiction clause 194]
196. $false <- (1) [resolution 124,119]
197. ~1 [avatar contradiction clause 196]
198. $false [avatar sat refutation 129,195,197]
% SZS output end Proof for 1440827341092774226961204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not happy.
Everyone who is both not quiet and wise is not kind or not brave and vice versa.
If someone is either not funny or brave then someone is either curious or not curious.
If fred is old or not strong then susan is funny or creative and vice versa.
Everyone who is strong or humble is kind.
Everyone who is not funny is humble or creative and vice versa.
Everyone who is not tall or curious is both humble and curious and vice versa.
If mary is not tall or not happy then someone is not rich and vice versa.
If someone is not tall then someone is brave or not tall and vice versa.
If alice is either not wise or not rich then mary is both patient and not humble and vice versa.
Everyone who is either curious or wise is either not rich or not old and vice versa.
If someone is either not strong or humble then someone is either quiet or not patient and vice versa.
If john is not wise or not brave then fred is both patient and not happy.
If someone is not generous or not patient then someone is either not quiet or wise and vice versa.
If susan is either humble or not creative then alice is funny or rich.
If lucy is both happy and not tall then alice is generous.
Paul is not calm.
Alice is not wise or creative.
Someone is curious.
Susan is both not wise and generous.
Someone is strong.
Alice is either not calm or not brave.
Alice is both not tall and generous.
Someone is not creative. | Susan is not brave. | contradiction | (![X]:(generous(X)=>~happy(X)))&
(![X]:((~quiet(X)&wise(X))<=>(~kind(X)|~brave(X))))&
((?[X]:((~funny(X)<~>brave(X))))=>(?[X]:((curious(X)<~>~curious(X)))))&
(((old(fred)|~strong(fred)))<=>((funny(susan)|creative(susan))))&
(![X]:((strong(X)|humble(X))=>kind(X)))&
(![X]:(~funny(X)<=>(humble(X)|creative(X))))&
(![X]:((~tall(X)|curious(X))<=>(humble(X)&curious(X))))&
(((~tall(mary)|~happy(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((brave(X)|~tall(X)))))&
(((~wise(alice)<~>~rich(alice)))<=>((patient(mary)&~humble(mary))))&
(![X]:((curious(X)<~>wise(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~strong(X)<~>humble(X))))<=>(?[X]:((quiet(X)<~>~patient(X)))))&
(((~wise(john)|~brave(john)))=>((patient(fred)&~happy(fred))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(((humble(susan)<~>~creative(susan)))=>((funny(alice)|rich(alice))))&
(((happy(lucy)&~tall(lucy)))=>(generous(alice)))&
(~calm(paul))&
((~wise(alice)|creative(alice)))&
(?[X]:(curious(X)))&
((~wise(susan)&generous(susan)))&
(?[X]:(strong(X)))&
((~calm(alice)<~>~brave(alice)))&
((~tall(alice)&generous(alice)))&
(?[X]:(~creative(X))) | ~brave(susan) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 425097518769996167339080
% SZS output start Proof for 425097518769996167339080
2. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (~brave(X0) | ~kind(X0))) [input p1]
20. generous(susan) & ~wise(susan) [input p19]
25. ~brave(susan) [input hypothesis]
38. ! [X0] : (((wise(X0) & ~quiet(X0)) | (brave(X0) & kind(X0))) & ((~brave(X0) | ~kind(X0)) | (~wise(X0) | quiet(X0)))) [nnf transformation 2]
39. ! [X0] : (((wise(X0) & ~quiet(X0)) | (brave(X0) & kind(X0))) & (~brave(X0) | ~kind(X0) | ~wise(X0) | quiet(X0))) [flattening 38]
86. brave(X0) | wise(X0) [cnf transformation 39]
149. ~wise(susan) [cnf transformation 20]
157. ~brave(susan) [cnf transformation 25]
368. wise(susan) [resolution 86,157]
370. $false [subsumption resolution 368,149]
% SZS output end Proof for 425097518769996167339080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Everyone who is not creative is not brave and vice versa.
Everyone who is both not humble and not quiet is either not brave or creative.
Everyone who is both calm and not humble is not brave and vice versa.
If susan is curious then lucy is either not kind or quiet.
Everyone who is brave or patient is tall or quiet and vice versa.
If john is tall then someone is either happy or wise and vice versa.
If someone is not rich or not wise then fred is both calm and curious and vice versa.
If someone is either not rich or not wise then someone is both creative and curious and vice versa.
If someone is both wise and not funny then someone is both not happy and kind.
Everyone who is either not strong or not brave is old or not brave and vice versa.
If paul is not calm or creative then alice is either humble or not calm.
Someone is not quiet.
Alice is funny or not old.
Someone is both funny and wise.
Mary is not curious.
Someone is kind.
Paul is either funny or curious.
Lucy is not patient. | Fred is not calm. | contradiction | (![X]:(~humble(X)<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~humble(X)&~quiet(X))=>(~brave(X)<~>creative(X))))&
(![X]:((calm(X)&~humble(X))<=>~brave(X)))&
((curious(susan))=>((~kind(lucy)<~>quiet(lucy))))&
(![X]:((brave(X)|patient(X))<=>(tall(X)|quiet(X))))&
((tall(john))<=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:((~rich(X)|~wise(X))))<=>((calm(fred)&curious(fred))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((creative(X)&curious(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(old(X)|~brave(X))))&
(((~calm(paul)|creative(paul)))=>((humble(alice)<~>~calm(alice))))&
(?[X]:(~quiet(X)))&
((funny(alice)|~old(alice)))&
(?[X]:((funny(X)&wise(X))))&
(~curious(mary))&
(?[X]:(kind(X)))&
((funny(paul)<~>curious(paul)))&
(~patient(lucy)) | ~calm(fred) | [
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 137574311235865322242066
% SZS output start Proof for 137574311235865322242066
2. (rich(mary) | brave(mary)) => ? [X0] : (curious(X0) & old(X0)) [input p1]
3. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p2]
12. ? [X0] : (~wise(X0) | ~rich(X0)) <=> (curious(fred) & calm(fred)) [input p11]
24. ~calm(fred) [input hypothesis]
27. ? [X0] : (curious(X0) & old(X0)) | (~rich(mary) & ~brave(mary)) [ennf transformation 2]
34. ? [X0] : (curious(X0) & old(X0)) => (curious(sK0) & old(sK0)) [choice axiom]
35. (curious(sK0) & old(sK0)) | (~rich(mary) & ~brave(mary)) [skolemisation 27,34]
36. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 3]
37. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 36]
52. (? [X0] : (~wise(X0) | ~rich(X0)) | (~curious(fred) | ~calm(fred))) & ((curious(fred) & calm(fred)) | ! [X0] : (wise(X0) & rich(X0))) [nnf transformation 12]
53. (? [X0] : (~wise(X0) | ~rich(X0)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X0] : (wise(X0) & rich(X0))) [flattening 52]
54. (? [X0] : (~wise(X0) | ~rich(X0)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X1] : (wise(X1) & rich(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) | ~rich(X0)) => (~wise(sK2) | ~rich(sK2)) [choice axiom]
56. ((~wise(sK2) | ~rich(sK2)) | ~curious(fred) | ~calm(fred)) & ((curious(fred) & calm(fred)) | ! [X1] : (wise(X1) & rich(X1))) [skolemisation 54,55]
80. curious(sK0) | ~rich(mary) [cnf transformation 35]
85. ~curious(X0) | ~rich(X0) [cnf transformation 37]
110. calm(fred) | rich(X1) [cnf transformation 56]
142. ~calm(fred) [cnf transformation 24]
146. 1 <=> rich(mary) [avatar definition]
148. ~rich(mary) <- (~1) [avatar component clause 146]
150. 2 <=> curious(sK0) [avatar definition]
152. curious(sK0) <- (2) [avatar component clause 150]
153. ~1 | 2 [avatar split clause 80,150,146]
204. 13 <=> calm(fred) [avatar definition]
225. 18 <=> ! [X1] : rich(X1) [avatar definition]
226. rich(X1) <- (18) [avatar component clause 225]
229. 18 | 13 [avatar split clause 110,204,225]
314. ~13 [avatar split clause 142,204]
316. $false <- (~1, 18) [subsumption resolution 148,226]
317. 1 | ~18 [avatar contradiction clause 316]
322. ~rich(sK0) <- (2) [resolution 85,152]
323. $false <- (2, 18) [subsumption resolution 322,226]
324. ~2 | ~18 [avatar contradiction clause 323]
325. $false [avatar sat refutation 153,229,314,317,324]
% SZS output end Proof for 137574311235865322242066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or brave is not curious or rich.
If someone is both not tall and calm then john is both creative and not happy and vice versa.
Everyone who is funny or not old is not patient or brave and vice versa.
If someone is not humble or curious then lucy is not creative.
Everyone who is both not humble and patient is not funny or not curious and vice versa.
If someone is either not creative or old then someone is wise or not patient and vice versa.
Everyone who is either quiet or not tall is wise and vice versa.
Everyone who is not generous or not quiet is not happy or funny and vice versa.
Everyone who is both kind and not quiet is not creative.
If fred is generous then someone is either wise or kind.
If someone is either kind or funny then alice is either not curious or curious.
Everyone who is either happy or creative is either not brave or wise.
If someone is either not kind or brave then someone is either strong or wise.
Everyone who is both happy and wise is either kind or not kind.
If someone is generous then someone is humble and vice versa.
Everyone who is both not funny and old is not wise or rich.
Someone is creative.
Someone is either not wise or calm.
Someone is not happy.
John is both quiet and humble.
Fred is both old and generous.
Someone is both creative and not wise.
Someone is either not tall or generous. | John is funny. | entailment | (![X]:((~curious(X)|brave(X))=>(~curious(X)|rich(X))))&
((?[X]:((~tall(X)&calm(X))))<=>((creative(john)&~happy(john))))&
(![X]:((funny(X)|~old(X))<=>(~patient(X)|brave(X))))&
((?[X]:((~humble(X)|curious(X))))=>(~creative(lucy)))&
(![X]:((~humble(X)&patient(X))<=>(~funny(X)|~curious(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((quiet(X)<~>~tall(X))<=>wise(X)))&
(![X]:((~generous(X)|~quiet(X))<=>(~happy(X)|funny(X))))&
(![X]:((kind(X)&~quiet(X))=>~creative(X)))&
((generous(fred))=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:((kind(X)<~>funny(X))))=>((~curious(alice)<~>curious(alice))))&
(![X]:((happy(X)<~>creative(X))=>(~brave(X)<~>wise(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>(?[X]:((strong(X)<~>wise(X)))))&
(![X]:((happy(X)&wise(X))=>(kind(X)<~>~kind(X))))&
((?[X]:(generous(X)))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)&old(X))=>(~wise(X)|rich(X))))&
(?[X]:(creative(X)))&
(?[X]:((~wise(X)<~>calm(X))))&
(?[X]:(~happy(X)))&
((quiet(john)&humble(john)))&
((old(fred)&generous(fred)))&
(?[X]:((creative(X)&~wise(X))))&
(?[X]:((~tall(X)<~>generous(X)))) | funny(john) | [
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5094468682067224044156701
% SZS output start Proof for 5094468682067224044156701
5. ! [X0] : ((patient(X0) & ~humble(X0)) <=> (~curious(X0) | ~funny(X0))) [input p4]
20. humble(john) & quiet(john) [input p19]
24. ~funny(john) [input hypothesis]
46. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~patient(X0) | humble(X0)))) [nnf transformation 5]
47. ! [X0] : (((patient(X0) & ~humble(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~patient(X0) | humble(X0))) [flattening 46]
94. ~humble(X0) | funny(X0) [cnf transformation 47]
136. humble(john) [cnf transformation 20]
143. ~funny(john) [cnf transformation 24]
286. funny(john) [resolution 94,136]
288. $false [subsumption resolution 286,143]
% SZS output end Proof for 5094468682067224044156701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and rich then lucy is either curious or not patient.
If lucy is patient or tall then someone is either not funny or not patient and vice versa.
If susan is generous or old then paul is not old and vice versa.
If someone is both not brave and curious then someone is not funny and vice versa.
Everyone who is either not humble or not strong is both calm and patient and vice versa.
Everyone who is both not creative and strong is both not calm and not humble.
Everyone who is either brave or not happy is both not patient and not funny and vice versa.
Everyone who is patient is both not humble and not calm.
If someone is humble then lucy is not rich or not generous.
Everyone who is both brave and wise is either kind or not curious and vice versa.
If someone is either curious or kind then john is both calm and not creative.
Everyone who is either not strong or not humble is both not calm and humble and vice versa.
If someone is happy or not quiet then someone is patient or kind and vice versa.
Everyone who is not rich is both not wise and humble.
If john is not curious or happy then someone is both humble and generous and vice versa.
Paul is either rich or not generous.
Alice is either curious or not tall.
Susan is not old.
Susan is either creative or not quiet.
Someone is both patient and rich.
Someone is not patient or tall. | John is not generous. | neutral | ((?[X]:((wise(X)&rich(X))))=>((curious(lucy)<~>~patient(lucy))))&
(((patient(lucy)|tall(lucy)))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
(((generous(susan)|old(susan)))<=>(~old(paul)))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(calm(X)&patient(X))))&
(![X]:((~creative(X)&strong(X))=>(~calm(X)&~humble(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)=>(~humble(X)&~calm(X))))&
((?[X]:(humble(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((brave(X)&wise(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((calm(john)&~creative(john))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)|~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:(~rich(X)=>(~wise(X)&humble(X))))&
(((~curious(john)|happy(john)))<=>(?[X]:((humble(X)&generous(X)))))&
((rich(paul)<~>~generous(paul)))&
((curious(alice)<~>~tall(alice)))&
(~old(susan))&
((creative(susan)<~>~quiet(susan)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((~patient(X)|tall(X)))) | ~generous(john) | [] | null | 0 |
If someone is both not old and not tall then mary is happy or kind.
If someone is not rich then someone is either strong or old.
Everyone who is generous or old is either not strong or not funny.
If fred is either not patient or not calm then alice is both strong and not strong.
If fred is either not brave or kind then mary is both not brave and generous and vice versa.
Everyone who is not old or not wise is curious or kind.
Everyone who is either not happy or generous is either brave or generous.
Everyone who is either not wise or not tall is not funny and vice versa.
If john is either old or not brave then someone is both funny and patient and vice versa.
If someone is either curious or not tall then alice is both strong and old and vice versa.
Everyone who is calm is both curious and calm.
If mary is either not old or curious then someone is both calm and not calm.
Everyone who is calm or old is not humble or patient.
Everyone who is either not old or rich is both quiet and humble and vice versa.
Everyone who is humble is both funny and humble and vice versa.
Everyone who is not rich or curious is both funny and not patient and vice versa.
Lucy is either patient or curious.
Someone is not tall.
Mary is tall or rich.
Susan is curious.
Paul is not funny.
Someone is both humble and tall.
Someone is either not strong or not wise. | Fred is not calm. | entailment | ((?[X]:((~old(X)&~tall(X))))=>((happy(mary)|kind(mary))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:((generous(X)|old(X))=>(~strong(X)<~>~funny(X))))&
(((~patient(fred)<~>~calm(fred)))=>((strong(alice)&~strong(alice))))&
(((~brave(fred)<~>kind(fred)))<=>((~brave(mary)&generous(mary))))&
(![X]:((~old(X)|~wise(X))=>(curious(X)|kind(X))))&
(![X]:((~happy(X)<~>generous(X))=>(brave(X)<~>generous(X))))&
(![X]:((~wise(X)<~>~tall(X))<=>~funny(X)))&
(((old(john)<~>~brave(john)))<=>(?[X]:((funny(X)&patient(X)))))&
((?[X]:((curious(X)<~>~tall(X))))<=>((strong(alice)&old(alice))))&
(![X]:(calm(X)=>(curious(X)&calm(X))))&
(((~old(mary)<~>curious(mary)))=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((calm(X)|old(X))=>(~humble(X)|patient(X))))&
(![X]:((~old(X)<~>rich(X))<=>(quiet(X)&humble(X))))&
(![X]:(humble(X)<=>(funny(X)&humble(X))))&
(![X]:((~rich(X)|curious(X))<=>(funny(X)&~patient(X))))&
((patient(lucy)<~>curious(lucy)))&
(?[X]:(~tall(X)))&
((tall(mary)|rich(mary)))&
(curious(susan))&
(~funny(paul))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:((~strong(X)<~>~wise(X)))) | ~calm(fred) | [
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1576338193320335953639689
% SZS output start Proof for 1576338193320335953639689
4. (~patient(fred) <~> ~calm(fred)) => (~strong(alice) & strong(alice)) [input p3]
11. ! [X0] : (calm(X0) => (calm(X0) & curious(X0))) [input p10]
16. ! [X0] : ((curious(X0) | ~rich(X0)) <=> (~patient(X0) & funny(X0))) [input p15]
24. calm(fred) [input hypothesis]
30. (~strong(alice) & strong(alice)) | (~patient(fred) <=> ~calm(fred)) [ennf transformation 4]
34. ! [X0] : ((calm(X0) & curious(X0)) | ~calm(X0)) [ennf transformation 11]
43. (~strong(alice) & strong(alice)) | ((~patient(fred) | calm(fred)) & (~calm(fred) | patient(fred))) [nnf transformation 30]
64. ! [X0] : (((curious(X0) | ~rich(X0)) | (patient(X0) | ~funny(X0))) & ((~patient(X0) & funny(X0)) | (~curious(X0) & rich(X0)))) [nnf transformation 16]
65. ! [X0] : ((curious(X0) | ~rich(X0) | patient(X0) | ~funny(X0)) & ((~patient(X0) & funny(X0)) | (~curious(X0) & rich(X0)))) [flattening 64]
81. strong(alice) | ~calm(fred) | patient(fred) [cnf transformation 43]
83. ~strong(alice) | ~calm(fred) | patient(fred) [cnf transformation 43]
113. ~calm(X0) | curious(X0) [cnf transformation 34]
133. ~curious(X0) | ~patient(X0) [cnf transformation 65]
145. calm(fred) [cnf transformation 24]
174. 7 <=> calm(fred) [avatar definition]
176. calm(fred) <- (7) [avatar component clause 174]
178. 8 <=> patient(fred) [avatar definition]
179. patient(fred) <- (8) [avatar component clause 178]
182. 9 <=> strong(alice) [avatar definition]
186. 8 | ~7 | ~9 [avatar split clause 83,182,174,178]
188. 8 | ~7 | 9 [avatar split clause 81,182,174,178]
304. 7 [avatar split clause 145,174]
305. curious(fred) <- (7) [resolution 113,176]
315. ~patient(fred) <- (7) [resolution 133,305]
316. $false <- (7, 8) [subsumption resolution 315,179]
317. ~7 | ~8 [avatar contradiction clause 316]
318. $false [avatar sat refutation 186,188,304,317]
% SZS output end Proof for 1576338193320335953639689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is both creative and generous and vice versa. If someone is quiet or not humble then alice is either happy or not funny and vice versa. Everyone who is wise or not rich is either generous or funny. Everyone who is both humble and not calm is both calm and not brave. Everyone who is brave is either not tall or calm and vice versa. Everyone who is not quiet or happy is both not wise and generous and vice versa. Everyone who is either old or generous is humble or wise. Everyone who is either calm or not happy is funny and vice versa. If someone is either humble or not curious then mary is either brave or wise and vice versa. If mary is not wise or not funny then someone is both not strong and not patient. If paul is old or not brave then paul is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Lucy is both not rich and wise. Someone is either patient or not quiet. Someone is not patient. Susan is both calm and quiet. Someone is both not kind and not wise. Someone is both strong and calm. Someone is both not patient and not calm. Someone is not strong. | Lucy is not calm. | contradiction | (![X]:((~funny(X)|funny(X))<=>(creative(X)&generous(X))))&
((?[X]:((quiet(X)|~humble(X))))<=>((happy(alice)<~>~funny(alice))))&
(![X]:((wise(X)|~rich(X))=>(generous(X)<~>funny(X))))&
(![X]:((humble(X)&~calm(X))=>(calm(X)&~brave(X))))&
(![X]:(brave(X)<=>(~tall(X)<~>calm(X))))&
(![X]:((~quiet(X)|happy(X))<=>(~wise(X)&generous(X))))&
(![X]:((old(X)<~>generous(X))=>(humble(X)|wise(X))))&
(![X]:((calm(X)<~>~happy(X))<=>funny(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>((brave(mary)<~>wise(mary))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((~strong(X)&~patient(X)))))&
(((old(paul)|~brave(paul)))=>((~quiet(paul)|~kind(paul))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
((~rich(lucy)&wise(lucy)))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
((calm(susan)&quiet(susan)))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:(~strong(X))) | ~calm(lucy) | [
"p0",
"p2",
"p5",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3704227269739638013522109
% SZS output start Proof for 3704227269739638013522109
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (generous(X0) & creative(X0))) [input p0]
3. ! [X0] : ((~rich(X0) | wise(X0)) => (generous(X0) <~> funny(X0))) [input p2]
6. ! [X0] : ((happy(X0) | ~quiet(X0)) <=> (generous(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((calm(X0) <~> ~happy(X0)) <=> funny(X0)) [input p7]
17. wise(lucy) & ~rich(lucy) [input p16]
25. ~calm(lucy) [input hypothesis]
26. ! [X0] : ((generous(X0) <~> funny(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 3]
40. ! [X0] : (((funny(X0) | ~funny(X0)) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
41. ! [X0] : ((funny(X0) | ~funny(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | (~funny(X0) & funny(X0)))) [flattening 40]
46. ! [X0] : (((~funny(X0) | ~generous(X0)) & (funny(X0) | generous(X0))) | (rich(X0) & ~wise(X0))) [nnf transformation 26]
48. ! [X0] : (((happy(X0) | ~quiet(X0)) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | (~happy(X0) & quiet(X0)))) [nnf transformation 6]
49. ! [X0] : ((happy(X0) | ~quiet(X0) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | (~happy(X0) & quiet(X0)))) [flattening 48]
51. ! [X0] : ((((happy(X0) | ~calm(X0)) & (~happy(X0) | calm(X0))) | ~funny(X0)) & (funny(X0) | ((calm(X0) | happy(X0)) & (~happy(X0) | ~calm(X0))))) [nnf transformation 8]
84. generous(X0) | funny(X0) [cnf transformation 41]
85. ~funny(X0) | generous(X0) [cnf transformation 41]
95. ~funny(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 46]
104. ~wise(X0) | ~happy(X0) [cnf transformation 49]
111. calm(X0) | funny(X0) | happy(X0) [cnf transformation 51]
139. wise(lucy) [cnf transformation 17]
152. ~calm(lucy) [cnf transformation 25]
154. generous(X0) [subsumption resolution 84,85]
185. ~wise(X0) | ~funny(X0) [subsumption resolution 95,154]
307. ~happy(lucy) [resolution 104,139]
309. ~funny(lucy) [resolution 185,139]
337. funny(lucy) | happy(lucy) [resolution 111,152]
341. happy(lucy) [subsumption resolution 337,309]
342. $false [subsumption resolution 341,307]
% SZS output end Proof for 3704227269739638013522109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and old then someone is both quiet and not happy and vice versa.
If mary is either not brave or not patient then someone is both creative and not rich and vice versa.
Everyone who is not humble or strong is not creative and vice versa.
Everyone who is both tall and wise is both not happy and not creative.
Everyone who is generous is creative or brave and vice versa.
Everyone who is calm is either calm or not kind and vice versa.
If alice is not old or not happy then someone is not old.
Everyone who is either kind or not humble is either humble or rich and vice versa.
If someone is curious or not quiet then someone is both brave and not quiet and vice versa.
If alice is not funny then mary is not calm or wise and vice versa.
Everyone who is not generous or rich is both not quiet and curious and vice versa.
If someone is either not strong or generous then someone is either brave or not funny.
Everyone who is not brave is quiet or wise and vice versa.
Everyone who is not curious or rich is curious or not curious.
Everyone who is not strong is both not patient and not curious and vice versa.
Everyone who is either funny or happy is not wise.
Someone is not generous.
Susan is either not generous or rich.
Someone is either happy or generous.
Someone is both tall and not funny.
Someone is creative or brave.
Someone is both not curious and quiet.
Someone is either wise or not wise.
Fred is not wise. | Alice is not curious. | neutral | ((?[X]:((curious(X)&old(X))))<=>(?[X]:((quiet(X)&~happy(X)))))&
(((~brave(mary)<~>~patient(mary)))<=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~humble(X)|strong(X))<=>~creative(X)))&
(![X]:((tall(X)&wise(X))=>(~happy(X)&~creative(X))))&
(![X]:(generous(X)<=>(creative(X)|brave(X))))&
(![X]:(calm(X)<=>(calm(X)<~>~kind(X))))&
(((~old(alice)|~happy(alice)))=>(?[X]:(~old(X))))&
(![X]:((kind(X)<~>~humble(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
((~funny(alice))<=>((~calm(mary)|wise(mary))))&
(![X]:((~generous(X)|rich(X))<=>(~quiet(X)&curious(X))))&
((?[X]:((~strong(X)<~>generous(X))))=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:(~brave(X)<=>(quiet(X)|wise(X))))&
(![X]:((~curious(X)|rich(X))=>(curious(X)|~curious(X))))&
(![X]:(~strong(X)<=>(~patient(X)&~curious(X))))&
(![X]:((funny(X)<~>happy(X))=>~wise(X)))&
(?[X]:(~generous(X)))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((tall(X)&~funny(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~curious(X)&quiet(X))))&
(?[X]:((wise(X)<~>~wise(X))))&
(~wise(fred)) | ~curious(alice) | [] | null | 0 |
Everyone who is strong is not tall or not kind and vice versa.
If someone is not quiet then someone is either not creative or not quiet.
Everyone who is tall or not funny is both brave and not generous and vice versa.
If lucy is both not strong and not quiet then someone is not kind and vice versa.
If someone is not strong then someone is either funny or not brave and vice versa.
If mary is not funny then fred is both strong and tall.
Everyone who is patient or not patient is both not old and generous.
If susan is both strong and happy then alice is both kind and not strong and vice versa.
If someone is not happy or patient then someone is either not patient or rich and vice versa.
If someone is both tall and calm then someone is not calm or humble.
If mary is both brave and funny then someone is not funny or rich and vice versa.
Everyone who is both not old and patient is either not rich or strong.
If someone is both rich and tall then someone is either humble or rich.
If lucy is creative or not happy then someone is calm or happy and vice versa.
Someone is either not humble or happy.
Susan is either strong or not strong.
Someone is humble.
Alice is kind.
Paul is either not creative or quiet. | Fred is rich. | contradiction | (![X]:(strong(X)<=>(~tall(X)|~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)|~funny(X))<=>(brave(X)&~generous(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
((~funny(mary))=>((strong(fred)&tall(fred))))&
(![X]:((patient(X)|~patient(X))=>(~old(X)&generous(X))))&
(((strong(susan)&happy(susan)))<=>((kind(alice)&~strong(alice))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((tall(X)&calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(((brave(mary)&funny(mary)))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~old(X)&patient(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((humble(X)<~>rich(X)))))&
(((creative(lucy)|~happy(lucy)))<=>(?[X]:((calm(X)|happy(X)))))&
(?[X]:((~humble(X)<~>happy(X))))&
((strong(susan)<~>~strong(susan)))&
(?[X]:(humble(X)))&
(kind(alice))&
((~creative(paul)<~>quiet(paul))) | rich(fred) | [
"p0",
"p2",
"p4",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4319459757727426525323294
% SZS output start Proof for 4319459757727426525323294
1. ! [X0] : (strong(X0) <=> (~kind(X0) | ~tall(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~generous(X0) & brave(X0))) [input p2]
5. ? [X0] : ~strong(X0) <=> ? [X0] : (funny(X0) <~> ~brave(X0)) [input p4]
7. ! [X0] : ((~patient(X0) | patient(X0)) => (generous(X0) & ~old(X0))) [input p6]
11. (funny(mary) & brave(mary)) <=> ? [X0] : (rich(X0) | ~funny(X0)) [input p10]
20. rich(fred) [input hypothesis]
22. ? [X0] : ~strong(X0) <=> ? [X1] : (funny(X1) <~> ~brave(X1)) [rectify 5]
28. ! [X0] : ((generous(X0) & ~old(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
33. ! [X0] : ((strong(X0) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | ~strong(X0))) [nnf transformation 1]
34. ! [X0] : ((strong(X0) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ~strong(X0))) [flattening 33]
39. ! [X0] : (((~funny(X0) | tall(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((~funny(X0) | tall(X0) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [flattening 39]
46. (? [X0] : ~strong(X0) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (? [X1] : ((brave(X1) | ~funny(X1)) & (~brave(X1) | funny(X1))) | ! [X0] : strong(X0)) [nnf transformation 22]
47. (? [X0] : ~strong(X0) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (? [X2] : ((brave(X2) | ~funny(X2)) & (~brave(X2) | funny(X2))) | ! [X3] : strong(X3)) [rectify 46]
48. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
49. ? [X2] : ((brave(X2) | ~funny(X2)) & (~brave(X2) | funny(X2))) => ((brave(sK3) | ~funny(sK3)) & (~brave(sK3) | funny(sK3))) [choice axiom]
50. (~strong(sK2) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (((brave(sK3) | ~funny(sK3)) & (~brave(sK3) | funny(sK3))) | ! [X3] : strong(X3)) [skolemisation 47,49,48]
61. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X0] : (rich(X0) | ~funny(X0)) | (~funny(mary) | ~brave(mary))) [nnf transformation 11]
62. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X0] : (rich(X0) | ~funny(X0)) | ~funny(mary) | ~brave(mary)) [flattening 61]
63. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X1] : (rich(X1) | ~funny(X1)) | ~funny(mary) | ~brave(mary)) [rectify 62]
64. ? [X1] : (rich(X1) | ~funny(X1)) => (rich(sK7) | ~funny(sK7)) [choice axiom]
65. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & ((rich(sK7) | ~funny(sK7)) | ~funny(mary) | ~brave(mary)) [skolemisation 63,64]
84. tall(X0) | strong(X0) [cnf transformation 34]
90. ~generous(X0) | ~tall(X0) [cnf transformation 40]
91. ~generous(X0) | funny(X0) [cnf transformation 40]
98. ~strong(sK2) | ~brave(X1) | ~funny(X1) [cnf transformation 50]
104. generous(X0) | ~patient(X0) [cnf transformation 28]
105. generous(X0) | patient(X0) [cnf transformation 28]
119. brave(mary) | ~rich(X0) [cnf transformation 65]
138. rich(fred) [cnf transformation 20]
171. 8 <=> ! [X1] : (~brave(X1) | ~funny(X1)) [avatar definition]
172. ~brave(X1) | ~funny(X1) <- (8) [avatar component clause 171]
174. 9 <=> strong(sK2) [avatar definition]
176. ~strong(sK2) <- (~9) [avatar component clause 174]
177. 8 | ~9 [avatar split clause 98,174,171]
180. 10 <=> ! [X3] : strong(X3) [avatar definition]
181. strong(X3) <- (10) [avatar component clause 180]
207. generous(X0) [subsumption resolution 104,105]
278. 31 <=> ! [X0] : ~rich(X0) [avatar definition]
279. ~rich(X0) <- (31) [avatar component clause 278]
282. 32 <=> ! [X0] : funny(X0) [avatar definition]
283. funny(X0) <- (32) [avatar component clause 282]
286. 33 <=> brave(mary) [avatar definition]
288. brave(mary) <- (33) [avatar component clause 286]
289. 31 | 33 [avatar split clause 119,286,278]
362. $false <- (~9, 10) [subsumption resolution 176,181]
363. 9 | ~10 [avatar contradiction clause 362]
366. ~brave(X1) <- (8, 32) [subsumption resolution 172,283]
369. $false <- (31) [resolution 279,138]
370. ~31 [avatar contradiction clause 369]
371. $false <- (8, 32, 33) [subsumption resolution 288,366]
372. ~8 | ~32 | ~33 [avatar contradiction clause 371]
380. ~tall(X0) [resolution 90,207]
381. strong(X0) [resolution 380,84]
382. 10 [avatar split clause 381,180]
383. funny(X0) [resolution 91,207]
384. 32 [avatar split clause 383,282]
385. $false [avatar sat refutation 177,289,363,370,372,382,384]
% SZS output end Proof for 4319459757727426525323294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and funny is either wise or creative. If someone is either not wise or tall then someone is both generous and curious. Everyone who is either not strong or strong is tall or happy. Everyone who is brave or creative is either brave or not curious. Everyone who is not wise is not quiet or not tall and vice versa. Everyone who is generous or tall is not patient. If lucy is creative then lucy is both humble and funny. Everyone who is either not patient or not strong is both creative and not curious. If someone is both not kind and not quiet then someone is kind or calm and vice versa. If someone is both happy and not humble then lucy is generous and vice versa. Everyone who is not tall or creative is both not rich and wise and vice versa. Everyone who is humble or creative is either not old or not curious and vice versa. Everyone who is either not tall or not happy is either wise or tall and vice versa. If someone is both not brave and tall then someone is either not patient or not strong and vice versa. Everyone who is both not creative and humble is either old or not curious. If someone is not rich then susan is not patient or humble. Alice is both not curious and not creative. Someone is both strong and funny. Fred is not rich. Someone is either not quiet or creative. Fred is not old or wise. Someone is either strong or creative. | Alice is strong. | contradiction | (![X]:((~old(X)&funny(X))=>(wise(X)<~>creative(X))))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((~strong(X)<~>strong(X))=>(tall(X)|happy(X))))&
(![X]:((brave(X)|creative(X))=>(brave(X)<~>~curious(X))))&
(![X]:(~wise(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((generous(X)|tall(X))=>~patient(X)))&
((creative(lucy))=>((humble(lucy)&funny(lucy))))&
(![X]:((~patient(X)<~>~strong(X))=>(creative(X)&~curious(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>(generous(lucy)))&
(![X]:((~tall(X)|creative(X))<=>(~rich(X)&wise(X))))&
(![X]:((humble(X)|creative(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:((~patient(X)<~>~strong(X)))))&
(![X]:((~creative(X)&humble(X))=>(old(X)<~>~curious(X))))&
((?[X]:(~rich(X)))=>((~patient(susan)|humble(susan))))&
((~curious(alice)&~creative(alice)))&
(?[X]:((strong(X)&funny(X))))&
(~rich(fred))&
(?[X]:((~quiet(X)<~>creative(X))))&
((~old(fred)|wise(fred)))&
(?[X]:((strong(X)<~>creative(X)))) | strong(alice) | [
"p4",
"p5",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 888305492610318722647851
% SZS output start Proof for 888305492610318722647851
5. ! [X0] : (~wise(X0) <=> (~tall(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((tall(X0) | generous(X0)) => ~patient(X0)) [input p5]
8. ! [X0] : ((~patient(X0) <~> ~strong(X0)) => (~curious(X0) & creative(X0))) [input p7]
11. ! [X0] : ((creative(X0) | ~tall(X0)) <=> (wise(X0) & ~rich(X0))) [input p10]
17. ~creative(alice) & ~curious(alice) [input p16]
23. strong(alice) [input hypothesis]
33. ! [X0] : (~patient(X0) | (~tall(X0) & ~generous(X0))) [ennf transformation 6]
35. ! [X0] : ((~curious(X0) & creative(X0)) | (~patient(X0) <=> ~strong(X0))) [ennf transformation 8]
47. ! [X0] : ((~wise(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | wise(X0))) [nnf transformation 5]
48. ! [X0] : ((~wise(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | wise(X0))) [flattening 47]
49. ! [X0] : ((~curious(X0) & creative(X0)) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) [nnf transformation 35]
59. ! [X0] : (((creative(X0) | ~tall(X0)) | (~wise(X0) | rich(X0))) & ((wise(X0) & ~rich(X0)) | (~creative(X0) & tall(X0)))) [nnf transformation 11]
60. ! [X0] : ((creative(X0) | ~tall(X0) | ~wise(X0) | rich(X0)) & ((wise(X0) & ~rich(X0)) | (~creative(X0) & tall(X0)))) [flattening 59]
92. ~wise(X0) | tall(X0) [cnf transformation 48]
94. ~patient(X0) | ~tall(X0) [cnf transformation 33]
97. ~strong(X0) | creative(X0) | patient(X0) [cnf transformation 49]
111. wise(X0) | tall(X0) [cnf transformation 60]
138. ~creative(alice) [cnf transformation 17]
147. strong(alice) [cnf transformation 23]
237. tall(X0) [subsumption resolution 111,92]
349. creative(alice) | patient(alice) [resolution 97,147]
353. patient(alice) [subsumption resolution 349,138]
367. ~tall(alice) [resolution 353,94]
369. $false [subsumption resolution 367,237]
% SZS output end Proof for 888305492610318722647851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or rich is kind.
If someone is both not funny and old then someone is wise.
If someone is not old or not wise then someone is either not old or not brave.
If someone is patient or creative then mary is not curious or quiet.
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Someone is calm or not patient.
Someone is not brave or not kind.
Someone is both not old and not happy.
Someone is calm or kind.
Someone is not rich.
Susan is either not creative or not generous.
Susan is not old or humble.
Fred is either calm or not happy. | Mary is kind. | neutral | (![X]:((humble(X)|rich(X))=>kind(X)))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((patient(X)|creative(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((~old(X)&~happy(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:(~rich(X)))&
((~creative(susan)<~>~generous(susan)))&
((~old(susan)|humble(susan)))&
((calm(fred)<~>~happy(fred))) | kind(mary) | [] | null | 0 |
Everyone who is either not calm or quiet is not brave or not wise. Everyone who is both tall and not funny is not happy or not quiet. Everyone who is not brave or not strong is either not brave or kind and vice versa. If someone is strong then someone is humble and vice versa. If someone is not old then someone is both quiet and not strong. Everyone who is not curious or not calm is both not funny and not calm. If susan is both not funny and not curious then john is either creative or not brave. Everyone who is both not happy and quiet is not kind or not rich and vice versa. If someone is wise or not brave then someone is not tall or calm and vice versa. Everyone who is either rich or not old is both happy and brave. Everyone who is calm is not curious and vice versa. Everyone who is either not tall or not humble is both humble and wise. Everyone who is not curious is tall. If susan is old then someone is not creative. If someone is both not wise and not creative then someone is not tall or not calm. If lucy is not quiet or tall then susan is either strong or brave and vice versa. Someone is not old. Someone is either not wise or not rich. Susan is not wise. Mary is calm or strong. Someone is patient. Someone is either humble or kind. Someone is not rich or not patient. | Susan is funny. | contradiction | (![X]:((~calm(X)<~>quiet(X))=>(~brave(X)|~wise(X))))&
(![X]:((tall(X)&~funny(X))=>(~happy(X)|~quiet(X))))&
(![X]:((~brave(X)|~strong(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:(humble(X))))&
((?[X]:(~old(X)))=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((~curious(X)|~calm(X))=>(~funny(X)&~calm(X))))&
(((~funny(susan)&~curious(susan)))=>((creative(john)<~>~brave(john))))&
(![X]:((~happy(X)&quiet(X))<=>(~kind(X)|~rich(X))))&
((?[X]:((wise(X)|~brave(X))))<=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((rich(X)<~>~old(X))=>(happy(X)&brave(X))))&
(![X]:(calm(X)<=>~curious(X)))&
(![X]:((~tall(X)<~>~humble(X))=>(humble(X)&wise(X))))&
(![X]:(~curious(X)=>tall(X)))&
((old(susan))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((~tall(X)|~calm(X)))))&
(((~quiet(lucy)|tall(lucy)))<=>((strong(susan)<~>brave(susan))))&
(?[X]:(~old(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~wise(susan))&
((calm(mary)|strong(mary)))&
(?[X]:(patient(X)))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((~rich(X)|~patient(X)))) | funny(susan) | [
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1161581359857205697296434
% SZS output start Proof for 1161581359857205697296434
6. ! [X0] : ((~calm(X0) | ~curious(X0)) => (~calm(X0) & ~funny(X0))) [input p5]
11. ! [X0] : (calm(X0) <=> ~curious(X0)) [input p10]
24. funny(susan) [input hypothesis]
34. ! [X0] : ((~calm(X0) & ~funny(X0)) | (calm(X0) & curious(X0))) [ennf transformation 6]
62. ! [X0] : ((calm(X0) | curious(X0)) & (~curious(X0) | ~calm(X0))) [nnf transformation 11]
97. ~funny(X0) | calm(X0) [cnf transformation 34]
98. ~calm(X0) | curious(X0) [cnf transformation 34]
115. ~curious(X0) | ~calm(X0) [cnf transformation 62]
116. calm(X0) | curious(X0) [cnf transformation 62]
139. funny(susan) [cnf transformation 24]
189. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
190. ~calm(X1) <- (11) [avatar component clause 189]
221. curious(X0) [subsumption resolution 116,98]
222. ~calm(X0) [subsumption resolution 115,221]
223. 11 [avatar split clause 222,189]
316. calm(susan) [resolution 97,139]
317. $false <- (11) [subsumption resolution 316,190]
318. ~11 [avatar contradiction clause 317]
319. $false [avatar sat refutation 223,318]
% SZS output end Proof for 1161581359857205697296434
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not generous is generous and vice versa.
If susan is not calm then someone is either not strong or not wise and vice versa.
Everyone who is either not wise or quiet is either not wise or curious.
Everyone who is either curious or not curious is either not tall or old and vice versa.
If someone is both rich and not old then someone is strong and vice versa.
If mary is happy then alice is both calm and not calm and vice versa.
If someone is not humble or not wise then fred is not patient and vice versa.
If someone is both not old and not creative then paul is not funny.
If fred is either tall or brave then lucy is either not creative or generous and vice versa.
If fred is both not funny and quiet then someone is both funny and rich and vice versa.
Everyone who is curious or wise is both calm and not tall.
Everyone who is brave or not kind is not kind or rich and vice versa.
If alice is generous or humble then paul is not calm.
If someone is either rich or kind then someone is wise and vice versa.
Someone is not kind or generous.
Paul is either kind or rich.
Someone is happy or not old.
Susan is either old or not funny.
Someone is either not wise or kind. | Fred is creative. | neutral | (![X]:((strong(X)<~>~generous(X))<=>generous(X)))&
((~calm(susan))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>(~wise(X)<~>curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:(strong(X))))&
((happy(mary))<=>((calm(alice)&~calm(alice))))&
((?[X]:((~humble(X)|~wise(X))))<=>(~patient(fred)))&
((?[X]:((~old(X)&~creative(X))))=>(~funny(paul)))&
(((tall(fred)<~>brave(fred)))<=>((~creative(lucy)<~>generous(lucy))))&
(((~funny(fred)&quiet(fred)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)&~tall(X))))&
(![X]:((brave(X)|~kind(X))<=>(~kind(X)|rich(X))))&
(((generous(alice)|humble(alice)))=>(~calm(paul)))&
((?[X]:((rich(X)<~>kind(X))))<=>(?[X]:(wise(X))))&
(?[X]:((~kind(X)|generous(X))))&
((kind(paul)<~>rich(paul)))&
(?[X]:((happy(X)|~old(X))))&
((old(susan)<~>~funny(susan)))&
(?[X]:((~wise(X)<~>kind(X)))) | creative(fred) | [] | null | 0 |
If someone is both brave and strong then someone is old.
If someone is either patient or not generous then fred is strong or generous.
Everyone who is either not rich or happy is not old or not strong.
Everyone who is old is funny.
If paul is tall or not brave then someone is not creative and vice versa.
If someone is funny then someone is both generous and not funny.
Everyone who is either old or patient is happy or generous and vice versa.
Everyone who is either calm or wise is not kind or not creative and vice versa.
Everyone who is not curious or wise is both curious and kind and vice versa.
If someone is not rich then lucy is both old and not old.
If alice is both kind and not quiet then someone is not strong and vice versa.
Everyone who is calm is both rich and creative.
Everyone who is not patient is either curious or not tall and vice versa.
If someone is either not quiet or old then fred is either not quiet or happy.
Everyone who is either not brave or not generous is not wise.
If someone is not brave then susan is kind or not wise and vice versa.
Fred is both kind and creative.
Susan is both funny and not kind.
Mary is not quiet.
Someone is not wise.
Alice is tall or not happy.
Someone is not happy or not rich.
Someone is not strong or tall.
Susan is curious. | Susan is wise. | contradiction | ((?[X]:((brave(X)&strong(X))))=>(?[X]:(old(X))))&
((?[X]:((patient(X)<~>~generous(X))))=>((strong(fred)|generous(fred))))&
(![X]:((~rich(X)<~>happy(X))=>(~old(X)|~strong(X))))&
(![X]:(old(X)=>funny(X)))&
(((tall(paul)|~brave(paul)))<=>(?[X]:(~creative(X))))&
((?[X]:(funny(X)))=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((old(X)<~>patient(X))<=>(happy(X)|generous(X))))&
(![X]:((calm(X)<~>wise(X))<=>(~kind(X)|~creative(X))))&
(![X]:((~curious(X)|wise(X))<=>(curious(X)&kind(X))))&
((?[X]:(~rich(X)))=>((old(lucy)&~old(lucy))))&
(((kind(alice)&~quiet(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(calm(X)=>(rich(X)&creative(X))))&
(![X]:(~patient(X)<=>(curious(X)<~>~tall(X))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~quiet(fred)<~>happy(fred))))&
(![X]:((~brave(X)<~>~generous(X))=>~wise(X)))&
((?[X]:(~brave(X)))<=>((kind(susan)|~wise(susan))))&
((kind(fred)&creative(fred)))&
((funny(susan)&~kind(susan)))&
(~quiet(mary))&
(?[X]:(~wise(X)))&
((tall(alice)|~happy(alice)))&
(?[X]:((~happy(X)|~rich(X))))&
(?[X]:((~strong(X)|tall(X))))&
(curious(susan)) | wise(susan) | [
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2710107957401280824854770
% SZS output start Proof for 2710107957401280824854770
9. ! [X0] : ((wise(X0) | ~curious(X0)) <=> (kind(X0) & curious(X0))) [input p8]
18. ~kind(susan) & funny(susan) [input p17]
25. wise(susan) [input hypothesis]
56. ! [X0] : (((wise(X0) | ~curious(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (~wise(X0) & curious(X0)))) [nnf transformation 9]
57. ! [X0] : ((wise(X0) | ~curious(X0) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | (~wise(X0) & curious(X0)))) [flattening 56]
103. ~wise(X0) | kind(X0) [cnf transformation 57]
128. ~kind(susan) [cnf transformation 18]
135. wise(susan) [cnf transformation 25]
241. 24 <=> wise(susan) [avatar definition]
243. wise(susan) <- (24) [avatar component clause 241]
250. 26 <=> kind(susan) [avatar definition]
252. ~kind(susan) <- (~26) [avatar component clause 250]
254. ~26 [avatar split clause 128,250]
282. 24 [avatar split clause 135,241]
289. kind(susan) <- (24) [resolution 103,243]
290. $false <- (24, ~26) [subsumption resolution 289,252]
291. ~24 | 26 [avatar contradiction clause 290]
292. $false [avatar sat refutation 254,282,291]
% SZS output end Proof for 2710107957401280824854770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or happy then someone is either not wise or happy and vice versa. Everyone who is happy is both not brave and tall and vice versa. If alice is not humble or not happy then paul is either tall or not brave. If someone is either brave or humble then someone is not patient or old and vice versa. If john is patient or humble then susan is brave and vice versa. If someone is brave or not brave then paul is not funny or brave. Everyone who is either patient or old is quiet or not calm and vice versa. If someone is both old and not brave then someone is both strong and not kind. If lucy is not humble then someone is not kind or not old and vice versa. Everyone who is both not generous and not kind is happy or wise and vice versa. If alice is not tall or not humble then lucy is not calm or brave. If john is calm then someone is either calm or not old and vice versa. Everyone who is funny is creative or not tall. Everyone who is either not strong or quiet is tall and vice versa. Everyone who is not quiet is curious. Everyone who is both not funny and tall is both patient and quiet. Alice is happy. Lucy is wise or not generous. Someone is not strong. Paul is strong or calm. Alice is wise. Susan is not kind. Someone is not old. Someone is either brave or patient. | John is curious. | neutral | ((?[X]:((calm(X)<~>happy(X))))<=>(?[X]:((~wise(X)<~>happy(X)))))&
(![X]:(happy(X)<=>(~brave(X)&tall(X))))&
(((~humble(alice)|~happy(alice)))=>((tall(paul)<~>~brave(paul))))&
((?[X]:((brave(X)<~>humble(X))))<=>(?[X]:((~patient(X)|old(X)))))&
(((patient(john)|humble(john)))<=>(brave(susan)))&
((?[X]:((brave(X)|~brave(X))))=>((~funny(paul)|brave(paul))))&
(![X]:((patient(X)<~>old(X))<=>(quiet(X)|~calm(X))))&
((?[X]:((old(X)&~brave(X))))=>(?[X]:((strong(X)&~kind(X)))))&
((~humble(lucy))<=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((~generous(X)&~kind(X))<=>(happy(X)|wise(X))))&
(((~tall(alice)|~humble(alice)))=>((~calm(lucy)|brave(lucy))))&
((calm(john))<=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:(funny(X)=>(creative(X)|~tall(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>tall(X)))&
(![X]:(~quiet(X)=>curious(X)))&
(![X]:((~funny(X)&tall(X))=>(patient(X)&quiet(X))))&
(happy(alice))&
((wise(lucy)|~generous(lucy)))&
(?[X]:(~strong(X)))&
((strong(paul)|calm(paul)))&
(wise(alice))&
(~kind(susan))&
(?[X]:(~old(X)))&
(?[X]:((brave(X)<~>patient(X)))) | curious(john) | [] | null | 0 |
If paul is both quiet and old then someone is both rich and happy and vice versa.
If someone is curious then fred is either strong or wise.
Everyone who is both not curious and not happy is humble or funny and vice versa.
If someone is either generous or tall then john is not patient or not brave and vice versa.
Everyone who is both humble and wise is either tall or humble.
If mary is creative or rich then john is old or not wise.
If paul is either not quiet or not patient then someone is both tall and humble.
Everyone who is both wise and not tall is not happy and vice versa.
Everyone who is both old and kind is not wise.
If someone is not wise then someone is not calm or calm and vice versa.
If lucy is creative then john is rich or creative.
Everyone who is generous or rich is wise.
Everyone who is both not old and quiet is not patient.
If someone is either humble or not humble then mary is both not strong and curious.
Everyone who is both tall and brave is either not calm or not rich.
Everyone who is not generous is either wise or tall and vice versa.
Fred is not brave.
John is curious or not tall.
Someone is quiet.
Someone is humble or kind.
Fred is both not strong and not brave.
Alice is both patient and not brave.
Someone is either patient or creative.
Someone is either not patient or not humble. | John is not patient. | neutral | (((quiet(paul)&old(paul)))<=>(?[X]:((rich(X)&happy(X)))))&
((?[X]:(curious(X)))=>((strong(fred)<~>wise(fred))))&
(![X]:((~curious(X)&~happy(X))<=>(humble(X)|funny(X))))&
((?[X]:((generous(X)<~>tall(X))))<=>((~patient(john)|~brave(john))))&
(![X]:((humble(X)&wise(X))=>(tall(X)<~>humble(X))))&
(((creative(mary)|rich(mary)))=>((old(john)|~wise(john))))&
(((~quiet(paul)<~>~patient(paul)))=>(?[X]:((tall(X)&humble(X)))))&
(![X]:((wise(X)&~tall(X))<=>~happy(X)))&
(![X]:((old(X)&kind(X))=>~wise(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)|calm(X)))))&
((creative(lucy))=>((rich(john)|creative(john))))&
(![X]:((generous(X)|rich(X))=>wise(X)))&
(![X]:((~old(X)&quiet(X))=>~patient(X)))&
((?[X]:((humble(X)<~>~humble(X))))=>((~strong(mary)&curious(mary))))&
(![X]:((tall(X)&brave(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(wise(X)<~>tall(X))))&
(~brave(fred))&
((curious(john)|~tall(john)))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|kind(X))))&
((~strong(fred)&~brave(fred)))&
((patient(alice)&~brave(alice)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((~patient(X)<~>~humble(X)))) | ~patient(john) | [] | null | 0 |
Everyone who is either not strong or not happy is either funny or not rich and vice versa. Everyone who is generous is curious or not creative and vice versa. Everyone who is either humble or old is both not humble and not patient and vice versa. If susan is quiet or not strong then someone is not kind or not old. Everyone who is not kind is rich or not calm and vice versa. If paul is both not happy and quiet then someone is happy. If paul is happy or calm then someone is either strong or not old and vice versa. If susan is either not tall or brave then someone is not strong or kind. Everyone who is either not happy or generous is not humble. Everyone who is strong or tall is funny and vice versa. Everyone who is both not brave and not calm is both creative and not patient and vice versa. Everyone who is not quiet is both not funny and not strong. Everyone who is both not wise and quiet is generous or not humble and vice versa. If lucy is generous or not tall then paul is either generous or wise. If fred is both not happy and funny then someone is both calm and patient and vice versa. If mary is rich or not happy then someone is either not rich or not patient and vice versa. Lucy is not strong or generous. Alice is both not strong and creative. Paul is both not wise and not happy. Someone is either humble or calm. Susan is either happy or strong. Someone is either curious or old. Someone is either funny or not brave. | Lucy is not tall. | neutral | (![X]:((~strong(X)<~>~happy(X))<=>(funny(X)<~>~rich(X))))&
(![X]:(generous(X)<=>(curious(X)|~creative(X))))&
(![X]:((humble(X)<~>old(X))<=>(~humble(X)&~patient(X))))&
(((quiet(susan)|~strong(susan)))=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:(~kind(X)<=>(rich(X)|~calm(X))))&
(((~happy(paul)&quiet(paul)))=>(?[X]:(happy(X))))&
(((happy(paul)|calm(paul)))<=>(?[X]:((strong(X)<~>~old(X)))))&
(((~tall(susan)<~>brave(susan)))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~happy(X)<~>generous(X))=>~humble(X)))&
(![X]:((strong(X)|tall(X))<=>funny(X)))&
(![X]:((~brave(X)&~calm(X))<=>(creative(X)&~patient(X))))&
(![X]:(~quiet(X)=>(~funny(X)&~strong(X))))&
(![X]:((~wise(X)&quiet(X))<=>(generous(X)|~humble(X))))&
(((generous(lucy)|~tall(lucy)))=>((generous(paul)<~>wise(paul))))&
(((~happy(fred)&funny(fred)))<=>(?[X]:((calm(X)&patient(X)))))&
(((rich(mary)|~happy(mary)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
((~strong(lucy)|generous(lucy)))&
((~strong(alice)&creative(alice)))&
((~wise(paul)&~happy(paul)))&
(?[X]:((humble(X)<~>calm(X))))&
((happy(susan)<~>strong(susan)))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((funny(X)<~>~brave(X)))) | ~tall(lucy) | [] | null | 0 |
If fred is both not tall and not patient then someone is either wise or not wise and vice versa.
If paul is both strong and rich then someone is both curious and not kind and vice versa.
If lucy is both curious and not funny then susan is either not generous or happy.
Everyone who is not tall or kind is both not calm and quiet.
If someone is both old and creative then someone is both not calm and strong and vice versa.
Everyone who is tall is not quiet.
Everyone who is not patient or funny is brave or not patient and vice versa.
Everyone who is either not rich or not strong is not tall or quiet.
Everyone who is old or creative is not tall.
Everyone who is not patient or not curious is either not rich or not humble and vice versa.
Everyone who is either rich or not calm is not wise and vice versa.
Everyone who is not old is both not happy and not funny and vice versa.
Everyone who is both not rich and not quiet is rich and vice versa.
Everyone who is kind or not curious is either not generous or not patient.
If someone is not funny or old then someone is either generous or not curious.
Everyone who is curious or not quiet is not calm or not happy and vice versa.
Fred is both brave and not strong.
Someone is either old or calm.
Someone is both not calm and old.
Paul is funny.
Paul is not calm.
Someone is strong.
Fred is either creative or strong. | Fred is not curious. | contradiction | (((~tall(fred)&~patient(fred)))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(((strong(paul)&rich(paul)))<=>(?[X]:((curious(X)&~kind(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~generous(susan)<~>happy(susan))))&
(![X]:((~tall(X)|kind(X))=>(~calm(X)&quiet(X))))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))<=>(brave(X)|~patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~tall(X)|quiet(X))))&
(![X]:((old(X)|creative(X))=>~tall(X)))&
(![X]:((~patient(X)|~curious(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((rich(X)<~>~calm(X))<=>~wise(X)))&
(![X]:(~old(X)<=>(~happy(X)&~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>rich(X)))&
(![X]:((kind(X)|~curious(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|~happy(X))))&
((brave(fred)&~strong(fred)))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((~calm(X)&old(X))))&
(funny(paul))&
(~calm(paul))&
(?[X]:(strong(X)))&
((creative(fred)<~>strong(fred))) | ~curious(fred) | [
"p3",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2718393269673299496240502
% SZS output start Proof for 2718393269673299496240502
4. ! [X0] : ((kind(X0) | ~tall(X0)) => (quiet(X0) & ~calm(X0))) [input p3]
6. ! [X0] : (tall(X0) => ~quiet(X0)) [input p5]
13. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> rich(X0)) [input p12]
16. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (~happy(X0) | ~calm(X0))) [input p15]
24. ~curious(fred) [input hypothesis]
29. ! [X0] : ((quiet(X0) & ~calm(X0)) | (~kind(X0) & tall(X0))) [ennf transformation 4]
30. ! [X0] : (~quiet(X0) | ~tall(X0)) [ennf transformation 6]
60. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 13]
61. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | quiet(X0) | rich(X0))) [flattening 60]
67. ! [X0] : (((~quiet(X0) | curious(X0)) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 16]
68. ! [X0] : ((~quiet(X0) | curious(X0) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | (quiet(X0) & ~curious(X0)))) [flattening 67]
89. ~calm(X0) | tall(X0) [cnf transformation 29]
97. ~quiet(X0) | ~tall(X0) [cnf transformation 30]
119. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 61]
120. ~rich(X0) | ~rich(X0) [cnf transformation 61]
132. ~quiet(X0) | curious(X0) | calm(X0) [cnf transformation 68]
145. ~curious(fred) [cnf transformation 24]
146. rich(X0) | quiet(X0) [duplicate literal removal 119]
147. ~rich(X0) [duplicate literal removal 120]
239. quiet(X0) [subsumption resolution 146,147]
259. calm(X0) | curious(X0) [subsumption resolution 132,239]
272. ~tall(X1) [resolution 97,239]
293. curious(X1) | tall(X1) [resolution 259,89]
298. curious(X1) [subsumption resolution 293,272]
300. $false [resolution 298,145]
% SZS output end Proof for 2718393269673299496240502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or strong is brave and vice versa.
Everyone who is not creative or funny is either not rich or happy and vice versa.
If john is not calm then alice is funny and vice versa.
Everyone who is either not creative or creative is either generous or not calm and vice versa.
If someone is not quiet or brave then mary is both generous and strong.
Everyone who is not kind or patient is either not strong or not generous.
If mary is old then mary is generous or not tall.
Everyone who is generous is both creative and kind.
If someone is either not curious or not calm then john is both not wise and not funny.
Everyone who is both happy and not patient is not creative and vice versa.
Everyone who is either not rich or not tall is humble or not generous and vice versa.
Everyone who is both not strong and not calm is both not brave and not old and vice versa.
If someone is calm or not strong then someone is not kind and vice versa.
If paul is either not tall or not quiet then mary is tall and vice versa.
Everyone who is either funny or not curious is either not calm or happy.
If someone is either tall or happy then someone is quiet or not generous and vice versa.
Lucy is both tall and calm.
Fred is either brave or not curious.
Lucy is kind or not tall.
Lucy is both creative and strong.
Someone is either quiet or not creative.
Someone is either generous or brave. | Paul is not generous. | neutral | (![X]:((~creative(X)|strong(X))<=>brave(X)))&
(![X]:((~creative(X)|funny(X))<=>(~rich(X)<~>happy(X))))&
((~calm(john))<=>(funny(alice)))&
(![X]:((~creative(X)<~>creative(X))<=>(generous(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|brave(X))))=>((generous(mary)&strong(mary))))&
(![X]:((~kind(X)|patient(X))=>(~strong(X)<~>~generous(X))))&
((old(mary))=>((generous(mary)|~tall(mary))))&
(![X]:(generous(X)=>(creative(X)&kind(X))))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~wise(john)&~funny(john))))&
(![X]:((happy(X)&~patient(X))<=>~creative(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(humble(X)|~generous(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~brave(X)&~old(X))))&
((?[X]:((calm(X)|~strong(X))))<=>(?[X]:(~kind(X))))&
(((~tall(paul)<~>~quiet(paul)))<=>(tall(mary)))&
(![X]:((funny(X)<~>~curious(X))=>(~calm(X)<~>happy(X))))&
((?[X]:((tall(X)<~>happy(X))))<=>(?[X]:((quiet(X)|~generous(X)))))&
((tall(lucy)&calm(lucy)))&
((brave(fred)<~>~curious(fred)))&
((kind(lucy)|~tall(lucy)))&
((creative(lucy)&strong(lucy)))&
(?[X]:((quiet(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>brave(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is wise or not rich is not quiet and vice versa.
If susan is happy or not generous then someone is either calm or generous.
Everyone who is either kind or not calm is funny or old and vice versa.
Everyone who is strong or not quiet is both calm and quiet.
Everyone who is not tall is brave.
Everyone who is either strong or not creative is not patient or not old.
If someone is either funny or kind then someone is either not creative or not humble and vice versa.
If john is either kind or not happy then lucy is either old or strong.
If lucy is either creative or calm then john is kind or generous.
Everyone who is both not happy and not tall is humble or not funny and vice versa.
Everyone who is either not happy or not curious is both not brave and kind.
If paul is both not brave and not rich then alice is not tall and vice versa.
Everyone who is not brave is strong or patient and vice versa.
Everyone who is kind is not quiet.
Everyone who is patient is not kind or not strong.
Lucy is not humble.
Someone is brave.
Someone is not brave or strong.
Someone is quiet or not generous.
John is not kind.
Mary is either not happy or patient. | Susan is strong. | contradiction | (![X]:((wise(X)|~rich(X))<=>~quiet(X)))&
(((happy(susan)|~generous(susan)))=>(?[X]:((calm(X)<~>generous(X)))))&
(![X]:((kind(X)<~>~calm(X))<=>(funny(X)|old(X))))&
(![X]:((strong(X)|~quiet(X))=>(calm(X)&quiet(X))))&
(![X]:(~tall(X)=>brave(X)))&
(![X]:((strong(X)<~>~creative(X))=>(~patient(X)|~old(X))))&
((?[X]:((funny(X)<~>kind(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(((kind(john)<~>~happy(john)))=>((old(lucy)<~>strong(lucy))))&
(((creative(lucy)<~>calm(lucy)))=>((kind(john)|generous(john))))&
(![X]:((~happy(X)&~tall(X))<=>(humble(X)|~funny(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(~brave(X)&kind(X))))&
(((~brave(paul)&~rich(paul)))<=>(~tall(alice)))&
(![X]:(~brave(X)<=>(strong(X)|patient(X))))&
(![X]:(kind(X)=>~quiet(X)))&
(![X]:(patient(X)=>(~kind(X)|~strong(X))))&
(~humble(lucy))&
(?[X]:(brave(X)))&
(?[X]:((~brave(X)|strong(X))))&
(?[X]:((quiet(X)|~generous(X))))&
(~kind(john))&
((~happy(mary)<~>patient(mary))) | strong(susan) | [
"p2",
"p3",
"p4",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5364094261695661387411551
% SZS output start Proof for 5364094261695661387411551
3. ! [X0] : ((kind(X0) <~> ~calm(X0)) <=> (old(X0) | funny(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) | strong(X0)) => (quiet(X0) & calm(X0))) [input p3]
5. ! [X0] : (~tall(X0) => brave(X0)) [input p4]
10. ! [X0] : ((~tall(X0) & ~happy(X0)) <=> (~funny(X0) | humble(X0))) [input p9]
13. ! [X0] : (~brave(X0) <=> (patient(X0) | strong(X0))) [input p12]
14. ! [X0] : (kind(X0) => ~quiet(X0)) [input p13]
22. strong(susan) [input hypothesis]
25. ! [X0] : ((quiet(X0) & calm(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 4]
26. ! [X0] : (brave(X0) | tall(X0)) [ennf transformation 5]
33. ! [X0] : (~quiet(X0) | ~kind(X0)) [ennf transformation 14]
41. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [nnf transformation 3]
42. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [flattening 41]
51. ! [X0] : (((~tall(X0) & ~happy(X0)) | (funny(X0) & ~humble(X0))) & ((~funny(X0) | humble(X0)) | (tall(X0) | happy(X0)))) [nnf transformation 10]
52. ! [X0] : (((~tall(X0) & ~happy(X0)) | (funny(X0) & ~humble(X0))) & (~funny(X0) | humble(X0) | tall(X0) | happy(X0))) [flattening 51]
56. ! [X0] : ((~brave(X0) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | brave(X0))) [nnf transformation 13]
57. ! [X0] : ((~brave(X0) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | brave(X0))) [flattening 56]
74. ~funny(X0) | kind(X0) | ~calm(X0) [cnf transformation 42]
78. ~strong(X0) | calm(X0) [cnf transformation 25]
81. quiet(X0) | quiet(X0) [cnf transformation 25]
82. brave(X0) | tall(X0) [cnf transformation 26]
103. ~tall(X0) | funny(X0) [cnf transformation 52]
112. ~brave(X0) | ~strong(X0) [cnf transformation 57]
114. ~quiet(X0) | ~kind(X0) [cnf transformation 33]
123. strong(susan) [cnf transformation 22]
124. quiet(X0) [duplicate literal removal 81]
230. ~kind(X0) [subsumption resolution 114,124]
246. calm(susan) [resolution 78,123]
254. ~strong(X0) | tall(X0) [resolution 112,82]
282. tall(susan) [resolution 254,123]
355. funny(susan) [resolution 282,103]
398. kind(susan) | ~calm(susan) [resolution 355,74]
399. ~calm(susan) [subsumption resolution 398,230]
400. $false [subsumption resolution 399,246]
% SZS output end Proof for 5364094261695661387411551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and not curious then someone is either not old or not wise and vice versa. Everyone who is not creative or not calm is both brave and humble. If susan is both not calm and not happy then someone is either wise or strong. Everyone who is both not rich and creative is not rich or wise and vice versa. If someone is either tall or old then someone is generous or not generous and vice versa. Everyone who is either not funny or not strong is both not generous and humble and vice versa. If someone is not humble then someone is not rich. Everyone who is both patient and happy is not rich. Everyone who is both not curious and generous is either not curious or not calm. Everyone who is both old and not funny is not patient and vice versa. Everyone who is not brave or not generous is both kind and not patient. If lucy is either happy or not tall then someone is either rich or not funny. If someone is either not curious or not brave then someone is not wise or patient and vice versa. If someone is both calm and not creative then alice is not curious and vice versa. Everyone who is curious or not brave is either not calm or tall and vice versa. If someone is either not creative or not calm then someone is either quiet or not curious and vice versa. Someone is rich. Someone is strong. Someone is both creative and humble. Paul is curious or not tall. Someone is quiet or old. Paul is calm or not funny. Lucy is not happy or not calm. | Susan is not funny. | neutral | ((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~old(X)<~>~wise(X)))))&
(![X]:((~creative(X)|~calm(X))=>(brave(X)&humble(X))))&
(((~calm(susan)&~happy(susan)))=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~rich(X)&creative(X))<=>(~rich(X)|wise(X))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((~funny(X)<~>~strong(X))<=>(~generous(X)&humble(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~rich(X))))&
(![X]:((patient(X)&happy(X))=>~rich(X)))&
(![X]:((~curious(X)&generous(X))=>(~curious(X)<~>~calm(X))))&
(![X]:((old(X)&~funny(X))<=>~patient(X)))&
(![X]:((~brave(X)|~generous(X))=>(kind(X)&~patient(X))))&
(((happy(lucy)<~>~tall(lucy)))=>(?[X]:((rich(X)<~>~funny(X)))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((~wise(X)|patient(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(~curious(alice)))&
(![X]:((curious(X)|~brave(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:((~creative(X)<~>~calm(X))))<=>(?[X]:((quiet(X)<~>~curious(X)))))&
(?[X]:(rich(X)))&
(?[X]:(strong(X)))&
(?[X]:((creative(X)&humble(X))))&
((curious(paul)|~tall(paul)))&
(?[X]:((quiet(X)|old(X))))&
((calm(paul)|~funny(paul)))&
((~happy(lucy)|~calm(lucy))) | ~funny(susan) | [] | null | 0 |
Everyone who is wise or not happy is both happy and brave.
Everyone who is quiet or not wise is funny.
If someone is either patient or wise then mary is either not quiet or not old and vice versa.
Everyone who is either not calm or not tall is not creative.
If john is rich then someone is not creative or creative.
If fred is both humble and not brave then someone is either not strong or not wise and vice versa.
Everyone who is either not brave or not curious is calm.
Everyone who is both creative and not calm is either humble or funny and vice versa.
Everyone who is not kind or strong is both patient and not tall.
Everyone who is not patient is either not curious or generous.
Everyone who is brave or funny is both rich and old and vice versa.
Everyone who is both not humble and not tall is either not happy or not quiet and vice versa.
Everyone who is not calm is both not funny and not creative and vice versa.
If lucy is both not tall and not strong then mary is both not funny and not kind.
If alice is not patient then susan is either humble or old.
If someone is not wise or rich then someone is both wise and not humble.
Someone is not creative or not old.
Paul is wise or not patient.
Someone is either quiet or strong.
Someone is strong.
Someone is both old and not tall.
Someone is either not creative or creative.
Someone is either old or funny.
Mary is humble. | Mary is not quiet. | contradiction | (![X]:((wise(X)|~happy(X))=>(happy(X)&brave(X))))&
(![X]:((quiet(X)|~wise(X))=>funny(X)))&
((?[X]:((patient(X)<~>wise(X))))<=>((~quiet(mary)<~>~old(mary))))&
(![X]:((~calm(X)<~>~tall(X))=>~creative(X)))&
((rich(john))=>(?[X]:((~creative(X)|creative(X)))))&
(((humble(fred)&~brave(fred)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:((~brave(X)<~>~curious(X))=>calm(X)))&
(![X]:((creative(X)&~calm(X))<=>(humble(X)<~>funny(X))))&
(![X]:((~kind(X)|strong(X))=>(patient(X)&~tall(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>generous(X))))&
(![X]:((brave(X)|funny(X))<=>(rich(X)&old(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~happy(X)<~>~quiet(X))))&
(![X]:(~calm(X)<=>(~funny(X)&~creative(X))))&
(((~tall(lucy)&~strong(lucy)))=>((~funny(mary)&~kind(mary))))&
((~patient(alice))=>((humble(susan)<~>old(susan))))&
((?[X]:((~wise(X)|rich(X))))=>(?[X]:((wise(X)&~humble(X)))))&
(?[X]:((~creative(X)|~old(X))))&
((wise(paul)|~patient(paul)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:(strong(X)))&
(?[X]:((old(X)&~tall(X))))&
(?[X]:((~creative(X)<~>creative(X))))&
(?[X]:((old(X)<~>funny(X))))&
(humble(mary)) | ~quiet(mary) | [
"p0",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 242356107142275458955019
% SZS output start Proof for 242356107142275458955019
1. ! [X0] : ((~happy(X0) | wise(X0)) => (brave(X0) & happy(X0))) [input p0]
12. ! [X0] : ((~tall(X0) & ~humble(X0)) <=> (~happy(X0) <~> ~quiet(X0))) [input p11]
24. humble(mary) [input p23]
25. ~quiet(mary) [input hypothesis]
27. ! [X0] : ((brave(X0) & happy(X0)) | (happy(X0) & ~wise(X0))) [ennf transformation 1]
56. ! [X0] : (((~tall(X0) & ~humble(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) & (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (tall(X0) | humble(X0)))) [nnf transformation 12]
57. ! [X0] : (((~tall(X0) & ~humble(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) & (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | tall(X0) | humble(X0))) [flattening 56]
80. happy(X0) | happy(X0) [cnf transformation 27]
124. ~humble(X0) | ~happy(X0) | quiet(X0) [cnf transformation 57]
149. humble(mary) [cnf transformation 24]
150. ~quiet(mary) [cnf transformation 25]
151. happy(X0) [duplicate literal removal 80]
157. 2 <=> quiet(mary) [avatar definition]
159. ~quiet(mary) <- (~2) [avatar component clause 157]
211. ~humble(X0) | quiet(X0) [subsumption resolution 124,151]
293. ~2 [avatar split clause 150,157]
350. quiet(mary) [resolution 211,149]
352. $false <- (~2) [subsumption resolution 350,159]
353. 2 [avatar contradiction clause 352]
354. $false [avatar sat refutation 293,353]
% SZS output end Proof for 242356107142275458955019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both strong and quiet then susan is not kind or not generous and vice versa. If someone is not old or quiet then someone is both old and not calm and vice versa. If lucy is not rich or funny then lucy is not calm and vice versa. If someone is tall or brave then someone is old and vice versa. If paul is either not old or patient then someone is either not curious or kind. Everyone who is both not patient and generous is not generous. If someone is not calm or not wise then someone is both not patient and patient and vice versa. Everyone who is creative or brave is either not kind or not generous. If someone is quiet or not kind then someone is not rich or strong and vice versa. If someone is not wise then fred is happy and vice versa. If someone is both not old and calm then someone is either happy or patient. Everyone who is both not funny and not quiet is not generous or kind and vice versa. Everyone who is either not brave or tall is both creative and not brave and vice versa. If someone is either generous or strong then someone is not calm or patient and vice versa. If paul is not creative then someone is both calm and kind and vice versa. Someone is not brave. Someone is curious or patient. Someone is not creative or rich. Fred is both curious and not humble. Lucy is either not creative or not brave. Paul is wise. Someone is either not generous or not kind. Someone is both calm and kind. | Susan is tall. | entailment | (((strong(paul)&quiet(paul)))<=>((~kind(susan)|~generous(susan))))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:((old(X)&~calm(X)))))&
(((~rich(lucy)|funny(lucy)))<=>(~calm(lucy)))&
((?[X]:((tall(X)|brave(X))))<=>(?[X]:(old(X))))&
(((~old(paul)<~>patient(paul)))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~patient(X)&generous(X))=>~generous(X)))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((creative(X)|brave(X))=>(~kind(X)<~>~generous(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(?[X]:((~rich(X)|strong(X)))))&
((?[X]:(~wise(X)))<=>(happy(fred)))&
((?[X]:((~old(X)&calm(X))))=>(?[X]:((happy(X)<~>patient(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(creative(X)&~brave(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~calm(X)|patient(X)))))&
((~creative(paul))<=>(?[X]:((calm(X)&kind(X)))))&
(?[X]:(~brave(X)))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((~creative(X)|rich(X))))&
((curious(fred)&~humble(fred)))&
((~creative(lucy)<~>~brave(lucy)))&
(wise(paul))&
(?[X]:((~generous(X)<~>~kind(X))))&
(?[X]:((calm(X)&kind(X)))) | tall(susan) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6467549350408559546584586
% SZS output start Proof for 6467549350408559546584586
1. (quiet(paul) & strong(paul)) <=> (~generous(susan) | ~kind(susan)) [input p0]
2. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X0] : (~calm(X0) & old(X0)) [input p1]
7. ? [X0] : (~wise(X0) | ~calm(X0)) <=> ? [X0] : (patient(X0) & ~patient(X0)) [input p6]
8. ! [X0] : ((brave(X0) | creative(X0)) => (~kind(X0) <~> ~generous(X0))) [input p7]
13. ! [X0] : ((~brave(X0) <~> tall(X0)) <=> (~brave(X0) & creative(X0))) [input p12]
24. ~tall(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X1] : (~calm(X1) & old(X1)) [rectify 2]
27. ? [X0] : (~wise(X0) | ~calm(X0)) <=> ? [X1] : (patient(X1) & ~patient(X1)) [rectify 7]
35. ! [X0] : ((~kind(X0) <~> ~generous(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 8]
37. ((quiet(paul) & strong(paul)) | (generous(susan) & kind(susan))) & ((~generous(susan) | ~kind(susan)) | (~quiet(paul) | ~strong(paul))) [nnf transformation 1]
38. ((quiet(paul) & strong(paul)) | (generous(susan) & kind(susan))) & (~generous(susan) | ~kind(susan) | ~quiet(paul) | ~strong(paul)) [flattening 37]
39. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : (calm(X1) | ~old(X1))) & (? [X1] : (~calm(X1) & old(X1)) | ! [X0] : (~quiet(X0) & old(X0))) [nnf transformation 25]
40. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : (calm(X1) | ~old(X1))) & (? [X2] : (~calm(X2) & old(X2)) | ! [X3] : (~quiet(X3) & old(X3))) [rectify 39]
41. ? [X0] : (quiet(X0) | ~old(X0)) => (quiet(sK0) | ~old(sK0)) [choice axiom]
42. ? [X2] : (~calm(X2) & old(X2)) => (~calm(sK1) & old(sK1)) [choice axiom]
43. ((quiet(sK0) | ~old(sK0)) | ! [X1] : (calm(X1) | ~old(X1))) & ((~calm(sK1) & old(sK1)) | ! [X3] : (~quiet(X3) & old(X3))) [skolemisation 40,42,41]
54. (? [X0] : (~wise(X0) | ~calm(X0)) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X1] : (patient(X1) & ~patient(X1)) | ! [X0] : (wise(X0) & calm(X0))) [nnf transformation 27]
55. (? [X0] : (~wise(X0) | ~calm(X0)) | ! [X1] : (~patient(X1) | patient(X1))) & (? [X2] : (patient(X2) & ~patient(X2)) | ! [X3] : (wise(X3) & calm(X3))) [rectify 54]
56. ? [X0] : (~wise(X0) | ~calm(X0)) => (~wise(sK5) | ~calm(sK5)) [choice axiom]
57. ? [X2] : (patient(X2) & ~patient(X2)) => (patient(sK6) & ~patient(sK6)) [choice axiom]
58. ((~wise(sK5) | ~calm(sK5)) | ! [X1] : (~patient(X1) | patient(X1))) & ((patient(sK6) & ~patient(sK6)) | ! [X3] : (wise(X3) & calm(X3))) [skolemisation 55,57,56]
59. ! [X0] : (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | (~brave(X0) & ~creative(X0))) [nnf transformation 35]
75. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | (brave(X0) | ~creative(X0))) & ((~brave(X0) & creative(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [nnf transformation 13]
76. ! [X0] : ((((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | brave(X0) | ~creative(X0)) & ((~brave(X0) & creative(X0)) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0))))) [flattening 75]
101. quiet(paul) | kind(susan) [cnf transformation 38]
102. quiet(paul) | generous(susan) [cnf transformation 38]
106. ~calm(sK1) | ~quiet(X3) [cnf transformation 43]
119. ~patient(sK6) | calm(X3) [cnf transformation 58]
121. patient(sK6) | calm(X3) [cnf transformation 58]
124. ~creative(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 59]
125. ~brave(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 59]
141. creative(X0) | tall(X0) | brave(X0) [cnf transformation 76]
167. ~tall(susan) [cnf transformation 24]
172. 1 <=> generous(susan) [avatar definition]
174. generous(susan) <- (1) [avatar component clause 172]
176. 2 <=> quiet(paul) [avatar definition]
178. quiet(paul) <- (2) [avatar component clause 176]
179. 1 | 2 [avatar split clause 102,176,172]
181. 3 <=> kind(susan) [avatar definition]
183. kind(susan) <- (3) [avatar component clause 181]
184. 3 | 2 [avatar split clause 101,176,181]
205. 8 <=> ! [X3] : ~quiet(X3) [avatar definition]
206. ~quiet(X3) <- (8) [avatar component clause 205]
208. 9 <=> calm(sK1) [avatar definition]
210. ~calm(sK1) <- (~9) [avatar component clause 208]
211. 8 | ~9 [avatar split clause 106,208,205]
285. 26 <=> patient(sK6) [avatar definition]
290. 27 <=> ! [X3] : calm(X3) [avatar definition]
291. calm(X3) <- (27) [avatar component clause 290]
292. 27 | 26 [avatar split clause 121,285,290]
294. 27 | ~26 [avatar split clause 119,285,290]
438. $false <- (2, 8) [subsumption resolution 178,206]
439. ~2 | ~8 [avatar contradiction clause 438]
442. $false <- (~9, 27) [subsumption resolution 210,291]
443. 9 | ~27 [avatar contradiction clause 442]
484. tall(X1) | brave(X1) | ~kind(X1) | ~generous(X1) [resolution 141,124]
488. ~generous(X1) | ~kind(X1) | tall(X1) [subsumption resolution 484,125]
573. ~kind(susan) | tall(susan) <- (1) [resolution 488,174]
576. tall(susan) <- (1, 3) [subsumption resolution 573,183]
577. $false <- (1, 3) [subsumption resolution 576,167]
578. ~1 | ~3 [avatar contradiction clause 577]
580. $false [avatar sat refutation 179,184,211,292,294,439,443,578]
% SZS output end Proof for 6467549350408559546584586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both humble and not curious then john is curious.
Everyone who is either tall or not strong is brave or not patient and vice versa.
If paul is generous then someone is both not old and rich.
If someone is kind or not rich then someone is quiet or not curious.
Everyone who is quiet is not creative and vice versa.
If someone is either not brave or not curious then someone is curious.
If susan is quiet or happy then john is not happy and vice versa.
If paul is quiet then paul is wise and vice versa.
If someone is either rich or not wise then someone is either strong or not humble.
Everyone who is not brave is happy and vice versa.
Everyone who is not wise is quiet.
Everyone who is either not patient or not funny is either strong or quiet.
Everyone who is either not old or not brave is creative or not quiet.
Everyone who is patient is not creative or brave and vice versa.
If john is creative then mary is funny or not funny.
Everyone who is not generous or not rich is funny or not wise.
Someone is either not patient or generous.
Mary is both calm and quiet.
Someone is both not funny and kind.
Susan is not rich or not tall.
Alice is both tall and strong.
Alice is not strong or not calm.
Paul is not generous or not creative. | Paul is not generous. | neutral | ((?[X]:((humble(X)&~curious(X))))=>(curious(john)))&
(![X]:((tall(X)<~>~strong(X))<=>(brave(X)|~patient(X))))&
((generous(paul))=>(?[X]:((~old(X)&rich(X)))))&
((?[X]:((kind(X)|~rich(X))))=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:(curious(X))))&
(((quiet(susan)|happy(susan)))<=>(~happy(john)))&
((quiet(paul))<=>(wise(paul)))&
((?[X]:((rich(X)<~>~wise(X))))=>(?[X]:((strong(X)<~>~humble(X)))))&
(![X]:(~brave(X)<=>happy(X)))&
(![X]:(~wise(X)=>quiet(X)))&
(![X]:((~patient(X)<~>~funny(X))=>(strong(X)<~>quiet(X))))&
(![X]:((~old(X)<~>~brave(X))=>(creative(X)|~quiet(X))))&
(![X]:(patient(X)<=>(~creative(X)|brave(X))))&
((creative(john))=>((funny(mary)|~funny(mary))))&
(![X]:((~generous(X)|~rich(X))=>(funny(X)|~wise(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((calm(mary)&quiet(mary)))&
(?[X]:((~funny(X)&kind(X))))&
((~rich(susan)|~tall(susan)))&
((tall(alice)&strong(alice)))&
((~strong(alice)|~calm(alice)))&
((~generous(paul)|~creative(paul))) | ~generous(paul) | [] | null | 0 |
Everyone who is tall is not funny or not humble.
If someone is old or curious then mary is both not strong and not calm.
Everyone who is either happy or not happy is either old or not generous.
Everyone who is patient or not tall is patient and vice versa.
Everyone who is either rich or not strong is both old and strong.
If someone is either not old or not tall then fred is both not calm and not wise and vice versa.
If someone is old or kind then john is not old or not tall and vice versa.
Everyone who is not old is either kind or not humble and vice versa.
Everyone who is not generous is quiet and vice versa.
If mary is both not funny and not quiet then susan is either rich or not humble and vice versa.
Everyone who is either not generous or patient is both not creative and happy and vice versa.
If someone is not strong or funny then mary is wise.
If someone is not generous or not curious then someone is humble.
Everyone who is both patient and not rich is either not quiet or funny.
If someone is not old then someone is quiet or not happy.
If mary is tall then someone is rich or patient.
Lucy is either wise or not calm.
Someone is both not creative and brave.
Mary is both not creative and strong.
Someone is either not happy or calm.
Susan is patient.
Someone is either not humble or not rich.
Lucy is either not creative or not old.
Alice is not generous or creative. | Lucy is old. | contradiction | (![X]:(tall(X)=>(~funny(X)|~humble(X))))&
((?[X]:((old(X)|curious(X))))=>((~strong(mary)&~calm(mary))))&
(![X]:((happy(X)<~>~happy(X))=>(old(X)<~>~generous(X))))&
(![X]:((patient(X)|~tall(X))<=>patient(X)))&
(![X]:((rich(X)<~>~strong(X))=>(old(X)&strong(X))))&
((?[X]:((~old(X)<~>~tall(X))))<=>((~calm(fred)&~wise(fred))))&
((?[X]:((old(X)|kind(X))))<=>((~old(john)|~tall(john))))&
(![X]:(~old(X)<=>(kind(X)<~>~humble(X))))&
(![X]:(~generous(X)<=>quiet(X)))&
(((~funny(mary)&~quiet(mary)))<=>((rich(susan)<~>~humble(susan))))&
(![X]:((~generous(X)<~>patient(X))<=>(~creative(X)&happy(X))))&
((?[X]:((~strong(X)|funny(X))))=>(wise(mary)))&
((?[X]:((~generous(X)|~curious(X))))=>(?[X]:(humble(X))))&
(![X]:((patient(X)&~rich(X))=>(~quiet(X)<~>funny(X))))&
((?[X]:(~old(X)))=>(?[X]:((quiet(X)|~happy(X)))))&
((tall(mary))=>(?[X]:((rich(X)|patient(X)))))&
((wise(lucy)<~>~calm(lucy)))&
(?[X]:((~creative(X)&brave(X))))&
((~creative(mary)&strong(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
(patient(susan))&
(?[X]:((~humble(X)<~>~rich(X))))&
((~creative(lucy)<~>~old(lucy)))&
((~generous(alice)|creative(alice))) | old(lucy) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1183928217062012822631589
% SZS output start Proof for 1183928217062012822631589
2. ? [X0] : (curious(X0) | old(X0)) => (~calm(mary) & ~strong(mary)) [input p1]
19. strong(mary) & ~creative(mary) [input p18]
25. old(lucy) [input hypothesis]
31. (~calm(mary) & ~strong(mary)) | ! [X0] : (~curious(X0) & ~old(X0)) [ennf transformation 2]
80. ~strong(mary) | ~old(X0) [cnf transformation 31]
135. strong(mary) [cnf transformation 19]
144. old(lucy) [cnf transformation 25]
159. 3 <=> ! [X0] : ~old(X0) [avatar definition]
160. ~old(X0) <- (3) [avatar component clause 159]
163. 4 <=> strong(mary) [avatar definition]
167. 3 | ~4 [avatar split clause 80,163,159]
302. 4 [avatar split clause 135,163]
328. 39 <=> old(lucy) [avatar definition]
330. old(lucy) <- (39) [avatar component clause 328]
342. 39 [avatar split clause 144,328]
347. $false <- (3, 39) [resolution 330,160]
348. ~3 | ~39 [avatar contradiction clause 347]
349. $false [avatar sat refutation 167,302,342,348]
% SZS output end Proof for 1183928217062012822631589
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not humble and not creative is humble and vice versa.
If john is not strong or not quiet then someone is both strong and rich.
If someone is both not tall and kind then paul is either generous or curious and vice versa.
Everyone who is either not patient or not curious is either old or not funny and vice versa.
If someone is either not calm or not tall then someone is both not tall and brave.
Everyone who is humble or kind is not curious and vice versa.
If someone is not generous or generous then someone is humble or strong and vice versa.
If someone is humble then john is either not generous or not happy.
If someone is kind then lucy is old and vice versa.
Everyone who is not humble or rich is happy or humble.
If someone is calm or quiet then someone is either creative or not kind and vice versa.
Everyone who is not generous or not patient is either not calm or curious and vice versa.
If someone is both kind and calm then someone is not humble or not funny.
Everyone who is not patient is not brave or not calm.
If mary is wise then someone is both not rich and not happy.
Everyone who is calm or not kind is not curious or creative and vice versa.
Susan is not humble.
Someone is not old.
Someone is either generous or old.
Fred is not kind or not happy.
Fred is old.
John is either creative or not funny. | Paul is not quiet. | neutral | (![X]:((~humble(X)&~creative(X))<=>humble(X)))&
(((~strong(john)|~quiet(john)))=>(?[X]:((strong(X)&rich(X)))))&
((?[X]:((~tall(X)&kind(X))))<=>((generous(paul)<~>curious(paul))))&
(![X]:((~patient(X)<~>~curious(X))<=>(old(X)<~>~funny(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((humble(X)|kind(X))<=>~curious(X)))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:((humble(X)|strong(X)))))&
((?[X]:(humble(X)))=>((~generous(john)<~>~happy(john))))&
((?[X]:(kind(X)))<=>(old(lucy)))&
(![X]:((~humble(X)|rich(X))=>(happy(X)|humble(X))))&
((?[X]:((calm(X)|quiet(X))))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~generous(X)|~patient(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((kind(X)&calm(X))))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:(~patient(X)=>(~brave(X)|~calm(X))))&
((wise(mary))=>(?[X]:((~rich(X)&~happy(X)))))&
(![X]:((calm(X)|~kind(X))<=>(~curious(X)|creative(X))))&
(~humble(susan))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>old(X))))&
((~kind(fred)|~happy(fred)))&
(old(fred))&
((creative(john)<~>~funny(john))) | ~quiet(paul) | [] | null | 0 |
If mary is not calm or not tall then mary is both calm and not curious.
Everyone who is either not rich or strong is both generous and quiet and vice versa.
If paul is not happy then someone is not generous.
If fred is happy or not strong then someone is not funny and vice versa.
If someone is both not curious and not creative then someone is either quiet or rich.
If paul is both brave and not kind then someone is patient and vice versa.
Everyone who is not funny or strong is either not wise or generous and vice versa.
If fred is both not happy and not humble then someone is curious.
Everyone who is old or not rich is not strong.
If fred is creative then mary is rich.
Everyone who is either not generous or not humble is either not humble or rich and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is creative is not humble.
Everyone who is both not creative and not kind is both brave and kind and vice versa.
Everyone who is not quiet or not patient is not rich and vice versa.
Paul is both wise and not kind.
Someone is both tall and rich.
Someone is brave.
Someone is not generous or not humble.
Someone is not generous or not funny.
Someone is old.
Someone is either calm or not rich. | Fred is not patient. | neutral | (((~calm(mary)|~tall(mary)))=>((calm(mary)&~curious(mary))))&
(![X]:((~rich(X)<~>strong(X))<=>(generous(X)&quiet(X))))&
((~happy(paul))=>(?[X]:(~generous(X))))&
(((happy(fred)|~strong(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((quiet(X)<~>rich(X)))))&
(((brave(paul)&~kind(paul)))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(~wise(X)<~>generous(X))))&
(((~happy(fred)&~humble(fred)))=>(?[X]:(curious(X))))&
(![X]:((old(X)|~rich(X))=>~strong(X)))&
((creative(fred))=>(rich(mary)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~humble(X)<~>rich(X))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:(creative(X)=>~humble(X)))&
(![X]:((~creative(X)&~kind(X))<=>(brave(X)&kind(X))))&
(![X]:((~quiet(X)|~patient(X))<=>~rich(X)))&
((wise(paul)&~kind(paul)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:(brave(X)))&
(?[X]:((~generous(X)|~humble(X))))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:(old(X)))&
(?[X]:((calm(X)<~>~rich(X)))) | ~patient(fred) | [] | null | 0 |
If lucy is not patient or humble then paul is not generous and vice versa.
Everyone who is both happy and not funny is both wise and not brave.
Everyone who is not old is either kind or happy and vice versa.
If susan is not brave or not curious then lucy is happy or not old.
If someone is rich then someone is both generous and not happy.
If mary is either not wise or not rich then fred is not creative or curious.
If someone is not tall or not brave then someone is either not quiet or not creative.
Everyone who is not happy is both generous and brave.
If paul is both not rich and funny then alice is strong and vice versa.
If mary is either old or not funny then someone is not kind or strong.
Everyone who is brave is both not brave and generous and vice versa.
If someone is both not brave and happy then someone is both quiet and not kind.
If someone is not tall or not quiet then someone is both strong and not curious.
If someone is both not quiet and not humble then someone is both not curious and not old.
If someone is either not humble or not brave then fred is both old and not tall and vice versa.
Everyone who is both not generous and old is both not strong and not wise.
Someone is either patient or not happy.
Someone is quiet or not strong.
Someone is not old.
Someone is either quiet or not rich.
Alice is not curious. | Alice is not generous. | entailment | (((~patient(lucy)|humble(lucy)))<=>(~generous(paul)))&
(![X]:((happy(X)&~funny(X))=>(wise(X)&~brave(X))))&
(![X]:(~old(X)<=>(kind(X)<~>happy(X))))&
(((~brave(susan)|~curious(susan)))=>((happy(lucy)|~old(lucy))))&
((?[X]:(rich(X)))=>(?[X]:((generous(X)&~happy(X)))))&
(((~wise(mary)<~>~rich(mary)))=>((~creative(fred)|curious(fred))))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(![X]:(~happy(X)=>(generous(X)&brave(X))))&
(((~rich(paul)&funny(paul)))<=>(strong(alice)))&
(((old(mary)<~>~funny(mary)))=>(?[X]:((~kind(X)|strong(X)))))&
(![X]:(brave(X)<=>(~brave(X)&generous(X))))&
((?[X]:((~brave(X)&happy(X))))=>(?[X]:((quiet(X)&~kind(X)))))&
((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:((strong(X)&~curious(X)))))&
((?[X]:((~quiet(X)&~humble(X))))=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((~humble(X)<~>~brave(X))))<=>((old(fred)&~tall(fred))))&
(![X]:((~generous(X)&old(X))=>(~strong(X)&~wise(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)<~>~rich(X))))&
(~curious(alice)) | ~generous(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1264738911426421767645639
% SZS output start Proof for 1264738911426421767645639
11. ! [X0] : (brave(X0) <=> (generous(X0) & ~brave(X0))) [input p10]
22. generous(alice) [input hypothesis]
59. ! [X0] : ((brave(X0) | (~generous(X0) | brave(X0))) & ((generous(X0) & ~brave(X0)) | ~brave(X0))) [nnf transformation 11]
60. ! [X0] : ((brave(X0) | ~generous(X0) | brave(X0)) & ((generous(X0) & ~brave(X0)) | ~brave(X0))) [flattening 59]
111. ~brave(X0) | ~brave(X0) [cnf transformation 60]
113. brave(X0) | ~generous(X0) | brave(X0) [cnf transformation 60]
137. generous(alice) [cnf transformation 22]
138. ~brave(X0) [duplicate literal removal 111]
139. ~generous(X0) | brave(X0) [duplicate literal removal 113]
362. brave(alice) [resolution 139,137]
363. $false [subsumption resolution 362,138]
% SZS output end Proof for 1264738911426421767645639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is either not tall or wise.
Everyone who is both not patient and humble is either brave or kind and vice versa.
If paul is not old or wise then someone is not creative and vice versa.
If fred is not happy or not wise then someone is both kind and not quiet.
Everyone who is either wise or old is not old and vice versa.
Everyone who is either not generous or happy is strong.
Everyone who is not patient or not rich is both curious and not patient and vice versa.
Everyone who is strong or kind is not kind.
Everyone who is not wise is both curious and generous and vice versa.
Everyone who is not humble is quiet or not rich and vice versa.
Everyone who is quiet is wise.
If someone is not curious or generous then someone is both not happy and happy.
If someone is not funny or not generous then john is either old or not old and vice versa.
If john is both generous and not creative then someone is quiet.
Everyone who is rich or happy is generous or not patient.
Lucy is either brave or tall.
Someone is both happy and funny.
Someone is not creative. | Lucy is old. | neutral | (![X]:(~strong(X)=>(~tall(X)<~>wise(X))))&
(![X]:((~patient(X)&humble(X))<=>(brave(X)<~>kind(X))))&
(((~old(paul)|wise(paul)))<=>(?[X]:(~creative(X))))&
(((~happy(fred)|~wise(fred)))=>(?[X]:((kind(X)&~quiet(X)))))&
(![X]:((wise(X)<~>old(X))<=>~old(X)))&
(![X]:((~generous(X)<~>happy(X))=>strong(X)))&
(![X]:((~patient(X)|~rich(X))<=>(curious(X)&~patient(X))))&
(![X]:((strong(X)|kind(X))=>~kind(X)))&
(![X]:(~wise(X)<=>(curious(X)&generous(X))))&
(![X]:(~humble(X)<=>(quiet(X)|~rich(X))))&
(![X]:(quiet(X)=>wise(X)))&
((?[X]:((~curious(X)|generous(X))))=>(?[X]:((~happy(X)&happy(X)))))&
((?[X]:((~funny(X)|~generous(X))))<=>((old(john)<~>~old(john))))&
(((generous(john)&~creative(john)))=>(?[X]:(quiet(X))))&
(![X]:((rich(X)|happy(X))=>(generous(X)|~patient(X))))&
((brave(lucy)<~>tall(lucy)))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:(~creative(X))) | old(lucy) | [] | null | 0 |
If someone is either brave or not wise then someone is creative and vice versa.
If someone is both creative and not quiet then lucy is either not generous or quiet.
Everyone who is both not rich and curious is not funny or rich and vice versa.
If someone is both old and not brave then alice is strong.
Everyone who is wise or not funny is both not curious and curious.
If susan is not strong or funny then someone is not kind.
If lucy is quiet then someone is either not wise or happy.
Everyone who is creative or quiet is calm or not humble.
Everyone who is quiet or wise is old and vice versa.
Everyone who is not kind or not strong is strong.
Everyone who is either not funny or not happy is not wise or happy and vice versa.
If paul is both rich and not wise then paul is generous and vice versa.
Everyone who is not wise or brave is not generous.
Everyone who is old or not rich is either not curious or creative.
If someone is either happy or curious then someone is either not kind or not happy and vice versa.
Lucy is not creative or tall.
Someone is not creative.
Susan is both quiet and not humble.
Susan is strong.
Paul is not kind or calm.
John is either calm or rich. | Lucy is not brave. | contradiction | ((?[X]:((brave(X)<~>~wise(X))))<=>(?[X]:(creative(X))))&
((?[X]:((creative(X)&~quiet(X))))=>((~generous(lucy)<~>quiet(lucy))))&
(![X]:((~rich(X)&curious(X))<=>(~funny(X)|rich(X))))&
((?[X]:((old(X)&~brave(X))))=>(strong(alice)))&
(![X]:((wise(X)|~funny(X))=>(~curious(X)&curious(X))))&
(((~strong(susan)|funny(susan)))=>(?[X]:(~kind(X))))&
((quiet(lucy))=>(?[X]:((~wise(X)<~>happy(X)))))&
(![X]:((creative(X)|quiet(X))=>(calm(X)|~humble(X))))&
(![X]:((quiet(X)|wise(X))<=>old(X)))&
(![X]:((~kind(X)|~strong(X))=>strong(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(~wise(X)|happy(X))))&
(((rich(paul)&~wise(paul)))<=>(generous(paul)))&
(![X]:((~wise(X)|brave(X))=>~generous(X)))&
(![X]:((old(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
((~creative(lucy)|tall(lucy)))&
(?[X]:(~creative(X)))&
((quiet(susan)&~humble(susan)))&
(strong(susan))&
((~kind(paul)|calm(paul)))&
((calm(john)<~>rich(john))) | ~brave(lucy) | [
"p0",
"p2",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3977744976918523257335389
% SZS output start Proof for 3977744976918523257335389
1. ? [X0] : (brave(X0) <~> ~wise(X0)) <=> ? [X0] : creative(X0) [input p0]
3. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (rich(X0) | ~funny(X0))) [input p2]
5. ! [X0] : ((~funny(X0) | wise(X0)) => (curious(X0) & ~curious(X0))) [input p4]
14. ! [X0] : ((~rich(X0) | old(X0)) => (~curious(X0) <~> creative(X0))) [input p13]
22. ~brave(lucy) [input hypothesis]
23. ? [X0] : (brave(X0) <~> ~wise(X0)) <=> ? [X1] : creative(X1) [rectify 1]
34. ! [X0] : ((curious(X0) & ~curious(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 5]
39. ! [X0] : ((~curious(X0) <~> creative(X0)) | (rich(X0) & ~old(X0))) [ennf transformation 14]
40. (? [X0] : ((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) [nnf transformation 23]
41. (? [X0] : ((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : ((brave(X3) | wise(X3)) & (~wise(X3) | ~brave(X3)))) [rectify 40]
42. ? [X0] : ((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) => ((wise(sK0) | ~brave(sK0)) & (~wise(sK0) | brave(sK0))) [choice axiom]
43. ? [X2] : creative(X2) => creative(sK1) [choice axiom]
44. (((wise(sK0) | ~brave(sK0)) & (~wise(sK0) | brave(sK0))) | ! [X1] : ~creative(X1)) & (creative(sK1) | ! [X3] : ((brave(X3) | wise(X3)) & (~wise(X3) | ~brave(X3)))) [skolemisation 41,43,42]
46. ! [X0] : (((curious(X0) & ~rich(X0)) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | (~curious(X0) | rich(X0)))) [nnf transformation 3]
47. ! [X0] : (((curious(X0) & ~rich(X0)) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ~curious(X0) | rich(X0))) [flattening 46]
57. ! [X0] : (((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | (rich(X0) & ~old(X0))) [nnf transformation 39]
67. creative(sK1) | brave(X3) | wise(X3) [cnf transformation 44]
72. rich(X0) | ~funny(X0) | ~curious(X0) | rich(X0) [cnf transformation 47]
74. ~rich(X0) | ~rich(X0) [cnf transformation 47]
75. funny(X0) | curious(X0) [cnf transformation 47]
77. ~curious(X0) | ~wise(X0) [cnf transformation 34]
78. ~curious(X0) | funny(X0) [cnf transformation 34]
79. ~wise(X0) | curious(X0) [cnf transformation 34]
100. ~creative(X0) | curious(X0) | rich(X0) [cnf transformation 57]
114. ~brave(lucy) [cnf transformation 22]
117. rich(X0) | ~funny(X0) | ~curious(X0) [duplicate literal removal 72]
118. ~rich(X0) [duplicate literal removal 74]
133. 4 <=> ! [X3] : (brave(X3) | wise(X3)) [avatar definition]
134. brave(X3) | wise(X3) <- (4) [avatar component clause 133]
136. 5 <=> creative(sK1) [avatar definition]
138. creative(sK1) <- (5) [avatar component clause 136]
139. 4 | 5 [avatar split clause 67,136,133]
157. ~funny(X0) | ~curious(X0) [subsumption resolution 117,118]
158. funny(X0) [subsumption resolution 78,75]
159. ~wise(X0) [subsumption resolution 77,79]
170. ~creative(X0) | curious(X0) [subsumption resolution 100,118]
185. 13 <=> ! [X3] : ~curious(X3) [avatar definition]
186. ~curious(X3) <- (13) [avatar component clause 185]
204. ~curious(X1) [resolution 157,158]
205. curious(sK1) <- (5) [resolution 170,138]
206. $false <- (5, 13) [subsumption resolution 205,186]
207. ~5 | ~13 [avatar contradiction clause 206]
208. brave(X3) <- (4) [subsumption resolution 134,159]
209. $false <- (4) [resolution 208,114]
212. ~4 [avatar contradiction clause 209]
213. 13 [avatar split clause 204,185]
216. $false [avatar sat refutation 139,207,212,213]
% SZS output end Proof for 3977744976918523257335389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not rich and not calm then john is both rich and not curious.
Everyone who is strong is not strong or quiet.
Everyone who is either not happy or creative is old or generous.
Everyone who is quiet or rich is either patient or not kind.
Everyone who is either generous or not rich is not calm or not brave.
If someone is either creative or calm then someone is either wise or calm and vice versa.
Everyone who is both tall and funny is either not happy or not humble and vice versa.
Everyone who is either happy or humble is either quiet or not curious and vice versa.
Everyone who is not rich or not calm is old or not old.
If someone is either generous or rich then paul is both generous and not curious.
Everyone who is not quiet is either not curious or not creative.
Everyone who is both curious and not humble is not brave or old and vice versa.
Everyone who is kind is both not patient and not creative.
Everyone who is calm is both not humble and not rich.
Everyone who is either calm or kind is not calm or not happy and vice versa.
If paul is both not tall and tall then someone is strong.
Someone is calm or not brave.
Someone is either not patient or not quiet.
Someone is either not curious or funny.
Someone is not funny.
Someone is either strong or not funny.
Someone is quiet.
Someone is both not kind and not strong.
John is either not quiet or brave. | Mary is rich. | contradiction | (((~rich(mary)&~calm(mary)))=>((rich(john)&~curious(john))))&
(![X]:(strong(X)=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)<~>creative(X))=>(old(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(patient(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~rich(X))=>(~calm(X)|~brave(X))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((tall(X)&funny(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((happy(X)<~>humble(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)|~calm(X))=>(old(X)|~old(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((generous(paul)&~curious(paul))))&
(![X]:(~quiet(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((curious(X)&~humble(X))<=>(~brave(X)|old(X))))&
(![X]:(kind(X)=>(~patient(X)&~creative(X))))&
(![X]:(calm(X)=>(~humble(X)&~rich(X))))&
(![X]:((calm(X)<~>kind(X))<=>(~calm(X)|~happy(X))))&
(((~tall(paul)&tall(paul)))=>(?[X]:(strong(X))))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:(~funny(X)))&
(?[X]:((strong(X)<~>~funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~kind(X)&~strong(X))))&
((~quiet(john)<~>brave(john))) | rich(mary) | [
"p3",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3955081512822311494983662
% SZS output start Proof for 3955081512822311494983662
4. ! [X0] : ((rich(X0) | quiet(X0)) => (patient(X0) <~> ~kind(X0))) [input p3]
13. ! [X0] : (kind(X0) => (~creative(X0) & ~patient(X0))) [input p12]
14. ! [X0] : (calm(X0) => (~rich(X0) & ~humble(X0))) [input p13]
15. ! [X0] : ((calm(X0) <~> kind(X0)) <=> (~happy(X0) | ~calm(X0))) [input p14]
25. rich(mary) [input hypothesis]
33. ! [X0] : ((patient(X0) <~> ~kind(X0)) | (~rich(X0) & ~quiet(X0))) [ennf transformation 4]
40. ! [X0] : ((~creative(X0) & ~patient(X0)) | ~kind(X0)) [ennf transformation 13]
41. ! [X0] : ((~rich(X0) & ~humble(X0)) | ~calm(X0)) [ennf transformation 14]
45. ! [X0] : (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~rich(X0) & ~quiet(X0))) [nnf transformation 33]
59. ! [X0] : ((((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0))))) [nnf transformation 15]
60. ! [X0] : ((((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0))))) [flattening 59]
87. ~kind(X0) | patient(X0) | ~rich(X0) [cnf transformation 45]
127. ~kind(X0) | ~patient(X0) [cnf transformation 40]
130. ~calm(X0) | ~rich(X0) [cnf transformation 41]
133. kind(X0) | calm(X0) | calm(X0) [cnf transformation 60]
151. rich(mary) [cnf transformation 25]
153. kind(X0) | calm(X0) [duplicate literal removal 133]
156. 1 <=> rich(mary) [avatar definition]
158. rich(mary) <- (1) [avatar component clause 156]
277. 1 [avatar split clause 151,156]
283. ~patient(X1) | calm(X1) [resolution 153,127]
295. patient(X0) | ~rich(X0) | calm(X0) [resolution 87,153]
296. ~rich(X0) | calm(X0) [subsumption resolution 295,283]
297. ~rich(X0) [subsumption resolution 296,130]
298. $false <- (1) [resolution 297,158]
299. ~1 [avatar contradiction clause 298]
300. $false [avatar sat refutation 277,299]
% SZS output end Proof for 3955081512822311494983662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not funny is either not quiet or not strong and vice versa.
Everyone who is not rich or strong is not creative or calm.
Everyone who is rich is either kind or old.
If paul is kind or not curious then someone is happy or tall and vice versa.
If john is both not curious and curious then someone is both wise and not patient and vice versa.
Everyone who is humble or not happy is either patient or not patient.
If someone is both calm and wise then fred is not brave or not old and vice versa.
If someone is both patient and not rich then someone is not brave or not rich and vice versa.
If fred is not brave then someone is not patient.
If john is not patient then someone is either not strong or rich.
Everyone who is not kind or kind is both brave and not creative and vice versa.
Everyone who is either creative or not strong is creative or not strong.
If someone is either not tall or not strong then lucy is funny or not happy and vice versa.
Everyone who is quiet or not curious is either not funny or not quiet.
If john is not humble then paul is not humble and vice versa.
If paul is either wise or quiet then lucy is funny or not creative and vice versa.
Someone is tall.
Someone is generous.
Someone is not strong.
Someone is not curious or not patient.
Mary is either not calm or tall.
Someone is curious or generous.
Fred is both not strong and not calm.
Someone is either tall or not curious. | Mary is not brave. | contradiction | (![X]:((happy(X)<~>~funny(X))<=>(~quiet(X)<~>~strong(X))))&
(![X]:((~rich(X)|strong(X))=>(~creative(X)|calm(X))))&
(![X]:(rich(X)=>(kind(X)<~>old(X))))&
(((kind(paul)|~curious(paul)))<=>(?[X]:((happy(X)|tall(X)))))&
(((~curious(john)&curious(john)))<=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((humble(X)|~happy(X))=>(patient(X)<~>~patient(X))))&
((?[X]:((calm(X)&wise(X))))<=>((~brave(fred)|~old(fred))))&
((?[X]:((patient(X)&~rich(X))))<=>(?[X]:((~brave(X)|~rich(X)))))&
((~brave(fred))=>(?[X]:(~patient(X))))&
((~patient(john))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((~kind(X)|kind(X))<=>(brave(X)&~creative(X))))&
(![X]:((creative(X)<~>~strong(X))=>(creative(X)|~strong(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((funny(lucy)|~happy(lucy))))&
(![X]:((quiet(X)|~curious(X))=>(~funny(X)<~>~quiet(X))))&
((~humble(john))<=>(~humble(paul)))&
(((wise(paul)<~>quiet(paul)))<=>((funny(lucy)|~creative(lucy))))&
(?[X]:(tall(X)))&
(?[X]:(generous(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~curious(X)|~patient(X))))&
((~calm(mary)<~>tall(mary)))&
(?[X]:((curious(X)|generous(X))))&
((~strong(fred)&~calm(fred)))&
(?[X]:((tall(X)<~>~curious(X)))) | ~brave(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7397318814152064309822061
% SZS output start Proof for 7397318814152064309822061
11. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~creative(X0) & brave(X0))) [input p10]
25. ~brave(mary) [input hypothesis]
66. ! [X0] : (((kind(X0) | ~kind(X0)) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 11]
67. ! [X0] : ((kind(X0) | ~kind(X0) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | (~kind(X0) & kind(X0)))) [flattening 66]
125. brave(X0) | kind(X0) [cnf transformation 67]
126. brave(X0) | ~kind(X0) [cnf transformation 67]
159. ~brave(mary) [cnf transformation 25]
231. 16 <=> ! [X1] : brave(X1) [avatar definition]
232. brave(X1) <- (16) [avatar component clause 231]
272. brave(X0) [subsumption resolution 125,126]
273. 16 [avatar split clause 272,231]
355. $false <- (16) [resolution 232,159]
356. ~16 [avatar contradiction clause 355]
357. $false [avatar sat refutation 273,356]
% SZS output end Proof for 7397318814152064309822061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either not kind or generous and vice versa.
If someone is either not generous or not tall then susan is curious and vice versa.
Everyone who is old or not happy is both not creative and not wise.
If someone is not kind then someone is not old or quiet.
Everyone who is not tall is both not happy and patient.
If someone is tall then lucy is quiet.
Everyone who is not generous or quiet is both not happy and tall and vice versa.
If someone is not creative then someone is not humble or not wise.
Everyone who is not humble or not brave is not old or rich and vice versa.
Everyone who is not rich is not humble and vice versa.
Everyone who is patient is both not old and creative.
If someone is creative or patient then susan is not patient or generous.
Everyone who is calm is wise and vice versa.
Everyone who is tall or not funny is either funny or tall.
If lucy is both curious and strong then someone is either patient or not tall and vice versa.
Everyone who is both quiet and not creative is both not curious and not calm.
Fred is either kind or not creative.
Someone is rich or not wise.
Someone is either not old or not kind.
Paul is quiet.
Mary is both curious and not old.
Someone is both tall and quiet.
Someone is either not creative or humble. | Susan is not generous. | entailment | (![X]:(~kind(X)<=>(~kind(X)<~>generous(X))))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(curious(susan)))&
(![X]:((old(X)|~happy(X))=>(~creative(X)&~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:(~tall(X)=>(~happy(X)&patient(X))))&
((?[X]:(tall(X)))=>(quiet(lucy)))&
(![X]:((~generous(X)|quiet(X))<=>(~happy(X)&tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:(patient(X)=>(~old(X)&creative(X))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(((curious(lucy)&strong(lucy)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((quiet(X)&~creative(X))=>(~curious(X)&~calm(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(quiet(paul))&
((curious(mary)&~old(mary)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~creative(X)<~>humble(X)))) | ~generous(susan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 711810395703751258662642
% SZS output start Proof for 711810395703751258662642
1. ! [X0] : (~kind(X0) <=> (~kind(X0) <~> generous(X0))) [input p0]
24. generous(susan) [input hypothesis]
43. ! [X0] : ((~kind(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | kind(X0))) [nnf transformation 1]
72. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 43]
74. ~kind(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 43]
122. generous(susan) [cnf transformation 24]
125. ~generous(X0) | kind(X0) [duplicate literal removal 72]
126. ~kind(X0) | ~generous(X0) [duplicate literal removal 74]
127. ~generous(X0) [subsumption resolution 125,126]
225. $false [subsumption resolution 122,127]
% SZS output end Proof for 711810395703751258662642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or quiet then paul is humble or creative and vice versa.
If someone is not brave or humble then someone is either not creative or not quiet.
Everyone who is not happy is not tall and vice versa.
If lucy is either not funny or rich then john is either patient or not tall and vice versa.
Everyone who is not curious or not kind is either tall or quiet.
If alice is old or not strong then someone is not patient or old and vice versa.
Everyone who is wise or brave is either not happy or brave.
Everyone who is not patient or creative is both not rich and not strong.
If someone is rich or not humble then someone is both not kind and rich and vice versa.
If susan is both not strong and generous then lucy is both quiet and not calm and vice versa.
If mary is not old then someone is either not strong or wise.
If susan is either generous or not strong then lucy is not tall or brave.
If paul is not humble then lucy is not old or old and vice versa.
Everyone who is either not happy or wise is both not rich and not funny and vice versa.
Everyone who is humble or brave is both curious and wise.
Everyone who is wise or not kind is not humble or wise.
Paul is both not creative and not rich.
Paul is either not creative or curious.
Someone is either not calm or curious.
John is strong.
Mary is either not brave or not strong.
Someone is not generous or strong.
Someone is not kind or old.
Susan is either not kind or old. | Lucy is not calm. | contradiction | ((?[X]:((~calm(X)|quiet(X))))<=>((humble(paul)|creative(paul))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:(~happy(X)<=>~tall(X)))&
(((~funny(lucy)<~>rich(lucy)))<=>((patient(john)<~>~tall(john))))&
(![X]:((~curious(X)|~kind(X))=>(tall(X)<~>quiet(X))))&
(((old(alice)|~strong(alice)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((wise(X)|brave(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~patient(X)|creative(X))=>(~rich(X)&~strong(X))))&
((?[X]:((rich(X)|~humble(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
(((~strong(susan)&generous(susan)))<=>((quiet(lucy)&~calm(lucy))))&
((~old(mary))=>(?[X]:((~strong(X)<~>wise(X)))))&
(((generous(susan)<~>~strong(susan)))=>((~tall(lucy)|brave(lucy))))&
((~humble(paul))<=>((~old(lucy)|old(lucy))))&
(![X]:((~happy(X)<~>wise(X))<=>(~rich(X)&~funny(X))))&
(![X]:((humble(X)|brave(X))=>(curious(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>(~humble(X)|wise(X))))&
((~creative(paul)&~rich(paul)))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((~calm(X)<~>curious(X))))&
(strong(john))&
((~brave(mary)<~>~strong(mary)))&
(?[X]:((~generous(X)|strong(X))))&
(?[X]:((~kind(X)|old(X))))&
((~kind(susan)<~>old(susan))) | ~calm(lucy) | [
"p0",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1552930841378676885826277
% SZS output start Proof for 1552930841378676885826277
1. ? [X0] : (quiet(X0) | ~calm(X0)) <=> (creative(paul) | humble(paul)) [input p0]
13. ~humble(paul) <=> (old(lucy) | ~old(lucy)) [input p12]
17. ~rich(paul) & ~creative(paul) [input p16]
25. ~calm(lucy) [input hypothesis]
38. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & ((creative(paul) | humble(paul)) | ! [X0] : (~quiet(X0) & calm(X0))) [nnf transformation 1]
39. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X0] : (~quiet(X0) & calm(X0))) [flattening 38]
40. (? [X0] : (quiet(X0) | ~calm(X0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X1] : (~quiet(X1) & calm(X1))) [rectify 39]
41. ? [X0] : (quiet(X0) | ~calm(X0)) => (quiet(sK0) | ~calm(sK0)) [choice axiom]
42. ((quiet(sK0) | ~calm(sK0)) | (~creative(paul) & ~humble(paul))) & (creative(paul) | humble(paul) | ! [X1] : (~quiet(X1) & calm(X1))) [skolemisation 40,41]
67. (~humble(paul) | (~old(lucy) & old(lucy))) & ((old(lucy) | ~old(lucy)) | humble(paul)) [nnf transformation 13]
68. (~humble(paul) | (~old(lucy) & old(lucy))) & (old(lucy) | ~old(lucy) | humble(paul)) [flattening 67]
81. creative(paul) | humble(paul) | calm(X1) [cnf transformation 42]
129. ~humble(paul) | old(lucy) [cnf transformation 68]
130. ~humble(paul) | ~old(lucy) [cnf transformation 68]
143. ~creative(paul) [cnf transformation 17]
156. ~calm(lucy) [cnf transformation 25]
159. 1 <=> creative(paul) [avatar definition]
172. 4 <=> humble(paul) [avatar definition]
181. 6 <=> ! [X1] : calm(X1) [avatar definition]
182. calm(X1) <- (6) [avatar component clause 181]
183. 6 | 4 | 1 [avatar split clause 81,159,172,181]
287. 29 <=> calm(lucy) [avatar definition]
288. ~calm(lucy) <- (~29) [avatar component clause 287]
327. 37 <=> old(lucy) [avatar definition]
330. ~37 | ~4 [avatar split clause 130,172,327]
331. 37 | ~4 [avatar split clause 129,172,327]
332. ~1 [avatar split clause 143,159]
387. ~29 [avatar split clause 156,287]
388. $false <- (6, ~29) [resolution 288,182]
389. ~6 | 29 [avatar contradiction clause 388]
390. $false [avatar sat refutation 183,330,331,332,387,389]
% SZS output end Proof for 1552930841378676885826277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is not creative. If someone is not happy then someone is not creative or not curious and vice versa. Everyone who is not generous or calm is kind. If lucy is either wise or creative then susan is brave and vice versa. Everyone who is both strong and curious is both not humble and not wise and vice versa. Everyone who is either kind or not wise is curious or not old and vice versa. If someone is not strong then someone is quiet. Everyone who is both not curious and quiet is not old and vice versa. Everyone who is both curious and calm is either not calm or not old and vice versa. Everyone who is either funny or not brave is either not quiet or not kind and vice versa. Everyone who is rich or humble is patient or not tall. Everyone who is both patient and humble is not happy. If someone is not tall or not brave then someone is either not tall or not funny. If someone is strong then someone is kind and vice versa. If fred is either tall or humble then alice is wise or not wise and vice versa. Everyone who is brave is both quiet and wise. Alice is not old or humble. John is happy or tall. Fred is tall. Someone is not rich. Someone is both not rich and quiet. Someone is either patient or wise. John is both creative and strong. Someone is either not humble or not calm. | Fred is kind. | entailment | ((?[X]:(~brave(X)))=>(?[X]:(~creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((~generous(X)|calm(X))=>kind(X)))&
(((wise(lucy)<~>creative(lucy)))<=>(brave(susan)))&
(![X]:((strong(X)&curious(X))<=>(~humble(X)&~wise(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(curious(X)|~old(X))))&
((?[X]:(~strong(X)))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&quiet(X))<=>~old(X)))&
(![X]:((curious(X)&calm(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((rich(X)|humble(X))=>(patient(X)|~tall(X))))&
(![X]:((patient(X)&humble(X))=>~happy(X)))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((?[X]:(strong(X)))<=>(?[X]:(kind(X))))&
(((tall(fred)<~>humble(fred)))<=>((wise(alice)|~wise(alice))))&
(![X]:(brave(X)=>(quiet(X)&wise(X))))&
((~old(alice)|humble(alice)))&
((happy(john)|tall(john)))&
(tall(fred))&
(?[X]:(~rich(X)))&
(?[X]:((~rich(X)&quiet(X))))&
(?[X]:((patient(X)<~>wise(X))))&
((creative(john)&strong(john)))&
(?[X]:((~humble(X)<~>~calm(X)))) | kind(fred) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4156718254493237022717744
% SZS output start Proof for 4156718254493237022717744
3. ! [X0] : ((calm(X0) | ~generous(X0)) => kind(X0)) [input p2]
5. ! [X0] : ((curious(X0) & strong(X0)) <=> (~wise(X0) & ~humble(X0))) [input p4]
6. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> (~old(X0) | curious(X0))) [input p5]
8. ! [X0] : ((quiet(X0) & ~curious(X0)) <=> ~old(X0)) [input p7]
9. ! [X0] : ((calm(X0) & curious(X0)) <=> (~calm(X0) <~> ~old(X0))) [input p8]
15. (tall(fred) <~> humble(fred)) <=> (~wise(alice) | wise(alice)) [input p14]
19. tall(fred) [input p18]
25. ~kind(fred) [input hypothesis]
34. ! [X0] : (calm(X0) => kind(X0)) [pure predicate removal 3]
36. ! [X0] : (kind(X0) | ~calm(X0)) [ennf transformation 34]
53. ! [X0] : (((curious(X0) & strong(X0)) | (wise(X0) | humble(X0))) & ((~wise(X0) & ~humble(X0)) | (~curious(X0) | ~strong(X0)))) [nnf transformation 5]
54. ! [X0] : (((curious(X0) & strong(X0)) | wise(X0) | humble(X0)) & ((~wise(X0) & ~humble(X0)) | ~curious(X0) | ~strong(X0))) [flattening 53]
55. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 6]
56. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [flattening 55]
60. ! [X0] : (((quiet(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | (~quiet(X0) | curious(X0)))) [nnf transformation 8]
61. ! [X0] : (((quiet(X0) & ~curious(X0)) | old(X0)) & (~old(X0) | ~quiet(X0) | curious(X0))) [flattening 60]
62. ! [X0] : (((calm(X0) & curious(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (~calm(X0) | ~curious(X0)))) [nnf transformation 9]
63. ! [X0] : (((calm(X0) & curious(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~calm(X0) | ~curious(X0))) [flattening 62]
74. (((~humble(fred) | ~tall(fred)) & (humble(fred) | tall(fred))) | (wise(alice) & ~wise(alice))) & ((~wise(alice) | wise(alice)) | ((tall(fred) | ~humble(fred)) & (humble(fred) | ~tall(fred)))) [nnf transformation 15]
75. (((~humble(fred) | ~tall(fred)) & (humble(fred) | tall(fred))) | (wise(alice) & ~wise(alice))) & (~wise(alice) | wise(alice) | ((tall(fred) | ~humble(fred)) & (humble(fred) | ~tall(fred)))) [flattening 74]
88. ~calm(X0) | kind(X0) [cnf transformation 36]
96. humble(X0) | wise(X0) | curious(X0) [cnf transformation 54]
100. ~wise(X0) | kind(X0) | old(X0) [cnf transformation 56]
105. ~curious(X0) | old(X0) [cnf transformation 61]
111. calm(X0) | ~old(X0) | calm(X0) [cnf transformation 63]
133. ~humble(fred) | ~tall(fred) | ~wise(alice) [cnf transformation 75]
134. ~humble(fred) | ~tall(fred) | wise(alice) [cnf transformation 75]
139. tall(fred) [cnf transformation 19]
147. ~kind(fred) [cnf transformation 25]
149. ~old(X0) | calm(X0) [duplicate literal removal 111]
240. 21 <=> wise(alice) [avatar definition]
244. 22 <=> tall(fred) [avatar definition]
248. 23 <=> humble(fred) [avatar definition]
250. ~humble(fred) <- (~23) [avatar component clause 248]
251. 21 | ~22 | ~23 [avatar split clause 134,248,244,240]
252. ~21 | ~22 | ~23 [avatar split clause 133,248,244,240]
273. 22 [avatar split clause 139,244]
337. 39 <=> wise(fred) [avatar definition]
339. wise(fred) <- (39) [avatar component clause 337]
341. wise(fred) | curious(fred) <- (~23) [resolution 96,250]
344. 40 <=> curious(fred) [avatar definition]
346. curious(fred) <- (40) [avatar component clause 344]
347. 40 | 39 | 23 [avatar split clause 341,248,337,344]
352. kind(fred) | old(fred) <- (39) [resolution 100,339]
353. old(fred) <- (39) [subsumption resolution 352,147]
478. calm(fred) <- (39) [resolution 353,149]
540. kind(fred) <- (39) [resolution 478,88]
541. $false <- (39) [subsumption resolution 540,147]
542. ~39 [avatar contradiction clause 541]
544. old(fred) <- (40) [resolution 346,105]
547. calm(fred) <- (40) [resolution 544,149]
588. kind(fred) <- (40) [resolution 547,88]
591. $false <- (40) [subsumption resolution 588,147]
592. ~40 [avatar contradiction clause 591]
593. $false [avatar sat refutation 251,252,273,347,542,592]
% SZS output end Proof for 4156718254493237022717744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is humble then paul is either not creative or brave and vice versa.
Everyone who is not creative is not curious and vice versa.
If alice is humble or not quiet then someone is kind.
Everyone who is patient or strong is either rich or funny.
Everyone who is both happy and not happy is not generous or tall.
Everyone who is not patient or patient is both not rich and not kind.
If fred is both old and wise then someone is kind.
If paul is happy then someone is either patient or not humble.
If someone is either quiet or not curious then mary is both wise and not rich and vice versa.
Everyone who is either old or kind is either not old or old.
If someone is brave or not quiet then fred is both not kind and creative.
Everyone who is not calm is not kind or not tall and vice versa.
If someone is quiet then someone is both not brave and not tall.
If mary is not calm or happy then lucy is old and vice versa.
If fred is humble then paul is either not strong or calm and vice versa.
Everyone who is not curious or calm is both humble and kind and vice versa.
Someone is not patient or calm.
Alice is both not humble and brave.
Someone is both not generous and old.
Someone is not tall.
Someone is either old or not rich. | Paul is not calm. | entailment | ((humble(john))<=>((~creative(paul)<~>brave(paul))))&
(![X]:(~creative(X)<=>~curious(X)))&
(((humble(alice)|~quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:((patient(X)|strong(X))=>(rich(X)<~>funny(X))))&
(![X]:((happy(X)&~happy(X))=>(~generous(X)|tall(X))))&
(![X]:((~patient(X)|patient(X))=>(~rich(X)&~kind(X))))&
(((old(fred)&wise(fred)))=>(?[X]:(kind(X))))&
((happy(paul))=>(?[X]:((patient(X)<~>~humble(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>((wise(mary)&~rich(mary))))&
(![X]:((old(X)<~>kind(X))=>(~old(X)<~>old(X))))&
((?[X]:((brave(X)|~quiet(X))))=>((~kind(fred)&creative(fred))))&
(![X]:(~calm(X)<=>(~kind(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(((~calm(mary)|happy(mary)))<=>(old(lucy)))&
((humble(fred))<=>((~strong(paul)<~>calm(paul))))&
(![X]:((~curious(X)|calm(X))<=>(humble(X)&kind(X))))&
(?[X]:((~patient(X)|calm(X))))&
((~humble(alice)&brave(alice)))&
(?[X]:((~generous(X)&old(X))))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)<~>~rich(X)))) | ~calm(paul) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2843432227567055914367975
% SZS output start Proof for 2843432227567055914367975
6. ! [X0] : ((patient(X0) | ~patient(X0)) => (~kind(X0) & ~rich(X0))) [input p5]
12. ! [X0] : (~calm(X0) <=> (~tall(X0) | ~kind(X0))) [input p11]
22. calm(paul) [input hypothesis]
28. ! [X0] : ((~kind(X0) & ~rich(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 6]
51. ! [X0] : ((~calm(X0) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | calm(X0))) [nnf transformation 12]
52. ! [X0] : ((~calm(X0) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | calm(X0))) [flattening 51]
84. ~kind(X0) | patient(X0) [cnf transformation 28]
85. ~kind(X0) | ~patient(X0) [cnf transformation 28]
104. ~calm(X0) | kind(X0) [cnf transformation 52]
127. calm(paul) [cnf transformation 22]
162. ~kind(X0) [subsumption resolution 84,85]
224. ~calm(X0) [subsumption resolution 104,162]
265. $false [subsumption resolution 127,224]
% SZS output end Proof for 2843432227567055914367975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is curious or funny then lucy is either not tall or not strong and vice versa. If mary is not calm or quiet then someone is not humble and vice versa. Everyone who is not quiet is not rich. Everyone who is either quiet or not calm is both not strong and not quiet and vice versa. Everyone who is wise or calm is not funny and vice versa. If someone is both humble and not patient then john is both quiet and creative and vice versa. If someone is not brave or not patient then alice is rich or humble. If mary is both humble and not patient then lucy is old or not tall and vice versa. If lucy is both not quiet and not creative then paul is either calm or brave and vice versa. Everyone who is both curious and not strong is either not wise or curious. Everyone who is either not calm or not generous is not brave or not rich and vice versa. If lucy is not old then someone is not kind and vice versa. Everyone who is either happy or not humble is not happy and vice versa. Everyone who is humble or rich is either calm or brave and vice versa. Everyone who is not humble or tall is either not brave or quiet. If someone is both tall and patient then someone is not happy. Someone is not old. Fred is either generous or patient. Alice is not funny or not humble. Lucy is not brave. Susan is curious. Someone is both rich and quiet. Susan is not quiet. | Fred is not calm. | entailment | (((curious(alice)|funny(alice)))<=>((~tall(lucy)<~>~strong(lucy))))&
(((~calm(mary)|quiet(mary)))<=>(?[X]:(~humble(X))))&
(![X]:(~quiet(X)=>~rich(X)))&
(![X]:((quiet(X)<~>~calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((wise(X)|calm(X))<=>~funny(X)))&
((?[X]:((humble(X)&~patient(X))))<=>((quiet(john)&creative(john))))&
((?[X]:((~brave(X)|~patient(X))))=>((rich(alice)|humble(alice))))&
(((humble(mary)&~patient(mary)))<=>((old(lucy)|~tall(lucy))))&
(((~quiet(lucy)&~creative(lucy)))<=>((calm(paul)<~>brave(paul))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
((~old(lucy))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~happy(X)))&
(![X]:((humble(X)|rich(X))<=>(calm(X)<~>brave(X))))&
(![X]:((~humble(X)|tall(X))=>(~brave(X)<~>quiet(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~happy(X))))&
(?[X]:(~old(X)))&
((generous(fred)<~>patient(fred)))&
((~funny(alice)|~humble(alice)))&
(~brave(lucy))&
(curious(susan))&
(?[X]:((rich(X)&quiet(X))))&
(~quiet(susan)) | ~calm(fred) | [
"p2",
"p3",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6296647610793334147522900
% SZS output start Proof for 6296647610793334147522900
3. ! [X0] : (~quiet(X0) => ~rich(X0)) [input p2]
4. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (~quiet(X0) & ~strong(X0))) [input p3]
13. ! [X0] : ((happy(X0) <~> ~humble(X0)) <=> ~happy(X0)) [input p12]
14. ! [X0] : ((rich(X0) | humble(X0)) <=> (calm(X0) <~> brave(X0))) [input p13]
15. ! [X0] : ((tall(X0) | ~humble(X0)) => (~brave(X0) <~> quiet(X0))) [input p14]
24. calm(fred) [input hypothesis]
26. ! [X0] : (~rich(X0) | quiet(X0)) [ennf transformation 3]
31. ! [X0] : ((~brave(X0) <~> quiet(X0)) | (~tall(X0) & humble(X0))) [ennf transformation 15]
40. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 4]
41. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 40]
60. ! [X0] : ((((humble(X0) | ~happy(X0)) & (~humble(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0))))) [nnf transformation 13]
61. ! [X0] : (((rich(X0) | humble(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~rich(X0) & ~humble(X0)))) [nnf transformation 14]
62. ! [X0] : ((rich(X0) | humble(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~rich(X0) & ~humble(X0)))) [flattening 61]
63. ! [X0] : (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | (~tall(X0) & humble(X0))) [nnf transformation 31]
81. ~rich(X0) | quiet(X0) [cnf transformation 26]
84. ~quiet(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 41]
118. ~happy(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 60]
120. ~humble(X0) | happy(X0) | happy(X0) [cnf transformation 60]
126. rich(X0) | humble(X0) | brave(X0) | ~calm(X0) [cnf transformation 62]
128. quiet(X0) | ~brave(X0) | humble(X0) [cnf transformation 63]
142. calm(fred) [cnf transformation 24]
143. ~happy(X0) | ~humble(X0) [duplicate literal removal 118]
144. ~humble(X0) | happy(X0) [duplicate literal removal 120]
146. ~quiet(X0) | ~calm(X0) [duplicate literal removal 84]
275. ~humble(X0) [subsumption resolution 143,144]
277. ~calm(X0) | brave(X0) | rich(X0) [subsumption resolution 126,275]
279. ~brave(X0) | quiet(X0) [subsumption resolution 128,275]
375. 36 <=> quiet(fred) [avatar definition]
376. ~quiet(fred) <- (~36) [avatar component clause 375]
377. quiet(fred) <- (36) [avatar component clause 375]
391. ~calm(fred) <- (36) [resolution 377,146]
397. 38 <=> brave(fred) [avatar definition]
399. brave(fred) <- (38) [avatar component clause 397]
402. $false <- (36) [subsumption resolution 391,142]
403. ~36 [avatar contradiction clause 402]
404. brave(fred) | rich(fred) [resolution 277,142]
406. 39 <=> rich(fred) [avatar definition]
408. rich(fred) <- (39) [avatar component clause 406]
409. 39 | 38 [avatar split clause 404,397,406]
422. quiet(fred) <- (39) [resolution 408,81]
423. $false <- (~36, 39) [subsumption resolution 422,376]
424. 36 | ~39 [avatar contradiction clause 423]
443. quiet(fred) <- (38) [resolution 399,279]
446. $false <- (~36, 38) [subsumption resolution 443,376]
447. 36 | ~38 [avatar contradiction clause 446]
448. $false [avatar sat refutation 403,409,424,447]
% SZS output end Proof for 6296647610793334147522900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind or not strong then someone is wise or not humble.
If someone is both strong and not wise then someone is either not wise or old.
Everyone who is curious is either not patient or kind.
Everyone who is either happy or not generous is either not creative or wise.
If someone is brave then someone is calm or generous and vice versa.
Everyone who is either not tall or funny is both old and not quiet.
If someone is either not old or not patient then mary is not funny and vice versa.
If someone is both wise and tall then susan is happy and vice versa.
If someone is not strong or rich then lucy is either calm or not tall and vice versa.
Everyone who is kind or creative is not quiet.
Everyone who is either strong or quiet is patient and vice versa.
Everyone who is either rich or not generous is both brave and not funny.
Everyone who is not quiet is both old and not tall.
Everyone who is patient is funny and vice versa.
If john is either not curious or funny then lucy is not funny.
If alice is either humble or not calm then john is both old and not brave.
Someone is either not generous or brave.
Someone is patient or brave.
Mary is both humble and brave.
Someone is humble or tall.
Susan is curious.
Someone is both not brave and old.
Susan is both funny and humble. | Lucy is not kind. | neutral | (((~kind(mary)|~strong(mary)))=>(?[X]:((wise(X)|~humble(X)))))&
((?[X]:((strong(X)&~wise(X))))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(curious(X)=>(~patient(X)<~>kind(X))))&
(![X]:((happy(X)<~>~generous(X))=>(~creative(X)<~>wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~tall(X)<~>funny(X))=>(old(X)&~quiet(X))))&
((?[X]:((~old(X)<~>~patient(X))))<=>(~funny(mary)))&
((?[X]:((wise(X)&tall(X))))<=>(happy(susan)))&
((?[X]:((~strong(X)|rich(X))))<=>((calm(lucy)<~>~tall(lucy))))&
(![X]:((kind(X)|creative(X))=>~quiet(X)))&
(![X]:((strong(X)<~>quiet(X))<=>patient(X)))&
(![X]:((rich(X)<~>~generous(X))=>(brave(X)&~funny(X))))&
(![X]:(~quiet(X)=>(old(X)&~tall(X))))&
(![X]:(patient(X)<=>funny(X)))&
(((~curious(john)<~>funny(john)))=>(~funny(lucy)))&
(((humble(alice)<~>~calm(alice)))=>((old(john)&~brave(john))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((patient(X)|brave(X))))&
((humble(mary)&brave(mary)))&
(?[X]:((humble(X)|tall(X))))&
(curious(susan))&
(?[X]:((~brave(X)&old(X))))&
((funny(susan)&humble(susan))) | ~kind(lucy) | [] | null | 0 |
Everyone who is not creative or not wise is both curious and quiet and vice versa.
Everyone who is both not brave and not generous is not rich or wise.
Everyone who is both patient and brave is not creative or not quiet.
If someone is either not wise or humble then alice is not creative and vice versa.
If someone is curious then mary is both creative and not tall.
Everyone who is quiet is both happy and curious.
If someone is both not funny and curious then someone is both patient and creative and vice versa.
If susan is either not happy or tall then mary is brave.
Everyone who is quiet is happy or humble.
If someone is not happy or not curious then mary is not patient or strong.
If someone is both not humble and not brave then john is not wise and vice versa.
Everyone who is both quiet and tall is not humble or not brave and vice versa.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Everyone who is either not brave or generous is both not old and rich and vice versa.
Lucy is not wise.
Someone is either happy or strong.
Someone is either kind or not strong.
Someone is not old.
Paul is not old.
Someone is not tall or wise.
Fred is old or not humble. | Alice is not curious. | contradiction | (![X]:((~creative(X)|~wise(X))<=>(curious(X)&quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((patient(X)&brave(X))=>(~creative(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(~creative(alice)))&
((?[X]:(curious(X)))=>((creative(mary)&~tall(mary))))&
(![X]:(quiet(X)=>(happy(X)&curious(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(((~happy(susan)<~>tall(susan)))=>(brave(mary)))&
(![X]:(quiet(X)=>(happy(X)|humble(X))))&
((?[X]:((~happy(X)|~curious(X))))=>((~patient(mary)|strong(mary))))&
((?[X]:((~humble(X)&~brave(X))))<=>(~wise(john)))&
(![X]:((quiet(X)&tall(X))<=>(~humble(X)|~brave(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
(~wise(lucy))&
(?[X]:((happy(X)<~>strong(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:(~old(X)))&
(~old(paul))&
(?[X]:((~tall(X)|wise(X))))&
((old(fred)|~humble(fred))) | ~curious(alice) | [
"p0",
"p3",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6749535440912875061337987
% SZS output start Proof for 6749535440912875061337987
1. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> (quiet(X0) & curious(X0))) [input p0]
4. ? [X0] : (~wise(X0) <~> humble(X0)) <=> ~creative(alice) [input p3]
6. ! [X0] : (quiet(X0) => (curious(X0) & happy(X0))) [input p5]
12. ! [X0] : ((tall(X0) & quiet(X0)) <=> (~brave(X0) | ~humble(X0))) [input p11]
24. ~curious(alice) [input hypothesis]
31. ! [X0] : ((curious(X0) & happy(X0)) | ~quiet(X0)) [ennf transformation 6]
37. ! [X0] : (((~wise(X0) | ~creative(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((~wise(X0) | ~creative(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [flattening 37]
39. (? [X0] : ((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | creative(alice)) & (~creative(alice) | ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) [nnf transformation 4]
40. (? [X0] : ((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | creative(alice)) & (~creative(alice) | ! [X1] : ((~wise(X1) | ~humble(X1)) & (humble(X1) | wise(X1)))) [rectify 39]
41. ? [X0] : ((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) => ((~humble(sK0) | wise(sK0)) & (humble(sK0) | ~wise(sK0))) [choice axiom]
42. (((~humble(sK0) | wise(sK0)) & (humble(sK0) | ~wise(sK0))) | creative(alice)) & (~creative(alice) | ! [X1] : ((~wise(X1) | ~humble(X1)) & (humble(X1) | wise(X1)))) [skolemisation 40,41]
53. ! [X0] : (((tall(X0) & quiet(X0)) | (brave(X0) & humble(X0))) & ((~brave(X0) | ~humble(X0)) | (~tall(X0) | ~quiet(X0)))) [nnf transformation 12]
54. ! [X0] : (((tall(X0) & quiet(X0)) | (brave(X0) & humble(X0))) & (~brave(X0) | ~humble(X0) | ~tall(X0) | ~quiet(X0))) [flattening 53]
76. curious(X0) | creative(X0) [cnf transformation 38]
79. quiet(X0) | wise(X0) [cnf transformation 38]
84. ~creative(alice) | ~wise(X1) | ~humble(X1) [cnf transformation 42]
90. ~quiet(X0) | curious(X0) [cnf transformation 31]
104. humble(X0) | quiet(X0) [cnf transformation 54]
135. ~curious(alice) [cnf transformation 24]
137. 1 <=> creative(alice) [avatar definition]
151. 4 <=> ! [X1] : (~wise(X1) | ~humble(X1)) [avatar definition]
152. ~humble(X1) | ~wise(X1) <- (4) [avatar component clause 151]
153. 4 | ~1 [avatar split clause 84,137,151]
212. 18 <=> ! [X0] : curious(X0) [avatar definition]
213. curious(X0) <- (18) [avatar component clause 212]
301. creative(alice) [resolution 76,135]
304. 1 [avatar split clause 301,137]
331. ~wise(X0) | quiet(X0) <- (4) [resolution 152,104]
332. quiet(X0) <- (4) [subsumption resolution 331,79]
345. curious(X0) <- (4) [resolution 332,90]
347. 18 | ~4 [avatar split clause 345,151,212]
349. $false <- (18) [resolution 213,135]
351. ~18 [avatar contradiction clause 349]
352. $false [avatar sat refutation 153,304,347,351]
% SZS output end Proof for 6749535440912875061337987
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not calm is both strong and not quiet. Everyone who is both not old and not happy is both not strong and generous and vice versa. Everyone who is old is not old. Everyone who is both quiet and brave is either rich or creative. Everyone who is either kind or funny is both kind and not strong. If john is strong then mary is tall. Everyone who is either not calm or strong is either funny or not tall. Everyone who is not tall is both funny and humble. Everyone who is both happy and not strong is both strong and curious and vice versa. Everyone who is not curious or not strong is both not kind and strong. Everyone who is old or not kind is humble or calm and vice versa. If lucy is either not humble or not generous then mary is both not humble and humble and vice versa. If paul is either not quiet or patient then fred is both not rich and not wise and vice versa. Someone is kind or strong. Susan is both brave and not quiet. Paul is either patient or not wise. Fred is kind or not calm. Fred is either not quiet or not tall. Mary is not wise or not strong. Someone is either not calm or creative. Fred is both not kind and not generous. | John is tall. | entailment | (![X]:((patient(X)|~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&generous(X))))&
(![X]:(old(X)=>~old(X)))&
(![X]:((quiet(X)&brave(X))=>(rich(X)<~>creative(X))))&
(![X]:((kind(X)<~>funny(X))=>(kind(X)&~strong(X))))&
((strong(john))=>(tall(mary)))&
(![X]:((~calm(X)<~>strong(X))=>(funny(X)<~>~tall(X))))&
(![X]:(~tall(X)=>(funny(X)&humble(X))))&
(![X]:((happy(X)&~strong(X))<=>(strong(X)&curious(X))))&
(![X]:((~curious(X)|~strong(X))=>(~kind(X)&strong(X))))&
(![X]:((old(X)|~kind(X))<=>(humble(X)|calm(X))))&
(((~humble(lucy)<~>~generous(lucy)))<=>((~humble(mary)&humble(mary))))&
(((~quiet(paul)<~>patient(paul)))<=>((~rich(fred)&~wise(fred))))&
(?[X]:((kind(X)|strong(X))))&
((brave(susan)&~quiet(susan)))&
((patient(paul)<~>~wise(paul)))&
((kind(fred)|~calm(fred)))&
((~quiet(fred)<~>~tall(fred)))&
((~wise(mary)|~strong(mary)))&
(?[X]:((~calm(X)<~>creative(X))))&
((~kind(fred)&~generous(fred))) | tall(john) | [
"p4",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5396793304193384116699704
% SZS output start Proof for 5396793304193384116699704
5. ! [X0] : ((kind(X0) <~> funny(X0)) => (~strong(X0) & kind(X0))) [input p4]
8. ! [X0] : (~tall(X0) => (humble(X0) & funny(X0))) [input p7]
9. ! [X0] : ((~strong(X0) & happy(X0)) <=> (curious(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~strong(X0) | ~curious(X0)) => (strong(X0) & ~kind(X0))) [input p9]
22. ~tall(john) [input hypothesis]
27. ! [X0] : ((~strong(X0) & kind(X0)) | (kind(X0) <=> funny(X0))) [ennf transformation 5]
30. ! [X0] : ((humble(X0) & funny(X0)) | tall(X0)) [ennf transformation 8]
31. ! [X0] : ((strong(X0) & ~kind(X0)) | (strong(X0) & curious(X0))) [ennf transformation 10]
35. ! [X0] : ((~strong(X0) & kind(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) [nnf transformation 27]
37. ! [X0] : (((~strong(X0) & happy(X0)) | (~curious(X0) | ~strong(X0))) & ((curious(X0) & strong(X0)) | (strong(X0) | ~happy(X0)))) [nnf transformation 9]
38. ! [X0] : (((~strong(X0) & happy(X0)) | ~curious(X0) | ~strong(X0)) & ((curious(X0) & strong(X0)) | strong(X0) | ~happy(X0))) [flattening 37]
64. kind(X0) | kind(X0) | ~funny(X0) [cnf transformation 35]
72. tall(X0) | funny(X0) [cnf transformation 30]
77. ~strong(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 38]
78. ~kind(X0) | curious(X0) [cnf transformation 31]
81. strong(X0) | strong(X0) [cnf transformation 31]
111. ~tall(john) [cnf transformation 22]
112. strong(X0) [duplicate literal removal 81]
114. ~curious(X0) | ~strong(X0) [duplicate literal removal 77]
115. ~funny(X0) | kind(X0) [duplicate literal removal 64]
200. funny(john) [resolution 72,111]
202. kind(john) [resolution 115,200]
203. curious(john) [resolution 202,78]
205. ~strong(john) [resolution 203,114]
206. $false [subsumption resolution 205,112]
% SZS output end Proof for 5396793304193384116699704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not old then paul is either not funny or curious and vice versa. Everyone who is curious or not tall is either humble or wise. Everyone who is both not patient and not quiet is not quiet. Everyone who is both not creative and kind is both rich and not old. Everyone who is either not patient or quiet is both brave and curious and vice versa. Everyone who is curious is not brave or not generous. Everyone who is either not generous or curious is not wise or funny and vice versa. Everyone who is not brave is quiet or not curious. Everyone who is both creative and wise is both not humble and not calm and vice versa. Everyone who is kind or not calm is either strong or not strong and vice versa. If someone is both not tall and wise then someone is brave or not generous. If someone is calm or humble then someone is not old. Everyone who is happy is not quiet. Everyone who is either calm or curious is not tall and vice versa. Everyone who is happy is both not rich and not happy and vice versa. Everyone who is not humble or not rich is not patient and vice versa. Someone is both not brave and humble. Someone is either curious or humble. Someone is either generous or not kind. Someone is either patient or tall. Someone is both generous and not kind. Susan is both patient and not generous. Paul is both creative and generous. Fred is curious or not creative. | Paul is generous. | entailment | ((?[X]:((~rich(X)|~old(X))))<=>((~funny(paul)<~>curious(paul))))&
(![X]:((curious(X)|~tall(X))=>(humble(X)<~>wise(X))))&
(![X]:((~patient(X)&~quiet(X))=>~quiet(X)))&
(![X]:((~creative(X)&kind(X))=>(rich(X)&~old(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(brave(X)&curious(X))))&
(![X]:(curious(X)=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)<~>curious(X))<=>(~wise(X)|funny(X))))&
(![X]:(~brave(X)=>(quiet(X)|~curious(X))))&
(![X]:((creative(X)&wise(X))<=>(~humble(X)&~calm(X))))&
(![X]:((kind(X)|~calm(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((~tall(X)&wise(X))))=>(?[X]:((brave(X)|~generous(X)))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:(~old(X))))&
(![X]:(happy(X)=>~quiet(X)))&
(![X]:((calm(X)<~>curious(X))<=>~tall(X)))&
(![X]:(happy(X)<=>(~rich(X)&~happy(X))))&
(![X]:((~humble(X)|~rich(X))<=>~patient(X)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
(?[X]:((patient(X)<~>tall(X))))&
(?[X]:((generous(X)&~kind(X))))&
((patient(susan)&~generous(susan)))&
((creative(paul)&generous(paul)))&
((curious(fred)|~creative(fred))) | generous(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8802347868827507521534076
% SZS output start Proof for 8802347868827507521534076
23. generous(paul) & creative(paul) [input p22]
25. ~generous(paul) [input hypothesis]
141. generous(paul) [cnf transformation 23]
143. ~generous(paul) [cnf transformation 25]
240. $false [subsumption resolution 143,141]
% SZS output end Proof for 8802347868827507521534076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then alice is not tall or creative.
Everyone who is either not generous or not strong is both generous and quiet and vice versa.
Everyone who is quiet is not kind and vice versa.
If someone is both not creative and happy then someone is either creative or not quiet.
Everyone who is not creative is both strong and not happy.
Everyone who is both happy and not brave is not funny and vice versa.
If someone is not funny or tall then fred is either strong or not rich.
Everyone who is old or creative is either not rich or curious.
Everyone who is either not generous or humble is not generous or calm.
If someone is not patient or strong then someone is old.
Everyone who is either happy or not rich is both not happy and old.
If someone is kind then alice is both generous and funny and vice versa.
Everyone who is tall or not wise is both not kind and patient and vice versa.
Everyone who is funny is both not quiet and not wise.
Everyone who is quiet is not generous and vice versa.
If someone is not funny then lucy is not patient.
Susan is kind or not kind.
Lucy is both not calm and creative.
Someone is both not generous and not tall.
Lucy is both not strong and humble.
Someone is not generous.
Susan is either generous or not curious. | Paul is not creative. | contradiction | ((humble(paul))=>((~tall(alice)|creative(alice))))&
(![X]:((~generous(X)<~>~strong(X))<=>(generous(X)&quiet(X))))&
(![X]:(quiet(X)<=>~kind(X)))&
((?[X]:((~creative(X)&happy(X))))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:(~creative(X)=>(strong(X)&~happy(X))))&
(![X]:((happy(X)&~brave(X))<=>~funny(X)))&
((?[X]:((~funny(X)|tall(X))))=>((strong(fred)<~>~rich(fred))))&
(![X]:((old(X)|creative(X))=>(~rich(X)<~>curious(X))))&
(![X]:((~generous(X)<~>humble(X))=>(~generous(X)|calm(X))))&
((?[X]:((~patient(X)|strong(X))))=>(?[X]:(old(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~happy(X)&old(X))))&
((?[X]:(kind(X)))<=>((generous(alice)&funny(alice))))&
(![X]:((tall(X)|~wise(X))<=>(~kind(X)&patient(X))))&
(![X]:(funny(X)=>(~quiet(X)&~wise(X))))&
(![X]:(quiet(X)<=>~generous(X)))&
((?[X]:(~funny(X)))=>(~patient(lucy)))&
((kind(susan)|~kind(susan)))&
((~calm(lucy)&creative(lucy)))&
(?[X]:((~generous(X)&~tall(X))))&
((~strong(lucy)&humble(lucy)))&
(?[X]:(~generous(X)))&
((generous(susan)<~>~curious(susan))) | ~creative(paul) | [
"p2",
"p4",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8822974989476731881634349
% SZS output start Proof for 8822974989476731881634349
3. ! [X0] : (quiet(X0) <=> ~kind(X0)) [input p2]
5. ! [X0] : (~creative(X0) => (~happy(X0) & strong(X0))) [input p4]
6. ! [X0] : ((~brave(X0) & happy(X0)) <=> ~funny(X0)) [input p5]
13. ! [X0] : ((~wise(X0) | tall(X0)) <=> (patient(X0) & ~kind(X0))) [input p12]
14. ! [X0] : (funny(X0) => (~wise(X0) & ~quiet(X0))) [input p13]
23. ~creative(paul) [input hypothesis]
29. ! [X0] : ((~happy(X0) & strong(X0)) | creative(X0)) [ennf transformation 5]
36. ! [X0] : ((~wise(X0) & ~quiet(X0)) | ~funny(X0)) [ennf transformation 14]
40. ! [X0] : ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))) [nnf transformation 3]
45. ! [X0] : (((~brave(X0) & happy(X0)) | funny(X0)) & (~funny(X0) | (brave(X0) | ~happy(X0)))) [nnf transformation 6]
46. ! [X0] : (((~brave(X0) & happy(X0)) | funny(X0)) & (~funny(X0) | brave(X0) | ~happy(X0))) [flattening 45]
59. ! [X0] : (((~wise(X0) | tall(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (wise(X0) & ~tall(X0)))) [nnf transformation 13]
60. ! [X0] : ((~wise(X0) | tall(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | (wise(X0) & ~tall(X0)))) [flattening 59]
75. kind(X0) | quiet(X0) [cnf transformation 40]
79. ~happy(X0) | creative(X0) [cnf transformation 29]
81. funny(X0) | happy(X0) [cnf transformation 46]
103. ~kind(X0) | wise(X0) [cnf transformation 60]
107. ~funny(X0) | ~quiet(X0) [cnf transformation 36]
108. ~wise(X0) | ~funny(X0) [cnf transformation 36]
122. ~creative(paul) [cnf transformation 23]
141. 4 <=> ! [X1] : (~happy(X1) | creative(X1)) [avatar definition]
142. ~happy(X1) | creative(X1) <- (4) [avatar component clause 141]
153. 4 [avatar split clause 79,141]
224. wise(X0) | quiet(X0) [resolution 103,75]
265. quiet(X0) | ~funny(X0) [resolution 224,108]
266. ~funny(X0) [subsumption resolution 265,107]
268. happy(X0) [resolution 266,81]
284. creative(X0) <- (4) [resolution 268,142]
289. $false <- (4) [resolution 284,122]
290. ~4 [avatar contradiction clause 289]
291. $false [avatar sat refutation 153,290]
% SZS output end Proof for 8822974989476731881634349
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is happy and vice versa. Everyone who is curious is calm. Everyone who is either curious or not brave is strong and vice versa. Everyone who is either not wise or not kind is both quiet and brave and vice versa. Everyone who is both curious and not creative is not funny or calm and vice versa. If fred is rich then someone is both not strong and kind. Everyone who is not brave or quiet is quiet and vice versa. If mary is not wise then someone is either not old or brave. Everyone who is not calm or not old is either not generous or calm and vice versa. If fred is calm or not kind then alice is old and vice versa. If someone is either generous or curious then someone is brave. Everyone who is not quiet or not funny is both strong and wise and vice versa. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. If alice is not funny or creative then someone is strong. Lucy is both brave and not kind. Susan is either not old or not happy. Someone is either humble or wise. Someone is not creative. Paul is not curious or not strong. John is both quiet and kind. | Paul is kind. | neutral | (![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(strong(X))))&
((brave(lucy)&~kind(lucy)))&
((~old(susan)<~>~happy(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
((~curious(paul)|~strong(paul)))&
((quiet(john)&kind(john))) | kind(paul) | [] | null | 0 |
If fred is old or patient then john is either creative or not creative. Everyone who is not old or creative is both not rich and not humble. Everyone who is old or not rich is both not curious and not wise and vice versa. Everyone who is rich is both rich and not happy. If john is either not patient or not kind then lucy is both not strong and not happy and vice versa. If susan is both not generous and generous then fred is both not strong and old and vice versa. If someone is either not strong or not kind then paul is happy. If someone is not calm or generous then mary is not rich or not funny. If someone is both old and not rich then alice is either not rich or brave. If john is either strong or not curious then someone is tall. Everyone who is both not kind and not creative is wise or kind and vice versa. Everyone who is either not wise or not quiet is not curious. If someone is not strong then someone is not kind or curious and vice versa. Everyone who is both not quiet and funny is both strong and not generous and vice versa. If paul is rich then lucy is either not strong or not quiet. Everyone who is either wise or not generous is either calm or not curious. Alice is either quiet or funny. Fred is either not patient or happy. Susan is funny or rich. Someone is either not strong or not calm. Someone is both not patient and old. Someone is either not kind or quiet. | Paul is kind. | contradiction | (((old(fred)|patient(fred)))=>((creative(john)<~>~creative(john))))&
(![X]:((~old(X)|creative(X))=>(~rich(X)&~humble(X))))&
(![X]:((old(X)|~rich(X))<=>(~curious(X)&~wise(X))))&
(![X]:(rich(X)=>(rich(X)&~happy(X))))&
(((~patient(john)<~>~kind(john)))<=>((~strong(lucy)&~happy(lucy))))&
(((~generous(susan)&generous(susan)))<=>((~strong(fred)&old(fred))))&
((?[X]:((~strong(X)<~>~kind(X))))=>(happy(paul)))&
((?[X]:((~calm(X)|generous(X))))=>((~rich(mary)|~funny(mary))))&
((?[X]:((old(X)&~rich(X))))=>((~rich(alice)<~>brave(alice))))&
(((strong(john)<~>~curious(john)))=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~creative(X))<=>(wise(X)|kind(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(strong(X)&~generous(X))))&
((rich(paul))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((wise(X)<~>~generous(X))=>(calm(X)<~>~curious(X))))&
((quiet(alice)<~>funny(alice)))&
((~patient(fred)<~>happy(fred)))&
((funny(susan)|rich(susan)))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~kind(X)<~>quiet(X)))) | kind(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1963526079285772406758902
% SZS output start Proof for 1963526079285772406758902
11. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (kind(X0) | wise(X0))) [input p10]
23. kind(paul) [input hypothesis]
46. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 11]
47. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | creative(X0) | kind(X0))) [flattening 46]
99. ~kind(X0) | ~kind(X0) [cnf transformation 47]
128. kind(paul) [cnf transformation 23]
130. ~kind(X0) [duplicate literal removal 99]
269. $false [subsumption resolution 128,130]
% SZS output end Proof for 1963526079285772406758902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or strong is either quiet or rich.
If paul is not kind then alice is both tall and not creative.
Everyone who is either not curious or not rich is either not kind or quiet and vice versa.
If alice is both patient and not kind then fred is both calm and patient and vice versa.
Everyone who is not happy is not creative or generous.
Everyone who is either tall or not generous is not rich and vice versa.
Everyone who is both quiet and not brave is either brave or not old and vice versa.
Everyone who is both brave and not wise is kind or not old and vice versa.
If someone is both not quiet and not creative then john is not tall.
Everyone who is either not funny or not wise is not quiet and vice versa.
If someone is not generous then alice is tall or not creative and vice versa.
Everyone who is both not patient and calm is quiet.
If lucy is either funny or not quiet then fred is quiet and vice versa.
If mary is generous then someone is either not calm or old and vice versa.
Everyone who is not tall is both strong and old.
Everyone who is curious is either not calm or generous and vice versa.
Mary is both brave and quiet.
Someone is wise or strong.
Alice is not brave or curious.
Mary is both curious and not wise.
Someone is tall.
Someone is either kind or quiet. | John is creative. | neutral | (![X]:((creative(X)<~>strong(X))=>(quiet(X)<~>rich(X))))&
((~kind(paul))=>((tall(alice)&~creative(alice))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~kind(X)<~>quiet(X))))&
(((patient(alice)&~kind(alice)))<=>((calm(fred)&patient(fred))))&
(![X]:(~happy(X)=>(~creative(X)|generous(X))))&
(![X]:((tall(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((quiet(X)&~brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:((brave(X)&~wise(X))<=>(kind(X)|~old(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(~tall(john)))&
(![X]:((~funny(X)<~>~wise(X))<=>~quiet(X)))&
((?[X]:(~generous(X)))<=>((tall(alice)|~creative(alice))))&
(![X]:((~patient(X)&calm(X))=>quiet(X)))&
(((funny(lucy)<~>~quiet(lucy)))<=>(quiet(fred)))&
((generous(mary))<=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~tall(X)=>(strong(X)&old(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>generous(X))))&
((brave(mary)&quiet(mary)))&
(?[X]:((wise(X)|strong(X))))&
((~brave(alice)|curious(alice)))&
((curious(mary)&~wise(mary)))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)<~>quiet(X)))) | creative(john) | [] | null | 0 |
Everyone who is not humble or brave is both not curious and not 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.
Everyone who is either not quiet or not curious is either not creative or not wise and vice versa.
If someone is either not wise or rich then someone is not creative or not calm.
Everyone who is not creative is calm.
Everyone who is either humble or quiet is both old and generous and vice versa.
If someone is not wise or not quiet then paul is humble.
If susan is both not curious and quiet then someone is curious or not tall.
If mary is either old or not rich then alice is not kind.
If john is both not wise and rich then lucy is not kind or not quiet.
Everyone who is either quiet or patient is not creative or kind and vice versa.
Someone is brave.
Someone is kind or calm.
Someone is either not tall or brave.
Fred is either not strong or kind.
Fred is happy.
Alice is either calm or brave.
Someone is kind or creative.
John is both not wise and not funny. | John is not humble. | contradiction | (![X]:((~humble(X)|brave(X))<=>(~curious(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))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>rich(X))))=>(?[X]:((~creative(X)|~calm(X)))))&
(![X]:(~creative(X)=>calm(X)))&
(![X]:((humble(X)<~>quiet(X))<=>(old(X)&generous(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(humble(paul)))&
(((~curious(susan)&quiet(susan)))=>(?[X]:((curious(X)|~tall(X)))))&
(((old(mary)<~>~rich(mary)))=>(~kind(alice)))&
(((~wise(john)&rich(john)))=>((~kind(lucy)|~quiet(lucy))))&
(![X]:((quiet(X)<~>patient(X))<=>(~creative(X)|kind(X))))&
(?[X]:(brave(X)))&
(?[X]:((kind(X)|calm(X))))&
(?[X]:((~tall(X)<~>brave(X))))&
((~strong(fred)<~>kind(fred)))&
(happy(fred))&
((calm(alice)<~>brave(alice)))&
(?[X]:((kind(X)|creative(X))))&
((~wise(john)&~funny(john))) | ~humble(john) | [
"p0",
"p5",
"p6",
"p7",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2561639500522999322947600
% SZS output start Proof for 2561639500522999322947600
1. ! [X0] : ((brave(X0) | ~humble(X0)) <=> (~calm(X0) & ~curious(X0))) [input p0]
6. ! [X0] : ((~creative(X0) | humble(X0)) <=> (~funny(X0) & calm(X0))) [input p5]
7. ! [X0] : (curious(X0) <=> (old(X0) | ~brave(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (~creative(X0) <~> ~wise(X0))) [input p7]
11. ! [X0] : ((humble(X0) <~> quiet(X0)) <=> (generous(X0) & old(X0))) [input p10]
24. ~funny(john) & ~wise(john) [input p23]
25. ~humble(john) [input hypothesis]
41. ! [X0] : (((brave(X0) | ~humble(X0)) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | (~brave(X0) & humble(X0)))) [nnf transformation 1]
42. ! [X0] : ((brave(X0) | ~humble(X0) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | (~brave(X0) & humble(X0)))) [flattening 41]
46. ! [X0] : (((~creative(X0) | humble(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [nnf transformation 6]
47. ! [X0] : ((~creative(X0) | humble(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (creative(X0) & ~humble(X0)))) [flattening 46]
48. ! [X0] : ((curious(X0) | (~old(X0) & brave(X0))) & ((old(X0) | ~brave(X0)) | ~curious(X0))) [nnf transformation 7]
49. ! [X0] : ((curious(X0) | (~old(X0) & brave(X0))) & (old(X0) | ~brave(X0) | ~curious(X0))) [flattening 48]
50. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 8]
55. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | (~generous(X0) | ~old(X0))) & ((generous(X0) & old(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ~generous(X0) | ~old(X0)) & ((generous(X0) & old(X0)) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0))))) [flattening 55]
73. ~curious(X0) | humble(X0) [cnf transformation 42]
75. ~calm(X0) | humble(X0) [cnf transformation 42]
89. creative(X0) | calm(X0) [cnf transformation 47]
95. ~old(X0) | curious(X0) [cnf transformation 49]
103. ~creative(X0) | quiet(X0) | curious(X0) | wise(X0) [cnf transformation 50]
108. ~quiet(X0) | humble(X0) | old(X0) [cnf transformation 56]
134. ~wise(john) [cnf transformation 24]
136. ~humble(john) [cnf transformation 25]
146. 3 <=> calm(john) [avatar definition]
148. calm(john) <- (3) [avatar component clause 146]
210. 18 <=> wise(john) [avatar definition]
211. ~wise(john) <- (~18) [avatar component clause 210]
273. ~18 [avatar split clause 134,210]
547. wise(X1) | curious(X1) | quiet(X1) | calm(X1) [resolution 103,89]
659. curious(john) | quiet(john) | calm(john) <- (~18) [resolution 547,211]
666. 70 <=> quiet(john) [avatar definition]
668. quiet(john) <- (70) [avatar component clause 666]
670. 71 <=> curious(john) [avatar definition]
671. ~curious(john) <- (~71) [avatar component clause 670]
672. curious(john) <- (71) [avatar component clause 670]
673. 3 | 70 | 71 | 18 [avatar split clause 659,210,670,666,146]
696. humble(john) | old(john) <- (70) [resolution 668,108]
722. old(john) <- (70) [subsumption resolution 696,136]
847. curious(john) <- (70) [resolution 722,95]
848. $false <- (70, ~71) [subsumption resolution 847,671]
849. ~70 | 71 [avatar contradiction clause 848]
874. humble(john) <- (71) [resolution 672,73]
877. $false <- (71) [subsumption resolution 874,136]
878. ~71 [avatar contradiction clause 877]
885. humble(john) <- (3) [resolution 148,75]
888. $false <- (3) [subsumption resolution 885,136]
889. ~3 [avatar contradiction clause 888]
890. $false [avatar sat refutation 273,673,849,878,889]
% SZS output end Proof for 2561639500522999322947600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not generous then lucy is not funny or humble and vice versa.
If alice is old or not curious then someone is kind and vice versa.
If someone is both strong and rich then paul is either curious or not brave.
Everyone who is kind is either curious or not funny and vice versa.
Everyone who is both brave and patient is rich or not quiet and vice versa.
Everyone who is either not old or not tall is both curious and wise.
Everyone who is not tall is either kind or humble and vice versa.
If someone is either wise or happy then someone is strong or rich.
If lucy is not brave then john is kind and vice versa.
Everyone who is either tall or quiet is both not wise and funny.
If fred is both not brave and creative then someone is either not brave or not old and vice versa.
If someone is not creative then someone is either brave or not generous and vice versa.
Everyone who is generous or patient is both happy and not kind and vice versa.
Everyone who is both not happy and not rich is either strong or brave and vice versa.
Everyone who is both generous and calm is not tall.
Everyone who is not happy or not old is not brave or not kind.
Paul is humble or curious.
Someone is not funny or not tall.
Someone is not tall or quiet.
Lucy is patient.
Someone is both not quiet and not humble.
Susan is both rich and calm.
Someone is not tall or not calm.
John is either not quiet or not generous. | Paul is not brave. | neutral | ((?[X]:((~rich(X)&~generous(X))))<=>((~funny(lucy)|humble(lucy))))&
(((old(alice)|~curious(alice)))<=>(?[X]:(kind(X))))&
((?[X]:((strong(X)&rich(X))))=>((curious(paul)<~>~brave(paul))))&
(![X]:(kind(X)<=>(curious(X)<~>~funny(X))))&
(![X]:((brave(X)&patient(X))<=>(rich(X)|~quiet(X))))&
(![X]:((~old(X)<~>~tall(X))=>(curious(X)&wise(X))))&
(![X]:(~tall(X)<=>(kind(X)<~>humble(X))))&
((?[X]:((wise(X)<~>happy(X))))=>(?[X]:((strong(X)|rich(X)))))&
((~brave(lucy))<=>(kind(john)))&
(![X]:((tall(X)<~>quiet(X))=>(~wise(X)&funny(X))))&
(((~brave(fred)&creative(fred)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((generous(X)|patient(X))<=>(happy(X)&~kind(X))))&
(![X]:((~happy(X)&~rich(X))<=>(strong(X)<~>brave(X))))&
(![X]:((generous(X)&calm(X))=>~tall(X)))&
(![X]:((~happy(X)|~old(X))=>(~brave(X)|~kind(X))))&
((humble(paul)|curious(paul)))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(patient(lucy))&
(?[X]:((~quiet(X)&~humble(X))))&
((rich(susan)&calm(susan)))&
(?[X]:((~tall(X)|~calm(X))))&
((~quiet(john)<~>~generous(john))) | ~brave(paul) | [] | null | 0 |
If someone is both rich and funny then someone is not funny.
Everyone who is not kind is either rich or humble and vice versa.
Everyone who is kind is not wise or not tall and vice versa.
Everyone who is humble is not rich or old.
If john is not rich then someone is either not old or patient and vice versa.
If mary is not rich or curious then alice is either not patient or not funny.
Everyone who is either funny or strong is not patient or curious and vice versa.
If fred is tall or not creative then mary is patient or strong.
Everyone who is both not generous and tall is either quiet or calm and vice versa.
Everyone who is either not funny or tall is both funny and kind.
If someone is wise or not happy then alice is both not quiet and not wise.
Everyone who is not kind is both not humble and happy and vice versa.
If fred is both curious and happy then someone is both wise and patient and vice versa.
If someone is either not old or happy then john is not calm.
Everyone who is kind or calm is creative and vice versa.
Everyone who is either not funny or not happy is both kind and patient and vice versa.
John is both not strong and not quiet.
Alice is not generous or wise.
Mary is either creative or not brave.
Someone is either not humble or kind.
Someone is not tall.
Someone is not wise or not old. | Alice is not funny. | neutral | ((?[X]:((rich(X)&funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(~kind(X)<=>(rich(X)<~>humble(X))))&
(![X]:(kind(X)<=>(~wise(X)|~tall(X))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(![X]:(~kind(X)<=>(~humble(X)&happy(X))))&
(((curious(fred)&happy(fred)))<=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((~old(X)<~>happy(X))))=>(~calm(john)))&
(![X]:((kind(X)|calm(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(kind(X)&patient(X))))&
((~strong(john)&~quiet(john)))&
((~generous(alice)|wise(alice)))&
((creative(mary)<~>~brave(mary)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)|~old(X)))) | ~funny(alice) | [] | null | 0 |
Everyone who is both not curious and creative is both not happy and not humble.
If john is not patient then susan is both creative and old and vice versa.
Everyone who is not generous or calm is not happy.
If someone is humble then mary is not quiet or not generous and vice versa.
Everyone who is both not happy and not kind is curious and vice versa.
If someone is both generous and not old then someone is happy.
If paul is kind then alice is either not wise or not quiet and vice versa.
If alice is not generous or generous then someone is curious or not old and vice versa.
If paul is not patient then someone is both humble and generous and vice versa.
Everyone who is either not happy or calm is generous and vice versa.
Everyone who is both brave and rich is not strong.
Everyone who is tall is not creative or not rich.
Everyone who is both curious and not humble is not rich or not generous and vice versa.
Everyone who is strong is calm and vice versa.
If someone is either kind or calm then fred is both creative and patient and vice versa.
Everyone who is patient is either not happy or generous and vice versa.
Susan is creative.
Someone is either not strong or not tall.
Susan is both tall and patient.
Someone is both funny and not creative.
Someone is either not wise or curious.
Someone is either funny or calm.
Someone is not brave or not generous.
Someone is either rich or not strong. | Susan is not strong. | contradiction | (![X]:((~curious(X)&creative(X))=>(~happy(X)&~humble(X))))&
((~patient(john))<=>((creative(susan)&old(susan))))&
(![X]:((~generous(X)|calm(X))=>~happy(X)))&
((?[X]:(humble(X)))<=>((~quiet(mary)|~generous(mary))))&
(![X]:((~happy(X)&~kind(X))<=>curious(X)))&
((?[X]:((generous(X)&~old(X))))=>(?[X]:(happy(X))))&
((kind(paul))<=>((~wise(alice)<~>~quiet(alice))))&
(((~generous(alice)|generous(alice)))<=>(?[X]:((curious(X)|~old(X)))))&
((~patient(paul))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~happy(X)<~>calm(X))<=>generous(X)))&
(![X]:((brave(X)&rich(X))=>~strong(X)))&
(![X]:(tall(X)=>(~creative(X)|~rich(X))))&
(![X]:((curious(X)&~humble(X))<=>(~rich(X)|~generous(X))))&
(![X]:(strong(X)<=>calm(X)))&
((?[X]:((kind(X)<~>calm(X))))<=>((creative(fred)&patient(fred))))&
(![X]:(patient(X)<=>(~happy(X)<~>generous(X))))&
(creative(susan))&
(?[X]:((~strong(X)<~>~tall(X))))&
((tall(susan)&patient(susan)))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((funny(X)<~>calm(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((rich(X)<~>~strong(X)))) | ~strong(susan) | [
"p2",
"p9",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2087645203618136428604032
% SZS output start Proof for 2087645203618136428604032
3. ! [X0] : ((calm(X0) | ~generous(X0)) => ~happy(X0)) [input p2]
10. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> generous(X0)) [input p9]
14. ! [X0] : (strong(X0) <=> calm(X0)) [input p13]
16. ! [X0] : (patient(X0) <=> (~happy(X0) <~> generous(X0))) [input p15]
19. patient(susan) & tall(susan) [input p18]
25. ~strong(susan) [input hypothesis]
31. ! [X0] : (~happy(X0) | (~calm(X0) & generous(X0))) [ennf transformation 3]
57. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | ~generous(X0)) & (generous(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 10]
60. ! [X0] : ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0))) [nnf transformation 14]
66. ! [X0] : ((patient(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ~patient(X0))) [nnf transformation 16]
86. ~happy(X0) | generous(X0) [cnf transformation 31]
87. ~calm(X0) | ~happy(X0) [cnf transformation 31]
106. generous(X0) | calm(X0) | happy(X0) [cnf transformation 57]
108. calm(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 57]
109. ~calm(X0) | happy(X0) | ~generous(X0) [cnf transformation 57]
117. ~calm(X0) | strong(X0) [cnf transformation 60]
125. ~generous(X0) | happy(X0) | ~patient(X0) [cnf transformation 66]
132. patient(susan) [cnf transformation 19]
141. ~strong(susan) [cnf transformation 25]
231. ~calm(X0) | ~generous(X0) [subsumption resolution 109,87]
232. ~happy(X0) | ~generous(X0) [subsumption resolution 108,231]
233. ~happy(X0) [subsumption resolution 232,86]
234. calm(X0) | generous(X0) [subsumption resolution 106,233]
264. ~generous(X0) | ~patient(X0) [subsumption resolution 125,233]
326. strong(X1) | generous(X1) [resolution 234,117]
371. generous(susan) [resolution 326,141]
379. ~patient(susan) [resolution 371,264]
381. $false [subsumption resolution 379,132]
% SZS output end Proof for 2087645203618136428604032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not tall is both not brave and not calm and vice versa.
If someone is both not funny and not curious then someone is either not kind or not brave.
Everyone who is not humble is both generous and not brave and vice versa.
Everyone who is both calm and not tall is not old.
Everyone who is rich is not tall.
Everyone who is both quiet and not curious is either not old or tall and vice versa.
Everyone who is not happy is not patient.
If someone is both strong and old then someone is not patient or strong.
If john is generous or not tall then susan is humble.
Everyone who is not strong or not funny is rich.
If someone is brave or happy then susan is both rich and happy.
Everyone who is either not quiet or not brave is both not funny and not brave.
If someone is both patient and not wise then someone is either not brave or quiet and vice versa.
Everyone who is humble is both not quiet and not rich.
Everyone who is both brave and generous is humble or strong.
If someone is tall then someone is either not curious or humble.
Someone is strong or not humble.
Someone is either creative or not wise.
Alice is old.
Someone is humble or not patient.
Someone is not funny or quiet.
Mary is both quiet and curious. | John is not rich. | entailment | (![X]:((~wise(X)|~tall(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:(~humble(X)<=>(generous(X)&~brave(X))))&
(![X]:((calm(X)&~tall(X))=>~old(X)))&
(![X]:(rich(X)=>~tall(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~old(X)<~>tall(X))))&
(![X]:(~happy(X)=>~patient(X)))&
((?[X]:((strong(X)&old(X))))=>(?[X]:((~patient(X)|strong(X)))))&
(((generous(john)|~tall(john)))=>(humble(susan)))&
(![X]:((~strong(X)|~funny(X))=>rich(X)))&
((?[X]:((brave(X)|happy(X))))=>((rich(susan)&happy(susan))))&
(![X]:((~quiet(X)<~>~brave(X))=>(~funny(X)&~brave(X))))&
((?[X]:((patient(X)&~wise(X))))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~quiet(X)&~rich(X))))&
(![X]:((brave(X)&generous(X))=>(humble(X)|strong(X))))&
((?[X]:(tall(X)))=>(?[X]:((~curious(X)<~>humble(X)))))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:((creative(X)<~>~wise(X))))&
(old(alice))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~funny(X)|quiet(X))))&
((quiet(mary)&curious(mary))) | ~rich(john) | [
"p2",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1448712333729205829581221
% SZS output start Proof for 1448712333729205829581221
3. ! [X0] : (~humble(X0) <=> (~brave(X0) & generous(X0))) [input p2]
7. ! [X0] : (~happy(X0) => ~patient(X0)) [input p6]
9. (~tall(john) | generous(john)) => humble(susan) [input p8]
11. ? [X0] : (happy(X0) | brave(X0)) => (happy(susan) & rich(susan)) [input p10]
12. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) => (~brave(X0) & ~funny(X0))) [input p11]
13. ? [X0] : (~wise(X0) & patient(X0)) <=> ? [X0] : (~brave(X0) <~> quiet(X0)) [input p12]
14. ! [X0] : (humble(X0) => (~rich(X0) & ~quiet(X0))) [input p13]
23. rich(john) [input hypothesis]
26. ? [X0] : (~wise(X0) & patient(X0)) <=> ? [X1] : (~brave(X1) <~> quiet(X1)) [rectify 13]
32. ! [X0] : (~patient(X0) | happy(X0)) [ennf transformation 7]
34. humble(susan) | (tall(john) & ~generous(john)) [ennf transformation 9]
36. (happy(susan) & rich(susan)) | ! [X0] : (~happy(X0) & ~brave(X0)) [ennf transformation 11]
37. ! [X0] : ((~brave(X0) & ~funny(X0)) | (~quiet(X0) <=> ~brave(X0))) [ennf transformation 12]
38. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~humble(X0)) [ennf transformation 14]
48. ! [X0] : ((~humble(X0) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | humble(X0))) [nnf transformation 3]
49. ! [X0] : ((~humble(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | humble(X0))) [flattening 48]
55. ! [X0] : ((~brave(X0) & ~funny(X0)) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0)))) [nnf transformation 37]
56. (? [X0] : (~wise(X0) & patient(X0)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X1] : ((~quiet(X1) | brave(X1)) & (quiet(X1) | ~brave(X1))) | ! [X0] : (wise(X0) | ~patient(X0))) [nnf transformation 26]
57. (? [X0] : (~wise(X0) & patient(X0)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) | ! [X3] : (wise(X3) | ~patient(X3))) [rectify 56]
58. ? [X0] : (~wise(X0) & patient(X0)) => (~wise(sK2) & patient(sK2)) [choice axiom]
59. ? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) => ((~quiet(sK3) | brave(sK3)) & (quiet(sK3) | ~brave(sK3))) [choice axiom]
60. ((~wise(sK2) & patient(sK2)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (((~quiet(sK3) | brave(sK3)) & (quiet(sK3) | ~brave(sK3))) | ! [X3] : (wise(X3) | ~patient(X3))) [skolemisation 57,59,58]
81. generous(X0) | humble(X0) [cnf transformation 49]
92. ~patient(X0) | happy(X0) [cnf transformation 32]
94. humble(susan) | ~generous(john) [cnf transformation 34]
99. rich(susan) | ~happy(X0) [cnf transformation 36]
104. ~brave(X0) | ~brave(X0) | quiet(X0) [cnf transformation 55]
108. patient(sK2) | quiet(X1) | brave(X1) [cnf transformation 60]
112. ~quiet(X0) | ~humble(X0) [cnf transformation 38]
113. ~rich(X0) | ~humble(X0) [cnf transformation 38]
125. rich(john) [cnf transformation 23]
126. ~brave(X0) | quiet(X0) [duplicate literal removal 104]
157. 8 <=> humble(susan) [avatar definition]
159. humble(susan) <- (8) [avatar component clause 157]
162. 9 <=> generous(john) [avatar definition]
164. ~generous(john) <- (~9) [avatar component clause 162]
165. ~9 | 8 [avatar split clause 94,157,162]
167. 10 <=> ! [X0] : ~happy(X0) [avatar definition]
168. ~happy(X0) <- (10) [avatar component clause 167]
179. 13 <=> rich(susan) [avatar definition]
181. rich(susan) <- (13) [avatar component clause 179]
182. 10 | 13 [avatar split clause 99,179,167]
192. 15 <=> ! [X1] : quiet(X1) [avatar definition]
193. quiet(X1) <- (15) [avatar component clause 192]
197. 16 <=> patient(sK2) [avatar definition]
199. patient(sK2) <- (16) [avatar component clause 197]
201. patient(sK2) | quiet(X1) [subsumption resolution 108,126]
202. 15 | 16 [avatar split clause 201,197,192]
267. humble(john) <- (~9) [resolution 81,164]
272. happy(sK2) <- (16) [resolution 92,199]
273. $false <- (10, 16) [subsumption resolution 272,168]
274. ~10 | ~16 [avatar contradiction clause 273]
278. ~humble(john) [resolution 113,125]
279. ~humble(susan) <- (13) [resolution 113,181]
281. $false <- (~9) [subsumption resolution 278,267]
282. 9 [avatar contradiction clause 281]
283. $false <- (8, 13) [subsumption resolution 279,159]
284. ~8 | ~13 [avatar contradiction clause 283]
288. ~humble(X0) <- (15) [resolution 193,112]
292. $false <- (8, 15) [resolution 288,159]
293. ~8 | ~15 [avatar contradiction clause 292]
294. $false [avatar sat refutation 165,182,202,274,282,284,293]
% SZS output end Proof for 1448712333729205829581221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then lucy is rich. If someone is either not funny or wise then someone is not brave and vice versa. Everyone who is not old is not wise or strong. Everyone who is generous is not creative or strong and vice versa. If susan is both not patient and not creative then someone is either not strong or creative and vice versa. Everyone who is both funny and rich is either not creative or curious and vice versa. Everyone who is either not curious or curious is both not happy and not generous. Everyone who is either kind or not wise is old and vice versa. If someone is patient then someone is calm and vice versa. Everyone who is not wise or not curious is quiet. If mary is not funny then someone is either creative or not patient and vice versa. If lucy is both generous and tall then someone is curious or not kind. If someone is funny then susan is either not happy or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. Mary is not calm. Someone is either not funny or not quiet. Mary is both not generous and not wise. John is both wise and not calm. Someone is either creative or not patient. Someone is not quiet. Mary is either not brave or quiet. | John is not funny. | neutral | ((brave(mary))=>(rich(lucy)))&
((?[X]:((~funny(X)<~>wise(X))))<=>(?[X]:(~brave(X))))&
(![X]:(~old(X)=>(~wise(X)|strong(X))))&
(![X]:(generous(X)<=>(~creative(X)|strong(X))))&
(((~patient(susan)&~creative(susan)))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(![X]:((funny(X)&rich(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((~curious(X)<~>curious(X))=>(~happy(X)&~generous(X))))&
(![X]:((kind(X)<~>~wise(X))<=>old(X)))&
((?[X]:(patient(X)))<=>(?[X]:(calm(X))))&
(![X]:((~wise(X)|~curious(X))=>quiet(X)))&
((~funny(mary))<=>(?[X]:((creative(X)<~>~patient(X)))))&
(((generous(lucy)&tall(lucy)))=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:(funny(X)))<=>((~happy(susan)<~>strong(susan))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
(~calm(mary))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((~generous(mary)&~wise(mary)))&
((wise(john)&~calm(john)))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:(~quiet(X)))&
((~brave(mary)<~>quiet(mary))) | ~funny(john) | [] | null | 0 |
Everyone who is not strong or curious is either happy or calm.
If alice is quiet then john is not rich or rich and vice versa.
If someone is either not kind or kind then susan is both humble and wise and vice versa.
Everyone who is either not quiet or not curious is both happy and not old.
If john is both quiet and strong then someone is not humble or not funny.
Everyone who is curious is tall and vice versa.
If someone is either generous or curious then mary is funny and vice versa.
If mary is either wise or not kind then lucy is either not old or not rich.
Everyone who is either generous or calm is both not happy and not humble and vice versa.
Everyone who is either kind or not quiet is either not patient or not old and vice versa.
Everyone who is both creative and not funny is both not calm and not curious.
Everyone who is calm or not calm is either not patient or not curious and vice versa.
Everyone who is both not happy and not patient is either creative or not old and vice versa.
Everyone who is either not curious or not funny is both patient and funny and vice versa.
Everyone who is either creative or kind is both happy and not tall.
If susan is both rich and not humble then someone is both not creative and not old.
Mary is not calm.
Someone is both not happy and curious.
Alice is creative.
Alice is not quiet or wise.
Someone is both not calm and strong.
Someone is either not strong or tall.
John is not strong. | Mary is strong. | neutral | (![X]:((~strong(X)|curious(X))=>(happy(X)<~>calm(X))))&
((quiet(alice))<=>((~rich(john)|rich(john))))&
((?[X]:((~kind(X)<~>kind(X))))<=>((humble(susan)&wise(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(happy(X)&~old(X))))&
(((quiet(john)&strong(john)))=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:(curious(X)<=>tall(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>(funny(mary)))&
(((wise(mary)<~>~kind(mary)))=>((~old(lucy)<~>~rich(lucy))))&
(![X]:((generous(X)<~>calm(X))<=>(~happy(X)&~humble(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((creative(X)&~funny(X))=>(~calm(X)&~curious(X))))&
(![X]:((calm(X)|~calm(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~happy(X)&~patient(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>(patient(X)&funny(X))))&
(![X]:((creative(X)<~>kind(X))=>(happy(X)&~tall(X))))&
(((rich(susan)&~humble(susan)))=>(?[X]:((~creative(X)&~old(X)))))&
(~calm(mary))&
(?[X]:((~happy(X)&curious(X))))&
(creative(alice))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~strong(X)<~>tall(X))))&
(~strong(john)) | strong(mary) | [] | null | 0 |
Everyone who is either quiet or not happy is either not happy or brave. Everyone who is not kind is both quiet and not brave and vice versa. Everyone who is both strong and happy is rich or creative. If someone is both not old and not humble then lucy is creative. If someone is either not rich or not kind then someone is happy and vice versa. If someone is not tall or not generous then paul is not brave. Everyone who is either not patient or not humble is not brave. If someone is both not patient and not brave then paul is kind or rich and vice versa. Everyone who is not strong is both not tall and tall and vice versa. Everyone who is not old or kind is both not quiet and brave. Everyone who is generous is tall or not happy and vice versa. Everyone who is both strong and kind is creative. Everyone who is both patient and not humble is strong or curious and vice versa. If someone is tall then mary is not humble or not tall and vice versa. Everyone who is kind is not patient. Everyone who is both creative and quiet is either funny or patient. Someone is both not funny and quiet. Lucy is wise or patient. Someone is both curious and not humble. Mary is wise or not quiet. Someone is either not funny or not generous. | Mary is wise. | entailment | (![X]:((quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(![X]:(~kind(X)<=>(quiet(X)&~brave(X))))&
(![X]:((strong(X)&happy(X))=>(rich(X)|creative(X))))&
((?[X]:((~old(X)&~humble(X))))=>(creative(lucy)))&
((?[X]:((~rich(X)<~>~kind(X))))<=>(?[X]:(happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(~brave(paul)))&
(![X]:((~patient(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((kind(paul)|rich(paul))))&
(![X]:(~strong(X)<=>(~tall(X)&tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)&brave(X))))&
(![X]:(generous(X)<=>(tall(X)|~happy(X))))&
(![X]:((strong(X)&kind(X))=>creative(X)))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|curious(X))))&
((?[X]:(tall(X)))<=>((~humble(mary)|~tall(mary))))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((creative(X)&quiet(X))=>(funny(X)<~>patient(X))))&
(?[X]:((~funny(X)&quiet(X))))&
((wise(lucy)|patient(lucy)))&
(?[X]:((curious(X)&~humble(X))))&
((wise(mary)|~quiet(mary)))&
(?[X]:((~funny(X)<~>~generous(X)))) | wise(mary) | [
"p1",
"p8",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6735699608281843290673103
% SZS output start Proof for 6735699608281843290673103
2. ! [X0] : (~kind(X0) <=> (~brave(X0) & quiet(X0))) [input p1]
9. ! [X0] : (~strong(X0) <=> (tall(X0) & ~tall(X0))) [input p8]
13. ! [X0] : ((~humble(X0) & patient(X0)) <=> (curious(X0) | strong(X0))) [input p12]
15. ! [X0] : (kind(X0) => ~patient(X0)) [input p14]
20. ~quiet(mary) | wise(mary) [input p19]
22. ~wise(mary) [input hypothesis]
34. ! [X0] : (~patient(X0) | ~kind(X0)) [ennf transformation 15]
38. ! [X0] : ((~kind(X0) | (brave(X0) | ~quiet(X0))) & ((~brave(X0) & quiet(X0)) | kind(X0))) [nnf transformation 2]
39. ! [X0] : ((~kind(X0) | brave(X0) | ~quiet(X0)) & ((~brave(X0) & quiet(X0)) | kind(X0))) [flattening 38]
51. ! [X0] : ((~strong(X0) | (~tall(X0) | tall(X0))) & ((tall(X0) & ~tall(X0)) | strong(X0))) [nnf transformation 9]
52. ! [X0] : ((~strong(X0) | ~tall(X0) | tall(X0)) & ((tall(X0) & ~tall(X0)) | strong(X0))) [flattening 51]
55. ! [X0] : (((~humble(X0) & patient(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (humble(X0) | ~patient(X0)))) [nnf transformation 13]
56. ! [X0] : (((~humble(X0) & patient(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | humble(X0) | ~patient(X0))) [flattening 55]
74. kind(X0) | quiet(X0) [cnf transformation 39]
91. ~tall(X0) | strong(X0) [cnf transformation 52]
92. tall(X0) | strong(X0) [cnf transformation 52]
101. patient(X0) | ~strong(X0) [cnf transformation 56]
108. ~patient(X0) | ~kind(X0) [cnf transformation 34]
116. ~quiet(mary) | wise(mary) [cnf transformation 20]
119. ~wise(mary) [cnf transformation 22]
183. strong(X0) [subsumption resolution 91,92]
186. patient(X0) [subsumption resolution 101,183]
198. ~kind(X0) [subsumption resolution 108,186]
201. 17 <=> wise(mary) [avatar definition]
205. 18 <=> quiet(mary) [avatar definition]
207. ~quiet(mary) <- (~18) [avatar component clause 205]
208. 17 | ~18 [avatar split clause 116,205,201]
219. ~17 [avatar split clause 119,201]
222. quiet(X0) [resolution 74,198]
223. $false <- (~18) [resolution 222,207]
224. 18 [avatar contradiction clause 223]
225. $false [avatar sat refutation 208,219,224]
% SZS output end Proof for 6735699608281843290673103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and kind is either happy or not tall.
If someone is both funny and not calm then susan is both not patient and generous.
Everyone who is quiet or not strong is not strong or not kind and vice versa.
If someone is both curious and kind then someone is both not rich and generous and vice versa.
If susan is both not quiet and not generous then someone is funny.
Everyone who is brave is not funny and vice versa.
Everyone who is calm is both not old and calm and vice versa.
If paul is not curious then john is patient and vice versa.
Everyone who is brave or not old is either not quiet or strong.
If john is not funny or not calm then someone is both not humble and not curious.
Everyone who is strong is both not strong and strong and vice versa.
Everyone who is both strong and funny is not quiet and vice versa.
If someone is both old and kind then lucy is either creative or not kind.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Lucy is either generous or tall.
John is not brave.
Someone is either not curious or strong.
Someone is wise.
Susan is not wise.
Someone is calm or not tall.
Paul is not humble or not calm.
Paul is both happy and not kind. | Lucy is funny. | entailment | (![X]:((~creative(X)&kind(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((funny(X)&~calm(X))))=>((~patient(susan)&generous(susan))))&
(![X]:((quiet(X)|~strong(X))<=>(~strong(X)|~kind(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(((~quiet(susan)&~generous(susan)))=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:(calm(X)<=>(~old(X)&calm(X))))&
((~curious(paul))<=>(patient(john)))&
(![X]:((brave(X)|~old(X))=>(~quiet(X)<~>strong(X))))&
(((~funny(john)|~calm(john)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:(strong(X)<=>(~strong(X)&strong(X))))&
(![X]:((strong(X)&funny(X))<=>~quiet(X)))&
((?[X]:((old(X)&kind(X))))=>((creative(lucy)<~>~kind(lucy))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((generous(lucy)<~>tall(lucy)))&
(~brave(john))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(wise(X)))&
(~wise(susan))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul))) | funny(lucy) | [
"p5",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1586194466498256717202107
% SZS output start Proof for 1586194466498256717202107
6. ! [X0] : (brave(X0) <=> ~funny(X0)) [input p5]
9. ! [X0] : ((~old(X0) | brave(X0)) => (~quiet(X0) <~> strong(X0))) [input p8]
11. ! [X0] : (strong(X0) <=> (strong(X0) & ~strong(X0))) [input p10]
12. ! [X0] : ((funny(X0) & strong(X0)) <=> ~quiet(X0)) [input p11]
25. ~funny(lucy) [input hypothesis]
35. ! [X0] : ((~quiet(X0) <~> strong(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 9]
53. ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))) [nnf transformation 6]
57. ! [X0] : (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (old(X0) & ~brave(X0))) [nnf transformation 35]
60. ! [X0] : ((strong(X0) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [nnf transformation 11]
61. ! [X0] : ((strong(X0) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ~strong(X0))) [flattening 60]
62. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) | ~strong(X0)))) [nnf transformation 12]
63. ! [X0] : (((funny(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | ~funny(X0) | ~strong(X0))) [flattening 62]
91. brave(X0) | funny(X0) [cnf transformation 53]
97. ~brave(X0) | ~quiet(X0) | strong(X0) [cnf transformation 57]
103. ~strong(X0) | ~strong(X0) [cnf transformation 61]
107. strong(X0) | quiet(X0) [cnf transformation 63]
128. ~funny(lucy) [cnf transformation 25]
129. ~strong(X0) [duplicate literal removal 103]
203. quiet(X0) [subsumption resolution 107,129]
257. ~quiet(X0) | strong(X0) | funny(X0) [resolution 97,91]
258. strong(X0) | funny(X0) [subsumption resolution 257,203]
259. funny(X0) [subsumption resolution 258,129]
263. $false [resolution 259,128]
% SZS output end Proof for 1586194466498256717202107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or strong is both brave and not wise and vice versa.
If susan is tall or generous then someone is humble or not generous.
Everyone who is both not creative and not calm is both not quiet and not calm and vice versa.
Everyone who is not old or humble is quiet or strong.
If susan is both old and not tall then susan is either not creative or patient and vice versa.
If lucy is not funny or not wise then mary is happy or generous.
If someone is both not calm and not humble then someone is either not wise or funny and vice versa.
If fred is either quiet or not calm then susan is either quiet or not generous and vice versa.
Everyone who is both curious and not tall is both patient and rich.
If someone is calm then paul is not quiet or not brave and vice versa.
If lucy is not happy then paul is not generous and vice versa.
Everyone who is either not rich or not curious is either generous or funny and vice versa.
Everyone who is both not rich and not creative is both not tall and not rich and vice versa.
If alice is both not old and tall then someone is not strong and vice versa.
Everyone who is not old is tall or kind.
Everyone who is not creative is both curious and strong and vice versa.
Alice is not happy or not tall.
Someone is not curious.
Paul is both brave and creative.
John is both not strong and not funny.
Someone is brave or not kind.
Fred is not brave.
Mary is not wise.
Lucy is happy or rich. | Alice is not old. | entailment | (![X]:((quiet(X)|strong(X))<=>(brave(X)&~wise(X))))&
(((tall(susan)|generous(susan)))=>(?[X]:((humble(X)|~generous(X)))))&
(![X]:((~creative(X)&~calm(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((~old(X)|humble(X))=>(quiet(X)|strong(X))))&
(((old(susan)&~tall(susan)))<=>((~creative(susan)<~>patient(susan))))&
(((~funny(lucy)|~wise(lucy)))=>((happy(mary)|generous(mary))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((~wise(X)<~>funny(X)))))&
(((quiet(fred)<~>~calm(fred)))<=>((quiet(susan)<~>~generous(susan))))&
(![X]:((curious(X)&~tall(X))=>(patient(X)&rich(X))))&
((?[X]:(calm(X)))<=>((~quiet(paul)|~brave(paul))))&
((~happy(lucy))<=>(~generous(paul)))&
(![X]:((~rich(X)<~>~curious(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~rich(X)&~creative(X))<=>(~tall(X)&~rich(X))))&
(((~old(alice)&tall(alice)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)=>(tall(X)|kind(X))))&
(![X]:(~creative(X)<=>(curious(X)&strong(X))))&
((~happy(alice)|~tall(alice)))&
(?[X]:(~curious(X)))&
((brave(paul)&creative(paul)))&
((~strong(john)&~funny(john)))&
(?[X]:((brave(X)|~kind(X))))&
(~brave(fred))&
(~wise(mary))&
((happy(lucy)|rich(lucy))) | ~old(alice) | [
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6882945821011374793790561
% SZS output start Proof for 6882945821011374793790561
14. (tall(alice) & ~old(alice)) <=> ? [X0] : ~strong(X0) [input p13]
20. ~funny(john) & ~strong(john) [input p19]
25. old(alice) [input hypothesis]
59. ((tall(alice) & ~old(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | (~tall(alice) | old(alice))) [nnf transformation 14]
60. ((tall(alice) & ~old(alice)) | ! [X0] : strong(X0)) & (? [X0] : ~strong(X0) | ~tall(alice) | old(alice)) [flattening 59]
61. ((tall(alice) & ~old(alice)) | ! [X0] : strong(X0)) & (? [X1] : ~strong(X1) | ~tall(alice) | old(alice)) [rectify 60]
62. ? [X1] : ~strong(X1) => ~strong(sK4) [choice axiom]
63. ((tall(alice) & ~old(alice)) | ! [X0] : strong(X0)) & (~strong(sK4) | ~tall(alice) | old(alice)) [skolemisation 61,62]
125. ~old(alice) | strong(X0) [cnf transformation 63]
135. ~strong(john) [cnf transformation 20]
141. old(alice) [cnf transformation 25]
277. 28 <=> ! [X0] : strong(X0) [avatar definition]
278. strong(X0) <- (28) [avatar component clause 277]
285. 30 <=> old(alice) [avatar definition]
288. 28 | ~30 [avatar split clause 125,285,277]
314. 30 [avatar split clause 141,285]
315. $false <- (28) [resolution 278,135]
316. ~28 [avatar contradiction clause 315]
317. $false [avatar sat refutation 288,314,316]
% SZS output end Proof for 6882945821011374793790561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not kind is both not tall and not creative. If someone is creative then mary is both not humble and humble. Everyone who is strong or tall is funny and vice versa. If mary is either not creative or not quiet then someone is both creative and not curious. If paul is either not strong or brave then someone is not tall or happy. If lucy is either not brave or patient then lucy is either not generous or quiet and vice versa. Everyone who is either curious or calm is both funny and curious and vice versa. If paul is not curious then alice is both not quiet and not patient. Everyone who is creative is curious. Everyone who is both not quiet and not tall is strong or old and vice versa. Everyone who is not quiet or not curious is either patient or not rich and vice versa. Everyone who is both brave and not happy is either strong or patient. Everyone who is not old or not patient is either generous or not kind and vice versa. Everyone who is rich or calm is both rich and calm and vice versa. Everyone who is not calm or not curious is either strong or calm and vice versa. If john is not humble or not strong then susan is both strong and not wise and vice versa. Someone is either not patient or brave. Susan is either rich or not calm. Someone is not brave. Alice is either old or not humble. Someone is not brave or not tall. Mary is not quiet. John is not creative or wise. | Lucy is funny. | entailment | (![X]:((~brave(X)&~kind(X))=>(~tall(X)&~creative(X))))&
((?[X]:(creative(X)))=>((~humble(mary)&humble(mary))))&
(![X]:((strong(X)|tall(X))<=>funny(X)))&
(((~creative(mary)<~>~quiet(mary)))=>(?[X]:((creative(X)&~curious(X)))))&
(((~strong(paul)<~>brave(paul)))=>(?[X]:((~tall(X)|happy(X)))))&
(((~brave(lucy)<~>patient(lucy)))<=>((~generous(lucy)<~>quiet(lucy))))&
(![X]:((curious(X)<~>calm(X))<=>(funny(X)&curious(X))))&
((~curious(paul))=>((~quiet(alice)&~patient(alice))))&
(![X]:(creative(X)=>curious(X)))&
(![X]:((~quiet(X)&~tall(X))<=>(strong(X)|old(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(patient(X)<~>~rich(X))))&
(![X]:((brave(X)&~happy(X))=>(strong(X)<~>patient(X))))&
(![X]:((~old(X)|~patient(X))<=>(generous(X)<~>~kind(X))))&
(![X]:((rich(X)|calm(X))<=>(rich(X)&calm(X))))&
(![X]:((~calm(X)|~curious(X))<=>(strong(X)<~>calm(X))))&
(((~humble(john)|~strong(john)))<=>((strong(susan)&~wise(susan))))&
(?[X]:((~patient(X)<~>brave(X))))&
((rich(susan)<~>~calm(susan)))&
(?[X]:(~brave(X)))&
((old(alice)<~>~humble(alice)))&
(?[X]:((~brave(X)|~tall(X))))&
(~quiet(mary))&
((~creative(john)|wise(john))) | funny(lucy) | [
"p2",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3135155617546091236248109
% SZS output start Proof for 3135155617546091236248109
3. ! [X0] : ((tall(X0) | strong(X0)) <=> funny(X0)) [input p2]
7. ! [X0] : ((curious(X0) <~> calm(X0)) <=> (curious(X0) & funny(X0))) [input p6]
15. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (strong(X0) <~> calm(X0))) [input p14]
24. ~funny(lucy) [input hypothesis]
33. ! [X0] : (((tall(X0) | strong(X0)) | ~funny(X0)) & (funny(X0) | (~tall(X0) & ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : ((tall(X0) | strong(X0) | ~funny(X0)) & (funny(X0) | (~tall(X0) & ~strong(X0)))) [flattening 33]
39. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (~curious(X0) | ~funny(X0))) & ((curious(X0) & funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [nnf transformation 7]
40. ! [X0] : ((((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | ~curious(X0) | ~funny(X0)) & ((curious(X0) & funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0))))) [flattening 39]
49. ! [X0] : (((~curious(X0) | ~calm(X0)) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (curious(X0) & calm(X0)))) [nnf transformation 15]
50. ! [X0] : ((~curious(X0) | ~calm(X0) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (curious(X0) & calm(X0)))) [flattening 49]
66. ~strong(X0) | funny(X0) [cnf transformation 34]
84. curious(X0) | curious(X0) | ~calm(X0) [cnf transformation 40]
112. calm(X0) | strong(X0) | calm(X0) [cnf transformation 50]
117. ~curious(X0) | ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 50]
133. ~funny(lucy) [cnf transformation 24]
134. calm(X0) | strong(X0) [duplicate literal removal 112]
135. ~curious(X0) | ~calm(X0) | strong(X0) [duplicate literal removal 117]
136. curious(X0) | ~calm(X0) [duplicate literal removal 84]
205. ~calm(X0) | strong(X0) [subsumption resolution 135,136]
207. strong(X0) [subsumption resolution 134,205]
259. funny(X0) [resolution 66,207]
260. $false [resolution 259,133]
% SZS output end Proof for 3135155617546091236248109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or not quiet is either humble or not wise and vice versa.
If someone is funny or creative then john is old or wise.
Everyone who is patient or not humble is not generous or curious and vice versa.
If mary is both not rich and funny then alice is not kind or kind and vice versa.
Everyone who is not old is both brave and wise.
Everyone who is either quiet or not old is old or not tall.
Everyone who is both creative and not patient is not tall or not strong and vice versa.
Everyone who is either brave or not old is humble and vice versa.
If someone is either not curious or not old then someone is both tall and wise and vice versa.
If someone is not generous or calm then fred is either not quiet or tall and vice versa.
Everyone who is both humble and happy is not old or strong and vice versa.
If someone is both not patient and brave then paul is tall or wise and vice versa.
Everyone who is either curious or not funny is both not wise and calm and vice versa.
If alice is both humble and patient then someone is both happy and calm.
If someone is not tall then mary is both not quiet and patient and vice versa.
Everyone who is both brave and curious is both quiet and creative and vice versa.
Someone is either not kind or not generous.
Someone is not tall or creative.
Someone is both not happy and not quiet.
Someone is patient.
Someone is either not creative or calm.
Someone is brave or rich.
Fred is not happy or not humble.
Someone is not happy or not rich. | Paul is brave. | entailment | (![X]:((~wise(X)<~>~quiet(X))<=>(humble(X)<~>~wise(X))))&
((?[X]:((funny(X)|creative(X))))=>((old(john)|wise(john))))&
(![X]:((patient(X)|~humble(X))<=>(~generous(X)|curious(X))))&
(((~rich(mary)&funny(mary)))<=>((~kind(alice)|kind(alice))))&
(![X]:(~old(X)=>(brave(X)&wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(old(X)|~tall(X))))&
(![X]:((creative(X)&~patient(X))<=>(~tall(X)|~strong(X))))&
(![X]:((brave(X)<~>~old(X))<=>humble(X)))&
((?[X]:((~curious(X)<~>~old(X))))<=>(?[X]:((tall(X)&wise(X)))))&
((?[X]:((~generous(X)|calm(X))))<=>((~quiet(fred)<~>tall(fred))))&
(![X]:((humble(X)&happy(X))<=>(~old(X)|strong(X))))&
((?[X]:((~patient(X)&brave(X))))<=>((tall(paul)|wise(paul))))&
(![X]:((curious(X)<~>~funny(X))<=>(~wise(X)&calm(X))))&
(((humble(alice)&patient(alice)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:(~tall(X)))<=>((~quiet(mary)&patient(mary))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)&creative(X))))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~happy(X)&~quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((brave(X)|rich(X))))&
((~happy(fred)|~humble(fred)))&
(?[X]:((~happy(X)|~rich(X)))) | brave(paul) | [
"p0",
"p4",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5480061899308742922646156
% SZS output start Proof for 5480061899308742922646156
1. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) <=> (humble(X0) <~> ~wise(X0))) [input p0]
5. ! [X0] : (~old(X0) => (wise(X0) & brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~strong(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> humble(X0)) [input p7]
11. ! [X0] : ((happy(X0) & humble(X0)) <=> (strong(X0) | ~old(X0))) [input p10]
16. ! [X0] : ((curious(X0) & brave(X0)) <=> (creative(X0) & quiet(X0))) [input p15]
25. ~brave(paul) [input hypothesis]
29. ! [X0] : ((wise(X0) & brave(X0)) | old(X0)) [ennf transformation 5]
34. ! [X0] : ((((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | ((humble(X0) | wise(X0)) & (~wise(X0) | ~humble(X0)))) & (((wise(X0) | ~humble(X0)) & (~wise(X0) | humble(X0))) | ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))))) [nnf transformation 1]
40. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 7]
41. ! [X0] : (((~patient(X0) & creative(X0)) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | patient(X0) | ~creative(X0))) [flattening 40]
42. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~humble(X0)) & (humble(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 8]
52. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 11]
53. ! [X0] : (((happy(X0) & humble(X0)) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ~happy(X0) | ~humble(X0))) [flattening 52]
68. ! [X0] : (((curious(X0) & brave(X0)) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 16]
69. ! [X0] : (((curious(X0) & brave(X0)) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 68]
87. ~wise(X0) | humble(X0) | ~wise(X0) | quiet(X0) [cnf transformation 34]
93. quiet(X0) | wise(X0) | humble(X0) | wise(X0) [cnf transformation 34]
105. brave(X0) | old(X0) [cnf transformation 29]
111. strong(X0) | creative(X0) [cnf transformation 41]
116. ~old(X0) | brave(X0) | ~humble(X0) [cnf transformation 42]
132. ~strong(X0) | humble(X0) [cnf transformation 53]
153. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 69]
166. ~brave(paul) [cnf transformation 25]
168. ~wise(X0) | humble(X0) | quiet(X0) [duplicate literal removal 87]
171. quiet(X0) | wise(X0) | humble(X0) [duplicate literal removal 93]
173. humble(X0) | quiet(X0) [subsumption resolution 168,171]
207. ~humble(X0) | brave(X0) [subsumption resolution 116,105]
385. creative(X0) | humble(X0) [resolution 132,111]
514. brave(X0) | ~quiet(X0) | humble(X0) [resolution 153,385]
519. brave(X0) | humble(X0) [subsumption resolution 514,173]
520. brave(X0) [subsumption resolution 519,207]
521. $false [resolution 520,166]
% SZS output end Proof for 5480061899308742922646156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and patient then someone is not quiet.
If susan is either calm or curious then someone is either tall or funny and vice versa.
If someone is either old or happy then lucy is not old and vice versa.
If john is happy then someone is both not calm and not patient and vice versa.
If lucy is not brave or not quiet then susan is not quiet or strong.
Everyone who is not funny is both strong and not happy and vice versa.
Everyone who is either rich or calm is either not happy or patient and vice versa.
If someone is both not patient and not strong then someone is both funny and not wise.
Everyone who is either wise or quiet is curious.
Everyone who is both not old and strong is wise or not brave.
Everyone who is both not kind and not calm is humble and vice versa.
If john is either not patient or curious then someone is both not happy and not kind.
Everyone who is humble is not quiet or not funny and vice versa.
Everyone who is not kind is both brave and funny.
Everyone who is both not brave and not quiet is not kind or tall.
Everyone who is not humble or not happy is both tall and quiet and vice versa.
Someone is both rich and not strong.
Susan is both not wise and curious.
Someone is not old or old.
John is both not generous and not strong.
Someone is either not old or not patient.
Someone is generous or not happy.
Mary is either rich or tall.
Someone is funny. | Lucy is not wise. | neutral | ((?[X]:((curious(X)&patient(X))))=>(?[X]:(~quiet(X))))&
(((calm(susan)<~>curious(susan)))<=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((old(X)<~>happy(X))))<=>(~old(lucy)))&
((happy(john))<=>(?[X]:((~calm(X)&~patient(X)))))&
(((~brave(lucy)|~quiet(lucy)))=>((~quiet(susan)|strong(susan))))&
(![X]:(~funny(X)<=>(strong(X)&~happy(X))))&
(![X]:((rich(X)<~>calm(X))<=>(~happy(X)<~>patient(X))))&
((?[X]:((~patient(X)&~strong(X))))=>(?[X]:((funny(X)&~wise(X)))))&
(![X]:((wise(X)<~>quiet(X))=>curious(X)))&
(![X]:((~old(X)&strong(X))=>(wise(X)|~brave(X))))&
(![X]:((~kind(X)&~calm(X))<=>humble(X)))&
(((~patient(john)<~>curious(john)))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~quiet(X)|~funny(X))))&
(![X]:(~kind(X)=>(brave(X)&funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~kind(X)|tall(X))))&
(![X]:((~humble(X)|~happy(X))<=>(tall(X)&quiet(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~wise(susan)&curious(susan)))&
(?[X]:((~old(X)|old(X))))&
((~generous(john)&~strong(john)))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((generous(X)|~happy(X))))&
((rich(mary)<~>tall(mary)))&
(?[X]:(funny(X))) | ~wise(lucy) | [] | null | 0 |
Everyone who is not strong is not brave or wise and vice versa.
Everyone who is either happy or funny is both curious and humble and vice versa.
If someone is patient or not creative then lucy is creative or not rich and vice versa.
Everyone who is not happy is either not curious or kind.
Everyone who is both curious and not tall is either quiet or not brave.
If paul is not old or not calm then lucy is either not tall or funny and vice versa.
Everyone who is not generous or calm is both old and not strong and vice versa.
If someone is funny or not quiet then john is not humble.
If someone is not tall or not humble then lucy is not rich.
If paul is both calm and humble then alice is strong or not happy and vice versa.
If someone is not wise or not curious then someone is not funny.
Everyone who is not brave or tall is tall or not quiet.
Everyone who is calm is either not generous or not patient and vice versa.
Everyone who is either not creative or calm is both not happy and not creative and vice versa.
Everyone who is wise is not funny or not wise and vice versa.
Everyone who is tall or kind is old.
Someone is both humble and not old.
Someone is not happy or funny.
Lucy is not calm or not generous.
Someone is not brave.
Susan is not calm.
Mary is tall or quiet.
Susan is brave. | Lucy is quiet. | neutral | (![X]:(~strong(X)<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)&humble(X))))&
((?[X]:((patient(X)|~creative(X))))<=>((creative(lucy)|~rich(lucy))))&
(![X]:(~happy(X)=>(~curious(X)<~>kind(X))))&
(![X]:((curious(X)&~tall(X))=>(quiet(X)<~>~brave(X))))&
(((~old(paul)|~calm(paul)))<=>((~tall(lucy)<~>funny(lucy))))&
(![X]:((~generous(X)|calm(X))<=>(old(X)&~strong(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(~humble(john)))&
((?[X]:((~tall(X)|~humble(X))))=>(~rich(lucy)))&
(((calm(paul)&humble(paul)))<=>((strong(alice)|~happy(alice))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)|tall(X))=>(tall(X)|~quiet(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>~patient(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&~creative(X))))&
(![X]:(wise(X)<=>(~funny(X)|~wise(X))))&
(![X]:((tall(X)|kind(X))=>old(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((~happy(X)|funny(X))))&
((~calm(lucy)|~generous(lucy)))&
(?[X]:(~brave(X)))&
(~calm(susan))&
((tall(mary)|quiet(mary)))&
(brave(susan)) | quiet(lucy) | [] | null | 0 |
Everyone who is both tall and not brave is both old and generous.
If alice is not old or generous then someone is both old and wise.
If paul is happy then fred is either generous or brave and vice versa.
If someone is brave or not rich then susan is either old or generous.
Everyone who is both old and not curious is either happy or not curious and vice versa.
If someone is tall then someone is both not rich and not wise.
Everyone who is either not happy or generous is not generous or not creative.
Everyone who is not strong or patient is generous and vice versa.
If someone is either not happy or quiet then someone is not curious or brave.
If someone is either quiet or not kind then john is not humble or not funny.
If someone is either not old or not curious then paul is either not rich or kind.
If paul is either generous or wise then someone is both not strong and not funny.
If susan is either curious or rich then someone is old.
Everyone who is either not generous or creative is not calm.
If fred is rich then someone is either not wise or calm and vice versa.
Everyone who is strong is happy and vice versa.
Paul is both not brave and strong.
Someone is old.
Paul is not creative.
Paul is kind.
Someone is either tall or not happy.
Fred is either not calm or not strong.
Someone is not rich or not calm.
Susan is either tall or not old. | Paul is creative. | contradiction | (![X]:((tall(X)&~brave(X))=>(old(X)&generous(X))))&
(((~old(alice)|generous(alice)))=>(?[X]:((old(X)&wise(X)))))&
((happy(paul))<=>((generous(fred)<~>brave(fred))))&
((?[X]:((brave(X)|~rich(X))))=>((old(susan)<~>generous(susan))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)<~>~curious(X))))&
((?[X]:(tall(X)))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((~happy(X)<~>generous(X))=>(~generous(X)|~creative(X))))&
(![X]:((~strong(X)|patient(X))<=>generous(X)))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((~curious(X)|brave(X)))))&
((?[X]:((quiet(X)<~>~kind(X))))=>((~humble(john)|~funny(john))))&
((?[X]:((~old(X)<~>~curious(X))))=>((~rich(paul)<~>kind(paul))))&
(((generous(paul)<~>wise(paul)))=>(?[X]:((~strong(X)&~funny(X)))))&
(((curious(susan)<~>rich(susan)))=>(?[X]:(old(X))))&
(![X]:((~generous(X)<~>creative(X))=>~calm(X)))&
((rich(fred))<=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(strong(X)<=>happy(X)))&
((~brave(paul)&strong(paul)))&
(?[X]:(old(X)))&
(~creative(paul))&
(kind(paul))&
(?[X]:((tall(X)<~>~happy(X))))&
((~calm(fred)<~>~strong(fred)))&
(?[X]:((~rich(X)|~calm(X))))&
((tall(susan)<~>~old(susan))) | creative(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7731647534864317204856809
% SZS output start Proof for 7731647534864317204856809
19. ~creative(paul) [input p18]
25. creative(paul) [input hypothesis]
128. ~creative(paul) [cnf transformation 19]
137. creative(paul) [cnf transformation 25]
329. $false [subsumption resolution 137,128]
% SZS output end Proof for 7731647534864317204856809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious then someone is not brave and vice versa. Everyone who is not brave is quiet or brave. If lucy is either not rich or not patient then susan is either not humble or generous. If someone is either not strong or old then someone is either not old or old. If someone is not patient or not wise then someone is both strong and tall and vice versa. If someone is calm then someone is either generous or strong. Everyone who is either happy or kind is brave or not happy and vice versa. Everyone who is both not quiet and old is both quiet and old and vice versa. If paul is both rich and patient then john is both not tall and generous. If mary is both not patient and not humble then lucy is either not curious or not strong. If someone is wise or tall then fred is either not funny or not wise and vice versa. Everyone who is not wise is creative or not quiet and vice versa. If fred is old then someone is both not strong and not old. Everyone who is either creative or not wise is both strong and not quiet. Everyone who is not old or humble is both not creative and calm and vice versa. If lucy is quiet then alice is not happy. Someone is both strong and funny. Mary is happy. Someone is rich. John is either not kind or happy. Fred is not patient or not creative. Susan is both not happy and not wise. | Fred is not creative. | entailment | ((~curious(paul))<=>(?[X]:(~brave(X))))&
(![X]:(~brave(X)=>(quiet(X)|brave(X))))&
(((~rich(lucy)<~>~patient(lucy)))=>((~humble(susan)<~>generous(susan))))&
((?[X]:((~strong(X)<~>old(X))))=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((~patient(X)|~wise(X))))<=>(?[X]:((strong(X)&tall(X)))))&
((?[X]:(calm(X)))=>(?[X]:((generous(X)<~>strong(X)))))&
(![X]:((happy(X)<~>kind(X))<=>(brave(X)|~happy(X))))&
(![X]:((~quiet(X)&old(X))<=>(quiet(X)&old(X))))&
(((rich(paul)&patient(paul)))=>((~tall(john)&generous(john))))&
(((~patient(mary)&~humble(mary)))=>((~curious(lucy)<~>~strong(lucy))))&
((?[X]:((wise(X)|tall(X))))<=>((~funny(fred)<~>~wise(fred))))&
(![X]:(~wise(X)<=>(creative(X)|~quiet(X))))&
((old(fred))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:((creative(X)<~>~wise(X))=>(strong(X)&~quiet(X))))&
(![X]:((~old(X)|humble(X))<=>(~creative(X)&calm(X))))&
((quiet(lucy))=>(~happy(alice)))&
(?[X]:((strong(X)&funny(X))))&
(happy(mary))&
(?[X]:(rich(X)))&
((~kind(john)<~>happy(john)))&
((~patient(fred)|~creative(fred)))&
((~happy(susan)&~wise(susan))) | ~creative(fred) | [
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4308810918570310138653486
% SZS output start Proof for 4308810918570310138653486
8. ! [X0] : ((old(X0) & ~quiet(X0)) <=> (old(X0) & quiet(X0))) [input p7]
15. ! [X0] : ((humble(X0) | ~old(X0)) <=> (calm(X0) & ~creative(X0))) [input p14]
23. creative(fred) [input hypothesis]
59. ! [X0] : (((old(X0) & ~quiet(X0)) | (~old(X0) | ~quiet(X0))) & ((old(X0) & quiet(X0)) | (~old(X0) | quiet(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & ~quiet(X0)) | ~old(X0) | ~quiet(X0)) & ((old(X0) & quiet(X0)) | ~old(X0) | quiet(X0))) [flattening 59]
71. ! [X0] : (((humble(X0) | ~old(X0)) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 15]
72. ! [X0] : ((humble(X0) | ~old(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | (~humble(X0) & old(X0)))) [flattening 71]
102. quiet(X0) | ~old(X0) | quiet(X0) [cnf transformation 60]
104. ~quiet(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 60]
125. ~creative(X0) | old(X0) [cnf transformation 72]
140. creative(fred) [cnf transformation 23]
141. quiet(X0) | ~old(X0) [duplicate literal removal 102]
142. ~quiet(X0) | ~old(X0) [duplicate literal removal 104]
223. ~old(X0) [subsumption resolution 141,142]
289. ~creative(X0) [subsumption resolution 125,223]
301. $false [subsumption resolution 140,289]
% SZS output end Proof for 4308810918570310138653486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is happy or not wise then someone is curious or not old.
If someone is both not brave and not curious then alice is both kind and tall.
If lucy is either rich or not happy then someone is kind or tall and vice versa.
Everyone who is both rich and brave is strong.
Everyone who is funny or quiet is either not curious or calm and vice versa.
If someone is brave or quiet then paul is both not happy and not strong and vice versa.
Everyone who is either not tall or not curious is not generous and vice versa.
If someone is either not wise or tall then fred is either old or not brave and vice versa.
If john is either not patient or generous then lucy is either calm or generous.
If someone is kind then someone is both creative and not brave and vice versa.
Everyone who is not calm or old is curious and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is both not old and quiet is both wise and old and vice versa.
If mary is quiet then someone is either not rich or not creative and vice versa.
Everyone who is not funny or curious is either not creative or not strong.
If someone is brave or creative then someone is generous.
Mary is not calm.
Lucy is either generous or happy.
Alice is not wise or tall.
Alice is kind.
Susan is patient or not strong.
Susan is patient or not generous. | Mary is wise. | contradiction | (((happy(paul)|~wise(paul)))=>(?[X]:((curious(X)|~old(X)))))&
((?[X]:((~brave(X)&~curious(X))))=>((kind(alice)&tall(alice))))&
(((rich(lucy)<~>~happy(lucy)))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((rich(X)&brave(X))=>strong(X)))&
(![X]:((funny(X)|quiet(X))<=>(~curious(X)<~>calm(X))))&
((?[X]:((brave(X)|quiet(X))))<=>((~happy(paul)&~strong(paul))))&
(![X]:((~tall(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:((~wise(X)<~>tall(X))))<=>((old(fred)<~>~brave(fred))))&
(((~patient(john)<~>generous(john)))=>((calm(lucy)<~>generous(lucy))))&
((?[X]:(kind(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((~calm(X)|old(X))<=>curious(X)))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~old(X)&quiet(X))<=>(wise(X)&old(X))))&
((quiet(mary))<=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((~funny(X)|curious(X))=>(~creative(X)<~>~strong(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:(generous(X))))&
(~calm(mary))&
((generous(lucy)<~>happy(lucy)))&
((~wise(alice)|tall(alice)))&
(kind(alice))&
((patient(susan)|~strong(susan)))&
((patient(susan)|~generous(susan))) | wise(mary) | [
"p4",
"p10",
"p11",
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 163203619328921879445953
% SZS output start Proof for 163203619328921879445953
5. ! [X0] : ((quiet(X0) | funny(X0)) <=> (~curious(X0) <~> calm(X0))) [input p4]
11. ! [X0] : ((old(X0) | ~calm(X0)) <=> curious(X0)) [input p10]
12. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p11]
13. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (old(X0) & wise(X0))) [input p12]
17. ~calm(mary) [input p16]
23. wise(mary) [input hypothesis]
31. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 12]
40. ! [X0] : (((quiet(X0) | funny(X0)) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) & (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : ((quiet(X0) | funny(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) & (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | (~quiet(X0) & ~funny(X0)))) [flattening 40]
58. ! [X0] : (((old(X0) | ~calm(X0)) | ~curious(X0)) & (curious(X0) | (~old(X0) & calm(X0)))) [nnf transformation 11]
59. ! [X0] : ((old(X0) | ~calm(X0) | ~curious(X0)) & (curious(X0) | (~old(X0) & calm(X0)))) [flattening 58]
60. ! [X0] : (((quiet(X0) & ~old(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 13]
61. ! [X0] : (((quiet(X0) & ~old(X0)) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | ~quiet(X0) | old(X0))) [flattening 60]
82. ~funny(X0) | ~curious(X0) | calm(X0) [cnf transformation 41]
112. calm(X0) | curious(X0) [cnf transformation 59]
115. funny(X0) | old(X0) [cnf transformation 31]
119. ~old(X0) | ~old(X0) | ~wise(X0) [cnf transformation 61]
131. ~calm(mary) [cnf transformation 17]
138. wise(mary) [cnf transformation 23]
140. ~old(X0) | ~wise(X0) [duplicate literal removal 119]
381. ~curious(X0) | calm(X0) | old(X0) [resolution 82,115]
382. calm(X0) | old(X0) [subsumption resolution 381,112]
398. old(mary) [resolution 382,131]
412. ~wise(mary) [resolution 398,140]
414. $false [subsumption resolution 412,138]
% SZS output end Proof for 163203619328921879445953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not patient then someone is brave or not patient.
Everyone who is both humble and brave is either happy or creative.
Everyone who is both not funny and not happy is not calm and vice versa.
Everyone who is both funny and not curious is both not generous and funny and vice versa.
Everyone who is both not brave and humble is old or not generous and vice versa.
If lucy is kind then someone is rich.
Everyone who is creative is not patient or not generous and vice versa.
Everyone who is not generous is both strong and not brave and vice versa.
Everyone who is both not calm and not brave is calm or tall and vice versa.
If susan is not brave or curious then susan is either not quiet or not happy.
If someone is both not rich and brave then john is either quiet or patient and vice versa.
Everyone who is both tall and not curious is both patient and not tall and vice versa.
If alice is both not strong and not curious then someone is calm and vice versa.
Everyone who is not creative is both not humble and creative.
Everyone who is either strong or not brave is both creative and not wise and vice versa.
If mary is not quiet or old then john is both not rich and calm and vice versa.
Alice is not happy or rich.
Fred is not happy.
Someone is not calm or not strong.
Someone is not brave.
Lucy is both not humble and wise.
Paul is not kind or creative.
Paul is either calm or old. | John is not humble. | neutral | ((?[X]:((~old(X)&~patient(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:((humble(X)&brave(X))=>(happy(X)<~>creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>~calm(X)))&
(![X]:((funny(X)&~curious(X))<=>(~generous(X)&funny(X))))&
(![X]:((~brave(X)&humble(X))<=>(old(X)|~generous(X))))&
((kind(lucy))=>(?[X]:(rich(X))))&
(![X]:(creative(X)<=>(~patient(X)|~generous(X))))&
(![X]:(~generous(X)<=>(strong(X)&~brave(X))))&
(![X]:((~calm(X)&~brave(X))<=>(calm(X)|tall(X))))&
(((~brave(susan)|curious(susan)))=>((~quiet(susan)<~>~happy(susan))))&
((?[X]:((~rich(X)&brave(X))))<=>((quiet(john)<~>patient(john))))&
(![X]:((tall(X)&~curious(X))<=>(patient(X)&~tall(X))))&
(((~strong(alice)&~curious(alice)))<=>(?[X]:(calm(X))))&
(![X]:(~creative(X)=>(~humble(X)&creative(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(creative(X)&~wise(X))))&
(((~quiet(mary)|old(mary)))<=>((~rich(john)&calm(john))))&
((~happy(alice)|rich(alice)))&
(~happy(fred))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:(~brave(X)))&
((~humble(lucy)&wise(lucy)))&
((~kind(paul)|creative(paul)))&
((calm(paul)<~>old(paul))) | ~humble(john) | [] | null | 0 |
Everyone who is either tall or patient is not humble or not rich and vice versa. Everyone who is kind or not humble is happy. Everyone who is both creative and not wise is both not creative and not generous and vice versa. Everyone who is generous is quiet. Everyone who is both not strong and not wise is not tall. Everyone who is both not strong and calm is both not patient and funny and vice versa. If someone is brave then alice is wise. Everyone who is old is brave or tall and vice versa. If someone is quiet then susan is both not creative and not rich and vice versa. If mary is both not creative and funny then lucy is either not quiet or old and vice versa. Everyone who is both not creative and tall is both funny and curious. Everyone who is not patient is either not old or calm and vice versa. If john is both not creative and happy then mary is either tall or not tall. Everyone who is happy is not humble or calm. Everyone who is curious is both tall and happy and vice versa. Everyone who is wise or not patient is both rich and not curious. Someone is wise or curious. Someone is either brave or happy. Mary is not funny. Alice is generous or not old. Someone is either kind or not kind. Someone is either kind or not brave. Someone is either not patient or kind. | Mary is not tall. | neutral | (![X]:((tall(X)<~>patient(X))<=>(~humble(X)|~rich(X))))&
(![X]:((kind(X)|~humble(X))=>happy(X)))&
(![X]:((creative(X)&~wise(X))<=>(~creative(X)&~generous(X))))&
(![X]:(generous(X)=>quiet(X)))&
(![X]:((~strong(X)&~wise(X))=>~tall(X)))&
(![X]:((~strong(X)&calm(X))<=>(~patient(X)&funny(X))))&
((?[X]:(brave(X)))=>(wise(alice)))&
(![X]:(old(X)<=>(brave(X)|tall(X))))&
((?[X]:(quiet(X)))<=>((~creative(susan)&~rich(susan))))&
(((~creative(mary)&funny(mary)))<=>((~quiet(lucy)<~>old(lucy))))&
(![X]:((~creative(X)&tall(X))=>(funny(X)&curious(X))))&
(![X]:(~patient(X)<=>(~old(X)<~>calm(X))))&
(((~creative(john)&happy(john)))=>((tall(mary)<~>~tall(mary))))&
(![X]:(happy(X)=>(~humble(X)|calm(X))))&
(![X]:(curious(X)<=>(tall(X)&happy(X))))&
(![X]:((wise(X)|~patient(X))=>(rich(X)&~curious(X))))&
(?[X]:((wise(X)|curious(X))))&
(?[X]:((brave(X)<~>happy(X))))&
(~funny(mary))&
((generous(alice)|~old(alice)))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((kind(X)<~>~brave(X))))&
(?[X]:((~patient(X)<~>kind(X)))) | ~tall(mary) | [] | null | 0 |
Everyone who is not happy is not generous and vice versa. If john is not brave or not creative then someone is both creative and not wise. Everyone who is either not quiet or patient is either not calm or wise and vice versa. If alice is either quiet or creative then someone is both quiet and tall and vice versa. Everyone who is both not generous and brave is both patient and humble and vice versa. If someone is either old or quiet then mary is both not wise and not old. Everyone who is quiet is rich and vice versa. If someone is both strong and not rich then paul is either old or funny. Everyone who is either creative or not strong is generous and vice versa. Everyone who is not brave or not tall is old and vice versa. If someone is both not generous and not happy then someone is not old and vice versa. Everyone who is both not creative and not quiet is kind or not creative and vice versa. Everyone who is not kind or not quiet is strong or curious. If john is either not old or not funny then mary is funny or brave. Everyone who is not wise is generous. Someone is either not patient or not creative. Someone is not rich. Alice is both funny and calm. Someone is either old or patient. Someone is not rich or not happy. Alice is either not old or happy. Someone is curious or tall. Someone is not humble or brave. | Paul is tall. | neutral | (![X]:(~happy(X)<=>~generous(X)))&
(((~brave(john)|~creative(john)))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~calm(X)<~>wise(X))))&
(((quiet(alice)<~>creative(alice)))<=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((~generous(X)&brave(X))<=>(patient(X)&humble(X))))&
((?[X]:((old(X)<~>quiet(X))))=>((~wise(mary)&~old(mary))))&
(![X]:(quiet(X)<=>rich(X)))&
((?[X]:((strong(X)&~rich(X))))=>((old(paul)<~>funny(paul))))&
(![X]:((creative(X)<~>~strong(X))<=>generous(X)))&
(![X]:((~brave(X)|~tall(X))<=>old(X)))&
((?[X]:((~generous(X)&~happy(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(kind(X)|~creative(X))))&
(![X]:((~kind(X)|~quiet(X))=>(strong(X)|curious(X))))&
(((~old(john)<~>~funny(john)))=>((funny(mary)|brave(mary))))&
(![X]:(~wise(X)=>generous(X)))&
(?[X]:((~patient(X)<~>~creative(X))))&
(?[X]:(~rich(X)))&
((funny(alice)&calm(alice)))&
(?[X]:((old(X)<~>patient(X))))&
(?[X]:((~rich(X)|~happy(X))))&
((~old(alice)<~>happy(alice)))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:((~humble(X)|brave(X)))) | tall(paul) | [] | null | 0 |
Everyone who is both kind and not patient is either rich or not curious and vice versa.
If someone is both not quiet and wise then lucy is not funny.
Everyone who is either not generous or not brave is not brave or humble and vice versa.
If someone is brave or not brave then lucy is either curious or generous and vice versa.
Everyone who is both not patient and not generous is not quiet or not creative.
If someone is strong or not tall then someone is both not patient and funny and vice versa.
Everyone who is either strong or tall is calm.
Everyone who is tall or not kind is both brave and generous and vice versa.
If susan is happy then someone is both not kind and not wise.
If someone is either not brave or funny then someone is happy and vice versa.
Everyone who is not calm is not brave or not tall and vice versa.
Everyone who is not strong or humble is either creative or happy.
Everyone who is old is either wise or happy.
Everyone who is both tall and not quiet is both not wise and not patient and vice versa.
If someone is either strong or not happy then susan is both funny and not wise and vice versa.
If someone is strong then mary is either rich or calm.
Susan is rich or not old.
Mary is both humble and not brave.
Mary is not happy.
Someone is both curious and not old.
Paul is either not kind or not tall.
Someone is either creative or not calm.
Susan is not strong or not kind. | Mary is quiet. | neutral | (![X]:((kind(X)&~patient(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))=>(~funny(lucy)))&
(![X]:((~generous(X)<~>~brave(X))<=>(~brave(X)|humble(X))))&
((?[X]:((brave(X)|~brave(X))))<=>((curious(lucy)<~>generous(lucy))))&
(![X]:((~patient(X)&~generous(X))=>(~quiet(X)|~creative(X))))&
((?[X]:((strong(X)|~tall(X))))<=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:((strong(X)<~>tall(X))=>calm(X)))&
(![X]:((tall(X)|~kind(X))<=>(brave(X)&generous(X))))&
((happy(susan))=>(?[X]:((~kind(X)&~wise(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(happy(X))))&
(![X]:(~calm(X)<=>(~brave(X)|~tall(X))))&
(![X]:((~strong(X)|humble(X))=>(creative(X)<~>happy(X))))&
(![X]:(old(X)=>(wise(X)<~>happy(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~wise(X)&~patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))<=>((funny(susan)&~wise(susan))))&
((?[X]:(strong(X)))=>((rich(mary)<~>calm(mary))))&
((rich(susan)|~old(susan)))&
((humble(mary)&~brave(mary)))&
(~happy(mary))&
(?[X]:((curious(X)&~old(X))))&
((~kind(paul)<~>~tall(paul)))&
(?[X]:((creative(X)<~>~calm(X))))&
((~strong(susan)|~kind(susan))) | quiet(mary) | [] | null | 0 |
Everyone who is calm is not happy. Everyone who is either not quiet or quiet is both humble and not quiet. Everyone who is not kind is either brave or kind. Everyone who is either not tall or wise is either humble or not wise. Everyone who is not happy or kind is not calm or humble. Everyone who is not kind or humble is both funny and creative and vice versa. If lucy is either old or wise then paul is both not creative and happy and vice versa. If john is not happy or calm then someone is wise or creative and vice versa. If someone is not creative or kind then john is both kind and curious. If alice is either curious or not humble then someone is old. If paul is both not wise and happy then fred is both wise and not patient. Everyone who is either calm or wise is not tall or not calm. Everyone who is patient is brave or not kind. Everyone who is not humble is kind or humble. If mary is creative then mary is not old. Everyone who is brave or not tall is either quiet or not brave and vice versa. Alice is either strong or not old. Susan is not generous or brave. Someone is both humble and not quiet. Lucy is either not generous or creative. Mary is either not happy or patient. Someone is either kind or not old. | Paul is brave. | contradiction | (![X]:(calm(X)=>~happy(X)))&
(![X]:((~quiet(X)<~>quiet(X))=>(humble(X)&~quiet(X))))&
(![X]:(~kind(X)=>(brave(X)<~>kind(X))))&
(![X]:((~tall(X)<~>wise(X))=>(humble(X)<~>~wise(X))))&
(![X]:((~happy(X)|kind(X))=>(~calm(X)|humble(X))))&
(![X]:((~kind(X)|humble(X))<=>(funny(X)&creative(X))))&
(((old(lucy)<~>wise(lucy)))<=>((~creative(paul)&happy(paul))))&
(((~happy(john)|calm(john)))<=>(?[X]:((wise(X)|creative(X)))))&
((?[X]:((~creative(X)|kind(X))))=>((kind(john)&curious(john))))&
(((curious(alice)<~>~humble(alice)))=>(?[X]:(old(X))))&
(((~wise(paul)&happy(paul)))=>((wise(fred)&~patient(fred))))&
(![X]:((calm(X)<~>wise(X))=>(~tall(X)|~calm(X))))&
(![X]:(patient(X)=>(brave(X)|~kind(X))))&
(![X]:(~humble(X)=>(kind(X)|humble(X))))&
((creative(mary))=>(~old(mary)))&
(![X]:((brave(X)|~tall(X))<=>(quiet(X)<~>~brave(X))))&
((strong(alice)<~>~old(alice)))&
((~generous(susan)|brave(susan)))&
(?[X]:((humble(X)&~quiet(X))))&
((~generous(lucy)<~>creative(lucy)))&
((~happy(mary)<~>patient(mary)))&
(?[X]:((kind(X)<~>~old(X)))) | brave(paul) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2142998937231220975207657
% SZS output start Proof for 2142998937231220975207657
2. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (~quiet(X0) & humble(X0))) [input p1]
16. ! [X0] : ((~tall(X0) | brave(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p15]
23. brave(paul) [input hypothesis]
25. ! [X0] : ((~quiet(X0) & humble(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 2]
41. ! [X0] : ((~quiet(X0) & humble(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 25]
57. ! [X0] : (((~tall(X0) | brave(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (tall(X0) & ~brave(X0)))) [nnf transformation 16]
58. ! [X0] : ((~tall(X0) | brave(X0) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (tall(X0) & ~brave(X0)))) [flattening 57]
71. ~quiet(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 41]
108. ~brave(X0) | quiet(X0) | ~brave(X0) [cnf transformation 58]
125. brave(paul) [cnf transformation 23]
126. ~brave(X0) | quiet(X0) [duplicate literal removal 108]
136. ~quiet(X0) [duplicate literal removal 71]
203. ~brave(X0) [subsumption resolution 126,136]
236. $false [subsumption resolution 125,203]
% SZS output end Proof for 2142998937231220975207657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then fred is not humble or creative.
Everyone who is not kind or quiet is either not wise or not humble.
If someone is quiet or old then john is funny or quiet and vice versa.
Everyone who is either not humble or funny is calm and vice versa.
Everyone who is tall is generous or not brave.
If someone is both not patient and quiet then mary is old or not wise.
Everyone who is not calm or humble is not rich or not quiet.
Everyone who is either generous or wise is either not brave or not calm.
If someone is curious then someone is both not calm and kind.
Everyone who is either not tall or generous is both not generous and not happy and vice versa.
Everyone who is not strong is not generous and vice versa.
Everyone who is both not wise and old is either not patient or rich.
Everyone who is both calm and creative is not patient or not funny and vice versa.
Everyone who is quiet is tall and vice versa.
If someone is calm or not calm then lucy is tall or not calm and vice versa.
If someone is either not curious or creative then fred is not generous.
Someone is both rich and quiet.
Someone is generous or not generous.
Alice is kind.
Alice is old or quiet.
Alice is both rich and not strong.
Someone is either not happy or strong.
Someone is both not wise and calm.
Someone is both not old and not funny. | Alice is kind. | entailment | ((?[X]:(creative(X)))=>((~humble(fred)|creative(fred))))&
(![X]:((~kind(X)|quiet(X))=>(~wise(X)<~>~humble(X))))&
((?[X]:((quiet(X)|old(X))))<=>((funny(john)|quiet(john))))&
(![X]:((~humble(X)<~>funny(X))<=>calm(X)))&
(![X]:(tall(X)=>(generous(X)|~brave(X))))&
((?[X]:((~patient(X)&quiet(X))))=>((old(mary)|~wise(mary))))&
(![X]:((~calm(X)|humble(X))=>(~rich(X)|~quiet(X))))&
(![X]:((generous(X)<~>wise(X))=>(~brave(X)<~>~calm(X))))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((~tall(X)<~>generous(X))<=>(~generous(X)&~happy(X))))&
(![X]:(~strong(X)<=>~generous(X)))&
(![X]:((~wise(X)&old(X))=>(~patient(X)<~>rich(X))))&
(![X]:((calm(X)&creative(X))<=>(~patient(X)|~funny(X))))&
(![X]:(quiet(X)<=>tall(X)))&
((?[X]:((calm(X)|~calm(X))))<=>((tall(lucy)|~calm(lucy))))&
((?[X]:((~curious(X)<~>creative(X))))=>(~generous(fred)))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:((generous(X)|~generous(X))))&
(kind(alice))&
((old(alice)|quiet(alice)))&
((rich(alice)&~strong(alice)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~wise(X)&calm(X))))&
(?[X]:((~old(X)&~funny(X)))) | kind(alice) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2041373698574440118670813
% SZS output start Proof for 2041373698574440118670813
19. kind(alice) [input p18]
25. ~kind(alice) [input hypothesis]
125. kind(alice) [cnf transformation 19]
135. ~kind(alice) [cnf transformation 25]
248. $false [subsumption resolution 135,125]
% SZS output end Proof for 2041373698574440118670813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not kind then someone is either curious or not wise and vice versa. If john is both quiet and creative then someone is not creative or patient and vice versa. If someone is either rich or not old then susan is both not quiet and not funny. If alice is not funny then fred is both not generous and not strong. If mary is both creative and not brave then paul is brave. Everyone who is happy or not funny is both rich and not tall. Everyone who is calm is both not quiet and not funny. Everyone who is either not funny or brave is calm and vice versa. If fred is patient then someone is both brave and quiet and vice versa. If someone is not patient then fred is either calm or not creative. Everyone who is either humble or kind is either not tall or not generous. Everyone who is brave or not patient is not curious and vice versa. Everyone who is both curious and tall is patient or curious. Everyone who is either kind or not quiet is both funny and patient and vice versa. If someone is either not happy or patient then someone is both happy and not kind. If someone is either not old or old then john is both not happy and calm and vice versa. Someone is either tall or curious. Paul is either not happy or humble. Fred is not generous. Someone is kind. Lucy is both not quiet and strong. Paul is either wise or not calm. Someone is not happy. | Lucy is kind. | entailment | (((patient(susan)|~kind(susan)))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((quiet(john)&creative(john)))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((rich(X)<~>~old(X))))=>((~quiet(susan)&~funny(susan))))&
((~funny(alice))=>((~generous(fred)&~strong(fred))))&
(((creative(mary)&~brave(mary)))=>(brave(paul)))&
(![X]:((happy(X)|~funny(X))=>(rich(X)&~tall(X))))&
(![X]:(calm(X)=>(~quiet(X)&~funny(X))))&
(![X]:((~funny(X)<~>brave(X))<=>calm(X)))&
((patient(fred))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:(~patient(X)))=>((calm(fred)<~>~creative(fred))))&
(![X]:((humble(X)<~>kind(X))=>(~tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~patient(X))<=>~curious(X)))&
(![X]:((curious(X)&tall(X))=>(patient(X)|curious(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(funny(X)&patient(X))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((happy(X)&~kind(X)))))&
((?[X]:((~old(X)<~>old(X))))<=>((~happy(john)&calm(john))))&
(?[X]:((tall(X)<~>curious(X))))&
((~happy(paul)<~>humble(paul)))&
(~generous(fred))&
(?[X]:(kind(X)))&
((~quiet(lucy)&strong(lucy)))&
((wise(paul)<~>~calm(paul)))&
(?[X]:(~happy(X))) | kind(lucy) | [
"p1",
"p6",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3202266702638943892225284
% SZS output start Proof for 3202266702638943892225284
2. (creative(john) & quiet(john)) <=> ? [X0] : (patient(X0) | ~creative(X0)) [input p1]
7. ! [X0] : (calm(X0) => (~funny(X0) & ~quiet(X0))) [input p6]
14. ! [X0] : ((kind(X0) <~> ~quiet(X0)) <=> (patient(X0) & funny(X0))) [input p13]
16. ? [X0] : (~old(X0) <~> old(X0)) <=> (calm(john) & ~happy(john)) [input p15]
21. strong(lucy) & ~quiet(lucy) [input p20]
24. ~kind(lucy) [input hypothesis]
31. ! [X0] : ((~funny(X0) & ~quiet(X0)) | ~calm(X0)) [ennf transformation 7]
42. ((creative(john) & quiet(john)) | ! [X0] : (~patient(X0) & creative(X0))) & (? [X0] : (patient(X0) | ~creative(X0)) | (~creative(john) | ~quiet(john))) [nnf transformation 2]
43. ((creative(john) & quiet(john)) | ! [X0] : (~patient(X0) & creative(X0))) & (? [X0] : (patient(X0) | ~creative(X0)) | ~creative(john) | ~quiet(john)) [flattening 42]
44. ((creative(john) & quiet(john)) | ! [X0] : (~patient(X0) & creative(X0))) & (? [X1] : (patient(X1) | ~creative(X1)) | ~creative(john) | ~quiet(john)) [rectify 43]
45. ? [X1] : (patient(X1) | ~creative(X1)) => (patient(sK1) | ~creative(sK1)) [choice axiom]
46. ((creative(john) & quiet(john)) | ! [X0] : (~patient(X0) & creative(X0))) & ((patient(sK1) | ~creative(sK1)) | ~creative(john) | ~quiet(john)) [skolemisation 44,45]
57. ! [X0] : ((((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | (~patient(X0) | ~funny(X0))) & ((patient(X0) & funny(X0)) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))))) [nnf transformation 14]
58. ! [X0] : ((((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ~patient(X0) | ~funny(X0)) & ((patient(X0) & funny(X0)) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))))) [flattening 57]
63. (? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (~calm(john) | happy(john))) & ((calm(john) & ~happy(john)) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 16]
64. (? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~calm(john) | happy(john)) & ((calm(john) & ~happy(john)) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [flattening 63]
65. (? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~calm(john) | happy(john)) & ((calm(john) & ~happy(john)) | ! [X1] : ((~old(X1) | ~old(X1)) & (old(X1) | old(X1)))) [rectify 64]
66. ? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) => ((~old(sK4) | old(sK4)) & (old(sK4) | ~old(sK4))) [choice axiom]
67. (((~old(sK4) | old(sK4)) & (old(sK4) | ~old(sK4))) | ~calm(john) | happy(john)) & ((calm(john) & ~happy(john)) | ! [X1] : ((~old(X1) | ~old(X1)) & (old(X1) | old(X1)))) [skolemisation 65,66]
85. quiet(john) | ~patient(X0) [cnf transformation 46]
99. ~calm(X0) | ~quiet(X0) [cnf transformation 31]
121. quiet(X0) | kind(X0) | patient(X0) [cnf transformation 58]
130. calm(john) | old(X1) | old(X1) [cnf transformation 67]
131. calm(john) | ~old(X1) | ~old(X1) [cnf transformation 67]
140. ~quiet(lucy) [cnf transformation 21]
145. ~kind(lucy) [cnf transformation 24]
148. calm(john) | old(X1) [duplicate literal removal 130]
149. calm(john) | ~old(X1) [duplicate literal removal 131]
179. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
180. ~patient(X0) <- (7) [avatar component clause 179]
191. 10 <=> quiet(john) [avatar definition]
194. 7 | 10 [avatar split clause 85,191,179]
302. 34 <=> ! [X1] : ~old(X1) [avatar definition]
303. ~old(X1) <- (34) [avatar component clause 302]
305. 35 <=> calm(john) [avatar definition]
307. calm(john) <- (35) [avatar component clause 305]
308. 34 | 35 [avatar split clause 149,305,302]
310. 36 <=> ! [X1] : old(X1) [avatar definition]
311. old(X1) <- (36) [avatar component clause 310]
312. 36 | 35 [avatar split clause 148,305,310]
355. ~quiet(john) <- (35) [resolution 99,307]
358. ~10 | ~35 [avatar split clause 355,305,191]
421. $false <- (34, 36) [subsumption resolution 303,311]
422. ~34 | ~36 [avatar contradiction clause 421]
440. kind(lucy) | patient(lucy) [resolution 121,140]
443. patient(lucy) [subsumption resolution 440,145]
444. $false <- (7) [subsumption resolution 443,180]
445. ~7 [avatar contradiction clause 444]
446. $false [avatar sat refutation 194,308,312,358,422,445]
% SZS output end Proof for 3202266702638943892225284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or generous then someone is not funny or funny.
Everyone who is quiet is not brave or calm.
If mary is either wise or not calm then someone is either humble or creative.
Everyone who is not brave or generous is both not humble and not curious.
Everyone who is both curious and not patient is not wise or not brave and vice versa.
Everyone who is either not tall or strong is both strong and funny.
Everyone who is humble or not brave is both not generous and calm.
Everyone who is brave is creative or brave.
Everyone who is both tall and calm is either not patient or patient and vice versa.
If susan is both creative and humble then someone is not funny or not rich.
If someone is either not funny or not rich then someone is both not funny and quiet and vice versa.
If susan is rich then someone is both kind and not wise and vice versa.
If fred is both generous and not tall then paul is both curious and not calm and vice versa.
Everyone who is either not kind or generous is not quiet.
Everyone who is both not strong and humble is not strong and vice versa.
Mary is not happy or not old.
Someone is either not kind or not creative.
Fred is both not generous and not humble.
Someone is either not humble or humble.
Someone is either not happy or strong.
Someone is not happy or generous.
Someone is both tall and not generous. | Mary is not humble. | neutral | ((?[X]:((old(X)|generous(X))))=>(?[X]:((~funny(X)|funny(X)))))&
(![X]:(quiet(X)=>(~brave(X)|calm(X))))&
(((wise(mary)<~>~calm(mary)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~brave(X)|generous(X))=>(~humble(X)&~curious(X))))&
(![X]:((curious(X)&~patient(X))<=>(~wise(X)|~brave(X))))&
(![X]:((~tall(X)<~>strong(X))=>(strong(X)&funny(X))))&
(![X]:((humble(X)|~brave(X))=>(~generous(X)&calm(X))))&
(![X]:(brave(X)=>(creative(X)|brave(X))))&
(![X]:((tall(X)&calm(X))<=>(~patient(X)<~>patient(X))))&
(((creative(susan)&humble(susan)))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>(?[X]:((~funny(X)&quiet(X)))))&
((rich(susan))<=>(?[X]:((kind(X)&~wise(X)))))&
(((generous(fred)&~tall(fred)))<=>((curious(paul)&~calm(paul))))&
(![X]:((~kind(X)<~>generous(X))=>~quiet(X)))&
(![X]:((~strong(X)&humble(X))<=>~strong(X)))&
((~happy(mary)|~old(mary)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((~generous(fred)&~humble(fred)))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:((tall(X)&~generous(X)))) | ~humble(mary) | [] | null | 0 |
If someone is both not kind and strong then someone is both kind and not curious.
If fred is both curious and not rich then someone is quiet or not rich.
If mary is both strong and not wise then someone is either generous or not patient and vice versa.
If someone is either not humble or kind then paul is happy and vice versa.
Everyone who is not curious or patient is either not creative or quiet and vice versa.
Everyone who is calm is both not wise and patient.
If fred is either creative or patient then john is humble or tall.
If lucy is either humble or quiet then paul is not generous.
Everyone who is not calm or curious is both tall and strong.
If someone is quiet or wise then someone is strong.
Everyone who is rich or not strong is either not tall or brave and vice versa.
If john is both not rich and strong then someone is not generous or patient.
Everyone who is both not brave and not strong is not tall or rich.
Everyone who is both not patient and not brave is both rich and not old.
Everyone who is wise is quiet or not tall.
If john is funny then paul is both not wise and brave and vice versa.
Someone is both not funny and humble.
Fred is both wise and not patient.
Fred is either not generous or calm.
Mary is not patient.
Alice is calm or not humble.
Someone is either happy or rich.
Someone is both generous and not strong.
Someone is not brave or not curious. | Fred is not strong. | contradiction | ((?[X]:((~kind(X)&strong(X))))=>(?[X]:((kind(X)&~curious(X)))))&
(((curious(fred)&~rich(fred)))=>(?[X]:((quiet(X)|~rich(X)))))&
(((strong(mary)&~wise(mary)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
((?[X]:((~humble(X)<~>kind(X))))<=>(happy(paul)))&
(![X]:((~curious(X)|patient(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(calm(X)=>(~wise(X)&patient(X))))&
(((creative(fred)<~>patient(fred)))=>((humble(john)|tall(john))))&
(((humble(lucy)<~>quiet(lucy)))=>(~generous(paul)))&
(![X]:((~calm(X)|curious(X))=>(tall(X)&strong(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:(strong(X))))&
(![X]:((rich(X)|~strong(X))<=>(~tall(X)<~>brave(X))))&
(((~rich(john)&strong(john)))=>(?[X]:((~generous(X)|patient(X)))))&
(![X]:((~brave(X)&~strong(X))=>(~tall(X)|rich(X))))&
(![X]:((~patient(X)&~brave(X))=>(rich(X)&~old(X))))&
(![X]:(wise(X)=>(quiet(X)|~tall(X))))&
((funny(john))<=>((~wise(paul)&brave(paul))))&
(?[X]:((~funny(X)&humble(X))))&
((wise(fred)&~patient(fred)))&
((~generous(fred)<~>calm(fred)))&
(~patient(mary))&
((calm(alice)|~humble(alice)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((~brave(X)|~curious(X)))) | ~strong(fred) | [
"p5",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 576093548536893230685989
% SZS output start Proof for 576093548536893230685989
6. ! [X0] : (calm(X0) => (patient(X0) & ~wise(X0))) [input p5]
9. ! [X0] : ((curious(X0) | ~calm(X0)) => (strong(X0) & tall(X0))) [input p8]
18. ~patient(fred) & wise(fred) [input p17]
25. ~strong(fred) [input hypothesis]
32. ! [X0] : ((patient(X0) & ~wise(X0)) | ~calm(X0)) [ennf transformation 6]
36. ! [X0] : ((strong(X0) & tall(X0)) | (~curious(X0) & calm(X0))) [ennf transformation 9]
102. ~calm(X0) | ~wise(X0) [cnf transformation 32]
110. calm(X0) | strong(X0) [cnf transformation 36]
129. wise(fred) [cnf transformation 18]
140. ~strong(fred) [cnf transformation 25]
303. 37 <=> calm(fred) [avatar definition]
304. calm(fred) <- (37) [avatar component clause 303]
305. ~calm(fred) <- (~37) [avatar component clause 303]
336. strong(fred) <- (~37) [resolution 110,305]
339. $false <- (~37) [subsumption resolution 336,140]
340. 37 [avatar contradiction clause 339]
342. ~wise(fred) <- (37) [resolution 304,102]
345. $false <- (37) [subsumption resolution 342,129]
346. ~37 [avatar contradiction clause 345]
347. $false [avatar sat refutation 340,346]
% SZS output end Proof for 576093548536893230685989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or tall. Everyone who is either creative or not funny is not old or not humble and vice versa. If fred is either old or not quiet then someone is either not strong or generous and vice versa. If someone is either not humble or funny then mary is not strong or tall and vice versa. Everyone who is funny or creative is both not strong and tall. Everyone who is not brave or not patient is not funny. Everyone who is happy or not tall is either not generous or generous and vice versa. Everyone who is happy or brave is rich and vice versa. Everyone who is curious or kind is both not old and not curious. If paul is either strong or humble then lucy is not rich or curious. If paul is generous or not kind then susan is creative and vice versa. If someone is calm or kind then someone is patient or old and vice versa. Everyone who is quiet or not funny is either not calm or curious. If alice is both curious and not old then someone is not strong or happy and vice versa. Everyone who is rich is not quiet or funny. If someone is not rich then someone is either not old or calm and vice versa. Paul is both not creative and not calm. Someone is either curious or quiet. Someone is either patient or rich. Someone is not creative. Lucy is old or rich. Someone is either not curious or wise. Susan is not quiet. Someone is either patient or not strong. | Lucy is not funny. | entailment | (![X]:(~patient(X)=>(patient(X)<~>tall(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~old(X)|~humble(X))))&
(((old(fred)<~>~quiet(fred)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((~humble(X)<~>funny(X))))<=>((~strong(mary)|tall(mary))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(((curious(alice)&~old(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
((~creative(paul)&~calm(paul)))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:(~creative(X)))&
((old(lucy)|rich(lucy)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~quiet(susan))&
(?[X]:((patient(X)<~>~strong(X)))) | ~funny(lucy) | [
"p4",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4213968234286625505912374
% SZS output start Proof for 4213968234286625505912374
5. ! [X0] : ((creative(X0) | funny(X0)) => (tall(X0) & ~strong(X0))) [input p4]
9. ! [X0] : ((kind(X0) | curious(X0)) => (~curious(X0) & ~old(X0))) [input p8]
14. (~old(alice) & curious(alice)) <=> ? [X0] : (happy(X0) | ~strong(X0)) [input p13]
25. funny(lucy) [input hypothesis]
29. ! [X0] : ((tall(X0) & ~strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 5]
31. ! [X0] : ((~curious(X0) & ~old(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 9]
62. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | (old(alice) | ~curious(alice))) [nnf transformation 14]
63. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X0] : (happy(X0) | ~strong(X0)) | old(alice) | ~curious(alice)) [flattening 62]
64. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & (? [X1] : (happy(X1) | ~strong(X1)) | old(alice) | ~curious(alice)) [rectify 63]
65. ? [X1] : (happy(X1) | ~strong(X1)) => (happy(sK4) | ~strong(sK4)) [choice axiom]
66. ((~old(alice) & curious(alice)) | ! [X0] : (~happy(X0) & strong(X0))) & ((happy(sK4) | ~strong(sK4)) | old(alice) | ~curious(alice)) [skolemisation 64,65]
108. ~strong(X0) | ~funny(X0) [cnf transformation 29]
125. ~curious(X0) | ~curious(X0) [cnf transformation 31]
141. curious(alice) | strong(X0) [cnf transformation 66]
163. funny(lucy) [cnf transformation 25]
164. ~curious(X0) [duplicate literal removal 125]
301. 29 <=> ! [X0] : strong(X0) [avatar definition]
302. strong(X0) <- (29) [avatar component clause 301]
306. strong(X0) [subsumption resolution 141,164]
307. 29 [avatar split clause 306,301]
368. ~funny(X0) <- (29) [resolution 108,302]
370. $false <- (29) [resolution 368,163]
371. ~29 [avatar contradiction clause 370]
372. $false [avatar sat refutation 307,371]
% SZS output end Proof for 4213968234286625505912374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or old is not patient or funny.
Everyone who is either happy or not patient is not patient and vice versa.
Everyone who is both not funny and generous is either creative or not wise and vice versa.
If john is not calm or not strong then mary is not kind.
Everyone who is either generous or patient is either quiet or not wise and vice versa.
Everyone who is either not happy or not tall is either humble or not tall and vice versa.
Everyone who is not old or not rich is both old and not happy and vice versa.
Everyone who is quiet or brave is not curious or kind and vice versa.
Everyone who is both calm and not tall is creative or patient and vice versa.
Everyone who is not humble or wise is not tall.
If alice is either wise or old then someone is either not quiet or not creative and vice versa.
If fred is either generous or tall then someone is funny or rich and vice versa.
If someone is either not calm or happy then john is either strong or brave.
If someone is either quiet or not funny then someone is kind.
If someone is either wise or not tall then someone is either happy or kind.
If someone is not creative then someone is both kind and not happy and vice versa.
Paul is either kind or brave.
Alice is both not funny and wise.
Someone is not wise or not creative.
Someone is either not wise or patient.
Paul is either not patient or not rich.
Someone is not curious. | John is not quiet. | neutral | (![X]:((~strong(X)|old(X))=>(~patient(X)|funny(X))))&
(![X]:((happy(X)<~>~patient(X))<=>~patient(X)))&
(![X]:((~funny(X)&generous(X))<=>(creative(X)<~>~wise(X))))&
(((~calm(john)|~strong(john)))=>(~kind(mary)))&
(![X]:((generous(X)<~>patient(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~tall(X))<=>(humble(X)<~>~tall(X))))&
(![X]:((~old(X)|~rich(X))<=>(old(X)&~happy(X))))&
(![X]:((quiet(X)|brave(X))<=>(~curious(X)|kind(X))))&
(![X]:((calm(X)&~tall(X))<=>(creative(X)|patient(X))))&
(![X]:((~humble(X)|wise(X))=>~tall(X)))&
(((wise(alice)<~>old(alice)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(((generous(fred)<~>tall(fred)))<=>(?[X]:((funny(X)|rich(X)))))&
((?[X]:((~calm(X)<~>happy(X))))=>((strong(john)<~>brave(john))))&
((?[X]:((quiet(X)<~>~funny(X))))=>(?[X]:(kind(X))))&
((?[X]:((wise(X)<~>~tall(X))))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&~happy(X)))))&
((kind(paul)<~>brave(paul)))&
((~funny(alice)&wise(alice)))&
(?[X]:((~wise(X)|~creative(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
((~patient(paul)<~>~rich(paul)))&
(?[X]:(~curious(X))) | ~quiet(john) | [] | null | 0 |
Everyone who is either not wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Paul is not rich. | neutral | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | ~rich(paul) | [] | null | 0 |
Everyone who is not kind is both not curious and patient and vice versa.
Everyone who is either patient or not brave is both not creative and not brave and vice versa.
If someone is not curious or not rich then alice is not creative or not brave.
If someone is both not old and not wise then alice is generous and vice versa.
If fred is not tall then fred is not strong or not creative.
If fred is humble then john is not old and vice versa.
If someone is either not funny or not old then paul is both tall and not rich and vice versa.
If someone is curious then fred is both not curious and creative and vice versa.
Everyone who is either rich or not kind is both wise and not old.
If mary is either brave or not quiet then lucy is either not creative or not generous.
Everyone who is old is rich and vice versa.
Everyone who is happy or not kind is either creative or not kind and vice versa.
If lucy is either not kind or quiet then alice is not rich.
If someone is either not funny or not tall then lucy is either quiet or not wise and vice versa.
If someone is either creative or not tall then alice is either curious or kind.
Everyone who is both quiet and not rich is both not generous and not patient and vice versa.
Someone is not creative or quiet.
Someone is either not brave or strong.
Fred is both not old and generous.
Paul is either not old or not humble.
Someone is either not curious or not wise.
Someone is not old or not rich.
Lucy is either not kind or not rich. | Mary is not old. | entailment | (![X]:(~kind(X)<=>(~curious(X)&patient(X))))&
(![X]:((patient(X)<~>~brave(X))<=>(~creative(X)&~brave(X))))&
((?[X]:((~curious(X)|~rich(X))))=>((~creative(alice)|~brave(alice))))&
((?[X]:((~old(X)&~wise(X))))<=>(generous(alice)))&
((~tall(fred))=>((~strong(fred)|~creative(fred))))&
((humble(fred))<=>(~old(john)))&
((?[X]:((~funny(X)<~>~old(X))))<=>((tall(paul)&~rich(paul))))&
((?[X]:(curious(X)))<=>((~curious(fred)&creative(fred))))&
(![X]:((rich(X)<~>~kind(X))=>(wise(X)&~old(X))))&
(((brave(mary)<~>~quiet(mary)))=>((~creative(lucy)<~>~generous(lucy))))&
(![X]:(old(X)<=>rich(X)))&
(![X]:((happy(X)|~kind(X))<=>(creative(X)<~>~kind(X))))&
(((~kind(lucy)<~>quiet(lucy)))=>(~rich(alice)))&
((?[X]:((~funny(X)<~>~tall(X))))<=>((quiet(lucy)<~>~wise(lucy))))&
((?[X]:((creative(X)<~>~tall(X))))=>((curious(alice)<~>kind(alice))))&
(![X]:((quiet(X)&~rich(X))<=>(~generous(X)&~patient(X))))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:((~brave(X)<~>strong(X))))&
((~old(fred)&generous(fred)))&
((~old(paul)<~>~humble(paul)))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((~old(X)|~rich(X))))&
((~kind(lucy)<~>~rich(lucy))) | ~old(mary) | [
"p0",
"p1",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 64298378153951995933156
% SZS output start Proof for 64298378153951995933156
1. ! [X0] : (~kind(X0) <=> (patient(X0) & ~curious(X0))) [input p0]
2. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> (~brave(X0) & ~creative(X0))) [input p1]
9. ! [X0] : ((rich(X0) <~> ~kind(X0)) => (~old(X0) & wise(X0))) [input p8]
11. ! [X0] : (old(X0) <=> rich(X0)) [input p10]
12. ! [X0] : ((~kind(X0) | happy(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p11]
24. old(mary) [input hypothesis]
29. ! [X0] : ((~old(X0) & wise(X0)) | (rich(X0) <=> ~kind(X0))) [ennf transformation 9]
33. ! [X0] : ((~kind(X0) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | kind(X0))) [nnf transformation 1]
34. ! [X0] : ((~kind(X0) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | kind(X0))) [flattening 33]
35. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 2]
36. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [flattening 35]
52. ! [X0] : ((~old(X0) & wise(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) [nnf transformation 29]
54. ! [X0] : ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0))) [nnf transformation 11]
55. ! [X0] : (((~kind(X0) | happy(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (kind(X0) & ~happy(X0)))) [nnf transformation 12]
56. ! [X0] : ((~kind(X0) | happy(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (kind(X0) & ~happy(X0)))) [flattening 55]
78. patient(X0) | kind(X0) [cnf transformation 34]
82. ~brave(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 36]
85. brave(X0) | ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 36]
105. ~old(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 52]
111. ~old(X0) | rich(X0) [cnf transformation 54]
116. kind(X0) | ~creative(X0) | kind(X0) [cnf transformation 56]
149. old(mary) [cnf transformation 24]
150. ~creative(X0) | kind(X0) [duplicate literal removal 116]
152. ~brave(X0) | ~patient(X0) [duplicate literal removal 82]
153. ~patient(X0) | brave(X0) | creative(X0) [duplicate literal removal 85]
383. rich(mary) [resolution 111,149]
488. ~kind(mary) | ~rich(mary) [resolution 105,149]
559. brave(X0) | creative(X0) | kind(X0) [resolution 153,78]
560. brave(X0) | kind(X0) [subsumption resolution 559,150]
563. kind(X0) | ~patient(X0) [resolution 560,152]
566. kind(X0) [subsumption resolution 563,78]
567. ~rich(mary) [subsumption resolution 488,566]
568. $false [subsumption resolution 567,383]
% SZS output end Proof for 64298378153951995933156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not generous then someone is not happy or not wise and vice versa. Everyone who is generous is either funny or not happy. If someone is not patient or patient then paul is either not calm or strong. Everyone who is both not wise and humble is either humble or not creative and vice versa. Everyone who is rich is either brave or not happy and vice versa. Everyone who is not happy is both strong and quiet. Everyone who is both rich and strong is either strong or not humble and vice versa. If someone is not tall or wise then fred is old or strong and vice versa. If someone is not old then someone is either calm or not humble. Everyone who is both not happy and old is both happy and strong. If mary is not wise then mary is not happy. If someone is both not rich and humble then someone is not rich. Everyone who is either not humble or not patient is not old. If someone is both rich and not happy then lucy is either brave or not strong and vice versa. Everyone who is funny or not tall is either generous or creative. Everyone who is strong or not creative is not patient. Someone is either not patient or kind. Someone is not quiet or not generous. Paul is either not patient or generous. John is both patient and not brave. Mary is both funny and not strong. Someone is both not quiet and funny. Someone is not wise. Someone is kind or generous. | Mary is creative. | contradiction | ((?[X]:((creative(X)|~generous(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:(generous(X)=>(funny(X)<~>~happy(X))))&
((?[X]:((~patient(X)|patient(X))))=>((~calm(paul)<~>strong(paul))))&
(![X]:((~wise(X)&humble(X))<=>(humble(X)<~>~creative(X))))&
(![X]:(rich(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~happy(X)=>(strong(X)&quiet(X))))&
(![X]:((rich(X)&strong(X))<=>(strong(X)<~>~humble(X))))&
((?[X]:((~tall(X)|wise(X))))<=>((old(fred)|strong(fred))))&
((?[X]:(~old(X)))=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:((~happy(X)&old(X))=>(happy(X)&strong(X))))&
((~wise(mary))=>(~happy(mary)))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:(~rich(X))))&
(![X]:((~humble(X)<~>~patient(X))=>~old(X)))&
((?[X]:((rich(X)&~happy(X))))<=>((brave(lucy)<~>~strong(lucy))))&
(![X]:((funny(X)|~tall(X))=>(generous(X)<~>creative(X))))&
(![X]:((strong(X)|~creative(X))=>~patient(X)))&
(?[X]:((~patient(X)<~>kind(X))))&
(?[X]:((~quiet(X)|~generous(X))))&
((~patient(paul)<~>generous(paul)))&
((patient(john)&~brave(john)))&
((funny(mary)&~strong(mary)))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|generous(X)))) | creative(mary) | [
"p3",
"p5",
"p6",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2738936416837918130586151
% SZS output start Proof for 2738936416837918130586151
4. ! [X0] : ((humble(X0) & ~wise(X0)) <=> (humble(X0) <~> ~creative(X0))) [input p3]
6. ! [X0] : (~happy(X0) => (quiet(X0) & strong(X0))) [input p5]
7. ! [X0] : ((strong(X0) & rich(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p6]
11. ~wise(mary) => ~happy(mary) [input p10]
21. ~strong(mary) & funny(mary) [input p20]
25. creative(mary) [input hypothesis]
31. ! [X0] : ((quiet(X0) & strong(X0)) | happy(X0)) [ennf transformation 6]
35. ~happy(mary) | wise(mary) [ennf transformation 11]
47. ! [X0] : (((humble(X0) & ~wise(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | (~humble(X0) | wise(X0)))) [nnf transformation 4]
48. ! [X0] : (((humble(X0) & ~wise(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | ~humble(X0) | wise(X0))) [flattening 47]
50. ! [X0] : (((strong(X0) & rich(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~strong(X0) | ~rich(X0)))) [nnf transformation 7]
51. ! [X0] : (((strong(X0) & rich(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ~strong(X0) | ~rich(X0))) [flattening 50]
94. ~humble(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 48]
102. strong(X0) | happy(X0) [cnf transformation 31]
109. strong(X0) | strong(X0) | humble(X0) [cnf transformation 51]
118. ~happy(mary) | wise(mary) [cnf transformation 35]
142. ~strong(mary) [cnf transformation 21]
147. creative(mary) [cnf transformation 25]
150. humble(X0) | strong(X0) [duplicate literal removal 109]
245. 22 <=> wise(mary) [avatar definition]
247. wise(mary) <- (22) [avatar component clause 245]
249. 23 <=> happy(mary) [avatar definition]
252. 22 | ~23 [avatar split clause 118,249,245]
324. happy(mary) [resolution 102,142]
329. 23 [avatar split clause 324,249]
365. ~wise(X1) | ~creative(X1) | strong(X1) [resolution 94,150]
474. ~creative(mary) | strong(mary) <- (22) [resolution 365,247]
477. strong(mary) <- (22) [subsumption resolution 474,147]
478. $false <- (22) [subsumption resolution 477,142]
479. ~22 [avatar contradiction clause 478]
480. $false [avatar sat refutation 252,329,479]
% SZS output end Proof for 2738936416837918130586151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either strong or curious then alice is both not quiet and not old and vice versa.
Everyone who is strong is kind or not strong and vice versa.
Everyone who is patient or not humble is not creative or not tall and vice versa.
If lucy is both not patient and not happy then someone is either patient or not calm.
Everyone who is not humble or not rich is either not wise or happy and vice versa.
If john is calm or quiet then mary is both not calm and kind.
If someone is either not old or not creative then someone is tall or not humble.
If paul is either not generous or not calm then paul is creative or not tall.
If someone is not old then someone is patient or not brave and vice versa.
Everyone who is both not old and kind is both not calm and not strong and vice versa.
Everyone who is both not patient and not generous is either strong or not tall.
If fred is not calm or not tall then someone is wise and vice versa.
If someone is both creative and not calm then someone is not rich or funny.
Everyone who is either not generous or not creative is either not humble or patient.
If someone is kind then mary is either tall or not patient and vice versa.
Everyone who is both not generous and old is not curious and vice versa.
Someone is not quiet.
Someone is rich or generous.
Someone is either not patient or not calm.
Someone is either not funny or not generous.
Someone is not brave or funny.
John is strong.
Someone is either not funny or not brave. | Fred is calm. | neutral | (((strong(fred)<~>curious(fred)))<=>((~quiet(alice)&~old(alice))))&
(![X]:(strong(X)<=>(kind(X)|~strong(X))))&
(![X]:((patient(X)|~humble(X))<=>(~creative(X)|~tall(X))))&
(((~patient(lucy)&~happy(lucy)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~rich(X))<=>(~wise(X)<~>happy(X))))&
(((calm(john)|quiet(john)))=>((~calm(mary)&kind(mary))))&
((?[X]:((~old(X)<~>~creative(X))))=>(?[X]:((tall(X)|~humble(X)))))&
(((~generous(paul)<~>~calm(paul)))=>((creative(paul)|~tall(paul))))&
((?[X]:(~old(X)))<=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~old(X)&kind(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&~generous(X))=>(strong(X)<~>~tall(X))))&
(((~calm(fred)|~tall(fred)))<=>(?[X]:(wise(X))))&
((?[X]:((creative(X)&~calm(X))))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))=>(~humble(X)<~>patient(X))))&
((?[X]:(kind(X)))<=>((tall(mary)<~>~patient(mary))))&
(![X]:((~generous(X)&old(X))<=>~curious(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:((~brave(X)|funny(X))))&
(strong(john))&
(?[X]:((~funny(X)<~>~brave(X)))) | calm(fred) | [] | null | 0 |
If someone is not quiet or not rich then fred is both not humble and wise and vice versa.
Everyone who is either calm or not tall is either brave or patient.
Everyone who is both tall and not patient is both calm and not wise.
If alice is not strong then someone is tall.
Everyone who is either patient or creative is not curious.
Everyone who is quiet or wise is not patient and vice versa.
Everyone who is both humble and brave is not kind or not strong.
Everyone who is patient or rich is funny or not calm.
If alice is not tall or funny then someone is not rich or calm and vice versa.
Everyone who is both not kind and not calm is not patient or humble and vice versa.
Everyone who is not kind is not old or not kind.
Everyone who is either not rich or not happy is either happy or not happy.
If susan is both not curious and brave then mary is both calm and not humble and vice versa.
If someone is generous or not creative then someone is both not patient and strong.
Everyone who is either not humble or calm is not funny or creative and vice versa.
Everyone who is not happy is curious or not humble.
Mary is either generous or not happy.
Alice is generous.
Lucy is either not tall or funny.
Susan is not curious.
Paul is not strong or patient.
Someone is either generous or not calm.
Fred is both not calm and not strong. | Mary is not humble. | neutral | ((?[X]:((~quiet(X)|~rich(X))))<=>((~humble(fred)&wise(fred))))&
(![X]:((calm(X)<~>~tall(X))=>(brave(X)<~>patient(X))))&
(![X]:((tall(X)&~patient(X))=>(calm(X)&~wise(X))))&
((~strong(alice))=>(?[X]:(tall(X))))&
(![X]:((patient(X)<~>creative(X))=>~curious(X)))&
(![X]:((quiet(X)|wise(X))<=>~patient(X)))&
(![X]:((humble(X)&brave(X))=>(~kind(X)|~strong(X))))&
(![X]:((patient(X)|rich(X))=>(funny(X)|~calm(X))))&
(((~tall(alice)|funny(alice)))<=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((~kind(X)&~calm(X))<=>(~patient(X)|humble(X))))&
(![X]:(~kind(X)=>(~old(X)|~kind(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(happy(X)<~>~happy(X))))&
(((~curious(susan)&brave(susan)))<=>((calm(mary)&~humble(mary))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~funny(X)|creative(X))))&
(![X]:(~happy(X)=>(curious(X)|~humble(X))))&
((generous(mary)<~>~happy(mary)))&
(generous(alice))&
((~tall(lucy)<~>funny(lucy)))&
(~curious(susan))&
((~strong(paul)|patient(paul)))&
(?[X]:((generous(X)<~>~calm(X))))&
((~calm(fred)&~strong(fred))) | ~humble(mary) | [] | null | 0 |
If someone is not funny or not wise then fred is quiet or not funny and vice versa.
Everyone who is either brave or kind is rich and vice versa.
Everyone who is either humble or generous is curious or not rich.
Everyone who is wise is not kind or kind.
Everyone who is both not happy and not funny is either quiet or patient and vice versa.
If someone is old or not rich then fred is either creative or not kind and vice versa.
Everyone who is either old or humble is both not funny and tall and vice versa.
If someone is both happy and rich then someone is not generous or humble.
Everyone who is both not wise and not brave is happy.
If john is brave or not quiet then someone is wise or not rich.
Everyone who is both not tall and not old is generous.
If someone is not brave or quiet then someone is both kind and not generous and vice versa.
If john is both humble and tall then someone is both not rich and not generous and vice versa.
Everyone who is generous or wise is both generous and not generous and vice versa.
If someone is both brave and not old then someone is not strong or funny and vice versa.
If someone is both happy and calm then paul is both patient and not kind.
John is brave or not humble.
Fred is either creative or not wise.
Mary is either calm or kind.
Susan is not tall.
Someone is either not wise or not kind.
Someone is humble.
Alice is both creative and not curious.
Paul is either funny or brave. | John is not generous. | entailment | ((?[X]:((~funny(X)|~wise(X))))<=>((quiet(fred)|~funny(fred))))&
(![X]:((brave(X)<~>kind(X))<=>rich(X)))&
(![X]:((humble(X)<~>generous(X))=>(curious(X)|~rich(X))))&
(![X]:(wise(X)=>(~kind(X)|kind(X))))&
(![X]:((~happy(X)&~funny(X))<=>(quiet(X)<~>patient(X))))&
((?[X]:((old(X)|~rich(X))))<=>((creative(fred)<~>~kind(fred))))&
(![X]:((old(X)<~>humble(X))<=>(~funny(X)&tall(X))))&
((?[X]:((happy(X)&rich(X))))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~wise(X)&~brave(X))=>happy(X)))&
(((brave(john)|~quiet(john)))=>(?[X]:((wise(X)|~rich(X)))))&
(![X]:((~tall(X)&~old(X))=>generous(X)))&
((?[X]:((~brave(X)|quiet(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
(((humble(john)&tall(john)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((generous(X)|wise(X))<=>(generous(X)&~generous(X))))&
((?[X]:((brave(X)&~old(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:((happy(X)&calm(X))))=>((patient(paul)&~kind(paul))))&
((brave(john)|~humble(john)))&
((creative(fred)<~>~wise(fred)))&
((calm(mary)<~>kind(mary)))&
(~tall(susan))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:(humble(X)))&
((creative(alice)&~curious(alice)))&
((funny(paul)<~>brave(paul))) | ~generous(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6360187706679141148922946
% SZS output start Proof for 6360187706679141148922946
14. ! [X0] : ((wise(X0) | generous(X0)) <=> (~generous(X0) & generous(X0))) [input p13]
25. generous(john) [input hypothesis]
70. ! [X0] : (((wise(X0) | generous(X0)) | (generous(X0) | ~generous(X0))) & ((~generous(X0) & generous(X0)) | (~wise(X0) & ~generous(X0)))) [nnf transformation 14]
71. ! [X0] : ((wise(X0) | generous(X0) | generous(X0) | ~generous(X0)) & ((~generous(X0) & generous(X0)) | (~wise(X0) & ~generous(X0)))) [flattening 70]
130. ~generous(X0) | ~generous(X0) [cnf transformation 71]
153. generous(john) [cnf transformation 25]
154. ~generous(X0) [duplicate literal removal 130]
361. $false [subsumption resolution 153,154]
% SZS output end Proof for 6360187706679141148922946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both generous and wise then alice is either not curious or happy and vice versa. Everyone who is both creative and quiet is quiet or happy and vice versa. If susan is either creative or not rich then lucy is both kind and not brave and vice versa. Everyone who is either not rich or funny is both patient and not patient and vice versa. Everyone who is not kind or funny is both not brave and not patient and vice versa. If someone is not wise or old then mary is not rich or patient and vice versa. If alice is both old and kind then john is creative and vice versa. If john is both not brave and not creative then alice is both not kind and wise. If someone is quiet or not creative then someone is either not funny or not curious. If fred is not funny or humble then someone is not happy or quiet and vice versa. Everyone who is both kind and old is not tall or humble. Everyone who is not wise is old or patient. If fred is both happy and rich then mary is both rich and not brave and vice versa. If someone is kind or patient then lucy is both not humble and creative and vice versa. If susan is not quiet or patient then someone is wise and vice versa. Everyone who is kind or not calm is both not patient and happy. John is either creative or brave. Someone is creative. Someone is patient or funny. Mary is not happy. Someone is either brave or funny. Someone is not quiet. Someone is quiet or happy. | Alice is tall. | neutral | (((generous(fred)&wise(fred)))<=>((~curious(alice)<~>happy(alice))))&
(![X]:((creative(X)&quiet(X))<=>(quiet(X)|happy(X))))&
(((creative(susan)<~>~rich(susan)))<=>((kind(lucy)&~brave(lucy))))&
(![X]:((~rich(X)<~>funny(X))<=>(patient(X)&~patient(X))))&
(![X]:((~kind(X)|funny(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~wise(X)|old(X))))<=>((~rich(mary)|patient(mary))))&
(((old(alice)&kind(alice)))<=>(creative(john)))&
(((~brave(john)&~creative(john)))=>((~kind(alice)&wise(alice))))&
((?[X]:((quiet(X)|~creative(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~funny(fred)|humble(fred)))<=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((kind(X)&old(X))=>(~tall(X)|humble(X))))&
(![X]:(~wise(X)=>(old(X)|patient(X))))&
(((happy(fred)&rich(fred)))<=>((rich(mary)&~brave(mary))))&
((?[X]:((kind(X)|patient(X))))<=>((~humble(lucy)&creative(lucy))))&
(((~quiet(susan)|patient(susan)))<=>(?[X]:(wise(X))))&
(![X]:((kind(X)|~calm(X))=>(~patient(X)&happy(X))))&
((creative(john)<~>brave(john)))&
(?[X]:(creative(X)))&
(?[X]:((patient(X)|funny(X))))&
(~happy(mary))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((quiet(X)|happy(X)))) | tall(alice) | [] | null | 0 |
Everyone who is not patient is not funny and vice versa.
Everyone who is happy or not brave is both not calm and not patient.
Everyone who is both not wise and not strong is both not quiet and not strong and vice versa.
If someone is both kind and not generous then alice is curious or not calm and vice versa.
Everyone who is rich or happy is not curious or happy and vice versa.
If someone is not quiet or not strong then someone is both not rich and calm.
If mary is brave or patient then someone is either creative or not creative and vice versa.
If someone is curious then fred is both not wise and not funny.
If someone is both curious and not creative then susan is both not generous and strong.
If someone is not tall then someone is not funny or not humble.
Everyone who is either patient or not curious is either kind or not funny.
Everyone who is both not tall and not strong is patient or not kind and vice versa.
Everyone who is both old and calm is calm or humble.
Everyone who is either tall or not wise is both not kind and curious.
If paul is both rich and strong then someone is both brave and strong.
Everyone who is old or not tall is funny or not generous and vice versa.
Paul is both not brave and not creative.
Someone is not old.
Someone is either curious or not curious.
Someone is both tall and not humble.
Someone is either strong or not rich.
Alice is both funny and creative.
Someone is either tall or not curious. | Paul is not funny. | entailment | (![X]:(~patient(X)<=>~funny(X)))&
(![X]:((happy(X)|~brave(X))=>(~calm(X)&~patient(X))))&
(![X]:((~wise(X)&~strong(X))<=>(~quiet(X)&~strong(X))))&
((?[X]:((kind(X)&~generous(X))))<=>((curious(alice)|~calm(alice))))&
(![X]:((rich(X)|happy(X))<=>(~curious(X)|happy(X))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:((~rich(X)&calm(X)))))&
(((brave(mary)|patient(mary)))<=>(?[X]:((creative(X)<~>~creative(X)))))&
((?[X]:(curious(X)))=>((~wise(fred)&~funny(fred))))&
((?[X]:((curious(X)&~creative(X))))=>((~generous(susan)&strong(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((~funny(X)|~humble(X)))))&
(![X]:((patient(X)<~>~curious(X))=>(kind(X)<~>~funny(X))))&
(![X]:((~tall(X)&~strong(X))<=>(patient(X)|~kind(X))))&
(![X]:((old(X)&calm(X))=>(calm(X)|humble(X))))&
(![X]:((tall(X)<~>~wise(X))=>(~kind(X)&curious(X))))&
(((rich(paul)&strong(paul)))=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((old(X)|~tall(X))<=>(funny(X)|~generous(X))))&
((~brave(paul)&~creative(paul)))&
(?[X]:(~old(X)))&
(?[X]:((curious(X)<~>~curious(X))))&
(?[X]:((tall(X)&~humble(X))))&
(?[X]:((strong(X)<~>~rich(X))))&
((funny(alice)&creative(alice)))&
(?[X]:((tall(X)<~>~curious(X)))) | ~funny(paul) | [
"p0",
"p1",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9198450760112161536689390
% SZS output start Proof for 9198450760112161536689390
1. ! [X0] : (~patient(X0) <=> ~funny(X0)) [input p0]
2. ! [X0] : ((~brave(X0) | happy(X0)) => (~patient(X0) & ~calm(X0))) [input p1]
17. ~creative(paul) & ~brave(paul) [input p16]
24. funny(paul) [input hypothesis]
27. ! [X0] : ((~patient(X0) & ~calm(X0)) | (brave(X0) & ~happy(X0))) [ennf transformation 2]
38. ! [X0] : ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))) [nnf transformation 1]
80. ~funny(X0) | patient(X0) [cnf transformation 38]
85. ~patient(X0) | brave(X0) [cnf transformation 27]
134. ~brave(paul) [cnf transformation 17]
147. funny(paul) [cnf transformation 24]
286. patient(paul) [resolution 80,147]
292. brave(paul) [resolution 85,286]
293. $false [subsumption resolution 292,134]
% SZS output end Proof for 9198450760112161536689390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Lucy is not calm.
Mary is either tall or quiet.
Someone is either brave or not curious.
Paul is either not calm or not kind.
Paul is either not wise or not kind.
Someone is not patient or brave. | Lucy is not wise. | contradiction | (![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(~calm(lucy))&
((tall(mary)<~>quiet(mary)))&
(?[X]:((brave(X)<~>~curious(X))))&
((~calm(paul)<~>~kind(paul)))&
((~wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)|brave(X)))) | ~wise(lucy) | [
"p0",
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1758056642625075855546771
% SZS output start Proof for 1758056642625075855546771
1. ! [X0] : (~kind(X0) => (wise(X0) & creative(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p3]
12. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (wise(X0) | ~creative(X0))) [input p11]
16. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | kind(X0)) [input p15]
23. ~wise(lucy) [input hypothesis]
24. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | kind(X1)) [rectify 16]
25. ! [X0] : ((wise(X0) & creative(X0)) | kind(X0)) [ennf transformation 1]
27. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 4]
56. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 12]
57. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 56]
60. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X1] : (humble(X1) | kind(X1)) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 24]
61. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X2] : (humble(X2) | kind(X2)) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 60]
62. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK3) & ~kind(sK3)) [choice axiom]
63. ? [X2] : (humble(X2) | kind(X2)) => (humble(sK4) | kind(sK4)) [choice axiom]
64. ((curious(sK3) & ~kind(sK3)) | ! [X1] : (~humble(X1) & ~kind(X1))) & ((humble(sK4) | kind(sK4)) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 61,63,62]
74. wise(X0) | kind(X0) [cnf transformation 25]
81. quiet(X0) | wise(X0) [cnf transformation 27]
83. ~curious(X0) | quiet(X0) [cnf transformation 27]
111. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 57]
113. curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 57]
124. ~kind(sK3) | ~kind(X1) [cnf transformation 64]
126. curious(sK3) | ~kind(X1) [cnf transformation 64]
138. ~wise(lucy) [cnf transformation 23]
183. quiet(X0) | ~wise(X0) [subsumption resolution 113,83]
184. quiet(X0) [subsumption resolution 183,81]
185. ~curious(X0) | ~wise(X0) [subsumption resolution 111,184]
194. 11 <=> curious(sK3) [avatar definition]
196. curious(sK3) <- (11) [avatar component clause 194]
199. 12 <=> ! [X1] : ~kind(X1) [avatar definition]
200. ~kind(X1) <- (12) [avatar component clause 199]
201. 12 | 11 [avatar split clause 126,194,199]
203. 13 <=> kind(sK3) [avatar definition]
205. ~kind(sK3) <- (~13) [avatar component clause 203]
207. 12 | ~13 [avatar split clause 124,203,199]
255. kind(lucy) [resolution 74,138]
259. ~wise(sK3) <- (11) [resolution 185,196]
261. kind(sK3) <- (11) [resolution 259,74]
262. $false <- (11, ~13) [subsumption resolution 261,205]
263. ~11 | 13 [avatar contradiction clause 262]
264. $false <- (12) [resolution 200,255]
265. ~12 [avatar contradiction clause 264]
266. $false [avatar sat refutation 201,207,263,265]
% SZS output end Proof for 1758056642625075855546771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and strong is funny. If someone is either kind or happy then someone is kind and vice versa. Everyone who is not patient is not old and vice versa. Everyone who is funny is either strong or humble and vice versa. Everyone who is generous or not calm is either not funny or not kind. If someone is not calm or not happy then paul is wise or not curious and vice versa. Everyone who is humble is both patient and not generous. Everyone who is not old or wise is both not funny and quiet. Everyone who is not patient or not funny is patient or not calm and vice versa. If someone is both quiet and not quiet then someone is not curious. If fred is both rich and kind then susan is not funny. If paul is both not old and not tall then someone is not brave or not happy. Everyone who is not happy or patient is both creative and not happy and vice versa. Everyone who is not humble or not wise is both generous and old. If someone is both wise and old then someone is either funny or not humble. Everyone who is both not wise and not quiet is not calm or funny and vice versa. Someone is patient or calm. John is wise or brave. Someone is either not strong or not creative. John is humble. Someone is both not rich and not generous. Someone is both not wise and not quiet. | Paul is not wise. | neutral | (![X]:((~curious(X)&strong(X))=>funny(X)))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:(kind(X))))&
(![X]:(~patient(X)<=>~old(X)))&
(![X]:(funny(X)<=>(strong(X)<~>humble(X))))&
(![X]:((generous(X)|~calm(X))=>(~funny(X)<~>~kind(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((wise(paul)|~curious(paul))))&
(![X]:(humble(X)=>(patient(X)&~generous(X))))&
(![X]:((~old(X)|wise(X))=>(~funny(X)&quiet(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)|~calm(X))))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:(~curious(X))))&
(((rich(fred)&kind(fred)))=>(~funny(susan)))&
(((~old(paul)&~tall(paul)))=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~happy(X)|patient(X))<=>(creative(X)&~happy(X))))&
(![X]:((~humble(X)|~wise(X))=>(generous(X)&old(X))))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~wise(X)&~quiet(X))<=>(~calm(X)|funny(X))))&
(?[X]:((patient(X)|calm(X))))&
((wise(john)|brave(john)))&
(?[X]:((~strong(X)<~>~creative(X))))&
(humble(john))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:((~wise(X)&~quiet(X)))) | ~wise(paul) | [] | null | 0 |
If someone is both not kind and wise then lucy is either curious or not funny and vice versa.
Everyone who is both not rich and wise is either brave or not quiet.
If fred is funny then someone is happy.
Everyone who is either not creative or not strong is not quiet or quiet.
If mary is both not rich and not old then susan is calm or not humble.
If someone is not creative then susan is brave or not curious.
Everyone who is either not curious or strong is not tall or not kind.
If someone is not quiet then someone is either not creative or not quiet.
Everyone who is tall or not funny is both brave and not generous and vice versa.
If lucy is both not strong and not quiet then someone is not kind and vice versa.
If someone is not strong then someone is either funny or not brave and vice versa.
If mary is not funny then fred is both strong and tall.
Everyone who is patient or not patient is both not old and generous.
If susan is both strong and happy then alice is both kind and not strong and vice versa.
If someone is not happy or patient then someone is either not patient or rich and vice versa.
If someone is both tall and calm then someone is not calm or humble.
Someone is both curious and not tall.
Mary is both creative and not tall.
Mary is not brave.
Lucy is both not wise and not brave.
Alice is both not tall and generous.
Someone is not happy or not patient. | Fred is tall. | contradiction | ((?[X]:((~kind(X)&wise(X))))<=>((curious(lucy)<~>~funny(lucy))))&
(![X]:((~rich(X)&wise(X))=>(brave(X)<~>~quiet(X))))&
((funny(fred))=>(?[X]:(happy(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(~quiet(X)|quiet(X))))&
(((~rich(mary)&~old(mary)))=>((calm(susan)|~humble(susan))))&
((?[X]:(~creative(X)))=>((brave(susan)|~curious(susan))))&
(![X]:((~curious(X)<~>strong(X))=>(~tall(X)|~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)|~funny(X))<=>(brave(X)&~generous(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
((~funny(mary))=>((strong(fred)&tall(fred))))&
(![X]:((patient(X)|~patient(X))=>(~old(X)&generous(X))))&
(((strong(susan)&happy(susan)))<=>((kind(alice)&~strong(alice))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((tall(X)&calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(?[X]:((curious(X)&~tall(X))))&
((creative(mary)&~tall(mary)))&
(~brave(mary))&
((~wise(lucy)&~brave(lucy)))&
((~tall(alice)&generous(alice)))&
(?[X]:((~happy(X)|~patient(X)))) | tall(fred) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6253860541401961861714765
% SZS output start Proof for 6253860541401961861714765
9. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~generous(X0) & brave(X0))) [input p8]
13. ! [X0] : ((~patient(X0) | patient(X0)) => (generous(X0) & ~old(X0))) [input p12]
23. tall(fred) [input hypothesis]
41. ! [X0] : ((generous(X0) & ~old(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 13]
56. ! [X0] : (((~funny(X0) | tall(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 9]
57. ! [X0] : ((~funny(X0) | tall(X0) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [flattening 56]
101. ~generous(X0) | ~tall(X0) [cnf transformation 57]
115. generous(X0) | ~patient(X0) [cnf transformation 41]
116. generous(X0) | patient(X0) [cnf transformation 41]
138. tall(fred) [cnf transformation 23]
261. 28 <=> tall(fred) [avatar definition]
263. tall(fred) <- (28) [avatar component clause 261]
270. generous(X0) [subsumption resolution 115,116]
347. 28 [avatar split clause 138,261]
362. ~tall(X0) [resolution 101,270]
364. $false <- (28) [resolution 362,263]
365. ~28 [avatar contradiction clause 364]
366. $false [avatar sat refutation 347,365]
% SZS output end Proof for 6253860541401961861714765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and strong then someone is curious.
Everyone who is not tall or not creative is both quiet and not brave and vice versa.
If someone is both old and happy then john is not wise or generous and vice versa.
If lucy is either old or not kind then paul is either not generous or creative.
If someone is creative or not tall then fred is not generous.
Everyone who is either not curious or kind is either not creative or not happy.
If someone is brave or not strong then susan is wise or tall and vice versa.
Everyone who is kind is both not quiet and creative and vice versa.
If someone is both kind and not wise then mary is not brave or not strong and vice versa.
Everyone who is both not wise and not patient is either generous or funny.
If someone is either not curious or not brave then alice is either not creative or not wise and vice versa.
Everyone who is not old is either rich or calm.
Everyone who is either not creative or not old is both brave and not happy.
Everyone who is not funny or brave is either not calm or humble.
Everyone who is both creative and not humble is both not rich and not creative.
If mary is both creative and quiet then someone is generous or humble and vice versa.
Paul is both creative and not old.
Someone is not quiet or not funny.
Someone is not kind or not rich.
Paul is not old or not quiet.
Alice is either not tall or wise.
Someone is not curious.
Alice is both not rich and not calm.
Paul is not generous. | Paul is calm. | entailment | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:(curious(X))))&
(![X]:((~tall(X)|~creative(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((old(X)&happy(X))))<=>((~wise(john)|generous(john))))&
(((old(lucy)<~>~kind(lucy)))=>((~generous(paul)<~>creative(paul))))&
((?[X]:((creative(X)|~tall(X))))=>(~generous(fred)))&
(![X]:((~curious(X)<~>kind(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((brave(X)|~strong(X))))<=>((wise(susan)|tall(susan))))&
(![X]:(kind(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)&~wise(X))))<=>((~brave(mary)|~strong(mary))))&
(![X]:((~wise(X)&~patient(X))=>(generous(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((~creative(alice)<~>~wise(alice))))&
(![X]:(~old(X)=>(rich(X)<~>calm(X))))&
(![X]:((~creative(X)<~>~old(X))=>(brave(X)&~happy(X))))&
(![X]:((~funny(X)|brave(X))=>(~calm(X)<~>humble(X))))&
(![X]:((creative(X)&~humble(X))=>(~rich(X)&~creative(X))))&
(((creative(mary)&quiet(mary)))<=>(?[X]:((generous(X)|humble(X)))))&
((creative(paul)&~old(paul)))&
(?[X]:((~quiet(X)|~funny(X))))&
(?[X]:((~kind(X)|~rich(X))))&
((~old(paul)|~quiet(paul)))&
((~tall(alice)<~>wise(alice)))&
(?[X]:(~curious(X)))&
((~rich(alice)&~calm(alice)))&
(~generous(paul)) | calm(paul) | [
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8293008519161084879969428
% SZS output start Proof for 8293008519161084879969428
13. ! [X0] : ((~creative(X0) <~> ~old(X0)) => (~happy(X0) & brave(X0))) [input p12]
14. ! [X0] : ((brave(X0) | ~funny(X0)) => (~calm(X0) <~> humble(X0))) [input p13]
15. ! [X0] : ((~humble(X0) & creative(X0)) => (~creative(X0) & ~rich(X0))) [input p14]
17. ~old(paul) & creative(paul) [input p16]
25. ~calm(paul) [input hypothesis]
33. ! [X0] : ((~happy(X0) & brave(X0)) | (~creative(X0) <=> ~old(X0))) [ennf transformation 13]
34. ! [X0] : ((~calm(X0) <~> humble(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 14]
35. ! [X0] : ((~creative(X0) & ~rich(X0)) | (humble(X0) | ~creative(X0))) [ennf transformation 15]
36. ! [X0] : ((~creative(X0) & ~rich(X0)) | humble(X0) | ~creative(X0)) [flattening 35]
66. ! [X0] : ((~happy(X0) & brave(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 33]
67. ! [X0] : (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~brave(X0) & funny(X0))) [nnf transformation 34]
124. ~creative(X0) | brave(X0) | old(X0) [cnf transformation 66]
130. ~humble(X0) | calm(X0) | ~brave(X0) [cnf transformation 67]
132. ~creative(X0) | humble(X0) | ~creative(X0) [cnf transformation 36]
138. creative(paul) [cnf transformation 17]
139. ~old(paul) [cnf transformation 17]
149. ~calm(paul) [cnf transformation 25]
150. ~creative(X0) | humble(X0) [duplicate literal removal 132]
196. 11 <=> creative(paul) [avatar definition]
197. creative(paul) <- (11) [avatar component clause 196]
324. 11 [avatar split clause 138,196]
361. humble(paul) <- (11) [resolution 150,197]
388. brave(paul) | old(paul) <- (11) [resolution 124,197]
394. brave(paul) <- (11) [subsumption resolution 388,139]
441. calm(paul) | ~brave(paul) <- (11) [resolution 130,361]
444. ~brave(paul) <- (11) [subsumption resolution 441,149]
445. $false <- (11) [subsumption resolution 444,394]
446. ~11 [avatar contradiction clause 445]
450. $false [avatar sat refutation 324,446]
% SZS output end Proof for 8293008519161084879969428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or patient then someone is either not quiet or not patient.
If someone is not curious or not kind then someone is both not kind and not brave and vice versa.
Everyone who is not strong or generous is calm or generous and vice versa.
If john is both not quiet and funny then someone is either not kind or not tall and vice versa.
If lucy is both not humble and not old then someone is wise and vice versa.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
Everyone who is either not funny or humble is patient.
If paul is either not tall or humble then someone is either happy or not humble.
Someone is either not tall or not creative.
Someone is both humble and creative.
Someone is not calm or strong.
Someone is either not funny or old.
Alice is brave or patient.
Susan is both generous and not wise.
Someone is either tall or creative. | Lucy is curious. | entailment | (((~wise(mary)|patient(mary)))=>(?[X]:((~quiet(X)<~>~patient(X)))))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)|generous(X))<=>(calm(X)|generous(X))))&
(((~quiet(john)&funny(john)))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~humble(lucy)&~old(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>patient(X)))&
(((~tall(paul)<~>humble(paul)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
((brave(alice)|patient(alice)))&
((generous(susan)&~wise(susan)))&
(?[X]:((tall(X)<~>creative(X)))) | curious(lucy) | [
"p3",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 572158326222381618199850
% SZS output start Proof for 572158326222381618199850
4. (funny(john) & ~quiet(john)) <=> ? [X0] : (~kind(X0) <~> ~tall(X0)) [input p3]
6. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p5]
8. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p7]
10. ! [X0] : ((kind(X0) | ~tall(X0)) <=> curious(X0)) [input p9]
12. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p11]
24. ~curious(lucy) [input hypothesis]
30. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 8]
46. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | (~funny(john) | quiet(john))) [nnf transformation 4]
47. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X0] : ((tall(X0) | kind(X0)) & (~tall(X0) | ~kind(X0))) | ~funny(john) | quiet(john)) [flattening 46]
48. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) | ~funny(john) | quiet(john)) [rectify 47]
49. ? [X1] : ((tall(X1) | kind(X1)) & (~tall(X1) | ~kind(X1))) => ((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) [choice axiom]
50. ((funny(john) & ~quiet(john)) | ! [X0] : ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) & (((tall(sK3) | kind(sK3)) & (~tall(sK3) | ~kind(sK3))) | ~funny(john) | quiet(john)) [skolemisation 48,49]
56. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 6]
60. ! [X0] : (((kind(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [nnf transformation 10]
61. ! [X0] : ((kind(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~kind(X0) & tall(X0)))) [flattening 60]
64. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 12]
65. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 64]
105. funny(john) | ~tall(X0) | kind(X0) [cnf transformation 50]
110. ~happy(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 56]
116. strong(X0) | happy(X0) [cnf transformation 30]
117. ~happy(X0) | strong(X0) [cnf transformation 30]
122. tall(X0) | curious(X0) [cnf transformation 61]
129. ~kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 65]
130. happy(X0) | happy(X0) [cnf transformation 65]
131. happy(X0) | kind(X0) [cnf transformation 65]
156. ~curious(lucy) [cnf transformation 24]
157. ~kind(X0) | ~happy(X0) [duplicate literal removal 129]
158. happy(X0) [duplicate literal removal 130]
202. 10 <=> ! [X3] : curious(X3) [avatar definition]
203. curious(X3) <- (10) [avatar component clause 202]
215. 13 <=> funny(john) [avatar definition]
217. funny(john) <- (13) [avatar component clause 215]
220. 14 <=> ! [X0] : (~tall(X0) | kind(X0)) [avatar definition]
221. ~tall(X0) | kind(X0) <- (14) [avatar component clause 220]
222. 14 | 13 [avatar split clause 105,215,220]
257. strong(X0) [subsumption resolution 116,117]
271. ~kind(X0) [subsumption resolution 157,158]
371. ~strong(X0) | ~funny(X0) | kind(X0) [resolution 110,131]
373. ~funny(X0) | kind(X0) [subsumption resolution 371,257]
374. ~funny(X0) [subsumption resolution 373,271]
377. $false <- (13) [resolution 374,217]
378. ~13 [avatar contradiction clause 377]
379. ~tall(X0) <- (14) [subsumption resolution 221,271]
380. curious(X0) <- (14) [resolution 379,122]
383. 10 | ~14 [avatar split clause 380,220,202]
384. $false <- (10) [resolution 203,156]
387. ~10 [avatar contradiction clause 384]
388. $false [avatar sat refutation 222,378,383,387]
% SZS output end Proof for 572158326222381618199850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is both funny and generous and vice versa. Everyone who is not brave is not wise or generous and vice versa. Everyone who is curious is either not patient or tall. Everyone who is not strong is either rich or not old and vice versa. If john is both not curious and not humble then someone is not humble and vice versa. Everyone who is not patient or not creative is either not calm or not happy. If someone is patient then someone is either not happy or not calm and vice versa. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Someone is humble. Lucy is not humble. Someone is either not strong or brave. Someone is both not wise and humble. Someone is not creative or strong. | Lucy is not strong. | entailment | (![X]:(happy(X)<=>(funny(X)&generous(X))))&
(![X]:(~brave(X)<=>(~wise(X)|generous(X))))&
(![X]:(curious(X)=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~creative(X)|strong(X)))) | ~strong(lucy) | [
"p3",
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9155223146956677010812382
% SZS output start Proof for 9155223146956677010812382
4. ! [X0] : (~strong(X0) <=> (rich(X0) <~> ~old(X0))) [input p3]
8. ! [X0] : ((kind(X0) | ~calm(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p7]
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (generous(X0) & ~calm(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (~funny(X0) & ~wise(X0))) [input p12]
15. ! [X0] : (calm(X0) <=> old(X0)) [input p14]
22. strong(lucy) [input hypothesis]
31. ! [X0] : ((generous(X0) & ~calm(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
39. ! [X0] : ((~strong(X0) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0)))) & (((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | strong(X0))) [nnf transformation 4]
51. ! [X0] : (((kind(X0) | ~calm(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((kind(X0) | ~calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [flattening 51]
56. ! [X0] : (((generous(X0) | ~brave(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | ~brave(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [flattening 56]
60. ! [X0] : ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))) [nnf transformation 15]
80. ~old(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 39]
95. wise(X0) | calm(X0) | calm(X0) [cnf transformation 52]
101. ~calm(X0) | rich(X0) [cnf transformation 31]
104. generous(X0) | generous(X0) [cnf transformation 31]
109. ~wise(X0) | ~generous(X0) [cnf transformation 57]
116. ~calm(X0) | old(X0) [cnf transformation 60]
125. strong(lucy) [cnf transformation 22]
126. generous(X0) [duplicate literal removal 104]
128. calm(X0) | wise(X0) [duplicate literal removal 95]
186. ~wise(X0) [subsumption resolution 109,126]
217. wise(X0) | old(X0) [resolution 128,116]
218. wise(X1) | rich(X1) [resolution 128,101]
221. old(X0) [subsumption resolution 217,186]
222. rich(X1) [subsumption resolution 218,186]
277. ~strong(X0) | ~rich(X0) [resolution 80,221]
278. ~strong(X0) [subsumption resolution 277,222]
280. $false [resolution 278,125]
% SZS output end Proof for 9155223146956677010812382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not kind then mary is happy and vice versa.
If someone is either not quiet or generous then alice is not happy or not curious and vice versa.
If susan is not patient or creative then john is not curious and vice versa.
If someone is strong or patient then someone is not patient or not wise.
Everyone who is both funny and strong is either old or not rich.
Everyone who is not generous is tall and vice versa.
Everyone who is both rich and not tall is not curious and vice versa.
Everyone who is either funny or quiet is not quiet.
If paul is both not calm and not curious then someone is either not curious or generous and vice versa.
Everyone who is either not generous or not old is both humble and not generous.
Everyone who is not kind is either humble or not funny.
If someone is not calm then someone is rich or funny and vice versa.
If mary is not rich then someone is brave or humble and vice versa.
If fred is either not brave or not generous then lucy is strong and vice versa.
If alice is not funny then someone is not funny and vice versa.
Everyone who is calm or not curious is quiet or not rich and vice versa.
Someone is not kind or not generous.
Someone is not patient or brave.
Someone is both not wise and funny.
Mary is either old or not tall.
Someone is not rich.
Susan is not kind or curious.
Mary is either not rich or creative.
Lucy is not rich. | Mary is not calm. | contradiction | ((?[X]:((tall(X)<~>~kind(X))))<=>(happy(mary)))&
((?[X]:((~quiet(X)<~>generous(X))))<=>((~happy(alice)|~curious(alice))))&
(((~patient(susan)|creative(susan)))<=>(~curious(john)))&
((?[X]:((strong(X)|patient(X))))=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((funny(X)&strong(X))=>(old(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>tall(X)))&
(![X]:((rich(X)&~tall(X))<=>~curious(X)))&
(![X]:((funny(X)<~>quiet(X))=>~quiet(X)))&
(((~calm(paul)&~curious(paul)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:((~generous(X)<~>~old(X))=>(humble(X)&~generous(X))))&
(![X]:(~kind(X)=>(humble(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((rich(X)|funny(X)))))&
((~rich(mary))<=>(?[X]:((brave(X)|humble(X)))))&
(((~brave(fred)<~>~generous(fred)))<=>(strong(lucy)))&
((~funny(alice))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)|~curious(X))<=>(quiet(X)|~rich(X))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((~wise(X)&funny(X))))&
((old(mary)<~>~tall(mary)))&
(?[X]:(~rich(X)))&
((~kind(susan)|curious(susan)))&
((~rich(mary)<~>creative(mary)))&
(~rich(lucy)) | ~calm(mary) | [
"p5",
"p6",
"p9",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4091383608442742494771319
% SZS output start Proof for 4091383608442742494771319
6. ! [X0] : (~generous(X0) <=> tall(X0)) [input p5]
7. ! [X0] : ((~tall(X0) & rich(X0)) <=> ~curious(X0)) [input p6]
10. ! [X0] : ((~generous(X0) <~> ~old(X0)) => (~generous(X0) & humble(X0))) [input p9]
13. ~rich(mary) <=> ? [X0] : (humble(X0) | brave(X0)) [input p12]
16. ! [X0] : ((~curious(X0) | calm(X0)) <=> (~rich(X0) | quiet(X0))) [input p15]
20. old(mary) <~> ~tall(mary) [input p19]
25. ~calm(mary) [input hypothesis]
33. ! [X0] : ((~generous(X0) & humble(X0)) | (~generous(X0) <=> ~old(X0))) [ennf transformation 10]
47. ! [X0] : ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0))) [nnf transformation 6]
48. ! [X0] : (((~tall(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | (tall(X0) | ~rich(X0)))) [nnf transformation 7]
49. ! [X0] : (((~tall(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | tall(X0) | ~rich(X0))) [flattening 48]
56. ! [X0] : ((~generous(X0) & humble(X0)) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) [nnf transformation 33]
63. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & (? [X0] : (humble(X0) | brave(X0)) | rich(mary)) [nnf transformation 13]
64. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & (? [X1] : (humble(X1) | brave(X1)) | rich(mary)) [rectify 63]
65. ? [X1] : (humble(X1) | brave(X1)) => (humble(sK5) | brave(sK5)) [choice axiom]
66. (~rich(mary) | ! [X0] : (~humble(X0) & ~brave(X0))) & ((humble(sK5) | brave(sK5)) | rich(mary)) [skolemisation 64,65]
72. ! [X0] : (((~curious(X0) | calm(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (curious(X0) & ~calm(X0)))) [nnf transformation 16]
73. ! [X0] : ((~curious(X0) | calm(X0) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | (curious(X0) & ~calm(X0)))) [flattening 72]
80. (tall(mary) | ~old(mary)) & (~tall(mary) | old(mary)) [nnf transformation 20]
99. generous(X0) | tall(X0) [cnf transformation 47]
100. ~generous(X0) | ~tall(X0) [cnf transformation 47]
102. rich(X0) | curious(X0) [cnf transformation 49]
112. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 56]
115. ~generous(X0) | ~generous(X0) | old(X0) [cnf transformation 56]
123. ~rich(mary) | ~humble(X0) [cnf transformation 66]
133. ~curious(X0) | calm(X0) | rich(X0) [cnf transformation 73]
137. ~tall(mary) | old(mary) [cnf transformation 80]
138. tall(mary) | ~old(mary) [cnf transformation 80]
144. ~calm(mary) [cnf transformation 25]
145. ~generous(X0) | old(X0) [duplicate literal removal 115]
265. 27 <=> ! [X0] : ~humble(X0) [avatar definition]
266. ~humble(X0) <- (27) [avatar component clause 265]
268. 28 <=> rich(mary) [avatar definition]
271. 27 | ~28 [avatar split clause 123,268,265]
314. calm(X0) | rich(X0) [subsumption resolution 133,102]
335. 42 <=> old(mary) [avatar definition]
336. old(mary) <- (42) [avatar component clause 335]
337. ~old(mary) <- (~42) [avatar component clause 335]
339. 43 <=> tall(mary) [avatar definition]
340. ~tall(mary) <- (~43) [avatar component clause 339]
341. tall(mary) <- (43) [avatar component clause 339]
342. ~42 | 43 [avatar split clause 138,339,335]
343. 42 | ~43 [avatar split clause 137,339,335]
379. old(X0) | tall(X0) [resolution 145,99]
397. rich(mary) [resolution 314,144]
401. 28 [avatar split clause 397,268]
522. tall(mary) <- (~42) [resolution 379,337]
525. $false <- (~42, ~43) [subsumption resolution 522,340]
526. 42 | 43 [avatar contradiction clause 525]
533. humble(mary) | generous(mary) <- (42) [resolution 336,112]
534. generous(mary) <- (27, 42) [subsumption resolution 533,266]
546. ~tall(mary) <- (27, 42) [resolution 534,100]
547. $false <- (27, 42, 43) [subsumption resolution 546,341]
548. ~27 | ~42 | ~43 [avatar contradiction clause 547]
549. $false [avatar sat refutation 271,342,343,401,526,548]
% SZS output end Proof for 4091383608442742494771319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not old then paul is both not generous and old and vice versa.
Everyone who is both patient and not rich is not brave.
Everyone who is both not tall and not strong is not old and vice versa.
If someone is both calm and tall then fred is both not strong and not curious and vice versa.
Everyone who is either strong or not happy is either not funny or not wise.
If someone is both not happy and calm then someone is calm or not humble.
Everyone who is both curious and not calm is both quiet and not funny and vice versa.
If someone is tall or quiet then someone is either calm or tall and vice versa.
Everyone who is either old or strong is not old or not kind.
If someone is not brave or not strong then someone is either not patient or not generous.
Everyone who is not calm or tall is either not humble or not brave.
If someone is either humble or not calm then someone is both not kind and tall and vice versa.
Everyone who is both calm and quiet is generous or wise.
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
Mary is tall or not patient.
Someone is either curious or humble.
Alice is quiet.
Susan is not old.
Someone is both kind and not wise.
Someone is not quiet or strong.
Someone is not happy or not calm. | Susan is calm. | neutral | (((patient(fred)<~>~old(fred)))<=>((~generous(paul)&old(paul))))&
(![X]:((patient(X)&~rich(X))=>~brave(X)))&
(![X]:((~tall(X)&~strong(X))<=>~old(X)))&
((?[X]:((calm(X)&tall(X))))<=>((~strong(fred)&~curious(fred))))&
(![X]:((strong(X)<~>~happy(X))=>(~funny(X)<~>~wise(X))))&
((?[X]:((~happy(X)&calm(X))))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((curious(X)&~calm(X))<=>(quiet(X)&~funny(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((old(X)<~>strong(X))=>(~old(X)|~kind(X))))&
((?[X]:((~brave(X)|~strong(X))))=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~calm(X)|tall(X))=>(~humble(X)<~>~brave(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:((~kind(X)&tall(X)))))&
(![X]:((calm(X)&quiet(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((tall(mary)|~patient(mary)))&
(?[X]:((curious(X)<~>humble(X))))&
(quiet(alice))&
(~old(susan))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((~happy(X)|~calm(X)))) | calm(susan) | [] | null | 0 |
Everyone who is both not patient and curious is not curious or creative and vice versa.
If someone is both not brave and calm then john is happy and vice versa.
Everyone who is not creative or not tall is either not humble or happy and vice versa.
If someone is not quiet or tall then someone is old or strong.
If someone is either not curious or not generous then paul is either calm or not old.
Everyone who is either calm or old is humble.
Everyone who is both creative and not patient is both not happy and not brave.
If someone is funny or not old then someone is creative or wise and vice versa.
Everyone who is both not funny and old is both quiet and generous.
If paul is either not creative or brave then lucy is happy or not generous.
Everyone who is old or not brave is both brave and not kind.
Everyone who is both brave and not creative is either not funny or not humble and vice versa.
If john is not strong then someone is both not old and not patient and vice versa.
Everyone who is tall is either kind or not brave and vice versa.
If someone is calm or not rich then susan is both patient and strong.
Everyone who is both old and wise is not quiet or not wise.
Someone is not rich or patient.
Susan is calm or not strong.
Someone is funny or not humble.
Someone is not kind or not strong.
Someone is creative or not calm.
Someone is quiet.
Paul is either not quiet or tall. | John is not calm. | neutral | (![X]:((~patient(X)&curious(X))<=>(~curious(X)|creative(X))))&
((?[X]:((~brave(X)&calm(X))))<=>(happy(john)))&
(![X]:((~creative(X)|~tall(X))<=>(~humble(X)<~>happy(X))))&
((?[X]:((~quiet(X)|tall(X))))=>(?[X]:((old(X)|strong(X)))))&
((?[X]:((~curious(X)<~>~generous(X))))=>((calm(paul)<~>~old(paul))))&
(![X]:((calm(X)<~>old(X))=>humble(X)))&
(![X]:((creative(X)&~patient(X))=>(~happy(X)&~brave(X))))&
((?[X]:((funny(X)|~old(X))))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~funny(X)&old(X))=>(quiet(X)&generous(X))))&
(((~creative(paul)<~>brave(paul)))=>((happy(lucy)|~generous(lucy))))&
(![X]:((old(X)|~brave(X))=>(brave(X)&~kind(X))))&
(![X]:((brave(X)&~creative(X))<=>(~funny(X)<~>~humble(X))))&
((~strong(john))<=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
((?[X]:((calm(X)|~rich(X))))=>((patient(susan)&strong(susan))))&
(![X]:((old(X)&wise(X))=>(~quiet(X)|~wise(X))))&
(?[X]:((~rich(X)|patient(X))))&
((calm(susan)|~strong(susan)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:(quiet(X)))&
((~quiet(paul)<~>tall(paul))) | ~calm(john) | [] | null | 0 |
Everyone who is both happy and not calm is both creative and not kind and vice versa. Everyone who is not funny or creative is not happy or curious. Everyone who is patient or not old is not old. Everyone who is both calm and not happy is happy or funny. If paul is not rich or not patient then susan is both kind and quiet. If someone is not generous or not wise then alice is not creative or not kind and vice versa. If lucy is not curious or wise then someone is either old or not kind and vice versa. If lucy is not wise or not creative then mary is either curious or not tall and vice versa. Everyone who is both not quiet and not creative is not tall. Everyone who is both creative and wise is calm or not patient and vice versa. If john is not tall or not wise then mary is either happy or not rich. Everyone who is both patient and humble is both not kind and not happy. If lucy is either not funny or generous then fred is patient or not old. If someone is strong or funny then mary is not creative and vice versa. If susan is both not wise and curious then someone is both old and not rich and vice versa. If someone is not curious or calm then john is both kind and not kind and vice versa. Someone is not creative. Someone is curious or calm. Mary is not old or happy. Someone is quiet. Paul is both brave and creative. Paul is either humble or tall. Someone is not tall or brave. | Susan is not calm. | entailment | (![X]:((happy(X)&~calm(X))<=>(creative(X)&~kind(X))))&
(![X]:((~funny(X)|creative(X))=>(~happy(X)|curious(X))))&
(![X]:((patient(X)|~old(X))=>~old(X)))&
(![X]:((calm(X)&~happy(X))=>(happy(X)|funny(X))))&
(((~rich(paul)|~patient(paul)))=>((kind(susan)&quiet(susan))))&
((?[X]:((~generous(X)|~wise(X))))<=>((~creative(alice)|~kind(alice))))&
(((~curious(lucy)|wise(lucy)))<=>(?[X]:((old(X)<~>~kind(X)))))&
(((~wise(lucy)|~creative(lucy)))<=>((curious(mary)<~>~tall(mary))))&
(![X]:((~quiet(X)&~creative(X))=>~tall(X)))&
(![X]:((creative(X)&wise(X))<=>(calm(X)|~patient(X))))&
(((~tall(john)|~wise(john)))=>((happy(mary)<~>~rich(mary))))&
(![X]:((patient(X)&humble(X))=>(~kind(X)&~happy(X))))&
(((~funny(lucy)<~>generous(lucy)))=>((patient(fred)|~old(fred))))&
((?[X]:((strong(X)|funny(X))))<=>(~creative(mary)))&
(((~wise(susan)&curious(susan)))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~curious(X)|calm(X))))<=>((kind(john)&~kind(john))))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)|calm(X))))&
((~old(mary)|happy(mary)))&
(?[X]:(quiet(X)))&
((brave(paul)&creative(paul)))&
((humble(paul)<~>tall(paul)))&
(?[X]:((~tall(X)|brave(X)))) | ~calm(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6908625256309698535156832
% SZS output start Proof for 6908625256309698535156832
16. ? [X0] : (calm(X0) | ~curious(X0)) <=> (~kind(john) & kind(john)) [input p15]
24. calm(susan) [input hypothesis]
68. (? [X0] : (calm(X0) | ~curious(X0)) | (kind(john) | ~kind(john))) & ((~kind(john) & kind(john)) | ! [X0] : (~calm(X0) & curious(X0))) [nnf transformation 16]
69. (? [X0] : (calm(X0) | ~curious(X0)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X0] : (~calm(X0) & curious(X0))) [flattening 68]
70. (? [X0] : (calm(X0) | ~curious(X0)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X1] : (~calm(X1) & curious(X1))) [rectify 69]
71. ? [X0] : (calm(X0) | ~curious(X0)) => (calm(sK4) | ~curious(sK4)) [choice axiom]
72. ((calm(sK4) | ~curious(sK4)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X1] : (~calm(X1) & curious(X1))) [skolemisation 70,71]
126. kind(john) | ~calm(X1) [cnf transformation 72]
128. ~kind(john) | ~calm(X1) [cnf transformation 72]
136. calm(susan) [cnf transformation 24]
305. 36 <=> ! [X1] : ~calm(X1) [avatar definition]
306. ~calm(X1) <- (36) [avatar component clause 305]
308. 37 <=> kind(john) [avatar definition]
311. 36 | ~37 [avatar split clause 128,308,305]
316. 36 | 37 [avatar split clause 126,308,305]
348. $false <- (36) [resolution 306,136]
349. ~36 [avatar contradiction clause 348]
350. $false [avatar sat refutation 311,316,349]
% SZS output end Proof for 6908625256309698535156832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not tall and not generous and vice versa.
If paul is strong or humble then someone is tall or not generous and vice versa.
Everyone who is either not happy or generous is both strong and old.
Everyone who is both strong and tall is both happy and calm and vice versa.
Everyone who is not kind is either strong or not rich and vice versa.
Everyone who is either rich or strong is both patient and not funny and vice versa.
If alice is generous then someone is either generous or not wise.
If mary is calm or not happy then someone is creative or not generous and vice versa.
If lucy is both quiet and kind then john is not old.
Everyone who is generous or not humble is strong or not humble.
Everyone who is either kind or not kind is both generous and not patient.
If someone is both not funny and not brave then someone is either generous or not kind and vice versa.
Everyone who is not kind or kind is both not funny and rich.
If someone is generous or not rich then someone is not calm or not rich.
Everyone who is both calm and brave is not calm or humble.
Alice is either not strong or not kind.
Someone is not creative or funny.
Fred is either curious or old.
Someone is not wise or not humble.
Someone is calm or not patient.
Lucy is creative or not strong. | John is brave. | entailment | (![X]:(~generous(X)<=>(~tall(X)&~generous(X))))&
(((strong(paul)|humble(paul)))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~happy(X)<~>generous(X))=>(strong(X)&old(X))))&
(![X]:((strong(X)&tall(X))<=>(happy(X)&calm(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>~rich(X))))&
(![X]:((rich(X)<~>strong(X))<=>(patient(X)&~funny(X))))&
((generous(alice))=>(?[X]:((generous(X)<~>~wise(X)))))&
(((calm(mary)|~happy(mary)))<=>(?[X]:((creative(X)|~generous(X)))))&
(((quiet(lucy)&kind(lucy)))=>(~old(john)))&
(![X]:((generous(X)|~humble(X))=>(strong(X)|~humble(X))))&
(![X]:((kind(X)<~>~kind(X))=>(generous(X)&~patient(X))))&
((?[X]:((~funny(X)&~brave(X))))<=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~kind(X)|kind(X))=>(~funny(X)&rich(X))))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((calm(X)&brave(X))=>(~calm(X)|humble(X))))&
((~strong(alice)<~>~kind(alice)))&
(?[X]:((~creative(X)|funny(X))))&
((curious(fred)<~>old(fred)))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((calm(X)|~patient(X))))&
((creative(lucy)|~strong(lucy))) | brave(john) | [
"p4",
"p5",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3681390295448127573323826
% SZS output start Proof for 3681390295448127573323826
5. ! [X0] : (~kind(X0) <=> (strong(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (~funny(X0) & patient(X0))) [input p5]
11. ! [X0] : ((kind(X0) <~> ~kind(X0)) => (~patient(X0) & generous(X0))) [input p10]
12. ? [X0] : (~brave(X0) & ~funny(X0)) <=> ? [X0] : (generous(X0) <~> ~kind(X0)) [input p11]
13. ! [X0] : ((kind(X0) | ~kind(X0)) => (rich(X0) & ~funny(X0))) [input p12]
22. ~brave(john) [input hypothesis]
23. ? [X0] : (~brave(X0) & ~funny(X0)) <=> ? [X1] : (generous(X1) <~> ~kind(X1)) [rectify 12]
30. ! [X0] : ((~patient(X0) & generous(X0)) | (kind(X0) <=> ~kind(X0))) [ennf transformation 11]
31. ! [X0] : ((rich(X0) & ~funny(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 13]
45. ! [X0] : ((~kind(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | kind(X0))) [nnf transformation 5]
46. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [flattening 46]
56. ! [X0] : ((~patient(X0) & generous(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 30]
57. (? [X0] : (~brave(X0) & ~funny(X0)) | ! [X1] : ((generous(X1) | kind(X1)) & (~kind(X1) | ~generous(X1)))) & (? [X1] : ((kind(X1) | ~generous(X1)) & (~kind(X1) | generous(X1))) | ! [X0] : (brave(X0) | funny(X0))) [nnf transformation 23]
58. (? [X0] : (~brave(X0) & ~funny(X0)) | ! [X1] : ((generous(X1) | kind(X1)) & (~kind(X1) | ~generous(X1)))) & (? [X2] : ((kind(X2) | ~generous(X2)) & (~kind(X2) | generous(X2))) | ! [X3] : (brave(X3) | funny(X3))) [rectify 57]
59. ? [X0] : (~brave(X0) & ~funny(X0)) => (~brave(sK3) & ~funny(sK3)) [choice axiom]
60. ? [X2] : ((kind(X2) | ~generous(X2)) & (~kind(X2) | generous(X2))) => ((kind(sK4) | ~generous(sK4)) & (~kind(sK4) | generous(sK4))) [choice axiom]
61. ((~brave(sK3) & ~funny(sK3)) | ! [X1] : ((generous(X1) | kind(X1)) & (~kind(X1) | ~generous(X1)))) & (((kind(sK4) | ~generous(sK4)) & (~kind(sK4) | generous(sK4))) | ! [X3] : (brave(X3) | funny(X3))) [skolemisation 58,60,59]
90. ~rich(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 45]
92. ~rich(X0) | strong(X0) | patient(X0) [cnf transformation 47]
107. generous(X0) | kind(X0) | kind(X0) [cnf transformation 56]
108. ~patient(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 56]
109. ~patient(X0) | kind(X0) | kind(X0) [cnf transformation 56]
111. kind(sK4) | ~generous(sK4) | brave(X3) | funny(X3) [cnf transformation 61]
116. ~funny(X0) | kind(X0) [cnf transformation 31]
117. ~funny(X0) | ~kind(X0) [cnf transformation 31]
118. rich(X0) | kind(X0) [cnf transformation 31]
119. ~kind(X0) | rich(X0) [cnf transformation 31]
131. ~brave(john) [cnf transformation 22]
134. kind(X0) | generous(X0) [duplicate literal removal 107]
135. ~patient(X0) | ~kind(X0) [duplicate literal removal 108]
136. ~patient(X0) | kind(X0) [duplicate literal removal 109]
200. ~patient(X0) [subsumption resolution 135,136]
216. kind(sK4) | brave(X3) | funny(X3) [subsumption resolution 111,134]
218. 18 <=> ! [X3] : (brave(X3) | funny(X3)) [avatar definition]
219. brave(X3) | funny(X3) <- (18) [avatar component clause 218]
221. 19 <=> kind(sK4) [avatar definition]
223. kind(sK4) <- (19) [avatar component clause 221]
224. 18 | 19 [avatar split clause 216,221,218]
231. rich(X0) [subsumption resolution 118,119]
232. ~funny(X0) [subsumption resolution 116,117]
281. brave(X3) <- (18) [subsumption resolution 219,232]
293. $false <- (18) [resolution 281,131]
294. ~18 [avatar contradiction clause 293]
317. ~kind(X0) | ~strong(X0) [resolution 90,231]
322. ~strong(sK4) <- (19) [resolution 317,223]
325. strong(X0) | patient(X0) [resolution 92,231]
326. strong(X0) [subsumption resolution 325,200]
342. $false <- (19) [resolution 322,326]
343. ~19 [avatar contradiction clause 342]
344. $false [avatar sat refutation 224,294,343]
% SZS output end Proof for 3681390295448127573323826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or quiet is either patient or wise and vice versa.
If someone is wise or creative then john is either not calm or not funny.
Everyone who is not funny or not old is old or curious.
Everyone who is quiet is not tall and vice versa.
Everyone who is both happy and not quiet is not quiet and vice versa.
Everyone who is both wise and creative is kind or strong.
Everyone who is not quiet is not rich.
If paul is both not brave and not tall then someone is both tall and not brave and vice versa.
Everyone who is happy or not funny is either not funny or funny.
Everyone who is not kind is not rich or not happy.
Everyone who is not creative or not humble is strong or not creative and vice versa.
If someone is both kind and funny then someone is either not tall or not wise and vice versa.
Everyone who is not patient is both strong and not kind.
If someone is old or not tall then someone is creative and vice versa.
If alice is either old or quiet then susan is not quiet or not curious and vice versa.
If alice is not kind then susan is both not happy and quiet and vice versa.
Mary is creative or wise.
Someone is happy or old.
Alice is either not calm or curious.
Mary is rich.
Alice is not funny or wise.
Someone is brave or generous.
Someone is either rich or funny. | John is not funny. | neutral | (![X]:((generous(X)<~>quiet(X))<=>(patient(X)<~>wise(X))))&
((?[X]:((wise(X)|creative(X))))=>((~calm(john)<~>~funny(john))))&
(![X]:((~funny(X)|~old(X))=>(old(X)|curious(X))))&
(![X]:(quiet(X)<=>~tall(X)))&
(![X]:((happy(X)&~quiet(X))<=>~quiet(X)))&
(![X]:((wise(X)&creative(X))=>(kind(X)|strong(X))))&
(![X]:(~quiet(X)=>~rich(X)))&
(((~brave(paul)&~tall(paul)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((happy(X)|~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:(~kind(X)=>(~rich(X)|~happy(X))))&
(![X]:((~creative(X)|~humble(X))<=>(strong(X)|~creative(X))))&
((?[X]:((kind(X)&funny(X))))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:(~patient(X)=>(strong(X)&~kind(X))))&
((?[X]:((old(X)|~tall(X))))<=>(?[X]:(creative(X))))&
(((old(alice)<~>quiet(alice)))<=>((~quiet(susan)|~curious(susan))))&
((~kind(alice))<=>((~happy(susan)&quiet(susan))))&
((creative(mary)|wise(mary)))&
(?[X]:((happy(X)|old(X))))&
((~calm(alice)<~>curious(alice)))&
(rich(mary))&
((~funny(alice)|wise(alice)))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((rich(X)<~>funny(X)))) | ~funny(john) | [] | null | 0 |
If someone is strong or not calm then mary is either not creative or not happy and vice versa.
Everyone who is tall or curious is both strong and not creative.
If fred is creative or quiet then john is either not strong or curious.
If mary is calm then lucy is not quiet and vice versa.
Everyone who is both quiet and not happy is not happy and vice versa.
Everyone who is creative is not wise or tall and vice versa.
If john is not patient then susan is either not curious or creative and vice versa.
If someone is both not funny and not generous then paul is strong or brave and vice versa.
If someone is humble then someone is both kind and not funny and vice versa.
Everyone who is not happy or strong is either not strong or not patient.
Everyone who is not funny is either not patient or strong.
Everyone who is not humble is calm or wise.
Everyone who is brave is not creative.
Everyone who is not happy is not strong or not calm and vice versa.
Everyone who is both brave and not patient is wise or brave.
If someone is not humble then someone is rich or generous.
Mary is either calm or not patient.
Someone is not patient.
Someone is either not calm or not old.
Someone is both funny and not wise. | Fred is not kind. | neutral | ((?[X]:((strong(X)|~calm(X))))<=>((~creative(mary)<~>~happy(mary))))&
(![X]:((tall(X)|curious(X))=>(strong(X)&~creative(X))))&
(((creative(fred)|quiet(fred)))=>((~strong(john)<~>curious(john))))&
((calm(mary))<=>(~quiet(lucy)))&
(![X]:((quiet(X)&~happy(X))<=>~happy(X)))&
(![X]:(creative(X)<=>(~wise(X)|tall(X))))&
((~patient(john))<=>((~curious(susan)<~>creative(susan))))&
((?[X]:((~funny(X)&~generous(X))))<=>((strong(paul)|brave(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((~happy(X)|strong(X))=>(~strong(X)<~>~patient(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>strong(X))))&
(![X]:(~humble(X)=>(calm(X)|wise(X))))&
(![X]:(brave(X)=>~creative(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~calm(X))))&
(![X]:((brave(X)&~patient(X))=>(wise(X)|brave(X))))&
((?[X]:(~humble(X)))=>(?[X]:((rich(X)|generous(X)))))&
((calm(mary)<~>~patient(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)<~>~old(X))))&
(?[X]:((funny(X)&~wise(X)))) | ~kind(fred) | [] | null | 0 |
Subsets and Splits