premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either wise or not kind is both generous and quiet and vice versa.
If someone is not wise or not rich then john is either not generous or creative and vice versa.
Everyone who is calm is both generous and not strong.
If mary is either strong or rich then someone is both kind and not strong.
If lucy is not generous or not brave then john is quiet or not quiet.
If someone is both tall and not happy then someone is not calm or not humble and vice versa.
If someone is old then someone is both humble and kind.
Everyone who is either old or not curious is not kind and vice versa.
Everyone who is both not kind and not brave is both not curious and not rich.
Everyone who is not kind or patient is not calm and vice versa.
If lucy is either funny or generous then paul is either old or not quiet and vice versa.
Everyone who is either wise or not brave is both not patient and not old and vice versa.
Everyone who is both quiet and generous is not brave and vice versa.
If fred is both not tall and brave then john is either not strong or generous and vice versa.
Everyone who is calm is either not brave or not strong and vice versa.
Everyone who is happy or not patient is generous and vice versa.
Fred is both quiet and rich.
Lucy is not tall.
John is either not generous or not kind.
Fred is either not tall or not humble.
Paul is not generous or not kind.
John is calm or not rich.
Mary is not wise or not creative.
Alice is curious or not rich. | John is not rich. | entailment | (![X]:((wise(X)<~>~kind(X))<=>(generous(X)&quiet(X))))&
((?[X]:((~wise(X)|~rich(X))))<=>((~generous(john)<~>creative(john))))&
(![X]:(calm(X)=>(generous(X)&~strong(X))))&
(((strong(mary)<~>rich(mary)))=>(?[X]:((kind(X)&~strong(X)))))&
(((~generous(lucy)|~brave(lucy)))=>((quiet(john)|~quiet(john))))&
((?[X]:((tall(X)&~happy(X))))<=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:(old(X)))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((old(X)<~>~curious(X))<=>~kind(X)))&
(![X]:((~kind(X)&~brave(X))=>(~curious(X)&~rich(X))))&
(![X]:((~kind(X)|patient(X))<=>~calm(X)))&
(((funny(lucy)<~>generous(lucy)))<=>((old(paul)<~>~quiet(paul))))&
(![X]:((wise(X)<~>~brave(X))<=>(~patient(X)&~old(X))))&
(![X]:((quiet(X)&generous(X))<=>~brave(X)))&
(((~tall(fred)&brave(fred)))<=>((~strong(john)<~>generous(john))))&
(![X]:(calm(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((happy(X)|~patient(X))<=>generous(X)))&
((quiet(fred)&rich(fred)))&
(~tall(lucy))&
((~generous(john)<~>~kind(john)))&
((~tall(fred)<~>~humble(fred)))&
((~generous(paul)|~kind(paul)))&
((calm(john)|~rich(john)))&
((~wise(mary)|~creative(mary)))&
((curious(alice)|~rich(alice))) | ~rich(john) | [
"p2",
"p9",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7404462906444921179317448
% SZS output start Proof for 7404462906444921179317448
3. ! [X0] : (calm(X0) => (~strong(X0) & generous(X0))) [input p2]
10. ! [X0] : ((patient(X0) | ~kind(X0)) <=> ~calm(X0)) [input p9]
19. ~generous(john) <~> ~kind(john) [input p18]
22. ~rich(john) | calm(john) [input p21]
25. rich(john) [input hypothesis]
28. ! [X0] : ((~strong(X0) & generous(X0)) | ~calm(X0)) [ennf transformation 3]
53. ! [X0] : (((patient(X0) | ~kind(X0)) | calm(X0)) & (~calm(X0) | (~patient(X0) & kind(X0)))) [nnf transformation 10]
54. ! [X0] : ((patient(X0) | ~kind(X0) | calm(X0)) & (~calm(X0) | (~patient(X0) & kind(X0)))) [flattening 53]
65. (kind(john) | generous(john)) & (~kind(john) | ~generous(john)) [nnf transformation 19]
79. ~calm(X0) | generous(X0) [cnf transformation 28]
100. ~calm(X0) | kind(X0) [cnf transformation 54]
136. ~kind(john) | ~generous(john) [cnf transformation 65]
141. ~rich(john) | calm(john) [cnf transformation 22]
144. rich(john) [cnf transformation 25]
150. 2 <=> generous(john) [avatar definition]
281. 28 <=> kind(john) [avatar definition]
282. ~kind(john) <- (~28) [avatar component clause 281]
285. ~2 | ~28 [avatar split clause 136,281,150]
302. 32 <=> calm(john) [avatar definition]
304. calm(john) <- (32) [avatar component clause 302]
306. 33 <=> rich(john) [avatar definition]
309. 32 | ~33 [avatar split clause 141,306,302]
328. 33 [avatar split clause 144,306]
339. generous(john) <- (32) [resolution 79,304]
342. 2 | ~32 [avatar split clause 339,302,150]
346. kind(john) <- (32) [resolution 100,304]
347. $false <- (~28, 32) [subsumption resolution 346,282]
348. 28 | ~32 [avatar contradiction clause 347]
349. $false [avatar sat refutation 285,309,328,342,348]
% SZS output end Proof for 7404462906444921179317448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not kind or old then mary is not happy or not humble. If mary is both quiet and not kind then mary is wise or old and vice versa. If susan is either not brave or not happy then alice is both not wise and happy. If lucy is funny then someone is humble or calm. If someone is either quiet or not rich then someone is tall or calm and vice versa. Everyone who is both patient and brave is not strong and vice versa. Everyone who is not happy or not funny is both quiet and happy and vice versa. Everyone who is either not happy or not patient is tall or happy and vice versa. Everyone who is both wise and not curious is both not humble and quiet and vice versa. If lucy is both old and happy then alice is calm or not calm and vice versa. Everyone who is not humble or quiet is not patient or wise and vice versa. Everyone who is both not quiet and happy is not creative. If paul is not strong then someone is patient and vice versa. If someone is both not quiet and kind then someone is both not funny and wise and vice versa. If fred is both not quiet and not funny then susan is either not brave or not calm and vice versa. Everyone who is both old and brave is not quiet and vice versa. John is generous. Paul is both not creative and not funny. Someone is both not patient and not quiet. Paul is rich. Someone is not wise. Someone is not calm. Fred is both not wise and not curious. Susan is either quiet or not quiet. | Lucy is humble. | neutral | (((~kind(paul)<~>old(paul)))=>((~happy(mary)|~humble(mary))))&
(((quiet(mary)&~kind(mary)))<=>((wise(mary)|old(mary))))&
(((~brave(susan)<~>~happy(susan)))=>((~wise(alice)&happy(alice))))&
((funny(lucy))=>(?[X]:((humble(X)|calm(X)))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((patient(X)&brave(X))<=>~strong(X)))&
(![X]:((~happy(X)|~funny(X))<=>(quiet(X)&happy(X))))&
(![X]:((~happy(X)<~>~patient(X))<=>(tall(X)|happy(X))))&
(![X]:((wise(X)&~curious(X))<=>(~humble(X)&quiet(X))))&
(((old(lucy)&happy(lucy)))<=>((calm(alice)|~calm(alice))))&
(![X]:((~humble(X)|quiet(X))<=>(~patient(X)|wise(X))))&
(![X]:((~quiet(X)&happy(X))=>~creative(X)))&
((~strong(paul))<=>(?[X]:(patient(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:((~funny(X)&wise(X)))))&
(((~quiet(fred)&~funny(fred)))<=>((~brave(susan)<~>~calm(susan))))&
(![X]:((old(X)&brave(X))<=>~quiet(X)))&
(generous(john))&
((~creative(paul)&~funny(paul)))&
(?[X]:((~patient(X)&~quiet(X))))&
(rich(paul))&
(?[X]:(~wise(X)))&
(?[X]:(~calm(X)))&
((~wise(fred)&~curious(fred)))&
((quiet(susan)<~>~quiet(susan))) | humble(lucy) | [] | null | 0 |
If john is not curious then fred is both not strong and creative and vice versa. If mary is not happy then fred is calm and vice versa. If mary is either calm or not patient then john is both generous and not brave and vice versa. If someone is both not rich and brave then someone is humble or not curious. Everyone who is both not generous and happy is either not tall or not creative and vice versa. Everyone who is either not kind or not happy is brave or not happy. Everyone who is either not brave or tall is both humble and curious and vice versa. If john is not rich or generous then someone is curious or wise and vice versa. Everyone who is both not rich and not wise is either not calm or not brave. If someone is wise then alice is either not creative or old. If mary is both happy and rich then someone is not kind. Everyone who is either humble or happy is both strong and not brave and vice versa. If john is not curious or not funny then someone is curious and vice versa. Everyone who is not old or not creative is either not quiet or not patient. Everyone who is not generous or creative is either rich or old. Everyone who is both quiet and strong is happy and vice versa. Someone is both strong and not calm. Someone is humble. Someone is brave. Someone is generous or funny. Someone is both rich and happy. John is strong. Paul is strong. Alice is either not brave or not rich. | Alice is old. | neutral | ((~curious(john))<=>((~strong(fred)&creative(fred))))&
((~happy(mary))<=>(calm(fred)))&
(((calm(mary)<~>~patient(mary)))<=>((generous(john)&~brave(john))))&
((?[X]:((~rich(X)&brave(X))))=>(?[X]:((humble(X)|~curious(X)))))&
(![X]:((~generous(X)&happy(X))<=>(~tall(X)<~>~creative(X))))&
(![X]:((~kind(X)<~>~happy(X))=>(brave(X)|~happy(X))))&
(![X]:((~brave(X)<~>tall(X))<=>(humble(X)&curious(X))))&
(((~rich(john)|generous(john)))<=>(?[X]:((curious(X)|wise(X)))))&
(![X]:((~rich(X)&~wise(X))=>(~calm(X)<~>~brave(X))))&
((?[X]:(wise(X)))=>((~creative(alice)<~>old(alice))))&
(((happy(mary)&rich(mary)))=>(?[X]:(~kind(X))))&
(![X]:((humble(X)<~>happy(X))<=>(strong(X)&~brave(X))))&
(((~curious(john)|~funny(john)))<=>(?[X]:(curious(X))))&
(![X]:((~old(X)|~creative(X))=>(~quiet(X)<~>~patient(X))))&
(![X]:((~generous(X)|creative(X))=>(rich(X)<~>old(X))))&
(![X]:((quiet(X)&strong(X))<=>happy(X)))&
(?[X]:((strong(X)&~calm(X))))&
(?[X]:(humble(X)))&
(?[X]:(brave(X)))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((rich(X)&happy(X))))&
(strong(john))&
(strong(paul))&
((~brave(alice)<~>~rich(alice))) | old(alice) | [] | null | 0 |
If someone is both not tall and creative then someone is either not tall or quiet and vice versa.
If someone is either not humble or kind then someone is both calm and creative.
If someone is either not quiet or not calm then someone is either not quiet or old and vice versa.
If fred is not kind or patient then someone is curious and vice versa.
If susan is not rich then someone is not rich and vice versa.
Everyone who is funny is not humble or wise and vice versa.
Everyone who is creative or kind is both quiet and strong and vice versa.
Everyone who is both old and not humble is not wise and vice versa.
If someone is both creative and not kind then paul is old or brave and vice versa.
If fred is both not rich and old then paul is both old and funny.
Everyone who is both not patient and strong is both quiet and not wise.
If fred is curious or not strong then lucy is both rich and not creative and vice versa.
Everyone who is both not wise and curious is either not quiet or not creative and vice versa.
Everyone who is either not funny or not calm is both rich and not creative.
If john is both not creative and patient then john is not strong and vice versa.
Everyone who is not generous is wise and vice versa.
John is not happy or generous.
Mary is either not kind or quiet.
John is patient.
Someone is calm or creative.
Someone is not curious or quiet.
Someone is both not happy and not calm.
Someone is creative or generous.
Someone is both strong and not old. | Lucy is wise. | neutral | ((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
((?[X]:((~humble(X)<~>kind(X))))=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((~quiet(X)<~>~calm(X))))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((~kind(fred)|patient(fred)))<=>(?[X]:(curious(X))))&
((~rich(susan))<=>(?[X]:(~rich(X))))&
(![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(![X]:((creative(X)|kind(X))<=>(quiet(X)&strong(X))))&
(![X]:((old(X)&~humble(X))<=>~wise(X)))&
((?[X]:((creative(X)&~kind(X))))<=>((old(paul)|brave(paul))))&
(((~rich(fred)&old(fred)))=>((old(paul)&funny(paul))))&
(![X]:((~patient(X)&strong(X))=>(quiet(X)&~wise(X))))&
(((curious(fred)|~strong(fred)))<=>((rich(lucy)&~creative(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(rich(X)&~creative(X))))&
(((~creative(john)&patient(john)))<=>(~strong(john)))&
(![X]:(~generous(X)<=>wise(X)))&
((~happy(john)|generous(john)))&
((~kind(mary)<~>quiet(mary)))&
(patient(john))&
(?[X]:((calm(X)|creative(X))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:((~happy(X)&~calm(X))))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:((strong(X)&~old(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is not wise or not generous is quiet or not rich.
Everyone who is generous or not tall is both brave and kind.
If john is funny or kind then someone is both not humble and not kind.
If someone is not rich or not creative then fred is both strong and generous.
Everyone who is tall or old is curious or not funny.
Everyone who is not wise or humble is not old or strong.
If lucy is tall then alice is both curious and patient.
If susan is either not humble or not curious then someone is either not calm or not brave and vice versa.
Everyone who is not old is either humble or old.
Everyone who is both patient and tall is both not humble and quiet.
Everyone who is both strong and not patient is not quiet or curious.
If fred is either not creative or not rich then someone is not strong.
If someone is not funny or happy then susan is either curious or not old.
If paul is not brave then someone is patient or kind and vice versa.
Someone is both not curious and wise.
Paul is either not quiet or wise.
Lucy is brave.
John is tall or not creative.
Alice is either happy or not funny.
Someone is both rich and funny.
Someone is not curious. | Alice is not calm. | neutral | (![X]:((~wise(X)|~generous(X))=>(quiet(X)|~rich(X))))&
(![X]:((generous(X)|~tall(X))=>(brave(X)&kind(X))))&
(((funny(john)|kind(john)))=>(?[X]:((~humble(X)&~kind(X)))))&
((?[X]:((~rich(X)|~creative(X))))=>((strong(fred)&generous(fred))))&
(![X]:((tall(X)|old(X))=>(curious(X)|~funny(X))))&
(![X]:((~wise(X)|humble(X))=>(~old(X)|strong(X))))&
((tall(lucy))=>((curious(alice)&patient(alice))))&
(((~humble(susan)<~>~curious(susan)))<=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:(~old(X)=>(humble(X)<~>old(X))))&
(![X]:((patient(X)&tall(X))=>(~humble(X)&quiet(X))))&
(![X]:((strong(X)&~patient(X))=>(~quiet(X)|curious(X))))&
(((~creative(fred)<~>~rich(fred)))=>(?[X]:(~strong(X))))&
((?[X]:((~funny(X)|happy(X))))=>((curious(susan)<~>~old(susan))))&
((~brave(paul))<=>(?[X]:((patient(X)|kind(X)))))&
(?[X]:((~curious(X)&wise(X))))&
((~quiet(paul)<~>wise(paul)))&
(brave(lucy))&
((tall(john)|~creative(john)))&
((happy(alice)<~>~funny(alice)))&
(?[X]:((rich(X)&funny(X))))&
(?[X]:(~curious(X))) | ~calm(alice) | [] | null | 0 |
If someone is wise then someone is tall or curious. If someone is not quiet or not brave then someone is happy and vice versa. Everyone who is either not wise or not creative is curious or not humble and vice versa. If someone is either generous or not happy then someone is kind. Everyone who is either curious or patient is curious and vice versa. Everyone who is curious is not happy. Everyone who is either rich or not old is kind or not curious. Everyone who is not creative or kind is kind and vice versa. Everyone who is either kind or happy is both happy and not patient and vice versa. If fred is old or not funny then lucy is either not curious or not quiet and vice versa. If someone is not wise then lucy is not curious or calm and vice versa. Everyone who is both not calm and patient is both not happy and curious. If lucy is both not generous and calm then someone is both wise and generous. If someone is either not generous or funny then someone is funny and vice versa. Everyone who is curious is either not humble or not rich. Everyone who is not creative is wise or tall and vice versa. Susan is not wise or not calm. Someone is creative or not curious. Lucy is either not wise or tall. Susan is both not patient and not generous. Fred is both not brave and strong. Someone is either not funny or not strong. | Lucy is not tall. | entailment | ((?[X]:(wise(X)))=>(?[X]:((tall(X)|curious(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(curious(X)|~humble(X))))&
((?[X]:((generous(X)<~>~happy(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>patient(X))<=>curious(X)))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((rich(X)<~>~old(X))=>(kind(X)|~curious(X))))&
(![X]:((~creative(X)|kind(X))<=>kind(X)))&
(![X]:((kind(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(((old(fred)|~funny(fred)))<=>((~curious(lucy)<~>~quiet(lucy))))&
((?[X]:(~wise(X)))<=>((~curious(lucy)|calm(lucy))))&
(![X]:((~calm(X)&patient(X))=>(~happy(X)&curious(X))))&
(((~generous(lucy)&calm(lucy)))=>(?[X]:((wise(X)&generous(X)))))&
((?[X]:((~generous(X)<~>funny(X))))<=>(?[X]:(funny(X))))&
(![X]:(curious(X)=>(~humble(X)<~>~rich(X))))&
(![X]:(~creative(X)<=>(wise(X)|tall(X))))&
((~wise(susan)|~calm(susan)))&
(?[X]:((creative(X)|~curious(X))))&
((~wise(lucy)<~>tall(lucy)))&
((~patient(susan)&~generous(susan)))&
((~brave(fred)&strong(fred)))&
(?[X]:((~funny(X)<~>~strong(X)))) | ~tall(lucy) | [
"p4",
"p7",
"p8",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 274178166936151874656306
% SZS output start Proof for 274178166936151874656306
5. ! [X0] : ((curious(X0) <~> patient(X0)) <=> curious(X0)) [input p4]
8. ! [X0] : ((kind(X0) | ~creative(X0)) <=> kind(X0)) [input p7]
9. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (~patient(X0) & happy(X0))) [input p8]
16. ! [X0] : (~creative(X0) <=> (tall(X0) | wise(X0))) [input p15]
19. ~wise(lucy) <~> tall(lucy) [input p18]
23. tall(lucy) [input hypothesis]
52. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | ~curious(X0)) & (curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 5]
54. ! [X0] : (((kind(X0) | ~creative(X0)) | ~kind(X0)) & (kind(X0) | (~kind(X0) & creative(X0)))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | ~creative(X0) | ~kind(X0)) & (kind(X0) | (~kind(X0) & creative(X0)))) [flattening 54]
56. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 9]
57. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 56]
73. ! [X0] : ((~creative(X0) | (~tall(X0) & ~wise(X0))) & ((tall(X0) | wise(X0)) | creative(X0))) [nnf transformation 16]
74. ! [X0] : ((~creative(X0) | (~tall(X0) & ~wise(X0))) & (tall(X0) | wise(X0) | creative(X0))) [flattening 73]
77. (~tall(lucy) | wise(lucy)) & (tall(lucy) | ~wise(lucy)) [nnf transformation 19]
94. curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 52]
96. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
100. kind(X0) | creative(X0) [cnf transformation 55]
103. happy(X0) | happy(X0) | ~kind(X0) [cnf transformation 57]
108. ~happy(X0) | ~kind(X0) | patient(X0) | ~happy(X0) [cnf transformation 57]
129. ~creative(X0) | ~wise(X0) [cnf transformation 74]
134. ~tall(lucy) | wise(lucy) [cnf transformation 77]
141. tall(lucy) [cnf transformation 23]
142. happy(X0) | ~kind(X0) [duplicate literal removal 103]
143. ~happy(X0) | ~kind(X0) | patient(X0) [duplicate literal removal 108]
144. curious(X0) | ~patient(X0) [duplicate literal removal 94]
145. ~patient(X0) | ~curious(X0) [duplicate literal removal 96]
147. 1 <=> ! [X1] : ~wise(X1) [avatar definition]
148. ~wise(X1) <- (1) [avatar component clause 147]
194. ~patient(X0) [subsumption resolution 144,145]
195. ~happy(X0) | ~kind(X0) [subsumption resolution 143,194]
196. ~kind(X0) [subsumption resolution 142,195]
291. 33 <=> wise(lucy) [avatar definition]
293. wise(lucy) <- (33) [avatar component clause 291]
295. 34 <=> tall(lucy) [avatar definition]
298. 33 | ~34 [avatar split clause 134,295,291]
310. 34 [avatar split clause 141,295]
314. creative(X0) [resolution 100,196]
315. ~wise(X0) [resolution 314,129]
316. 1 [avatar split clause 315,147]
317. $false <- (1, 33) [resolution 148,293]
318. ~1 | ~33 [avatar contradiction clause 317]
319. $false [avatar sat refutation 298,310,316,318]
% SZS output end Proof for 274178166936151874656306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not rich then someone is both tall and generous.
Everyone who is not creative is kind.
If alice is calm then someone is not patient or not rich.
Everyone who is both not calm and strong is not rich or patient.
Everyone who is happy or curious is either tall or not tall and vice versa.
If john is quiet or wise then john is both patient and not curious and vice versa.
Everyone who is tall is tall or not funny.
If someone is not quiet or strong then someone is calm.
If paul is both curious and not funny then someone is humble and vice versa.
If alice is either wise or not creative then paul is not creative or creative.
If someone is both not wise and not curious then alice is not calm or strong and vice versa.
Everyone who is both strong and not generous is not tall and vice versa.
Everyone who is both patient and funny is not old or not funny.
If someone is tall then mary is not patient and vice versa.
If lucy is not creative then someone is both not generous and generous.
If someone is funny or brave then lucy is either not old or not curious and vice versa.
Susan is not creative.
Lucy is either wise or not strong.
Lucy is rich.
Someone is either not calm or rich.
Someone is not old.
Alice is either curious or brave.
Someone is not quiet or wise.
Paul is either not happy or curious. | Alice is calm. | neutral | ((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((tall(X)&generous(X)))))&
(![X]:(~creative(X)=>kind(X)))&
((calm(alice))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((~calm(X)&strong(X))=>(~rich(X)|patient(X))))&
(![X]:((happy(X)|curious(X))<=>(tall(X)<~>~tall(X))))&
(((quiet(john)|wise(john)))<=>((patient(john)&~curious(john))))&
(![X]:(tall(X)=>(tall(X)|~funny(X))))&
((?[X]:((~quiet(X)|strong(X))))=>(?[X]:(calm(X))))&
(((curious(paul)&~funny(paul)))<=>(?[X]:(humble(X))))&
(((wise(alice)<~>~creative(alice)))=>((~creative(paul)|creative(paul))))&
((?[X]:((~wise(X)&~curious(X))))<=>((~calm(alice)|strong(alice))))&
(![X]:((strong(X)&~generous(X))<=>~tall(X)))&
(![X]:((patient(X)&funny(X))=>(~old(X)|~funny(X))))&
((?[X]:(tall(X)))<=>(~patient(mary)))&
((~creative(lucy))=>(?[X]:((~generous(X)&generous(X)))))&
((?[X]:((funny(X)|brave(X))))<=>((~old(lucy)<~>~curious(lucy))))&
(~creative(susan))&
((wise(lucy)<~>~strong(lucy)))&
(rich(lucy))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:(~old(X)))&
((curious(alice)<~>brave(alice)))&
(?[X]:((~quiet(X)|wise(X))))&
((~happy(paul)<~>curious(paul))) | calm(alice) | [] | null | 0 |
Everyone who is either brave or wise is rich and vice versa.
If someone is brave or creative then paul is not tall and vice versa.
If paul is either not kind or generous then mary is both not brave and not generous.
If someone is happy or not brave then fred is both funny and calm and vice versa.
Everyone who is either not creative or not rich is either not patient or strong.
Everyone who is both strong and not creative is not patient or quiet and vice versa.
If someone is not patient or curious then someone is generous or not curious.
Everyone who is happy is not humble and vice versa.
Everyone who is both funny and old is not tall.
Everyone who is both kind and not patient is both wise and tall and vice versa.
Everyone who is humble is either wise or not humble and vice versa.
Everyone who is wise is either not brave or humble.
Everyone who is not happy or not quiet is brave and vice versa.
Everyone who is calm is either calm or not strong and vice versa.
If susan is not curious then paul is kind or quiet and vice versa.
If mary is wise or happy then fred is generous or not tall.
Susan is both wise and not creative.
Lucy is not creative.
Alice is both not patient and not funny.
Someone is not calm or brave.
Alice is funny or not quiet.
Someone is not patient.
Someone is both curious and tall. | Lucy is not quiet. | neutral | (![X]:((brave(X)<~>wise(X))<=>rich(X)))&
((?[X]:((brave(X)|creative(X))))<=>(~tall(paul)))&
(((~kind(paul)<~>generous(paul)))=>((~brave(mary)&~generous(mary))))&
((?[X]:((happy(X)|~brave(X))))<=>((funny(fred)&calm(fred))))&
(![X]:((~creative(X)<~>~rich(X))=>(~patient(X)<~>strong(X))))&
(![X]:((strong(X)&~creative(X))<=>(~patient(X)|quiet(X))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:(happy(X)<=>~humble(X)))&
(![X]:((funny(X)&old(X))=>~tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(wise(X)&tall(X))))&
(![X]:(humble(X)<=>(wise(X)<~>~humble(X))))&
(![X]:(wise(X)=>(~brave(X)<~>humble(X))))&
(![X]:((~happy(X)|~quiet(X))<=>brave(X)))&
(![X]:(calm(X)<=>(calm(X)<~>~strong(X))))&
((~curious(susan))<=>((kind(paul)|quiet(paul))))&
(((wise(mary)|happy(mary)))=>((generous(fred)|~tall(fred))))&
((wise(susan)&~creative(susan)))&
(~creative(lucy))&
((~patient(alice)&~funny(alice)))&
(?[X]:((~calm(X)|brave(X))))&
((funny(alice)|~quiet(alice)))&
(?[X]:(~patient(X)))&
(?[X]:((curious(X)&tall(X)))) | ~quiet(lucy) | [] | null | 0 |
If someone is both patient and brave then lucy is wise or not creative and vice versa.
If someone is tall or rich then susan is not old or not curious.
Everyone who is not calm or not brave is both happy and not wise and vice versa.
Everyone who is either happy or not creative is either not calm or not curious and vice versa.
If fred is not funny or not kind then someone is funny.
Everyone who is not kind or not quiet is both not humble and happy and vice versa.
Everyone who is both happy and not kind is not old.
If someone is either not rich or creative then alice is creative and vice versa.
Everyone who is creative or curious is not kind or not creative.
Everyone who is not brave is not curious or not humble and vice versa.
If someone is either happy or not rich then someone is either not humble or not rich and vice versa.
If john is both funny and tall then susan is either not humble or funny.
Everyone who is not calm or not curious is kind.
If someone is both not quiet and patient then fred is patient and vice versa.
If john is both quiet and old then susan is not humble and vice versa.
Everyone who is not generous is not brave and vice versa.
Lucy is either not kind or not rich.
Someone is generous.
Someone is not old.
Someone is not wise.
Someone is both tall and strong. | Lucy is generous. | contradiction | ((?[X]:((patient(X)&brave(X))))<=>((wise(lucy)|~creative(lucy))))&
((?[X]:((tall(X)|rich(X))))=>((~old(susan)|~curious(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(happy(X)&~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~curious(X))))&
(((~funny(fred)|~kind(fred)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((?[X]:((~rich(X)<~>creative(X))))<=>(creative(alice)))&
(![X]:((creative(X)|curious(X))=>(~kind(X)|~creative(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((funny(john)&tall(john)))=>((~humble(susan)<~>funny(susan))))&
(![X]:((~calm(X)|~curious(X))=>kind(X)))&
((?[X]:((~quiet(X)&patient(X))))<=>(patient(fred)))&
(((quiet(john)&old(john)))<=>(~humble(susan)))&
(![X]:(~generous(X)<=>~brave(X)))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
(?[X]:((tall(X)&strong(X)))) | generous(lucy) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 57095076304412402306988
% SZS output start Proof for 57095076304412402306988
4. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (~calm(X0) <~> ~curious(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (happy(X0) & ~humble(X0))) [input p5]
8. ? [X0] : (~rich(X0) <~> creative(X0)) <=> creative(alice) [input p7]
9. ! [X0] : ((curious(X0) | creative(X0)) => (~creative(X0) | ~kind(X0))) [input p8]
10. ! [X0] : (~brave(X0) <=> (~humble(X0) | ~curious(X0))) [input p9]
13. ! [X0] : ((~curious(X0) | ~calm(X0)) => kind(X0)) [input p12]
16. ! [X0] : (~generous(X0) <=> ~brave(X0)) [input p15]
17. ~kind(lucy) <~> ~rich(lucy) [input p16]
22. generous(lucy) [input hypothesis]
24. ! [X0] : (~brave(X0) => ~generous(X0)) [unused predicate definition removal 16]
31. ! [X0] : ((~creative(X0) | ~kind(X0)) | (~curious(X0) & ~creative(X0))) [ennf transformation 9]
32. ! [X0] : (~creative(X0) | ~kind(X0) | (~curious(X0) & ~creative(X0))) [flattening 31]
35. ! [X0] : (kind(X0) | (curious(X0) & calm(X0))) [ennf transformation 13]
36. ! [X0] : (~generous(X0) | brave(X0)) [ennf transformation 24]
44. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0)))) & (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 4]
47. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 6]
48. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [flattening 47]
49. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 8]
50. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [rectify 49]
51. ? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) => ((~creative(sK2) | rich(sK2)) & (creative(sK2) | ~rich(sK2))) [choice axiom]
52. (((~creative(sK2) | rich(sK2)) & (creative(sK2) | ~rich(sK2))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [skolemisation 50,51]
53. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & ((~humble(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 10]
54. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & (~humble(X0) | ~curious(X0) | brave(X0))) [flattening 53]
67. (rich(lucy) | kind(lucy)) & (~rich(lucy) | ~kind(lucy)) [nnf transformation 17]
88. ~happy(X0) | ~calm(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 44]
98. ~humble(X0) | kind(X0) [cnf transformation 48]
100. kind(X0) | happy(X0) [cnf transformation 48]
104. creative(alice) | creative(X1) | rich(X1) [cnf transformation 52]
108. ~creative(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 32]
109. ~kind(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 32]
111. ~brave(X0) | curious(X0) [cnf transformation 54]
112. ~brave(X0) | humble(X0) [cnf transformation 54]
123. kind(X0) | calm(X0) [cnf transformation 35]
124. kind(X0) | curious(X0) [cnf transformation 35]
131. ~generous(X0) | brave(X0) [cnf transformation 36]
132. ~rich(lucy) | ~kind(lucy) [cnf transformation 67]
138. generous(lucy) [cnf transformation 22]
139. ~kind(X0) | ~creative(X0) [duplicate literal removal 108]
141. 1 <=> creative(lucy) [avatar definition]
142. ~creative(lucy) <- (~1) [avatar component clause 141]
200. 13 <=> creative(alice) [avatar definition]
201. creative(alice) <- (13) [avatar component clause 200]
218. 17 <=> ! [X1] : (creative(X1) | rich(X1)) [avatar definition]
219. rich(X1) | creative(X1) <- (17) [avatar component clause 218]
220. 17 | 13 [avatar split clause 104,200,218]
305. 36 <=> kind(lucy) [avatar definition]
307. kind(lucy) <- (36) [avatar component clause 305]
309. 37 <=> rich(lucy) [avatar definition]
310. ~rich(lucy) <- (~37) [avatar component clause 309]
313. ~36 | ~37 [avatar split clause 132,309,305]
329. brave(lucy) [resolution 131,138]
332. ~creative(X0) | curious(X0) [resolution 139,124]
333. ~creative(X1) | calm(X1) [resolution 139,123]
334. ~creative(X2) | happy(X2) [resolution 139,100]
338. humble(lucy) [resolution 329,112]
339. curious(lucy) [resolution 329,111]
371. 41 <=> curious(alice) [avatar definition]
375. 42 <=> happy(alice) [avatar definition]
377. happy(alice) <- (42) [avatar component clause 375]
380. creative(lucy) <- (17, ~37) [resolution 219,310]
384. $false <- (~1, 17, ~37) [subsumption resolution 380,142]
385. 1 | ~17 | 37 [avatar contradiction clause 384]
470. kind(lucy) [resolution 338,98]
473. 36 [avatar split clause 470,305]
478. ~creative(lucy) | ~curious(lucy) <- (36) [resolution 307,109]
486. ~creative(lucy) <- (36) [subsumption resolution 478,339]
487. ~1 | ~36 [avatar split clause 486,305,141]
490. calm(alice) <- (13) [resolution 201,333]
491. curious(alice) <- (13) [resolution 201,332]
500. happy(alice) <- (13) [resolution 334,201]
502. 42 | ~13 [avatar split clause 500,200,375]
504. ~calm(alice) | ~creative(alice) | ~curious(alice) <- (42) [resolution 377,88]
506. ~creative(alice) | ~curious(alice) <- (13, 42) [subsumption resolution 504,490]
507. ~curious(alice) <- (13, 42) [subsumption resolution 506,201]
520. ~41 | ~13 | ~42 [avatar split clause 507,375,200,371]
521. 41 | ~13 [avatar split clause 491,200,371]
522. $false [avatar sat refutation 220,313,385,473,487,502,520,521]
% SZS output end Proof for 57095076304412402306988
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not funny or not happy and vice versa.
Everyone who is humble is patient or strong and vice versa.
If someone is wise or not calm then someone is not curious or not calm and vice versa.
Everyone who is both tall and not wise is either not creative or not tall and vice versa.
Everyone who is both tall and curious is not wise and vice versa.
Everyone who is either not rich or not old is not quiet.
If mary is either not funny or rich then john is rich and vice versa.
Everyone who is either humble or generous is not humble or not generous.
Everyone who is calm or happy is both funny and wise.
Everyone who is either patient or not creative is both not creative and brave and vice versa.
Everyone who is curious is both calm and not kind and vice versa.
Everyone who is not generous is either strong or not strong and vice versa.
If someone is not old or generous then alice is not generous.
Everyone who is either not rich or humble is kind and vice versa.
Everyone who is not generous is not happy or tall and vice versa.
Everyone who is either not humble or not brave is kind or tall.
Someone is not kind.
Mary is humble or not quiet.
Someone is either not old or not tall.
Alice is both kind and not calm.
Someone is not creative or not old.
John is either not humble or creative. | Mary is happy. | entailment | ((?[X]:(~wise(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(humble(X)<=>(patient(X)|strong(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((tall(X)&~wise(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((tall(X)&curious(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~old(X))=>~quiet(X)))&
(((~funny(mary)<~>rich(mary)))<=>(rich(john)))&
(![X]:((humble(X)<~>generous(X))=>(~humble(X)|~generous(X))))&
(![X]:((calm(X)|happy(X))=>(funny(X)&wise(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~creative(X)&brave(X))))&
(![X]:(curious(X)<=>(calm(X)&~kind(X))))&
(![X]:(~generous(X)<=>(strong(X)<~>~strong(X))))&
((?[X]:((~old(X)|generous(X))))=>(~generous(alice)))&
(![X]:((~rich(X)<~>humble(X))<=>kind(X)))&
(![X]:(~generous(X)<=>(~happy(X)|tall(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(kind(X)|tall(X))))&
(?[X]:(~kind(X)))&
((humble(mary)|~quiet(mary)))&
(?[X]:((~old(X)<~>~tall(X))))&
((kind(alice)&~calm(alice)))&
(?[X]:((~creative(X)|~old(X))))&
((~humble(john)<~>creative(john))) | happy(mary) | [
"p0",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6031600602826953032565241
% SZS output start Proof for 6031600602826953032565241
1. ? [X0] : ~wise(X0) <=> ? [X0] : (~happy(X0) | ~funny(X0)) [input p0]
5. ! [X0] : ((curious(X0) & tall(X0)) <=> ~wise(X0)) [input p4]
9. ! [X0] : ((happy(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p8]
11. ! [X0] : (curious(X0) <=> (~kind(X0) & calm(X0))) [input p10]
23. ~happy(mary) [input hypothesis]
24. ? [X0] : ~wise(X0) <=> ? [X1] : (~happy(X1) | ~funny(X1)) [rectify 1]
30. ! [X0] : ((wise(X0) & funny(X0)) | (~happy(X0) & ~calm(X0))) [ennf transformation 9]
34. (? [X0] : ~wise(X0) | ! [X1] : (happy(X1) & funny(X1))) & (? [X1] : (~happy(X1) | ~funny(X1)) | ! [X0] : wise(X0)) [nnf transformation 24]
35. (? [X0] : ~wise(X0) | ! [X1] : (happy(X1) & funny(X1))) & (? [X2] : (~happy(X2) | ~funny(X2)) | ! [X3] : wise(X3)) [rectify 34]
36. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
37. ? [X2] : (~happy(X2) | ~funny(X2)) => (~happy(sK1) | ~funny(sK1)) [choice axiom]
38. (~wise(sK0) | ! [X1] : (happy(X1) & funny(X1))) & ((~happy(sK1) | ~funny(sK1)) | ! [X3] : wise(X3)) [skolemisation 35,37,36]
48. ! [X0] : (((curious(X0) & tall(X0)) | wise(X0)) & (~wise(X0) | (~curious(X0) | ~tall(X0)))) [nnf transformation 5]
49. ! [X0] : (((curious(X0) & tall(X0)) | wise(X0)) & (~wise(X0) | ~curious(X0) | ~tall(X0))) [flattening 48]
54. ! [X0] : ((curious(X0) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | ~curious(X0))) [nnf transformation 11]
55. ! [X0] : ((curious(X0) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | ~curious(X0))) [flattening 54]
71. ~wise(sK0) | happy(X1) [cnf transformation 38]
87. curious(X0) | wise(X0) [cnf transformation 49]
96. ~calm(X0) | wise(X0) [cnf transformation 30]
104. ~curious(X0) | calm(X0) [cnf transformation 55]
130. ~happy(mary) [cnf transformation 23]
140. 1 <=> ! [X1] : happy(X1) [avatar definition]
141. happy(X1) <- (1) [avatar component clause 140]
143. 2 <=> wise(sK0) [avatar definition]
145. ~wise(sK0) <- (~2) [avatar component clause 143]
146. 1 | ~2 [avatar split clause 71,143,140]
152. 4 <=> ! [X3] : wise(X3) [avatar definition]
153. wise(X3) <- (4) [avatar component clause 152]
242. calm(X0) | wise(X0) [resolution 104,87]
243. wise(X0) [subsumption resolution 242,96]
244. 4 [avatar split clause 243,152]
245. $false <- (~2, 4) [resolution 153,145]
246. 2 | ~4 [avatar contradiction clause 245]
247. $false <- (1) [resolution 141,130]
252. ~1 [avatar contradiction clause 247]
253. $false [avatar sat refutation 146,244,246,252]
% SZS output end Proof for 6031600602826953032565241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or strong then lucy is either not patient or not strong and vice versa.
Everyone who is either brave or old is either happy or old and vice versa.
If susan is both funny and patient then someone is not brave or not quiet and vice versa.
Everyone who is creative or wise is either not patient or strong.
Everyone who is creative is not creative or calm.
Everyone who is not curious or patient is not creative or not quiet and vice versa.
If someone is funny then someone is not strong.
If someone is not tall then someone is curious or not calm and vice versa.
If john is patient then mary is not creative and vice versa.
If someone is both rich and not brave then someone is both wise and humble.
Everyone who is not curious is generous or creative and vice versa.
If mary is either funny or not creative then someone is both happy and not generous.
Everyone who is both brave and humble is not rich or not generous and vice versa.
If someone is quiet or wise then someone is generous or strong.
Everyone who is either wise or happy is both not humble and not patient and vice versa.
Everyone who is either not kind or not happy is not curious.
Someone is both not rich and funny.
Fred is rich.
Someone is funny.
Someone is both not curious and not humble.
Someone is curious or not patient.
Someone is wise or humble. | Fred is funny. | neutral | ((?[X]:((humble(X)|strong(X))))<=>((~patient(lucy)<~>~strong(lucy))))&
(![X]:((brave(X)<~>old(X))<=>(happy(X)<~>old(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((creative(X)|wise(X))=>(~patient(X)<~>strong(X))))&
(![X]:(creative(X)=>(~creative(X)|calm(X))))&
(![X]:((~curious(X)|patient(X))<=>(~creative(X)|~quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~strong(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((curious(X)|~calm(X)))))&
((patient(john))<=>(~creative(mary)))&
((?[X]:((rich(X)&~brave(X))))=>(?[X]:((wise(X)&humble(X)))))&
(![X]:(~curious(X)<=>(generous(X)|creative(X))))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~kind(X)<~>~happy(X))=>~curious(X)))&
(?[X]:((~rich(X)&funny(X))))&
(rich(fred))&
(?[X]:(funny(X)))&
(?[X]:((~curious(X)&~humble(X))))&
(?[X]:((curious(X)|~patient(X))))&
(?[X]:((wise(X)|humble(X)))) | funny(fred) | [] | null | 0 |
Everyone who is not old is not rich and vice versa.
Everyone who is not funny is not generous and vice versa.
If someone is not rich then someone is wise or quiet and vice versa.
If someone is both kind and creative then paul is wise or old.
If alice is wise then someone is either old or not quiet and vice versa.
Everyone who is either not tall or strong is either not creative or not calm and vice versa.
If someone is both generous and curious then someone is not patient or not rich.
Everyone who is quiet or strong is not happy or not creative and vice versa.
Everyone who is either wise or not creative is not kind.
If fred is not wise or wise then someone is not quiet or rich.
If paul is either calm or not funny then john is either quiet or not happy and vice versa.
If lucy is not funny then someone is creative or funny.
If lucy is brave then lucy is both not wise and not brave and vice versa.
If paul is both not kind and not curious then john is not creative and vice versa.
If someone is both not old and patient then alice is either creative or generous and vice versa.
Everyone who is not quiet is both not humble and tall and vice versa.
Someone is both not brave and not strong.
Susan is both rich and not creative.
Lucy is not calm.
John is strong or kind.
Someone is not strong or not curious.
Someone is not funny or strong.
Someone is patient.
Someone is either not quiet or not patient. | Susan is old. | entailment | (![X]:(~old(X)<=>~rich(X)))&
(![X]:(~funny(X)<=>~generous(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((wise(X)|quiet(X)))))&
((?[X]:((kind(X)&creative(X))))=>((wise(paul)|old(paul))))&
((wise(alice))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:((generous(X)&curious(X))))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((quiet(X)|strong(X))<=>(~happy(X)|~creative(X))))&
(![X]:((wise(X)<~>~creative(X))=>~kind(X)))&
(((~wise(fred)|wise(fred)))=>(?[X]:((~quiet(X)|rich(X)))))&
(((calm(paul)<~>~funny(paul)))<=>((quiet(john)<~>~happy(john))))&
((~funny(lucy))=>(?[X]:((creative(X)|funny(X)))))&
((brave(lucy))<=>((~wise(lucy)&~brave(lucy))))&
(((~kind(paul)&~curious(paul)))<=>(~creative(john)))&
((?[X]:((~old(X)&patient(X))))<=>((creative(alice)<~>generous(alice))))&
(![X]:(~quiet(X)<=>(~humble(X)&tall(X))))&
(?[X]:((~brave(X)&~strong(X))))&
((rich(susan)&~creative(susan)))&
(~calm(lucy))&
((strong(john)|kind(john)))&
(?[X]:((~strong(X)|~curious(X))))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)<~>~patient(X)))) | old(susan) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6052390673390632449729795
% SZS output start Proof for 6052390673390632449729795
1. ! [X0] : (~old(X0) <=> ~rich(X0)) [input p0]
18. ~creative(susan) & rich(susan) [input p17]
25. ~old(susan) [input hypothesis]
34. ! [X0] : ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))) [nnf transformation 1]
78. ~rich(X0) | old(X0) [cnf transformation 34]
133. rich(susan) [cnf transformation 18]
142. ~old(susan) [cnf transformation 25]
354. old(susan) [resolution 78,133]
355. $false [subsumption resolution 354,142]
% SZS output end Proof for 6052390673390632449729795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not brave is not calm and vice versa.
If someone is either wise or not quiet then someone is either not brave or humble.
Everyone who is not tall is both not happy and creative.
Everyone who is kind or not happy is both not funny and funny.
If someone is not kind then susan is tall and vice versa.
Everyone who is either happy or kind is either not curious or not tall and vice versa.
If john is either patient or not creative then someone is not happy.
If alice is not calm then someone is either not brave or not humble.
If someone is not generous then someone is both quiet and not funny and vice versa.
If alice is quiet or brave then john is kind or not rich and vice versa.
Everyone who is both brave and wise is rich and vice versa.
Everyone who is strong or generous is both not old and funny and vice versa.
If someone is not quiet then fred is humble or not strong.
If someone is tall then lucy is creative or not wise.
Everyone who is both generous and not creative is either not brave or not kind.
Everyone who is calm or not wise is not creative and vice versa.
Someone is generous or calm.
Fred is either humble or quiet.
Someone is both not curious and creative.
Someone is not tall or not strong.
Someone is quiet.
Someone is not wise or not calm.
Someone is both patient and not quiet.
Lucy is both calm and not old. | Lucy is not rich. | entailment | (![X]:((~patient(X)&~brave(X))<=>~calm(X)))&
((?[X]:((wise(X)<~>~quiet(X))))=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:(~tall(X)=>(~happy(X)&creative(X))))&
(![X]:((kind(X)|~happy(X))=>(~funny(X)&funny(X))))&
((?[X]:(~kind(X)))<=>(tall(susan)))&
(![X]:((happy(X)<~>kind(X))<=>(~curious(X)<~>~tall(X))))&
(((patient(john)<~>~creative(john)))=>(?[X]:(~happy(X))))&
((~calm(alice))=>(?[X]:((~brave(X)<~>~humble(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((quiet(X)&~funny(X)))))&
(((quiet(alice)|brave(alice)))<=>((kind(john)|~rich(john))))&
(![X]:((brave(X)&wise(X))<=>rich(X)))&
(![X]:((strong(X)|generous(X))<=>(~old(X)&funny(X))))&
((?[X]:(~quiet(X)))=>((humble(fred)|~strong(fred))))&
((?[X]:(tall(X)))=>((creative(lucy)|~wise(lucy))))&
(![X]:((generous(X)&~creative(X))=>(~brave(X)<~>~kind(X))))&
(![X]:((calm(X)|~wise(X))<=>~creative(X)))&
(?[X]:((generous(X)|calm(X))))&
((humble(fred)<~>quiet(fred)))&
(?[X]:((~curious(X)&creative(X))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((patient(X)&~quiet(X))))&
((calm(lucy)&~old(lucy))) | ~rich(lucy) | [
"p2",
"p3",
"p10",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1584256301292651400531405
% SZS output start Proof for 1584256301292651400531405
3. ! [X0] : (~tall(X0) => (creative(X0) & ~happy(X0))) [input p2]
4. ! [X0] : ((~happy(X0) | kind(X0)) => (funny(X0) & ~funny(X0))) [input p3]
11. ! [X0] : ((wise(X0) & brave(X0)) <=> rich(X0)) [input p10]
14. ? [X0] : tall(X0) => (~wise(lucy) | creative(lucy)) [input p13]
16. ! [X0] : ((~wise(X0) | calm(X0)) <=> ~creative(X0)) [input p15]
24. ~old(lucy) & calm(lucy) [input p23]
25. rich(lucy) [input hypothesis]
29. ! [X0] : ((creative(X0) & ~happy(X0)) | tall(X0)) [ennf transformation 3]
30. ! [X0] : ((funny(X0) & ~funny(X0)) | (happy(X0) & ~kind(X0))) [ennf transformation 4]
35. (~wise(lucy) | creative(lucy)) | ! [X0] : ~tall(X0) [ennf transformation 14]
36. ~wise(lucy) | creative(lucy) | ! [X0] : ~tall(X0) [flattening 35]
63. ! [X0] : (((wise(X0) & brave(X0)) | ~rich(X0)) & (rich(X0) | (~wise(X0) | ~brave(X0)))) [nnf transformation 11]
64. ! [X0] : (((wise(X0) & brave(X0)) | ~rich(X0)) & (rich(X0) | ~wise(X0) | ~brave(X0))) [flattening 63]
68. ! [X0] : (((~wise(X0) | calm(X0)) | creative(X0)) & (~creative(X0) | (wise(X0) & ~calm(X0)))) [nnf transformation 16]
69. ! [X0] : ((~wise(X0) | calm(X0) | creative(X0)) & (~creative(X0) | (wise(X0) & ~calm(X0)))) [flattening 68]
90. ~happy(X0) | tall(X0) [cnf transformation 29]
93. ~funny(X0) | happy(X0) [cnf transformation 30]
95. funny(X0) | happy(X0) [cnf transformation 30]
119. ~rich(X0) | wise(X0) [cnf transformation 64]
126. ~wise(lucy) | creative(lucy) | ~tall(X0) [cnf transformation 36]
129. ~creative(X0) | ~calm(X0) [cnf transformation 69]
142. calm(lucy) [cnf transformation 24]
144. rich(lucy) [cnf transformation 25]
163. happy(X0) [subsumption resolution 93,95]
245. 21 <=> ! [X0] : ~tall(X0) [avatar definition]
246. ~tall(X0) <- (21) [avatar component clause 245]
248. 22 <=> creative(lucy) [avatar definition]
250. creative(lucy) <- (22) [avatar component clause 248]
252. 23 <=> wise(lucy) [avatar definition]
255. 21 | 22 | ~23 [avatar split clause 126,252,248,245]
293. tall(X0) [resolution 90,163]
296. wise(lucy) [resolution 119,144]
300. 23 [avatar split clause 296,252]
301. $false <- (21) [subsumption resolution 246,293]
302. ~21 [avatar contradiction clause 301]
309. ~calm(lucy) <- (22) [resolution 129,250]
313. $false <- (22) [subsumption resolution 309,142]
314. ~22 [avatar contradiction clause 313]
315. $false [avatar sat refutation 255,300,302,314]
% SZS output end Proof for 1584256301292651400531405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is calm then john is either rich or not old.
If susan is either wise or patient then someone is happy and vice versa.
Everyone who is not funny is not patient and vice versa.
Everyone who is not wise is either not generous or generous.
If someone is both quiet and not funny then someone is either not curious or not calm and vice versa.
If someone is brave or not funny then someone is both not kind and strong.
If mary is not creative or not humble then susan is not patient and vice versa.
If lucy is not old or patient then someone is both old and not strong and vice versa.
Everyone who is creative is patient or calm and vice versa.
Everyone who is either kind or not rich is not rich and vice versa.
If alice is patient then someone is either creative or patient and vice versa.
If someone is both not humble and curious then fred is tall or not patient and vice versa.
Everyone who is either calm or generous is kind or calm and vice versa.
Everyone who is not calm is both not strong and not calm.
Everyone who is both not funny and old is not patient or kind and vice versa.
If someone is both not creative and not brave then someone is not strong and vice versa.
Someone is both not humble and not calm.
Lucy is not humble.
Someone is either curious or not old.
Someone is either old or humble.
Someone is happy.
Someone is not kind or not tall.
Alice is either happy or calm. | Lucy is kind. | contradiction | ((calm(lucy))=>((rich(john)<~>~old(john))))&
(((wise(susan)<~>patient(susan)))<=>(?[X]:(happy(X))))&
(![X]:(~funny(X)<=>~patient(X)))&
(![X]:(~wise(X)=>(~generous(X)<~>generous(X))))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
((?[X]:((brave(X)|~funny(X))))=>(?[X]:((~kind(X)&strong(X)))))&
(((~creative(mary)|~humble(mary)))<=>(~patient(susan)))&
(((~old(lucy)|patient(lucy)))<=>(?[X]:((old(X)&~strong(X)))))&
(![X]:(creative(X)<=>(patient(X)|calm(X))))&
(![X]:((kind(X)<~>~rich(X))<=>~rich(X)))&
((patient(alice))<=>(?[X]:((creative(X)<~>patient(X)))))&
((?[X]:((~humble(X)&curious(X))))<=>((tall(fred)|~patient(fred))))&
(![X]:((calm(X)<~>generous(X))<=>(kind(X)|calm(X))))&
(![X]:(~calm(X)=>(~strong(X)&~calm(X))))&
(![X]:((~funny(X)&old(X))<=>(~patient(X)|kind(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:(~strong(X))))&
(?[X]:((~humble(X)&~calm(X))))&
(~humble(lucy))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((old(X)<~>humble(X))))&
(?[X]:(happy(X)))&
(?[X]:((~kind(X)|~tall(X))))&
((happy(alice)<~>calm(alice))) | kind(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 9214259519204273905353688
% SZS output start Proof for 9214259519204273905353688
10. ! [X0] : ((kind(X0) <~> ~rich(X0)) <=> ~rich(X0)) [input p9]
24. kind(lucy) [input hypothesis]
56. ! [X0] : ((((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | rich(X0)) & (~rich(X0) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0))))) [nnf transformation 10]
119. ~rich(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 56]
122. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 56]
159. kind(lucy) [cnf transformation 24]
162. ~rich(X0) | ~kind(X0) [duplicate literal removal 119]
163. rich(X0) | ~kind(X0) [duplicate literal removal 122]
281. ~kind(X0) [subsumption resolution 162,163]
379. $false [subsumption resolution 159,281]
% SZS output end Proof for 9214259519204273905353688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not strong or kind then lucy is strong.
Everyone who is both not rich and not calm is not kind or calm and vice versa.
Everyone who is curious is generous or not curious and vice versa.
If paul is both not kind and generous then someone is generous and vice versa.
If someone is strong or wise then someone is not kind or rich and vice versa.
Everyone who is either not quiet or not kind is either not humble or brave and vice versa.
If someone is patient then someone is not funny and vice versa.
Everyone who is both patient and not quiet is either patient or not humble.
If someone is either not kind or tall then someone is either calm or not creative.
If someone is both curious and wise then lucy is either not patient or generous.
Everyone who is not happy is either not old or strong and vice versa.
If paul is either brave or not tall then fred is both not humble and kind and vice versa.
Everyone who is not kind is not calm and vice versa.
Everyone who is either not happy or funny is not generous and vice versa.
If john is either not old or not happy then someone is both not wise and quiet.
If susan is kind or happy then susan is both not generous and funny.
Lucy is either creative or not old.
Someone is either not strong or rich.
Fred is not quiet or tall.
John is old.
Lucy is not quiet or not brave. | Fred is tall. | neutral | (((~strong(alice)<~>kind(alice)))=>(strong(lucy)))&
(![X]:((~rich(X)&~calm(X))<=>(~kind(X)|calm(X))))&
(![X]:(curious(X)<=>(generous(X)|~curious(X))))&
(((~kind(paul)&generous(paul)))<=>(?[X]:(generous(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~humble(X)<~>brave(X))))&
((?[X]:(patient(X)))<=>(?[X]:(~funny(X))))&
(![X]:((patient(X)&~quiet(X))=>(patient(X)<~>~humble(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:((calm(X)<~>~creative(X)))))&
((?[X]:((curious(X)&wise(X))))=>((~patient(lucy)<~>generous(lucy))))&
(![X]:(~happy(X)<=>(~old(X)<~>strong(X))))&
(((brave(paul)<~>~tall(paul)))<=>((~humble(fred)&kind(fred))))&
(![X]:(~kind(X)<=>~calm(X)))&
(![X]:((~happy(X)<~>funny(X))<=>~generous(X)))&
(((~old(john)<~>~happy(john)))=>(?[X]:((~wise(X)&quiet(X)))))&
(((kind(susan)|happy(susan)))=>((~generous(susan)&funny(susan))))&
((creative(lucy)<~>~old(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
((~quiet(fred)|tall(fred)))&
(old(john))&
((~quiet(lucy)|~brave(lucy))) | tall(fred) | [] | null | 0 |
Everyone who is funny or not patient is either not old or brave and vice versa.
Everyone who is kind is curious and vice versa.
Everyone who is both not tall and curious is calm and vice versa.
Everyone who is funny is not kind or not calm.
If paul is either patient or not curious then someone is creative or strong.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If mary is not curious then mary is not quiet and vice versa.
If someone is not brave then someone is both happy and rich.
Everyone who is both not humble and not funny is humble.
Someone is both not funny and not creative.
Someone is rich or happy.
Alice is either not patient or not kind.
Someone is both not patient and not strong.
Someone is tall or not generous.
Someone is tall or not old. | Alice is not happy. | neutral | (![X]:((funny(X)|~patient(X))<=>(~old(X)<~>brave(X))))&
(![X]:(kind(X)<=>curious(X)))&
(![X]:((~tall(X)&curious(X))<=>calm(X)))&
(![X]:(funny(X)=>(~kind(X)|~calm(X))))&
(((patient(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|strong(X)))))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((~curious(mary))<=>(~quiet(mary)))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:((~humble(X)&~funny(X))=>humble(X)))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((rich(X)|happy(X))))&
((~patient(alice)<~>~kind(alice)))&
(?[X]:((~patient(X)&~strong(X))))&
(?[X]:((tall(X)|~generous(X))))&
(?[X]:((tall(X)|~old(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is happy is wise or not strong and vice versa.
Everyone who is not patient is either calm or strong.
Everyone who is either not rich or not funny is both funny and not generous.
If someone is old then john is both not funny and not quiet.
If someone is rich or not curious then someone is both quiet and not curious.
If someone is patient or not creative then fred is both not wise and not brave.
Everyone who is both patient and humble is not funny or not calm.
If susan is either not humble or funny then someone is both creative and not brave.
If someone is not tall then paul is funny.
Everyone who is both not rich and not humble is either humble or old.
Everyone who is both not curious and kind is either not brave or not funny and vice versa.
If someone is both strong and not funny then mary is both not curious and tall and vice versa.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
If fred is both not old and calm then susan is either not happy or not humble and vice versa.
If someone is either strong or funny then someone is either patient or rich and vice versa.
Someone is not rich or not creative.
Someone is either wise or funny.
Lucy is both not kind and not rich.
Alice is both not patient and tall.
Mary is not calm or not humble.
John is not patient or not generous.
Mary is not quiet or happy. | Mary is happy. | neutral | (![X]:(happy(X)<=>(wise(X)|~strong(X))))&
(![X]:(~patient(X)=>(calm(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(funny(X)&~generous(X))))&
((?[X]:(old(X)))=>((~funny(john)&~quiet(john))))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((quiet(X)&~curious(X)))))&
((?[X]:((patient(X)|~creative(X))))=>((~wise(fred)&~brave(fred))))&
(![X]:((patient(X)&humble(X))=>(~funny(X)|~calm(X))))&
(((~humble(susan)<~>funny(susan)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:(~tall(X)))=>(funny(paul)))&
(![X]:((~rich(X)&~humble(X))=>(humble(X)<~>old(X))))&
(![X]:((~curious(X)&kind(X))<=>(~brave(X)<~>~funny(X))))&
((?[X]:((strong(X)&~funny(X))))<=>((~curious(mary)&tall(mary))))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
(((~old(fred)&calm(fred)))<=>((~happy(susan)<~>~humble(susan))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~kind(lucy)&~rich(lucy)))&
((~patient(alice)&tall(alice)))&
((~calm(mary)|~humble(mary)))&
((~patient(john)|~generous(john)))&
((~quiet(mary)|happy(mary))) | happy(mary) | [] | null | 0 |
Everyone who is both not rich and not happy is either not quiet or patient and vice versa.
Everyone who is both brave and tall is humble or brave and vice versa.
If alice is not happy then someone is not generous or not old and vice versa.
If alice is both kind and not humble then fred is not wise and vice versa.
If someone is either curious or brave then someone is either not creative or tall and vice versa.
Everyone who is quiet or not calm is either not tall or old and vice versa.
Everyone who is both brave and not wise is both wise and not old.
Everyone who is both not patient and not kind is both not brave and not strong and vice versa.
Everyone who is not curious or creative is both tall and not wise.
If someone is both not brave and quiet then paul is either not rich or calm and vice versa.
If paul is not curious then susan is either strong or not calm and vice versa.
Everyone who is curious is not patient.
Everyone who is not humble is strong or quiet and vice versa.
If someone is not quiet then susan is both not calm and not quiet and vice versa.
Everyone who is both strong and funny is not rich or patient.
Everyone who is both strong and not wise is both happy and quiet and vice versa.
Lucy is kind.
Susan is not generous.
Someone is wise or strong.
Someone is calm.
Someone is either humble or calm.
Someone is either funny or tall.
Susan is either not brave or wise. | Susan is wise. | neutral | (![X]:((~rich(X)&~happy(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))<=>(humble(X)|brave(X))))&
((~happy(alice))<=>(?[X]:((~generous(X)|~old(X)))))&
(((kind(alice)&~humble(alice)))<=>(~wise(fred)))&
((?[X]:((curious(X)<~>brave(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:((quiet(X)|~calm(X))<=>(~tall(X)<~>old(X))))&
(![X]:((brave(X)&~wise(X))=>(wise(X)&~old(X))))&
(![X]:((~patient(X)&~kind(X))<=>(~brave(X)&~strong(X))))&
(![X]:((~curious(X)|creative(X))=>(tall(X)&~wise(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>((~rich(paul)<~>calm(paul))))&
((~curious(paul))<=>((strong(susan)<~>~calm(susan))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:(~humble(X)<=>(strong(X)|quiet(X))))&
((?[X]:(~quiet(X)))<=>((~calm(susan)&~quiet(susan))))&
(![X]:((strong(X)&funny(X))=>(~rich(X)|patient(X))))&
(![X]:((strong(X)&~wise(X))<=>(happy(X)&quiet(X))))&
(kind(lucy))&
(~generous(susan))&
(?[X]:((wise(X)|strong(X))))&
(?[X]:(calm(X)))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:((funny(X)<~>tall(X))))&
((~brave(susan)<~>wise(susan))) | wise(susan) | [] | null | 0 |
If alice is either not old or curious then someone is either not curious or wise and vice versa.
Everyone who is patient is both not happy and not quiet.
Everyone who is not humble or tall is either not patient or not kind.
Everyone who is not old or not brave is not tall or not happy and vice versa.
If someone is creative or patient then someone is both not humble and creative.
Everyone who is both not quiet and not old is quiet.
Everyone who is creative or old is not generous or not curious and vice versa.
Everyone who is rich or not strong is both not rich and creative.
Everyone who is humble or not patient is not quiet and vice versa.
If someone is both patient and not strong then alice is either wise or generous and vice versa.
If alice is either curious or not strong then paul is either not happy or not generous.
Everyone who is either not wise or not rich is rich and vice versa.
If susan is not patient or not tall then someone is both not calm and not old and vice versa.
If someone is not generous then mary is both not brave and not funny and vice versa.
If john is curious or not quiet then john is both not curious and not strong.
If someone is both not tall and not curious then mary is either not strong or not calm and vice versa.
Lucy is tall or not quiet.
Someone is either curious or strong.
Lucy is not brave.
Someone is tall.
Someone is happy or not kind.
Someone is either funny or tall.
Someone is either calm or not quiet. | Lucy is not creative. | neutral | (((~old(alice)<~>curious(alice)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:(patient(X)=>(~happy(X)&~quiet(X))))&
(![X]:((~humble(X)|tall(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~old(X)|~brave(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((creative(X)|patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~quiet(X)&~old(X))=>quiet(X)))&
(![X]:((creative(X)|old(X))<=>(~generous(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))=>(~rich(X)&creative(X))))&
(![X]:((humble(X)|~patient(X))<=>~quiet(X)))&
((?[X]:((patient(X)&~strong(X))))<=>((wise(alice)<~>generous(alice))))&
(((curious(alice)<~>~strong(alice)))=>((~happy(paul)<~>~generous(paul))))&
(![X]:((~wise(X)<~>~rich(X))<=>rich(X)))&
(((~patient(susan)|~tall(susan)))<=>(?[X]:((~calm(X)&~old(X)))))&
((?[X]:(~generous(X)))<=>((~brave(mary)&~funny(mary))))&
(((curious(john)|~quiet(john)))=>((~curious(john)&~strong(john))))&
((?[X]:((~tall(X)&~curious(X))))<=>((~strong(mary)<~>~calm(mary))))&
((tall(lucy)|~quiet(lucy)))&
(?[X]:((curious(X)<~>strong(X))))&
(~brave(lucy))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(?[X]:((calm(X)<~>~quiet(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is not happy or kind is wise or rich and vice versa.
Everyone who is not happy is creative or not funny and vice versa.
Everyone who is happy or not generous is tall and vice versa.
If someone is both not old and not wise then fred is happy.
Everyone who is either not generous or not happy is either humble or not brave.
If someone is calm then someone is both not happy and not brave and vice versa.
Everyone who is wise is either not tall or curious and vice versa.
If alice is not patient or generous then fred is not rich.
Everyone who is happy or not tall is not quiet and vice versa.
If lucy is both not humble and kind then susan is both not curious and happy and vice versa.
If john is either not quiet or not humble then someone is strong.
Everyone who is either happy or creative is tall and vice versa.
Everyone who is funny or not rich is either old or not calm and vice versa.
If someone is both not happy and not humble then someone is not tall or not old.
Everyone who is not patient is not tall or not creative and vice versa.
Everyone who is strong is either not rich or not strong and vice versa.
Someone is both not tall and generous.
John is either old or not humble.
Mary is not quiet or not wise.
Alice is not wise or not humble.
Someone is either not wise or strong.
Alice is not patient or patient.
Someone is not strong.
Mary is both humble and happy. | Fred is happy. | neutral | (![X]:((~happy(X)|kind(X))<=>(wise(X)|rich(X))))&
(![X]:(~happy(X)<=>(creative(X)|~funny(X))))&
(![X]:((happy(X)|~generous(X))<=>tall(X)))&
((?[X]:((~old(X)&~wise(X))))=>(happy(fred)))&
(![X]:((~generous(X)<~>~happy(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)<=>(~tall(X)<~>curious(X))))&
(((~patient(alice)|generous(alice)))=>(~rich(fred)))&
(![X]:((happy(X)|~tall(X))<=>~quiet(X)))&
(((~humble(lucy)&kind(lucy)))<=>((~curious(susan)&happy(susan))))&
(((~quiet(john)<~>~humble(john)))=>(?[X]:(strong(X))))&
(![X]:((happy(X)<~>creative(X))<=>tall(X)))&
(![X]:((funny(X)|~rich(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(~patient(X)<=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>~strong(X))))&
(?[X]:((~tall(X)&generous(X))))&
((old(john)<~>~humble(john)))&
((~quiet(mary)|~wise(mary)))&
((~wise(alice)|~humble(alice)))&
(?[X]:((~wise(X)<~>strong(X))))&
((~patient(alice)|patient(alice)))&
(?[X]:(~strong(X)))&
((humble(mary)&happy(mary))) | happy(fred) | [] | null | 0 |
Everyone who is tall is not patient. Everyone who is brave is both tall and not funny and vice versa. If someone is not strong or not generous then someone is either not funny or not old and vice versa. Everyone who is not wise or happy is not rich and vice versa. Everyone who is both humble and brave is not tall. Everyone who is not curious is both generous and not kind and vice versa. Everyone who is not brave is both quiet and humble. Everyone who is both not quiet and quiet is not humble or kind and vice versa. If someone is not quiet or funny then someone is not creative or old and vice versa. If susan is both humble and calm then someone is not curious or not strong. Everyone who is either creative or quiet is both not patient and not generous. Everyone who is either rich or not humble is old and vice versa. Everyone who is either not happy or patient is both funny and not creative and vice versa. Everyone who is either old or creative is either not calm or not tall. Everyone who is rich is tall or old and vice versa. If someone is tall or not rich then someone is either quiet or creative and vice versa. Someone is not tall or not generous. Someone is either strong or not quiet. Lucy is not patient. John is not generous or generous. Mary is tall or not strong. Lucy is not calm or not humble. Someone is generous or patient. Alice is both generous and not rich. | Alice is not creative. | contradiction | (![X]:(tall(X)=>~patient(X)))&
(![X]:(brave(X)<=>(tall(X)&~funny(X))))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((~wise(X)|happy(X))<=>~rich(X)))&
(![X]:((humble(X)&brave(X))=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(?[X]:((~tall(X)|~generous(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
(~patient(lucy))&
((~generous(john)|generous(john)))&
((tall(mary)|~strong(mary)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice))) | ~creative(alice) | [
"p1",
"p4",
"p6",
"p7",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 881133487807830381988191
% SZS output start Proof for 881133487807830381988191
2. ! [X0] : (brave(X0) <=> (~funny(X0) & tall(X0))) [input p1]
5. ! [X0] : ((brave(X0) & humble(X0)) => ~tall(X0)) [input p4]
7. ! [X0] : (~brave(X0) => (humble(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (kind(X0) | ~humble(X0))) [input p7]
11. ! [X0] : ((creative(X0) <~> quiet(X0)) => (~generous(X0) & ~patient(X0))) [input p10]
24. ~rich(alice) & generous(alice) [input p23]
25. ~creative(alice) [input hypothesis]
31. ! [X0] : (~tall(X0) | (~brave(X0) | ~humble(X0))) [ennf transformation 5]
32. ! [X0] : (~tall(X0) | ~brave(X0) | ~humble(X0)) [flattening 31]
34. ! [X0] : ((humble(X0) & quiet(X0)) | brave(X0)) [ennf transformation 7]
37. ! [X0] : ((~generous(X0) & ~patient(X0)) | (creative(X0) <=> quiet(X0))) [ennf transformation 11]
39. ! [X0] : ((brave(X0) | (funny(X0) | ~tall(X0))) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [nnf transformation 2]
40. ! [X0] : ((brave(X0) | funny(X0) | ~tall(X0)) & ((~funny(X0) & tall(X0)) | ~brave(X0))) [flattening 39]
48. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 8]
49. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~quiet(X0) | quiet(X0))) [flattening 48]
57. ! [X0] : ((~generous(X0) & ~patient(X0)) | ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0)))) [nnf transformation 37]
77. ~brave(X0) | tall(X0) [cnf transformation 40]
89. ~tall(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 32]
92. quiet(X0) | brave(X0) [cnf transformation 34]
95. ~quiet(X0) | humble(X0) [cnf transformation 49]
97. quiet(X0) | humble(X0) [cnf transformation 49]
107. ~quiet(X0) | creative(X0) | ~generous(X0) [cnf transformation 57]
139. generous(alice) [cnf transformation 24]
141. ~creative(alice) [cnf transformation 25]
176. ~humble(X0) | ~brave(X0) [subsumption resolution 89,77]
178. humble(X0) [subsumption resolution 95,97]
311. ~brave(X1) [resolution 176,178]
324. creative(X1) | ~generous(X1) | brave(X1) [resolution 107,92]
328. ~generous(X1) | creative(X1) [subsumption resolution 324,311]
329. creative(alice) [resolution 328,139]
331. $false [subsumption resolution 329,141]
% SZS output end Proof for 881133487807830381988191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or brave is both not creative and strong and vice versa.
Everyone who is not curious is either not kind or not humble.
If john is generous then mary is funny.
Everyone who is both not generous and wise is either strong or not wise.
Everyone who is both not old and brave is not brave and vice versa.
If alice is not kind or humble then john is either not kind or kind and vice versa.
If someone is either not wise or patient then someone is both brave and not old and vice versa.
If fred is either happy or not wise then someone is both not curious and not humble.
Everyone who is old is either not strong or not happy and vice versa.
If someone is either not curious or not calm then someone is both funny and generous and vice versa.
Everyone who is both not tall and wise is kind or not brave.
Everyone who is quiet is both not kind and wise.
If fred is either not strong or not rich then someone is not rich and vice versa.
Everyone who is not happy or not patient is either not tall or not brave and vice versa.
If someone is either generous or creative then someone is both not old and not tall.
Someone is not creative or generous.
Mary is not creative.
Someone is both brave and not funny.
Lucy is not calm or not creative.
Mary is either not kind or not happy.
Someone is both not creative and not funny.
Someone is not funny or not quiet. | Lucy is not quiet. | entailment | (![X]:((~creative(X)<~>brave(X))<=>(~creative(X)&strong(X))))&
(![X]:(~curious(X)=>(~kind(X)<~>~humble(X))))&
((generous(john))=>(funny(mary)))&
(![X]:((~generous(X)&wise(X))=>(strong(X)<~>~wise(X))))&
(![X]:((~old(X)&brave(X))<=>~brave(X)))&
(((~kind(alice)|humble(alice)))<=>((~kind(john)<~>kind(john))))&
((?[X]:((~wise(X)<~>patient(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(((happy(fred)<~>~wise(fred)))=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:(old(X)<=>(~strong(X)<~>~happy(X))))&
((?[X]:((~curious(X)<~>~calm(X))))<=>(?[X]:((funny(X)&generous(X)))))&
(![X]:((~tall(X)&wise(X))=>(kind(X)|~brave(X))))&
(![X]:(quiet(X)=>(~kind(X)&wise(X))))&
(((~strong(fred)<~>~rich(fred)))<=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|~patient(X))<=>(~tall(X)<~>~brave(X))))&
((?[X]:((generous(X)<~>creative(X))))=>(?[X]:((~old(X)&~tall(X)))))&
(?[X]:((~creative(X)|generous(X))))&
(~creative(mary))&
(?[X]:((brave(X)&~funny(X))))&
((~calm(lucy)|~creative(lucy)))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((~funny(X)|~quiet(X)))) | ~quiet(lucy) | [
"p0",
"p3",
"p4",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8312559262946973293838699
% SZS output start Proof for 8312559262946973293838699
1. ! [X0] : ((~creative(X0) <~> brave(X0)) <=> (strong(X0) & ~creative(X0))) [input p0]
4. ! [X0] : ((wise(X0) & ~generous(X0)) => (strong(X0) <~> ~wise(X0))) [input p3]
5. ! [X0] : ((brave(X0) & ~old(X0)) <=> ~brave(X0)) [input p4]
12. ! [X0] : (quiet(X0) => (wise(X0) & ~kind(X0))) [input p11]
15. ? [X0] : (generous(X0) <~> creative(X0)) => ? [X0] : (~tall(X0) & ~old(X0)) [input p14]
23. quiet(lucy) [input hypothesis]
26. ? [X0] : (generous(X0) <~> creative(X0)) => ? [X1] : (~tall(X1) & ~old(X1)) [rectify 15]
29. ! [X0] : ((strong(X0) <~> ~wise(X0)) | (~wise(X0) | generous(X0))) [ennf transformation 4]
30. ! [X0] : ((strong(X0) <~> ~wise(X0)) | ~wise(X0) | generous(X0)) [flattening 29]
34. ! [X0] : ((wise(X0) & ~kind(X0)) | ~quiet(X0)) [ennf transformation 12]
35. ? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) <=> creative(X0)) [ennf transformation 26]
36. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~strong(X0) | creative(X0))) & ((strong(X0) & ~creative(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ~strong(X0) | creative(X0)) & ((strong(X0) & ~creative(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0))))) [flattening 36]
39. ! [X0] : (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ~wise(X0) | generous(X0)) [nnf transformation 30]
40. ! [X0] : (((brave(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) | old(X0)))) [nnf transformation 5]
41. ! [X0] : (((brave(X0) & ~old(X0)) | brave(X0)) & (~brave(X0) | ~brave(X0) | old(X0))) [flattening 40]
64. ? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0))) [nnf transformation 35]
65. ? [X0] : (~tall(X0) & ~old(X0)) | ! [X1] : ((generous(X1) | ~creative(X1)) & (creative(X1) | ~generous(X1))) [rectify 64]
66. ? [X0] : (~tall(X0) & ~old(X0)) => (~tall(sK6) & ~old(sK6)) [choice axiom]
67. (~tall(sK6) & ~old(sK6)) | ! [X1] : ((generous(X1) | ~creative(X1)) & (creative(X1) | ~generous(X1))) [skolemisation 65,66]
78. ~creative(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 37]
82. ~brave(X0) | creative(X0) | ~strong(X0) | creative(X0) [cnf transformation 37]
86. ~wise(X0) | strong(X0) | ~wise(X0) | generous(X0) [cnf transformation 39]
88. ~brave(X0) | ~brave(X0) | old(X0) [cnf transformation 41]
90. brave(X0) | brave(X0) [cnf transformation 41]
119. ~quiet(X0) | wise(X0) [cnf transformation 34]
130. ~old(sK6) | creative(X1) | ~generous(X1) [cnf transformation 67]
144. quiet(lucy) [cnf transformation 23]
147. ~brave(X0) | old(X0) [duplicate literal removal 88]
148. brave(X0) [duplicate literal removal 90]
149. ~wise(X0) | strong(X0) | generous(X0) [duplicate literal removal 86]
150. ~brave(X0) | ~creative(X0) [duplicate literal removal 78]
151. ~strong(X0) | creative(X0) | ~brave(X0) [duplicate literal removal 82]
161. old(X0) [subsumption resolution 147,148]
263. 23 <=> ! [X1] : (creative(X1) | ~generous(X1)) [avatar definition]
264. ~generous(X1) | creative(X1) <- (23) [avatar component clause 263]
268. creative(X1) | ~generous(X1) [subsumption resolution 130,161]
269. 23 [avatar split clause 268,263]
310. wise(lucy) [resolution 119,144]
311. ~creative(X0) [resolution 150,148]
320. strong(lucy) | generous(lucy) [resolution 149,310]
322. 32 <=> generous(lucy) [avatar definition]
324. generous(lucy) <- (32) [avatar component clause 322]
326. 33 <=> strong(lucy) [avatar definition]
328. strong(lucy) <- (33) [avatar component clause 326]
329. 32 | 33 [avatar split clause 320,326,322]
345. creative(lucy) <- (23, 32) [resolution 324,264]
346. $false <- (23, 32) [subsumption resolution 345,311]
347. ~23 | ~32 [avatar contradiction clause 346]
361. creative(lucy) | ~brave(lucy) <- (33) [resolution 328,151]
362. ~brave(lucy) <- (33) [subsumption resolution 361,311]
363. $false <- (33) [subsumption resolution 362,148]
364. ~33 [avatar contradiction clause 363]
365. $false [avatar sat refutation 269,329,347,364]
% SZS output end Proof for 8312559262946973293838699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not generous then someone is either strong or old.
Everyone who is kind is either old or not brave and vice versa.
Everyone who is either funny or wise is either not kind or not strong.
Everyone who is kind is rich or not tall.
If mary is not kind then someone is not creative and vice versa.
Everyone who is not generous is creative or kind.
Everyone who is not creative or not quiet is brave and vice versa.
Everyone who is either not patient or not curious is either not patient or rich and vice versa.
Everyone who is either not quiet or not patient is curious and vice versa.
If lucy is either not curious or not rich then alice is wise or not rich and vice versa.
If someone is not patient or calm then susan is both creative and quiet.
Everyone who is not old or not kind is both kind and happy and vice versa.
Everyone who is generous or not calm is strong or not kind and vice versa.
If someone is both not rich and humble then lucy is not rich and vice versa.
Everyone who is either not brave or wise is rich.
Everyone who is either not kind or curious is both not old and not quiet and vice versa.
Someone is kind.
Someone is both brave and humble.
John is either wise or not tall.
Someone is strong or not quiet.
Someone is either not brave or humble.
Lucy is brave.
Someone is both not tall and kind. | Lucy is quiet. | contradiction | ((?[X]:((~funny(X)|~generous(X))))=>(?[X]:((strong(X)<~>old(X)))))&
(![X]:(kind(X)<=>(old(X)<~>~brave(X))))&
(![X]:((funny(X)<~>wise(X))=>(~kind(X)<~>~strong(X))))&
(![X]:(kind(X)=>(rich(X)|~tall(X))))&
((~kind(mary))<=>(?[X]:(~creative(X))))&
(![X]:(~generous(X)=>(creative(X)|kind(X))))&
(![X]:((~creative(X)|~quiet(X))<=>brave(X)))&
(![X]:((~patient(X)<~>~curious(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((~quiet(X)<~>~patient(X))<=>curious(X)))&
(((~curious(lucy)<~>~rich(lucy)))<=>((wise(alice)|~rich(alice))))&
((?[X]:((~patient(X)|calm(X))))=>((creative(susan)&quiet(susan))))&
(![X]:((~old(X)|~kind(X))<=>(kind(X)&happy(X))))&
(![X]:((generous(X)|~calm(X))<=>(strong(X)|~kind(X))))&
((?[X]:((~rich(X)&humble(X))))<=>(~rich(lucy)))&
(![X]:((~brave(X)<~>wise(X))=>rich(X)))&
(![X]:((~kind(X)<~>curious(X))<=>(~old(X)&~quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)&humble(X))))&
((wise(john)<~>~tall(john)))&
(?[X]:((strong(X)|~quiet(X))))&
(?[X]:((~brave(X)<~>humble(X))))&
(brave(lucy))&
(?[X]:((~tall(X)&kind(X)))) | quiet(lucy) | [
"p4",
"p6",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 279668664029147176130670
% SZS output start Proof for 279668664029147176130670
5. ~kind(mary) <=> ? [X0] : ~creative(X0) [input p4]
7. ! [X0] : ((~quiet(X0) | ~creative(X0)) <=> brave(X0)) [input p6]
12. ! [X0] : ((~kind(X0) | ~old(X0)) <=> (happy(X0) & kind(X0))) [input p11]
22. brave(lucy) [input p21]
24. quiet(lucy) [input hypothesis]
40. (~kind(mary) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | kind(mary)) [nnf transformation 5]
41. (~kind(mary) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | kind(mary)) [rectify 40]
42. ? [X1] : ~creative(X1) => ~creative(sK1) [choice axiom]
43. (~kind(mary) | ! [X0] : creative(X0)) & (~creative(sK1) | kind(mary)) [skolemisation 41,42]
44. ! [X0] : (((~quiet(X0) | ~creative(X0)) | ~brave(X0)) & (brave(X0) | (quiet(X0) & creative(X0)))) [nnf transformation 7]
45. ! [X0] : ((~quiet(X0) | ~creative(X0) | ~brave(X0)) & (brave(X0) | (quiet(X0) & creative(X0)))) [flattening 44]
50. ! [X0] : (((~kind(X0) | ~old(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (kind(X0) & old(X0)))) [nnf transformation 12]
51. ! [X0] : ((~kind(X0) | ~old(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (kind(X0) & old(X0)))) [flattening 50]
87. ~kind(mary) | creative(X0) [cnf transformation 43]
91. ~quiet(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 45]
115. kind(X0) | kind(X0) [cnf transformation 51]
142. brave(lucy) [cnf transformation 22]
145. quiet(lucy) [cnf transformation 24]
146. kind(X0) [duplicate literal removal 115]
171. 5 <=> ! [X0] : creative(X0) [avatar definition]
172. creative(X0) <- (5) [avatar component clause 171]
174. 6 <=> kind(mary) [avatar definition]
176. ~kind(mary) <- (~6) [avatar component clause 174]
177. 5 | ~6 [avatar split clause 87,174,171]
271. $false <- (~6) [subsumption resolution 176,146]
272. 6 [avatar contradiction clause 271]
307. ~creative(lucy) | ~brave(lucy) [resolution 91,145]
309. ~brave(lucy) <- (5) [subsumption resolution 307,172]
310. $false <- (5) [subsumption resolution 309,142]
311. ~5 [avatar contradiction clause 310]
312. $false [avatar sat refutation 177,272,311]
% SZS output end Proof for 279668664029147176130670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and funny is quiet and vice versa.
Everyone who is rich or not happy is funny.
If someone is kind then someone is humble and vice versa.
If susan is tall or not curious then someone is not kind or old.
Everyone who is both not wise and happy is both kind and not funny.
If paul is both not calm and not quiet then someone is both old and not creative and vice versa.
If alice is both not funny and not calm then someone is either not quiet or not brave.
Everyone who is generous or patient is not happy and vice versa.
Everyone who is tall is humble.
Everyone who is either rich or not patient is either not wise or not rich.
Everyone who is either kind or not wise is both not wise and happy and vice versa.
Everyone who is not generous is not tall and vice versa.
Everyone who is funny or not strong is strong or not happy and vice versa.
Everyone who is calm is not generous and vice versa.
If someone is both not tall and funny then someone is both tall and brave.
If someone is either not happy or creative then fred is either not generous or not curious and vice versa.
Mary is either not creative or not calm.
Someone is either not tall or wise.
Alice is not quiet or not old.
Someone is quiet.
Someone is not kind.
Someone is curious.
Mary is calm or strong. | Alice is not rich. | neutral | (![X]:((kind(X)&funny(X))<=>quiet(X)))&
(![X]:((rich(X)|~happy(X))=>funny(X)))&
((?[X]:(kind(X)))<=>(?[X]:(humble(X))))&
(((tall(susan)|~curious(susan)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~wise(X)&happy(X))=>(kind(X)&~funny(X))))&
(((~calm(paul)&~quiet(paul)))<=>(?[X]:((old(X)&~creative(X)))))&
(((~funny(alice)&~calm(alice)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((generous(X)|patient(X))<=>~happy(X)))&
(![X]:(tall(X)=>humble(X)))&
(![X]:((rich(X)<~>~patient(X))=>(~wise(X)<~>~rich(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~wise(X)&happy(X))))&
(![X]:(~generous(X)<=>~tall(X)))&
(![X]:((funny(X)|~strong(X))<=>(strong(X)|~happy(X))))&
(![X]:(calm(X)<=>~generous(X)))&
((?[X]:((~tall(X)&funny(X))))=>(?[X]:((tall(X)&brave(X)))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~generous(fred)<~>~curious(fred))))&
((~creative(mary)<~>~calm(mary)))&
(?[X]:((~tall(X)<~>wise(X))))&
((~quiet(alice)|~old(alice)))&
(?[X]:(quiet(X)))&
(?[X]:(~kind(X)))&
(?[X]:(curious(X)))&
((calm(mary)|strong(mary))) | ~rich(alice) | [] | null | 0 |
Everyone who is generous or not calm is not curious.
Everyone who is both not strong and not generous is both humble and patient.
Everyone who is both not strong and not old is either not strong or not old.
Everyone who is quiet or curious is either not kind or old.
Everyone who is not brave is funny or brave.
Everyone who is not patient or patient is not rich.
Everyone who is humble is either kind or not humble and vice versa.
Everyone who is not humble or not tall is both not tall and not creative.
If fred is not patient or tall then someone is both not curious and generous and vice versa.
Everyone who is not old or not calm is curious.
Everyone who is either quiet or humble is rich.
Everyone who is not tall or kind is creative or curious and vice versa.
Everyone who is funny or not generous is not kind or wise and vice versa.
Everyone who is not patient or not curious is either creative or strong and vice versa.
Everyone who is happy or old is either not calm or tall and vice versa.
Everyone who is both not patient and quiet is not kind or rich.
Someone is either not brave or kind.
Lucy is either wise or not brave.
Someone is both tall and wise.
Someone is either tall or not funny.
Someone is curious.
Lucy is both humble and patient. | Lucy is old. | entailment | (![X]:((generous(X)|~calm(X))=>~curious(X)))&
(![X]:((~strong(X)&~generous(X))=>(humble(X)&patient(X))))&
(![X]:((~strong(X)&~old(X))=>(~strong(X)<~>~old(X))))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)<~>old(X))))&
(![X]:(~brave(X)=>(funny(X)|brave(X))))&
(![X]:((~patient(X)|patient(X))=>~rich(X)))&
(![X]:(humble(X)<=>(kind(X)<~>~humble(X))))&
(![X]:((~humble(X)|~tall(X))=>(~tall(X)&~creative(X))))&
(((~patient(fred)|tall(fred)))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:((~old(X)|~calm(X))=>curious(X)))&
(![X]:((quiet(X)<~>humble(X))=>rich(X)))&
(![X]:((~tall(X)|kind(X))<=>(creative(X)|curious(X))))&
(![X]:((funny(X)|~generous(X))<=>(~kind(X)|wise(X))))&
(![X]:((~patient(X)|~curious(X))<=>(creative(X)<~>strong(X))))&
(![X]:((happy(X)|old(X))<=>(~calm(X)<~>tall(X))))&
(![X]:((~patient(X)&quiet(X))=>(~kind(X)|rich(X))))&
(?[X]:((~brave(X)<~>kind(X))))&
((wise(lucy)<~>~brave(lucy)))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:(curious(X)))&
((humble(lucy)&patient(lucy))) | old(lucy) | [
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1704704993659835702223405
% SZS output start Proof for 1704704993659835702223405
4. ! [X0] : ((curious(X0) | quiet(X0)) => (~kind(X0) <~> old(X0))) [input p3]
7. ! [X0] : (humble(X0) <=> (kind(X0) <~> ~humble(X0))) [input p6]
10. ! [X0] : ((~calm(X0) | ~old(X0)) => curious(X0)) [input p9]
23. ~old(lucy) [input hypothesis]
29. ! [X0] : ((~kind(X0) <~> old(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 4]
34. ! [X0] : (curious(X0) | (calm(X0) & old(X0))) [ennf transformation 10]
39. ! [X0] : (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (~curious(X0) & ~quiet(X0))) [nnf transformation 29]
40. ! [X0] : ((humble(X0) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | ~humble(X0))) [nnf transformation 7]
73. ~kind(X0) | old(X0) | ~curious(X0) [cnf transformation 39]
79. ~humble(X0) | kind(X0) | ~humble(X0) [cnf transformation 40]
82. humble(X0) | kind(X0) | humble(X0) [cnf transformation 40]
92. old(X0) | curious(X0) [cnf transformation 34]
128. ~old(lucy) [cnf transformation 23]
129. ~humble(X0) | kind(X0) [duplicate literal removal 79]
130. kind(X0) | humble(X0) [duplicate literal removal 82]
134. kind(X0) [subsumption resolution 129,130]
229. old(X1) | ~curious(X1) [resolution 73,134]
231. old(X1) [subsumption resolution 229,92]
232. $false [resolution 231,128]
% SZS output end Proof for 1704704993659835702223405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not curious is either happy or not strong and vice versa.
If mary is not wise then mary is not brave or strong.
If susan is either wise or kind then mary is brave or strong and vice versa.
If lucy is quiet or happy then mary is not curious and vice versa.
If someone is both strong and not humble then someone is both not wise and funny and vice versa.
Everyone who is either old or not funny is strong.
Everyone who is either not kind or humble is either not rich or funny.
Everyone who is not tall or not quiet is both not creative and curious.
If someone is generous or humble then john is both not humble and not old.
If someone is generous then susan is both not brave and not patient.
Everyone who is happy is calm or brave.
Everyone who is generous is old or not curious and vice versa.
If mary is curious or quiet then lucy is either not generous or quiet.
Everyone who is either old or rich is both wise and not funny and vice versa.
If someone is happy then john is rich and vice versa.
Everyone who is both not old and quiet is not kind or calm.
Alice is creative.
Someone is either not wise or quiet.
Someone is either generous or wise.
Someone is not brave or brave.
Paul is not happy or kind.
Lucy is either funny or not wise.
Someone is not rich.
John is calm. | Mary is curious. | neutral | (![X]:((~wise(X)&~curious(X))<=>(happy(X)<~>~strong(X))))&
((~wise(mary))=>((~brave(mary)|strong(mary))))&
(((wise(susan)<~>kind(susan)))<=>((brave(mary)|strong(mary))))&
(((quiet(lucy)|happy(lucy)))<=>(~curious(mary)))&
((?[X]:((strong(X)&~humble(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((old(X)<~>~funny(X))=>strong(X)))&
(![X]:((~kind(X)<~>humble(X))=>(~rich(X)<~>funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~creative(X)&curious(X))))&
((?[X]:((generous(X)|humble(X))))=>((~humble(john)&~old(john))))&
((?[X]:(generous(X)))=>((~brave(susan)&~patient(susan))))&
(![X]:(happy(X)=>(calm(X)|brave(X))))&
(![X]:(generous(X)<=>(old(X)|~curious(X))))&
(((curious(mary)|quiet(mary)))=>((~generous(lucy)<~>quiet(lucy))))&
(![X]:((old(X)<~>rich(X))<=>(wise(X)&~funny(X))))&
((?[X]:(happy(X)))<=>(rich(john)))&
(![X]:((~old(X)&quiet(X))=>(~kind(X)|calm(X))))&
(creative(alice))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((~brave(X)|brave(X))))&
((~happy(paul)|kind(paul)))&
((funny(lucy)<~>~wise(lucy)))&
(?[X]:(~rich(X)))&
(calm(john)) | curious(mary) | [] | null | 0 |
Everyone who is both kind and humble is quiet or humble and vice versa.
Everyone who is either funny or humble is either not funny or patient and vice versa.
Everyone who is both curious and patient is not patient or not quiet and vice versa.
Everyone who is either strong or not creative is tall or not tall.
If someone is not brave then someone is not curious or strong.
Everyone who is either not humble or quiet is old.
If mary is both not happy and curious then someone is either not tall or patient.
If paul is both calm and not humble then someone is both quiet and wise and vice versa.
If lucy is strong then alice is not brave and vice versa.
Everyone who is not humble is either wise or not creative.
If lucy is either not generous or not quiet then someone is not quiet or wise and vice versa.
If susan is either not quiet or wise then lucy is either generous or not rich and vice versa.
Everyone who is old is both not humble and not calm and vice versa.
Everyone who is not old is both brave and not wise.
If alice is either not tall or kind then someone is happy and vice versa.
If someone is both quiet and not brave then fred is not tall.
Someone is not tall or not funny.
Fred is humble or strong.
Mary is either not strong or not wise.
Mary is funny.
Someone is strong or not creative. | Fred is funny. | neutral | (![X]:((kind(X)&humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((curious(X)&patient(X))<=>(~patient(X)|~quiet(X))))&
(![X]:((strong(X)<~>~creative(X))=>(tall(X)|~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~humble(X)<~>quiet(X))=>old(X)))&
(((~happy(mary)&curious(mary)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((calm(paul)&~humble(paul)))<=>(?[X]:((quiet(X)&wise(X)))))&
((strong(lucy))<=>(~brave(alice)))&
(![X]:(~humble(X)=>(wise(X)<~>~creative(X))))&
(((~generous(lucy)<~>~quiet(lucy)))<=>(?[X]:((~quiet(X)|wise(X)))))&
(((~quiet(susan)<~>wise(susan)))<=>((generous(lucy)<~>~rich(lucy))))&
(![X]:(old(X)<=>(~humble(X)&~calm(X))))&
(![X]:(~old(X)=>(brave(X)&~wise(X))))&
(((~tall(alice)<~>kind(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((quiet(X)&~brave(X))))=>(~tall(fred)))&
(?[X]:((~tall(X)|~funny(X))))&
((humble(fred)|strong(fred)))&
((~strong(mary)<~>~wise(mary)))&
(funny(mary))&
(?[X]:((strong(X)|~creative(X)))) | funny(fred) | [] | null | 0 |
If john is either generous or not funny then mary is both not curious and kind. Everyone who is not kind is both not funny and creative and vice versa. If fred is not kind then someone is quiet or rich. Everyone who is both strong and old is humble or not happy. Everyone who is either not strong or not tall is not happy or patient and vice versa. Everyone who is either strong or quiet is either not patient or not tall and vice versa. If john is either creative or not curious then someone is not quiet or not generous and vice versa. Everyone who is either not calm or curious is not rich. If someone is both not humble and old then someone is old or humble. Everyone who is both not humble and not kind is either strong or funny and vice versa. If someone is either not curious or creative then someone is happy. Everyone who is either not wise or humble is not kind or kind. If susan is either not strong or curious then mary is either not creative or quiet. Everyone who is not strong or curious is strong and vice versa. If john is not calm then someone is tall or not patient. If someone is both not curious and not wise then someone is either not tall or not strong and vice versa. Someone is not patient or not curious. Someone is happy or old. Someone is not brave. Someone is either not patient or kind. John is both strong and tall. Fred is not patient or not kind. Someone is funny or not brave. Paul is rich or not old. | Mary is funny. | entailment | (((generous(john)<~>~funny(john)))=>((~curious(mary)&kind(mary))))&
(![X]:(~kind(X)<=>(~funny(X)&creative(X))))&
((~kind(fred))=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((strong(X)&old(X))=>(humble(X)|~happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~happy(X)|patient(X))))&
(![X]:((strong(X)<~>quiet(X))<=>(~patient(X)<~>~tall(X))))&
(((creative(john)<~>~curious(john)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(![X]:((~calm(X)<~>curious(X))=>~rich(X)))&
((?[X]:((~humble(X)&old(X))))=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~humble(X)&~kind(X))<=>(strong(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>creative(X))))=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>humble(X))=>(~kind(X)|kind(X))))&
(((~strong(susan)<~>curious(susan)))=>((~creative(mary)<~>quiet(mary))))&
(![X]:((~strong(X)|curious(X))<=>strong(X)))&
((~calm(john))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(?[X]:((~patient(X)|~curious(X))))&
(?[X]:((happy(X)|old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~patient(X)<~>kind(X))))&
((strong(john)&tall(john)))&
((~patient(fred)|~kind(fred)))&
(?[X]:((funny(X)|~brave(X))))&
((rich(paul)|~old(paul))) | funny(mary) | [
"p1",
"p4",
"p5",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8476517070705732551275384
% SZS output start Proof for 8476517070705732551275384
2. ! [X0] : (~kind(X0) <=> (creative(X0) & ~funny(X0))) [input p1]
5. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (patient(X0) | ~happy(X0))) [input p4]
6. ! [X0] : ((strong(X0) <~> quiet(X0)) <=> (~patient(X0) <~> ~tall(X0))) [input p5]
10. ! [X0] : ((~kind(X0) & ~humble(X0)) <=> (strong(X0) <~> funny(X0))) [input p9]
13. (~strong(susan) <~> curious(susan)) => (~creative(mary) <~> quiet(mary)) [input p12]
14. ! [X0] : ((curious(X0) | ~strong(X0)) <=> strong(X0)) [input p13]
16. ? [X0] : (~wise(X0) & ~curious(X0)) <=> ? [X0] : (~tall(X0) <~> ~strong(X0)) [input p15]
25. ~funny(mary) [input hypothesis]
28. ? [X0] : (~wise(X0) & ~curious(X0)) <=> ? [X1] : (~tall(X1) <~> ~strong(X1)) [rectify 16]
40. (~creative(mary) <~> quiet(mary)) | (~strong(susan) <=> curious(susan)) [ennf transformation 13]
43. ! [X0] : ((~kind(X0) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 2]
44. ! [X0] : ((~kind(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | kind(X0))) [flattening 43]
47. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~patient(X0) & happy(X0))) & ((patient(X0) | ~happy(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 5]
48. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~patient(X0) & happy(X0))) & (patient(X0) | ~happy(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [flattening 47]
49. ! [X0] : ((((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0)))) & (((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0))))) [nnf transformation 6]
58. ! [X0] : (((~kind(X0) & ~humble(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | (kind(X0) | humble(X0)))) [nnf transformation 10]
59. ! [X0] : (((~kind(X0) & ~humble(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | kind(X0) | humble(X0))) [flattening 58]
65. ((~quiet(mary) | creative(mary)) & (quiet(mary) | ~creative(mary))) | ((~strong(susan) | ~curious(susan)) & (curious(susan) | strong(susan))) [nnf transformation 40]
66. ! [X0] : (((curious(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~curious(X0) & strong(X0)))) [nnf transformation 14]
67. ! [X0] : ((curious(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (~curious(X0) & strong(X0)))) [flattening 66]
70. (? [X0] : (~wise(X0) & ~curious(X0)) | ! [X1] : ((~tall(X1) | strong(X1)) & (~strong(X1) | tall(X1)))) & (? [X1] : ((strong(X1) | tall(X1)) & (~strong(X1) | ~tall(X1))) | ! [X0] : (wise(X0) | curious(X0))) [nnf transformation 28]
71. (? [X0] : (~wise(X0) & ~curious(X0)) | ! [X1] : ((~tall(X1) | strong(X1)) & (~strong(X1) | tall(X1)))) & (? [X2] : ((strong(X2) | tall(X2)) & (~strong(X2) | ~tall(X2))) | ! [X3] : (wise(X3) | curious(X3))) [rectify 70]
72. ? [X0] : (~wise(X0) & ~curious(X0)) => (~wise(sK5) & ~curious(sK5)) [choice axiom]
73. ? [X2] : ((strong(X2) | tall(X2)) & (~strong(X2) | ~tall(X2))) => ((strong(sK6) | tall(sK6)) & (~strong(sK6) | ~tall(sK6))) [choice axiom]
74. ((~wise(sK5) & ~curious(sK5)) | ! [X1] : ((~tall(X1) | strong(X1)) & (~strong(X1) | tall(X1)))) & (((strong(sK6) | tall(sK6)) & (~strong(sK6) | ~tall(sK6))) | ! [X3] : (wise(X3) | curious(X3))) [skolemisation 71,73,72]
87. creative(X0) | kind(X0) [cnf transformation 44]
94. ~patient(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 48]
103. ~quiet(X0) | ~strong(X0) | ~tall(X0) | patient(X0) [cnf transformation 49]
118. ~strong(X0) | funny(X0) | ~kind(X0) [cnf transformation 59]
125. quiet(mary) | ~creative(mary) | ~strong(susan) | ~curious(susan) [cnf transformation 65]
128. strong(X0) | strong(X0) [cnf transformation 67]
130. curious(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 67]
134. ~curious(sK5) | ~strong(X1) | tall(X1) [cnf transformation 74]
146. ~funny(mary) [cnf transformation 25]
147. strong(X0) [duplicate literal removal 128]
148. ~strong(X0) | curious(X0) [duplicate literal removal 130]
158. 3 <=> kind(mary) [avatar definition]
160. kind(mary) <- (3) [avatar component clause 158]
183. ~tall(X0) | ~strong(X0) | ~quiet(X0) [subsumption resolution 103,94]
241. 20 <=> curious(susan) [avatar definition]
243. ~curious(susan) <- (~20) [avatar component clause 241]
245. 21 <=> strong(susan) [avatar definition]
247. ~strong(susan) <- (~21) [avatar component clause 245]
249. 22 <=> creative(mary) [avatar definition]
250. ~creative(mary) <- (~22) [avatar component clause 249]
253. 23 <=> quiet(mary) [avatar definition]
254. quiet(mary) <- (23) [avatar component clause 253]
258. ~20 | ~21 | ~22 | 23 [avatar split clause 125,253,249,245,241]
275. 27 <=> ! [X1] : tall(X1) [avatar definition]
276. tall(X1) <- (27) [avatar component clause 275]
282. ~curious(sK5) | tall(X1) [subsumption resolution 134,147]
284. 29 <=> curious(sK5) [avatar definition]
286. ~curious(sK5) <- (~29) [avatar component clause 284]
287. 27 | ~29 [avatar split clause 282,284,275]
340. kind(mary) <- (~22) [resolution 87,250]
341. 3 | 22 [avatar split clause 340,249,158]
342. curious(X0) [resolution 148,147]
345. $false <- (~20) [resolution 342,243]
346. $false <- (~29) [resolution 342,286]
347. 29 [avatar contradiction clause 346]
348. 20 [avatar contradiction clause 345]
361. ~kind(X0) | funny(X0) [resolution 118,147]
363. funny(mary) <- (3) [resolution 361,160]
364. $false <- (3) [subsumption resolution 363,146]
365. ~3 [avatar contradiction clause 364]
366. $false <- (~21) [subsumption resolution 247,147]
367. 21 [avatar contradiction clause 366]
373. ~strong(X1) | ~quiet(X1) <- (27) [resolution 183,276]
375. ~quiet(X1) <- (27) [subsumption resolution 373,147]
377. $false <- (23, 27) [resolution 375,254]
378. ~23 | ~27 [avatar contradiction clause 377]
379. $false [avatar sat refutation 258,287,341,347,348,365,367,378]
% SZS output end Proof for 8476517070705732551275384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not old or not kind then someone is not tall. If someone is not brave then fred is not patient or not happy and vice versa. Everyone who is either not strong or tall is funny or not quiet and vice versa. If fred is curious or kind then john is humble. If john is both curious and not quiet then fred is both rich and not generous. If someone is either patient or happy then mary is tall or not strong. If someone is both patient and not generous then lucy is both not kind and calm. Everyone who is not patient or brave is not calm or curious and vice versa. Everyone who is not old is either tall or kind. Everyone who is not humble or calm is quiet and vice versa. If lucy is either kind or not generous then fred is happy and vice versa. Everyone who is either not rich or not curious is wise or not tall. If mary is either not happy or not creative then lucy is not calm and vice versa. If john is brave or not old then someone is not creative or tall. Everyone who is not generous is either rich or creative. Everyone who is either funny or kind is not curious or creative. Lucy is not brave or not calm. John is either not rich or not calm. Lucy is happy. Lucy is both humble and rich. Someone is kind or patient. Fred is both not calm and quiet. Susan is rich or not generous. Someone is not funny or not happy. | John is not calm. | neutral | (((~old(paul)|~kind(paul)))=>(?[X]:(~tall(X))))&
((?[X]:(~brave(X)))<=>((~patient(fred)|~happy(fred))))&
(![X]:((~strong(X)<~>tall(X))<=>(funny(X)|~quiet(X))))&
(((curious(fred)|kind(fred)))=>(humble(john)))&
(((curious(john)&~quiet(john)))=>((rich(fred)&~generous(fred))))&
((?[X]:((patient(X)<~>happy(X))))=>((tall(mary)|~strong(mary))))&
((?[X]:((patient(X)&~generous(X))))=>((~kind(lucy)&calm(lucy))))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)|curious(X))))&
(![X]:(~old(X)=>(tall(X)<~>kind(X))))&
(![X]:((~humble(X)|calm(X))<=>quiet(X)))&
(((kind(lucy)<~>~generous(lucy)))<=>(happy(fred)))&
(![X]:((~rich(X)<~>~curious(X))=>(wise(X)|~tall(X))))&
(((~happy(mary)<~>~creative(mary)))<=>(~calm(lucy)))&
(((brave(john)|~old(john)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:(~generous(X)=>(rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>kind(X))=>(~curious(X)|creative(X))))&
((~brave(lucy)|~calm(lucy)))&
((~rich(john)<~>~calm(john)))&
(happy(lucy))&
((humble(lucy)&rich(lucy)))&
(?[X]:((kind(X)|patient(X))))&
((~calm(fred)&quiet(fred)))&
((rich(susan)|~generous(susan)))&
(?[X]:((~funny(X)|~happy(X)))) | ~calm(john) | [] | null | 0 |
If alice is either calm or not generous then paul is both not kind and humble. If mary is not rich then alice is either happy or generous. Everyone who is either old or not happy is calm or patient and vice versa. If susan is both calm and not curious then paul is both funny and not happy and vice versa. If john is funny or not brave then susan is either not strong or not wise and vice versa. If john is not strong or happy then john is curious and vice versa. If paul is either wise or patient then someone is both tall and not creative. Everyone who is patient is both not patient and humble and vice versa. Everyone who is both not calm and not quiet is either not wise or not generous and vice versa. Everyone who is both strong and curious is calm and vice versa. If someone is either not tall or quiet then john is either funny or kind. If paul is both not patient and quiet then someone is not quiet. Everyone who is either calm or not brave is either brave or not brave and vice versa. If mary is not brave then someone is strong. If john is kind then someone is either not quiet or not creative and vice versa. If fred is not brave then someone is patient and vice versa. Susan is old. Someone is either not old or not calm. Paul is not wise or kind. Mary is either patient or creative. Someone is not kind or not rich. Someone is not rich. Paul is not calm or calm. | Mary is patient. | contradiction | (((calm(alice)<~>~generous(alice)))=>((~kind(paul)&humble(paul))))&
((~rich(mary))=>((happy(alice)<~>generous(alice))))&
(![X]:((old(X)<~>~happy(X))<=>(calm(X)|patient(X))))&
(((calm(susan)&~curious(susan)))<=>((funny(paul)&~happy(paul))))&
(((funny(john)|~brave(john)))<=>((~strong(susan)<~>~wise(susan))))&
(((~strong(john)|happy(john)))<=>(curious(john)))&
(((wise(paul)<~>patient(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:(patient(X)<=>(~patient(X)&humble(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~wise(X)<~>~generous(X))))&
(![X]:((strong(X)&curious(X))<=>calm(X)))&
((?[X]:((~tall(X)<~>quiet(X))))=>((funny(john)<~>kind(john))))&
(((~patient(paul)&quiet(paul)))=>(?[X]:(~quiet(X))))&
(![X]:((calm(X)<~>~brave(X))<=>(brave(X)<~>~brave(X))))&
((~brave(mary))=>(?[X]:(strong(X))))&
((kind(john))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
((~brave(fred))<=>(?[X]:(patient(X))))&
(old(susan))&
(?[X]:((~old(X)<~>~calm(X))))&
((~wise(paul)|kind(paul)))&
((patient(mary)<~>creative(mary)))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:(~rich(X)))&
((~calm(paul)|calm(paul))) | patient(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4051650036644165702195907
% SZS output start Proof for 4051650036644165702195907
8. ! [X0] : (patient(X0) <=> (humble(X0) & ~patient(X0))) [input p7]
24. patient(mary) [input hypothesis]
45. ! [X0] : ((patient(X0) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
46. ! [X0] : ((patient(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | ~patient(X0))) [flattening 45]
102. ~patient(X0) | ~patient(X0) [cnf transformation 46]
143. patient(mary) [cnf transformation 24]
152. ~patient(X0) [duplicate literal removal 102]
334. $false [subsumption resolution 143,152]
% SZS output end Proof for 4051650036644165702195907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not patient is calm or not rich and vice versa.
If someone is either not creative or not tall then someone is either not rich or not curious and vice versa.
If someone is both strong and wise then mary is both not humble and not generous and vice versa.
If someone is either creative or not creative then mary is generous and vice versa.
If lucy is either generous or rich then alice is both not generous and curious.
If paul is both humble and not calm then someone is either not patient or not humble.
If alice is both not creative and not patient then someone is either brave or wise and vice versa.
Everyone who is either wise or not rich is patient.
Everyone who is both not tall and wise is either curious or creative.
Everyone who is both wise and humble is both not tall and rich and vice versa.
If john is both kind and not rich then john is not creative.
If someone is either kind or generous then someone is not brave.
Everyone who is not old or creative is old or not wise and vice versa.
Everyone who is not wise is both not calm and not tall and vice versa.
Everyone who is not quiet is both not funny and kind.
Everyone who is both patient and creative is both not creative and old and vice versa.
Someone is both curious and creative.
Someone is not generous.
Alice is both not patient and old.
Someone is funny.
Someone is either not quiet or old.
Paul is both generous and calm. | Alice is humble. | contradiction | (![X]:((old(X)|~patient(X))<=>(calm(X)|~rich(X))))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:((strong(X)&wise(X))))<=>((~humble(mary)&~generous(mary))))&
((?[X]:((creative(X)<~>~creative(X))))<=>(generous(mary)))&
(((generous(lucy)<~>rich(lucy)))=>((~generous(alice)&curious(alice))))&
(((humble(paul)&~calm(paul)))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((~creative(alice)&~patient(alice)))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~rich(X))=>patient(X)))&
(![X]:((~tall(X)&wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((wise(X)&humble(X))<=>(~tall(X)&rich(X))))&
(((kind(john)&~rich(john)))=>(~creative(john)))&
((?[X]:((kind(X)<~>generous(X))))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|creative(X))<=>(old(X)|~wise(X))))&
(![X]:(~wise(X)<=>(~calm(X)&~tall(X))))&
(![X]:(~quiet(X)=>(~funny(X)&kind(X))))&
(![X]:((patient(X)&creative(X))<=>(~creative(X)&old(X))))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(~generous(X)))&
((~patient(alice)&old(alice)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)<~>old(X))))&
((generous(paul)&calm(paul))) | humble(alice) | [
"p7",
"p9",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2307916634464358214960504
% SZS output start Proof for 2307916634464358214960504
8. ! [X0] : ((wise(X0) <~> ~rich(X0)) => patient(X0)) [input p7]
10. ! [X0] : ((humble(X0) & wise(X0)) <=> (rich(X0) & ~tall(X0))) [input p9]
14. ! [X0] : (~wise(X0) <=> (~tall(X0) & ~calm(X0))) [input p13]
19. old(alice) & ~patient(alice) [input p18]
23. humble(alice) [input hypothesis]
29. ! [X0] : (patient(X0) | (wise(X0) <=> ~rich(X0))) [ennf transformation 8]
61. ! [X0] : (patient(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0)))) [nnf transformation 29]
63. ! [X0] : (((humble(X0) & wise(X0)) | (~rich(X0) | tall(X0))) & ((rich(X0) & ~tall(X0)) | (~humble(X0) | ~wise(X0)))) [nnf transformation 10]
64. ! [X0] : (((humble(X0) & wise(X0)) | ~rich(X0) | tall(X0)) & ((rich(X0) & ~tall(X0)) | ~humble(X0) | ~wise(X0))) [flattening 63]
71. ! [X0] : ((~wise(X0) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [nnf transformation 14]
72. ! [X0] : ((~wise(X0) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | wise(X0))) [flattening 71]
116. ~wise(X0) | ~rich(X0) | patient(X0) [cnf transformation 61]
117. wise(X0) | patient(X0) | rich(X0) [cnf transformation 61]
120. ~humble(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 64]
121. ~humble(X0) | rich(X0) | ~wise(X0) [cnf transformation 64]
122. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 64]
132. ~tall(X0) | wise(X0) [cnf transformation 72]
143. ~patient(alice) [cnf transformation 19]
150. humble(alice) [cnf transformation 23]
266. 25 <=> patient(alice) [avatar definition]
268. ~patient(alice) <- (~25) [avatar component clause 266]
315. ~25 [avatar split clause 143,266]
365. ~tall(alice) | ~wise(alice) [resolution 120,150]
366. ~tall(alice) [subsumption resolution 365,132]
367. rich(alice) | ~wise(alice) [resolution 121,150]
369. 41 <=> wise(alice) [avatar definition]
370. wise(alice) <- (41) [avatar component clause 369]
371. ~wise(alice) <- (~41) [avatar component clause 369]
373. 42 <=> rich(alice) [avatar definition]
375. rich(alice) <- (42) [avatar component clause 373]
376. ~41 | 42 [avatar split clause 367,373,369]
377. patient(alice) | rich(alice) <- (~41) [resolution 371,117]
378. rich(alice) <- (~25, ~41) [subsumption resolution 377,268]
379. 42 | 25 | 41 [avatar split clause 378,369,266,373]
380. wise(alice) | tall(alice) <- (42) [resolution 375,122]
387. wise(alice) <- (42) [subsumption resolution 380,366]
388. 41 | ~42 [avatar split clause 387,373,369]
390. ~rich(alice) | patient(alice) <- (41) [resolution 370,116]
394. patient(alice) <- (41, 42) [subsumption resolution 390,375]
395. $false <- (~25, 41, 42) [subsumption resolution 394,268]
396. 25 | ~41 | ~42 [avatar contradiction clause 395]
397. $false [avatar sat refutation 315,376,379,388,396]
% SZS output end Proof for 2307916634464358214960504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not quiet then mary is brave or creative. If fred is either patient or not brave then someone is both not tall and tall. If john is both not creative and happy then someone is either not creative or not strong and vice versa. If alice is not funny or not strong then fred is both kind and not rich. Everyone who is either not tall or not kind is creative and vice versa. If someone is either not brave or brave then someone is both not calm and old and vice versa. Everyone who is not humble or not rich is rich. If someone is either not happy or not humble then someone is both not quiet and humble and vice versa. Everyone who is either not brave or not calm is either not generous or wise and vice versa. Everyone who is humble or strong is wise. Everyone who is not rich is both not funny and not rich. If someone is humble or not rich then someone is either strong or not funny and vice versa. Everyone who is not happy is generous and vice versa. Everyone who is either quiet or old is both happy and rich and vice versa. Everyone who is both not calm and not rich is either not brave or calm and vice versa. If paul is not tall or not calm then someone is either kind or not happy and vice versa. Someone is creative or happy. Alice is not funny or not quiet. Someone is both generous and not kind. Alice is creative or old. Fred is both not happy and brave. Someone is either not happy or not wise. Alice is both wise and not tall. | Alice is not funny. | contradiction | ((~quiet(fred))=>((brave(mary)|creative(mary))))&
(((patient(fred)<~>~brave(fred)))=>(?[X]:((~tall(X)&tall(X)))))&
(((~creative(john)&happy(john)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((~funny(alice)|~strong(alice)))=>((kind(fred)&~rich(fred))))&
(![X]:((~tall(X)<~>~kind(X))<=>creative(X)))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:((~humble(X)|~rich(X))=>rich(X)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((humble(X)|strong(X))=>wise(X)))&
(![X]:(~rich(X)=>(~funny(X)&~rich(X))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:((strong(X)<~>~funny(X)))))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:((quiet(X)<~>old(X))<=>(happy(X)&rich(X))))&
(![X]:((~calm(X)&~rich(X))<=>(~brave(X)<~>calm(X))))&
(((~tall(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(?[X]:((creative(X)|happy(X))))&
((~funny(alice)|~quiet(alice)))&
(?[X]:((generous(X)&~kind(X))))&
((creative(alice)|old(alice)))&
((~happy(fred)&brave(fred)))&
(?[X]:((~happy(X)<~>~wise(X))))&
((wise(alice)&~tall(alice))) | ~funny(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6426927247549608020770395
% SZS output start Proof for 6426927247549608020770395
4. (~strong(alice) | ~funny(alice)) => (~rich(fred) & kind(fred)) [input p3]
7. ! [X0] : ((~rich(X0) | ~humble(X0)) => rich(X0)) [input p6]
24. ~funny(alice) [input hypothesis]
31. (~rich(fred) & kind(fred)) | (strong(alice) & funny(alice)) [ennf transformation 4]
32. ! [X0] : (rich(X0) | (rich(X0) & humble(X0))) [ennf transformation 7]
90. ~rich(fred) | funny(alice) [cnf transformation 31]
103. rich(X0) | rich(X0) [cnf transformation 32]
159. ~funny(alice) [cnf transformation 24]
162. rich(X0) [duplicate literal removal 103]
229. 14 <=> rich(fred) [avatar definition]
231. ~rich(fred) <- (~14) [avatar component clause 229]
234. 15 <=> funny(alice) [avatar definition]
237. 15 | ~14 [avatar split clause 90,229,234]
386. ~15 [avatar split clause 159,234]
387. $false <- (~14) [subsumption resolution 231,162]
388. 14 [avatar contradiction clause 387]
389. $false [avatar sat refutation 237,386,388]
% SZS output end Proof for 6426927247549608020770395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is generous and vice versa.
Everyone who is both not curious and happy is either not old or humble and vice versa.
Everyone who is both curious and happy is both patient and generous.
If someone is not rich then someone is either calm or happy.
Everyone who is quiet or strong is both kind and curious and vice versa.
Everyone who is patient or not brave is not creative or old.
If fred is either not humble or rich then fred is wise and vice versa.
Everyone who is either funny or kind is both not tall and not rich and vice versa.
If mary is not patient or humble then paul is either not rich or brave and vice versa.
If someone is either creative or not strong then someone is generous and vice versa.
Everyone who is either creative or not humble is either not tall or brave and vice versa.
Everyone who is not old is not creative or generous and vice versa.
Everyone who is either creative or not creative is both curious and humble.
Everyone who is patient or not quiet is not funny or not wise.
Everyone who is both not quiet and not strong is both patient and kind and vice versa.
If someone is not quiet then lucy is both not generous and curious.
Fred is quiet.
Someone is either not old or not calm.
Someone is strong or rich.
Someone is not humble or curious.
Someone is kind.
Susan is not happy or not brave. | Paul is rich. | neutral | (![X]:(~tall(X)<=>generous(X)))&
(![X]:((~curious(X)&happy(X))<=>(~old(X)<~>humble(X))))&
(![X]:((curious(X)&happy(X))=>(patient(X)&generous(X))))&
((?[X]:(~rich(X)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((quiet(X)|strong(X))<=>(kind(X)&curious(X))))&
(![X]:((patient(X)|~brave(X))=>(~creative(X)|old(X))))&
(((~humble(fred)<~>rich(fred)))<=>(wise(fred)))&
(![X]:((funny(X)<~>kind(X))<=>(~tall(X)&~rich(X))))&
(((~patient(mary)|humble(mary)))<=>((~rich(paul)<~>brave(paul))))&
((?[X]:((creative(X)<~>~strong(X))))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(~tall(X)<~>brave(X))))&
(![X]:(~old(X)<=>(~creative(X)|generous(X))))&
(![X]:((creative(X)<~>~creative(X))=>(curious(X)&humble(X))))&
(![X]:((patient(X)|~quiet(X))=>(~funny(X)|~wise(X))))&
(![X]:((~quiet(X)&~strong(X))<=>(patient(X)&kind(X))))&
((?[X]:(~quiet(X)))=>((~generous(lucy)&curious(lucy))))&
(quiet(fred))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:(kind(X)))&
((~happy(susan)|~brave(susan))) | rich(paul) | [] | null | 0 |
Everyone who is both kind and brave is humble.
Everyone who is not curious is either strong or kind and vice versa.
Everyone who is either not humble or strong is both not calm and not wise.
Everyone who is either not funny or not creative is strong or happy.
If paul is either not rich or quiet then someone is both not kind and not quiet.
If john is both tall and not funny then john is generous.
If fred is both not funny and not wise then alice is both not quiet and not curious.
If someone is both happy and not kind then someone is generous.
If fred is not rich or quiet then someone is either not tall or generous.
Everyone who is not brave is either not quiet or old and vice versa.
If someone is not patient or funny then mary is both not humble and not funny and vice versa.
Everyone who is not tall is either humble or not tall.
If someone is both humble and not kind then someone is either calm or strong.
If lucy is brave or not old then someone is both wise and not wise and vice versa.
Everyone who is not kind is happy or funny.
Everyone who is both funny and old is both not curious and not calm and vice versa.
Someone is rich or funny.
John is creative or not calm.
Paul is funny or generous.
Someone is not kind or not funny.
Someone is not tall.
Alice is both old and kind.
John is humble or old.
Susan is not happy. | Susan is funny. | neutral | (![X]:((kind(X)&brave(X))=>humble(X)))&
(![X]:(~curious(X)<=>(strong(X)<~>kind(X))))&
(![X]:((~humble(X)<~>strong(X))=>(~calm(X)&~wise(X))))&
(![X]:((~funny(X)<~>~creative(X))=>(strong(X)|happy(X))))&
(((~rich(paul)<~>quiet(paul)))=>(?[X]:((~kind(X)&~quiet(X)))))&
(((tall(john)&~funny(john)))=>(generous(john)))&
(((~funny(fred)&~wise(fred)))=>((~quiet(alice)&~curious(alice))))&
((?[X]:((happy(X)&~kind(X))))=>(?[X]:(generous(X))))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:((~patient(X)|funny(X))))<=>((~humble(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(((brave(lucy)|~old(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
(?[X]:((rich(X)|funny(X))))&
((creative(john)|~calm(john)))&
((funny(paul)|generous(paul)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:(~tall(X)))&
((old(alice)&kind(alice)))&
((humble(john)|old(john)))&
(~happy(susan)) | funny(susan) | [] | null | 0 |
Everyone who is either not calm or curious is not kind or not humble.
Everyone who is not quiet or brave is not wise and vice versa.
If fred is humble then someone is both strong and old and vice versa.
Everyone who is not curious is creative or not curious.
Everyone who is either funny or not old is either not brave or humble and vice versa.
Everyone who is both not old and not calm is either not curious or not strong.
If someone is both not old and happy then alice is not funny or not tall and vice versa.
If someone is either not humble or not wise then someone is funny and vice versa.
If someone is both not humble and not quiet then someone is either not creative or funny and vice versa.
If alice is both not creative and not strong then mary is old or strong.
Everyone who is not old is not wise and vice versa.
If someone is wise then someone is both not creative and not strong and vice versa.
If someone is either not rich or not curious then someone is wise or not curious and vice versa.
Everyone who is not happy or not humble is both not strong and not creative and vice versa.
If mary is both old and not funny then alice is not strong or not kind and vice versa.
If someone is not patient then alice is not tall or not wise and vice versa.
Susan is both rich and brave.
Fred is tall or kind.
Someone is tall.
Someone is not brave.
John is either tall or calm.
Someone is patient or not kind.
Someone is humble or not old.
Alice is either funny or strong. | John is humble. | neutral | (![X]:((~calm(X)<~>curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~quiet(X)|brave(X))<=>~wise(X)))&
((humble(fred))<=>(?[X]:((strong(X)&old(X)))))&
(![X]:(~curious(X)=>(creative(X)|~curious(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~brave(X)<~>humble(X))))&
(![X]:((~old(X)&~calm(X))=>(~curious(X)<~>~strong(X))))&
((?[X]:((~old(X)&happy(X))))<=>((~funny(alice)|~tall(alice))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
(((~creative(alice)&~strong(alice)))=>((old(mary)|strong(mary))))&
(![X]:(~old(X)<=>~wise(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~creative(X)&~strong(X)))))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((~happy(X)|~humble(X))<=>(~strong(X)&~creative(X))))&
(((old(mary)&~funny(mary)))<=>((~strong(alice)|~kind(alice))))&
((?[X]:(~patient(X)))<=>((~tall(alice)|~wise(alice))))&
((rich(susan)&brave(susan)))&
((tall(fred)|kind(fred)))&
(?[X]:(tall(X)))&
(?[X]:(~brave(X)))&
((tall(john)<~>calm(john)))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:((humble(X)|~old(X))))&
((funny(alice)<~>strong(alice))) | humble(john) | [] | null | 0 |
If someone is not old then alice is not creative or not brave. If mary is either not tall or happy then someone is not rich or not wise. Everyone who is not old is either creative or not calm. If someone is either not creative or creative then someone is wise or not tall. Everyone who is not strong is old or not rich. If paul is both not generous and calm then someone is either not quiet or old and vice versa. If lucy is kind or not old then someone is strong or kind. If fred is creative or curious then susan is not quiet or not tall. Everyone who is both not curious and old is not calm and vice versa. Everyone who is creative is quiet and vice versa. Everyone who is calm is both rich and not rich and vice versa. Everyone who is either not brave or not rich is both strong and curious. If someone is both happy and humble then someone is humble or calm. Everyone who is both rich and calm is both kind and not humble. If paul is not wise or generous then someone is kind and vice versa. Someone is either not strong or not tall. Someone is not kind. Alice is both wise and not funny. Susan is curious or old. Someone is strong. Someone is both not tall and not wise. Alice is either quiet or not happy. Someone is both not patient and not calm. | Mary is creative. | contradiction | ((?[X]:(~old(X)))=>((~creative(alice)|~brave(alice))))&
(((~tall(mary)<~>happy(mary)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~old(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~strong(X)=>(old(X)|~rich(X))))&
(((~generous(paul)&calm(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((kind(lucy)|~old(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(((creative(fred)|curious(fred)))=>((~quiet(susan)|~tall(susan))))&
(![X]:((~curious(X)&old(X))<=>~calm(X)))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:(calm(X)<=>(rich(X)&~rich(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(strong(X)&curious(X))))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((rich(X)&calm(X))=>(kind(X)&~humble(X))))&
(((~wise(paul)|generous(paul)))<=>(?[X]:(kind(X))))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:(~kind(X)))&
((wise(alice)&~funny(alice)))&
((curious(susan)|old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)&~wise(X))))&
((quiet(alice)<~>~happy(alice)))&
(?[X]:((~patient(X)&~calm(X)))) | creative(mary) | [
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7697666462003529276163856
% SZS output start Proof for 7697666462003529276163856
6. (calm(paul) & ~generous(paul)) <=> ? [X0] : (~quiet(X0) <~> old(X0)) [input p5]
9. ! [X0] : ((old(X0) & ~curious(X0)) <=> ~calm(X0)) [input p8]
10. ! [X0] : (creative(X0) <=> quiet(X0)) [input p9]
11. ! [X0] : (calm(X0) <=> (~rich(X0) & rich(X0))) [input p10]
24. creative(mary) [input hypothesis]
51. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~calm(paul) | generous(paul))) [nnf transformation 6]
52. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~calm(paul) | generous(paul)) [flattening 51]
53. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) | ~calm(paul) | generous(paul)) [rectify 52]
54. ? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) => ((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) [choice axiom]
55. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) | ~calm(paul) | generous(paul)) [skolemisation 53,54]
58. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~old(X0) | curious(X0)))) [nnf transformation 9]
59. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~old(X0) | curious(X0))) [flattening 58]
60. ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0))) [nnf transformation 10]
61. ! [X0] : ((calm(X0) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 11]
62. ! [X0] : ((calm(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [flattening 61]
97. calm(paul) | ~quiet(X0) | ~old(X0) [cnf transformation 55]
104. calm(X0) | old(X0) [cnf transformation 59]
105. ~creative(X0) | quiet(X0) [cnf transformation 60]
107. rich(X0) | ~calm(X0) [cnf transformation 62]
108. ~calm(X0) | ~rich(X0) [cnf transformation 62]
131. creative(mary) [cnf transformation 24]
135. 1 <=> ! [X0] : old(X0) [avatar definition]
136. old(X0) <- (1) [avatar component clause 135]
181. 12 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
182. ~quiet(X0) | ~old(X0) <- (12) [avatar component clause 181]
184. 13 <=> calm(paul) [avatar definition]
186. calm(paul) <- (13) [avatar component clause 184]
187. 12 | 13 [avatar split clause 97,184,181]
244. ~calm(X0) [subsumption resolution 107,108]
297. $false <- (13) [subsumption resolution 186,244]
298. ~13 [avatar contradiction clause 297]
302. old(X0) [resolution 104,244]
303. 1 [avatar split clause 302,135]
306. quiet(mary) [resolution 105,131]
309. ~old(mary) <- (12) [resolution 182,306]
310. $false <- (1, 12) [subsumption resolution 309,136]
311. ~1 | ~12 [avatar contradiction clause 310]
312. $false [avatar sat refutation 187,298,303,311]
% SZS output end Proof for 7697666462003529276163856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or funny then mary is either brave or not curious and vice versa.
Everyone who is not curious or curious is both not humble and not funny and vice versa.
If someone is both happy and not calm then someone is calm or rich and vice versa.
Everyone who is either not brave or not happy is not old or not strong and vice versa.
Everyone who is both not wise and patient is either creative or not tall and vice versa.
If someone is not kind then john is both creative and kind.
If paul is not tall or not strong then fred is happy.
Everyone who is both not calm and not kind is either calm or quiet and vice versa.
Everyone who is either old or not tall is creative or humble and vice versa.
Everyone who is both wise and not kind is both wise and quiet.
Everyone who is not strong or calm is both not tall and tall.
If alice is not rich then someone is both not rich and not calm.
If someone is rich or strong then paul is not wise or not calm and vice versa.
If john is not tall then someone is not happy.
If someone is humble then someone is quiet or not creative and vice versa.
Everyone who is not calm or calm is not creative or curious.
Someone is rich or not tall.
Someone is either not curious or patient.
Alice is brave or strong.
Someone is either old or not happy.
Someone is generous or not brave. | Mary is old. | neutral | (((~tall(alice)<~>funny(alice)))<=>((brave(mary)<~>~curious(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((happy(X)&~calm(X))))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~brave(X)<~>~happy(X))<=>(~old(X)|~strong(X))))&
(![X]:((~wise(X)&patient(X))<=>(creative(X)<~>~tall(X))))&
((?[X]:(~kind(X)))=>((creative(john)&kind(john))))&
(((~tall(paul)|~strong(paul)))=>(happy(fred)))&
(![X]:((~calm(X)&~kind(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(creative(X)|humble(X))))&
(![X]:((wise(X)&~kind(X))=>(wise(X)&quiet(X))))&
(![X]:((~strong(X)|calm(X))=>(~tall(X)&tall(X))))&
((~rich(alice))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((rich(X)|strong(X))))<=>((~wise(paul)|~calm(paul))))&
((~tall(john))=>(?[X]:(~happy(X))))&
((?[X]:(humble(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(?[X]:((rich(X)|~tall(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((brave(alice)|strong(alice)))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((generous(X)|~brave(X)))) | old(mary) | [] | null | 0 |
If susan is old then paul is not tall or strong.
Everyone who is not generous is both generous and patient and vice versa.
If someone is brave then susan is not rich or curious.
If someone is not calm then paul is curious or creative.
Everyone who is not wise or curious is both not generous and kind and vice versa.
If john is both not old and happy then john is not generous or wise and vice versa.
Everyone who is either rich or not tall is both not quiet and tall.
Everyone who is not calm is both not happy and tall.
Everyone who is either not generous or calm is funny and vice versa.
Everyone who is happy is either tall or not creative.
If someone is either creative or brave then fred is not creative or not quiet and vice versa.
Everyone who is not wise or not rich is both not old and tall and vice versa.
If someone is both not tall and quiet then someone is both not wise and not rich.
Everyone who is both patient and happy is either not strong or not happy and vice versa.
Someone is quiet.
Mary is not tall or funny.
Mary is either rich or not kind.
Paul is not calm.
Lucy is not rich or patient. | Mary is calm. | entailment | ((old(susan))=>((~tall(paul)|strong(paul))))&
(![X]:(~generous(X)<=>(generous(X)&patient(X))))&
((?[X]:(brave(X)))=>((~rich(susan)|curious(susan))))&
((?[X]:(~calm(X)))=>((curious(paul)|creative(paul))))&
(![X]:((~wise(X)|curious(X))<=>(~generous(X)&kind(X))))&
(((~old(john)&happy(john)))<=>((~generous(john)|wise(john))))&
(![X]:((rich(X)<~>~tall(X))=>(~quiet(X)&tall(X))))&
(![X]:(~calm(X)=>(~happy(X)&tall(X))))&
(![X]:((~generous(X)<~>calm(X))<=>funny(X)))&
(![X]:(happy(X)=>(tall(X)<~>~creative(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~creative(fred)|~quiet(fred))))&
(![X]:((~wise(X)|~rich(X))<=>(~old(X)&tall(X))))&
((?[X]:((~tall(X)&quiet(X))))=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:((patient(X)&happy(X))<=>(~strong(X)<~>~happy(X))))&
(?[X]:(quiet(X)))&
((~tall(mary)|funny(mary)))&
((rich(mary)<~>~kind(mary)))&
(~calm(paul))&
((~rich(lucy)|patient(lucy))) | calm(mary) | [
"p1",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6138171565134683036977794
% SZS output start Proof for 6138171565134683036977794
2. ! [X0] : (~generous(X0) <=> (patient(X0) & generous(X0))) [input p1]
8. ! [X0] : (~calm(X0) => (tall(X0) & ~happy(X0))) [input p7]
9. ! [X0] : ((~generous(X0) <~> calm(X0)) <=> funny(X0)) [input p8]
16. funny(mary) | ~tall(mary) [input p15]
20. ~calm(mary) [input hypothesis]
22. ! [X0] : (funny(X0) => (~generous(X0) <~> calm(X0))) [unused predicate definition removal 9]
30. ! [X0] : ((tall(X0) & ~happy(X0)) | calm(X0)) [ennf transformation 8]
31. ! [X0] : ((~generous(X0) <~> calm(X0)) | ~funny(X0)) [ennf transformation 22]
34. ! [X0] : ((~generous(X0) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | generous(X0))) [nnf transformation 2]
35. ! [X0] : ((~generous(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | generous(X0))) [flattening 34]
41. ! [X0] : (((~calm(X0) | generous(X0)) & (calm(X0) | ~generous(X0))) | ~funny(X0)) [nnf transformation 31]
59. generous(X0) | generous(X0) [cnf transformation 35]
79. calm(X0) | tall(X0) [cnf transformation 30]
80. calm(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 41]
104. funny(mary) | ~tall(mary) [cnf transformation 16]
109. ~calm(mary) [cnf transformation 20]
113. generous(X0) [duplicate literal removal 59]
156. ~funny(X0) | calm(X0) [subsumption resolution 80,113]
198. 18 <=> tall(mary) [avatar definition]
202. 19 <=> funny(mary) [avatar definition]
204. funny(mary) <- (19) [avatar component clause 202]
205. ~18 | 19 [avatar split clause 104,202,198]
234. tall(mary) [resolution 79,109]
238. 18 [avatar split clause 234,198]
243. calm(mary) <- (19) [resolution 156,204]
244. $false <- (19) [subsumption resolution 243,109]
245. ~19 [avatar contradiction clause 244]
246. $false [avatar sat refutation 205,238,245]
% SZS output end Proof for 6138171565134683036977794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not calm or not brave then someone is not strong and vice versa.
If someone is not curious or patient then fred is not wise.
Everyone who is generous is either not humble or not generous.
Everyone who is old is both rich and generous.
If john is not generous or not creative then someone is either not rich or funny.
If someone is either not patient or not rich then john is not kind.
Everyone who is humble or not old is both generous and curious.
Everyone who is humble or not generous is not rich or tall and vice versa.
Everyone who is calm or tall is either funny or calm and vice versa.
Everyone who is both not old and creative is both humble and old and vice versa.
Everyone who is either calm or happy is either strong or not brave and vice versa.
Everyone who is both calm and not quiet is not patient or quiet.
Everyone who is either happy or not curious is wise.
Everyone who is not wise is not tall or not wise.
Everyone who is either patient or not creative is both not patient and not generous and vice versa.
Everyone who is not funny or not patient is not generous or quiet and vice versa.
Someone is not creative.
Fred is not strong.
Someone is not curious or not brave.
Someone is either not happy or not humble.
Paul is not old or not happy.
Someone is either not kind or not calm.
Someone is not curious or kind. | Paul is creative. | neutral | (((~calm(mary)|~brave(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:((~curious(X)|patient(X))))=>(~wise(fred)))&
(![X]:(generous(X)=>(~humble(X)<~>~generous(X))))&
(![X]:(old(X)=>(rich(X)&generous(X))))&
(((~generous(john)|~creative(john)))=>(?[X]:((~rich(X)<~>funny(X)))))&
((?[X]:((~patient(X)<~>~rich(X))))=>(~kind(john)))&
(![X]:((humble(X)|~old(X))=>(generous(X)&curious(X))))&
(![X]:((humble(X)|~generous(X))<=>(~rich(X)|tall(X))))&
(![X]:((calm(X)|tall(X))<=>(funny(X)<~>calm(X))))&
(![X]:((~old(X)&creative(X))<=>(humble(X)&old(X))))&
(![X]:((calm(X)<~>happy(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((calm(X)&~quiet(X))=>(~patient(X)|quiet(X))))&
(![X]:((happy(X)<~>~curious(X))=>wise(X)))&
(![X]:(~wise(X)=>(~tall(X)|~wise(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~patient(X)&~generous(X))))&
(![X]:((~funny(X)|~patient(X))<=>(~generous(X)|quiet(X))))&
(?[X]:(~creative(X)))&
(~strong(fred))&
(?[X]:((~curious(X)|~brave(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
((~old(paul)|~happy(paul)))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((~curious(X)|kind(X)))) | creative(paul) | [] | null | 0 |
If mary is strong or not brave then mary is both not rich and quiet.
If someone is both tall and not generous then someone is either not strong or creative.
Everyone who is either not happy or calm is not creative.
If alice is both not happy and not funny then lucy is not strong or quiet and vice versa.
Everyone who is not curious or quiet is calm.
Everyone who is both brave and generous is not calm or quiet.
Everyone who is both not brave and happy is quiet and vice versa.
If someone is either curious or not wise then someone is not old or not tall.
If someone is either wise or strong then someone is not humble.
If alice is both not humble and brave then someone is both not happy and calm.
Everyone who is patient is either not quiet or strong and vice versa.
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Someone is not patient or brave.
Alice is wise or not quiet.
Someone is not creative.
Susan is funny or not rich.
Lucy is not creative or not funny.
Paul is not kind.
Someone is kind.
John is either curious or not brave. | Alice is funny. | neutral | (((strong(mary)|~brave(mary)))=>((~rich(mary)&quiet(mary))))&
((?[X]:((tall(X)&~generous(X))))=>(?[X]:((~strong(X)<~>creative(X)))))&
(![X]:((~happy(X)<~>calm(X))=>~creative(X)))&
(((~happy(alice)&~funny(alice)))<=>((~strong(lucy)|quiet(lucy))))&
(![X]:((~curious(X)|quiet(X))=>calm(X)))&
(![X]:((brave(X)&generous(X))=>(~calm(X)|quiet(X))))&
(![X]:((~brave(X)&happy(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>~wise(X))))=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:((wise(X)<~>strong(X))))=>(?[X]:(~humble(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(?[X]:((~patient(X)|brave(X))))&
((wise(alice)|~quiet(alice)))&
(?[X]:(~creative(X)))&
((funny(susan)|~rich(susan)))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john))) | funny(alice) | [] | null | 0 |
If lucy is both humble and brave then susan is either humble or not humble. If someone is both not quiet and not curious then paul is happy and vice versa. 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. If john is either not patient or kind then someone is not generous and vice versa. Everyone who is either not curious or not brave is either not old or not calm. If someone is either creative or not tall then someone is both old and not strong. Mary is not quiet. John is not creative or wise. Fred is either not funny or happy. Someone is either brave or not rich. Paul is not wise. Alice is either not rich or not strong. Someone is either not quiet or rich. | Lucy is quiet. | contradiction | (((humble(lucy)&brave(lucy)))=>((humble(susan)<~>~humble(susan))))&
((?[X]:((~quiet(X)&~curious(X))))<=>(happy(paul)))&
(((~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))))&
(((~patient(john)<~>kind(john)))<=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>~brave(X))=>(~old(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>~tall(X))))=>(?[X]:((old(X)&~strong(X)))))&
(~quiet(mary))&
((~creative(john)|wise(john)))&
((~funny(fred)<~>happy(fred)))&
(?[X]:((brave(X)<~>~rich(X))))&
(~wise(paul))&
((~rich(alice)<~>~strong(alice)))&
(?[X]:((~quiet(X)<~>rich(X)))) | quiet(lucy) | [
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3022598910256878385330346
% SZS output start Proof for 3022598910256878385330346
4. ! [X0] : ((curious(X0) <~> calm(X0)) <=> (curious(X0) & funny(X0))) [input p3]
7. ! [X0] : ((~tall(X0) & ~quiet(X0)) <=> (old(X0) | strong(X0))) [input p6]
12. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (strong(X0) <~> calm(X0))) [input p11]
24. quiet(lucy) [input hypothesis]
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))))) [nnf transformation 4]
41. ! [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 40]
42. ! [X0] : (((~tall(X0) & ~quiet(X0)) | (~old(X0) & ~strong(X0))) & ((old(X0) | strong(X0)) | (tall(X0) | quiet(X0)))) [nnf transformation 7]
43. ! [X0] : (((~tall(X0) & ~quiet(X0)) | (~old(X0) & ~strong(X0))) & (old(X0) | strong(X0) | tall(X0) | quiet(X0))) [flattening 42]
51. ! [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 12]
52. ! [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 51]
88. curious(X0) | curious(X0) | ~calm(X0) [cnf transformation 41]
95. ~strong(X0) | ~quiet(X0) [cnf transformation 43]
118. calm(X0) | strong(X0) | calm(X0) [cnf transformation 52]
123. ~curious(X0) | ~calm(X0) | strong(X0) | ~calm(X0) [cnf transformation 52]
152. quiet(lucy) [cnf transformation 24]
153. calm(X0) | strong(X0) [duplicate literal removal 118]
154. ~curious(X0) | ~calm(X0) | strong(X0) [duplicate literal removal 123]
155. curious(X0) | ~calm(X0) [duplicate literal removal 88]
176. 5 <=> quiet(lucy) [avatar definition]
177. quiet(lucy) <- (5) [avatar component clause 176]
213. ~calm(X0) | strong(X0) [subsumption resolution 154,155]
215. strong(X0) [subsumption resolution 153,213]
291. 5 [avatar split clause 152,176]
292. ~quiet(X0) [resolution 95,215]
293. $false <- (5) [resolution 292,177]
294. ~5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 291,294]
% SZS output end Proof for 3022598910256878385330346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny then someone is both not humble and curious and vice versa.
Everyone who is not curious is not generous or not kind.
If susan is not generous then alice is strong or rich and vice versa.
Everyone who is patient is creative and vice versa.
If susan is either not creative or creative then someone is not strong.
Everyone who is either not strong or not creative is not brave and vice versa.
Everyone who is wise or not calm is both not kind and patient and vice versa.
If paul is not happy then susan is either not brave or old.
Everyone who is creative or generous is both not old and not calm and vice versa.
If john is both not quiet and creative then john is calm and vice versa.
Everyone who is both not creative and not curious is both rich and patient and vice versa.
If someone is not wise or tall then someone is both not wise and not patient.
If john is either happy or quiet then someone is both calm and not calm.
If someone is both not strong and not happy then someone is both patient and creative and vice versa.
Everyone who is both funny and not old is both not brave and wise.
Everyone who is not funny or humble is not creative or not humble.
Someone is not calm.
Someone is either not brave or not wise.
Susan is curious or not generous.
Mary is humble.
Someone is both kind and happy.
Someone is not funny.
Someone is either not tall or tall.
Paul is not strong or strong. | Lucy is not tall. | neutral | ((funny(lucy))<=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
((~generous(susan))<=>((strong(alice)|rich(alice))))&
(![X]:(patient(X)<=>creative(X)))&
(((~creative(susan)<~>creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((wise(X)|~calm(X))<=>(~kind(X)&patient(X))))&
((~happy(paul))=>((~brave(susan)<~>old(susan))))&
(![X]:((creative(X)|generous(X))<=>(~old(X)&~calm(X))))&
(((~quiet(john)&creative(john)))<=>(calm(john)))&
(![X]:((~creative(X)&~curious(X))<=>(rich(X)&patient(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(((happy(john)<~>quiet(john)))=>(?[X]:((calm(X)&~calm(X)))))&
((?[X]:((~strong(X)&~happy(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((funny(X)&~old(X))=>(~brave(X)&wise(X))))&
(![X]:((~funny(X)|humble(X))=>(~creative(X)|~humble(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((curious(susan)|~generous(susan)))&
(humble(mary))&
(?[X]:((kind(X)&happy(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~tall(X)<~>tall(X))))&
((~strong(paul)|strong(paul))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either creative or quiet is not tall or wise and vice versa.
Everyone who is kind is both not funny and not strong.
Everyone who is not patient is not happy or humble.
If someone is not rich or strong then someone is both not calm and brave.
If paul is kind or not rich then someone is either not strong or not tall and vice versa.
Everyone who is kind is both not quiet and not creative and vice versa.
Everyone who is not humble is either rich or not tall and vice versa.
Everyone who is both creative and not creative is not creative or not humble and vice versa.
If paul is not quiet then alice is both not brave and not strong.
If mary is both not humble and calm then someone is either not rich or brave.
Everyone who is quiet or calm is either not calm or not quiet and vice versa.
If someone is either creative or not creative then lucy is rich or wise.
Everyone who is not wise is old or curious and vice versa.
If alice is not brave then someone is both generous and not generous and vice versa.
Everyone who is either quiet or tall is either not wise or generous and vice versa.
Everyone who is old or kind is both not tall and curious.
John is wise or not generous.
Susan is not strong.
Someone is either strong or not strong.
Susan is both not old and not patient.
Someone is not happy or not creative. | John is calm. | neutral | (![X]:((creative(X)<~>quiet(X))<=>(~tall(X)|wise(X))))&
(![X]:(kind(X)=>(~funny(X)&~strong(X))))&
(![X]:(~patient(X)=>(~happy(X)|humble(X))))&
((?[X]:((~rich(X)|strong(X))))=>(?[X]:((~calm(X)&brave(X)))))&
(((kind(paul)|~rich(paul)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:(kind(X)<=>(~quiet(X)&~creative(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>~tall(X))))&
(![X]:((creative(X)&~creative(X))<=>(~creative(X)|~humble(X))))&
((~quiet(paul))=>((~brave(alice)&~strong(alice))))&
(((~humble(mary)&calm(mary)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~calm(X)<~>~quiet(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>((rich(lucy)|wise(lucy))))&
(![X]:(~wise(X)<=>(old(X)|curious(X))))&
((~brave(alice))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((old(X)|kind(X))=>(~tall(X)&curious(X))))&
((wise(john)|~generous(john)))&
(~strong(susan))&
(?[X]:((strong(X)<~>~strong(X))))&
((~old(susan)&~patient(susan)))&
(?[X]:((~happy(X)|~creative(X)))) | calm(john) | [] | null | 0 |
Everyone who is funny is rich and vice versa.
Everyone who is either not creative or calm is patient or not rich.
Everyone who is either happy or curious is kind.
If alice is both kind and not kind then someone is patient or calm.
Everyone who is either brave or strong is both not rich and brave.
Everyone who is either generous or not patient is not creative or not wise and vice versa.
If lucy is not calm then someone is not wise.
If someone is calm then paul is both not strong and not happy.
Everyone who is brave or quiet is either not wise or not humble and vice versa.
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.
Someone is both strong and not happy.
Alice is both calm and not happy.
Someone is not strong or not humble.
Lucy is both not wise and old.
John is both creative and calm.
Someone is not funny.
Someone is not quiet. | Paul is not strong. | entailment | (![X]:(funny(X)<=>rich(X)))&
(![X]:((~creative(X)<~>calm(X))=>(patient(X)|~rich(X))))&
(![X]:((happy(X)<~>curious(X))=>kind(X)))&
(((kind(alice)&~kind(alice)))=>(?[X]:((patient(X)|calm(X)))))&
(![X]:((brave(X)<~>strong(X))=>(~rich(X)&brave(X))))&
(![X]:((generous(X)<~>~patient(X))<=>(~creative(X)|~wise(X))))&
((~calm(lucy))=>(?[X]:(~wise(X))))&
((?[X]:(calm(X)))=>((~strong(paul)&~happy(paul))))&
(![X]:((brave(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]:((strong(X)&~happy(X))))&
((calm(alice)&~happy(alice)))&
(?[X]:((~strong(X)|~humble(X))))&
((~wise(lucy)&old(lucy)))&
((creative(john)&calm(john)))&
(?[X]:(~funny(X)))&
(?[X]:(~quiet(X))) | ~strong(paul) | [
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 662930827963179983430850
% SZS output start Proof for 662930827963179983430850
8. ? [X0] : calm(X0) => (~happy(paul) & ~strong(paul)) [input p7]
18. ~happy(alice) & calm(alice) [input p17]
24. strong(paul) [input hypothesis]
34. (~happy(paul) & ~strong(paul)) | ! [X0] : ~calm(X0) [ennf transformation 8]
89. ~strong(paul) | ~calm(X0) [cnf transformation 34]
116. calm(alice) [cnf transformation 18]
125. strong(paul) [cnf transformation 24]
137. 3 <=> ! [X0] : ~calm(X0) [avatar definition]
138. ~calm(X0) <- (3) [avatar component clause 137]
145. 5 <=> strong(paul) [avatar definition]
148. 3 | ~5 [avatar split clause 89,145,137]
209. 5 [avatar split clause 125,145]
210. $false <- (3) [resolution 138,116]
213. ~3 [avatar contradiction clause 210]
214. $false [avatar sat refutation 148,209,213]
% SZS output end Proof for 662930827963179983430850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not funny then fred is brave. If someone is either calm or not rich then someone is both not curious and tall and vice versa. If someone is curious or not old then someone is either tall or not strong and vice versa. Everyone who is not kind is not brave or not curious. Everyone who is either curious or tall is either not tall or generous. Everyone who is patient is not old. If susan is not calm then lucy is tall and vice versa. If susan is not old or curious then someone is not quiet and vice versa. If someone is not creative or not curious then someone is either quiet or not calm and vice versa. Everyone who is either not patient or old is not happy. If someone is both happy and strong then someone is either patient or brave. Everyone who is either not wise or funny is not wise or not rich and vice versa. If fred is humble then someone is happy or curious. Everyone who is not brave is not creative and vice versa. If someone is both rich and curious then someone is not humble or humble. If lucy is not kind or not strong then someone is either not brave or not generous. John is either quiet or creative. John is calm or creative. Someone is not funny. Alice is not rich or not strong. Susan is both strong and not brave. Alice is not tall or not quiet. Someone is generous or kind. Someone is creative. | Lucy is strong. | neutral | ((?[X]:((~humble(X)|~funny(X))))=>(brave(fred)))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:((~curious(X)&tall(X)))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(~brave(X)|~curious(X))))&
(![X]:((curious(X)<~>tall(X))=>(~tall(X)<~>generous(X))))&
(![X]:(patient(X)=>~old(X)))&
((~calm(susan))<=>(tall(lucy)))&
(((~old(susan)|curious(susan)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~patient(X)<~>old(X))=>~happy(X)))&
((?[X]:((happy(X)&strong(X))))=>(?[X]:((patient(X)<~>brave(X)))))&
(![X]:((~wise(X)<~>funny(X))<=>(~wise(X)|~rich(X))))&
((humble(fred))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
((?[X]:((rich(X)&curious(X))))=>(?[X]:((~humble(X)|humble(X)))))&
(((~kind(lucy)|~strong(lucy)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
((quiet(john)<~>creative(john)))&
((calm(john)|creative(john)))&
(?[X]:(~funny(X)))&
((~rich(alice)|~strong(alice)))&
((strong(susan)&~brave(susan)))&
((~tall(alice)|~quiet(alice)))&
(?[X]:((generous(X)|kind(X))))&
(?[X]:(creative(X))) | strong(lucy) | [] | null | 0 |
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.
Everyone who is either not kind or patient is either not kind or rich and vice versa.
If john is quiet then paul is either rich or not funny.
Everyone who is either not quiet or humble is either creative or calm.
Everyone who is not patient is either not curious or curious.
Everyone who is both old and not humble is either not quiet or generous.
Everyone who is either not funny or not calm is either strong or creative.
If paul is both wise and strong then someone is tall.
Everyone who is brave is both not humble and curious and vice versa.
Everyone who is calm is both strong and funny and vice versa.
If alice is both creative and not patient then someone is wise.
Everyone who is not brave is calm and vice versa.
Everyone who is both not calm and not generous is either quiet or calm and vice versa.
John is wise.
Fred is tall.
Alice is both tall and old.
Someone is not strong or wise.
Paul is both not calm and not humble.
Lucy is not old or not humble.
Someone is both creative and quiet.
Someone is happy or generous. | Alice is not humble. | contradiction | (![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)))))&
(![X]:((~kind(X)<~>patient(X))<=>(~kind(X)<~>rich(X))))&
((quiet(john))=>((rich(paul)<~>~funny(paul))))&
(![X]:((~quiet(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>curious(X))))&
(![X]:((old(X)&~humble(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~calm(X))=>(strong(X)<~>creative(X))))&
(((wise(paul)&strong(paul)))=>(?[X]:(tall(X))))&
(![X]:(brave(X)<=>(~humble(X)&curious(X))))&
(![X]:(calm(X)<=>(strong(X)&funny(X))))&
(((creative(alice)&~patient(alice)))=>(?[X]:(wise(X))))&
(![X]:(~brave(X)<=>calm(X)))&
(![X]:((~calm(X)&~generous(X))<=>(quiet(X)<~>calm(X))))&
(wise(john))&
(tall(fred))&
((tall(alice)&old(alice)))&
(?[X]:((~strong(X)|wise(X))))&
((~calm(paul)&~humble(paul)))&
((~old(lucy)|~humble(lucy)))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:((happy(X)|generous(X)))) | ~humble(alice) | [
"p0",
"p8",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3421656829398357520499308
% SZS output start Proof for 3421656829398357520499308
1. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (humble(X0) & ~calm(X0))) [input p0]
9. ! [X0] : ((~humble(X0) & old(X0)) => (~quiet(X0) <~> generous(X0))) [input p8]
13. ! [X0] : (calm(X0) <=> (funny(X0) & strong(X0))) [input p12]
16. ! [X0] : ((~generous(X0) & ~calm(X0)) <=> (quiet(X0) <~> calm(X0))) [input p15]
19. old(alice) & tall(alice) [input p18]
25. ~humble(alice) [input hypothesis]
29. old(alice) [pure predicate removal 19]
34. ! [X0] : ((~quiet(X0) <~> generous(X0)) | (humble(X0) | ~old(X0))) [ennf transformation 9]
35. ! [X0] : ((~quiet(X0) <~> generous(X0)) | humble(X0) | ~old(X0)) [flattening 34]
39. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 1]
40. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 39]
55. ! [X0] : (((~generous(X0) | quiet(X0)) & (generous(X0) | ~quiet(X0))) | humble(X0) | ~old(X0)) [nnf transformation 35]
59. ! [X0] : ((calm(X0) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ~calm(X0))) [nnf transformation 13]
60. ! [X0] : ((calm(X0) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ~calm(X0))) [flattening 59]
64. ! [X0] : (((~generous(X0) & ~calm(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (generous(X0) | calm(X0)))) [nnf transformation 16]
65. ! [X0] : (((~generous(X0) & ~calm(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | generous(X0) | calm(X0))) [flattening 64]
75. humble(X0) | ~strong(X0) | humble(X0) [cnf transformation 40]
105. ~old(X0) | ~quiet(X0) | humble(X0) | generous(X0) [cnf transformation 55]
106. ~old(X0) | quiet(X0) | humble(X0) | ~generous(X0) [cnf transformation 55]
114. ~calm(X0) | strong(X0) [cnf transformation 60]
120. calm(X0) | quiet(X0) | generous(X0) | calm(X0) [cnf transformation 65]
123. ~calm(X0) | quiet(X0) | ~calm(X0) [cnf transformation 65]
124. ~generous(X0) | calm(X0) | ~quiet(X0) [cnf transformation 65]
127. old(alice) [cnf transformation 29]
135. ~humble(alice) [cnf transformation 25]
136. calm(X0) | quiet(X0) | generous(X0) [duplicate literal removal 120]
137. ~calm(X0) | quiet(X0) [duplicate literal removal 123]
142. ~strong(X0) | humble(X0) [duplicate literal removal 75]
229. generous(X0) | quiet(X0) [subsumption resolution 136,137]
346. ~quiet(alice) | humble(alice) | generous(alice) [resolution 105,127]
353. quiet(alice) | humble(alice) | ~generous(alice) [resolution 106,127]
364. quiet(alice) | ~generous(alice) [subsumption resolution 353,135]
365. quiet(alice) [subsumption resolution 364,229]
366. humble(alice) | generous(alice) [subsumption resolution 346,365]
367. generous(alice) [subsumption resolution 366,135]
394. calm(alice) | ~quiet(alice) [resolution 367,124]
395. calm(alice) [subsumption resolution 394,365]
418. strong(alice) [resolution 395,114]
421. humble(alice) [resolution 418,142]
422. $false [subsumption resolution 421,135]
% SZS output end Proof for 3421656829398357520499308
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious or kind then mary is not strong and vice versa.
If fred is quiet then someone is either calm or creative.
Everyone who is old or not happy is kind.
Everyone who is strong is either quiet or old and vice versa.
If john is both not patient and creative then someone is both not kind and wise.
If fred is not brave or strong then susan is both not generous and not tall.
If john is both not funny and curious then lucy is old or kind.
If someone is calm or kind then susan is either not brave or not humble.
Everyone who is rich or not wise is creative and vice versa.
Everyone who is old is either not wise or kind.
Everyone who is rich is generous or not humble and vice versa.
Everyone who is either tall or not generous is either not patient or calm and vice versa.
Everyone who is both rich and strong is both happy and wise.
If susan is rich or brave then someone is both generous and calm.
If someone is either not funny or not creative then paul is both not creative and strong and vice versa.
Everyone who is either not curious or quiet is either quiet or not patient and vice versa.
Fred is kind.
Susan is not kind or not calm.
Someone is both creative and generous.
Mary is both not tall and rich.
Lucy is both patient and quiet.
Someone is both not strong and not wise.
Lucy is not funny or not calm.
Someone is not generous. | Susan is humble. | neutral | (((curious(susan)|kind(susan)))<=>(~strong(mary)))&
((quiet(fred))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((old(X)|~happy(X))=>kind(X)))&
(![X]:(strong(X)<=>(quiet(X)<~>old(X))))&
(((~patient(john)&creative(john)))=>(?[X]:((~kind(X)&wise(X)))))&
(((~brave(fred)|strong(fred)))=>((~generous(susan)&~tall(susan))))&
(((~funny(john)&curious(john)))=>((old(lucy)|kind(lucy))))&
((?[X]:((calm(X)|kind(X))))=>((~brave(susan)<~>~humble(susan))))&
(![X]:((rich(X)|~wise(X))<=>creative(X)))&
(![X]:(old(X)=>(~wise(X)<~>kind(X))))&
(![X]:(rich(X)<=>(generous(X)|~humble(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((rich(X)&strong(X))=>(happy(X)&wise(X))))&
(((rich(susan)|brave(susan)))=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((~creative(paul)&strong(paul))))&
(![X]:((~curious(X)<~>quiet(X))<=>(quiet(X)<~>~patient(X))))&
(kind(fred))&
((~kind(susan)|~calm(susan)))&
(?[X]:((creative(X)&generous(X))))&
((~tall(mary)&rich(mary)))&
((patient(lucy)&quiet(lucy)))&
(?[X]:((~strong(X)&~wise(X))))&
((~funny(lucy)|~calm(lucy)))&
(?[X]:(~generous(X))) | humble(susan) | [] | null | 0 |
Everyone who is either creative or not tall is not humble or calm and vice versa.
If someone is either curious or tall then someone is not strong or humble and vice versa.
If someone is either curious or creative then paul is either not funny or not brave.
If susan is both patient and not brave then someone is not funny or not brave and vice versa.
Everyone who is not calm or creative is both humble and tall.
If someone is either not patient or funny then lucy is quiet or not funny and vice versa.
If someone is calm then fred is wise or not funny.
Everyone who is both brave and not curious is both not calm and not happy.
Everyone who is strong or humble is either quiet or not old.
If paul is both old and not happy then someone is either funny or patient and vice versa.
Everyone who is either not wise or calm is not humble or tall.
If lucy is either not tall or not humble then someone is not brave and vice versa.
Everyone who is either quiet or generous is either not old or not tall.
Everyone who is not kind is not quiet or curious.
Everyone who is not rich or not creative is generous or not quiet.
Everyone who is old or not old is both not wise and not kind and vice versa.
Someone is either not calm or not curious.
Someone is not kind or wise.
Mary is both not strong and generous.
Mary is calm.
Paul is both not patient and not generous.
Paul is tall. | Lucy is not creative. | entailment | (![X]:((creative(X)<~>~tall(X))<=>(~humble(X)|calm(X))))&
((?[X]:((curious(X)<~>tall(X))))<=>(?[X]:((~strong(X)|humble(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>((~funny(paul)<~>~brave(paul))))&
(((patient(susan)&~brave(susan)))<=>(?[X]:((~funny(X)|~brave(X)))))&
(![X]:((~calm(X)|creative(X))=>(humble(X)&tall(X))))&
((?[X]:((~patient(X)<~>funny(X))))<=>((quiet(lucy)|~funny(lucy))))&
((?[X]:(calm(X)))=>((wise(fred)|~funny(fred))))&
(![X]:((brave(X)&~curious(X))=>(~calm(X)&~happy(X))))&
(![X]:((strong(X)|humble(X))=>(quiet(X)<~>~old(X))))&
(((old(paul)&~happy(paul)))<=>(?[X]:((funny(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>calm(X))=>(~humble(X)|tall(X))))&
(((~tall(lucy)<~>~humble(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~old(X)<~>~tall(X))))&
(![X]:(~kind(X)=>(~quiet(X)|curious(X))))&
(![X]:((~rich(X)|~creative(X))=>(generous(X)|~quiet(X))))&
(![X]:((old(X)|~old(X))<=>(~wise(X)&~kind(X))))&
(?[X]:((~calm(X)<~>~curious(X))))&
(?[X]:((~kind(X)|wise(X))))&
((~strong(mary)&generous(mary)))&
(calm(mary))&
((~patient(paul)&~generous(paul)))&
(tall(paul)) | ~creative(lucy) | [
"p3",
"p4",
"p6",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4044452030238898362963163
% SZS output start Proof for 4044452030238898362963163
4. (~brave(susan) & patient(susan)) <=> ? [X0] : (~brave(X0) | ~funny(X0)) [input p3]
5. ! [X0] : ((creative(X0) | ~calm(X0)) => (tall(X0) & humble(X0))) [input p4]
7. ? [X0] : calm(X0) => (~funny(fred) | wise(fred)) [input p6]
12. (~tall(lucy) <~> ~humble(lucy)) <=> ? [X0] : ~brave(X0) [input p11]
16. ! [X0] : ((~old(X0) | old(X0)) <=> (~kind(X0) & ~wise(X0))) [input p15]
20. calm(mary) [input p19]
23. creative(lucy) [input hypothesis]
27. ! [X0] : ((tall(X0) & humble(X0)) | (~creative(X0) & calm(X0))) [ennf transformation 5]
28. (~funny(fred) | wise(fred)) | ! [X0] : ~calm(X0) [ennf transformation 7]
29. ~funny(fred) | wise(fred) | ! [X0] : ~calm(X0) [flattening 28]
48. ((~brave(susan) & patient(susan)) | ! [X0] : (brave(X0) & funny(X0))) & (? [X0] : (~brave(X0) | ~funny(X0)) | (brave(susan) | ~patient(susan))) [nnf transformation 4]
49. ((~brave(susan) & patient(susan)) | ! [X0] : (brave(X0) & funny(X0))) & (? [X0] : (~brave(X0) | ~funny(X0)) | brave(susan) | ~patient(susan)) [flattening 48]
50. ((~brave(susan) & patient(susan)) | ! [X0] : (brave(X0) & funny(X0))) & (? [X1] : (~brave(X1) | ~funny(X1)) | brave(susan) | ~patient(susan)) [rectify 49]
51. ? [X1] : (~brave(X1) | ~funny(X1)) => (~brave(sK2) | ~funny(sK2)) [choice axiom]
52. ((~brave(susan) & patient(susan)) | ! [X0] : (brave(X0) & funny(X0))) & ((~brave(sK2) | ~funny(sK2)) | brave(susan) | ~patient(susan)) [skolemisation 50,51]
65. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [nnf transformation 12]
66. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [rectify 65]
67. ? [X1] : ~brave(X1) => ~brave(sK5) [choice axiom]
68. (((humble(lucy) | tall(lucy)) & (~humble(lucy) | ~tall(lucy))) | ! [X0] : brave(X0)) & (~brave(sK5) | ((~tall(lucy) | humble(lucy)) & (~humble(lucy) | tall(lucy)))) [skolemisation 66,67]
70. ! [X0] : (((~old(X0) | old(X0)) | (kind(X0) | wise(X0))) & ((~kind(X0) & ~wise(X0)) | (old(X0) & ~old(X0)))) [nnf transformation 16]
71. ! [X0] : ((~old(X0) | old(X0) | kind(X0) | wise(X0)) & ((~kind(X0) & ~wise(X0)) | (old(X0) & ~old(X0)))) [flattening 70]
96. ~brave(susan) | funny(X0) [cnf transformation 52]
99. ~creative(X0) | humble(X0) [cnf transformation 27]
101. ~creative(X0) | tall(X0) [cnf transformation 27]
108. ~funny(fred) | wise(fred) | ~calm(X0) [cnf transformation 29]
125. ~humble(lucy) | ~tall(lucy) | brave(X0) [cnf transformation 68]
133. ~wise(X0) | ~old(X0) [cnf transformation 71]
134. ~wise(X0) | old(X0) [cnf transformation 71]
143. calm(mary) [cnf transformation 20]
147. creative(lucy) [cnf transformation 23]
201. 13 <=> ! [X0] : brave(X0) [avatar definition]
202. brave(X0) <- (13) [avatar component clause 201]
204. 14 <=> brave(susan) [avatar definition]
206. ~brave(susan) <- (~14) [avatar component clause 204]
209. 15 <=> ! [X0] : funny(X0) [avatar definition]
210. funny(X0) <- (15) [avatar component clause 209]
211. 15 | ~14 [avatar split clause 96,204,209]
256. 25 <=> ! [X0] : ~calm(X0) [avatar definition]
257. ~calm(X0) <- (25) [avatar component clause 256]
259. 26 <=> wise(fred) [avatar definition]
261. wise(fred) <- (26) [avatar component clause 259]
263. 27 <=> funny(fred) [avatar definition]
265. ~funny(fred) <- (~27) [avatar component clause 263]
266. 25 | 26 | ~27 [avatar split clause 108,263,259,256]
297. 34 <=> tall(lucy) [avatar definition]
298. ~tall(lucy) <- (~34) [avatar component clause 297]
301. 35 <=> humble(lucy) [avatar definition]
305. 13 | ~34 | ~35 [avatar split clause 125,301,297,201]
313. ~wise(X0) [subsumption resolution 133,134]
332. $false <- (13, ~14) [subsumption resolution 206,202]
333. ~13 | 14 [avatar contradiction clause 332]
339. $false <- (15, ~27) [resolution 265,210]
340. ~15 | 27 [avatar contradiction clause 339]
341. $false <- (25) [resolution 257,143]
342. ~25 [avatar contradiction clause 341]
343. $false <- (26) [subsumption resolution 261,313]
344. ~26 [avatar contradiction clause 343]
351. humble(lucy) [resolution 99,147]
354. 35 [avatar split clause 351,301]
355. tall(lucy) [resolution 101,147]
356. $false <- (~34) [subsumption resolution 355,298]
357. 34 [avatar contradiction clause 356]
358. $false [avatar sat refutation 211,266,305,333,340,342,344,354,357]
% SZS output end Proof for 4044452030238898362963163
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both not old and not patient is either quiet or not old.
If someone is not funny or old then someone is either curious or rich.
If alice is both old and rich then lucy is not rich and vice versa.
Everyone who is both not patient and not rich is either creative or humble and vice versa.
Everyone who is funny or generous is both not strong and not kind.
If paul is either not old or not rich then paul is not creative and vice versa.
Everyone who is not old is both rich and patient and vice versa.
Everyone who is not calm is happy and vice versa.
Everyone who is both not patient and not happy is both not funny and quiet and vice versa.
Everyone who is calm is both not old and not kind and vice versa.
If john is both not kind and creative then lucy is both brave and creative and vice versa.
If lucy is not wise then paul is quiet.
Everyone who is old is either not old or quiet.
Everyone who is happy or calm is both creative and not wise.
If someone is not rich then john is both not kind and not quiet and vice versa.
Lucy is either not patient or strong.
Susan is either not curious or not funny.
Susan is either tall or not old.
Someone is quiet or not rich.
Susan is not rich.
Someone is not creative or quiet.
Someone is wise or not generous. | Paul is not rich. | contradiction | (![X]:((~old(X)&~patient(X))=>(quiet(X)<~>~old(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((curious(X)<~>rich(X)))))&
(((old(alice)&rich(alice)))<=>(~rich(lucy)))&
(![X]:((~patient(X)&~rich(X))<=>(creative(X)<~>humble(X))))&
(![X]:((funny(X)|generous(X))=>(~strong(X)&~kind(X))))&
(((~old(paul)<~>~rich(paul)))<=>(~creative(paul)))&
(![X]:(~old(X)<=>(rich(X)&patient(X))))&
(![X]:(~calm(X)<=>happy(X)))&
(![X]:((~patient(X)&~happy(X))<=>(~funny(X)&quiet(X))))&
(![X]:(calm(X)<=>(~old(X)&~kind(X))))&
(((~kind(john)&creative(john)))<=>((brave(lucy)&creative(lucy))))&
((~wise(lucy))=>(quiet(paul)))&
(![X]:(old(X)=>(~old(X)<~>quiet(X))))&
(![X]:((happy(X)|calm(X))=>(creative(X)&~wise(X))))&
((?[X]:(~rich(X)))<=>((~kind(john)&~quiet(john))))&
((~patient(lucy)<~>strong(lucy)))&
((~curious(susan)<~>~funny(susan)))&
((tall(susan)<~>~old(susan)))&
(?[X]:((quiet(X)|~rich(X))))&
(~rich(susan))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:((wise(X)|~generous(X)))) | ~rich(paul) | [
"p5",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3367386238249716049784677
% SZS output start Proof for 3367386238249716049784677
6. (~old(paul) <~> ~rich(paul)) <=> ~creative(paul) [input p5]
7. ! [X0] : (~old(X0) <=> (patient(X0) & rich(X0))) [input p6]
8. ! [X0] : (~calm(X0) <=> happy(X0)) [input p7]
14. ! [X0] : ((calm(X0) | happy(X0)) => (~wise(X0) & creative(X0))) [input p13]
23. ~rich(paul) [input hypothesis]
33. ! [X0] : ((~wise(X0) & creative(X0)) | (~calm(X0) & ~happy(X0))) [ennf transformation 14]
43. (((rich(paul) | old(paul)) & (~rich(paul) | ~old(paul))) | creative(paul)) & (~creative(paul) | ((~old(paul) | rich(paul)) & (~rich(paul) | old(paul)))) [nnf transformation 6]
44. ! [X0] : ((~old(X0) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | old(X0))) [nnf transformation 7]
45. ! [X0] : ((~old(X0) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | old(X0))) [flattening 44]
46. ! [X0] : ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))) [nnf transformation 8]
84. ~creative(paul) | ~old(paul) | rich(paul) [cnf transformation 43]
87. rich(X0) | old(X0) [cnf transformation 45]
90. happy(X0) | calm(X0) [cnf transformation 46]
106. ~happy(X0) | creative(X0) [cnf transformation 33]
107. ~calm(X0) | creative(X0) [cnf transformation 33]
122. ~rich(paul) [cnf transformation 23]
159. 8 <=> creative(paul) [avatar definition]
160. ~creative(paul) <- (~8) [avatar component clause 159]
163. 9 <=> old(paul) [avatar definition]
167. 10 <=> rich(paul) [avatar definition]
168. ~rich(paul) <- (~10) [avatar component clause 167]
172. 10 | ~9 | ~8 [avatar split clause 84,159,163,167]
265. ~10 [avatar split clause 122,167]
266. old(paul) <- (~10) [resolution 87,168]
275. 9 | 10 [avatar split clause 266,167,163]
279. creative(X0) | calm(X0) [resolution 106,90]
280. creative(X0) [subsumption resolution 279,107]
283. $false <- (~8) [resolution 280,160]
284. 8 [avatar contradiction clause 283]
287. $false [avatar sat refutation 172,265,275,284]
% SZS output end Proof for 3367386238249716049784677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either not funny or tall and vice versa. If someone is not humble or strong then susan is rich or kind and vice versa. Everyone who is rich is both not happy and kind and vice versa. If someone is old then fred is funny. Everyone who is not patient is not kind or curious. If someone is creative then someone is either not kind or humble. If john is both patient and not happy then lucy is either quiet or not strong. If susan is strong then susan is calm. If john is kind then paul is either not humble or not kind and vice versa. If someone is either creative or not generous then someone is not rich. If paul is either not strong or quiet then susan is either quiet or not generous. If paul is either not generous or not humble then someone is creative. If someone is humble or calm then someone is strong and vice versa. Everyone who is not wise is either not happy or calm. If susan is both not humble and not quiet then someone is quiet or not old and vice versa. If lucy is not patient then someone is not tall. Susan is quiet or creative. Alice is either not kind or not curious. Someone is not funny or not old. Someone is either not patient or not funny. Mary is either not strong or old. Someone is either not curious or not creative. Someone is creative or not strong. Mary is both generous and strong. | Susan is creative. | entailment | (![X]:(~curious(X)<=>(~funny(X)<~>tall(X))))&
((?[X]:((~humble(X)|strong(X))))<=>((rich(susan)|kind(susan))))&
(![X]:(rich(X)<=>(~happy(X)&kind(X))))&
((?[X]:(old(X)))=>(funny(fred)))&
(![X]:(~patient(X)=>(~kind(X)|curious(X))))&
((?[X]:(creative(X)))=>(?[X]:((~kind(X)<~>humble(X)))))&
(((patient(john)&~happy(john)))=>((quiet(lucy)<~>~strong(lucy))))&
((strong(susan))=>(calm(susan)))&
((kind(john))<=>((~humble(paul)<~>~kind(paul))))&
((?[X]:((creative(X)<~>~generous(X))))=>(?[X]:(~rich(X))))&
(((~strong(paul)<~>quiet(paul)))=>((quiet(susan)<~>~generous(susan))))&
(((~generous(paul)<~>~humble(paul)))=>(?[X]:(creative(X))))&
((?[X]:((humble(X)|calm(X))))<=>(?[X]:(strong(X))))&
(![X]:(~wise(X)=>(~happy(X)<~>calm(X))))&
(((~humble(susan)&~quiet(susan)))<=>(?[X]:((quiet(X)|~old(X)))))&
((~patient(lucy))=>(?[X]:(~tall(X))))&
((quiet(susan)|creative(susan)))&
((~kind(alice)<~>~curious(alice)))&
(?[X]:((~funny(X)|~old(X))))&
(?[X]:((~patient(X)<~>~funny(X))))&
((~strong(mary)<~>old(mary)))&
(?[X]:((~curious(X)<~>~creative(X))))&
(?[X]:((creative(X)|~strong(X))))&
((generous(mary)&strong(mary))) | creative(susan) | [
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2893749552913481952517412
% SZS output start Proof for 2893749552913481952517412
15. (~quiet(susan) & ~humble(susan)) <=> ? [X0] : (~old(X0) | quiet(X0)) [input p14]
17. creative(susan) | quiet(susan) [input p16]
25. ~creative(susan) [input hypothesis]
68. ((~quiet(susan) & ~humble(susan)) | ! [X0] : (old(X0) & ~quiet(X0))) & (? [X0] : (~old(X0) | quiet(X0)) | (quiet(susan) | humble(susan))) [nnf transformation 15]
69. ((~quiet(susan) & ~humble(susan)) | ! [X0] : (old(X0) & ~quiet(X0))) & (? [X0] : (~old(X0) | quiet(X0)) | quiet(susan) | humble(susan)) [flattening 68]
70. ((~quiet(susan) & ~humble(susan)) | ! [X0] : (old(X0) & ~quiet(X0))) & (? [X1] : (~old(X1) | quiet(X1)) | quiet(susan) | humble(susan)) [rectify 69]
71. ? [X1] : (~old(X1) | quiet(X1)) => (~old(sK6) | quiet(sK6)) [choice axiom]
72. ((~quiet(susan) & ~humble(susan)) | ! [X0] : (old(X0) & ~quiet(X0))) & ((~old(sK6) | quiet(sK6)) | quiet(susan) | humble(susan)) [skolemisation 70,71]
123. ~quiet(susan) | ~quiet(X0) [cnf transformation 72]
126. creative(susan) | quiet(susan) [cnf transformation 17]
139. ~creative(susan) [cnf transformation 25]
251. 26 <=> quiet(susan) [avatar definition]
252. quiet(susan) <- (26) [avatar component clause 251]
298. 36 <=> ! [X0] : ~quiet(X0) [avatar definition]
299. ~quiet(X0) <- (36) [avatar component clause 298]
300. 36 | ~26 [avatar split clause 123,251,298]
326. 42 <=> creative(susan) [avatar definition]
329. 26 | 42 [avatar split clause 126,326,251]
389. ~42 [avatar split clause 139,326]
390. $false <- (26, 36) [subsumption resolution 252,299]
391. ~26 | ~36 [avatar contradiction clause 390]
396. $false [avatar sat refutation 300,329,389,391]
% SZS output end Proof for 2893749552913481952517412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then john is not calm or strong and vice versa.
If paul is not happy or not curious then someone is kind.
If lucy is patient then someone is not curious.
If someone is both brave and happy then fred is not old.
If alice is funny then john is both funny and not kind.
Everyone who is curious or not happy is wise and vice versa.
Everyone who is not wise is not generous or calm and vice versa.
Everyone who is brave is generous or wise.
Everyone who is not creative or not patient is either not old or not humble.
Everyone who is either generous or creative is not happy or funny and vice versa.
If susan is either not funny or strong then someone is either funny or not generous.
If someone is both curious and not happy then lucy is either not creative or kind and vice versa.
If someone is curious then someone is either not calm or kind and vice versa.
Everyone who is not creative is both not wise and not quiet and vice versa.
If someone is not quiet then susan is not humble and vice versa.
If alice is either not generous or calm then alice is creative and vice versa.
Lucy is humble.
Alice is tall.
Someone is quiet.
Someone is wise or not calm.
Fred is not wise.
Someone is either brave or calm. | Lucy is creative. | neutral | ((?[X]:(~rich(X)))<=>((~calm(john)|strong(john))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:(kind(X))))&
((patient(lucy))=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)&happy(X))))=>(~old(fred)))&
((funny(alice))=>((funny(john)&~kind(john))))&
(![X]:((curious(X)|~happy(X))<=>wise(X)))&
(![X]:(~wise(X)<=>(~generous(X)|calm(X))))&
(![X]:(brave(X)=>(generous(X)|wise(X))))&
(![X]:((~creative(X)|~patient(X))=>(~old(X)<~>~humble(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~happy(X)|funny(X))))&
(((~funny(susan)<~>strong(susan)))=>(?[X]:((funny(X)<~>~generous(X)))))&
((?[X]:((curious(X)&~happy(X))))<=>((~creative(lucy)<~>kind(lucy))))&
((?[X]:(curious(X)))<=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:(~creative(X)<=>(~wise(X)&~quiet(X))))&
((?[X]:(~quiet(X)))<=>(~humble(susan)))&
(((~generous(alice)<~>calm(alice)))<=>(creative(alice)))&
(humble(lucy))&
(tall(alice))&
(?[X]:(quiet(X)))&
(?[X]:((wise(X)|~calm(X))))&
(~wise(fred))&
(?[X]:((brave(X)<~>calm(X)))) | creative(lucy) | [] | null | 0 |
If someone is humble or curious then john is either calm or creative and vice versa.
If someone is either not strong or tall then someone is rich or happy.
Everyone who is not tall is generous.
If mary is humble then susan is quiet or calm and vice versa.
Everyone who is either not curious or quiet is either happy or tall and vice versa.
Everyone who is both funny and rich is kind or old.
If someone is not quiet then someone is both funny and not funny and vice versa.
If someone is either happy or not calm then mary is either wise or happy and vice versa.
Everyone who is not quiet or strong is either generous or not tall and vice versa.
Everyone who is patient is not tall.
If paul is not wise then someone is quiet or happy and vice versa.
Everyone who is rich or humble is either curious or not wise.
Everyone who is either not quiet or not kind is not calm or happy.
Everyone who is both rich and creative is not humble or generous and vice versa.
If someone is not humble or calm then someone is not quiet.
Everyone who is happy or not tall is either patient or not rich and vice versa.
John is either not quiet or strong.
Someone is not wise.
Someone is either creative or not tall.
Lucy is either creative or curious.
Someone is either quiet or calm.
Alice is either strong or generous. | Paul is not strong. | entailment | ((?[X]:((humble(X)|curious(X))))<=>((calm(john)<~>creative(john))))&
((?[X]:((~strong(X)<~>tall(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:(~tall(X)=>generous(X)))&
((humble(mary))<=>((quiet(susan)|calm(susan))))&
(![X]:((~curious(X)<~>quiet(X))<=>(happy(X)<~>tall(X))))&
(![X]:((funny(X)&rich(X))=>(kind(X)|old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((funny(X)&~funny(X)))))&
((?[X]:((happy(X)<~>~calm(X))))<=>((wise(mary)<~>happy(mary))))&
(![X]:((~quiet(X)|strong(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(patient(X)=>~tall(X)))&
((~wise(paul))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((rich(X)|humble(X))=>(curious(X)<~>~wise(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~calm(X)|happy(X))))&
(![X]:((rich(X)&creative(X))<=>(~humble(X)|generous(X))))&
((?[X]:((~humble(X)|calm(X))))=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)|~tall(X))<=>(patient(X)<~>~rich(X))))&
((~quiet(john)<~>strong(john)))&
(?[X]:(~wise(X)))&
(?[X]:((creative(X)<~>~tall(X))))&
((creative(lucy)<~>curious(lucy)))&
(?[X]:((quiet(X)<~>calm(X))))&
((strong(alice)<~>generous(alice))) | ~strong(paul) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1167955587805535221406678
% SZS output start Proof for 1167955587805535221406678
3. ! [X0] : (~tall(X0) => generous(X0)) [input p2]
5. ! [X0] : ((~curious(X0) <~> quiet(X0)) <=> (happy(X0) <~> tall(X0))) [input p4]
7. ? [X0] : ~quiet(X0) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p6]
9. ! [X0] : ((strong(X0) | ~quiet(X0)) <=> (generous(X0) <~> ~tall(X0))) [input p8]
10. ! [X0] : (patient(X0) => ~tall(X0)) [input p9]
11. ~wise(paul) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p10]
12. ! [X0] : ((humble(X0) | rich(X0)) => (curious(X0) <~> ~wise(X0))) [input p11]
14. ! [X0] : ((creative(X0) & rich(X0)) <=> (generous(X0) | ~humble(X0))) [input p13]
16. ! [X0] : ((~tall(X0) | happy(X0)) <=> (patient(X0) <~> ~rich(X0))) [input p15]
23. strong(paul) [input hypothesis]
25. ? [X0] : ~quiet(X0) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 7]
29. ! [X0] : (generous(X0) | tall(X0)) [ennf transformation 3]
30. ! [X0] : (~tall(X0) | ~patient(X0)) [ennf transformation 10]
31. ! [X0] : ((curious(X0) <~> ~wise(X0)) | (~humble(X0) & ~rich(X0))) [ennf transformation 12]
45. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) & (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [nnf transformation 5]
46. (? [X0] : ~quiet(X0) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : quiet(X0)) [nnf transformation 25]
47. (? [X0] : ~quiet(X0) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : quiet(X3)) [rectify 46]
48. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
49. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK3) & funny(sK3)) [choice axiom]
50. (~quiet(sK2) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK3) & funny(sK3)) | ! [X3] : quiet(X3)) [skolemisation 47,49,48]
55. ! [X0] : (((strong(X0) | ~quiet(X0)) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (~strong(X0) & quiet(X0)))) [nnf transformation 9]
56. ! [X0] : ((strong(X0) | ~quiet(X0) | ((generous(X0) | tall(X0)) & (~tall(X0) | ~generous(X0)))) & (((tall(X0) | ~generous(X0)) & (~tall(X0) | generous(X0))) | (~strong(X0) & quiet(X0)))) [flattening 55]
57. (~wise(paul) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | wise(paul)) [nnf transformation 11]
58. (~wise(paul) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | wise(paul)) [rectify 57]
59. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK5) | quiet(sK5)) [choice axiom]
60. (~wise(paul) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK5) | quiet(sK5)) | wise(paul)) [skolemisation 58,59]
61. ! [X0] : (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | (~humble(X0) & ~rich(X0))) [nnf transformation 31]
63. ! [X0] : (((creative(X0) & rich(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (~creative(X0) | ~rich(X0)))) [nnf transformation 14]
64. ! [X0] : (((creative(X0) & rich(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ~creative(X0) | ~rich(X0))) [flattening 63]
68. ! [X0] : (((~tall(X0) | happy(X0)) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (tall(X0) & ~happy(X0)))) [nnf transformation 16]
69. ! [X0] : ((~tall(X0) | happy(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | (tall(X0) & ~happy(X0)))) [flattening 68]
89. generous(X0) | tall(X0) [cnf transformation 29]
100. ~quiet(X0) | curious(X0) | happy(X0) | ~tall(X0) [cnf transformation 45]
101. funny(sK3) | quiet(X3) [cnf transformation 50]
102. ~funny(sK3) | quiet(X3) [cnf transformation 50]
113. ~tall(X0) | generous(X0) | ~strong(X0) [cnf transformation 56]
115. tall(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 56]
118. ~patient(X0) | ~tall(X0) [cnf transformation 30]
120. ~wise(paul) | ~quiet(X0) [cnf transformation 60]
124. ~rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 61]
130. ~generous(X0) | rich(X0) [cnf transformation 64]
135. ~happy(X0) | patient(X0) | ~rich(X0) [cnf transformation 69]
152. strong(paul) [cnf transformation 23]
213. 14 <=> ! [X3] : quiet(X3) [avatar definition]
214. quiet(X3) <- (14) [avatar component clause 213]
216. 15 <=> funny(sK3) [avatar definition]
219. 14 | ~15 [avatar split clause 102,216,213]
220. 14 | 15 [avatar split clause 101,216,213]
251. ~strong(X0) | tall(X0) [subsumption resolution 115,89]
253. ~strong(X0) | generous(X0) [subsumption resolution 113,89]
259. 23 <=> wise(paul) [avatar definition]
261. ~wise(paul) <- (~23) [avatar component clause 259]
264. 24 <=> ! [X0] : ~quiet(X0) [avatar definition]
265. ~quiet(X0) <- (24) [avatar component clause 264]
266. 24 | ~23 [avatar split clause 120,259,264]
334. $false <- (14, 24) [subsumption resolution 214,265]
335. ~14 | ~24 [avatar contradiction clause 334]
349. tall(paul) [resolution 251,152]
351. generous(paul) [resolution 253,152]
354. rich(paul) [resolution 351,130]
393. ~curious(paul) | wise(paul) [resolution 354,124]
394. ~curious(paul) <- (~23) [subsumption resolution 393,261]
525. ~tall(X3) | happy(X3) | curious(X3) <- (14) [resolution 100,214]
616. happy(paul) | curious(paul) <- (14) [resolution 525,349]
620. happy(paul) <- (14, ~23) [subsumption resolution 616,394]
638. patient(paul) | ~rich(paul) <- (14, ~23) [resolution 620,135]
639. patient(paul) <- (14, ~23) [subsumption resolution 638,354]
692. ~tall(paul) <- (14, ~23) [resolution 639,118]
693. $false <- (14, ~23) [subsumption resolution 692,349]
694. ~14 | 23 [avatar contradiction clause 693]
695. $false [avatar sat refutation 219,220,266,335,694]
% SZS output end Proof for 1167955587805535221406678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not humble is both patient and old and vice versa.
Everyone who is both not calm and not rich is curious.
If alice is either brave or not humble then someone is not calm.
If someone is either happy or tall then susan is not tall.
If paul is both kind and rich then someone is either curious or not happy.
Everyone who is quiet or not tall is not happy and vice versa.
Everyone who is not brave is both rich and creative and vice versa.
Everyone who is kind or not calm is both not humble and creative.
Everyone who is old is not creative.
Everyone who is both not creative and not happy is either brave or rich.
Everyone who is not creative or not wise is either not wise or calm.
Everyone who is brave is both strong and happy and vice versa.
If fred is humble then mary is rich.
Everyone who is rich is both not curious and not calm.
If someone is either rich or not strong then paul is both not old and humble and vice versa.
If someone is strong then mary is not wise.
Someone is creative.
Mary is generous or not calm.
Someone is old or wise.
Lucy is both tall and generous.
Someone is kind.
Alice is either not wise or wise. | Alice is quiet. | contradiction | (![X]:((curious(X)<~>~humble(X))<=>(patient(X)&old(X))))&
(![X]:((~calm(X)&~rich(X))=>curious(X)))&
(((brave(alice)<~>~humble(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((happy(X)<~>tall(X))))=>(~tall(susan)))&
(((kind(paul)&rich(paul)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~tall(X))<=>~happy(X)))&
(![X]:(~brave(X)<=>(rich(X)&creative(X))))&
(![X]:((kind(X)|~calm(X))=>(~humble(X)&creative(X))))&
(![X]:(old(X)=>~creative(X)))&
(![X]:((~creative(X)&~happy(X))=>(brave(X)<~>rich(X))))&
(![X]:((~creative(X)|~wise(X))=>(~wise(X)<~>calm(X))))&
(![X]:(brave(X)<=>(strong(X)&happy(X))))&
((humble(fred))=>(rich(mary)))&
(![X]:(rich(X)=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>((~old(paul)&humble(paul))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(?[X]:(creative(X)))&
((generous(mary)|~calm(mary)))&
(?[X]:((old(X)|wise(X))))&
((tall(lucy)&generous(lucy)))&
(?[X]:(kind(X)))&
((~wise(alice)<~>wise(alice))) | quiet(alice) | [
"p0",
"p5",
"p6",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8439159065556842943648667
% SZS output start Proof for 8439159065556842943648667
1. ! [X0] : ((curious(X0) <~> ~humble(X0)) <=> (old(X0) & patient(X0))) [input p0]
6. ! [X0] : ((~tall(X0) | quiet(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : (~brave(X0) <=> (creative(X0) & rich(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | kind(X0)) => (creative(X0) & ~humble(X0))) [input p7]
9. ! [X0] : (old(X0) => ~creative(X0)) [input p8]
12. ! [X0] : (brave(X0) <=> (happy(X0) & strong(X0))) [input p11]
14. ! [X0] : (rich(X0) => (~calm(X0) & ~curious(X0))) [input p13]
23. quiet(alice) [input hypothesis]
32. ! [X0] : ((creative(X0) & ~humble(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 8]
33. ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) & ~curious(X0)) | ~rich(X0)) [ennf transformation 14]
40. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [nnf transformation 1]
41. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [flattening 40]
49. ! [X0] : (((~tall(X0) | quiet(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) & ~quiet(X0)))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | quiet(X0) | happy(X0)) & (~happy(X0) | (tall(X0) & ~quiet(X0)))) [flattening 49]
51. ! [X0] : ((~brave(X0) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | brave(X0))) [nnf transformation 7]
52. ! [X0] : ((~brave(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | brave(X0))) [flattening 51]
55. ! [X0] : ((brave(X0) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | ~brave(X0))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | ~brave(X0))) [flattening 55]
72. old(X0) | curious(X0) | humble(X0) [cnf transformation 41]
82. ~quiet(X0) | ~happy(X0) [cnf transformation 50]
85. brave(X0) | rich(X0) [cnf transformation 52]
89. ~humble(X0) | calm(X0) [cnf transformation 32]
91. creative(X0) | calm(X0) [cnf transformation 32]
92. ~creative(X0) | ~old(X0) [cnf transformation 33]
100. ~brave(X0) | happy(X0) [cnf transformation 56]
103. ~rich(X0) | ~curious(X0) [cnf transformation 38]
104. ~rich(X0) | ~calm(X0) [cnf transformation 38]
118. quiet(alice) [cnf transformation 23]
220. ~happy(alice) [resolution 82,118]
225. ~old(X0) | calm(X0) [resolution 92,91]
230. happy(X0) | rich(X0) [resolution 100,85]
249. curious(X0) | humble(X0) | calm(X0) [resolution 72,225]
253. calm(X0) | curious(X0) [subsumption resolution 249,89]
348. rich(alice) [resolution 230,220]
356. ~calm(alice) [resolution 348,104]
357. ~curious(alice) [resolution 348,103]
388. curious(alice) [resolution 356,253]
389. $false [subsumption resolution 388,357]
% SZS output end Proof for 8439159065556842943648667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or tall is both patient and not creative.
Everyone who is funny or old is both not funny and not rich and vice versa.
Everyone who is not humble or humble is either kind or funny and vice versa.
If alice is both not humble and rich then alice is both curious and not generous and vice versa.
If someone is either not generous or calm then mary is both curious and not wise and vice versa.
If alice is both wise and not funny then someone is not funny or not happy.
Everyone who is patient or not generous is either rich or not creative.
Everyone who is wise or not strong is both not old and generous.
Everyone who is not strong is not patient.
If fred is not curious then susan is either not patient or creative.
If someone is both kind and not generous then someone is either wise or curious and vice versa.
If someone is not tall then someone is either not old or humble and vice versa.
If someone is not strong or not quiet then someone is both old and humble and vice versa.
Everyone who is calm is either calm or creative and vice versa.
Everyone who is generous is not old or not humble.
If mary is not generous then susan is both creative and not kind and vice versa.
Susan is not tall or humble.
Alice is both not curious and humble.
Someone is not humble.
John is brave or not rich.
Alice is not curious.
Someone is both not creative and old.
John is not curious or rich. | Mary is not wise. | entailment | (![X]:((generous(X)|tall(X))=>(patient(X)&~creative(X))))&
(![X]:((funny(X)|old(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~humble(X)|humble(X))<=>(kind(X)<~>funny(X))))&
(((~humble(alice)&rich(alice)))<=>((curious(alice)&~generous(alice))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((curious(mary)&~wise(mary))))&
(((wise(alice)&~funny(alice)))=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:((patient(X)|~generous(X))=>(rich(X)<~>~creative(X))))&
(![X]:((wise(X)|~strong(X))=>(~old(X)&generous(X))))&
(![X]:(~strong(X)=>~patient(X)))&
((~curious(fred))=>((~patient(susan)<~>creative(susan))))&
((?[X]:((kind(X)&~generous(X))))<=>(?[X]:((wise(X)<~>curious(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~old(X)<~>humble(X)))))&
((?[X]:((~strong(X)|~quiet(X))))<=>(?[X]:((old(X)&humble(X)))))&
(![X]:(calm(X)<=>(calm(X)<~>creative(X))))&
(![X]:(generous(X)=>(~old(X)|~humble(X))))&
((~generous(mary))<=>((creative(susan)&~kind(susan))))&
((~tall(susan)|humble(susan)))&
((~curious(alice)&humble(alice)))&
(?[X]:(~humble(X)))&
((brave(john)|~rich(john)))&
(~curious(alice))&
(?[X]:((~creative(X)&old(X))))&
((~curious(john)|rich(john))) | ~wise(mary) | [
"p0",
"p1",
"p2",
"p6",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6111143607290746209780864
% SZS output start Proof for 6111143607290746209780864
1. ! [X0] : ((tall(X0) | generous(X0)) => (~creative(X0) & patient(X0))) [input p0]
2. ! [X0] : ((old(X0) | funny(X0)) <=> (~rich(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((humble(X0) | ~humble(X0)) <=> (kind(X0) <~> funny(X0))) [input p2]
7. ! [X0] : ((~generous(X0) | patient(X0)) => (rich(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((~strong(X0) | wise(X0)) => (generous(X0) & ~old(X0))) [input p7]
14. ! [X0] : (calm(X0) <=> (calm(X0) <~> creative(X0))) [input p13]
16. ~generous(mary) <=> (~kind(susan) & creative(susan)) [input p15]
24. wise(mary) [input hypothesis]
30. ! [X0] : ((~creative(X0) & patient(X0)) | (~tall(X0) & ~generous(X0))) [ennf transformation 1]
31. ! [X0] : ((rich(X0) <~> ~creative(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 7]
32. ! [X0] : ((generous(X0) & ~old(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 8]
37. ! [X0] : (((old(X0) | funny(X0)) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [nnf transformation 2]
38. ! [X0] : ((old(X0) | funny(X0) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | (~old(X0) & ~funny(X0)))) [flattening 37]
39. ! [X0] : (((humble(X0) | ~humble(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~humble(X0) & humble(X0)))) [nnf transformation 3]
40. ! [X0] : ((humble(X0) | ~humble(X0) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~humble(X0) & humble(X0)))) [flattening 39]
48. ! [X0] : (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (generous(X0) & ~patient(X0))) [nnf transformation 31]
65. ! [X0] : ((calm(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~calm(X0))) [nnf transformation 14]
66. (~generous(mary) | (kind(susan) | ~creative(susan))) & ((~kind(susan) & creative(susan)) | generous(mary)) [nnf transformation 16]
67. (~generous(mary) | kind(susan) | ~creative(susan)) & ((~kind(susan) & creative(susan)) | generous(mary)) [flattening 66]
72. ~generous(X0) | patient(X0) [cnf transformation 30]
76. ~funny(X0) | ~funny(X0) [cnf transformation 38]
80. old(X0) | funny(X0) | rich(X0) | funny(X0) [cnf transformation 38]
81. funny(X0) | kind(X0) | humble(X0) [cnf transformation 40]
82. funny(X0) | kind(X0) | ~humble(X0) [cnf transformation 40]
99. ~rich(X0) | creative(X0) | ~patient(X0) [cnf transformation 48]
101. ~wise(X0) | ~old(X0) [cnf transformation 32]
124. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 65]
126. calm(X0) | calm(X0) | ~creative(X0) [cnf transformation 65]
129. ~kind(susan) | generous(mary) [cnf transformation 67]
139. wise(mary) [cnf transformation 24]
140. ~creative(X0) | ~calm(X0) [duplicate literal removal 124]
141. ~creative(X0) | calm(X0) [duplicate literal removal 126]
142. ~funny(X0) [duplicate literal removal 76]
143. rich(X0) | funny(X0) | old(X0) [duplicate literal removal 80]
144. ~humble(X0) | kind(X0) [subsumption resolution 82,142]
145. kind(X0) | humble(X0) [subsumption resolution 81,142]
146. kind(X0) [subsumption resolution 145,144]
172. 6 <=> wise(mary) [avatar definition]
174. wise(mary) <- (6) [avatar component clause 172]
289. ~creative(X0) [subsumption resolution 140,141]
290. generous(mary) [subsumption resolution 129,146]
312. 6 [avatar split clause 139,172]
321. patient(mary) [resolution 72,290]
325. ~old(mary) <- (6) [resolution 101,174]
347. funny(X1) | old(X1) | creative(X1) | ~patient(X1) [resolution 143,99]
352. old(X1) | creative(X1) | ~patient(X1) [subsumption resolution 347,142]
353. ~patient(X1) | old(X1) [subsumption resolution 352,289]
373. old(mary) [resolution 353,321]
377. $false <- (6) [subsumption resolution 373,325]
378. ~6 [avatar contradiction clause 377]
383. $false [avatar sat refutation 312,378]
% SZS output end Proof for 6111143607290746209780864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not humble is both rich and happy.
Everyone who is either not brave or creative is both rich and generous.
Everyone who is both not strong and not kind is both not patient and humble and vice versa.
If someone is either not wise or calm then someone is either funny or generous and vice versa.
If mary is both not curious and not humble then someone is both not calm and not kind and vice versa.
Everyone who is either not funny or not old is either not calm or not funny.
Everyone who is patient is both wise and not wise and vice versa.
Everyone who is both patient and rich is both not patient and strong and vice versa.
Everyone who is wise or funny is both tall and strong.
Everyone who is either curious or not calm is not patient or funny and vice versa.
If someone is either calm or not happy then someone is tall or not tall.
If susan is either creative or curious then lucy is not calm and vice versa.
If someone is creative then someone is strong or tall and vice versa.
If mary is either not creative or generous then john is both not wise and not generous.
If someone is not wise then alice is both not generous and not tall and vice versa.
Someone is either generous or not happy.
John is tall or wise.
Alice is not generous or old.
Someone is not rich or not humble.
Lucy is not happy or not tall.
John is either not curious or quiet.
Alice is not tall or not quiet. | Lucy is happy. | entailment | (![X]:((~happy(X)|~humble(X))=>(rich(X)&happy(X))))&
(![X]:((~brave(X)<~>creative(X))=>(rich(X)&generous(X))))&
(![X]:((~strong(X)&~kind(X))<=>(~patient(X)&humble(X))))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(((~curious(mary)&~humble(mary)))<=>(?[X]:((~calm(X)&~kind(X)))))&
(![X]:((~funny(X)<~>~old(X))=>(~calm(X)<~>~funny(X))))&
(![X]:(patient(X)<=>(wise(X)&~wise(X))))&
(![X]:((patient(X)&rich(X))<=>(~patient(X)&strong(X))))&
(![X]:((wise(X)|funny(X))=>(tall(X)&strong(X))))&
(![X]:((curious(X)<~>~calm(X))<=>(~patient(X)|funny(X))))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:((tall(X)|~tall(X)))))&
(((creative(susan)<~>curious(susan)))<=>(~calm(lucy)))&
((?[X]:(creative(X)))<=>(?[X]:((strong(X)|tall(X)))))&
(((~creative(mary)<~>generous(mary)))=>((~wise(john)&~generous(john))))&
((?[X]:(~wise(X)))<=>((~generous(alice)&~tall(alice))))&
(?[X]:((generous(X)<~>~happy(X))))&
((tall(john)|wise(john)))&
((~generous(alice)|old(alice)))&
(?[X]:((~rich(X)|~humble(X))))&
((~happy(lucy)|~tall(lucy)))&
((~curious(john)<~>quiet(john)))&
((~tall(alice)|~quiet(alice))) | happy(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1151598636199915598565915
% SZS output start Proof for 1151598636199915598565915
1. ! [X0] : ((~humble(X0) | ~happy(X0)) => (happy(X0) & rich(X0))) [input p0]
23. ~happy(lucy) [input hypothesis]
27. ! [X0] : ((happy(X0) & rich(X0)) | (humble(X0) & happy(X0))) [ennf transformation 1]
77. happy(X0) | happy(X0) [cnf transformation 27]
145. ~happy(lucy) [cnf transformation 23]
150. happy(X0) [duplicate literal removal 77]
288. $false [subsumption resolution 145,150]
% SZS output end Proof for 1151598636199915598565915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or old is both wise and not strong.
If someone is not kind then paul is both not rich and tall and vice versa.
If someone is either patient or not generous then fred is kind or not brave and vice versa.
If someone is old then lucy is both brave and not tall and vice versa.
Everyone who is either not old or humble is patient and vice versa.
Everyone who is both not wise and not rich is either not tall or not creative.
If lucy is both not patient and not humble then susan is rich or old.
If someone is either not patient or not funny then someone is either not wise or not old and vice versa.
If paul is happy then someone is either generous or curious.
If someone is quiet or happy then mary is not old and vice versa.
If someone is generous or not happy then someone is both quiet and brave.
If someone is not wise or not funny then someone is either not happy or strong.
Everyone who is either not old or not kind is calm and vice versa.
Everyone who is not happy or rich is either quiet or creative.
Everyone who is either not strong or not calm is either not old or brave and vice versa.
Everyone who is not humble is either not patient or not tall and vice versa.
Lucy is not calm or not happy.
Mary is both not patient and not rich.
John is not kind.
Mary is either old or not happy.
Susan is either tall or not creative.
Someone is either creative or kind.
Someone is not creative. | Mary is humble. | entailment | (![X]:((funny(X)|old(X))=>(wise(X)&~strong(X))))&
((?[X]:(~kind(X)))<=>((~rich(paul)&tall(paul))))&
((?[X]:((patient(X)<~>~generous(X))))<=>((kind(fred)|~brave(fred))))&
((?[X]:(old(X)))<=>((brave(lucy)&~tall(lucy))))&
(![X]:((~old(X)<~>humble(X))<=>patient(X)))&
(![X]:((~wise(X)&~rich(X))=>(~tall(X)<~>~creative(X))))&
(((~patient(lucy)&~humble(lucy)))=>((rich(susan)|old(susan))))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(?[X]:((~wise(X)<~>~old(X)))))&
((happy(paul))=>(?[X]:((generous(X)<~>curious(X)))))&
((?[X]:((quiet(X)|happy(X))))<=>(~old(mary)))&
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((quiet(X)&brave(X)))))&
((?[X]:((~wise(X)|~funny(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~kind(X))<=>calm(X)))&
(![X]:((~happy(X)|rich(X))=>(quiet(X)<~>creative(X))))&
(![X]:((~strong(X)<~>~calm(X))<=>(~old(X)<~>brave(X))))&
(![X]:(~humble(X)<=>(~patient(X)<~>~tall(X))))&
((~calm(lucy)|~happy(lucy)))&
((~patient(mary)&~rich(mary)))&
(~kind(john))&
((old(mary)<~>~happy(mary)))&
((tall(susan)<~>~creative(susan)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:(~creative(X))) | humble(mary) | [
"p4",
"p9",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4091934705046150210994656
% SZS output start Proof for 4091934705046150210994656
5. ! [X0] : ((~old(X0) <~> humble(X0)) <=> patient(X0)) [input p4]
10. ? [X0] : (happy(X0) | quiet(X0)) <=> ~old(mary) [input p9]
11. ? [X0] : (~happy(X0) | generous(X0)) => ? [X0] : (brave(X0) & quiet(X0)) [input p10]
18. ~rich(mary) & ~patient(mary) [input p17]
24. ~humble(mary) [input hypothesis]
26. ? [X0] : (~happy(X0) | generous(X0)) => ? [X1] : (brave(X1) & quiet(X1)) [rectify 11]
34. ? [X1] : (brave(X1) & quiet(X1)) | ! [X0] : (happy(X0) & ~generous(X0)) [ennf transformation 26]
52. ! [X0] : ((((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | ~patient(X0)) & (patient(X0) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0))))) [nnf transformation 5]
62. (? [X0] : (happy(X0) | quiet(X0)) | old(mary)) & (~old(mary) | ! [X0] : (~happy(X0) & ~quiet(X0))) [nnf transformation 10]
63. (? [X0] : (happy(X0) | quiet(X0)) | old(mary)) & (~old(mary) | ! [X1] : (~happy(X1) & ~quiet(X1))) [rectify 62]
64. ? [X0] : (happy(X0) | quiet(X0)) => (happy(sK6) | quiet(sK6)) [choice axiom]
65. ((happy(sK6) | quiet(sK6)) | old(mary)) & (~old(mary) | ! [X1] : (~happy(X1) & ~quiet(X1))) [skolemisation 63,64]
66. ? [X0] : (brave(X0) & quiet(X0)) | ! [X1] : (happy(X1) & ~generous(X1)) [rectify 34]
67. ? [X0] : (brave(X0) & quiet(X0)) => (brave(sK7) & quiet(sK7)) [choice axiom]
68. (brave(sK7) & quiet(sK7)) | ! [X1] : (happy(X1) & ~generous(X1)) [skolemisation 66,67]
100. humble(X0) | patient(X0) | old(X0) [cnf transformation 52]
117. ~old(mary) | ~quiet(X1) [cnf transformation 65]
118. ~old(mary) | ~happy(X1) [cnf transformation 65]
121. quiet(sK7) | happy(X1) [cnf transformation 68]
149. ~patient(mary) [cnf transformation 18]
159. ~humble(mary) [cnf transformation 24]
277. 26 <=> happy(paul) [avatar definition]
278. happy(paul) <- (26) [avatar component clause 277]
279. ~happy(paul) <- (~26) [avatar component clause 277]
291. 29 <=> old(mary) [avatar definition]
304. 32 <=> ! [X1] : ~happy(X1) [avatar definition]
305. ~happy(X1) <- (32) [avatar component clause 304]
306. 32 | ~29 [avatar split clause 118,291,304]
308. 33 <=> ! [X1] : ~quiet(X1) [avatar definition]
309. ~quiet(X1) <- (33) [avatar component clause 308]
310. 33 | ~29 [avatar split clause 117,291,308]
312. 34 <=> ! [X1] : happy(X1) [avatar definition]
313. happy(X1) <- (34) [avatar component clause 312]
324. 37 <=> quiet(sK7) [avatar definition]
326. quiet(sK7) <- (37) [avatar component clause 324]
327. 34 | 37 [avatar split clause 121,324,312]
386. $false <- (~26, 34) [subsumption resolution 279,313]
387. 26 | ~34 [avatar contradiction clause 386]
397. patient(mary) | old(mary) [resolution 100,159]
398. old(mary) [subsumption resolution 397,149]
401. 29 [avatar split clause 398,291]
403. $false <- (26, 32) [resolution 305,278]
404. ~26 | ~32 [avatar contradiction clause 403]
406. $false <- (33, 37) [resolution 309,326]
407. ~33 | ~37 [avatar contradiction clause 406]
409. $false [avatar sat refutation 306,310,327,387,401,404,407]
% SZS output end Proof for 4091934705046150210994656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then john is not kind or brave. If paul is not old then mary is either quiet or calm. If someone is both not old and happy then someone is not rich or old and vice versa. If john is either not humble or patient then fred is both not strong and curious. Everyone who is not generous or not happy is not happy. If someone is both patient and not generous then john is not calm and vice versa. Everyone who is either calm or not creative is either not brave or not generous and vice versa. If john is either not generous or not creative then john is not curious and vice versa. Everyone who is humble is either wise or creative and vice versa. If someone is tall or not humble then alice is curious or creative and vice versa. If alice is funny then alice is kind or not happy. If susan is either wise or old then alice is not rich or not brave and vice versa. Everyone who is kind or generous is both not brave and quiet and vice versa. Everyone who is both not old and curious is old or wise. Everyone who is wise or happy is both not happy and not strong and vice versa. Everyone who is both calm and funny is not kind or not generous. Someone is both not quiet and not curious. Someone is not creative. Alice is either not tall or old. Susan is either generous or humble. Susan is patient or not creative. Paul is both funny and not wise. | Mary is creative. | neutral | ((?[X]:(curious(X)))=>((~kind(john)|brave(john))))&
((~old(paul))=>((quiet(mary)<~>calm(mary))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((~rich(X)|old(X)))))&
(((~humble(john)<~>patient(john)))=>((~strong(fred)&curious(fred))))&
(![X]:((~generous(X)|~happy(X))=>~happy(X)))&
((?[X]:((patient(X)&~generous(X))))<=>(~calm(john)))&
(![X]:((calm(X)<~>~creative(X))<=>(~brave(X)<~>~generous(X))))&
(((~generous(john)<~>~creative(john)))<=>(~curious(john)))&
(![X]:(humble(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((tall(X)|~humble(X))))<=>((curious(alice)|creative(alice))))&
((funny(alice))=>((kind(alice)|~happy(alice))))&
(((wise(susan)<~>old(susan)))<=>((~rich(alice)|~brave(alice))))&
(![X]:((kind(X)|generous(X))<=>(~brave(X)&quiet(X))))&
(![X]:((~old(X)&curious(X))=>(old(X)|wise(X))))&
(![X]:((wise(X)|happy(X))<=>(~happy(X)&~strong(X))))&
(![X]:((calm(X)&funny(X))=>(~kind(X)|~generous(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
(?[X]:(~creative(X)))&
((~tall(alice)<~>old(alice)))&
((generous(susan)<~>humble(susan)))&
((patient(susan)|~creative(susan)))&
((funny(paul)&~wise(paul))) | creative(mary) | [] | null | 0 |
If someone is not tall then alice is humble or not old and vice versa.
If fred is both wise and patient then someone is not wise and vice versa.
Everyone who is both creative and patient is quiet.
If someone is patient or calm then mary is both tall and not curious and vice versa.
If someone is kind then someone is curious or not quiet.
Everyone who is kind or not curious is happy or not funny and vice versa.
If mary is brave then mary is wise or not tall and vice versa.
If someone is both tall and not funny then paul is both patient and calm and vice versa.
If someone is not curious or not generous then alice is both brave and happy.
If susan is either not funny or not strong then fred is both not funny and funny and vice versa.
If lucy is humble or not old then someone is funny and vice versa.
Everyone who is funny or not quiet is both not patient and rich and vice versa.
Everyone who is rich is either humble or funny and vice versa.
Everyone who is generous or not humble is both not brave and not old.
Everyone who is either not funny or not old is patient or not strong and vice versa.
If someone is both patient and generous then someone is both curious and not strong and vice versa.
Paul is either quiet or not funny.
Someone is both not brave and creative.
Lucy is either kind or not quiet.
Lucy is either not patient or not old.
Paul is generous or quiet.
Someone is not wise or rich.
John is curious. | Lucy is not humble. | contradiction | ((?[X]:(~tall(X)))<=>((humble(alice)|~old(alice))))&
(((wise(fred)&patient(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((creative(X)&patient(X))=>quiet(X)))&
((?[X]:((patient(X)|calm(X))))<=>((tall(mary)&~curious(mary))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((kind(X)|~curious(X))<=>(happy(X)|~funny(X))))&
((brave(mary))<=>((wise(mary)|~tall(mary))))&
((?[X]:((tall(X)&~funny(X))))<=>((patient(paul)&calm(paul))))&
((?[X]:((~curious(X)|~generous(X))))=>((brave(alice)&happy(alice))))&
(((~funny(susan)<~>~strong(susan)))<=>((~funny(fred)&funny(fred))))&
(((humble(lucy)|~old(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~patient(X)&rich(X))))&
(![X]:(rich(X)<=>(humble(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))=>(~brave(X)&~old(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(patient(X)|~strong(X))))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((curious(X)&~strong(X)))))&
((quiet(paul)<~>~funny(paul)))&
(?[X]:((~brave(X)&creative(X))))&
((kind(lucy)<~>~quiet(lucy)))&
((~patient(lucy)<~>~old(lucy)))&
((generous(paul)|quiet(paul)))&
(?[X]:((~wise(X)|rich(X))))&
(curious(john)) | ~humble(lucy) | [
"p11",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 641563840796503244575936
% SZS output start Proof for 641563840796503244575936
12. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (rich(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((~humble(X0) | generous(X0)) => (~old(X0) & ~brave(X0))) [input p13]
15. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (~strong(X0) | patient(X0))) [input p14]
20. ~patient(lucy) <~> ~old(lucy) [input p19]
24. ~humble(lucy) [input hypothesis]
31. ! [X0] : ((~old(X0) & ~brave(X0)) | (humble(X0) & ~generous(X0))) [ennf transformation 14]
66. ! [X0] : (((~quiet(X0) | funny(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [nnf transformation 12]
67. ! [X0] : ((~quiet(X0) | funny(X0) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [flattening 66]
69. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (strong(X0) & ~patient(X0))) & ((~strong(X0) | patient(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 15]
70. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (strong(X0) & ~patient(X0))) & (~strong(X0) | patient(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [flattening 69]
80. (old(lucy) | patient(lucy)) & (~old(lucy) | ~patient(lucy)) [nnf transformation 20]
120. ~funny(X0) | ~patient(X0) [cnf transformation 67]
132. ~old(X0) | humble(X0) [cnf transformation 31]
137. old(X0) | funny(X0) | ~patient(X0) [cnf transformation 70]
150. old(lucy) | patient(lucy) [cnf transformation 80]
154. ~humble(lucy) [cnf transformation 24]
302. 33 <=> humble(lucy) [avatar definition]
303. ~humble(lucy) <- (~33) [avatar component clause 302]
306. 34 <=> old(lucy) [avatar definition]
307. old(lucy) <- (34) [avatar component clause 306]
318. old(X0) | ~patient(X0) [subsumption resolution 137,120]
366. old(lucy) [subsumption resolution 150,318]
367. 34 [avatar split clause 366,306]
383. ~33 [avatar split clause 154,302]
426. humble(lucy) <- (34) [resolution 132,307]
427. $false <- (~33, 34) [subsumption resolution 426,303]
428. 33 | ~34 [avatar contradiction clause 427]
429. $false [avatar sat refutation 367,383,428]
% SZS output end Proof for 641563840796503244575936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either brave or not generous then lucy is either not quiet or not rich.
If alice is both not patient and not kind then someone is tall or patient.
If john is either calm or quiet then mary is both tall and not quiet.
Everyone who is both brave and not quiet is both not patient and not tall and vice versa.
If lucy is curious then someone is not old and vice versa.
Everyone who is both patient and old is either not wise or not old and vice versa.
If lucy is either not calm or funny then john is not curious or not patient.
Everyone who is both not generous and quiet is either not calm or not creative.
If someone is either old or patient then someone is both not calm and quiet and vice versa.
Everyone who is either old or not quiet is patient or not old and vice versa.
If lucy is not rich or not creative then lucy is both not curious and tall and vice versa.
If susan is not quiet or not funny then someone is not patient and vice versa.
Everyone who is either patient or rich is not strong or not happy.
Everyone who is either not kind or kind is generous or not curious and vice versa.
Everyone who is either not creative or not quiet is not funny.
If john is quiet then someone is humble.
Fred is not wise or generous.
Someone is either kind or happy.
Susan is tall or patient.
Someone is either generous or humble.
Fred is either strong or not quiet.
Alice is either not curious or calm.
Alice is both not calm and quiet.
Someone is both not generous and not funny. | Alice is not wise. | entailment | (((brave(fred)<~>~generous(fred)))=>((~quiet(lucy)<~>~rich(lucy))))&
(((~patient(alice)&~kind(alice)))=>(?[X]:((tall(X)|patient(X)))))&
(((calm(john)<~>quiet(john)))=>((tall(mary)&~quiet(mary))))&
(![X]:((brave(X)&~quiet(X))<=>(~patient(X)&~tall(X))))&
((curious(lucy))<=>(?[X]:(~old(X))))&
(![X]:((patient(X)&old(X))<=>(~wise(X)<~>~old(X))))&
(((~calm(lucy)<~>funny(lucy)))=>((~curious(john)|~patient(john))))&
(![X]:((~generous(X)&quiet(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:((old(X)<~>patient(X))))<=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((old(X)<~>~quiet(X))<=>(patient(X)|~old(X))))&
(((~rich(lucy)|~creative(lucy)))<=>((~curious(lucy)&tall(lucy))))&
(((~quiet(susan)|~funny(susan)))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)<~>rich(X))=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>~funny(X)))&
((quiet(john))=>(?[X]:(humble(X))))&
((~wise(fred)|generous(fred)))&
(?[X]:((kind(X)<~>happy(X))))&
((tall(susan)|patient(susan)))&
(?[X]:((generous(X)<~>humble(X))))&
((strong(fred)<~>~quiet(fred)))&
((~curious(alice)<~>calm(alice)))&
((~calm(alice)&quiet(alice)))&
(?[X]:((~generous(X)&~funny(X)))) | ~wise(alice) | [
"p5",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3547963154948344479641551
% SZS output start Proof for 3547963154948344479641551
6. ! [X0] : ((old(X0) & patient(X0)) <=> (~wise(X0) <~> ~old(X0))) [input p5]
10. ! [X0] : ((old(X0) <~> ~quiet(X0)) <=> (~old(X0) | patient(X0))) [input p9]
23. quiet(alice) & ~calm(alice) [input p22]
25. wise(alice) [input hypothesis]
49. ! [X0] : (((old(X0) & patient(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | (~old(X0) | ~patient(X0)))) [nnf transformation 6]
50. ! [X0] : (((old(X0) & patient(X0)) | ((~wise(X0) | old(X0)) & (~old(X0) | wise(X0)))) & (((old(X0) | wise(X0)) & (~old(X0) | ~wise(X0))) | ~old(X0) | ~patient(X0))) [flattening 49]
58. ! [X0] : ((((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (old(X0) & ~patient(X0))) & ((~old(X0) | patient(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))))) [nnf transformation 10]
59. ! [X0] : ((((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (old(X0) & ~patient(X0))) & (~old(X0) | patient(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0))))) [flattening 58]
98. ~old(X0) | ~wise(X0) | ~old(X0) | ~patient(X0) [cnf transformation 50]
103. old(X0) | ~wise(X0) | old(X0) [cnf transformation 50]
114. ~old(X0) | patient(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 59]
117. ~quiet(X0) | old(X0) | old(X0) [cnf transformation 59]
150. quiet(alice) [cnf transformation 23]
153. wise(alice) [cnf transformation 25]
156. ~old(X0) | patient(X0) | ~quiet(X0) [duplicate literal removal 114]
157. ~quiet(X0) | old(X0) [duplicate literal removal 117]
158. ~old(X0) | ~wise(X0) | ~patient(X0) [duplicate literal removal 98]
159. ~wise(X0) | old(X0) [duplicate literal removal 103]
181. 5 <=> patient(alice) [avatar definition]
182. ~patient(alice) <- (~5) [avatar component clause 181]
230. ~wise(X0) | ~patient(X0) [subsumption resolution 158,159]
280. ~quiet(X0) | patient(X0) [subsumption resolution 156,157]
376. ~patient(alice) [resolution 230,153]
379. ~5 [avatar split clause 376,181]
386. patient(alice) [resolution 280,150]
388. $false <- (~5) [subsumption resolution 386,182]
389. 5 [avatar contradiction clause 388]
390. $false [avatar sat refutation 379,389]
% SZS output end Proof for 3547963154948344479641551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or not patient then lucy is not generous or not creative and vice versa.
Everyone who is either not curious or creative is both not old and curious.
Everyone who is curious or not kind is wise and vice versa.
Everyone who is calm is kind or not calm and vice versa.
If mary is curious then alice is funny or not curious.
Everyone who is not patient is not tall or patient and vice versa.
Everyone who is wise or not funny is tall or not quiet.
If someone is both strong and not wise then someone is kind or tall and vice versa.
If someone is not curious then someone is both not rich and creative.
Everyone who is not brave or calm is either not creative or strong.
Everyone who is either not rich or not kind is kind and vice versa.
Everyone who is both rich and not brave is not old or tall and vice versa.
If someone is not tall or not wise then someone is not brave or creative.
If mary is either not kind or not brave then susan is both not funny and not kind.
If someone is tall or not kind then someone is both curious and tall.
Everyone who is both not calm and rich is either not curious or funny.
Paul is strong.
Mary is both not patient and not funny.
Lucy is humble or quiet.
Mary is not strong.
Alice is either humble or curious.
Alice is wise. | Paul is calm. | entailment | ((?[X]:((rich(X)<~>~patient(X))))<=>((~generous(lucy)|~creative(lucy))))&
(![X]:((~curious(X)<~>creative(X))=>(~old(X)&curious(X))))&
(![X]:((curious(X)|~kind(X))<=>wise(X)))&
(![X]:(calm(X)<=>(kind(X)|~calm(X))))&
((curious(mary))=>((funny(alice)|~curious(alice))))&
(![X]:(~patient(X)<=>(~tall(X)|patient(X))))&
(![X]:((wise(X)|~funny(X))=>(tall(X)|~quiet(X))))&
((?[X]:((strong(X)&~wise(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:((~brave(X)|calm(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~kind(X))<=>kind(X)))&
(![X]:((rich(X)&~brave(X))<=>(~old(X)|tall(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((~brave(X)|creative(X)))))&
(((~kind(mary)<~>~brave(mary)))=>((~funny(susan)&~kind(susan))))&
((?[X]:((tall(X)|~kind(X))))=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((~calm(X)&rich(X))=>(~curious(X)<~>funny(X))))&
(strong(paul))&
((~patient(mary)&~funny(mary)))&
((humble(lucy)|quiet(lucy)))&
(~strong(mary))&
((humble(alice)<~>curious(alice)))&
(wise(alice)) | calm(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6916416519286367388959313
% SZS output start Proof for 6916416519286367388959313
4. ! [X0] : (calm(X0) <=> (~calm(X0) | kind(X0))) [input p3]
23. ~calm(paul) [input hypothesis]
48. ! [X0] : ((calm(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | ~calm(X0))) [nnf transformation 4]
49. ! [X0] : ((calm(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | ~calm(X0))) [flattening 48]
88. calm(X0) | calm(X0) [cnf transformation 49]
135. ~calm(paul) [cnf transformation 23]
141. calm(X0) [duplicate literal removal 88]
238. $false [subsumption resolution 135,141]
% SZS output end Proof for 6916416519286367388959313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not kind or strong then someone is both creative and not strong and vice versa. If lucy is both patient and funny then paul is either not brave or not curious and vice versa. Everyone who is either not wise or not funny is calm and vice versa. If paul is not patient then someone is not humble. Everyone who is either not brave or not creative is not calm and vice versa. Everyone who is not funny or not patient is both not wise and not humble and vice versa. Everyone who is not humble is happy. Everyone who is either kind or not strong is both not rich and happy and vice versa. If someone is old then john is either patient or not wise. If alice is happy then someone is humble or calm and vice versa. If john is both not patient and quiet then someone is brave or rich and vice versa. Everyone who is both tall and wise is patient or not calm and vice versa. Everyone who is both tall and not curious is both tall and wise. Everyone who is both not brave and wise is both strong and wise. Everyone who is not kind is both not calm and quiet and vice versa. Everyone who is either funny or not creative is both creative and not kind and vice versa. Someone is either not old or not brave. Alice is not old. Someone is generous or not patient. Mary is not happy. Someone is either not funny or not happy. Someone is both patient and not calm. Someone is not strong. | Mary is not tall. | contradiction | (((~kind(susan)|strong(susan)))<=>(?[X]:((creative(X)&~strong(X)))))&
(((patient(lucy)&funny(lucy)))<=>((~brave(paul)<~>~curious(paul))))&
(![X]:((~wise(X)<~>~funny(X))<=>calm(X)))&
((~patient(paul))=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)<~>~creative(X))<=>~calm(X)))&
(![X]:((~funny(X)|~patient(X))<=>(~wise(X)&~humble(X))))&
(![X]:(~humble(X)=>happy(X)))&
(![X]:((kind(X)<~>~strong(X))<=>(~rich(X)&happy(X))))&
((?[X]:(old(X)))=>((patient(john)<~>~wise(john))))&
((happy(alice))<=>(?[X]:((humble(X)|calm(X)))))&
(((~patient(john)&quiet(john)))<=>(?[X]:((brave(X)|rich(X)))))&
(![X]:((tall(X)&wise(X))<=>(patient(X)|~calm(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)&wise(X))))&
(![X]:((~brave(X)&wise(X))=>(strong(X)&wise(X))))&
(![X]:(~kind(X)<=>(~calm(X)&quiet(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~kind(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
(~old(alice))&
(?[X]:((generous(X)|~patient(X))))&
(~happy(mary))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(~strong(X))) | ~tall(mary) | [
"p5",
"p6",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2273483016855477403901115
% SZS output start Proof for 2273483016855477403901115
6. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> (~humble(X0) & ~wise(X0))) [input p5]
7. ! [X0] : (~humble(X0) => happy(X0)) [input p6]
12. ! [X0] : ((wise(X0) & tall(X0)) <=> (~calm(X0) | patient(X0))) [input p11]
20. ~happy(mary) [input p19]
24. ~tall(mary) [input hypothesis]
27. ! [X0] : (happy(X0) | humble(X0)) [ennf transformation 7]
44. ! [X0] : (((~patient(X0) | ~funny(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (patient(X0) & funny(X0)))) [nnf transformation 6]
45. ! [X0] : ((~patient(X0) | ~funny(X0) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | (patient(X0) & funny(X0)))) [flattening 44]
58. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~wise(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((wise(X0) & tall(X0)) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | ~wise(X0) | ~tall(X0))) [flattening 58]
97. ~humble(X0) | patient(X0) [cnf transformation 45]
99. happy(X0) | humble(X0) [cnf transformation 27]
117. ~patient(X0) | tall(X0) [cnf transformation 59]
137. ~happy(mary) [cnf transformation 20]
143. ~tall(mary) [cnf transformation 24]
277. humble(mary) [resolution 99,137]
288. patient(mary) [resolution 277,97]
311. tall(mary) [resolution 288,117]
312. $false [subsumption resolution 311,143]
% SZS output end Proof for 2273483016855477403901115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is either not quiet or not wise.
Everyone who is not wise or not strong is tall and vice versa.
Everyone who is both humble and not calm is calm.
If fred is not creative or funny then someone is either brave or kind and vice versa.
If john is not rich or not kind then mary is not kind.
If someone is both not creative and not funny then someone is not happy or creative and vice versa.
If john is either not funny or strong then paul is not happy and vice versa.
If someone is old or not humble then someone is not curious and vice versa.
If mary is either not wise or quiet then alice is both not tall and not generous and vice versa.
Everyone who is not rich or calm is either quiet or funny and vice versa.
Everyone who is wise is not strong and vice versa.
If someone is both tall and not strong then someone is not creative or quiet and vice versa.
If alice is either rich or strong then alice is both not tall and not funny and vice versa.
Everyone who is curious or kind is wise.
Everyone who is not wise or kind is not old or not quiet and vice versa.
Someone is rich.
Someone is either not patient or creative.
Mary is both not happy and not curious.
Paul is not wise.
Someone is generous or not tall.
Susan is not generous or wise.
John is wise or not generous.
Someone is humble or not funny. | Paul is old. | contradiction | (![X]:(~quiet(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((~wise(X)|~strong(X))<=>tall(X)))&
(![X]:((humble(X)&~calm(X))=>calm(X)))&
(((~creative(fred)|funny(fred)))<=>(?[X]:((brave(X)<~>kind(X)))))&
(((~rich(john)|~kind(john)))=>(~kind(mary)))&
((?[X]:((~creative(X)&~funny(X))))<=>(?[X]:((~happy(X)|creative(X)))))&
(((~funny(john)<~>strong(john)))<=>(~happy(paul)))&
((?[X]:((old(X)|~humble(X))))<=>(?[X]:(~curious(X))))&
(((~wise(mary)<~>quiet(mary)))<=>((~tall(alice)&~generous(alice))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(![X]:(wise(X)<=>~strong(X)))&
((?[X]:((tall(X)&~strong(X))))<=>(?[X]:((~creative(X)|quiet(X)))))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(![X]:((~wise(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
((~happy(mary)&~curious(mary)))&
(~wise(paul))&
(?[X]:((generous(X)|~tall(X))))&
((~generous(susan)|wise(susan)))&
((wise(john)|~generous(john)))&
(?[X]:((humble(X)|~funny(X)))) | old(paul) | [
"p0",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5156082197389034159139772
% SZS output start Proof for 5156082197389034159139772
1. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> ~wise(X0))) [input p0]
15. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (~quiet(X0) | ~old(X0))) [input p14]
19. ~wise(paul) [input p18]
24. old(paul) [input hypothesis]
28. ! [X0] : ((~quiet(X0) <~> ~wise(X0)) | quiet(X0)) [ennf transformation 1]
33. ! [X0] : (((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 28]
64. ! [X0] : (((kind(X0) | ~wise(X0)) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | (~kind(X0) & wise(X0)))) [nnf transformation 15]
65. ! [X0] : ((kind(X0) | ~wise(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | (~kind(X0) & wise(X0)))) [flattening 64]
76. wise(X0) | quiet(X0) | quiet(X0) [cnf transformation 33]
128. ~quiet(X0) | ~old(X0) | wise(X0) [cnf transformation 65]
137. ~wise(paul) [cnf transformation 19]
142. old(paul) [cnf transformation 24]
144. wise(X0) | quiet(X0) [duplicate literal removal 76]
330. ~old(X0) | wise(X0) [subsumption resolution 128,144]
407. wise(paul) [resolution 330,142]
408. $false [subsumption resolution 407,137]
% SZS output end Proof for 5156082197389034159139772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not quiet or not tall then someone is both tall and rich. Everyone who is calm or not quiet is either not curious or happy and vice versa. Everyone who is either not curious or brave is not old and vice versa. If someone is calm then someone is not rich or not happy and vice versa. Everyone who is not generous or not funny is both old and curious. If someone is not curious then someone is both old and not calm. Everyone who is both curious and not kind is creative. Everyone who is both not humble and not brave is humble and vice versa. If alice is tall then someone is both kind and patient and vice versa. If lucy is either wise or tall then mary is both curious and not funny. If someone is both quiet and not generous then someone is either calm or not humble. If someone is both not funny and humble then someone is either not rich or curious. Everyone who is either not kind or rich is either rich or kind. If someone is tall or patient then lucy is curious and vice versa. Everyone who is both curious and not strong is both calm and creative. If paul is either calm or not tall then lucy is rich or not humble and vice versa. Mary is quiet or brave. Someone is either calm or not humble. Paul is either strong or kind. Someone is both strong and not humble. Someone is funny or creative. Alice is brave or old. Someone is both old and not patient. Someone is not patient or wise. | Alice is not funny. | contradiction | (((~quiet(john)<~>~tall(john)))=>(?[X]:((tall(X)&rich(X)))))&
(![X]:((calm(X)|~quiet(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>~old(X)))&
((?[X]:(calm(X)))<=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((~generous(X)|~funny(X))=>(old(X)&curious(X))))&
((?[X]:(~curious(X)))=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((curious(X)&~kind(X))=>creative(X)))&
(![X]:((~humble(X)&~brave(X))<=>humble(X)))&
((tall(alice))<=>(?[X]:((kind(X)&patient(X)))))&
(((wise(lucy)<~>tall(lucy)))=>((curious(mary)&~funny(mary))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
((?[X]:((~funny(X)&humble(X))))=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(rich(X)<~>kind(X))))&
((?[X]:((tall(X)|patient(X))))<=>(curious(lucy)))&
(![X]:((curious(X)&~strong(X))=>(calm(X)&creative(X))))&
(((calm(paul)<~>~tall(paul)))<=>((rich(lucy)|~humble(lucy))))&
((quiet(mary)|brave(mary)))&
(?[X]:((calm(X)<~>~humble(X))))&
((strong(paul)<~>kind(paul)))&
(?[X]:((strong(X)&~humble(X))))&
(?[X]:((funny(X)|creative(X))))&
((brave(alice)|old(alice)))&
(?[X]:((old(X)&~patient(X))))&
(?[X]:((~patient(X)|wise(X)))) | ~funny(alice) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6567818366048679380599439
% SZS output start Proof for 6567818366048679380599439
3. ! [X0] : ((~curious(X0) <~> brave(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : ((~funny(X0) | ~generous(X0)) => (curious(X0) & old(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> humble(X0)) [input p7]
25. ~funny(alice) [input hypothesis]
30. ! [X0] : ((~curious(X0) <~> brave(X0)) => ~old(X0)) [unused predicate definition removal 3]
35. ! [X0] : (~funny(X0) => (curious(X0) & old(X0))) [pure predicate removal 5]
37. ! [X0] : (~old(X0) | (~curious(X0) <=> brave(X0))) [ennf transformation 30]
38. ! [X0] : ((curious(X0) & old(X0)) | funny(X0)) [ennf transformation 35]
50. ! [X0] : (~old(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) [nnf transformation 37]
59. ! [X0] : (((~brave(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) | humble(X0)))) [nnf transformation 8]
60. ! [X0] : (((~brave(X0) & ~humble(X0)) | ~humble(X0)) & (humble(X0) | brave(X0) | humble(X0))) [flattening 59]
98. ~old(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 50]
102. funny(X0) | old(X0) [cnf transformation 38]
103. funny(X0) | curious(X0) [cnf transformation 38]
106. humble(X0) | brave(X0) | humble(X0) [cnf transformation 60]
107. ~humble(X0) | ~humble(X0) [cnf transformation 60]
143. ~funny(alice) [cnf transformation 25]
146. humble(X0) | brave(X0) [duplicate literal removal 106]
147. ~humble(X0) [duplicate literal removal 107]
205. brave(X0) [subsumption resolution 146,147]
303. old(alice) [resolution 102,143]
304. curious(alice) [resolution 103,143]
321. ~curious(alice) | ~brave(alice) [resolution 98,303]
328. ~curious(alice) [subsumption resolution 321,205]
344. $false [subsumption resolution 304,328]
% SZS output end Proof for 6567818366048679380599439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not curious then paul is not old or calm.
If john is not wise then fred is both creative and calm and vice versa.
Everyone who is both not curious and not quiet is either not tall or not rich.
If mary is either generous or not creative then susan is either brave or not strong and vice versa.
Everyone who is both not funny and patient is both rich and tall.
Everyone who is brave is not creative or strong.
Everyone who is patient is either not happy or creative.
If someone is both not old and funny then alice is both not creative and not curious.
Everyone who is both generous and not generous is not curious or not generous and vice versa.
If fred is brave then someone is not generous and vice versa.
Everyone who is not quiet or not patient is not curious.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
If someone is both not kind and not patient then john is not strong or not brave and vice versa.
Everyone who is rich is not quiet or old and vice versa.
Someone is either curious or funny.
Lucy is not rich or not brave.
Someone is generous or not brave.
Fred is not humble or quiet.
Susan is both brave and strong. | Mary is not old. | contradiction | (((rich(paul)|~curious(paul)))=>((~old(paul)|calm(paul))))&
((~wise(john))<=>((creative(fred)&calm(fred))))&
(![X]:((~curious(X)&~quiet(X))=>(~tall(X)<~>~rich(X))))&
(((generous(mary)<~>~creative(mary)))<=>((brave(susan)<~>~strong(susan))))&
(![X]:((~funny(X)&patient(X))=>(rich(X)&tall(X))))&
(![X]:(brave(X)=>(~creative(X)|strong(X))))&
(![X]:(patient(X)=>(~happy(X)<~>creative(X))))&
((?[X]:((~old(X)&funny(X))))=>((~creative(alice)&~curious(alice))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)|~generous(X))))&
((brave(fred))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)|~patient(X))=>~curious(X)))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)&~patient(X))))<=>((~strong(john)|~brave(john))))&
(![X]:(rich(X)<=>(~quiet(X)|old(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((~rich(lucy)|~brave(lucy)))&
(?[X]:((generous(X)|~brave(X))))&
((~humble(fred)|quiet(fred)))&
((brave(susan)&strong(susan))) | ~old(mary) | [
"p4",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8678918348487556306296552
% SZS output start Proof for 8678918348487556306296552
5. ! [X0] : ((patient(X0) & ~funny(X0)) => (tall(X0) & rich(X0))) [input p4]
8. ? [X0] : (funny(X0) & ~old(X0)) => (~curious(alice) & ~creative(alice)) [input p7]
9. ! [X0] : ((~generous(X0) & generous(X0)) <=> (~generous(X0) | ~curious(X0))) [input p8]
11. ! [X0] : ((~patient(X0) | ~quiet(X0)) => ~curious(X0)) [input p10]
16. ! [X0] : (rich(X0) <=> (old(X0) | ~quiet(X0))) [input p15]
22. ~old(mary) [input hypothesis]
29. ! [X0] : ((tall(X0) & rich(X0)) | (~patient(X0) | funny(X0))) [ennf transformation 5]
30. ! [X0] : ((tall(X0) & rich(X0)) | ~patient(X0) | funny(X0)) [flattening 29]
34. (~curious(alice) & ~creative(alice)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 8]
35. ! [X0] : (~curious(X0) | (patient(X0) & quiet(X0))) [ennf transformation 11]
42. ! [X0] : (((~generous(X0) & generous(X0)) | (generous(X0) & curious(X0))) & ((~generous(X0) | ~curious(X0)) | (generous(X0) | ~generous(X0)))) [nnf transformation 9]
43. ! [X0] : (((~generous(X0) & generous(X0)) | (generous(X0) & curious(X0))) & (~generous(X0) | ~curious(X0) | generous(X0) | ~generous(X0))) [flattening 42]
63. ! [X0] : ((rich(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | ~rich(X0))) [nnf transformation 16]
64. ! [X0] : ((rich(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~rich(X0))) [flattening 63]
85. ~patient(X0) | rich(X0) | funny(X0) [cnf transformation 30]
91. ~curious(alice) | ~funny(X0) | old(X0) [cnf transformation 34]
94. generous(X0) | generous(X0) [cnf transformation 43]
95. ~generous(X0) | curious(X0) [cnf transformation 43]
99. ~curious(X0) | quiet(X0) [cnf transformation 35]
100. ~curious(X0) | patient(X0) [cnf transformation 35]
121. ~quiet(X0) | old(X0) | ~rich(X0) [cnf transformation 64]
123. ~old(X0) | rich(X0) [cnf transformation 64]
130. ~old(mary) [cnf transformation 22]
132. generous(X0) [duplicate literal removal 94]
191. 12 <=> ! [X0] : (~funny(X0) | old(X0)) [avatar definition]
192. ~funny(X0) | old(X0) <- (12) [avatar component clause 191]
194. 13 <=> curious(alice) [avatar definition]
196. ~curious(alice) <- (~13) [avatar component clause 194]
197. 12 | ~13 [avatar split clause 91,194,191]
317. curious(X0) [resolution 95,132]
319. $false <- (~13) [resolution 317,196]
321. quiet(X0) [resolution 317,99]
323. 13 [avatar contradiction clause 319]
325. patient(X0) [resolution 100,317]
332. funny(X0) | rich(X0) [resolution 85,325]
341. rich(X0) | old(X0) <- (12) [resolution 332,192]
344. rich(X0) <- (12) [subsumption resolution 341,123]
359. old(X0) | ~rich(X0) [resolution 121,321]
362. old(X0) <- (12) [subsumption resolution 359,344]
367. $false <- (12) [resolution 362,130]
371. ~12 [avatar contradiction clause 367]
372. $false [avatar sat refutation 197,323,371]
% SZS output end Proof for 8678918348487556306296552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then alice is both not tall and quiet. Everyone who is creative or calm is both not patient and not creative. Everyone who is not old is either not rich or not funny. If paul is happy or not quiet then someone is not calm and vice versa. If someone is both tall and not rich then susan is either not funny or not tall. If someone is either kind or tall then lucy is wise. If someone is both creative and happy then alice is either not patient or old and vice versa. Everyone who is either not generous or not creative is either not happy or not curious and vice versa. If someone is both not strong and not wise then fred is not kind or old. If lucy is tall or old then lucy is patient or kind and vice versa. Everyone who is not brave is calm or kind. If someone is curious then someone is either not humble or not strong. If paul is brave then alice is funny. Everyone who is either not generous or not funny is not generous or calm and vice versa. Everyone who is not brave or calm is either not calm or creative and vice versa. If susan is quiet then someone is either happy or curious. Paul is either rich or not rich. Someone is either not funny or not calm. Someone is either not humble or not brave. Fred is either not wise or happy. Someone is either not quiet or not funny. Someone is not brave. Someone is either humble or strong. | Paul is calm. | contradiction | ((?[X]:(~humble(X)))=>((~tall(alice)&quiet(alice))))&
(![X]:((creative(X)|calm(X))=>(~patient(X)&~creative(X))))&
(![X]:(~old(X)=>(~rich(X)<~>~funny(X))))&
(((happy(paul)|~quiet(paul)))<=>(?[X]:(~calm(X))))&
((?[X]:((tall(X)&~rich(X))))=>((~funny(susan)<~>~tall(susan))))&
((?[X]:((kind(X)<~>tall(X))))=>(wise(lucy)))&
((?[X]:((creative(X)&happy(X))))<=>((~patient(alice)<~>old(alice))))&
(![X]:((~generous(X)<~>~creative(X))<=>(~happy(X)<~>~curious(X))))&
((?[X]:((~strong(X)&~wise(X))))=>((~kind(fred)|old(fred))))&
(((tall(lucy)|old(lucy)))<=>((patient(lucy)|kind(lucy))))&
(![X]:(~brave(X)=>(calm(X)|kind(X))))&
((?[X]:(curious(X)))=>(?[X]:((~humble(X)<~>~strong(X)))))&
((brave(paul))=>(funny(alice)))&
(![X]:((~generous(X)<~>~funny(X))<=>(~generous(X)|calm(X))))&
(![X]:((~brave(X)|calm(X))<=>(~calm(X)<~>creative(X))))&
((quiet(susan))=>(?[X]:((happy(X)<~>curious(X)))))&
((rich(paul)<~>~rich(paul)))&
(?[X]:((~funny(X)<~>~calm(X))))&
(?[X]:((~humble(X)<~>~brave(X))))&
((~wise(fred)<~>happy(fred)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)<~>strong(X)))) | calm(paul) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 799657745180690784123010
% SZS output start Proof for 799657745180690784123010
2. ! [X0] : ((calm(X0) | creative(X0)) => (~creative(X0) & ~patient(X0))) [input p1]
15. ! [X0] : ((calm(X0) | ~brave(X0)) <=> (~calm(X0) <~> creative(X0))) [input p14]
24. calm(paul) [input hypothesis]
27. ! [X0] : ((~creative(X0) & ~patient(X0)) | (~calm(X0) & ~creative(X0))) [ennf transformation 2]
59. ! [X0] : (((calm(X0) | ~brave(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~calm(X0) & brave(X0)))) [nnf transformation 15]
60. ! [X0] : ((calm(X0) | ~brave(X0) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~calm(X0) & brave(X0)))) [flattening 59]
84. ~creative(X0) | ~creative(X0) [cnf transformation 27]
125. creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 60]
145. calm(paul) [cnf transformation 24]
146. creative(X0) | ~calm(X0) [duplicate literal removal 125]
150. ~creative(X0) [duplicate literal removal 84]
285. ~calm(X0) [subsumption resolution 146,150]
340. $false [subsumption resolution 145,285]
% SZS output end Proof for 799657745180690784123010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is either funny or not rich. Everyone who is either kind or strong is either not funny or calm. If someone is calm or creative then someone is both brave and rich. Everyone who is either brave or patient is not rich and vice versa. Everyone who is not tall is not happy. Everyone who is either calm or tall is both not rich and not tall and vice versa. Everyone who is not kind is both not kind and kind. Everyone who is either not happy or creative is either old or not calm and vice versa. Everyone who is either creative or not kind is patient. Everyone who is humble is wise or happy and vice versa. If alice is either quiet or not creative then someone is not strong. Everyone who is generous or not rich is either not curious or creative. If someone is not humble or curious then paul is either not humble or not generous. Everyone who is either not rich or humble is either generous or not tall and vice versa. Everyone who is wise is either not tall or happy. Paul is not old or old. Someone is kind or rich. Someone is generous. Alice is not wise or quiet. Someone is old or brave. Mary is old or tall. | Paul is funny. | neutral | ((?[X]:(~brave(X)))=>(?[X]:((funny(X)<~>~rich(X)))))&
(![X]:((kind(X)<~>strong(X))=>(~funny(X)<~>calm(X))))&
((?[X]:((calm(X)|creative(X))))=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((brave(X)<~>patient(X))<=>~rich(X)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((calm(X)<~>tall(X))<=>(~rich(X)&~tall(X))))&
(![X]:(~kind(X)=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(old(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~kind(X))=>patient(X)))&
(![X]:(humble(X)<=>(wise(X)|happy(X))))&
(((quiet(alice)<~>~creative(alice)))=>(?[X]:(~strong(X))))&
(![X]:((generous(X)|~rich(X))=>(~curious(X)<~>creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(generous(X)<~>~tall(X))))&
(![X]:(wise(X)=>(~tall(X)<~>happy(X))))&
((~old(paul)|old(paul)))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:(generous(X)))&
((~wise(alice)|quiet(alice)))&
(?[X]:((old(X)|brave(X))))&
((old(mary)|tall(mary))) | funny(paul) | [] | null | 0 |
If susan is both brave and old then fred is either not brave or not humble.
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.
Everyone who is humble is tall or curious.
Everyone who is either not old or not quiet is brave or not curious and vice versa.
Everyone who is not kind is either not generous or not brave and vice versa.
Alice is both not strong and patient.
John is both not tall and humble.
Someone is either not happy or not tall.
Lucy is both funny and not brave.
Someone is either happy or kind.
John is either not generous or not wise.
Paul is both brave and not patient.
Mary is generous. | Alice is not strong. | entailment | (((brave(susan)&old(susan)))=>((~brave(fred)<~>~humble(fred))))&
(![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)))))&
(![X]:(humble(X)=>(tall(X)|curious(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(brave(X)|~curious(X))))&
(![X]:(~kind(X)<=>(~generous(X)<~>~brave(X))))&
((~strong(alice)&patient(alice)))&
((~tall(john)&humble(john)))&
(?[X]:((~happy(X)<~>~tall(X))))&
((funny(lucy)&~brave(lucy)))&
(?[X]:((happy(X)<~>kind(X))))&
((~generous(john)<~>~wise(john)))&
((brave(paul)&~patient(paul)))&
(generous(mary)) | ~strong(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1185034827238091348694888
% SZS output start Proof for 1185034827238091348694888
17. patient(alice) & ~strong(alice) [input p16]
25. strong(alice) [input hypothesis]
133. ~strong(alice) [cnf transformation 17]
148. strong(alice) [cnf transformation 25]
290. $false [subsumption resolution 148,133]
% SZS output end Proof for 1185034827238091348694888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then someone is curious.
If someone is not tall then someone is not rich.
Everyone who is either not patient or creative is both not patient and creative.
Everyone who is both kind and not curious is not strong and vice versa.
If john is not quiet then alice is not tall or calm.
Everyone who is patient is both not creative and quiet.
If mary is not funny or not brave then alice is not funny and vice versa.
If someone is either brave or not creative then someone is both not creative and happy.
Everyone who is either not calm or not humble is not strong.
Everyone who is both not quiet and not wise is both happy and quiet and vice versa.
Everyone who is curious or quiet is both humble and rich and vice versa.
Everyone who is not quiet is not calm or not happy.
If fred is both not tall and not old then someone is not rich or brave and vice versa.
Everyone who is both not creative and funny is curious.
If someone is not rich then paul is both not old and not curious.
If alice is quiet then john is either not rich or not kind and vice versa.
Paul is both not rich and not humble.
Alice is strong.
Someone is not kind.
Someone is either not patient or not quiet.
Someone is rich or calm.
Susan is not wise.
Someone is calm.
Alice is either not kind or brave. | Paul is not brave. | entailment | ((?[X]:(old(X)))=>(?[X]:(curious(X))))&
((?[X]:(~tall(X)))=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~patient(X)&creative(X))))&
(![X]:((kind(X)&~curious(X))<=>~strong(X)))&
((~quiet(john))=>((~tall(alice)|calm(alice))))&
(![X]:(patient(X)=>(~creative(X)&quiet(X))))&
(((~funny(mary)|~brave(mary)))<=>(~funny(alice)))&
((?[X]:((brave(X)<~>~creative(X))))=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((~calm(X)<~>~humble(X))=>~strong(X)))&
(![X]:((~quiet(X)&~wise(X))<=>(happy(X)&quiet(X))))&
(![X]:((curious(X)|quiet(X))<=>(humble(X)&rich(X))))&
(![X]:(~quiet(X)=>(~calm(X)|~happy(X))))&
(((~tall(fred)&~old(fred)))<=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~creative(X)&funny(X))=>curious(X)))&
((?[X]:(~rich(X)))=>((~old(paul)&~curious(paul))))&
((quiet(alice))<=>((~rich(john)<~>~kind(john))))&
((~rich(paul)&~humble(paul)))&
(strong(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((rich(X)|calm(X))))&
(~wise(susan))&
(?[X]:(calm(X)))&
((~kind(alice)<~>brave(alice))) | ~brave(paul) | [
"p2",
"p5",
"p7",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 50334495813608464548793
% SZS output start Proof for 50334495813608464548793
3. ! [X0] : ((~patient(X0) <~> creative(X0)) => (creative(X0) & ~patient(X0))) [input p2]
6. ! [X0] : (patient(X0) => (quiet(X0) & ~creative(X0))) [input p5]
8. ? [X0] : (brave(X0) <~> ~creative(X0)) => ? [X0] : (happy(X0) & ~creative(X0)) [input p7]
10. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (quiet(X0) & happy(X0))) [input p9]
11. ! [X0] : ((quiet(X0) | curious(X0)) <=> (rich(X0) & humble(X0))) [input p10]
17. ~humble(paul) & ~rich(paul) [input p16]
25. brave(paul) [input hypothesis]
28. ? [X0] : (brave(X0) <~> ~creative(X0)) => ? [X1] : (happy(X1) & ~creative(X1)) [rectify 8]
31. ! [X0] : ((creative(X0) & ~patient(X0)) | (~patient(X0) <=> creative(X0))) [ennf transformation 3]
34. ! [X0] : ((quiet(X0) & ~creative(X0)) | ~patient(X0)) [ennf transformation 6]
35. ? [X1] : (happy(X1) & ~creative(X1)) | ! [X0] : (brave(X0) <=> ~creative(X0)) [ennf transformation 28]
48. ! [X0] : ((creative(X0) & ~patient(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 31]
53. ? [X1] : (happy(X1) & ~creative(X1)) | ! [X0] : ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))) [nnf transformation 35]
54. ? [X0] : (happy(X0) & ~creative(X0)) | ! [X1] : ((brave(X1) | creative(X1)) & (~creative(X1) | ~brave(X1))) [rectify 53]
55. ? [X0] : (happy(X0) & ~creative(X0)) => (happy(sK2) & ~creative(sK2)) [choice axiom]
56. (happy(sK2) & ~creative(sK2)) | ! [X1] : ((brave(X1) | creative(X1)) & (~creative(X1) | ~brave(X1))) [skolemisation 54,55]
58. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 10]
59. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | wise(X0) | quiet(X0))) [flattening 58]
60. ! [X0] : (((quiet(X0) | curious(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 11]
61. ! [X0] : ((quiet(X0) | curious(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~quiet(X0) & ~curious(X0)))) [flattening 60]
82. creative(X0) | creative(X0) | patient(X0) [cnf transformation 48]
89. ~patient(X0) | quiet(X0) [cnf transformation 34]
93. ~creative(sK2) | ~creative(X1) | ~brave(X1) [cnf transformation 56]
95. happy(sK2) | ~creative(X1) | ~brave(X1) [cnf transformation 56]
101. ~quiet(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 59]
104. ~quiet(X0) | humble(X0) [cnf transformation 61]
122. ~humble(paul) [cnf transformation 17]
132. brave(paul) [cnf transformation 25]
134. ~happy(X0) | ~quiet(X0) [duplicate literal removal 101]
136. creative(X0) | patient(X0) [duplicate literal removal 82]
185. 12 <=> happy(sK2) [avatar definition]
187. happy(sK2) <- (12) [avatar component clause 185]
190. 13 <=> ! [X1] : (~creative(X1) | ~brave(X1)) [avatar definition]
191. ~brave(X1) | ~creative(X1) <- (13) [avatar component clause 190]
192. 13 | 12 [avatar split clause 95,185,190]
194. 14 <=> creative(sK2) [avatar definition]
196. ~creative(sK2) <- (~14) [avatar component clause 194]
198. 13 | ~14 [avatar split clause 93,194,190]
282. ~quiet(sK2) <- (12) [resolution 134,187]
283. patient(sK2) <- (~14) [resolution 136,196]
285. quiet(sK2) <- (~14) [resolution 283,89]
286. $false <- (12, ~14) [subsumption resolution 285,282]
287. ~12 | 14 [avatar contradiction clause 286]
290. ~creative(paul) <- (13) [resolution 191,132]
292. patient(paul) <- (13) [resolution 290,136]
320. quiet(paul) <- (13) [resolution 292,89]
351. humble(paul) <- (13) [resolution 320,104]
354. $false <- (13) [subsumption resolution 351,122]
355. ~13 [avatar contradiction clause 354]
356. $false [avatar sat refutation 192,198,287,355]
% SZS output end Proof for 50334495813608464548793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is not creative.
Everyone who is either not brave or rich is both not curious and calm.
If someone is either not curious or not tall then someone is both kind and not calm and vice versa.
If susan is not kind or not happy then someone is both humble and not humble.
Everyone who is old is not calm and vice versa.
Everyone who is funny or not happy is not humble and vice versa.
Everyone who is not happy or creative is both funny and happy and vice versa.
If john is creative then paul is not patient and vice versa.
If someone is both not curious and not wise then someone is either not tall or not generous and vice versa.
Everyone who is not brave or not humble is either not strong or old and vice versa.
Everyone who is both not calm and not old is not curious or rich and vice versa.
If john is curious then someone is either patient or happy and vice versa.
If someone is humble or not old then john is either not rich or happy and vice versa.
Everyone who is quiet or not happy is both not patient and happy and vice versa.
If someone is not humble or tall then someone is not rich or brave and vice versa.
Someone is not rich.
Someone is either not wise or quiet.
Susan is not generous.
Paul is old or not curious.
Someone is happy.
Someone is either not rich or not generous. | John is not strong. | contradiction | (![X]:(~quiet(X)=>~creative(X)))&
(![X]:((~brave(X)<~>rich(X))=>(~curious(X)&calm(X))))&
((?[X]:((~curious(X)<~>~tall(X))))<=>(?[X]:((kind(X)&~calm(X)))))&
(((~kind(susan)|~happy(susan)))=>(?[X]:((humble(X)&~humble(X)))))&
(![X]:(old(X)<=>~calm(X)))&
(![X]:((funny(X)|~happy(X))<=>~humble(X)))&
(![X]:((~happy(X)|creative(X))<=>(funny(X)&happy(X))))&
((creative(john))<=>(~patient(paul)))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(~strong(X)<~>old(X))))&
(![X]:((~calm(X)&~old(X))<=>(~curious(X)|rich(X))))&
((curious(john))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((humble(X)|~old(X))))<=>((~rich(john)<~>happy(john))))&
(![X]:((quiet(X)|~happy(X))<=>(~patient(X)&happy(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:(~rich(X)))&
(?[X]:((~wise(X)<~>quiet(X))))&
(~generous(susan))&
((old(paul)|~curious(paul)))&
(?[X]:(happy(X)))&
(?[X]:((~rich(X)<~>~generous(X)))) | ~strong(john) | [
"p4",
"p6",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 395373593644875710578098
% SZS output start Proof for 395373593644875710578098
5. ! [X0] : (old(X0) <=> ~calm(X0)) [input p4]
7. ! [X0] : ((creative(X0) | ~happy(X0)) <=> (happy(X0) & funny(X0))) [input p6]
10. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (~strong(X0) <~> old(X0))) [input p9]
11. ! [X0] : ((~old(X0) & ~calm(X0)) <=> (rich(X0) | ~curious(X0))) [input p10]
13. ? [X0] : (~old(X0) | humble(X0)) <=> (~rich(john) <~> happy(john)) [input p12]
22. ~strong(john) [input hypothesis]
37. ! [X0] : ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))) [nnf transformation 5]
40. ! [X0] : (((creative(X0) | ~happy(X0)) | (~happy(X0) | ~funny(X0))) & ((happy(X0) & funny(X0)) | (~creative(X0) & happy(X0)))) [nnf transformation 7]
41. ! [X0] : ((creative(X0) | ~happy(X0) | ~happy(X0) | ~funny(X0)) & ((happy(X0) & funny(X0)) | (~creative(X0) & happy(X0)))) [flattening 40]
48. ! [X0] : (((~humble(X0) | ~brave(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (humble(X0) & brave(X0)))) [nnf transformation 10]
49. ! [X0] : ((~humble(X0) | ~brave(X0) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) & (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | (humble(X0) & brave(X0)))) [flattening 48]
50. ! [X0] : (((~old(X0) & ~calm(X0)) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | (old(X0) | calm(X0)))) [nnf transformation 11]
51. ! [X0] : (((~old(X0) & ~calm(X0)) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | old(X0) | calm(X0))) [flattening 50]
56. (? [X0] : (~old(X0) | humble(X0)) | ((~rich(john) | ~happy(john)) & (happy(john) | rich(john)))) & (((~happy(john) | rich(john)) & (happy(john) | ~rich(john))) | ! [X0] : (old(X0) & ~humble(X0))) [nnf transformation 13]
57. (? [X0] : (~old(X0) | humble(X0)) | ((~rich(john) | ~happy(john)) & (happy(john) | rich(john)))) & (((~happy(john) | rich(john)) & (happy(john) | ~rich(john))) | ! [X1] : (old(X1) & ~humble(X1))) [rectify 56]
58. ? [X0] : (~old(X0) | humble(X0)) => (~old(sK6) | humble(sK6)) [choice axiom]
59. ((~old(sK6) | humble(sK6)) | ((~rich(john) | ~happy(john)) & (happy(john) | rich(john)))) & (((~happy(john) | rich(john)) & (happy(john) | ~rich(john))) | ! [X1] : (old(X1) & ~humble(X1))) [skolemisation 57,58]
93. old(X0) | calm(X0) [cnf transformation 37]
99. happy(X0) | happy(X0) [cnf transformation 41]
113. ~old(X0) | strong(X0) | humble(X0) [cnf transformation 49]
118. ~calm(X0) | ~rich(X0) [cnf transformation 51]
120. ~old(X0) | ~rich(X0) [cnf transformation 51]
127. ~happy(john) | rich(john) | ~humble(X1) [cnf transformation 59]
128. ~happy(john) | rich(john) | old(X1) [cnf transformation 59]
148. ~strong(john) [cnf transformation 22]
151. happy(X0) [duplicate literal removal 99]
258. 23 <=> rich(john) [avatar definition]
259. rich(john) <- (23) [avatar component clause 258]
270. rich(john) | old(X1) [subsumption resolution 128,151]
272. 26 <=> ! [X1] : old(X1) [avatar definition]
273. old(X1) <- (26) [avatar component clause 272]
274. 26 | 23 [avatar split clause 270,258,272]
275. rich(john) | ~humble(X1) [subsumption resolution 127,151]
277. 27 <=> ! [X1] : ~humble(X1) [avatar definition]
278. ~humble(X1) <- (27) [avatar component clause 277]
279. 27 | 23 [avatar split clause 275,258,277]
356. ~rich(X0) | calm(X0) [resolution 120,93]
358. ~rich(X0) [subsumption resolution 356,118]
359. $false <- (23) [resolution 358,259]
362. ~23 [avatar contradiction clause 359]
398. strong(X0) | humble(X0) <- (26) [resolution 113,273]
401. strong(X0) <- (26, 27) [subsumption resolution 398,278]
404. $false <- (26, 27) [resolution 401,148]
407. ~26 | ~27 [avatar contradiction clause 404]
408. $false [avatar sat refutation 274,279,362,407]
% SZS output end Proof for 395373593644875710578098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or not wise then someone is not kind and vice versa.
If someone is kind or not generous then someone is either brave or happy and vice versa.
Everyone who is both quiet and not strong is either tall or not kind and vice versa.
If someone is either not patient or kind then john is old and vice versa.
If someone is not brave or not creative then mary is either humble or brave and vice versa.
If someone is both strong and not rich then someone is either strong or rich.
If susan is both kind and not old then fred is either not kind or not humble and vice versa.
If someone is either tall or rich then someone is not happy or not tall.
If someone is both curious and not kind then lucy is not wise or calm.
If someone is both not patient and not strong then lucy is both generous and not wise and vice versa.
Everyone who is calm or humble is either not strong or generous.
Everyone who is not quiet is both not happy and not wise and vice versa.
Everyone who is tall is both not humble and not patient.
Everyone who is either strong or calm is not kind or patient.
If someone is both old and calm then someone is not funny.
Everyone who is generous is either generous or old and vice versa.
Mary is both rich and not curious.
Someone is not strong.
Someone is both not happy and patient.
John is not kind.
Paul is old or not humble.
Paul is not kind or not tall.
Alice is strong.
Mary is both calm and wise. | Mary is rich. | entailment | ((?[X]:((calm(X)<~>~wise(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((quiet(X)&~strong(X))<=>(tall(X)<~>~kind(X))))&
((?[X]:((~patient(X)<~>kind(X))))<=>(old(john)))&
((?[X]:((~brave(X)|~creative(X))))<=>((humble(mary)<~>brave(mary))))&
((?[X]:((strong(X)&~rich(X))))=>(?[X]:((strong(X)<~>rich(X)))))&
(((kind(susan)&~old(susan)))<=>((~kind(fred)<~>~humble(fred))))&
((?[X]:((tall(X)<~>rich(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((curious(X)&~kind(X))))=>((~wise(lucy)|calm(lucy))))&
((?[X]:((~patient(X)&~strong(X))))<=>((generous(lucy)&~wise(lucy))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)<~>generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)&~wise(X))))&
(![X]:(tall(X)=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:(generous(X)<=>(generous(X)<~>old(X))))&
((rich(mary)&~curious(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)&patient(X))))&
(~kind(john))&
((old(paul)|~humble(paul)))&
((~kind(paul)|~tall(paul)))&
(strong(alice))&
((calm(mary)&wise(mary))) | rich(mary) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1323350160843672311864539
% SZS output start Proof for 1323350160843672311864539
17. ~curious(mary) & rich(mary) [input p16]
25. ~rich(mary) [input hypothesis]
33. rich(mary) [pure predicate removal 17]
139. rich(mary) [cnf transformation 33]
149. ~rich(mary) [cnf transformation 25]
346. $false [subsumption resolution 149,139]
% SZS output end Proof for 1323350160843672311864539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both patient and not generous and vice versa.
Everyone who is not quiet is either calm or not generous and vice versa.
If someone is not kind or old then someone is creative.
Everyone who is not creative is kind or not brave.
If john is either quiet or curious then someone is both curious and tall.
Everyone who is either curious or humble is both generous and tall and vice versa.
If someone is both not rich and generous then john is not curious or not quiet.
If paul is tall or wise then someone is strong or not quiet and vice versa.
Everyone who is either not rich or calm is both not quiet and kind.
If paul is either happy or quiet then someone is both not kind and not humble.
If someone is patient or creative then mary is both not wise and happy and vice versa.
Everyone who is not kind is not rich or not wise and vice versa.
Everyone who is either rich or not tall is both not strong and not generous.
If someone is either funny or rich then someone is both not rich and wise and vice versa.
Everyone who is both not creative and tall is not strong or not creative and vice versa.
If alice is not curious then john is both creative and humble.
Mary is not strong or not creative.
Alice is tall or old.
Someone is both curious and not calm.
Lucy is happy.
Susan is not old.
Fred is not patient.
Someone is both wise and rich.
Susan is both not tall and not old. | Mary is not happy. | contradiction | (![X]:(~humble(X)<=>(patient(X)&~generous(X))))&
(![X]:(~quiet(X)<=>(calm(X)<~>~generous(X))))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(kind(X)|~brave(X))))&
(((quiet(john)<~>curious(john)))=>(?[X]:((curious(X)&tall(X)))))&
(![X]:((curious(X)<~>humble(X))<=>(generous(X)&tall(X))))&
((?[X]:((~rich(X)&generous(X))))=>((~curious(john)|~quiet(john))))&
(((tall(paul)|wise(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((~rich(X)<~>calm(X))=>(~quiet(X)&kind(X))))&
(((happy(paul)<~>quiet(paul)))=>(?[X]:((~kind(X)&~humble(X)))))&
((?[X]:((patient(X)|creative(X))))<=>((~wise(mary)&happy(mary))))&
(![X]:(~kind(X)<=>(~rich(X)|~wise(X))))&
(![X]:((rich(X)<~>~tall(X))=>(~strong(X)&~generous(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
(![X]:((~creative(X)&tall(X))<=>(~strong(X)|~creative(X))))&
((~curious(alice))=>((creative(john)&humble(john))))&
((~strong(mary)|~creative(mary)))&
((tall(alice)|old(alice)))&
(?[X]:((curious(X)&~calm(X))))&
(happy(lucy))&
(~old(susan))&
(~patient(fred))&
(?[X]:((wise(X)&rich(X))))&
((~tall(susan)&~old(susan))) | ~happy(mary) | [
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8974460613770324135654365
% SZS output start Proof for 8974460613770324135654365
11. ? [X0] : (creative(X0) | patient(X0)) <=> (happy(mary) & ~wise(mary)) [input p10]
15. ! [X0] : ((tall(X0) & ~creative(X0)) <=> (~creative(X0) | ~strong(X0))) [input p14]
24. ~old(susan) & ~tall(susan) [input p23]
25. ~happy(mary) [input hypothesis]
57. (? [X0] : (creative(X0) | patient(X0)) | (~happy(mary) | wise(mary))) & ((happy(mary) & ~wise(mary)) | ! [X0] : (~creative(X0) & ~patient(X0))) [nnf transformation 11]
58. (? [X0] : (creative(X0) | patient(X0)) | ~happy(mary) | wise(mary)) & ((happy(mary) & ~wise(mary)) | ! [X0] : (~creative(X0) & ~patient(X0))) [flattening 57]
59. (? [X0] : (creative(X0) | patient(X0)) | ~happy(mary) | wise(mary)) & ((happy(mary) & ~wise(mary)) | ! [X1] : (~creative(X1) & ~patient(X1))) [rectify 58]
60. ? [X0] : (creative(X0) | patient(X0)) => (creative(sK4) | patient(sK4)) [choice axiom]
61. ((creative(sK4) | patient(sK4)) | ~happy(mary) | wise(mary)) & ((happy(mary) & ~wise(mary)) | ! [X1] : (~creative(X1) & ~patient(X1))) [skolemisation 59,60]
70. ! [X0] : (((tall(X0) & ~creative(X0)) | (creative(X0) & strong(X0))) & ((~creative(X0) | ~strong(X0)) | (~tall(X0) | creative(X0)))) [nnf transformation 15]
71. ! [X0] : (((tall(X0) & ~creative(X0)) | (creative(X0) & strong(X0))) & (~creative(X0) | ~strong(X0) | ~tall(X0) | creative(X0))) [flattening 70]
111. happy(mary) | ~creative(X1) [cnf transformation 61]
130. tall(X0) | creative(X0) [cnf transformation 71]
142. ~tall(susan) [cnf transformation 24]
144. ~happy(mary) [cnf transformation 25]
234. 20 <=> happy(mary) [avatar definition]
247. 23 <=> ! [X1] : ~creative(X1) [avatar definition]
248. ~creative(X1) <- (23) [avatar component clause 247]
249. 23 | 20 [avatar split clause 111,234,247]
311. ~20 [avatar split clause 144,234]
321. creative(susan) [resolution 130,142]
322. $false <- (23) [subsumption resolution 321,248]
323. ~23 [avatar contradiction clause 322]
324. $false [avatar sat refutation 249,311,323]
% SZS output end Proof for 8974460613770324135654365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and brave is either not wise or not brave. If someone is tall then someone is both not patient and generous. Everyone who is either rich or not wise is happy and vice versa. If someone is both not creative and not kind then john is rich and vice versa. If lucy is creative or not happy then someone is calm or happy and vice versa. If someone is brave or not brave then fred is not calm. Everyone who is either patient or wise is both humble and kind. Everyone who is either not old or wise is either humble or not rich and vice versa. Everyone who is either wise or not strong is not happy. Everyone who is rich or not happy is both not happy and curious. Everyone who is not old or curious is not patient or brave. If someone is either not quiet or patient then someone is not old. Everyone who is both not calm and tall is not rich and vice versa. If someone is either happy or not tall then lucy is either not happy or kind. Everyone who is both calm and not funny is happy or not generous and vice versa. Everyone who is both not old and creative is both kind and not funny. Someone is generous or not funny. Someone is not brave. Susan is either not quiet or calm. Paul is both not rich and not quiet. Fred is both not strong and quiet. Someone is not strong or not tall. Paul is wise or not funny. Someone is not tall. | John is not happy. | entailment | (![X]:((creative(X)&brave(X))=>(~wise(X)<~>~brave(X))))&
((?[X]:(tall(X)))=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>happy(X)))&
((?[X]:((~creative(X)&~kind(X))))<=>(rich(john)))&
(((creative(lucy)|~happy(lucy)))<=>(?[X]:((calm(X)|happy(X)))))&
((?[X]:((brave(X)|~brave(X))))=>(~calm(fred)))&
(![X]:((patient(X)<~>wise(X))=>(humble(X)&kind(X))))&
(![X]:((~old(X)<~>wise(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((wise(X)<~>~strong(X))=>~happy(X)))&
(![X]:((rich(X)|~happy(X))=>(~happy(X)&curious(X))))&
(![X]:((~old(X)|curious(X))=>(~patient(X)|brave(X))))&
((?[X]:((~quiet(X)<~>patient(X))))=>(?[X]:(~old(X))))&
(![X]:((~calm(X)&tall(X))<=>~rich(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>((~happy(lucy)<~>kind(lucy))))&
(![X]:((calm(X)&~funny(X))<=>(happy(X)|~generous(X))))&
(![X]:((~old(X)&creative(X))=>(kind(X)&~funny(X))))&
(?[X]:((generous(X)|~funny(X))))&
(?[X]:(~brave(X)))&
((~quiet(susan)<~>calm(susan)))&
((~rich(paul)&~quiet(paul)))&
((~strong(fred)&quiet(fred)))&
(?[X]:((~strong(X)|~tall(X))))&
((wise(paul)|~funny(paul)))&
(?[X]:(~tall(X))) | ~happy(john) | [
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8875095740205359147922572
% SZS output start Proof for 8875095740205359147922572
10. ! [X0] : ((~happy(X0) | rich(X0)) => (curious(X0) & ~happy(X0))) [input p9]
13. ! [X0] : ((tall(X0) & ~calm(X0)) <=> ~rich(X0)) [input p12]
15. ! [X0] : ((~funny(X0) & calm(X0)) <=> (~generous(X0) | happy(X0))) [input p14]
25. happy(john) [input hypothesis]
34. ! [X0] : ((curious(X0) & ~happy(X0)) | (happy(X0) & ~rich(X0))) [ennf transformation 10]
62. ! [X0] : (((tall(X0) & ~calm(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) | calm(X0)))) [nnf transformation 13]
63. ! [X0] : (((tall(X0) & ~calm(X0)) | rich(X0)) & (~rich(X0) | ~tall(X0) | calm(X0))) [flattening 62]
65. ! [X0] : (((~funny(X0) & calm(X0)) | (generous(X0) & ~happy(X0))) & ((~generous(X0) | happy(X0)) | (funny(X0) | ~calm(X0)))) [nnf transformation 15]
66. ! [X0] : (((~funny(X0) & calm(X0)) | (generous(X0) & ~happy(X0))) & (~generous(X0) | happy(X0) | funny(X0) | ~calm(X0))) [flattening 65]
107. ~happy(X0) | ~rich(X0) [cnf transformation 34]
116. ~calm(X0) | rich(X0) [cnf transformation 63]
123. ~happy(X0) | calm(X0) [cnf transformation 66]
140. happy(john) [cnf transformation 25]
156. 4 <=> rich(john) [avatar definition]
158. ~rich(john) <- (~4) [avatar component clause 156]
265. ~rich(john) [resolution 107,140]
268. ~4 [avatar split clause 265,156]
274. calm(john) [resolution 123,140]
278. rich(john) [resolution 274,116]
279. $false <- (~4) [subsumption resolution 278,158]
280. 4 [avatar contradiction clause 279]
281. $false [avatar sat refutation 268,280]
% SZS output end Proof for 8875095740205359147922572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and not curious then mary is both rich and not old.
Everyone who is calm is both humble and not patient and vice versa.
Everyone who is both quiet and not old is not happy and vice versa.
If someone is both old and not brave then john is old or not old and vice versa.
If someone is both not creative and rich then mary is not quiet and vice versa.
If john is either patient or not happy then someone is not creative and vice versa.
Everyone who is both happy and funny is not curious.
If susan is not humble then someone is not funny or old and vice versa.
Everyone who is not strong is either not wise or old.
If someone is not quiet or not patient then susan is not tall or not wise and vice versa.
If lucy is funny or old then john is calm or funny.
If someone is not humble then paul is not tall or funny.
If someone is not strong then someone is not old.
Everyone who is not strong is either old or not rich and vice versa.
Everyone who is brave or quiet is kind and vice versa.
Everyone who is not tall or not funny is not kind.
Someone is humble or not generous.
Someone is happy or not generous.
Someone is either generous or not creative.
Someone is either not tall or curious.
Alice is either not quiet or not tall.
Someone is both calm and not kind.
Someone is calm. | Paul is funny. | neutral | (((generous(susan)&~curious(susan)))=>((rich(mary)&~old(mary))))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
(![X]:((quiet(X)&~old(X))<=>~happy(X)))&
((?[X]:((old(X)&~brave(X))))<=>((old(john)|~old(john))))&
((?[X]:((~creative(X)&rich(X))))<=>(~quiet(mary)))&
(((patient(john)<~>~happy(john)))<=>(?[X]:(~creative(X))))&
(![X]:((happy(X)&funny(X))=>~curious(X)))&
((~humble(susan))<=>(?[X]:((~funny(X)|old(X)))))&
(![X]:(~strong(X)=>(~wise(X)<~>old(X))))&
((?[X]:((~quiet(X)|~patient(X))))<=>((~tall(susan)|~wise(susan))))&
(((funny(lucy)|old(lucy)))=>((calm(john)|funny(john))))&
((?[X]:(~humble(X)))=>((~tall(paul)|funny(paul))))&
((?[X]:(~strong(X)))=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(old(X)<~>~rich(X))))&
(![X]:((brave(X)|quiet(X))<=>kind(X)))&
(![X]:((~tall(X)|~funny(X))=>~kind(X)))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((generous(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>curious(X))))&
((~quiet(alice)<~>~tall(alice)))&
(?[X]:((calm(X)&~kind(X))))&
(?[X]:(calm(X))) | funny(paul) | [] | null | 0 |
If someone is not patient then susan is both not tall and not generous. Everyone who is generous is both creative and old. If someone is either tall or not happy then someone is not strong or kind. Everyone who is not quiet or not brave is both not patient and not strong and vice versa. Everyone who is not tall or not strong is either calm or generous. Everyone who is both not brave and not funny is happy and vice versa. If john is either kind or funny then lucy is not patient or not tall. If paul is not quiet or not humble then someone is brave or not happy. Everyone who is both quiet and not kind is either not brave or not rich and vice versa. If alice is not rich or creative then someone is either generous or funny and vice versa. If someone is not wise or creative then someone is either not brave or not funny and vice versa. Everyone who is calm is not brave and vice versa. If paul is either not rich or not quiet then john is funny and vice versa. Everyone who is curious is happy. Everyone who is either generous or not curious is curious and vice versa. Everyone who is either not wise or not brave is not creative or not kind. Alice is humble. Someone is calm or old. Fred is both patient and strong. Someone is both tall and rich. Someone is not funny or not humble. | Lucy is generous. | entailment | ((?[X]:(~patient(X)))=>((~tall(susan)&~generous(susan))))&
(![X]:(generous(X)=>(creative(X)&old(X))))&
((?[X]:((tall(X)<~>~happy(X))))=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>(~patient(X)&~strong(X))))&
(![X]:((~tall(X)|~strong(X))=>(calm(X)<~>generous(X))))&
(![X]:((~brave(X)&~funny(X))<=>happy(X)))&
(((kind(john)<~>funny(john)))=>((~patient(lucy)|~tall(lucy))))&
(((~quiet(paul)|~humble(paul)))=>(?[X]:((brave(X)|~happy(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~brave(X)<~>~rich(X))))&
(((~rich(alice)|creative(alice)))<=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:((~wise(X)|creative(X))))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(![X]:(calm(X)<=>~brave(X)))&
(((~rich(paul)<~>~quiet(paul)))<=>(funny(john)))&
(![X]:(curious(X)=>happy(X)))&
(![X]:((generous(X)<~>~curious(X))<=>curious(X)))&
(![X]:((~wise(X)<~>~brave(X))=>(~creative(X)|~kind(X))))&
(humble(alice))&
(?[X]:((calm(X)|old(X))))&
((patient(fred)&strong(fred)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((~funny(X)|~humble(X)))) | generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8073256461925992391441465
% SZS output start Proof for 8073256461925992391441465
15. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> curious(X0)) [input p14]
22. ~generous(lucy) [input hypothesis]
63. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | ~curious(X0)) & (curious(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 15]
116. curious(X0) | generous(X0) | curious(X0) [cnf transformation 63]
117. ~curious(X0) | generous(X0) | ~curious(X0) [cnf transformation 63]
127. ~generous(lucy) [cnf transformation 22]
128. curious(X0) | generous(X0) [duplicate literal removal 116]
129. ~curious(X0) | generous(X0) [duplicate literal removal 117]
263. generous(X0) [subsumption resolution 128,129]
273. $false [subsumption resolution 127,263]
% SZS output end Proof for 8073256461925992391441465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and old is not old and vice versa.
If someone is both not humble and not generous then someone is both not kind and generous.
If someone is creative or calm then someone is strong or brave.
If susan is both not rich and not brave then fred is funny.
Everyone who is either creative or old is either not generous or not creative and vice versa.
If susan is not creative then someone is either creative or not tall.
If lucy is both curious and old then susan is both rich and not wise and vice versa.
If someone is either funny or not humble then john is tall.
If someone is not patient then someone is not wise and vice versa.
If susan is not humble or not calm then someone is not strong or not curious and vice versa.
Everyone who is not patient is not old and vice versa.
Everyone who is not creative is creative or not humble and vice versa.
Everyone who is not funny is not quiet or not humble and vice versa.
Everyone who is both not curious and funny is not strong and vice versa.
If someone is either not old or not generous then alice is either tall or not rich and vice versa.
Someone is brave or curious.
Susan is either wise or not calm.
Someone is not generous or happy.
Someone is quiet or kind.
Fred is both generous and happy. | John is old. | entailment | (![X]:((~calm(X)&old(X))<=>~old(X)))&
((?[X]:((~humble(X)&~generous(X))))=>(?[X]:((~kind(X)&generous(X)))))&
((?[X]:((creative(X)|calm(X))))=>(?[X]:((strong(X)|brave(X)))))&
(((~rich(susan)&~brave(susan)))=>(funny(fred)))&
(![X]:((creative(X)<~>old(X))<=>(~generous(X)<~>~creative(X))))&
((~creative(susan))=>(?[X]:((creative(X)<~>~tall(X)))))&
(((curious(lucy)&old(lucy)))<=>((rich(susan)&~wise(susan))))&
((?[X]:((funny(X)<~>~humble(X))))=>(tall(john)))&
((?[X]:(~patient(X)))<=>(?[X]:(~wise(X))))&
(((~humble(susan)|~calm(susan)))<=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:(~patient(X)<=>~old(X)))&
(![X]:(~creative(X)<=>(creative(X)|~humble(X))))&
(![X]:(~funny(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((~curious(X)&funny(X))<=>~strong(X)))&
((?[X]:((~old(X)<~>~generous(X))))<=>((tall(alice)<~>~rich(alice))))&
(?[X]:((brave(X)|curious(X))))&
((wise(susan)<~>~calm(susan)))&
(?[X]:((~generous(X)|happy(X))))&
(?[X]:((quiet(X)|kind(X))))&
((generous(fred)&happy(fred))) | old(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 634706619447016640891899
% SZS output start Proof for 634706619447016640891899
1. ! [X0] : ((old(X0) & ~calm(X0)) <=> ~old(X0)) [input p0]
21. ~old(john) [input hypothesis]
33. ! [X0] : (((old(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | (~old(X0) | calm(X0)))) [nnf transformation 1]
34. ! [X0] : (((old(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | ~old(X0) | calm(X0))) [flattening 33]
71. old(X0) | old(X0) [cnf transformation 34]
119. ~old(john) [cnf transformation 21]
127. old(X0) [duplicate literal removal 71]
258. $false [subsumption resolution 119,127]
% SZS output end Proof for 634706619447016640891899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not humble or not calm then alice is curious and vice versa. Everyone who is happy or not humble is either not rich or not wise. If someone is both tall and happy then someone is not generous and vice versa. Everyone who is either not brave or brave is either not funny or not calm and vice versa. Everyone who is tall is either not tall or rich. Everyone who is either not happy or not funny is both brave and not happy and vice versa. Everyone who is either generous or humble is both not rich and not humble. Everyone who is not strong or brave is not kind and vice versa. Everyone who is kind is not humble or not strong. Everyone who is strong or not creative is not curious or not patient. Everyone who is not kind or rich is not generous or brave. Everyone who is funny is happy or not tall and vice versa. Everyone who is not quiet is not humble or generous and vice versa. Everyone who is not old is both not happy and calm. Everyone who is either not happy or not kind is either humble or old. Alice is both old and tall. Someone is not humble or rich. Someone is both brave and not calm. Someone is either brave or humble. Fred is either happy or quiet. Someone is patient or not quiet. Paul is either calm or not curious. | Paul is not tall. | neutral | (((~humble(alice)<~>~calm(alice)))<=>(curious(alice)))&
(![X]:((happy(X)|~humble(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:((tall(X)&happy(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~brave(X)<~>brave(X))<=>(~funny(X)<~>~calm(X))))&
(![X]:(tall(X)=>(~tall(X)<~>rich(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(brave(X)&~happy(X))))&
(![X]:((generous(X)<~>humble(X))=>(~rich(X)&~humble(X))))&
(![X]:((~strong(X)|brave(X))<=>~kind(X)))&
(![X]:(kind(X)=>(~humble(X)|~strong(X))))&
(![X]:((strong(X)|~creative(X))=>(~curious(X)|~patient(X))))&
(![X]:((~kind(X)|rich(X))=>(~generous(X)|brave(X))))&
(![X]:(funny(X)<=>(happy(X)|~tall(X))))&
(![X]:(~quiet(X)<=>(~humble(X)|generous(X))))&
(![X]:(~old(X)=>(~happy(X)&calm(X))))&
(![X]:((~happy(X)<~>~kind(X))=>(humble(X)<~>old(X))))&
((old(alice)&tall(alice)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((brave(X)<~>humble(X))))&
((happy(fred)<~>quiet(fred)))&
(?[X]:((patient(X)|~quiet(X))))&
((calm(paul)<~>~curious(paul))) | ~tall(paul) | [] | null | 0 |
Everyone who is funny is either curious or strong.
If mary is not calm then fred is either not brave or not happy.
Everyone who is either not old or kind is calm or not humble.
Everyone who is humble is rich or not wise and vice versa.
Everyone who is strong is curious or calm.
If someone is both not kind and strong then someone is not quiet and vice versa.
Everyone who is humble is either old or not creative.
Everyone who is both not old and not calm is calm or not brave and vice versa.
If someone is brave or not rich then someone is old or not tall and vice versa.
If susan is not calm then fred is brave and vice versa.
Everyone who is both not strong and not happy is either funny or not happy.
If someone is rich or not creative then someone is not funny or not rich.
If someone is generous or not creative then someone is both happy and not happy.
If someone is not humble or not generous then someone is both curious and kind and vice versa.
If mary is either not curious or strong then paul is either happy or kind and vice versa.
Everyone who is both not strong and not tall is both not curious and quiet and vice versa.
Someone is not patient or not kind.
John is quiet.
Someone is both curious and not funny.
Someone is creative or quiet.
Lucy is funny. | Fred is tall. | neutral | (![X]:(funny(X)=>(curious(X)<~>strong(X))))&
((~calm(mary))=>((~brave(fred)<~>~happy(fred))))&
(![X]:((~old(X)<~>kind(X))=>(calm(X)|~humble(X))))&
(![X]:(humble(X)<=>(rich(X)|~wise(X))))&
(![X]:(strong(X)=>(curious(X)|calm(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(humble(X)=>(old(X)<~>~creative(X))))&
(![X]:((~old(X)&~calm(X))<=>(calm(X)|~brave(X))))&
((?[X]:((brave(X)|~rich(X))))<=>(?[X]:((old(X)|~tall(X)))))&
((~calm(susan))<=>(brave(fred)))&
(![X]:((~strong(X)&~happy(X))=>(funny(X)<~>~happy(X))))&
((?[X]:((rich(X)|~creative(X))))=>(?[X]:((~funny(X)|~rich(X)))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((happy(X)&~happy(X)))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:((curious(X)&kind(X)))))&
(((~curious(mary)<~>strong(mary)))<=>((happy(paul)<~>kind(paul))))&
(![X]:((~strong(X)&~tall(X))<=>(~curious(X)&quiet(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(quiet(john))&
(?[X]:((curious(X)&~funny(X))))&
(?[X]:((creative(X)|quiet(X))))&
(funny(lucy)) | tall(fred) | [] | null | 0 |
If susan is both kind and not creative then alice is either not tall or not patient and vice versa.
Everyone who is not wise is either calm or not calm and vice versa.
If alice is not humble then john is humble and vice versa.
Everyone who is both not quiet and not kind is either not happy or strong and vice versa.
If someone is either not old or not generous then someone is both not wise and strong and vice versa.
Everyone who is not happy or not kind is kind or patient and vice versa.
Everyone who is either not quiet or rich is not happy or not curious and vice versa.
If lucy is not old or creative then alice is happy or calm.
Everyone who is either tall or old is not strong and vice versa.
If alice is not tall then mary is patient.
If fred is kind then someone is either brave or quiet and vice versa.
Everyone who is either generous or not rich is calm or wise and vice versa.
If someone is either not humble or not creative then lucy is creative or kind.
If someone is both creative and happy then someone is either not funny or quiet and vice versa.
Everyone who is both creative and generous is either not funny or wise and vice versa.
If someone is either not strong or patient then someone is not tall or not generous.
Someone is not happy.
Paul is both curious and humble.
Someone is both rich and quiet.
Lucy is funny.
Fred is old or kind.
Someone is either not creative or strong.
Fred is not rich or not old. | John is creative. | neutral | (((kind(susan)&~creative(susan)))<=>((~tall(alice)<~>~patient(alice))))&
(![X]:(~wise(X)<=>(calm(X)<~>~calm(X))))&
((~humble(alice))<=>(humble(john)))&
(![X]:((~quiet(X)&~kind(X))<=>(~happy(X)<~>strong(X))))&
((?[X]:((~old(X)<~>~generous(X))))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:((~happy(X)|~kind(X))<=>(kind(X)|patient(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(~happy(X)|~curious(X))))&
(((~old(lucy)|creative(lucy)))=>((happy(alice)|calm(alice))))&
(![X]:((tall(X)<~>old(X))<=>~strong(X)))&
((~tall(alice))=>(patient(mary)))&
((kind(fred))<=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:((generous(X)<~>~rich(X))<=>(calm(X)|wise(X))))&
((?[X]:((~humble(X)<~>~creative(X))))=>((creative(lucy)|kind(lucy))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
(![X]:((creative(X)&generous(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((~strong(X)<~>patient(X))))=>(?[X]:((~tall(X)|~generous(X)))))&
(?[X]:(~happy(X)))&
((curious(paul)&humble(paul)))&
(?[X]:((rich(X)&quiet(X))))&
(funny(lucy))&
((old(fred)|kind(fred)))&
(?[X]:((~creative(X)<~>strong(X))))&
((~rich(fred)|~old(fred))) | creative(john) | [] | null | 0 |
If john is either not funny or quiet then alice is quiet or generous.
Everyone who is humble or tall is not patient and vice versa.
If someone is not kind or not tall then someone is humble or not rich and vice versa.
Everyone who is both strong and wise is not humble or kind.
Everyone who is not strong or old is either wise or not strong and vice versa.
Everyone who is both rich and not quiet is not brave or not strong and vice versa.
Everyone who is either not tall or tall is either not old or not tall and vice versa.
Everyone who is either rich or brave is both creative and kind.
Everyone who is both curious and rich is not old.
If someone is either quiet or not happy then someone is not humble or not creative.
If someone is not old or not happy then john is both strong and not wise.
If someone is not patient then fred is either kind or happy.
If someone is either not wise or funny then someone is wise or rich.
Everyone who is generous is both kind and old and vice versa.
Everyone who is either not kind or brave is patient or generous and vice versa.
Someone is either generous or not calm.
Someone is rich or creative.
Paul is not humble.
Mary is not wise or not patient.
Someone is quiet or curious. | Fred is wise. | neutral | (((~funny(john)<~>quiet(john)))=>((quiet(alice)|generous(alice))))&
(![X]:((humble(X)|tall(X))<=>~patient(X)))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((strong(X)&wise(X))=>(~humble(X)|kind(X))))&
(![X]:((~strong(X)|old(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((rich(X)&~quiet(X))<=>(~brave(X)|~strong(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((rich(X)<~>brave(X))=>(creative(X)&kind(X))))&
(![X]:((curious(X)&rich(X))=>~old(X)))&
((?[X]:((quiet(X)<~>~happy(X))))=>(?[X]:((~humble(X)|~creative(X)))))&
((?[X]:((~old(X)|~happy(X))))=>((strong(john)&~wise(john))))&
((?[X]:(~patient(X)))=>((kind(fred)<~>happy(fred))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(generous(X)<=>(kind(X)&old(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(patient(X)|generous(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((rich(X)|creative(X))))&
(~humble(paul))&
((~wise(mary)|~patient(mary)))&
(?[X]:((quiet(X)|curious(X)))) | wise(fred) | [] | null | 0 |
If mary is not quiet or not creative then someone is kind and vice versa.
If someone is both not wise and wise then someone is not calm or not patient and vice versa.
Everyone who is both not creative and funny is calm and vice versa.
Everyone who is not curious is not rich and vice versa.
If fred is either not rich or not calm then fred is humble and vice versa.
If paul is both funny and curious then mary is both not calm and not old.
If someone is not tall then someone is either patient or strong.
Everyone who is either not rich or not quiet is both humble and quiet and vice versa.
If someone is tall then someone is generous and vice versa.
Everyone who is not tall or not creative is either brave or not patient.
If lucy is either not happy or not curious then someone is not happy and vice versa.
Everyone who is generous or not patient is not old or not kind and vice versa.
Everyone who is both calm and patient is funny and vice versa.
Everyone who is both curious and strong is either not quiet or patient and vice versa.
Everyone who is quiet or strong is strong or not curious.
Everyone who is not happy is old or generous.
Someone is patient or brave.
Fred is either curious or not brave.
Paul is funny.
Paul is either not rich or creative.
Mary is either old or wise.
Someone is funny or not calm.
Alice is both tall and not kind. | Fred is calm. | entailment | (((~quiet(mary)|~creative(mary)))<=>(?[X]:(kind(X))))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((~creative(X)&funny(X))<=>calm(X)))&
(![X]:(~curious(X)<=>~rich(X)))&
(((~rich(fred)<~>~calm(fred)))<=>(humble(fred)))&
(((funny(paul)&curious(paul)))=>((~calm(mary)&~old(mary))))&
((?[X]:(~tall(X)))=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(humble(X)&quiet(X))))&
((?[X]:(tall(X)))<=>(?[X]:(generous(X))))&
(![X]:((~tall(X)|~creative(X))=>(brave(X)<~>~patient(X))))&
(((~happy(lucy)<~>~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((generous(X)|~patient(X))<=>(~old(X)|~kind(X))))&
(![X]:((calm(X)&patient(X))<=>funny(X)))&
(![X]:((curious(X)&strong(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((quiet(X)|strong(X))=>(strong(X)|~curious(X))))&
(![X]:(~happy(X)=>(old(X)|generous(X))))&
(?[X]:((patient(X)|brave(X))))&
((curious(fred)<~>~brave(fred)))&
(funny(paul))&
((~rich(paul)<~>creative(paul)))&
((old(mary)<~>wise(mary)))&
(?[X]:((funny(X)|~calm(X))))&
((tall(alice)&~kind(alice))) | calm(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8890993306100924990672730
% SZS output start Proof for 8890993306100924990672730
2. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X0] : (~patient(X0) | ~calm(X0)) [input p1]
24. ~calm(fred) [input hypothesis]
25. ? [X0] : (wise(X0) & ~wise(X0)) <=> ? [X1] : (~patient(X1) | ~calm(X1)) [rectify 2]
41. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (patient(X1) & calm(X1))) & (? [X1] : (~patient(X1) | ~calm(X1)) | ! [X0] : (~wise(X0) | wise(X0))) [nnf transformation 25]
42. (? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (patient(X1) & calm(X1))) & (? [X2] : (~patient(X2) | ~calm(X2)) | ! [X3] : (~wise(X3) | wise(X3))) [rectify 41]
43. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
44. ? [X2] : (~patient(X2) | ~calm(X2)) => (~patient(sK2) | ~calm(sK2)) [choice axiom]
45. ((wise(sK1) & ~wise(sK1)) | ! [X1] : (patient(X1) & calm(X1))) & ((~patient(sK2) | ~calm(sK2)) | ! [X3] : (~wise(X3) | wise(X3))) [skolemisation 42,44,43]
83. ~wise(sK1) | calm(X1) [cnf transformation 45]
85. wise(sK1) | calm(X1) [cnf transformation 45]
143. ~calm(fred) [cnf transformation 24]
168. 6 <=> wise(sK1) [avatar definition]
173. 7 <=> ! [X1] : calm(X1) [avatar definition]
174. calm(X1) <- (7) [avatar component clause 173]
175. 7 | 6 [avatar split clause 85,168,173]
177. 7 | ~6 [avatar split clause 83,168,173]
187. 10 <=> calm(fred) [avatar definition]
188. ~calm(fred) <- (~10) [avatar component clause 187]
296. ~10 [avatar split clause 143,187]
299. $false <- (7, ~10) [resolution 188,174]
300. ~7 | 10 [avatar contradiction clause 299]
301. $false [avatar sat refutation 175,177,296,300]
% SZS output end Proof for 8890993306100924990672730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then susan is both old and brave.
Everyone who is humble or rich is not old.
Everyone who is funny is either not humble or curious and vice versa.
If john is not happy then someone is not humble.
Everyone who is both calm and not wise is not quiet and vice versa.
Everyone who is both curious and not wise is either not kind or not rich and vice versa.
If susan is not rich or generous then john is not calm or creative and vice versa.
Everyone who is either not wise or wise is not quiet or not generous and vice versa.
If someone is either not quiet or strong then someone is both patient and humble.
If john is both not happy and old then fred is not creative and vice versa.
If someone is not curious or rich then someone is either not generous or not kind and vice versa.
Everyone who is either brave or not strong is both tall and creative and vice versa.
Everyone who is tall or kind is curious or happy and vice versa.
If someone is not patient or wise then someone is not creative and vice versa.
If susan is both strong and not funny then someone is patient or humble.
Everyone who is either brave or calm is both not humble and patient.
Someone is not rich.
Mary is not calm or not patient.
Mary is both wise and funny.
Paul is generous or not patient.
Someone is curious.
Someone is both rich and happy.
Paul is humble.
John is humble. | Mary is patient. | neutral | ((?[X]:(~quiet(X)))=>((old(susan)&brave(susan))))&
(![X]:((humble(X)|rich(X))=>~old(X)))&
(![X]:(funny(X)<=>(~humble(X)<~>curious(X))))&
((~happy(john))=>(?[X]:(~humble(X))))&
(![X]:((calm(X)&~wise(X))<=>~quiet(X)))&
(![X]:((curious(X)&~wise(X))<=>(~kind(X)<~>~rich(X))))&
(((~rich(susan)|generous(susan)))<=>((~calm(john)|creative(john))))&
(![X]:((~wise(X)<~>wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~quiet(X)<~>strong(X))))=>(?[X]:((patient(X)&humble(X)))))&
(((~happy(john)&old(john)))<=>(~creative(fred)))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~generous(X)<~>~kind(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(tall(X)&creative(X))))&
(![X]:((tall(X)|kind(X))<=>(curious(X)|happy(X))))&
((?[X]:((~patient(X)|wise(X))))<=>(?[X]:(~creative(X))))&
(((strong(susan)&~funny(susan)))=>(?[X]:((patient(X)|humble(X)))))&
(![X]:((brave(X)<~>calm(X))=>(~humble(X)&patient(X))))&
(?[X]:(~rich(X)))&
((~calm(mary)|~patient(mary)))&
((wise(mary)&funny(mary)))&
((generous(paul)|~patient(paul)))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)&happy(X))))&
(humble(paul))&
(humble(john)) | patient(mary) | [] | null | 0 |
If alice is either calm or patient then someone is either curious or not funny and vice versa.
If someone is either curious or not calm then someone is not patient.
Everyone who is both not brave and patient is kind.
If someone is either not rich or calm then lucy is either not happy or happy.
Everyone who is tall is either not creative or not tall.
If someone is not brave then someone is either not happy or not rich.
Everyone who is either humble or not rich is strong or humble and vice versa.
If fred is quiet or not creative then someone is not old and vice versa.
If someone is old then alice is either wise or generous and vice versa.
Everyone who is both patient and not creative is funny.
Everyone who is generous or strong is both not rich and not tall.
Everyone who is wise or not happy is either strong or old.
Everyone who is not humble is not strong and vice versa.
Everyone who is both strong and not quiet is both tall and old.
Everyone who is patient is rich and vice versa.
If john is both not kind and brave then someone is not generous or happy and vice versa.
Alice is creative.
Fred is old.
Lucy is either wise or quiet.
Mary is old.
Lucy is either funny or wise. | Fred is generous. | contradiction | (((calm(alice)<~>patient(alice)))<=>(?[X]:((curious(X)<~>~funny(X)))))&
((?[X]:((curious(X)<~>~calm(X))))=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)&patient(X))=>kind(X)))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(lucy)<~>happy(lucy))))&
(![X]:(tall(X)=>(~creative(X)<~>~tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(strong(X)|humble(X))))&
(((quiet(fred)|~creative(fred)))<=>(?[X]:(~old(X))))&
((?[X]:(old(X)))<=>((wise(alice)<~>generous(alice))))&
(![X]:((patient(X)&~creative(X))=>funny(X)))&
(![X]:((generous(X)|strong(X))=>(~rich(X)&~tall(X))))&
(![X]:((wise(X)|~happy(X))=>(strong(X)<~>old(X))))&
(![X]:(~humble(X)<=>~strong(X)))&
(![X]:((strong(X)&~quiet(X))=>(tall(X)&old(X))))&
(![X]:(patient(X)<=>rich(X)))&
(((~kind(john)&brave(john)))<=>(?[X]:((~generous(X)|happy(X)))))&
(creative(alice))&
(old(fred))&
((wise(lucy)<~>quiet(lucy)))&
(old(mary))&
((funny(lucy)<~>wise(lucy))) | generous(fred) | [
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4567095510958960373417839
% SZS output start Proof for 4567095510958960373417839
7. ! [X0] : ((humble(X0) <~> ~rich(X0)) <=> (humble(X0) | strong(X0))) [input p6]
11. ! [X0] : ((strong(X0) | generous(X0)) => (~tall(X0) & ~rich(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> ~strong(X0)) [input p12]
22. generous(fred) [input hypothesis]
33. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 11]
51. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [nnf transformation 7]
52. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [flattening 51]
63. ! [X0] : ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))) [nnf transformation 13]
92. humble(X0) | strong(X0) | humble(X0) | rich(X0) [cnf transformation 52]
96. rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 52]
105. ~generous(X0) | ~rich(X0) [cnf transformation 33]
113. ~strong(X0) | humble(X0) [cnf transformation 63]
131. generous(fred) [cnf transformation 22]
132. humble(X0) | strong(X0) | rich(X0) [duplicate literal removal 92]
133. ~humble(X0) | rich(X0) [duplicate literal removal 96]
190. strong(X0) | rich(X0) [subsumption resolution 132,133]
272. ~rich(fred) [resolution 105,131]
286. rich(X0) | humble(X0) [resolution 190,113]
289. rich(X0) [subsumption resolution 286,133]
291. $false [resolution 289,272]
% SZS output end Proof for 4567095510958960373417839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is not tall then someone is both patient and generous. Everyone who is both not old and not strong is both tall and funny and vice versa. Everyone who is either not creative or not wise is either not old or tall. If alice is either generous or wise then john is both wise and old. Everyone who is both not humble and humble is tall or not curious and vice versa. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. Someone is either not creative or wise. Someone is happy or not kind. Someone is humble. Someone is patient or generous. Lucy is not old. John is not strong or generous. Someone is not calm or not patient. | John is not kind. | entailment | ((~tall(mary))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((~old(X)&~strong(X))<=>(tall(X)&funny(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(~old(X)<~>tall(X))))&
(((generous(alice)<~>wise(alice)))=>((wise(john)&old(john))))&
(![X]:((~humble(X)&humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:(humble(X)))&
(?[X]:((patient(X)|generous(X))))&
(~old(lucy))&
((~strong(john)|generous(john)))&
(?[X]:((~calm(X)|~patient(X)))) | ~kind(john) | [
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 710084811975542635453555
% SZS output start Proof for 710084811975542635453555
6. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p5]
8. ! [X0] : (~kind(X0) <=> funny(X0)) [input p7]
9. ! [X0] : (humble(X0) <=> (old(X0) <~> ~brave(X0))) [input p8]
10. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p9]
11. brave(john) <=> ? [X0] : (creative(X0) & generous(X0)) [input p10]
14. ! [X0] : ((~old(X0) & happy(X0)) <=> creative(X0)) [input p13]
15. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (~brave(X0) | ~curious(X0))) [input p14]
24. kind(john) [input hypothesis]
26. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X1] : (humble(X1) & ~humble(X1)) [rectify 10]
33. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 26]
43. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 43]
48. ! [X0] : ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))) [nnf transformation 8]
49. ! [X0] : ((humble(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0)))) & (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ~humble(X0))) [nnf transformation 9]
50. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 33]
51. ? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [rectify 50]
52. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
53. (humble(sK2) & ~humble(sK2)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [skolemisation 51,52]
54. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X0] : (creative(X0) & generous(X0)) | ~brave(john)) [nnf transformation 11]
55. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & (? [X1] : (creative(X1) & generous(X1)) | ~brave(john)) [rectify 54]
56. ? [X1] : (creative(X1) & generous(X1)) => (creative(sK3) & generous(sK3)) [choice axiom]
57. (brave(john) | ! [X0] : (~creative(X0) | ~generous(X0))) & ((creative(sK3) & generous(sK3)) | ~brave(john)) [skolemisation 55,56]
63. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 14]
64. ! [X0] : (((~old(X0) & happy(X0)) | ~creative(X0)) & (creative(X0) | old(X0) | ~happy(X0))) [flattening 63]
65. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 15]
66. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 65]
99. ~happy(X0) | rich(X0) | ~brave(X0) [cnf transformation 44]
101. ~rich(X0) | funny(X0) | brave(X0) [cnf transformation 44]
105. ~kind(X0) | ~funny(X0) [cnf transformation 48]
106. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 49]
109. brave(X0) | old(X0) | humble(X0) [cnf transformation 49]
110. ~humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 53]
111. ~humble(sK2) | ~humble(X1) | rich(X1) [cnf transformation 53]
112. humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 53]
113. humble(sK2) | ~humble(X1) | rich(X1) [cnf transformation 53]
115. creative(sK3) | ~brave(john) [cnf transformation 57]
124. ~creative(X0) | happy(X0) [cnf transformation 64]
125. ~creative(X0) | ~old(X0) [cnf transformation 64]
129. ~creative(X0) | old(X0) | brave(X0) [cnf transformation 66]
131. creative(X0) | ~old(X0) | brave(X0) [cnf transformation 66]
143. kind(john) [cnf transformation 24]
171. 6 <=> old(john) [avatar definition]
172. ~old(john) <- (~6) [avatar component clause 171]
173. old(john) <- (6) [avatar component clause 171]
193. 10 <=> ! [X1] : (~humble(X1) | rich(X1)) [avatar definition]
194. ~humble(X1) | rich(X1) <- (10) [avatar component clause 193]
196. 11 <=> humble(sK2) [avatar definition]
199. 10 | 11 [avatar split clause 113,196,193]
201. 12 <=> ! [X1] : (~rich(X1) | humble(X1)) [avatar definition]
202. ~rich(X1) | humble(X1) <- (12) [avatar component clause 201]
203. 12 | 11 [avatar split clause 112,196,201]
204. 10 | ~11 [avatar split clause 111,196,193]
205. 12 | ~11 [avatar split clause 110,196,201]
210. 14 <=> brave(john) [avatar definition]
211. ~brave(john) <- (~14) [avatar component clause 210]
215. 15 <=> creative(sK3) [avatar definition]
217. creative(sK3) <- (15) [avatar component clause 215]
218. ~14 | 15 [avatar split clause 115,215,210]
236. ~old(X0) | brave(X0) [subsumption resolution 131,125]
237. ~creative(X0) | brave(X0) [subsumption resolution 129,236]
295. ~funny(john) [resolution 105,143]
305. brave(john) <- (6) [resolution 173,236]
308. 14 | ~6 [avatar split clause 305,171,210]
309. brave(sK3) <- (15) [resolution 217,237]
311. ~old(sK3) <- (15) [resolution 217,125]
312. happy(sK3) <- (15) [resolution 217,124]
323. rich(sK3) | ~brave(sK3) <- (15) [resolution 99,312]
324. rich(sK3) <- (15) [subsumption resolution 323,309]
327. humble(sK3) <- (12, 15) [resolution 324,202]
352. old(sK3) | ~humble(sK3) <- (15) [resolution 106,309]
354. ~humble(sK3) <- (15) [subsumption resolution 352,311]
355. $false <- (12, 15) [subsumption resolution 354,327]
356. ~12 | ~15 [avatar contradiction clause 355]
370. old(john) | humble(john) <- (~14) [resolution 109,211]
373. humble(john) <- (~6, ~14) [subsumption resolution 370,172]
375. rich(john) <- (~6, 10, ~14) [resolution 373,194]
377. funny(john) | brave(john) <- (~6, 10, ~14) [resolution 375,101]
380. brave(john) <- (~6, 10, ~14) [subsumption resolution 377,295]
381. $false <- (~6, 10, ~14) [subsumption resolution 380,211]
382. 6 | ~10 | 14 [avatar contradiction clause 381]
383. $false [avatar sat refutation 199,203,204,205,218,308,356,382]
% SZS output end Proof for 710084811975542635453555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not generous is both generous and not happy. If someone is creative or not humble then paul is not tall and vice versa. If lucy is not calm or not wise then alice is both creative and kind. Everyone who is both old and not tall is either not rich or not curious and vice versa. Everyone who is happy or not patient is generous. Everyone who is either brave or not funny is calm and vice versa. Everyone who is both not wise and not happy is not generous or creative. Everyone who is both brave and rich is either curious or brave. If someone is not patient then someone is kind. Everyone who is not quiet or old is both not humble and not funny. If someone is curious then susan is rich and vice versa. If someone is funny or not wise then susan is both not strong and not quiet. If someone is either not quiet or brave then someone is rich or generous and vice versa. Everyone who is not quiet or not wise is both strong and not calm and vice versa. If mary is kind or curious then someone is brave and vice versa. If someone is both rich and humble then paul is both not tall and not brave and vice versa. Someone is not patient or not quiet. Paul is either funny or not rich. Mary is both brave and not old. Someone is both not funny and creative. Someone is both not kind and curious. Mary is old or not funny. Paul is both not brave and creative. | Alice is not patient. | neutral | (![X]:((~patient(X)<~>~generous(X))=>(generous(X)&~happy(X))))&
((?[X]:((creative(X)|~humble(X))))<=>(~tall(paul)))&
(((~calm(lucy)|~wise(lucy)))=>((creative(alice)&kind(alice))))&
(![X]:((old(X)&~tall(X))<=>(~rich(X)<~>~curious(X))))&
(![X]:((happy(X)|~patient(X))=>generous(X)))&
(![X]:((brave(X)<~>~funny(X))<=>calm(X)))&
(![X]:((~wise(X)&~happy(X))=>(~generous(X)|creative(X))))&
(![X]:((brave(X)&rich(X))=>(curious(X)<~>brave(X))))&
((?[X]:(~patient(X)))=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)|old(X))=>(~humble(X)&~funny(X))))&
((?[X]:(curious(X)))<=>(rich(susan)))&
((?[X]:((funny(X)|~wise(X))))=>((~strong(susan)&~quiet(susan))))&
((?[X]:((~quiet(X)<~>brave(X))))<=>(?[X]:((rich(X)|generous(X)))))&
(![X]:((~quiet(X)|~wise(X))<=>(strong(X)&~calm(X))))&
(((kind(mary)|curious(mary)))<=>(?[X]:(brave(X))))&
((?[X]:((rich(X)&humble(X))))<=>((~tall(paul)&~brave(paul))))&
(?[X]:((~patient(X)|~quiet(X))))&
((funny(paul)<~>~rich(paul)))&
((brave(mary)&~old(mary)))&
(?[X]:((~funny(X)&creative(X))))&
(?[X]:((~kind(X)&curious(X))))&
((old(mary)|~funny(mary)))&
((~brave(paul)&creative(paul))) | ~patient(alice) | [] | null | 0 |
Everyone who is calm or old is strong or curious. Everyone who is either patient or not rich is both wise and rich. If someone is not generous or not quiet then someone is both not quiet and patient and vice versa. Everyone who is not funny is either not tall or not happy and vice versa. Everyone who is both happy and not wise is either not patient or not calm and vice versa. If someone is funny then fred is brave. Everyone who is not rich or not quiet is not wise and vice versa. If someone is not creative then someone is both wise and creative. If someone is not tall then someone is not rich. Everyone who is not generous or not rich is happy or humble and vice versa. If paul is not funny then someone is old. Everyone who is curious or humble is not old and vice versa. Everyone who is either generous or not curious is not creative. If susan is either creative or not funny then someone is either not funny or not brave. Everyone who is not wise or not rich is patient. Everyone who is both creative and not curious is strong or not brave. Someone is not tall. Someone is calm. Alice is either kind or not quiet. Someone is either creative or not tall. Lucy is either tall or brave. John is both rich and generous. Mary is calm or patient. | Fred is humble. | neutral | (![X]:((calm(X)|old(X))=>(strong(X)|curious(X))))&
(![X]:((patient(X)<~>~rich(X))=>(wise(X)&rich(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(~funny(X)<=>(~tall(X)<~>~happy(X))))&
(![X]:((happy(X)&~wise(X))<=>(~patient(X)<~>~calm(X))))&
((?[X]:(funny(X)))=>(brave(fred)))&
(![X]:((~rich(X)|~quiet(X))<=>~wise(X)))&
((?[X]:(~creative(X)))=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:(~rich(X))))&
(![X]:((~generous(X)|~rich(X))<=>(happy(X)|humble(X))))&
((~funny(paul))=>(?[X]:(old(X))))&
(![X]:((curious(X)|humble(X))<=>~old(X)))&
(![X]:((generous(X)<~>~curious(X))=>~creative(X)))&
(((creative(susan)<~>~funny(susan)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((~wise(X)|~rich(X))=>patient(X)))&
(![X]:((creative(X)&~curious(X))=>(strong(X)|~brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:(calm(X)))&
((kind(alice)<~>~quiet(alice)))&
(?[X]:((creative(X)<~>~tall(X))))&
((tall(lucy)<~>brave(lucy)))&
((rich(john)&generous(john)))&
((calm(mary)|patient(mary))) | humble(fred) | [] | null | 0 |
If lucy is either wise or not generous then someone is not tall and vice versa.
Everyone who is not creative or patient is either calm or rich and vice versa.
Everyone who is both calm and creative is tall.
Everyone who is both rich and happy is both not creative and not quiet and vice versa.
If someone is not rich then someone is both not wise and not calm and vice versa.
Everyone who is not creative or quiet is not funny or funny.
Everyone who is both creative and not creative is brave or not wise and vice versa.
Everyone who is either not calm or creative is funny and vice versa.
Everyone who is not wise or wise is humble or curious.
Everyone who is both quiet and not patient is strong and vice versa.
If someone is both not calm and not old then someone is curious and vice versa.
If alice is both funny and calm then someone is not calm.
Everyone who is not tall is either not curious or not creative and vice versa.
If john is both not funny and rich then mary is both not rich and not strong.
Everyone who is calm is both not old and not quiet and vice versa.
Everyone who is creative is both not humble and rich and vice versa.
Someone is old.
Lucy is either quiet or curious.
John is both not calm and curious.
Someone is both not generous and funny.
Someone is funny or not humble.
Alice is both not humble and quiet.
Someone is rich or wise.
Lucy is kind or not generous. | Alice is patient. | entailment | (((wise(lucy)<~>~generous(lucy)))<=>(?[X]:(~tall(X))))&
(![X]:((~creative(X)|patient(X))<=>(calm(X)<~>rich(X))))&
(![X]:((calm(X)&creative(X))=>tall(X)))&
(![X]:((rich(X)&happy(X))<=>(~creative(X)&~quiet(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~creative(X)|quiet(X))=>(~funny(X)|funny(X))))&
(![X]:((creative(X)&~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((~calm(X)<~>creative(X))<=>funny(X)))&
(![X]:((~wise(X)|wise(X))=>(humble(X)|curious(X))))&
(![X]:((quiet(X)&~patient(X))<=>strong(X)))&
((?[X]:((~calm(X)&~old(X))))<=>(?[X]:(curious(X))))&
(((funny(alice)&calm(alice)))=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)<=>(~curious(X)<~>~creative(X))))&
(((~funny(john)&rich(john)))=>((~rich(mary)&~strong(mary))))&
(![X]:(calm(X)<=>(~old(X)&~quiet(X))))&
(![X]:(creative(X)<=>(~humble(X)&rich(X))))&
(?[X]:(old(X)))&
((quiet(lucy)<~>curious(lucy)))&
((~calm(john)&curious(john)))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:((funny(X)|~humble(X))))&
((~humble(alice)&quiet(alice)))&
(?[X]:((rich(X)|wise(X))))&
((kind(lucy)|~generous(lucy))) | patient(alice) | [
"p1",
"p4",
"p6",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5696612283621120829743857
% SZS output start Proof for 5696612283621120829743857
2. ! [X0] : ((patient(X0) | ~creative(X0)) <=> (calm(X0) <~> rich(X0))) [input p1]
5. ? [X0] : ~rich(X0) <=> ? [X0] : (~calm(X0) & ~wise(X0)) [input p4]
7. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~wise(X0) | brave(X0))) [input p6]
15. ! [X0] : (calm(X0) <=> (~quiet(X0) & ~old(X0))) [input p14]
16. ! [X0] : (creative(X0) <=> (rich(X0) & ~humble(X0))) [input p15]
22. quiet(alice) & ~humble(alice) [input p21]
25. ~patient(alice) [input hypothesis]
26. ? [X0] : ~rich(X0) <=> ? [X1] : (~calm(X1) & ~wise(X1)) [rectify 5]
46. ! [X0] : (((patient(X0) | ~creative(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (~patient(X0) & creative(X0)))) [nnf transformation 2]
47. ! [X0] : ((patient(X0) | ~creative(X0) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (~patient(X0) & creative(X0)))) [flattening 46]
50. (? [X0] : ~rich(X0) | ! [X1] : (calm(X1) | wise(X1))) & (? [X1] : (~calm(X1) & ~wise(X1)) | ! [X0] : rich(X0)) [nnf transformation 26]
51. (? [X0] : ~rich(X0) | ! [X1] : (calm(X1) | wise(X1))) & (? [X2] : (~calm(X2) & ~wise(X2)) | ! [X3] : rich(X3)) [rectify 50]
52. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
53. ? [X2] : (~calm(X2) & ~wise(X2)) => (~calm(sK2) & ~wise(sK2)) [choice axiom]
54. (~rich(sK1) | ! [X1] : (calm(X1) | wise(X1))) & ((~calm(sK2) & ~wise(sK2)) | ! [X3] : rich(X3)) [skolemisation 51,53,52]
55. ! [X0] : (((~creative(X0) & creative(X0)) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 7]
56. ! [X0] : (((~creative(X0) & creative(X0)) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | creative(X0) | ~creative(X0))) [flattening 55]
66. ! [X0] : ((calm(X0) | (quiet(X0) | old(X0))) & ((~quiet(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 15]
67. ! [X0] : ((calm(X0) | quiet(X0) | old(X0)) & ((~quiet(X0) & ~old(X0)) | ~calm(X0))) [flattening 66]
68. ! [X0] : ((creative(X0) | (~rich(X0) | humble(X0))) & ((rich(X0) & ~humble(X0)) | ~creative(X0))) [nnf transformation 16]
69. ! [X0] : ((creative(X0) | ~rich(X0) | humble(X0)) & ((rich(X0) & ~humble(X0)) | ~creative(X0))) [flattening 68]
83. rich(X0) | calm(X0) | creative(X0) [cnf transformation 47]
85. ~rich(X0) | ~calm(X0) | creative(X0) [cnf transformation 47]
88. ~rich(X0) | ~creative(X0) | calm(X0) | patient(X0) [cnf transformation 47]
94. ~wise(sK2) | rich(X3) [cnf transformation 54]
101. creative(X0) | wise(X0) [cnf transformation 56]
103. ~creative(X0) | wise(X0) [cnf transformation 56]
122. ~quiet(X0) | ~calm(X0) [cnf transformation 67]
126. ~rich(X0) | creative(X0) | humble(X0) [cnf transformation 69]
135. ~humble(alice) [cnf transformation 22]
136. quiet(alice) [cnf transformation 22]
138. ~patient(alice) [cnf transformation 25]
167. 7 <=> ! [X3] : rich(X3) [avatar definition]
168. rich(X3) <- (7) [avatar component clause 167]
175. 9 <=> wise(sK2) [avatar definition]
177. ~wise(sK2) <- (~9) [avatar component clause 175]
178. 7 | ~9 [avatar split clause 94,175,167]
179. wise(X0) [subsumption resolution 101,103]
208. 16 <=> calm(alice) [avatar definition]
210. ~calm(alice) <- (~16) [avatar component clause 208]
253. $false <- (~9) [subsumption resolution 177,179]
254. 9 [avatar contradiction clause 253]
264. ~calm(alice) [resolution 122,136]
266. ~16 [avatar split clause 264,208]
277. ~calm(X1) | creative(X1) <- (7) [resolution 85,168]
364. creative(X0) | humble(X0) | calm(X0) | creative(X0) [resolution 126,83]
366. creative(X0) | humble(X0) | calm(X0) [duplicate literal removal 364]
367. humble(X0) | creative(X0) <- (7) [subsumption resolution 366,277]
371. ~creative(X1) | calm(X1) | patient(X1) <- (7) [resolution 88,168]
386. creative(alice) <- (7) [resolution 367,135]
395. calm(alice) | patient(alice) <- (7) [resolution 371,386]
396. patient(alice) <- (7, ~16) [subsumption resolution 395,210]
397. $false <- (7, ~16) [subsumption resolution 396,138]
398. ~7 | 16 [avatar contradiction clause 397]
399. $false [avatar sat refutation 178,254,266,398]
% SZS output end Proof for 5696612283621120829743857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not quiet and rich then someone is not patient or not strong and vice versa.
If lucy is curious then susan is both humble and not calm.
Everyone who is both quiet and not rich is calm and vice versa.
If susan is either not strong or wise then someone is either not happy or old and vice versa.
Everyone who is both calm and curious is kind or curious.
If someone is old then fred is either humble or quiet and vice versa.
Everyone who is both brave and kind is not calm or strong and vice versa.
Everyone who is brave is either wise or humble.
Everyone who is not old or humble is strong or not rich.
Everyone who is humble is old or not curious.
Everyone who is either patient or not humble is not patient.
Everyone who is not patient is humble.
Everyone who is kind is either not quiet or creative and vice versa.
Everyone who is not wise or not quiet is both happy and not curious and vice versa.
If mary is calm or not patient then someone is either calm or not tall.
Everyone who is not curious or not strong is either patient or strong and vice versa.
Someone is either creative or humble.
Paul is not humble or creative.
Susan is either patient or curious.
Paul is either humble or happy.
Someone is happy. | Susan is not creative. | neutral | (((~quiet(fred)&rich(fred)))<=>(?[X]:((~patient(X)|~strong(X)))))&
((curious(lucy))=>((humble(susan)&~calm(susan))))&
(![X]:((quiet(X)&~rich(X))<=>calm(X)))&
(((~strong(susan)<~>wise(susan)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((calm(X)&curious(X))=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>((humble(fred)<~>quiet(fred))))&
(![X]:((brave(X)&kind(X))<=>(~calm(X)|strong(X))))&
(![X]:(brave(X)=>(wise(X)<~>humble(X))))&
(![X]:((~old(X)|humble(X))=>(strong(X)|~rich(X))))&
(![X]:(humble(X)=>(old(X)|~curious(X))))&
(![X]:((patient(X)<~>~humble(X))=>~patient(X)))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(kind(X)<=>(~quiet(X)<~>creative(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(happy(X)&~curious(X))))&
(((calm(mary)|~patient(mary)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((~curious(X)|~strong(X))<=>(patient(X)<~>strong(X))))&
(?[X]:((creative(X)<~>humble(X))))&
((~humble(paul)|creative(paul)))&
((patient(susan)<~>curious(susan)))&
((humble(paul)<~>happy(paul)))&
(?[X]:(happy(X))) | ~creative(susan) | [] | null | 0 |
Everyone who is not wise or not tall is both not calm and not funny and vice versa. Everyone who is both quiet and curious is either brave or not patient. If fred is generous then lucy is either curious or calm. If someone is kind then paul is both not funny and not tall and vice versa. If lucy is both curious and humble then john is either curious or rich. If someone is creative or not kind then someone is not kind or not strong. Everyone who is both generous and not old is either curious or not quiet. If someone is both not curious and not happy then susan is either not quiet or not humble and vice versa. Everyone who is not rich is not quiet and vice versa. Everyone who is either patient or curious is not tall. If someone is both not creative and brave then someone is happy or not curious. If someone is quiet or strong then mary is both not creative and funny. If paul is either not happy or not humble then lucy is not brave. Everyone who is either calm or brave is not strong or tall and vice versa. If someone is not creative then someone is both brave and humble. If someone is rich then someone is not quiet and vice versa. Susan is either calm or not old. Susan is either not old or curious. Mary is both not humble and quiet. John is both not brave and quiet. Someone is not funny. Fred is patient. Mary is either not brave or not tall. Someone is wise or happy. | John is not rich. | contradiction | (![X]:((~wise(X)|~tall(X))<=>(~calm(X)&~funny(X))))&
(![X]:((quiet(X)&curious(X))=>(brave(X)<~>~patient(X))))&
((generous(fred))=>((curious(lucy)<~>calm(lucy))))&
((?[X]:(kind(X)))<=>((~funny(paul)&~tall(paul))))&
(((curious(lucy)&humble(lucy)))=>((curious(john)<~>rich(john))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:((~kind(X)|~strong(X)))))&
(![X]:((generous(X)&~old(X))=>(curious(X)<~>~quiet(X))))&
((?[X]:((~curious(X)&~happy(X))))<=>((~quiet(susan)<~>~humble(susan))))&
(![X]:(~rich(X)<=>~quiet(X)))&
(![X]:((patient(X)<~>curious(X))=>~tall(X)))&
((?[X]:((~creative(X)&brave(X))))=>(?[X]:((happy(X)|~curious(X)))))&
((?[X]:((quiet(X)|strong(X))))=>((~creative(mary)&funny(mary))))&
(((~happy(paul)<~>~humble(paul)))=>(~brave(lucy)))&
(![X]:((calm(X)<~>brave(X))<=>(~strong(X)|tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((brave(X)&humble(X)))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
((calm(susan)<~>~old(susan)))&
((~old(susan)<~>curious(susan)))&
((~humble(mary)&quiet(mary)))&
((~brave(john)&quiet(john)))&
(?[X]:(~funny(X)))&
(patient(fred))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:((wise(X)|happy(X)))) | ~rich(john) | [
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6168977290292085191904794
% SZS output start Proof for 6168977290292085191904794
9. ! [X0] : (~rich(X0) <=> ~quiet(X0)) [input p8]
20. quiet(john) & ~brave(john) [input p19]
25. ~rich(john) [input hypothesis]
58. ! [X0] : ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0))) [nnf transformation 9]
101. ~quiet(X0) | rich(X0) [cnf transformation 58]
129. quiet(john) [cnf transformation 20]
135. ~rich(john) [cnf transformation 25]
168. 8 <=> rich(john) [avatar definition]
170. ~rich(john) <- (~8) [avatar component clause 168]
324. ~8 [avatar split clause 135,168]
346. rich(john) [resolution 101,129]
348. $false <- (~8) [subsumption resolution 346,170]
349. 8 [avatar contradiction clause 348]
350. $false [avatar sat refutation 324,349]
% SZS output end Proof for 6168977290292085191904794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or rich is both not wise and not calm.
If someone is not happy or not generous then paul is either happy or not generous and vice versa.
Everyone who is both tall and generous is not happy or not kind and vice versa.
Everyone who is both not funny and brave is creative and vice versa.
If someone is not generous or strong then someone is both quiet and not humble and vice versa.
If lucy is not happy or humble then someone is generous or not strong.
If someone is not brave or not creative then paul is not wise or tall.
Everyone who is both not curious and old is creative or not curious and vice versa.
Everyone who is either not happy or not strong is either wise or not brave.
Everyone who is either not creative or creative is rich or not strong and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Fred is not calm. | entailment | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>((happy(paul)<~>~generous(paul))))&
(![X]:((tall(X)&generous(X))<=>(~happy(X)|~kind(X))))&
(![X]:((~funny(X)&brave(X))<=>creative(X)))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((~happy(lucy)|humble(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((?[X]:((~brave(X)|~creative(X))))=>((~wise(paul)|tall(paul))))&
(![X]:((~curious(X)&old(X))<=>(creative(X)|~curious(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)<~>~brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(rich(X)|~strong(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | ~calm(fred) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p11",
"p13",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3473992208190521179273807
% SZS output start Proof for 3473992208190521179273807
1. ! [X0] : ((rich(X0) | generous(X0)) => (~calm(X0) & ~wise(X0))) [input p0]
2. ? [X0] : (~generous(X0) | ~happy(X0)) <=> (happy(paul) <~> ~generous(paul)) [input p1]
3. ! [X0] : ((generous(X0) & tall(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
9. ! [X0] : ((~happy(X0) <~> ~strong(X0)) => (wise(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~strong(X0) | rich(X0))) [input p9]
12. ! [X0] : (funny(X0) <=> ~wise(X0)) [input p11]
14. ? [X0] : (~funny(X0) | ~brave(X0)) <=> ~tall(fred) [input p13]
21. ~rich(fred) <~> ~tall(fred) [input p20]
23. ~quiet(paul) & ~rich(paul) [input p22]
25. calm(fred) [input hypothesis]
29. ! [X0] : ((~calm(X0) & ~wise(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 1]
33. ! [X0] : ((wise(X0) <~> ~brave(X0)) | (~happy(X0) <=> ~strong(X0))) [ennf transformation 9]
35. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X0] : (generous(X0) & happy(X0))) [nnf transformation 2]
36. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [rectify 35]
37. ? [X0] : (~generous(X0) | ~happy(X0)) => (~generous(sK0) | ~happy(sK0)) [choice axiom]
38. ((~generous(sK0) | ~happy(sK0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [skolemisation 36,37]
39. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 3]
40. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~generous(X0) | ~tall(X0))) [flattening 39]
52. ! [X0] : (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) [nnf transformation 33]
53. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 53]
58. ! [X0] : ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))) [nnf transformation 12]
64. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X0] : (funny(X0) & brave(X0))) [nnf transformation 14]
65. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [rectify 64]
66. ? [X0] : (~funny(X0) | ~brave(X0)) => (~funny(sK7) | ~brave(sK7)) [choice axiom]
67. ((~funny(sK7) | ~brave(sK7)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [skolemisation 65,66]
75. (tall(fred) | rich(fred)) & (~tall(fred) | ~rich(fred)) [nnf transformation 21]
83. ~calm(X0) | ~rich(X0) [cnf transformation 29]
84. ~generous(paul) | happy(paul) | happy(X1) [cnf transformation 38]
93. happy(X0) | generous(X0) [cnf transformation 40]
113. ~brave(X0) | wise(X0) | ~happy(X0) | strong(X0) [cnf transformation 52]
116. ~strong(X0) | rich(X0) | creative(X0) | creative(X0) [cnf transformation 54]
117. ~strong(X0) | rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 54]
124. ~funny(X0) | ~wise(X0) [cnf transformation 58]
129. ~tall(fred) | brave(X1) [cnf transformation 67]
130. ~tall(fred) | funny(X1) [cnf transformation 67]
153. tall(fred) | rich(fred) [cnf transformation 75]
156. ~rich(paul) [cnf transformation 23]
159. calm(fred) [cnf transformation 25]
162. ~strong(X0) | rich(X0) | creative(X0) [duplicate literal removal 116]
163. ~strong(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 117]
165. 1 <=> generous(paul) [avatar definition]
166. ~generous(paul) <- (~1) [avatar component clause 165]
169. 2 <=> happy(paul) [avatar definition]
170. ~happy(paul) <- (~2) [avatar component clause 169]
171. happy(paul) <- (2) [avatar component clause 169]
187. 6 <=> ! [X1] : happy(X1) [avatar definition]
188. happy(X1) <- (6) [avatar component clause 187]
191. 6 | 2 | ~1 [avatar split clause 84,165,169,187]
241. 18 <=> wise(paul) [avatar definition]
242. wise(paul) <- (18) [avatar component clause 241]
243. ~wise(paul) <- (~18) [avatar component clause 241]
250. 20 <=> ! [X0] : brave(X0) [avatar definition]
251. brave(X0) <- (20) [avatar component clause 250]
253. ~strong(X0) | rich(X0) [subsumption resolution 162,163]
273. 25 <=> tall(fred) [avatar definition]
286. 28 <=> ! [X1] : funny(X1) [avatar definition]
287. funny(X1) <- (28) [avatar component clause 286]
288. 28 | ~25 [avatar split clause 130,273,286]
289. 20 | ~25 [avatar split clause 129,273,250]
325. 35 <=> rich(fred) [avatar definition]
328. 35 | 25 [avatar split clause 153,273,325]
335. ~rich(fred) [resolution 83,159]
336. generous(paul) <- (~2) [resolution 93,170]
337. $false <- (~1, ~2) [subsumption resolution 336,166]
338. 1 | 2 [avatar contradiction clause 337]
352. ~happy(X0) | wise(X0) | strong(X0) <- (20) [resolution 113,251]
360. ~35 [avatar split clause 335,325]
418. ~wise(X0) <- (28) [resolution 287,124]
470. wise(paul) | strong(paul) <- (2, 20) [resolution 352,171]
475. strong(paul) <- (2, ~18, 20) [subsumption resolution 470,243]
481. rich(paul) <- (2, ~18, 20) [resolution 475,253]
486. $false <- (2, ~18, 20) [subsumption resolution 481,156]
487. ~2 | 18 | ~20 [avatar contradiction clause 486]
489. $false <- (18, 28) [subsumption resolution 242,418]
490. ~18 | ~28 [avatar contradiction clause 489]
491. $false <- (~2, 6) [subsumption resolution 170,188]
492. 2 | ~6 [avatar contradiction clause 491]
493. $false [avatar sat refutation 191,288,289,328,338,360,487,490,492]
% SZS output end Proof for 3473992208190521179273807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or quiet then someone is either not kind or wise.
Everyone who is patient is both not patient and quiet and vice versa.
If paul is strong then someone is strong.
Everyone who is old or not quiet is both curious and not brave.
If paul is either wise or not old then fred is tall.
Everyone who is both not quiet and not patient is both not tall and old.
Everyone who is both not quiet and quiet is either not generous or not curious and vice versa.
If someone is not creative then alice is either not brave or not curious.
If alice is curious then someone is either not humble or not creative and vice versa.
Everyone who is both creative and not creative is both not strong and strong.
Everyone who is both not strong and generous is quiet and vice versa.
Everyone who is both kind and not old is either not strong or not funny and vice versa.
If john is either kind or quiet then paul is either kind or tall.
Everyone who is both not brave and happy is both tall and wise.
Everyone who is either old or tall is old and vice versa.
Everyone who is not humble or tall is not wise.
Someone is kind or not happy.
Someone is not kind.
Lucy is either calm or happy.
Paul is not funny or generous.
Someone is generous. | Paul is not happy. | entailment | ((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(patient(X)<=>(~patient(X)&quiet(X))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
(((wise(paul)<~>~old(paul)))=>(tall(fred)))&
(![X]:((~quiet(X)&~patient(X))=>(~tall(X)&old(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>((~brave(alice)<~>~curious(alice))))&
((curious(alice))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((creative(X)&~creative(X))=>(~strong(X)&strong(X))))&
(![X]:((~strong(X)&generous(X))<=>quiet(X)))&
(![X]:((kind(X)&~old(X))<=>(~strong(X)<~>~funny(X))))&
(((kind(john)<~>quiet(john)))=>((kind(paul)<~>tall(paul))))&
(![X]:((~brave(X)&happy(X))=>(tall(X)&wise(X))))&
(![X]:((old(X)<~>tall(X))<=>old(X)))&
(![X]:((~humble(X)|tall(X))=>~wise(X)))&
(?[X]:((kind(X)|~happy(X))))&
(?[X]:(~kind(X)))&
((calm(lucy)<~>happy(lucy)))&
((~funny(paul)|generous(paul)))&
(?[X]:(generous(X))) | ~happy(paul) | [
"p1",
"p3",
"p6",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1108067419609928493298543
% SZS output start Proof for 1108067419609928493298543
2. ! [X0] : (patient(X0) <=> (quiet(X0) & ~patient(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) | old(X0)) => (~brave(X0) & curious(X0))) [input p3]
7. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p6]
11. ! [X0] : ((generous(X0) & ~strong(X0)) <=> quiet(X0)) [input p10]
14. ! [X0] : ((happy(X0) & ~brave(X0)) => (wise(X0) & tall(X0))) [input p13]
15. ! [X0] : ((old(X0) <~> tall(X0)) <=> old(X0)) [input p14]
22. happy(paul) [input hypothesis]
26. ! [X0] : ((~brave(X0) & curious(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 4]
34. ! [X0] : ((wise(X0) & tall(X0)) | (~happy(X0) | brave(X0))) [ennf transformation 14]
35. ! [X0] : ((wise(X0) & tall(X0)) | ~happy(X0) | brave(X0)) [flattening 34]
41. ! [X0] : ((patient(X0) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 2]
42. ! [X0] : ((patient(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | ~patient(X0))) [flattening 41]
46. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (~quiet(X0) | quiet(X0)))) [nnf transformation 7]
47. ! [X0] : (((quiet(X0) & ~quiet(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | ~quiet(X0) | quiet(X0))) [flattening 46]
53. ! [X0] : (((generous(X0) & ~strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) | strong(X0)))) [nnf transformation 11]
54. ! [X0] : (((generous(X0) & ~strong(X0)) | ~quiet(X0)) & (quiet(X0) | ~generous(X0) | strong(X0))) [flattening 53]
58. ! [X0] : ((((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | ~old(X0)) & (old(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0))))) [nnf transformation 15]
70. ~patient(X0) | ~patient(X0) [cnf transformation 42]
72. patient(X0) | ~quiet(X0) | patient(X0) [cnf transformation 42]
75. curious(X0) | quiet(X0) [cnf transformation 26]
77. ~brave(X0) | quiet(X0) [cnf transformation 26]
86. quiet(X0) | ~curious(X0) | generous(X0) [cnf transformation 47]
96. quiet(X0) | ~generous(X0) | strong(X0) [cnf transformation 54]
97. ~strong(X0) | ~quiet(X0) [cnf transformation 54]
98. generous(X0) | ~quiet(X0) [cnf transformation 54]
109. ~happy(X0) | tall(X0) | brave(X0) [cnf transformation 35]
112. old(X0) | old(X0) | ~tall(X0) [cnf transformation 58]
114. ~tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 58]
123. happy(paul) [cnf transformation 22]
124. old(X0) | ~tall(X0) [duplicate literal removal 112]
125. ~tall(X0) | ~old(X0) [duplicate literal removal 114]
126. ~patient(X0) [duplicate literal removal 70]
127. ~quiet(X0) | patient(X0) [duplicate literal removal 72]
147. 5 <=> strong(paul) [avatar definition]
148. strong(paul) <- (5) [avatar component clause 147]
149. ~strong(paul) <- (~5) [avatar component clause 147]
172. generous(X0) | quiet(X0) [subsumption resolution 86,75]
206. generous(X0) [subsumption resolution 98,172]
207. strong(X0) | quiet(X0) [subsumption resolution 96,206]
228. ~tall(X0) [subsumption resolution 124,125]
270. quiet(paul) <- (~5) [resolution 207,149]
272. patient(paul) <- (~5) [resolution 270,127]
273. $false <- (~5) [subsumption resolution 272,126]
274. 5 [avatar contradiction clause 273]
275. ~quiet(paul) <- (5) [resolution 148,97]
306. tall(paul) | brave(paul) [resolution 109,123]
307. brave(paul) [subsumption resolution 306,228]
315. quiet(paul) [resolution 307,77]
317. $false <- (5) [subsumption resolution 315,275]
318. ~5 [avatar contradiction clause 317]
321. $false [avatar sat refutation 274,318]
% SZS output end Proof for 1108067419609928493298543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not calm is not kind and vice versa.
Everyone who is either funny or not quiet is happy or not wise and vice versa.
Everyone who is old or brave is both tall and not humble and vice versa.
Everyone who is either not happy or happy is both not curious and quiet.
Everyone who is not calm is both curious and not strong and vice versa.
Everyone who is not kind or not brave is either creative or not wise and vice versa.
Everyone who is both calm and wise is not old or not generous and vice versa.
Everyone who is old is not humble.
Everyone who is not funny or not brave is either not rich or brave.
Everyone who is calm or not curious is not kind and vice versa.
Everyone who is not funny or not quiet is quiet or not funny.
Everyone who is not brave is either rich or not generous and vice versa.
Everyone who is both calm and not creative is wise.
Everyone who is not tall or rich is tall or creative and vice versa.
If mary is both not humble and not happy then paul is both happy and not generous.
Someone is either patient or calm.
Someone is not brave or not funny.
Lucy is humble or calm.
Fred is either humble or brave.
Paul is not happy or not curious. | Mary is not generous. | entailment | (![X]:((~brave(X)|~calm(X))<=>~kind(X)))&
(![X]:((funny(X)<~>~quiet(X))<=>(happy(X)|~wise(X))))&
(![X]:((old(X)|brave(X))<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)<~>happy(X))=>(~curious(X)&quiet(X))))&
(![X]:(~calm(X)<=>(curious(X)&~strong(X))))&
(![X]:((~kind(X)|~brave(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((calm(X)&wise(X))<=>(~old(X)|~generous(X))))&
(![X]:(old(X)=>~humble(X)))&
(![X]:((~funny(X)|~brave(X))=>(~rich(X)<~>brave(X))))&
(![X]:((calm(X)|~curious(X))<=>~kind(X)))&
(![X]:((~funny(X)|~quiet(X))=>(quiet(X)|~funny(X))))&
(![X]:(~brave(X)<=>(rich(X)<~>~generous(X))))&
(![X]:((calm(X)&~creative(X))=>wise(X)))&
(![X]:((~tall(X)|rich(X))<=>(tall(X)|creative(X))))&
(((~humble(mary)&~happy(mary)))=>((happy(paul)&~generous(paul))))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~brave(X)|~funny(X))))&
((humble(lucy)|calm(lucy)))&
((humble(fred)<~>brave(fred)))&
((~happy(paul)|~curious(paul))) | ~generous(mary) | [
"p0",
"p3",
"p4",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2156846028920679663231412
% SZS output start Proof for 2156846028920679663231412
1. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> ~kind(X0)) [input p0]
4. ! [X0] : ((~happy(X0) <~> happy(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (~strong(X0) & curious(X0))) [input p4]
9. ! [X0] : ((~brave(X0) | ~funny(X0)) => (~rich(X0) <~> brave(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | calm(X0)) <=> ~kind(X0)) [input p9]
12. ! [X0] : (~brave(X0) <=> (rich(X0) <~> ~generous(X0))) [input p11]
21. generous(mary) [input hypothesis]
22. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 4]
24. ! [X0] : ((~rich(X0) <~> brave(X0)) | (brave(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : (((~calm(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [nnf transformation 1]
32. ! [X0] : ((~calm(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (calm(X0) & brave(X0)))) [flattening 31]
37. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 22]
38. ! [X0] : ((~calm(X0) | (strong(X0) | ~curious(X0))) & ((~strong(X0) & curious(X0)) | calm(X0))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | strong(X0) | ~curious(X0)) & ((~strong(X0) & curious(X0)) | calm(X0))) [flattening 38]
44. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (brave(X0) & funny(X0))) [nnf transformation 24]
45. ! [X0] : (((~curious(X0) | calm(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~curious(X0) | calm(X0) | kind(X0)) & (~kind(X0) | (curious(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : ((~brave(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | brave(X0))) [nnf transformation 12]
58. ~calm(X0) | ~brave(X0) | kind(X0) [cnf transformation 32]
70. ~curious(X0) | happy(X0) | happy(X0) [cnf transformation 37]
71. ~curious(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 37]
74. curious(X0) | calm(X0) [cnf transformation 39]
90. brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 44]
94. ~kind(X0) | curious(X0) [cnf transformation 46]
98. ~generous(X0) | rich(X0) | brave(X0) [cnf transformation 47]
100. ~brave(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 47]
116. generous(mary) [cnf transformation 21]
120. ~rich(X0) | brave(X0) [duplicate literal removal 90]
121. ~curious(X0) | happy(X0) [duplicate literal removal 70]
122. ~curious(X0) | ~happy(X0) [duplicate literal removal 71]
126. ~curious(X0) [subsumption resolution 121,122]
127. calm(X0) [subsumption resolution 74,126]
131. ~kind(X0) [subsumption resolution 94,126]
132. ~rich(X0) | ~generous(X0) [subsumption resolution 100,120]
133. ~generous(X0) | brave(X0) [subsumption resolution 98,132]
178. brave(mary) [resolution 133,116]
182. ~brave(X0) | kind(X0) [resolution 58,127]
183. ~brave(X0) [subsumption resolution 182,131]
184. $false [resolution 183,178]
% SZS output end Proof for 2156846028920679663231412
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not happy is not humble and vice versa. Everyone who is either not humble or happy is either not brave or not patient. Everyone who is not happy is calm. If someone is both not humble and kind then someone is either funny or not funny. Everyone who is either old or wise is either calm or not calm and vice versa. If someone is both kind and not funny then someone is both quiet and not rich and vice versa. If someone is both funny and humble then someone is not patient and vice versa. Everyone who is not kind is both not kind and not wise. If fred is either not humble or patient then fred is either not calm or not humble. Everyone who is not patient or not quiet is patient and vice versa. Everyone who is both strong and tall is brave or curious and vice versa. Everyone who is patient is both not strong and funny and vice versa. Everyone who is either brave or happy is either not humble or not wise and vice versa. If alice is either happy or rich then someone is both not humble and not quiet. Everyone who is rich is not curious and vice versa. Everyone who is not strong is either not generous or patient. Someone is both calm and happy. Lucy is kind or not wise. Someone is rich. John is generous or funny. Lucy is patient or old. | Fred is not humble. | entailment | (![X]:((~curious(X)|~happy(X))<=>~humble(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~brave(X)<~>~patient(X))))&
(![X]:(~happy(X)=>calm(X)))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:((old(X)<~>wise(X))<=>(calm(X)<~>~calm(X))))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((quiet(X)&~rich(X)))))&
((?[X]:((funny(X)&humble(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~kind(X)&~wise(X))))&
(((~humble(fred)<~>patient(fred)))=>((~calm(fred)<~>~humble(fred))))&
(![X]:((~patient(X)|~quiet(X))<=>patient(X)))&
(![X]:((strong(X)&tall(X))<=>(brave(X)|curious(X))))&
(![X]:(patient(X)<=>(~strong(X)&funny(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~humble(X)<~>~wise(X))))&
(((happy(alice)<~>rich(alice)))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:(rich(X)<=>~curious(X)))&
(![X]:(~strong(X)=>(~generous(X)<~>patient(X))))&
(?[X]:((calm(X)&happy(X))))&
((kind(lucy)|~wise(lucy)))&
(?[X]:(rich(X)))&
((generous(john)|funny(john)))&
((patient(lucy)|old(lucy))) | ~humble(fred) | [
"p0",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 192762994293656073518609
% SZS output start Proof for 192762994293656073518609
1. ! [X0] : ((~happy(X0) | ~curious(X0)) <=> ~humble(X0)) [input p0]
10. ! [X0] : ((~quiet(X0) | ~patient(X0)) <=> patient(X0)) [input p9]
11. ! [X0] : ((tall(X0) & strong(X0)) <=> (curious(X0) | brave(X0))) [input p10]
12. ! [X0] : (patient(X0) <=> (funny(X0) & ~strong(X0))) [input p11]
22. humble(fred) [input hypothesis]
33. ! [X0] : (((~happy(X0) | ~curious(X0)) | humble(X0)) & (~humble(X0) | (happy(X0) & curious(X0)))) [nnf transformation 1]
34. ! [X0] : ((~happy(X0) | ~curious(X0) | humble(X0)) & (~humble(X0) | (happy(X0) & curious(X0)))) [flattening 33]
52. ! [X0] : (((~quiet(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (quiet(X0) & patient(X0)))) [nnf transformation 10]
53. ! [X0] : ((~quiet(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (quiet(X0) & patient(X0)))) [flattening 52]
54. ! [X0] : (((tall(X0) & strong(X0)) | (~curious(X0) & ~brave(X0))) & ((curious(X0) | brave(X0)) | (~tall(X0) | ~strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((tall(X0) & strong(X0)) | (~curious(X0) & ~brave(X0))) & (curious(X0) | brave(X0) | ~tall(X0) | ~strong(X0))) [flattening 54]
56. ! [X0] : ((patient(X0) | (~funny(X0) | strong(X0))) & ((funny(X0) & ~strong(X0)) | ~patient(X0))) [nnf transformation 12]
57. ! [X0] : ((patient(X0) | ~funny(X0) | strong(X0)) & ((funny(X0) & ~strong(X0)) | ~patient(X0))) [flattening 56]
68. ~humble(X0) | curious(X0) [cnf transformation 34]
99. patient(X0) | patient(X0) [cnf transformation 53]
104. ~curious(X0) | strong(X0) [cnf transformation 55]
107. ~strong(X0) | ~patient(X0) [cnf transformation 57]
132. humble(fred) [cnf transformation 22]
133. patient(X0) [duplicate literal removal 99]
174. 7 <=> ! [X1] : patient(X1) [avatar definition]
175. patient(X1) <- (7) [avatar component clause 174]
203. 14 <=> humble(fred) [avatar definition]
205. humble(fred) <- (14) [avatar component clause 203]
208. 7 [avatar split clause 133,174]
252. 14 [avatar split clause 132,203]
255. curious(fred) <- (14) [resolution 68,205]
258. strong(fred) <- (14) [resolution 104,255]
260. ~patient(fred) <- (14) [resolution 107,258]
261. $false <- (7, 14) [subsumption resolution 260,175]
262. ~7 | ~14 [avatar contradiction clause 261]
263. $false [avatar sat refutation 208,252,262]
% SZS output end Proof for 192762994293656073518609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and curious is not curious or happy. If paul is happy or tall then mary is kind and vice versa. If fred is both not brave and not wise then paul is rich and vice versa. Everyone who is either kind or not quiet is strong. If someone is either calm or not quiet then someone is either calm or not calm. Everyone who is both not humble and not creative is not generous. If someone is brave then someone is not wise or tall. Everyone who is either wise or rich is not generous or not funny. Everyone who is either quiet or old is patient or not old and vice versa. Everyone who is humble is not calm and vice versa. If lucy is curious or not patient then john is not generous or not creative and vice versa. Everyone who is both not calm and patient is not wise or funny and vice versa. If alice is creative then someone is not patient or wise. Everyone who is wise or not creative is both not rich and curious and vice versa. Everyone who is both curious and funny is both not curious and curious and vice versa. If john is either curious or patient then mary is both brave and generous and vice versa. Alice is rich. Someone is either not patient or rich. John is either kind or generous. Alice is both brave and strong. John is both wise and not patient. Lucy is curious. Susan is either not patient or creative. | Lucy is old. | neutral | (![X]:((~wise(X)&curious(X))=>(~curious(X)|happy(X))))&
(((happy(paul)|tall(paul)))<=>(kind(mary)))&
(((~brave(fred)&~wise(fred)))<=>(rich(paul)))&
(![X]:((kind(X)<~>~quiet(X))=>strong(X)))&
((?[X]:((calm(X)<~>~quiet(X))))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~humble(X)&~creative(X))=>~generous(X)))&
((?[X]:(brave(X)))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((wise(X)<~>rich(X))=>(~generous(X)|~funny(X))))&
(![X]:((quiet(X)<~>old(X))<=>(patient(X)|~old(X))))&
(![X]:(humble(X)<=>~calm(X)))&
(((curious(lucy)|~patient(lucy)))<=>((~generous(john)|~creative(john))))&
(![X]:((~calm(X)&patient(X))<=>(~wise(X)|funny(X))))&
((creative(alice))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((wise(X)|~creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((curious(X)&funny(X))<=>(~curious(X)&curious(X))))&
(((curious(john)<~>patient(john)))<=>((brave(mary)&generous(mary))))&
(rich(alice))&
(?[X]:((~patient(X)<~>rich(X))))&
((kind(john)<~>generous(john)))&
((brave(alice)&strong(alice)))&
((wise(john)&~patient(john)))&
(curious(lucy))&
((~patient(susan)<~>creative(susan))) | old(lucy) | [] | null | 0 |
Everyone who is kind is both not tall and not creative. If someone is either old or creative then alice is not wise or quiet and vice versa. Everyone who is brave or tall is both not patient and old and vice versa. If someone is either calm or not strong then mary is either not old or kind. Everyone who is either old or not strong is not kind or not funny. If paul is both not patient and not rich then someone is not generous. Everyone who is not strong or quiet is either not creative or not quiet and vice versa. If alice is funny then someone is funny or wise and vice versa. Everyone who is not kind is quiet and vice versa. If john is either generous or rich then someone is either curious or wise and vice versa. Everyone who is not humble or old is brave or generous and vice versa. Everyone who is both calm and tall is both not tall and not generous. If susan is both quiet and not quiet then someone is not generous and vice versa. If john is either kind or generous then john is either funny or rich and vice versa. If someone is humble or calm then someone is not curious and vice versa. Everyone who is generous is rich or not kind and vice versa. Someone is either rich or generous. Someone is not humble or patient. Alice is wise or happy. John is not happy. Alice is kind or not wise. Fred is not calm. | Mary is not generous. | contradiction | (![X]:(kind(X)=>(~tall(X)&~creative(X))))&
((?[X]:((old(X)<~>creative(X))))<=>((~wise(alice)|quiet(alice))))&
(![X]:((brave(X)|tall(X))<=>(~patient(X)&old(X))))&
((?[X]:((calm(X)<~>~strong(X))))=>((~old(mary)<~>kind(mary))))&
(![X]:((old(X)<~>~strong(X))=>(~kind(X)|~funny(X))))&
(((~patient(paul)&~rich(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~strong(X)|quiet(X))<=>(~creative(X)<~>~quiet(X))))&
((funny(alice))<=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~kind(X)<=>quiet(X)))&
(((generous(john)<~>rich(john)))<=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~humble(X)|old(X))<=>(brave(X)|generous(X))))&
(![X]:((calm(X)&tall(X))=>(~tall(X)&~generous(X))))&
(((quiet(susan)&~quiet(susan)))<=>(?[X]:(~generous(X))))&
(((kind(john)<~>generous(john)))<=>((funny(john)<~>rich(john))))&
((?[X]:((humble(X)|calm(X))))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(rich(X)|~kind(X))))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~humble(X)|patient(X))))&
((wise(alice)|happy(alice)))&
(~happy(john))&
((kind(alice)|~wise(alice)))&
(~calm(fred)) | ~generous(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1686388707844808813344937
% SZS output start Proof for 1686388707844808813344937
13. (~quiet(susan) & quiet(susan)) <=> ? [X0] : ~generous(X0) [input p12]
23. ~generous(mary) [input hypothesis]
57. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (quiet(susan) | ~quiet(susan))) [nnf transformation 13]
58. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | quiet(susan) | ~quiet(susan)) [flattening 57]
59. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | quiet(susan) | ~quiet(susan)) [rectify 58]
60. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
61. ((~quiet(susan) & quiet(susan)) | ! [X0] : generous(X0)) & (~generous(sK4) | quiet(susan) | ~quiet(susan)) [skolemisation 59,60]
121. quiet(susan) | generous(X0) [cnf transformation 61]
122. ~quiet(susan) | generous(X0) [cnf transformation 61]
144. ~generous(mary) [cnf transformation 23]
259. 25 <=> ! [X0] : generous(X0) [avatar definition]
260. generous(X0) <- (25) [avatar component clause 259]
262. 26 <=> quiet(susan) [avatar definition]
265. 25 | ~26 [avatar split clause 122,262,259]
266. 25 | 26 [avatar split clause 121,262,259]
345. $false <- (25) [resolution 260,144]
346. ~25 [avatar contradiction clause 345]
347. $false [avatar sat refutation 265,266,346]
% SZS output end Proof for 1686388707844808813344937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then someone is either not calm or tall. If someone is old or not patient then someone is both not old and humble. Everyone who is not patient or not generous is either not calm or not wise. If susan is generous or not strong then someone is not funny. If someone is either not patient or not curious then someone is both wise and not calm and vice versa. If mary is both not kind and not old then someone is either not kind or strong and vice versa. Everyone who is either patient or not kind is old and vice versa. Everyone who is not funny is either not tall or not brave and vice versa. Everyone who is both wise and not patient is both humble and generous and vice versa. If someone is not old then someone is either not wise or not brave. If someone is not calm or not patient then lucy is both kind and not old and vice versa. Everyone who is either brave or humble is either not creative or happy and vice versa. If someone is not rich or not tall then someone is wise or not creative and vice versa. Everyone who is humble is brave or humble. Everyone who is both not curious and not old is rich or calm. Everyone who is either not patient or not generous is either funny or not quiet. Lucy is both not creative and not quiet. Someone is not wise. Someone is calm or not tall. Someone is both not wise and kind. Someone is funny or quiet. John is both not curious and not strong. John is not calm or not funny. | Susan is tall. | neutral | ((?[X]:(~calm(X)))=>(?[X]:((~calm(X)<~>tall(X)))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:((~old(X)&humble(X)))))&
(![X]:((~patient(X)|~generous(X))=>(~calm(X)<~>~wise(X))))&
(((generous(susan)|~strong(susan)))=>(?[X]:(~funny(X))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
(((~kind(mary)&~old(mary)))<=>(?[X]:((~kind(X)<~>strong(X)))))&
(![X]:((patient(X)<~>~kind(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~tall(X)<~>~brave(X))))&
(![X]:((wise(X)&~patient(X))<=>(humble(X)&generous(X))))&
((?[X]:(~old(X)))=>(?[X]:((~wise(X)<~>~brave(X)))))&
((?[X]:((~calm(X)|~patient(X))))<=>((kind(lucy)&~old(lucy))))&
(![X]:((brave(X)<~>humble(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~rich(X)|~tall(X))))<=>(?[X]:((wise(X)|~creative(X)))))&
(![X]:(humble(X)=>(brave(X)|humble(X))))&
(![X]:((~curious(X)&~old(X))=>(rich(X)|calm(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(funny(X)<~>~quiet(X))))&
((~creative(lucy)&~quiet(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((funny(X)|quiet(X))))&
((~curious(john)&~strong(john)))&
((~calm(john)|~funny(john))) | tall(susan) | [] | null | 0 |
Everyone who is not brave or rich is not calm or not wise and vice versa.
Everyone who is both not tall and not curious is calm or generous and vice versa.
Everyone who is both calm and funny is not curious.
Everyone who is brave or not funny is either not funny or not wise and vice versa.
Everyone who is either not kind or not creative is not strong or not wise.
If alice is either strong or not funny then susan is both funny and not patient and vice versa.
Everyone who is both not rich and not wise is curious.
Everyone who is either old or humble is patient or wise.
Everyone who is funny or not tall is either rich or wise and vice versa.
Everyone who is either not old or tall is either not generous or calm and vice versa.
If alice is not calm or not curious then someone is either creative or not generous.
Everyone who is not brave or not humble is either kind or creative and vice versa.
Everyone who is not happy or not old is not curious or not strong and vice versa.
If susan is both rich and funny then susan is quiet.
If john is either not funny or curious then someone is strong or not generous.
Everyone who is generous or brave is not kind or not tall and vice versa.
Mary is not curious or not wise.
Someone is not curious.
John is wise or kind.
Fred is either not brave or kind.
John is patient.
Someone is both not strong and not happy.
Someone is both happy and not quiet.
Alice is both not tall and generous. | Alice is not curious. | entailment | (![X]:((~brave(X)|rich(X))<=>(~calm(X)|~wise(X))))&
(![X]:((~tall(X)&~curious(X))<=>(calm(X)|generous(X))))&
(![X]:((calm(X)&funny(X))=>~curious(X)))&
(![X]:((brave(X)|~funny(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(~strong(X)|~wise(X))))&
(((strong(alice)<~>~funny(alice)))<=>((funny(susan)&~patient(susan))))&
(![X]:((~rich(X)&~wise(X))=>curious(X)))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|wise(X))))&
(![X]:((funny(X)|~tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>calm(X))))&
(((~calm(alice)|~curious(alice)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)|~strong(X))))&
(((rich(susan)&funny(susan)))=>(quiet(susan)))&
(((~funny(john)<~>curious(john)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((generous(X)|brave(X))<=>(~kind(X)|~tall(X))))&
((~curious(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((wise(john)|kind(john)))&
((~brave(fred)<~>kind(fred)))&
(patient(john))&
(?[X]:((~strong(X)&~happy(X))))&
(?[X]:((happy(X)&~quiet(X))))&
((~tall(alice)&generous(alice))) | ~curious(alice) | [
"p1",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3576636057127278775628985
% SZS output start Proof for 3576636057127278775628985
2. ! [X0] : ((~curious(X0) & ~tall(X0)) <=> (generous(X0) | calm(X0))) [input p1]
24. generous(alice) & ~tall(alice) [input p23]
25. curious(alice) [input hypothesis]
40. ! [X0] : (((~curious(X0) & ~tall(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (curious(X0) | tall(X0)))) [nnf transformation 2]
41. ! [X0] : (((~curious(X0) & ~tall(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | curious(X0) | tall(X0))) [flattening 40]
78. ~generous(X0) | ~curious(X0) [cnf transformation 41]
143. generous(alice) [cnf transformation 24]
144. curious(alice) [cnf transformation 25]
177. 5 <=> curious(alice) [avatar definition]
179. curious(alice) <- (5) [avatar component clause 177]
251. 5 [avatar split clause 144,177]
255. ~curious(alice) [resolution 78,143]
256. $false <- (5) [subsumption resolution 255,179]
257. ~5 [avatar contradiction clause 256]
258. $false [avatar sat refutation 251,257]
% SZS output end Proof for 3576636057127278775628985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or quiet is strong. If alice is both not rich and patient then someone is tall or not strong and vice versa. If paul is kind then mary is rich and vice versa. If someone is not wise then paul is not kind or old. Everyone who is both wise and rich is both not patient and not calm and vice versa. Everyone who is both not strong and old is either wise or curious. Everyone who is funny is both brave and not happy. Everyone who is either not humble or not wise is strong or kind and vice versa. Everyone who is either not quiet or wise is not creative or tall. If fred is not curious then mary is either brave or not old. If john is not curious then lucy is not funny. If someone is both generous and curious then susan is not patient or quiet. If susan is not quiet or brave then someone is either not patient or not creative. Everyone who is happy or not wise is generous and vice versa. Everyone who is both generous and not tall is not generous. Everyone who is both creative and not curious is both not old and not creative. Paul is both generous and humble. John is not strong or not creative. Paul is not creative or not humble. Alice is both not kind and not happy. Paul is not kind. Someone is not curious or kind. Someone is either not curious or patient. | Fred is humble. | neutral | (![X]:((strong(X)|quiet(X))=>strong(X)))&
(((~rich(alice)&patient(alice)))<=>(?[X]:((tall(X)|~strong(X)))))&
((kind(paul))<=>(rich(mary)))&
((?[X]:(~wise(X)))=>((~kind(paul)|old(paul))))&
(![X]:((wise(X)&rich(X))<=>(~patient(X)&~calm(X))))&
(![X]:((~strong(X)&old(X))=>(wise(X)<~>curious(X))))&
(![X]:(funny(X)=>(brave(X)&~happy(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(strong(X)|kind(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(~creative(X)|tall(X))))&
((~curious(fred))=>((brave(mary)<~>~old(mary))))&
((~curious(john))=>(~funny(lucy)))&
((?[X]:((generous(X)&curious(X))))=>((~patient(susan)|quiet(susan))))&
(((~quiet(susan)|brave(susan)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((happy(X)|~wise(X))<=>generous(X)))&
(![X]:((generous(X)&~tall(X))=>~generous(X)))&
(![X]:((creative(X)&~curious(X))=>(~old(X)&~creative(X))))&
((generous(paul)&humble(paul)))&
((~strong(john)|~creative(john)))&
((~creative(paul)|~humble(paul)))&
((~kind(alice)&~happy(alice)))&
(~kind(paul))&
(?[X]:((~curious(X)|kind(X))))&
(?[X]:((~curious(X)<~>patient(X)))) | humble(fred) | [] | null | 0 |
Everyone who is either generous or not curious is either rich or not kind. Everyone who is both not humble and generous is both humble and wise and vice versa. Everyone who is patient or not calm is either curious or brave and vice versa. If susan is strong then susan is tall and vice versa. Everyone who is both brave and rich is not humble and vice versa. If someone is not patient or not funny then lucy is not tall or calm and vice versa. Everyone who is strong or quiet is old or not tall and vice versa. If someone is either not strong or strong then someone is either not kind or kind and vice versa. If someone is both not creative and not kind then lucy is not curious or not wise and vice versa. If someone is tall or brave then susan is both not calm and brave. Everyone who is either not curious or not creative is either not brave or not curious and vice versa. Everyone who is humble or brave is both tall and generous. If someone is wise then someone is both not humble and not kind. Everyone who is funny or not humble is either not brave or old and vice versa. Everyone who is either not kind or funny is strong or funny and vice versa. If alice is either not curious or not rich then lucy is not rich and vice versa. John is old. Mary is not funny or calm. Lucy is either not wise or not quiet. Someone is wise or humble. Lucy is either quiet or wise. Lucy is humble or kind. Alice is either curious or quiet. | Lucy is old. | entailment | (![X]:((generous(X)<~>~curious(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~humble(X)&generous(X))<=>(humble(X)&wise(X))))&
(![X]:((patient(X)|~calm(X))<=>(curious(X)<~>brave(X))))&
((strong(susan))<=>(tall(susan)))&
(![X]:((brave(X)&rich(X))<=>~humble(X)))&
((?[X]:((~patient(X)|~funny(X))))<=>((~tall(lucy)|calm(lucy))))&
(![X]:((strong(X)|quiet(X))<=>(old(X)|~tall(X))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((humble(X)|brave(X))=>(tall(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(strong(X)|funny(X))))&
(((~curious(alice)<~>~rich(alice)))<=>(~rich(lucy)))&
(old(john))&
((~funny(mary)|calm(mary)))&
((~wise(lucy)<~>~quiet(lucy)))&
(?[X]:((wise(X)|humble(X))))&
((quiet(lucy)<~>wise(lucy)))&
((humble(lucy)|kind(lucy)))&
((curious(alice)<~>quiet(alice))) | old(lucy) | [
"p1",
"p4",
"p6",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6320749710682026445239217
% SZS output start Proof for 6320749710682026445239217
2. ! [X0] : ((generous(X0) & ~humble(X0)) <=> (wise(X0) & humble(X0))) [input p1]
5. ! [X0] : ((rich(X0) & brave(X0)) <=> ~humble(X0)) [input p4]
7. ! [X0] : ((quiet(X0) | strong(X0)) <=> (~tall(X0) | old(X0))) [input p6]
12. ! [X0] : ((brave(X0) | humble(X0)) => (generous(X0) & tall(X0))) [input p11]
13. ? [X0] : wise(X0) => ? [X0] : (~kind(X0) & ~humble(X0)) [input p12]
21. quiet(lucy) <~> wise(lucy) [input p20]
24. ~old(lucy) [input hypothesis]
26. ? [X0] : wise(X0) => ? [X1] : (~kind(X1) & ~humble(X1)) [rectify 13]
29. ! [X0] : ((generous(X0) & tall(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 12]
30. ? [X1] : (~kind(X1) & ~humble(X1)) | ! [X0] : ~wise(X0) [ennf transformation 26]
32. ! [X0] : (((generous(X0) & ~humble(X0)) | (~wise(X0) | ~humble(X0))) & ((wise(X0) & humble(X0)) | (~generous(X0) | humble(X0)))) [nnf transformation 2]
33. ! [X0] : (((generous(X0) & ~humble(X0)) | ~wise(X0) | ~humble(X0)) & ((wise(X0) & humble(X0)) | ~generous(X0) | humble(X0))) [flattening 32]
37. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) | ~brave(X0)))) [nnf transformation 5]
38. ! [X0] : (((rich(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | ~rich(X0) | ~brave(X0))) [flattening 37]
44. ! [X0] : (((quiet(X0) | strong(X0)) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((quiet(X0) | strong(X0) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | (~quiet(X0) & ~strong(X0)))) [flattening 44]
57. ? [X0] : (~kind(X0) & ~humble(X0)) | ! [X1] : ~wise(X1) [rectify 30]
58. ? [X0] : (~kind(X0) & ~humble(X0)) => (~kind(sK4) & ~humble(sK4)) [choice axiom]
59. (~kind(sK4) & ~humble(sK4)) | ! [X1] : ~wise(X1) [skolemisation 57,58]
68. (~wise(lucy) | ~quiet(lucy)) & (wise(lucy) | quiet(lucy)) [nnf transformation 21]
74. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 33]
87. brave(X0) | humble(X0) [cnf transformation 38]
94. ~quiet(X0) | old(X0) | ~tall(X0) [cnf transformation 45]
122. ~humble(X0) | tall(X0) [cnf transformation 29]
123. ~brave(X0) | tall(X0) [cnf transformation 29]
125. ~brave(X0) | generous(X0) [cnf transformation 29]
126. ~humble(sK4) | ~wise(X1) [cnf transformation 59]
149. wise(lucy) | quiet(lucy) [cnf transformation 68]
154. ~old(lucy) [cnf transformation 24]
169. ~generous(X0) | humble(X0) [duplicate literal removal 74]
208. 9 <=> wise(lucy) [avatar definition]
210. wise(lucy) <- (9) [avatar component clause 208]
252. 18 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (18) [avatar component clause 252]
260. 20 <=> humble(sK4) [avatar definition]
262. ~humble(sK4) <- (~20) [avatar component clause 260]
263. 18 | ~20 [avatar split clause 126,260,252]
293. 26 <=> quiet(lucy) [avatar definition]
295. quiet(lucy) <- (26) [avatar component clause 293]
308. 26 | 9 [avatar split clause 149,208,293]
339. tall(X0) | humble(X0) [resolution 123,87]
342. tall(X0) [subsumption resolution 339,122]
351. generous(X0) | humble(X0) [resolution 125,87]
353. humble(X0) [subsumption resolution 351,169]
355. $false <- (~20) [resolution 353,262]
360. 20 [avatar contradiction clause 355]
361. $false <- (9, 18) [resolution 253,210]
364. ~9 | ~18 [avatar contradiction clause 361]
407. old(lucy) | ~tall(lucy) <- (26) [resolution 94,295]
408. ~tall(lucy) <- (26) [subsumption resolution 407,154]
409. $false <- (26) [subsumption resolution 408,342]
410. ~26 [avatar contradiction clause 409]
411. $false [avatar sat refutation 263,308,360,364,410]
% SZS output end Proof for 6320749710682026445239217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or quiet then someone is both not patient and wise and vice versa.
If mary is both humble and not brave then john is not creative.
Everyone who is old or strong is both funny and not quiet and vice versa.
If someone is both strong and not creative then alice is either not tall or patient and vice versa.
Everyone who is either not strong or old is strong or quiet.
Everyone who is either not generous or not old is both not calm and patient and vice versa.
Everyone who is old is both not brave and patient.
Everyone who is not rich or not old is quiet and vice versa.
If lucy is both not happy and not old then someone is rich or generous and vice versa.
If lucy is either funny or not funny then someone is either not wise or not patient and vice versa.
If someone is both not strong and not kind then someone is not creative and vice versa.
If john is not tall then fred is patient and vice versa.
Everyone who is patient or calm is either not funny or not kind and vice versa.
If someone is both strong and not generous then someone is either old or not kind.
Everyone who is either brave or not old is not calm and vice versa.
If someone is both not humble and funny then someone is both funny and happy and vice versa.
Mary is not calm.
Alice is either old or strong.
Paul is not calm.
Lucy is patient.
Someone is either generous or patient.
Someone is not brave or quiet.
Someone is either generous or rich.
Someone is not curious or not patient. | Paul is strong. | contradiction | ((?[X]:((calm(X)<~>quiet(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(((humble(mary)&~brave(mary)))=>(~creative(john)))&
(![X]:((old(X)|strong(X))<=>(funny(X)&~quiet(X))))&
((?[X]:((strong(X)&~creative(X))))<=>((~tall(alice)<~>patient(alice))))&
(![X]:((~strong(X)<~>old(X))=>(strong(X)|quiet(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~calm(X)&patient(X))))&
(![X]:(old(X)=>(~brave(X)&patient(X))))&
(![X]:((~rich(X)|~old(X))<=>quiet(X)))&
(((~happy(lucy)&~old(lucy)))<=>(?[X]:((rich(X)|generous(X)))))&
(((funny(lucy)<~>~funny(lucy)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:(~creative(X))))&
((~tall(john))<=>(patient(fred)))&
(![X]:((patient(X)|calm(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((brave(X)<~>~old(X))<=>~calm(X)))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((funny(X)&happy(X)))))&
(~calm(mary))&
((old(alice)<~>strong(alice)))&
(~calm(paul))&
(patient(lucy))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(?[X]:((~curious(X)|~patient(X)))) | strong(paul) | [
"p2",
"p6",
"p7",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2625892517014009725888079
% SZS output start Proof for 2625892517014009725888079
3. ! [X0] : ((strong(X0) | old(X0)) <=> (~quiet(X0) & funny(X0))) [input p2]
7. ! [X0] : (old(X0) => (patient(X0) & ~brave(X0))) [input p6]
8. ! [X0] : ((~old(X0) | ~rich(X0)) <=> quiet(X0)) [input p7]
15. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> ~calm(X0)) [input p14]
19. ~calm(paul) [input p18]
25. strong(paul) [input hypothesis]
35. ! [X0] : ((patient(X0) & ~brave(X0)) | ~old(X0)) [ennf transformation 7]
42. ! [X0] : (((strong(X0) | old(X0)) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | (~strong(X0) & ~old(X0)))) [nnf transformation 3]
43. ! [X0] : ((strong(X0) | old(X0) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | (~strong(X0) & ~old(X0)))) [flattening 42]
51. ! [X0] : (((~old(X0) | ~rich(X0)) | ~quiet(X0)) & (quiet(X0) | (old(X0) & rich(X0)))) [nnf transformation 8]
52. ! [X0] : ((~old(X0) | ~rich(X0) | ~quiet(X0)) & (quiet(X0) | (old(X0) & rich(X0)))) [flattening 51]
74. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | calm(X0)) & (~calm(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 15]
99. ~strong(X0) | ~quiet(X0) [cnf transformation 43]
115. ~old(X0) | ~brave(X0) [cnf transformation 35]
118. old(X0) | quiet(X0) [cnf transformation 52]
148. ~old(X0) | brave(X0) | calm(X0) [cnf transformation 74]
149. old(X0) | ~brave(X0) | calm(X0) [cnf transformation 74]
157. ~calm(paul) [cnf transformation 19]
164. strong(paul) [cnf transformation 25]
326. ~brave(X0) | calm(X0) [subsumption resolution 149,115]
327. ~old(X0) | calm(X0) [subsumption resolution 148,326]
401. ~quiet(paul) [resolution 99,164]
431. quiet(X0) | calm(X0) [resolution 327,118]
627. calm(paul) [resolution 431,401]
630. $false [subsumption resolution 627,157]
% SZS output end Proof for 2625892517014009725888079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or wise is both rich and kind.
Everyone who is both not curious and tall is not creative and vice versa.
Everyone who is not brave is either quiet or not wise and vice versa.
Everyone who is both not brave and calm is not creative or kind and vice versa.
If someone is both humble and not quiet then paul is either kind or funny.
If someone is not strong or generous then mary is not brave or strong and vice versa.
If alice is both happy and quiet then someone is not brave and vice versa.
If mary is either tall or generous then someone is generous and vice versa.
Everyone who is either tall or not creative is not strong and vice versa.
If susan is either not strong or happy then mary is either kind or curious and vice versa.
If fred is either old or brave then someone is creative or not humble and vice versa.
Everyone who is both not strong and brave is both funny and not curious and vice versa.
Everyone who is both not old and not brave is either not curious or rich.
Everyone who is both not strong and not brave is both wise and generous and vice versa.
Everyone who is either not quiet or generous is not quiet or rich and vice versa.
Mary is not funny.
Susan is quiet.
Someone is both not calm and wise.
Someone is humble.
Fred is tall. | Mary is not calm. | contradiction | (![X]:((~calm(X)<~>wise(X))=>(rich(X)&kind(X))))&
(![X]:((~curious(X)&tall(X))<=>~creative(X)))&
(![X]:(~brave(X)<=>(quiet(X)<~>~wise(X))))&
(![X]:((~brave(X)&calm(X))<=>(~creative(X)|kind(X))))&
((?[X]:((humble(X)&~quiet(X))))=>((kind(paul)<~>funny(paul))))&
((?[X]:((~strong(X)|generous(X))))<=>((~brave(mary)|strong(mary))))&
(((happy(alice)&quiet(alice)))<=>(?[X]:(~brave(X))))&
(((tall(mary)<~>generous(mary)))<=>(?[X]:(generous(X))))&
(![X]:((tall(X)<~>~creative(X))<=>~strong(X)))&
(((~strong(susan)<~>happy(susan)))<=>((kind(mary)<~>curious(mary))))&
(((old(fred)<~>brave(fred)))<=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:((~strong(X)&brave(X))<=>(funny(X)&~curious(X))))&
(![X]:((~old(X)&~brave(X))=>(~curious(X)<~>rich(X))))&
(![X]:((~strong(X)&~brave(X))<=>(wise(X)&generous(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(~quiet(X)|rich(X))))&
(~funny(mary))&
(quiet(susan))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:(humble(X)))&
(tall(fred)) | ~calm(mary) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7495779967888856913641028
% SZS output start Proof for 7495779967888856913641028
1. ! [X0] : ((~calm(X0) <~> wise(X0)) => (kind(X0) & rich(X0))) [input p0]
2. ! [X0] : ((tall(X0) & ~curious(X0)) <=> ~creative(X0)) [input p1]
4. ! [X0] : ((calm(X0) & ~brave(X0)) <=> (kind(X0) | ~creative(X0))) [input p3]
6. ? [X0] : (generous(X0) | ~strong(X0)) <=> (strong(mary) | ~brave(mary)) [input p5]
8. (tall(mary) <~> generous(mary)) <=> ? [X0] : generous(X0) [input p7]
9. ! [X0] : ((tall(X0) <~> ~creative(X0)) <=> ~strong(X0)) [input p8]
12. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (~curious(X0) & funny(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~strong(X0)) <=> (generous(X0) & wise(X0))) [input p13]
21. ~calm(mary) [input hypothesis]
22. ! [X0] : ((kind(X0) & rich(X0)) | (~calm(X0) <=> wise(X0))) [ennf transformation 1]
26. ! [X0] : ((kind(X0) & rich(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) [nnf transformation 22]
27. ! [X0] : (((tall(X0) & ~curious(X0)) | creative(X0)) & (~creative(X0) | (~tall(X0) | curious(X0)))) [nnf transformation 2]
28. ! [X0] : (((tall(X0) & ~curious(X0)) | creative(X0)) & (~creative(X0) | ~tall(X0) | curious(X0))) [flattening 27]
30. ! [X0] : (((calm(X0) & ~brave(X0)) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | (~calm(X0) | brave(X0)))) [nnf transformation 4]
31. ! [X0] : (((calm(X0) & ~brave(X0)) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | ~calm(X0) | brave(X0))) [flattening 30]
33. (? [X0] : (generous(X0) | ~strong(X0)) | (~strong(mary) & brave(mary))) & ((strong(mary) | ~brave(mary)) | ! [X0] : (~generous(X0) & strong(X0))) [nnf transformation 6]
34. (? [X0] : (generous(X0) | ~strong(X0)) | (~strong(mary) & brave(mary))) & (strong(mary) | ~brave(mary) | ! [X0] : (~generous(X0) & strong(X0))) [flattening 33]
35. (? [X0] : (generous(X0) | ~strong(X0)) | (~strong(mary) & brave(mary))) & (strong(mary) | ~brave(mary) | ! [X1] : (~generous(X1) & strong(X1))) [rectify 34]
36. ? [X0] : (generous(X0) | ~strong(X0)) => (generous(sK0) | ~strong(sK0)) [choice axiom]
37. ((generous(sK0) | ~strong(sK0)) | (~strong(mary) & brave(mary))) & (strong(mary) | ~brave(mary) | ! [X1] : (~generous(X1) & strong(X1))) [skolemisation 35,36]
43. (((~generous(mary) | ~tall(mary)) & (generous(mary) | tall(mary))) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ((tall(mary) | ~generous(mary)) & (generous(mary) | ~tall(mary)))) [nnf transformation 8]
44. (((~generous(mary) | ~tall(mary)) & (generous(mary) | tall(mary))) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ((tall(mary) | ~generous(mary)) & (generous(mary) | ~tall(mary)))) [rectify 43]
45. ? [X1] : generous(X1) => generous(sK2) [choice axiom]
46. (((~generous(mary) | ~tall(mary)) & (generous(mary) | tall(mary))) | ! [X0] : ~generous(X0)) & (generous(sK2) | ((tall(mary) | ~generous(mary)) & (generous(mary) | ~tall(mary)))) [skolemisation 44,45]
47. ! [X0] : ((((creative(X0) | ~tall(X0)) & (~creative(X0) | tall(X0))) | strong(X0)) & (~strong(X0) | ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))))) [nnf transformation 9]
53. ! [X0] : (((brave(X0) & ~strong(X0)) | (curious(X0) | ~funny(X0))) & ((~curious(X0) & funny(X0)) | (~brave(X0) | strong(X0)))) [nnf transformation 12]
54. ! [X0] : (((brave(X0) & ~strong(X0)) | curious(X0) | ~funny(X0)) & ((~curious(X0) & funny(X0)) | ~brave(X0) | strong(X0))) [flattening 53]
56. ! [X0] : (((~brave(X0) & ~strong(X0)) | (~generous(X0) | ~wise(X0))) & ((generous(X0) & wise(X0)) | (brave(X0) | strong(X0)))) [nnf transformation 14]
57. ! [X0] : (((~brave(X0) & ~strong(X0)) | ~generous(X0) | ~wise(X0)) & ((generous(X0) & wise(X0)) | brave(X0) | strong(X0))) [flattening 56]
66. kind(X0) | wise(X0) | calm(X0) [cnf transformation 26]
68. ~creative(X0) | ~tall(X0) | curious(X0) [cnf transformation 28]
69. ~curious(X0) | creative(X0) [cnf transformation 28]
70. creative(X0) | tall(X0) [cnf transformation 28]
78. creative(X0) | calm(X0) [cnf transformation 31]
79. ~kind(X0) | calm(X0) [cnf transformation 31]
82. strong(mary) | ~brave(mary) | strong(X1) [cnf transformation 37]
85. generous(sK0) | ~strong(sK0) | ~strong(mary) [cnf transformation 37]
91. generous(mary) | tall(mary) | ~generous(X0) [cnf transformation 46]
92. ~generous(mary) | ~tall(mary) | ~generous(X0) [cnf transformation 46]
93. ~strong(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 47]
95. ~creative(X0) | tall(X0) | strong(X0) [cnf transformation 47]
96. creative(X0) | ~tall(X0) | strong(X0) [cnf transformation 47]
112. ~brave(X0) | ~curious(X0) | strong(X0) [cnf transformation 54]
118. generous(X0) | brave(X0) | strong(X0) [cnf transformation 57]
119. ~generous(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 57]
133. ~calm(mary) [cnf transformation 21]
150. 4 <=> strong(mary) [avatar definition]
151. strong(mary) <- (4) [avatar component clause 150]
152. ~strong(mary) <- (~4) [avatar component clause 150]
154. 5 <=> strong(sK0) [avatar definition]
156. ~strong(sK0) <- (~5) [avatar component clause 154]
158. 6 <=> generous(sK0) [avatar definition]
159. ~generous(sK0) <- (~6) [avatar component clause 158]
160. generous(sK0) <- (6) [avatar component clause 158]
161. ~4 | ~5 | 6 [avatar split clause 85,158,154,150]
163. 7 <=> brave(mary) [avatar definition]
164. ~brave(mary) <- (~7) [avatar component clause 163]
168. 8 <=> ! [X1] : ~generous(X1) [avatar definition]
169. ~generous(X1) <- (8) [avatar component clause 168]
172. 9 <=> ! [X1] : strong(X1) [avatar definition]
173. strong(X1) <- (9) [avatar component clause 172]
174. 9 | ~7 | 4 [avatar split clause 82,150,163,172]
194. 14 <=> tall(mary) [avatar definition]
195. tall(mary) <- (14) [avatar component clause 194]
198. 15 <=> generous(mary) [avatar definition]
199. generous(mary) <- (15) [avatar component clause 198]
200. ~generous(mary) <- (~15) [avatar component clause 198]
201. 8 | ~14 | ~15 [avatar split clause 92,198,194,168]
202. 8 | 14 | 15 [avatar split clause 91,198,194,168]
209. strong(X0) | creative(X0) [subsumption resolution 96,70]
210. strong(X0) | tall(X0) [subsumption resolution 95,209]
212. 17 <=> curious(mary) [avatar definition]
213. curious(mary) <- (17) [avatar component clause 212]
278. wise(X0) | calm(X0) | calm(X0) [resolution 66,79]
279. wise(X0) | calm(X0) [duplicate literal removal 278]
286. ~tall(X0) | curious(X0) | calm(X0) [resolution 68,78]
387. brave(mary) | strong(mary) <- (~15) [resolution 118,200]
423. $false <- (6, 8) [subsumption resolution 160,169]
424. ~6 | ~8 [avatar contradiction clause 423]
466. ~creative(X1) | ~tall(X1) <- (9) [resolution 173,93]
500. 41 <=> brave(sK0) [avatar definition]
502. brave(sK0) <- (41) [avatar component clause 500]
514. 44 <=> curious(sK0) [avatar definition]
515. ~curious(sK0) <- (~44) [avatar component clause 514]
587. 55 <=> wise(mary) [avatar definition]
588. ~wise(mary) <- (~55) [avatar component clause 587]
589. wise(mary) <- (55) [avatar component clause 587]
597. creative(mary) <- (17) [resolution 213,69]
701. calm(mary) <- (~55) [resolution 588,279]
702. $false <- (~55) [subsumption resolution 701,133]
703. 55 [avatar contradiction clause 702]
712. ~tall(mary) <- (9, 17) [resolution 597,466]
715. $false <- (9, 14, 17) [subsumption resolution 712,195]
716. ~9 | ~14 | ~17 [avatar contradiction clause 715]
722. ~curious(sK0) | strong(sK0) <- (41) [resolution 502,112]
728. curious(mary) | calm(mary) <- (14) [resolution 286,195]
738. 5 | ~44 | ~41 [avatar split clause 722,500,514,154]
739. strong(mary) <- (~7, ~15) [subsumption resolution 387,164]
740. 4 | 7 | 15 [avatar split clause 739,198,163,150]
771. curious(mary) <- (14) [subsumption resolution 728,133]
772. 17 | ~14 [avatar split clause 771,194,212]
784. ~creative(mary) | ~tall(mary) <- (4) [resolution 151,93]
785. ~creative(mary) <- (4, 14) [subsumption resolution 784,195]
791. creative(mary) <- (17) [resolution 213,69]
792. $false <- (4, 14, 17) [subsumption resolution 791,785]
793. ~4 | ~14 | ~17 [avatar contradiction clause 792]
795. tall(mary) <- (~4) [resolution 152,210]
798. tall(sK0) <- (~5) [resolution 156,210]
799. creative(sK0) <- (~5) [resolution 156,209]
807. 14 | 4 [avatar split clause 795,150,194]
810. brave(sK0) | strong(sK0) <- (~6) [resolution 159,118]
814. brave(sK0) <- (~5, ~6) [subsumption resolution 810,156]
815. 41 | 5 | 6 [avatar split clause 814,158,154,500]
818. ~strong(mary) | ~wise(mary) <- (15) [resolution 199,119]
826. ~strong(mary) <- (15, 55) [subsumption resolution 818,589]
827. ~4 | ~15 | ~55 [avatar split clause 826,587,198,150]
837. $false <- (8, 15) [resolution 169,199]
838. ~8 | ~15 [avatar contradiction clause 837]
862. ~tall(sK0) | curious(sK0) <- (~5) [resolution 799,68]
863. curious(sK0) <- (~5) [subsumption resolution 862,798]
864. $false <- (~5, ~44) [subsumption resolution 863,515]
865. 5 | 44 [avatar contradiction clause 864]
866. $false [avatar sat refutation 161,174,201,202,424,703,716,738,740,772,793,807,815,827,838,865]
% SZS output end Proof for 7495779967888856913641028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
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