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 not funny or patient is both not creative and not generous.
If someone is either curious or funny then susan is not rich.
Everyone who is both not creative and old is not wise.
Everyone who is either not kind or strong is both rich and not rich.
Everyone who is not strong or happy is both generous and not creative.
Everyone who is patient is happy and vice versa.
If alice is both curious and not wise then someone is either not creative or funny.
If someone is either not patient or old then someone is either not happy or rich.
If someone is either not happy or not calm then someone is either old or not brave.
If paul is old or humble then someone is patient or curious.
Everyone who is both old and wise is either not old or wise and vice versa.
Everyone who is either not wise or not creative is kind and vice versa.
Everyone who is both brave and not generous is not kind.
Everyone who is calm or not old is not curious.
If fred is both not funny and not humble then someone is not creative.
Someone is either not strong or not old.
Someone is either not creative or rich.
Susan is not kind.
Someone is not curious or not humble.
Lucy is not curious or humble.
Someone is either not funny or creative.
Someone is either not happy or wise.
Someone is either not happy or not strong. | Lucy is strong. | neutral | (![X]:((~funny(X)|patient(X))=>(~creative(X)&~generous(X))))&
((?[X]:((curious(X)<~>funny(X))))=>(~rich(susan)))&
(![X]:((~creative(X)&old(X))=>~wise(X)))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&~rich(X))))&
(![X]:((~strong(X)|happy(X))=>(generous(X)&~creative(X))))&
(![X]:(patient(X)<=>happy(X)))&
(((curious(alice)&~wise(alice)))=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((~patient(X)<~>old(X))))=>(?[X]:((~happy(X)<~>rich(X)))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(?[X]:((old(X)<~>~brave(X)))))&
(((old(paul)|humble(paul)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((old(X)&wise(X))<=>(~old(X)<~>wise(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>kind(X)))&
(![X]:((brave(X)&~generous(X))=>~kind(X)))&
(![X]:((calm(X)|~old(X))=>~curious(X)))&
(((~funny(fred)&~humble(fred)))=>(?[X]:(~creative(X))))&
(?[X]:((~strong(X)<~>~old(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
(~kind(susan))&
(?[X]:((~curious(X)|~humble(X))))&
((~curious(lucy)|humble(lucy)))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((~happy(X)<~>~strong(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is not strong or old is humble or not brave.
If alice is either happy or not curious then alice is either old or not generous and vice versa.
If someone is creative or funny then alice is strong or humble.
Everyone who is creative or humble is not tall or tall and vice versa.
Everyone who is either generous or not humble is happy.
If paul is not tall or not old then someone is both not strong and not quiet and vice versa.
If mary is not calm then fred is kind or not funny.
Everyone who is both not generous and happy is either happy or not kind.
Everyone who is curious or not patient is not old or rich and vice versa.
Everyone who is patient is not humble.
Everyone who is happy or curious is not generous and vice versa.
If paul is humble or tall then paul is both creative and calm and vice versa.
Everyone who is both not happy and not kind is either calm or not kind and vice versa.
If mary is not tall or not humble then someone is both wise and brave.
If someone is either not wise or not humble then someone is tall.
If paul is not patient or not kind then fred is both wise and creative and vice versa.
Mary is not humble.
Alice is both not old and kind.
Someone is strong or not calm.
Mary is either strong or not calm.
Someone is either quiet or creative.
Someone is both not tall and old. | Paul is tall. | contradiction | (![X]:((~strong(X)|old(X))=>(humble(X)|~brave(X))))&
(((happy(alice)<~>~curious(alice)))<=>((old(alice)<~>~generous(alice))))&
((?[X]:((creative(X)|funny(X))))=>((strong(alice)|humble(alice))))&
(![X]:((creative(X)|humble(X))<=>(~tall(X)|tall(X))))&
(![X]:((generous(X)<~>~humble(X))=>happy(X)))&
(((~tall(paul)|~old(paul)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
((~calm(mary))=>((kind(fred)|~funny(fred))))&
(![X]:((~generous(X)&happy(X))=>(happy(X)<~>~kind(X))))&
(![X]:((curious(X)|~patient(X))<=>(~old(X)|rich(X))))&
(![X]:(patient(X)=>~humble(X)))&
(![X]:((happy(X)|curious(X))<=>~generous(X)))&
(((humble(paul)|tall(paul)))<=>((creative(paul)&calm(paul))))&
(![X]:((~happy(X)&~kind(X))<=>(calm(X)<~>~kind(X))))&
(((~tall(mary)|~humble(mary)))=>(?[X]:((wise(X)&brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(tall(X))))&
(((~patient(paul)|~kind(paul)))<=>((wise(fred)&creative(fred))))&
(~humble(mary))&
((~old(alice)&kind(alice)))&
(?[X]:((strong(X)|~calm(X))))&
((strong(mary)<~>~calm(mary)))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:((~tall(X)&old(X)))) | tall(paul) | [
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3401437375220051929209085
% SZS output start Proof for 3401437375220051929209085
8. ! [X0] : ((happy(X0) & ~generous(X0)) => (happy(X0) <~> ~kind(X0))) [input p7]
11. ! [X0] : ((curious(X0) | happy(X0)) <=> ~generous(X0)) [input p10]
12. (tall(paul) | humble(paul)) <=> (calm(paul) & creative(paul)) [input p11]
13. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p12]
23. tall(paul) [input hypothesis]
32. ! [X0] : ((happy(X0) <~> ~kind(X0)) | (~happy(X0) | generous(X0))) [ennf transformation 8]
33. ! [X0] : ((happy(X0) <~> ~kind(X0)) | ~happy(X0) | generous(X0)) [flattening 32]
46. ! [X0] : (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ~happy(X0) | generous(X0)) [nnf transformation 33]
49. ! [X0] : (((curious(X0) | happy(X0)) | generous(X0)) & (~generous(X0) | (~curious(X0) & ~happy(X0)))) [nnf transformation 11]
50. ! [X0] : ((curious(X0) | happy(X0) | generous(X0)) & (~generous(X0) | (~curious(X0) & ~happy(X0)))) [flattening 49]
51. ((tall(paul) | humble(paul)) | (~calm(paul) | ~creative(paul))) & ((calm(paul) & creative(paul)) | (~tall(paul) & ~humble(paul))) [nnf transformation 12]
52. (tall(paul) | humble(paul) | ~calm(paul) | ~creative(paul)) & ((calm(paul) & creative(paul)) | (~tall(paul) & ~humble(paul))) [flattening 51]
53. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 13]
54. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | kind(X0) | happy(X0))) [flattening 53]
94. kind(X0) | ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 46]
100. ~generous(X0) | ~happy(X0) [cnf transformation 50]
106. calm(paul) | ~tall(paul) [cnf transformation 52]
109. kind(X0) | ~calm(X0) | kind(X0) | happy(X0) [cnf transformation 54]
112. ~kind(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 54]
135. tall(paul) [cnf transformation 23]
136. kind(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 109]
137. ~kind(X0) | ~calm(X0) [duplicate literal removal 112]
138. ~happy(X0) | kind(X0) | generous(X0) [duplicate literal removal 94]
180. 9 <=> tall(paul) [avatar definition]
202. 13 <=> calm(paul) [avatar definition]
203. calm(paul) <- (13) [avatar component clause 202]
210. ~9 | 13 [avatar split clause 106,202,180]
219. ~calm(X0) | happy(X0) [subsumption resolution 136,137]
265. 26 <=> kind(paul) [avatar definition]
266. kind(paul) <- (26) [avatar component clause 265]
267. ~kind(paul) <- (~26) [avatar component clause 265]
304. 9 [avatar split clause 135,180]
309. happy(paul) <- (13) [resolution 219,203]
368. kind(paul) | generous(paul) <- (13) [resolution 138,309]
370. generous(paul) <- (13, ~26) [subsumption resolution 368,267]
374. ~happy(paul) <- (13, ~26) [resolution 370,100]
375. $false <- (13, ~26) [subsumption resolution 374,309]
376. ~13 | 26 [avatar contradiction clause 375]
382. ~calm(paul) <- (26) [resolution 266,137]
383. $false <- (13, 26) [subsumption resolution 382,203]
384. ~13 | ~26 [avatar contradiction clause 383]
385. $false [avatar sat refutation 210,304,376,384]
% SZS output end Proof for 3401437375220051929209085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or happy then someone is both not kind and not brave and vice versa. Everyone who is either quiet or creative is both not quiet and not calm. If john is not funny or not strong then fred is either rich or not creative. Everyone who is both not creative and quiet is not strong or tall and vice versa. If lucy is not brave then someone is both funny and not old and vice versa. If lucy is both funny and not happy then someone is brave or old. If fred is both happy and creative then mary is not strong. Everyone who is brave is not curious or strong. Everyone who is either kind or not happy is not generous or brave. If someone is either kind or not generous then mary is funny. Everyone who is both funny and patient is wise or not kind. If someone is not wise or creative then fred is not wise or humble. If someone is not patient or not calm then someone is either not happy or strong and vice versa. Everyone who is not creative is rich or not tall and vice versa. If someone is not kind then someone is both wise and humble and vice versa. If someone is both strong and not calm then paul is either not rich or not quiet and vice versa. Lucy is not creative or brave. Lucy is both not brave and curious. Someone is either not creative or not funny. Paul is curious. Susan is both brave and not curious. John is not wise or wise. John is not curious. Someone is creative or funny. | John is not tall. | entailment | ((?[X]:((wise(X)|happy(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((quiet(X)<~>creative(X))=>(~quiet(X)&~calm(X))))&
(((~funny(john)|~strong(john)))=>((rich(fred)<~>~creative(fred))))&
(![X]:((~creative(X)&quiet(X))<=>(~strong(X)|tall(X))))&
((~brave(lucy))<=>(?[X]:((funny(X)&~old(X)))))&
(((funny(lucy)&~happy(lucy)))=>(?[X]:((brave(X)|old(X)))))&
(((happy(fred)&creative(fred)))=>(~strong(mary)))&
(![X]:(brave(X)=>(~curious(X)|strong(X))))&
(![X]:((kind(X)<~>~happy(X))=>(~generous(X)|brave(X))))&
((?[X]:((kind(X)<~>~generous(X))))=>(funny(mary)))&
(![X]:((funny(X)&patient(X))=>(wise(X)|~kind(X))))&
((?[X]:((~wise(X)|creative(X))))=>((~wise(fred)|humble(fred))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((wise(X)&humble(X)))))&
((?[X]:((strong(X)&~calm(X))))<=>((~rich(paul)<~>~quiet(paul))))&
((~creative(lucy)|brave(lucy)))&
((~brave(lucy)&curious(lucy)))&
(?[X]:((~creative(X)<~>~funny(X))))&
(curious(paul))&
((brave(susan)&~curious(susan)))&
((~wise(john)|wise(john)))&
(~curious(john))&
(?[X]:((creative(X)|funny(X)))) | ~tall(john) | [
"p1",
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2534704093102109434252175
% SZS output start Proof for 2534704093102109434252175
2. ! [X0] : ((quiet(X0) <~> creative(X0)) => (~calm(X0) & ~quiet(X0))) [input p1]
4. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> (tall(X0) | ~strong(X0))) [input p3]
14. ! [X0] : (~creative(X0) <=> (~tall(X0) | rich(X0))) [input p13]
25. tall(john) [input hypothesis]
29. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (quiet(X0) <=> creative(X0))) [ennf transformation 2]
49. ! [X0] : ((~calm(X0) & ~quiet(X0)) | ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0)))) [nnf transformation 29]
51. ! [X0] : (((quiet(X0) & ~creative(X0)) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | (~quiet(X0) | creative(X0)))) [nnf transformation 4]
52. ! [X0] : (((quiet(X0) & ~creative(X0)) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~quiet(X0) | creative(X0))) [flattening 51]
66. ! [X0] : ((~creative(X0) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | creative(X0))) [nnf transformation 14]
67. ! [X0] : ((~creative(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | creative(X0))) [flattening 66]
87. ~quiet(X0) | creative(X0) | ~quiet(X0) [cnf transformation 49]
97. ~tall(X0) | ~creative(X0) [cnf transformation 52]
99. ~tall(X0) | quiet(X0) [cnf transformation 52]
121. ~creative(X0) | tall(X0) [cnf transformation 67]
142. tall(john) [cnf transformation 25]
143. ~quiet(X0) | creative(X0) [duplicate literal removal 87]
251. 25 <=> ! [X0] : ~creative(X0) [avatar definition]
252. ~creative(X0) <- (25) [avatar component clause 251]
300. ~creative(X0) [subsumption resolution 121,97]
301. 25 [avatar split clause 300,251]
388. quiet(john) [resolution 99,142]
391. creative(john) [resolution 143,388]
396. $false <- (25) [subsumption resolution 391,252]
397. ~25 [avatar contradiction clause 396]
398. $false [avatar sat refutation 301,397]
% SZS output end Proof for 2534704093102109434252175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not curious then someone is curious or not brave and vice versa. Everyone who is not tall is humble and vice versa. Everyone who is either not rich or not quiet is not creative. If john is either not wise or patient then someone is either calm or strong and vice versa. If someone is strong then alice is not old or not creative and vice versa. Everyone who is either not funny or creative is not wise or not tall. If someone is not wise then someone is quiet. If fred is not humble then someone is funny and vice versa. If fred is not patient then fred is both calm and strong and vice versa. Everyone who is not creative is either not humble or not funny. Everyone who is both generous and humble is calm and vice versa. If someone is either not wise or creative then someone is tall or humble. Everyone who is not happy or happy is either not generous or not funny. Everyone who is either curious or creative is both curious and tall. If mary is either generous or funny then someone is not strong or humble and vice versa. Everyone who is both not quiet and not generous is old or generous and vice versa. Lucy is both not patient and strong. Paul is brave. John is both not tall and creative. Someone is humble or kind. Someone is either rich or not patient. Fred is not kind or not humble. | John is not funny. | contradiction | ((?[X]:((calm(X)|~curious(X))))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(~tall(X)<=>humble(X)))&
(![X]:((~rich(X)<~>~quiet(X))=>~creative(X)))&
(((~wise(john)<~>patient(john)))<=>(?[X]:((calm(X)<~>strong(X)))))&
((?[X]:(strong(X)))<=>((~old(alice)|~creative(alice))))&
(![X]:((~funny(X)<~>creative(X))=>(~wise(X)|~tall(X))))&
((?[X]:(~wise(X)))=>(?[X]:(quiet(X))))&
((~humble(fred))<=>(?[X]:(funny(X))))&
((~patient(fred))<=>((calm(fred)&strong(fred))))&
(![X]:(~creative(X)=>(~humble(X)<~>~funny(X))))&
(![X]:((generous(X)&humble(X))<=>calm(X)))&
((?[X]:((~wise(X)<~>creative(X))))=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((~happy(X)|happy(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((curious(X)<~>creative(X))=>(curious(X)&tall(X))))&
(((generous(mary)<~>funny(mary)))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:((~quiet(X)&~generous(X))<=>(old(X)|generous(X))))&
((~patient(lucy)&strong(lucy)))&
(brave(paul))&
((~tall(john)&creative(john)))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
((~kind(fred)|~humble(fred))) | ~funny(john) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3581125353518775859927837
% SZS output start Proof for 3581125353518775859927837
13. ! [X0] : ((happy(X0) | ~happy(X0)) => (~generous(X0) <~> ~funny(X0))) [input p12]
16. ! [X0] : ((~generous(X0) & ~quiet(X0)) <=> (generous(X0) | old(X0))) [input p15]
23. ~funny(john) [input hypothesis]
33. ! [X0] : ((~generous(X0) <~> ~funny(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 13]
68. ! [X0] : (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (~happy(X0) & happy(X0))) [nnf transformation 33]
74. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | (generous(X0) | quiet(X0)))) [nnf transformation 16]
75. ! [X0] : (((~generous(X0) & ~quiet(X0)) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | generous(X0) | quiet(X0))) [flattening 74]
117. funny(X0) | generous(X0) | happy(X0) [cnf transformation 68]
118. funny(X0) | generous(X0) | ~happy(X0) [cnf transformation 68]
133. ~generous(X0) | ~generous(X0) [cnf transformation 75]
143. ~funny(john) [cnf transformation 23]
145. ~generous(X0) [duplicate literal removal 133]
263. generous(X0) | funny(X0) [subsumption resolution 117,118]
318. funny(X0) [resolution 263,145]
337. $false [resolution 318,143]
% SZS output end Proof for 3581125353518775859927837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not calm or not tall then someone is strong.
If someone is both not curious and not generous then someone is both not creative and not wise.
If someone is both strong and old then someone is not patient and vice versa.
Everyone who is either curious or quiet is not creative or not old and vice versa.
If someone is either not humble or not happy then john is both old and rich and vice versa.
Everyone who is happy or brave is both quiet and not strong and vice versa.
Everyone who is either not humble or not tall is kind and vice versa.
Everyone who is not strong or not humble is brave.
If someone is curious then someone is not kind or funny and vice versa.
Everyone who is both not quiet and not old is either not generous or creative and vice versa.
Everyone who is either wise or happy is both not old and strong.
If lucy is old or not brave then fred is both not old and happy and vice versa.
Everyone who is either not patient or not creative is either happy or curious.
If paul is both creative and not curious then someone is not generous.
If someone is rich then someone is not humble.
Everyone who is both not funny and kind is either not funny or not curious and vice versa.
Mary is generous.
Paul is both curious and creative.
Someone is both not rich and funny.
Lucy is curious or happy.
Someone is both curious and humble.
Alice is not brave or not old.
Someone is humble.
Lucy is both generous and brave. | Lucy is not creative. | entailment | (((~calm(mary)<~>~tall(mary)))=>(?[X]:(strong(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~creative(X)&~wise(X)))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:(~patient(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~creative(X)|~old(X))))&
((?[X]:((~humble(X)<~>~happy(X))))<=>((old(john)&rich(john))))&
(![X]:((happy(X)|brave(X))<=>(quiet(X)&~strong(X))))&
(![X]:((~humble(X)<~>~tall(X))<=>kind(X)))&
(![X]:((~strong(X)|~humble(X))=>brave(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:((~quiet(X)&~old(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((wise(X)<~>happy(X))=>(~old(X)&strong(X))))&
(((old(lucy)|~brave(lucy)))<=>((~old(fred)&happy(fred))))&
(![X]:((~patient(X)<~>~creative(X))=>(happy(X)<~>curious(X))))&
(((creative(paul)&~curious(paul)))=>(?[X]:(~generous(X))))&
((?[X]:(rich(X)))=>(?[X]:(~humble(X))))&
(![X]:((~funny(X)&kind(X))<=>(~funny(X)<~>~curious(X))))&
(generous(mary))&
((curious(paul)&creative(paul)))&
(?[X]:((~rich(X)&funny(X))))&
((curious(lucy)|happy(lucy)))&
(?[X]:((curious(X)&humble(X))))&
((~brave(alice)|~old(alice)))&
(?[X]:(humble(X)))&
((generous(lucy)&brave(lucy))) | ~creative(lucy) | [
"p5",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1137759282526987960958986
% SZS output start Proof for 1137759282526987960958986
6. ! [X0] : ((brave(X0) | happy(X0)) <=> (~strong(X0) & quiet(X0))) [input p5]
10. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (~generous(X0) <~> creative(X0))) [input p9]
24. brave(lucy) & generous(lucy) [input p23]
25. creative(lucy) [input hypothesis]
56. ! [X0] : (((brave(X0) | happy(X0)) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 6]
57. ! [X0] : ((brave(X0) | happy(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 56]
64. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 10]
65. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0)))) & (((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | old(X0) | quiet(X0))) [flattening 64]
103. ~brave(X0) | quiet(X0) [cnf transformation 57]
119. ~quiet(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 65]
153. generous(lucy) [cnf transformation 24]
154. brave(lucy) [cnf transformation 24]
155. creative(lucy) [cnf transformation 25]
272. 27 <=> brave(lucy) [avatar definition]
273. brave(lucy) <- (27) [avatar component clause 272]
322. 27 [avatar split clause 154,272]
325. quiet(lucy) <- (27) [resolution 103,273]
436. ~generous(lucy) | ~creative(lucy) <- (27) [resolution 119,325]
440. ~creative(lucy) <- (27) [subsumption resolution 436,153]
441. $false <- (27) [subsumption resolution 440,155]
442. ~27 [avatar contradiction clause 441]
444. $false [avatar sat refutation 322,442]
% SZS output end Proof for 1137759282526987960958986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both not humble and not rich and vice versa. Everyone who is either tall or not humble is both not curious and patient and vice versa. Everyone who is either creative or not rich is curious. If mary is creative or not old then someone is either tall or not old. If someone is both creative and not calm then someone is both quiet and not quiet and vice versa. If someone is either not curious or not old then mary is not brave or not curious. Everyone who is patient or quiet is both not kind and not strong and vice versa. If fred is generous then fred is not tall or creative and vice versa. Everyone who is either not calm or not strong is either kind or not rich and vice versa. If someone is both not kind and old then someone is not humble and vice versa. Everyone who is either not quiet or not calm is both not strong and quiet and vice versa. Everyone who is both patient and not humble is strong or not strong. Everyone who is not funny is not kind and vice versa. Everyone who is either not strong or strong is brave or not curious. If someone is not kind then fred is both not generous and humble. Everyone who is curious or not humble is both not brave and not quiet. Alice is generous. Mary is both not calm and funny. Someone is not wise or not quiet. Alice is patient or not funny. Mary is not humble or not creative. Someone is either not brave or brave. Susan is rich. Alice is both not tall and not kind. | Alice is not quiet. | contradiction | (![X]:(~humble(X)<=>(~humble(X)&~rich(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(~curious(X)&patient(X))))&
(![X]:((creative(X)<~>~rich(X))=>curious(X)))&
(((creative(mary)|~old(mary)))=>(?[X]:((tall(X)<~>~old(X)))))&
((?[X]:((creative(X)&~calm(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>((~brave(mary)|~curious(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~kind(X)&~strong(X))))&
((generous(fred))<=>((~tall(fred)|creative(fred))))&
(![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)&quiet(X))))&
(![X]:((patient(X)&~humble(X))=>(strong(X)|~strong(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(![X]:((~strong(X)<~>strong(X))=>(brave(X)|~curious(X))))&
((?[X]:(~kind(X)))=>((~generous(fred)&humble(fred))))&
(![X]:((curious(X)|~humble(X))=>(~brave(X)&~quiet(X))))&
(generous(alice))&
((~calm(mary)&funny(mary)))&
(?[X]:((~wise(X)|~quiet(X))))&
((patient(alice)|~funny(alice)))&
((~humble(mary)|~creative(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(rich(susan))&
((~tall(alice)&~kind(alice))) | ~quiet(alice) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p8",
"p10",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2963188468272012686335027
% SZS output start Proof for 2963188468272012686335027
1. ! [X0] : (~humble(X0) <=> (~rich(X0) & ~humble(X0))) [input p0]
2. ! [X0] : ((tall(X0) <~> ~humble(X0)) <=> (patient(X0) & ~curious(X0))) [input p1]
3. ! [X0] : ((creative(X0) <~> ~rich(X0)) => curious(X0)) [input p2]
5. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p4]
7. ! [X0] : ((quiet(X0) | patient(X0)) <=> (~strong(X0) & ~kind(X0))) [input p6]
9. ! [X0] : ((~calm(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~rich(X0))) [input p8]
11. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p10]
14. ! [X0] : ((~strong(X0) <~> strong(X0)) => (~curious(X0) | brave(X0))) [input p13]
16. ! [X0] : ((~humble(X0) | curious(X0)) => (~quiet(X0) & ~brave(X0))) [input p15]
24. ~kind(alice) & ~tall(alice) [input p23]
25. ~quiet(alice) [input hypothesis]
26. ? [X0] : (~calm(X0) & creative(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 5]
29. ! [X0] : (curious(X0) | (creative(X0) <=> ~rich(X0))) [ennf transformation 3]
35. ! [X0] : ((~curious(X0) | brave(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 14]
36. ! [X0] : (~curious(X0) | brave(X0) | (~strong(X0) <=> strong(X0))) [flattening 35]
38. ! [X0] : ((~quiet(X0) & ~brave(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 16]
39. ! [X0] : ((~humble(X0) | (rich(X0) | humble(X0))) & ((~rich(X0) & ~humble(X0)) | humble(X0))) [nnf transformation 1]
40. ! [X0] : ((~humble(X0) | rich(X0) | humble(X0)) & ((~rich(X0) & ~humble(X0)) | humble(X0))) [flattening 39]
41. ! [X0] : ((((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))))) [nnf transformation 2]
42. ! [X0] : ((((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))))) [flattening 41]
43. ! [X0] : (curious(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 29]
47. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : (calm(X0) | ~creative(X0))) [nnf transformation 26]
48. (? [X0] : (~calm(X0) & creative(X0)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : (calm(X3) | ~creative(X3))) [rectify 47]
49. ? [X0] : (~calm(X0) & creative(X0)) => (~calm(sK1) & creative(sK1)) [choice axiom]
50. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK2) & quiet(sK2)) [choice axiom]
51. ((~calm(sK1) & creative(sK1)) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK2) & quiet(sK2)) | ! [X3] : (calm(X3) | ~creative(X3))) [skolemisation 48,50,49]
53. ! [X0] : (((quiet(X0) | patient(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [nnf transformation 7]
54. ! [X0] : ((quiet(X0) | patient(X0) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | (~quiet(X0) & ~patient(X0)))) [flattening 53]
57. ! [X0] : ((((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ((kind(X0) | rich(X0)) & (~rich(X0) | ~kind(X0)))) & (((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0))))) [nnf transformation 9]
63. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 11]
64. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 63]
66. ! [X0] : (~curious(X0) | brave(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 36]
71. ~rich(X0) | humble(X0) [cnf transformation 40]
77. ~patient(X0) | tall(X0) | ~humble(X0) | curious(X0) [cnf transformation 42]
80. creative(X0) | curious(X0) | rich(X0) [cnf transformation 43]
85. quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 51]
86. ~quiet(sK2) | calm(X3) | ~creative(X3) [cnf transformation 51]
94. ~strong(X0) | ~quiet(X0) [cnf transformation 54]
95. strong(X0) | patient(X0) | quiet(X0) | kind(X0) [cnf transformation 54]
99. ~strong(X0) | kind(X0) | ~rich(X0) | calm(X0) [cnf transformation 57]
112. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 64]
114. ~calm(X0) | ~quiet(X0) | ~quiet(X0) | strong(X0) [cnf transformation 64]
119. ~curious(X0) | brave(X0) | strong(X0) | strong(X0) [cnf transformation 66]
120. ~curious(X0) | brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 66]
123. ~brave(X0) | ~curious(X0) [cnf transformation 38]
135. ~tall(alice) [cnf transformation 24]
136. ~kind(alice) [cnf transformation 24]
137. ~quiet(alice) [cnf transformation 25]
138. ~curious(X0) | brave(X0) | strong(X0) [duplicate literal removal 119]
139. ~strong(X0) | brave(X0) | ~curious(X0) [duplicate literal removal 120]
140. quiet(X0) | ~calm(X0) [duplicate literal removal 112]
141. ~calm(X0) | ~quiet(X0) | strong(X0) [duplicate literal removal 114]
163. 5 <=> ! [X3] : (calm(X3) | ~creative(X3)) [avatar definition]
164. calm(X3) | ~creative(X3) <- (5) [avatar component clause 163]
166. 6 <=> quiet(sK2) [avatar definition]
169. 5 | ~6 [avatar split clause 86,166,163]
170. 5 | 6 [avatar split clause 85,166,163]
203. 14 <=> ! [X1] : humble(X1) [avatar definition]
204. humble(X1) <- (14) [avatar component clause 203]
223. ~quiet(X0) | ~calm(X0) [subsumption resolution 141,94]
224. ~calm(X0) [subsumption resolution 140,223]
225. ~curious(X0) | brave(X0) [subsumption resolution 138,139]
235. ~curious(X0) [subsumption resolution 123,225]
237. 21 <=> patient(alice) [avatar definition]
239. patient(alice) <- (21) [avatar component clause 237]
250. ~creative(X3) <- (5) [subsumption resolution 164,224]
272. curious(X1) | rich(X1) <- (5) [resolution 80,250]
274. rich(X1) <- (5) [subsumption resolution 272,235]
275. humble(X0) <- (5) [resolution 274,71]
285. kind(X0) | ~rich(X0) | calm(X0) | patient(X0) | quiet(X0) | kind(X0) [resolution 99,95]
286. kind(X0) | ~rich(X0) | calm(X0) | patient(X0) | quiet(X0) [duplicate literal removal 285]
287. kind(X0) | calm(X0) | patient(X0) | quiet(X0) <- (5) [subsumption resolution 286,274]
288. kind(X0) | patient(X0) | quiet(X0) <- (5) [subsumption resolution 287,224]
289. patient(alice) | quiet(alice) <- (5) [resolution 288,136]
293. patient(alice) <- (5) [subsumption resolution 289,137]
294. 21 | ~5 [avatar split clause 293,163,237]
296. tall(alice) | ~humble(alice) | curious(alice) <- (21) [resolution 239,77]
297. ~humble(alice) | curious(alice) <- (21) [subsumption resolution 296,135]
298. curious(alice) <- (14, 21) [subsumption resolution 297,204]
299. $false <- (14, 21) [subsumption resolution 298,235]
300. ~14 | ~21 [avatar contradiction clause 299]
302. 14 | ~5 [avatar split clause 275,163,203]
314. $false [avatar sat refutation 169,170,294,300,302]
% SZS output end Proof for 2963188468272012686335027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and old is both not wise and curious.
Everyone who is not wise is rich or kind.
Everyone who is not wise or not rich is old or not funny and vice versa.
If someone is both not quiet and wise then someone is not rich.
Everyone who is both not generous and not happy is both not happy and tall and vice versa.
Everyone who is not happy is not curious or not happy and vice versa.
If fred is not wise then mary is not humble or not creative and vice versa.
Everyone who is rich or not humble is strong.
If john is kind then someone is wise or not brave.
If paul is not quiet then mary is calm or funny and vice versa.
Everyone who is tall is generous or not wise and vice versa.
Everyone who is patient or strong is both tall and not strong and vice versa.
Everyone who is old or generous is not humble and vice versa.
Everyone who is creative or not rich is not calm.
Everyone who is generous is both not kind and not wise.
If fred is both not generous and not calm then someone is old or happy.
Paul is not generous or curious.
Lucy is not creative or brave.
Alice is not calm.
Someone is both kind and wise. | Lucy is not happy. | neutral | (![X]:((calm(X)&old(X))=>(~wise(X)&curious(X))))&
(![X]:(~wise(X)=>(rich(X)|kind(X))))&
(![X]:((~wise(X)|~rich(X))<=>(old(X)|~funny(X))))&
((?[X]:((~quiet(X)&wise(X))))=>(?[X]:(~rich(X))))&
(![X]:((~generous(X)&~happy(X))<=>(~happy(X)&tall(X))))&
(![X]:(~happy(X)<=>(~curious(X)|~happy(X))))&
((~wise(fred))<=>((~humble(mary)|~creative(mary))))&
(![X]:((rich(X)|~humble(X))=>strong(X)))&
((kind(john))=>(?[X]:((wise(X)|~brave(X)))))&
((~quiet(paul))<=>((calm(mary)|funny(mary))))&
(![X]:(tall(X)<=>(generous(X)|~wise(X))))&
(![X]:((patient(X)|strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((old(X)|generous(X))<=>~humble(X)))&
(![X]:((creative(X)|~rich(X))=>~calm(X)))&
(![X]:(generous(X)=>(~kind(X)&~wise(X))))&
(((~generous(fred)&~calm(fred)))=>(?[X]:((old(X)|happy(X)))))&
((~generous(paul)|curious(paul)))&
((~creative(lucy)|brave(lucy)))&
(~calm(alice))&
(?[X]:((kind(X)&wise(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is either not strong or not funny is either generous or wise. If someone is funny or not brave then lucy is rich and vice versa. Everyone who is either not creative or not happy is rich and vice versa. Everyone who is either patient or not old is both generous and humble and vice versa. Everyone who is not rich is either patient or not happy and vice versa. If someone is not happy then someone is not calm and vice versa. Everyone who is either funny or old is either not old or rich and vice versa. Everyone who is not strong or calm is funny or not calm. If someone is not patient then fred is funny. Everyone who is quiet or kind is tall. Everyone who is either quiet or funny is not curious or creative and vice versa. Everyone who is not curious is curious. If someone is patient or rich then lucy is both not patient and not tall and vice versa. If susan is wise or strong then someone is not tall or not strong and vice versa. Everyone who is either not strong or old is not brave. If someone is both curious and not creative then lucy is not curious or old. Lucy is both wise and not funny. Susan is not calm or strong. Someone is old. Someone is not creative or not rich. Someone is both humble and generous. Someone is not patient or not rich. Susan is both not calm and not rich. | Susan is not kind. | neutral | (![X]:((~strong(X)<~>~funny(X))=>(generous(X)<~>wise(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(rich(lucy)))&
(![X]:((~creative(X)<~>~happy(X))<=>rich(X)))&
(![X]:((patient(X)<~>~old(X))<=>(generous(X)&humble(X))))&
(![X]:(~rich(X)<=>(patient(X)<~>~happy(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~calm(X))))&
(![X]:((funny(X)<~>old(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~strong(X)|calm(X))=>(funny(X)|~calm(X))))&
((?[X]:(~patient(X)))=>(funny(fred)))&
(![X]:((quiet(X)|kind(X))=>tall(X)))&
(![X]:((quiet(X)<~>funny(X))<=>(~curious(X)|creative(X))))&
(![X]:(~curious(X)=>curious(X)))&
((?[X]:((patient(X)|rich(X))))<=>((~patient(lucy)&~tall(lucy))))&
(((wise(susan)|strong(susan)))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~strong(X)<~>old(X))=>~brave(X)))&
((?[X]:((curious(X)&~creative(X))))=>((~curious(lucy)|old(lucy))))&
((wise(lucy)&~funny(lucy)))&
((~calm(susan)|strong(susan)))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:((~patient(X)|~rich(X))))&
((~calm(susan)&~rich(susan))) | ~kind(susan) | [] | null | 0 |
Everyone who is not creative is both not calm and not humble and vice versa. Everyone who is either happy or strong is not quiet or not patient and vice versa. Everyone who is not creative or not curious is both not old and tall and vice versa. If someone is both not curious and not happy then lucy is both wise and not calm and vice versa. Everyone who is either not strong or wise is not quiet. Everyone who is humble is brave and vice versa. Everyone who is not funny is not old and vice versa. Everyone who is either not rich or humble is either not funny or happy and vice versa. Everyone who is curious or quiet is both not tall and not quiet. Everyone who is kind is either not old or not kind. If someone is either not old or not quiet then someone is either curious or not brave and vice versa. If someone is both wise and not creative then someone is both humble and kind. If someone is both kind and not patient then mary is not tall or quiet. Everyone who is not wise is both funny and not rich and vice versa. Everyone who is strong is kind or not patient. If alice is generous or strong then mary is not humble or generous. Lucy is tall. Mary is both not generous and not quiet. Someone is not strong or not happy. Lucy is both wise and not kind. Paul is both generous and tall. Mary is strong. | Mary is wise. | neutral | (![X]:(~creative(X)<=>(~calm(X)&~humble(X))))&
(![X]:((happy(X)<~>strong(X))<=>(~quiet(X)|~patient(X))))&
(![X]:((~creative(X)|~curious(X))<=>(~old(X)&tall(X))))&
((?[X]:((~curious(X)&~happy(X))))<=>((wise(lucy)&~calm(lucy))))&
(![X]:((~strong(X)<~>wise(X))=>~quiet(X)))&
(![X]:(humble(X)<=>brave(X)))&
(![X]:(~funny(X)<=>~old(X)))&
(![X]:((~rich(X)<~>humble(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((curious(X)|quiet(X))=>(~tall(X)&~quiet(X))))&
(![X]:(kind(X)=>(~old(X)<~>~kind(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((wise(X)&~creative(X))))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((kind(X)&~patient(X))))=>((~tall(mary)|quiet(mary))))&
(![X]:(~wise(X)<=>(funny(X)&~rich(X))))&
(![X]:(strong(X)=>(kind(X)|~patient(X))))&
(((generous(alice)|strong(alice)))=>((~humble(mary)|generous(mary))))&
(tall(lucy))&
((~generous(mary)&~quiet(mary)))&
(?[X]:((~strong(X)|~happy(X))))&
((wise(lucy)&~kind(lucy)))&
((generous(paul)&tall(paul)))&
(strong(mary)) | wise(mary) | [] | null | 0 |
Everyone who is either not curious or not tall is either not curious or not patient and vice versa.
If someone is not curious then mary is either strong or generous.
If lucy is both not rich and quiet then susan is either creative or rich and vice versa.
If paul is not rich then someone is both not happy and happy.
If someone is either not wise or tall then lucy is both not calm and not happy.
Everyone who is both not kind and brave is not strong.
Everyone who is either not rich or strong is not patient and vice versa.
Everyone who is either wise or kind is both not curious and not generous and vice versa.
If fred is patient or strong then alice is wise and vice versa.
If alice is not rich then someone is either patient or generous.
Everyone who is not happy or not calm is both humble and not brave and vice versa.
If john is both not quiet and not funny then alice is quiet.
Everyone who is both curious and quiet is either not generous or not brave.
Everyone who is both old and not happy is not wise or not patient and vice versa.
Everyone who is both wise and calm is generous or quiet.
Everyone who is either not curious or not wise is not rich.
Someone is humble or kind.
Someone is either not funny or not patient.
Someone is either not wise or curious.
Lucy is rich.
Someone is not tall or kind.
Mary is happy.
Lucy is either happy or not strong.
Someone is not creative or not funny. | Paul is not rich. | contradiction | (![X]:((~curious(X)<~>~tall(X))<=>(~curious(X)<~>~patient(X))))&
((?[X]:(~curious(X)))=>((strong(mary)<~>generous(mary))))&
(((~rich(lucy)&quiet(lucy)))<=>((creative(susan)<~>rich(susan))))&
((~rich(paul))=>(?[X]:((~happy(X)&happy(X)))))&
((?[X]:((~wise(X)<~>tall(X))))=>((~calm(lucy)&~happy(lucy))))&
(![X]:((~kind(X)&brave(X))=>~strong(X)))&
(![X]:((~rich(X)<~>strong(X))<=>~patient(X)))&
(![X]:((wise(X)<~>kind(X))<=>(~curious(X)&~generous(X))))&
(((patient(fred)|strong(fred)))<=>(wise(alice)))&
((~rich(alice))=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~happy(X)|~calm(X))<=>(humble(X)&~brave(X))))&
(((~quiet(john)&~funny(john)))=>(quiet(alice)))&
(![X]:((curious(X)&quiet(X))=>(~generous(X)<~>~brave(X))))&
(![X]:((old(X)&~happy(X))<=>(~wise(X)|~patient(X))))&
(![X]:((wise(X)&calm(X))=>(generous(X)|quiet(X))))&
(![X]:((~curious(X)<~>~wise(X))=>~rich(X)))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
(rich(lucy))&
(?[X]:((~tall(X)|kind(X))))&
(happy(mary))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~creative(X)|~funny(X)))) | ~rich(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5113272295649817559190935
% SZS output start Proof for 5113272295649817559190935
4. ~rich(paul) => ? [X0] : (happy(X0) & ~happy(X0)) [input p3]
25. ~rich(paul) [input hypothesis]
27. ? [X0] : (happy(X0) & ~happy(X0)) | rich(paul) [ennf transformation 4]
43. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK0) & ~happy(sK0)) [choice axiom]
44. (happy(sK0) & ~happy(sK0)) | rich(paul) [skolemisation 27,43]
89. ~happy(sK0) | rich(paul) [cnf transformation 44]
90. happy(sK0) | rich(paul) [cnf transformation 44]
138. ~rich(paul) [cnf transformation 25]
181. 8 <=> rich(paul) [avatar definition]
185. 9 <=> happy(sK0) [avatar definition]
188. 8 | 9 [avatar split clause 90,185,181]
189. 8 | ~9 [avatar split clause 89,185,181]
304. ~8 [avatar split clause 138,181]
305. $false [avatar sat refutation 188,189,304]
% SZS output end Proof for 5113272295649817559190935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is either not patient or funny and vice versa.
Everyone who is not quiet or not calm is both humble and not creative and vice versa.
Everyone who is not brave or not calm is curious and vice versa.
Everyone who is both creative and not brave is either not tall or not humble.
If mary is funny or not kind then someone is funny or not strong and vice versa.
Everyone who is strong is either not old or not tall and vice versa.
Everyone who is kind or humble is not strong and vice versa.
If paul is not patient or not calm then someone is curious and vice versa.
If mary is not calm or rich then alice is creative or tall.
Everyone who is not creative is not patient or happy.
If someone is either calm or strong then john is both not tall and funny.
If paul is both not calm and not brave then someone is either happy or generous and vice versa.
Everyone who is both brave and not funny is both tall and happy.
If susan is either creative or not humble then lucy is either not old or not funny.
Everyone who is either patient or quiet is either brave or tall.
Everyone who is not generous or not humble is either curious or humble and vice versa.
Someone is generous.
Lucy is either not wise or generous.
Lucy is calm.
Someone is either not humble or not calm.
Someone is not funny or not brave.
Someone is both strong and patient.
Lucy is either not happy or generous. | Lucy is funny. | contradiction | (![X]:(~patient(X)<=>(~patient(X)<~>funny(X))))&
(![X]:((~quiet(X)|~calm(X))<=>(humble(X)&~creative(X))))&
(![X]:((~brave(X)|~calm(X))<=>curious(X)))&
(![X]:((creative(X)&~brave(X))=>(~tall(X)<~>~humble(X))))&
(((funny(mary)|~kind(mary)))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:(strong(X)<=>(~old(X)<~>~tall(X))))&
(![X]:((kind(X)|humble(X))<=>~strong(X)))&
(((~patient(paul)|~calm(paul)))<=>(?[X]:(curious(X))))&
(((~calm(mary)|rich(mary)))=>((creative(alice)|tall(alice))))&
(![X]:(~creative(X)=>(~patient(X)|happy(X))))&
((?[X]:((calm(X)<~>strong(X))))=>((~tall(john)&funny(john))))&
(((~calm(paul)&~brave(paul)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:((brave(X)&~funny(X))=>(tall(X)&happy(X))))&
(((creative(susan)<~>~humble(susan)))=>((~old(lucy)<~>~funny(lucy))))&
(![X]:((patient(X)<~>quiet(X))=>(brave(X)<~>tall(X))))&
(![X]:((~generous(X)|~humble(X))<=>(curious(X)<~>humble(X))))&
(?[X]:(generous(X)))&
((~wise(lucy)<~>generous(lucy)))&
(calm(lucy))&
(?[X]:((~humble(X)<~>~calm(X))))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:((strong(X)&patient(X))))&
((~happy(lucy)<~>generous(lucy))) | funny(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 4543494451734219556368947
% SZS output start Proof for 4543494451734219556368947
1. ! [X0] : (~patient(X0) <=> (~patient(X0) <~> funny(X0))) [input p0]
24. funny(lucy) [input hypothesis]
37. ! [X0] : ((~patient(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | patient(X0))) [nnf transformation 1]
78. ~funny(X0) | patient(X0) | patient(X0) [cnf transformation 37]
80. ~patient(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 37]
144. funny(lucy) [cnf transformation 24]
147. ~funny(X0) | patient(X0) [duplicate literal removal 78]
148. ~patient(X0) | ~funny(X0) [duplicate literal removal 80]
149. ~funny(X0) [subsumption resolution 147,148]
269. $false [subsumption resolution 144,149]
% SZS output end Proof for 4543494451734219556368947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not tall then susan is not quiet.
If someone is not strong then someone is either happy or calm.
Everyone who is humble or not humble is both not creative and curious.
Everyone who is patient is either not old or not creative and vice versa.
Everyone who is strong or happy is strong or not happy and vice versa.
If someone is generous then someone is both not rich and calm.
Everyone who is not strong is either funny or not creative and vice versa.
Everyone who is not quiet is both curious and not strong.
Everyone who is both not curious and not old is both rich and patient.
If fred is not wise then mary is wise or not tall and vice versa.
Everyone who is either not tall or not quiet is either generous or not humble.
Everyone who is not strong is humble.
If someone is not humble or curious then paul is either tall or patient.
If paul is happy or not tall then someone is quiet.
If john is both rich and not rich then paul is either not creative or not wise and vice versa.
If paul is both not rich and happy then someone is either calm or humble.
Paul is not funny or quiet.
Someone is funny.
Someone is not old or not patient.
Alice is either not generous or not kind.
Lucy is either not kind or not creative.
Alice is curious. | Alice is not kind. | contradiction | ((?[X]:((~rich(X)|~tall(X))))=>(~quiet(susan)))&
((?[X]:(~strong(X)))=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((humble(X)|~humble(X))=>(~creative(X)&curious(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~creative(X))))&
(![X]:((strong(X)|happy(X))<=>(strong(X)|~happy(X))))&
((?[X]:(generous(X)))=>(?[X]:((~rich(X)&calm(X)))))&
(![X]:(~strong(X)<=>(funny(X)<~>~creative(X))))&
(![X]:(~quiet(X)=>(curious(X)&~strong(X))))&
(![X]:((~curious(X)&~old(X))=>(rich(X)&patient(X))))&
((~wise(fred))<=>((wise(mary)|~tall(mary))))&
(![X]:((~tall(X)<~>~quiet(X))=>(generous(X)<~>~humble(X))))&
(![X]:(~strong(X)=>humble(X)))&
((?[X]:((~humble(X)|curious(X))))=>((tall(paul)<~>patient(paul))))&
(((happy(paul)|~tall(paul)))=>(?[X]:(quiet(X))))&
(((rich(john)&~rich(john)))<=>((~creative(paul)<~>~wise(paul))))&
(((~rich(paul)&happy(paul)))=>(?[X]:((calm(X)<~>humble(X)))))&
((~funny(paul)|quiet(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|~patient(X))))&
((~generous(alice)<~>~kind(alice)))&
((~kind(lucy)<~>~creative(lucy)))&
(curious(alice)) | ~kind(alice) | [
"p0",
"p4",
"p5",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3480565157710957715466535
% SZS output start Proof for 3480565157710957715466535
1. ? [X0] : (~tall(X0) | ~rich(X0)) => ~quiet(susan) [input p0]
5. ! [X0] : ((happy(X0) | strong(X0)) <=> (~happy(X0) | strong(X0))) [input p4]
6. ? [X0] : generous(X0) => ? [X0] : (calm(X0) & ~rich(X0)) [input p5]
8. ! [X0] : (~quiet(X0) => (~strong(X0) & curious(X0))) [input p7]
20. ~generous(alice) <~> ~kind(alice) [input p19]
23. ~kind(alice) [input hypothesis]
25. ? [X0] : generous(X0) => ? [X1] : (calm(X1) & ~rich(X1)) [rectify 6]
26. ~quiet(susan) | ! [X0] : (tall(X0) & rich(X0)) [ennf transformation 1]
29. ? [X1] : (calm(X1) & ~rich(X1)) | ! [X0] : ~generous(X0) [ennf transformation 25]
30. ! [X0] : ((~strong(X0) & curious(X0)) | quiet(X0)) [ennf transformation 8]
44. ! [X0] : (((happy(X0) | strong(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (~happy(X0) & ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : ((happy(X0) | strong(X0) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | (~happy(X0) & ~strong(X0)))) [flattening 44]
46. ? [X0] : (calm(X0) & ~rich(X0)) | ! [X1] : ~generous(X1) [rectify 29]
47. ? [X0] : (calm(X0) & ~rich(X0)) => (calm(sK1) & ~rich(sK1)) [choice axiom]
48. (calm(sK1) & ~rich(sK1)) | ! [X1] : ~generous(X1) [skolemisation 46,47]
65. (kind(alice) | generous(alice)) & (~kind(alice) | ~generous(alice)) [nnf transformation 20]
67. ~quiet(susan) | rich(X0) [cnf transformation 26]
80. ~happy(X0) | strong(X0) | ~happy(X0) [cnf transformation 45]
82. happy(X0) | strong(X0) | happy(X0) [cnf transformation 45]
83. ~rich(sK1) | ~generous(X1) [cnf transformation 48]
90. ~strong(X0) | quiet(X0) [cnf transformation 30]
119. kind(alice) | generous(alice) [cnf transformation 65]
123. ~kind(alice) [cnf transformation 23]
124. ~happy(X0) | strong(X0) [duplicate literal removal 80]
125. happy(X0) | strong(X0) [duplicate literal removal 82]
130. 2 <=> quiet(susan) [avatar definition]
132. ~quiet(susan) <- (~2) [avatar component clause 130]
135. 3 <=> ! [X0] : rich(X0) [avatar definition]
136. rich(X0) <- (3) [avatar component clause 135]
137. 3 | ~2 [avatar split clause 67,130,135]
139. 4 <=> ! [X1] : strong(X1) [avatar definition]
140. strong(X1) <- (4) [avatar component clause 139]
155. strong(X0) [subsumption resolution 124,125]
156. 4 [avatar split clause 155,139]
158. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
159. ~generous(X1) <- (7) [avatar component clause 158]
166. 9 <=> rich(sK1) [avatar definition]
168. ~rich(sK1) <- (~9) [avatar component clause 166]
169. 7 | ~9 [avatar split clause 83,166,158]
251. 25 <=> generous(alice) [avatar definition]
253. generous(alice) <- (25) [avatar component clause 251]
255. 26 <=> kind(alice) [avatar definition]
258. 25 | 26 [avatar split clause 119,255,251]
261. ~26 [avatar split clause 123,255]
262. $false <- (7, 25) [resolution 253,159]
263. ~7 | ~25 [avatar contradiction clause 262]
264. quiet(X0) <- (4) [resolution 90,140]
265. $false <- (~2, 4) [resolution 264,132]
266. 2 | ~4 [avatar contradiction clause 265]
269. $false <- (3, ~9) [resolution 136,168]
270. ~3 | 9 [avatar contradiction clause 269]
271. $false [avatar sat refutation 137,156,169,258,261,263,266,270]
% SZS output end Proof for 3480565157710957715466535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not quiet is both quiet and patient.
Everyone who is both kind and rich is both humble and not funny and vice versa.
Everyone who is either not funny or not generous is not tall or not humble and vice versa.
If someone is not kind then alice is creative.
Everyone who is not brave or brave is either not patient or not brave.
Everyone who is both not strong and strong is either rich or quiet and vice versa.
If paul is both calm and humble then someone is either humble or creative and vice versa.
Everyone who is either not kind or calm is rich or old and vice versa.
Everyone who is curious is not calm or not old.
If fred is humble or brave then susan is both not brave and tall.
If mary is either wise or creative then susan is both tall and not creative.
Everyone who is either creative or calm is either old or not tall and vice versa.
If someone is either tall or not strong then fred is not creative or brave and vice versa.
Everyone who is either wise or calm is humble or not patient and vice versa.
Everyone who is quiet or not humble is either not creative or funny and vice versa.
If someone is both quiet and humble then mary is both not curious and old.
Mary is either not patient or not kind.
Someone is not humble.
Someone is either happy or not old.
Alice is both not calm and not kind.
Someone is not brave.
Someone is either not generous or old.
Mary is both not happy and funny.
Someone is either tall or not happy. | Susan is not rich. | contradiction | (![X]:((~strong(X)|~quiet(X))=>(quiet(X)&patient(X))))&
(![X]:((kind(X)&rich(X))<=>(humble(X)&~funny(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~tall(X)|~humble(X))))&
((?[X]:(~kind(X)))=>(creative(alice)))&
(![X]:((~brave(X)|brave(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~strong(X)&strong(X))<=>(rich(X)<~>quiet(X))))&
(((calm(paul)&humble(paul)))<=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(rich(X)|old(X))))&
(![X]:(curious(X)=>(~calm(X)|~old(X))))&
(((humble(fred)|brave(fred)))=>((~brave(susan)&tall(susan))))&
(((wise(mary)<~>creative(mary)))=>((tall(susan)&~creative(susan))))&
(![X]:((creative(X)<~>calm(X))<=>(old(X)<~>~tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))<=>((~creative(fred)|brave(fred))))&
(![X]:((wise(X)<~>calm(X))<=>(humble(X)|~patient(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:((quiet(X)&humble(X))))=>((~curious(mary)&old(mary))))&
((~patient(mary)<~>~kind(mary)))&
(?[X]:(~humble(X)))&
(?[X]:((happy(X)<~>~old(X))))&
((~calm(alice)&~kind(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((~generous(X)<~>old(X))))&
((~happy(mary)&funny(mary)))&
(?[X]:((tall(X)<~>~happy(X)))) | ~rich(susan) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7655938207476221474188937
% SZS output start Proof for 7655938207476221474188937
1. ! [X0] : ((~quiet(X0) | ~strong(X0)) => (patient(X0) & quiet(X0))) [input p0]
6. ! [X0] : ((strong(X0) & ~strong(X0)) <=> (rich(X0) <~> quiet(X0))) [input p5]
25. ~rich(susan) [input hypothesis]
28. ! [X0] : ((patient(X0) & quiet(X0)) | (quiet(X0) & strong(X0))) [ennf transformation 1]
39. ! [X0] : (((strong(X0) & ~strong(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~strong(X0) | strong(X0)))) [nnf transformation 6]
40. ! [X0] : (((strong(X0) & ~strong(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) & (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | ~strong(X0) | strong(X0))) [flattening 39]
74. quiet(X0) | quiet(X0) [cnf transformation 28]
95. ~strong(X0) | rich(X0) | ~quiet(X0) [cnf transformation 40]
97. strong(X0) | rich(X0) | ~quiet(X0) [cnf transformation 40]
159. ~rich(susan) [cnf transformation 25]
162. quiet(X0) [duplicate literal removal 74]
171. strong(X0) | rich(X0) [subsumption resolution 97,162]
172. ~strong(X0) | rich(X0) [subsumption resolution 95,162]
173. rich(X0) [subsumption resolution 172,171]
315. $false [subsumption resolution 159,173]
% SZS output end Proof for 7655938207476221474188937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or tall is generous or not calm.
If susan is both kind and curious then someone is either curious or not patient.
Everyone who is both patient and strong is happy or not kind.
Everyone who is both not quiet and rich is both brave and old.
Everyone who is not patient or not creative is both generous and not generous.
Everyone who is either not creative or not generous is not rich and vice versa.
Everyone who is curious or creative is both not curious and wise and vice versa.
If someone is quiet then someone is not patient or wise.
Everyone who is both not strong and strong is tall and vice versa.
If someone is both curious and wise then someone is not wise.
Everyone who is quiet is strong.
Everyone who is humble or not humble is creative.
Everyone who is either not curious or not funny is both not quiet and old.
Everyone who is either tall or creative is both calm and wise.
Everyone who is generous or not quiet is not quiet or kind.
Everyone who is both not old and calm is both not curious and not funny and vice versa.
Paul is both strong and generous.
Someone is kind or not creative.
Fred is humble.
Fred is strong.
Someone is either not strong or humble. | Paul is not wise. | contradiction | (![X]:((~rich(X)<~>tall(X))=>(generous(X)|~calm(X))))&
(((kind(susan)&curious(susan)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((patient(X)&strong(X))=>(happy(X)|~kind(X))))&
(![X]:((~quiet(X)&rich(X))=>(brave(X)&old(X))))&
(![X]:((~patient(X)|~creative(X))=>(generous(X)&~generous(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>~rich(X)))&
(![X]:((curious(X)|creative(X))<=>(~curious(X)&wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((~strong(X)&strong(X))<=>tall(X)))&
((?[X]:((curious(X)&wise(X))))=>(?[X]:(~wise(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((humble(X)|~humble(X))=>creative(X)))&
(![X]:((~curious(X)<~>~funny(X))=>(~quiet(X)&old(X))))&
(![X]:((tall(X)<~>creative(X))=>(calm(X)&wise(X))))&
(![X]:((generous(X)|~quiet(X))=>(~quiet(X)|kind(X))))&
(![X]:((~old(X)&calm(X))<=>(~curious(X)&~funny(X))))&
((strong(paul)&generous(paul)))&
(?[X]:((kind(X)|~creative(X))))&
(humble(fred))&
(strong(fred))&
(?[X]:((~strong(X)<~>humble(X)))) | ~wise(paul) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6218139171312560794664352
% SZS output start Proof for 6218139171312560794664352
5. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~generous(X0) & generous(X0))) [input p4]
7. ! [X0] : ((creative(X0) | curious(X0)) <=> (wise(X0) & ~curious(X0))) [input p6]
22. ~wise(paul) [input hypothesis]
33. ! [X0] : ((~generous(X0) & generous(X0)) | (creative(X0) & patient(X0))) [ennf transformation 5]
47. ! [X0] : (((creative(X0) | curious(X0)) | (~wise(X0) | curious(X0))) & ((wise(X0) & ~curious(X0)) | (~creative(X0) & ~curious(X0)))) [nnf transformation 7]
48. ! [X0] : ((creative(X0) | curious(X0) | ~wise(X0) | curious(X0)) & ((wise(X0) & ~curious(X0)) | (~creative(X0) & ~curious(X0)))) [flattening 47]
72. generous(X0) | creative(X0) [cnf transformation 33]
74. ~generous(X0) | creative(X0) [cnf transformation 33]
82. wise(X0) | ~creative(X0) [cnf transformation 48]
113. ~wise(paul) [cnf transformation 22]
134. creative(X0) [subsumption resolution 72,74]
138. wise(X0) [subsumption resolution 82,134]
157. $false [subsumption resolution 113,138]
% SZS output end Proof for 6218139171312560794664352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not happy is not patient and vice versa.
Everyone who is curious is creative and vice versa.
Everyone who is both not patient and curious is not tall or not quiet and vice versa.
Everyone who is not funny is either old or not generous.
Everyone who is both not humble and not wise is not calm and vice versa.
Everyone who is either humble or not rich is both generous and not wise and vice versa.
Everyone who is either not strong or not humble is either strong or quiet and vice versa.
If someone is curious then someone is humble or wise and vice versa.
Everyone who is not happy or not tall is either not wise or not funny.
If someone is either not humble or not rich then john is both rich and not patient.
Everyone who is either not creative or old is either not wise or not tall.
Everyone who is either tall or brave is curious.
If someone is not generous then someone is not happy or generous.
If john is either not funny or not humble then susan is both not quiet and creative and vice versa.
If susan is quiet or not old then john is not quiet and vice versa.
If mary is humble or not patient then fred is happy or brave and vice versa.
Someone is kind.
John is not creative.
Someone is creative.
Someone is either not old or humble.
Someone is both brave and not funny.
Someone is either old or quiet.
Paul is not wise.
Alice is funny or not wise. | Alice is not generous. | contradiction | (![X]:((~quiet(X)&~happy(X))<=>~patient(X)))&
(![X]:(curious(X)<=>creative(X)))&
(![X]:((~patient(X)&curious(X))<=>(~tall(X)|~quiet(X))))&
(![X]:(~funny(X)=>(old(X)<~>~generous(X))))&
(![X]:((~humble(X)&~wise(X))<=>~calm(X)))&
(![X]:((humble(X)<~>~rich(X))<=>(generous(X)&~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((~happy(X)|~tall(X))=>(~wise(X)<~>~funny(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>((rich(john)&~patient(john))))&
(![X]:((~creative(X)<~>old(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((tall(X)<~>brave(X))=>curious(X)))&
((?[X]:(~generous(X)))=>(?[X]:((~happy(X)|generous(X)))))&
(((~funny(john)<~>~humble(john)))<=>((~quiet(susan)&creative(susan))))&
(((quiet(susan)|~old(susan)))<=>(~quiet(john)))&
(((humble(mary)|~patient(mary)))<=>((happy(fred)|brave(fred))))&
(?[X]:(kind(X)))&
(~creative(john))&
(?[X]:(creative(X)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((old(X)<~>quiet(X))))&
(~wise(paul))&
((funny(alice)|~wise(alice))) | ~generous(alice) | [
"p0",
"p1",
"p2",
"p5",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7725829944754443035528842
% SZS output start Proof for 7725829944754443035528842
1. ! [X0] : ((~happy(X0) & ~quiet(X0)) <=> ~patient(X0)) [input p0]
2. ! [X0] : (curious(X0) <=> creative(X0)) [input p1]
3. ! [X0] : ((curious(X0) & ~patient(X0)) <=> (~quiet(X0) | ~tall(X0))) [input p2]
6. ! [X0] : ((humble(X0) <~> ~rich(X0)) <=> (~wise(X0) & generous(X0))) [input p5]
10. ? [X0] : (~humble(X0) <~> ~rich(X0)) => (~patient(john) & rich(john)) [input p9]
18. ~creative(john) [input p17]
25. ~generous(alice) [input hypothesis]
31. (~patient(john) & rich(john)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 10]
35. ! [X0] : (((~happy(X0) & ~quiet(X0)) | patient(X0)) & (~patient(X0) | (happy(X0) | quiet(X0)))) [nnf transformation 1]
36. ! [X0] : (((~happy(X0) & ~quiet(X0)) | patient(X0)) & (~patient(X0) | happy(X0) | quiet(X0))) [flattening 35]
37. ! [X0] : ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0))) [nnf transformation 2]
38. ! [X0] : (((curious(X0) & ~patient(X0)) | (quiet(X0) & tall(X0))) & ((~quiet(X0) | ~tall(X0)) | (~curious(X0) | patient(X0)))) [nnf transformation 3]
39. ! [X0] : (((curious(X0) & ~patient(X0)) | (quiet(X0) & tall(X0))) & (~quiet(X0) | ~tall(X0) | ~curious(X0) | patient(X0))) [flattening 38]
41. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [nnf transformation 6]
42. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [flattening 41]
50. (~patient(john) & rich(john)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 31]
73. ~quiet(X0) | patient(X0) [cnf transformation 36]
75. ~curious(X0) | creative(X0) [cnf transformation 37]
81. curious(X0) | quiet(X0) [cnf transformation 39]
84. ~rich(X0) | generous(X0) | ~humble(X0) [cnf transformation 42]
85. rich(X0) | humble(X0) | generous(X0) [cnf transformation 42]
107. ~patient(john) | ~rich(X0) | humble(X0) [cnf transformation 50]
108. ~patient(john) | ~humble(X0) | rich(X0) [cnf transformation 50]
129. ~creative(john) [cnf transformation 18]
139. ~generous(alice) [cnf transformation 25]
171. 7 <=> ! [X0] : (~humble(X0) | rich(X0)) [avatar definition]
172. ~humble(X0) | rich(X0) <- (7) [avatar component clause 171]
174. 8 <=> patient(john) [avatar definition]
177. 7 | ~8 [avatar split clause 108,174,171]
179. 9 <=> ! [X0] : (~rich(X0) | humble(X0)) [avatar definition]
180. ~rich(X0) | humble(X0) <- (9) [avatar component clause 179]
181. 9 | ~8 [avatar split clause 107,174,179]
190. 11 <=> ! [X1] : generous(X1) [avatar definition]
191. generous(X1) <- (11) [avatar component clause 190]
224. 18 <=> quiet(john) [avatar definition]
226. quiet(john) <- (18) [avatar component clause 224]
289. creative(X0) | quiet(X0) [resolution 81,75]
298. quiet(john) [resolution 289,129]
305. 18 [avatar split clause 298,224]
308. patient(john) <- (18) [resolution 226,73]
313. 8 | ~18 [avatar split clause 308,224,174]
350. humble(X1) | generous(X1) | humble(X1) <- (9) [resolution 85,180]
351. humble(X1) | generous(X1) <- (9) [duplicate literal removal 350]
567. rich(X1) | generous(X1) <- (7, 9) [resolution 351,172]
652. generous(X2) | generous(X2) | ~humble(X2) <- (7, 9) [resolution 567,84]
654. generous(X2) | ~humble(X2) <- (7, 9) [duplicate literal removal 652]
656. generous(X2) <- (7, 9) [subsumption resolution 654,351]
657. 11 | ~7 | ~9 [avatar split clause 656,179,171,190]
658. $false <- (11) [resolution 191,139]
660. ~11 [avatar contradiction clause 658]
661. $false [avatar sat refutation 177,181,305,313,657,660]
% SZS output end Proof for 7725829944754443035528842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not quiet then someone is generous or creative and vice versa.
Everyone who is both kind and curious is not quiet.
Everyone who is generous or not generous is both not calm and not tall.
Everyone who is quiet or wise is either not humble or rich and vice versa.
If susan is not generous or not wise then someone is not kind or creative and vice versa.
Everyone who is both creative and not tall is not wise or funny and vice versa.
If fred is either not generous or wise then someone is both not wise and not curious and vice versa.
Everyone who is brave or humble is either not quiet or humble and vice versa.
If someone is either not humble or rich then john is wise.
If someone is both rich and not tall then alice is not quiet.
If fred is creative or funny then fred is not old or not tall.
Everyone who is brave or quiet is either not tall or not kind.
If fred is patient then mary is both humble and not kind.
Everyone who is not brave or tall is both funny and not strong.
Everyone who is patient is either curious or wise and vice versa.
Lucy is kind.
Fred is not happy.
Someone is either not calm or old.
John is either not tall or not kind.
Susan is both not wise and not funny.
Someone is not rich.
Someone is generous.
Someone is not patient or creative. | Fred is funny. | neutral | ((?[X]:((kind(X)<~>~quiet(X))))<=>(?[X]:((generous(X)|creative(X)))))&
(![X]:((kind(X)&curious(X))=>~quiet(X)))&
(![X]:((generous(X)|~generous(X))=>(~calm(X)&~tall(X))))&
(![X]:((quiet(X)|wise(X))<=>(~humble(X)<~>rich(X))))&
(((~generous(susan)|~wise(susan)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((creative(X)&~tall(X))<=>(~wise(X)|funny(X))))&
(((~generous(fred)<~>wise(fred)))<=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|humble(X))<=>(~quiet(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>rich(X))))=>(wise(john)))&
((?[X]:((rich(X)&~tall(X))))=>(~quiet(alice)))&
(((creative(fred)|funny(fred)))=>((~old(fred)|~tall(fred))))&
(![X]:((brave(X)|quiet(X))=>(~tall(X)<~>~kind(X))))&
((patient(fred))=>((humble(mary)&~kind(mary))))&
(![X]:((~brave(X)|tall(X))=>(funny(X)&~strong(X))))&
(![X]:(patient(X)<=>(curious(X)<~>wise(X))))&
(kind(lucy))&
(~happy(fred))&
(?[X]:((~calm(X)<~>old(X))))&
((~tall(john)<~>~kind(john)))&
((~wise(susan)&~funny(susan)))&
(?[X]:(~rich(X)))&
(?[X]:(generous(X)))&
(?[X]:((~patient(X)|creative(X)))) | funny(fred) | [] | null | 0 |
If someone is not old or old then someone is either not funny or brave and vice versa.
Everyone who is not curious is both quiet and curious and vice versa.
Everyone who is either not happy or funny is both not tall and old.
If paul is both not happy and happy then someone is brave and vice versa.
Everyone who is either kind or funny is calm and vice versa.
If someone is either strong or not generous then someone is both quiet and not tall.
If john is both strong and not brave then susan is not generous or creative.
Everyone who is either not kind or not creative is both not brave and not creative.
If someone is either not rich or not calm then alice is not kind or not tall.
Everyone who is not strong is not rich.
Everyone who is old is both brave and creative and vice versa.
Everyone who is strong or creative is both not wise and old.
Everyone who is either curious or not curious is either calm or not curious and vice versa.
Everyone who is either happy or wise is kind or funny and vice versa.
If someone is happy then someone is not brave or not curious.
Someone is both calm and not tall.
Someone is kind.
Someone is not generous or not old.
Someone is either rich or calm.
Alice is either not humble or not creative.
Someone is not happy.
Susan is either not tall or not curious. | Paul is quiet. | contradiction | ((?[X]:((~old(X)|old(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:(~curious(X)<=>(quiet(X)&curious(X))))&
(![X]:((~happy(X)<~>funny(X))=>(~tall(X)&old(X))))&
(((~happy(paul)&happy(paul)))<=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>funny(X))<=>calm(X)))&
((?[X]:((strong(X)<~>~generous(X))))=>(?[X]:((quiet(X)&~tall(X)))))&
(((strong(john)&~brave(john)))=>((~generous(susan)|creative(susan))))&
(![X]:((~kind(X)<~>~creative(X))=>(~brave(X)&~creative(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~kind(alice)|~tall(alice))))&
(![X]:(~strong(X)=>~rich(X)))&
(![X]:(old(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)|creative(X))=>(~wise(X)&old(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)|funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((~brave(X)|~curious(X)))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~generous(X)|~old(X))))&
(?[X]:((rich(X)<~>calm(X))))&
((~humble(alice)<~>~creative(alice)))&
(?[X]:(~happy(X)))&
((~tall(susan)<~>~curious(susan))) | quiet(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3972503898640519473550055
% SZS output start Proof for 3972503898640519473550055
2. ! [X0] : (~curious(X0) <=> (curious(X0) & quiet(X0))) [input p1]
23. quiet(paul) [input hypothesis]
42. ! [X0] : ((~curious(X0) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | curious(X0))) [nnf transformation 2]
43. ! [X0] : ((~curious(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | curious(X0))) [flattening 42]
85. curious(X0) | curious(X0) [cnf transformation 43]
86. ~curious(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 43]
143. quiet(paul) [cnf transformation 23]
153. curious(X0) [duplicate literal removal 85]
154. ~quiet(X0) | ~curious(X0) [duplicate literal removal 86]
264. ~curious(paul) [resolution 154,143]
265. $false [subsumption resolution 264,153]
% SZS output end Proof for 3972503898640519473550055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not quiet or not old then someone is not generous or strong and vice versa. Everyone who is either not wise or tall is either not funny or patient and vice versa. If john is both not humble and not curious then john is brave. Everyone who is strong is both funny and wise and vice versa. If someone is brave or creative then someone is either not calm or strong. Everyone who is not strong or not creative is old. If mary is both wise and tall then someone is not quiet or not curious and vice versa. Everyone who is brave or strong is not happy or not tall. If lucy is old or brave then lucy is not kind. Everyone who is both not curious and not creative is either not patient or not brave and vice versa. If someone is not curious then someone is either brave or not wise and vice versa. Everyone who is not generous is either not old or tall. Everyone who is not strong is not funny or not rich and vice versa. If someone is not happy or rich then fred is either humble or not strong. Everyone who is both not wise and old is generous or brave and vice versa. Everyone who is not quiet is not kind. Lucy is either not calm or not generous. Susan is tall. Someone is patient. Someone is calm or not calm. Someone is not funny or not generous. Someone is either generous or not funny. Someone is either not wise or patient. Alice is either not curious or not brave. | Mary is not brave. | entailment | (((~quiet(mary)|~old(mary)))<=>(?[X]:((~generous(X)|strong(X)))))&
(![X]:((~wise(X)<~>tall(X))<=>(~funny(X)<~>patient(X))))&
(((~humble(john)&~curious(john)))=>(brave(john)))&
(![X]:(strong(X)<=>(funny(X)&wise(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~strong(X)|~creative(X))=>old(X)))&
(((wise(mary)&tall(mary)))<=>(?[X]:((~quiet(X)|~curious(X)))))&
(![X]:((brave(X)|strong(X))=>(~happy(X)|~tall(X))))&
(((old(lucy)|brave(lucy)))=>(~kind(lucy)))&
(![X]:((~curious(X)&~creative(X))<=>(~patient(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(~funny(X)|~rich(X))))&
((?[X]:((~happy(X)|rich(X))))=>((humble(fred)<~>~strong(fred))))&
(![X]:((~wise(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
((~calm(lucy)<~>~generous(lucy)))&
(tall(susan))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
((~curious(alice)<~>~brave(alice))) | ~brave(mary) | [
"p0",
"p6",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6218159191301844670227858
% SZS output start Proof for 6218159191301844670227858
1. (~old(mary) | ~quiet(mary)) <=> ? [X0] : (strong(X0) | ~generous(X0)) [input p0]
7. (tall(mary) & wise(mary)) <=> ? [X0] : (~curious(X0) | ~quiet(X0)) [input p6]
11. ? [X0] : ~curious(X0) <=> ? [X0] : (brave(X0) <~> ~wise(X0)) [input p10]
15. ! [X0] : ((old(X0) & ~wise(X0)) <=> (brave(X0) | generous(X0))) [input p14]
24. ~curious(alice) <~> ~brave(alice) [input p23]
25. brave(mary) [input hypothesis]
27. ? [X0] : ~curious(X0) <=> ? [X1] : (brave(X1) <~> ~wise(X1)) [rectify 11]
38. ((~old(mary) | ~quiet(mary)) | ! [X0] : (~strong(X0) & generous(X0))) & (? [X0] : (strong(X0) | ~generous(X0)) | (old(mary) & quiet(mary))) [nnf transformation 1]
39. (~old(mary) | ~quiet(mary) | ! [X0] : (~strong(X0) & generous(X0))) & (? [X0] : (strong(X0) | ~generous(X0)) | (old(mary) & quiet(mary))) [flattening 38]
40. (~old(mary) | ~quiet(mary) | ! [X0] : (~strong(X0) & generous(X0))) & (? [X1] : (strong(X1) | ~generous(X1)) | (old(mary) & quiet(mary))) [rectify 39]
41. ? [X1] : (strong(X1) | ~generous(X1)) => (strong(sK0) | ~generous(sK0)) [choice axiom]
42. (~old(mary) | ~quiet(mary) | ! [X0] : (~strong(X0) & generous(X0))) & ((strong(sK0) | ~generous(sK0)) | (old(mary) & quiet(mary))) [skolemisation 40,41]
50. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | (~tall(mary) | ~wise(mary))) [nnf transformation 7]
51. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X0] : (~curious(X0) | ~quiet(X0)) | ~tall(mary) | ~wise(mary)) [flattening 50]
52. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & (? [X1] : (~curious(X1) | ~quiet(X1)) | ~tall(mary) | ~wise(mary)) [rectify 51]
53. ? [X1] : (~curious(X1) | ~quiet(X1)) => (~curious(sK2) | ~quiet(sK2)) [choice axiom]
54. ((tall(mary) & wise(mary)) | ! [X0] : (curious(X0) & quiet(X0))) & ((~curious(sK2) | ~quiet(sK2)) | ~tall(mary) | ~wise(mary)) [skolemisation 52,53]
57. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X1] : ((wise(X1) | ~brave(X1)) & (~wise(X1) | brave(X1))) | ! [X0] : curious(X0)) [nnf transformation 27]
58. (? [X0] : ~curious(X0) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) | ! [X3] : curious(X3)) [rectify 57]
59. ? [X0] : ~curious(X0) => ~curious(sK3) [choice axiom]
60. ? [X2] : ((wise(X2) | ~brave(X2)) & (~wise(X2) | brave(X2))) => ((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) [choice axiom]
61. (~curious(sK3) | ! [X1] : ((brave(X1) | wise(X1)) & (~wise(X1) | ~brave(X1)))) & (((wise(sK4) | ~brave(sK4)) & (~wise(sK4) | brave(sK4))) | ! [X3] : curious(X3)) [skolemisation 58,60,59]
66. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 15]
67. ! [X0] : (((old(X0) & ~wise(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | wise(X0))) [flattening 66]
81. (brave(alice) | curious(alice)) & (~brave(alice) | ~curious(alice)) [nnf transformation 24]
84. ~old(mary) | ~quiet(mary) | generous(X0) [cnf transformation 42]
105. wise(mary) | quiet(X0) [cnf transformation 54]
106. wise(mary) | curious(X0) [cnf transformation 54]
120. ~curious(sK3) | brave(X1) | wise(X1) [cnf transformation 61]
131. ~wise(X0) | ~generous(X0) [cnf transformation 67]
132. ~wise(X0) | ~brave(X0) [cnf transformation 67]
134. ~brave(X0) | old(X0) [cnf transformation 67]
145. ~brave(alice) | ~curious(alice) [cnf transformation 81]
147. brave(mary) [cnf transformation 25]
152. 2 <=> quiet(mary) [avatar definition]
154. ~quiet(mary) <- (~2) [avatar component clause 152]
156. 3 <=> old(mary) [avatar definition]
161. 4 <=> ! [X0] : generous(X0) [avatar definition]
162. generous(X0) <- (4) [avatar component clause 161]
163. 4 | ~2 | ~3 [avatar split clause 84,156,152,161]
206. 14 <=> ! [X0] : curious(X0) [avatar definition]
207. curious(X0) <- (14) [avatar component clause 206]
214. 16 <=> ! [X0] : quiet(X0) [avatar definition]
215. quiet(X0) <- (16) [avatar component clause 214]
218. 17 <=> wise(mary) [avatar definition]
221. 14 | 17 [avatar split clause 106,218,206]
222. 16 | 17 [avatar split clause 105,218,214]
233. 20 <=> ! [X1] : (brave(X1) | wise(X1)) [avatar definition]
234. brave(X1) | wise(X1) <- (20) [avatar component clause 233]
236. 21 <=> curious(sK3) [avatar definition]
238. ~curious(sK3) <- (~21) [avatar component clause 236]
239. 20 | ~21 [avatar split clause 120,236,233]
241. 22 <=> ! [X1] : (~wise(X1) | ~brave(X1)) [avatar definition]
242. ~brave(X1) | ~wise(X1) <- (22) [avatar component clause 241]
272. 22 [avatar split clause 132,241]
313. 37 <=> curious(alice) [avatar definition]
314. ~curious(alice) <- (~37) [avatar component clause 313]
317. 38 <=> brave(alice) [avatar definition]
318. ~brave(alice) <- (~38) [avatar component clause 317]
321. ~37 | ~38 [avatar split clause 145,317,313]
322. $false <- (14, ~21) [resolution 238,207]
323. ~14 | 21 [avatar contradiction clause 322]
330. old(mary) [resolution 134,147]
333. 3 [avatar split clause 330,156]
334. $false <- (~2, 16) [subsumption resolution 154,215]
335. 2 | ~16 [avatar contradiction clause 334]
336. ~wise(mary) <- (22) [resolution 242,147]
339. ~17 | ~22 [avatar split clause 336,241,218]
351. wise(alice) <- (20, ~38) [resolution 234,318]
360. ~generous(alice) <- (20, ~38) [resolution 351,131]
361. $false <- (4, 20, ~38) [subsumption resolution 360,162]
362. ~4 | ~20 | 38 [avatar contradiction clause 361]
363. $false <- (14, ~37) [subsumption resolution 314,207]
364. ~14 | 37 [avatar contradiction clause 363]
365. $false [avatar sat refutation 163,221,222,239,272,321,323,333,335,339,362,364]
% SZS output end Proof for 6218159191301844670227858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then john is not rich or not wise.
If someone is either happy or not old then paul is both calm and not humble.
Everyone who is strong or not patient is brave and vice versa.
Everyone who is both rich and creative is old and vice versa.
Everyone who is patient or brave is either kind or not humble.
If paul is not patient or humble then john is either calm or funny and vice versa.
If someone is both quiet and not brave then someone is either not wise or tall and vice versa.
If someone is not creative then paul is either old or kind and vice versa.
Everyone who is not brave or strong is humble or not brave.
If paul is not quiet or not tall then fred is not creative or not brave.
If mary is both kind and brave then john is both kind and wise.
Everyone who is tall or not calm is not curious.
If susan is old or kind then someone is both not kind and not happy and vice versa.
Everyone who is not curious is both not patient and patient.
Everyone who is either not humble or kind is either not calm or not brave and vice versa.
If alice is both not funny and not quiet then fred is either not brave or old.
Someone is not creative.
Alice is both generous and not happy.
Lucy is quiet.
Someone is either patient or not wise.
Someone is either funny or not patient.
Someone is either old or not quiet.
Mary is not generous or not kind. | Alice is patient. | entailment | ((?[X]:(quiet(X)))=>((~rich(john)|~wise(john))))&
((?[X]:((happy(X)<~>~old(X))))=>((calm(paul)&~humble(paul))))&
(![X]:((strong(X)|~patient(X))<=>brave(X)))&
(![X]:((rich(X)&creative(X))<=>old(X)))&
(![X]:((patient(X)|brave(X))=>(kind(X)<~>~humble(X))))&
(((~patient(paul)|humble(paul)))<=>((calm(john)<~>funny(john))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~creative(X)))<=>((old(paul)<~>kind(paul))))&
(![X]:((~brave(X)|strong(X))=>(humble(X)|~brave(X))))&
(((~quiet(paul)|~tall(paul)))=>((~creative(fred)|~brave(fred))))&
(((kind(mary)&brave(mary)))=>((kind(john)&wise(john))))&
(![X]:((tall(X)|~calm(X))=>~curious(X)))&
(((old(susan)|kind(susan)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(~curious(X)=>(~patient(X)&patient(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(~calm(X)<~>~brave(X))))&
(((~funny(alice)&~quiet(alice)))=>((~brave(fred)<~>old(fred))))&
(?[X]:(~creative(X)))&
((generous(alice)&~happy(alice)))&
(quiet(lucy))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
((~generous(mary)|~kind(mary))) | patient(alice) | [
"p2",
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 413839620583120241333855
% SZS output start Proof for 413839620583120241333855
3. ! [X0] : ((~patient(X0) | strong(X0)) <=> brave(X0)) [input p2]
5. ! [X0] : ((brave(X0) | patient(X0)) => (kind(X0) <~> ~humble(X0))) [input p4]
12. ! [X0] : ((~calm(X0) | tall(X0)) => ~curious(X0)) [input p11]
14. ! [X0] : (~curious(X0) => (patient(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~calm(X0) <~> ~brave(X0))) [input p14]
24. ~patient(alice) [input hypothesis]
29. ! [X0] : ((kind(X0) <~> ~humble(X0)) | (~brave(X0) & ~patient(X0))) [ennf transformation 5]
36. ! [X0] : (~curious(X0) | (calm(X0) & ~tall(X0))) [ennf transformation 12]
37. ! [X0] : ((patient(X0) & ~patient(X0)) | curious(X0)) [ennf transformation 14]
41. ! [X0] : (((~patient(X0) | strong(X0)) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((~patient(X0) | strong(X0) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [flattening 41]
45. ! [X0] : (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~brave(X0) & ~patient(X0))) [nnf transformation 29]
62. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 15]
81. brave(X0) | patient(X0) [cnf transformation 42]
87. ~humble(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
89. humble(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 45]
113. ~curious(X0) | calm(X0) [cnf transformation 36]
119. ~patient(X0) | curious(X0) [cnf transformation 37]
120. curious(X0) | patient(X0) [cnf transformation 37]
121. ~brave(X0) | ~calm(X0) | kind(X0) | humble(X0) [cnf transformation 62]
122. ~brave(X0) | ~calm(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 62]
126. kind(X0) | ~humble(X0) | ~calm(X0) | brave(X0) [cnf transformation 62]
142. ~patient(alice) [cnf transformation 24]
298. curious(X0) [subsumption resolution 119,120]
300. kind(X0) | ~humble(X0) | ~calm(X0) [subsumption resolution 126,87]
301. ~brave(X0) | ~calm(X0) | ~kind(X0) [subsumption resolution 122,89]
302. ~brave(X0) | ~calm(X0) | kind(X0) [subsumption resolution 121,300]
303. ~brave(X0) | ~calm(X0) [subsumption resolution 302,301]
355. calm(X0) [resolution 113,298]
375. ~calm(X0) | patient(X0) [resolution 303,81]
376. patient(X0) [subsumption resolution 375,355]
379. $false [resolution 376,142]
% SZS output end Proof for 413839620583120241333855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not wise is both creative and generous.
Everyone who is either not patient or funny is funny and vice versa.
If someone is both old and not creative then someone is both not wise and not humble.
Everyone who is not humble is not old or happy and vice versa.
Everyone who is curious or not patient is either tall or not strong.
Everyone who is generous or curious is both calm and curious and vice versa.
Everyone who is old is either not brave or funny.
Everyone who is wise is wise or patient.
Everyone who is not funny or creative is not creative or not old.
Everyone who is funny or strong is strong and vice versa.
If alice is tall then mary is patient.
Everyone who is both not humble and not creative is humble.
Everyone who is creative is not funny.
Everyone who is either kind or wise is either generous or not calm.
If john is either not happy or not brave then someone is wise or tall.
If someone is both quiet and kind then someone is both patient and not old.
Someone is not humble.
Someone is not humble or humble.
Someone is creative or not rich.
Mary is either calm or brave.
Someone is either not funny or patient.
Someone is either not strong or strong.
Fred is curious.
Alice is not brave. | John is rich. | neutral | (![X]:((strong(X)<~>~wise(X))=>(creative(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))<=>funny(X)))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:(~humble(X)<=>(~old(X)|happy(X))))&
(![X]:((curious(X)|~patient(X))=>(tall(X)<~>~strong(X))))&
(![X]:((generous(X)|curious(X))<=>(calm(X)&curious(X))))&
(![X]:(old(X)=>(~brave(X)<~>funny(X))))&
(![X]:(wise(X)=>(wise(X)|patient(X))))&
(![X]:((~funny(X)|creative(X))=>(~creative(X)|~old(X))))&
(![X]:((funny(X)|strong(X))<=>strong(X)))&
((tall(alice))=>(patient(mary)))&
(![X]:((~humble(X)&~creative(X))=>humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:((kind(X)<~>wise(X))=>(generous(X)<~>~calm(X))))&
(((~happy(john)<~>~brave(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((patient(X)&~old(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((creative(X)|~rich(X))))&
((calm(mary)<~>brave(mary)))&
(?[X]:((~funny(X)<~>patient(X))))&
(?[X]:((~strong(X)<~>strong(X))))&
(curious(fred))&
(~brave(alice)) | rich(john) | [] | 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. | Alice is calm. | 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)))) | calm(alice) | [] | null | 0 |
If someone is either not funny or funny then someone is both quiet and not strong and vice versa.
Everyone who is not rich or not wise is either not tall or generous and vice versa.
Everyone who is either humble or not humble is old and vice versa.
If someone is both generous and strong then someone is either not generous or not wise and vice versa.
If someone is humble or not creative then alice is not tall and vice versa.
If someone is funny then someone is funny or quiet and vice versa.
Everyone who is either curious or not generous is both not rich and not humble.
Everyone who is both brave and humble is either not rich or not funny and vice versa.
Everyone who is both kind and happy is curious and vice versa.
Everyone who is patient or not rich is creative.
If lucy is both strong and wise then someone is not humble or not generous.
If paul is either strong or tall then alice is either curious or not patient and vice versa.
If someone is either rich or wise then someone is both old and quiet and vice versa.
Everyone who is either tall or happy is either not creative or not happy.
Everyone who is either patient or not generous is both not patient and not rich and vice versa.
Everyone who is either not tall or happy is both happy and wise.
Someone is either rich or creative.
Someone is funny.
Someone is not old or humble.
Fred is quiet or not strong.
Lucy is creative or brave.
Someone is either not curious or not wise.
Someone is humble or quiet. | Alice is not happy. | contradiction | ((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((~rich(X)|~wise(X))<=>(~tall(X)<~>generous(X))))&
(![X]:((humble(X)<~>~humble(X))<=>old(X)))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((humble(X)|~creative(X))))<=>(~tall(alice)))&
((?[X]:(funny(X)))<=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(~rich(X)&~humble(X))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((kind(X)&happy(X))<=>curious(X)))&
(![X]:((patient(X)|~rich(X))=>creative(X)))&
(((strong(lucy)&wise(lucy)))=>(?[X]:((~humble(X)|~generous(X)))))&
(((strong(paul)<~>tall(paul)))<=>((curious(alice)<~>~patient(alice))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((tall(X)<~>happy(X))=>(~creative(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(~patient(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))=>(happy(X)&wise(X))))&
(?[X]:((rich(X)<~>creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)|humble(X))))&
((quiet(fred)|~strong(fred)))&
((creative(lucy)|brave(lucy)))&
(?[X]:((~curious(X)<~>~wise(X))))&
(?[X]:((humble(X)|quiet(X)))) | ~happy(alice) | [
"p2",
"p4",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8350858678228210674348045
% SZS output start Proof for 8350858678228210674348045
3. ! [X0] : ((humble(X0) <~> ~humble(X0)) <=> old(X0)) [input p2]
5. ? [X0] : (~creative(X0) | humble(X0)) <=> ~tall(alice) [input p4]
16. ! [X0] : ((~tall(X0) <~> happy(X0)) => (wise(X0) & happy(X0))) [input p15]
19. ? [X0] : (humble(X0) | ~old(X0)) [input p18]
24. ~happy(alice) [input hypothesis]
34. ! [X0] : ((wise(X0) & happy(X0)) | (~tall(X0) <=> happy(X0))) [ennf transformation 16]
42. ! [X0] : ((((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ~old(X0)) & (old(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0))))) [nnf transformation 3]
48. (? [X0] : (~creative(X0) | humble(X0)) | tall(alice)) & (~tall(alice) | ! [X0] : (creative(X0) & ~humble(X0))) [nnf transformation 5]
49. (? [X0] : (~creative(X0) | humble(X0)) | tall(alice)) & (~tall(alice) | ! [X1] : (creative(X1) & ~humble(X1))) [rectify 48]
50. ? [X0] : (~creative(X0) | humble(X0)) => (~creative(sK4) | humble(sK4)) [choice axiom]
51. ((~creative(sK4) | humble(sK4)) | tall(alice)) & (~tall(alice) | ! [X1] : (creative(X1) & ~humble(X1))) [skolemisation 49,50]
73. ! [X0] : ((wise(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0)))) [nnf transformation 34]
79. ? [X0] : (humble(X0) | ~old(X0)) => (humble(sK12) | ~old(sK12)) [choice axiom]
80. humble(sK12) | ~old(sK12) [skolemisation 19,79]
98. old(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
99. old(X0) | humble(X0) | humble(X0) [cnf transformation 42]
108. ~tall(alice) | ~humble(X1) [cnf transformation 51]
154. happy(X0) | happy(X0) | tall(X0) [cnf transformation 73]
161. humble(sK12) | ~old(sK12) [cnf transformation 80]
167. ~happy(alice) [cnf transformation 24]
168. happy(X0) | tall(X0) [duplicate literal removal 154]
173. old(X0) | ~humble(X0) [duplicate literal removal 98]
174. old(X0) | humble(X0) [duplicate literal removal 99]
197. old(X0) [subsumption resolution 173,174]
230. 12 <=> tall(alice) [avatar definition]
247. 16 <=> ! [X1] : ~humble(X1) [avatar definition]
248. ~humble(X1) <- (16) [avatar component clause 247]
249. 16 | ~12 [avatar split clause 108,230,247]
342. humble(sK12) [subsumption resolution 161,197]
386. tall(alice) [resolution 168,167]
389. 12 [avatar split clause 386,230]
392. $false <- (16) [resolution 248,342]
395. ~16 [avatar contradiction clause 392]
396. $false [avatar sat refutation 249,389,395]
% SZS output end Proof for 8350858678228210674348045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is old or not generous and vice versa.
Everyone who is either not quiet or not old is not wise or not humble and vice versa.
If someone is either not quiet or humble then someone is not creative or patient and vice versa.
If someone is both not quiet and not humble then someone is not generous or humble.
Everyone who is not quiet or generous is either tall or old.
Everyone who is either curious or not curious is not rich or generous.
Everyone who is not creative is not happy or tall.
Everyone who is old or not humble is not old or creative and vice versa.
If someone is not calm or quiet then someone is not strong or funny and vice versa.
If alice is tall or not patient then someone is both not rich and not quiet and vice versa.
If someone is happy or not funny then susan is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
If fred is not wise or kind then someone is rich or patient.
John is not quiet or happy.
Someone is not patient.
Someone is either creative or rich.
Paul is both not wise and not brave.
Lucy is calm or not generous.
Paul is not patient or not creative.
John is either not generous or calm.
Fred is humble or not quiet. | Mary is not generous. | neutral | ((?[X]:(~strong(X)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~quiet(X)<~>~old(X))<=>(~wise(X)|~humble(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((~quiet(X)&~humble(X))))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~quiet(X)|generous(X))=>(tall(X)<~>old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~rich(X)|generous(X))))&
(![X]:(~creative(X)=>(~happy(X)|tall(X))))&
(![X]:((old(X)|~humble(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
((~quiet(john)|happy(john)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((~wise(paul)&~brave(paul)))&
((calm(lucy)|~generous(lucy)))&
((~patient(paul)|~creative(paul)))&
((~generous(john)<~>calm(john)))&
((humble(fred)|~quiet(fred))) | ~generous(mary) | [] | null | 0 |
If someone is both not curious and kind then someone is both not old and not quiet and vice versa.
Everyone who is humble or not generous is either old or funny.
Everyone who is either rich or generous is both patient and funny and vice versa.
If someone is not old then someone is generous or not tall.
Everyone who is either not quiet or generous is kind or not funny and vice versa.
If lucy is either tall or not kind then alice is not brave and vice versa.
Everyone who is either quiet or rich is both patient and not generous and vice versa.
If paul is calm or not kind then fred is both not creative and old and vice versa.
Everyone who is either calm or not curious is not calm.
If someone is not brave or curious then someone is both tall and strong.
If someone is either generous or wise then someone is both funny and not patient.
Everyone who is quiet or humble is either not happy or not creative.
Everyone who is either rich or not old is not strong.
If lucy is either not wise or generous then someone is either tall or not patient and vice versa.
Everyone who is not funny or funny is both calm and strong.
If someone is rich then someone is not tall and vice versa.
John is calm.
Fred is not creative or rich.
Someone is generous or funny.
Susan is either patient or not humble.
Lucy is either creative or not quiet.
Alice is either not tall or not wise.
Lucy is strong. | Fred is calm. | entailment | ((?[X]:((~curious(X)&kind(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((humble(X)|~generous(X))=>(old(X)<~>funny(X))))&
(![X]:((rich(X)<~>generous(X))<=>(patient(X)&funny(X))))&
((?[X]:(~old(X)))=>(?[X]:((generous(X)|~tall(X)))))&
(![X]:((~quiet(X)<~>generous(X))<=>(kind(X)|~funny(X))))&
(((tall(lucy)<~>~kind(lucy)))<=>(~brave(alice)))&
(![X]:((quiet(X)<~>rich(X))<=>(patient(X)&~generous(X))))&
(((calm(paul)|~kind(paul)))<=>((~creative(fred)&old(fred))))&
(![X]:((calm(X)<~>~curious(X))=>~calm(X)))&
((?[X]:((~brave(X)|curious(X))))=>(?[X]:((tall(X)&strong(X)))))&
((?[X]:((generous(X)<~>wise(X))))=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:((quiet(X)|humble(X))=>(~happy(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~old(X))=>~strong(X)))&
(((~wise(lucy)<~>generous(lucy)))<=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((~funny(X)|funny(X))=>(calm(X)&strong(X))))&
((?[X]:(rich(X)))<=>(?[X]:(~tall(X))))&
(calm(john))&
((~creative(fred)|rich(fred)))&
(?[X]:((generous(X)|funny(X))))&
((patient(susan)<~>~humble(susan)))&
((creative(lucy)<~>~quiet(lucy)))&
((~tall(alice)<~>~wise(alice)))&
(strong(lucy)) | calm(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7419840346015488434864571
% SZS output start Proof for 7419840346015488434864571
15. ! [X0] : ((funny(X0) | ~funny(X0)) => (strong(X0) & calm(X0))) [input p14]
24. ~calm(fred) [input hypothesis]
37. ! [X0] : ((strong(X0) & calm(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 15]
140. calm(X0) | funny(X0) [cnf transformation 37]
141. calm(X0) | ~funny(X0) [cnf transformation 37]
156. ~calm(fred) [cnf transformation 24]
301. calm(X0) [subsumption resolution 140,141]
362. $false [subsumption resolution 156,301]
% SZS output end Proof for 7419840346015488434864571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either old or not brave then susan is quiet and vice versa. Everyone who is either not old or not quiet is not kind. Everyone who is both kind and old is both not strong and brave. If alice is both funny and not funny then mary is both not wise and not calm. Everyone who is both not calm and not brave is kind and vice versa. If fred is not old or not quiet then lucy is either not calm or brave and vice versa. If someone is calm or not creative then someone is either humble or not old. Everyone who is strong or not brave is quiet or not humble and vice versa. Everyone who is either not happy or not wise is not creative. If susan is both curious and patient then susan is either strong or tall. If someone is both calm and happy then mary is either kind or not quiet. Everyone who is both not calm and not wise is both wise and calm and vice versa. If paul is both not wise and rich then someone is tall. Everyone who is not creative or not calm is both not kind and creative and vice versa. Everyone who is rich is both not kind and creative and vice versa. Everyone who is either strong or tall is not rich and vice versa. Mary is not curious or not humble. John is either not patient or calm. Mary is creative or not brave. Someone is not quiet. Someone is funny or old. Fred is both old and generous. | John is wise. | entailment | (((old(susan)<~>~brave(susan)))<=>(quiet(susan)))&
(![X]:((~old(X)<~>~quiet(X))=>~kind(X)))&
(![X]:((kind(X)&old(X))=>(~strong(X)&brave(X))))&
(((funny(alice)&~funny(alice)))=>((~wise(mary)&~calm(mary))))&
(![X]:((~calm(X)&~brave(X))<=>kind(X)))&
(((~old(fred)|~quiet(fred)))<=>((~calm(lucy)<~>brave(lucy))))&
((?[X]:((calm(X)|~creative(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
(![X]:((strong(X)|~brave(X))<=>(quiet(X)|~humble(X))))&
(![X]:((~happy(X)<~>~wise(X))=>~creative(X)))&
(((curious(susan)&patient(susan)))=>((strong(susan)<~>tall(susan))))&
((?[X]:((calm(X)&happy(X))))=>((kind(mary)<~>~quiet(mary))))&
(![X]:((~calm(X)&~wise(X))<=>(wise(X)&calm(X))))&
(((~wise(paul)&rich(paul)))=>(?[X]:(tall(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&creative(X))))&
(![X]:(rich(X)<=>(~kind(X)&creative(X))))&
(![X]:((strong(X)<~>tall(X))<=>~rich(X)))&
((~curious(mary)|~humble(mary)))&
((~patient(john)<~>calm(john)))&
((creative(mary)|~brave(mary)))&
(?[X]:(~quiet(X)))&
(?[X]:((funny(X)|old(X))))&
((old(fred)&generous(fred))) | wise(john) | [
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4504797672446879880853689
% SZS output start Proof for 4504797672446879880853689
5. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> kind(X0)) [input p4]
12. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> (calm(X0) & wise(X0))) [input p11]
14. ! [X0] : ((~calm(X0) | ~creative(X0)) <=> (creative(X0) & ~kind(X0))) [input p13]
23. ~wise(john) [input hypothesis]
40. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | (brave(X0) | calm(X0)))) [nnf transformation 5]
41. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | brave(X0) | calm(X0))) [flattening 40]
52. ! [X0] : (((~wise(X0) & ~calm(X0)) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | (wise(X0) | calm(X0)))) [nnf transformation 12]
53. ! [X0] : (((~wise(X0) & ~calm(X0)) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | wise(X0) | calm(X0))) [flattening 52]
56. ! [X0] : (((~calm(X0) | ~creative(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (calm(X0) & creative(X0)))) [nnf transformation 14]
57. ! [X0] : ((~calm(X0) | ~creative(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | (calm(X0) & creative(X0)))) [flattening 56]
77. ~calm(X0) | ~kind(X0) [cnf transformation 41]
98. calm(X0) | wise(X0) | calm(X0) [cnf transformation 53]
104. creative(X0) | creative(X0) [cnf transformation 57]
106. ~calm(X0) | ~creative(X0) | ~creative(X0) | kind(X0) [cnf transformation 57]
120. ~wise(john) [cnf transformation 23]
121. creative(X0) [duplicate literal removal 104]
122. ~calm(X0) | ~creative(X0) | kind(X0) [duplicate literal removal 106]
124. calm(X0) | wise(X0) [duplicate literal removal 98]
166. 8 <=> ! [X1] : creative(X1) [avatar definition]
167. creative(X1) <- (8) [avatar component clause 166]
178. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
179. ~calm(X1) <- (11) [avatar component clause 178]
209. ~creative(X0) | ~calm(X0) [subsumption resolution 122,77]
210. 8 [avatar split clause 121,166]
218. 19 <=> calm(john) [avatar definition]
219. calm(john) <- (19) [avatar component clause 218]
220. ~calm(john) <- (~19) [avatar component clause 218]
243. wise(john) <- (~19) [resolution 124,220]
245. $false <- (~19) [subsumption resolution 243,120]
246. 19 [avatar contradiction clause 245]
251. ~calm(X1) <- (8) [resolution 209,167]
252. 11 | ~8 [avatar split clause 251,166,178]
254. $false <- (11, 19) [resolution 179,219]
255. ~11 | ~19 [avatar contradiction clause 254]
256. $false [avatar sat refutation 210,246,252,255]
% SZS output end Proof for 4504797672446879880853689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or creative is either not rich or not patient and vice versa.
If someone is not curious or not rich then someone is tall.
Everyone who is wise or happy is not strong or strong.
If someone is both calm and curious then someone is wise and vice versa.
If mary is either brave or creative then susan is both not wise and not funny and vice versa.
If lucy is both not calm and not humble then alice is not kind and vice versa.
Everyone who is either brave or not old is quiet and vice versa.
If john is both happy and rich then someone is not humble or funny and vice versa.
If paul is not funny or creative then alice is both not curious and not strong and vice versa.
Everyone who is both patient and not tall is rich or not patient and vice versa.
Everyone who is quiet or wise is not quiet or not funny.
If john is kind then susan is calm or not humble and vice versa.
Everyone who is either funny or strong is tall.
If someone is not wise then paul is both brave and creative and vice versa.
Everyone who is either not old or funny is either not quiet or creative and vice versa.
If john is both patient and tall then someone is brave and vice versa.
Someone is not rich.
Someone is rich or patient.
Someone is either funny or quiet.
Someone is wise or kind.
Fred is both not curious and not kind.
Someone is both not creative and curious. | Mary is brave. | contradiction | (![X]:((curious(X)<~>creative(X))<=>(~rich(X)<~>~patient(X))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:(tall(X))))&
(![X]:((wise(X)|happy(X))=>(~strong(X)|strong(X))))&
((?[X]:((calm(X)&curious(X))))<=>(?[X]:(wise(X))))&
(((brave(mary)<~>creative(mary)))<=>((~wise(susan)&~funny(susan))))&
(((~calm(lucy)&~humble(lucy)))<=>(~kind(alice)))&
(![X]:((brave(X)<~>~old(X))<=>quiet(X)))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((patient(X)&~tall(X))<=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
((?[X]:(~wise(X)))<=>((brave(paul)&creative(paul))))&
(![X]:((~old(X)<~>funny(X))<=>(~quiet(X)<~>creative(X))))&
(((patient(john)&tall(john)))<=>(?[X]:(brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((funny(X)<~>quiet(X))))&
(?[X]:((wise(X)|kind(X))))&
((~curious(fred)&~kind(fred)))&
(?[X]:((~creative(X)&curious(X)))) | brave(mary) | [
"p4",
"p6",
"p7",
"p9",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4843254314452711057777830
% SZS output start Proof for 4843254314452711057777830
5. (brave(mary) <~> creative(mary)) <=> (~funny(susan) & ~wise(susan)) [input p4]
7. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> quiet(X0)) [input p6]
8. (rich(john) & happy(john)) <=> ? [X0] : (funny(X0) | ~humble(X0)) [input p7]
10. ! [X0] : ((~tall(X0) & patient(X0)) <=> (~patient(X0) | rich(X0))) [input p9]
11. ! [X0] : ((wise(X0) | quiet(X0)) => (~funny(X0) | ~quiet(X0))) [input p10]
14. ? [X0] : ~wise(X0) <=> (creative(paul) & brave(paul)) [input p13]
15. ! [X0] : ((~old(X0) <~> funny(X0)) <=> (~quiet(X0) <~> creative(X0))) [input p14]
16. (tall(john) & patient(john)) <=> ? [X0] : brave(X0) [input p15]
23. brave(mary) [input hypothesis]
29. ! [X0] : ((~funny(X0) | ~quiet(X0)) | (~wise(X0) & ~quiet(X0))) [ennf transformation 11]
30. ! [X0] : (~funny(X0) | ~quiet(X0) | (~wise(X0) & ~quiet(X0))) [flattening 29]
41. (((~creative(mary) | ~brave(mary)) & (creative(mary) | brave(mary))) | (funny(susan) | wise(susan))) & ((~funny(susan) & ~wise(susan)) | ((brave(mary) | ~creative(mary)) & (creative(mary) | ~brave(mary)))) [nnf transformation 5]
42. (((~creative(mary) | ~brave(mary)) & (creative(mary) | brave(mary))) | funny(susan) | wise(susan)) & ((~funny(susan) & ~wise(susan)) | ((brave(mary) | ~creative(mary)) & (creative(mary) | ~brave(mary)))) [flattening 41]
45. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | ~quiet(X0)) & (quiet(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 7]
46. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | (~rich(john) | ~happy(john))) [nnf transformation 8]
47. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | ~rich(john) | ~happy(john)) [flattening 46]
48. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X1] : (funny(X1) | ~humble(X1)) | ~rich(john) | ~happy(john)) [rectify 47]
49. ? [X1] : (funny(X1) | ~humble(X1)) => (funny(sK3) | ~humble(sK3)) [choice axiom]
50. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & ((funny(sK3) | ~humble(sK3)) | ~rich(john) | ~happy(john)) [skolemisation 48,49]
53. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & ((~patient(X0) | rich(X0)) | (tall(X0) | ~patient(X0)))) [nnf transformation 10]
54. ! [X0] : (((~tall(X0) & patient(X0)) | (patient(X0) & ~rich(X0))) & (~patient(X0) | rich(X0) | tall(X0) | ~patient(X0))) [flattening 53]
58. (? [X0] : ~wise(X0) | (~creative(paul) | ~brave(paul))) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [nnf transformation 14]
59. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [flattening 58]
60. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [rectify 59]
61. ? [X0] : ~wise(X0) => ~wise(sK4) [choice axiom]
62. (~wise(sK4) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [skolemisation 60,61]
63. ! [X0] : ((((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0)))) & (((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))))) [nnf transformation 15]
64. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~tall(john) | ~patient(john))) [nnf transformation 16]
65. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~tall(john) | ~patient(john)) [flattening 64]
66. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~tall(john) | ~patient(john)) [rectify 65]
67. ? [X1] : brave(X1) => brave(sK5) [choice axiom]
68. ((tall(john) & patient(john)) | ! [X0] : ~brave(X0)) & (brave(sK5) | ~tall(john) | ~patient(john)) [skolemisation 66,67]
95. ~wise(susan) | creative(mary) | ~brave(mary) [cnf transformation 42]
104. ~old(X0) | quiet(X0) | ~brave(X0) [cnf transformation 45]
107. ~quiet(X0) | ~brave(X0) | old(X0) [cnf transformation 45]
112. rich(john) | ~funny(X0) [cnf transformation 50]
121. ~tall(X0) | ~rich(X0) [cnf transformation 54]
123. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 30]
130. brave(paul) | wise(X1) [cnf transformation 62]
131. creative(paul) | wise(X1) [cnf transformation 62]
135. ~creative(X0) | quiet(X0) | funny(X0) | old(X0) [cnf transformation 63]
138. funny(X0) | ~old(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 63]
143. tall(john) | ~brave(X0) [cnf transformation 68]
153. brave(mary) [cnf transformation 23]
154. ~quiet(X0) | ~funny(X0) [duplicate literal removal 123]
191. 9 <=> wise(susan) [avatar definition]
192. ~wise(susan) <- (~9) [avatar component clause 191]
199. 11 <=> brave(mary) [avatar definition]
200. brave(mary) <- (11) [avatar component clause 199]
203. 12 <=> creative(mary) [avatar definition]
204. creative(mary) <- (12) [avatar component clause 203]
211. ~11 | 12 | ~9 [avatar split clause 95,191,203,199]
228. 16 <=> ! [X0] : ~funny(X0) [avatar definition]
229. ~funny(X0) <- (16) [avatar component clause 228]
231. 17 <=> rich(john) [avatar definition]
234. 16 | 17 [avatar split clause 112,231,228]
267. 25 <=> creative(paul) [avatar definition]
269. creative(paul) <- (25) [avatar component clause 267]
292. 29 <=> brave(paul) [avatar definition]
293. brave(paul) <- (29) [avatar component clause 292]
301. 31 <=> ! [X1] : wise(X1) [avatar definition]
302. wise(X1) <- (31) [avatar component clause 301]
303. 31 | 25 [avatar split clause 131,267,301]
304. 31 | 29 [avatar split clause 130,292,301]
306. ~quiet(X0) | ~old(X0) | ~creative(X0) [subsumption resolution 138,154]
310. 32 <=> ! [X0] : ~brave(X0) [avatar definition]
311. ~brave(X0) <- (32) [avatar component clause 310]
313. 33 <=> tall(john) [avatar definition]
315. tall(john) <- (33) [avatar component clause 313]
316. 32 | 33 [avatar split clause 143,313,310]
341. 11 [avatar split clause 153,199]
346. $false <- (11, 32) [subsumption resolution 200,311]
347. ~11 | ~32 [avatar contradiction clause 346]
355. ~rich(john) <- (33) [resolution 121,315]
358. ~17 | ~33 [avatar split clause 355,313,231]
455. quiet(paul) | funny(paul) | old(paul) <- (25) [resolution 135,269]
457. quiet(paul) | old(paul) <- (16, 25) [subsumption resolution 455,229]
459. 47 <=> old(paul) [avatar definition]
461. old(paul) <- (47) [avatar component clause 459]
463. 48 <=> quiet(paul) [avatar definition]
465. quiet(paul) <- (48) [avatar component clause 463]
466. 47 | 48 | ~16 | ~25 [avatar split clause 457,267,228,463,459]
476. quiet(paul) | ~brave(paul) <- (47) [resolution 461,104]
477. quiet(paul) <- (29, 47) [subsumption resolution 476,293]
478. 48 | ~29 | ~47 [avatar split clause 477,459,292,463]
480. ~old(paul) | ~creative(paul) <- (48) [resolution 465,306]
482. ~brave(paul) | old(paul) <- (48) [resolution 465,107]
494. $false <- (~9, 31) [resolution 302,192]
495. 9 | ~31 [avatar contradiction clause 494]
497. quiet(mary) | funny(mary) | old(mary) <- (12) [resolution 204,135]
499. quiet(mary) | old(mary) <- (12, 16) [subsumption resolution 497,229]
501. 49 <=> old(mary) [avatar definition]
503. old(mary) <- (49) [avatar component clause 501]
505. 50 <=> quiet(mary) [avatar definition]
507. quiet(mary) <- (50) [avatar component clause 505]
508. 49 | 50 | ~12 | ~16 [avatar split clause 499,228,203,505,501]
513. quiet(mary) | ~brave(mary) <- (49) [resolution 503,104]
514. quiet(mary) <- (11, 49) [subsumption resolution 513,200]
515. 50 | ~11 | ~49 [avatar split clause 514,501,199,505]
517. ~old(mary) | ~creative(mary) <- (50) [resolution 507,306]
519. ~brave(mary) | old(mary) <- (50) [resolution 507,107]
525. old(mary) <- (11, 50) [subsumption resolution 519,200]
526. 49 | ~11 | ~50 [avatar split clause 525,505,199,501]
529. ~12 | ~49 | ~50 [avatar split clause 517,505,501,203]
532. old(paul) <- (29, 48) [subsumption resolution 482,293]
533. 47 | ~29 | ~48 [avatar split clause 532,463,292,459]
534. ~25 | ~47 | ~48 [avatar split clause 480,463,459,267]
535. $false [avatar sat refutation 211,234,303,304,316,341,347,358,466,478,495,508,515,526,529,533,534]
% SZS output end Proof for 4843254314452711057777830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and old then lucy is both not curious and not kind.
If someone is old or brave then fred is not patient and vice versa.
Everyone who is either brave or not generous is quiet or old.
Everyone who is not patient or humble is not tall and vice versa.
If someone is not happy then mary is not happy.
Everyone who is generous or rich is either curious or not funny.
Everyone who is both not happy and happy is quiet or not curious and vice versa.
If alice is not wise or not rich then susan is either calm or not quiet and vice versa.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
If lucy is both calm and tall then someone is not generous and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
If someone is creative or humble then lucy is not calm.
Fred is not calm.
Someone is either not creative or not curious.
Someone is not kind or not creative.
John is curious.
Someone is both wise and happy.
Alice is either tall or funny. | Susan is funny. | entailment | (((~rich(lucy)&old(lucy)))=>((~curious(lucy)&~kind(lucy))))&
((?[X]:((old(X)|brave(X))))<=>(~patient(fred)))&
(![X]:((brave(X)<~>~generous(X))=>(quiet(X)|old(X))))&
(![X]:((~patient(X)|humble(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(~happy(mary)))&
(![X]:((generous(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))<=>(quiet(X)|~curious(X))))&
(((~wise(alice)|~rich(alice)))<=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
((?[X]:((creative(X)|humble(X))))=>(~calm(lucy)))&
(~calm(fred))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(curious(john))&
(?[X]:((wise(X)&happy(X))))&
((tall(alice)<~>funny(alice))) | funny(susan) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 641904208070819655932838
% SZS output start Proof for 641904208070819655932838
2. ? [X0] : (brave(X0) | old(X0)) <=> ~patient(fred) [input p1]
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (old(X0) | quiet(X0))) [input p2]
4. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~tall(X0)) [input p3]
6. ! [X0] : ((rich(X0) | generous(X0)) => (curious(X0) <~> ~funny(X0))) [input p5]
7. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~curious(X0) | quiet(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p9]
13. ! [X0] : (kind(X0) => patient(X0)) [input p12]
15. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p14]
23. ~funny(susan) [input hypothesis]
26. ! [X0] : ((old(X0) | quiet(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
27. ! [X0] : (old(X0) | quiet(X0) | (brave(X0) <=> ~generous(X0))) [flattening 26]
29. ! [X0] : ((curious(X0) <~> ~funny(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 6]
32. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 13]
36. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (~brave(X0) & ~old(X0))) [nnf transformation 2]
37. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [rectify 36]
38. ? [X0] : (brave(X0) | old(X0)) => (brave(sK0) | old(sK0)) [choice axiom]
39. ((brave(sK0) | old(sK0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [skolemisation 37,38]
40. ! [X0] : (old(X0) | quiet(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 27]
41. ! [X0] : (((humble(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [flattening 41]
43. ! [X0] : (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 29]
44. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 7]
45. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~happy(X0) | happy(X0))) [flattening 44]
49. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 10]
57. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 15]
68. ~patient(fred) | ~old(X1) [cnf transformation 39]
69. ~patient(fred) | ~brave(X1) [cnf transformation 39]
72. quiet(X0) | old(X0) | brave(X0) | generous(X0) [cnf transformation 40]
73. ~tall(X0) | patient(X0) [cnf transformation 42]
79. ~generous(X0) | ~curious(X0) | funny(X0) [cnf transformation 43]
82. ~happy(X0) | ~quiet(X0) [cnf transformation 45]
83. ~happy(X0) | curious(X0) [cnf transformation 45]
84. ~quiet(X0) | happy(X0) [cnf transformation 45]
85. happy(X0) | curious(X0) [cnf transformation 45]
96. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
107. ~kind(X0) | patient(X0) [cnf transformation 32]
110. ~generous(X0) | kind(X0) [cnf transformation 57]
122. ~funny(susan) [cnf transformation 23]
142. 5 <=> patient(fred) [avatar definition]
143. ~patient(fred) <- (~5) [avatar component clause 142]
155. 8 <=> ! [X1] : ~brave(X1) [avatar definition]
156. ~brave(X1) <- (8) [avatar component clause 155]
157. 8 | ~5 [avatar split clause 69,142,155]
159. 9 <=> ! [X1] : ~old(X1) [avatar definition]
160. ~old(X1) <- (9) [avatar component clause 159]
161. 9 | ~5 [avatar split clause 68,142,159]
170. curious(X0) [subsumption resolution 83,85]
171. ~quiet(X0) [subsumption resolution 82,84]
191. tall(X0) | generous(X0) [subsumption resolution 96,171]
193. 15 <=> ! [X0] : generous(X0) [avatar definition]
194. generous(X0) <- (15) [avatar component clause 193]
259. generous(X2) | patient(X2) [resolution 191,73]
262. patient(X0) | kind(X0) [resolution 259,110]
266. patient(X0) [subsumption resolution 262,107]
268. $false <- (~5) [resolution 266,143]
270. 5 [avatar contradiction clause 268]
291. old(X1) | brave(X1) | generous(X1) [resolution 72,171]
296. brave(X1) | generous(X1) <- (9) [subsumption resolution 291,160]
297. generous(X1) <- (8, 9) [subsumption resolution 296,156]
300. 15 | ~8 | ~9 [avatar split clause 297,159,155,193]
302. ~curious(X1) | funny(X1) <- (15) [resolution 194,79]
308. funny(X1) <- (15) [subsumption resolution 302,170]
327. $false <- (15) [resolution 308,122]
330. ~15 [avatar contradiction clause 327]
331. $false [avatar sat refutation 157,161,270,300,330]
% SZS output end Proof for 641904208070819655932838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not brave is both not kind and not creative. Everyone who is not strong or brave is not quiet or strong. Everyone who is not happy or not strong is rich or not rich. Everyone who is not curious or humble is both not funny and not humble. If someone is not rich then someone is both not tall and not patient and vice versa. If someone is not calm or happy then mary is not humble or not kind. If someone is either funny or not humble then someone is both tall and not generous. If john is either funny or wise then mary is not curious or curious. Everyone who is generous or curious is rich or wise and vice versa. If someone is both funny and not tall then lucy is both wise and not strong and vice versa. If someone is both rich and not creative then someone is either funny or humble. Everyone who is happy is either not humble or not brave and vice versa. Everyone who is either not humble or not funny is both not kind and rich and vice versa. Everyone who is both strong and tall is generous and vice versa. Everyone who is not happy or calm is not patient. If someone is either not old or humble then mary is both tall and not patient. Someone is both wise and calm. Lucy is either not rich or not wise. Fred is not strong. Mary is not tall or not generous. Someone is both not humble and not generous. Someone is either not happy or not creative. Someone is both not happy and funny. | Mary is old. | neutral | (![X]:((~kind(X)&~brave(X))=>(~kind(X)&~creative(X))))&
(![X]:((~strong(X)|brave(X))=>(~quiet(X)|strong(X))))&
(![X]:((~happy(X)|~strong(X))=>(rich(X)|~rich(X))))&
(![X]:((~curious(X)|humble(X))=>(~funny(X)&~humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~tall(X)&~patient(X)))))&
((?[X]:((~calm(X)|happy(X))))=>((~humble(mary)|~kind(mary))))&
((?[X]:((funny(X)<~>~humble(X))))=>(?[X]:((tall(X)&~generous(X)))))&
(((funny(john)<~>wise(john)))=>((~curious(mary)|curious(mary))))&
(![X]:((generous(X)|curious(X))<=>(rich(X)|wise(X))))&
((?[X]:((funny(X)&~tall(X))))<=>((wise(lucy)&~strong(lucy))))&
((?[X]:((rich(X)&~creative(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:(happy(X)<=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(~kind(X)&rich(X))))&
(![X]:((strong(X)&tall(X))<=>generous(X)))&
(![X]:((~happy(X)|calm(X))=>~patient(X)))&
((?[X]:((~old(X)<~>humble(X))))=>((tall(mary)&~patient(mary))))&
(?[X]:((wise(X)&calm(X))))&
((~rich(lucy)<~>~wise(lucy)))&
(~strong(fred))&
((~tall(mary)|~generous(mary)))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:((~happy(X)&funny(X)))) | old(mary) | [] | null | 0 |
If someone is both rich and creative then someone is both not funny and not strong.
Everyone who is either not calm or not wise is either happy or not happy and vice versa.
Everyone who is either generous or not old is not patient or not kind and vice versa.
If lucy is either curious or brave then paul is both rich and happy and vice versa.
If someone is both not strong and generous then john is either brave or not generous.
Everyone who is not curious is both not tall and not funny.
Everyone who is not wise is either not old or creative.
If someone is either old or not wise then alice is not tall and vice versa.
If john is not kind then someone is both not wise and not humble.
If someone is either rich or strong then mary is not brave.
Everyone who is rich is both not kind and not quiet and vice versa.
Everyone who is not funny is not calm or humble and vice versa.
Everyone who is either patient or kind is not calm or not humble.
Everyone who is either not strong or funny is both strong and not brave.
If someone is both not patient and wise then someone is strong.
If john is either not wise or tall then someone is both patient and old.
Alice is funny.
Someone is both not tall and funny.
Alice is either not brave or humble.
Alice is either not funny or tall.
Lucy is both rich and patient.
Fred is not kind.
Someone is not curious.
Someone is either not quiet or not calm. | Lucy is not generous. | entailment | ((?[X]:((rich(X)&creative(X))))=>(?[X]:((~funny(X)&~strong(X)))))&
(![X]:((~calm(X)<~>~wise(X))<=>(happy(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~old(X))<=>(~patient(X)|~kind(X))))&
(((curious(lucy)<~>brave(lucy)))<=>((rich(paul)&happy(paul))))&
((?[X]:((~strong(X)&generous(X))))=>((brave(john)<~>~generous(john))))&
(![X]:(~curious(X)=>(~tall(X)&~funny(X))))&
(![X]:(~wise(X)=>(~old(X)<~>creative(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>(~tall(alice)))&
((~kind(john))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((rich(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:(rich(X)<=>(~kind(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~calm(X)|humble(X))))&
(![X]:((patient(X)<~>kind(X))=>(~calm(X)|~humble(X))))&
(![X]:((~strong(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:((~patient(X)&wise(X))))=>(?[X]:(strong(X))))&
(((~wise(john)<~>tall(john)))=>(?[X]:((patient(X)&old(X)))))&
(funny(alice))&
(?[X]:((~tall(X)&funny(X))))&
((~brave(alice)<~>humble(alice)))&
((~funny(alice)<~>tall(alice)))&
((rich(lucy)&patient(lucy)))&
(~kind(fred))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)<~>~calm(X)))) | ~generous(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p10",
"p13",
"p16",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8562674721076786732584046
% SZS output start Proof for 8562674721076786732584046
1. ? [X0] : (creative(X0) & rich(X0)) => ? [X0] : (~strong(X0) & ~funny(X0)) [input p0]
3. ! [X0] : ((generous(X0) <~> ~old(X0)) <=> (~kind(X0) | ~patient(X0))) [input p2]
7. ! [X0] : (~wise(X0) => (~old(X0) <~> creative(X0))) [input p6]
8. ? [X0] : (old(X0) <~> ~wise(X0)) <=> ~tall(alice) [input p7]
11. ! [X0] : (rich(X0) <=> (~quiet(X0) & ~kind(X0))) [input p10]
14. ! [X0] : ((~strong(X0) <~> funny(X0)) => (~brave(X0) & strong(X0))) [input p13]
17. funny(alice) [input p16]
20. ~funny(alice) <~> tall(alice) [input p19]
21. patient(lucy) & rich(lucy) [input p20]
25. generous(lucy) [input hypothesis]
26. ? [X0] : (creative(X0) & rich(X0)) => ? [X1] : (~strong(X1) & ~funny(X1)) [rectify 1]
28. ? [X1] : (~strong(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) | ~rich(X0)) [ennf transformation 26]
31. ! [X0] : ((~old(X0) <~> creative(X0)) | wise(X0)) [ennf transformation 7]
36. ! [X0] : ((~brave(X0) & strong(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 14]
39. ? [X0] : (~strong(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) | ~rich(X1)) [rectify 28]
40. ? [X0] : (~strong(X0) & ~funny(X0)) => (~strong(sK0) & ~funny(sK0)) [choice axiom]
41. (~strong(sK0) & ~funny(sK0)) | ! [X1] : (~creative(X1) | ~rich(X1)) [skolemisation 39,40]
43. ! [X0] : ((((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (kind(X0) & patient(X0))) & ((~kind(X0) | ~patient(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0))))) [nnf transformation 3]
44. ! [X0] : ((((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (kind(X0) & patient(X0))) & (~kind(X0) | ~patient(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0))))) [flattening 43]
48. ! [X0] : (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | wise(X0)) [nnf transformation 31]
49. (? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | tall(alice)) & (~tall(alice) | ! [X0] : ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) [nnf transformation 8]
50. (? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | tall(alice)) & (~tall(alice) | ! [X1] : ((old(X1) | wise(X1)) & (~wise(X1) | ~old(X1)))) [rectify 49]
51. ? [X0] : ((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) => ((wise(sK1) | ~old(sK1)) & (~wise(sK1) | old(sK1))) [choice axiom]
52. (((wise(sK1) | ~old(sK1)) & (~wise(sK1) | old(sK1))) | tall(alice)) & (~tall(alice) | ! [X1] : ((old(X1) | wise(X1)) & (~wise(X1) | ~old(X1)))) [skolemisation 50,51]
56. ! [X0] : ((rich(X0) | (quiet(X0) | kind(X0))) & ((~quiet(X0) & ~kind(X0)) | ~rich(X0))) [nnf transformation 11]
57. ! [X0] : ((rich(X0) | quiet(X0) | kind(X0)) & ((~quiet(X0) & ~kind(X0)) | ~rich(X0))) [flattening 56]
61. ! [X0] : ((~brave(X0) & strong(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 36]
71. (~tall(alice) | funny(alice)) & (tall(alice) | ~funny(alice)) [nnf transformation 20]
77. ~funny(sK0) | ~creative(X1) | ~rich(X1) [cnf transformation 41]
78. ~strong(sK0) | ~creative(X1) | ~rich(X1) [cnf transformation 41]
92. ~generous(X0) | old(X0) | kind(X0) [cnf transformation 44]
103. ~old(X0) | creative(X0) | wise(X0) [cnf transformation 48]
105. ~tall(alice) | ~wise(X1) | ~old(X1) [cnf transformation 52]
106. ~tall(alice) | old(X1) | wise(X1) [cnf transformation 52]
113. ~kind(X0) | ~rich(X0) [cnf transformation 57]
121. strong(X0) | funny(X0) | strong(X0) [cnf transformation 61]
130. funny(alice) [cnf transformation 17]
135. tall(alice) | ~funny(alice) [cnf transformation 71]
137. rich(lucy) [cnf transformation 21]
143. generous(lucy) [cnf transformation 25]
144. strong(X0) | funny(X0) [duplicate literal removal 121]
150. 1 <=> ! [X1] : (~creative(X1) | ~rich(X1)) [avatar definition]
151. ~creative(X1) | ~rich(X1) <- (1) [avatar component clause 150]
153. 2 <=> strong(sK0) [avatar definition]
155. ~strong(sK0) <- (~2) [avatar component clause 153]
156. 1 | ~2 [avatar split clause 78,153,150]
158. 3 <=> funny(sK0) [avatar definition]
160. ~funny(sK0) <- (~3) [avatar component clause 158]
161. 1 | ~3 [avatar split clause 77,158,150]
200. 11 <=> tall(alice) [avatar definition]
214. 14 <=> ! [X1] : (old(X1) | wise(X1)) [avatar definition]
215. old(X1) | wise(X1) <- (14) [avatar component clause 214]
216. 14 | ~11 [avatar split clause 106,200,214]
218. 15 <=> ! [X1] : (~wise(X1) | ~old(X1)) [avatar definition]
219. ~old(X1) | ~wise(X1) <- (15) [avatar component clause 218]
220. 15 | ~11 [avatar split clause 105,200,218]
285. tall(alice) [subsumption resolution 135,130]
286. 11 [avatar split clause 285,200]
304. funny(sK0) <- (~2) [resolution 144,155]
305. $false <- (~2, ~3) [subsumption resolution 304,160]
306. 2 | 3 [avatar contradiction clause 305]
316. old(lucy) | kind(lucy) [resolution 92,143]
318. 32 <=> kind(lucy) [avatar definition]
320. kind(lucy) <- (32) [avatar component clause 318]
322. 33 <=> old(lucy) [avatar definition]
324. old(lucy) <- (33) [avatar component clause 322]
325. 32 | 33 [avatar split clause 316,322,318]
326. creative(X0) | wise(X0) | wise(X0) <- (14) [resolution 103,215]
327. wise(X0) | creative(X0) <- (14) [duplicate literal removal 326]
358. ~rich(lucy) <- (32) [resolution 320,113]
359. $false <- (32) [subsumption resolution 358,137]
360. ~32 [avatar contradiction clause 359]
364. ~wise(lucy) <- (15, 33) [resolution 324,219]
385. creative(lucy) <- (14, 15, 33) [resolution 327,364]
431. ~rich(lucy) <- (1, 14, 15, 33) [resolution 385,151]
432. $false <- (1, 14, 15, 33) [subsumption resolution 431,137]
433. ~1 | ~14 | ~15 | ~33 [avatar contradiction clause 432]
434. $false [avatar sat refutation 156,161,216,220,286,306,325,360,433]
% SZS output end Proof for 8562674721076786732584046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not calm and vice versa.
Everyone who is either humble or creative is either not old or creative and vice versa.
If john is both patient and not calm then someone is kind and vice versa.
If someone is either wise or not tall then susan is either not patient or not curious and vice versa.
Everyone who is old or strong is creative and vice versa.
Everyone who is either brave or funny is strong.
Everyone who is happy is either quiet or happy.
If fred is not brave or not happy then someone is both not quiet and old and vice versa.
Everyone who is happy is calm and vice versa.
If someone is rich or wise then someone is not strong or quiet.
If someone is either not rich or not humble then john is either not tall or quiet and vice versa.
If someone is both humble and not rich then someone is not strong and vice versa.
Everyone who is old is not wise and vice versa.
If alice is curious then susan is both not creative and creative.
Everyone who is either curious or not creative is both not tall and calm.
Everyone who is calm is funny or humble and vice versa.
Someone is either old or not funny.
Susan is either not brave or wise.
Lucy is brave.
Paul is not calm or not quiet.
Fred is either not happy or curious.
Fred is both not old and funny.
Someone is not quiet. | Alice is not humble. | neutral | (![X]:(creative(X)<=>~calm(X)))&
(![X]:((humble(X)<~>creative(X))<=>(~old(X)<~>creative(X))))&
(((patient(john)&~calm(john)))<=>(?[X]:(kind(X))))&
((?[X]:((wise(X)<~>~tall(X))))<=>((~patient(susan)<~>~curious(susan))))&
(![X]:((old(X)|strong(X))<=>creative(X)))&
(![X]:((brave(X)<~>funny(X))=>strong(X)))&
(![X]:(happy(X)=>(quiet(X)<~>happy(X))))&
(((~brave(fred)|~happy(fred)))<=>(?[X]:((~quiet(X)&old(X)))))&
(![X]:(happy(X)<=>calm(X)))&
((?[X]:((rich(X)|wise(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>((~tall(john)<~>quiet(john))))&
((?[X]:((humble(X)&~rich(X))))<=>(?[X]:(~strong(X))))&
(![X]:(old(X)<=>~wise(X)))&
((curious(alice))=>((~creative(susan)&creative(susan))))&
(![X]:((curious(X)<~>~creative(X))=>(~tall(X)&calm(X))))&
(![X]:(calm(X)<=>(funny(X)|humble(X))))&
(?[X]:((old(X)<~>~funny(X))))&
((~brave(susan)<~>wise(susan)))&
(brave(lucy))&
((~calm(paul)|~quiet(paul)))&
((~happy(fred)<~>curious(fred)))&
((~old(fred)&funny(fred)))&
(?[X]:(~quiet(X))) | ~humble(alice) | [] | null | 0 |
Everyone who is both tall and not wise is either curious or not generous and vice versa.
Everyone who is either patient or not generous is not wise or old.
If someone is old then fred is not funny and vice versa.
If mary is either not wise or not kind then susan is not quiet or not calm and vice versa.
Everyone who is not generous or quiet is both patient and not tall and vice versa.
Everyone who is either not curious or not funny is kind and vice versa.
If someone is both not calm and patient then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Someone is both creative and old.
Lucy is wise.
Fred is strong or not quiet.
Someone is not humble. | Lucy is strong. | entailment | (![X]:((tall(X)&~wise(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((patient(X)<~>~generous(X))=>(~wise(X)|old(X))))&
((?[X]:(old(X)))<=>(~funny(fred)))&
(((~wise(mary)<~>~kind(mary)))<=>((~quiet(susan)|~calm(susan))))&
(![X]:((~generous(X)|quiet(X))<=>(patient(X)&~tall(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>kind(X)))&
((?[X]:((~calm(X)&patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(?[X]:((creative(X)&old(X))))&
(wise(lucy))&
((strong(fred)|~quiet(fred)))&
(?[X]:(~humble(X))) | strong(lucy) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1234166540848218776976029
% SZS output start Proof for 1234166540848218776976029
10. ? [X0] : (~strong(X0) | ~tall(X0)) <=> humble(john) [input p9]
15. ? [X0] : humble(X0) => ~humble(john) [input p14]
21. ~strong(lucy) [input hypothesis]
30. ~humble(john) | ! [X0] : ~humble(X0) [ennf transformation 15]
53. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X0] : (strong(X0) & tall(X0))) [nnf transformation 10]
54. (? [X0] : (~strong(X0) | ~tall(X0)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [rectify 53]
55. ? [X0] : (~strong(X0) | ~tall(X0)) => (~strong(sK5) | ~tall(sK5)) [choice axiom]
56. ((~strong(sK5) | ~tall(sK5)) | ~humble(john)) & (humble(john) | ! [X1] : (strong(X1) & tall(X1))) [skolemisation 54,55]
106. humble(john) | strong(X1) [cnf transformation 56]
129. ~humble(john) | ~humble(X0) [cnf transformation 30]
138. ~strong(lucy) [cnf transformation 21]
238. 23 <=> humble(john) [avatar definition]
239. humble(john) <- (23) [avatar component clause 238]
251. 26 <=> ! [X1] : strong(X1) [avatar definition]
252. strong(X1) <- (26) [avatar component clause 251]
253. 26 | 23 [avatar split clause 106,238,251]
326. 42 <=> ! [X0] : ~humble(X0) [avatar definition]
327. ~humble(X0) <- (42) [avatar component clause 326]
328. 42 | ~23 [avatar split clause 129,238,326]
340. $false <- (26) [resolution 252,138]
341. ~26 [avatar contradiction clause 340]
344. $false <- (23, 42) [subsumption resolution 239,327]
345. ~23 | ~42 [avatar contradiction clause 344]
346. $false [avatar sat refutation 253,328,341,345]
% SZS output end Proof for 1234166540848218776976029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not generous is not kind or not old and vice versa.
If someone is not creative then fred is not curious.
If paul is rich or not creative then someone is either not tall or not creative.
If alice is not strong or not humble then alice is rich or not curious.
If someone is wise or generous then john is either not humble or rich and vice versa.
Everyone who is creative or not wise is rich and vice versa.
Everyone who is curious or not happy is not tall or not happy and vice versa.
Everyone who is either not curious or brave is both funny and tall and vice versa.
Everyone who is not curious is not kind or humble and vice versa.
Everyone who is old is humble or rich.
Everyone who is creative is either humble or not wise and vice versa.
Everyone who is either not tall or not generous is not happy or strong and vice versa.
If someone is both not strong and not humble then susan is either not generous or not quiet.
If john is both tall and not generous then someone is either brave or not wise and vice versa.
Everyone who is both not rich and not humble is both brave and not old and vice versa.
Everyone who is wise or not generous is either not curious or rich.
Someone is either calm or tall.
Fred is not tall.
Someone is old or not brave.
John is both not old and not calm.
Someone is not tall or generous. | Susan is rich. | entailment | (![X]:((kind(X)|~generous(X))<=>(~kind(X)|~old(X))))&
((?[X]:(~creative(X)))=>(~curious(fred)))&
(((rich(paul)|~creative(paul)))=>(?[X]:((~tall(X)<~>~creative(X)))))&
(((~strong(alice)|~humble(alice)))=>((rich(alice)|~curious(alice))))&
((?[X]:((wise(X)|generous(X))))<=>((~humble(john)<~>rich(john))))&
(![X]:((creative(X)|~wise(X))<=>rich(X)))&
(![X]:((curious(X)|~happy(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~curious(X)<~>brave(X))<=>(funny(X)&tall(X))))&
(![X]:(~curious(X)<=>(~kind(X)|humble(X))))&
(![X]:(old(X)=>(humble(X)|rich(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>~generous(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~strong(X)&~humble(X))))=>((~generous(susan)<~>~quiet(susan))))&
(((tall(john)&~generous(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)&~old(X))))&
(![X]:((wise(X)|~generous(X))=>(~curious(X)<~>rich(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(~tall(fred))&
(?[X]:((old(X)|~brave(X))))&
((~old(john)&~calm(john)))&
(?[X]:((~tall(X)|generous(X)))) | rich(susan) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p8",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3066165977499452971912770
% SZS output start Proof for 3066165977499452971912770
1. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~old(X0) | ~kind(X0))) [input p0]
2. ? [X0] : ~creative(X0) => ~curious(fred) [input p1]
6. ! [X0] : ((~wise(X0) | creative(X0)) <=> rich(X0)) [input p5]
7. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~happy(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~curious(X0) <~> brave(X0)) <=> (tall(X0) & funny(X0))) [input p7]
9. ! [X0] : (~curious(X0) <=> (humble(X0) | ~kind(X0))) [input p8]
12. ! [X0] : ((~tall(X0) <~> ~generous(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
15. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (~old(X0) & brave(X0))) [input p14]
18. ~tall(fred) [input p17]
22. ~rich(susan) [input hypothesis]
23. ~curious(fred) | ! [X0] : creative(X0) [ennf transformation 2]
31. ! [X0] : (((~generous(X0) | kind(X0)) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 1]
32. ! [X0] : ((~generous(X0) | kind(X0) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | (generous(X0) & ~kind(X0)))) [flattening 31]
40. ! [X0] : (((~wise(X0) | creative(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [nnf transformation 6]
41. ! [X0] : ((~wise(X0) | creative(X0) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~creative(X0)))) [flattening 40]
42. ! [X0] : (((~happy(X0) | curious(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 7]
43. ! [X0] : ((~happy(X0) | curious(X0) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | (happy(X0) & ~curious(X0)))) [flattening 42]
44. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (~tall(X0) | ~funny(X0))) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [nnf transformation 8]
45. ! [X0] : ((((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | ~tall(X0) | ~funny(X0)) & ((tall(X0) & funny(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0))))) [flattening 44]
46. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | curious(X0))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | curious(X0))) [flattening 46]
49. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [nnf transformation 12]
50. ! [X0] : ((((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0))))) [flattening 49]
57. ! [X0] : (((~humble(X0) & ~rich(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 15]
58. ! [X0] : (((~humble(X0) & ~rich(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | humble(X0) | rich(X0))) [flattening 57]
67. ~old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 32]
69. ~generous(X0) | kind(X0) | kind(X0) [cnf transformation 32]
71. ~curious(fred) | creative(X0) [cnf transformation 23]
84. ~creative(X0) | rich(X0) [cnf transformation 41]
89. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 43]
93. brave(X0) | tall(X0) | curious(X0) [cnf transformation 45]
97. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 47]
99. ~humble(X0) | ~curious(X0) [cnf transformation 47]
109. happy(X0) | tall(X0) | generous(X0) [cnf transformation 50]
122. ~brave(X0) | old(X0) | ~humble(X0) [cnf transformation 58]
129. ~tall(fred) [cnf transformation 18]
134. ~rich(susan) [cnf transformation 22]
135. ~old(X0) | ~kind(X0) [duplicate literal removal 67]
136. ~generous(X0) | kind(X0) [duplicate literal removal 69]
138. 1 <=> ! [X0] : creative(X0) [avatar definition]
139. creative(X0) <- (1) [avatar component clause 138]
141. 2 <=> curious(fred) [avatar definition]
143. ~curious(fred) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 71,141,138]
375. tall(X0) | generous(X0) | curious(X0) | tall(X0) [resolution 109,89]
377. tall(X0) | generous(X0) | curious(X0) [duplicate literal removal 375]
454. old(X1) | ~humble(X1) | tall(X1) | curious(X1) [resolution 122,93]
478. ~humble(X1) | old(X1) | tall(X1) [subsumption resolution 454,99]
551. generous(fred) | curious(fred) [resolution 377,129]
555. generous(fred) <- (~2) [subsumption resolution 551,143]
618. kind(fred) <- (~2) [resolution 555,136]
620. 62 <=> old(fred) [avatar definition]
622. old(fred) <- (62) [avatar component clause 620]
624. 63 <=> kind(fred) [avatar definition]
626. kind(fred) <- (63) [avatar component clause 624]
628. 63 | 2 [avatar split clause 618,141,624]
667. humble(fred) | curious(fred) <- (63) [resolution 626,97]
668. humble(fred) <- (~2, 63) [subsumption resolution 667,143]
713. old(fred) | tall(fred) <- (~2, 63) [resolution 668,478]
717. old(fred) <- (~2, 63) [subsumption resolution 713,129]
718. 62 | 2 | ~63 [avatar split clause 717,624,141,620]
730. ~kind(fred) <- (62) [resolution 622,135]
740. ~63 | ~62 [avatar split clause 730,620,624]
742. rich(X1) <- (1) [resolution 139,84]
768. $false <- (1) [resolution 742,134]
771. ~1 [avatar contradiction clause 768]
773. $false [avatar sat refutation 144,628,718,740,771]
% SZS output end Proof for 3066165977499452971912770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not brave is not old or not brave and vice versa. If someone is either generous or curious then someone is strong or not tall. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. If susan is not kind then susan is both generous and not old and vice versa. Everyone who is funny or tall is patient and vice versa. Someone is either not calm or humble. John is both humble and patient. Susan is both not rich and funny. Someone is both not quiet and funny. John is both not brave and not quiet. Someone is either patient or curious. Alice is creative or curious. Someone is both not wise and not creative. | Paul is strong. | neutral | (![X]:((~wise(X)<~>~brave(X))<=>(~old(X)|~brave(X))))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(?[X]:((~calm(X)<~>humble(X))))&
((humble(john)&patient(john)))&
((~rich(susan)&funny(susan)))&
(?[X]:((~quiet(X)&funny(X))))&
((~brave(john)&~quiet(john)))&
(?[X]:((patient(X)<~>curious(X))))&
((creative(alice)|curious(alice)))&
(?[X]:((~wise(X)&~creative(X)))) | strong(paul) | [] | null | 0 |
Everyone who is not patient is not humble and vice versa.
Everyone who is brave is either not happy or happy and vice versa.
If susan is not funny or not kind then someone is not tall.
Everyone who is not creative is not rich.
Everyone who is either not funny or humble is curious or not happy.
If fred is calm or brave then someone is strong.
Everyone who is brave is either not calm or not old and vice versa.
If paul is funny or not tall then paul is either patient or calm.
If someone is both not brave and wise then susan is both rich and not rich and vice versa.
Everyone who is happy or not rich is patient or not calm and vice versa.
If someone is either not wise or not brave then fred is either patient or not calm.
If someone is not strong or happy then someone is brave.
Everyone who is both patient and happy is either curious or not wise.
If someone is both strong and not rich then someone is either not brave or happy and vice versa.
Everyone who is either not curious or not calm is not brave.
Everyone who is both not funny and not strong is both not creative and not generous and vice versa.
John is either kind or not tall.
Someone is either not generous or not creative.
Mary is either tall or not strong.
Someone is happy or curious.
Someone is not calm or not wise.
Fred is not humble.
Someone is either not tall or not rich.
Susan is not old or not wise. | Susan is curious. | neutral | (![X]:(~patient(X)<=>~humble(X)))&
(![X]:(brave(X)<=>(~happy(X)<~>happy(X))))&
(((~funny(susan)|~kind(susan)))=>(?[X]:(~tall(X))))&
(![X]:(~creative(X)=>~rich(X)))&
(![X]:((~funny(X)<~>humble(X))=>(curious(X)|~happy(X))))&
(((calm(fred)|brave(fred)))=>(?[X]:(strong(X))))&
(![X]:(brave(X)<=>(~calm(X)<~>~old(X))))&
(((funny(paul)|~tall(paul)))=>((patient(paul)<~>calm(paul))))&
((?[X]:((~brave(X)&wise(X))))<=>((rich(susan)&~rich(susan))))&
(![X]:((happy(X)|~rich(X))<=>(patient(X)|~calm(X))))&
((?[X]:((~wise(X)<~>~brave(X))))=>((patient(fred)<~>~calm(fred))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:(brave(X))))&
(![X]:((patient(X)&happy(X))=>(curious(X)<~>~wise(X))))&
((?[X]:((strong(X)&~rich(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~curious(X)<~>~calm(X))=>~brave(X)))&
(![X]:((~funny(X)&~strong(X))<=>(~creative(X)&~generous(X))))&
((kind(john)<~>~tall(john)))&
(?[X]:((~generous(X)<~>~creative(X))))&
((tall(mary)<~>~strong(mary)))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~calm(X)|~wise(X))))&
(~humble(fred))&
(?[X]:((~tall(X)<~>~rich(X))))&
((~old(susan)|~wise(susan))) | curious(susan) | [] | null | 0 |
If someone is both not patient and not funny then fred is not creative and vice versa.
Everyone who is either kind or brave is both patient and not strong.
If someone is both kind and rich then someone is both patient and tall.
Everyone who is either rich or funny is quiet and vice versa.
If lucy is both not old and not wise then susan is either happy or creative and vice versa.
If someone is either quiet or not humble then someone is not brave.
If john is either funny or not kind then mary is strong.
Everyone who is curious is both not humble and creative.
Everyone who is either patient or not generous is both curious and not tall.
Everyone who is either not tall or rich is kind or not tall.
If someone is both brave and not quiet then lucy is both quiet and curious.
If someone is either not rich or not humble then someone is not old or humble and vice versa.
If someone is either strong or not tall then someone is both rich and not kind and vice versa.
If john is either kind or not tall then fred is both not humble and old and vice versa.
If someone is patient then someone is not creative or wise.
Everyone who is either not creative or calm is either humble or funny.
Mary is wise.
Susan is not curious.
Lucy is either happy or not strong.
Someone is either kind or rich.
Lucy is both humble and patient.
Susan is patient or not generous.
Someone is not happy.
Fred is both not humble and patient. | Lucy is generous. | contradiction | ((?[X]:((~patient(X)&~funny(X))))<=>(~creative(fred)))&
(![X]:((kind(X)<~>brave(X))=>(patient(X)&~strong(X))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((rich(X)<~>funny(X))<=>quiet(X)))&
(((~old(lucy)&~wise(lucy)))<=>((happy(susan)<~>creative(susan))))&
((?[X]:((quiet(X)<~>~humble(X))))=>(?[X]:(~brave(X))))&
(((funny(john)<~>~kind(john)))=>(strong(mary)))&
(![X]:(curious(X)=>(~humble(X)&creative(X))))&
(![X]:((patient(X)<~>~generous(X))=>(curious(X)&~tall(X))))&
(![X]:((~tall(X)<~>rich(X))=>(kind(X)|~tall(X))))&
((?[X]:((brave(X)&~quiet(X))))=>((quiet(lucy)&curious(lucy))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((~old(X)|humble(X)))))&
((?[X]:((strong(X)<~>~tall(X))))<=>(?[X]:((rich(X)&~kind(X)))))&
(((kind(john)<~>~tall(john)))<=>((~humble(fred)&old(fred))))&
((?[X]:(patient(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))=>(humble(X)<~>funny(X))))&
(wise(mary))&
(~curious(susan))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((kind(X)<~>rich(X))))&
((humble(lucy)&patient(lucy)))&
((patient(susan)|~generous(susan)))&
(?[X]:(~happy(X)))&
((~humble(fred)&patient(fred))) | generous(lucy) | [
"p7",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 640388557906561180142731
% SZS output start Proof for 640388557906561180142731
8. ! [X0] : (curious(X0) => (creative(X0) & ~humble(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> ~generous(X0)) => (~tall(X0) & curious(X0))) [input p8]
21. patient(lucy) & humble(lucy) [input p20]
25. generous(lucy) [input hypothesis]
35. ! [X0] : ((creative(X0) & ~humble(X0)) | ~curious(X0)) [ennf transformation 8]
36. ! [X0] : ((~tall(X0) & curious(X0)) | (patient(X0) <=> ~generous(X0))) [ennf transformation 9]
58. ! [X0] : ((~tall(X0) & curious(X0)) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) [nnf transformation 36]
105. ~curious(X0) | ~humble(X0) [cnf transformation 35]
107. ~generous(X0) | curious(X0) | ~patient(X0) [cnf transformation 58]
144. humble(lucy) [cnf transformation 21]
145. patient(lucy) [cnf transformation 21]
150. generous(lucy) [cnf transformation 25]
235. 19 <=> curious(lucy) [avatar definition]
237. curious(lucy) <- (19) [avatar component clause 235]
457. curious(lucy) | ~patient(lucy) [resolution 107,150]
458. curious(lucy) [subsumption resolution 457,145]
459. 19 [avatar split clause 458,235]
461. ~humble(lucy) <- (19) [resolution 237,105]
462. $false <- (19) [subsumption resolution 461,144]
463. ~19 [avatar contradiction clause 462]
464. $false [avatar sat refutation 459,463]
% SZS output end Proof for 640388557906561180142731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is both not kind and wise and vice versa. If someone is happy then paul is both happy and not patient. If someone is both not patient and not curious then lucy is both not brave and quiet and vice versa. Everyone who is either wise or brave is not humble or brave and vice versa. Everyone who is both curious and humble is both not happy and brave. Everyone who is both not humble and not happy is not brave and vice versa. Everyone who is calm or not old is calm or not rich and vice versa. Everyone who is either funny or wise is either not strong or not calm and vice versa. Everyone who is not old is not happy or funny. If someone is either not old or not patient then someone is not wise. Everyone who is curious is not kind and vice versa. Everyone who is wise is both not rich and patient. Everyone who is rich or not happy is both not quiet and not curious. If someone is not kind then john is not old and vice versa. Everyone who is humble or calm is not funny or happy and vice versa. Everyone who is brave or kind is rich and vice versa. Paul is not quiet or brave. Fred is both not curious and generous. Someone is wise or not strong. Mary is either not old or not happy. Someone is humble. | Lucy is calm. | neutral | (![X]:((~rich(X)&~generous(X))<=>(~kind(X)&wise(X))))&
((?[X]:(happy(X)))=>((happy(paul)&~patient(paul))))&
((?[X]:((~patient(X)&~curious(X))))<=>((~brave(lucy)&quiet(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~humble(X)|brave(X))))&
(![X]:((curious(X)&humble(X))=>(~happy(X)&brave(X))))&
(![X]:((~humble(X)&~happy(X))<=>~brave(X)))&
(![X]:((calm(X)|~old(X))<=>(calm(X)|~rich(X))))&
(![X]:((funny(X)<~>wise(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:(~old(X)=>(~happy(X)|funny(X))))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:(~wise(X))))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:(wise(X)=>(~rich(X)&patient(X))))&
(![X]:((rich(X)|~happy(X))=>(~quiet(X)&~curious(X))))&
((?[X]:(~kind(X)))<=>(~old(john)))&
(![X]:((humble(X)|calm(X))<=>(~funny(X)|happy(X))))&
(![X]:((brave(X)|kind(X))<=>rich(X)))&
((~quiet(paul)|brave(paul)))&
((~curious(fred)&generous(fred)))&
(?[X]:((wise(X)|~strong(X))))&
((~old(mary)<~>~happy(mary)))&
(?[X]:(humble(X))) | calm(lucy) | [] | null | 0 |
If lucy is not old then fred is either kind or not curious and vice versa.
Everyone who is either calm or not wise is funny or not humble and vice versa.
If someone is both not quiet and strong then someone is strong.
If susan is either curious or patient then someone is humble and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
Everyone who is wise or not calm is both happy and calm.
If someone is not creative or not humble then someone is not kind and vice versa.
If someone is not wise then mary is not creative and vice versa.
Everyone who is tall is either not rich or not patient.
Everyone who is rich or humble is not patient and vice versa.
If fred is either funny or not old then john is either creative or patient and vice versa.
Everyone who is wise is both not patient and not kind and vice versa.
If lucy is not happy or old then someone is either creative or kind and vice versa.
If john is both patient and not strong then someone is not old or kind and vice versa.
If someone is either not old or not quiet then alice is both not humble and not generous.
Everyone who is happy or not funny is either not old or brave.
Paul is quiet.
Lucy is not curious.
Someone is not tall or tall.
John is curious.
Someone is either wise or humble. | Paul is wise. | entailment | ((~old(lucy))<=>((kind(fred)<~>~curious(fred))))&
(![X]:((calm(X)<~>~wise(X))<=>(funny(X)|~humble(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:(strong(X))))&
(((curious(susan)<~>patient(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
(![X]:((wise(X)|~calm(X))=>(happy(X)&calm(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))<=>(~creative(mary)))&
(![X]:(tall(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)|humble(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>((creative(john)<~>patient(john))))&
(![X]:(wise(X)<=>(~patient(X)&~kind(X))))&
(((~happy(lucy)|old(lucy)))<=>(?[X]:((creative(X)<~>kind(X)))))&
(((patient(john)&~strong(john)))<=>(?[X]:((~old(X)|kind(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~humble(alice)&~generous(alice))))&
(![X]:((happy(X)|~funny(X))=>(~old(X)<~>brave(X))))&
(quiet(paul))&
(~curious(lucy))&
(?[X]:((~tall(X)|tall(X))))&
(curious(john))&
(?[X]:((wise(X)<~>humble(X)))) | wise(paul) | [
"p4",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 675182462332977169628748
% SZS output start Proof for 675182462332977169628748
5. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p4]
10. ! [X0] : ((humble(X0) | rich(X0)) <=> ~patient(X0)) [input p9]
12. ! [X0] : (wise(X0) <=> (~kind(X0) & ~patient(X0))) [input p11]
14. (~strong(john) & patient(john)) <=> ? [X0] : (kind(X0) | ~old(X0)) [input p13]
22. ~wise(paul) [input hypothesis]
41. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 5]
42. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 41]
53. ! [X0] : (((humble(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 10]
54. ! [X0] : ((humble(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~humble(X0) & ~rich(X0)))) [flattening 53]
56. ! [X0] : ((wise(X0) | (kind(X0) | patient(X0))) & ((~kind(X0) & ~patient(X0)) | ~wise(X0))) [nnf transformation 12]
57. ! [X0] : ((wise(X0) | kind(X0) | patient(X0)) & ((~kind(X0) & ~patient(X0)) | ~wise(X0))) [flattening 56]
63. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | (strong(john) | ~patient(john))) [nnf transformation 14]
64. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X0] : (kind(X0) | ~old(X0)) | strong(john) | ~patient(john)) [flattening 63]
65. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & (? [X1] : (kind(X1) | ~old(X1)) | strong(john) | ~patient(john)) [rectify 64]
66. ? [X1] : (kind(X1) | ~old(X1)) => (kind(sK6) | ~old(sK6)) [choice axiom]
67. ((~strong(john) & patient(john)) | ! [X0] : (~kind(X0) & old(X0))) & ((kind(sK6) | ~old(sK6)) | strong(john) | ~patient(john)) [skolemisation 65,66]
91. ~patient(X0) | humble(X0) [cnf transformation 42]
107. ~patient(X0) | ~humble(X0) [cnf transformation 54]
119. wise(X0) | kind(X0) | patient(X0) [cnf transformation 57]
128. patient(john) | ~kind(X0) [cnf transformation 67]
143. ~wise(paul) [cnf transformation 22]
228. ~patient(X0) [subsumption resolution 107,91]
249. wise(X0) | kind(X0) [subsumption resolution 119,228]
275. 27 <=> ! [X0] : ~kind(X0) [avatar definition]
276. ~kind(X0) <- (27) [avatar component clause 275]
286. ~kind(X0) [subsumption resolution 128,228]
287. 27 [avatar split clause 286,275]
325. kind(paul) [resolution 249,143]
329. $false <- (27) [subsumption resolution 325,276]
330. ~27 [avatar contradiction clause 329]
334. $false [avatar sat refutation 287,330]
% SZS output end Proof for 675182462332977169628748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is either not patient or not quiet.
Everyone who is brave or not patient is not humble or not generous and vice versa.
Everyone who is humble is generous or wise and vice versa.
Everyone who is both generous and funny is brave or happy.
Everyone who is either not quiet or wise is curious.
Everyone who is either not creative or not generous is funny and vice versa.
If john is not rich or rich then fred is creative.
Everyone who is not funny or generous is either humble or rich and vice versa.
If someone is both not quiet and not generous then paul is both not funny and not generous and vice versa.
If alice is both funny and not curious then susan is either creative or not quiet.
Everyone who is either not quiet or creative is not rich or quiet and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is either wise or patient is both not funny and wise and vice versa.
If someone is either not quiet or not rich then someone is not quiet or funny and vice versa.
Everyone who is quiet is strong or patient and vice versa.
If someone is both generous and not strong then someone is either not creative or not strong and vice versa.
Someone is funny or calm.
Susan is not wise or wise.
Fred is not wise.
Alice is creative or not rich.
Lucy is strong.
Someone is either not old or not patient.
Someone is either not wise or calm.
Lucy is not tall or not happy. | Paul is generous. | contradiction | (![X]:((~wise(X)<~>~strong(X))=>(~patient(X)<~>~quiet(X))))&
(![X]:((brave(X)|~patient(X))<=>(~humble(X)|~generous(X))))&
(![X]:(humble(X)<=>(generous(X)|wise(X))))&
(![X]:((generous(X)&funny(X))=>(brave(X)|happy(X))))&
(![X]:((~quiet(X)<~>wise(X))=>curious(X)))&
(![X]:((~creative(X)<~>~generous(X))<=>funny(X)))&
(((~rich(john)|rich(john)))=>(creative(fred)))&
(![X]:((~funny(X)|generous(X))<=>(humble(X)<~>rich(X))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~funny(paul)&~generous(paul))))&
(((funny(alice)&~curious(alice)))=>((creative(susan)<~>~quiet(susan))))&
(![X]:((~quiet(X)<~>creative(X))<=>(~rich(X)|quiet(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((wise(X)<~>patient(X))<=>(~funny(X)&wise(X))))&
((?[X]:((~quiet(X)<~>~rich(X))))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:(quiet(X)<=>(strong(X)|patient(X))))&
((?[X]:((generous(X)&~strong(X))))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(?[X]:((funny(X)|calm(X))))&
((~wise(susan)|wise(susan)))&
(~wise(fred))&
((creative(alice)|~rich(alice)))&
(strong(lucy))&
(?[X]:((~old(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>calm(X))))&
((~tall(lucy)|~happy(lucy))) | generous(paul) | [
"p1",
"p2",
"p5",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1434216197055916543548835
% SZS output start Proof for 1434216197055916543548835
2. ! [X0] : ((~patient(X0) | brave(X0)) <=> (~generous(X0) | ~humble(X0))) [input p1]
3. ! [X0] : (humble(X0) <=> (wise(X0) | generous(X0))) [input p2]
6. ! [X0] : ((~creative(X0) <~> ~generous(X0)) <=> funny(X0)) [input p5]
9. ? [X0] : (~generous(X0) & ~quiet(X0)) <=> (~generous(paul) & ~funny(paul)) [input p8]
11. ! [X0] : ((~quiet(X0) <~> creative(X0)) <=> (quiet(X0) | ~rich(X0))) [input p10]
13. ! [X0] : ((wise(X0) <~> patient(X0)) <=> (wise(X0) & ~funny(X0))) [input p12]
15. ! [X0] : (quiet(X0) <=> (patient(X0) | strong(X0))) [input p14]
25. generous(paul) [input hypothesis]
36. ! [X0] : (((~patient(X0) | brave(X0)) | (generous(X0) & humble(X0))) & ((~generous(X0) | ~humble(X0)) | (patient(X0) & ~brave(X0)))) [nnf transformation 2]
37. ! [X0] : ((~patient(X0) | brave(X0) | (generous(X0) & humble(X0))) & (~generous(X0) | ~humble(X0) | (patient(X0) & ~brave(X0)))) [flattening 36]
38. ! [X0] : ((humble(X0) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | ~humble(X0))) [nnf transformation 3]
39. ! [X0] : ((humble(X0) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | ~humble(X0))) [flattening 38]
40. ! [X0] : ((((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | ~funny(X0)) & (funny(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0))))) [nnf transformation 6]
43. (? [X0] : (~generous(X0) & ~quiet(X0)) | (generous(paul) | funny(paul))) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (generous(X0) | quiet(X0))) [nnf transformation 9]
44. (? [X0] : (~generous(X0) & ~quiet(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X0] : (generous(X0) | quiet(X0))) [flattening 43]
45. (? [X0] : (~generous(X0) & ~quiet(X0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (generous(X1) | quiet(X1))) [rectify 44]
46. ? [X0] : (~generous(X0) & ~quiet(X0)) => (~generous(sK0) & ~quiet(sK0)) [choice axiom]
47. ((~generous(sK0) & ~quiet(sK0)) | generous(paul) | funny(paul)) & ((~generous(paul) & ~funny(paul)) | ! [X1] : (generous(X1) | quiet(X1))) [skolemisation 45,46]
48. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [nnf transformation 11]
49. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [flattening 48]
50. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [nnf transformation 13]
51. ! [X0] : ((((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))))) [flattening 50]
57. ! [X0] : ((quiet(X0) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 15]
58. ! [X0] : ((quiet(X0) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ~quiet(X0))) [flattening 57]
77. ~generous(X0) | ~humble(X0) | patient(X0) [cnf transformation 37]
81. ~generous(X0) | humble(X0) [cnf transformation 39]
85. ~creative(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 40]
95. ~funny(paul) | generous(X1) | quiet(X1) [cnf transformation 47]
102. creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 49]
108. wise(X0) | wise(X0) | ~patient(X0) [cnf transformation 51]
110. ~patient(X0) | ~wise(X0) | ~wise(X0) | funny(X0) [cnf transformation 51]
119. ~patient(X0) | quiet(X0) [cnf transformation 58]
135. generous(paul) [cnf transformation 25]
136. ~patient(X0) | wise(X0) [duplicate literal removal 108]
137. ~patient(X0) | ~wise(X0) | funny(X0) [duplicate literal removal 110]
139. ~quiet(X0) | creative(X0) [duplicate literal removal 102]
153. 3 <=> funny(paul) [avatar definition]
155. funny(paul) <- (3) [avatar component clause 153]
157. 4 <=> generous(paul) [avatar definition]
159. generous(paul) <- (4) [avatar component clause 157]
171. 7 <=> ! [X1] : (generous(X1) | quiet(X1)) [avatar definition]
172. generous(X1) | quiet(X1) <- (7) [avatar component clause 171]
174. 7 | ~3 [avatar split clause 95,153,171]
189. 11 <=> ! [X1] : quiet(X1) [avatar definition]
190. quiet(X1) <- (11) [avatar component clause 189]
270. 4 [avatar split clause 135,157]
271. humble(paul) <- (4) [resolution 81,159]
275. humble(X0) | quiet(X0) <- (7) [resolution 172,81]
297. ~humble(paul) | patient(paul) <- (4) [resolution 77,159]
298. ~humble(X0) | patient(X0) | quiet(X0) <- (7) [resolution 77,172]
299. patient(paul) <- (4) [subsumption resolution 297,271]
301. wise(paul) <- (4) [resolution 299,136]
355. ~humble(X0) | quiet(X0) <- (7) [subsumption resolution 298,119]
356. quiet(X0) <- (7) [subsumption resolution 355,275]
357. 11 | ~7 [avatar split clause 356,171,189]
362. creative(X0) <- (11) [resolution 190,139]
457. ~funny(X1) | ~generous(X1) <- (11) [resolution 362,85]
460. ~wise(paul) | funny(paul) <- (4) [resolution 137,299]
461. funny(paul) <- (4) [subsumption resolution 460,301]
462. 3 | ~4 [avatar split clause 461,157,153]
611. ~generous(paul) <- (3, 11) [resolution 457,155]
614. $false <- (3, 4, 11) [subsumption resolution 611,159]
615. ~3 | ~4 | ~11 [avatar contradiction clause 614]
619. $false [avatar sat refutation 174,270,357,462,615]
% SZS output end Proof for 1434216197055916543548835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or curious is wise or generous.
If lucy is funny or old then someone is quiet and vice versa.
If someone is brave or not patient then alice is patient or not kind.
If someone is either happy or not kind then someone is either not tall or tall and vice versa.
Everyone who is calm or not generous is curious or not funny.
Everyone who is both not rich and funny is happy or not kind.
If someone is both tall and not tall then someone is old or not rich and vice versa.
If mary is both strong and rich then john is either not tall or not rich.
If paul is not rich then mary is not curious.
Everyone who is not wise is either not calm or funny.
Everyone who is patient is either happy or brave.
Everyone who is patient is not wise and vice versa.
Everyone who is not patient or not creative is either wise or not creative.
If someone is calm or patient then someone is either creative or not calm and vice versa.
Everyone who is both not calm and not rich is not calm and vice versa.
If lucy is not patient then fred is happy and vice versa.
Mary is not creative.
Someone is quiet.
Someone is not rich or strong.
Someone is old or happy.
Someone is both patient and not kind.
Susan is not patient.
Susan is not tall. | Mary is not curious. | contradiction | (![X]:((kind(X)<~>curious(X))=>(wise(X)|generous(X))))&
(((funny(lucy)|old(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~patient(X))))=>((patient(alice)|~kind(alice))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((calm(X)|~generous(X))=>(curious(X)|~funny(X))))&
(![X]:((~rich(X)&funny(X))=>(happy(X)|~kind(X))))&
((?[X]:((tall(X)&~tall(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(((strong(mary)&rich(mary)))=>((~tall(john)<~>~rich(john))))&
((~rich(paul))=>(~curious(mary)))&
(![X]:(~wise(X)=>(~calm(X)<~>funny(X))))&
(![X]:(patient(X)=>(happy(X)<~>brave(X))))&
(![X]:(patient(X)<=>~wise(X)))&
(![X]:((~patient(X)|~creative(X))=>(wise(X)<~>~creative(X))))&
((?[X]:((calm(X)|patient(X))))<=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((~calm(X)&~rich(X))<=>~calm(X)))&
((~patient(lucy))<=>(happy(fred)))&
(~creative(mary))&
(?[X]:(quiet(X)))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((old(X)|happy(X))))&
(?[X]:((patient(X)&~kind(X))))&
(~patient(susan))&
(~tall(susan)) | ~curious(mary) | [
"p4",
"p6",
"p9",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2099270377850453403660425
% SZS output start Proof for 2099270377850453403660425
5. ! [X0] : ((~generous(X0) | calm(X0)) => (~funny(X0) | curious(X0))) [input p4]
7. ? [X0] : (~tall(X0) & tall(X0)) <=> ? [X0] : (~rich(X0) | old(X0)) [input p6]
10. ! [X0] : (~wise(X0) => (~calm(X0) <~> funny(X0))) [input p9]
13. ! [X0] : ((~creative(X0) | ~patient(X0)) => (wise(X0) <~> ~creative(X0))) [input p12]
15. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> ~calm(X0)) [input p14]
17. ~creative(mary) [input p16]
24. ~curious(mary) [input hypothesis]
26. ? [X0] : (~tall(X0) & tall(X0)) <=> ? [X1] : (~rich(X1) | old(X1)) [rectify 7]
29. ! [X0] : (calm(X0) => (~funny(X0) | curious(X0))) [pure predicate removal 5]
32. ! [X0] : ((~funny(X0) | curious(X0)) | ~calm(X0)) [ennf transformation 29]
33. ! [X0] : (~funny(X0) | curious(X0) | ~calm(X0)) [flattening 32]
39. ! [X0] : ((~calm(X0) <~> funny(X0)) | wise(X0)) [ennf transformation 10]
41. ! [X0] : ((wise(X0) <~> ~creative(X0)) | (creative(X0) & patient(X0))) [ennf transformation 13]
52. (? [X0] : (~tall(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~old(X1))) & (? [X1] : (~rich(X1) | old(X1)) | ! [X0] : (tall(X0) | ~tall(X0))) [nnf transformation 26]
53. (? [X0] : (~tall(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~old(X1))) & (? [X2] : (~rich(X2) | old(X2)) | ! [X3] : (tall(X3) | ~tall(X3))) [rectify 52]
54. ? [X0] : (~tall(X0) & tall(X0)) => (~tall(sK3) & tall(sK3)) [choice axiom]
55. ? [X2] : (~rich(X2) | old(X2)) => (~rich(sK4) | old(sK4)) [choice axiom]
56. ((~tall(sK3) & tall(sK3)) | ! [X1] : (rich(X1) & ~old(X1))) & ((~rich(sK4) | old(sK4)) | ! [X3] : (tall(X3) | ~tall(X3))) [skolemisation 53,55,54]
58. ! [X0] : (((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | wise(X0)) [nnf transformation 39]
61. ! [X0] : (((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | (creative(X0) & patient(X0))) [nnf transformation 41]
67. ! [X0] : (((~rich(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | (rich(X0) | calm(X0)))) [nnf transformation 15]
68. ! [X0] : (((~rich(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | rich(X0) | calm(X0))) [flattening 67]
91. ~calm(X0) | curious(X0) | ~funny(X0) [cnf transformation 33]
95. tall(sK3) | rich(X1) [cnf transformation 56]
97. ~tall(sK3) | rich(X1) [cnf transformation 56]
101. ~calm(X0) | funny(X0) | wise(X0) [cnf transformation 58]
110. creative(X0) | ~wise(X0) | creative(X0) [cnf transformation 61]
119. ~rich(X0) | calm(X0) [cnf transformation 68]
122. ~creative(mary) [cnf transformation 17]
130. ~curious(mary) [cnf transformation 24]
131. ~wise(X0) | creative(X0) [duplicate literal removal 110]
189. 13 <=> ! [X1] : rich(X1) [avatar definition]
190. rich(X1) <- (13) [avatar component clause 189]
192. 14 <=> tall(sK3) [avatar definition]
195. 13 | ~14 [avatar split clause 97,192,189]
200. 13 | 14 [avatar split clause 95,192,189]
225. 21 <=> curious(mary) [avatar definition]
227. ~curious(mary) <- (~21) [avatar component clause 225]
291. ~21 [avatar split clause 130,225]
302. calm(X0) <- (13) [resolution 119,190]
308. ~funny(X0) | curious(X0) <- (13) [resolution 91,302]
319. funny(X0) | wise(X0) <- (13) [resolution 101,302]
380. wise(X0) | curious(X0) <- (13) [resolution 319,308]
385. creative(X0) | curious(X0) <- (13) [resolution 380,131]
386. curious(mary) <- (13) [resolution 385,122]
387. $false <- (13, ~21) [subsumption resolution 386,227]
388. ~13 | 21 [avatar contradiction clause 387]
389. $false [avatar sat refutation 195,200,291,388]
% SZS output end Proof for 2099270377850453403660425
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not brave is both not calm and not curious and vice versa.
If someone is humble then alice is not humble or generous and vice versa.
If paul is either not creative or curious then alice is both not old and not brave.
Everyone who is kind is both not humble and not funny.
Everyone who is generous is strong or wise and vice versa.
Everyone who is calm or happy is either creative or not funny.
Everyone who is curious or not patient is either tall or not strong and vice versa.
If alice is humble or not quiet then fred is either patient or happy.
Everyone who is not creative is kind.
Everyone who is both not strong and rich is both kind and not old.
If susan is not wise then someone is not generous or funny and vice versa.
Everyone who is both old and wise is either not brave or not patient and vice versa.
If someone is both not old and old then mary is both not tall and quiet and vice versa.
Everyone who is either kind or not old is brave or kind and vice versa.
Everyone who is tall is kind or curious.
Everyone who is either not strong or creative is either not strong or not tall and vice versa.
Lucy is old.
Mary is not brave.
Mary is strong.
Fred is not wise or curious.
Susan is not curious.
Fred is both humble and not tall. | Lucy is not curious. | neutral | (![X]:((~generous(X)<~>~brave(X))<=>(~calm(X)&~curious(X))))&
((?[X]:(humble(X)))<=>((~humble(alice)|generous(alice))))&
(((~creative(paul)<~>curious(paul)))=>((~old(alice)&~brave(alice))))&
(![X]:(kind(X)=>(~humble(X)&~funny(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((calm(X)|happy(X))=>(creative(X)<~>~funny(X))))&
(![X]:((curious(X)|~patient(X))<=>(tall(X)<~>~strong(X))))&
(((humble(alice)|~quiet(alice)))=>((patient(fred)<~>happy(fred))))&
(![X]:(~creative(X)=>kind(X)))&
(![X]:((~strong(X)&rich(X))=>(kind(X)&~old(X))))&
((~wise(susan))<=>(?[X]:((~generous(X)|funny(X)))))&
(![X]:((old(X)&wise(X))<=>(~brave(X)<~>~patient(X))))&
((?[X]:((~old(X)&old(X))))<=>((~tall(mary)&quiet(mary))))&
(![X]:((kind(X)<~>~old(X))<=>(brave(X)|kind(X))))&
(![X]:(tall(X)=>(kind(X)|curious(X))))&
(![X]:((~strong(X)<~>creative(X))<=>(~strong(X)<~>~tall(X))))&
(old(lucy))&
(~brave(mary))&
(strong(mary))&
((~wise(fred)|curious(fred)))&
(~curious(susan))&
((humble(fred)&~tall(fred))) | ~curious(lucy) | [] | null | 0 |
Everyone who is not patient or not creative is curious or funny. Everyone who is not tall is either not wise or calm. If someone is funny then someone is either not generous or not calm. Everyone who is both calm and tall is not generous. Everyone who is not brave is both not funny and not calm. If someone is both not generous and humble then john is both quiet and generous and vice versa. Everyone who is both happy and funny is not brave and vice versa. Everyone who is both wise and not wise is both not brave and not calm and vice versa. If paul is either wise or curious then someone is not humble or not kind. If someone is either not happy or not humble then someone is either not humble or not curious and vice versa. Everyone who is not curious or not tall is kind and vice versa. If lucy is both not happy and funny then alice is not kind and vice versa. Everyone who is not strong is calm. Everyone who is both rich and strong is either kind or not quiet. Everyone who is either kind or happy is not wise. Everyone who is both not curious and not brave is humble or not curious and vice versa. Alice is not happy. Someone is not kind. Someone is either not calm or strong. Someone is not creative. Someone is old or humble. Lucy is either curious or not funny. Someone is both strong and patient. | Alice is humble. | contradiction | (![X]:((~patient(X)|~creative(X))=>(curious(X)|funny(X))))&
(![X]:(~tall(X)=>(~wise(X)<~>calm(X))))&
((?[X]:(funny(X)))=>(?[X]:((~generous(X)<~>~calm(X)))))&
(![X]:((calm(X)&tall(X))=>~generous(X)))&
(![X]:(~brave(X)=>(~funny(X)&~calm(X))))&
((?[X]:((~generous(X)&humble(X))))<=>((quiet(john)&generous(john))))&
(![X]:((happy(X)&funny(X))<=>~brave(X)))&
(![X]:((wise(X)&~wise(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~humble(X)<~>~curious(X)))))&
(![X]:((~curious(X)|~tall(X))<=>kind(X)))&
(((~happy(lucy)&funny(lucy)))<=>(~kind(alice)))&
(![X]:(~strong(X)=>calm(X)))&
(![X]:((rich(X)&strong(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((kind(X)<~>happy(X))=>~wise(X)))&
(![X]:((~curious(X)&~brave(X))<=>(humble(X)|~curious(X))))&
(~happy(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)<~>strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)|humble(X))))&
((curious(lucy)<~>~funny(lucy)))&
(?[X]:((strong(X)&patient(X)))) | humble(alice) | [
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 760096732060725611919362
% SZS output start Proof for 760096732060725611919362
5. ! [X0] : (~brave(X0) => (~calm(X0) & ~funny(X0))) [input p4]
7. ! [X0] : ((funny(X0) & happy(X0)) <=> ~brave(X0)) [input p6]
16. ! [X0] : ((~brave(X0) & ~curious(X0)) <=> (~curious(X0) | humble(X0))) [input p15]
24. humble(alice) [input hypothesis]
37. ! [X0] : ((~calm(X0) & ~funny(X0)) | brave(X0)) [ennf transformation 5]
51. ! [X0] : (((funny(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) | ~happy(X0)))) [nnf transformation 7]
52. ! [X0] : (((funny(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | ~funny(X0) | ~happy(X0))) [flattening 51]
68. ! [X0] : (((~brave(X0) & ~curious(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (brave(X0) | curious(X0)))) [nnf transformation 16]
69. ! [X0] : (((~brave(X0) & ~curious(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | brave(X0) | curious(X0))) [flattening 68]
86. ~funny(X0) | brave(X0) [cnf transformation 37]
94. funny(X0) | brave(X0) [cnf transformation 52]
121. ~brave(X0) | ~humble(X0) [cnf transformation 69]
131. humble(alice) [cnf transformation 24]
168. brave(X0) [subsumption resolution 94,86]
241. ~humble(X0) [subsumption resolution 121,168]
246. $false [subsumption resolution 131,241]
% SZS output end Proof for 760096732060725611919362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and not calm is kind.
If fred is not generous then mary is both not happy and creative and vice versa.
If alice is either not tall or funny then someone is either not funny or not patient.
If someone is either not patient or strong then someone is old or not generous.
Everyone who is not wise or brave is not tall or humble.
Everyone who is not tall or humble is funny.
If someone is calm then paul is not generous or wise and vice versa.
Everyone who is patient is either not patient or old.
Everyone who is both kind and not old is tall or generous and vice versa.
If alice is either old or not creative then someone is generous or not happy.
If paul is both not tall and not brave then someone is both not creative and not tall and vice versa.
Everyone who is both not brave and brave is either not creative or funny and vice versa.
If someone is both curious and not old then someone is calm or happy.
Everyone who is not tall is not strong.
If fred is both happy and not quiet then someone is both not quiet and creative and vice versa.
If mary is not generous or not old then paul is not brave or curious.
John is not quiet or brave.
Lucy is both humble and patient.
Someone is quiet or not brave.
Mary is brave.
Someone is either not happy or not old.
Someone is not wise.
Lucy is rich.
Someone is creative. | Paul is creative. | contradiction | (![X]:((~tall(X)&~calm(X))=>kind(X)))&
((~generous(fred))<=>((~happy(mary)&creative(mary))))&
(((~tall(alice)<~>funny(alice)))=>(?[X]:((~funny(X)<~>~patient(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~wise(X)|brave(X))=>(~tall(X)|humble(X))))&
(![X]:((~tall(X)|humble(X))=>funny(X)))&
((?[X]:(calm(X)))<=>((~generous(paul)|wise(paul))))&
(![X]:(patient(X)=>(~patient(X)<~>old(X))))&
(![X]:((kind(X)&~old(X))<=>(tall(X)|generous(X))))&
(((old(alice)<~>~creative(alice)))=>(?[X]:((generous(X)|~happy(X)))))&
(((~tall(paul)&~brave(paul)))<=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~brave(X)&brave(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:((curious(X)&~old(X))))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:(~tall(X)=>~strong(X)))&
(((happy(fred)&~quiet(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(((~generous(mary)|~old(mary)))=>((~brave(paul)|curious(paul))))&
((~quiet(john)|brave(john)))&
((humble(lucy)&patient(lucy)))&
(?[X]:((quiet(X)|~brave(X))))&
(brave(mary))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:(~wise(X)))&
(rich(lucy))&
(?[X]:(creative(X))) | creative(paul) | [
"p5",
"p7",
"p8",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8846052030205860679705242
% SZS output start Proof for 8846052030205860679705242
6. ! [X0] : ((humble(X0) | ~tall(X0)) => funny(X0)) [input p5]
8. ! [X0] : (patient(X0) => (~patient(X0) <~> old(X0))) [input p7]
9. ! [X0] : ((~old(X0) & kind(X0)) <=> (generous(X0) | tall(X0))) [input p8]
11. (~brave(paul) & ~tall(paul)) <=> ? [X0] : (~tall(X0) & ~creative(X0)) [input p10]
12. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (~creative(X0) <~> funny(X0))) [input p11]
18. patient(lucy) & humble(lucy) [input p17]
25. creative(paul) [input hypothesis]
35. ! [X0] : (funny(X0) | (~humble(X0) & tall(X0))) [ennf transformation 6]
36. ! [X0] : ((~patient(X0) <~> old(X0)) | ~patient(X0)) [ennf transformation 8]
56. ! [X0] : (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ~patient(X0)) [nnf transformation 36]
57. ! [X0] : (((~old(X0) & kind(X0)) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | (old(X0) | ~kind(X0)))) [nnf transformation 9]
58. ! [X0] : (((~old(X0) & kind(X0)) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | old(X0) | ~kind(X0))) [flattening 57]
62. ((~brave(paul) & ~tall(paul)) | ! [X0] : (tall(X0) | creative(X0))) & (? [X0] : (~tall(X0) & ~creative(X0)) | (brave(paul) | tall(paul))) [nnf transformation 11]
63. ((~brave(paul) & ~tall(paul)) | ! [X0] : (tall(X0) | creative(X0))) & (? [X0] : (~tall(X0) & ~creative(X0)) | brave(paul) | tall(paul)) [flattening 62]
64. ((~brave(paul) & ~tall(paul)) | ! [X0] : (tall(X0) | creative(X0))) & (? [X1] : (~tall(X1) & ~creative(X1)) | brave(paul) | tall(paul)) [rectify 63]
65. ? [X1] : (~tall(X1) & ~creative(X1)) => (~tall(sK4) & ~creative(sK4)) [choice axiom]
66. ((~brave(paul) & ~tall(paul)) | ! [X0] : (tall(X0) | creative(X0))) & ((~tall(sK4) & ~creative(sK4)) | brave(paul) | tall(paul)) [skolemisation 64,65]
67. ! [X0] : (((brave(X0) & ~brave(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (~brave(X0) | brave(X0)))) [nnf transformation 12]
68. ! [X0] : (((brave(X0) & ~brave(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | ~brave(X0) | brave(X0))) [flattening 67]
98. funny(X0) | tall(X0) [cnf transformation 35]
103. old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 56]
108. ~old(X0) | ~tall(X0) [cnf transformation 58]
114. ~tall(paul) | tall(X0) | creative(X0) [cnf transformation 66]
119. ~brave(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 68]
121. ~funny(X0) | ~creative(X0) | brave(X0) [cnf transformation 68]
132. patient(lucy) [cnf transformation 18]
139. creative(paul) [cnf transformation 25]
140. ~patient(X0) | old(X0) [duplicate literal removal 103]
229. 20 <=> ! [X0] : (tall(X0) | creative(X0)) [avatar definition]
230. tall(X0) | creative(X0) <- (20) [avatar component clause 229]
237. 22 <=> tall(paul) [avatar definition]
240. 20 | ~22 [avatar split clause 114,237,229]
251. ~funny(X0) | ~creative(X0) [subsumption resolution 119,121]
331. old(lucy) [resolution 140,132]
333. ~creative(X0) | tall(X0) [resolution 251,98]
338. ~tall(lucy) [resolution 331,108]
362. tall(paul) [resolution 333,139]
368. 22 [avatar split clause 362,237]
369. tall(X0) <- (20) [subsumption resolution 230,333]
382. $false <- (20) [resolution 369,338]
385. ~20 [avatar contradiction clause 382]
388. $false [avatar sat refutation 240,368,385]
% SZS output end Proof for 8846052030205860679705242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and humble then mary is either happy or not patient and vice versa.
If someone is not quiet or strong then someone is old or not generous and vice versa.
If someone is both not humble and not quiet then someone is brave or patient.
If someone is not brave then someone is either humble or rich.
If susan is either not creative or not old then someone is both rich and not patient and vice versa.
Everyone who is humble or not happy is happy or old and vice versa.
Everyone who is old is both not rich and creative and vice versa.
If someone is not humble or not wise then someone is both not curious and patient and vice versa.
If paul is both not wise and not funny then paul is wise or brave.
Everyone who is not rich or patient is creative or not calm and vice versa.
Everyone who is not rich is both humble and patient.
If paul is both generous and not generous then someone is not rich or kind and vice versa.
Everyone who is either not strong or not calm is patient.
Everyone who is either strong or brave is either not creative or humble.
If mary is rich then alice is not patient or not happy and vice versa.
Someone is either not strong or not tall.
Mary is generous or not funny.
Someone is not patient or not tall.
Someone is either happy or old.
Susan is either not tall or not happy. | Mary is not brave. | contradiction | (((~old(fred)&humble(fred)))<=>((happy(mary)<~>~patient(mary))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((old(X)|~generous(X)))))&
((?[X]:((~humble(X)&~quiet(X))))=>(?[X]:((brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)<~>rich(X)))))&
(((~creative(susan)<~>~old(susan)))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((humble(X)|~happy(X))<=>(happy(X)|old(X))))&
(![X]:(old(X)<=>(~rich(X)&creative(X))))&
((?[X]:((~humble(X)|~wise(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(((~wise(paul)&~funny(paul)))=>((wise(paul)|brave(paul))))&
(![X]:((~rich(X)|patient(X))<=>(creative(X)|~calm(X))))&
(![X]:(~rich(X)=>(humble(X)&patient(X))))&
(((generous(paul)&~generous(paul)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))=>patient(X)))&
(![X]:((strong(X)<~>brave(X))=>(~creative(X)<~>humble(X))))&
((rich(mary))<=>((~patient(alice)|~happy(alice))))&
(?[X]:((~strong(X)<~>~tall(X))))&
((generous(mary)|~funny(mary)))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((happy(X)<~>old(X))))&
((~tall(susan)<~>~happy(susan))) | ~brave(mary) | [
"p3",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2043927019298991501103325
% SZS output start Proof for 2043927019298991501103325
4. ? [X0] : ~brave(X0) => ? [X0] : (humble(X0) <~> rich(X0)) [input p3]
6. ! [X0] : ((~happy(X0) | humble(X0)) <=> (old(X0) | happy(X0))) [input p5]
7. ! [X0] : (old(X0) <=> (creative(X0) & ~rich(X0))) [input p6]
12. (~generous(paul) & generous(paul)) <=> ? [X0] : (kind(X0) | ~rich(X0)) [input p11]
21. ~brave(mary) [input hypothesis]
24. ? [X0] : ~brave(X0) => ? [X1] : (humble(X1) <~> rich(X1)) [rectify 4]
27. ? [X1] : (humble(X1) <~> rich(X1)) | ! [X0] : brave(X0) [ennf transformation 24]
43. ? [X1] : ((~rich(X1) | ~humble(X1)) & (rich(X1) | humble(X1))) | ! [X0] : brave(X0) [nnf transformation 27]
44. ? [X0] : ((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ! [X1] : brave(X1) [rectify 43]
45. ? [X0] : ((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) => ((~rich(sK3) | ~humble(sK3)) & (rich(sK3) | humble(sK3))) [choice axiom]
46. ((~rich(sK3) | ~humble(sK3)) & (rich(sK3) | humble(sK3))) | ! [X1] : brave(X1) [skolemisation 44,45]
51. ! [X0] : (((~happy(X0) | humble(X0)) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | (happy(X0) & ~humble(X0)))) [nnf transformation 6]
52. ! [X0] : ((~happy(X0) | humble(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | (happy(X0) & ~humble(X0)))) [flattening 51]
53. ! [X0] : ((old(X0) | (~creative(X0) | rich(X0))) & ((creative(X0) & ~rich(X0)) | ~old(X0))) [nnf transformation 7]
54. ! [X0] : ((old(X0) | ~creative(X0) | rich(X0)) & ((creative(X0) & ~rich(X0)) | ~old(X0))) [flattening 53]
62. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | (generous(paul) | ~generous(paul))) [nnf transformation 12]
63. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X0] : (kind(X0) | ~rich(X0)) | generous(paul) | ~generous(paul)) [flattening 62]
64. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & (? [X1] : (kind(X1) | ~rich(X1)) | generous(paul) | ~generous(paul)) [rectify 63]
65. ? [X1] : (kind(X1) | ~rich(X1)) => (kind(sK7) | ~rich(sK7)) [choice axiom]
66. ((~generous(paul) & generous(paul)) | ! [X0] : (~kind(X0) & rich(X0))) & ((kind(sK7) | ~rich(sK7)) | generous(paul) | ~generous(paul)) [skolemisation 64,65]
92. ~rich(sK3) | ~humble(sK3) | brave(X1) [cnf transformation 46]
100. old(X0) | happy(X0) | happy(X0) [cnf transformation 52]
101. ~happy(X0) | humble(X0) | ~happy(X0) [cnf transformation 52]
103. ~rich(X0) | ~old(X0) [cnf transformation 54]
119. generous(paul) | rich(X0) [cnf transformation 66]
121. ~generous(paul) | rich(X0) [cnf transformation 66]
140. ~brave(mary) [cnf transformation 21]
142. happy(X0) | old(X0) [duplicate literal removal 100]
143. ~happy(X0) | humble(X0) [duplicate literal removal 101]
179. 8 <=> ! [X1] : ~old(X1) [avatar definition]
180. ~old(X1) <- (8) [avatar component clause 179]
211. 16 <=> ! [X1] : brave(X1) [avatar definition]
212. brave(X1) <- (16) [avatar component clause 211]
214. 17 <=> humble(sK3) [avatar definition]
216. ~humble(sK3) <- (~17) [avatar component clause 214]
218. 18 <=> rich(sK3) [avatar definition]
220. ~rich(sK3) <- (~18) [avatar component clause 218]
221. 16 | ~17 | ~18 [avatar split clause 92,218,214,211]
269. 29 <=> ! [X3] : humble(X3) [avatar definition]
270. humble(X3) <- (29) [avatar component clause 269]
295. 35 <=> generous(paul) [avatar definition]
300. 36 <=> ! [X0] : rich(X0) [avatar definition]
301. rich(X0) <- (36) [avatar component clause 300]
302. 36 | ~35 [avatar split clause 121,295,300]
304. 36 | 35 [avatar split clause 119,295,300]
368. $false <- (16) [resolution 212,140]
369. ~16 [avatar contradiction clause 368]
370. ~old(X0) <- (36) [resolution 103,301]
372. 8 | ~36 [avatar split clause 370,300,179]
395. humble(X0) | old(X0) [resolution 143,142]
400. humble(X0) <- (8) [subsumption resolution 395,180]
401. 29 | ~8 [avatar split clause 400,179,269]
403. $false <- (~17, 29) [resolution 270,216]
404. 17 | ~29 [avatar contradiction clause 403]
406. $false <- (~18, 36) [subsumption resolution 220,301]
407. 18 | ~36 [avatar contradiction clause 406]
408. $false [avatar sat refutation 221,302,304,369,372,401,404,407]
% SZS output end Proof for 2043927019298991501103325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is kind or not creative then fred is either not kind or not generous and vice versa.
Everyone who is not old is patient.
Everyone who is both generous and patient is strong or not quiet and vice versa.
If someone is both humble and patient then someone is both not patient and not brave and vice versa.
If john is both tall and rich then someone is creative.
If susan is not humble then someone is both not humble and not wise.
Everyone who is strong or generous is not happy.
Everyone who is not patient or not old is either not rich or not creative and vice versa.
If alice is strong then mary is brave.
If someone is humble then fred is both not old and not generous and vice versa.
Everyone who is either not quiet or tall is either not curious or kind.
Everyone who is either not humble or wise is funny and vice versa.
Everyone who is not wise or not rich is both not quiet and old and vice versa.
If mary is either not happy or not rich then someone is either funny or not happy.
Everyone who is quiet is both old and not humble.
Everyone who is both creative and funny is brave or calm and vice versa.
Someone is old or kind.
Fred is either not creative or not kind.
Someone is not strong.
Fred is not brave.
Someone is either rich or not tall.
Mary is not creative. | Mary is not happy. | entailment | (((kind(paul)|~creative(paul)))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((generous(X)&patient(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((tall(john)&rich(john)))=>(?[X]:(creative(X))))&
((~humble(susan))=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((strong(X)|generous(X))=>~happy(X)))&
(![X]:((~patient(X)|~old(X))<=>(~rich(X)<~>~creative(X))))&
((strong(alice))=>(brave(mary)))&
((?[X]:(humble(X)))<=>((~old(fred)&~generous(fred))))&
(![X]:((~quiet(X)<~>tall(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>funny(X)))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(?[X]:((old(X)|kind(X))))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:(~strong(X)))&
(~brave(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(~creative(mary)) | ~happy(mary) | [
"p2",
"p3",
"p6",
"p7",
"p9",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3946579633806177990894128
% SZS output start Proof for 3946579633806177990894128
3. ! [X0] : ((patient(X0) & generous(X0)) <=> (~quiet(X0) | strong(X0))) [input p2]
4. ? [X0] : (patient(X0) & humble(X0)) <=> ? [X0] : (~brave(X0) & ~patient(X0)) [input p3]
7. ! [X0] : ((generous(X0) | strong(X0)) => ~happy(X0)) [input p6]
8. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (~rich(X0) <~> ~creative(X0))) [input p7]
10. ? [X0] : humble(X0) <=> (~generous(fred) & ~old(fred)) [input p9]
13. ! [X0] : ((~rich(X0) | ~wise(X0)) <=> (old(X0) & ~quiet(X0))) [input p12]
15. ! [X0] : (quiet(X0) => (~humble(X0) & old(X0))) [input p14]
16. ! [X0] : ((funny(X0) & creative(X0)) <=> (calm(X0) | brave(X0))) [input p15]
22. ~creative(mary) [input p21]
23. happy(mary) [input hypothesis]
24. ? [X0] : (patient(X0) & humble(X0)) <=> ? [X1] : (~brave(X1) & ~patient(X1)) [rectify 4]
29. ! [X0] : (~happy(X0) | (~generous(X0) & ~strong(X0))) [ennf transformation 7]
33. ! [X0] : ((~humble(X0) & old(X0)) | ~quiet(X0)) [ennf transformation 15]
36. ! [X0] : (((patient(X0) & generous(X0)) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | (~patient(X0) | ~generous(X0)))) [nnf transformation 3]
37. ! [X0] : (((patient(X0) & generous(X0)) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~patient(X0) | ~generous(X0))) [flattening 36]
38. (? [X0] : (patient(X0) & humble(X0)) | ! [X1] : (brave(X1) | patient(X1))) & (? [X1] : (~brave(X1) & ~patient(X1)) | ! [X0] : (~patient(X0) | ~humble(X0))) [nnf transformation 24]
39. (? [X0] : (patient(X0) & humble(X0)) | ! [X1] : (brave(X1) | patient(X1))) & (? [X2] : (~brave(X2) & ~patient(X2)) | ! [X3] : (~patient(X3) | ~humble(X3))) [rectify 38]
40. ? [X0] : (patient(X0) & humble(X0)) => (patient(sK0) & humble(sK0)) [choice axiom]
41. ? [X2] : (~brave(X2) & ~patient(X2)) => (~brave(sK1) & ~patient(sK1)) [choice axiom]
42. ((patient(sK0) & humble(sK0)) | ! [X1] : (brave(X1) | patient(X1))) & ((~brave(sK1) & ~patient(sK1)) | ! [X3] : (~patient(X3) | ~humble(X3))) [skolemisation 39,41,40]
47. ! [X0] : (((~old(X0) | ~patient(X0)) | ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0)))) & (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (old(X0) & patient(X0)))) [nnf transformation 8]
48. ! [X0] : ((~old(X0) | ~patient(X0) | ((~rich(X0) | creative(X0)) & (~creative(X0) | rich(X0)))) & (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (old(X0) & patient(X0)))) [flattening 47]
49. (? [X0] : humble(X0) | (generous(fred) | old(fred))) & ((~generous(fred) & ~old(fred)) | ! [X0] : ~humble(X0)) [nnf transformation 10]
50. (? [X0] : humble(X0) | generous(fred) | old(fred)) & ((~generous(fred) & ~old(fred)) | ! [X0] : ~humble(X0)) [flattening 49]
51. (? [X0] : humble(X0) | generous(fred) | old(fred)) & ((~generous(fred) & ~old(fred)) | ! [X1] : ~humble(X1)) [rectify 50]
52. ? [X0] : humble(X0) => humble(sK4) [choice axiom]
53. (humble(sK4) | generous(fred) | old(fred)) & ((~generous(fred) & ~old(fred)) | ! [X1] : ~humble(X1)) [skolemisation 51,52]
56. ! [X0] : (((~rich(X0) | ~wise(X0)) | (~old(X0) | quiet(X0))) & ((old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [nnf transformation 13]
57. ! [X0] : ((~rich(X0) | ~wise(X0) | ~old(X0) | quiet(X0)) & ((old(X0) & ~quiet(X0)) | (rich(X0) & wise(X0)))) [flattening 56]
61. ! [X0] : (((funny(X0) & creative(X0)) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | (~funny(X0) | ~creative(X0)))) [nnf transformation 16]
62. ! [X0] : (((funny(X0) & creative(X0)) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | ~funny(X0) | ~creative(X0))) [flattening 61]
80. quiet(X0) | generous(X0) [cnf transformation 37]
82. quiet(X0) | patient(X0) [cnf transformation 37]
85. humble(sK0) | brave(X1) | patient(X1) [cnf transformation 42]
91. ~happy(X0) | ~generous(X0) [cnf transformation 29]
92. ~rich(X0) | ~creative(X0) | patient(X0) [cnf transformation 48]
97. ~rich(X0) | ~patient(X0) | ~old(X0) | creative(X0) [cnf transformation 48]
99. ~old(fred) | ~humble(X1) [cnf transformation 53]
100. ~generous(fred) | ~humble(X1) [cnf transformation 53]
111. ~quiet(X0) | rich(X0) [cnf transformation 57]
119. ~quiet(X0) | old(X0) [cnf transformation 33]
122. ~brave(X0) | creative(X0) [cnf transformation 62]
133. ~creative(mary) [cnf transformation 22]
134. happy(mary) [cnf transformation 23]
136. 1 <=> generous(fred) [avatar definition]
137. ~generous(fred) <- (~1) [avatar component clause 136]
158. 5 <=> ! [X1] : (brave(X1) | patient(X1)) [avatar definition]
159. brave(X1) | patient(X1) <- (5) [avatar component clause 158]
166. 7 <=> humble(sK0) [avatar definition]
168. humble(sK0) <- (7) [avatar component clause 166]
169. 5 | 7 [avatar split clause 85,166,158]
220. 19 <=> old(fred) [avatar definition]
221. ~old(fred) <- (~19) [avatar component clause 220]
229. 21 <=> ! [X1] : ~humble(X1) [avatar definition]
230. ~humble(X1) <- (21) [avatar component clause 229]
231. 21 | ~1 [avatar split clause 100,136,229]
232. 21 | ~19 [avatar split clause 99,220,229]
234. 22 <=> rich(mary) [avatar definition]
235. ~rich(mary) <- (~22) [avatar component clause 234]
236. rich(mary) <- (22) [avatar component clause 234]
238. 23 <=> happy(mary) [avatar definition]
239. happy(mary) <- (23) [avatar component clause 238]
278. 23 [avatar split clause 134,238]
281. ~generous(mary) <- (23) [resolution 91,239]
284. rich(X0) | patient(X0) [resolution 111,82]
285. rich(X1) | generous(X1) [resolution 111,80]
290. old(X1) | generous(X1) [resolution 119,80]
407. ~patient(mary) | ~old(mary) | creative(mary) <- (22) [resolution 97,236]
417. ~patient(mary) | ~old(mary) <- (22) [subsumption resolution 407,133]
419. 44 <=> old(mary) [avatar definition]
421. ~old(mary) <- (~44) [avatar component clause 419]
423. 45 <=> patient(mary) [avatar definition]
425. ~patient(mary) <- (~45) [avatar component clause 423]
426. ~44 | ~45 | ~22 [avatar split clause 417,234,423,419]
486. patient(X2) | ~creative(X2) | patient(X2) [resolution 284,92]
487. patient(X2) | ~creative(X2) [duplicate literal removal 486]
493. generous(fred) <- (~19) [resolution 290,221]
496. $false <- (~1, ~19) [subsumption resolution 493,137]
497. 1 | 19 [avatar contradiction clause 496]
499. $false <- (7, 21) [resolution 230,168]
500. ~7 | ~21 [avatar contradiction clause 499]
506. patient(X1) | creative(X1) <- (5) [resolution 159,122]
507. patient(X1) <- (5) [subsumption resolution 506,487]
517. $false <- (5, ~45) [resolution 507,425]
518. ~5 | 45 [avatar contradiction clause 517]
521. generous(mary) <- (~22) [resolution 235,285]
526. $false <- (~22, 23) [subsumption resolution 521,281]
527. 22 | ~23 [avatar contradiction clause 526]
535. generous(mary) <- (~44) [resolution 421,290]
536. $false <- (23, ~44) [subsumption resolution 535,281]
537. ~23 | 44 [avatar contradiction clause 536]
538. $false [avatar sat refutation 169,231,232,278,426,497,500,518,527,537]
% SZS output end Proof for 3946579633806177990894128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or wise then someone is not old or not kind and vice versa. Everyone who is either generous or funny is humble or not curious. Everyone who is not curious or creative is patient or not generous and vice versa. If susan is not tall then paul is both happy and not funny. If someone is generous then alice is creative and vice versa. Everyone who is either not curious or rich is either tall or not calm and vice versa. Everyone who is both not wise and not kind is either wise or not wise. Everyone who is kind is both rich and not strong. If paul is calm or not brave then paul is wise and vice versa. Everyone who is wise is either calm or happy and vice versa. If someone is either old or brave then john is not old or not creative. If someone is kind then paul is not patient or kind and vice versa. Everyone who is funny is creative or not brave and vice versa. If someone is humble then lucy is not old or not quiet and vice versa. Everyone who is both patient and old is either not tall or not strong and vice versa. Everyone who is brave is both not strong and happy. Paul is either humble or not old. John is both not old and not tall. Susan is wise. Lucy is either generous or kind. Someone is both funny and rich. Susan is funny or patient. Fred is calm. Fred is strong or not tall. | Paul is brave. | contradiction | ((?[X]:((~strong(X)|wise(X))))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((generous(X)<~>funny(X))=>(humble(X)|~curious(X))))&
(![X]:((~curious(X)|creative(X))<=>(patient(X)|~generous(X))))&
((~tall(susan))=>((happy(paul)&~funny(paul))))&
((?[X]:(generous(X)))<=>(creative(alice)))&
(![X]:((~curious(X)<~>rich(X))<=>(tall(X)<~>~calm(X))))&
(![X]:((~wise(X)&~kind(X))=>(wise(X)<~>~wise(X))))&
(![X]:(kind(X)=>(rich(X)&~strong(X))))&
(((calm(paul)|~brave(paul)))<=>(wise(paul)))&
(![X]:(wise(X)<=>(calm(X)<~>happy(X))))&
((?[X]:((old(X)<~>brave(X))))=>((~old(john)|~creative(john))))&
((?[X]:(kind(X)))<=>((~patient(paul)|kind(paul))))&
(![X]:(funny(X)<=>(creative(X)|~brave(X))))&
((?[X]:(humble(X)))<=>((~old(lucy)|~quiet(lucy))))&
(![X]:((patient(X)&old(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:(brave(X)=>(~strong(X)&happy(X))))&
((humble(paul)<~>~old(paul)))&
((~old(john)&~tall(john)))&
(wise(susan))&
((generous(lucy)<~>kind(lucy)))&
(?[X]:((funny(X)&rich(X))))&
((funny(susan)|patient(susan)))&
(calm(fred))&
((strong(fred)|~tall(fred))) | brave(paul) | [
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 931397273958746724278261
% SZS output start Proof for 931397273958746724278261
9. (~brave(paul) | calm(paul)) <=> wise(paul) [input p8]
10. ! [X0] : (wise(X0) <=> (calm(X0) <~> happy(X0))) [input p9]
16. ! [X0] : (brave(X0) => (happy(X0) & ~strong(X0))) [input p15]
25. brave(paul) [input hypothesis]
35. ! [X0] : ((happy(X0) & ~strong(X0)) | ~brave(X0)) [ennf transformation 16]
50. ((~brave(paul) | calm(paul)) | ~wise(paul)) & (wise(paul) | (brave(paul) & ~calm(paul))) [nnf transformation 9]
51. (~brave(paul) | calm(paul) | ~wise(paul)) & (wise(paul) | (brave(paul) & ~calm(paul))) [flattening 50]
52. ! [X0] : ((wise(X0) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ~wise(X0))) [nnf transformation 10]
98. wise(paul) | ~calm(paul) [cnf transformation 51]
100. ~brave(paul) | calm(paul) | ~wise(paul) [cnf transformation 51]
102. ~calm(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 52]
104. ~happy(X0) | calm(X0) | wise(X0) [cnf transformation 52]
123. ~brave(X0) | happy(X0) [cnf transformation 35]
136. brave(paul) [cnf transformation 25]
181. 11 <=> happy(paul) [avatar definition]
183. happy(paul) <- (11) [avatar component clause 181]
199. 15 <=> wise(paul) [avatar definition]
200. wise(paul) <- (15) [avatar component clause 199]
203. 16 <=> calm(paul) [avatar definition]
205. calm(paul) <- (16) [avatar component clause 203]
207. 17 <=> brave(paul) [avatar definition]
208. brave(paul) <- (17) [avatar component clause 207]
210. ~15 | 16 | ~17 [avatar split clause 100,207,203,199]
212. ~16 | 15 [avatar split clause 98,199,203]
304. 17 [avatar split clause 136,207]
310. happy(paul) <- (17) [resolution 123,208]
312. 11 | ~17 [avatar split clause 310,207,181]
360. calm(paul) | wise(paul) <- (11) [resolution 104,183]
366. 15 | 16 | ~11 [avatar split clause 360,181,203,199]
369. ~happy(paul) | ~wise(paul) <- (16) [resolution 205,102]
370. ~wise(paul) <- (11, 16) [subsumption resolution 369,183]
371. $false <- (11, 15, 16) [subsumption resolution 370,200]
372. ~11 | ~15 | ~16 [avatar contradiction clause 371]
373. $false [avatar sat refutation 210,212,304,312,366,372]
% SZS output end Proof for 931397273958746724278261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not funny is both not patient and quiet and vice versa. If lucy is both not strong and not brave then someone is funny or calm and vice versa. Everyone who is rich or creative is humble and vice versa. If susan is both not brave and patient then mary is not humble or not calm. If someone is both not quiet and old then someone is not quiet and vice versa. Everyone who is brave is not funny. If lucy is both happy and not tall then someone is both not humble and not patient. Everyone who is not calm is either rich or humble. If someone is not funny or happy then mary is not tall or not strong and vice versa. If mary is creative then someone is either not funny or patient. Everyone who is kind is either not creative or funny and vice versa. Everyone who is generous or not humble is not generous or generous and vice versa. If mary is both patient and rich then someone is not patient or happy. If john is not strong or brave then someone is not tall or not generous. If john is both not wise and not humble then john is both happy and old and vice versa. Everyone who is not curious or not patient is both quiet and curious and vice versa. John is patient or generous. Paul is either not brave or old. Someone is not funny. John is not happy. Mary is tall. Someone is kind or strong. Someone is not generous. Someone is quiet. | Paul is quiet. | entailment | (![X]:((~brave(X)|~funny(X))<=>(~patient(X)&quiet(X))))&
(((~strong(lucy)&~brave(lucy)))<=>(?[X]:((funny(X)|calm(X)))))&
(![X]:((rich(X)|creative(X))<=>humble(X)))&
(((~brave(susan)&patient(susan)))=>((~humble(mary)|~calm(mary))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>~funny(X)))&
(((happy(lucy)&~tall(lucy)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:(~calm(X)=>(rich(X)<~>humble(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
(((patient(mary)&rich(mary)))=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(john)|brave(john)))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~wise(john)&~humble(john)))<=>((happy(john)&old(john))))&
(![X]:((~curious(X)|~patient(X))<=>(quiet(X)&curious(X))))&
((patient(john)|generous(john)))&
((~brave(paul)<~>old(paul)))&
(?[X]:(~funny(X)))&
(~happy(john))&
(tall(mary))&
(?[X]:((kind(X)|strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:(quiet(X))) | quiet(paul) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4682335626260311829277234
% SZS output start Proof for 4682335626260311829277234
1. ! [X0] : ((~funny(X0) | ~brave(X0)) <=> (quiet(X0) & ~patient(X0))) [input p0]
6. ! [X0] : (brave(X0) => ~funny(X0)) [input p5]
25. ~quiet(paul) [input hypothesis]
30. ! [X0] : (~funny(X0) | ~brave(X0)) [ennf transformation 6]
39. ! [X0] : (((~funny(X0) | ~brave(X0)) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | (funny(X0) & brave(X0)))) [nnf transformation 1]
40. ! [X0] : ((~funny(X0) | ~brave(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | (funny(X0) & brave(X0)))) [flattening 39]
86. quiet(X0) | brave(X0) [cnf transformation 40]
87. quiet(X0) | funny(X0) [cnf transformation 40]
101. ~funny(X0) | ~brave(X0) [cnf transformation 30]
139. ~quiet(paul) [cnf transformation 25]
316. 39 <=> brave(paul) [avatar definition]
318. brave(paul) <- (39) [avatar component clause 316]
341. brave(paul) [resolution 86,139]
346. 39 [avatar split clause 341,316]
347. funny(paul) [resolution 87,139]
351. ~brave(paul) [resolution 101,347]
356. $false <- (39) [subsumption resolution 351,318]
357. ~39 [avatar contradiction clause 356]
360. $false [avatar sat refutation 346,357]
% SZS output end Proof for 4682335626260311829277234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich then mary is patient and vice versa.
Everyone who is either calm or not calm is both not funny and curious and vice versa.
Everyone who is both generous and patient is either not strong or not humble and vice versa.
Everyone who is either not quiet or not generous is both kind and tall.
Everyone who is either not quiet or strong is both kind and not kind.
If paul is either not humble or not funny then someone is calm or not funny and vice versa.
Everyone who is either rich or not old is both calm and quiet.
Everyone who is either not tall or creative is not patient and vice versa.
Everyone who is not quiet is either not funny or not generous and vice versa.
Everyone who is both wise and patient is either not quiet or rich.
Everyone who is both humble and happy is quiet.
If lucy is both kind and not wise then someone is either tall or not happy and vice versa.
Everyone who is not happy is either funny or not rich and vice versa.
If alice is either calm or happy then alice is happy and vice versa.
If someone is either not patient or not brave then susan is both not tall and kind and vice versa.
Someone is both happy and calm.
Susan is not generous.
Lucy is old.
Susan is old or not calm.
Someone is old or brave. | Lucy is not strong. | neutral | ((?[X]:(rich(X)))<=>(patient(mary)))&
(![X]:((calm(X)<~>~calm(X))<=>(~funny(X)&curious(X))))&
(![X]:((generous(X)&patient(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>~generous(X))=>(kind(X)&tall(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(kind(X)&~kind(X))))&
(((~humble(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:((rich(X)<~>~old(X))=>(calm(X)&quiet(X))))&
(![X]:((~tall(X)<~>creative(X))<=>~patient(X)))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~generous(X))))&
(![X]:((wise(X)&patient(X))=>(~quiet(X)<~>rich(X))))&
(![X]:((humble(X)&happy(X))=>quiet(X)))&
(((kind(lucy)&~wise(lucy)))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:(~happy(X)<=>(funny(X)<~>~rich(X))))&
(((calm(alice)<~>happy(alice)))<=>(happy(alice)))&
((?[X]:((~patient(X)<~>~brave(X))))<=>((~tall(susan)&kind(susan))))&
(?[X]:((happy(X)&calm(X))))&
(~generous(susan))&
(old(lucy))&
((old(susan)|~calm(susan)))&
(?[X]:((old(X)|brave(X)))) | ~strong(lucy) | [] | null | 0 |
If lucy is not creative then susan is not calm or not creative. Everyone who is either not funny or strong is either generous or not creative. Everyone who is both not creative and not patient is not calm and vice versa. If mary is either old or tall then alice is rich and vice versa. If lucy is not strong then someone is both rich and happy. If someone is both funny and not strong then alice is not creative or not strong. Everyone who is both creative and not rich is both not happy and tall and vice versa. Everyone who is strong is either not creative or funny and vice versa. Everyone who is both not rich and wise is not strong or strong. If someone is either quiet or not calm then someone is both generous and not strong and vice versa. If someone is not generous then someone is tall or curious and vice versa. If john is not tall then someone is not humble. Everyone who is not generous or not tall is both not tall and not strong. If someone is not quiet then someone is both not patient and not humble. If someone is either tall or brave then lucy is not kind. If someone is not rich or not old then susan is not brave or not generous and vice versa. Someone is curious or brave. Alice is either strong or not curious. Someone is wise or brave. Lucy is both not funny and not kind. Mary is both not patient and not funny. Fred is brave or old. Someone is either patient or not curious. Susan is both old and not strong. | Lucy is funny. | contradiction | ((~creative(lucy))=>((~calm(susan)|~creative(susan))))&
(![X]:((~funny(X)<~>strong(X))=>(generous(X)<~>~creative(X))))&
(![X]:((~creative(X)&~patient(X))<=>~calm(X)))&
(((old(mary)<~>tall(mary)))<=>(rich(alice)))&
((~strong(lucy))=>(?[X]:((rich(X)&happy(X)))))&
((?[X]:((funny(X)&~strong(X))))=>((~creative(alice)|~strong(alice))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&tall(X))))&
(![X]:(strong(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((~rich(X)&wise(X))=>(~strong(X)|strong(X))))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((tall(X)|curious(X)))))&
((~tall(john))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|~tall(X))=>(~tall(X)&~strong(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
((?[X]:((tall(X)<~>brave(X))))=>(~kind(lucy)))&
((?[X]:((~rich(X)|~old(X))))<=>((~brave(susan)|~generous(susan))))&
(?[X]:((curious(X)|brave(X))))&
((strong(alice)<~>~curious(alice)))&
(?[X]:((wise(X)|brave(X))))&
((~funny(lucy)&~kind(lucy)))&
((~patient(mary)&~funny(mary)))&
((brave(fred)|old(fred)))&
(?[X]:((patient(X)<~>~curious(X))))&
((old(susan)&~strong(susan))) | funny(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 651601886675568227230711
% SZS output start Proof for 651601886675568227230711
20. ~kind(lucy) & ~funny(lucy) [input p19]
25. funny(lucy) [input hypothesis]
30. ~funny(lucy) [pure predicate removal 20]
124. ~funny(lucy) [cnf transformation 30]
132. funny(lucy) [cnf transformation 25]
320. $false [subsumption resolution 132,124]
% SZS output end Proof for 651601886675568227230711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not curious or happy then john is not patient and vice versa. If someone is not strong or funny then fred is not old or humble and vice versa. If someone is both not tall and not quiet then someone is either calm or not wise and vice versa. If someone is both not rich and generous then someone is happy or old and vice versa. If someone is not old then alice is not kind or quiet and vice versa. Everyone who is funny is both humble and creative. Everyone who is kind is not quiet and vice versa. Everyone who is either rich or not brave is either wise or not quiet and vice versa. If someone is either not generous or generous then someone is funny and vice versa. If someone is quiet then someone is rich or not wise and vice versa. Everyone who is not rich or wise is both not humble and curious and vice versa. Everyone who is not humble is both not humble and not generous and vice versa. If someone is both tall and not brave then john is creative or curious. Everyone who is either patient or curious is both strong and rich and vice versa. Everyone who is either not wise or not patient is either not generous or patient. John is strong. Someone is humble or not calm. Someone is either not generous or generous. Paul is not humble or kind. Someone is curious. | Alice is patient. | neutral | (((~curious(lucy)<~>happy(lucy)))<=>(~patient(john)))&
((?[X]:((~strong(X)|funny(X))))<=>((~old(fred)|humble(fred))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(?[X]:((calm(X)<~>~wise(X)))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(wise(X)<~>~quiet(X))))&
((?[X]:((~generous(X)<~>generous(X))))<=>(?[X]:(funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((~rich(X)|wise(X))<=>(~humble(X)&curious(X))))&
(![X]:(~humble(X)<=>(~humble(X)&~generous(X))))&
((?[X]:((tall(X)&~brave(X))))=>((creative(john)|curious(john))))&
(![X]:((patient(X)<~>curious(X))<=>(strong(X)&rich(X))))&
(![X]:((~wise(X)<~>~patient(X))=>(~generous(X)<~>patient(X))))&
(strong(john))&
(?[X]:((humble(X)|~calm(X))))&
(?[X]:((~generous(X)<~>generous(X))))&
((~humble(paul)|kind(paul)))&
(?[X]:(curious(X))) | patient(alice) | [] | null | 0 |
If someone is both not humble and kind then fred is rich or not kind and vice versa.
If someone is not curious then fred is kind and vice versa.
Everyone who is tall or curious is not brave and vice versa.
Everyone who is not quiet or not strong is not curious or not funny and vice versa.
If lucy is either not old or rich then someone is both not strong and not rich.
If lucy is not creative or not tall then someone is either rich or wise and vice versa.
If someone is both brave and quiet then someone is tall or not funny.
If someone is brave then susan is not tall.
Everyone who is either not tall or patient is either creative or kind and vice versa.
Everyone who is either not patient or not kind is wise.
If someone is both not creative and kind then susan is not tall or not kind.
If susan is either kind or not kind then someone is old or not creative and vice versa.
If alice is either not generous or not happy then lucy is rich and vice versa.
Everyone who is not creative is either not kind or not quiet and vice versa.
If lucy is creative then mary is either not generous or not tall and vice versa.
Everyone who is creative is both not funny and wise and vice versa.
Fred is either not tall or wise.
Someone is not humble.
Someone is not creative or tall.
Someone is both patient and old.
Mary is curious or not curious.
Someone is curious.
Someone is both brave and not strong.
Someone is not quiet or brave. | Fred is not wise. | contradiction | ((?[X]:((~humble(X)&kind(X))))<=>((rich(fred)|~kind(fred))))&
((?[X]:(~curious(X)))<=>(kind(fred)))&
(![X]:((tall(X)|curious(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~strong(X))<=>(~curious(X)|~funny(X))))&
(((~old(lucy)<~>rich(lucy)))=>(?[X]:((~strong(X)&~rich(X)))))&
(((~creative(lucy)|~tall(lucy)))<=>(?[X]:((rich(X)<~>wise(X)))))&
((?[X]:((brave(X)&quiet(X))))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(brave(X)))=>(~tall(susan)))&
(![X]:((~tall(X)<~>patient(X))<=>(creative(X)<~>kind(X))))&
(![X]:((~patient(X)<~>~kind(X))=>wise(X)))&
((?[X]:((~creative(X)&kind(X))))=>((~tall(susan)|~kind(susan))))&
(((kind(susan)<~>~kind(susan)))<=>(?[X]:((old(X)|~creative(X)))))&
(((~generous(alice)<~>~happy(alice)))<=>(rich(lucy)))&
(![X]:(~creative(X)<=>(~kind(X)<~>~quiet(X))))&
((creative(lucy))<=>((~generous(mary)<~>~tall(mary))))&
(![X]:(creative(X)<=>(~funny(X)&wise(X))))&
((~tall(fred)<~>wise(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)|tall(X))))&
(?[X]:((patient(X)&old(X))))&
((curious(mary)|~curious(mary)))&
(?[X]:(curious(X)))&
(?[X]:((brave(X)&~strong(X))))&
(?[X]:((~quiet(X)|brave(X)))) | ~wise(fred) | [
"p1",
"p2",
"p8",
"p9",
"p15",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6944713115088122576262038
% SZS output start Proof for 6944713115088122576262038
2. ? [X0] : ~curious(X0) <=> kind(fred) [input p1]
3. ! [X0] : ((curious(X0) | tall(X0)) <=> ~brave(X0)) [input p2]
9. ! [X0] : ((~tall(X0) <~> patient(X0)) <=> (creative(X0) <~> kind(X0))) [input p8]
10. ! [X0] : ((~patient(X0) <~> ~kind(X0)) => wise(X0)) [input p9]
16. ! [X0] : (creative(X0) <=> (wise(X0) & ~funny(X0))) [input p15]
17. ~tall(fred) <~> wise(fred) [input p16]
23. ? [X0] : (~strong(X0) & brave(X0)) [input p22]
25. ~wise(fred) [input hypothesis]
30. ! [X0] : (wise(X0) | (~patient(X0) <=> ~kind(X0))) [ennf transformation 10]
38. (? [X0] : ~curious(X0) | ~kind(fred)) & (kind(fred) | ! [X0] : curious(X0)) [nnf transformation 2]
39. (? [X0] : ~curious(X0) | ~kind(fred)) & (kind(fred) | ! [X1] : curious(X1)) [rectify 38]
40. ? [X0] : ~curious(X0) => ~curious(sK1) [choice axiom]
41. (~curious(sK1) | ~kind(fred)) & (kind(fred) | ! [X1] : curious(X1)) [skolemisation 39,40]
42. ! [X0] : (((curious(X0) | tall(X0)) | brave(X0)) & (~brave(X0) | (~curious(X0) & ~tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((curious(X0) | tall(X0) | brave(X0)) & (~brave(X0) | (~curious(X0) & ~tall(X0)))) [flattening 42]
57. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) & (((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [nnf transformation 9]
58. ! [X0] : (wise(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) [nnf transformation 30]
66. ! [X0] : ((creative(X0) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | ~creative(X0))) [nnf transformation 16]
67. ! [X0] : ((creative(X0) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0))) [flattening 66]
68. (~wise(fred) | tall(fred)) & (wise(fred) | ~tall(fred)) [nnf transformation 17]
77. ? [X0] : (~strong(X0) & brave(X0)) => (~strong(sK10) & brave(sK10)) [choice axiom]
78. ~strong(sK10) & brave(sK10) [skolemisation 23,77]
86. kind(fred) | curious(X1) [cnf transformation 41]
89. ~brave(X0) | ~curious(X0) [cnf transformation 43]
114. ~patient(X0) | tall(X0) | creative(X0) | ~kind(X0) [cnf transformation 57]
115. ~kind(X0) | wise(X0) | patient(X0) [cnf transformation 58]
137. ~creative(X0) | wise(X0) [cnf transformation 67]
139. wise(fred) | ~tall(fred) [cnf transformation 68]
147. brave(sK10) [cnf transformation 78]
150. ~wise(fred) [cnf transformation 25]
154. 1 <=> kind(fred) [avatar definition]
156. kind(fred) <- (1) [avatar component clause 154]
183. 7 <=> ! [X1] : curious(X1) [avatar definition]
184. curious(X1) <- (7) [avatar component clause 183]
185. 7 | 1 [avatar split clause 86,154,183]
297. 31 <=> tall(fred) [avatar definition]
298. ~tall(fred) <- (~31) [avatar component clause 297]
301. 32 <=> wise(fred) [avatar definition]
303. ~wise(fred) <- (~32) [avatar component clause 301]
305. ~31 | 32 [avatar split clause 139,301,297]
324. ~32 [avatar split clause 150,301]
326. ~curious(sK10) [resolution 89,147]
327. $false <- (7) [subsumption resolution 326,184]
328. ~7 [avatar contradiction clause 327]
337. wise(fred) | patient(fred) <- (1) [resolution 115,156]
347. patient(fred) <- (1, ~32) [subsumption resolution 337,303]
481. tall(fred) | creative(fred) | ~kind(fred) <- (1, ~32) [resolution 114,347]
487. creative(fred) | ~kind(fred) <- (1, ~31, ~32) [subsumption resolution 481,298]
488. creative(fred) <- (1, ~31, ~32) [subsumption resolution 487,156]
523. wise(fred) <- (1, ~31, ~32) [resolution 488,137]
526. $false <- (1, ~31, ~32) [subsumption resolution 523,303]
527. ~1 | 31 | 32 [avatar contradiction clause 526]
528. $false [avatar sat refutation 185,305,324,328,527]
% SZS output end Proof for 6944713115088122576262038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not calm is not tall or wise.
Everyone who is not rich or kind is not calm.
If john is happy then someone is wise and vice versa.
Everyone who is strong or calm is either wise or not humble and vice versa.
If someone is happy or not rich then someone is either not wise or not happy.
Everyone who is either creative or not generous is both not funny and generous.
Everyone who is not tall or not patient is rich and vice versa.
Everyone who is funny or creative is old or not humble.
If lucy is rich then fred is curious or tall.
If someone is not kind or happy then mary is not rich and vice versa.
If fred is either happy or quiet then someone is both not patient and not tall.
Everyone who is either not generous or not tall is either not funny or not brave.
If paul is either calm or not generous then lucy is not curious and vice versa.
If alice is either curious or not strong then someone is either not patient or not creative.
Everyone who is either humble or not brave is both not funny and not kind and vice versa.
Everyone who is either wise or curious is rich.
Someone is not creative.
Someone is either wise or calm.
Lucy is not strong or not quiet.
Someone is both humble and not funny.
Someone is either quiet or not calm.
Paul is patient or curious.
Alice is rich or not kind.
Alice is not strong or not brave. | John is happy. | entailment | (![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
(![X]:((~rich(X)|kind(X))=>~calm(X)))&
((happy(john))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)|calm(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:((happy(X)|~rich(X))))=>(?[X]:((~wise(X)<~>~happy(X)))))&
(![X]:((creative(X)<~>~generous(X))=>(~funny(X)&generous(X))))&
(![X]:((~tall(X)|~patient(X))<=>rich(X)))&
(![X]:((funny(X)|creative(X))=>(old(X)|~humble(X))))&
((rich(lucy))=>((curious(fred)|tall(fred))))&
((?[X]:((~kind(X)|happy(X))))<=>(~rich(mary)))&
(((happy(fred)<~>quiet(fred)))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(~funny(X)<~>~brave(X))))&
(((calm(paul)<~>~generous(paul)))<=>(~curious(lucy)))&
(((curious(alice)<~>~strong(alice)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((humble(X)<~>~brave(X))<=>(~funny(X)&~kind(X))))&
(![X]:((wise(X)<~>curious(X))=>rich(X)))&
(?[X]:(~creative(X)))&
(?[X]:((wise(X)<~>calm(X))))&
((~strong(lucy)|~quiet(lucy)))&
(?[X]:((humble(X)&~funny(X))))&
(?[X]:((quiet(X)<~>~calm(X))))&
((patient(paul)|curious(paul)))&
((rich(alice)|~kind(alice)))&
((~strong(alice)|~brave(alice))) | happy(john) | [
"p0",
"p1",
"p2",
"p6",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6739978045098044219446247
% SZS output start Proof for 6739978045098044219446247
1. ! [X0] : ((wise(X0) <~> ~calm(X0)) => (wise(X0) | ~tall(X0))) [input p0]
2. ! [X0] : ((kind(X0) | ~rich(X0)) => ~calm(X0)) [input p1]
3. happy(john) <=> ? [X0] : wise(X0) [input p2]
7. ! [X0] : ((~patient(X0) | ~tall(X0)) <=> rich(X0)) [input p6]
10. ? [X0] : (happy(X0) | ~kind(X0)) <=> ~rich(mary) [input p9]
18. ? [X0] : (wise(X0) <~> calm(X0)) [input p17]
25. ~happy(john) [input hypothesis]
28. ! [X0] : ((wise(X0) | ~tall(X0)) | (wise(X0) <=> ~calm(X0))) [ennf transformation 1]
29. ! [X0] : (wise(X0) | ~tall(X0) | (wise(X0) <=> ~calm(X0))) [flattening 28]
30. ! [X0] : (~calm(X0) | (~kind(X0) & rich(X0))) [ennf transformation 2]
39. ! [X0] : (wise(X0) | ~tall(X0) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) [nnf transformation 29]
40. (happy(john) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ~happy(john)) [nnf transformation 3]
41. (happy(john) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ~happy(john)) [rectify 40]
42. ? [X1] : wise(X1) => wise(sK0) [choice axiom]
43. (happy(john) | ! [X0] : ~wise(X0)) & (wise(sK0) | ~happy(john)) [skolemisation 41,42]
51. ! [X0] : (((~patient(X0) | ~tall(X0)) | ~rich(X0)) & (rich(X0) | (patient(X0) & tall(X0)))) [nnf transformation 7]
52. ! [X0] : ((~patient(X0) | ~tall(X0) | ~rich(X0)) & (rich(X0) | (patient(X0) & tall(X0)))) [flattening 51]
53. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~happy(X0) & kind(X0))) [nnf transformation 10]
54. (? [X0] : (happy(X0) | ~kind(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [rectify 53]
55. ? [X0] : (happy(X0) | ~kind(X0)) => (happy(sK2) | ~kind(sK2)) [choice axiom]
56. ((happy(sK2) | ~kind(sK2)) | rich(mary)) & (~rich(mary) | ! [X1] : (~happy(X1) & kind(X1))) [skolemisation 54,55]
70. ? [X0] : ((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) [nnf transformation 18]
71. ? [X0] : ((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) => ((~calm(sK6) | ~wise(sK6)) & (calm(sK6) | wise(sK6))) [choice axiom]
72. (~calm(sK6) | ~wise(sK6)) & (calm(sK6) | wise(sK6)) [skolemisation 70,71]
79. wise(X0) | ~tall(X0) | wise(X0) | calm(X0) [cnf transformation 39]
80. ~calm(X0) | rich(X0) [cnf transformation 30]
81. ~kind(X0) | ~calm(X0) [cnf transformation 30]
83. happy(john) | ~wise(X0) [cnf transformation 43]
98. rich(X0) | tall(X0) [cnf transformation 52]
102. ~rich(mary) | kind(X1) [cnf transformation 56]
130. calm(sK6) | wise(sK6) [cnf transformation 72]
140. ~happy(john) [cnf transformation 25]
142. ~tall(X0) | wise(X0) | calm(X0) [duplicate literal removal 79]
144. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
145. ~wise(X0) <- (1) [avatar component clause 144]
147. 2 <=> happy(john) [avatar definition]
150. 1 | 2 [avatar split clause 83,147,144]
188. 11 <=> rich(mary) [avatar definition]
189. ~rich(mary) <- (~11) [avatar component clause 188]
202. 14 <=> ! [X1] : kind(X1) [avatar definition]
203. kind(X1) <- (14) [avatar component clause 202]
204. 14 | ~11 [avatar split clause 102,188,202]
262. 26 <=> wise(sK6) [avatar definition]
263. wise(sK6) <- (26) [avatar component clause 262]
266. 27 <=> calm(sK6) [avatar definition]
267. calm(sK6) <- (27) [avatar component clause 266]
270. 26 | 27 [avatar split clause 130,266,262]
313. ~2 [avatar split clause 140,147]
316. $false <- (1, 26) [resolution 263,145]
317. ~1 | ~26 [avatar contradiction clause 316]
320. tall(mary) <- (~11) [resolution 98,189]
343. wise(mary) | calm(mary) <- (~11) [resolution 142,320]
345. calm(mary) <- (1, ~11) [subsumption resolution 343,145]
360. rich(mary) <- (1, ~11) [resolution 345,80]
361. $false <- (1, ~11) [subsumption resolution 360,189]
362. ~1 | 11 [avatar contradiction clause 361]
368. ~calm(X1) <- (14) [resolution 203,81]
371. $false <- (14, 27) [resolution 368,267]
372. ~14 | ~27 [avatar contradiction clause 371]
373. $false [avatar sat refutation 150,204,270,313,317,362,372]
% SZS output end Proof for 6739978045098044219446247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not funny is both kind and old. Everyone who is either not creative or quiet is either quiet or not patient and vice versa. Everyone who is both old and not generous is not strong and vice versa. If mary is both not brave and creative then mary is not kind or not happy. If alice is both curious and funny then susan is both generous and not humble. Everyone who is both curious and not quiet is either calm or not patient and vice versa. Everyone who is both not tall and tall is both happy and brave and vice versa. If john is strong or not old then someone is either not old or kind. Everyone who is both funny and not happy is either not calm or not old. If susan is either not funny or patient then paul is either funny or not funny and vice versa. Everyone who is brave or patient is curious and vice versa. Everyone who is wise is either not patient or old. If fred is curious or not funny then susan is both humble and not creative. If alice is strong or not rich then paul is not brave. If someone is not happy then john is not generous or kind and vice versa. Everyone who is both not rich and not happy is both strong and not kind. Susan is both funny and patient. Susan is old or creative. Someone is both not old and not tall. Someone is either not kind or not tall. Alice is both not kind and not old. Paul is not quiet or not curious. Fred is not old or not brave. Someone is patient or kind. | Susan is not funny. | contradiction | (![X]:((~patient(X)<~>~funny(X))=>(kind(X)&old(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((old(X)&~generous(X))<=>~strong(X)))&
(((~brave(mary)&creative(mary)))=>((~kind(mary)|~happy(mary))))&
(((curious(alice)&funny(alice)))=>((generous(susan)&~humble(susan))))&
(![X]:((curious(X)&~quiet(X))<=>(calm(X)<~>~patient(X))))&
(![X]:((~tall(X)&tall(X))<=>(happy(X)&brave(X))))&
(((strong(john)|~old(john)))=>(?[X]:((~old(X)<~>kind(X)))))&
(![X]:((funny(X)&~happy(X))=>(~calm(X)<~>~old(X))))&
(((~funny(susan)<~>patient(susan)))<=>((funny(paul)<~>~funny(paul))))&
(![X]:((brave(X)|patient(X))<=>curious(X)))&
(![X]:(wise(X)=>(~patient(X)<~>old(X))))&
(((curious(fred)|~funny(fred)))=>((humble(susan)&~creative(susan))))&
(((strong(alice)|~rich(alice)))=>(~brave(paul)))&
((?[X]:(~happy(X)))<=>((~generous(john)|kind(john))))&
(![X]:((~rich(X)&~happy(X))=>(strong(X)&~kind(X))))&
((funny(susan)&patient(susan)))&
((old(susan)|creative(susan)))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
((~kind(alice)&~old(alice)))&
((~quiet(paul)|~curious(paul)))&
((~old(fred)|~brave(fred)))&
(?[X]:((patient(X)|kind(X)))) | ~funny(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1666173390667003234687194
% SZS output start Proof for 1666173390667003234687194
17. patient(susan) & funny(susan) [input p16]
25. ~funny(susan) [input hypothesis]
118. funny(susan) [cnf transformation 17]
130. ~funny(susan) [cnf transformation 25]
202. 14 <=> funny(susan) [avatar definition]
257. 14 [avatar split clause 118,202]
300. ~14 [avatar split clause 130,202]
301. $false [avatar sat refutation 257,300]
% SZS output end Proof for 1666173390667003234687194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then john is either funny or wise and vice versa.
Everyone who is tall or not generous is kind and vice versa.
If paul is brave or not old then someone is not curious or not creative.
Everyone who is not kind is either not kind or not old.
Everyone who is both not quiet and humble is both patient and not patient and vice versa.
Everyone who is not strong is both generous and not calm and vice versa.
Everyone who is patient or not patient is strong.
If john is rich or strong then someone is not funny and vice versa.
Everyone who is both calm and generous is both funny and old and vice versa.
Everyone who is humble is both patient and not rich.
If lucy is not old then mary is both patient and generous.
If someone is not humble or not rich then john is quiet.
Everyone who is not funny or not brave is either not wise or not kind.
If someone is both rich and wise then someone is quiet or not strong and vice versa.
Everyone who is not brave is not wise or kind and vice versa.
If someone is strong then someone is either not generous or not patient and vice versa.
Paul is not happy.
Susan is either humble or not funny.
Someone is either quiet or patient.
Mary is not calm.
Someone is not kind or curious.
Susan is brave.
Someone is not happy or not old.
Someone is not old or creative. | Paul is not strong. | contradiction | ((?[X]:(happy(X)))<=>((funny(john)<~>wise(john))))&
(![X]:((tall(X)|~generous(X))<=>kind(X)))&
(((brave(paul)|~old(paul)))=>(?[X]:((~curious(X)|~creative(X)))))&
(![X]:(~kind(X)=>(~kind(X)<~>~old(X))))&
(![X]:((~quiet(X)&humble(X))<=>(patient(X)&~patient(X))))&
(![X]:(~strong(X)<=>(generous(X)&~calm(X))))&
(![X]:((patient(X)|~patient(X))=>strong(X)))&
(((rich(john)|strong(john)))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&generous(X))<=>(funny(X)&old(X))))&
(![X]:(humble(X)=>(patient(X)&~rich(X))))&
((~old(lucy))=>((patient(mary)&generous(mary))))&
((?[X]:((~humble(X)|~rich(X))))=>(quiet(john)))&
(![X]:((~funny(X)|~brave(X))=>(~wise(X)<~>~kind(X))))&
((?[X]:((rich(X)&wise(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:(~brave(X)<=>(~wise(X)|kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~generous(X)<~>~patient(X)))))&
(~happy(paul))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((quiet(X)<~>patient(X))))&
(~calm(mary))&
(?[X]:((~kind(X)|curious(X))))&
(brave(susan))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~old(X)|creative(X)))) | ~strong(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 808665911669768791661320
% SZS output start Proof for 808665911669768791661320
7. ! [X0] : ((~patient(X0) | patient(X0)) => strong(X0)) [input p6]
25. ~strong(paul) [input hypothesis]
30. ! [X0] : (strong(X0) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
96. strong(X0) | ~patient(X0) [cnf transformation 30]
97. strong(X0) | patient(X0) [cnf transformation 30]
137. ~strong(paul) [cnf transformation 25]
177. strong(X0) [subsumption resolution 96,97]
287. $false [subsumption resolution 137,177]
% SZS output end Proof for 808665911669768791661320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both brave and not creative then someone is both not rich and not humble. Everyone who is funny or kind is not calm. Everyone who is either kind or not rich is not patient or tall and vice versa. If someone is happy or quiet then fred is generous or not quiet. Everyone who is either patient or not happy is either not old or patient. If someone is not old then someone is brave or curious and vice versa. Everyone who is not creative or not happy is both curious and wise and vice versa. Everyone who is not creative is old. Everyone who is both funny and not calm is either tall or not tall. Everyone who is not strong or not quiet is patient. Everyone who is either kind or not curious is not quiet or strong and vice versa. Everyone who is not quiet or funny is quiet or not kind and vice versa. Everyone who is both not calm and old is both kind and not rich and vice versa. Everyone who is both not patient and creative is quiet or not tall. If someone is tall or humble then fred is generous. Everyone who is not quiet or not strong is either generous or curious. Mary is both strong and quiet. Someone is not brave or not rich. John is both brave and patient. Lucy is not quiet or brave. Lucy is patient. Someone is creative or not curious. | Paul is calm. | neutral | (((brave(paul)&~creative(paul)))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((funny(X)|kind(X))=>~calm(X)))&
(![X]:((kind(X)<~>~rich(X))<=>(~patient(X)|tall(X))))&
((?[X]:((happy(X)|quiet(X))))=>((generous(fred)|~quiet(fred))))&
(![X]:((patient(X)<~>~happy(X))=>(~old(X)<~>patient(X))))&
((?[X]:(~old(X)))<=>(?[X]:((brave(X)|curious(X)))))&
(![X]:((~creative(X)|~happy(X))<=>(curious(X)&wise(X))))&
(![X]:(~creative(X)=>old(X)))&
(![X]:((funny(X)&~calm(X))=>(tall(X)<~>~tall(X))))&
(![X]:((~strong(X)|~quiet(X))=>patient(X)))&
(![X]:((kind(X)<~>~curious(X))<=>(~quiet(X)|strong(X))))&
(![X]:((~quiet(X)|funny(X))<=>(quiet(X)|~kind(X))))&
(![X]:((~calm(X)&old(X))<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)&creative(X))=>(quiet(X)|~tall(X))))&
((?[X]:((tall(X)|humble(X))))=>(generous(fred)))&
(![X]:((~quiet(X)|~strong(X))=>(generous(X)<~>curious(X))))&
((strong(mary)&quiet(mary)))&
(?[X]:((~brave(X)|~rich(X))))&
((brave(john)&patient(john)))&
((~quiet(lucy)|brave(lucy)))&
(patient(lucy))&
(?[X]:((creative(X)|~curious(X)))) | calm(paul) | [] | null | 0 |
If someone is either not brave or not rich then mary is quiet or not old and vice versa. Everyone who is both not patient and quiet is not happy. Everyone who is old or kind is old and vice versa. If susan is either generous or not quiet then lucy is not rich. Everyone who is wise is creative or happy and vice versa. Everyone who is funny is both not creative and generous and vice versa. If paul is either tall or not creative then lucy is calm or not creative and vice versa. Everyone who is not happy or not humble is rich and vice versa. If someone is not strong or creative then mary is not rich and vice versa. If someone is both calm and not humble then fred is either not humble or funny. Everyone who is brave is either not patient or calm. Everyone who is kind or not creative is not curious or kind and vice versa. If lucy is both strong and old then someone is both quiet and strong. Everyone who is old is both not humble and not funny. If someone is not patient then fred is not happy. Everyone who is old is happy or not kind and vice versa. Someone is either not humble or not strong. Mary is not kind or wise. John is not happy. Alice is curious or not curious. Someone is either not old or kind. Someone is either not generous or quiet. | Lucy is not curious. | neutral | ((?[X]:((~brave(X)<~>~rich(X))))<=>((quiet(mary)|~old(mary))))&
(![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X)))) | ~curious(lucy) | [] | null | 0 |
If paul is either quiet or curious then alice is rich and vice versa.
Everyone who is creative or funny is either not funny or kind.
If someone is either not humble or quiet then someone is both not brave and generous.
If john is not creative or quiet then someone is not strong.
Everyone who is both not patient and not curious is both old and not brave and vice versa.
Everyone who is either not strong or curious is either wise or humble.
If someone is generous or wise then someone is both not wise and not brave.
If lucy is either rich or not tall then paul is both not quiet and quiet and vice versa.
If someone is either not generous or not tall then lucy is not creative or not funny.
If paul is both not generous and curious then mary is not calm or generous.
Everyone who is either calm or rich is curious and vice versa.
Everyone who is either happy or curious is both rich and tall.
If someone is curious then someone is both not generous and rich and vice versa.
Everyone who is happy or not kind is not quiet or not funny.
Everyone who is either calm or not kind is both not curious and strong.
Everyone who is both not brave and creative is either humble or not creative.
Lucy is kind or funny.
Someone is not strong.
John is kind or not wise.
Susan is both not tall and funny.
Paul is strong or calm.
Lucy is both old and not strong.
Someone is both not happy and not rich. | Lucy is not calm. | entailment | (((quiet(paul)<~>curious(paul)))<=>(rich(alice)))&
(![X]:((creative(X)|funny(X))=>(~funny(X)<~>kind(X))))&
((?[X]:((~humble(X)<~>quiet(X))))=>(?[X]:((~brave(X)&generous(X)))))&
(((~creative(john)|quiet(john)))=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)&~curious(X))<=>(old(X)&~brave(X))))&
(![X]:((~strong(X)<~>curious(X))=>(wise(X)<~>humble(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~wise(X)&~brave(X)))))&
(((rich(lucy)<~>~tall(lucy)))<=>((~quiet(paul)&quiet(paul))))&
((?[X]:((~generous(X)<~>~tall(X))))=>((~creative(lucy)|~funny(lucy))))&
(((~generous(paul)&curious(paul)))=>((~calm(mary)|generous(mary))))&
(![X]:((calm(X)<~>rich(X))<=>curious(X)))&
(![X]:((happy(X)<~>curious(X))=>(rich(X)&tall(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~generous(X)&rich(X)))))&
(![X]:((happy(X)|~kind(X))=>(~quiet(X)|~funny(X))))&
(![X]:((calm(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(![X]:((~brave(X)&creative(X))=>(humble(X)<~>~creative(X))))&
((kind(lucy)|funny(lucy)))&
(?[X]:(~strong(X)))&
((kind(john)|~wise(john)))&
((~tall(susan)&funny(susan)))&
((strong(paul)|calm(paul)))&
((old(lucy)&~strong(lucy)))&
(?[X]:((~happy(X)&~rich(X)))) | ~calm(lucy) | [
"p1",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1015308632846082602538729
% SZS output start Proof for 1015308632846082602538729
2. ! [X0] : ((funny(X0) | creative(X0)) => (~funny(X0) <~> kind(X0))) [input p1]
15. ! [X0] : ((calm(X0) <~> ~kind(X0)) => (strong(X0) & ~curious(X0))) [input p14]
17. funny(lucy) | kind(lucy) [input p16]
22. ~strong(lucy) & old(lucy) [input p21]
24. calm(lucy) [input hypothesis]
28. ! [X0] : ((~funny(X0) <~> kind(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 2]
40. ! [X0] : ((strong(X0) & ~curious(X0)) | (calm(X0) <=> ~kind(X0))) [ennf transformation 15]
44. ! [X0] : (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (~funny(X0) & ~creative(X0))) [nnf transformation 28]
67. ! [X0] : ((strong(X0) & ~curious(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) [nnf transformation 40]
78. kind(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 44]
123. ~calm(X0) | ~kind(X0) | strong(X0) [cnf transformation 67]
127. funny(lucy) | kind(lucy) [cnf transformation 17]
134. ~strong(lucy) [cnf transformation 22]
137. calm(lucy) [cnf transformation 24]
139. ~funny(X0) | kind(X0) [duplicate literal removal 78]
268. kind(lucy) [subsumption resolution 127,139]
471. ~kind(lucy) | strong(lucy) [resolution 123,137]
473. strong(lucy) [subsumption resolution 471,268]
474. $false [subsumption resolution 473,134]
% SZS output end Proof for 1015308632846082602538729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not rich is either strong or not funny and vice versa. Everyone who is either not tall or kind is either humble or wise and vice versa. If alice is both generous and not kind then someone is either quiet or rich. Everyone who is wise or not old is either tall or not curious. Everyone who is both not brave and not humble is both not wise and not tall and vice versa. If fred is either happy or brave then someone is happy and vice versa. Everyone who is calm is either not rich or not quiet and vice versa. Everyone who is both quiet and kind is both not quiet and not old and vice versa. If someone is not rich or not happy then someone is both patient and not funny. Everyone who is not humble is not curious or not brave and vice versa. If mary is brave or not patient then mary is not patient and vice versa. Everyone who is wise is both not happy and quiet. Everyone who is both kind and not wise is both wise and brave. If someone is both creative and strong then fred is tall or wise and vice versa. Everyone who is wise or calm is not quiet and vice versa. Everyone who is not funny or not humble is not funny or not calm and vice versa. John is either rich or not creative. Alice is creative or not quiet. John is not patient. Someone is not rich or calm. Lucy is either not happy or rich. Someone is both brave and happy. Lucy is either quiet or not patient. | Lucy is not tall. | contradiction | (![X]:((tall(X)<~>~rich(X))<=>(strong(X)<~>~funny(X))))&
(![X]:((~tall(X)<~>kind(X))<=>(humble(X)<~>wise(X))))&
(((generous(alice)&~kind(alice)))=>(?[X]:((quiet(X)<~>rich(X)))))&
(![X]:((wise(X)|~old(X))=>(tall(X)<~>~curious(X))))&
(![X]:((~brave(X)&~humble(X))<=>(~wise(X)&~tall(X))))&
(((happy(fred)<~>brave(fred)))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)<=>(~rich(X)<~>~quiet(X))))&
(![X]:((quiet(X)&kind(X))<=>(~quiet(X)&~old(X))))&
((?[X]:((~rich(X)|~happy(X))))=>(?[X]:((patient(X)&~funny(X)))))&
(![X]:(~humble(X)<=>(~curious(X)|~brave(X))))&
(((brave(mary)|~patient(mary)))<=>(~patient(mary)))&
(![X]:(wise(X)=>(~happy(X)&quiet(X))))&
(![X]:((kind(X)&~wise(X))=>(wise(X)&brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((tall(fred)|wise(fred))))&
(![X]:((wise(X)|calm(X))<=>~quiet(X)))&
(![X]:((~funny(X)|~humble(X))<=>(~funny(X)|~calm(X))))&
((rich(john)<~>~creative(john)))&
((creative(alice)|~quiet(alice)))&
(~patient(john))&
(?[X]:((~rich(X)|calm(X))))&
((~happy(lucy)<~>rich(lucy)))&
(?[X]:((brave(X)&happy(X))))&
((quiet(lucy)<~>~patient(lucy))) | ~tall(lucy) | [
"p1",
"p4",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 498756572319418452123530
% SZS output start Proof for 498756572319418452123530
2. ! [X0] : ((~tall(X0) <~> kind(X0)) <=> (humble(X0) <~> wise(X0))) [input p1]
5. ! [X0] : ((~humble(X0) & ~brave(X0)) <=> (~tall(X0) & ~wise(X0))) [input p4]
10. ! [X0] : (~humble(X0) <=> (~brave(X0) | ~curious(X0))) [input p9]
12. ! [X0] : (wise(X0) => (quiet(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((~wise(X0) & kind(X0)) => (brave(X0) & wise(X0))) [input p12]
15. ! [X0] : ((calm(X0) | wise(X0)) <=> ~quiet(X0)) [input p14]
24. ~tall(lucy) [input hypothesis]
29. ! [X0] : ((quiet(X0) & ~happy(X0)) | ~wise(X0)) [ennf transformation 12]
30. ! [X0] : ((brave(X0) & wise(X0)) | (wise(X0) | ~kind(X0))) [ennf transformation 13]
31. ! [X0] : ((brave(X0) & wise(X0)) | wise(X0) | ~kind(X0)) [flattening 30]
33. ! [X0] : ((((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))))) [nnf transformation 2]
35. ! [X0] : (((~humble(X0) & ~brave(X0)) | (tall(X0) | wise(X0))) & ((~tall(X0) & ~wise(X0)) | (humble(X0) | brave(X0)))) [nnf transformation 5]
36. ! [X0] : (((~humble(X0) & ~brave(X0)) | tall(X0) | wise(X0)) & ((~tall(X0) & ~wise(X0)) | humble(X0) | brave(X0))) [flattening 35]
47. ! [X0] : ((~humble(X0) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | humble(X0))) [nnf transformation 10]
48. ! [X0] : ((~humble(X0) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | humble(X0))) [flattening 47]
56. ! [X0] : (((calm(X0) | wise(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & ~wise(X0)))) [nnf transformation 15]
57. ! [X0] : ((calm(X0) | wise(X0) | quiet(X0)) & (~quiet(X0) | (~calm(X0) & ~wise(X0)))) [flattening 56]
75. wise(X0) | humble(X0) | kind(X0) | tall(X0) [cnf transformation 33]
87. ~wise(X0) | humble(X0) | brave(X0) [cnf transformation 36]
88. ~tall(X0) | humble(X0) | brave(X0) [cnf transformation 36]
89. ~brave(X0) | tall(X0) | wise(X0) [cnf transformation 36]
109. ~humble(X0) | brave(X0) [cnf transformation 48]
114. ~wise(X0) | quiet(X0) [cnf transformation 29]
115. wise(X0) | wise(X0) | ~kind(X0) [cnf transformation 31]
122. ~quiet(X0) | ~wise(X0) [cnf transformation 57]
140. ~tall(lucy) [cnf transformation 24]
141. ~kind(X0) | wise(X0) [duplicate literal removal 115]
215. ~wise(X0) [subsumption resolution 122,114]
389. humble(X0) | kind(X0) | tall(X0) | humble(X0) | brave(X0) [resolution 75,87]
393. humble(X0) | kind(X0) | tall(X0) | brave(X0) [duplicate literal removal 389]
394. humble(X0) | kind(X0) | brave(X0) [subsumption resolution 393,88]
395. brave(X0) | kind(X0) [subsumption resolution 394,109]
405. kind(X1) | tall(X1) | wise(X1) [resolution 395,89]
406. kind(X1) | tall(X1) [subsumption resolution 405,215]
570. tall(X3) | wise(X3) [resolution 406,141]
573. tall(X3) [subsumption resolution 570,215]
587. $false [resolution 573,140]
% SZS output end Proof for 498756572319418452123530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not humble or not rich is either not rich or not strong and vice versa. Everyone who is not rich is not calm or strong and vice versa. If someone is not old or strong then someone is either kind or not quiet. Everyone who is creative is not tall. Everyone who is both not calm and not kind is creative and vice versa. Everyone who is either creative or calm is either kind or not humble and vice versa. If someone is either humble or not generous then someone is not old. Everyone who is creative is creative or not generous and vice versa. If someone is both funny and wise then someone is not kind. Everyone who is either not strong or tall is both not curious and not rich and vice versa. If paul is either not generous or not happy then someone is either generous or calm and vice versa. If john is not kind then alice is both creative and generous and vice versa. If someone is either not tall or happy then someone is not brave. Everyone who is either old or strong is happy or not humble and vice versa. Everyone who is both not strong and not patient is both patient and not tall and vice versa. Everyone who is both brave and not rich is not creative or humble and vice versa. Someone is either old or not tall. Fred is both not humble and quiet. Someone is not old or kind. Alice is either rich or not creative. Someone is both not humble and not wise. Lucy is either not humble or humble. Someone is either creative or not wise. | Fred is not curious. | contradiction | (![X]:((~humble(X)<~>~rich(X))<=>(~rich(X)<~>~strong(X))))&
(![X]:(~rich(X)<=>(~calm(X)|strong(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>~tall(X)))&
(![X]:((~calm(X)&~kind(X))<=>creative(X)))&
(![X]:((creative(X)<~>calm(X))<=>(kind(X)<~>~humble(X))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~curious(X)&~rich(X))))&
(((~generous(paul)<~>~happy(paul)))<=>(?[X]:((generous(X)<~>calm(X)))))&
((~kind(john))<=>((creative(alice)&generous(alice))))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:(~brave(X))))&
(![X]:((old(X)<~>strong(X))<=>(happy(X)|~humble(X))))&
(![X]:((~strong(X)&~patient(X))<=>(patient(X)&~tall(X))))&
(![X]:((brave(X)&~rich(X))<=>(~creative(X)|humble(X))))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)&~wise(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X)))) | ~curious(fred) | [
"p0",
"p1",
"p3",
"p9",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 47263372136549528624833
% SZS output start Proof for 47263372136549528624833
1. ! [X0] : ((~humble(X0) <~> ~rich(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p0]
2. ! [X0] : (~rich(X0) <=> (strong(X0) | ~calm(X0))) [input p1]
4. ! [X0] : (creative(X0) => ~tall(X0)) [input p3]
10. ! [X0] : ((~strong(X0) <~> tall(X0)) <=> (~rich(X0) & ~curious(X0))) [input p9]
15. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> (~tall(X0) & patient(X0))) [input p14]
16. ! [X0] : ((~rich(X0) & brave(X0)) <=> (humble(X0) | ~creative(X0))) [input p15]
18. quiet(fred) & ~humble(fred) [input p17]
24. ~curious(fred) [input hypothesis]
31. ! [X0] : (~tall(X0) | ~creative(X0)) [ennf transformation 4]
34. ! [X0] : ((((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | rich(X0))) [nnf transformation 2]
36. ! [X0] : ((~rich(X0) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | rich(X0))) [flattening 35]
50. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (rich(X0) | curious(X0))) & ((~rich(X0) & ~curious(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [nnf transformation 10]
51. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | rich(X0) | curious(X0)) & ((~rich(X0) & ~curious(X0)) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [flattening 50]
64. ! [X0] : (((~patient(X0) & ~strong(X0)) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | (patient(X0) | strong(X0)))) [nnf transformation 15]
65. ! [X0] : (((~patient(X0) & ~strong(X0)) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | patient(X0) | strong(X0))) [flattening 64]
66. ! [X0] : (((~rich(X0) & brave(X0)) | (~humble(X0) & creative(X0))) & ((humble(X0) | ~creative(X0)) | (rich(X0) | ~brave(X0)))) [nnf transformation 16]
67. ! [X0] : (((~rich(X0) & brave(X0)) | (~humble(X0) & creative(X0))) & (humble(X0) | ~creative(X0) | rich(X0) | ~brave(X0))) [flattening 66]
80. ~strong(X0) | ~rich(X0) | ~rich(X0) | humble(X0) [cnf transformation 34]
86. rich(X0) | humble(X0) | ~strong(X0) | rich(X0) [cnf transformation 34]
90. ~strong(X0) | ~rich(X0) [cnf transformation 36]
95. ~tall(X0) | ~creative(X0) [cnf transformation 31]
114. ~rich(X0) | tall(X0) | strong(X0) [cnf transformation 51]
117. ~tall(X0) | strong(X0) | rich(X0) | curious(X0) [cnf transformation 51]
137. patient(X0) | patient(X0) | strong(X0) [cnf transformation 65]
140. ~patient(X0) | tall(X0) | ~patient(X0) [cnf transformation 65]
144. ~rich(X0) | creative(X0) [cnf transformation 67]
148. ~humble(fred) [cnf transformation 18]
159. ~curious(fred) [cnf transformation 24]
160. patient(X0) | strong(X0) [duplicate literal removal 137]
161. ~patient(X0) | tall(X0) [duplicate literal removal 140]
162. ~strong(X0) | ~rich(X0) | humble(X0) [duplicate literal removal 80]
165. ~strong(X0) | humble(X0) | rich(X0) [duplicate literal removal 86]
167. ~strong(X0) | humble(X0) [subsumption resolution 162,165]
204. ~rich(X0) | tall(X0) [subsumption resolution 114,90]
306. tall(X0) | strong(X0) [resolution 161,160]
451. strong(X0) | strong(X0) | rich(X0) | curious(X0) [resolution 306,117]
455. curious(X0) | rich(X0) | strong(X0) [duplicate literal removal 451]
709. rich(fred) | strong(fred) [resolution 455,159]
714. 57 <=> strong(fred) [avatar definition]
716. strong(fred) <- (57) [avatar component clause 714]
718. 58 <=> rich(fred) [avatar definition]
720. rich(fred) <- (58) [avatar component clause 718]
721. 57 | 58 [avatar split clause 709,718,714]
962. humble(fred) <- (57) [resolution 716,167]
967. $false <- (57) [subsumption resolution 962,148]
968. ~57 [avatar contradiction clause 967]
971. tall(fred) <- (58) [resolution 720,204]
973. creative(fred) <- (58) [resolution 720,144]
1055. ~creative(fred) <- (58) [resolution 971,95]
1056. $false <- (58) [subsumption resolution 1055,973]
1057. ~58 [avatar contradiction clause 1056]
1058. $false [avatar sat refutation 721,968,1057]
% SZS output end Proof for 47263372136549528624833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not humble is not calm and vice versa. If alice is humble then someone is not creative or patient. Everyone who is not generous or humble is both not funny and tall and vice versa. Everyone who is curious or happy is both curious and not happy. If mary is either humble or kind then someone is either not rich or quiet and vice versa. If someone is either not happy or quiet then paul is not strong or strong and vice versa. If paul is both not rich and not quiet then paul is either not funny or not curious. If someone is both brave and not calm then someone is not strong or brave. Everyone who is both not tall and not brave is wise or not wise. Everyone who is either not happy or creative is not funny and vice versa. Everyone who is not old or not wise is both not curious and rich. Everyone who is either funny or not tall is both not strong and brave. If someone is curious or not curious then someone is humble or not generous. If alice is not patient or not generous then lucy is funny. Everyone who is both not quiet and not old is both not creative and not calm. If someone is old then lucy is either tall or humble and vice versa. Someone is not tall. Someone is not brave. Someone is either rich or not patient. Paul is old or calm. Someone is both rich and not calm. Someone is either not funny or kind. | Lucy is humble. | contradiction | (![X]:((humble(X)<~>~humble(X))<=>~calm(X)))&
((humble(alice))=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:((~generous(X)|humble(X))<=>(~funny(X)&tall(X))))&
(![X]:((curious(X)|happy(X))=>(curious(X)&~happy(X))))&
(((humble(mary)<~>kind(mary)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
((?[X]:((~happy(X)<~>quiet(X))))<=>((~strong(paul)|strong(paul))))&
(((~rich(paul)&~quiet(paul)))=>((~funny(paul)<~>~curious(paul))))&
((?[X]:((brave(X)&~calm(X))))=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:((~tall(X)&~brave(X))=>(wise(X)|~wise(X))))&
(![X]:((~happy(X)<~>creative(X))<=>~funny(X)))&
(![X]:((~old(X)|~wise(X))=>(~curious(X)&rich(X))))&
(![X]:((funny(X)<~>~tall(X))=>(~strong(X)&brave(X))))&
((?[X]:((curious(X)|~curious(X))))=>(?[X]:((humble(X)|~generous(X)))))&
(((~patient(alice)|~generous(alice)))=>(funny(lucy)))&
(![X]:((~quiet(X)&~old(X))=>(~creative(X)&~calm(X))))&
((?[X]:(old(X)))<=>((tall(lucy)<~>humble(lucy))))&
(?[X]:(~tall(X)))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>~patient(X))))&
((old(paul)|calm(paul)))&
(?[X]:((rich(X)&~calm(X))))&
(?[X]:((~funny(X)<~>kind(X)))) | humble(lucy) | [
"p0",
"p2",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 830807912004867589377084
% SZS output start Proof for 830807912004867589377084
1. ! [X0] : ((humble(X0) <~> ~humble(X0)) <=> ~calm(X0)) [input p0]
3. ! [X0] : ((humble(X0) | ~generous(X0)) <=> (tall(X0) & ~funny(X0))) [input p2]
16. ? [X0] : old(X0) <=> (tall(lucy) <~> humble(lucy)) [input p15]
20. calm(paul) | old(paul) [input p19]
23. humble(lucy) [input hypothesis]
39. ! [X0] : ((((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | calm(X0)) & (~calm(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0))))) [nnf transformation 1]
42. ! [X0] : (((humble(X0) | ~generous(X0)) | (~tall(X0) | funny(X0))) & ((tall(X0) & ~funny(X0)) | (~humble(X0) & generous(X0)))) [nnf transformation 3]
43. ! [X0] : ((humble(X0) | ~generous(X0) | ~tall(X0) | funny(X0)) & ((tall(X0) & ~funny(X0)) | (~humble(X0) & generous(X0)))) [flattening 42]
62. (? [X0] : old(X0) | ((tall(lucy) | ~humble(lucy)) & (humble(lucy) | ~tall(lucy)))) & (((~humble(lucy) | ~tall(lucy)) & (humble(lucy) | tall(lucy))) | ! [X0] : ~old(X0)) [nnf transformation 16]
63. (? [X0] : old(X0) | ((tall(lucy) | ~humble(lucy)) & (humble(lucy) | ~tall(lucy)))) & (((~humble(lucy) | ~tall(lucy)) & (humble(lucy) | tall(lucy))) | ! [X1] : ~old(X1)) [rectify 62]
64. ? [X0] : old(X0) => old(sK5) [choice axiom]
65. (old(sK5) | ((tall(lucy) | ~humble(lucy)) & (humble(lucy) | ~tall(lucy)))) & (((~humble(lucy) | ~tall(lucy)) & (humble(lucy) | tall(lucy))) | ! [X1] : ~old(X1)) [skolemisation 63,64]
78. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 39]
79. ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 39]
86. tall(X0) | ~humble(X0) [cnf transformation 43]
129. ~humble(lucy) | ~tall(lucy) | ~old(X1) [cnf transformation 65]
136. calm(paul) | old(paul) [cnf transformation 20]
141. humble(lucy) [cnf transformation 23]
143. ~calm(X0) | ~humble(X0) [duplicate literal removal 78]
144. ~calm(X0) | humble(X0) [duplicate literal removal 79]
145. ~calm(X0) [subsumption resolution 143,144]
269. 27 <=> humble(lucy) [avatar definition]
277. ~humble(lucy) | ~old(X1) [subsumption resolution 129,86]
279. 29 <=> ! [X1] : ~old(X1) [avatar definition]
280. ~old(X1) <- (29) [avatar component clause 279]
281. 29 | ~27 [avatar split clause 277,269,279]
294. old(paul) [subsumption resolution 136,145]
305. 27 [avatar split clause 141,269]
306. $false <- (29) [resolution 294,280]
307. ~29 [avatar contradiction clause 306]
308. $false [avatar sat refutation 281,305,307]
% SZS output end Proof for 830807912004867589377084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is calm or creative then someone is not quiet.
If mary is curious or not humble then someone is happy and vice versa.
If lucy is both not generous and patient then someone is both not creative and not calm and vice versa.
If alice is both quiet and calm then someone is not rich.
If someone is old or not humble then lucy is brave or rich and vice versa.
Everyone who is kind is both generous and not curious.
Everyone who is both old and patient is humble.
Everyone who is both old and curious is happy.
Everyone who is kind is not curious.
Everyone who is humble is not calm and vice versa.
If alice is both curious and not creative then fred is strong or not patient.
If mary is either patient or not creative then fred is humble and vice versa.
Everyone who is tall or not quiet is humble and vice versa.
Everyone who is curious or not wise is either not calm or humble and vice versa.
If someone is either not curious or not wise then someone is either not calm or not creative and vice versa.
If alice is happy then john is either not old or generous.
John is both not strong and creative.
John is generous or not creative.
Someone is both not creative and not kind.
Someone is not tall or funny.
Mary is not creative or not strong.
Someone is both not quiet and generous.
Paul is either happy or not patient. | Lucy is rich. | neutral | (((calm(mary)|creative(mary)))=>(?[X]:(~quiet(X))))&
(((curious(mary)|~humble(mary)))<=>(?[X]:(happy(X))))&
(((~generous(lucy)&patient(lucy)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(((quiet(alice)&calm(alice)))=>(?[X]:(~rich(X))))&
((?[X]:((old(X)|~humble(X))))<=>((brave(lucy)|rich(lucy))))&
(![X]:(kind(X)=>(generous(X)&~curious(X))))&
(![X]:((old(X)&patient(X))=>humble(X)))&
(![X]:((old(X)&curious(X))=>happy(X)))&
(![X]:(kind(X)=>~curious(X)))&
(![X]:(humble(X)<=>~calm(X)))&
(((curious(alice)&~creative(alice)))=>((strong(fred)|~patient(fred))))&
(((patient(mary)<~>~creative(mary)))<=>(humble(fred)))&
(![X]:((tall(X)|~quiet(X))<=>humble(X)))&
(![X]:((curious(X)|~wise(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~creative(X)))))&
((happy(alice))=>((~old(john)<~>generous(john))))&
((~strong(john)&creative(john)))&
((generous(john)|~creative(john)))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((~tall(X)|funny(X))))&
((~creative(mary)|~strong(mary)))&
(?[X]:((~quiet(X)&generous(X))))&
((happy(paul)<~>~patient(paul))) | rich(lucy) | [] | null | 0 |
Everyone who is quiet or curious is brave or strong and vice versa. Everyone who is strong is either not rich or rich and vice versa. Everyone who is not happy or rich is either old or rich and vice versa. Everyone who is rich is not generous. If susan is not strong then lucy is either not rich or not wise. If someone is wise then john is both not patient and not calm and vice versa. If someone is both curious and not curious then lucy is not rich and vice versa. Everyone who is not tall or rich is both not tall and humble and vice versa. Everyone who is calm is either not wise or tall. If lucy is either not strong or wise then someone is curious or calm. If someone is patient then paul is either tall or generous and vice versa. Everyone who is both kind and not patient is not wise and vice versa. If mary is either quiet or brave then someone is both not happy and calm. Everyone who is either quiet or rich is not rich and vice versa. Everyone who is either patient or not happy is either happy or generous and vice versa. Everyone who is not quiet is wise or not curious. Paul is both not rich and tall. Susan is old. Susan is either tall or not generous. Someone is both not kind and brave. Someone is both not curious and not brave. Someone is both not kind and not funny. Alice is either not rich or not creative. Mary is not rich or not wise. | Paul is not generous. | entailment | (![X]:((quiet(X)|curious(X))<=>(brave(X)|strong(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>rich(X))))&
(![X]:((~happy(X)|rich(X))<=>(old(X)<~>rich(X))))&
(![X]:(rich(X)=>~generous(X)))&
((~strong(susan))=>((~rich(lucy)<~>~wise(lucy))))&
((?[X]:(wise(X)))<=>((~patient(john)&~calm(john))))&
((?[X]:((curious(X)&~curious(X))))<=>(~rich(lucy)))&
(![X]:((~tall(X)|rich(X))<=>(~tall(X)&humble(X))))&
(![X]:(calm(X)=>(~wise(X)<~>tall(X))))&
(((~strong(lucy)<~>wise(lucy)))=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:(patient(X)))<=>((tall(paul)<~>generous(paul))))&
(![X]:((kind(X)&~patient(X))<=>~wise(X)))&
(((quiet(mary)<~>brave(mary)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:((quiet(X)<~>rich(X))<=>~rich(X)))&
(![X]:((patient(X)<~>~happy(X))<=>(happy(X)<~>generous(X))))&
(![X]:(~quiet(X)=>(wise(X)|~curious(X))))&
((~rich(paul)&tall(paul)))&
(old(susan))&
((tall(susan)<~>~generous(susan)))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~curious(X)&~brave(X))))&
(?[X]:((~kind(X)&~funny(X))))&
((~rich(alice)<~>~creative(alice)))&
((~rich(mary)|~wise(mary))) | ~generous(paul) | [
"p3",
"p6",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5089091297303193074916094
% SZS output start Proof for 5089091297303193074916094
4. ! [X0] : (rich(X0) => ~generous(X0)) [input p3]
7. ? [X0] : (~curious(X0) & curious(X0)) <=> ~rich(lucy) [input p6]
11. ? [X0] : patient(X0) <=> (tall(paul) <~> generous(paul)) [input p10]
15. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (happy(X0) <~> generous(X0))) [input p14]
17. tall(paul) & ~rich(paul) [input p16]
25. generous(paul) [input hypothesis]
27. ! [X0] : (~generous(X0) | ~rich(X0)) [ennf transformation 4]
45. (? [X0] : (~curious(X0) & curious(X0)) | rich(lucy)) & (~rich(lucy) | ! [X0] : (curious(X0) | ~curious(X0))) [nnf transformation 7]
46. (? [X0] : (~curious(X0) & curious(X0)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (curious(X1) | ~curious(X1))) [rectify 45]
47. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK1) & curious(sK1)) [choice axiom]
48. ((~curious(sK1) & curious(sK1)) | rich(lucy)) & (~rich(lucy) | ! [X1] : (curious(X1) | ~curious(X1))) [skolemisation 46,47]
55. (? [X0] : patient(X0) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X0] : ~patient(X0)) [nnf transformation 11]
56. (? [X0] : patient(X0) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X1] : ~patient(X1)) [rectify 55]
57. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
58. (patient(sK3) | ((tall(paul) | ~generous(paul)) & (generous(paul) | ~tall(paul)))) & (((~generous(paul) | ~tall(paul)) & (generous(paul) | tall(paul))) | ! [X1] : ~patient(X1)) [skolemisation 56,57]
65. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 15]
88. ~generous(X0) | ~rich(X0) [cnf transformation 27]
95. curious(sK1) | rich(lucy) [cnf transformation 48]
96. ~curious(sK1) | rich(lucy) [cnf transformation 48]
107. ~generous(paul) | ~tall(paul) | ~patient(X1) [cnf transformation 58]
122. generous(X0) | happy(X0) | patient(X0) | happy(X0) [cnf transformation 65]
125. ~happy(X0) | patient(X0) | generous(X0) | ~happy(X0) [cnf transformation 65]
131. tall(paul) [cnf transformation 17]
143. generous(paul) [cnf transformation 25]
144. generous(X0) | happy(X0) | patient(X0) [duplicate literal removal 122]
146. ~happy(X0) | patient(X0) | generous(X0) [duplicate literal removal 125]
174. 5 <=> rich(lucy) [avatar definition]
176. rich(lucy) <- (5) [avatar component clause 174]
178. 6 <=> curious(sK1) [avatar definition]
181. 5 | ~6 [avatar split clause 96,178,174]
182. 5 | 6 [avatar split clause 95,178,174]
198. 10 <=> generous(paul) [avatar definition]
202. 11 <=> tall(paul) [avatar definition]
212. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
213. ~patient(X1) <- (13) [avatar component clause 212]
214. 13 | ~11 | ~10 [avatar split clause 107,198,202,212]
238. patient(X0) | generous(X0) [subsumption resolution 144,146]
239. 11 [avatar split clause 131,202]
269. 10 [avatar split clause 143,198]
288. generous(X2) <- (13) [resolution 238,213]
290. ~rich(X0) <- (13) [resolution 288,88]
293. $false <- (5, 13) [resolution 290,176]
297. ~5 | ~13 [avatar contradiction clause 293]
298. $false [avatar sat refutation 181,182,214,239,269,297]
% SZS output end Proof for 5089091297303193074916094
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and creative is rich or not old and vice versa. If someone is not humble then alice is not curious. Everyone who is old or not calm is humble and vice versa. If someone is either tall or patient then alice is strong and vice versa. If someone is not strong or not funny then lucy is happy. If someone is not calm then someone is both not kind and not funny and vice versa. If fred is not brave then someone is not patient or funny and vice versa. Everyone who is either humble or not calm is generous. Everyone who is either rich or brave is both not strong and happy. Everyone who is humble or not tall is not happy or not calm and vice versa. Everyone who is either not kind or tall is either not humble or not calm and vice versa. Everyone who is either humble or rich is both not rich and not generous and vice versa. Everyone who is either quiet or generous is both tall and calm. Everyone who is not wise is both quiet and not strong and vice versa. If lucy is curious or not old then mary is curious or not old. If paul is not patient then paul is either not wise or not rich. Mary is not generous. Lucy is patient or not kind. Paul is not tall or generous. Alice is both not wise and not humble. Someone is happy or not creative. Someone is not creative or old. Someone is funny or generous. Someone is kind. | Alice is patient. | entailment | (![X]:((tall(X)&creative(X))<=>(rich(X)|~old(X))))&
((?[X]:(~humble(X)))=>(~curious(alice)))&
(![X]:((old(X)|~calm(X))<=>humble(X)))&
((?[X]:((tall(X)<~>patient(X))))<=>(strong(alice)))&
((?[X]:((~strong(X)|~funny(X))))=>(happy(lucy)))&
((?[X]:(~calm(X)))<=>(?[X]:((~kind(X)&~funny(X)))))&
((~brave(fred))<=>(?[X]:((~patient(X)|funny(X)))))&
(![X]:((humble(X)<~>~calm(X))=>generous(X)))&
(![X]:((rich(X)<~>brave(X))=>(~strong(X)&happy(X))))&
(![X]:((humble(X)|~tall(X))<=>(~happy(X)|~calm(X))))&
(![X]:((~kind(X)<~>tall(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:((humble(X)<~>rich(X))<=>(~rich(X)&~generous(X))))&
(![X]:((quiet(X)<~>generous(X))=>(tall(X)&calm(X))))&
(![X]:(~wise(X)<=>(quiet(X)&~strong(X))))&
(((curious(lucy)|~old(lucy)))=>((curious(mary)|~old(mary))))&
((~patient(paul))=>((~wise(paul)<~>~rich(paul))))&
(~generous(mary))&
((patient(lucy)|~kind(lucy)))&
((~tall(paul)|generous(paul)))&
((~wise(alice)&~humble(alice)))&
(?[X]:((happy(X)|~creative(X))))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((funny(X)|generous(X))))&
(?[X]:(kind(X))) | patient(alice) | [
"p0",
"p2",
"p3",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5601473316632749186539
% SZS output start Proof for 5601473316632749186539
1. ! [X0] : ((creative(X0) & tall(X0)) <=> (~old(X0) | rich(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | old(X0)) <=> humble(X0)) [input p2]
4. ? [X0] : (tall(X0) <~> patient(X0)) <=> strong(alice) [input p3]
14. ! [X0] : (~wise(X0) <=> (~strong(X0) & quiet(X0))) [input p13]
20. ~humble(alice) & ~wise(alice) [input p19]
25. ~patient(alice) [input hypothesis]
35. ! [X0] : (((creative(X0) & tall(X0)) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | (~creative(X0) | ~tall(X0)))) [nnf transformation 1]
36. ! [X0] : (((creative(X0) & tall(X0)) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | ~creative(X0) | ~tall(X0))) [flattening 35]
37. ! [X0] : (((~calm(X0) | old(X0)) | ~humble(X0)) & (humble(X0) | (calm(X0) & ~old(X0)))) [nnf transformation 3]
38. ! [X0] : ((~calm(X0) | old(X0) | ~humble(X0)) & (humble(X0) | (calm(X0) & ~old(X0)))) [flattening 37]
39. (? [X0] : ((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~strong(alice)) & (strong(alice) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) [nnf transformation 4]
40. (? [X0] : ((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~strong(alice)) & (strong(alice) | ! [X1] : ((tall(X1) | ~patient(X1)) & (patient(X1) | ~tall(X1)))) [rectify 39]
41. ? [X0] : ((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) => ((~patient(sK0) | ~tall(sK0)) & (patient(sK0) | tall(sK0))) [choice axiom]
42. (((~patient(sK0) | ~tall(sK0)) & (patient(sK0) | tall(sK0))) | ~strong(alice)) & (strong(alice) | ! [X1] : ((tall(X1) | ~patient(X1)) & (patient(X1) | ~tall(X1)))) [skolemisation 40,41]
60. ! [X0] : ((~wise(X0) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | wise(X0))) [nnf transformation 14]
61. ! [X0] : ((~wise(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | wise(X0))) [flattening 60]
73. old(X0) | tall(X0) [cnf transformation 36]
77. ~old(X0) | humble(X0) [cnf transformation 38]
80. strong(alice) | patient(X1) | ~tall(X1) [cnf transformation 42]
121. ~strong(X0) | wise(X0) [cnf transformation 61]
130. ~wise(alice) [cnf transformation 20]
131. ~humble(alice) [cnf transformation 20]
136. ~patient(alice) [cnf transformation 25]
148. 3 <=> strong(alice) [avatar definition]
149. strong(alice) <- (3) [avatar component clause 148]
166. 7 <=> ! [X1] : (patient(X1) | ~tall(X1)) [avatar definition]
167. ~tall(X1) | patient(X1) <- (7) [avatar component clause 166]
168. 7 | 3 [avatar split clause 80,148,166]
300. humble(X1) | tall(X1) [resolution 77,73]
303. wise(alice) <- (3) [resolution 121,149]
304. $false <- (3) [subsumption resolution 303,130]
305. ~3 [avatar contradiction clause 304]
319. tall(alice) [resolution 300,131]
320. patient(alice) <- (7) [resolution 319,167]
321. $false <- (7) [subsumption resolution 320,136]
322. ~7 [avatar contradiction clause 321]
323. $false [avatar sat refutation 168,305,322]
% SZS output end Proof for 5601473316632749186539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is rich or humble then someone is both not wise and happy. If someone is calm then someone is both generous and funny. If someone is wise then fred is either creative or not rich. Everyone who is both not strong and curious is not humble and vice versa. If lucy is patient or creative then someone is both kind and creative. Everyone who is not patient is wise or strong and vice versa. If someone is either funny or happy then someone is not strong or brave. If someone is either wise or not rich then fred is not happy or not kind and vice versa. Everyone who is brave or creative is either funny or curious and vice versa. If alice is not calm then fred is either not funny or not brave and vice versa. If lucy is either not humble or happy then alice is both strong and not tall. If susan is happy or not rich then paul is both calm and kind. If mary is rich then fred is both old and generous. Everyone who is both not curious and not humble is not generous or calm and vice versa. If someone is kind or not tall then john is either quiet or not brave and vice versa. If someone is both patient and happy then john is old. Someone is happy. Someone is either not brave or not patient. Mary is patient. Someone is both quiet and not tall. Paul is either strong or rich. Fred is not curious or creative. Susan is either not brave or not generous. John is either not curious or not calm. | Mary is calm. | contradiction | (((rich(lucy)|humble(lucy)))=>(?[X]:((~wise(X)&happy(X)))))&
((?[X]:(calm(X)))=>(?[X]:((generous(X)&funny(X)))))&
((?[X]:(wise(X)))=>((creative(fred)<~>~rich(fred))))&
(![X]:((~strong(X)&curious(X))<=>~humble(X)))&
(((patient(lucy)|creative(lucy)))=>(?[X]:((kind(X)&creative(X)))))&
(![X]:(~patient(X)<=>(wise(X)|strong(X))))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((~strong(X)|brave(X)))))&
((?[X]:((wise(X)<~>~rich(X))))<=>((~happy(fred)|~kind(fred))))&
(![X]:((brave(X)|creative(X))<=>(funny(X)<~>curious(X))))&
((~calm(alice))<=>((~funny(fred)<~>~brave(fred))))&
(((~humble(lucy)<~>happy(lucy)))=>((strong(alice)&~tall(alice))))&
(((happy(susan)|~rich(susan)))=>((calm(paul)&kind(paul))))&
((rich(mary))=>((old(fred)&generous(fred))))&
(![X]:((~curious(X)&~humble(X))<=>(~generous(X)|calm(X))))&
((?[X]:((kind(X)|~tall(X))))<=>((quiet(john)<~>~brave(john))))&
((?[X]:((patient(X)&happy(X))))=>(old(john)))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)<~>~patient(X))))&
(patient(mary))&
(?[X]:((quiet(X)&~tall(X))))&
((strong(paul)<~>rich(paul)))&
((~curious(fred)|creative(fred)))&
((~brave(susan)<~>~generous(susan)))&
((~curious(john)<~>~calm(john))) | calm(mary) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 203025114313743099380583
% SZS output start Proof for 203025114313743099380583
4. ! [X0] : ((curious(X0) & ~strong(X0)) <=> ~humble(X0)) [input p3]
14. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> (calm(X0) | ~generous(X0))) [input p13]
25. calm(mary) [input hypothesis]
44. ! [X0] : (((curious(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | (~curious(X0) | strong(X0)))) [nnf transformation 4]
45. ! [X0] : (((curious(X0) & ~strong(X0)) | humble(X0)) & (~humble(X0) | ~curious(X0) | strong(X0))) [flattening 44]
63. ! [X0] : (((~humble(X0) & ~curious(X0)) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | (humble(X0) | curious(X0)))) [nnf transformation 14]
64. ! [X0] : (((~humble(X0) & ~curious(X0)) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | humble(X0) | curious(X0))) [flattening 63]
89. curious(X0) | humble(X0) [cnf transformation 45]
126. ~curious(X0) | ~calm(X0) [cnf transformation 64]
128. ~humble(X0) | ~calm(X0) [cnf transformation 64]
148. calm(mary) [cnf transformation 25]
170. 5 <=> ! [X1] : ~calm(X1) [avatar definition]
171. ~calm(X1) <- (5) [avatar component clause 170]
392. $false <- (5) [resolution 171,148]
393. ~5 [avatar contradiction clause 392]
402. ~calm(X0) | humble(X0) [resolution 126,89]
404. ~calm(X0) [subsumption resolution 402,128]
405. 5 [avatar split clause 404,170]
406. $false [avatar sat refutation 393,405]
% SZS output end Proof for 203025114313743099380583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both calm and funny and vice versa.
If someone is either not patient or quiet then susan is curious and vice versa.
If fred is strong then susan is not curious or not humble and vice versa.
Everyone who is either not happy or curious is calm and vice versa.
Everyone who is not strong or not quiet is not brave or not kind.
Everyone who is both not rich and old is either patient or happy.
Everyone who is old or kind is not curious.
Everyone who is either humble or curious is not funny and vice versa.
Everyone who is both patient and not happy is tall or not calm.
Everyone who is not funny or not calm is either kind or generous.
Everyone who is patient is both kind and tall.
If lucy is either not generous or brave then someone is both curious and not curious and vice versa.
Everyone who is not patient is wise or not calm.
If someone is both generous and not brave then john is kind and vice versa.
If someone is tall or rich then someone is both happy and humble and vice versa.
If susan is both not generous and kind then paul is kind or not rich and vice versa.
Someone is not tall.
Paul is not wise.
Someone is not patient or not kind.
Alice is not brave.
Alice is generous.
Paul is either not tall or tall. | John is not quiet. | contradiction | (![X]:(~funny(X)<=>(calm(X)&funny(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(curious(susan)))&
((strong(fred))<=>((~curious(susan)|~humble(susan))))&
(![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:((~strong(X)|~quiet(X))=>(~brave(X)|~kind(X))))&
(![X]:((~rich(X)&old(X))=>(patient(X)<~>happy(X))))&
(![X]:((old(X)|kind(X))=>~curious(X)))&
(![X]:((humble(X)<~>curious(X))<=>~funny(X)))&
(![X]:((patient(X)&~happy(X))=>(tall(X)|~calm(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)<~>generous(X))))&
(![X]:(patient(X)=>(kind(X)&tall(X))))&
(((~generous(lucy)<~>brave(lucy)))<=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:(~patient(X)=>(wise(X)|~calm(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(kind(john)))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:((happy(X)&humble(X)))))&
(((~generous(susan)&kind(susan)))<=>((kind(paul)|~rich(paul))))&
(?[X]:(~tall(X)))&
(~wise(paul))&
(?[X]:((~patient(X)|~kind(X))))&
(~brave(alice))&
(generous(alice))&
((~tall(paul)<~>tall(paul))) | ~quiet(john) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5001219827046494098411786
% SZS output start Proof for 5001219827046494098411786
1. ! [X0] : (~funny(X0) <=> (funny(X0) & calm(X0))) [input p0]
2. ? [X0] : (~patient(X0) <~> quiet(X0)) <=> curious(susan) [input p1]
4. ! [X0] : ((~happy(X0) <~> curious(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((kind(X0) | old(X0)) => ~curious(X0)) [input p6]
8. ! [X0] : ((humble(X0) <~> curious(X0)) <=> ~funny(X0)) [input p7]
11. ! [X0] : (patient(X0) => (tall(X0) & kind(X0))) [input p10]
15. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X0] : (humble(X0) & happy(X0)) [input p14]
16. (kind(susan) & ~generous(susan)) <=> (~rich(paul) | kind(paul)) [input p15]
23. ~quiet(john) [input hypothesis]
24. ? [X0] : (rich(X0) | tall(X0)) <=> ? [X1] : (humble(X1) & happy(X1)) [rectify 15]
26. ! [X0] : (kind(X0) => ~curious(X0)) [pure predicate removal 7]
29. ! [X0] : (~curious(X0) | ~kind(X0)) [ennf transformation 26]
33. ! [X0] : ((tall(X0) & kind(X0)) | ~patient(X0)) [ennf transformation 11]
36. ! [X0] : ((~funny(X0) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | funny(X0))) [nnf transformation 1]
37. ! [X0] : ((~funny(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | funny(X0))) [flattening 36]
38. (? [X0] : ((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~curious(susan)) & (curious(susan) | ! [X0] : ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) [nnf transformation 2]
39. (? [X0] : ((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~curious(susan)) & (curious(susan) | ! [X1] : ((~patient(X1) | ~quiet(X1)) & (quiet(X1) | patient(X1)))) [rectify 38]
40. ? [X0] : ((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) => ((~quiet(sK0) | patient(sK0)) & (quiet(sK0) | ~patient(sK0))) [choice axiom]
41. (((~quiet(sK0) | patient(sK0)) & (quiet(sK0) | ~patient(sK0))) | ~curious(susan)) & (curious(susan) | ! [X1] : ((~patient(X1) | ~quiet(X1)) & (quiet(X1) | patient(X1)))) [skolemisation 39,40]
44. ! [X0] : ((((~curious(X0) | happy(X0)) & (curious(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))))) [nnf transformation 4]
45. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | funny(X0)) & (~funny(X0) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 8]
55. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : (~humble(X1) | ~happy(X1))) & (? [X1] : (humble(X1) & happy(X1)) | ! [X0] : (~rich(X0) & ~tall(X0))) [nnf transformation 24]
56. (? [X0] : (rich(X0) | tall(X0)) | ! [X1] : (~humble(X1) | ~happy(X1))) & (? [X2] : (humble(X2) & happy(X2)) | ! [X3] : (~rich(X3) & ~tall(X3))) [rectify 55]
57. ? [X0] : (rich(X0) | tall(X0)) => (rich(sK3) | tall(sK3)) [choice axiom]
58. ? [X2] : (humble(X2) & happy(X2)) => (humble(sK4) & happy(sK4)) [choice axiom]
59. ((rich(sK3) | tall(sK3)) | ! [X1] : (~humble(X1) | ~happy(X1))) & ((humble(sK4) & happy(sK4)) | ! [X3] : (~rich(X3) & ~tall(X3))) [skolemisation 56,58,57]
60. ((kind(susan) & ~generous(susan)) | (rich(paul) & ~kind(paul))) & ((~rich(paul) | kind(paul)) | (~kind(susan) | generous(susan))) [nnf transformation 16]
61. ((kind(susan) & ~generous(susan)) | (rich(paul) & ~kind(paul))) & (~rich(paul) | kind(paul) | ~kind(susan) | generous(susan)) [flattening 60]
68. funny(X0) | funny(X0) [cnf transformation 37]
69. ~funny(X0) | ~funny(X0) | ~calm(X0) [cnf transformation 37]
70. curious(susan) | quiet(X1) | patient(X1) [cnf transformation 41]
78. ~happy(X0) | calm(X0) | ~curious(X0) [cnf transformation 44]
83. ~kind(X0) | ~curious(X0) [cnf transformation 29]
84. ~funny(X0) | curious(X0) | ~humble(X0) [cnf transformation 45]
94. ~patient(X0) | tall(X0) [cnf transformation 33]
105. happy(sK4) | ~tall(X3) [cnf transformation 59]
106. happy(sK4) | ~rich(X3) [cnf transformation 59]
107. humble(sK4) | ~tall(X3) [cnf transformation 59]
108. humble(sK4) | ~rich(X3) [cnf transformation 59]
114. kind(susan) | rich(paul) [cnf transformation 61]
122. ~quiet(john) [cnf transformation 23]
123. funny(X0) [duplicate literal removal 68]
124. ~calm(X0) | ~funny(X0) [duplicate literal removal 69]
126. 1 <=> curious(susan) [avatar definition]
127. curious(susan) <- (1) [avatar component clause 126]
144. 5 <=> ! [X1] : (quiet(X1) | patient(X1)) [avatar definition]
145. quiet(X1) | patient(X1) <- (5) [avatar component clause 144]
146. 5 | 1 [avatar split clause 70,126,144]
159. ~humble(X0) | curious(X0) [subsumption resolution 84,123]
207. 18 <=> ! [X3] : ~rich(X3) [avatar definition]
208. ~rich(X3) <- (18) [avatar component clause 207]
210. 19 <=> humble(sK4) [avatar definition]
212. humble(sK4) <- (19) [avatar component clause 210]
213. 18 | 19 [avatar split clause 108,210,207]
215. 20 <=> ! [X3] : ~tall(X3) [avatar definition]
216. ~tall(X3) <- (20) [avatar component clause 215]
217. 20 | 19 [avatar split clause 107,210,215]
219. 21 <=> happy(sK4) [avatar definition]
221. happy(sK4) <- (21) [avatar component clause 219]
222. 18 | 21 [avatar split clause 106,219,207]
223. 20 | 21 [avatar split clause 105,219,215]
225. 22 <=> rich(paul) [avatar definition]
227. rich(paul) <- (22) [avatar component clause 225]
229. 23 <=> kind(susan) [avatar definition]
231. kind(susan) <- (23) [avatar component clause 229]
232. 22 | 23 [avatar split clause 114,229,225]
246. $false <- (18, 22) [resolution 227,208]
247. ~18 | ~22 [avatar contradiction clause 246]
249. patient(john) <- (5) [resolution 145,122]
251. tall(john) <- (5) [resolution 249,94]
253. $false <- (5, 20) [subsumption resolution 251,216]
254. ~5 | ~20 [avatar contradiction clause 253]
255. curious(sK4) <- (19) [resolution 159,212]
260. calm(sK4) | ~curious(sK4) <- (21) [resolution 78,221]
263. calm(sK4) <- (19, 21) [subsumption resolution 260,255]
267. ~funny(sK4) <- (19, 21) [resolution 263,124]
268. $false <- (19, 21) [subsumption resolution 267,123]
269. ~19 | ~21 [avatar contradiction clause 268]
278. ~curious(susan) <- (23) [resolution 231,83]
279. $false <- (1, 23) [subsumption resolution 278,127]
280. ~1 | ~23 [avatar contradiction clause 279]
281. $false [avatar sat refutation 146,213,217,222,223,232,247,254,269,280]
% SZS output end Proof for 5001219827046494098411786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not curious then susan is both not calm and not rich and vice versa. Everyone who is funny or wise is not old or strong and vice versa. If alice is not quiet then someone is humble and vice versa. If someone is not curious then alice is both wise and not kind and vice versa. If paul is either not humble or quiet then mary is either not wise or tall and vice versa. If mary is either not rich or not creative then fred is either kind or not creative. If someone is either not creative or brave then someone is kind or not calm. Everyone who is either humble or not happy is funny. If someone is not wise or humble then someone is either wise or not creative and vice versa. If mary is both wise and not humble then someone is either not tall or calm. Everyone who is generous is both not wise and generous. If lucy is not kind then susan is not rich. Everyone who is not funny is calm or not funny and vice versa. Everyone who is not generous is tall or not happy and vice versa. Everyone who is calm is either creative or calm. Everyone who is either wise or curious is not generous and vice versa. Someone is not humble or not rich. Someone is curious or quiet. Someone is both not happy and tall. Someone is either patient or rich. Someone is both not tall and not funny. Mary is not old. Paul is both not calm and not quiet. Someone is strong or quiet. | Mary is wise. | neutral | ((~curious(john))<=>((~calm(susan)&~rich(susan))))&
(![X]:((funny(X)|wise(X))<=>(~old(X)|strong(X))))&
((~quiet(alice))<=>(?[X]:(humble(X))))&
((?[X]:(~curious(X)))<=>((wise(alice)&~kind(alice))))&
(((~humble(paul)<~>quiet(paul)))<=>((~wise(mary)<~>tall(mary))))&
(((~rich(mary)<~>~creative(mary)))=>((kind(fred)<~>~creative(fred))))&
((?[X]:((~creative(X)<~>brave(X))))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:((humble(X)<~>~happy(X))=>funny(X)))&
((?[X]:((~wise(X)|humble(X))))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((wise(mary)&~humble(mary)))=>(?[X]:((~tall(X)<~>calm(X)))))&
(![X]:(generous(X)=>(~wise(X)&generous(X))))&
((~kind(lucy))=>(~rich(susan)))&
(![X]:(~funny(X)<=>(calm(X)|~funny(X))))&
(![X]:(~generous(X)<=>(tall(X)|~happy(X))))&
(![X]:(calm(X)=>(creative(X)<~>calm(X))))&
(![X]:((wise(X)<~>curious(X))<=>~generous(X)))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:((~tall(X)&~funny(X))))&
(~old(mary))&
((~calm(paul)&~quiet(paul)))&
(?[X]:((strong(X)|quiet(X)))) | wise(mary) | [] | null | 0 |
If mary is generous or not brave then susan is not rich or not curious.
Everyone who is either rich or not kind is patient.
If someone is both humble and not generous then mary is strong and vice versa.
If lucy is not strong then someone is not happy or not wise.
Everyone who is both rich and not generous is either tall or not strong and vice versa.
Everyone who is both not old and not rich is not happy or not strong.
If mary is funny or tall then lucy is funny or not tall and vice versa.
Everyone who is curious or not humble is not kind and vice versa.
Everyone who is both wise and kind is not wise.
Everyone who is either not rich or generous is not tall and vice versa.
If john is both brave and generous then susan is not funny.
Everyone who is both not humble and not strong is kind and vice versa.
If john is either tall or not funny then someone is old.
If someone is not old then fred is happy or patient.
Everyone who is not generous is patient or not old and vice versa.
Everyone who is either kind or not creative is not humble and vice versa.
Someone is strong or happy.
Someone is both creative and wise.
John is either patient or strong.
Alice is generous or old.
Someone is wise.
Someone is both humble and not wise.
Alice is both not funny and wise.
Fred is both generous and brave. | Susan is not creative. | neutral | (((generous(mary)|~brave(mary)))=>((~rich(susan)|~curious(susan))))&
(![X]:((rich(X)<~>~kind(X))=>patient(X)))&
((?[X]:((humble(X)&~generous(X))))<=>(strong(mary)))&
((~strong(lucy))=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:((rich(X)&~generous(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((~old(X)&~rich(X))=>(~happy(X)|~strong(X))))&
(((funny(mary)|tall(mary)))<=>((funny(lucy)|~tall(lucy))))&
(![X]:((curious(X)|~humble(X))<=>~kind(X)))&
(![X]:((wise(X)&kind(X))=>~wise(X)))&
(![X]:((~rich(X)<~>generous(X))<=>~tall(X)))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
((?[X]:(~old(X)))=>((happy(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(patient(X)|~old(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~humble(X)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((creative(X)&wise(X))))&
((patient(john)<~>strong(john)))&
((generous(alice)|old(alice)))&
(?[X]:(wise(X)))&
(?[X]:((humble(X)&~wise(X))))&
((~funny(alice)&wise(alice)))&
((generous(fred)&brave(fred))) | ~creative(susan) | [] | null | 0 |
Everyone who is curious is either not calm or humble and vice versa. If someone is either not curious or not wise then someone is either not calm or not creative and vice versa. If alice is happy then john is either not old or generous. If someone is rich or not funny then john is generous or not creative and vice versa. Everyone who is not tall is both curious and old and vice versa. If someone is not calm or not tall then mary is either tall or not generous and vice versa. Everyone who is not strong or not quiet is brave or not patient. Everyone who is either not patient or not calm is either strong or patient and vice versa. Everyone who is not curious or rich is either rich or not old. If lucy is not calm or not humble then someone is old or happy. If lucy is either not curious or strong then john is wise. If someone is brave then someone is quiet or not creative and vice versa. If someone is not curious or kind then alice is both humble and not happy. If lucy is both not generous and kind then john is either kind or not happy. If someone is not kind or not brave then paul is both not humble and not creative and vice versa. Everyone who is not generous or quiet is not quiet and vice versa. Lucy is old. Mary is wise. Someone is not old. Someone is not generous or funny. Someone is either old or not tall. Paul is both not happy and not patient. Mary is not tall or creative. | Alice is humble. | entailment | (![X]:(curious(X)<=>(~calm(X)<~>humble(X))))&
((?[X]:((~curious(X)<~>~wise(X))))<=>(?[X]:((~calm(X)<~>~creative(X)))))&
((happy(alice))=>((~old(john)<~>generous(john))))&
((?[X]:((rich(X)|~funny(X))))<=>((generous(john)|~creative(john))))&
(![X]:(~tall(X)<=>(curious(X)&old(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>((tall(mary)<~>~generous(mary))))&
(![X]:((~strong(X)|~quiet(X))=>(brave(X)|~patient(X))))&
(![X]:((~patient(X)<~>~calm(X))<=>(strong(X)<~>patient(X))))&
(![X]:((~curious(X)|rich(X))=>(rich(X)<~>~old(X))))&
(((~calm(lucy)|~humble(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((~curious(lucy)<~>strong(lucy)))=>(wise(john)))&
((?[X]:(brave(X)))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((~curious(X)|kind(X))))=>((humble(alice)&~happy(alice))))&
(((~generous(lucy)&kind(lucy)))=>((kind(john)<~>~happy(john))))&
((?[X]:((~kind(X)|~brave(X))))<=>((~humble(paul)&~creative(paul))))&
(![X]:((~generous(X)|quiet(X))<=>~quiet(X)))&
(old(lucy))&
(wise(mary))&
(?[X]:(~old(X)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:((old(X)<~>~tall(X))))&
((~happy(paul)&~patient(paul)))&
((~tall(mary)|creative(mary))) | humble(alice) | [
"p4",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5263481472854675001208455
% SZS output start Proof for 5263481472854675001208455
5. ! [X0] : (~tall(X0) <=> (old(X0) & curious(X0))) [input p4]
13. ? [X0] : (kind(X0) | ~curious(X0)) => (~happy(alice) & humble(alice)) [input p12]
21. ? [X0] : (old(X0) <~> ~tall(X0)) [input p20]
24. ~humble(alice) [input hypothesis]
33. (~happy(alice) & humble(alice)) | ! [X0] : (~kind(X0) & curious(X0)) [ennf transformation 13]
48. ! [X0] : ((~tall(X0) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | tall(X0))) [nnf transformation 5]
49. ! [X0] : ((~tall(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | tall(X0))) [flattening 48]
76. ? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) [nnf transformation 21]
77. ? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) => ((tall(sK10) | ~old(sK10)) & (~tall(sK10) | old(sK10))) [choice axiom]
78. (tall(sK10) | ~old(sK10)) & (~tall(sK10) | old(sK10)) [skolemisation 76,77]
98. tall(X0) | old(X0) [cnf transformation 49]
99. ~tall(X0) | ~old(X0) | ~curious(X0) [cnf transformation 49]
127. humble(alice) | curious(X0) [cnf transformation 33]
145. ~tall(sK10) | old(sK10) [cnf transformation 78]
146. tall(sK10) | ~old(sK10) [cnf transformation 78]
150. ~humble(alice) [cnf transformation 24]
321. 37 <=> ! [X0] : curious(X0) [avatar definition]
322. curious(X0) <- (37) [avatar component clause 321]
325. 38 <=> humble(alice) [avatar definition]
329. 37 | 38 [avatar split clause 127,325,321]
385. tall(sK10) [subsumption resolution 146,98]
386. old(sK10) [subsumption resolution 145,385]
392. ~38 [avatar split clause 150,325]
412. ~old(sK10) | ~curious(sK10) [resolution 99,385]
415. ~curious(sK10) [subsumption resolution 412,386]
416. $false <- (37) [subsumption resolution 415,322]
417. ~37 [avatar contradiction clause 416]
418. $false [avatar sat refutation 329,392,417]
% SZS output end Proof for 5263481472854675001208455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous is not happy and vice versa.
Everyone who is both not generous and not old is old or tall.
Everyone who is either creative or calm is either not funny or curious.
If paul is not curious or not tall then someone is both not curious and not old.
Everyone who is old or not quiet is both not happy and funny.
Everyone who is not tall is either not wise or wise.
Everyone who is either strong or not generous is not happy.
If someone is creative or calm then someone is both not patient and not old.
Everyone who is either brave or rich is not patient and vice versa.
Everyone who is creative is either quiet or funny and vice versa.
Everyone who is either not generous or not rich is not humble or not creative.
Everyone who is both funny and kind is either not wise or not quiet.
Everyone who is funny is not brave.
If paul is not funny then mary is not kind or quiet.
If someone is generous or happy then mary is both not wise and quiet and vice versa.
Everyone who is patient is quiet and vice versa.
Fred is rich.
Someone is rich or not quiet.
Someone is humble or not curious.
Someone is either wise or kind.
Someone is both not old and not creative.
Paul is generous.
Fred is not funny.
Someone is both funny and not kind. | Paul is strong. | contradiction | (![X]:(~generous(X)<=>~happy(X)))&
(![X]:((~generous(X)&~old(X))=>(old(X)|tall(X))))&
(![X]:((creative(X)<~>calm(X))=>(~funny(X)<~>curious(X))))&
(((~curious(paul)|~tall(paul)))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((old(X)|~quiet(X))=>(~happy(X)&funny(X))))&
(![X]:(~tall(X)=>(~wise(X)<~>wise(X))))&
(![X]:((strong(X)<~>~generous(X))=>~happy(X)))&
((?[X]:((creative(X)|calm(X))))=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((brave(X)<~>rich(X))<=>~patient(X)))&
(![X]:(creative(X)<=>(quiet(X)<~>funny(X))))&
(![X]:((~generous(X)<~>~rich(X))=>(~humble(X)|~creative(X))))&
(![X]:((funny(X)&kind(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(funny(X)=>~brave(X)))&
((~funny(paul))=>((~kind(mary)|quiet(mary))))&
((?[X]:((generous(X)|happy(X))))<=>((~wise(mary)&quiet(mary))))&
(![X]:(patient(X)<=>quiet(X)))&
(rich(fred))&
(?[X]:((rich(X)|~quiet(X))))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((wise(X)<~>kind(X))))&
(?[X]:((~old(X)&~creative(X))))&
(generous(paul))&
(~funny(fred))&
(?[X]:((funny(X)&~kind(X)))) | strong(paul) | [
"p0",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2851538686318884352134130
% SZS output start Proof for 2851538686318884352134130
1. ! [X0] : (~generous(X0) <=> ~happy(X0)) [input p0]
7. ! [X0] : ((strong(X0) <~> ~generous(X0)) => ~happy(X0)) [input p6]
22. generous(paul) [input p21]
25. strong(paul) [input hypothesis]
37. ! [X0] : (~happy(X0) | (strong(X0) <=> ~generous(X0))) [ennf transformation 7]
46. ! [X0] : ((~generous(X0) | happy(X0)) & (~happy(X0) | generous(X0))) [nnf transformation 1]
50. ! [X0] : (~happy(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) [nnf transformation 37]
75. ~happy(X0) | generous(X0) [cnf transformation 46]
76. ~generous(X0) | happy(X0) [cnf transformation 46]
84. ~happy(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 50]
115. generous(paul) [cnf transformation 22]
119. strong(paul) [cnf transformation 25]
129. ~strong(X0) | ~happy(X0) [subsumption resolution 84,75]
207. happy(paul) [resolution 76,115]
218. ~happy(paul) [resolution 129,119]
219. $false [subsumption resolution 218,207]
% SZS output end Proof for 2851538686318884352134130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or generous then someone is both not humble and wise and vice versa.
If alice is wise then someone is old.
Everyone who is not patient or patient is both not brave and quiet and vice versa.
Everyone who is either not quiet or not brave is not happy.
If alice is either strong or happy then alice is funny.
Everyone who is either not brave or tall is funny and vice versa.
Everyone who is old or humble is old or not funny and vice versa.
Everyone who is strong or not tall is both creative and wise.
If someone is not wise or old then someone is either quiet or calm.
Everyone who is happy is both not tall and funny and vice versa.
Everyone who is both not patient and not tall is either brave or strong.
Everyone who is humble or not quiet is brave.
Everyone who is happy is both wise and not calm and vice versa.
If someone is humble then lucy is not generous or not wise and vice versa.
If someone is either not patient or curious then someone is both curious and not generous and vice versa.
If someone is either humble or not happy then alice is either not rich or not happy and vice versa.
John is not funny.
Alice is not generous or happy.
Someone is either patient or strong.
Someone is not kind or curious.
Someone is quiet or wise. | Lucy is not humble. | entailment | ((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
((wise(alice))=>(?[X]:(old(X))))&
(![X]:((~patient(X)|patient(X))<=>(~brave(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~brave(X))=>~happy(X)))&
(((strong(alice)<~>happy(alice)))=>(funny(alice)))&
(![X]:((~brave(X)<~>tall(X))<=>funny(X)))&
(![X]:((old(X)|humble(X))<=>(old(X)|~funny(X))))&
(![X]:((strong(X)|~tall(X))=>(creative(X)&wise(X))))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:(happy(X)<=>(~tall(X)&funny(X))))&
(![X]:((~patient(X)&~tall(X))=>(brave(X)<~>strong(X))))&
(![X]:((humble(X)|~quiet(X))=>brave(X)))&
(![X]:(happy(X)<=>(wise(X)&~calm(X))))&
((?[X]:(humble(X)))<=>((~generous(lucy)|~wise(lucy))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((curious(X)&~generous(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~rich(alice)<~>~happy(alice))))&
(~funny(john))&
((~generous(alice)|happy(alice)))&
(?[X]:((patient(X)<~>strong(X))))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:((quiet(X)|wise(X)))) | ~humble(lucy) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7938801889150956415633484
% SZS output start Proof for 7938801889150956415633484
3. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (quiet(X0) & ~brave(X0))) [input p2]
12. ! [X0] : ((~quiet(X0) | humble(X0)) => brave(X0)) [input p11]
22. humble(lucy) [input hypothesis]
34. ! [X0] : (brave(X0) | (quiet(X0) & ~humble(X0))) [ennf transformation 12]
42. ! [X0] : (((patient(X0) | ~patient(X0)) | (~quiet(X0) | brave(X0))) & ((quiet(X0) & ~brave(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 3]
43. ! [X0] : ((patient(X0) | ~patient(X0) | ~quiet(X0) | brave(X0)) & ((quiet(X0) & ~brave(X0)) | (~patient(X0) & patient(X0)))) [flattening 42]
85. ~brave(X0) | patient(X0) [cnf transformation 43]
86. ~brave(X0) | ~patient(X0) [cnf transformation 43]
113. brave(X0) | ~humble(X0) [cnf transformation 34]
141. humble(lucy) [cnf transformation 22]
182. ~brave(X0) [subsumption resolution 85,86]
213. ~humble(X0) [subsumption resolution 113,182]
271. $false [subsumption resolution 141,213]
% SZS output end Proof for 7938801889150956415633484
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not humble is not old or kind.
If lucy is rich or not strong then susan is either rich or not brave.
Everyone who is either not wise or kind is quiet or happy.
If mary is either strong or not tall then someone is both not rich and not quiet.
If alice is not old or kind then fred is either not kind or not old and vice versa.
Everyone who is both humble and not old is either patient or kind and vice versa.
If someone is humble then someone is not humble or humble.
Everyone who is either quiet or funny is curious.
Everyone who is either not brave or not happy is either not funny or brave.
If someone is not brave then alice is not curious and vice versa.
Everyone who is old is both not kind and not rich and vice versa.
If mary is either not happy or not quiet then mary is both wise and patient and vice versa.
If someone is both not funny and calm then someone is not creative and vice versa.
Everyone who is not patient is either brave or tall and vice versa.
If someone is tall or old then someone is either not tall or not calm and vice versa.
Everyone who is not humble or not kind is not rich or calm.
Fred is either curious or not quiet.
Someone is both not calm and not creative.
Susan is both not creative and rich.
Someone is both not patient and generous.
Someone is both not strong and curious.
Mary is either funny or calm.
Fred is quiet or kind. | Mary is wise. | neutral | (![X]:((rich(X)&~humble(X))=>(~old(X)|kind(X))))&
(((rich(lucy)|~strong(lucy)))=>((rich(susan)<~>~brave(susan))))&
(![X]:((~wise(X)<~>kind(X))=>(quiet(X)|happy(X))))&
(((strong(mary)<~>~tall(mary)))=>(?[X]:((~rich(X)&~quiet(X)))))&
(((~old(alice)|kind(alice)))<=>((~kind(fred)<~>~old(fred))))&
(![X]:((humble(X)&~old(X))<=>(patient(X)<~>kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~humble(X)|humble(X)))))&
(![X]:((quiet(X)<~>funny(X))=>curious(X)))&
(![X]:((~brave(X)<~>~happy(X))=>(~funny(X)<~>brave(X))))&
((?[X]:(~brave(X)))<=>(~curious(alice)))&
(![X]:(old(X)<=>(~kind(X)&~rich(X))))&
(((~happy(mary)<~>~quiet(mary)))<=>((wise(mary)&patient(mary))))&
((?[X]:((~funny(X)&calm(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~patient(X)<=>(brave(X)<~>tall(X))))&
((?[X]:((tall(X)|old(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((~humble(X)|~kind(X))=>(~rich(X)|calm(X))))&
((curious(fred)<~>~quiet(fred)))&
(?[X]:((~calm(X)&~creative(X))))&
((~creative(susan)&rich(susan)))&
(?[X]:((~patient(X)&generous(X))))&
(?[X]:((~strong(X)&curious(X))))&
((funny(mary)<~>calm(mary)))&
((quiet(fred)|kind(fred))) | wise(mary) | [] | null | 0 |
Everyone who is either calm or not kind is both not rich and funny.
Everyone who is both brave and kind is not brave and vice versa.
If someone is either not quiet or not humble then someone is either rich or not curious.
Everyone who is either creative or rich is either quiet or tall and vice versa.
Everyone who is both not tall and generous is not old and vice versa.
If someone is both kind and calm then mary is not wise and vice versa.
If someone is not rich or not brave then someone is both old and not curious and vice versa.
If john is not generous or old then mary is curious.
Everyone who is not funny is quiet or happy.
Everyone who is either not funny or not calm is either not funny or kind and vice versa.
Everyone who is not curious or brave is both not old and not kind.
If alice is both quiet and not rich then someone is both funny and tall.
If someone is creative then someone is either funny or not calm.
If someone is either brave or strong then someone is both creative and not old and vice versa.
Everyone who is not rich is tall.
Everyone who is calm or not generous is not patient or not curious and vice versa.
Fred is either not calm or not old.
Someone is both not patient and quiet.
Someone is either happy or curious.
Someone is both not quiet and not curious.
Someone is not happy.
Mary is not quiet.
Someone is patient or not tall. | Mary is not creative. | contradiction | (![X]:((calm(X)<~>~kind(X))=>(~rich(X)&funny(X))))&
(![X]:((brave(X)&kind(X))<=>~brave(X)))&
((?[X]:((~quiet(X)<~>~humble(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(quiet(X)<~>tall(X))))&
(![X]:((~tall(X)&generous(X))<=>~old(X)))&
((?[X]:((kind(X)&calm(X))))<=>(~wise(mary)))&
((?[X]:((~rich(X)|~brave(X))))<=>(?[X]:((old(X)&~curious(X)))))&
(((~generous(john)|old(john)))=>(curious(mary)))&
(![X]:(~funny(X)=>(quiet(X)|happy(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~curious(X)|brave(X))=>(~old(X)&~kind(X))))&
(((quiet(alice)&~rich(alice)))=>(?[X]:((funny(X)&tall(X)))))&
((?[X]:(creative(X)))=>(?[X]:((funny(X)<~>~calm(X)))))&
((?[X]:((brave(X)<~>strong(X))))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:(~rich(X)=>tall(X)))&
(![X]:((calm(X)|~generous(X))<=>(~patient(X)|~curious(X))))&
((~calm(fred)<~>~old(fred)))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
(?[X]:(~happy(X)))&
(~quiet(mary))&
(?[X]:((patient(X)|~tall(X)))) | ~creative(mary) | [
"p1",
"p3",
"p4",
"p6",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1288080666253797686219059
% SZS output start Proof for 1288080666253797686219059
2. ! [X0] : ((kind(X0) & brave(X0)) <=> ~brave(X0)) [input p1]
4. ! [X0] : ((creative(X0) <~> rich(X0)) <=> (quiet(X0) <~> tall(X0))) [input p3]
5. ! [X0] : ((generous(X0) & ~tall(X0)) <=> ~old(X0)) [input p4]
7. ? [X0] : (~brave(X0) | ~rich(X0)) <=> ? [X0] : (~curious(X0) & old(X0)) [input p6]
11. ! [X0] : ((brave(X0) | ~curious(X0)) => (~kind(X0) & ~old(X0))) [input p10]
22. ~quiet(mary) [input p21]
24. ~creative(mary) [input hypothesis]
26. ? [X0] : (~brave(X0) | ~rich(X0)) <=> ? [X1] : (~curious(X1) & old(X1)) [rectify 7]
34. ! [X0] : ((~kind(X0) & ~old(X0)) | (~brave(X0) & curious(X0))) [ennf transformation 11]
40. ! [X0] : (((kind(X0) & brave(X0)) | brave(X0)) & (~brave(X0) | (~kind(X0) | ~brave(X0)))) [nnf transformation 2]
41. ! [X0] : (((kind(X0) & brave(X0)) | brave(X0)) & (~brave(X0) | ~kind(X0) | ~brave(X0))) [flattening 40]
46. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 4]
47. ! [X0] : (((generous(X0) & ~tall(X0)) | old(X0)) & (~old(X0) | (~generous(X0) | tall(X0)))) [nnf transformation 5]
48. ! [X0] : (((generous(X0) & ~tall(X0)) | old(X0)) & (~old(X0) | ~generous(X0) | tall(X0))) [flattening 47]
53. (? [X0] : (~brave(X0) | ~rich(X0)) | ! [X1] : (curious(X1) | ~old(X1))) & (? [X1] : (~curious(X1) & old(X1)) | ! [X0] : (brave(X0) & rich(X0))) [nnf transformation 26]
54. (? [X0] : (~brave(X0) | ~rich(X0)) | ! [X1] : (curious(X1) | ~old(X1))) & (? [X2] : (~curious(X2) & old(X2)) | ! [X3] : (brave(X3) & rich(X3))) [rectify 53]
55. ? [X0] : (~brave(X0) | ~rich(X0)) => (~brave(sK2) | ~rich(sK2)) [choice axiom]
56. ? [X2] : (~curious(X2) & old(X2)) => (~curious(sK3) & old(sK3)) [choice axiom]
57. ((~brave(sK2) | ~rich(sK2)) | ! [X1] : (curious(X1) | ~old(X1))) & ((~curious(sK3) & old(sK3)) | ! [X3] : (brave(X3) & rich(X3))) [skolemisation 54,56,55]
89. brave(X0) | brave(X0) [cnf transformation 41]
96. ~rich(X0) | quiet(X0) | creative(X0) | tall(X0) [cnf transformation 46]
104. ~tall(X0) | old(X0) [cnf transformation 48]
109. old(sK3) | rich(X3) [cnf transformation 57]
126. ~old(X0) | ~brave(X0) [cnf transformation 34]
153. ~quiet(mary) [cnf transformation 22]
155. ~creative(mary) [cnf transformation 24]
161. brave(X0) [duplicate literal removal 89]
202. 9 <=> ! [X3] : rich(X3) [avatar definition]
203. rich(X3) <- (9) [avatar component clause 202]
210. 11 <=> old(sK3) [avatar definition]
212. old(sK3) <- (11) [avatar component clause 210]
213. 9 | 11 [avatar split clause 109,210,202]
229. ~old(X0) [subsumption resolution 126,161]
302. $false <- (11) [subsumption resolution 212,229]
303. ~11 [avatar contradiction clause 302]
328. tall(X0) | creative(X0) | quiet(X0) <- (9) [resolution 96,203]
352. creative(X2) | quiet(X2) | old(X2) <- (9) [resolution 328,104]
363. creative(X2) | quiet(X2) <- (9) [subsumption resolution 352,229]
396. quiet(mary) <- (9) [resolution 363,155]
400. $false <- (9) [subsumption resolution 396,153]
401. ~9 [avatar contradiction clause 400]
402. $false [avatar sat refutation 213,303,401]
% SZS output end Proof for 1288080666253797686219059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not brave then someone is either not curious or not tall and vice versa. Everyone who is either patient or not quiet is humble. Everyone who is either tall or not curious is both wise and not kind. Everyone who is either patient or not tall is both not humble and quiet and vice versa. If someone is tall then someone is either not creative or not tall. Everyone who is not brave or not humble is tall. Everyone who is not calm or not generous is generous or not quiet and vice versa. If someone is not generous or brave then someone is funny and vice versa. Everyone who is both not quiet and tall is not humble. Everyone who is both kind and calm is both patient and funny. Everyone who is either not generous or generous is not happy. Everyone who is rich is tall or not funny and vice versa. Everyone who is either not calm or not rich is kind. Everyone who is kind is either not humble or wise and vice versa. If someone is not patient or not wise then alice is not funny or not rich and vice versa. If someone is creative or humble then fred is either humble or not creative. Someone is either not patient or humble. Someone is tall. Someone is quiet. Someone is not quiet. Someone is humble or not tall. Someone is both brave and old. | Alice is not funny. | entailment | ((~brave(alice))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:((patient(X)<~>~quiet(X))=>humble(X)))&
(![X]:((tall(X)<~>~curious(X))=>(wise(X)&~kind(X))))&
(![X]:((patient(X)<~>~tall(X))<=>(~humble(X)&quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((~brave(X)|~humble(X))=>tall(X)))&
(![X]:((~calm(X)|~generous(X))<=>(generous(X)|~quiet(X))))&
((?[X]:((~generous(X)|brave(X))))<=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)&tall(X))=>~humble(X)))&
(![X]:((kind(X)&calm(X))=>(patient(X)&funny(X))))&
(![X]:((~generous(X)<~>generous(X))=>~happy(X)))&
(![X]:(rich(X)<=>(tall(X)|~funny(X))))&
(![X]:((~calm(X)<~>~rich(X))=>kind(X)))&
(![X]:(kind(X)<=>(~humble(X)<~>wise(X))))&
((?[X]:((~patient(X)|~wise(X))))<=>((~funny(alice)|~rich(alice))))&
((?[X]:((creative(X)|humble(X))))=>((humble(fred)<~>~creative(fred))))&
(?[X]:((~patient(X)<~>humble(X))))&
(?[X]:(tall(X)))&
(?[X]:(quiet(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((brave(X)&old(X)))) | ~funny(alice) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p11",
"p13",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3591072120518186202623954
% SZS output start Proof for 3591072120518186202623954
1. ~brave(alice) <=> ? [X0] : (~curious(X0) <~> ~tall(X0)) [input p0]
2. ! [X0] : ((patient(X0) <~> ~quiet(X0)) => humble(X0)) [input p1]
3. ! [X0] : ((tall(X0) <~> ~curious(X0)) => (~kind(X0) & wise(X0))) [input p2]
4. ! [X0] : ((patient(X0) <~> ~tall(X0)) <=> (quiet(X0) & ~humble(X0))) [input p3]
6. ! [X0] : ((~humble(X0) | ~brave(X0)) => tall(X0)) [input p5]
12. ! [X0] : (rich(X0) <=> (~funny(X0) | tall(X0))) [input p11]
14. ! [X0] : (kind(X0) <=> (~humble(X0) <~> wise(X0))) [input p13]
15. ? [X0] : (~wise(X0) | ~patient(X0)) <=> (~rich(alice) | ~funny(alice)) [input p14]
17. ? [X0] : (~patient(X0) <~> humble(X0)) [input p16]
18. ? [X0] : tall(X0) [input p17]
23. funny(alice) [input hypothesis]
28. ! [X0] : (humble(X0) | (patient(X0) <=> ~quiet(X0))) [ennf transformation 2]
29. ! [X0] : ((~kind(X0) & wise(X0)) | (tall(X0) <=> ~curious(X0))) [ennf transformation 3]
31. ! [X0] : (tall(X0) | (humble(X0) & brave(X0))) [ennf transformation 6]
38. (~brave(alice) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X0] : ((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | brave(alice)) [nnf transformation 1]
39. (~brave(alice) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) | brave(alice)) [rectify 38]
40. ? [X1] : ((tall(X1) | curious(X1)) & (~tall(X1) | ~curious(X1))) => ((tall(sK0) | curious(sK0)) & (~tall(sK0) | ~curious(sK0))) [choice axiom]
41. (~brave(alice) | ! [X0] : ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(sK0) | curious(sK0)) & (~tall(sK0) | ~curious(sK0))) | brave(alice)) [skolemisation 39,40]
42. ! [X0] : (humble(X0) | ((patient(X0) | quiet(X0)) & (~quiet(X0) | ~patient(X0)))) [nnf transformation 28]
43. ! [X0] : ((~kind(X0) & wise(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) [nnf transformation 29]
44. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [nnf transformation 4]
45. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [flattening 44]
57. ! [X0] : ((rich(X0) | (funny(X0) & ~tall(X0))) & ((~funny(X0) | tall(X0)) | ~rich(X0))) [nnf transformation 12]
58. ! [X0] : ((rich(X0) | (funny(X0) & ~tall(X0))) & (~funny(X0) | tall(X0) | ~rich(X0))) [flattening 57]
60. ! [X0] : ((kind(X0) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) & (((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | ~kind(X0))) [nnf transformation 14]
61. (? [X0] : (~wise(X0) | ~patient(X0)) | (rich(alice) & funny(alice))) & ((~rich(alice) | ~funny(alice)) | ! [X0] : (wise(X0) & patient(X0))) [nnf transformation 15]
62. (? [X0] : (~wise(X0) | ~patient(X0)) | (rich(alice) & funny(alice))) & (~rich(alice) | ~funny(alice) | ! [X0] : (wise(X0) & patient(X0))) [flattening 61]
63. (? [X0] : (~wise(X0) | ~patient(X0)) | (rich(alice) & funny(alice))) & (~rich(alice) | ~funny(alice) | ! [X1] : (wise(X1) & patient(X1))) [rectify 62]
64. ? [X0] : (~wise(X0) | ~patient(X0)) => (~wise(sK4) | ~patient(sK4)) [choice axiom]
65. ((~wise(sK4) | ~patient(sK4)) | (rich(alice) & funny(alice))) & (~rich(alice) | ~funny(alice) | ! [X1] : (wise(X1) & patient(X1))) [skolemisation 63,64]
67. ? [X0] : ((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) [nnf transformation 17]
68. ? [X0] : ((~humble(X0) | patient(X0)) & (humble(X0) | ~patient(X0))) => ((~humble(sK5) | patient(sK5)) & (humble(sK5) | ~patient(sK5))) [choice axiom]
69. (~humble(sK5) | patient(sK5)) & (humble(sK5) | ~patient(sK5)) [skolemisation 67,68]
70. ? [X0] : tall(X0) => tall(sK6) [choice axiom]
71. tall(sK6) [skolemisation 18,70]
83. ~brave(alice) | ~curious(X0) | tall(X0) [cnf transformation 41]
84. ~quiet(X0) | humble(X0) | ~patient(X0) [cnf transformation 42]
85. humble(X0) | patient(X0) | quiet(X0) [cnf transformation 42]
87. wise(X0) | tall(X0) | curious(X0) [cnf transformation 43]
89. ~kind(X0) | tall(X0) | curious(X0) [cnf transformation 43]
90. ~humble(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 45]
92. ~patient(X0) | ~tall(X0) | quiet(X0) [cnf transformation 45]
94. ~tall(X0) | patient(X0) | ~quiet(X0) | humble(X0) [cnf transformation 45]
98. tall(X0) | brave(X0) [cnf transformation 31]
99. humble(X0) | tall(X0) [cnf transformation 31]
111. ~tall(X0) | rich(X0) [cnf transformation 58]
118. ~wise(X0) | ~humble(X0) | kind(X0) [cnf transformation 60]
119. ~rich(alice) | ~funny(alice) | patient(X1) [cnf transformation 65]
127. humble(sK5) | ~patient(sK5) [cnf transformation 69]
128. ~humble(sK5) | patient(sK5) [cnf transformation 69]
129. tall(sK6) [cnf transformation 71]
134. funny(alice) [cnf transformation 23]
138. 1 <=> ! [X0] : (~curious(X0) | tall(X0)) [avatar definition]
139. ~curious(X0) | tall(X0) <- (1) [avatar component clause 138]
141. 2 <=> brave(alice) [avatar definition]
143. ~brave(alice) <- (~2) [avatar component clause 141]
144. 1 | ~2 [avatar split clause 83,141,138]
159. ~tall(X0) | patient(X0) | humble(X0) [subsumption resolution 94,85]
198. 15 <=> rich(alice) [avatar definition]
199. ~rich(alice) <- (~15) [avatar component clause 198]
211. 18 <=> funny(alice) [avatar definition]
220. 20 <=> ! [X1] : patient(X1) [avatar definition]
221. patient(X1) <- (20) [avatar component clause 220]
222. 20 | ~18 | ~15 [avatar split clause 119,198,211,220]
242. 25 <=> patient(sK5) [avatar definition]
243. ~patient(sK5) <- (~25) [avatar component clause 242]
244. patient(sK5) <- (25) [avatar component clause 242]
246. 26 <=> humble(sK5) [avatar definition]
247. humble(sK5) <- (26) [avatar component clause 246]
248. ~humble(sK5) <- (~26) [avatar component clause 246]
249. 25 | ~26 [avatar split clause 128,246,242]
250. ~25 | 26 [avatar split clause 127,246,242]
252. 18 [avatar split clause 134,211]
258. tall(sK5) <- (~26) [resolution 99,248]
260. rich(X0) | brave(X0) [resolution 111,98]
377. 41 <=> patient(sK6) [avatar definition]
378. ~patient(sK6) <- (~41) [avatar component clause 377]
379. patient(sK6) <- (41) [avatar component clause 377]
397. 42 <=> humble(sK6) [avatar definition]
399. humble(sK6) <- (42) [avatar component clause 397]
401. ~humble(X0) | kind(X0) | tall(X0) | curious(X0) [resolution 118,87]
403. kind(X0) | tall(X0) | curious(X0) [subsumption resolution 401,99]
404. tall(X0) | curious(X0) [subsumption resolution 403,89]
410. patient(sK5) | humble(sK5) <- (~26) [resolution 159,258]
412. humble(sK5) <- (~25, ~26) [subsumption resolution 410,243]
413. $false <- (~25, ~26) [subsumption resolution 412,248]
414. 25 | 26 [avatar contradiction clause 413]
423. 44 <=> tall(sK5) [avatar definition]
425. ~tall(sK5) <- (~44) [avatar component clause 423]
429. ~tall(sK5) | ~patient(sK5) <- (26) [resolution 247,90]
431. brave(alice) <- (~15) [resolution 260,199]
434. $false <- (~2, ~15) [subsumption resolution 431,143]
435. 2 | 15 [avatar contradiction clause 434]
485. ~tall(X0) | quiet(X0) <- (20) [resolution 221,92]
536. quiet(sK6) <- (20) [resolution 485,129]
560. humble(sK6) | ~patient(sK6) <- (20) [resolution 536,84]
565. humble(sK6) <- (20, 41) [subsumption resolution 560,379]
566. 42 | ~20 | ~41 [avatar split clause 565,377,220,397]
587. ~tall(sK5) <- (25, 26) [subsumption resolution 429,244]
588. ~44 | ~25 | ~26 [avatar split clause 587,246,242,423]
591. tall(X0) <- (1) [subsumption resolution 139,404]
595. $false <- (1, ~44) [subsumption resolution 425,591]
596. ~1 | 44 [avatar contradiction clause 595]
696. ~tall(sK6) | ~patient(sK6) <- (42) [resolution 399,90]
697. ~patient(sK6) <- (42) [subsumption resolution 696,129]
700. $false <- (20, 42) [subsumption resolution 697,221]
701. ~20 | ~42 [avatar contradiction clause 700]
702. $false <- (20, ~41) [subsumption resolution 378,221]
703. ~20 | 41 [avatar contradiction clause 702]
704. $false [avatar sat refutation 144,222,249,250,252,414,435,566,588,596,701,703]
% SZS output end Proof for 3591072120518186202623954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and not old then someone is not funny.
If someone is both not generous and not creative then mary is both funny and not wise and vice versa.
Everyone who is funny is either old or not calm and vice versa.
If someone is both calm and rich then fred is either not kind or funny and vice versa.
Everyone who is both strong and not quiet is either strong or funny.
If someone is not generous then someone is both not quiet and happy.
If someone is not creative then someone is curious and vice versa.
If someone is both not kind and not humble then lucy is either kind or not strong and vice versa.
If someone is not generous then someone is not patient or strong and vice versa.
Everyone who is both rich and patient is both strong and not patient.
Everyone who is both tall and not quiet is both not patient and patient and vice versa.
If mary is either not wise or old then mary is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Paul is both happy and rich.
Someone is curious.
Fred is both tall and kind.
Someone is both quiet and not curious.
Someone is either not calm or not strong.
John is both rich and not tall.
Alice is either not generous or funny.
Susan is either not kind or not funny. | Mary is not calm. | neutral | ((?[X]:((patient(X)&~old(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~generous(X)&~creative(X))))<=>((funny(mary)&~wise(mary))))&
(![X]:(funny(X)<=>(old(X)<~>~calm(X))))&
((?[X]:((calm(X)&rich(X))))<=>((~kind(fred)<~>funny(fred))))&
(![X]:((strong(X)&~quiet(X))=>(strong(X)<~>funny(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:(curious(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>((kind(lucy)<~>~strong(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((rich(X)&patient(X))=>(strong(X)&~patient(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~patient(X)&patient(X))))&
(((~wise(mary)<~>old(mary)))=>((~happy(mary)<~>rich(mary))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
((happy(paul)&rich(paul)))&
(?[X]:(curious(X)))&
((tall(fred)&kind(fred)))&
(?[X]:((quiet(X)&~curious(X))))&
(?[X]:((~calm(X)<~>~strong(X))))&
((rich(john)&~tall(john)))&
((~generous(alice)<~>funny(alice)))&
((~kind(susan)<~>~funny(susan))) | ~calm(mary) | [] | null | 0 |
If someone is either not happy or not humble then fred is either curious or happy.
If someone is not brave or not rich then john is either generous or wise.
If lucy is strong then someone is either not kind or not rich and vice versa.
Everyone who is either not curious or rich is not creative or not brave and vice versa.
Everyone who is not kind or not patient is both rich and funny.
Everyone who is brave or not patient is both not funny and old.
If someone is both tall and not kind then alice is not creative and vice versa.
Everyone who is either not funny or not happy is either rich or not generous and vice versa.
Everyone who is both not wise and not old is both happy and kind.
Everyone who is either not rich or not generous is quiet and vice versa.
Everyone who is not strong or old is either wise or not curious and vice versa.
If someone is not rich or patient then someone is either not quiet or not old.
Everyone who is not calm is both kind and not patient and vice versa.
If someone is generous or not humble then someone is not calm or not strong.
If someone is both wise and not creative then susan is both rich and not calm and vice versa.
Someone is either not quiet or not funny.
Someone is wise or generous.
Someone is quiet or funny.
Someone is both curious and quiet.
Alice is either calm or quiet.
Mary is both not brave and not curious.
Susan is not happy or not calm.
John is tall or not kind. | Alice is not calm. | contradiction | ((?[X]:((~happy(X)<~>~humble(X))))=>((curious(fred)<~>happy(fred))))&
((?[X]:((~brave(X)|~rich(X))))=>((generous(john)<~>wise(john))))&
((strong(lucy))<=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~kind(X)|~patient(X))=>(rich(X)&funny(X))))&
(![X]:((brave(X)|~patient(X))=>(~funny(X)&old(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~creative(alice)))&
(![X]:((~funny(X)<~>~happy(X))<=>(rich(X)<~>~generous(X))))&
(![X]:((~wise(X)&~old(X))=>(happy(X)&kind(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>quiet(X)))&
(![X]:((~strong(X)|old(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:((~rich(X)|patient(X))))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(![X]:(~calm(X)<=>(kind(X)&~patient(X))))&
((?[X]:((generous(X)|~humble(X))))=>(?[X]:((~calm(X)|~strong(X)))))&
((?[X]:((wise(X)&~creative(X))))<=>((rich(susan)&~calm(susan))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:((curious(X)&quiet(X))))&
((calm(alice)<~>quiet(alice)))&
((~brave(mary)&~curious(mary)))&
((~happy(susan)|~calm(susan)))&
((tall(john)|~kind(john))) | ~calm(alice) | [
"p4",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 166387177467667195478320
% SZS output start Proof for 166387177467667195478320
5. ! [X0] : ((~patient(X0) | ~kind(X0)) => (funny(X0) & rich(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | brave(X0)) => (old(X0) & ~funny(X0))) [input p5]
13. ! [X0] : (~calm(X0) <=> (~patient(X0) & kind(X0))) [input p12]
24. ~calm(alice) [input hypothesis]
29. ! [X0] : ((funny(X0) & rich(X0)) | (patient(X0) & kind(X0))) [ennf transformation 5]
30. ! [X0] : ((old(X0) & ~funny(X0)) | (patient(X0) & ~brave(X0))) [ennf transformation 6]
55. ! [X0] : ((~calm(X0) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | calm(X0))) [nnf transformation 13]
56. ! [X0] : ((~calm(X0) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | calm(X0))) [flattening 55]
96. funny(X0) | patient(X0) [cnf transformation 29]
98. ~funny(X0) | patient(X0) [cnf transformation 30]
129. ~patient(X0) | calm(X0) [cnf transformation 56]
149. ~calm(alice) [cnf transformation 24]
208. patient(X0) [subsumption resolution 98,96]
241. calm(X0) [subsumption resolution 129,208]
296. $false [subsumption resolution 149,241]
% SZS output end Proof for 166387177467667195478320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not old is both not quiet and old. If susan is humble then mary is either not calm or not kind. Everyone who is both happy and humble is both humble and not strong and vice versa. Everyone who is both not funny and happy is both not generous and patient and vice versa. If susan is both rich and not humble then john is not generous. Everyone who is old is either happy or tall and vice versa. Everyone who is not happy is both calm and not curious and vice versa. Everyone who is both not tall and creative is either quiet or tall. Everyone who is either strong or not tall is both not calm and old. Everyone who is both patient and not brave is either generous or kind. If someone is not humble or not generous then someone is both not patient and strong. Everyone who is calm is either not brave or strong. If lucy is curious then fred is both not funny and happy and vice versa. If mary is not calm then lucy is both not generous and not calm. Everyone who is rich or not calm is both strong and tall. If someone is happy then fred is either not curious or quiet and vice versa. Someone is both strong and not quiet. Someone is either not funny or strong. Someone is both wise and not rich. Someone is not generous. Someone is funny or kind. Mary is either not generous or wise. Mary is both curious and brave. | Lucy is curious. | contradiction | (![X]:((~tall(X)<~>~old(X))=>(~quiet(X)&old(X))))&
((humble(susan))=>((~calm(mary)<~>~kind(mary))))&
(![X]:((happy(X)&humble(X))<=>(humble(X)&~strong(X))))&
(![X]:((~funny(X)&happy(X))<=>(~generous(X)&patient(X))))&
(((rich(susan)&~humble(susan)))=>(~generous(john)))&
(![X]:(old(X)<=>(happy(X)<~>tall(X))))&
(![X]:(~happy(X)<=>(calm(X)&~curious(X))))&
(![X]:((~tall(X)&creative(X))=>(quiet(X)<~>tall(X))))&
(![X]:((strong(X)<~>~tall(X))=>(~calm(X)&old(X))))&
(![X]:((patient(X)&~brave(X))=>(generous(X)<~>kind(X))))&
((?[X]:((~humble(X)|~generous(X))))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:(calm(X)=>(~brave(X)<~>strong(X))))&
((curious(lucy))<=>((~funny(fred)&happy(fred))))&
((~calm(mary))=>((~generous(lucy)&~calm(lucy))))&
(![X]:((rich(X)|~calm(X))=>(strong(X)&tall(X))))&
((?[X]:(happy(X)))<=>((~curious(fred)<~>quiet(fred))))&
(?[X]:((strong(X)&~quiet(X))))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((wise(X)&~rich(X))))&
(?[X]:(~generous(X)))&
(?[X]:((funny(X)|kind(X))))&
((~generous(mary)<~>wise(mary)))&
((curious(mary)&brave(mary))) | curious(lucy) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7639792870242964669919324
% SZS output start Proof for 7639792870242964669919324
1. ! [X0] : ((~tall(X0) <~> ~old(X0)) => (old(X0) & ~quiet(X0))) [input p0]
6. ! [X0] : (old(X0) <=> (happy(X0) <~> tall(X0))) [input p5]
7. ! [X0] : (~happy(X0) <=> (~curious(X0) & calm(X0))) [input p6]
13. curious(lucy) <=> (happy(fred) & ~funny(fred)) [input p12]
15. ! [X0] : ((~calm(X0) | rich(X0)) => (tall(X0) & strong(X0))) [input p14]
16. ? [X0] : happy(X0) <=> (~curious(fred) <~> quiet(fred)) [input p15]
23. brave(mary) & curious(mary) [input p22]
24. curious(lucy) [input hypothesis]
28. ! [X0] : (~calm(X0) => (tall(X0) & strong(X0))) [pure predicate removal 15]
30. ! [X0] : ((old(X0) & ~quiet(X0)) | (~tall(X0) <=> ~old(X0))) [ennf transformation 1]
38. ! [X0] : ((tall(X0) & strong(X0)) | calm(X0)) [ennf transformation 28]
39. ! [X0] : ((old(X0) & ~quiet(X0)) | ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0)))) [nnf transformation 30]
45. ! [X0] : ((old(X0) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0)))) & (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | ~old(X0))) [nnf transformation 6]
46. ! [X0] : ((~happy(X0) | (curious(X0) | ~calm(X0))) & ((~curious(X0) & calm(X0)) | happy(X0))) [nnf transformation 7]
47. ! [X0] : ((~happy(X0) | curious(X0) | ~calm(X0)) & ((~curious(X0) & calm(X0)) | happy(X0))) [flattening 46]
54. (curious(lucy) | (~happy(fred) | funny(fred))) & ((happy(fred) & ~funny(fred)) | ~curious(lucy)) [nnf transformation 13]
55. (curious(lucy) | ~happy(fred) | funny(fred)) & ((happy(fred) & ~funny(fred)) | ~curious(lucy)) [flattening 54]
56. (? [X0] : happy(X0) | ((~curious(fred) | ~quiet(fred)) & (quiet(fred) | curious(fred)))) & (((~quiet(fred) | curious(fred)) & (quiet(fred) | ~curious(fred))) | ! [X0] : ~happy(X0)) [nnf transformation 16]
57. (? [X0] : happy(X0) | ((~curious(fred) | ~quiet(fred)) & (quiet(fred) | curious(fred)))) & (((~quiet(fred) | curious(fred)) & (quiet(fred) | ~curious(fred))) | ! [X1] : ~happy(X1)) [rectify 56]
58. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
59. (happy(sK1) | ((~curious(fred) | ~quiet(fred)) & (quiet(fred) | curious(fred)))) & (((~quiet(fred) | curious(fred)) & (quiet(fred) | ~curious(fred))) | ! [X1] : ~happy(X1)) [skolemisation 57,58]
72. ~quiet(X0) | ~old(X0) | tall(X0) [cnf transformation 39]
75. old(X0) | ~tall(X0) | old(X0) [cnf transformation 39]
87. ~tall(X0) | ~happy(X0) | ~old(X0) [cnf transformation 45]
88. old(X0) | tall(X0) | ~happy(X0) [cnf transformation 45]
90. happy(X0) | calm(X0) [cnf transformation 47]
91. ~curious(X0) | happy(X0) [cnf transformation 47]
92. ~happy(X0) | curious(X0) | ~calm(X0) [cnf transformation 47]
106. happy(fred) | ~curious(lucy) [cnf transformation 55]
111. calm(X0) | tall(X0) [cnf transformation 38]
112. quiet(fred) | ~curious(fred) | ~happy(X1) [cnf transformation 59]
125. curious(mary) [cnf transformation 23]
127. curious(lucy) [cnf transformation 24]
128. ~tall(X0) | old(X0) [duplicate literal removal 75]
143. ~happy(X0) | old(X0) [subsumption resolution 88,128]
144. ~happy(X0) | ~tall(X0) [subsumption resolution 87,143]
169. 9 <=> happy(fred) [avatar definition]
170. happy(fred) <- (9) [avatar component clause 169]
173. 10 <=> curious(lucy) [avatar definition]
177. ~10 | 9 [avatar split clause 106,169,173]
190. 13 <=> quiet(fred) [avatar definition]
191. quiet(fred) <- (13) [avatar component clause 190]
194. 14 <=> curious(fred) [avatar definition]
204. 16 <=> ! [X1] : ~happy(X1) [avatar definition]
205. ~happy(X1) <- (16) [avatar component clause 204]
207. 16 | ~14 | 13 [avatar split clause 112,190,194,204]
237. 10 [avatar split clause 127,173]
238. happy(mary) [resolution 91,125]
246. old(fred) <- (9) [resolution 143,170]
248. ~tall(X0) | calm(X0) [resolution 144,90]
251. ~tall(fred) <- (9) [resolution 144,170]
253. calm(X0) [subsumption resolution 248,111]
331. curious(fred) | ~calm(fred) <- (9) [resolution 92,170]
337. curious(fred) <- (9) [subsumption resolution 331,253]
338. 14 | ~9 [avatar split clause 337,169,194]
341. $false <- (16) [resolution 205,238]
348. ~16 [avatar contradiction clause 341]
349. ~old(fred) | tall(fred) <- (13) [resolution 191,72]
350. tall(fred) <- (9, 13) [subsumption resolution 349,246]
351. $false <- (9, 13) [subsumption resolution 350,251]
352. ~9 | ~13 [avatar contradiction clause 351]
353. $false [avatar sat refutation 177,207,237,338,348,352]
% SZS output end Proof for 7639792870242964669919324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or not brave is either happy or not wise and vice versa. If someone is both not kind and not happy then lucy is kind or not creative and vice versa. Everyone who is either wise or kind is not old or not funny. Everyone who is not creative or not happy is generous. Everyone who is either humble or old is both not curious and not humble and vice versa. Everyone who is patient or not generous is rich. Everyone who is either generous or rich is generous and vice versa. Everyone who is not humble is both happy and strong and vice versa. If someone is not wise then fred is both happy and not happy. If someone is tall then lucy is not generous or not patient and vice versa. If someone is not kind then someone is quiet or generous. If fred is brave or not kind then mary is humble. If someone is either not strong or strong then someone is not tall or strong and vice versa. If someone is both happy and not calm then lucy is not creative or strong. Everyone who is either not curious or not strong is calm or not quiet. If susan is wise or not old then someone is curious or rich. Susan is not old. Someone is strong or funny. Alice is both funny and old. Susan is calm or not happy. Alice is not tall or rich. Someone is not strong or not tall. | Lucy is not old. | neutral | (![X]:((~kind(X)<~>~brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((kind(lucy)|~creative(lucy))))&
(![X]:((wise(X)<~>kind(X))=>(~old(X)|~funny(X))))&
(![X]:((~creative(X)|~happy(X))=>generous(X)))&
(![X]:((humble(X)<~>old(X))<=>(~curious(X)&~humble(X))))&
(![X]:((patient(X)|~generous(X))=>rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>generous(X)))&
(![X]:(~humble(X)<=>(happy(X)&strong(X))))&
((?[X]:(~wise(X)))=>((happy(fred)&~happy(fred))))&
((?[X]:(tall(X)))<=>((~generous(lucy)|~patient(lucy))))&
((?[X]:(~kind(X)))=>(?[X]:((quiet(X)|generous(X)))))&
(((brave(fred)|~kind(fred)))=>(humble(mary)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
((?[X]:((happy(X)&~calm(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((~curious(X)<~>~strong(X))=>(calm(X)|~quiet(X))))&
(((wise(susan)|~old(susan)))=>(?[X]:((curious(X)|rich(X)))))&
(~old(susan))&
(?[X]:((strong(X)|funny(X))))&
((funny(alice)&old(alice)))&
((calm(susan)|~happy(susan)))&
((~tall(alice)|rich(alice)))&
(?[X]:((~strong(X)|~tall(X)))) | ~old(lucy) | [] | null | 0 |
If fred is either not quiet or curious then someone is either happy or not wise. Everyone who is both calm and not funny is not curious. Everyone who is rich is not happy. If someone is either patient or creative then someone is patient or curious and vice versa. Everyone who is either rich or wise is either not funny or not brave and vice versa. Everyone who is both curious and brave is not humble or not generous. If someone is both rich and not generous then fred is not strong and vice versa. Everyone who is either tall or not old is both kind and not curious. If someone is quiet or not funny then paul is old or not funny and vice versa. Everyone who is wise or not rich is either wise or not strong. If someone is both not funny and wise then someone is both old and strong. Everyone who is not old or not wise is generous and vice versa. If someone is kind then someone is both not humble and not old and vice versa. Everyone who is either not strong or rich is not curious or not calm and vice versa. Everyone who is both kind and wise is wise. Everyone who is either funny or not happy is not happy and vice versa. Someone is either patient or not brave. Someone is not curious or tall. Someone is both not kind and not calm. Fred is funny or not rich. John is not brave. Someone is not humble or not old. Alice is either not old or generous. Mary is both rich and wise. | Mary is not happy. | entailment | (((~quiet(fred)<~>curious(fred)))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((calm(X)&~funny(X))=>~curious(X)))&
(![X]:(rich(X)=>~happy(X)))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((rich(X)<~>wise(X))<=>(~funny(X)<~>~brave(X))))&
(![X]:((curious(X)&brave(X))=>(~humble(X)|~generous(X))))&
((?[X]:((rich(X)&~generous(X))))<=>(~strong(fred)))&
(![X]:((tall(X)<~>~old(X))=>(kind(X)&~curious(X))))&
((?[X]:((quiet(X)|~funny(X))))<=>((old(paul)|~funny(paul))))&
(![X]:((wise(X)|~rich(X))=>(wise(X)<~>~strong(X))))&
((?[X]:((~funny(X)&wise(X))))=>(?[X]:((old(X)&strong(X)))))&
(![X]:((~old(X)|~wise(X))<=>generous(X)))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~strong(X)<~>rich(X))<=>(~curious(X)|~calm(X))))&
(![X]:((kind(X)&wise(X))=>wise(X)))&
(![X]:((funny(X)<~>~happy(X))<=>~happy(X)))&
(?[X]:((patient(X)<~>~brave(X))))&
(?[X]:((~curious(X)|tall(X))))&
(?[X]:((~kind(X)&~calm(X))))&
((funny(fred)|~rich(fred)))&
(~brave(john))&
(?[X]:((~humble(X)|~old(X))))&
((~old(alice)<~>generous(alice)))&
((rich(mary)&wise(mary))) | ~happy(mary) | [
"p2",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3102613011833289431476263
% SZS output start Proof for 3102613011833289431476263
3. ! [X0] : (rich(X0) => ~happy(X0)) [input p2]
24. wise(mary) & rich(mary) [input p23]
25. happy(mary) [input hypothesis]
32. ! [X0] : (~happy(X0) | ~rich(X0)) [ennf transformation 3]
88. ~rich(X0) | ~happy(X0) [cnf transformation 32]
148. rich(mary) [cnf transformation 24]
150. happy(mary) [cnf transformation 25]
321. ~happy(mary) [resolution 88,148]
323. $false [subsumption resolution 321,150]
% SZS output end Proof for 3102613011833289431476263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is not humble or funny is both not curious and tall.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
Everyone who is creative is both strong and not creative.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Everyone who is either humble or not humble is not humble.
Someone is not brave or patient.
Someone is either not old or tall.
Susan is not brave.
Fred is both funny and not creative.
Susan is either old or kind. | Fred is not quiet. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((~humble(X)|funny(X))=>(~curious(X)&tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>(strong(X)&~creative(X))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
(![X]:((humble(X)<~>~humble(X))=>~humble(X)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~old(X)<~>tall(X))))&
(~brave(susan))&
((funny(fred)&~creative(fred)))&
((old(susan)<~>kind(susan))) | ~quiet(fred) | [
"p2",
"p3",
"p7",
"p8",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 342997813456658284226854
% SZS output start Proof for 342997813456658284226854
3. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p2]
4. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p3]
8. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p7]
9. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p8]
12. ? [X0] : ~wise(X0) <=> ? [X0] : (~calm(X0) <~> ~quiet(X0)) [input p11]
13. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
20. ~creative(fred) & funny(fred) [input p19]
22. quiet(fred) [input hypothesis]
23. ? [X0] : ~wise(X0) <=> ? [X1] : (~calm(X1) <~> ~quiet(X1)) [rectify 12]
25. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 3]
32. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 13]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 4]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 8]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
45. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 9]
46. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 45]
55. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X1] : ((quiet(X1) | calm(X1)) & (~quiet(X1) | ~calm(X1))) | ! [X0] : wise(X0)) [nnf transformation 23]
56. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) | ! [X3] : wise(X3)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. ? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) => ((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) [choice axiom]
59. (~wise(sK3) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) | ! [X3] : wise(X3)) [skolemisation 56,58,57]
63. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 63]
80. ~rich(X0) | happy(X0) [cnf transformation 25]
84. ~happy(X0) | creative(X0) | patient(X0) [cnf transformation 36]
93. ~funny(fred) | wise(X1) [cnf transformation 44]
96. ~patient(fred) | creative(alice) [cnf transformation 46]
109. ~wise(sK3) | ~quiet(X1) | calm(X1) [cnf transformation 59]
112. ~creative(X0) | ~creative(X0) [cnf transformation 32]
117. rich(X0) | ~calm(X0) | rich(X0) | happy(X0) [cnf transformation 64]
129. funny(fred) [cnf transformation 20]
133. quiet(fred) [cnf transformation 22]
136. rich(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 117]
138. ~creative(X0) [duplicate literal removal 112]
144. 2 <=> funny(fred) [avatar definition]
153. 4 <=> ! [X1] : wise(X1) [avatar definition]
154. wise(X1) <- (4) [avatar component clause 153]
155. 4 | ~2 [avatar split clause 93,144,153]
158. 5 <=> patient(fred) [avatar definition]
170. 8 <=> creative(alice) [avatar definition]
171. creative(alice) <- (8) [avatar component clause 170]
176. 8 | ~5 [avatar split clause 96,158,170]
216. 17 <=> wise(sK3) [avatar definition]
218. ~wise(sK3) <- (~17) [avatar component clause 216]
221. 18 <=> ! [X1] : (~quiet(X1) | calm(X1)) [avatar definition]
222. ~quiet(X1) | calm(X1) <- (18) [avatar component clause 221]
223. 18 | ~17 [avatar split clause 109,216,221]
248. ~calm(X0) | happy(X0) [subsumption resolution 136,80]
268. 2 [avatar split clause 129,144]
279. $false <- (4, ~17) [resolution 218,154]
280. ~4 | 17 [avatar contradiction clause 279]
292. calm(fred) <- (18) [resolution 222,133]
294. happy(fred) <- (18) [resolution 248,292]
307. creative(fred) | patient(fred) <- (18) [resolution 84,294]
309. patient(fred) <- (18) [subsumption resolution 307,138]
312. 5 | ~18 [avatar split clause 309,221,158]
313. $false <- (8) [subsumption resolution 171,138]
314. ~8 [avatar contradiction clause 313]
315. $false [avatar sat refutation 155,176,223,268,280,312,314]
% SZS output end Proof for 342997813456658284226854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or humble then someone is not kind or not humble and vice versa.
Everyone who is both curious and rich is not happy or not tall.
Everyone who is creative is not funny or not quiet and vice versa.
If paul is not old or patient then fred is both tall and not creative and vice versa.
Everyone who is quiet is not rich or tall and vice versa.
Everyone who is either kind or curious is wise or generous.
If lucy is funny or old then someone is quiet and vice versa.
If someone is brave or not patient then alice is patient or not kind.
If someone is either happy or not kind then someone is either not tall or tall and vice versa.
Everyone who is calm or not generous is curious or not funny.
Everyone who is both not rich and funny is happy or not kind.
If someone is both tall and not tall then someone is old or not rich and vice versa.
If mary is both strong and rich then john is either not tall or not rich.
If paul is not rich then mary is not curious.
Everyone who is not wise is either not calm or funny.
Everyone who is patient is either happy or brave.
Someone is not creative or not humble.
Someone is both brave and not creative.
Fred is either generous or not creative.
Someone is patient.
Someone is both tall and not old.
Susan is both curious and not creative.
Paul is both not patient and not happy.
Someone is both not funny and tall. | Fred is rich. | entailment | ((?[X]:((brave(X)|humble(X))))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((curious(X)&rich(X))=>(~happy(X)|~tall(X))))&
(![X]:(creative(X)<=>(~funny(X)|~quiet(X))))&
(((~old(paul)|patient(paul)))<=>((tall(fred)&~creative(fred))))&
(![X]:(quiet(X)<=>(~rich(X)|tall(X))))&
(![X]:((kind(X)<~>curious(X))=>(wise(X)|generous(X))))&
(((funny(lucy)|old(lucy)))<=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~patient(X))))=>((patient(alice)|~kind(alice))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((~tall(X)<~>tall(X)))))&
(![X]:((calm(X)|~generous(X))=>(curious(X)|~funny(X))))&
(![X]:((~rich(X)&funny(X))=>(happy(X)|~kind(X))))&
((?[X]:((tall(X)&~tall(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(((strong(mary)&rich(mary)))=>((~tall(john)<~>~rich(john))))&
((~rich(paul))=>(~curious(mary)))&
(![X]:(~wise(X)=>(~calm(X)<~>funny(X))))&
(![X]:(patient(X)=>(happy(X)<~>brave(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:((brave(X)&~creative(X))))&
((generous(fred)<~>~creative(fred)))&
(?[X]:(patient(X)))&
(?[X]:((tall(X)&~old(X))))&
((curious(susan)&~creative(susan)))&
((~patient(paul)&~happy(paul)))&
(?[X]:((~funny(X)&tall(X)))) | rich(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5153095041657279760162600
% SZS output start Proof for 5153095041657279760162600
12. ? [X0] : (~tall(X0) & tall(X0)) <=> ? [X0] : (~rich(X0) | old(X0)) [input p11]
25. ~rich(fred) [input hypothesis]
28. ? [X0] : (~tall(X0) & tall(X0)) <=> ? [X1] : (~rich(X1) | old(X1)) [rectify 12]
64. (? [X0] : (~tall(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~old(X1))) & (? [X1] : (~rich(X1) | old(X1)) | ! [X0] : (tall(X0) | ~tall(X0))) [nnf transformation 28]
65. (? [X0] : (~tall(X0) & tall(X0)) | ! [X1] : (rich(X1) & ~old(X1))) & (? [X2] : (~rich(X2) | old(X2)) | ! [X3] : (tall(X3) | ~tall(X3))) [rectify 64]
66. ? [X0] : (~tall(X0) & tall(X0)) => (~tall(sK5) & tall(sK5)) [choice axiom]
67. ? [X2] : (~rich(X2) | old(X2)) => (~rich(sK6) | old(sK6)) [choice axiom]
68. ((~tall(sK5) & tall(sK5)) | ! [X1] : (rich(X1) & ~old(X1))) & ((~rich(sK6) | old(sK6)) | ! [X3] : (tall(X3) | ~tall(X3))) [skolemisation 65,67,66]
114. tall(sK5) | rich(X1) [cnf transformation 68]
116. ~tall(sK5) | rich(X1) [cnf transformation 68]
134. ~rich(fred) [cnf transformation 25]
242. 24 <=> ! [X1] : rich(X1) [avatar definition]
243. rich(X1) <- (24) [avatar component clause 242]
245. 25 <=> tall(sK5) [avatar definition]
248. 24 | ~25 [avatar split clause 116,245,242]
253. 24 | 25 [avatar split clause 114,245,242]
284. $false <- (24) [resolution 243,134]
285. ~24 [avatar contradiction clause 284]
286. $false [avatar sat refutation 248,253,285]
% SZS output end Proof for 5153095041657279760162600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and patient is both quiet and not curious and vice versa.
If alice is not happy or not humble then someone is both strong and not creative.
Everyone who is either humble or not kind is not brave or not funny and vice versa.
Everyone who is both not calm and not happy is not generous or not rich.
Everyone who is either funny or creative is kind or funny and vice versa.
Everyone who is not quiet is calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Someone is not creative.
Someone is either not calm or not rich.
Someone is not creative or humble.
Someone is either old or not tall.
Fred is both not humble and quiet.
Someone is not old or kind.
Alice is either rich or not creative. | Lucy is kind. | neutral | (![X]:((happy(X)&patient(X))<=>(quiet(X)&~curious(X))))&
(((~happy(alice)|~humble(alice)))=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((humble(X)<~>~kind(X))<=>(~brave(X)|~funny(X))))&
(![X]:((~calm(X)&~happy(X))=>(~generous(X)|~rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>(kind(X)|funny(X))))&
(![X]:(~quiet(X)<=>calm(X)))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(?[X]:(~creative(X)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred)))&
(?[X]:((~old(X)|kind(X))))&
((rich(alice)<~>~creative(alice))) | kind(lucy) | [] | null | 0 |
Everyone who is both not brave and not kind is not generous or patient.
Everyone who is either curious or not rich is either tall or rich.
If mary is not generous or patient then john is not kind.
If someone is happy then alice is creative or funny.
Everyone who is either creative or not brave is not brave or not tall.
If mary is either curious or not generous then paul is either not generous or not wise.
Everyone who is not funny or not happy is generous.
Everyone who is either funny or not creative is both creative and not wise and vice versa.
Everyone who is not wise is quiet or not patient.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
Lucy is not calm or not funny.
Someone is rich.
Someone is either not quiet or not kind.
Someone is both strong and calm.
Someone is both not brave and strong.
John is kind or wise.
Alice is brave.
Someone is either not rich or quiet. | Paul is not rich. | neutral | (![X]:((~brave(X)&~kind(X))=>(~generous(X)|patient(X))))&
(![X]:((curious(X)<~>~rich(X))=>(tall(X)<~>rich(X))))&
(((~generous(mary)|patient(mary)))=>(~kind(john)))&
((?[X]:(happy(X)))=>((creative(alice)|funny(alice))))&
(![X]:((creative(X)<~>~brave(X))=>(~brave(X)|~tall(X))))&
(((curious(mary)<~>~generous(mary)))=>((~generous(paul)<~>~wise(paul))))&
(![X]:((~funny(X)|~happy(X))=>generous(X)))&
(![X]:((funny(X)<~>~creative(X))<=>(creative(X)&~wise(X))))&
(![X]:(~wise(X)=>(quiet(X)|~patient(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
((~calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((~brave(X)&strong(X))))&
((kind(john)|wise(john)))&
(brave(alice))&
(?[X]:((~rich(X)<~>quiet(X)))) | ~rich(paul) | [] | null | 0 |
If paul is strong then someone is wise and vice versa.
If alice is either not rich or not funny then someone is wise and vice versa.
Everyone who is both not generous and not funny is both wise and humble.
If someone is not rich then alice is wise and vice versa.
If someone is either rich or quiet then fred is both wise and not patient.
Everyone who is either not old or not wise is either old or strong.
If someone is patient or funny then paul is patient and vice versa.
If someone is both not creative and not tall then someone is funny.
If john is both creative and old then someone is strong and vice versa.
If someone is strong then someone is both not happy and happy and vice versa.
Everyone who is either old or not kind is either not patient or kind.
If someone is either curious or not brave then mary is quiet.
Everyone who is either not generous or not happy is both not brave and creative.
Everyone who is both generous and not kind is either not funny or not quiet.
Everyone who is both kind and generous is either generous or not happy.
If susan is both patient and not rich then fred is creative and vice versa.
John is either not kind or not patient.
Someone is either tall or humble.
Someone is old or not generous.
Lucy is not happy.
Someone is both quiet and not old.
Someone is either curious or funny.
Fred is humble or strong. | Fred is not kind. | neutral | ((strong(paul))<=>(?[X]:(wise(X))))&
(((~rich(alice)<~>~funny(alice)))<=>(?[X]:(wise(X))))&
(![X]:((~generous(X)&~funny(X))=>(wise(X)&humble(X))))&
((?[X]:(~rich(X)))<=>(wise(alice)))&
((?[X]:((rich(X)<~>quiet(X))))=>((wise(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~wise(X))=>(old(X)<~>strong(X))))&
((?[X]:((patient(X)|funny(X))))<=>(patient(paul)))&
((?[X]:((~creative(X)&~tall(X))))=>(?[X]:(funny(X))))&
(((creative(john)&old(john)))<=>(?[X]:(strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>kind(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(quiet(mary)))&
(![X]:((~generous(X)<~>~happy(X))=>(~brave(X)&creative(X))))&
(![X]:((generous(X)&~kind(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)<~>~happy(X))))&
(((patient(susan)&~rich(susan)))<=>(creative(fred)))&
((~kind(john)<~>~patient(john)))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((old(X)|~generous(X))))&
(~happy(lucy))&
(?[X]:((quiet(X)&~old(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((humble(fred)|strong(fred))) | ~kind(fred) | [] | null | 0 |
If someone is not kind then fred is generous and vice versa. If paul is generous then fred is both not quiet and not wise. If susan is humble or strong then mary is either rich or old and vice versa. If someone is patient or generous then mary is either not creative or curious and vice versa. Everyone who is both calm and not brave is either quiet or not brave and vice versa. If alice is not old then someone is both tall and old. If paul is both funny and not creative then someone is not creative or curious and vice versa. If lucy is not wise then paul is both not funny and wise and vice versa. If someone is tall or generous then fred is not curious and vice versa. Everyone who is both generous and wise is either wise or kind. If someone is not wise then someone is not rich or wise. Everyone who is both not funny and happy is funny and vice versa. If someone is either rich or creative then john is not generous. Everyone who is either not patient or not happy is not brave. If someone is not patient or quiet then john is either not calm or happy. Someone is creative. Susan is curious or rich. Fred is curious or not happy. Someone is both kind and tall. | Susan is not curious. | entailment | ((?[X]:(~kind(X)))<=>(generous(fred)))&
((generous(paul))=>((~quiet(fred)&~wise(fred))))&
(((humble(susan)|strong(susan)))<=>((rich(mary)<~>old(mary))))&
((?[X]:((patient(X)|generous(X))))<=>((~creative(mary)<~>curious(mary))))&
(![X]:((calm(X)&~brave(X))<=>(quiet(X)<~>~brave(X))))&
((~old(alice))=>(?[X]:((tall(X)&old(X)))))&
(((funny(paul)&~creative(paul)))<=>(?[X]:((~creative(X)|curious(X)))))&
((~wise(lucy))<=>((~funny(paul)&wise(paul))))&
((?[X]:((tall(X)|generous(X))))<=>(~curious(fred)))&
(![X]:((generous(X)&wise(X))=>(wise(X)<~>kind(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~funny(X)&happy(X))<=>funny(X)))&
((?[X]:((rich(X)<~>creative(X))))=>(~generous(john)))&
(![X]:((~patient(X)<~>~happy(X))=>~brave(X)))&
((?[X]:((~patient(X)|quiet(X))))=>((~calm(john)<~>happy(john))))&
(?[X]:(creative(X)))&
((curious(susan)|rich(susan)))&
((curious(fred)|~happy(fred)))&
(?[X]:((kind(X)&tall(X)))) | ~curious(susan) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 932785879087237925233202
% SZS output start Proof for 932785879087237925233202
7. (~creative(paul) & funny(paul)) <=> ? [X0] : (curious(X0) | ~creative(X0)) [input p6]
12. ! [X0] : ((happy(X0) & ~funny(X0)) <=> funny(X0)) [input p11]
20. curious(susan) [input hypothesis]
44. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X0] : (curious(X0) | ~creative(X0)) | (creative(paul) | ~funny(paul))) [nnf transformation 7]
45. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X0] : (curious(X0) | ~creative(X0)) | creative(paul) | ~funny(paul)) [flattening 44]
46. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & (? [X1] : (curious(X1) | ~creative(X1)) | creative(paul) | ~funny(paul)) [rectify 45]
47. ? [X1] : (curious(X1) | ~creative(X1)) => (curious(sK3) | ~creative(sK3)) [choice axiom]
48. ((~creative(paul) & funny(paul)) | ! [X0] : (~curious(X0) & creative(X0))) & ((curious(sK3) | ~creative(sK3)) | creative(paul) | ~funny(paul)) [skolemisation 46,47]
59. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | funny(X0)))) [nnf transformation 12]
60. ! [X0] : (((happy(X0) & ~funny(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | funny(X0))) [flattening 59]
94. funny(paul) | ~curious(X0) [cnf transformation 48]
107. ~funny(X0) | ~funny(X0) [cnf transformation 60]
122. curious(susan) [cnf transformation 20]
124. ~funny(X0) [duplicate literal removal 107]
221. 20 <=> ! [X0] : ~curious(X0) [avatar definition]
222. ~curious(X0) <- (20) [avatar component clause 221]
233. 23 <=> funny(paul) [avatar definition]
235. funny(paul) <- (23) [avatar component clause 233]
236. 20 | 23 [avatar split clause 94,233,221]
317. 41 <=> curious(susan) [avatar definition]
319. curious(susan) <- (41) [avatar component clause 317]
325. 41 [avatar split clause 122,317]
332. $false <- (23) [subsumption resolution 235,124]
333. ~23 [avatar contradiction clause 332]
340. $false <- (20, 41) [resolution 319,222]
341. ~20 | ~41 [avatar contradiction clause 340]
342. $false [avatar sat refutation 236,325,333,341]
% SZS output end Proof for 932785879087237925233202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not funny is both wise and not humble.
If someone is not calm or brave then susan is not happy or not calm and vice versa.
Everyone who is either not wise or old is either creative or old and vice versa.
Everyone who is wise or generous is both not old and happy.
Everyone who is both not curious and not happy is wise.
Everyone who is both funny and not quiet is both funny and brave and vice versa.
Everyone who is both happy and patient is not calm.
If someone is either funny or not quiet then fred is not wise or strong.
Everyone who is both not wise and not funny is not tall or not rich and vice versa.
If someone is either wise or rich then alice is either funny or not rich.
If someone is not quiet then fred is either humble or patient.
Everyone who is either happy or not old is calm and vice versa.
If someone is not quiet or not strong then john is either not humble or not curious and vice versa.
Everyone who is either not old or calm is either not rich or wise and vice versa.
If john is either not generous or not wise then john is both not calm and patient.
Everyone who is both not curious and creative is brave and vice versa.
Someone is either tall or brave.
John is not kind or not rich.
Mary is kind.
Lucy is either not curious or not quiet.
Someone is humble or not old.
Paul is either patient or calm.
Susan is either quiet or humble.
Susan is tall or wise. | Mary is not kind. | contradiction | (![X]:((~strong(X)&~funny(X))=>(wise(X)&~humble(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((~happy(susan)|~calm(susan))))&
(![X]:((~wise(X)<~>old(X))<=>(creative(X)<~>old(X))))&
(![X]:((wise(X)|generous(X))=>(~old(X)&happy(X))))&
(![X]:((~curious(X)&~happy(X))=>wise(X)))&
(![X]:((funny(X)&~quiet(X))<=>(funny(X)&brave(X))))&
(![X]:((happy(X)&patient(X))=>~calm(X)))&
((?[X]:((funny(X)<~>~quiet(X))))=>((~wise(fred)|strong(fred))))&
(![X]:((~wise(X)&~funny(X))<=>(~tall(X)|~rich(X))))&
((?[X]:((wise(X)<~>rich(X))))=>((funny(alice)<~>~rich(alice))))&
((?[X]:(~quiet(X)))=>((humble(fred)<~>patient(fred))))&
(![X]:((happy(X)<~>~old(X))<=>calm(X)))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~humble(john)<~>~curious(john))))&
(![X]:((~old(X)<~>calm(X))<=>(~rich(X)<~>wise(X))))&
(((~generous(john)<~>~wise(john)))=>((~calm(john)&patient(john))))&
(![X]:((~curious(X)&creative(X))<=>brave(X)))&
(?[X]:((tall(X)<~>brave(X))))&
((~kind(john)|~rich(john)))&
(kind(mary))&
((~curious(lucy)<~>~quiet(lucy)))&
(?[X]:((humble(X)|~old(X))))&
((patient(paul)<~>calm(paul)))&
((quiet(susan)<~>humble(susan)))&
((tall(susan)|wise(susan))) | ~kind(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4017117079917568154640786
% SZS output start Proof for 4017117079917568154640786
19. kind(mary) [input p18]
25. ~kind(mary) [input hypothesis]
133. kind(mary) [cnf transformation 19]
142. ~kind(mary) [cnf transformation 25]
326. $false [subsumption resolution 142,133]
% SZS output end Proof for 4017117079917568154640786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or old is not wise or not tall and vice versa.
Everyone who is not tall is happy or not humble.
Everyone who is either not tall or humble is either strong or not quiet.
Everyone who is both not brave and not generous is strong or rich.
Everyone who is not old is both calm and rich.
Everyone who is not tall is either creative or not humble and vice versa.
If paul is not calm or not quiet then alice is either not funny or strong.
Everyone who is not funny or wise is not tall or not strong and vice versa.
If someone is either curious or not funny then someone is curious or happy.
If someone is either tall or calm then paul is both generous and not calm and vice versa.
Everyone who is brave or not humble is both wise and patient and vice versa.
If someone is either tall or wise then susan is not calm.
Everyone who is both not patient and not wise is curious or not curious.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
Someone is either funny or happy.
Paul is both not tall and not generous.
Paul is either old or generous.
Alice is both kind and not wise.
Someone is not generous.
Someone is not patient.
Someone is either old or wise.
Alice is not curious. | Paul is not generous. | entailment | (![X]:((happy(X)|old(X))<=>(~wise(X)|~tall(X))))&
(![X]:(~tall(X)=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>humble(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(strong(X)|rich(X))))&
(![X]:(~old(X)=>(calm(X)&rich(X))))&
(![X]:(~tall(X)<=>(creative(X)<~>~humble(X))))&
(((~calm(paul)|~quiet(paul)))=>((~funny(alice)<~>strong(alice))))&
(![X]:((~funny(X)|wise(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((curious(X)|happy(X)))))&
((?[X]:((tall(X)<~>calm(X))))<=>((generous(paul)&~calm(paul))))&
(![X]:((brave(X)|~humble(X))<=>(wise(X)&patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(~calm(susan)))&
(![X]:((~patient(X)&~wise(X))=>(curious(X)|~curious(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
(?[X]:((funny(X)<~>happy(X))))&
((~tall(paul)&~generous(paul)))&
((old(paul)<~>generous(paul)))&
((kind(alice)&~wise(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)<~>wise(X))))&
(~curious(alice)) | ~generous(paul) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4906474000683124210121548
% SZS output start Proof for 4906474000683124210121548
18. ~generous(paul) & ~tall(paul) [input p17]
25. generous(paul) [input hypothesis]
123. ~generous(paul) [cnf transformation 18]
132. generous(paul) [cnf transformation 25]
170. 9 <=> generous(paul) [avatar definition]
236. ~9 [avatar split clause 123,170]
253. 9 [avatar split clause 132,170]
254. $false [avatar sat refutation 236,253]
% SZS output end Proof for 4906474000683124210121548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not rich and quiet then someone is either not creative or not strong. Everyone who is curious is not kind. If someone is strong then john is either wise or not patient and vice versa. If fred is both not curious and rich then mary is either not patient or quiet. Everyone who is not quiet is either not humble or not strong and vice versa. Everyone who is both creative and rich is either not patient or creative and vice versa. Everyone who is both generous and patient is either not happy or not creative and vice versa. Everyone who is funny is strong or old. Everyone who is both not humble and funny is not humble or patient and vice versa. Everyone who is not strong or not curious is either generous or wise. If someone is both humble and kind then alice is both not patient and old and vice versa. Everyone who is either not creative or humble is both generous and old and vice versa. If susan is not quiet or generous then mary is either strong or brave. Everyone who is both tall and brave is funny and vice versa. Everyone who is funny or wise is quiet and vice versa. If alice is not curious or kind then susan is both not wise and quiet and vice versa. Lucy is quiet or happy. Someone is not curious. Someone is humble. John is quiet or rich. Someone is not rich or rich. Someone is patient or kind. Paul is both not kind and not rich. | Alice is not curious. | neutral | (((~rich(lucy)&quiet(lucy)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(curious(X)=>~kind(X)))&
((?[X]:(strong(X)))<=>((wise(john)<~>~patient(john))))&
(((~curious(fred)&rich(fred)))=>((~patient(mary)<~>quiet(mary))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)&rich(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((generous(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(funny(X)=>(strong(X)|old(X))))&
(![X]:((~humble(X)&funny(X))<=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)|~curious(X))=>(generous(X)<~>wise(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~patient(alice)&old(alice))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)&old(X))))&
(((~quiet(susan)|generous(susan)))=>((strong(mary)<~>brave(mary))))&
(![X]:((tall(X)&brave(X))<=>funny(X)))&
(![X]:((funny(X)|wise(X))<=>quiet(X)))&
(((~curious(alice)|kind(alice)))<=>((~wise(susan)&quiet(susan))))&
((quiet(lucy)|happy(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:(humble(X)))&
((quiet(john)|rich(john)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((patient(X)|kind(X))))&
((~kind(paul)&~rich(paul))) | ~curious(alice) | [] | null | 0 |
If someone is both not wise and not calm then mary is either not creative or not tall.
Everyone who is humble or not calm is not quiet or not tall.
Everyone who is not creative or creative is tall or quiet and vice versa.
Everyone who is both not curious and wise is either not humble or not brave.
Everyone who is both funny and not old is both not creative and not quiet and vice versa.
If someone is not rich or not calm then susan is both not old and old and vice versa.
If fred is both not rich and happy then someone is either not strong or not happy and vice versa.
If susan is wise or old then fred is both not funny and wise.
Everyone who is either not happy or not quiet is not tall and vice versa.
If someone is both wise and not curious then someone is both not calm and not kind and vice versa.
If someone is not tall then paul is both generous and old and vice versa.
Everyone who is not humble or not generous is both not curious and not old.
If lucy is not curious or kind then someone is not wise or not calm.
If someone is quiet or funny then someone is both wise and kind.
If susan is either wise or not strong then someone is both not calm and creative.
Everyone who is either humble or rich is wise or not rich.
Someone is funny or not brave.
Susan is patient or not wise.
Someone is both not strong and not kind.
Fred is either creative or old.
Mary is not strong or curious.
Mary is either not old or not creative. | Lucy is rich. | entailment | ((?[X]:((~wise(X)&~calm(X))))=>((~creative(mary)<~>~tall(mary))))&
(![X]:((humble(X)|~calm(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~creative(X)|creative(X))<=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((funny(X)&~old(X))<=>(~creative(X)&~quiet(X))))&
((?[X]:((~rich(X)|~calm(X))))<=>((~old(susan)&old(susan))))&
(((~rich(fred)&happy(fred)))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(((wise(susan)|old(susan)))=>((~funny(fred)&wise(fred))))&
(![X]:((~happy(X)<~>~quiet(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~tall(X)))<=>((generous(paul)&old(paul))))&
(![X]:((~humble(X)|~generous(X))=>(~curious(X)&~old(X))))&
(((~curious(lucy)|kind(lucy)))=>(?[X]:((~wise(X)|~calm(X)))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((wise(X)&kind(X)))))&
(((wise(susan)<~>~strong(susan)))=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((humble(X)<~>rich(X))=>(wise(X)|~rich(X))))&
(?[X]:((funny(X)|~brave(X))))&
((patient(susan)|~wise(susan)))&
(?[X]:((~strong(X)&~kind(X))))&
((creative(fred)<~>old(fred)))&
((~strong(mary)|curious(mary)))&
((~old(mary)<~>~creative(mary))) | rich(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5168383966278273123388992
% SZS output start Proof for 5168383966278273123388992
6. ? [X0] : (~calm(X0) | ~rich(X0)) <=> (old(susan) & ~old(susan)) [input p5]
23. ~rich(lucy) [input hypothesis]
45. (? [X0] : (~calm(X0) | ~rich(X0)) | (~old(susan) | old(susan))) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [nnf transformation 6]
46. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X0] : (calm(X0) & rich(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) | ~rich(X0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [rectify 46]
48. ? [X0] : (~calm(X0) | ~rich(X0)) => (~calm(sK0) | ~rich(sK0)) [choice axiom]
49. ((~calm(sK0) | ~rich(sK0)) | ~old(susan) | old(susan)) & ((old(susan) & ~old(susan)) | ! [X1] : (calm(X1) & rich(X1))) [skolemisation 47,48]
95. ~old(susan) | rich(X1) [cnf transformation 49]
97. old(susan) | rich(X1) [cnf transformation 49]
145. ~rich(lucy) [cnf transformation 23]
165. 5 <=> old(susan) [avatar definition]
170. 6 <=> ! [X1] : rich(X1) [avatar definition]
171. rich(X1) <- (6) [avatar component clause 170]
172. 6 | 5 [avatar split clause 97,165,170]
174. 6 | ~5 [avatar split clause 95,165,170]
351. $false <- (6) [resolution 171,145]
352. ~6 [avatar contradiction clause 351]
353. $false [avatar sat refutation 172,174,352]
% SZS output end Proof for 5168383966278273123388992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is tall or not quiet and vice versa.
Everyone who is both not quiet and not kind is happy.
If john is either not calm or tall then fred is both not humble and not patient and vice versa.
If lucy is not rich then someone is not humble.
Everyone who is not brave or strong is not patient or not strong and vice versa.
Everyone who is both not humble and generous is rich and vice versa.
If someone is curious then someone is not creative or not curious and vice versa.
Everyone who is curious or not curious is both not patient and not strong.
If someone is either not happy or tall then someone is not patient or not curious and vice versa.
Everyone who is either not calm or calm is curious or creative and vice versa.
Everyone who is both not rich and not calm is creative or calm.
Everyone who is both not humble and not strong is either not wise or not calm.
Everyone who is either creative or quiet is either not rich or humble and vice versa.
Everyone who is either curious or not funny is curious or not wise and vice versa.
Everyone who is happy is not happy or funny.
Everyone who is rich or not creative is either not tall or curious.
Someone is either not happy or patient.
Someone is both kind and tall.
Someone is both calm and not strong.
Susan is not humble or old.
Someone is not patient.
Someone is not calm or creative.
Mary is either happy or tall.
Fred is wise. | Susan is patient. | contradiction | (![X]:(funny(X)<=>(tall(X)|~quiet(X))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(((~calm(john)<~>tall(john)))<=>((~humble(fred)&~patient(fred))))&
((~rich(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((curious(X)|~curious(X))=>(~patient(X)&~strong(X))))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
(![X]:(happy(X)=>(~happy(X)|funny(X))))&
(![X]:((rich(X)|~creative(X))=>(~tall(X)<~>curious(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((calm(X)&~strong(X))))&
((~humble(susan)|old(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)|creative(X))))&
((happy(mary)<~>tall(mary)))&
(wise(fred)) | patient(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4900292541666750559851387
% SZS output start Proof for 4900292541666750559851387
8. ! [X0] : ((~curious(X0) | curious(X0)) => (~strong(X0) & ~patient(X0))) [input p7]
25. patient(susan) [input hypothesis]
32. ! [X0] : ((~strong(X0) & ~patient(X0)) | (curious(X0) & ~curious(X0))) [ennf transformation 8]
99. ~patient(X0) | ~curious(X0) [cnf transformation 32]
100. ~patient(X0) | curious(X0) [cnf transformation 32]
147. patient(susan) [cnf transformation 25]
212. ~patient(X0) [subsumption resolution 99,100]
256. $false [subsumption resolution 147,212]
% SZS output end Proof for 4900292541666750559851387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is either not strong or not quiet and vice versa.
Everyone who is not generous is not old.
Everyone who is either happy or quiet is not creative or not kind and vice versa.
Everyone who is either happy or old is both funny and not old and vice versa.
Everyone who is both not creative and quiet is not strong or not happy and vice versa.
If fred is either rich or kind then someone is not patient or not funny and vice versa.
If someone is both not rich and not happy then lucy is not tall or not humble.
Everyone who is not brave is either not calm or brave.
If susan is creative then paul is not tall or patient and vice versa.
If someone is rich then someone is wise and vice versa.
Everyone who is quiet or not creative is not calm or tall and vice versa.
If fred is not kind or kind then someone is both not curious and not kind and vice versa.
Everyone who is not calm or patient is not generous.
If susan is old or not curious then mary is either not calm or happy and vice versa.
If fred is either not humble or patient then paul is kind.
Everyone who is not humble or rich is not generous.
Someone is both not wise and brave.
Someone is not tall.
Someone is either not quiet or not brave.
Fred is patient.
Lucy is both not strong and not tall.
Someone is both not curious and not rich.
Someone is generous or creative.
Someone is humble or not rich. | Lucy is old. | contradiction | ((?[X]:(~rich(X)))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~generous(X)=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))<=>(~creative(X)|~kind(X))))&
(![X]:((happy(X)<~>old(X))<=>(funny(X)&~old(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~strong(X)|~happy(X))))&
(((rich(fred)<~>kind(fred)))<=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:((~rich(X)&~happy(X))))=>((~tall(lucy)|~humble(lucy))))&
(![X]:(~brave(X)=>(~calm(X)<~>brave(X))))&
((creative(susan))<=>((~tall(paul)|patient(paul))))&
((?[X]:(rich(X)))<=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|~creative(X))<=>(~calm(X)|tall(X))))&
(((~kind(fred)|kind(fred)))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((~calm(X)|patient(X))=>~generous(X)))&
(((old(susan)|~curious(susan)))<=>((~calm(mary)<~>happy(mary))))&
(((~humble(fred)<~>patient(fred)))=>(kind(paul)))&
(![X]:((~humble(X)|rich(X))=>~generous(X)))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(patient(fred))&
((~strong(lucy)&~tall(lucy)))&
(?[X]:((~curious(X)&~rich(X))))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:((humble(X)|~rich(X)))) | old(lucy) | [
"p2",
"p3",
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6242468789753641490806098
% SZS output start Proof for 6242468789753641490806098
3. ! [X0] : ((happy(X0) <~> quiet(X0)) <=> (~kind(X0) | ~creative(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> old(X0)) <=> (~old(X0) & funny(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> (~happy(X0) | ~strong(X0))) [input p4]
21. ~tall(lucy) & ~strong(lucy) [input p20]
25. old(lucy) [input hypothesis]
40. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~quiet(X0) | ~happy(X0)) & (quiet(X0) | happy(X0))) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ((happy(X0) | ~quiet(X0)) & (quiet(X0) | ~happy(X0))))) [flattening 40]
42. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | (old(X0) | ~funny(X0))) & ((~old(X0) & funny(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | old(X0) | ~funny(X0)) & ((~old(X0) & funny(X0)) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0))))) [flattening 42]
44. ! [X0] : (((quiet(X0) & ~creative(X0)) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | (~quiet(X0) | creative(X0)))) [nnf transformation 5]
45. ! [X0] : (((quiet(X0) & ~creative(X0)) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | ~quiet(X0) | creative(X0))) [flattening 44]
90. ~happy(X0) | ~quiet(X0) | creative(X0) [cnf transformation 41]
95. ~old(X0) | happy(X0) | ~old(X0) [cnf transformation 43]
99. ~creative(X0) | strong(X0) [cnf transformation 45]
101. quiet(X0) | strong(X0) [cnf transformation 45]
144. ~strong(lucy) [cnf transformation 21]
150. old(lucy) [cnf transformation 25]
152. ~old(X0) | happy(X0) [duplicate literal removal 95]
346. happy(lucy) [resolution 152,150]
354. ~quiet(lucy) | creative(lucy) [resolution 90,346]
356. 38 <=> creative(lucy) [avatar definition]
358. creative(lucy) <- (38) [avatar component clause 356]
360. 39 <=> quiet(lucy) [avatar definition]
362. ~quiet(lucy) <- (~39) [avatar component clause 360]
363. 38 | ~39 [avatar split clause 354,360,356]
364. strong(lucy) <- (~39) [resolution 362,101]
365. $false <- (~39) [subsumption resolution 364,144]
366. 39 [avatar contradiction clause 365]
381. strong(lucy) <- (38) [resolution 358,99]
382. $false <- (38) [subsumption resolution 381,144]
383. ~38 [avatar contradiction clause 382]
384. $false [avatar sat refutation 363,366,383]
% SZS output end Proof for 6242468789753641490806098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both funny and not strong. If lucy is not quiet then fred is either not happy or not brave. If someone is both happy and funny then someone is both not patient and brave. Everyone who is not calm or happy is either not quiet or patient. Everyone who is curious is patient. Everyone who is rich is brave or kind and vice versa. Everyone who is both calm and creative is kind or not quiet. Everyone who is both not funny and not brave is generous or not curious and vice versa. If someone is both old and kind then john is wise or not rich. Everyone who is not creative or rich is both not calm and old. Everyone who is either curious or not patient is quiet or brave and vice versa. If someone is not rich then someone is not wise or not brave. Everyone who is both not patient and strong is strong or calm. If paul is happy then paul is curious or happy and vice versa. If someone is both not brave and creative then john is both strong and not kind and vice versa. If susan is either not strong or wise then someone is both not happy and not rich. Fred is both not tall and generous. Someone is not strong or quiet. Paul is not funny. Alice is not generous. Someone is not curious or not patient. Someone is calm or kind. | John is not funny. | entailment | (![X]:(~calm(X)=>(funny(X)&~strong(X))))&
((~quiet(lucy))=>((~happy(fred)<~>~brave(fred))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:((~patient(X)&brave(X)))))&
(![X]:((~calm(X)|happy(X))=>(~quiet(X)<~>patient(X))))&
(![X]:(curious(X)=>patient(X)))&
(![X]:(rich(X)<=>(brave(X)|kind(X))))&
(![X]:((calm(X)&creative(X))=>(kind(X)|~quiet(X))))&
(![X]:((~funny(X)&~brave(X))<=>(generous(X)|~curious(X))))&
((?[X]:((old(X)&kind(X))))=>((wise(john)|~rich(john))))&
(![X]:((~creative(X)|rich(X))=>(~calm(X)&old(X))))&
(![X]:((curious(X)<~>~patient(X))<=>(quiet(X)|brave(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:((~patient(X)&strong(X))=>(strong(X)|calm(X))))&
((happy(paul))<=>((curious(paul)|happy(paul))))&
((?[X]:((~brave(X)&creative(X))))<=>((strong(john)&~kind(john))))&
(((~strong(susan)<~>wise(susan)))=>(?[X]:((~happy(X)&~rich(X)))))&
((~tall(fred)&generous(fred)))&
(?[X]:((~strong(X)|quiet(X))))&
(~funny(paul))&
(~generous(alice))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((calm(X)|kind(X)))) | ~funny(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5149614878991073893237066
% SZS output start Proof for 5149614878991073893237066
1. ! [X0] : (~calm(X0) => (~strong(X0) & funny(X0))) [input p0]
5. ! [X0] : (curious(X0) => patient(X0)) [input p4]
6. ! [X0] : (rich(X0) <=> (kind(X0) | brave(X0))) [input p5]
7. ! [X0] : ((creative(X0) & calm(X0)) => (~quiet(X0) | kind(X0))) [input p6]
8. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (~curious(X0) | generous(X0))) [input p7]
10. ! [X0] : ((rich(X0) | ~creative(X0)) => (old(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) <~> ~patient(X0)) <=> (brave(X0) | quiet(X0))) [input p10]
15. ? [X0] : (creative(X0) & ~brave(X0)) <=> (~kind(john) & strong(john)) [input p14]
17. generous(fred) & ~tall(fred) [input p16]
23. funny(john) [input hypothesis]
26. generous(fred) [pure predicate removal 17]
27. ! [X0] : ((~strong(X0) & funny(X0)) | calm(X0)) [ennf transformation 1]
31. ! [X0] : (patient(X0) | ~curious(X0)) [ennf transformation 5]
32. ! [X0] : ((~quiet(X0) | kind(X0)) | (~creative(X0) | ~calm(X0))) [ennf transformation 7]
33. ! [X0] : (~quiet(X0) | kind(X0) | ~creative(X0) | ~calm(X0)) [flattening 32]
36. ! [X0] : ((old(X0) & ~calm(X0)) | (~rich(X0) & creative(X0))) [ennf transformation 10]
46. ! [X0] : ((rich(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 6]
47. ! [X0] : ((rich(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | ~rich(X0))) [flattening 46]
48. ! [X0] : (((~brave(X0) & ~funny(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 8]
49. ! [X0] : (((~brave(X0) & ~funny(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | brave(X0) | funny(X0))) [flattening 48]
50. ! [X0] : ((((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) & ((brave(X0) | quiet(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))))) [nnf transformation 11]
51. ! [X0] : ((((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (~brave(X0) & ~quiet(X0))) & (brave(X0) | quiet(X0) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0))))) [flattening 50]
57. (? [X0] : (creative(X0) & ~brave(X0)) | (kind(john) | ~strong(john))) & ((~kind(john) & strong(john)) | ! [X0] : (~creative(X0) | brave(X0))) [nnf transformation 15]
58. (? [X0] : (creative(X0) & ~brave(X0)) | kind(john) | ~strong(john)) & ((~kind(john) & strong(john)) | ! [X0] : (~creative(X0) | brave(X0))) [flattening 57]
59. (? [X0] : (creative(X0) & ~brave(X0)) | kind(john) | ~strong(john)) & ((~kind(john) & strong(john)) | ! [X1] : (~creative(X1) | brave(X1))) [rectify 58]
60. ? [X0] : (creative(X0) & ~brave(X0)) => (creative(sK2) & ~brave(sK2)) [choice axiom]
61. ((creative(sK2) & ~brave(sK2)) | kind(john) | ~strong(john)) & ((~kind(john) & strong(john)) | ! [X1] : (~creative(X1) | brave(X1))) [skolemisation 59,60]
71. funny(X0) | calm(X0) [cnf transformation 27]
72. ~strong(X0) | calm(X0) [cnf transformation 27]
81. ~curious(X0) | patient(X0) [cnf transformation 31]
83. ~brave(X0) | rich(X0) [cnf transformation 47]
84. ~kind(X0) | rich(X0) [cnf transformation 47]
85. ~creative(X0) | kind(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 33]
87. ~generous(X0) | ~funny(X0) [cnf transformation 49]
88. ~funny(X0) | curious(X0) [cnf transformation 49]
89. ~generous(X0) | ~brave(X0) [cnf transformation 49]
92. ~calm(X0) | creative(X0) [cnf transformation 36]
93. ~rich(X0) | ~calm(X0) [cnf transformation 36]
96. brave(X0) | quiet(X0) | ~patient(X0) | ~curious(X0) [cnf transformation 51]
107. strong(john) | ~creative(X1) | brave(X1) [cnf transformation 61]
115. generous(fred) [cnf transformation 26]
121. funny(john) [cnf transformation 23]
131. 3 <=> brave(fred) [avatar definition]
157. 9 <=> rich(john) [avatar definition]
158. rich(john) <- (9) [avatar component clause 157]
159. ~rich(john) <- (~9) [avatar component clause 157]
163. ~curious(X0) | quiet(X0) | brave(X0) [subsumption resolution 96,81]
186. 15 <=> strong(john) [avatar definition]
187. strong(john) <- (15) [avatar component clause 186]
190. 16 <=> kind(john) [avatar definition]
192. kind(john) <- (16) [avatar component clause 190]
204. 19 <=> ! [X1] : (~creative(X1) | brave(X1)) [avatar definition]
205. ~creative(X1) | brave(X1) <- (19) [avatar component clause 204]
207. 19 | 15 [avatar split clause 107,186,204]
248. calm(john) <- (15) [resolution 72,187]
249. ~funny(fred) [resolution 87,115]
250. calm(fred) [resolution 249,71]
251. curious(john) [resolution 88,121]
254. ~brave(fred) [resolution 89,115]
255. creative(fred) [resolution 92,250]
256. creative(john) <- (15) [resolution 92,248]
279. 29 <=> quiet(john) [avatar definition]
281. quiet(john) <- (29) [avatar component clause 279]
295. quiet(john) | brave(john) [resolution 163,251]
298. 32 <=> brave(john) [avatar definition]
300. brave(john) <- (32) [avatar component clause 298]
301. 32 | 29 [avatar split clause 295,279,298]
304. kind(john) | ~quiet(john) | ~calm(john) <- (15) [resolution 85,256]
352. kind(john) | ~calm(john) <- (15, 29) [subsumption resolution 304,281]
353. kind(john) <- (15, 29) [subsumption resolution 352,248]
354. 16 | ~15 | ~29 [avatar split clause 353,279,186,190]
355. rich(john) <- (16) [resolution 192,84]
358. 9 | ~16 [avatar split clause 355,190,157]
361. ~calm(john) <- (9) [resolution 158,93]
362. $false <- (9, 15) [subsumption resolution 361,248]
363. ~9 | ~15 [avatar contradiction clause 362]
365. brave(fred) <- (19) [resolution 205,255]
374. 3 | ~19 [avatar split clause 365,204,131]
375. ~3 [avatar split clause 254,131]
383. rich(john) <- (32) [resolution 300,83]
384. $false <- (~9, 32) [subsumption resolution 383,159]
385. 9 | ~32 [avatar contradiction clause 384]
386. $false [avatar sat refutation 207,301,354,358,363,374,375,385]
% SZS output end Proof for 5149614878991073893237066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not brave is not quiet or humble.
Everyone who is curious is either tall or not generous.
If john is both not wise and wise then someone is either happy or not humble.
Everyone who is not patient is either not kind or not creative and vice versa.
If someone is both not wise and not rich then john is not tall.
Everyone who is either not strong or not quiet is both generous and not curious and vice versa.
Everyone who is both curious and not humble is either generous or patient and vice versa.
Everyone who is not happy or not rich is not calm or funny.
If someone is either not old or rich then someone is not kind or not curious and vice versa.
Everyone who is either not generous or not kind is both not humble and quiet.
Everyone who is humble or strong is either not wise or not kind and vice versa.
If alice is curious then someone is not old or generous and vice versa.
If alice is not tall then fred is not humble or curious and vice versa.
Everyone who is either not calm or curious is either quiet or curious.
Everyone who is not kind is wise and vice versa.
If susan is old then someone is patient or not happy.
John is either not rich or not quiet.
Alice is creative or not old.
Someone is both humble and wise.
Fred is either not calm or strong.
Someone is not calm or rich.
Someone is either not wise or not creative.
Someone is not curious or creative. | John is old. | neutral | (![X]:((~funny(X)|~brave(X))=>(~quiet(X)|humble(X))))&
(![X]:(curious(X)=>(tall(X)<~>~generous(X))))&
(((~wise(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~patient(X)<=>(~kind(X)<~>~creative(X))))&
((?[X]:((~wise(X)&~rich(X))))=>(~tall(john)))&
(![X]:((~strong(X)<~>~quiet(X))<=>(generous(X)&~curious(X))))&
(![X]:((curious(X)&~humble(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~happy(X)|~rich(X))=>(~calm(X)|funny(X))))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((~kind(X)|~curious(X)))))&
(![X]:((~generous(X)<~>~kind(X))=>(~humble(X)&quiet(X))))&
(![X]:((humble(X)|strong(X))<=>(~wise(X)<~>~kind(X))))&
((curious(alice))<=>(?[X]:((~old(X)|generous(X)))))&
((~tall(alice))<=>((~humble(fred)|curious(fred))))&
(![X]:((~calm(X)<~>curious(X))=>(quiet(X)<~>curious(X))))&
(![X]:(~kind(X)<=>wise(X)))&
((old(susan))=>(?[X]:((patient(X)|~happy(X)))))&
((~rich(john)<~>~quiet(john)))&
((creative(alice)|~old(alice)))&
(?[X]:((humble(X)&wise(X))))&
((~calm(fred)<~>strong(fred)))&
(?[X]:((~calm(X)|rich(X))))&
(?[X]:((~wise(X)<~>~creative(X))))&
(?[X]:((~curious(X)|creative(X)))) | old(john) | [] | null | 0 |
Everyone who is either not brave or not old is funny or not happy.
If mary is either not kind or not old then someone is either not rich or not old.
If someone is kind or creative then mary is either strong or not funny and vice versa.
Everyone who is patient or humble is strong or not strong and vice versa.
Everyone who is both not generous and wise is either humble or patient and vice versa.
Everyone who is patient is either funny or not quiet.
If someone is either wise or not humble then someone is funny or kind and vice versa.
If susan is either quiet or not brave then someone is not happy or not calm and vice versa.
Everyone who is either not calm or quiet is not curious and vice versa.
Everyone who is not quiet is either brave or kind and vice versa.
Everyone who is either generous or not funny is not brave or not generous and vice versa.
Everyone who is not curious or tall is either humble or not curious.
Everyone who is curious is both patient and not quiet.
Everyone who is not wise is both kind and creative and vice versa.
If john is creative then someone is either not kind or tall and vice versa.
If someone is both old and rich then someone is both not rich and not wise.
John is wise or not calm.
Someone is either not patient or generous.
Paul is either not kind or not funny.
Mary is strong or calm.
Lucy is not kind or not strong.
Someone is generous. | Paul is quiet. | contradiction | (![X]:((~brave(X)<~>~old(X))=>(funny(X)|~happy(X))))&
(((~kind(mary)<~>~old(mary)))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((kind(X)|creative(X))))<=>((strong(mary)<~>~funny(mary))))&
(![X]:((patient(X)|humble(X))<=>(strong(X)|~strong(X))))&
(![X]:((~generous(X)&wise(X))<=>(humble(X)<~>patient(X))))&
(![X]:(patient(X)=>(funny(X)<~>~quiet(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(((quiet(susan)<~>~brave(susan)))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~quiet(X)<=>(brave(X)<~>kind(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|tall(X))=>(humble(X)<~>~curious(X))))&
(![X]:(curious(X)=>(patient(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(kind(X)&creative(X))))&
((creative(john))<=>(?[X]:((~kind(X)<~>tall(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
((wise(john)|~calm(john)))&
(?[X]:((~patient(X)<~>generous(X))))&
((~kind(paul)<~>~funny(paul)))&
((strong(mary)|calm(mary)))&
((~kind(lucy)|~strong(lucy)))&
(?[X]:(generous(X))) | quiet(paul) | [
"p3",
"p4",
"p5",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2635514519000153311413201
% SZS output start Proof for 2635514519000153311413201
4. ! [X0] : ((humble(X0) | patient(X0)) <=> (~strong(X0) | strong(X0))) [input p3]
5. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (humble(X0) <~> patient(X0))) [input p4]
6. ! [X0] : (patient(X0) => (funny(X0) <~> ~quiet(X0))) [input p5]
11. ! [X0] : ((generous(X0) <~> ~funny(X0)) <=> (~generous(X0) | ~brave(X0))) [input p10]
12. ! [X0] : ((tall(X0) | ~curious(X0)) => (humble(X0) <~> ~curious(X0))) [input p11]
13. ! [X0] : (curious(X0) => (~quiet(X0) & patient(X0))) [input p12]
23. quiet(paul) [input hypothesis]
29. ! [X0] : ((funny(X0) <~> ~quiet(X0)) | ~patient(X0)) [ennf transformation 6]
30. ! [X0] : ((humble(X0) <~> ~curious(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 12]
31. ! [X0] : ((~quiet(X0) & patient(X0)) | ~curious(X0)) [ennf transformation 13]
41. ! [X0] : (((humble(X0) | patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~humble(X0) & ~patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | patient(X0) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | (~humble(X0) & ~patient(X0)))) [flattening 41]
43. ! [X0] : (((wise(X0) & ~generous(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~wise(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((wise(X0) & ~generous(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | ~wise(X0) | generous(X0))) [flattening 43]
45. ! [X0] : (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | ~patient(X0)) [nnf transformation 29]
57. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [nnf transformation 11]
58. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [flattening 57]
59. ! [X0] : (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~tall(X0) & curious(X0))) [nnf transformation 30]
89. humble(X0) | patient(X0) | ~strong(X0) [cnf transformation 42]
90. humble(X0) | patient(X0) | strong(X0) [cnf transformation 42]
94. ~generous(X0) | humble(X0) | ~patient(X0) [cnf transformation 44]
97. ~quiet(X0) | funny(X0) | ~patient(X0) [cnf transformation 45]
122. ~funny(X0) | generous(X0) | generous(X0) [cnf transformation 58]
127. curious(X0) | ~humble(X0) | curious(X0) [cnf transformation 59]
129. ~curious(X0) | patient(X0) [cnf transformation 31]
130. ~curious(X0) | ~quiet(X0) [cnf transformation 31]
148. quiet(paul) [cnf transformation 23]
149. ~humble(X0) | curious(X0) [duplicate literal removal 127]
151. ~funny(X0) | generous(X0) [duplicate literal removal 122]
200. humble(X0) | patient(X0) [subsumption resolution 89,90]
203. ~generous(X0) | humble(X0) [subsumption resolution 94,200]
323. 36 <=> funny(paul) [avatar definition]
325. funny(paul) <- (36) [avatar component clause 323]
356. patient(X0) | curious(X0) [resolution 200,149]
357. patient(X0) [subsumption resolution 356,129]
384. funny(paul) | ~patient(paul) [resolution 97,148]
388. funny(paul) [subsumption resolution 384,357]
389. 36 [avatar split clause 388,323]
391. generous(paul) <- (36) [resolution 325,151]
396. humble(paul) <- (36) [resolution 391,203]
432. 44 <=> curious(paul) [avatar definition]
433. ~curious(paul) <- (~44) [avatar component clause 432]
434. curious(paul) <- (44) [avatar component clause 432]
442. ~quiet(paul) <- (44) [resolution 434,130]
446. $false <- (44) [subsumption resolution 442,148]
447. ~44 [avatar contradiction clause 446]
669. curious(paul) <- (36) [resolution 396,149]
670. $false <- (36, ~44) [subsumption resolution 669,433]
671. ~36 | 44 [avatar contradiction clause 670]
672. $false [avatar sat refutation 389,447,671]
% SZS output end Proof for 2635514519000153311413201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not happy or not wise then someone is either tall or quiet and vice versa.
If lucy is not calm or not funny then someone is curious and vice versa.
If someone is both not funny and funny then someone is happy and vice versa.
Everyone who is not kind or not tall is old or creative and vice versa.
Everyone who is either not happy or happy is not generous and vice versa.
Everyone who is not rich or not generous is brave and vice versa.
Everyone who is either curious or not quiet is either not old or tall.
If someone is both curious and not curious then susan is not calm or strong.
Everyone who is either not strong or happy is both not generous and not old and vice versa.
Everyone who is not quiet is either not kind or tall.
If lucy is not brave then someone is both rich and not calm.
Everyone who is both not strong and not funny is both curious and patient.
If lucy is either tall or creative then susan is brave.
Everyone who is not calm is either not patient or not tall and vice versa.
Everyone who is either not kind or not brave is curious and vice versa.
Everyone who is generous or not strong is not brave.
Someone is not creative.
Paul is both not rich and humble.
Someone is either not tall or tall.
Paul is both not curious and funny.
Fred is either calm or not creative.
Mary is curious.
Someone is either old or not wise. | Paul is not old. | contradiction | (((~happy(alice)|~wise(alice)))<=>(?[X]:((tall(X)<~>quiet(X)))))&
(((~calm(lucy)|~funny(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~kind(X)|~tall(X))<=>(old(X)|creative(X))))&
(![X]:((~happy(X)<~>happy(X))<=>~generous(X)))&
(![X]:((~rich(X)|~generous(X))<=>brave(X)))&
(![X]:((curious(X)<~>~quiet(X))=>(~old(X)<~>tall(X))))&
((?[X]:((curious(X)&~curious(X))))=>((~calm(susan)|strong(susan))))&
(![X]:((~strong(X)<~>happy(X))<=>(~generous(X)&~old(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>tall(X))))&
((~brave(lucy))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~strong(X)&~funny(X))=>(curious(X)&patient(X))))&
(((tall(lucy)<~>creative(lucy)))=>(brave(susan)))&
(![X]:(~calm(X)<=>(~patient(X)<~>~tall(X))))&
(![X]:((~kind(X)<~>~brave(X))<=>curious(X)))&
(![X]:((generous(X)|~strong(X))=>~brave(X)))&
(?[X]:(~creative(X)))&
((~rich(paul)&humble(paul)))&
(?[X]:((~tall(X)<~>tall(X))))&
((~curious(paul)&funny(paul)))&
((calm(fred)<~>~creative(fred)))&
(curious(mary))&
(?[X]:((old(X)<~>~wise(X)))) | ~old(paul) | [
"p2",
"p4",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7414026378403931631689363
% SZS output start Proof for 7414026378403931631689363
3. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X0] : happy(X0) [input p2]
5. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> ~generous(X0)) [input p4]
6. ! [X0] : ((~generous(X0) | ~rich(X0)) <=> brave(X0)) [input p5]
9. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~old(X0) & ~generous(X0))) [input p8]
16. ! [X0] : ((~strong(X0) | generous(X0)) => ~brave(X0)) [input p15]
24. ~old(paul) [input hypothesis]
25. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X1] : happy(X1) [rectify 3]
35. ! [X0] : (~brave(X0) | (strong(X0) & ~generous(X0))) [ennf transformation 16]
46. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (~funny(X0) | funny(X0))) [nnf transformation 25]
47. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (~funny(X3) | funny(X3))) [rectify 46]
48. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK2) & ~funny(sK2)) [choice axiom]
49. ? [X2] : happy(X2) => happy(sK3) [choice axiom]
50. ((funny(sK2) & ~funny(sK2)) | ! [X1] : ~happy(X1)) & (happy(sK3) | ! [X3] : (~funny(X3) | funny(X3))) [skolemisation 47,49,48]
53. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | generous(X0)) & (~generous(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 5]
54. ! [X0] : (((~generous(X0) | ~rich(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) & rich(X0)))) [nnf transformation 6]
55. ! [X0] : ((~generous(X0) | ~rich(X0) | ~brave(X0)) & (brave(X0) | (generous(X0) & rich(X0)))) [flattening 54]
57. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 57]
84. ~funny(sK2) | ~happy(X1) [cnf transformation 50]
85. funny(sK2) | ~happy(X1) [cnf transformation 50]
90. ~generous(X0) | happy(X0) | happy(X0) [cnf transformation 53]
91. ~generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 53]
95. brave(X0) | generous(X0) [cnf transformation 55]
106. happy(X0) | ~strong(X0) | old(X0) | generous(X0) [cnf transformation 58]
125. ~brave(X0) | strong(X0) [cnf transformation 35]
137. ~old(paul) [cnf transformation 24]
138. ~generous(X0) | happy(X0) [duplicate literal removal 90]
139. ~generous(X0) | ~happy(X0) [duplicate literal removal 91]
187. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
188. ~happy(X1) <- (11) [avatar component clause 187]
190. 12 <=> funny(sK2) [avatar definition]
193. 11 | 12 [avatar split clause 85,190,187]
194. 11 | ~12 [avatar split clause 84,190,187]
195. ~generous(X0) [subsumption resolution 138,139]
196. brave(X0) [subsumption resolution 95,195]
198. ~strong(X0) | happy(X0) | old(X0) [subsumption resolution 106,195]
201. strong(X0) [subsumption resolution 125,196]
291. happy(X1) | old(X1) [resolution 198,201]
293. old(X1) <- (11) [subsumption resolution 291,188]
301. $false <- (11) [resolution 293,137]
307. ~11 [avatar contradiction clause 301]
308. $false [avatar sat refutation 193,194,307]
% SZS output end Proof for 7414026378403931631689363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and humble then mary is either calm or not old and vice versa. Everyone who is either strong or old is both not creative and not curious. Everyone who is both not curious and humble is either humble or creative and vice versa. If lucy is calm then mary is not curious or curious and vice versa. Everyone who is not wise or strong is not creative and vice versa. If lucy is not brave or not curious then someone is not tall or not patient. Everyone who is both not curious and rich is both not creative and not kind. Everyone who is either not strong or not humble is both funny and not tall and vice versa. Everyone who is either creative or not wise is both strong and not curious and vice versa. Everyone who is both generous and not kind is both not tall and not funny and vice versa. Everyone who is not funny is both not generous and not brave. Everyone who is either not rich or not tall is not patient and vice versa. If paul is both strong and not happy then lucy is not old or not rich. If fred is either creative or not generous then alice is both not strong and curious. Everyone who is happy is both old and not funny. Everyone who is not kind is both humble and kind and vice versa. Lucy is not curious. Someone is both quiet and not calm. Someone is strong or not happy. | Alice is old. | neutral | ((?[X]:((~creative(X)&humble(X))))<=>((calm(mary)<~>~old(mary))))&
(![X]:((strong(X)<~>old(X))=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&humble(X))<=>(humble(X)<~>creative(X))))&
((calm(lucy))<=>((~curious(mary)|curious(mary))))&
(![X]:((~wise(X)|strong(X))<=>~creative(X)))&
(((~brave(lucy)|~curious(lucy)))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((~curious(X)&rich(X))=>(~creative(X)&~kind(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(funny(X)&~tall(X))))&
(![X]:((creative(X)<~>~wise(X))<=>(strong(X)&~curious(X))))&
(![X]:((generous(X)&~kind(X))<=>(~tall(X)&~funny(X))))&
(![X]:(~funny(X)=>(~generous(X)&~brave(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>~patient(X)))&
(((strong(paul)&~happy(paul)))=>((~old(lucy)|~rich(lucy))))&
(((creative(fred)<~>~generous(fred)))=>((~strong(alice)&curious(alice))))&
(![X]:(happy(X)=>(old(X)&~funny(X))))&
(![X]:(~kind(X)<=>(humble(X)&kind(X))))&
(~curious(lucy))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((strong(X)|~happy(X)))) | old(alice) | [] | null | 0 |
Everyone who is either not generous or happy is both not patient and not happy.
Everyone who is creative or brave is not strong or not happy.
If someone is quiet then mary is not creative and vice versa.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
Lucy is either tall or not funny.
Someone is either tall or not humble.
Someone is not kind or strong.
Someone is both not curious and quiet.
Fred is not curious or brave.
Mary is both not patient and not creative.
Fred is not patient or humble.
Someone is both wise and not rich. | Paul is not wise. | contradiction | (![X]:((~generous(X)<~>happy(X))=>(~patient(X)&~happy(X))))&
(![X]:((creative(X)|brave(X))=>(~strong(X)|~happy(X))))&
((?[X]:(quiet(X)))<=>(~creative(mary)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(mary)&~creative(mary)))&
((~patient(fred)|humble(fred)))&
(?[X]:((wise(X)&~rich(X)))) | ~wise(paul) | [
"p4",
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 48509618923509120356497
% SZS output start Proof for 48509618923509120356497
5. ! [X0] : ((~wise(X0) | patient(X0)) => ~curious(X0)) [input p4]
7. ! [X0] : ((strong(X0) | patient(X0)) <=> (happy(X0) & kind(X0))) [input p6]
15. ? [X0] : happy(X0) <=> (curious(lucy) & ~wise(lucy)) [input p14]
16. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
25. ~wise(paul) [input hypothesis]
31. ! [X0] : (~curious(X0) | (wise(X0) & ~patient(X0))) [ennf transformation 5]
51. ! [X0] : (((strong(X0) | patient(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [nnf transformation 7]
52. ! [X0] : ((strong(X0) | patient(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (~strong(X0) & ~patient(X0)))) [flattening 51]
67. (? [X0] : happy(X0) | (~curious(lucy) | wise(lucy))) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [nnf transformation 15]
68. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X0] : ~happy(X0)) [flattening 67]
69. (? [X0] : happy(X0) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [rectify 68]
70. ? [X0] : happy(X0) => happy(sK7) [choice axiom]
71. (happy(sK7) | ~curious(lucy) | wise(lucy)) & ((curious(lucy) & ~wise(lucy)) | ! [X1] : ~happy(X1)) [skolemisation 69,70]
72. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 16]
73. ! [X0] : (((~patient(X0) & strong(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | patient(X0) | ~strong(X0))) [flattening 72]
98. ~curious(X0) | wise(X0) [cnf transformation 31]
108. ~strong(X0) | happy(X0) [cnf transformation 52]
136. ~wise(lucy) | ~happy(X1) [cnf transformation 71]
137. curious(lucy) | ~happy(X1) [cnf transformation 71]
140. wise(X0) | strong(X0) [cnf transformation 73]
157. ~wise(paul) [cnf transformation 25]
175. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
176. ~happy(X0) <- (4) [avatar component clause 175]
300. 32 <=> curious(lucy) [avatar definition]
302. curious(lucy) <- (32) [avatar component clause 300]
303. 4 | 32 [avatar split clause 137,300,175]
305. 33 <=> wise(lucy) [avatar definition]
307. ~wise(lucy) <- (~33) [avatar component clause 305]
308. 4 | ~33 [avatar split clause 136,305,175]
352. strong(paul) [resolution 140,157]
354. happy(paul) [resolution 352,108]
356. $false <- (4) [subsumption resolution 354,176]
357. ~4 [avatar contradiction clause 356]
360. wise(lucy) <- (32) [resolution 302,98]
362. $false <- (32, ~33) [subsumption resolution 360,307]
363. ~32 | 33 [avatar contradiction clause 362]
364. $false [avatar sat refutation 303,308,357,363]
% SZS output end Proof for 48509618923509120356497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then john is not quiet or humble and vice versa.
Everyone who is not generous is not generous or old and vice versa.
If susan is generous then alice is both not kind and not wise and vice versa.
Everyone who is either not quiet or funny is rich.
If someone is either old or curious then lucy is either not brave or strong and vice versa.
If someone is both strong and brave then someone is curious and vice versa.
Everyone who is either funny or not calm is not humble.
If fred is either not humble or quiet then fred is strong and vice versa.
Everyone who is humble is either not curious or not brave.
Everyone who is not generous is both not old and not curious and vice versa.
Everyone who is patient is not creative or wise.
If alice is funny or not tall then someone is generous or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
Someone is either not old or brave.
Alice is both not creative and strong.
Someone is generous or not old.
Someone is both not brave and quiet.
John is not strong or not quiet.
Paul is generous or not generous. | Alice is not patient. | contradiction | ((?[X]:(kind(X)))<=>((~quiet(john)|humble(john))))&
(![X]:(~generous(X)<=>(~generous(X)|old(X))))&
((generous(susan))<=>((~kind(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>funny(X))=>rich(X)))&
((?[X]:((old(X)<~>curious(X))))<=>((~brave(lucy)<~>strong(lucy))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((funny(X)<~>~calm(X))=>~humble(X)))&
(((~humble(fred)<~>quiet(fred)))<=>(strong(fred)))&
(![X]:(humble(X)=>(~curious(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~old(X)&~curious(X))))&
(![X]:(patient(X)=>(~creative(X)|wise(X))))&
(((funny(alice)|~tall(alice)))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul))) | ~patient(alice) | [
"p1",
"p5",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8471079788074634399775729
% SZS output start Proof for 8471079788074634399775729
2. ! [X0] : (~generous(X0) <=> (old(X0) | ~generous(X0))) [input p1]
6. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X0] : curious(X0) [input p5]
10. ! [X0] : (~generous(X0) <=> (~curious(X0) & ~old(X0))) [input p9]
12. (~tall(alice) | funny(alice)) => ? [X0] : (brave(X0) | generous(X0)) [input p11]
13. ! [X0] : ((tall(X0) | ~wise(X0)) => patient(X0)) [input p12]
16. ! [X0] : ((~patient(X0) & ~brave(X0)) <=> (humble(X0) | brave(X0))) [input p15]
23. ~patient(alice) [input hypothesis]
24. ? [X0] : (brave(X0) & strong(X0)) <=> ? [X1] : curious(X1) [rectify 6]
30. ? [X0] : (brave(X0) | generous(X0)) | (tall(alice) & ~funny(alice)) [ennf transformation 12]
31. ! [X0] : (patient(X0) | (~tall(X0) & wise(X0))) [ennf transformation 13]
38. ! [X0] : ((~generous(X0) | (~old(X0) & generous(X0))) & ((old(X0) | ~generous(X0)) | generous(X0))) [nnf transformation 2]
39. ! [X0] : ((~generous(X0) | (~old(X0) & generous(X0))) & (old(X0) | ~generous(X0) | generous(X0))) [flattening 38]
46. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (~brave(X0) | ~strong(X0))) [nnf transformation 24]
47. (? [X0] : (brave(X0) & strong(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (~brave(X3) | ~strong(X3))) [rectify 46]
48. ? [X0] : (brave(X0) & strong(X0)) => (brave(sK2) & strong(sK2)) [choice axiom]
49. ? [X2] : curious(X2) => curious(sK3) [choice axiom]
50. ((brave(sK2) & strong(sK2)) | ! [X1] : ~curious(X1)) & (curious(sK3) | ! [X3] : (~brave(X3) | ~strong(X3))) [skolemisation 47,49,48]
54. ! [X0] : ((~generous(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | generous(X0))) [nnf transformation 10]
55. ! [X0] : ((~generous(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | generous(X0))) [flattening 54]
56. ? [X0] : (brave(X0) | generous(X0)) => (brave(sK4) | generous(sK4)) [choice axiom]
57. (brave(sK4) | generous(sK4)) | (tall(alice) & ~funny(alice)) [skolemisation 30,56]
60. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (patient(X0) | brave(X0)))) [nnf transformation 16]
61. ! [X0] : (((~patient(X0) & ~brave(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | patient(X0) | brave(X0))) [flattening 60]
74. ~old(X0) | ~generous(X0) [cnf transformation 39]
88. brave(sK2) | ~curious(X1) [cnf transformation 50]
99. ~generous(X0) | curious(X0) | old(X0) [cnf transformation 55]
101. brave(sK4) | generous(sK4) | tall(alice) [cnf transformation 57]
103. ~tall(X0) | patient(X0) [cnf transformation 31]
112. ~brave(X0) | ~brave(X0) [cnf transformation 61]
124. ~patient(alice) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 112]
191. 14 <=> ! [X1] : ~curious(X1) [avatar definition]
192. ~curious(X1) <- (14) [avatar component clause 191]
194. 15 <=> brave(sK2) [avatar definition]
196. brave(sK2) <- (15) [avatar component clause 194]
197. 14 | 15 [avatar split clause 88,194,191]
227. ~generous(X0) | curious(X0) [subsumption resolution 99,74]
230. 22 <=> tall(alice) [avatar definition]
232. tall(alice) <- (22) [avatar component clause 230]
234. 23 <=> generous(sK4) [avatar definition]
236. generous(sK4) <- (23) [avatar component clause 234]
238. 24 <=> brave(sK4) [avatar definition]
240. brave(sK4) <- (24) [avatar component clause 238]
241. 22 | 23 | 24 [avatar split clause 101,238,234,230]
257. $false <- (15) [subsumption resolution 196,126]
258. ~15 [avatar contradiction clause 257]
265. patient(alice) <- (22) [resolution 103,232]
266. $false <- (22) [subsumption resolution 265,124]
267. ~22 [avatar contradiction clause 266]
268. $false <- (24) [subsumption resolution 240,126]
269. ~24 [avatar contradiction clause 268]
281. curious(sK4) <- (23) [resolution 227,236]
282. $false <- (14, 23) [subsumption resolution 281,192]
283. ~14 | ~23 [avatar contradiction clause 282]
284. $false [avatar sat refutation 197,241,258,267,269,283]
% SZS output end Proof for 8471079788074634399775729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not rich is both tall and curious and vice versa.
Everyone who is both patient and generous is happy or not old.
Everyone who is both rich and not tall is kind.
If someone is both patient and brave then someone is both not kind and happy and vice versa.
Everyone who is not patient is not calm or not old and vice versa.
Everyone who is either not happy or funny is rich.
Everyone who is generous or kind is not old or not quiet and vice versa.
Everyone who is quiet or happy is not calm.
Everyone who is humble or not wise is either patient or not old and vice versa.
Everyone who is both creative and patient is either not curious or not patient and vice versa.
If john is not rich or not generous then fred is both not happy and not humble and vice versa.
Everyone who is both strong and creative is both not rich and not funny.
Everyone who is either not brave or not curious is either quiet or old and vice versa.
Everyone who is both not strong and not creative is wise or creative.
Susan is not brave or not calm.
Paul is both calm and not funny.
Someone is not rich.
Mary is not patient or patient.
John is kind.
Someone is kind. | Fred is strong. | entailment | (![X]:((rich(X)<~>~rich(X))<=>(tall(X)&curious(X))))&
(![X]:((patient(X)&generous(X))=>(happy(X)|~old(X))))&
(![X]:((rich(X)&~tall(X))=>kind(X)))&
((?[X]:((patient(X)&brave(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:(~patient(X)<=>(~calm(X)|~old(X))))&
(![X]:((~happy(X)<~>funny(X))=>rich(X)))&
(![X]:((generous(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(![X]:((quiet(X)|happy(X))=>~calm(X)))&
(![X]:((humble(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((creative(X)&patient(X))<=>(~curious(X)<~>~patient(X))))&
(((~rich(john)|~generous(john)))<=>((~happy(fred)&~humble(fred))))&
(![X]:((strong(X)&creative(X))=>(~rich(X)&~funny(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~strong(X)&~creative(X))=>(wise(X)|creative(X))))&
((~brave(susan)|~calm(susan)))&
((calm(paul)&~funny(paul)))&
(?[X]:(~rich(X)))&
((~patient(mary)|patient(mary)))&
(kind(john))&
(?[X]:(kind(X))) | strong(fred) | [
"p0",
"p1",
"p4",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5063362540863440451899911
% SZS output start Proof for 5063362540863440451899911
1. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (curious(X0) & tall(X0))) [input p0]
2. ! [X0] : ((generous(X0) & patient(X0)) => (~old(X0) | happy(X0))) [input p1]
5. ! [X0] : (~patient(X0) <=> (~old(X0) | ~calm(X0))) [input p4]
8. ! [X0] : ((happy(X0) | quiet(X0)) => ~calm(X0)) [input p7]
9. ! [X0] : ((~wise(X0) | humble(X0)) <=> (patient(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : ((patient(X0) & creative(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p9]
11. (~generous(john) | ~rich(john)) <=> (~humble(fred) & ~happy(fred)) [input p10]
14. ! [X0] : ((~creative(X0) & ~strong(X0)) => (creative(X0) | wise(X0))) [input p13]
21. ~strong(fred) [input hypothesis]
23. ! [X0] : ((~old(X0) | happy(X0)) | (~generous(X0) | ~patient(X0))) [ennf transformation 2]
24. ! [X0] : (~old(X0) | happy(X0) | ~generous(X0) | ~patient(X0)) [flattening 23]
28. ! [X0] : (~calm(X0) | (~happy(X0) & ~quiet(X0))) [ennf transformation 8]
31. ! [X0] : ((creative(X0) | wise(X0)) | (creative(X0) | strong(X0))) [ennf transformation 14]
32. ! [X0] : (creative(X0) | wise(X0) | creative(X0) | strong(X0)) [flattening 31]
33. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 1]
34. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [flattening 33]
40. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & ((~old(X0) | ~calm(X0)) | patient(X0))) [nnf transformation 5]
41. ! [X0] : ((~patient(X0) | (old(X0) & calm(X0))) & (~old(X0) | ~calm(X0) | patient(X0))) [flattening 40]
45. ! [X0] : (((~wise(X0) | humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~humble(X0)))) [nnf transformation 9]
46. ! [X0] : ((~wise(X0) | humble(X0) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (wise(X0) & ~humble(X0)))) [flattening 45]
47. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (~patient(X0) | ~creative(X0)))) [nnf transformation 10]
48. ! [X0] : (((patient(X0) & creative(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~patient(X0) | ~creative(X0))) [flattening 47]
49. ((~generous(john) | ~rich(john)) | (humble(fred) | happy(fred))) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [nnf transformation 11]
50. (~generous(john) | ~rich(john) | humble(fred) | happy(fred)) & ((~humble(fred) & ~happy(fred)) | (generous(john) & rich(john))) [flattening 49]
58. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 34]
59. curious(X0) | rich(X0) | rich(X0) [cnf transformation 34]
62. ~old(X0) | happy(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 24]
69. ~patient(X0) | calm(X0) [cnf transformation 41]
70. ~patient(X0) | old(X0) [cnf transformation 41]
78. ~calm(X0) | ~happy(X0) [cnf transformation 28]
83. ~wise(X0) | humble(X0) | ~old(X0) | ~patient(X0) [cnf transformation 46]
85. ~patient(X0) | ~curious(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 48]
90. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 48]
94. ~humble(fred) | generous(john) [cnf transformation 50]
106. creative(X0) | wise(X0) | creative(X0) | strong(X0) [cnf transformation 32]
114. ~strong(fred) [cnf transformation 21]
115. creative(X0) | wise(X0) | strong(X0) [duplicate literal removal 106]
116. ~patient(X0) | ~curious(X0) | ~creative(X0) [duplicate literal removal 85]
117. patient(X0) | ~curious(X0) [duplicate literal removal 90]
120. curious(X0) | ~rich(X0) [duplicate literal removal 58]
121. curious(X0) | rich(X0) [duplicate literal removal 59]
122. curious(X0) [subsumption resolution 120,121]
151. ~wise(X0) | humble(X0) | ~patient(X0) [subsumption resolution 83,70]
152. patient(X0) [subsumption resolution 117,122]
153. ~curious(X0) | ~creative(X0) [subsumption resolution 116,152]
154. ~creative(X0) [subsumption resolution 153,122]
160. 8 <=> humble(fred) [avatar definition]
168. 10 <=> generous(john) [avatar definition]
169. generous(john) <- (10) [avatar component clause 168]
172. 10 | ~8 [avatar split clause 94,160,168]
180. strong(X0) | wise(X0) [subsumption resolution 115,154]
193. calm(X0) [resolution 69,152]
196. old(X0) [resolution 70,152]
198. ~happy(X0) [resolution 78,193]
199. wise(fred) [resolution 180,114]
212. humble(fred) | ~patient(fred) [resolution 151,199]
216. humble(fred) [subsumption resolution 212,152]
217. 8 [avatar split clause 216,160]
228. happy(X0) | ~generous(X0) | ~patient(X0) [resolution 62,196]
229. ~generous(X0) | ~patient(X0) [subsumption resolution 228,198]
230. ~generous(X0) [subsumption resolution 229,152]
231. $false <- (10) [resolution 230,169]
232. ~10 [avatar contradiction clause 231]
233. $false [avatar sat refutation 172,217,232]
% SZS output end Proof for 5063362540863440451899911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either wise or creative then fred is either tall or rich.
If someone is funny then john is generous and vice versa.
If mary is kind or not curious then john is both not humble and creative and vice versa.
Everyone who is both old and not funny is not funny.
Everyone who is not funny is creative or calm and vice versa.
If fred is both curious and not old then susan is either not quiet or generous and vice versa.
Everyone who is not quiet or not generous is not patient.
Everyone who is either generous or not patient is not happy or not rich and vice versa.
Everyone who is not kind is quiet and vice versa.
If john is both old and kind then someone is not curious or old.
If john is brave then someone is both not creative and not kind.
If john is both creative and not strong then mary is either not quiet or happy.
If john is both not quiet and rich then someone is brave and vice versa.
Everyone who is both brave and not brave is both kind and not generous and vice versa.
Everyone who is not strong or old is both not kind and not tall and vice versa.
Everyone who is both not strong and curious is kind or not generous.
Mary is either generous or humble.
Someone is either kind or not strong.
Paul is either creative or not curious.
Alice is both generous and wise.
Alice is not quiet.
Alice is either rich or not kind.
Someone is not kind.
Someone is rich. | Mary is creative. | neutral | (((wise(lucy)<~>creative(lucy)))=>((tall(fred)<~>rich(fred))))&
((?[X]:(funny(X)))<=>(generous(john)))&
(((kind(mary)|~curious(mary)))<=>((~humble(john)&creative(john))))&
(![X]:((old(X)&~funny(X))=>~funny(X)))&
(![X]:(~funny(X)<=>(creative(X)|calm(X))))&
(((curious(fred)&~old(fred)))<=>((~quiet(susan)<~>generous(susan))))&
(![X]:((~quiet(X)|~generous(X))=>~patient(X)))&
(![X]:((generous(X)<~>~patient(X))<=>(~happy(X)|~rich(X))))&
(![X]:(~kind(X)<=>quiet(X)))&
(((old(john)&kind(john)))=>(?[X]:((~curious(X)|old(X)))))&
((brave(john))=>(?[X]:((~creative(X)&~kind(X)))))&
(((creative(john)&~strong(john)))=>((~quiet(mary)<~>happy(mary))))&
(((~quiet(john)&rich(john)))<=>(?[X]:(brave(X))))&
(![X]:((brave(X)&~brave(X))<=>(kind(X)&~generous(X))))&
(![X]:((~strong(X)|old(X))<=>(~kind(X)&~tall(X))))&
(![X]:((~strong(X)&curious(X))=>(kind(X)|~generous(X))))&
((generous(mary)<~>humble(mary)))&
(?[X]:((kind(X)<~>~strong(X))))&
((creative(paul)<~>~curious(paul)))&
((generous(alice)&wise(alice)))&
(~quiet(alice))&
((rich(alice)<~>~kind(alice)))&
(?[X]:(~kind(X)))&
(?[X]:(rich(X))) | creative(mary) | [] | null | 0 |
If lucy is patient or not strong then someone is both not happy and kind and vice versa.
Everyone who is both calm and strong is either not wise or old.
If someone is tall or not humble then someone is either creative or generous.
Everyone who is not tall or not rich is both old and not curious.
If john is either not funny or creative then paul is humble or curious and vice versa.
Everyone who is wise is old or strong.
Everyone who is not funny or brave is curious and vice versa.
Everyone who is humble is both not curious and not kind and vice versa.
Everyone who is either not tall or old is both not creative and patient.
If someone is kind then someone is curious and vice versa.
Everyone who is not kind is humble or not generous.
Everyone who is either not generous or calm is not quiet or not tall and vice versa.
Everyone who is both brave and not happy is old or not creative and vice versa.
Everyone who is not old is curious.
Everyone who is happy or old is not old and vice versa.
Someone is both generous and curious.
Mary is rich or curious.
John is creative or not curious.
Someone is rich or strong.
Mary is both generous and not brave.
Someone is either kind or not funny. | Mary is kind. | entailment | (((patient(lucy)|~strong(lucy)))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:(curious(X))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((brave(X)&~happy(X))<=>(old(X)|~creative(X))))&
(![X]:(~old(X)=>curious(X)))&
(![X]:((happy(X)|old(X))<=>~old(X)))&
(?[X]:((generous(X)&curious(X))))&
((rich(mary)|curious(mary)))&
((creative(john)|~curious(john)))&
(?[X]:((rich(X)|strong(X))))&
((generous(mary)&~brave(mary)))&
(?[X]:((kind(X)<~>~funny(X)))) | kind(mary) | [
"p7",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7191761709609832548759020
% SZS output start Proof for 7191761709609832548759020
8. ! [X0] : (humble(X0) <=> (~kind(X0) & ~curious(X0))) [input p7]
11. ! [X0] : (~kind(X0) => (~generous(X0) | humble(X0))) [input p10]
14. ! [X0] : (~old(X0) => curious(X0)) [input p13]
15. ! [X0] : ((old(X0) | happy(X0)) <=> ~old(X0)) [input p14]
20. ~brave(mary) & generous(mary) [input p19]
22. ~kind(mary) [input hypothesis]
35. ! [X0] : ((~generous(X0) | humble(X0)) | kind(X0)) [ennf transformation 11]
36. ! [X0] : (~generous(X0) | humble(X0) | kind(X0)) [flattening 35]
37. ! [X0] : (curious(X0) | old(X0)) [ennf transformation 14]
52. ! [X0] : ((humble(X0) | (kind(X0) | curious(X0))) & ((~kind(X0) & ~curious(X0)) | ~humble(X0))) [nnf transformation 8]
53. ! [X0] : ((humble(X0) | kind(X0) | curious(X0)) & ((~kind(X0) & ~curious(X0)) | ~humble(X0))) [flattening 52]
64. ! [X0] : (((old(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [nnf transformation 15]
65. ! [X0] : ((old(X0) | happy(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [flattening 64]
94. ~curious(X0) | ~humble(X0) [cnf transformation 53]
103. ~generous(X0) | humble(X0) | kind(X0) [cnf transformation 36]
115. curious(X0) | old(X0) [cnf transformation 37]
117. ~old(X0) | ~old(X0) [cnf transformation 65]
122. generous(mary) [cnf transformation 20]
126. ~kind(mary) [cnf transformation 22]
127. ~old(X0) [duplicate literal removal 117]
244. old(X0) | ~humble(X0) [resolution 115,94]
250. ~humble(X0) [subsumption resolution 244,127]
281. humble(mary) | kind(mary) [resolution 103,122]
283. kind(mary) [subsumption resolution 281,250]
284. $false [subsumption resolution 283,126]
% SZS output end Proof for 7191761709609832548759020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not kind is not funny or not kind.
Everyone who is not creative or creative is both not generous and not tall.
Everyone who is either not creative or funny is not generous and vice versa.
Everyone who is both not patient and not humble is both tall and not humble and vice versa.
If someone is both kind and creative then someone is either tall or not calm and vice versa.
If john is both rich and not brave then someone is strong and vice versa.
If someone is not patient or not strong then someone is humble and vice versa.
If someone is wise then someone is both happy and not strong.
Everyone who is strong or not creative is creative or tall.
Everyone who is not old is curious and vice versa.
If lucy is strong or kind then someone is both generous and rich and vice versa.
Everyone who is both brave and wise is creative and vice versa.
Everyone who is brave or humble is both humble and not patient.
If someone is not creative or generous then mary is not wise.
If someone is not generous or not tall then alice is either not calm or not old and vice versa.
Someone is either not tall or not curious.
Alice is both wise and not generous.
Alice is creative.
Someone is both not patient and not generous.
Someone is both brave and not calm.
Someone is humble or not quiet.
Someone is not patient or brave.
Someone is either quiet or not generous. | Lucy is not strong. | entailment | (![X]:((~happy(X)|~kind(X))=>(~funny(X)|~kind(X))))&
(![X]:((~creative(X)|creative(X))=>(~generous(X)&~tall(X))))&
(![X]:((~creative(X)<~>funny(X))<=>~generous(X)))&
(![X]:((~patient(X)&~humble(X))<=>(tall(X)&~humble(X))))&
((?[X]:((kind(X)&creative(X))))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((rich(john)&~brave(john)))<=>(?[X]:(strong(X))))&
((?[X]:((~patient(X)|~strong(X))))<=>(?[X]:(humble(X))))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)&~strong(X)))))&
(![X]:((strong(X)|~creative(X))=>(creative(X)|tall(X))))&
(![X]:(~old(X)<=>curious(X)))&
(((strong(lucy)|kind(lucy)))<=>(?[X]:((generous(X)&rich(X)))))&
(![X]:((brave(X)&wise(X))<=>creative(X)))&
(![X]:((brave(X)|humble(X))=>(humble(X)&~patient(X))))&
((?[X]:((~creative(X)|generous(X))))=>(~wise(mary)))&
((?[X]:((~generous(X)|~tall(X))))<=>((~calm(alice)<~>~old(alice))))&
(?[X]:((~tall(X)<~>~curious(X))))&
((wise(alice)&~generous(alice)))&
(creative(alice))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:((humble(X)|~quiet(X))))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((quiet(X)<~>~generous(X)))) | ~strong(lucy) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2607457646103369835260703
% SZS output start Proof for 2607457646103369835260703
2. ! [X0] : ((creative(X0) | ~creative(X0)) => (~tall(X0) & ~generous(X0))) [input p1]
11. (kind(lucy) | strong(lucy)) <=> ? [X0] : (rich(X0) & generous(X0)) [input p10]
24. strong(lucy) [input hypothesis]
32. ! [X0] : ((~tall(X0) & ~generous(X0)) | (~creative(X0) & creative(X0))) [ennf transformation 2]
60. ((kind(lucy) | strong(lucy)) | ! [X0] : (~rich(X0) | ~generous(X0))) & (? [X0] : (rich(X0) & generous(X0)) | (~kind(lucy) & ~strong(lucy))) [nnf transformation 11]
61. (kind(lucy) | strong(lucy) | ! [X0] : (~rich(X0) | ~generous(X0))) & (? [X0] : (rich(X0) & generous(X0)) | (~kind(lucy) & ~strong(lucy))) [flattening 60]
62. (kind(lucy) | strong(lucy) | ! [X0] : (~rich(X0) | ~generous(X0))) & (? [X1] : (rich(X1) & generous(X1)) | (~kind(lucy) & ~strong(lucy))) [rectify 61]
63. ? [X1] : (rich(X1) & generous(X1)) => (rich(sK6) & generous(sK6)) [choice axiom]
64. (kind(lucy) | strong(lucy) | ! [X0] : (~rich(X0) | ~generous(X0))) & ((rich(sK6) & generous(sK6)) | (~kind(lucy) & ~strong(lucy))) [skolemisation 62,63]
86. ~generous(X0) | creative(X0) [cnf transformation 32]
87. ~generous(X0) | ~creative(X0) [cnf transformation 32]
115. generous(sK6) | ~strong(lucy) [cnf transformation 64]
148. strong(lucy) [cnf transformation 24]
151. ~generous(X0) [subsumption resolution 86,87]
240. 20 <=> strong(lucy) [avatar definition]
246. ~strong(lucy) [subsumption resolution 115,151]
247. ~20 [avatar split clause 246,240]
270. 20 [avatar split clause 148,240]
271. $false [avatar sat refutation 247,270]
% SZS output end Proof for 2607457646103369835260703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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