premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If lucy is funny or brave then someone is rich or brave and vice versa. Everyone who is both kind and wise is both kind and not old. Everyone who is creative is curious and vice versa. If mary is humble or not curious then someone is not calm. Everyone who is strong or not quiet is both not creative and happy. Everyone who is wise is either not strong or not old. Everyone who is happy is both not curious and not calm. Everyone who is not funny is either not strong or not kind and vice versa. Everyone who is funny is either creative or happy and vice versa. Everyone who is both not happy and patient is both old and not brave. If someone is either curious or not creative then someone is both not patient and tall. If someone is either not humble or not patient then someone is both patient and happy and vice versa. Everyone who is not kind is both humble and strong and vice versa. If someone is either not quiet or not happy then fred is both not curious and not creative and vice versa. Everyone who is calm is strong or not rich. If alice is both strong and not curious then paul is either not wise or curious and vice versa. John is humble. Lucy is not wise. Alice is both not happy and not curious. Someone is both quiet and old. Someone is tall or wise. Fred is both not wise and not humble. | Alice is quiet. | entailment | (((funny(lucy)|brave(lucy)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)&~old(X))))&
(![X]:(creative(X)<=>curious(X)))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(![X]:(happy(X)=>(~curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((~happy(X)&patient(X))=>(old(X)&~brave(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:(~kind(X)<=>(humble(X)&strong(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((~curious(fred)&~creative(fred))))&
(![X]:(calm(X)=>(strong(X)|~rich(X))))&
(((strong(alice)&~curious(alice)))<=>((~wise(paul)<~>curious(paul))))&
(humble(john))&
(~wise(lucy))&
((~happy(alice)&~curious(alice)))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((tall(X)|wise(X))))&
((~wise(fred)&~humble(fred))) | quiet(alice) | [
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4616762624409657633543513
% SZS output start Proof for 4616762624409657633543513
5. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p4]
19. ~curious(alice) & ~happy(alice) [input p18]
23. ~quiet(alice) [input hypothesis]
33. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 5]
79. happy(X0) | quiet(X0) [cnf transformation 33]
118. ~happy(alice) [cnf transformation 19]
124. ~quiet(alice) [cnf transformation 23]
254. quiet(alice) [resolution 79,118]
255. $false [subsumption resolution 254,124]
% SZS output end Proof for 4616762624409657633543513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or tall is both kind and not brave and vice versa.
If alice is not curious or not quiet then someone is funny and vice versa.
Everyone who is calm or not strong is not quiet or not wise and vice versa.
If lucy is humble or strong then someone is either not curious or not happy.
Everyone who is not strong is calm or tall and vice versa.
If john is not funny then alice is not curious.
If someone is both not generous and humble then fred is creative.
If someone is kind then someone is calm.
If someone is strong then someone is both not happy and kind.
If john is strong or not generous then fred is both not wise and kind.
Everyone who is not calm is kind or not old and vice versa.
Everyone who is both not curious and not old is both not calm and strong.
If lucy is both not tall and not quiet then someone is both not humble and quiet and vice versa.
If john is not generous or not wise then fred is strong or tall and vice versa.
Everyone who is not generous or quiet is both strong and not happy.
If susan is not kind or brave then mary is either wise or kind.
John is both wise and old.
Fred is quiet or creative.
Someone is both old and not humble.
Someone is happy.
Susan is tall or not wise.
Someone is both tall and humble.
Someone is not old or humble.
Someone is both tall and not calm. | Susan is generous. | entailment | (![X]:((~quiet(X)<~>tall(X))<=>(kind(X)&~brave(X))))&
(((~curious(alice)|~quiet(alice)))<=>(?[X]:(funny(X))))&
(![X]:((calm(X)|~strong(X))<=>(~quiet(X)|~wise(X))))&
(((humble(lucy)|strong(lucy)))=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:(~strong(X)<=>(calm(X)|tall(X))))&
((~funny(john))=>(~curious(alice)))&
((?[X]:((~generous(X)&humble(X))))=>(creative(fred)))&
((?[X]:(kind(X)))=>(?[X]:(calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~happy(X)&kind(X)))))&
(((strong(john)|~generous(john)))=>((~wise(fred)&kind(fred))))&
(![X]:(~calm(X)<=>(kind(X)|~old(X))))&
(![X]:((~curious(X)&~old(X))=>(~calm(X)&strong(X))))&
(((~tall(lucy)&~quiet(lucy)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((~generous(john)|~wise(john)))<=>((strong(fred)|tall(fred))))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~happy(X))))&
(((~kind(susan)|brave(susan)))=>((wise(mary)<~>kind(mary))))&
((wise(john)&old(john)))&
((quiet(fred)|creative(fred)))&
(?[X]:((old(X)&~humble(X))))&
(?[X]:(happy(X)))&
((tall(susan)|~wise(susan)))&
(?[X]:((tall(X)&humble(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((tall(X)&~calm(X)))) | generous(susan) | [
"p2",
"p4",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5001755669464180121362408
% SZS output start Proof for 5001755669464180121362408
3. ! [X0] : ((~strong(X0) | calm(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p2]
5. ! [X0] : (~strong(X0) <=> (tall(X0) | calm(X0))) [input p4]
15. ! [X0] : ((quiet(X0) | ~generous(X0)) => (~happy(X0) & strong(X0))) [input p14]
21. ~wise(susan) | tall(susan) [input p20]
25. ~generous(susan) [input hypothesis]
37. ! [X0] : ((~happy(X0) & strong(X0)) | (~quiet(X0) & generous(X0))) [ennf transformation 15]
46. ! [X0] : (((~strong(X0) | calm(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (strong(X0) & ~calm(X0)))) [nnf transformation 3]
47. ! [X0] : ((~strong(X0) | calm(X0) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | (strong(X0) & ~calm(X0)))) [flattening 46]
51. ! [X0] : ((~strong(X0) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | strong(X0))) [nnf transformation 5]
52. ! [X0] : ((~strong(X0) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | strong(X0))) [flattening 51]
91. ~strong(X0) | calm(X0) | wise(X0) [cnf transformation 47]
97. ~strong(X0) | ~calm(X0) [cnf transformation 52]
98. ~strong(X0) | ~tall(X0) [cnf transformation 52]
120. generous(X0) | strong(X0) [cnf transformation 37]
133. ~wise(susan) | tall(susan) [cnf transformation 21]
139. ~generous(susan) [cnf transformation 25]
285. 31 <=> tall(susan) [avatar definition]
289. 32 <=> wise(susan) [avatar definition]
291. ~wise(susan) <- (~32) [avatar component clause 289]
292. 31 | ~32 [avatar split clause 133,289,285]
302. strong(susan) [resolution 120,139]
316. ~tall(susan) [resolution 302,98]
317. ~calm(susan) [resolution 302,97]
318. ~31 [avatar split clause 316,285]
382. calm(susan) | wise(susan) [resolution 91,302]
384. wise(susan) [subsumption resolution 382,317]
385. $false <- (~32) [subsumption resolution 384,291]
386. 32 [avatar contradiction clause 385]
387. $false [avatar sat refutation 292,318,386]
% SZS output end Proof for 5001755669464180121362408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or generous then lucy is patient and vice versa.
If fred is either not calm or not wise then someone is both not generous and not funny and vice versa.
Everyone who is either not curious or tall is generous.
If someone is not calm or not wise then lucy is either humble or funny.
If someone is either not brave or not tall then someone is either not curious or quiet and vice versa.
If john is creative or not brave then someone is either brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
If someone is not creative or not tall then susan is not brave and vice versa.
Everyone who is creative or kind is both patient and not creative and vice versa.
Someone is not brave or not strong.
Someone is both not brave and not rich.
Someone is either not funny or not old.
Someone is either happy or humble.
Lucy is either patient or strong.
Someone is rich.
Fred is either generous or curious. | Lucy is calm. | entailment | ((?[X]:((~humble(X)<~>generous(X))))<=>(patient(lucy)))&
(((~calm(fred)<~>~wise(fred)))<=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((~curious(X)<~>tall(X))=>generous(X)))&
((?[X]:((~calm(X)|~wise(X))))=>((humble(lucy)<~>funny(lucy))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((creative(john)|~brave(john)))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>(~brave(susan)))&
(![X]:((creative(X)|kind(X))<=>(patient(X)&~creative(X))))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~brave(X)&~rich(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((patient(lucy)<~>strong(lucy)))&
(?[X]:(rich(X)))&
((generous(fred)<~>curious(fred))) | calm(lucy) | [
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4855865391325561227186273
% SZS output start Proof for 4855865391325561227186273
12. ! [X0] : ((~calm(X0) | creative(X0)) => (generous(X0) & creative(X0))) [input p11]
16. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) & patient(X0))) [input p15]
24. ~calm(lucy) [input hypothesis]
33. ! [X0] : ((generous(X0) & creative(X0)) | (calm(X0) & ~creative(X0))) [ennf transformation 12]
77. ! [X0] : (((kind(X0) | creative(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 16]
78. ! [X0] : ((kind(X0) | creative(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 77]
148. creative(X0) | calm(X0) [cnf transformation 33]
168. ~creative(X0) | ~creative(X0) [cnf transformation 78]
183. ~calm(lucy) [cnf transformation 24]
184. ~creative(X0) [duplicate literal removal 168]
248. 14 <=> ! [X0] : calm(X0) [avatar definition]
249. calm(X0) <- (14) [avatar component clause 248]
458. calm(X0) [resolution 148,184]
459. 14 [avatar split clause 458,248]
460. $false <- (14) [resolution 249,183]
463. ~14 [avatar contradiction clause 460]
464. $false [avatar sat refutation 459,463]
% SZS output end Proof for 4855865391325561227186273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not brave is both not old and creative and vice versa.
Everyone who is either not quiet or wise is not rich and vice versa.
If someone is either curious or not generous then someone is both funny and not humble and vice versa.
Everyone who is both not curious and not wise is not happy and vice versa.
If lucy is either not rich or patient then lucy is curious or humble and vice versa.
Everyone who is both kind and old is funny and vice versa.
If someone is not calm or not generous then someone is both not creative and humble.
Everyone who is both not funny and not old is quiet or not quiet.
If john is humble then mary is either generous or not creative.
Everyone who is not humble or not old is both generous and not tall.
Everyone who is both curious and funny is either not funny or curious and vice versa.
Everyone who is both not funny and not tall is not kind or humble.
Everyone who is both generous and funny is both not kind and creative.
If paul is not humble then fred is both not curious and not tall.
Everyone who is both brave and not quiet is funny or not tall.
Everyone who is either not humble or humble is not generous and vice versa.
John is both not wise and happy.
Lucy is not funny.
Someone is either not strong or not patient.
Paul is both not generous and patient.
Someone is either wise or calm.
Someone is not kind.
Fred is either kind or humble. | Paul is not kind. | neutral | (![X]:((~old(X)|~brave(X))<=>(~old(X)&creative(X))))&
(![X]:((~quiet(X)<~>wise(X))<=>~rich(X)))&
((?[X]:((curious(X)<~>~generous(X))))<=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((~curious(X)&~wise(X))<=>~happy(X)))&
(((~rich(lucy)<~>patient(lucy)))<=>((curious(lucy)|humble(lucy))))&
(![X]:((kind(X)&old(X))<=>funny(X)))&
((?[X]:((~calm(X)|~generous(X))))=>(?[X]:((~creative(X)&humble(X)))))&
(![X]:((~funny(X)&~old(X))=>(quiet(X)|~quiet(X))))&
((humble(john))=>((generous(mary)<~>~creative(mary))))&
(![X]:((~humble(X)|~old(X))=>(generous(X)&~tall(X))))&
(![X]:((curious(X)&funny(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~funny(X)&~tall(X))=>(~kind(X)|humble(X))))&
(![X]:((generous(X)&funny(X))=>(~kind(X)&creative(X))))&
((~humble(paul))=>((~curious(fred)&~tall(fred))))&
(![X]:((brave(X)&~quiet(X))=>(funny(X)|~tall(X))))&
(![X]:((~humble(X)<~>humble(X))<=>~generous(X)))&
((~wise(john)&happy(john)))&
(~funny(lucy))&
(?[X]:((~strong(X)<~>~patient(X))))&
((~generous(paul)&patient(paul)))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:(~kind(X)))&
((kind(fred)<~>humble(fred))) | ~kind(paul) | [] | null | 0 |
Everyone who is not brave is not patient. If someone is creative or not patient then someone is patient or not quiet. Everyone who is either patient or old is either not happy or not old. Everyone who is funny or generous is not brave or creative and vice versa. If someone is wise or not tall then someone is not old and vice versa. Everyone who is not calm is not curious. Everyone who is not happy is curious and vice versa. Everyone who is either quiet or curious is either not kind or strong and vice versa. Everyone who is kind is calm or not quiet and vice versa. If susan is not rich or funny then someone is both not strong and not calm. If alice is quiet or generous then someone is not kind or quiet. Everyone who is old is not happy or tall. If paul is both not patient and not wise then someone is either not tall or not calm and vice versa. Everyone who is both quiet and old is either not strong or calm and vice versa. Everyone who is either not patient or old is both calm and not patient and vice versa. Everyone who is both not quiet and strong is humble or brave. Someone is both not old and not generous. John is either not happy or not generous. Someone is both not old and not quiet. Lucy is either funny or not strong. John is both not wise and rich. John is brave or not brave. Susan is both not tall and kind. | John is kind. | entailment | (![X]:(~brave(X)=>~patient(X)))&
((?[X]:((creative(X)|~patient(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((patient(X)<~>old(X))=>(~happy(X)<~>~old(X))))&
(![X]:((funny(X)|generous(X))<=>(~brave(X)|creative(X))))&
((?[X]:((wise(X)|~tall(X))))<=>(?[X]:(~old(X))))&
(![X]:(~calm(X)=>~curious(X)))&
(![X]:(~happy(X)<=>curious(X)))&
(![X]:((quiet(X)<~>curious(X))<=>(~kind(X)<~>strong(X))))&
(![X]:(kind(X)<=>(calm(X)|~quiet(X))))&
(((~rich(susan)|funny(susan)))=>(?[X]:((~strong(X)&~calm(X)))))&
(((quiet(alice)|generous(alice)))=>(?[X]:((~kind(X)|quiet(X)))))&
(![X]:(old(X)=>(~happy(X)|tall(X))))&
(((~patient(paul)&~wise(paul)))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((quiet(X)&old(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((~patient(X)<~>old(X))<=>(calm(X)&~patient(X))))&
(![X]:((~quiet(X)&strong(X))=>(humble(X)|brave(X))))&
(?[X]:((~old(X)&~generous(X))))&
((~happy(john)<~>~generous(john)))&
(?[X]:((~old(X)&~quiet(X))))&
((funny(lucy)<~>~strong(lucy)))&
((~wise(john)&rich(john)))&
((brave(john)|~brave(john)))&
((~tall(susan)&kind(susan))) | kind(john) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6326886747526354095229352
% SZS output start Proof for 6326886747526354095229352
3. ! [X0] : ((patient(X0) <~> old(X0)) => (~happy(X0) <~> ~old(X0))) [input p2]
6. ! [X0] : (~calm(X0) => ~curious(X0)) [input p5]
7. ! [X0] : (~happy(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (~kind(X0) <~> strong(X0))) [input p7]
9. ! [X0] : (kind(X0) <=> (~quiet(X0) | calm(X0))) [input p8]
14. ! [X0] : ((old(X0) & quiet(X0)) <=> (~strong(X0) <~> calm(X0))) [input p13]
15. ! [X0] : ((~patient(X0) <~> old(X0)) <=> (~patient(X0) & calm(X0))) [input p14]
24. ~kind(john) [input hypothesis]
32. ! [X0] : ((~happy(X0) <~> ~old(X0)) | (patient(X0) <=> old(X0))) [ennf transformation 3]
33. ! [X0] : (~curious(X0) | calm(X0)) [ennf transformation 6]
41. ! [X0] : (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) [nnf transformation 32]
49. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 7]
50. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0)))) & (((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 8]
51. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & ((~quiet(X0) | calm(X0)) | ~kind(X0))) [nnf transformation 9]
52. ! [X0] : ((kind(X0) | (quiet(X0) & ~calm(X0))) & (~quiet(X0) | calm(X0) | ~kind(X0))) [flattening 51]
62. ! [X0] : (((old(X0) & quiet(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (~old(X0) | ~quiet(X0)))) [nnf transformation 14]
63. ! [X0] : (((old(X0) & quiet(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | ~old(X0) | ~quiet(X0))) [flattening 62]
64. ! [X0] : ((((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))))) [nnf transformation 15]
65. ! [X0] : ((((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))))) [flattening 64]
76. ~old(X0) | ~happy(X0) | patient(X0) | ~old(X0) [cnf transformation 41]
86. ~curious(X0) | calm(X0) [cnf transformation 33]
87. curious(X0) | happy(X0) [cnf transformation 49]
91. ~strong(X0) | kind(X0) | curious(X0) | ~quiet(X0) [cnf transformation 50]
94. ~strong(X0) | quiet(X0) | ~kind(X0) | curious(X0) [cnf transformation 50]
97. ~kind(X0) | calm(X0) | ~quiet(X0) [cnf transformation 52]
98. ~calm(X0) | kind(X0) [cnf transformation 52]
99. kind(X0) | quiet(X0) [cnf transformation 52]
115. strong(X0) | calm(X0) | old(X0) [cnf transformation 63]
120. ~patient(X0) | ~patient(X0) | ~old(X0) [cnf transformation 65]
122. ~old(X0) | patient(X0) | patient(X0) | ~calm(X0) [cnf transformation 65]
135. ~kind(john) [cnf transformation 24]
136. ~old(X0) | ~patient(X0) [duplicate literal removal 120]
137. ~calm(X0) | patient(X0) | ~old(X0) [duplicate literal removal 122]
138. ~happy(X0) | ~old(X0) | patient(X0) [duplicate literal removal 76]
258. calm(X0) | happy(X0) [resolution 87,86]
372. patient(X1) | ~old(X1) | happy(X1) [resolution 137,258]
374. patient(X1) | ~old(X1) [subsumption resolution 372,138]
375. ~old(X1) [subsumption resolution 374,136]
415. kind(X0) | curious(X0) | ~quiet(X0) | calm(X0) | old(X0) [resolution 91,115]
417. kind(X0) | curious(X0) | ~quiet(X0) | calm(X0) [subsumption resolution 415,375]
418. kind(X0) | curious(X0) | calm(X0) [subsumption resolution 417,99]
419. kind(X0) | curious(X0) [subsumption resolution 418,98]
440. quiet(X1) | ~kind(X1) | curious(X1) | calm(X1) | old(X1) [resolution 94,115]
444. quiet(X1) | ~kind(X1) | curious(X1) | calm(X1) [subsumption resolution 440,375]
445. ~kind(X1) | curious(X1) | calm(X1) [subsumption resolution 444,97]
446. curious(X1) | calm(X1) [subsumption resolution 445,419]
447. calm(X1) [subsumption resolution 446,86]
449. kind(X1) [resolution 447,98]
452. $false [resolution 449,135]
% SZS output end Proof for 6326886747526354095229352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either creative or generous.
Everyone who is both patient and calm is both not rich and not happy and vice versa.
If alice is both humble and not tall then someone is humble.
Everyone who is both happy and not curious is not happy or curious.
Everyone who is not curious is both not generous and not humble.
If someone is either patient or funny then someone is either brave or wise and vice versa.
Everyone who is not creative is not patient.
If someone is not old then someone is both not brave and not tall.
Everyone who is both calm and not old is either brave or not tall.
Everyone who is both not generous and not rich is either not creative or rich and vice versa.
Everyone who is both not quiet and kind is creative or not generous.
If someone is old or not tall then alice is both patient and calm and vice versa.
Everyone who is either tall or calm is not tall or not rich and vice versa.
Everyone who is humble or not funny is either not tall or not kind and vice versa.
If someone is both creative and generous then someone is either calm or rich and vice versa.
Everyone who is either not wise or not brave is old.
Alice is not happy or kind.
Someone is either not kind or quiet.
Someone is not rich or brave.
Someone is not happy.
Mary is not patient.
Someone is quiet or old.
Alice is not quiet.
Someone is either not funny or not wise. | Fred is creative. | neutral | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((patient(X)&calm(X))<=>(~rich(X)&~happy(X))))&
(((humble(alice)&~tall(alice)))=>(?[X]:(humble(X))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>old(X)))&
((~happy(alice)|kind(alice)))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:((~rich(X)|brave(X))))&
(?[X]:(~happy(X)))&
(~patient(mary))&
(?[X]:((quiet(X)|old(X))))&
(~quiet(alice))&
(?[X]:((~funny(X)<~>~wise(X)))) | creative(fred) | [] | null | 0 |
Everyone who is either not kind or brave is patient.
If someone is not generous then lucy is patient or kind and vice versa.
Everyone who is both not creative and not calm is both happy and not funny and vice versa.
If susan is not curious or not calm then someone is both not generous and not calm and vice versa.
Everyone who is either not wise or kind is both not brave and not humble.
Everyone who is both not kind and rich is funny and vice versa.
Everyone who is both not quiet and rich is either not old or kind and vice versa.
Everyone who is both humble and brave is not tall and vice versa.
If mary is either not rich or wise then susan is happy and vice versa.
If lucy is both not strong and strong then someone is both not brave and calm and vice versa.
Everyone who is not strong or calm is either not happy or calm.
If someone is not rich or strong then paul is quiet and vice versa.
Everyone who is not wise is both not quiet and not rich and vice versa.
If susan is either not calm or not patient then someone is humble or not quiet.
Everyone who is creative is both not brave and not quiet and vice versa.
Everyone who is either wise or not old is either humble or brave.
Someone is quiet or patient.
Someone is tall.
Fred is both old and not happy.
Someone is both not calm and rich.
Someone is both not brave and quiet.
Lucy is both rich and curious.
Someone is not curious.
Someone is either not curious or not humble. | Fred is quiet. | contradiction | (![X]:((~kind(X)<~>brave(X))=>patient(X)))&
((?[X]:(~generous(X)))<=>((patient(lucy)|kind(lucy))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~funny(X))))&
(((~curious(susan)|~calm(susan)))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~wise(X)<~>kind(X))=>(~brave(X)&~humble(X))))&
(![X]:((~kind(X)&rich(X))<=>funny(X)))&
(![X]:((~quiet(X)&rich(X))<=>(~old(X)<~>kind(X))))&
(![X]:((humble(X)&brave(X))<=>~tall(X)))&
(((~rich(mary)<~>wise(mary)))<=>(happy(susan)))&
(((~strong(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~strong(X)|calm(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(quiet(paul)))&
(![X]:(~wise(X)<=>(~quiet(X)&~rich(X))))&
(((~calm(susan)<~>~patient(susan)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:(creative(X)<=>(~brave(X)&~quiet(X))))&
(![X]:((wise(X)<~>~old(X))=>(humble(X)<~>brave(X))))&
(?[X]:((quiet(X)|patient(X))))&
(?[X]:(tall(X)))&
((old(fred)&~happy(fred)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((rich(lucy)&curious(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:((~curious(X)<~>~humble(X)))) | quiet(fred) | [
"p2",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 557005314732286034963858
% SZS output start Proof for 557005314732286034963858
3. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (~funny(X0) & happy(X0))) [input p2]
11. ! [X0] : ((calm(X0) | ~strong(X0)) => (~happy(X0) <~> calm(X0))) [input p10]
15. ! [X0] : (creative(X0) <=> (~quiet(X0) & ~brave(X0))) [input p14]
19. ~happy(fred) & old(fred) [input p18]
25. quiet(fred) [input hypothesis]
31. ! [X0] : ((~happy(X0) <~> calm(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 11]
40. ! [X0] : (((~calm(X0) & ~creative(X0)) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 3]
41. ! [X0] : (((~calm(X0) & ~creative(X0)) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | calm(X0) | creative(X0))) [flattening 40]
58. ! [X0] : (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~calm(X0) & strong(X0))) [nnf transformation 31]
68. ! [X0] : ((creative(X0) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | ~creative(X0))) [nnf transformation 15]
69. ! [X0] : ((creative(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | ~creative(X0))) [flattening 68]
89. happy(X0) | calm(X0) | creative(X0) [cnf transformation 41]
123. ~calm(X0) | happy(X0) | ~calm(X0) [cnf transformation 58]
133. ~quiet(X0) | ~creative(X0) [cnf transformation 69]
142. ~happy(fred) [cnf transformation 19]
152. quiet(fred) [cnf transformation 25]
153. ~calm(X0) | happy(X0) [duplicate literal removal 123]
282. ~creative(fred) [resolution 133,152]
285. calm(fred) | creative(fred) [resolution 89,142]
286. calm(fred) [subsumption resolution 285,282]
299. happy(fred) [resolution 286,153]
300. $false [subsumption resolution 299,142]
% SZS output end Proof for 557005314732286034963858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is either rich or not curious and vice versa.
Everyone who is either brave or funny is not kind.
Everyone who is not funny or generous is both not humble and not kind and vice versa.
Everyone who is either not rich or curious is both not humble and not curious and vice versa.
If susan is wise or creative then lucy is either not tall or not patient and vice versa.
Everyone who is creative is either not kind or not patient and vice versa.
Everyone who is either not old or not kind is either rich or brave.
Everyone who is either not quiet or brave is not quiet or creative and vice versa.
If alice is rich then susan is either wise or generous.
Everyone who is calm or not patient is both rich and not happy and vice versa.
Everyone who is not calm is not wise or not humble.
Everyone who is not rich or rich is either not tall or brave and vice versa.
If mary is both not patient and curious then someone is brave or not old.
Everyone who is both funny and not creative is both not curious and not humble and vice versa.
Everyone who is not wise is either calm or not tall and vice versa.
If someone is brave or rich then fred is strong and vice versa.
Fred is tall or patient.
Someone is not curious.
Alice is humble or not humble.
Paul is either curious or not brave.
Someone is not generous.
Lucy is happy.
Someone is either not old or not wise. | Paul is not creative. | contradiction | (![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((brave(X)<~>funny(X))=>~kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~humble(X)&~kind(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~humble(X)&~curious(X))))&
(((wise(susan)|creative(susan)))<=>((~tall(lucy)<~>~patient(lucy))))&
(![X]:(creative(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)<~>~kind(X))=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>brave(X))<=>(~quiet(X)|creative(X))))&
((rich(alice))=>((wise(susan)<~>generous(susan))))&
(![X]:((calm(X)|~patient(X))<=>(rich(X)&~happy(X))))&
(![X]:(~calm(X)=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|rich(X))<=>(~tall(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((funny(X)&~creative(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((brave(X)|rich(X))))<=>(strong(fred)))&
((tall(fred)|patient(fred)))&
(?[X]:(~curious(X)))&
((humble(alice)|~humble(alice)))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~generous(X)))&
(happy(lucy))&
(?[X]:((~old(X)<~>~wise(X)))) | ~creative(paul) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2560883782327125964508914
% SZS output start Proof for 2560883782327125964508914
2. ! [X0] : ((brave(X0) <~> funny(X0)) => ~kind(X0)) [input p1]
3. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (~kind(X0) & ~humble(X0))) [input p2]
4. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> (~curious(X0) & ~humble(X0))) [input p3]
6. ! [X0] : (creative(X0) <=> (~kind(X0) <~> ~patient(X0))) [input p5]
8. ! [X0] : ((~quiet(X0) <~> brave(X0)) <=> (creative(X0) | ~quiet(X0))) [input p7]
10. ! [X0] : ((~patient(X0) | calm(X0)) <=> (~happy(X0) & rich(X0))) [input p9]
14. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~humble(X0) & ~curious(X0))) [input p13]
24. ~creative(paul) [input hypothesis]
25. ! [X0] : (~kind(X0) | (brave(X0) <=> funny(X0))) [ennf transformation 2]
33. ! [X0] : (~kind(X0) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) [nnf transformation 25]
34. ! [X0] : (((generous(X0) | ~funny(X0)) | (kind(X0) | humble(X0))) & ((~kind(X0) & ~humble(X0)) | (~generous(X0) & funny(X0)))) [nnf transformation 3]
35. ! [X0] : ((generous(X0) | ~funny(X0) | kind(X0) | humble(X0)) & ((~kind(X0) & ~humble(X0)) | (~generous(X0) & funny(X0)))) [flattening 34]
36. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 4]
37. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [flattening 36]
40. ! [X0] : ((creative(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 6]
42. ! [X0] : ((((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0))))) [nnf transformation 8]
43. ! [X0] : ((((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0))))) [flattening 42]
45. ! [X0] : (((~patient(X0) | calm(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~patient(X0) | calm(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | (patient(X0) & ~calm(X0)))) [flattening 45]
51. ! [X0] : (((~creative(X0) & funny(X0)) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 14]
52. ! [X0] : (((~creative(X0) & funny(X0)) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | creative(X0) | ~funny(X0))) [flattening 51]
71. ~kind(X0) | brave(X0) | ~funny(X0) [cnf transformation 33]
72. ~humble(X0) | funny(X0) [cnf transformation 35]
74. ~kind(X0) | funny(X0) [cnf transformation 35]
80. ~curious(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 37]
81. curious(X0) | ~rich(X0) | curious(X0) | humble(X0) [cnf transformation 37]
91. ~patient(X0) | creative(X0) | kind(X0) [cnf transformation 40]
98. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 43]
101. ~brave(X0) | quiet(X0) | quiet(X0) [cnf transformation 43]
106. patient(X0) | rich(X0) [cnf transformation 46]
119. ~humble(X0) | creative(X0) | ~funny(X0) [cnf transformation 52]
138. ~creative(paul) [cnf transformation 24]
139. creative(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 98]
140. ~brave(X0) | quiet(X0) [duplicate literal removal 101]
141. ~curious(X0) | ~rich(X0) [duplicate literal removal 80]
142. ~rich(X0) | curious(X0) | humble(X0) [duplicate literal removal 81]
165. ~brave(X0) | creative(X0) [subsumption resolution 139,140]
196. ~humble(X0) | creative(X0) [subsumption resolution 119,72]
228. 18 <=> curious(paul) [avatar definition]
229. curious(paul) <- (18) [avatar component clause 228]
230. ~curious(paul) <- (~18) [avatar component clause 228]
232. 19 <=> brave(paul) [avatar definition]
233. ~brave(paul) <- (~19) [avatar component clause 232]
234. brave(paul) <- (19) [avatar component clause 232]
306. creative(X0) | kind(X0) | rich(X0) [resolution 91,106]
513. kind(paul) | rich(paul) [resolution 306,138]
521. 54 <=> rich(paul) [avatar definition]
523. rich(paul) <- (54) [avatar component clause 521]
525. 55 <=> kind(paul) [avatar definition]
527. kind(paul) <- (55) [avatar component clause 525]
528. 54 | 55 [avatar split clause 513,525,521]
567. curious(paul) | humble(paul) <- (54) [resolution 523,142]
569. humble(paul) <- (~18, 54) [subsumption resolution 567,230]
624. brave(paul) | ~funny(paul) <- (55) [resolution 527,71]
626. funny(paul) <- (55) [resolution 527,74]
628. ~funny(paul) <- (~19, 55) [subsumption resolution 624,233]
629. $false <- (~19, 55) [subsumption resolution 626,628]
630. 19 | ~55 [avatar contradiction clause 629]
647. creative(paul) <- (~18, 54) [resolution 569,196]
650. $false <- (~18, 54) [subsumption resolution 647,138]
651. 18 | ~54 [avatar contradiction clause 650]
656. ~rich(paul) <- (18) [resolution 229,141]
663. ~54 | ~18 [avatar split clause 656,228,521]
666. creative(paul) <- (19) [resolution 234,165]
668. $false <- (19) [subsumption resolution 666,138]
669. ~19 [avatar contradiction clause 668]
670. $false [avatar sat refutation 528,630,651,663,669]
% SZS output end Proof for 2560883782327125964508914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and strong is not rich or not curious. Everyone who is both not humble and old is quiet and vice versa. Everyone who is either not brave or not happy is either not patient or kind. Everyone who is old or wise is brave or not rich. If lucy is not strong then someone is both not creative and happy. Everyone who is brave or strong is humble and vice versa. Everyone who is humble or calm is creative and vice versa. If someone is both funny and brave then someone is not strong and vice versa. If someone is both not funny and not generous then fred is not rich or not funny. Everyone who is wise or old is brave and vice versa. Everyone who is quiet is rich. If mary is rich or kind then lucy is not strong or curious. If someone is either not humble or rich then someone is both not tall and not old and vice versa. Everyone who is both not kind and patient is both brave and patient and vice versa. Everyone who is either happy or not kind is calm or rich and vice versa. Everyone who is either generous or not humble is not patient or brave. Susan is tall. Mary is not funny or not rich. Someone is strong. Mary is either quiet or kind. Lucy is not calm or patient. Someone is both funny and not kind. Fred is both brave and not patient. Someone is old. | Susan is funny. | neutral | (![X]:((~generous(X)&strong(X))=>(~rich(X)|~curious(X))))&
(![X]:((~humble(X)&old(X))<=>quiet(X)))&
(![X]:((~brave(X)<~>~happy(X))=>(~patient(X)<~>kind(X))))&
(![X]:((old(X)|wise(X))=>(brave(X)|~rich(X))))&
((~strong(lucy))=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((brave(X)|strong(X))<=>humble(X)))&
(![X]:((humble(X)|calm(X))<=>creative(X)))&
((?[X]:((funny(X)&brave(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~funny(X)&~generous(X))))=>((~rich(fred)|~funny(fred))))&
(![X]:((wise(X)|old(X))<=>brave(X)))&
(![X]:(quiet(X)=>rich(X)))&
(((rich(mary)|kind(mary)))=>((~strong(lucy)|curious(lucy))))&
((?[X]:((~humble(X)<~>rich(X))))<=>(?[X]:((~tall(X)&~old(X)))))&
(![X]:((~kind(X)&patient(X))<=>(brave(X)&patient(X))))&
(![X]:((happy(X)<~>~kind(X))<=>(calm(X)|rich(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~patient(X)|brave(X))))&
(tall(susan))&
((~funny(mary)|~rich(mary)))&
(?[X]:(strong(X)))&
((quiet(mary)<~>kind(mary)))&
((~calm(lucy)|patient(lucy)))&
(?[X]:((funny(X)&~kind(X))))&
((brave(fred)&~patient(fred)))&
(?[X]:(old(X))) | funny(susan) | [] | null | 0 |
If someone is not curious or happy then someone is calm or wise. Everyone who is curious or tall is funny and vice versa. If fred is not happy or kind then someone is both patient and not old and vice versa. Everyone who is both rich and not curious is either happy or kind and vice versa. Everyone who is both not patient and strong is both not rich and generous. Everyone who is both not brave and funny is patient or not creative and vice versa. If fred is either creative or not happy then lucy is either creative or not tall and vice versa. Everyone who is both not quiet and not creative is not happy. Everyone who is either not quiet or quiet is tall. If fred is curious then mary is either tall or humble and vice versa. Everyone who is both not patient and not tall is either calm or old and vice versa. If someone is not generous then alice is both quiet and happy. Everyone who is both funny and humble is both calm and not quiet and vice versa. Everyone who is either old or kind is happy and vice versa. Susan is either not patient or strong. Paul is both creative and not kind. Someone is not kind or old. Someone is not rich or wise. John is strong. Lucy is old. Someone is either quiet or creative. | Lucy is not calm. | contradiction | ((?[X]:((~curious(X)|happy(X))))=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((curious(X)|tall(X))<=>funny(X)))&
(((~happy(fred)|kind(fred)))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~curious(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)&strong(X))=>(~rich(X)&generous(X))))&
(![X]:((~brave(X)&funny(X))<=>(patient(X)|~creative(X))))&
(((creative(fred)<~>~happy(fred)))<=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((~quiet(X)&~creative(X))=>~happy(X)))&
(![X]:((~quiet(X)<~>quiet(X))=>tall(X)))&
((curious(fred))<=>((tall(mary)<~>humble(mary))))&
(![X]:((~patient(X)&~tall(X))<=>(calm(X)<~>old(X))))&
((?[X]:(~generous(X)))=>((quiet(alice)&happy(alice))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&~quiet(X))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
((~patient(susan)<~>strong(susan)))&
((creative(paul)&~kind(paul)))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:((~rich(X)|wise(X))))&
(strong(john))&
(old(lucy))&
(?[X]:((quiet(X)<~>creative(X)))) | ~calm(lucy) | [
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6124639257015380024337985
% SZS output start Proof for 6124639257015380024337985
9. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => tall(X0)) [input p8]
11. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (calm(X0) <~> old(X0))) [input p10]
20. old(lucy) [input p19]
22. ~calm(lucy) [input hypothesis]
32. ! [X0] : (tall(X0) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 9]
45. ! [X0] : (tall(X0) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 32]
47. ! [X0] : (((~tall(X0) & ~patient(X0)) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0)))) & (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | (tall(X0) | patient(X0)))) [nnf transformation 11]
48. ! [X0] : (((~tall(X0) & ~patient(X0)) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0)))) & (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | tall(X0) | patient(X0))) [flattening 47]
87. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 45]
88. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 45]
98. ~tall(X0) | calm(X0) | ~old(X0) [cnf transformation 48]
113. old(lucy) [cnf transformation 20]
116. ~calm(lucy) [cnf transformation 22]
117. tall(X0) | quiet(X0) [duplicate literal removal 87]
118. ~quiet(X0) | tall(X0) [duplicate literal removal 88]
163. tall(X0) [subsumption resolution 117,118]
176. ~old(X0) | calm(X0) [subsumption resolution 98,163]
214. calm(lucy) [resolution 176,113]
215. $false [subsumption resolution 214,116]
% SZS output end Proof for 6124639257015380024337985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either patient or not curious then john is strong. Everyone who is not quiet is not rich and vice versa. Everyone who is both creative and not creative is kind and vice versa. Everyone who is both humble and generous is either not tall or not funny and vice versa. Everyone who is humble or not kind is either not strong or not quiet. Everyone who is both rich and patient is tall or happy and vice versa. Everyone who is either brave or not humble is both not calm and old. If someone is not calm then someone is both strong and not creative and vice versa. If john is creative then someone is either humble or not humble and vice versa. Everyone who is curious or not funny is old and vice versa. Everyone who is not wise or humble is either wise or strong. Everyone who is calm or not patient is either funny or curious. If susan is not strong then paul is not curious or humble. If someone is both not brave and tall then someone is not funny or not curious. If someone is not strong then paul is either creative or not old and vice versa. If someone is either not rich or not wise then someone is both not wise and humble. Paul is funny. Susan is either tall or not happy. Lucy is not strong or patient. John is either not kind or not humble. Fred is both not wise and brave. Someone is either curious or funny. Someone is happy. Paul is either patient or not creative. | Paul is not curious. | neutral | (((patient(fred)<~>~curious(fred)))=>(strong(john)))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:((creative(X)&~creative(X))<=>kind(X)))&
(![X]:((humble(X)&generous(X))<=>(~tall(X)<~>~funny(X))))&
(![X]:((humble(X)|~kind(X))=>(~strong(X)<~>~quiet(X))))&
(![X]:((rich(X)&patient(X))<=>(tall(X)|happy(X))))&
(![X]:((brave(X)<~>~humble(X))=>(~calm(X)&old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((strong(X)&~creative(X)))))&
((creative(john))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((curious(X)|~funny(X))<=>old(X)))&
(![X]:((~wise(X)|humble(X))=>(wise(X)<~>strong(X))))&
(![X]:((calm(X)|~patient(X))=>(funny(X)<~>curious(X))))&
((~strong(susan))=>((~curious(paul)|humble(paul))))&
((?[X]:((~brave(X)&tall(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
((?[X]:(~strong(X)))<=>((creative(paul)<~>~old(paul))))&
((?[X]:((~rich(X)<~>~wise(X))))=>(?[X]:((~wise(X)&humble(X)))))&
(funny(paul))&
((tall(susan)<~>~happy(susan)))&
((~strong(lucy)|patient(lucy)))&
((~kind(john)<~>~humble(john)))&
((~wise(fred)&brave(fred)))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:(happy(X)))&
((patient(paul)<~>~creative(paul))) | ~curious(paul) | [] | null | 0 |
If someone is either not quiet or happy then paul is either not generous or not wise and vice versa. Everyone who is both curious and calm is not happy or brave and vice versa. If paul is generous then someone is both not funny and generous. If someone is either not strong or not tall then mary is both quiet and not kind. Everyone who is both old and not generous is not funny and vice versa. Everyone who is not quiet or not wise is generous and vice versa. Everyone who is either happy or generous is patient and vice versa. If mary is not tall then paul is creative or not old and vice versa. If mary is either not calm or strong then someone is not kind and vice versa. If john is both creative and not quiet then someone is not quiet. If paul is rich then someone is not wise or tall. Everyone who is both humble and not old is not wise or not tall and vice versa. If someone is either not quiet or not kind then alice is not old or funny. If someone is both creative and not wise then lucy is either not wise or not brave. If someone is both generous and not calm then lucy is both not kind and kind and vice versa. Everyone who is either not kind or funny is either rich or brave and vice versa. Susan is old or funny. Mary is not wise. Someone is either funny or not wise. Alice is both old and humble. Lucy is either not quiet or curious. Someone is not generous or not tall. Susan is quiet. | Mary is funny. | entailment | ((?[X]:((~quiet(X)<~>happy(X))))<=>((~generous(paul)<~>~wise(paul))))&
(![X]:((curious(X)&calm(X))<=>(~happy(X)|brave(X))))&
((generous(paul))=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~strong(X)<~>~tall(X))))=>((quiet(mary)&~kind(mary))))&
(![X]:((old(X)&~generous(X))<=>~funny(X)))&
(![X]:((~quiet(X)|~wise(X))<=>generous(X)))&
(![X]:((happy(X)<~>generous(X))<=>patient(X)))&
((~tall(mary))<=>((creative(paul)|~old(paul))))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:(~kind(X))))&
(((creative(john)&~quiet(john)))=>(?[X]:(~quiet(X))))&
((rich(paul))=>(?[X]:((~wise(X)|tall(X)))))&
(![X]:((humble(X)&~old(X))<=>(~wise(X)|~tall(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>((~old(alice)|funny(alice))))&
((?[X]:((creative(X)&~wise(X))))=>((~wise(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)&~calm(X))))<=>((~kind(lucy)&kind(lucy))))&
(![X]:((~kind(X)<~>funny(X))<=>(rich(X)<~>brave(X))))&
((old(susan)|funny(susan)))&
(~wise(mary))&
(?[X]:((funny(X)<~>~wise(X))))&
((old(alice)&humble(alice)))&
((~quiet(lucy)<~>curious(lucy)))&
(?[X]:((~generous(X)|~tall(X))))&
(quiet(susan)) | funny(mary) | [
"p4",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2579199081701497003153272
% SZS output start Proof for 2579199081701497003153272
5. ! [X0] : ((~generous(X0) & old(X0)) <=> ~funny(X0)) [input p4]
6. ! [X0] : ((~wise(X0) | ~quiet(X0)) <=> generous(X0)) [input p5]
18. ~wise(mary) [input p17]
24. ~funny(mary) [input hypothesis]
42. ! [X0] : (((~generous(X0) & old(X0)) | funny(X0)) & (~funny(X0) | (generous(X0) | ~old(X0)))) [nnf transformation 5]
43. ! [X0] : (((~generous(X0) & old(X0)) | funny(X0)) & (~funny(X0) | generous(X0) | ~old(X0))) [flattening 42]
44. ! [X0] : (((~wise(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (wise(X0) & quiet(X0)))) [nnf transformation 6]
45. ! [X0] : ((~wise(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (wise(X0) & quiet(X0)))) [flattening 44]
93. ~generous(X0) | funny(X0) [cnf transformation 43]
95. wise(X0) | generous(X0) [cnf transformation 45]
128. ~wise(mary) [cnf transformation 18]
137. ~funny(mary) [cnf transformation 24]
326. generous(mary) [resolution 95,128]
338. funny(mary) [resolution 326,93]
339. $false [subsumption resolution 338,137]
% SZS output end Proof for 2579199081701497003153272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not brave is not calm.
Everyone who is both not happy and generous is patient.
If someone is wise or creative then alice is both patient and not calm.
Everyone who is not strong is both not generous and not kind and vice versa.
Everyone who is not strong or not happy is both rich and not curious.
Everyone who is not kind or not patient is calm or wise and vice versa.
Everyone who is brave or generous is tall or not tall and vice versa.
If john is either not happy or kind then someone is not rich or not quiet and vice versa.
If someone is both curious and not kind then john is not creative.
Everyone who is rich is brave and vice versa.
If someone is calm then someone is not funny.
If lucy is either not brave or rich then someone is both generous and calm and vice versa.
If someone is either generous or calm then susan is either not quiet or humble.
If someone is rich or not strong then someone is both not old and funny and vice versa.
Everyone who is both not rich and generous is either rich or calm and vice versa.
If susan is not patient or not creative then someone is either not tall or quiet.
Someone is both not kind and not humble.
Someone is patient.
Susan is not happy.
Someone is not rich.
Someone is both not old and generous.
Someone is both not creative and brave.
Someone is not patient or calm.
Someone is tall or humble. | Alice is wise. | contradiction | (![X]:((creative(X)&~brave(X))=>~calm(X)))&
(![X]:((~happy(X)&generous(X))=>patient(X)))&
((?[X]:((wise(X)|creative(X))))=>((patient(alice)&~calm(alice))))&
(![X]:(~strong(X)<=>(~generous(X)&~kind(X))))&
(![X]:((~strong(X)|~happy(X))=>(rich(X)&~curious(X))))&
(![X]:((~kind(X)|~patient(X))<=>(calm(X)|wise(X))))&
(![X]:((brave(X)|generous(X))<=>(tall(X)|~tall(X))))&
(((~happy(john)<~>kind(john)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((?[X]:((curious(X)&~kind(X))))=>(~creative(john)))&
(![X]:(rich(X)<=>brave(X)))&
((?[X]:(calm(X)))=>(?[X]:(~funny(X))))&
(((~brave(lucy)<~>rich(lucy)))<=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((generous(X)<~>calm(X))))=>((~quiet(susan)<~>humble(susan))))&
((?[X]:((rich(X)|~strong(X))))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((~rich(X)&generous(X))<=>(rich(X)<~>calm(X))))&
(((~patient(susan)|~creative(susan)))=>(?[X]:((~tall(X)<~>quiet(X)))))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:(patient(X)))&
(~happy(susan))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((tall(X)|humble(X)))) | wise(alice) | [
"p2",
"p6",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5647252828609499971205525
% SZS output start Proof for 5647252828609499971205525
3. ? [X0] : (creative(X0) | wise(X0)) => (~calm(alice) & patient(alice)) [input p2]
7. ! [X0] : ((generous(X0) | brave(X0)) <=> (~tall(X0) | tall(X0))) [input p6]
10. ! [X0] : (rich(X0) <=> brave(X0)) [input p9]
15. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (rich(X0) <~> calm(X0))) [input p14]
25. wise(alice) [input hypothesis]
34. (~calm(alice) & patient(alice)) | ! [X0] : (~creative(X0) & ~wise(X0)) [ennf transformation 3]
43. ! [X0] : (((generous(X0) | brave(X0)) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | (~generous(X0) & ~brave(X0)))) [nnf transformation 7]
44. ! [X0] : ((generous(X0) | brave(X0) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | (~generous(X0) & ~brave(X0)))) [flattening 43]
49. ! [X0] : ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0))) [nnf transformation 10]
63. ! [X0] : (((generous(X0) & ~rich(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~generous(X0) | rich(X0)))) [nnf transformation 15]
64. ! [X0] : (((generous(X0) & ~rich(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | ~generous(X0) | rich(X0))) [flattening 63]
86. ~calm(alice) | ~wise(X0) [cnf transformation 34]
99. generous(X0) | brave(X0) | ~tall(X0) [cnf transformation 44]
100. tall(X0) | brave(X0) | generous(X0) [cnf transformation 44]
108. ~brave(X0) | rich(X0) [cnf transformation 49]
125. calm(X0) | rich(X0) | ~generous(X0) | rich(X0) [cnf transformation 64]
127. ~rich(X0) | calm(X0) | ~rich(X0) [cnf transformation 64]
146. wise(alice) [cnf transformation 25]
147. calm(X0) | rich(X0) | ~generous(X0) [duplicate literal removal 125]
148. ~rich(X0) | calm(X0) [duplicate literal removal 127]
153. 2 <=> calm(alice) [avatar definition]
155. ~calm(alice) <- (~2) [avatar component clause 153]
158. 3 <=> ! [X0] : ~wise(X0) [avatar definition]
159. ~wise(X0) <- (3) [avatar component clause 158]
160. 3 | ~2 [avatar split clause 86,153,158]
167. generous(X0) | brave(X0) [subsumption resolution 99,100]
237. 19 <=> ! [X0] : (calm(X0) | ~generous(X0)) [avatar definition]
238. ~generous(X0) | calm(X0) <- (19) [avatar component clause 237]
269. calm(X0) | ~generous(X0) [subsumption resolution 147,148]
270. 19 [avatar split clause 269,237]
323. calm(X0) | brave(X0) <- (19) [resolution 238,167]
451. brave(alice) <- (~2, 19) [resolution 323,155]
456. rich(alice) <- (~2, 19) [resolution 451,108]
496. calm(alice) <- (~2, 19) [resolution 456,148]
499. $false <- (~2, 19) [subsumption resolution 496,155]
500. 2 | ~19 [avatar contradiction clause 499]
513. $false <- (3) [resolution 159,146]
518. ~3 [avatar contradiction clause 513]
519. $false [avatar sat refutation 160,270,500,518]
% SZS output end Proof for 5647252828609499971205525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If fred is creative or not generous then someone is brave or old.
Everyone who is brave is wise or kind and vice versa.
If someone is not curious then john is either not strong or not kind.
If someone is either kind or brave then someone is both patient and not strong.
Everyone who is either not kind or not generous is generous.
If someone is both kind and quiet then someone is either not old or strong and vice versa.
If paul is happy or not quiet then john is curious or not humble and vice versa.
If someone is happy or not humble then fred is quiet or not kind and vice versa.
If fred is not wise or not creative then someone is rich or not brave.
If someone is either not brave or humble then fred is either kind or not rich.
Everyone who is quiet is not curious.
Everyone who is humble or not humble is both not quiet and not patient.
If john is kind then paul is either not rich or old.
If alice is both kind and not rich then someone is creative or generous and vice versa.
If susan is both strong and not wise then fred is old or funny.
Paul is either not generous or not tall.
Someone is not patient or creative.
Mary is old or quiet.
Someone is happy.
Lucy is not patient.
Someone is not patient or calm.
Someone is either not wise or not rich.
Mary is not brave or not curious. | Lucy is not quiet. | entailment | (((creative(fred)|~generous(fred)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:(brave(X)<=>(wise(X)|kind(X))))&
((?[X]:(~curious(X)))=>((~strong(john)<~>~kind(john))))&
((?[X]:((kind(X)<~>brave(X))))=>(?[X]:((patient(X)&~strong(X)))))&
(![X]:((~kind(X)<~>~generous(X))=>generous(X)))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((~old(X)<~>strong(X)))))&
(((happy(paul)|~quiet(paul)))<=>((curious(john)|~humble(john))))&
((?[X]:((happy(X)|~humble(X))))<=>((quiet(fred)|~kind(fred))))&
(((~wise(fred)|~creative(fred)))=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:((~brave(X)<~>humble(X))))=>((kind(fred)<~>~rich(fred))))&
(![X]:(quiet(X)=>~curious(X)))&
(![X]:((humble(X)|~humble(X))=>(~quiet(X)&~patient(X))))&
((kind(john))=>((~rich(paul)<~>old(paul))))&
(((kind(alice)&~rich(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(((strong(susan)&~wise(susan)))=>((old(fred)|funny(fred))))&
((~generous(paul)<~>~tall(paul)))&
(?[X]:((~patient(X)|creative(X))))&
((old(mary)|quiet(mary)))&
(?[X]:(happy(X)))&
(~patient(lucy))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
((~brave(mary)|~curious(mary))) | ~quiet(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 403279875593153886257281
% SZS output start Proof for 403279875593153886257281
12. ! [X0] : ((~humble(X0) | humble(X0)) => (~patient(X0) & ~quiet(X0))) [input p11]
24. quiet(lucy) [input hypothesis]
36. ! [X0] : ((~patient(X0) & ~quiet(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 12]
111. ~quiet(X0) | ~humble(X0) [cnf transformation 36]
112. ~quiet(X0) | humble(X0) [cnf transformation 36]
131. quiet(lucy) [cnf transformation 24]
283. ~quiet(X0) [subsumption resolution 111,112]
351. $false [subsumption resolution 131,283]
% SZS output end Proof for 403279875593153886257281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not tall is either kind or generous.
Everyone who is either not patient or not curious is either happy or generous and vice versa.
Everyone who is either tall or not generous is both not wise and patient.
If someone is not funny then susan is kind.
If fred is both not strong and not old then someone is not happy and vice versa.
Everyone who is either generous or not calm is not quiet.
Everyone who is both kind and patient is either generous or tall and vice versa.
Everyone who is quiet is not curious.
If someone is either not rich or not brave then fred is either not calm or happy.
If alice is both not brave and funny then fred is patient.
Everyone who is patient is either quiet or brave.
If susan is both tall and calm then someone is not calm and vice versa.
Everyone who is both funny and rich is not happy.
Everyone who is wise is old or not funny.
Everyone who is not happy is not curious.
Paul is both brave and not calm.
Paul is not kind.
Someone is creative or brave.
Someone is both not calm and old.
Someone is either tall or quiet.
Susan is not wise.
Someone is tall or strong.
Paul is either creative or funny. | Paul is quiet. | contradiction | (![X]:((humble(X)|~tall(X))=>(kind(X)<~>generous(X))))&
(![X]:((~patient(X)<~>~curious(X))<=>(happy(X)<~>generous(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~wise(X)&patient(X))))&
((?[X]:(~funny(X)))=>(kind(susan)))&
(((~strong(fred)&~old(fred)))<=>(?[X]:(~happy(X))))&
(![X]:((generous(X)<~>~calm(X))=>~quiet(X)))&
(![X]:((kind(X)&patient(X))<=>(generous(X)<~>tall(X))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~rich(X)<~>~brave(X))))=>((~calm(fred)<~>happy(fred))))&
(((~brave(alice)&funny(alice)))=>(patient(fred)))&
(![X]:(patient(X)=>(quiet(X)<~>brave(X))))&
(((tall(susan)&calm(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((funny(X)&rich(X))=>~happy(X)))&
(![X]:(wise(X)=>(old(X)|~funny(X))))&
(![X]:(~happy(X)=>~curious(X)))&
((brave(paul)&~calm(paul)))&
(~kind(paul))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~calm(X)&old(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(~wise(susan))&
(?[X]:((tall(X)|strong(X))))&
((creative(paul)<~>funny(paul))) | quiet(paul) | [
"p2",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 812245659010464636285836
% SZS output start Proof for 812245659010464636285836
3. ! [X0] : ((tall(X0) <~> ~generous(X0)) => (patient(X0) & ~wise(X0))) [input p2]
7. ! [X0] : ((patient(X0) & kind(X0)) <=> (generous(X0) <~> tall(X0))) [input p6]
11. ! [X0] : (patient(X0) => (quiet(X0) <~> brave(X0))) [input p10]
16. ~calm(paul) & brave(paul) [input p15]
24. quiet(paul) [input hypothesis]
26. ! [X0] : ((tall(X0) <~> ~generous(X0)) => patient(X0)) [pure predicate removal 3]
30. ! [X0] : (patient(X0) | (tall(X0) <=> ~generous(X0))) [ennf transformation 26]
37. ! [X0] : ((quiet(X0) <~> brave(X0)) | ~patient(X0)) [ennf transformation 11]
43. ! [X0] : (patient(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 30]
50. ! [X0] : (((patient(X0) & kind(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (~patient(X0) | ~kind(X0)))) [nnf transformation 7]
51. ! [X0] : (((patient(X0) & kind(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0)))) & (((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ~patient(X0) | ~kind(X0))) [flattening 50]
53. ! [X0] : (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~patient(X0)) [nnf transformation 37]
79. patient(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 43]
80. patient(X0) | tall(X0) | generous(X0) [cnf transformation 43]
91. patient(X0) | tall(X0) | ~generous(X0) [cnf transformation 51]
92. patient(X0) | generous(X0) | ~tall(X0) [cnf transformation 51]
100. ~brave(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 53]
106. brave(paul) [cnf transformation 16]
117. quiet(paul) [cnf transformation 24]
144. patient(X0) | generous(X0) [subsumption resolution 92,80]
145. patient(X0) | ~generous(X0) [subsumption resolution 91,79]
146. patient(X0) [subsumption resolution 145,144]
171. ~brave(X0) | ~quiet(X0) [subsumption resolution 100,146]
240. ~quiet(paul) [resolution 171,106]
241. $false [subsumption resolution 240,117]
% SZS output end Proof for 812245659010464636285836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and happy then john is curious or generous and vice versa.
Everyone who is not generous is both not tall and not old.
Everyone who is either happy or brave is generous or old and vice versa.
If someone is not wise or tall then fred is not funny or not tall and vice versa.
If someone is both not patient and creative then susan is brave.
If lucy is strong or not kind then someone is not calm or rich.
Everyone who is not quiet is both not patient and brave and vice versa.
Everyone who is strong or funny is either not wise or patient and vice versa.
If mary is either not funny or calm then someone is not wise.
If someone is either wise or brave then someone is not humble and vice versa.
Everyone who is either not tall or not wise is not funny or happy.
Everyone who is strong is either not old or not calm and vice versa.
Everyone who is not strong is either not quiet or strong and vice versa.
Everyone who is both calm and funny is wise.
If someone is old then someone is both rich and strong and vice versa.
If lucy is not rich or rich then lucy is both not strong and wise and vice versa.
Susan is both not generous and not funny.
Someone is either not patient or kind.
Susan is not wise or calm.
Someone is either not brave or wise.
Someone is old.
John is not curious.
Someone is not generous or tall. | John is quiet. | contradiction | (((funny(mary)&happy(mary)))<=>((curious(john)|generous(john))))&
(![X]:(~generous(X)=>(~tall(X)&~old(X))))&
(![X]:((happy(X)<~>brave(X))<=>(generous(X)|old(X))))&
((?[X]:((~wise(X)|tall(X))))<=>((~funny(fred)|~tall(fred))))&
((?[X]:((~patient(X)&creative(X))))=>(brave(susan)))&
(((strong(lucy)|~kind(lucy)))=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:(~quiet(X)<=>(~patient(X)&brave(X))))&
(![X]:((strong(X)|funny(X))<=>(~wise(X)<~>patient(X))))&
(((~funny(mary)<~>calm(mary)))=>(?[X]:(~wise(X))))&
((?[X]:((wise(X)<~>brave(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>~wise(X))=>(~funny(X)|happy(X))))&
(![X]:(strong(X)<=>(~old(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((calm(X)&funny(X))=>wise(X)))&
((?[X]:(old(X)))<=>(?[X]:((rich(X)&strong(X)))))&
(((~rich(lucy)|rich(lucy)))<=>((~strong(lucy)&wise(lucy))))&
((~generous(susan)&~funny(susan)))&
(?[X]:((~patient(X)<~>kind(X))))&
((~wise(susan)|calm(susan)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(old(X)))&
(~curious(john))&
(?[X]:((~generous(X)|tall(X)))) | quiet(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8084389719132788950579983
% SZS output start Proof for 8084389719132788950579983
13. ! [X0] : (~strong(X0) <=> (~quiet(X0) <~> strong(X0))) [input p12]
24. quiet(john) [input hypothesis]
60. ! [X0] : ((~strong(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | strong(X0))) [nnf transformation 13]
118. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 60]
121. ~strong(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 60]
141. quiet(john) [cnf transformation 24]
142. strong(X0) | ~quiet(X0) [duplicate literal removal 118]
143. ~strong(X0) | ~quiet(X0) [duplicate literal removal 121]
246. ~quiet(X0) [subsumption resolution 142,143]
319. $false [subsumption resolution 141,246]
% SZS output end Proof for 8084389719132788950579983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not old or calm then lucy is tall or not calm and vice versa.
Everyone who is both not quiet and generous is either humble or funny and vice versa.
Everyone who is creative or old is both strong and creative and vice versa.
Everyone who is either not patient or creative is calm or old and vice versa.
Everyone who is either not patient or quiet is old or not tall.
Everyone who is either tall or patient is either not happy or wise and vice versa.
If someone is not happy then someone is both not rich and not funny.
Everyone who is both not happy and generous is curious and vice versa.
If paul is not rich or strong then fred is both funny and not generous.
Everyone who is either not creative or not generous is both not happy and kind.
Everyone who is not strong or wise is not humble and vice versa.
If someone is not happy or not brave then someone is happy.
If someone is not rich then lucy is generous and vice versa.
Everyone who is either tall or not brave is not old.
Everyone who is both not generous and strong is either not generous or generous and vice versa.
If susan is not tall then someone is both rich and calm.
Someone is either kind or not tall.
Someone is both patient and quiet.
Alice is not wise.
Fred is either not generous or kind.
Someone is both not quiet and rich.
Mary is either generous or not generous.
Alice is either strong or curious. | Fred is creative. | contradiction | ((?[X]:((~old(X)<~>calm(X))))<=>((tall(lucy)|~calm(lucy))))&
(![X]:((~quiet(X)&generous(X))<=>(humble(X)<~>funny(X))))&
(![X]:((creative(X)|old(X))<=>(strong(X)&creative(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(calm(X)|old(X))))&
(![X]:((~patient(X)<~>quiet(X))=>(old(X)|~tall(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~happy(X)<~>wise(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((~happy(X)&generous(X))<=>curious(X)))&
(((~rich(paul)|strong(paul)))=>((funny(fred)&~generous(fred))))&
(![X]:((~creative(X)<~>~generous(X))=>(~happy(X)&kind(X))))&
(![X]:((~strong(X)|wise(X))<=>~humble(X)))&
((?[X]:((~happy(X)|~brave(X))))=>(?[X]:(happy(X))))&
((?[X]:(~rich(X)))<=>(generous(lucy)))&
(![X]:((tall(X)<~>~brave(X))=>~old(X)))&
(![X]:((~generous(X)&strong(X))<=>(~generous(X)<~>generous(X))))&
((~tall(susan))=>(?[X]:((rich(X)&calm(X)))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:((patient(X)&quiet(X))))&
(~wise(alice))&
((~generous(fred)<~>kind(fred)))&
(?[X]:((~quiet(X)&rich(X))))&
((generous(mary)<~>~generous(mary)))&
((strong(alice)<~>curious(alice))) | creative(fred) | [
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1094351684221277316837235
% SZS output start Proof for 1094351684221277316837235
7. ? [X0] : ~happy(X0) => ? [X0] : (~funny(X0) & ~rich(X0)) [input p6]
10. ! [X0] : ((~creative(X0) <~> ~generous(X0)) => (kind(X0) & ~happy(X0))) [input p9]
13. ? [X0] : ~rich(X0) <=> generous(lucy) [input p12]
15. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~generous(X0) <~> generous(X0))) [input p14]
24. creative(fred) [input hypothesis]
25. ? [X0] : ~happy(X0) => ? [X1] : (~funny(X1) & ~rich(X1)) [rectify 7]
29. ? [X1] : (~funny(X1) & ~rich(X1)) | ! [X0] : happy(X0) [ennf transformation 25]
31. ! [X0] : ((kind(X0) & ~happy(X0)) | (~creative(X0) <=> ~generous(X0))) [ennf transformation 10]
48. ? [X0] : (~funny(X0) & ~rich(X0)) | ! [X1] : happy(X1) [rectify 29]
49. ? [X0] : (~funny(X0) & ~rich(X0)) => (~funny(sK1) & ~rich(sK1)) [choice axiom]
50. (~funny(sK1) & ~rich(sK1)) | ! [X1] : happy(X1) [skolemisation 48,49]
53. ! [X0] : ((kind(X0) & ~happy(X0)) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) [nnf transformation 31]
59. (? [X0] : ~rich(X0) | ~generous(lucy)) & (generous(lucy) | ! [X0] : rich(X0)) [nnf transformation 13]
60. (? [X0] : ~rich(X0) | ~generous(lucy)) & (generous(lucy) | ! [X1] : rich(X1)) [rectify 59]
61. ? [X0] : ~rich(X0) => ~rich(sK3) [choice axiom]
62. (~rich(sK3) | ~generous(lucy)) & (generous(lucy) | ! [X1] : rich(X1)) [skolemisation 60,61]
64. ! [X0] : (((strong(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | (~strong(X0) | generous(X0)))) [nnf transformation 15]
65. ! [X0] : (((strong(X0) & ~generous(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | ~strong(X0) | generous(X0))) [flattening 64]
111. ~rich(sK1) | happy(X1) [cnf transformation 50]
121. ~happy(X0) | ~creative(X0) | generous(X0) [cnf transformation 53]
129. generous(lucy) | rich(X1) [cnf transformation 62]
136. ~generous(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 65]
154. creative(fred) [cnf transformation 24]
158. ~generous(X0) [duplicate literal removal 136]
193. 7 <=> ! [X1] : happy(X1) [avatar definition]
194. happy(X1) <- (7) [avatar component clause 193]
201. 9 <=> rich(sK1) [avatar definition]
203. ~rich(sK1) <- (~9) [avatar component clause 201]
204. 7 | ~9 [avatar split clause 111,201,193]
235. 16 <=> generous(lucy) [avatar definition]
236. generous(lucy) <- (16) [avatar component clause 235]
244. 18 <=> ! [X1] : rich(X1) [avatar definition]
245. rich(X1) <- (18) [avatar component clause 244]
246. 18 | 16 [avatar split clause 129,235,244]
274. $false <- (16) [subsumption resolution 236,158]
275. ~16 [avatar contradiction clause 274]
318. ~creative(X0) | generous(X0) <- (7) [resolution 121,194]
319. ~creative(X0) <- (7) [subsumption resolution 318,158]
320. $false <- (7) [resolution 319,154]
321. ~7 [avatar contradiction clause 320]
322. $false <- (~9, 18) [subsumption resolution 203,245]
323. 9 | ~18 [avatar contradiction clause 322]
324. $false [avatar sat refutation 204,246,275,321,323]
% SZS output end Proof for 1094351684221277316837235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or strong then paul is either curious or not tall and vice versa.
If someone is patient then someone is both tall and funny and vice versa.
Everyone who is curious is both not patient and not funny and vice versa.
Everyone who is either tall or calm is not calm or not brave and vice versa.
If lucy is not generous or not happy then someone is either patient or not old.
Everyone who is both humble and brave is both generous and not happy and vice versa.
Everyone who is not generous or curious is funny and vice versa.
If fred is funny then someone is both patient and not calm and vice versa.
Everyone who is not wise is both creative and strong.
If alice is not tall then susan is either not curious or kind and vice versa.
If paul is either not happy or not brave then mary is not strong or not calm.
If someone is not rich or not calm then someone is both not calm and not funny.
Everyone who is not generous is tall or not happy and vice versa.
Everyone who is calm is either creative or calm.
If paul is both quiet and funny then susan is not funny or not brave and vice versa.
Mary is tall.
Someone is either patient or rich.
Mary is not old.
Someone is strong or quiet.
John is kind or patient.
Someone is wise or strong. | Susan is not calm. | contradiction | ((?[X]:((wise(X)|strong(X))))<=>((curious(paul)<~>~tall(paul))))&
((?[X]:(patient(X)))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~funny(X))))&
(![X]:((tall(X)<~>calm(X))<=>(~calm(X)|~brave(X))))&
(((~generous(lucy)|~happy(lucy)))=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((humble(X)&brave(X))<=>(generous(X)&~happy(X))))&
(![X]:((~generous(X)|curious(X))<=>funny(X)))&
((funny(fred))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:(~wise(X)=>(creative(X)&strong(X))))&
((~tall(alice))<=>((~curious(susan)<~>kind(susan))))&
(((~happy(paul)<~>~brave(paul)))=>((~strong(mary)|~calm(mary))))&
((?[X]:((~rich(X)|~calm(X))))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:(~generous(X)<=>(tall(X)|~happy(X))))&
(![X]:(calm(X)=>(creative(X)<~>calm(X))))&
(((quiet(paul)&funny(paul)))<=>((~funny(susan)|~brave(susan))))&
(tall(mary))&
(?[X]:((patient(X)<~>rich(X))))&
(~old(mary))&
(?[X]:((strong(X)|quiet(X))))&
((kind(john)|patient(john)))&
(?[X]:((wise(X)|strong(X)))) | ~calm(susan) | [
"p3",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2397885318704009267146864
% SZS output start Proof for 2397885318704009267146864
4. ! [X0] : ((tall(X0) <~> calm(X0)) <=> (~brave(X0) | ~calm(X0))) [input p3]
7. ! [X0] : ((curious(X0) | ~generous(X0)) <=> funny(X0)) [input p6]
12. ? [X0] : (~calm(X0) | ~rich(X0)) => ? [X0] : (~funny(X0) & ~calm(X0)) [input p11]
13. ! [X0] : (~generous(X0) <=> (~happy(X0) | tall(X0))) [input p12]
22. ~calm(susan) [input hypothesis]
24. ? [X0] : (~calm(X0) | ~rich(X0)) => ? [X1] : (~funny(X1) & ~calm(X1)) [rectify 12]
29. ? [X1] : (~funny(X1) & ~calm(X1)) | ! [X0] : (calm(X0) & rich(X0)) [ennf transformation 24]
42. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))))) [flattening 42]
49. ! [X0] : (((curious(X0) | ~generous(X0)) | ~funny(X0)) & (funny(X0) | (~curious(X0) & generous(X0)))) [nnf transformation 7]
50. ! [X0] : ((curious(X0) | ~generous(X0) | ~funny(X0)) & (funny(X0) | (~curious(X0) & generous(X0)))) [flattening 49]
57. ? [X0] : (~funny(X0) & ~calm(X0)) | ! [X1] : (calm(X1) & rich(X1)) [rectify 29]
58. ? [X0] : (~funny(X0) & ~calm(X0)) => (~funny(sK5) & ~calm(sK5)) [choice axiom]
59. (~funny(sK5) & ~calm(sK5)) | ! [X1] : (calm(X1) & rich(X1)) [skolemisation 57,58]
60. ! [X0] : ((~generous(X0) | (happy(X0) & ~tall(X0))) & ((~happy(X0) | tall(X0)) | generous(X0))) [nnf transformation 13]
61. ! [X0] : ((~generous(X0) | (happy(X0) & ~tall(X0))) & (~happy(X0) | tall(X0) | generous(X0))) [flattening 60]
86. calm(X0) | tall(X0) | calm(X0) [cnf transformation 43]
98. generous(X0) | funny(X0) [cnf transformation 50]
113. ~calm(sK5) | calm(X1) [cnf transformation 59]
115. ~funny(sK5) | calm(X1) [cnf transformation 59]
117. ~generous(X0) | ~tall(X0) [cnf transformation 61]
133. ~calm(susan) [cnf transformation 22]
136. calm(X0) | tall(X0) [duplicate literal removal 86]
258. 26 <=> ! [X1] : calm(X1) [avatar definition]
259. calm(X1) <- (26) [avatar component clause 258]
261. 27 <=> funny(sK5) [avatar definition]
264. 26 | ~27 [avatar split clause 115,261,258]
270. 29 <=> calm(sK5) [avatar definition]
272. ~calm(sK5) <- (~29) [avatar component clause 270]
273. 26 | ~29 [avatar split clause 113,270,258]
329. ~tall(X0) | funny(X0) [resolution 117,98]
340. tall(sK5) <- (~29) [resolution 136,272]
387. funny(sK5) <- (~29) [resolution 329,340]
390. 27 | 29 [avatar split clause 387,270,261]
392. $false <- (26) [resolution 259,133]
399. ~26 [avatar contradiction clause 392]
400. $false [avatar sat refutation 264,273,390,399]
% SZS output end Proof for 2397885318704009267146864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both rich and happy then someone is brave.
Everyone who is not calm or generous is not kind or tall.
Everyone who is not funny or not quiet is both not patient and not kind and vice versa.
If someone is calm or humble then someone is wise and vice versa.
Everyone who is not tall or tall is generous.
Everyone who is not creative is either quiet or happy and vice versa.
If lucy is creative or curious then lucy is funny.
Everyone who is not curious or calm is not tall.
Everyone who is happy is not quiet.
If someone is both not happy and not humble then someone is either not patient or not happy and vice versa.
Everyone who is both patient and happy is old and vice versa.
Everyone who is not creative is either kind or not generous.
Everyone who is both not strong and not wise is not happy.
Everyone who is both not tall and happy is either not kind or generous and vice versa.
Everyone who is either tall or strong is calm or kind.
If lucy is funny then john is kind or brave and vice versa.
Someone is not kind.
Someone is not strong.
Fred is both wise and not calm.
Fred is wise or not funny.
Paul is both not brave and not old.
John is kind or brave.
Someone is not brave or wise. | Lucy is quiet. | contradiction | (((rich(susan)&happy(susan)))=>(?[X]:(brave(X))))&
(![X]:((~calm(X)|generous(X))=>(~kind(X)|tall(X))))&
(![X]:((~funny(X)|~quiet(X))<=>(~patient(X)&~kind(X))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)|tall(X))=>generous(X)))&
(![X]:(~creative(X)<=>(quiet(X)<~>happy(X))))&
(((creative(lucy)|curious(lucy)))=>(funny(lucy)))&
(![X]:((~curious(X)|calm(X))=>~tall(X)))&
(![X]:(happy(X)=>~quiet(X)))&
((?[X]:((~happy(X)&~humble(X))))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((patient(X)&happy(X))<=>old(X)))&
(![X]:(~creative(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~strong(X)&~wise(X))=>~happy(X)))&
(![X]:((~tall(X)&happy(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((tall(X)<~>strong(X))=>(calm(X)|kind(X))))&
((funny(lucy))<=>((kind(john)|brave(john))))&
(?[X]:(~kind(X)))&
(?[X]:(~strong(X)))&
((wise(fred)&~calm(fred)))&
((wise(fred)|~funny(fred)))&
((~brave(paul)&~old(paul)))&
((kind(john)|brave(john)))&
(?[X]:((~brave(X)|wise(X)))) | quiet(lucy) | [
"p4",
"p5",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5843209547294228541374200
% SZS output start Proof for 5843209547294228541374200
5. ! [X0] : ((tall(X0) | ~tall(X0)) => generous(X0)) [input p4]
6. ! [X0] : (~creative(X0) <=> (quiet(X0) <~> happy(X0))) [input p5]
9. ! [X0] : (happy(X0) => ~quiet(X0)) [input p8]
12. ! [X0] : (~creative(X0) => (kind(X0) <~> ~generous(X0))) [input p11]
14. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (~kind(X0) <~> generous(X0))) [input p13]
24. quiet(lucy) [input hypothesis]
31. ! [X0] : (generous(X0) | (~tall(X0) & tall(X0))) [ennf transformation 5]
34. ! [X0] : (~quiet(X0) | ~happy(X0)) [ennf transformation 9]
37. ! [X0] : ((kind(X0) <~> ~generous(X0)) | creative(X0)) [ennf transformation 12]
49. ! [X0] : ((~creative(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | creative(X0))) [nnf transformation 6]
55. ! [X0] : (((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | creative(X0)) [nnf transformation 37]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~happy(X0) | tall(X0)))) [nnf transformation 14]
57. ! [X0] : (((happy(X0) & ~tall(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | ~happy(X0) | tall(X0))) [flattening 56]
77. generous(X0) | tall(X0) [cnf transformation 31]
78. ~tall(X0) | generous(X0) [cnf transformation 31]
81. ~creative(X0) | happy(X0) | ~quiet(X0) [cnf transformation 49]
87. ~quiet(X0) | ~happy(X0) [cnf transformation 34]
95. ~generous(X0) | kind(X0) | creative(X0) [cnf transformation 55]
103. happy(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 57]
118. quiet(lucy) [cnf transformation 24]
143. generous(X0) [subsumption resolution 77,78]
189. creative(X0) | kind(X0) [subsumption resolution 95,143]
190. ~kind(X0) | happy(X0) [subsumption resolution 103,143]
223. happy(X1) | ~quiet(X1) | kind(X1) [resolution 81,189]
225. happy(X1) | ~quiet(X1) [subsumption resolution 223,190]
226. ~quiet(X1) [subsumption resolution 225,87]
231. $false [resolution 226,118]
% SZS output end Proof for 5843209547294228541374200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is both creative and generous and vice versa. If someone is quiet or not humble then alice is either happy or not funny and vice versa. Everyone who is wise or not rich is either generous or funny. Everyone who is both humble and not calm is both calm and not brave. Everyone who is brave is either not tall or calm and vice versa. Everyone who is not quiet or happy is both not wise and generous and vice versa. Everyone who is either old or generous is humble or wise. Everyone who is either calm or not happy is funny and vice versa. If someone is either humble or not curious then mary is either brave or wise and vice versa. If mary is not wise or not funny then someone is both not strong and not patient. If paul is old or not brave then paul is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Lucy is both not rich and wise. Someone is either patient or not quiet. Someone is not patient. Susan is both calm and quiet. Someone is both not kind and not wise. Someone is both strong and calm. Someone is both not patient and not calm. Someone is not strong. | Lucy is not happy. | entailment | (![X]:((~funny(X)|funny(X))<=>(creative(X)&generous(X))))&
((?[X]:((quiet(X)|~humble(X))))<=>((happy(alice)<~>~funny(alice))))&
(![X]:((wise(X)|~rich(X))=>(generous(X)<~>funny(X))))&
(![X]:((humble(X)&~calm(X))=>(calm(X)&~brave(X))))&
(![X]:(brave(X)<=>(~tall(X)<~>calm(X))))&
(![X]:((~quiet(X)|happy(X))<=>(~wise(X)&generous(X))))&
(![X]:((old(X)<~>generous(X))=>(humble(X)|wise(X))))&
(![X]:((calm(X)<~>~happy(X))<=>funny(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>((brave(mary)<~>wise(mary))))&
(((~wise(mary)|~funny(mary)))=>(?[X]:((~strong(X)&~patient(X)))))&
(((old(paul)|~brave(paul)))=>((~quiet(paul)|~kind(paul))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
((~rich(lucy)&wise(lucy)))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:(~patient(X)))&
((calm(susan)&quiet(susan)))&
(?[X]:((~kind(X)&~wise(X))))&
(?[X]:((strong(X)&calm(X))))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:(~strong(X))) | ~happy(lucy) | [
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3473023486387579162910711
% SZS output start Proof for 3473023486387579162910711
6. ! [X0] : ((happy(X0) | ~quiet(X0)) <=> (generous(X0) & ~wise(X0))) [input p5]
17. wise(lucy) & ~rich(lucy) [input p16]
25. happy(lucy) [input hypothesis]
48. ! [X0] : (((happy(X0) | ~quiet(X0)) | (~generous(X0) | wise(X0))) & ((generous(X0) & ~wise(X0)) | (~happy(X0) & quiet(X0)))) [nnf transformation 6]
49. ! [X0] : ((happy(X0) | ~quiet(X0) | ~generous(X0) | wise(X0)) & ((generous(X0) & ~wise(X0)) | (~happy(X0) & quiet(X0)))) [flattening 48]
104. ~wise(X0) | ~happy(X0) [cnf transformation 49]
139. wise(lucy) [cnf transformation 17]
152. happy(lucy) [cnf transformation 25]
307. ~happy(lucy) [resolution 104,139]
309. $false [subsumption resolution 307,152]
% SZS output end Proof for 3473023486387579162910711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not happy then susan is not brave. Everyone who is either brave or not creative is kind and vice versa. Everyone who is both not old and quiet is happy. If lucy is both quiet and not wise then mary is both wise and not patient. Everyone who is creative or humble is either not patient or rich. Everyone who is either not creative or generous is not brave. Everyone who is brave is not calm or humble and vice versa. If fred is either not strong or not wise then paul is both strong and old. Everyone who is old is either not funny or not brave. Everyone who is both not brave and patient is both not wise and brave and vice versa. If someone is not quiet or not brave then someone is both not kind and humble. Everyone who is patient or not tall is either not humble or wise. Everyone who is both kind and not funny is not patient and vice versa. If someone is not calm or patient then paul is generous. Everyone who is either not wise or not strong is either not rich or strong and vice versa. Someone is brave. Mary is either funny or curious. Someone is creative. Someone is not patient or wise. Someone is either happy or not old. Mary is not tall or not kind. | Lucy is patient. | contradiction | ((?[X]:((strong(X)&~happy(X))))=>(~brave(susan)))&
(![X]:((brave(X)<~>~creative(X))<=>kind(X)))&
(![X]:((~old(X)&quiet(X))=>happy(X)))&
(((quiet(lucy)&~wise(lucy)))=>((wise(mary)&~patient(mary))))&
(![X]:((creative(X)|humble(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~creative(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)<=>(~calm(X)|humble(X))))&
(((~strong(fred)<~>~wise(fred)))=>((strong(paul)&old(paul))))&
(![X]:(old(X)=>(~funny(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~wise(X)&brave(X))))&
((?[X]:((~quiet(X)|~brave(X))))=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((patient(X)|~tall(X))=>(~humble(X)<~>wise(X))))&
(![X]:((kind(X)&~funny(X))<=>~patient(X)))&
((?[X]:((~calm(X)|patient(X))))=>(generous(paul)))&
(![X]:((~wise(X)<~>~strong(X))<=>(~rich(X)<~>strong(X))))&
(?[X]:(brave(X)))&
((funny(mary)<~>curious(mary)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
((~tall(mary)|~kind(mary))) | patient(lucy) | [
"p4",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2390803591208282699249570
% SZS output start Proof for 2390803591208282699249570
5. ! [X0] : ((humble(X0) | creative(X0)) => (~patient(X0) <~> rich(X0))) [input p4]
10. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (brave(X0) & ~wise(X0))) [input p9]
12. ! [X0] : ((~tall(X0) | patient(X0)) => (~humble(X0) <~> wise(X0))) [input p11]
15. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~rich(X0) <~> strong(X0))) [input p14]
22. patient(lucy) [input hypothesis]
29. ! [X0] : ((~patient(X0) <~> rich(X0)) | (~humble(X0) & ~creative(X0))) [ennf transformation 5]
34. ! [X0] : ((~humble(X0) <~> wise(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 12]
37. ! [X0] : (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~humble(X0) & ~creative(X0))) [nnf transformation 29]
43. ! [X0] : (((patient(X0) & ~brave(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 10]
44. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | ~patient(X0) | brave(X0))) [flattening 43]
48. ! [X0] : (((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (tall(X0) & ~patient(X0))) [nnf transformation 34]
51. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 15]
71. ~humble(X0) | ~patient(X0) | rich(X0) [cnf transformation 37]
86. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 44]
87. ~brave(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
95. ~patient(X0) | humble(X0) | ~wise(X0) [cnf transformation 48]
103. strong(X0) | ~rich(X0) | ~wise(X0) | strong(X0) [cnf transformation 51]
107. ~strong(X0) | ~wise(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 51]
118. patient(lucy) [cnf transformation 22]
119. strong(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 103]
121. ~strong(X0) | ~wise(X0) | ~rich(X0) [duplicate literal removal 107]
123. ~patient(X0) | brave(X0) [duplicate literal removal 86]
124. ~brave(X0) | wise(X0) [duplicate literal removal 87]
138. 4 <=> wise(lucy) [avatar definition]
140. wise(lucy) <- (4) [avatar component clause 138]
202. ~rich(X0) | ~wise(X0) [subsumption resolution 119,121]
245. brave(lucy) [resolution 123,118]
250. wise(lucy) [resolution 124,245]
251. 4 [avatar split clause 250,138]
291. 29 <=> rich(lucy) [avatar definition]
293. rich(lucy) <- (29) [avatar component clause 291]
371. humble(lucy) | ~wise(lucy) [resolution 95,118]
375. humble(lucy) <- (4) [subsumption resolution 371,140]
381. ~patient(lucy) | rich(lucy) <- (4) [resolution 375,71]
383. rich(lucy) <- (4) [subsumption resolution 381,118]
384. 29 | ~4 [avatar split clause 383,138,291]
393. ~wise(lucy) <- (29) [resolution 293,202]
394. $false <- (4, 29) [subsumption resolution 393,140]
395. ~4 | ~29 [avatar contradiction clause 394]
396. $false [avatar sat refutation 251,384,395]
% SZS output end Proof for 2390803591208282699249570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or strong then someone is both not old and not curious and vice versa.
Everyone who is not quiet is curious and vice versa.
If someone is either rich or brave then alice is either funny or wise and vice versa.
Everyone who is not strong is both wise and not kind.
Everyone who is either not quiet or not creative is either quiet or humble and vice versa.
If someone is not wise then someone is either not brave or creative.
Everyone who is rich is either wise or happy and vice versa.
Everyone who is not rich is not old and vice versa.
If someone is not generous then someone is either not generous or not strong and vice versa.
Everyone who is not wise is not generous and vice versa.
If lucy is both funny and not funny then alice is not kind or not tall.
If someone is both not quiet and generous then someone is both generous and not humble.
Everyone who is either funny or not humble is funny or humble.
Everyone who is happy or not curious is tall and vice versa.
If paul is both generous and wise then someone is not humble.
Everyone who is not generous or tall is both not funny and not strong.
John is curious or creative.
John is not patient or patient.
Lucy is wise or not kind.
Someone is not funny or old.
Mary is both funny and not creative.
Someone is quiet or calm.
Mary is both brave and generous. | Mary is not old. | contradiction | ((?[X]:((curious(X)<~>strong(X))))<=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((rich(X)<~>brave(X))))<=>((funny(alice)<~>wise(alice))))&
(![X]:(~strong(X)=>(wise(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~brave(X)<~>creative(X)))))&
(![X]:(rich(X)<=>(wise(X)<~>happy(X))))&
(![X]:(~rich(X)<=>~old(X)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>~generous(X)))&
(((funny(lucy)&~funny(lucy)))=>((~kind(alice)|~tall(alice))))&
((?[X]:((~quiet(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(funny(X)|humble(X))))&
(![X]:((happy(X)|~curious(X))<=>tall(X)))&
(((generous(paul)&wise(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)|tall(X))=>(~funny(X)&~strong(X))))&
((curious(john)|creative(john)))&
((~patient(john)|patient(john)))&
((wise(lucy)|~kind(lucy)))&
(?[X]:((~funny(X)|old(X))))&
((funny(mary)&~creative(mary)))&
(?[X]:((quiet(X)|calm(X))))&
((brave(mary)&generous(mary))) | ~old(mary) | [
"p3",
"p6",
"p7",
"p8",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8550811848278518440404874
% SZS output start Proof for 8550811848278518440404874
4. ! [X0] : (~strong(X0) => (~kind(X0) & wise(X0))) [input p3]
7. ! [X0] : (rich(X0) <=> (wise(X0) <~> happy(X0))) [input p6]
8. ! [X0] : (~rich(X0) <=> ~old(X0)) [input p7]
9. ? [X0] : ~generous(X0) <=> ? [X0] : (~generous(X0) <~> ~strong(X0)) [input p8]
10. ! [X0] : (~wise(X0) <=> ~generous(X0)) [input p9]
14. ! [X0] : ((~curious(X0) | happy(X0)) <=> tall(X0)) [input p13]
16. ! [X0] : ((tall(X0) | ~generous(X0)) => (~strong(X0) & ~funny(X0))) [input p15]
24. ~old(mary) [input hypothesis]
27. ? [X0] : ~generous(X0) <=> ? [X1] : (~generous(X1) <~> ~strong(X1)) [rectify 9]
29. ! [X0] : ((~curious(X0) | happy(X0)) => tall(X0)) [unused predicate definition removal 14]
33. ! [X0] : (~strong(X0) => wise(X0)) [pure predicate removal 4]
34. ! [X0] : (wise(X0) | strong(X0)) [ennf transformation 33]
39. ! [X0] : (tall(X0) | (curious(X0) & ~happy(X0))) [ennf transformation 29]
42. ! [X0] : ((~strong(X0) & ~funny(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 16]
58. ! [X0] : ((rich(X0) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0)))) & (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | ~rich(X0))) [nnf transformation 7]
59. ! [X0] : ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))) [nnf transformation 8]
60. (? [X0] : ~generous(X0) | ! [X1] : ((~generous(X1) | strong(X1)) & (~strong(X1) | generous(X1)))) & (? [X1] : ((strong(X1) | generous(X1)) & (~strong(X1) | ~generous(X1))) | ! [X0] : generous(X0)) [nnf transformation 27]
61. (? [X0] : ~generous(X0) | ! [X1] : ((~generous(X1) | strong(X1)) & (~strong(X1) | generous(X1)))) & (? [X2] : ((strong(X2) | generous(X2)) & (~strong(X2) | ~generous(X2))) | ! [X3] : generous(X3)) [rectify 60]
62. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
63. ? [X2] : ((strong(X2) | generous(X2)) & (~strong(X2) | ~generous(X2))) => ((strong(sK5) | generous(sK5)) & (~strong(sK5) | ~generous(sK5))) [choice axiom]
64. (~generous(sK4) | ! [X1] : ((~generous(X1) | strong(X1)) & (~strong(X1) | generous(X1)))) & (((strong(sK5) | generous(sK5)) & (~strong(sK5) | ~generous(sK5))) | ! [X3] : generous(X3)) [skolemisation 61,63,62]
65. ! [X0] : ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))) [nnf transformation 10]
90. wise(X0) | strong(X0) [cnf transformation 34]
103. ~wise(X0) | happy(X0) | rich(X0) [cnf transformation 58]
106. ~rich(X0) | old(X0) [cnf transformation 59]
110. ~generous(sK4) | ~generous(X1) | strong(X1) [cnf transformation 64]
111. ~generous(X0) | wise(X0) [cnf transformation 65]
112. ~wise(X0) | generous(X0) [cnf transformation 65]
117. ~happy(X0) | tall(X0) [cnf transformation 39]
122. ~strong(X0) | generous(X0) [cnf transformation 42]
123. ~tall(X0) | ~strong(X0) [cnf transformation 42]
131. ~old(mary) [cnf transformation 24]
201. 14 <=> ! [X1] : wise(X1) [avatar definition]
202. wise(X1) <- (14) [avatar component clause 201]
214. 17 <=> ! [X1] : (~generous(X1) | strong(X1)) [avatar definition]
215. ~generous(X1) | strong(X1) <- (17) [avatar component clause 214]
217. 18 <=> generous(sK4) [avatar definition]
219. ~generous(sK4) <- (~18) [avatar component clause 217]
220. 17 | ~18 [avatar split clause 110,217,214]
222. 19 <=> ! [X1] : (~strong(X1) | generous(X1)) [avatar definition]
223. ~strong(X1) | generous(X1) <- (19) [avatar component clause 222]
226. 20 <=> ! [X3] : generous(X3) [avatar definition]
227. generous(X3) <- (20) [avatar component clause 226]
261. 19 [avatar split clause 122,222]
280. $false <- (~18, 20) [subsumption resolution 219,227]
281. 18 | ~20 [avatar contradiction clause 280]
292. generous(X0) | strong(X0) [resolution 112,90]
302. generous(X0) <- (19) [subsumption resolution 292,223]
303. 20 | ~19 [avatar split clause 302,222,226]
304. strong(X1) <- (17, 20) [subsumption resolution 215,227]
305. wise(X0) <- (20) [resolution 227,111]
306. 14 | ~20 [avatar split clause 305,226,201]
335. happy(X0) | rich(X0) <- (14) [resolution 103,202]
348. tall(X2) | rich(X2) <- (14) [resolution 335,117]
351. rich(X0) | ~strong(X0) <- (14) [resolution 348,123]
353. rich(X0) <- (14, 17, 20) [subsumption resolution 351,304]
355. old(X1) <- (14, 17, 20) [resolution 353,106]
356. $false <- (14, 17, 20) [resolution 355,131]
360. ~14 | ~17 | ~20 [avatar contradiction clause 356]
361. $false [avatar sat refutation 220,261,281,303,306,360]
% SZS output end Proof for 8550811848278518440404874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet or not rich then alice is rich or not calm. Everyone who is either not creative or calm is not curious or kind and vice versa. Everyone who is not calm or not quiet is not strong or quiet and vice versa. Everyone who is either not curious or humble is patient or rich. Everyone who is either not old or generous is not calm and vice versa. Everyone who is brave or not quiet is humble or not calm and vice versa. If john is rich or not wise then john is quiet or not generous. If someone is not calm or not funny then lucy is not strong and vice versa. Everyone who is old is wise and vice versa. Everyone who is either not tall or funny is not kind or wise and vice versa. Everyone who is either brave or not curious is either humble or not creative. Everyone who is both not patient and strong is either not curious or not quiet. Everyone who is brave is happy and vice versa. Everyone who is not brave or not creative is both calm and funny and vice versa. Everyone who is both creative and not quiet is not happy and vice versa. If mary is both happy and wise then john is funny or not patient. Someone is patient. Someone is either not brave or not curious. Fred is both not kind and patient. Susan is not quiet or wise. Someone is either not old or brave. Someone is not wise or not strong. Paul is both curious and creative. | Alice is humble. | entailment | (((~quiet(paul)|~rich(paul)))=>((rich(alice)|~calm(alice))))&
(![X]:((~creative(X)<~>calm(X))<=>(~curious(X)|kind(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(~strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>humble(X))=>(patient(X)|rich(X))))&
(![X]:((~old(X)<~>generous(X))<=>~calm(X)))&
(![X]:((brave(X)|~quiet(X))<=>(humble(X)|~calm(X))))&
(((rich(john)|~wise(john)))=>((quiet(john)|~generous(john))))&
((?[X]:((~calm(X)|~funny(X))))<=>(~strong(lucy)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((~tall(X)<~>funny(X))<=>(~kind(X)|wise(X))))&
(![X]:((brave(X)<~>~curious(X))=>(humble(X)<~>~creative(X))))&
(![X]:((~patient(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:(brave(X)<=>happy(X)))&
(![X]:((~brave(X)|~creative(X))<=>(calm(X)&funny(X))))&
(![X]:((creative(X)&~quiet(X))<=>~happy(X)))&
(((happy(mary)&wise(mary)))=>((funny(john)|~patient(john))))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
((~kind(fred)&patient(fred)))&
((~quiet(susan)|wise(susan)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((~wise(X)|~strong(X))))&
((curious(paul)&creative(paul))) | humble(alice) | [
"p1",
"p2",
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2514337928386437867451022
% SZS output start Proof for 2514337928386437867451022
2. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> (kind(X0) | ~curious(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) | ~calm(X0)) <=> (quiet(X0) | ~strong(X0))) [input p2]
6. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (~calm(X0) | humble(X0))) [input p5]
11. ! [X0] : ((brave(X0) <~> ~curious(X0)) => (humble(X0) <~> ~creative(X0))) [input p10]
14. ! [X0] : ((~creative(X0) | ~brave(X0)) <=> (funny(X0) & calm(X0))) [input p13]
24. ~humble(alice) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> ~creative(X0)) | (brave(X0) <=> ~curious(X0))) [ennf transformation 11]
36. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [flattening 36]
38. ! [X0] : (((~quiet(X0) | ~calm(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (quiet(X0) & calm(X0)))) [nnf transformation 3]
39. ! [X0] : ((~quiet(X0) | ~calm(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | (quiet(X0) & calm(X0)))) [flattening 38]
42. ! [X0] : (((~quiet(X0) | brave(X0)) | (calm(X0) & ~humble(X0))) & ((~calm(X0) | humble(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 6]
43. ! [X0] : ((~quiet(X0) | brave(X0) | (calm(X0) & ~humble(X0))) & (~calm(X0) | humble(X0) | (quiet(X0) & ~brave(X0)))) [flattening 42]
51. ! [X0] : (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0)))) [nnf transformation 31]
54. ! [X0] : (((~creative(X0) | ~brave(X0)) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | (creative(X0) & brave(X0)))) [nnf transformation 14]
55. ! [X0] : ((~creative(X0) | ~brave(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | (creative(X0) & brave(X0)))) [flattening 54]
72. ~creative(X0) | calm(X0) | curious(X0) [cnf transformation 37]
79. ~quiet(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 39]
87. ~calm(X0) | humble(X0) | quiet(X0) [cnf transformation 43]
103. ~brave(X0) | humble(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 51]
111. brave(X0) | calm(X0) [cnf transformation 55]
112. creative(X0) | calm(X0) [cnf transformation 55]
131. ~humble(alice) [cnf transformation 24]
133. ~calm(X0) | ~quiet(X0) [duplicate literal removal 79]
153. ~calm(X0) | humble(X0) [subsumption resolution 87,133]
257. calm(X0) | curious(X0) | calm(X0) [resolution 72,112]
258. curious(X0) | calm(X0) [duplicate literal removal 257]
373. humble(X1) | ~curious(X1) | ~creative(X1) | calm(X1) [resolution 103,111]
374. humble(X1) | ~curious(X1) | calm(X1) [subsumption resolution 373,112]
375. ~curious(X1) | humble(X1) [subsumption resolution 374,153]
381. humble(X0) | calm(X0) [resolution 375,258]
383. humble(X0) [subsumption resolution 381,153]
398. $false [resolution 383,131]
% SZS output end Proof for 2514337928386437867451022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not calm or brave.
If mary is either not strong or tall then someone is not happy or not quiet and vice versa.
If someone is not wise or not old then someone is not tall or generous and vice versa.
If someone is either not wise or wise then lucy is kind or wise and vice versa.
Everyone who is not old or generous is not old.
Everyone who is both patient and not happy is either not tall or not rich.
If someone is either generous or not patient then someone is both not kind and curious and vice versa.
Everyone who is both not generous and brave is either not happy or quiet.
Everyone who is both not rich and strong is tall and vice versa.
If john is either funny or not curious then paul is not kind or not calm.
If paul is strong then someone is old.
Everyone who is happy or not old is patient or not strong and vice versa.
Everyone who is both tall and not tall is rich or not strong and vice versa.
If paul is both not calm and not humble then mary is either brave or creative.
Everyone who is tall or rich is either not wise or brave.
Everyone who is both not humble and funny is either not quiet or not generous and vice versa.
Mary is both creative and not humble.
Someone is creative.
Paul is not wise.
Someone is not strong or not quiet.
Someone is curious.
Someone is not funny.
Fred is both not curious and brave.
Lucy is either old or not tall. | Lucy is old. | entailment | (![X]:(~happy(X)=>(~calm(X)<~>brave(X))))&
(((~strong(mary)<~>tall(mary)))<=>(?[X]:((~happy(X)|~quiet(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((kind(lucy)|wise(lucy))))&
(![X]:((~old(X)|generous(X))=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(~tall(X)<~>~rich(X))))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((~generous(X)&brave(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)&strong(X))<=>tall(X)))&
(((funny(john)<~>~curious(john)))=>((~kind(paul)|~calm(paul))))&
((strong(paul))=>(?[X]:(old(X))))&
(![X]:((happy(X)|~old(X))<=>(patient(X)|~strong(X))))&
(![X]:((tall(X)&~tall(X))<=>(rich(X)|~strong(X))))&
(((~calm(paul)&~humble(paul)))=>((brave(mary)<~>creative(mary))))&
(![X]:((tall(X)|rich(X))=>(~wise(X)<~>brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(~quiet(X)<~>~generous(X))))&
((creative(mary)&~humble(mary)))&
(?[X]:(creative(X)))&
(~wise(paul))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:(curious(X)))&
(?[X]:(~funny(X)))&
((~curious(fred)&brave(fred)))&
((old(lucy)<~>~tall(lucy))) | old(lucy) | [
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8775472653271096015559846
% SZS output start Proof for 8775472653271096015559846
9. ! [X0] : ((strong(X0) & ~rich(X0)) <=> tall(X0)) [input p8]
13. ! [X0] : ((~tall(X0) & tall(X0)) <=> (~strong(X0) | rich(X0))) [input p12]
24. old(lucy) <~> ~tall(lucy) [input p23]
25. ~old(lucy) [input hypothesis]
62. ! [X0] : (((strong(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | (~strong(X0) | rich(X0)))) [nnf transformation 9]
63. ! [X0] : (((strong(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | ~strong(X0) | rich(X0))) [flattening 62]
69. ! [X0] : (((~tall(X0) & tall(X0)) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | (tall(X0) | ~tall(X0)))) [nnf transformation 13]
70. ! [X0] : (((~tall(X0) & tall(X0)) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | tall(X0) | ~tall(X0))) [flattening 69]
83. (tall(lucy) | ~old(lucy)) & (~tall(lucy) | old(lucy)) [nnf transformation 24]
114. ~strong(X0) | tall(X0) | rich(X0) [cnf transformation 63]
115. ~rich(X0) | ~tall(X0) [cnf transformation 63]
116. ~tall(X0) | strong(X0) [cnf transformation 63]
125. tall(X0) | ~rich(X0) [cnf transformation 70]
126. tall(X0) | strong(X0) [cnf transformation 70]
150. ~tall(lucy) | old(lucy) [cnf transformation 83]
152. ~old(lucy) [cnf transformation 25]
196. 10 <=> ! [X1] : tall(X1) [avatar definition]
197. tall(X1) <- (10) [avatar component clause 196]
286. strong(X0) [subsumption resolution 126,116]
287. ~rich(X0) [subsumption resolution 125,115]
305. 34 <=> old(lucy) [avatar definition]
309. 35 <=> tall(lucy) [avatar definition]
310. ~tall(lucy) <- (~35) [avatar component clause 309]
313. 34 | ~35 [avatar split clause 150,309,305]
314. ~34 [avatar split clause 152,305]
336. tall(X0) | rich(X0) [resolution 114,286]
337. tall(X0) [subsumption resolution 336,287]
338. 10 [avatar split clause 337,196]
340. $false <- (10, ~35) [resolution 197,310]
342. ~10 | 35 [avatar contradiction clause 340]
344. $false [avatar sat refutation 313,314,338,342]
% SZS output end Proof for 8775472653271096015559846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or funny is strong and vice versa. If paul is either not old or brave then fred is either creative or happy. Everyone who is wise is not curious or quiet and vice versa. If paul is happy then someone is not humble. Everyone who is either happy or not rich is creative or not tall. If alice is happy then mary is not wise. Everyone who is rich or kind is either generous or not funny. If someone is both creative and not calm then alice is either strong or quiet. Everyone who is not calm is both old and not generous and vice versa. If someone is old or not happy then lucy is not kind and vice versa. Everyone who is not old is quiet or funny and vice versa. If lucy is either not curious or not old then someone is not wise or strong. If alice is old then someone is strong. Everyone who is not strong or not patient is creative or not quiet and vice versa. Everyone who is not humble or old is both tall and patient. Everyone who is both not generous and not patient is not patient or wise and vice versa. Someone is not funny. Someone is not funny or curious. Someone is either calm or happy. Someone is strong or not brave. Paul is not tall or rich. Lucy is not happy. Lucy is not brave. | Mary is old. | contradiction | (![X]:((patient(X)<~>funny(X))<=>strong(X)))&
(((~old(paul)<~>brave(paul)))=>((creative(fred)<~>happy(fred))))&
(![X]:(wise(X)<=>(~curious(X)|quiet(X))))&
((happy(paul))=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>~rich(X))=>(creative(X)|~tall(X))))&
((happy(alice))=>(~wise(mary)))&
(![X]:((rich(X)|kind(X))=>(generous(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>((strong(alice)<~>quiet(alice))))&
(![X]:(~calm(X)<=>(old(X)&~generous(X))))&
((?[X]:((old(X)|~happy(X))))<=>(~kind(lucy)))&
(![X]:(~old(X)<=>(quiet(X)|funny(X))))&
(((~curious(lucy)<~>~old(lucy)))=>(?[X]:((~wise(X)|strong(X)))))&
((old(alice))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)|~patient(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~humble(X)|old(X))=>(tall(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)|wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((strong(X)|~brave(X))))&
((~tall(paul)|rich(paul)))&
(~happy(lucy))&
(~brave(lucy)) | old(mary) | [
"p0",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3064666869444825381598088
% SZS output start Proof for 3064666869444825381598088
1. ! [X0] : ((patient(X0) <~> funny(X0)) <=> strong(X0)) [input p0]
11. ! [X0] : (~old(X0) <=> (funny(X0) | quiet(X0))) [input p10]
14. ! [X0] : ((~patient(X0) | ~strong(X0)) <=> (~quiet(X0) | creative(X0))) [input p13]
15. ! [X0] : ((old(X0) | ~humble(X0)) => (patient(X0) & tall(X0))) [input p14]
24. old(mary) [input hypothesis]
34. ! [X0] : ((patient(X0) & tall(X0)) | (~old(X0) & humble(X0))) [ennf transformation 15]
35. ! [X0] : ((((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | ~strong(X0)) & (strong(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0))))) [nnf transformation 1]
50. ! [X0] : ((~old(X0) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | old(X0))) [nnf transformation 11]
51. ! [X0] : ((~old(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | old(X0))) [flattening 50]
57. ! [X0] : (((~patient(X0) | ~strong(X0)) | (quiet(X0) & ~creative(X0))) & ((~quiet(X0) | creative(X0)) | (patient(X0) & strong(X0)))) [nnf transformation 14]
58. ! [X0] : ((~patient(X0) | ~strong(X0) | (quiet(X0) & ~creative(X0))) & (~quiet(X0) | creative(X0) | (patient(X0) & strong(X0)))) [flattening 57]
70. ~patient(X0) | funny(X0) | strong(X0) [cnf transformation 35]
98. ~quiet(X0) | ~old(X0) [cnf transformation 51]
99. ~old(X0) | ~funny(X0) [cnf transformation 51]
106. ~strong(X0) | ~patient(X0) | quiet(X0) [cnf transformation 58]
110. ~old(X0) | patient(X0) [cnf transformation 34]
124. old(mary) [cnf transformation 24]
261. ~funny(mary) [resolution 99,124]
269. patient(mary) [resolution 110,124]
271. funny(mary) | strong(mary) [resolution 70,269]
273. strong(mary) [subsumption resolution 271,261]
297. ~patient(mary) | quiet(mary) [resolution 106,273]
299. quiet(mary) [subsumption resolution 297,269]
303. ~old(mary) [resolution 299,98]
305. $false [subsumption resolution 303,124]
% SZS output end Proof for 3064666869444825381598088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is not kind or not funny and vice versa. Everyone who is both not generous and happy is either not brave or not happy and vice versa. Everyone who is both tall and humble is not curious or not brave and vice versa. Everyone who is not patient or happy is not calm or not tall and vice versa. Everyone who is both not funny and not strong is humble or wise. Everyone who is either curious or kind is both not generous and humble and vice versa. If someone is both not brave and not calm then someone is patient or not kind and vice versa. Everyone who is patient or humble is either not rich or calm and vice versa. Everyone who is not wise is brave or old. Everyone who is either not quiet or not brave is both strong and patient and vice versa. If someone is both kind and not old then someone is not brave and vice versa. Everyone who is either not happy or calm is kind or brave. If susan is either not rich or wise then alice is not humble. Everyone who is curious or old is tall or happy. Everyone who is both rich and not happy is not wise or tall and vice versa. Someone is strong. Someone is either wise or not brave. Someone is either not strong or old. John is funny or old. Susan is humble or funny. Someone is generous. | Alice is not strong. | neutral | (![X]:(~brave(X)<=>(~kind(X)|~funny(X))))&
(![X]:((~generous(X)&happy(X))<=>(~brave(X)<~>~happy(X))))&
(![X]:((tall(X)&humble(X))<=>(~curious(X)|~brave(X))))&
(![X]:((~patient(X)|happy(X))<=>(~calm(X)|~tall(X))))&
(![X]:((~funny(X)&~strong(X))=>(humble(X)|wise(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~generous(X)&humble(X))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((patient(X)|~kind(X)))))&
(![X]:((patient(X)|humble(X))<=>(~rich(X)<~>calm(X))))&
(![X]:(~wise(X)=>(brave(X)|old(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>(strong(X)&patient(X))))&
((?[X]:((kind(X)&~old(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~happy(X)<~>calm(X))=>(kind(X)|brave(X))))&
(((~rich(susan)<~>wise(susan)))=>(~humble(alice)))&
(![X]:((curious(X)|old(X))=>(tall(X)|happy(X))))&
(![X]:((rich(X)&~happy(X))<=>(~wise(X)|tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~strong(X)<~>old(X))))&
((funny(john)|old(john)))&
((humble(susan)|funny(susan)))&
(?[X]:(generous(X))) | ~strong(alice) | [] | null | 0 |
If someone is either happy or funny then fred is not quiet or not funny and vice versa. Everyone who is both not happy and not quiet is either wise or not happy and vice versa. Everyone who is either not wise or not brave is both curious and not strong. If fred is old then lucy is either wise or not creative and vice versa. Everyone who is either brave or tall is both wise and not brave. If susan is both generous and not generous then someone is strong or generous and vice versa. If alice is kind then someone is humble or old. Everyone who is not wise or generous is both not strong and quiet and vice versa. Everyone who is both kind and humble is either humble or not old and vice versa. If someone is either kind or old then mary is tall or not kind. Everyone who is not calm or not happy is both strong and not tall. Everyone who is calm is curious or strong. If alice is both not humble and brave then someone is both not happy and calm. Everyone who is patient is either not quiet or strong and vice versa. Everyone who is funny or wise is happy. Everyone who is both patient and rich is not funny and vice versa. Someone is brave. Mary is creative or not patient. Fred is happy. Someone is happy or not happy. Someone is either not tall or humble. | Alice is not funny. | contradiction | ((?[X]:((happy(X)<~>funny(X))))<=>((~quiet(fred)|~funny(fred))))&
(![X]:((~happy(X)&~quiet(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~brave(X))=>(curious(X)&~strong(X))))&
((old(fred))<=>((wise(lucy)<~>~creative(lucy))))&
(![X]:((brave(X)<~>tall(X))=>(wise(X)&~brave(X))))&
(((generous(susan)&~generous(susan)))<=>(?[X]:((strong(X)|generous(X)))))&
((kind(alice))=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(?[X]:(brave(X)))&
((creative(mary)|~patient(mary)))&
(happy(fred))&
(?[X]:((happy(X)|~happy(X))))&
(?[X]:((~tall(X)<~>humble(X)))) | ~funny(alice) | [
"p1",
"p5",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 460343008697929867531132
% SZS output start Proof for 460343008697929867531132
2. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (wise(X0) <~> ~happy(X0))) [input p1]
6. (~generous(susan) & generous(susan)) <=> ? [X0] : (generous(X0) | strong(X0)) [input p5]
8. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p7]
14. ! [X0] : (patient(X0) <=> (~quiet(X0) <~> strong(X0))) [input p13]
16. ! [X0] : ((rich(X0) & patient(X0)) <=> ~funny(X0)) [input p15]
22. ~funny(alice) [input hypothesis]
41. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) & (((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | (quiet(X0) | happy(X0)))) [nnf transformation 2]
42. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) & (((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | quiet(X0) | happy(X0))) [flattening 41]
46. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X0] : (generous(X0) | strong(X0)) | (generous(susan) | ~generous(susan))) [nnf transformation 6]
47. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X0] : (generous(X0) | strong(X0)) | generous(susan) | ~generous(susan)) [flattening 46]
48. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & (? [X1] : (generous(X1) | strong(X1)) | generous(susan) | ~generous(susan)) [rectify 47]
49. ? [X1] : (generous(X1) | strong(X1)) => (generous(sK1) | strong(sK1)) [choice axiom]
50. ((~generous(susan) & generous(susan)) | ! [X0] : (~generous(X0) & ~strong(X0))) & ((generous(sK1) | strong(sK1)) | generous(susan) | ~generous(susan)) [skolemisation 48,49]
53. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 8]
54. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 53]
60. ! [X0] : ((patient(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~patient(X0))) [nnf transformation 14]
61. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | ~patient(X0)))) [nnf transformation 16]
62. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | ~patient(X0))) [flattening 61]
77. happy(X0) | ~wise(X0) | quiet(X0) | happy(X0) [cnf transformation 42]
78. ~happy(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 42]
93. generous(susan) | ~strong(X0) [cnf transformation 50]
95. ~generous(susan) | ~strong(X0) [cnf transformation 50]
100. quiet(X0) | wise(X0) [cnf transformation 54]
114. strong(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 60]
121. patient(X0) | funny(X0) [cnf transformation 62]
129. ~funny(alice) [cnf transformation 22]
133. happy(X0) | ~wise(X0) | quiet(X0) [duplicate literal removal 77]
134. ~wise(X0) | ~happy(X0) [duplicate literal removal 78]
163. ~wise(X0) | quiet(X0) [subsumption resolution 133,134]
184. 11 <=> generous(susan) [avatar definition]
189. 12 <=> ! [X0] : ~strong(X0) [avatar definition]
190. ~strong(X0) <- (12) [avatar component clause 189]
191. 12 | ~11 [avatar split clause 95,184,189]
193. 12 | 11 [avatar split clause 93,184,189]
208. quiet(X0) [subsumption resolution 100,163]
236. ~patient(X0) | strong(X0) [subsumption resolution 114,208]
278. strong(X0) | funny(X0) [resolution 236,121]
279. funny(X0) <- (12) [subsumption resolution 278,190]
282. $false <- (12) [resolution 279,129]
285. ~12 [avatar contradiction clause 282]
287. $false [avatar sat refutation 191,193,285]
% SZS output end Proof for 460343008697929867531132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or funny is strong. If someone is calm then fred is tall or funny. Everyone who is humble is kind and vice versa. If someone is not generous then someone is funny and vice versa. Everyone who is quiet or not creative is wise or calm and vice versa. If paul is not creative then paul is not humble and vice versa. Everyone who is both funny and kind is either wise or not happy and vice versa. If mary is both tall and not strong then fred is both not patient and brave and vice versa. Everyone who is generous or tall is both not creative and humble. Everyone who is not rich or not kind is either not happy or not generous. If alice is not funny then john is both not tall and rich. If susan is both old and strong then john is either not quiet or not calm and vice versa. Everyone who is funny or not funny is not curious. Everyone who is both not kind and not wise is both not creative and quiet. Everyone who is kind or tall is either not happy or happy and vice versa. Everyone who is not kind is humble or tall. Someone is strong. Someone is not wise or not creative. Someone is not old. Fred is either not patient or funny. Someone is not quiet. John is funny or calm. Someone is both not patient and not funny. | Susan is humble. | entailment | (![X]:((~patient(X)|funny(X))=>strong(X)))&
((?[X]:(calm(X)))=>((tall(fred)|funny(fred))))&
(![X]:(humble(X)<=>kind(X)))&
((?[X]:(~generous(X)))<=>(?[X]:(funny(X))))&
(![X]:((quiet(X)|~creative(X))<=>(wise(X)|calm(X))))&
((~creative(paul))<=>(~humble(paul)))&
(![X]:((funny(X)&kind(X))<=>(wise(X)<~>~happy(X))))&
(((tall(mary)&~strong(mary)))<=>((~patient(fred)&brave(fred))))&
(![X]:((generous(X)|tall(X))=>(~creative(X)&humble(X))))&
(![X]:((~rich(X)|~kind(X))=>(~happy(X)<~>~generous(X))))&
((~funny(alice))=>((~tall(john)&rich(john))))&
(((old(susan)&strong(susan)))<=>((~quiet(john)<~>~calm(john))))&
(![X]:((funny(X)|~funny(X))=>~curious(X)))&
(![X]:((~kind(X)&~wise(X))=>(~creative(X)&quiet(X))))&
(![X]:((kind(X)|tall(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(~kind(X)=>(humble(X)|tall(X))))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)|~creative(X))))&
(?[X]:(~old(X)))&
((~patient(fred)<~>funny(fred)))&
(?[X]:(~quiet(X)))&
((funny(john)|calm(john)))&
(?[X]:((~patient(X)&~funny(X)))) | humble(susan) | [
"p2",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 639937653763279579979104
% SZS output start Proof for 639937653763279579979104
3. ! [X0] : (humble(X0) <=> kind(X0)) [input p2]
9. ! [X0] : ((tall(X0) | generous(X0)) => (humble(X0) & ~creative(X0))) [input p8]
15. ! [X0] : ((tall(X0) | kind(X0)) <=> (~happy(X0) <~> happy(X0))) [input p14]
24. ~humble(susan) [input hypothesis]
32. ! [X0] : ((humble(X0) & ~creative(X0)) | (~tall(X0) & ~generous(X0))) [ennf transformation 9]
39. ! [X0] : ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))) [nnf transformation 3]
55. ! [X0] : (((tall(X0) | kind(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~tall(X0) & ~kind(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | kind(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~tall(X0) & ~kind(X0)))) [flattening 55]
72. ~kind(X0) | humble(X0) [cnf transformation 39]
94. ~tall(X0) | humble(X0) [cnf transformation 32]
110. tall(X0) | kind(X0) | happy(X0) | happy(X0) [cnf transformation 56]
111. tall(X0) | kind(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
122. ~humble(susan) [cnf transformation 24]
123. tall(X0) | kind(X0) | happy(X0) [duplicate literal removal 110]
124. tall(X0) | kind(X0) | ~happy(X0) [duplicate literal removal 111]
214. kind(X0) | tall(X0) [subsumption resolution 123,124]
235. tall(X0) | humble(X0) [resolution 214,72]
236. humble(X0) [subsumption resolution 235,94]
239. $false [resolution 236,122]
% SZS output end Proof for 639937653763279579979104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and happy then someone is both generous and curious and vice versa.
Everyone who is both kind and not happy is both calm and rich.
If someone is both quiet and not calm then lucy is either not quiet or not funny and vice versa.
Everyone who is not wise is not calm.
Everyone who is rich is patient and vice versa.
Everyone who is creative or humble is not tall.
Everyone who is either not brave or humble is both not happy and funny.
Everyone who is both funny and wise is both funny and not quiet and vice versa.
If lucy is either not tall or not funny then someone is both funny and not patient and vice versa.
Everyone who is creative is both humble and funny.
Everyone who is creative is either happy or funny.
Everyone who is either not brave or not calm is either not calm or not rich.
Everyone who is both not humble and creative is kind and vice versa.
If mary is either not creative or not rich then john is not quiet.
Everyone who is not happy or tall is either old or calm.
Everyone who is not strong or strong is both tall and rich and vice versa.
Someone is rich or not quiet.
Someone is humble or not brave.
Alice is old.
Someone is both not funny and old.
Lucy is both patient and calm.
Susan is happy or not strong.
Susan is not funny. | Alice is tall. | entailment | ((?[X]:((~happy(X)&happy(X))))<=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((kind(X)&~happy(X))=>(calm(X)&rich(X))))&
((?[X]:((quiet(X)&~calm(X))))<=>((~quiet(lucy)<~>~funny(lucy))))&
(![X]:(~wise(X)=>~calm(X)))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((creative(X)|humble(X))=>~tall(X)))&
(![X]:((~brave(X)<~>humble(X))=>(~happy(X)&funny(X))))&
(![X]:((funny(X)&wise(X))<=>(funny(X)&~quiet(X))))&
(((~tall(lucy)<~>~funny(lucy)))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(creative(X)=>(humble(X)&funny(X))))&
(![X]:(creative(X)=>(happy(X)<~>funny(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~humble(X)&creative(X))<=>kind(X)))&
(((~creative(mary)<~>~rich(mary)))=>(~quiet(john)))&
(![X]:((~happy(X)|tall(X))=>(old(X)<~>calm(X))))&
(![X]:((~strong(X)|strong(X))<=>(tall(X)&rich(X))))&
(?[X]:((rich(X)|~quiet(X))))&
(?[X]:((humble(X)|~brave(X))))&
(old(alice))&
(?[X]:((~funny(X)&old(X))))&
((patient(lucy)&calm(lucy)))&
((happy(susan)|~strong(susan)))&
(~funny(susan)) | tall(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 155788243597194853870802
% SZS output start Proof for 155788243597194853870802
16. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & tall(X0))) [input p15]
24. ~tall(alice) [input hypothesis]
60. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~tall(X0))) & ((rich(X0) & tall(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 16]
61. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~tall(X0)) & ((rich(X0) & tall(X0)) | (~strong(X0) & strong(X0)))) [flattening 60]
114. tall(X0) | strong(X0) [cnf transformation 61]
115. tall(X0) | ~strong(X0) [cnf transformation 61]
128. ~tall(alice) [cnf transformation 24]
202. tall(X0) [subsumption resolution 114,115]
221. $false [subsumption resolution 128,202]
% SZS output end Proof for 155788243597194853870802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not creative is both patient and funny and vice versa.
If someone is either strong or not patient then someone is not old or patient and vice versa.
If john is not happy then paul is not humble or not generous.
If someone is humble or funny then paul is not strong.
If someone is brave or strong then paul is creative or not brave and vice versa.
If someone is kind or generous then someone is both patient and not calm.
If alice is not old then fred is wise or not patient and vice versa.
Everyone who is creative is both not strong and not calm.
If someone is not rich or strong then lucy is happy and vice versa.
Everyone who is not tall or not generous is both not rich and patient.
If alice is not rich then alice is both not quiet and not rich.
If someone is not happy then fred is not strong and vice versa.
If someone is both wise and not humble then someone is calm.
Everyone who is not kind is not humble or funny.
Everyone who is rich or not old is both not wise and calm and vice versa.
Everyone who is both not quiet and strong is both not rich and not tall.
Someone is either not patient or creative.
Fred is either humble or not quiet.
Someone is kind or not wise.
Someone is both calm and not generous.
John is both not quiet and strong.
Fred is either not generous or humble.
Fred is either happy or creative.
Paul is happy or strong. | Lucy is not calm. | neutral | (![X]:((happy(X)&~creative(X))<=>(patient(X)&funny(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>(?[X]:((~old(X)|patient(X)))))&
((~happy(john))=>((~humble(paul)|~generous(paul))))&
((?[X]:((humble(X)|funny(X))))=>(~strong(paul)))&
((?[X]:((brave(X)|strong(X))))<=>((creative(paul)|~brave(paul))))&
((?[X]:((kind(X)|generous(X))))=>(?[X]:((patient(X)&~calm(X)))))&
((~old(alice))<=>((wise(fred)|~patient(fred))))&
(![X]:(creative(X)=>(~strong(X)&~calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(happy(lucy)))&
(![X]:((~tall(X)|~generous(X))=>(~rich(X)&patient(X))))&
((~rich(alice))=>((~quiet(alice)&~rich(alice))))&
((?[X]:(~happy(X)))<=>(~strong(fred)))&
((?[X]:((wise(X)&~humble(X))))=>(?[X]:(calm(X))))&
(![X]:(~kind(X)=>(~humble(X)|funny(X))))&
(![X]:((rich(X)|~old(X))<=>(~wise(X)&calm(X))))&
(![X]:((~quiet(X)&strong(X))=>(~rich(X)&~tall(X))))&
(?[X]:((~patient(X)<~>creative(X))))&
((humble(fred)<~>~quiet(fred)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((calm(X)&~generous(X))))&
((~quiet(john)&strong(john)))&
((~generous(fred)<~>humble(fred)))&
((happy(fred)<~>creative(fred)))&
((happy(paul)|strong(paul))) | ~calm(lucy) | [] | null | 0 |
If mary is not creative then someone is either not wise or patient and vice versa. Everyone who is either not wise or kind is not calm and vice versa. If john is humble then john is not quiet. Everyone who is either old or not generous is strong and vice versa. If lucy is either rich or not curious then alice is either not rich or not creative. If someone is either not happy or not humble then paul is patient. Everyone who is both strong and happy is not happy. Everyone who is both not old and not tall is not quiet. Everyone who is calm or kind is either not patient or funny and vice versa. If john is humble then mary is patient. Everyone who is both wise and kind is not strong and vice versa. Everyone who is not curious or not humble is either brave or generous. If someone is both not creative and old then someone is either kind or not patient. If someone is either wise or not kind then john is not strong and vice versa. Everyone who is curious or funny is either patient or old. Everyone who is not humble is wise or brave and vice versa. Someone is funny or old. Someone is not brave or patient. Alice is either not kind or funny. Mary is both rich and not happy. Fred is both not patient and happy. Someone is strong. Alice is both not patient and not quiet. Someone is not kind. | Alice is not calm. | contradiction | ((~creative(mary))<=>(?[X]:((~wise(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>kind(X))<=>~calm(X)))&
((humble(john))=>(~quiet(john)))&
(![X]:((old(X)<~>~generous(X))<=>strong(X)))&
(((rich(lucy)<~>~curious(lucy)))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((~happy(X)<~>~humble(X))))=>(patient(paul)))&
(![X]:((strong(X)&happy(X))=>~happy(X)))&
(![X]:((~old(X)&~tall(X))=>~quiet(X)))&
(![X]:((calm(X)|kind(X))<=>(~patient(X)<~>funny(X))))&
((humble(john))=>(patient(mary)))&
(![X]:((wise(X)&kind(X))<=>~strong(X)))&
(![X]:((~curious(X)|~humble(X))=>(brave(X)<~>generous(X))))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((wise(X)<~>~kind(X))))<=>(~strong(john)))&
(![X]:((curious(X)|funny(X))=>(patient(X)<~>old(X))))&
(![X]:(~humble(X)<=>(wise(X)|brave(X))))&
(?[X]:((funny(X)|old(X))))&
(?[X]:((~brave(X)|patient(X))))&
((~kind(alice)<~>funny(alice)))&
((rich(mary)&~happy(mary)))&
((~patient(fred)&happy(fred)))&
(?[X]:(strong(X)))&
((~patient(alice)&~quiet(alice)))&
(?[X]:(~kind(X))) | ~calm(alice) | [
"p8",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9181579032292408896393376
% SZS output start Proof for 9181579032292408896393376
9. ! [X0] : ((kind(X0) | calm(X0)) <=> (~patient(X0) <~> funny(X0))) [input p8]
19. ~kind(alice) <~> funny(alice) [input p18]
23. ~quiet(alice) & ~patient(alice) [input p22]
25. ~calm(alice) [input hypothesis]
29. ~patient(alice) [pure predicate removal 23]
46. ! [X0] : (((kind(X0) | calm(X0)) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~calm(X0)))) [nnf transformation 9]
47. ! [X0] : ((kind(X0) | calm(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~calm(X0)))) [flattening 46]
66. (~funny(alice) | kind(alice)) & (funny(alice) | ~kind(alice)) [nnf transformation 19]
93. ~funny(X0) | patient(X0) | ~kind(X0) [cnf transformation 47]
94. funny(X0) | calm(X0) | kind(X0) | patient(X0) [cnf transformation 47]
119. funny(alice) | ~kind(alice) [cnf transformation 66]
120. ~funny(alice) | kind(alice) [cnf transformation 66]
126. ~patient(alice) [cnf transformation 29]
128. ~calm(alice) [cnf transformation 25]
247. 27 <=> kind(alice) [avatar definition]
248. ~kind(alice) <- (~27) [avatar component clause 247]
249. kind(alice) <- (27) [avatar component clause 247]
251. 28 <=> funny(alice) [avatar definition]
252. funny(alice) <- (28) [avatar component clause 251]
253. ~funny(alice) <- (~28) [avatar component clause 251]
254. 27 | ~28 [avatar split clause 120,251,247]
255. ~27 | 28 [avatar split clause 119,251,247]
378. patient(alice) | ~kind(alice) <- (28) [resolution 93,252]
384. ~kind(alice) <- (28) [subsumption resolution 378,126]
385. $false <- (27, 28) [subsumption resolution 384,249]
386. ~27 | ~28 [avatar contradiction clause 385]
466. calm(alice) | kind(alice) | patient(alice) <- (~28) [resolution 94,253]
470. kind(alice) | patient(alice) <- (~28) [subsumption resolution 466,128]
471. patient(alice) <- (~27, ~28) [subsumption resolution 470,248]
472. $false <- (~27, ~28) [subsumption resolution 471,126]
473. 27 | 28 [avatar contradiction clause 472]
474. $false [avatar sat refutation 254,255,386,473]
% SZS output end Proof for 9181579032292408896393376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then susan is either not kind or happy and vice versa.
If paul is not wise then mary is not tall and vice versa.
If fred is either humble or old then someone is not brave and vice versa.
If someone is both old and not rich then someone is either not brave or strong and vice versa.
Everyone who is both patient and not kind is both calm and not kind.
Everyone who is either brave or not rich is creative or happy and vice versa.
If lucy is both curious and not tall then someone is both funny and not creative.
If someone is either not kind or creative then mary is not brave or curious.
Everyone who is curious is either not creative or not tall and vice versa.
Everyone who is not humble is not kind or not wise and vice versa.
Everyone who is either humble or not happy is both not brave and not generous and vice versa.
Everyone who is either not strong or brave is not old and vice versa.
If someone is both not old and not humble then someone is both creative and wise and vice versa.
If someone is not kind then lucy is both brave and not creative.
Everyone who is either strong or not patient is either generous or not quiet and vice versa.
Everyone who is both not strong and not humble is not kind or not old.
Alice is curious or not funny.
Paul is either not rich or not quiet.
Paul is either curious or creative.
Someone is not old or generous.
Lucy is curious.
Paul is not brave.
Susan is not generous.
Mary is either curious or not tall. | Fred is not old. | neutral | ((?[X]:(~calm(X)))<=>((~kind(susan)<~>happy(susan))))&
((~wise(paul))<=>(~tall(mary)))&
(((humble(fred)<~>old(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((old(X)&~rich(X))))<=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:((patient(X)&~kind(X))=>(calm(X)&~kind(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(creative(X)|happy(X))))&
(((curious(lucy)&~tall(lucy)))=>(?[X]:((funny(X)&~creative(X)))))&
((?[X]:((~kind(X)<~>creative(X))))=>((~brave(mary)|curious(mary))))&
(![X]:(curious(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:(~humble(X)<=>(~kind(X)|~wise(X))))&
(![X]:((humble(X)<~>~happy(X))<=>(~brave(X)&~generous(X))))&
(![X]:((~strong(X)<~>brave(X))<=>~old(X)))&
((?[X]:((~old(X)&~humble(X))))<=>(?[X]:((creative(X)&wise(X)))))&
((?[X]:(~kind(X)))=>((brave(lucy)&~creative(lucy))))&
(![X]:((strong(X)<~>~patient(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:((~strong(X)&~humble(X))=>(~kind(X)|~old(X))))&
((curious(alice)|~funny(alice)))&
((~rich(paul)<~>~quiet(paul)))&
((curious(paul)<~>creative(paul)))&
(?[X]:((~old(X)|generous(X))))&
(curious(lucy))&
(~brave(paul))&
(~generous(susan))&
((curious(mary)<~>~tall(mary))) | ~old(fred) | [] | null | 0 |
Everyone who is not brave is old. Everyone who is not calm is both funny and not patient. If someone is not curious or generous then lucy is either curious or kind. Everyone who is either calm or not funny is not kind or not brave and vice versa. Everyone who is humble or not creative is either patient or happy. If john is not humble or strong then someone is not happy. If someone is both not quiet and not calm then susan is both generous and not quiet and vice versa. Everyone who is not funny is not quiet. Everyone who is either not quiet or not kind is either happy or not kind and vice versa. If john is either calm or generous then someone is curious and vice versa. Everyone who is not kind or happy is both not humble and happy. Everyone who is kind is humble and vice versa. Everyone who is both not wise and not patient is either not happy or not quiet. Everyone who is strong or not quiet is not old. If fred is both not strong and curious then someone is not humble or kind and vice versa. Everyone who is either old or not kind is both funny and not happy and vice versa. Someone is not funny or not tall. John is either not generous or generous. Lucy is both curious and creative. Alice is kind or happy. Someone is wise. Fred is both kind and calm. | Lucy is generous. | contradiction | (![X]:(~brave(X)=>old(X)))&
(![X]:(~calm(X)=>(funny(X)&~patient(X))))&
((?[X]:((~curious(X)|generous(X))))=>((curious(lucy)<~>kind(lucy))))&
(![X]:((calm(X)<~>~funny(X))<=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)|~creative(X))=>(patient(X)<~>happy(X))))&
(((~humble(john)|strong(john)))=>(?[X]:(~happy(X))))&
((?[X]:((~quiet(X)&~calm(X))))<=>((generous(susan)&~quiet(susan))))&
(![X]:(~funny(X)=>~quiet(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(happy(X)<~>~kind(X))))&
(((calm(john)<~>generous(john)))<=>(?[X]:(curious(X))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(?[X]:((~funny(X)|~tall(X))))&
((~generous(john)<~>generous(john)))&
((curious(lucy)&creative(lucy)))&
((kind(alice)|happy(alice)))&
(?[X]:(wise(X)))&
((kind(fred)&calm(fred))) | generous(lucy) | [
"p2",
"p8",
"p10",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 169736115471492950393546
% SZS output start Proof for 169736115471492950393546
3. ? [X0] : (generous(X0) | ~curious(X0)) => (curious(lucy) <~> kind(lucy)) [input p2]
9. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (happy(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p10]
14. ! [X0] : ((~quiet(X0) | strong(X0)) => ~old(X0)) [input p13]
16. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (~happy(X0) & funny(X0))) [input p15]
19. creative(lucy) & curious(lucy) [input p18]
23. generous(lucy) [input hypothesis]
27. curious(lucy) [pure predicate removal 19]
31. (curious(lucy) <~> kind(lucy)) | ! [X0] : (~generous(X0) & curious(X0)) [ennf transformation 3]
35. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 11]
36. ! [X0] : (~old(X0) | (quiet(X0) & ~strong(X0))) [ennf transformation 14]
37. ((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ! [X0] : (~generous(X0) & curious(X0)) [nnf transformation 31]
48. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) & (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 9]
59. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 16]
60. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [flattening 59]
68. ~kind(lucy) | ~curious(lucy) | ~generous(X0) [cnf transformation 37]
87. kind(X0) | ~happy(X0) | ~quiet(X0) | kind(X0) [cnf transformation 48]
88. ~kind(X0) | ~quiet(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 48]
98. happy(X0) | kind(X0) [cnf transformation 35]
103. ~old(X0) | quiet(X0) [cnf transformation 36]
112. ~happy(X0) | old(X0) | kind(X0) [cnf transformation 60]
117. curious(lucy) [cnf transformation 27]
121. generous(lucy) [cnf transformation 23]
123. kind(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 87]
124. ~quiet(X0) | ~kind(X0) | ~happy(X0) [duplicate literal removal 88]
127. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
128. ~generous(X0) <- (1) [avatar component clause 127]
130. 2 <=> curious(lucy) [avatar definition]
134. 3 <=> kind(lucy) [avatar definition]
136. ~kind(lucy) <- (~3) [avatar component clause 134]
137. 1 | ~2 | ~3 [avatar split clause 68,134,130,127]
185. ~quiet(X0) | ~happy(X0) [subsumption resolution 123,124]
225. kind(X0) | old(X0) [subsumption resolution 112,98]
227. 2 [avatar split clause 117,130]
246. old(lucy) <- (~3) [resolution 225,136]
264. quiet(lucy) <- (~3) [resolution 246,103]
297. ~happy(lucy) <- (~3) [resolution 264,185]
444. kind(lucy) <- (~3) [resolution 297,98]
445. $false <- (~3) [subsumption resolution 444,136]
446. 3 [avatar contradiction clause 445]
447. $false <- (1) [resolution 128,121]
450. ~1 [avatar contradiction clause 447]
451. $false [avatar sat refutation 137,227,446,450]
% SZS output end Proof for 169736115471492950393546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not wise is both quiet and not brave and vice versa.
Everyone who is not patient or funny is either not kind or not humble and vice versa.
If someone is either wise or not funny then john is humble or rich.
If john is either not kind or not quiet then someone is funny and vice versa.
Everyone who is not calm or not curious is not quiet and vice versa.
If someone is creative then lucy is not quiet.
If someone is both brave and not strong then someone is either not happy or old.
If someone is both generous and humble then someone is not tall.
If someone is both kind and strong then someone is both not old and not generous.
If someone is both not humble and funny then susan is not rich or patient and vice versa.
Everyone who is either not quiet or not wise is either strong or not wise.
Everyone who is both tall and generous is both old and not tall and vice versa.
If fred is not patient then someone is either not happy or calm.
Everyone who is both funny and not happy is patient or old.
Everyone who is either rich or brave is not brave or not patient and vice versa.
Everyone who is both not calm and creative is not generous and vice versa.
John is not calm or tall.
Someone is old.
Fred is both old and not kind.
Someone is either curious or brave.
Susan is both calm and quiet.
Someone is happy.
Someone is either not patient or wise. | Lucy is quiet. | contradiction | (![X]:((~curious(X)|~wise(X))<=>(quiet(X)&~brave(X))))&
(![X]:((~patient(X)|funny(X))<=>(~kind(X)<~>~humble(X))))&
((?[X]:((wise(X)<~>~funny(X))))=>((humble(john)|rich(john))))&
(((~kind(john)<~>~quiet(john)))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|~curious(X))<=>~quiet(X)))&
((?[X]:(creative(X)))=>(~quiet(lucy)))&
((?[X]:((brave(X)&~strong(X))))=>(?[X]:((~happy(X)<~>old(X)))))&
((?[X]:((generous(X)&humble(X))))=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)&strong(X))))=>(?[X]:((~old(X)&~generous(X)))))&
((?[X]:((~humble(X)&funny(X))))<=>((~rich(susan)|patient(susan))))&
(![X]:((~quiet(X)<~>~wise(X))=>(strong(X)<~>~wise(X))))&
(![X]:((tall(X)&generous(X))<=>(old(X)&~tall(X))))&
((~patient(fred))=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((funny(X)&~happy(X))=>(patient(X)|old(X))))&
(![X]:((rich(X)<~>brave(X))<=>(~brave(X)|~patient(X))))&
(![X]:((~calm(X)&creative(X))<=>~generous(X)))&
((~calm(john)|tall(john)))&
(?[X]:(old(X)))&
((old(fred)&~kind(fred)))&
(?[X]:((curious(X)<~>brave(X))))&
((calm(susan)&quiet(susan)))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)<~>wise(X)))) | quiet(lucy) | [
"p5",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2203283484231455990254006
% SZS output start Proof for 2203283484231455990254006
6. ? [X0] : creative(X0) => ~quiet(lucy) [input p5]
12. ! [X0] : ((generous(X0) & tall(X0)) <=> (~tall(X0) & old(X0))) [input p11]
16. ! [X0] : ((creative(X0) & ~calm(X0)) <=> ~generous(X0)) [input p15]
18. ? [X0] : old(X0) [input p17]
24. quiet(lucy) [input hypothesis]
30. ~quiet(lucy) | ! [X0] : ~creative(X0) [ennf transformation 6]
65. ! [X0] : (((generous(X0) & tall(X0)) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 12]
66. ! [X0] : (((generous(X0) & tall(X0)) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | ~generous(X0) | ~tall(X0))) [flattening 65]
72. ! [X0] : (((creative(X0) & ~calm(X0)) | generous(X0)) & (~generous(X0) | (~creative(X0) | calm(X0)))) [nnf transformation 16]
73. ! [X0] : (((creative(X0) & ~calm(X0)) | generous(X0)) & (~generous(X0) | ~creative(X0) | calm(X0))) [flattening 72]
74. ? [X0] : old(X0) => old(sK6) [choice axiom]
75. old(sK6) [skolemisation 18,74]
104. ~quiet(lucy) | ~creative(X0) [cnf transformation 30]
120. ~tall(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 66]
121. tall(X0) | tall(X0) | ~old(X0) [cnf transformation 66]
134. generous(X0) | creative(X0) [cnf transformation 73]
136. old(sK6) [cnf transformation 75]
146. quiet(lucy) [cnf transformation 24]
149. ~tall(X0) | ~generous(X0) [duplicate literal removal 120]
150. ~old(X0) | tall(X0) [duplicate literal removal 121]
191. 9 <=> ! [X0] : ~creative(X0) [avatar definition]
192. ~creative(X0) <- (9) [avatar component clause 191]
194. 10 <=> quiet(lucy) [avatar definition]
197. 9 | ~10 [avatar split clause 104,194,191]
293. 10 [avatar split clause 146,194]
310. tall(sK6) [resolution 150,136]
312. ~generous(sK6) [resolution 310,149]
316. creative(sK6) [resolution 312,134]
317. $false <- (9) [subsumption resolution 316,192]
318. ~9 [avatar contradiction clause 317]
319. $false [avatar sat refutation 197,293,318]
% SZS output end Proof for 2203283484231455990254006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then john is both not brave and not tall and vice versa.
Everyone who is either not strong or not quiet is both old and brave and vice versa.
Everyone who is not patient or wise is both not wise and not funny.
Everyone who is funny is both calm and funny and vice versa.
Everyone who is both not happy and not humble is not creative or calm and vice versa.
Everyone who is happy is generous or happy.
If lucy is not strong then paul is old or rich.
If someone is either not curious or not quiet then someone is either generous or not tall.
Everyone who is both not kind and not patient is not calm and vice versa.
If paul is either curious or not creative then someone is tall.
If someone is both not quiet and brave then someone is both calm and strong.
Everyone who is quiet or not quiet is not creative and vice versa.
If mary is either not creative or not curious then someone is not funny and vice versa.
If susan is patient or not brave then alice is both not humble and not tall.
Everyone who is both strong and tall is funny or not humble.
Mary is either not strong or tall.
Susan is not brave.
Paul is creative or not patient.
Mary is either generous or not generous.
Susan is either curious or wise.
Someone is either not wise or rich. | Mary is not wise. | entailment | ((~creative(john))<=>((~brave(john)&~tall(john))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(old(X)&brave(X))))&
(![X]:((~patient(X)|wise(X))=>(~wise(X)&~funny(X))))&
(![X]:(funny(X)<=>(calm(X)&funny(X))))&
(![X]:((~happy(X)&~humble(X))<=>(~creative(X)|calm(X))))&
(![X]:(happy(X)=>(generous(X)|happy(X))))&
((~strong(lucy))=>((old(paul)|rich(paul))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((~kind(X)&~patient(X))<=>~calm(X)))&
(((curious(paul)<~>~creative(paul)))=>(?[X]:(tall(X))))&
((?[X]:((~quiet(X)&brave(X))))=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((quiet(X)|~quiet(X))<=>~creative(X)))&
(((~creative(mary)<~>~curious(mary)))<=>(?[X]:(~funny(X))))&
(((patient(susan)|~brave(susan)))=>((~humble(alice)&~tall(alice))))&
(![X]:((strong(X)&tall(X))=>(funny(X)|~humble(X))))&
((~strong(mary)<~>tall(mary)))&
(~brave(susan))&
((creative(paul)|~patient(paul)))&
((generous(mary)<~>~generous(mary)))&
((curious(susan)<~>wise(susan)))&
(?[X]:((~wise(X)<~>rich(X)))) | ~wise(mary) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2605833887486558719305928
% SZS output start Proof for 2605833887486558719305928
3. ! [X0] : ((wise(X0) | ~patient(X0)) => (~funny(X0) & ~wise(X0))) [input p2]
22. wise(mary) [input hypothesis]
25. ! [X0] : ((~funny(X0) & ~wise(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 3]
78. ~wise(X0) | ~wise(X0) [cnf transformation 25]
124. wise(mary) [cnf transformation 22]
125. ~wise(X0) [duplicate literal removal 78]
249. $false [subsumption resolution 124,125]
% SZS output end Proof for 2605833887486558719305928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not rich is either not generous or curious and vice versa. Everyone who is either brave or curious is not creative and vice versa. If someone is not happy or not kind then alice is quiet or not quiet. If alice is both patient and wise then someone is both tall and not quiet and vice versa. If mary is humble then someone is both not rich and not calm and vice versa. Everyone who is happy or not calm is either quiet or not happy. Everyone who is humble or not brave is both not creative and not humble. If alice is either brave or not strong then someone is not old. If lucy is both not funny and not brave then alice is both not happy and not generous. Everyone who is not kind is either kind or calm and vice versa. If fred is both not calm and not funny then someone is both not tall and not calm and vice versa. Everyone who is wise is both humble and brave and vice versa. If someone is either not funny or generous then john is either not curious or not quiet and vice versa. If someone is rich then john is not brave. Everyone who is both calm and wise is not old and vice versa. Someone is both patient and not tall. Someone is either not happy or not calm. Someone is not creative. John is not brave or not patient. Someone is funny. Paul is either not rich or not curious. Paul is humble or not brave. Mary is either not funny or not happy. | Paul is humble. | contradiction | (![X]:((~strong(X)<~>~rich(X))<=>(~generous(X)<~>curious(X))))&
(![X]:((brave(X)<~>curious(X))<=>~creative(X)))&
((?[X]:((~happy(X)|~kind(X))))=>((quiet(alice)|~quiet(alice))))&
(((patient(alice)&wise(alice)))<=>(?[X]:((tall(X)&~quiet(X)))))&
((humble(mary))<=>(?[X]:((~rich(X)&~calm(X)))))&
(![X]:((happy(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((humble(X)|~brave(X))=>(~creative(X)&~humble(X))))&
(((brave(alice)<~>~strong(alice)))=>(?[X]:(~old(X))))&
(((~funny(lucy)&~brave(lucy)))=>((~happy(alice)&~generous(alice))))&
(![X]:(~kind(X)<=>(kind(X)<~>calm(X))))&
(((~calm(fred)&~funny(fred)))<=>(?[X]:((~tall(X)&~calm(X)))))&
(![X]:(wise(X)<=>(humble(X)&brave(X))))&
((?[X]:((~funny(X)<~>generous(X))))<=>((~curious(john)<~>~quiet(john))))&
((?[X]:(rich(X)))=>(~brave(john)))&
(![X]:((calm(X)&wise(X))<=>~old(X)))&
(?[X]:((patient(X)&~tall(X))))&
(?[X]:((~happy(X)<~>~calm(X))))&
(?[X]:(~creative(X)))&
((~brave(john)|~patient(john)))&
(?[X]:(funny(X)))&
((~rich(paul)<~>~curious(paul)))&
((humble(paul)|~brave(paul)))&
((~funny(mary)<~>~happy(mary))) | humble(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8315605855275776055466657
% SZS output start Proof for 8315605855275776055466657
7. ! [X0] : ((~brave(X0) | humble(X0)) => (~humble(X0) & ~creative(X0))) [input p6]
24. humble(paul) [input hypothesis]
31. ! [X0] : ((~humble(X0) & ~creative(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 7]
100. ~humble(X0) | ~humble(X0) [cnf transformation 31]
140. humble(paul) [cnf transformation 24]
143. ~humble(X0) [duplicate literal removal 100]
286. $false [subsumption resolution 140,143]
% SZS output end Proof for 8315605855275776055466657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or creative is patient or not old and vice versa. If susan is either not funny or kind then someone is either not rich or calm and vice versa. Everyone who is either not patient or tall is generous or kind. Everyone who is kind is generous. Everyone who is not quiet is either not humble or humble and vice versa. Everyone who is not generous or tall is not happy or patient and vice versa. If lucy is not rich then someone is both not wise and not funny and vice versa. Everyone who is creative is both creative and tall. Everyone who is not generous or happy is wise or not curious. If susan is both not calm and strong then susan is both creative and wise and vice versa. If someone is either old or not wise then someone is patient or not creative and vice versa. Everyone who is both not wise and quiet is not quiet or not curious. Everyone who is both not humble and not strong is both creative and not kind and vice versa. If someone is both creative and not rich then someone is creative. Everyone who is both strong and tall is not happy. Everyone who is brave or not happy is not quiet. Paul is calm or not happy. Someone is both not curious and funny. Someone is patient or brave. Alice is strong. Someone is not humble. Someone is quiet or wise. Someone is not kind. Someone is either not patient or kind. | Lucy is happy. | neutral | (![X]:((~rich(X)|creative(X))<=>(patient(X)|~old(X))))&
(((~funny(susan)<~>kind(susan)))<=>(?[X]:((~rich(X)<~>calm(X)))))&
(![X]:((~patient(X)<~>tall(X))=>(generous(X)|kind(X))))&
(![X]:(kind(X)=>generous(X)))&
(![X]:(~quiet(X)<=>(~humble(X)<~>humble(X))))&
(![X]:((~generous(X)|tall(X))<=>(~happy(X)|patient(X))))&
((~rich(lucy))<=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:(creative(X)=>(creative(X)&tall(X))))&
(![X]:((~generous(X)|happy(X))=>(wise(X)|~curious(X))))&
(((~calm(susan)&strong(susan)))<=>((creative(susan)&wise(susan))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((patient(X)|~creative(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)|~curious(X))))&
(![X]:((~humble(X)&~strong(X))<=>(creative(X)&~kind(X))))&
((?[X]:((creative(X)&~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((strong(X)&tall(X))=>~happy(X)))&
(![X]:((brave(X)|~happy(X))=>~quiet(X)))&
((calm(paul)|~happy(paul)))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((patient(X)|brave(X))))&
(strong(alice))&
(?[X]:(~humble(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~patient(X)<~>kind(X)))) | happy(lucy) | [] | null | 0 |
Everyone who is not generous or patient is both not kind and not creative. If someone is either tall or not rich then someone is either not strong or not tall and vice versa. If someone is calm or tall then someone is both not calm and not quiet. Everyone who is either wise or not funny is not happy and vice versa. If someone is patient or not kind then mary is both not creative and strong. If someone is either not generous or quiet then susan is both creative and tall and vice versa. Everyone who is not creative or not funny is kind and vice versa. If someone is quiet or happy then lucy is either calm or old. Everyone who is not quiet or not old is both kind and not tall and vice versa. If mary is tall or creative then someone is not generous or curious and vice versa. If fred is not old or strong then someone is not rich or curious and vice versa. Everyone who is generous or not humble is rich or not creative. Everyone who is not curious is either not kind or not patient and vice versa. Everyone who is not quiet or creative is not tall or not wise and vice versa. If someone is not creative or humble then someone is either rich or not generous and vice versa. If mary is wise then someone is both not generous and happy and vice versa. Someone is both not happy and quiet. Fred is both not strong and not quiet. Someone is strong or kind. Someone is wise or brave. Fred is either not rich or tall. Someone is either not generous or funny. Someone is strong or not funny. | Lucy is not curious. | entailment | (![X]:((~generous(X)|patient(X))=>(~kind(X)&~creative(X))))&
((?[X]:((tall(X)<~>~rich(X))))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
((?[X]:((calm(X)|tall(X))))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((wise(X)<~>~funny(X))<=>~happy(X)))&
((?[X]:((patient(X)|~kind(X))))=>((~creative(mary)&strong(mary))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((creative(susan)&tall(susan))))&
(![X]:((~creative(X)|~funny(X))<=>kind(X)))&
((?[X]:((quiet(X)|happy(X))))=>((calm(lucy)<~>old(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)&~tall(X))))&
(((tall(mary)|creative(mary)))<=>(?[X]:((~generous(X)|curious(X)))))&
(((~old(fred)|strong(fred)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((generous(X)|~humble(X))=>(rich(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~kind(X)<~>~patient(X))))&
(![X]:((~quiet(X)|creative(X))<=>(~tall(X)|~wise(X))))&
((?[X]:((~creative(X)|humble(X))))<=>(?[X]:((rich(X)<~>~generous(X)))))&
((wise(mary))<=>(?[X]:((~generous(X)&happy(X)))))&
(?[X]:((~happy(X)&quiet(X))))&
((~strong(fred)&~quiet(fred)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((wise(X)|brave(X))))&
((~rich(fred)<~>tall(fred)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((strong(X)|~funny(X)))) | ~curious(lucy) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2314839483014150492894803
% SZS output start Proof for 2314839483014150492894803
1. ! [X0] : ((patient(X0) | ~generous(X0)) => (~creative(X0) & ~kind(X0))) [input p0]
5. ? [X0] : (~kind(X0) | patient(X0)) => (strong(mary) & ~creative(mary)) [input p4]
7. ! [X0] : ((~funny(X0) | ~creative(X0)) <=> kind(X0)) [input p6]
9. ! [X0] : ((~old(X0) | ~quiet(X0)) <=> (~tall(X0) & kind(X0))) [input p8]
10. (creative(mary) | tall(mary)) <=> ? [X0] : (curious(X0) | ~generous(X0)) [input p9]
13. ! [X0] : (~curious(X0) <=> (~kind(X0) <~> ~patient(X0))) [input p12]
14. ! [X0] : ((creative(X0) | ~quiet(X0)) <=> (~wise(X0) | ~tall(X0))) [input p13]
16. wise(mary) <=> ? [X0] : (happy(X0) & ~generous(X0)) [input p15]
24. curious(lucy) [input hypothesis]
29. ! [X0] : ((~creative(X0) & ~kind(X0)) | (~patient(X0) & generous(X0))) [ennf transformation 1]
31. (strong(mary) & ~creative(mary)) | ! [X0] : (kind(X0) & ~patient(X0)) [ennf transformation 5]
49. ! [X0] : (((~funny(X0) | ~creative(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) & creative(X0)))) [nnf transformation 7]
50. ! [X0] : ((~funny(X0) | ~creative(X0) | ~kind(X0)) & (kind(X0) | (funny(X0) & creative(X0)))) [flattening 49]
52. ! [X0] : (((~old(X0) | ~quiet(X0)) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | (old(X0) & quiet(X0)))) [nnf transformation 9]
53. ! [X0] : ((~old(X0) | ~quiet(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | (old(X0) & quiet(X0)))) [flattening 52]
54. ((creative(mary) | tall(mary)) | ! [X0] : (~curious(X0) & generous(X0))) & (? [X0] : (curious(X0) | ~generous(X0)) | (~creative(mary) & ~tall(mary))) [nnf transformation 10]
55. (creative(mary) | tall(mary) | ! [X0] : (~curious(X0) & generous(X0))) & (? [X0] : (curious(X0) | ~generous(X0)) | (~creative(mary) & ~tall(mary))) [flattening 54]
56. (creative(mary) | tall(mary) | ! [X0] : (~curious(X0) & generous(X0))) & (? [X1] : (curious(X1) | ~generous(X1)) | (~creative(mary) & ~tall(mary))) [rectify 55]
57. ? [X1] : (curious(X1) | ~generous(X1)) => (curious(sK4) | ~generous(sK4)) [choice axiom]
58. (creative(mary) | tall(mary) | ! [X0] : (~curious(X0) & generous(X0))) & ((curious(sK4) | ~generous(sK4)) | (~creative(mary) & ~tall(mary))) [skolemisation 56,57]
64. ! [X0] : ((~curious(X0) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | curious(X0))) [nnf transformation 13]
65. ! [X0] : (((creative(X0) | ~quiet(X0)) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | (~creative(X0) & quiet(X0)))) [nnf transformation 14]
66. ! [X0] : ((creative(X0) | ~quiet(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | (~creative(X0) & quiet(X0)))) [flattening 65]
72. (wise(mary) | ! [X0] : (~happy(X0) | generous(X0))) & (? [X0] : (happy(X0) & ~generous(X0)) | ~wise(mary)) [nnf transformation 16]
73. (wise(mary) | ! [X0] : (~happy(X0) | generous(X0))) & (? [X1] : (happy(X1) & ~generous(X1)) | ~wise(mary)) [rectify 72]
74. ? [X1] : (happy(X1) & ~generous(X1)) => (happy(sK8) & ~generous(sK8)) [choice axiom]
75. (wise(mary) | ! [X0] : (~happy(X0) | generous(X0))) & ((happy(sK8) & ~generous(sK8)) | ~wise(mary)) [skolemisation 73,74]
86. ~kind(X0) | generous(X0) [cnf transformation 29]
87. ~kind(X0) | ~patient(X0) [cnf transformation 29]
88. ~creative(X0) | generous(X0) [cnf transformation 29]
107. ~creative(mary) | kind(X0) [cnf transformation 31]
116. creative(X0) | kind(X0) [cnf transformation 50]
125. ~tall(X0) | quiet(X0) [cnf transformation 53]
131. creative(mary) | tall(mary) | ~curious(X0) [cnf transformation 58]
141. ~curious(X0) | ~kind(X0) | patient(X0) [cnf transformation 64]
145. ~quiet(X0) | creative(X0) | wise(X0) [cnf transformation 66]
152. ~generous(sK8) | ~wise(mary) [cnf transformation 75]
165. curious(lucy) [cnf transformation 24]
221. 13 <=> ! [X0] : kind(X0) [avatar definition]
222. kind(X0) <- (13) [avatar component clause 221]
233. 16 <=> creative(mary) [avatar definition]
235. ~creative(mary) <- (~16) [avatar component clause 233]
236. 13 | ~16 [avatar split clause 107,233,221]
285. 27 <=> ! [X0] : ~curious(X0) [avatar definition]
286. ~curious(X0) <- (27) [avatar component clause 285]
288. 28 <=> tall(mary) [avatar definition]
290. tall(mary) <- (28) [avatar component clause 288]
291. 27 | 28 | 16 [avatar split clause 131,233,288,285]
293. 29 <=> ! [X0] : generous(X0) [avatar definition]
294. generous(X0) <- (29) [avatar component clause 293]
330. ~curious(X0) | ~kind(X0) [subsumption resolution 141,87]
370. 46 <=> wise(mary) [avatar definition]
380. 48 <=> generous(sK8) [avatar definition]
382. ~generous(sK8) <- (~48) [avatar component clause 380]
383. ~46 | ~48 [avatar split clause 152,380,370]
430. kind(X1) | generous(X1) [resolution 116,88]
431. generous(X1) [subsumption resolution 430,86]
432. 29 [avatar split clause 431,293]
441. $false <- (27) [resolution 286,165]
442. ~27 [avatar contradiction clause 441]
459. ~kind(lucy) [resolution 330,165]
461. $false <- (13) [subsumption resolution 459,222]
462. ~13 [avatar contradiction clause 461]
469. quiet(mary) <- (28) [resolution 290,125]
547. creative(mary) | wise(mary) <- (28) [resolution 145,469]
550. wise(mary) <- (~16, 28) [subsumption resolution 547,235]
563. 46 | 16 | ~28 [avatar split clause 550,288,233,370]
564. $false <- (29, ~48) [subsumption resolution 382,294]
565. ~29 | 48 [avatar contradiction clause 564]
566. $false [avatar sat refutation 236,291,383,432,442,462,563,565]
% SZS output end Proof for 2314839483014150492894803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is not quiet then alice is not patient and vice versa.
If someone is patient then fred is both not patient and generous and vice versa.
If fred is both happy and not quiet then mary is not curious or not old.
Everyone who is both not kind and not generous is happy.
If someone is not funny then lucy is both rich and not creative.
If lucy is not creative or rich then alice is not tall and vice versa.
If someone is both not kind and wise then susan is either creative or not kind.
Everyone who is both kind and funny is generous and vice versa.
If someone is either not tall or not wise then someone is old and vice versa.
Everyone who is either calm or funny is either not old or not strong.
If john is both kind and not humble then susan is both not quiet and not calm and vice versa.
Everyone who is either curious or patient is either curious or not calm and vice versa.
Everyone who is both humble and strong is patient or kind and vice versa.
If someone is either not kind or patient then fred is patient.
If fred is old then fred is either not funny or rich.
Everyone who is both not old and quiet is both patient and not humble and vice versa.
Paul is either not strong or quiet.
Fred is old or wise.
Someone is both generous and not old.
Someone is both tall and not creative.
John is both not funny and not old.
Someone is both wise and funny.
Lucy is not kind. | Paul is not old. | contradiction | ((~quiet(john))<=>(~patient(alice)))&
((?[X]:(patient(X)))<=>((~patient(fred)&generous(fred))))&
(((happy(fred)&~quiet(fred)))=>((~curious(mary)|~old(mary))))&
(![X]:((~kind(X)&~generous(X))=>happy(X)))&
((?[X]:(~funny(X)))=>((rich(lucy)&~creative(lucy))))&
(((~creative(lucy)|rich(lucy)))<=>(~tall(alice)))&
((?[X]:((~kind(X)&wise(X))))=>((creative(susan)<~>~kind(susan))))&
(![X]:((kind(X)&funny(X))<=>generous(X)))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>funny(X))=>(~old(X)<~>~strong(X))))&
(((kind(john)&~humble(john)))<=>((~quiet(susan)&~calm(susan))))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)&strong(X))<=>(patient(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(patient(fred)))&
((old(fred))=>((~funny(fred)<~>rich(fred))))&
(![X]:((~old(X)&quiet(X))<=>(patient(X)&~humble(X))))&
((~strong(paul)<~>quiet(paul)))&
((old(fred)|wise(fred)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((tall(X)&~creative(X))))&
((~funny(john)&~old(john)))&
(?[X]:((wise(X)&funny(X))))&
(~kind(lucy)) | ~old(paul) | [
"p1",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6690869472156564867844093
% SZS output start Proof for 6690869472156564867844093
2. ? [X0] : patient(X0) <=> (generous(fred) & ~patient(fred)) [input p1]
13. ! [X0] : ((strong(X0) & humble(X0)) <=> (kind(X0) | patient(X0))) [input p12]
14. ? [X0] : (~kind(X0) <~> patient(X0)) => patient(fred) [input p13]
16. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (~humble(X0) & patient(X0))) [input p15]
17. ~strong(paul) <~> quiet(paul) [input p16]
24. ~old(paul) [input hypothesis]
33. patient(fred) | ! [X0] : (~kind(X0) <=> patient(X0)) [ennf transformation 14]
36. (? [X0] : patient(X0) | (~generous(fred) | patient(fred))) & ((generous(fred) & ~patient(fred)) | ! [X0] : ~patient(X0)) [nnf transformation 2]
37. (? [X0] : patient(X0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X0] : ~patient(X0)) [flattening 36]
38. (? [X0] : patient(X0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X1] : ~patient(X1)) [rectify 37]
39. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
40. (patient(sK0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X1] : ~patient(X1)) [skolemisation 38,39]
55. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~strong(X0) | ~humble(X0)))) [nnf transformation 13]
56. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~strong(X0) | ~humble(X0))) [flattening 55]
57. patient(fred) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))) [nnf transformation 33]
59. ! [X0] : (((quiet(X0) & ~old(X0)) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 16]
60. ! [X0] : (((quiet(X0) & ~old(X0)) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | ~quiet(X0) | old(X0))) [flattening 59]
61. (~quiet(paul) | strong(paul)) & (quiet(paul) | ~strong(paul)) [nnf transformation 17]
70. ~patient(fred) | ~patient(X1) [cnf transformation 40]
106. ~patient(X0) | humble(X0) [cnf transformation 56]
107. ~kind(X0) | humble(X0) [cnf transformation 56]
108. ~patient(X0) | strong(X0) [cnf transformation 56]
109. ~kind(X0) | strong(X0) [cnf transformation 56]
110. patient(fred) | patient(X0) | kind(X0) [cnf transformation 57]
115. ~humble(X0) | ~quiet(X0) | old(X0) [cnf transformation 60]
118. quiet(paul) | ~strong(paul) [cnf transformation 61]
130. ~old(paul) [cnf transformation 24]
146. 3 <=> patient(fred) [avatar definition]
148. patient(fred) <- (3) [avatar component clause 146]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
162. 6 | ~3 [avatar split clause 70,146,159]
265. 29 <=> ! [X0] : (patient(X0) | kind(X0)) [avatar definition]
266. kind(X0) | patient(X0) <- (29) [avatar component clause 265]
267. 29 | 3 [avatar split clause 110,146,265]
283. 33 <=> strong(paul) [avatar definition]
284. ~strong(paul) <- (~33) [avatar component clause 283]
287. 34 <=> quiet(paul) [avatar definition]
288. quiet(paul) <- (34) [avatar component clause 287]
291. ~33 | 34 [avatar split clause 118,287,283]
297. $false <- (3, 6) [subsumption resolution 148,160]
298. ~3 | ~6 [avatar contradiction clause 297]
327. patient(X1) | strong(X1) <- (29) [resolution 266,109]
328. patient(X2) | humble(X2) <- (29) [resolution 266,107]
332. strong(X1) <- (29) [subsumption resolution 327,108]
333. humble(X2) <- (29) [subsumption resolution 328,106]
388. $false <- (29, ~33) [resolution 332,284]
389. ~29 | 33 [avatar contradiction clause 388]
394. ~quiet(X0) | old(X0) <- (29) [resolution 115,333]
475. old(paul) <- (29, 34) [resolution 394,288]
476. $false <- (29, 34) [subsumption resolution 475,130]
477. ~29 | ~34 [avatar contradiction clause 476]
478. $false [avatar sat refutation 162,267,291,298,389,477]
% SZS output end Proof for 6690869472156564867844093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either quiet or not curious then someone is either not curious or not old and vice versa.
If mary is either calm or quiet then someone is not happy or old and vice versa.
If john is kind or old then someone is both tall and not kind and vice versa.
Everyone who is either wise or not tall is either happy or curious and vice versa.
If someone is strong then lucy is both creative and not strong.
If mary is creative or happy then someone is both not humble and generous and vice versa.
Everyone who is either quiet or not wise is quiet and vice versa.
Everyone who is both not curious and not quiet is either curious or not brave.
If someone is either not tall or wise then someone is both wise and humble and vice versa.
If paul is not creative or patient then someone is both not curious and not kind and vice versa.
Everyone who is not humble or wise is not happy and vice versa.
Everyone who is either not brave or patient is both curious and old.
Everyone who is not humble is either calm or patient.
Everyone who is old or not quiet is not strong or tall and vice versa.
Everyone who is not funny or not wise is both not generous and not rich.
Everyone who is not brave or not calm is either not wise or brave and vice versa.
Someone is funny or not patient.
Mary is calm or brave.
John is both kind and not humble.
Susan is either rich or not old.
Susan is both patient and strong.
Someone is strong or generous.
Alice is generous.
Mary is both not old and strong. | John is not wise. | contradiction | (((quiet(paul)<~>~curious(paul)))<=>(?[X]:((~curious(X)<~>~old(X)))))&
(((calm(mary)<~>quiet(mary)))<=>(?[X]:((~happy(X)|old(X)))))&
(((kind(john)|old(john)))<=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((wise(X)<~>~tall(X))<=>(happy(X)<~>curious(X))))&
((?[X]:(strong(X)))=>((creative(lucy)&~strong(lucy))))&
(((creative(mary)|happy(mary)))<=>(?[X]:((~humble(X)&generous(X)))))&
(![X]:((quiet(X)<~>~wise(X))<=>quiet(X)))&
(![X]:((~curious(X)&~quiet(X))=>(curious(X)<~>~brave(X))))&
((?[X]:((~tall(X)<~>wise(X))))<=>(?[X]:((wise(X)&humble(X)))))&
(((~creative(paul)|patient(paul)))<=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((~humble(X)|wise(X))<=>~happy(X)))&
(![X]:((~brave(X)<~>patient(X))=>(curious(X)&old(X))))&
(![X]:(~humble(X)=>(calm(X)<~>patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~strong(X)|tall(X))))&
(![X]:((~funny(X)|~wise(X))=>(~generous(X)&~rich(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~wise(X)<~>brave(X))))&
(?[X]:((funny(X)|~patient(X))))&
((calm(mary)|brave(mary)))&
((kind(john)&~humble(john)))&
((rich(susan)<~>~old(susan)))&
((patient(susan)&strong(susan)))&
(?[X]:((strong(X)|generous(X))))&
(generous(alice))&
((~old(mary)&strong(mary))) | ~wise(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2595262908106113236841490
% SZS output start Proof for 2595262908106113236841490
7. ! [X0] : ((quiet(X0) <~> ~wise(X0)) <=> quiet(X0)) [input p6]
25. ~wise(john) [input hypothesis]
54. ! [X0] : ((((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))))) [nnf transformation 7]
112. quiet(X0) | quiet(X0) | wise(X0) [cnf transformation 54]
114. wise(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
160. ~wise(john) [cnf transformation 25]
164. quiet(X0) | wise(X0) [duplicate literal removal 112]
165. wise(X0) | ~quiet(X0) [duplicate literal removal 114]
285. wise(X0) [subsumption resolution 164,165]
353. $false [subsumption resolution 160,285]
% SZS output end Proof for 2595262908106113236841490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or happy is either not strong or tall and vice versa.
Everyone who is both creative and not funny is calm and vice versa.
If paul is old or not funny then lucy is not funny or not tall.
If paul is either not patient or strong then fred is patient.
If fred is both brave and not quiet then someone is humble.
If paul is not quiet then someone is strong or rich and vice versa.
If someone is both not quiet and not generous then lucy is either not kind or quiet and vice versa.
If someone is generous then susan is calm.
Everyone who is not kind or not generous is both not old and not quiet.
Everyone who is either creative or tall is both happy and humble.
Everyone who is not patient or brave is either not calm or not happy and vice versa.
Everyone who is either generous or not funny is both not strong and quiet and vice versa.
Everyone who is old or strong is not patient or strong.
Everyone who is both kind and old is both humble and not rich.
Everyone who is either not generous or not tall is either tall or calm and vice versa.
Everyone who is humble is both not quiet and creative and vice versa.
Mary is not curious or tall.
John is not happy.
Lucy is not strong or not old.
Alice is quiet.
Someone is both kind and not funny.
Lucy is both quiet and not old.
Susan is not happy or not quiet. | John is not calm. | entailment | (![X]:((~strong(X)<~>happy(X))<=>(~strong(X)<~>tall(X))))&
(![X]:((creative(X)&~funny(X))<=>calm(X)))&
(((old(paul)|~funny(paul)))=>((~funny(lucy)|~tall(lucy))))&
(((~patient(paul)<~>strong(paul)))=>(patient(fred)))&
(((brave(fred)&~quiet(fred)))=>(?[X]:(humble(X))))&
((~quiet(paul))<=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:((~quiet(X)&~generous(X))))<=>((~kind(lucy)<~>quiet(lucy))))&
((?[X]:(generous(X)))=>(calm(susan)))&
(![X]:((~kind(X)|~generous(X))=>(~old(X)&~quiet(X))))&
(![X]:((creative(X)<~>tall(X))=>(happy(X)&humble(X))))&
(![X]:((~patient(X)|brave(X))<=>(~calm(X)<~>~happy(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~strong(X)&quiet(X))))&
(![X]:((old(X)|strong(X))=>(~patient(X)|strong(X))))&
(![X]:((kind(X)&old(X))=>(humble(X)&~rich(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(tall(X)<~>calm(X))))&
(![X]:(humble(X)<=>(~quiet(X)&creative(X))))&
((~curious(mary)|tall(mary)))&
(~happy(john))&
((~strong(lucy)|~old(lucy)))&
(quiet(alice))&
(?[X]:((kind(X)&~funny(X))))&
((quiet(lucy)&~old(lucy)))&
((~happy(susan)|~quiet(susan))) | ~calm(john) | [
"p0",
"p1",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7837793874032734723123532
% SZS output start Proof for 7837793874032734723123532
1. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~strong(X0) <~> tall(X0))) [input p0]
2. ! [X0] : ((~funny(X0) & creative(X0)) <=> calm(X0)) [input p1]
10. ! [X0] : ((creative(X0) <~> tall(X0)) => (humble(X0) & happy(X0))) [input p9]
18. ~happy(john) [input p17]
24. calm(john) [input hypothesis]
40. ! [X0] : ((humble(X0) & happy(X0)) | (creative(X0) <=> tall(X0))) [ennf transformation 10]
44. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) & (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 1]
45. ! [X0] : (((~funny(X0) & creative(X0)) | ~calm(X0)) & (calm(X0) | (funny(X0) | ~creative(X0)))) [nnf transformation 2]
46. ! [X0] : (((~funny(X0) & creative(X0)) | ~calm(X0)) & (calm(X0) | funny(X0) | ~creative(X0))) [flattening 45]
58. ! [X0] : ((humble(X0) & happy(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) [nnf transformation 40]
67. tall(X0) | ~strong(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 44]
68. ~tall(X0) | strong(X0) | happy(X0) | strong(X0) [cnf transformation 44]
71. happy(X0) | ~strong(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 44]
72. ~happy(X0) | strong(X0) | tall(X0) | strong(X0) [cnf transformation 44]
75. ~calm(X0) | creative(X0) [cnf transformation 46]
93. happy(X0) | tall(X0) | ~creative(X0) [cnf transformation 58]
120. ~happy(john) [cnf transformation 18]
126. calm(john) [cnf transformation 24]
131. tall(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 67]
132. ~tall(X0) | strong(X0) | happy(X0) [duplicate literal removal 68]
133. happy(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 71]
134. ~happy(X0) | strong(X0) | tall(X0) [duplicate literal removal 72]
135. ~tall(X0) | happy(X0) [subsumption resolution 132,133]
136. ~happy(X0) | tall(X0) [subsumption resolution 131,134]
231. ~creative(X0) | tall(X0) [subsumption resolution 93,136]
248. creative(john) [resolution 75,126]
264. tall(john) [resolution 231,248]
279. happy(john) [resolution 264,135]
280. $false [subsumption resolution 279,120]
% SZS output end Proof for 7837793874032734723123532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and brave is not funny and vice versa.
If lucy is funny then fred is both tall and strong and vice versa.
Everyone who is calm or brave is both curious and not happy.
If john is either not brave or not generous then someone is not rich and vice versa.
If someone is patient then paul is not funny and vice versa.
If someone is not generous or calm then lucy is both not creative and strong and vice versa.
Everyone who is both not humble and not generous is curious and vice versa.
Everyone who is wise is not strong.
Everyone who is both not calm and rich is not brave or calm.
Everyone who is not patient or rich is either not creative or not quiet and vice versa.
Everyone who is either not funny or not rich is quiet and vice versa.
If someone is not rich then someone is curious and vice versa.
Everyone who is both not funny and calm is funny or not patient.
Everyone who is either not old or not creative is not old or not quiet.
Mary is both not wise and not strong.
Alice is creative or not patient.
Someone is not rich or old.
Someone is either calm or not wise. | John is tall. | neutral | (![X]:((~brave(X)&brave(X))<=>~funny(X)))&
((funny(lucy))<=>((tall(fred)&strong(fred))))&
(![X]:((calm(X)|brave(X))=>(curious(X)&~happy(X))))&
(((~brave(john)<~>~generous(john)))<=>(?[X]:(~rich(X))))&
((?[X]:(patient(X)))<=>(~funny(paul)))&
((?[X]:((~generous(X)|calm(X))))<=>((~creative(lucy)&strong(lucy))))&
(![X]:((~humble(X)&~generous(X))<=>curious(X)))&
(![X]:(wise(X)=>~strong(X)))&
(![X]:((~calm(X)&rich(X))=>(~brave(X)|calm(X))))&
(![X]:((~patient(X)|rich(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>quiet(X)))&
((?[X]:(~rich(X)))<=>(?[X]:(curious(X))))&
(![X]:((~funny(X)&calm(X))=>(funny(X)|~patient(X))))&
(![X]:((~old(X)<~>~creative(X))=>(~old(X)|~quiet(X))))&
((~wise(mary)&~strong(mary)))&
((creative(alice)|~patient(alice)))&
(?[X]:((~rich(X)|old(X))))&
(?[X]:((calm(X)<~>~wise(X)))) | tall(john) | [] | null | 0 |
Everyone who is both not patient and old is not humble. Everyone who is both brave and not quiet is calm and vice versa. Everyone who is quiet or not curious is rich. If someone is either wise or calm then someone is both not funny and not happy. Everyone who is not humble is either calm or brave and vice versa. Everyone who is not calm or calm is not strong or not wise. Everyone who is both rich and happy is both not happy and not kind. If john is both not brave and not strong then mary is both not rich and quiet. If mary is not patient or not generous then someone is both not calm and not funny. Everyone who is either humble or patient is not calm or patient and vice versa. Everyone who is either not wise or not patient is both not humble and not tall and vice versa. If someone is either not curious or calm then john is both not creative and calm. If someone is both curious and not strong then mary is either not patient or quiet and vice versa. If paul is calm or not calm then someone is not calm or not wise and vice versa. If someone is brave then someone is either not patient or old. Everyone who is either tall or not happy is calm and vice versa. Someone is either not old or not creative. John is rich. Someone is rich or not generous. John is not patient. Someone is patient. Someone is either not old or not quiet. Someone is creative. Someone is either generous or strong. | Paul is calm. | contradiction | (![X]:((~patient(X)&old(X))=>~humble(X)))&
(![X]:((brave(X)&~quiet(X))<=>calm(X)))&
(![X]:((quiet(X)|~curious(X))=>rich(X)))&
((?[X]:((wise(X)<~>calm(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(~humble(X)<=>(calm(X)<~>brave(X))))&
(![X]:((~calm(X)|calm(X))=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&happy(X))=>(~happy(X)&~kind(X))))&
(((~brave(john)&~strong(john)))=>((~rich(mary)&quiet(mary))))&
(((~patient(mary)|~generous(mary)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((humble(X)<~>patient(X))<=>(~calm(X)|patient(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~humble(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))=>((~creative(john)&calm(john))))&
((?[X]:((curious(X)&~strong(X))))<=>((~patient(mary)<~>quiet(mary))))&
(((calm(paul)|~calm(paul)))<=>(?[X]:((~calm(X)|~wise(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:((tall(X)<~>~happy(X))<=>calm(X)))&
(?[X]:((~old(X)<~>~creative(X))))&
(rich(john))&
(?[X]:((rich(X)|~generous(X))))&
(~patient(john))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)<~>~quiet(X))))&
(?[X]:(creative(X)))&
(?[X]:((generous(X)<~>strong(X)))) | calm(paul) | [
"p1",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6146153339911883622389849
% SZS output start Proof for 6146153339911883622389849
2. ! [X0] : ((~quiet(X0) & brave(X0)) <=> calm(X0)) [input p1]
5. ! [X0] : (~humble(X0) <=> (calm(X0) <~> brave(X0))) [input p4]
10. ! [X0] : ((humble(X0) <~> patient(X0)) <=> (patient(X0) | ~calm(X0))) [input p9]
25. calm(paul) [input hypothesis]
44. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | ~brave(X0)))) [nnf transformation 2]
45. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | ~brave(X0))) [flattening 44]
50. ! [X0] : ((~humble(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | humble(X0))) [nnf transformation 5]
53. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [flattening 53]
89. brave(X0) | ~calm(X0) [cnf transformation 45]
96. ~brave(X0) | ~calm(X0) | humble(X0) [cnf transformation 50]
106. patient(X0) | ~calm(X0) | patient(X0) | ~humble(X0) [cnf transformation 54]
111. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 54]
149. calm(paul) [cnf transformation 25]
150. patient(X0) | ~calm(X0) | ~humble(X0) [duplicate literal removal 106]
151. ~patient(X0) | ~humble(X0) [duplicate literal removal 111]
165. ~calm(X0) | humble(X0) [subsumption resolution 96,89]
201. ~calm(X0) | ~humble(X0) [subsumption resolution 150,151]
202. ~calm(X0) [subsumption resolution 201,165]
274. $false [subsumption resolution 149,202]
% SZS output end Proof for 6146153339911883622389849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or brave is not strong and vice versa.
Everyone who is either calm or not creative is either old or curious.
Everyone who is either old or tall is not funny or patient and vice versa.
If john is both brave and not old then someone is not happy or calm.
Everyone who is either curious or not generous is both creative and not humble.
Everyone who is both not curious and patient is calm or generous and vice versa.
Everyone who is not old or not humble is either curious or not tall.
Everyone who is either curious or tall is either not generous or not brave and vice versa.
If someone is either rich or not strong then someone is both brave and patient and vice versa.
If someone is either generous or not curious then someone is not patient or not funny.
If someone is not tall then someone is creative.
Everyone who is funny or generous is not curious.
If john is either rich or not tall then someone is both quiet and not quiet and vice versa.
If someone is not rich then someone is either kind or wise and vice versa.
If john is not old or tall then someone is strong or funny and vice versa.
Everyone who is generous is either not wise or creative.
Someone is creative or not wise.
Someone is not brave or not generous.
Someone is both patient and rich.
Susan is either kind or not old.
Mary is brave.
Someone is not humble.
Fred is not kind or happy.
Lucy is strong or curious. | Mary is tall. | contradiction | (![X]:((~patient(X)<~>brave(X))<=>~strong(X)))&
(![X]:((calm(X)<~>~creative(X))=>(old(X)<~>curious(X))))&
(![X]:((old(X)<~>tall(X))<=>(~funny(X)|patient(X))))&
(((brave(john)&~old(john)))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(creative(X)&~humble(X))))&
(![X]:((~curious(X)&patient(X))<=>(calm(X)|generous(X))))&
(![X]:((~old(X)|~humble(X))=>(curious(X)<~>~tall(X))))&
(![X]:((curious(X)<~>tall(X))<=>(~generous(X)<~>~brave(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((?[X]:((generous(X)<~>~curious(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:(~tall(X)))=>(?[X]:(creative(X))))&
(![X]:((funny(X)|generous(X))=>~curious(X)))&
(((rich(john)<~>~tall(john)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((kind(X)<~>wise(X)))))&
(((~old(john)|tall(john)))<=>(?[X]:((strong(X)|funny(X)))))&
(![X]:(generous(X)=>(~wise(X)<~>creative(X))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((patient(X)&rich(X))))&
((kind(susan)<~>~old(susan)))&
(brave(mary))&
(?[X]:(~humble(X)))&
((~kind(fred)|happy(fred)))&
((strong(lucy)|curious(lucy))) | tall(mary) | [
"p4",
"p5",
"p6",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6024761783090573338591334
% SZS output start Proof for 6024761783090573338591334
5. ! [X0] : ((curious(X0) <~> ~generous(X0)) => (~humble(X0) & creative(X0))) [input p4]
6. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (generous(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~humble(X0) | ~old(X0)) => (curious(X0) <~> ~tall(X0))) [input p6]
8. ! [X0] : ((curious(X0) <~> tall(X0)) <=> (~generous(X0) <~> ~brave(X0))) [input p7]
21. brave(mary) [input p20]
25. tall(mary) [input hypothesis]
33. ! [X0] : ((~humble(X0) & creative(X0)) | (curious(X0) <=> ~generous(X0))) [ennf transformation 5]
34. ! [X0] : ((curious(X0) <~> ~tall(X0)) | (humble(X0) & old(X0))) [ennf transformation 7]
45. ! [X0] : ((~humble(X0) & creative(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 33]
46. ! [X0] : (((patient(X0) & ~curious(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~patient(X0) | curious(X0)))) [nnf transformation 6]
47. ! [X0] : (((patient(X0) & ~curious(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | ~patient(X0) | curious(X0))) [flattening 46]
48. ! [X0] : (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (humble(X0) & old(X0))) [nnf transformation 34]
49. ! [X0] : ((((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0)))) & (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0))))) [nnf transformation 8]
104. ~humble(X0) | curious(X0) | generous(X0) [cnf transformation 45]
107. ~generous(X0) | ~curious(X0) [cnf transformation 47]
111. ~tall(X0) | curious(X0) | humble(X0) [cnf transformation 48]
115. ~brave(X0) | ~generous(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
120. ~tall(X0) | ~curious(X0) | ~brave(X0) | generous(X0) [cnf transformation 49]
155. brave(mary) [cnf transformation 21]
159. tall(mary) [cnf transformation 25]
177. ~tall(X0) | ~curious(X0) | ~brave(X0) [subsumption resolution 120,107]
180. ~generous(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 115,177]
525. curious(mary) | humble(mary) [resolution 111,159]
552. ~curious(mary) | ~brave(mary) [resolution 177,159]
558. ~curious(mary) [subsumption resolution 552,155]
559. humble(mary) [subsumption resolution 525,558]
590. curious(mary) | generous(mary) [resolution 559,104]
592. generous(mary) [subsumption resolution 590,558]
827. ~brave(mary) | ~tall(mary) [resolution 592,180]
833. ~tall(mary) [subsumption resolution 827,155]
834. $false [subsumption resolution 833,159]
% SZS output end Proof for 6024761783090573338591334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then susan is not kind or not wise.
Everyone who is happy or not humble is patient or humble.
Everyone who is not brave or tall is both not patient and not humble and vice versa.
Everyone who is both not old and tall is both not calm and not tall and vice versa.
If john is not kind or not strong then fred is either not kind or wise and vice versa.
Everyone who is either not funny or patient is either not humble or not quiet.
Everyone who is either happy or calm is tall.
If someone is not tall or not brave then susan is either rich or funny and vice versa.
If fred is both not patient and not wise then someone is both not rich and not generous and vice versa.
Everyone who is not happy or generous is kind or generous.
Everyone who is not wise is humble and vice versa.
Everyone who is old is both curious and quiet and vice versa.
If fred is both kind and strong then lucy is calm and vice versa.
Everyone who is patient or generous is curious or kind.
If someone is both not quiet and not rich then someone is not humble or not brave and vice versa.
If mary is patient or funny then someone is both not curious and not happy and vice versa.
Lucy is either not happy or not funny.
Fred is rich or not curious.
Someone is strong or kind.
Someone is either generous or rich.
Lucy is either brave or not strong.
Fred is both humble and rich. | Fred is strong. | entailment | ((?[X]:(wise(X)))=>((~kind(susan)|~wise(susan))))&
(![X]:((happy(X)|~humble(X))=>(patient(X)|humble(X))))&
(![X]:((~brave(X)|tall(X))<=>(~patient(X)&~humble(X))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)&~tall(X))))&
(((~kind(john)|~strong(john)))<=>((~kind(fred)<~>wise(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((happy(X)<~>calm(X))=>tall(X)))&
((?[X]:((~tall(X)|~brave(X))))<=>((rich(susan)<~>funny(susan))))&
(((~patient(fred)&~wise(fred)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:((~happy(X)|generous(X))=>(kind(X)|generous(X))))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:(old(X)<=>(curious(X)&quiet(X))))&
(((kind(fred)&strong(fred)))<=>(calm(lucy)))&
(![X]:((patient(X)|generous(X))=>(curious(X)|kind(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~humble(X)|~brave(X)))))&
(((patient(mary)|funny(mary)))<=>(?[X]:((~curious(X)&~happy(X)))))&
((~happy(lucy)<~>~funny(lucy)))&
((rich(fred)|~curious(fred)))&
(?[X]:((strong(X)|kind(X))))&
(?[X]:((generous(X)<~>rich(X))))&
((brave(lucy)<~>~strong(lucy)))&
((humble(fred)&rich(fred))) | strong(fred) | [
"p1",
"p2",
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2577316170954057342602471
% SZS output start Proof for 2577316170954057342602471
2. ! [X0] : ((~humble(X0) | happy(X0)) => (humble(X0) | patient(X0))) [input p1]
3. ! [X0] : ((tall(X0) | ~brave(X0)) <=> (~humble(X0) & ~patient(X0))) [input p2]
4. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~tall(X0) & ~calm(X0))) [input p3]
13. (strong(fred) & kind(fred)) <=> calm(lucy) [input p12]
23. ~strong(fred) [input hypothesis]
27. ! [X0] : ((humble(X0) | patient(X0)) | (humble(X0) & ~happy(X0))) [ennf transformation 2]
28. ! [X0] : (humble(X0) | patient(X0) | (humble(X0) & ~happy(X0))) [flattening 27]
35. ! [X0] : (((tall(X0) | ~brave(X0)) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | (~tall(X0) & brave(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | ~brave(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | (~tall(X0) & brave(X0)))) [flattening 35]
37. ! [X0] : (((tall(X0) & ~old(X0)) | (tall(X0) | calm(X0))) & ((~tall(X0) & ~calm(X0)) | (~tall(X0) | old(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & ~old(X0)) | tall(X0) | calm(X0)) & ((~tall(X0) & ~calm(X0)) | ~tall(X0) | old(X0))) [flattening 37]
55. ((strong(fred) & kind(fred)) | ~calm(lucy)) & (calm(lucy) | (~strong(fred) | ~kind(fred))) [nnf transformation 13]
56. ((strong(fred) & kind(fred)) | ~calm(lucy)) & (calm(lucy) | ~strong(fred) | ~kind(fred)) [flattening 55]
76. humble(X0) | patient(X0) | humble(X0) [cnf transformation 28]
78. ~tall(X0) | ~patient(X0) [cnf transformation 36]
80. ~tall(X0) | ~humble(X0) [cnf transformation 36]
85. tall(X0) | tall(X0) | calm(X0) [cnf transformation 38]
117. strong(fred) | ~calm(lucy) [cnf transformation 56]
140. ~strong(fred) [cnf transformation 23]
142. calm(X0) | tall(X0) [duplicate literal removal 85]
143. patient(X0) | humble(X0) [duplicate literal removal 76]
229. 18 <=> calm(lucy) [avatar definition]
231. ~calm(lucy) <- (~18) [avatar component clause 229]
233. 19 <=> strong(fred) [avatar definition]
236. ~18 | 19 [avatar split clause 117,233,229]
336. ~19 [avatar split clause 140,233]
342. tall(lucy) <- (~18) [resolution 142,231]
344. ~humble(lucy) <- (~18) [resolution 342,80]
345. ~patient(lucy) <- (~18) [resolution 342,78]
377. humble(lucy) <- (~18) [resolution 345,143]
378. $false <- (~18) [subsumption resolution 377,344]
379. 18 [avatar contradiction clause 378]
380. $false [avatar sat refutation 236,336,379]
% SZS output end Proof for 2577316170954057342602471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is patient or not rich then someone is kind or not funny and vice versa.
Everyone who is both not brave and not creative is both not quiet and curious.
Everyone who is patient or quiet is either generous or wise and vice versa.
Everyone who is both not strong and not funny is not brave.
Everyone who is both rich and strong is not old or not tall.
Everyone who is either not quiet or not strong is not strong and vice versa.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
If john is either wise or kind then someone is rich or not kind and vice versa.
Everyone who is either not wise or curious is not brave and vice versa.
Someone is both brave and not kind.
Someone is either creative or kind.
Susan is not kind or brave.
Fred is not funny or not tall.
Someone is either not curious or strong.
John is both not old and humble. | Susan is wise. | neutral | (((patient(susan)|~rich(susan)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~brave(X)&~creative(X))=>(~quiet(X)&curious(X))))&
(![X]:((patient(X)|quiet(X))<=>(generous(X)<~>wise(X))))&
(![X]:((~strong(X)&~funny(X))=>~brave(X)))&
(![X]:((rich(X)&strong(X))=>(~old(X)|~tall(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
(((wise(john)<~>kind(john)))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>~brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((~kind(susan)|brave(susan)))&
((~funny(fred)|~tall(fred)))&
(?[X]:((~curious(X)<~>strong(X))))&
((~old(john)&humble(john))) | wise(susan) | [] | null | 0 |
If someone is generous or funny then someone is both quiet and creative. Everyone who is happy is either patient or wise. If susan is not rich or curious then someone is both not brave and rich and vice versa. Everyone who is not humble or not happy is brave and vice versa. Everyone who is not creative or humble is both not tall and tall. If someone is either old or not happy then alice is humble or not creative. If paul is either patient or not humble then someone is either not brave or not generous. Everyone who is kind is generous or not tall and vice versa. If someone is either strong or not patient then someone is not humble or kind. If mary is strong then someone is not tall or not quiet and vice versa. Everyone who is both tall and patient is both not generous and creative. Everyone who is not kind is both not rich and curious. Everyone who is not humble is not funny or creative. If someone is curious or tall then someone is either not strong or not quiet and vice versa. Everyone who is not kind is either not generous or quiet. Mary is either wise or not happy. Someone is either quiet or funny. Fred is not calm or tall. Paul is both creative and brave. Mary is wise or happy. Someone is rich. Lucy is either generous or not wise. | Mary is strong. | entailment | ((?[X]:((generous(X)|funny(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:(happy(X)=>(patient(X)<~>wise(X))))&
(((~rich(susan)|curious(susan)))<=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((~humble(X)|~happy(X))<=>brave(X)))&
(![X]:((~creative(X)|humble(X))=>(~tall(X)&tall(X))))&
((?[X]:((old(X)<~>~happy(X))))=>((humble(alice)|~creative(alice))))&
(((patient(paul)<~>~humble(paul)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:(kind(X)<=>(generous(X)|~tall(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~humble(X)|kind(X)))))&
((strong(mary))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((tall(X)&patient(X))=>(~generous(X)&creative(X))))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(![X]:(~humble(X)=>(~funny(X)|creative(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((wise(mary)<~>~happy(mary)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~calm(fred)|tall(fred)))&
((creative(paul)&brave(paul)))&
((wise(mary)|happy(mary)))&
(?[X]:(rich(X)))&
((generous(lucy)<~>~wise(lucy))) | strong(mary) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4521815207287726265107807
% SZS output start Proof for 4521815207287726265107807
4. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> brave(X0)) [input p3]
5. ! [X0] : ((humble(X0) | ~creative(X0)) => (tall(X0) & ~tall(X0))) [input p4]
7. (patient(paul) <~> ~humble(paul)) => ? [X0] : (~brave(X0) <~> ~generous(X0)) [input p6]
8. ! [X0] : (kind(X0) <=> (~tall(X0) | generous(X0))) [input p7]
10. strong(mary) <=> ? [X0] : (~quiet(X0) | ~tall(X0)) [input p9]
11. ! [X0] : ((patient(X0) & tall(X0)) => (creative(X0) & ~generous(X0))) [input p10]
15. ! [X0] : (~kind(X0) => (~generous(X0) <~> quiet(X0))) [input p14]
23. ~strong(mary) [input hypothesis]
27. ! [X0] : (kind(X0) => (~tall(X0) | generous(X0))) [unused predicate definition removal 8]
31. ! [X0] : ((tall(X0) & ~tall(X0)) | (~humble(X0) & creative(X0))) [ennf transformation 5]
34. ? [X0] : (~brave(X0) <~> ~generous(X0)) | (patient(paul) <=> ~humble(paul)) [ennf transformation 7]
35. ! [X0] : ((~tall(X0) | generous(X0)) | ~kind(X0)) [ennf transformation 27]
36. ! [X0] : (~tall(X0) | generous(X0) | ~kind(X0)) [flattening 35]
38. ! [X0] : ((creative(X0) & ~generous(X0)) | (~patient(X0) | ~tall(X0))) [ennf transformation 11]
39. ! [X0] : ((creative(X0) & ~generous(X0)) | ~patient(X0) | ~tall(X0)) [flattening 38]
43. ! [X0] : ((~generous(X0) <~> quiet(X0)) | kind(X0)) [ennf transformation 15]
53. ! [X0] : (((~happy(X0) | ~humble(X0)) | ~brave(X0)) & (brave(X0) | (happy(X0) & humble(X0)))) [nnf transformation 4]
54. ! [X0] : ((~happy(X0) | ~humble(X0) | ~brave(X0)) & (brave(X0) | (happy(X0) & humble(X0)))) [flattening 53]
56. ? [X0] : ((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ((patient(paul) | humble(paul)) & (~humble(paul) | ~patient(paul))) [nnf transformation 34]
57. ? [X0] : ((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) => ((generous(sK2) | brave(sK2)) & (~generous(sK2) | ~brave(sK2))) [choice axiom]
58. ((generous(sK2) | brave(sK2)) & (~generous(sK2) | ~brave(sK2))) | ((patient(paul) | humble(paul)) & (~humble(paul) | ~patient(paul))) [skolemisation 56,57]
63. (strong(mary) | ! [X0] : (quiet(X0) & tall(X0))) & (? [X0] : (~quiet(X0) | ~tall(X0)) | ~strong(mary)) [nnf transformation 10]
64. (strong(mary) | ! [X0] : (quiet(X0) & tall(X0))) & (? [X1] : (~quiet(X1) | ~tall(X1)) | ~strong(mary)) [rectify 63]
65. ? [X1] : (~quiet(X1) | ~tall(X1)) => (~quiet(sK4) | ~tall(sK4)) [choice axiom]
66. (strong(mary) | ! [X0] : (quiet(X0) & tall(X0))) & ((~quiet(sK4) | ~tall(sK4)) | ~strong(mary)) [skolemisation 64,65]
72. ! [X0] : (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | kind(X0)) [nnf transformation 43]
91. humble(X0) | brave(X0) [cnf transformation 54]
95. ~tall(X0) | ~humble(X0) [cnf transformation 31]
97. ~humble(X0) | tall(X0) [cnf transformation 31]
101. ~generous(sK2) | ~brave(sK2) | patient(paul) | humble(paul) [cnf transformation 58]
104. ~kind(X0) | generous(X0) | ~tall(X0) [cnf transformation 36]
108. strong(mary) | tall(X0) [cnf transformation 66]
109. strong(mary) | quiet(X0) [cnf transformation 66]
110. ~tall(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 39]
122. ~quiet(X0) | generous(X0) | kind(X0) [cnf transformation 72]
133. ~strong(mary) [cnf transformation 23]
176. ~humble(X0) [subsumption resolution 95,97]
184. 10 <=> patient(paul) [avatar definition]
186. patient(paul) <- (10) [avatar component clause 184]
188. 11 <=> brave(sK2) [avatar definition]
189. ~brave(sK2) <- (~11) [avatar component clause 188]
192. 12 <=> generous(sK2) [avatar definition]
193. ~generous(sK2) <- (~12) [avatar component clause 192]
196. ~generous(sK2) | ~brave(sK2) | patient(paul) [subsumption resolution 101,176]
197. 10 | ~11 | ~12 [avatar split clause 196,192,188,184]
199. 13 <=> ! [X0] : quiet(X0) [avatar definition]
200. quiet(X0) <- (13) [avatar component clause 199]
202. 14 <=> strong(mary) [avatar definition]
205. 13 | 14 [avatar split clause 109,202,199]
207. 15 <=> ! [X0] : tall(X0) [avatar definition]
208. tall(X0) <- (15) [avatar component clause 207]
209. 15 | 14 [avatar split clause 108,202,207]
284. ~14 [avatar split clause 133,202]
287. brave(X0) [resolution 91,176]
308. ~patient(X1) | ~generous(X1) <- (15) [resolution 110,208]
312. kind(X0) | generous(X0) <- (13) [resolution 122,200]
315. ~generous(paul) <- (10, 15) [resolution 308,186]
316. generous(X0) | generous(X0) | ~tall(X0) <- (13) [resolution 312,104]
317. generous(X0) | ~tall(X0) <- (13) [duplicate literal removal 316]
318. generous(X0) <- (13, 15) [subsumption resolution 317,208]
321. $false <- (10, 13, 15) [resolution 318,315]
322. ~10 | ~13 | ~15 [avatar contradiction clause 321]
324. $false <- (~12, 13, 15) [subsumption resolution 193,318]
325. 12 | ~13 | ~15 [avatar contradiction clause 324]
326. $false <- (~11) [subsumption resolution 189,287]
327. 11 [avatar contradiction clause 326]
328. $false [avatar sat refutation 197,205,209,284,322,325,327]
% SZS output end Proof for 4521815207287726265107807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or not funny then paul is both creative and generous. Everyone who is brave or curious is either not humble or not old. If someone is humble then alice is both not creative and not calm and vice versa. If alice is quiet then someone is not wise and vice versa. If someone is strong or not funny then someone is not creative and vice versa. If alice is not creative or patient then fred is either not kind or not quiet and vice versa. If someone is not brave then someone is either not curious or strong and vice versa. Everyone who is either not tall or not curious is not brave or not funny. Everyone who is not curious is either not creative or not happy. Everyone who is not quiet or not patient is either not quiet or not old. Everyone who is both not rich and brave is brave and vice versa. Everyone who is creative is not calm and vice versa. Everyone who is either not brave or not tall is either not happy or not calm and vice versa. Everyone who is both not quiet and not humble is quiet or not old. Everyone who is both not happy and not creative is not quiet and vice versa. If someone is not kind or not calm then someone is funny or patient. Fred is either calm or not funny. Alice is old or not kind. Someone is both wise and generous. Someone is not patient or not quiet. Someone is generous. Susan is not tall. Alice is rich or not brave. | Fred is not funny. | neutral | (((patient(mary)<~>~funny(mary)))=>((creative(paul)&generous(paul))))&
(![X]:((brave(X)|curious(X))=>(~humble(X)<~>~old(X))))&
((?[X]:(humble(X)))<=>((~creative(alice)&~calm(alice))))&
((quiet(alice))<=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:(~creative(X))))&
(((~creative(alice)|patient(alice)))<=>((~kind(fred)<~>~quiet(fred))))&
((?[X]:(~brave(X)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((~tall(X)<~>~curious(X))=>(~brave(X)|~funny(X))))&
(![X]:(~curious(X)=>(~creative(X)<~>~happy(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~rich(X)&brave(X))<=>brave(X)))&
(![X]:(creative(X)<=>~calm(X)))&
(![X]:((~brave(X)<~>~tall(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((~quiet(X)&~humble(X))=>(quiet(X)|~old(X))))&
(![X]:((~happy(X)&~creative(X))<=>~quiet(X)))&
((?[X]:((~kind(X)|~calm(X))))=>(?[X]:((funny(X)|patient(X)))))&
((calm(fred)<~>~funny(fred)))&
((old(alice)|~kind(alice)))&
(?[X]:((wise(X)&generous(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:(generous(X)))&
(~tall(susan))&
((rich(alice)|~brave(alice))) | ~funny(fred) | [] | null | 0 |
If someone is either kind or not happy then lucy is both not rich and old and vice versa. Everyone who is rich or not kind is both not happy and not creative and vice versa. If someone is curious or generous then susan is either patient or old. Everyone who is humble or not old is not humble or happy. If paul is not rich then paul is either not patient or not kind. Everyone who is calm or not happy is humble or wise. If someone is strong or wise then someone is either not calm or calm and vice versa. Everyone who is not old or rich is patient. Everyone who is either patient or not patient is both not brave and not wise and vice versa. Everyone who is kind or not creative is both happy and not calm. If lucy is both not quiet and wise then someone is not wise. If lucy is either not calm or not humble then paul is both generous and not wise. Everyone who is both not happy and not old is either humble or creative and vice versa. Fred is not humble or old. Someone is not patient or funny. Someone is both not old and funny. Fred is either funny or rich. Fred is either generous or not humble. | Fred is not funny. | contradiction | ((?[X]:((kind(X)<~>~happy(X))))<=>((~rich(lucy)&old(lucy))))&
(![X]:((rich(X)|~kind(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((curious(X)|generous(X))))=>((patient(susan)<~>old(susan))))&
(![X]:((humble(X)|~old(X))=>(~humble(X)|happy(X))))&
((~rich(paul))=>((~patient(paul)<~>~kind(paul))))&
(![X]:((calm(X)|~happy(X))=>(humble(X)|wise(X))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:((patient(X)<~>~patient(X))<=>(~brave(X)&~wise(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&~calm(X))))&
(((~quiet(lucy)&wise(lucy)))=>(?[X]:(~wise(X))))&
(((~calm(lucy)<~>~humble(lucy)))=>((generous(paul)&~wise(paul))))&
(![X]:((~happy(X)&~old(X))<=>(humble(X)<~>creative(X))))&
((~humble(fred)|old(fred)))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((~old(X)&funny(X))))&
((funny(fred)<~>rich(fred)))&
((generous(fred)<~>~humble(fred))) | ~funny(fred) | [
"p1",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6560255554556265898939024
% SZS output start Proof for 6560255554556265898939024
2. ! [X0] : ((~kind(X0) | rich(X0)) <=> (~creative(X0) & ~happy(X0))) [input p1]
10. ! [X0] : ((~creative(X0) | kind(X0)) => (~calm(X0) & happy(X0))) [input p9]
17. funny(fred) <~> rich(fred) [input p16]
19. ~funny(fred) [input hypothesis]
30. ! [X0] : ((~calm(X0) & happy(X0)) | (creative(X0) & ~kind(X0))) [ennf transformation 10]
37. ! [X0] : (((~kind(X0) | rich(X0)) | (creative(X0) | happy(X0))) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~kind(X0) | rich(X0) | creative(X0) | happy(X0)) & ((~creative(X0) & ~happy(X0)) | (kind(X0) & ~rich(X0)))) [flattening 37]
55. (~rich(fred) | ~funny(fred)) & (rich(fred) | funny(fred)) [nnf transformation 17]
63. ~rich(X0) | ~happy(X0) [cnf transformation 38]
65. ~creative(X0) | ~rich(X0) [cnf transformation 38]
91. creative(X0) | happy(X0) [cnf transformation 30]
108. rich(fred) | funny(fred) [cnf transformation 55]
112. ~funny(fred) [cnf transformation 19]
228. 24 <=> funny(fred) [avatar definition]
232. 25 <=> rich(fred) [avatar definition]
233. rich(fred) <- (25) [avatar component clause 232]
236. 24 | 25 [avatar split clause 108,232,228]
243. ~24 [avatar split clause 112,228]
251. happy(X1) | ~rich(X1) [resolution 91,65]
253. ~rich(X1) [subsumption resolution 251,63]
258. $false <- (25) [resolution 253,233]
259. ~25 [avatar contradiction clause 258]
261. $false [avatar sat refutation 236,243,259]
% SZS output end Proof for 6560255554556265898939024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not old or humble then fred is not wise or tall. If paul is humble or not tall then someone is either kind or tall. Everyone who is either generous or not patient is either creative or not kind. Everyone who is both not creative and quiet is either not happy or not curious. If fred is curious then someone is funny and vice versa. Everyone who is both not tall and creative is either not strong or humble and vice versa. Everyone who is old or not brave is both patient and rich. Everyone who is both not wise and happy is brave. Everyone who is not calm or not patient is both not humble and rich. If someone is either not rich or not funny then someone is rich or strong. Everyone who is both not calm and curious is not rich or not happy and vice versa. Everyone who is either wise or humble is not wise and vice versa. If someone is both not rich and calm then susan is both generous and not old and vice versa. If someone is both not curious and creative then someone is both not quiet and not strong and vice versa. If john is both not funny and not wise then paul is both generous and not tall and vice versa. Everyone who is kind or funny is both not kind and quiet. Someone is not funny or creative. Someone is both calm and not creative. Someone is either generous or not rich. Someone is both generous and not strong. Alice is rich or not patient. Someone is either not creative or not wise. Someone is either not strong or not tall. | Mary is not rich. | contradiction | (((~old(mary)<~>humble(mary)))=>((~wise(fred)|tall(fred))))&
(((humble(paul)|~tall(paul)))=>(?[X]:((kind(X)<~>tall(X)))))&
(![X]:((generous(X)<~>~patient(X))=>(creative(X)<~>~kind(X))))&
(![X]:((~creative(X)&quiet(X))=>(~happy(X)<~>~curious(X))))&
((curious(fred))<=>(?[X]:(funny(X))))&
(![X]:((~tall(X)&creative(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((old(X)|~brave(X))=>(patient(X)&rich(X))))&
(![X]:((~wise(X)&happy(X))=>brave(X)))&
(![X]:((~calm(X)|~patient(X))=>(~humble(X)&rich(X))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((~calm(X)&curious(X))<=>(~rich(X)|~happy(X))))&
(![X]:((wise(X)<~>humble(X))<=>~wise(X)))&
((?[X]:((~rich(X)&calm(X))))<=>((generous(susan)&~old(susan))))&
((?[X]:((~curious(X)&creative(X))))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(((~funny(john)&~wise(john)))<=>((generous(paul)&~tall(paul))))&
(![X]:((kind(X)|funny(X))=>(~kind(X)&quiet(X))))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((generous(X)&~strong(X))))&
((rich(alice)|~patient(alice)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((~strong(X)<~>~tall(X)))) | ~rich(mary) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2971914914584451722278794
% SZS output start Proof for 2971914914584451722278794
9. ! [X0] : ((~patient(X0) | ~calm(X0)) => (rich(X0) & ~humble(X0))) [input p8]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~happy(X0) | ~rich(X0))) [input p10]
24. ~rich(mary) [input hypothesis]
36. ! [X0] : ((rich(X0) & ~humble(X0)) | (patient(X0) & calm(X0))) [ennf transformation 9]
55. ! [X0] : (((curious(X0) & ~calm(X0)) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
56. ! [X0] : (((curious(X0) & ~calm(X0)) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | ~curious(X0) | calm(X0))) [flattening 55]
109. rich(X0) | calm(X0) [cnf transformation 36]
114. ~calm(X0) | rich(X0) [cnf transformation 56]
150. ~rich(mary) [cnf transformation 24]
221. rich(X0) [subsumption resolution 114,109]
311. $false [subsumption resolution 150,221]
% SZS output end Proof for 2971914914584451722278794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is calm then lucy is both brave and generous and vice versa.
Everyone who is not wise is not funny.
Everyone who is both kind and not happy is either not curious or not quiet and vice versa.
If someone is either funny or brave then someone is not wise or happy.
Everyone who is patient is both not calm and creative and vice versa.
Everyone who is not calm or creative is both funny and not quiet and vice versa.
Everyone who is quiet or creative is both not rich and not old and vice versa.
Everyone who is both not kind and brave is quiet or wise and vice versa.
If someone is not creative then someone is quiet or not funny.
If fred is both humble and not wise then someone is both not rich and quiet and vice versa.
Everyone who is not rich or not old is either old or wise.
If fred is not wise or strong then lucy is humble or not strong.
If someone is rich or patient then paul is both old and not creative and vice versa.
Everyone who is either not wise or brave is both not brave and funny.
If someone is not wise or not quiet then someone is either not wise or strong.
Paul is not funny or not calm.
Someone is either not brave or tall.
Mary is not tall.
Susan is not generous or not strong.
Alice is both brave and not creative.
Susan is both old and not generous. | Susan is creative. | contradiction | ((calm(paul))<=>((brave(lucy)&generous(lucy))))&
(![X]:(~wise(X)=>~funny(X)))&
(![X]:((kind(X)&~happy(X))<=>(~curious(X)<~>~quiet(X))))&
((?[X]:((funny(X)<~>brave(X))))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:(patient(X)<=>(~calm(X)&creative(X))))&
(![X]:((~calm(X)|creative(X))<=>(funny(X)&~quiet(X))))&
(![X]:((quiet(X)|creative(X))<=>(~rich(X)&~old(X))))&
(![X]:((~kind(X)&brave(X))<=>(quiet(X)|wise(X))))&
((?[X]:(~creative(X)))=>(?[X]:((quiet(X)|~funny(X)))))&
(((humble(fred)&~wise(fred)))<=>(?[X]:((~rich(X)&quiet(X)))))&
(![X]:((~rich(X)|~old(X))=>(old(X)<~>wise(X))))&
(((~wise(fred)|strong(fred)))=>((humble(lucy)|~strong(lucy))))&
((?[X]:((rich(X)|patient(X))))<=>((old(paul)&~creative(paul))))&
(![X]:((~wise(X)<~>brave(X))=>(~brave(X)&funny(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:((~wise(X)<~>strong(X)))))&
((~funny(paul)|~calm(paul)))&
(?[X]:((~brave(X)<~>tall(X))))&
(~tall(mary))&
((~generous(susan)|~strong(susan)))&
((brave(alice)&~creative(alice)))&
((old(susan)&~generous(susan))) | creative(susan) | [
"p1",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7048270024512491277446013
% SZS output start Proof for 7048270024512491277446013
2. ! [X0] : (~wise(X0) => ~funny(X0)) [input p1]
6. ! [X0] : ((creative(X0) | ~calm(X0)) <=> (~quiet(X0) & funny(X0))) [input p5]
8. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (wise(X0) | quiet(X0))) [input p7]
14. ! [X0] : ((~wise(X0) <~> brave(X0)) => (funny(X0) & ~brave(X0))) [input p13]
22. creative(susan) [input hypothesis]
26. ! [X0] : (~funny(X0) | wise(X0)) [ennf transformation 2]
32. ! [X0] : ((funny(X0) & ~brave(X0)) | (~wise(X0) <=> brave(X0))) [ennf transformation 14]
44. ! [X0] : (((creative(X0) | ~calm(X0)) | (quiet(X0) | ~funny(X0))) & ((~quiet(X0) & funny(X0)) | (~creative(X0) & calm(X0)))) [nnf transformation 6]
45. ! [X0] : ((creative(X0) | ~calm(X0) | quiet(X0) | ~funny(X0)) & ((~quiet(X0) & funny(X0)) | (~creative(X0) & calm(X0)))) [flattening 44]
48. ! [X0] : (((brave(X0) & ~kind(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (~brave(X0) | kind(X0)))) [nnf transformation 8]
49. ! [X0] : (((brave(X0) & ~kind(X0)) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | ~brave(X0) | kind(X0))) [flattening 48]
64. ! [X0] : ((funny(X0) & ~brave(X0)) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) [nnf transformation 32]
75. ~funny(X0) | wise(X0) [cnf transformation 26]
88. ~creative(X0) | funny(X0) [cnf transformation 45]
101. brave(X0) | ~wise(X0) [cnf transformation 49]
119. ~brave(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 64]
135. creative(susan) [cnf transformation 22]
136. ~brave(X0) | ~wise(X0) [duplicate literal removal 119]
250. ~wise(X0) [subsumption resolution 136,101]
291. funny(susan) [resolution 88,135]
295. wise(susan) [resolution 291,75]
296. $false [subsumption resolution 295,250]
% SZS output end Proof for 7048270024512491277446013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then paul is humble. If john is not tall then alice is both not curious and creative. Everyone who is not strong or not old is either tall or not rich and vice versa. Everyone who is either generous or not strong is both not funny and not humble. If john is both quiet and not curious then someone is curious and vice versa. If someone is not patient then someone is both not funny and generous and vice versa. If someone is either not tall or brave then someone is both humble and curious. Everyone who is not patient or not generous is funny or curious and vice versa. If alice is either calm or brave then someone is old and vice versa. If alice is both not generous and not creative then someone is either not tall or not humble. Everyone who is not strong or generous is both tall and not humble and vice versa. If alice is curious then someone is both happy and not wise and vice versa. If john is both not creative and not funny then fred is either not tall or strong. If someone is humble or not curious then someone is not curious and vice versa. If someone is happy or funny then mary is not strong and vice versa. If someone is either tall or not curious then john is not quiet. Alice is either creative or brave. Alice is not creative. John is not brave or not humble. Someone is brave. Fred is both not wise and not rich. Lucy is not humble. Someone is happy. Someone is either not patient or wise. | Alice is not brave. | contradiction | ((?[X]:(~happy(X)))=>(humble(paul)))&
((~tall(john))=>((~curious(alice)&creative(alice))))&
(![X]:((~strong(X)|~old(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((generous(X)<~>~strong(X))=>(~funny(X)&~humble(X))))&
(((quiet(john)&~curious(john)))<=>(?[X]:(curious(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((~tall(X)<~>brave(X))))=>(?[X]:((humble(X)&curious(X)))))&
(![X]:((~patient(X)|~generous(X))<=>(funny(X)|curious(X))))&
(((calm(alice)<~>brave(alice)))<=>(?[X]:(old(X))))&
(((~generous(alice)&~creative(alice)))=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~strong(X)|generous(X))<=>(tall(X)&~humble(X))))&
((curious(alice))<=>(?[X]:((happy(X)&~wise(X)))))&
(((~creative(john)&~funny(john)))=>((~tall(fred)<~>strong(fred))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((happy(X)|funny(X))))<=>(~strong(mary)))&
((?[X]:((tall(X)<~>~curious(X))))=>(~quiet(john)))&
((creative(alice)<~>brave(alice)))&
(~creative(alice))&
((~brave(john)|~humble(john)))&
(?[X]:(brave(X)))&
((~wise(fred)&~rich(fred)))&
(~humble(lucy))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)<~>wise(X)))) | ~brave(alice) | [
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2455757208769012802941511
% SZS output start Proof for 2455757208769012802941511
17. creative(alice) <~> brave(alice) [input p16]
18. ~creative(alice) [input p17]
25. ~brave(alice) [input hypothesis]
81. (~brave(alice) | ~creative(alice)) & (brave(alice) | creative(alice)) [nnf transformation 17]
140. brave(alice) | creative(alice) [cnf transformation 81]
142. ~creative(alice) [cnf transformation 18]
151. ~brave(alice) [cnf transformation 25]
165. 4 <=> creative(alice) [avatar definition]
239. 21 <=> brave(alice) [avatar definition]
349. 4 | 21 [avatar split clause 140,239,165]
350. ~4 [avatar split clause 142,165]
370. ~21 [avatar split clause 151,239]
371. $false [avatar sat refutation 349,350,370]
% SZS output end Proof for 2455757208769012802941511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and creative is both not patient and curious. Everyone who is either quiet or not humble is humble or not kind. Everyone who is not funny is calm. If mary is either generous or curious then mary is brave or not happy. Everyone who is not funny or curious is either not old or wise and vice versa. Everyone who is either wise or not happy is either not humble or tall. If alice is not rich then susan is quiet or not happy and vice versa. If someone is not quiet or creative then someone is either funny or not old and vice versa. Everyone who is both not old and not patient is kind or wise and vice versa. If someone is not tall then someone is both generous and not rich. Everyone who is both not old and not wise is not quiet or not curious and vice versa. Everyone who is brave or not kind is not kind and vice versa. If someone is strong then someone is kind and vice versa. If john is not quiet then someone is rich or not funny and vice versa. Everyone who is wise or tall is both not happy and not old. Everyone who is not curious or not strong is not happy. Fred is both not funny and strong. Someone is both calm and not curious. Alice is either strong or not rich. Someone is not happy. Susan is both not humble and generous. John is not strong. Susan is generous or not kind. Someone is either not happy or wise. | Mary is not wise. | entailment | (![X]:((rich(X)&creative(X))=>(~patient(X)&curious(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(humble(X)|~kind(X))))&
(![X]:(~funny(X)=>calm(X)))&
(((generous(mary)<~>curious(mary)))=>((brave(mary)|~happy(mary))))&
(![X]:((~funny(X)|curious(X))<=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)<~>~happy(X))=>(~humble(X)<~>tall(X))))&
((~rich(alice))<=>((quiet(susan)|~happy(susan))))&
((?[X]:((~quiet(X)|creative(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((~old(X)&~patient(X))<=>(kind(X)|wise(X))))&
((?[X]:(~tall(X)))=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:((~old(X)&~wise(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((brave(X)|~kind(X))<=>~kind(X)))&
((?[X]:(strong(X)))<=>(?[X]:(kind(X))))&
((~quiet(john))<=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:((wise(X)|tall(X))=>(~happy(X)&~old(X))))&
(![X]:((~curious(X)|~strong(X))=>~happy(X)))&
((~funny(fred)&strong(fred)))&
(?[X]:((calm(X)&~curious(X))))&
((strong(alice)<~>~rich(alice)))&
(?[X]:(~happy(X)))&
((~humble(susan)&generous(susan)))&
(~strong(john))&
((generous(susan)|~kind(susan)))&
(?[X]:((~happy(X)<~>wise(X)))) | ~wise(mary) | [
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1196615003937200870597429
% SZS output start Proof for 1196615003937200870597429
5. ! [X0] : ((curious(X0) | ~funny(X0)) <=> (~old(X0) <~> wise(X0))) [input p4]
9. ! [X0] : ((~patient(X0) & ~old(X0)) <=> (wise(X0) | kind(X0))) [input p8]
11. ! [X0] : ((~wise(X0) & ~old(X0)) <=> (~curious(X0) | ~quiet(X0))) [input p10]
25. wise(mary) [input hypothesis]
43. ! [X0] : (((curious(X0) | ~funny(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) & (((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~curious(X0) & funny(X0)))) [nnf transformation 5]
44. ! [X0] : ((curious(X0) | ~funny(X0) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0)))) & (((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~curious(X0) & funny(X0)))) [flattening 43]
53. ! [X0] : (((~patient(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & ((wise(X0) | kind(X0)) | (patient(X0) | old(X0)))) [nnf transformation 9]
54. ! [X0] : (((~patient(X0) & ~old(X0)) | (~wise(X0) & ~kind(X0))) & (wise(X0) | kind(X0) | patient(X0) | old(X0))) [flattening 53]
58. ! [X0] : (((~wise(X0) & ~old(X0)) | (curious(X0) & quiet(X0))) & ((~curious(X0) | ~quiet(X0)) | (wise(X0) | old(X0)))) [nnf transformation 11]
59. ! [X0] : (((~wise(X0) & ~old(X0)) | (curious(X0) & quiet(X0))) & (~curious(X0) | ~quiet(X0) | wise(X0) | old(X0))) [flattening 58]
88. ~wise(X0) | old(X0) | ~curious(X0) [cnf transformation 44]
106. ~wise(X0) | ~old(X0) [cnf transformation 54]
115. ~wise(X0) | curious(X0) [cnf transformation 59]
142. wise(mary) [cnf transformation 25]
145. 1 <=> curious(mary) [avatar definition]
146. curious(mary) <- (1) [avatar component clause 145]
274. ~old(mary) [resolution 106,142]
278. curious(mary) [resolution 115,142]
279. 1 [avatar split clause 278,145]
285. old(mary) | ~curious(mary) [resolution 88,142]
286. ~curious(mary) [subsumption resolution 285,274]
287. $false <- (1) [subsumption resolution 286,146]
288. ~1 [avatar contradiction clause 287]
289. $false [avatar sat refutation 279,288]
% SZS output end Proof for 1196615003937200870597429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is not generous or humble and vice versa.
Everyone who is either creative or curious is old or not tall and vice versa.
Everyone who is either brave or curious is humble and vice versa.
If someone is both kind and not wise then someone is both funny and not funny and vice versa.
Everyone who is either rich or not humble is not curious.
If fred is not humble then john is not generous and vice versa.
If john is both funny and wise then fred is funny or patient.
Everyone who is either happy or wise is not tall.
Everyone who is both not creative and not quiet is not creative or generous and vice versa.
Everyone who is not old or generous is patient and vice versa.
Everyone who is either not kind or not old is both brave and not humble.
Everyone who is both not quiet and brave is both not curious and not patient and vice versa.
If john is tall or not humble then someone is not kind or not brave and vice versa.
Everyone who is both strong and old is either rich or generous and vice versa.
If john is both not quiet and wise then someone is either not strong or not brave and vice versa.
Everyone who is not rich is either not patient or not quiet.
Alice is happy.
Alice is not quiet.
Susan is both calm and wise.
Susan is not wise or kind.
John is not funny or not generous.
Someone is both not strong and humble.
Fred is not rich or not creative.
Someone is either not old or not patient. | Fred is not rich. | entailment | (![X]:((kind(X)|tall(X))<=>(~generous(X)|humble(X))))&
(![X]:((creative(X)<~>curious(X))<=>(old(X)|~tall(X))))&
(![X]:((brave(X)<~>curious(X))<=>humble(X)))&
((?[X]:((kind(X)&~wise(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((rich(X)<~>~humble(X))=>~curious(X)))&
((~humble(fred))<=>(~generous(john)))&
(((funny(john)&wise(john)))=>((funny(fred)|patient(fred))))&
(![X]:((happy(X)<~>wise(X))=>~tall(X)))&
(![X]:((~creative(X)&~quiet(X))<=>(~creative(X)|generous(X))))&
(![X]:((~old(X)|generous(X))<=>patient(X)))&
(![X]:((~kind(X)<~>~old(X))=>(brave(X)&~humble(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~curious(X)&~patient(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:((~kind(X)|~brave(X)))))&
(![X]:((strong(X)&old(X))<=>(rich(X)<~>generous(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~rich(X)=>(~patient(X)<~>~quiet(X))))&
(happy(alice))&
(~quiet(alice))&
((calm(susan)&wise(susan)))&
((~wise(susan)|kind(susan)))&
((~funny(john)|~generous(john)))&
(?[X]:((~strong(X)&humble(X))))&
((~rich(fred)|~creative(fred)))&
(?[X]:((~old(X)<~>~patient(X)))) | ~rich(fred) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p9",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3562788167191315540945718
% SZS output start Proof for 3562788167191315540945718
1. ! [X0] : ((tall(X0) | kind(X0)) <=> (humble(X0) | ~generous(X0))) [input p0]
2. ! [X0] : ((creative(X0) <~> curious(X0)) <=> (~tall(X0) | old(X0))) [input p1]
3. ! [X0] : ((brave(X0) <~> curious(X0)) <=> humble(X0)) [input p2]
5. ! [X0] : ((rich(X0) <~> ~humble(X0)) => ~curious(X0)) [input p4]
9. ! [X0] : ((~quiet(X0) & ~creative(X0)) <=> (generous(X0) | ~creative(X0))) [input p8]
10. ! [X0] : ((generous(X0) | ~old(X0)) <=> patient(X0)) [input p9]
12. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~patient(X0) & ~curious(X0))) [input p11]
14. ! [X0] : ((old(X0) & strong(X0)) <=> (rich(X0) <~> generous(X0))) [input p13]
23. ~creative(fred) | ~rich(fred) [input p22]
25. rich(fred) [input hypothesis]
28. ! [X0] : (~curious(X0) | (rich(X0) <=> ~humble(X0))) [ennf transformation 5]
34. ! [X0] : (((tall(X0) | kind(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 1]
35. ! [X0] : ((tall(X0) | kind(X0) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | (~tall(X0) & ~kind(X0)))) [flattening 34]
36. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | (tall(X0) & ~old(X0))) & ((~tall(X0) | old(X0)) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | (tall(X0) & ~old(X0))) & (~tall(X0) | old(X0) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [flattening 36]
38. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ~humble(X0)) & (humble(X0) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 3]
44. ! [X0] : (~curious(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) [nnf transformation 28]
47. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (quiet(X0) | creative(X0)))) [nnf transformation 9]
48. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | quiet(X0) | creative(X0))) [flattening 47]
49. ! [X0] : (((generous(X0) | ~old(X0)) | ~patient(X0)) & (patient(X0) | (~generous(X0) & old(X0)))) [nnf transformation 10]
50. ! [X0] : ((generous(X0) | ~old(X0) | ~patient(X0)) & (patient(X0) | (~generous(X0) & old(X0)))) [flattening 49]
52. ! [X0] : (((brave(X0) & ~quiet(X0)) | (patient(X0) | curious(X0))) & ((~patient(X0) & ~curious(X0)) | (~brave(X0) | quiet(X0)))) [nnf transformation 12]
53. ! [X0] : (((brave(X0) & ~quiet(X0)) | patient(X0) | curious(X0)) & ((~patient(X0) & ~curious(X0)) | ~brave(X0) | quiet(X0))) [flattening 52]
59. ! [X0] : (((old(X0) & strong(X0)) | ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | (~old(X0) | ~strong(X0)))) [nnf transformation 14]
60. ! [X0] : (((old(X0) & strong(X0)) | ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ~old(X0) | ~strong(X0))) [flattening 59]
73. ~generous(X0) | humble(X0) | ~tall(X0) [cnf transformation 35]
78. ~old(X0) | creative(X0) | curious(X0) [cnf transformation 37]
79. curious(X0) | creative(X0) | tall(X0) [cnf transformation 37]
81. ~curious(X0) | ~creative(X0) | tall(X0) [cnf transformation 37]
83. ~curious(X0) | brave(X0) | humble(X0) [cnf transformation 38]
84. ~humble(X0) | brave(X0) | curious(X0) [cnf transformation 38]
90. ~rich(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 44]
100. ~quiet(X0) | creative(X0) [cnf transformation 48]
103. ~generous(X0) | patient(X0) [cnf transformation 50]
109. ~brave(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
110. ~patient(X0) | ~brave(X0) | quiet(X0) [cnf transformation 53]
121. ~rich(X0) | generous(X0) | old(X0) [cnf transformation 60]
138. ~creative(fred) | ~rich(fred) [cnf transformation 23]
141. rich(fred) [cnf transformation 25]
156. 4 <=> humble(fred) [avatar definition]
157. humble(fred) <- (4) [avatar component clause 156]
158. ~humble(fred) <- (~4) [avatar component clause 156]
174. 8 <=> patient(fred) [avatar definition]
176. patient(fred) <- (8) [avatar component clause 174]
231. 20 <=> rich(fred) [avatar definition]
232. rich(fred) <- (20) [avatar component clause 231]
235. 21 <=> creative(fred) [avatar definition]
237. ~creative(fred) <- (~21) [avatar component clause 235]
238. ~20 | ~21 [avatar split clause 138,235,231]
248. 20 [avatar split clause 141,231]
271. brave(X0) | humble(X0) | creative(X0) | tall(X0) [resolution 83,79]
284. ~humble(fred) | ~curious(fred) <- (20) [resolution 90,232]
377. 42 <=> generous(fred) [avatar definition]
379. generous(fred) <- (42) [avatar component clause 377]
384. generous(fred) | old(fred) <- (20) [resolution 121,232]
386. 43 <=> old(fred) [avatar definition]
388. old(fred) <- (43) [avatar component clause 386]
389. 43 | 42 | ~20 [avatar split clause 384,231,377,386]
393. creative(fred) | curious(fred) <- (43) [resolution 388,78]
394. curious(fred) <- (~21, 43) [subsumption resolution 393,237]
446. brave(fred) | humble(fred) <- (~21, 43) [resolution 394,83]
476. 52 <=> tall(fred) [avatar definition]
477. ~tall(fred) <- (~52) [avatar component clause 476]
506. humble(X1) | creative(X1) | tall(X1) | ~curious(X1) | quiet(X1) [resolution 271,109]
516. ~curious(X1) | tall(X1) | humble(X1) | quiet(X1) [subsumption resolution 506,81]
593. brave(fred) <- (~4, ~21, 43) [subsumption resolution 446,158]
838. ~curious(fred) | quiet(fred) <- (~4, ~21, 43) [resolution 593,109]
844. quiet(fred) <- (~4, ~21, 43) [subsumption resolution 838,394]
881. tall(X0) | humble(X0) | quiet(X0) | creative(X0) | tall(X0) [resolution 516,79]
886. tall(X0) | humble(X0) | quiet(X0) | creative(X0) [duplicate literal removal 881]
887. creative(X0) | humble(X0) | tall(X0) [subsumption resolution 886,100]
899. creative(fred) <- (~4, ~21, 43) [resolution 844,100]
900. $false <- (~4, ~21, 43) [subsumption resolution 899,237]
901. 4 | 21 | ~43 [avatar contradiction clause 900]
908. 81 <=> brave(fred) [avatar definition]
910. brave(fred) <- (81) [avatar component clause 908]
912. 4 | 81 | 21 | ~43 [avatar split clause 446,386,235,908,156]
914. ~humble(fred) <- (20, ~21, 43) [subsumption resolution 284,394]
915. ~4 | ~20 | 21 | ~43 [avatar split clause 914,386,235,231,156]
916. ~curious(fred) <- (4, 20) [subsumption resolution 284,157]
941. brave(fred) | curious(fred) <- (4) [resolution 157,84]
945. brave(fred) <- (4, 20) [subsumption resolution 941,916]
946. 81 | ~4 | ~20 [avatar split clause 945,231,156,908]
955. humble(fred) | ~tall(fred) <- (42) [resolution 379,73]
957. patient(fred) <- (42) [resolution 379,103]
958. 8 | ~42 [avatar split clause 957,377,174]
959. ~brave(fred) | quiet(fred) <- (8) [resolution 176,110]
961. quiet(fred) <- (8, 81) [subsumption resolution 959,910]
982. creative(fred) <- (8, 81) [resolution 961,100]
985. $false <- (8, ~21, 81) [subsumption resolution 982,237]
986. ~8 | 21 | ~81 [avatar contradiction clause 985]
1002. ~tall(fred) <- (~4, 42) [subsumption resolution 955,158]
1003. ~52 | 4 | ~42 [avatar split clause 1002,377,156,476]
1020. humble(fred) | tall(fred) <- (~21) [resolution 887,237]
1024. tall(fred) <- (~4, ~21) [subsumption resolution 1020,158]
1025. $false <- (~4, ~21, ~52) [subsumption resolution 1024,477]
1026. 4 | 21 | 52 [avatar contradiction clause 1025]
1027. $false [avatar sat refutation 238,248,389,901,912,915,946,958,986,1003,1026]
% SZS output end Proof for 3562788167191315540945718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then john is not creative or not happy and vice versa.
Everyone who is either funny or happy is not wise and vice versa.
Everyone who is both quiet and curious is happy or tall and vice versa.
If john is wise then john is patient.
If someone is both brave and not curious then someone is either not strong or not humble and vice versa.
Everyone who is funny or not patient is both not brave and creative and vice versa.
Everyone who is both humble and old is either happy or not happy and vice versa.
Everyone who is not kind is either not rich or not wise.
Everyone who is wise is both wise and not rich and vice versa.
If someone is not funny or tall then fred is not creative.
If paul is either rich or calm then someone is both not kind and funny.
If paul is rich or not brave then fred is both rich and kind and vice versa.
If fred is either tall or not brave then someone is either tall or kind.
Everyone who is tall is either not strong or patient and vice versa.
Everyone who is not funny is both curious and not calm.
Everyone who is both patient and wise is either generous or not humble.
Alice is curious or humble.
Someone is tall.
Paul is either not creative or not quiet.
Fred is both not happy and old.
Someone is curious.
Susan is not calm.
Susan is both creative and not generous. | Paul is not brave. | contradiction | ((?[X]:(tall(X)))<=>((~creative(john)|~happy(john))))&
(![X]:((funny(X)<~>happy(X))<=>~wise(X)))&
(![X]:((quiet(X)&curious(X))<=>(happy(X)|tall(X))))&
((wise(john))=>(patient(john)))&
((?[X]:((brave(X)&~curious(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((funny(X)|~patient(X))<=>(~brave(X)&creative(X))))&
(![X]:((humble(X)&old(X))<=>(happy(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(wise(X)&~rich(X))))&
((?[X]:((~funny(X)|tall(X))))=>(~creative(fred)))&
(((rich(paul)<~>calm(paul)))=>(?[X]:((~kind(X)&funny(X)))))&
(((rich(paul)|~brave(paul)))<=>((rich(fred)&kind(fred))))&
(((tall(fred)<~>~brave(fred)))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(~strong(X)<~>patient(X))))&
(![X]:(~funny(X)=>(curious(X)&~calm(X))))&
(![X]:((patient(X)&wise(X))=>(generous(X)<~>~humble(X))))&
((curious(alice)|humble(alice)))&
(?[X]:(tall(X)))&
((~creative(paul)<~>~quiet(paul)))&
((~happy(fred)&old(fred)))&
(?[X]:(curious(X)))&
(~calm(susan))&
((creative(susan)&~generous(susan))) | ~brave(paul) | [
"p1",
"p5",
"p8",
"p9",
"p11",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 893129431216061152272860
% SZS output start Proof for 893129431216061152272860
2. ! [X0] : ((funny(X0) <~> happy(X0)) <=> ~wise(X0)) [input p1]
6. ! [X0] : ((~patient(X0) | funny(X0)) <=> (creative(X0) & ~brave(X0))) [input p5]
9. ! [X0] : (wise(X0) <=> (~rich(X0) & wise(X0))) [input p8]
10. ? [X0] : (tall(X0) | ~funny(X0)) => ~creative(fred) [input p9]
12. (~brave(paul) | rich(paul)) <=> (kind(fred) & rich(fred)) [input p11]
18. ? [X0] : tall(X0) [input p17]
20. old(fred) & ~happy(fred) [input p19]
24. ~brave(paul) [input hypothesis]
28. ~creative(fred) | ! [X0] : (~tall(X0) & funny(X0)) [ennf transformation 10]
39. ! [X0] : ((((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | wise(X0)) & (~wise(X0) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))))) [nnf transformation 2]
47. ! [X0] : (((~patient(X0) | funny(X0)) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | (patient(X0) & ~funny(X0)))) [nnf transformation 6]
48. ! [X0] : ((~patient(X0) | funny(X0) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | (patient(X0) & ~funny(X0)))) [flattening 47]
52. ! [X0] : ((wise(X0) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ~wise(X0))) [nnf transformation 9]
53. ! [X0] : ((wise(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ~wise(X0))) [flattening 52]
57. ((~brave(paul) | rich(paul)) | (~kind(fred) | ~rich(fred))) & ((kind(fred) & rich(fred)) | (brave(paul) & ~rich(paul))) [nnf transformation 12]
58. (~brave(paul) | rich(paul) | ~kind(fred) | ~rich(fred)) & ((kind(fred) & rich(fred)) | (brave(paul) & ~rich(paul))) [flattening 57]
64. ? [X0] : tall(X0) => tall(sK5) [choice axiom]
65. tall(sK5) [skolemisation 18,64]
74. wise(X0) | funny(X0) | happy(X0) [cnf transformation 39]
90. ~funny(X0) | creative(X0) [cnf transformation 48]
102. ~rich(X0) | ~wise(X0) [cnf transformation 53]
105. ~creative(fred) | ~tall(X0) [cnf transformation 28]
111. rich(fred) | brave(paul) [cnf transformation 58]
128. tall(sK5) [cnf transformation 65]
131. ~happy(fred) [cnf transformation 20]
137. ~brave(paul) [cnf transformation 24]
157. 4 <=> ! [X1] : ~tall(X1) [avatar definition]
158. ~tall(X1) <- (4) [avatar component clause 157]
203. 14 <=> creative(fred) [avatar definition]
206. 4 | ~14 [avatar split clause 105,203,157]
232. 20 <=> rich(fred) [avatar definition]
233. rich(fred) <- (20) [avatar component clause 232]
240. 22 <=> brave(paul) [avatar definition]
246. 22 | 20 [avatar split clause 111,232,240]
279. ~22 [avatar split clause 137,240]
287. ~wise(fred) <- (20) [resolution 102,233]
290. funny(fred) | happy(fred) <- (20) [resolution 74,287]
299. funny(fred) <- (20) [subsumption resolution 290,131]
340. creative(fred) <- (20) [resolution 299,90]
343. 14 | ~20 [avatar split clause 340,232,203]
344. $false <- (4) [resolution 158,128]
349. ~4 [avatar contradiction clause 344]
350. $false [avatar sat refutation 206,246,279,343,349]
% SZS output end Proof for 893129431216061152272860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is wise or brave. If someone is both tall and funny then john is old. Everyone who is brave is either tall or strong. Everyone who is creative or not curious is both patient and quiet and vice versa. Everyone who is both strong and not brave is strong or not rich and vice versa. Everyone who is both funny and generous is either not wise or not patient and vice versa. If alice is not curious or not kind then someone is funny or quiet. If someone is not tall or rich then someone is both not rich and not wise. Everyone who is both brave and not brave is funny and vice versa. Everyone who is either old or brave is creative and vice versa. Everyone who is humble or not quiet is either not quiet or not rich and vice versa. If someone is not old then susan is happy or not creative and vice versa. Everyone who is both rich and not humble is both not humble and not brave and vice versa. If someone is either not funny or curious then lucy is not creative or not humble. Someone is humble. Someone is both not brave and strong. John is either not rich or generous. Someone is tall or curious. Mary is not funny. | Mary is quiet. | entailment | (![X]:(~rich(X)=>(wise(X)|brave(X))))&
((?[X]:((tall(X)&funny(X))))=>(old(john)))&
(![X]:(brave(X)=>(tall(X)<~>strong(X))))&
(![X]:((creative(X)|~curious(X))<=>(patient(X)&quiet(X))))&
(![X]:((strong(X)&~brave(X))<=>(strong(X)|~rich(X))))&
(![X]:((funny(X)&generous(X))<=>(~wise(X)<~>~patient(X))))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((funny(X)|quiet(X)))))&
((?[X]:((~tall(X)|rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((brave(X)&~brave(X))<=>funny(X)))&
(![X]:((old(X)<~>brave(X))<=>creative(X)))&
(![X]:((humble(X)|~quiet(X))<=>(~quiet(X)<~>~rich(X))))&
((?[X]:(~old(X)))<=>((happy(susan)|~creative(susan))))&
(![X]:((rich(X)&~humble(X))<=>(~humble(X)&~brave(X))))&
((?[X]:((~funny(X)<~>curious(X))))=>((~creative(lucy)|~humble(lucy))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)&strong(X))))&
((~rich(john)<~>generous(john)))&
(?[X]:((tall(X)|curious(X))))&
(~funny(mary)) | quiet(mary) | [
"p0",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 430945493002555913562824
% SZS output start Proof for 430945493002555913562824
1. ! [X0] : (~rich(X0) => (brave(X0) | wise(X0))) [input p0]
5. ! [X0] : ((~brave(X0) & strong(X0)) <=> (~rich(X0) | strong(X0))) [input p4]
8. ? [X0] : (rich(X0) | ~tall(X0)) => ? [X0] : (~wise(X0) & ~rich(X0)) [input p7]
11. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (~quiet(X0) <~> ~rich(X0))) [input p10]
20. ~quiet(mary) [input hypothesis]
21. ? [X0] : (rich(X0) | ~tall(X0)) => ? [X1] : (~wise(X1) & ~rich(X1)) [rectify 8]
23. ! [X0] : ((brave(X0) | wise(X0)) | rich(X0)) [ennf transformation 1]
24. ! [X0] : (brave(X0) | wise(X0) | rich(X0)) [flattening 23]
28. ? [X1] : (~wise(X1) & ~rich(X1)) | ! [X0] : (~rich(X0) & tall(X0)) [ennf transformation 21]
34. ! [X0] : (((~brave(X0) & strong(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (brave(X0) | ~strong(X0)))) [nnf transformation 5]
35. ! [X0] : (((~brave(X0) & strong(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | brave(X0) | ~strong(X0))) [flattening 34]
40. ? [X0] : (~wise(X0) & ~rich(X0)) | ! [X1] : (~rich(X1) & tall(X1)) [rectify 28]
41. ? [X0] : (~wise(X0) & ~rich(X0)) => (~wise(sK1) & ~rich(sK1)) [choice axiom]
42. (~wise(sK1) & ~rich(sK1)) | ! [X1] : (~rich(X1) & tall(X1)) [skolemisation 40,41]
46. ! [X0] : (((~quiet(X0) | humble(X0)) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | (quiet(X0) & ~humble(X0)))) [nnf transformation 11]
47. ! [X0] : ((~quiet(X0) | humble(X0) | ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0)))) & (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | (quiet(X0) & ~humble(X0)))) [flattening 46]
63. brave(X0) | wise(X0) | rich(X0) [cnf transformation 24]
76. ~brave(X0) | rich(X0) [cnf transformation 35]
85. ~rich(sK1) | ~rich(X1) [cnf transformation 42]
87. ~wise(sK1) | ~rich(X1) [cnf transformation 42]
98. rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 47]
117. ~quiet(mary) [cnf transformation 20]
118. quiet(X0) | rich(X0) [duplicate literal removal 98]
142. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
143. ~rich(X1) <- (6) [avatar component clause 142]
145. 7 <=> wise(sK1) [avatar definition]
147. ~wise(sK1) <- (~7) [avatar component clause 145]
148. 6 | ~7 [avatar split clause 87,145,142]
154. 9 <=> rich(sK1) [avatar definition]
156. ~rich(sK1) <- (~9) [avatar component clause 154]
157. 6 | ~9 [avatar split clause 85,154,142]
215. rich(mary) [resolution 118,117]
219. wise(X1) | rich(X1) | rich(X1) [resolution 63,76]
220. wise(X1) | rich(X1) [duplicate literal removal 219]
231. rich(sK1) <- (~7) [resolution 220,147]
232. $false <- (~7, ~9) [subsumption resolution 231,156]
233. 7 | 9 [avatar contradiction clause 232]
234. $false <- (6) [resolution 143,215]
239. ~6 [avatar contradiction clause 234]
240. $false [avatar sat refutation 148,157,233,239]
% SZS output end Proof for 430945493002555913562824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either not patient or brave and vice versa.
Everyone who is either old or not rich is creative or not wise.
If someone is either not kind or curious then susan is wise and vice versa.
If someone is kind then fred is either not old or rich.
Everyone who is generous or not patient is both funny and happy.
Everyone who is either not funny or not generous is either calm or generous and vice versa.
If someone is both not happy and happy then someone is not wise and vice versa.
Everyone who is either calm or creative is either not tall or strong.
If susan is both tall and old then someone is both generous and wise and vice versa.
Everyone who is either not brave or generous is either not creative or not calm and vice versa.
Everyone who is creative is both generous and strong and vice versa.
Everyone who is not brave or not quiet is generous and vice versa.
If mary is either calm or not kind then someone is not quiet.
Everyone who is either brave or calm is wise or not curious.
Everyone who is both not creative and not strong is tall.
Everyone who is either brave or not calm is not wise.
Paul is either kind or not quiet.
Mary is both not generous and humble.
Someone is curious or not creative.
Alice is both patient and not humble.
Mary is creative or not tall. | Susan is not calm. | contradiction | (![X]:(~tall(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((old(X)<~>~rich(X))=>(creative(X)|~wise(X))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(wise(susan)))&
((?[X]:(kind(X)))=>((~old(fred)<~>rich(fred))))&
(![X]:((generous(X)|~patient(X))=>(funny(X)&happy(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(calm(X)<~>generous(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)<~>creative(X))=>(~tall(X)<~>strong(X))))&
(((tall(susan)&old(susan)))<=>(?[X]:((generous(X)&wise(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:(creative(X)<=>(generous(X)&strong(X))))&
(![X]:((~brave(X)|~quiet(X))<=>generous(X)))&
(((calm(mary)<~>~kind(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)<~>calm(X))=>(wise(X)|~curious(X))))&
(![X]:((~creative(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)<~>~calm(X))=>~wise(X)))&
((kind(paul)<~>~quiet(paul)))&
((~generous(mary)&humble(mary)))&
(?[X]:((curious(X)|~creative(X))))&
((patient(alice)&~humble(alice)))&
((creative(mary)|~tall(mary))) | ~calm(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1662128935610947260282932
% SZS output start Proof for 1662128935610947260282932
1. ! [X0] : (~tall(X0) <=> (~patient(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((old(X0) <~> ~rich(X0)) => (~wise(X0) | creative(X0))) [input p1]
4. ? [X0] : kind(X0) => (~old(fred) <~> rich(fred)) [input p3]
5. ! [X0] : ((~patient(X0) | generous(X0)) => (happy(X0) & funny(X0))) [input p4]
6. ! [X0] : ((~funny(X0) <~> ~generous(X0)) <=> (calm(X0) <~> generous(X0))) [input p5]
7. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X0] : ~wise(X0) [input p6]
9. (old(susan) & tall(susan)) <=> ? [X0] : (wise(X0) & generous(X0)) [input p8]
11. ! [X0] : (creative(X0) <=> (strong(X0) & generous(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> generous(X0)) [input p11]
17. kind(paul) <~> ~quiet(paul) [input p16]
22. ~calm(susan) [input hypothesis]
23. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X1] : ~wise(X1) [rectify 7]
24. ! [X0] : ((~wise(X0) | creative(X0)) | (old(X0) <=> ~rich(X0))) [ennf transformation 2]
25. ! [X0] : (~wise(X0) | creative(X0) | (old(X0) <=> ~rich(X0))) [flattening 24]
26. (~old(fred) <~> rich(fred)) | ! [X0] : ~kind(X0) [ennf transformation 4]
27. ! [X0] : ((happy(X0) & funny(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 5]
35. ! [X0] : ((~tall(X0) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) & (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | tall(X0))) [nnf transformation 1]
36. ! [X0] : (~wise(X0) | creative(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0)))) [nnf transformation 25]
41. ((~rich(fred) | old(fred)) & (rich(fred) | ~old(fred))) | ! [X0] : ~kind(X0) [nnf transformation 26]
42. ! [X0] : ((((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0))))) [nnf transformation 6]
43. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~happy(X0) | happy(X0))) [nnf transformation 23]
44. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~happy(X3) | happy(X3))) [rectify 43]
45. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK1) & ~happy(sK1)) [choice axiom]
46. ? [X2] : ~wise(X2) => ~wise(sK2) [choice axiom]
47. ((happy(sK1) & ~happy(sK1)) | ! [X1] : wise(X1)) & (~wise(sK2) | ! [X3] : (~happy(X3) | happy(X3))) [skolemisation 44,46,45]
49. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X0] : (wise(X0) & generous(X0)) | (~old(susan) | ~tall(susan))) [nnf transformation 9]
50. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X0] : (wise(X0) & generous(X0)) | ~old(susan) | ~tall(susan)) [flattening 49]
51. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & (? [X1] : (wise(X1) & generous(X1)) | ~old(susan) | ~tall(susan)) [rectify 50]
52. ? [X1] : (wise(X1) & generous(X1)) => (wise(sK3) & generous(sK3)) [choice axiom]
53. ((old(susan) & tall(susan)) | ! [X0] : (~wise(X0) | ~generous(X0))) & ((wise(sK3) & generous(sK3)) | ~old(susan) | ~tall(susan)) [skolemisation 51,52]
55. ! [X0] : ((creative(X0) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | ~creative(X0))) [nnf transformation 11]
56. ! [X0] : ((creative(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | ~creative(X0))) [flattening 55]
57. ! [X0] : (((~quiet(X0) | ~brave(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) & brave(X0)))) [nnf transformation 12]
58. ! [X0] : ((~quiet(X0) | ~brave(X0) | ~generous(X0)) & (generous(X0) | (quiet(X0) & brave(X0)))) [flattening 57]
64. (quiet(paul) | ~kind(paul)) & (~quiet(paul) | kind(paul)) [nnf transformation 17]
70. ~brave(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 35]
71. ~wise(X0) | creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 36]
72. ~wise(X0) | creative(X0) | old(X0) | rich(X0) [cnf transformation 36]
77. rich(fred) | ~old(fred) | ~kind(X0) [cnf transformation 41]
78. ~rich(fred) | old(fred) | ~kind(X0) [cnf transformation 41]
79. ~generous(X0) | funny(X0) [cnf transformation 27]
80. funny(X0) | patient(X0) [cnf transformation 27]
84. generous(X0) | calm(X0) | ~funny(X0) | generous(X0) [cnf transformation 42]
88. ~generous(X0) | ~funny(X0) | calm(X0) | ~generous(X0) [cnf transformation 42]
92. ~happy(sK1) | wise(X1) [cnf transformation 47]
93. happy(sK1) | wise(X1) [cnf transformation 47]
100. tall(susan) | ~wise(X0) | ~generous(X0) [cnf transformation 53]
110. ~creative(X0) | generous(X0) [cnf transformation 56]
113. generous(X0) | brave(X0) [cnf transformation 58]
114. quiet(X0) | generous(X0) [cnf transformation 58]
123. ~quiet(paul) | kind(paul) [cnf transformation 64]
131. ~calm(susan) [cnf transformation 22]
132. generous(X0) | calm(X0) | ~funny(X0) [duplicate literal removal 84]
134. ~generous(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 88]
159. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
160. ~kind(X0) <- (6) [avatar component clause 159]
162. 7 <=> old(fred) [avatar definition]
164. old(fred) <- (7) [avatar component clause 162]
166. 8 <=> rich(fred) [avatar definition]
167. rich(fred) <- (8) [avatar component clause 166]
168. ~rich(fred) <- (~8) [avatar component clause 166]
169. 6 | 7 | ~8 [avatar split clause 78,166,162,159]
170. 6 | ~7 | 8 [avatar split clause 77,166,162,159]
172. ~generous(X0) | calm(X0) [subsumption resolution 134,79]
173. ~funny(X0) | calm(X0) [subsumption resolution 132,172]
175. 9 <=> ! [X1] : wise(X1) [avatar definition]
176. wise(X1) <- (9) [avatar component clause 175]
178. 10 <=> happy(sK1) [avatar definition]
181. 9 | 10 [avatar split clause 93,178,175]
182. 9 | ~10 [avatar split clause 92,178,175]
184. 11 <=> ! [X0] : (~wise(X0) | ~generous(X0)) [avatar definition]
185. ~generous(X0) | ~wise(X0) <- (11) [avatar component clause 184]
192. 13 <=> tall(susan) [avatar definition]
195. 11 | 13 [avatar split clause 100,192,184]
226. 19 <=> kind(paul) [avatar definition]
227. kind(paul) <- (19) [avatar component clause 226]
230. 20 <=> quiet(paul) [avatar definition]
231. ~quiet(paul) <- (~20) [avatar component clause 230]
234. 19 | ~20 [avatar split clause 123,230,226]
259. generous(paul) <- (~20) [resolution 114,231]
271. calm(X0) | brave(X0) [resolution 172,113]
274. calm(X0) | patient(X0) [resolution 173,80]
278. ~wise(paul) <- (11, ~20) [resolution 185,259]
282. $false <- (9, 11, ~20) [subsumption resolution 278,176]
283. ~9 | ~11 | 20 [avatar contradiction clause 282]
303. 27 <=> patient(susan) [avatar definition]
307. 28 <=> brave(susan) [avatar definition]
309. brave(susan) <- (28) [avatar component clause 307]
339. ~rich(X0) | creative(X0) | ~old(X0) <- (9) [resolution 71,176]
341. creative(X0) | old(X0) | rich(X0) <- (9) [resolution 72,176]
342. brave(susan) [resolution 271,131]
345. 28 [avatar split clause 342,307]
358. ~patient(susan) | ~tall(susan) <- (28) [resolution 309,70]
415. patient(susan) [resolution 274,131]
429. ~13 | ~27 | ~28 [avatar split clause 358,307,303,192]
431. 27 [avatar split clause 415,303]
432. ~generous(X0) <- (9, 11) [subsumption resolution 185,176]
466. old(X3) | rich(X3) | generous(X3) <- (9) [resolution 341,110]
478. rich(X3) | old(X3) <- (9, 11) [subsumption resolution 466,432]
500. old(fred) <- (~8, 9, 11) [resolution 478,168]
504. 7 | 8 | ~9 | ~11 [avatar split clause 500,184,175,166,162]
507. $false <- (6, 19) [resolution 160,227]
508. ~6 | ~19 [avatar contradiction clause 507]
511. creative(fred) | ~old(fred) <- (8, 9) [resolution 167,339]
512. creative(fred) <- (7, 8, 9) [subsumption resolution 511,164]
517. generous(fred) <- (7, 8, 9) [resolution 512,110]
519. $false <- (7, 8, 9, 11) [subsumption resolution 517,432]
520. ~7 | ~8 | ~9 | ~11 [avatar contradiction clause 519]
521. $false [avatar sat refutation 169,170,181,182,195,234,283,345,429,431,504,508,520]
% SZS output end Proof for 1662128935610947260282932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then someone is either not patient or generous and vice versa.
If someone is either not creative or not rich then someone is happy and vice versa.
If alice is not strong then someone is either not generous or calm and vice versa.
If someone is either not wise or not patient then someone is not calm and vice versa.
If someone is either creative or humble then mary is both kind and funny.
Everyone who is brave or not patient is both not strong and not humble.
Everyone who is not creative is both not old and humble.
Everyone who is not generous is both humble and happy.
Everyone who is both not curious and not rich is curious or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Everyone who is both not quiet and not wise is creative.
If someone is not brave then someone is either tall or old.
Everyone who is either kind or curious is both generous and curious.
Everyone who is not creative or happy is either funny or not patient and vice versa.
Mary is tall.
Someone is both creative and not old.
John is either old or humble.
Paul is not brave or not funny.
Someone is either wise or generous.
John is not tall. | John is rich. | contradiction | ((?[X]:(kind(X)))<=>(?[X]:((~patient(X)<~>generous(X)))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:(happy(X))))&
((~strong(alice))<=>(?[X]:((~generous(X)<~>calm(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((creative(X)<~>humble(X))))=>((kind(mary)&funny(mary))))&
(![X]:((brave(X)|~patient(X))=>(~strong(X)&~humble(X))))&
(![X]:(~creative(X)=>(~old(X)&humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|funny(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
(![X]:((~quiet(X)&~wise(X))=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((kind(X)<~>curious(X))=>(generous(X)&curious(X))))&
(![X]:((~creative(X)|happy(X))<=>(funny(X)<~>~patient(X))))&
(tall(mary))&
(?[X]:((creative(X)&~old(X))))&
((old(john)<~>humble(john)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((wise(X)<~>generous(X))))&
(~tall(john)) | rich(john) | [
"p0",
"p4",
"p5",
"p6",
"p7",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4962504437110033829344442
% SZS output start Proof for 4962504437110033829344442
1. ? [X0] : kind(X0) <=> ? [X0] : (~patient(X0) <~> generous(X0)) [input p0]
5. ? [X0] : (creative(X0) <~> humble(X0)) => (funny(mary) & kind(mary)) [input p4]
6. ! [X0] : ((~patient(X0) | brave(X0)) => (~humble(X0) & ~strong(X0))) [input p5]
7. ! [X0] : (~creative(X0) => (humble(X0) & ~old(X0))) [input p6]
8. ! [X0] : (~generous(X0) => (happy(X0) & humble(X0))) [input p7]
9. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) | curious(X0))) [input p8]
14. ! [X0] : ((kind(X0) <~> curious(X0)) => (curious(X0) & generous(X0))) [input p13]
15. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (funny(X0) <~> ~patient(X0))) [input p14]
22. rich(john) [input hypothesis]
23. ? [X0] : kind(X0) <=> ? [X1] : (~patient(X1) <~> generous(X1)) [rectify 1]
28. (funny(mary) & kind(mary)) | ! [X0] : (creative(X0) <=> humble(X0)) [ennf transformation 5]
29. ! [X0] : ((~humble(X0) & ~strong(X0)) | (patient(X0) & ~brave(X0))) [ennf transformation 6]
30. ! [X0] : ((humble(X0) & ~old(X0)) | creative(X0)) [ennf transformation 7]
31. ! [X0] : ((happy(X0) & humble(X0)) | generous(X0)) [ennf transformation 8]
35. ! [X0] : ((curious(X0) & generous(X0)) | (kind(X0) <=> curious(X0))) [ennf transformation 14]
36. (? [X0] : kind(X0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (? [X1] : ((~generous(X1) | patient(X1)) & (generous(X1) | ~patient(X1))) | ! [X0] : ~kind(X0)) [nnf transformation 23]
37. (? [X0] : kind(X0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (? [X2] : ((~generous(X2) | patient(X2)) & (generous(X2) | ~patient(X2))) | ! [X3] : ~kind(X3)) [rectify 36]
38. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
39. ? [X2] : ((~generous(X2) | patient(X2)) & (generous(X2) | ~patient(X2))) => ((~generous(sK1) | patient(sK1)) & (generous(sK1) | ~patient(sK1))) [choice axiom]
40. (kind(sK0) | ! [X1] : ((~patient(X1) | ~generous(X1)) & (generous(X1) | patient(X1)))) & (((~generous(sK1) | patient(sK1)) & (generous(sK1) | ~patient(sK1))) | ! [X3] : ~kind(X3)) [skolemisation 37,39,38]
55. (funny(mary) & kind(mary)) | ! [X0] : ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0))) [nnf transformation 28]
56. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 9]
57. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 56]
62. ! [X0] : ((curious(X0) & generous(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) [nnf transformation 35]
63. ! [X0] : (((happy(X0) | ~creative(X0)) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~happy(X0) & creative(X0)))) [nnf transformation 15]
64. ! [X0] : ((happy(X0) | ~creative(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0)))) & (((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | (~happy(X0) & creative(X0)))) [flattening 63]
74. kind(sK0) | ~patient(X1) | ~generous(X1) [cnf transformation 40]
87. kind(mary) | humble(X0) | ~creative(X0) [cnf transformation 55]
88. kind(mary) | creative(X0) | ~humble(X0) [cnf transformation 55]
94. ~humble(X0) | patient(X0) [cnf transformation 29]
96. humble(X0) | creative(X0) [cnf transformation 30]
98. happy(X0) | generous(X0) [cnf transformation 31]
100. ~curious(X0) | ~curious(X0) [cnf transformation 57]
103. ~funny(X0) | ~rich(X0) [cnf transformation 57]
111. curious(X0) | curious(X0) | ~kind(X0) [cnf transformation 62]
114. ~happy(X0) | funny(X0) | ~patient(X0) [cnf transformation 64]
128. rich(john) [cnf transformation 22]
129. curious(X0) | ~kind(X0) [duplicate literal removal 111]
131. ~curious(X0) [duplicate literal removal 100]
133. 1 <=> ! [X1] : (~patient(X1) | ~generous(X1)) [avatar definition]
134. ~generous(X1) | ~patient(X1) <- (1) [avatar component clause 133]
136. 2 <=> kind(sK0) [avatar definition]
138. kind(sK0) <- (2) [avatar component clause 136]
139. 1 | 2 [avatar split clause 74,136,133]
145. 4 <=> ! [X3] : ~kind(X3) [avatar definition]
146. ~kind(X3) <- (4) [avatar component clause 145]
230. 24 <=> ! [X0] : (creative(X0) | ~humble(X0)) [avatar definition]
231. creative(X0) | ~humble(X0) <- (24) [avatar component clause 230]
238. 26 <=> ! [X0] : (humble(X0) | ~creative(X0)) [avatar definition]
239. humble(X0) | ~creative(X0) <- (26) [avatar component clause 238]
242. 27 <=> kind(mary) [avatar definition]
244. kind(mary) <- (27) [avatar component clause 242]
245. 24 | 27 [avatar split clause 88,242,230]
246. 26 | 27 [avatar split clause 87,242,238]
261. ~kind(X0) [subsumption resolution 129,131]
262. 4 [avatar split clause 261,145]
269. 32 <=> humble(john) [avatar definition]
270. humble(john) <- (32) [avatar component clause 269]
271. ~humble(john) <- (~32) [avatar component clause 269]
293. humble(X0) <- (26) [subsumption resolution 239,96]
297. $false <- (2, 4) [subsumption resolution 138,146]
298. ~2 | ~4 [avatar contradiction clause 297]
305. $false <- (26, ~32) [resolution 293,271]
306. ~26 | 32 [avatar contradiction clause 305]
307. creative(X0) <- (24) [subsumption resolution 231,96]
308. $false <- (4, 27) [subsumption resolution 244,146]
309. ~4 | ~27 [avatar contradiction clause 308]
310. humble(X0) <- (24, 26) [subsumption resolution 239,307]
318. patient(john) <- (32) [resolution 94,270]
319. patient(X0) <- (24, 26) [resolution 94,310]
348. funny(X0) | ~patient(X0) | generous(X0) [resolution 114,98]
350. funny(X0) | generous(X0) <- (24, 26) [subsumption resolution 348,319]
374. ~rich(X3) | generous(X3) <- (24, 26) [resolution 350,103]
388. generous(john) <- (24, 26) [resolution 374,128]
389. ~patient(john) <- (1, 24, 26) [resolution 388,134]
390. $false <- (1, 24, 26, 32) [subsumption resolution 389,318]
391. ~1 | ~24 | ~26 | ~32 [avatar contradiction clause 390]
392. $false [avatar sat refutation 139,245,246,262,298,306,309,391]
% SZS output end Proof for 4962504437110033829344442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or funny is curious or funny and vice versa.
Everyone who is tall or humble is either not happy or not brave and vice versa.
If someone is either funny or not creative then someone is both old and rich and vice versa.
Everyone who is kind or quiet is either generous or not strong and vice versa.
If someone is calm or not wise then someone is both not quiet and not brave.
Everyone who is not tall or not kind is not old and vice versa.
If someone is either not funny or not brave then someone is both rich and not strong and vice versa.
Everyone who is not happy is both not wise and humble and vice versa.
If paul is not patient or brave then someone is quiet and vice versa.
Everyone who is calm or not humble is not happy or not curious and vice versa.
Everyone who is not old or not quiet is not brave and vice versa.
Everyone who is old is patient and vice versa.
Everyone who is not humble is brave and vice versa.
If someone is either not calm or happy then someone is not old or not wise.
Everyone who is not kind is not humble and vice versa.
If someone is both not brave and not old then someone is both not tall and not generous and vice versa.
Someone is curious or tall.
Someone is both happy and humble.
Someone is curious or not quiet.
Alice is both old and not calm.
Susan is calm or not wise.
John is not generous or tall. | Alice is not generous. | neutral | (![X]:((~kind(X)<~>funny(X))<=>(curious(X)|funny(X))))&
(![X]:((tall(X)|humble(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:((old(X)&rich(X)))))&
(![X]:((kind(X)|quiet(X))<=>(generous(X)<~>~strong(X))))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:((~tall(X)|~kind(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>~brave(X))))<=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:(~happy(X)<=>(~wise(X)&humble(X))))&
(((~patient(paul)|brave(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:((happy(X)&humble(X))))&
(?[X]:((curious(X)|~quiet(X))))&
((old(alice)&~calm(alice)))&
((calm(susan)|~wise(susan)))&
((~generous(john)|tall(john))) | ~generous(alice) | [] | null | 0 |
If mary is curious or strong then paul is both not quiet and not brave and vice versa. Everyone who is not rich is humble or generous and vice versa. Everyone who is both old and humble is not quiet. Everyone who is both not calm and not patient is not humble or not quiet and vice versa. Everyone who is wise is not old. Everyone who is humble is not strong or not creative and vice versa. Everyone who is both not funny and rich is either quiet or old. If alice is either tall or calm then someone is funny or not creative. If mary is either not old or curious then john is patient and vice versa. Everyone who is wise or not generous is either patient or not wise. If paul is not curious or not humble then someone is either curious or quiet and vice versa. Everyone who is both not kind and not brave is quiet or generous and vice versa. Everyone who is either funny or not generous is not patient or strong. If john is kind then someone is not curious or strong and vice versa. Everyone who is not creative or tall is either brave or not curious and vice versa. If someone is not creative then mary is not rich. John is not calm. Paul is either not wise or quiet. Someone is tall. Mary is not brave or not generous. Someone is either not generous or generous. Someone is either not tall or not humble. Alice is both not funny and not quiet. | Paul is funny. | neutral | (((curious(mary)|strong(mary)))<=>((~quiet(paul)&~brave(paul))))&
(![X]:(~rich(X)<=>(humble(X)|generous(X))))&
(![X]:((old(X)&humble(X))=>~quiet(X)))&
(![X]:((~calm(X)&~patient(X))<=>(~humble(X)|~quiet(X))))&
(![X]:(wise(X)=>~old(X)))&
(![X]:(humble(X)<=>(~strong(X)|~creative(X))))&
(![X]:((~funny(X)&rich(X))=>(quiet(X)<~>old(X))))&
(((tall(alice)<~>calm(alice)))=>(?[X]:((funny(X)|~creative(X)))))&
(((~old(mary)<~>curious(mary)))<=>(patient(john)))&
(![X]:((wise(X)|~generous(X))=>(patient(X)<~>~wise(X))))&
(((~curious(paul)|~humble(paul)))<=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:((~kind(X)&~brave(X))<=>(quiet(X)|generous(X))))&
(![X]:((funny(X)<~>~generous(X))=>(~patient(X)|strong(X))))&
((kind(john))<=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~creative(X)|tall(X))<=>(brave(X)<~>~curious(X))))&
((?[X]:(~creative(X)))=>(~rich(mary)))&
(~calm(john))&
((~wise(paul)<~>quiet(paul)))&
(?[X]:(tall(X)))&
((~brave(mary)|~generous(mary)))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((~tall(X)<~>~humble(X))))&
((~funny(alice)&~quiet(alice))) | funny(paul) | [] | null | 0 |
Everyone who is both creative and not kind is either not kind or old and vice versa.
If alice is both old and not kind then john is strong or brave.
Everyone who is both brave and curious is either patient or generous and vice versa.
If susan is generous then lucy is not kind or wise and vice versa.
If lucy is either quiet or rich then someone is brave or not humble.
Everyone who is kind or rich is either patient or brave and vice versa.
If fred is not brave then alice is both strong and tall.
Everyone who is either not curious or not funny is both patient and not wise and vice versa.
Everyone who is not creative or creative is both not happy and calm and vice versa.
Everyone who is not brave or strong is strong.
If lucy is not wise then fred is both creative and not patient.
Everyone who is both not quiet and not calm is both wise and creative.
Everyone who is both curious and not patient is happy or quiet.
If fred is both calm and not calm then someone is not rich and vice versa.
If someone is both not humble and creative then someone is either old or kind and vice versa.
If alice is either not rich or not quiet then paul is either calm or humble.
Someone is either strong or generous.
Paul is both not wise and brave.
Mary is not funny or not humble.
Someone is brave or not generous.
Susan is both not tall and quiet.
Paul is both humble and funny.
Someone is patient. | John is not happy. | entailment | (![X]:((creative(X)&~kind(X))<=>(~kind(X)<~>old(X))))&
(((old(alice)&~kind(alice)))=>((strong(john)|brave(john))))&
(![X]:((brave(X)&curious(X))<=>(patient(X)<~>generous(X))))&
((generous(susan))<=>((~kind(lucy)|wise(lucy))))&
(((quiet(lucy)<~>rich(lucy)))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((kind(X)|rich(X))<=>(patient(X)<~>brave(X))))&
((~brave(fred))=>((strong(alice)&tall(alice))))&
(![X]:((~curious(X)<~>~funny(X))<=>(patient(X)&~wise(X))))&
(![X]:((~creative(X)|creative(X))<=>(~happy(X)&calm(X))))&
(![X]:((~brave(X)|strong(X))=>strong(X)))&
((~wise(lucy))=>((creative(fred)&~patient(fred))))&
(![X]:((~quiet(X)&~calm(X))=>(wise(X)&creative(X))))&
(![X]:((curious(X)&~patient(X))=>(happy(X)|quiet(X))))&
(((calm(fred)&~calm(fred)))<=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((old(X)<~>kind(X)))))&
(((~rich(alice)<~>~quiet(alice)))=>((calm(paul)<~>humble(paul))))&
(?[X]:((strong(X)<~>generous(X))))&
((~wise(paul)&brave(paul)))&
((~funny(mary)|~humble(mary)))&
(?[X]:((brave(X)|~generous(X))))&
((~tall(susan)&quiet(susan)))&
((humble(paul)&funny(paul)))&
(?[X]:(patient(X))) | ~happy(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5678471380453835560262682
% SZS output start Proof for 5678471380453835560262682
9. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (calm(X0) & ~happy(X0))) [input p8]
24. happy(john) [input hypothesis]
50. ! [X0] : (((creative(X0) | ~creative(X0)) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 9]
51. ! [X0] : ((creative(X0) | ~creative(X0) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | (~creative(X0) & creative(X0)))) [flattening 50]
102. ~happy(X0) | creative(X0) [cnf transformation 51]
103. ~happy(X0) | ~creative(X0) [cnf transformation 51]
138. happy(john) [cnf transformation 24]
204. ~happy(X0) [subsumption resolution 102,103]
291. $false [subsumption resolution 138,204]
% SZS output end Proof for 5678471380453835560262682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or old is strong or calm and vice versa.
Everyone who is not strong or curious is both not tall and not brave and vice versa.
Everyone who is both not tall and creative is either not patient or not funny and vice versa.
Everyone who is both funny and not creative is either not old or quiet and vice versa.
If mary is not rich or humble then someone is both not old and tall and vice versa.
If someone is kind then paul is creative.
Everyone who is happy is patient or calm.
Everyone who is both not creative and not generous is both not humble and not wise and vice versa.
Everyone who is either curious or happy is both generous and not funny.
Everyone who is old or funny is not creative or curious.
Everyone who is not funny or not kind is either tall or funny and vice versa.
If someone is not brave then lucy is either not rich or not old and vice versa.
Everyone who is not kind is not old.
If lucy is not humble then paul is either rich or not curious and vice versa.
If someone is not humble or generous then someone is either not rich or not wise.
Everyone who is both not rich and wise is happy.
Someone is both not humble and not patient.
Someone is not rich or not curious.
Someone is not tall.
Someone is either happy or not curious.
John is funny.
Lucy is both rich and wise.
Lucy is both humble and not funny. | Paul is not patient. | entailment | (![X]:((~humble(X)<~>old(X))<=>(strong(X)|calm(X))))&
(![X]:((~strong(X)|curious(X))<=>(~tall(X)&~brave(X))))&
(![X]:((~tall(X)&creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((funny(X)&~creative(X))<=>(~old(X)<~>quiet(X))))&
(((~rich(mary)|humble(mary)))<=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(kind(X)))=>(creative(paul)))&
(![X]:(happy(X)=>(patient(X)|calm(X))))&
(![X]:((~creative(X)&~generous(X))<=>(~humble(X)&~wise(X))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~funny(X))))&
(![X]:((old(X)|funny(X))=>(~creative(X)|curious(X))))&
(![X]:((~funny(X)|~kind(X))<=>(tall(X)<~>funny(X))))&
((?[X]:(~brave(X)))<=>((~rich(lucy)<~>~old(lucy))))&
(![X]:(~kind(X)=>~old(X)))&
((~humble(lucy))<=>((rich(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|generous(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~rich(X)&wise(X))=>happy(X)))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~rich(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(funny(john))&
((rich(lucy)&wise(lucy)))&
((humble(lucy)&~funny(lucy))) | ~patient(paul) | [
"p0",
"p1",
"p2",
"p5",
"p9",
"p10",
"p11",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4503761443785148275797296
% SZS output start Proof for 4503761443785148275797296
1. ! [X0] : ((~humble(X0) <~> old(X0)) <=> (calm(X0) | strong(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (~brave(X0) & ~tall(X0))) [input p1]
3. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~funny(X0))) [input p2]
6. ? [X0] : kind(X0) => creative(paul) [input p5]
10. ! [X0] : ((funny(X0) | old(X0)) => (curious(X0) | ~creative(X0))) [input p9]
11. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (tall(X0) <~> funny(X0))) [input p10]
12. ? [X0] : ~brave(X0) <=> (~rich(lucy) <~> ~old(lucy)) [input p11]
13. ! [X0] : (~kind(X0) => ~old(X0)) [input p12]
22. wise(lucy) & rich(lucy) [input p21]
23. ~funny(lucy) & humble(lucy) [input p22]
24. patient(paul) [input hypothesis]
26. creative(paul) | ! [X0] : ~kind(X0) [ennf transformation 6]
30. ! [X0] : ((curious(X0) | ~creative(X0)) | (~funny(X0) & ~old(X0))) [ennf transformation 10]
31. ! [X0] : (curious(X0) | ~creative(X0) | (~funny(X0) & ~old(X0))) [flattening 30]
32. ! [X0] : (~old(X0) | kind(X0)) [ennf transformation 13]
36. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & ((calm(X0) | strong(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) | (~calm(X0) & ~strong(X0))) & (calm(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0))))) [flattening 36]
38. ! [X0] : (((curious(X0) | ~strong(X0)) | (brave(X0) | tall(X0))) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~strong(X0) | brave(X0) | tall(X0)) & ((~brave(X0) & ~tall(X0)) | (~curious(X0) & strong(X0)))) [flattening 38]
40. ! [X0] : (((creative(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~creative(X0) | tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((creative(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0)))) & (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~creative(X0) | tall(X0))) [flattening 40]
52. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 11]
53. ! [X0] : ((~kind(X0) | ~funny(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (kind(X0) & funny(X0)))) [flattening 52]
54. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X0] : brave(X0)) [nnf transformation 12]
55. (? [X0] : ~brave(X0) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [rectify 54]
56. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
57. (~brave(sK1) | ((~rich(lucy) | old(lucy)) & (~old(lucy) | rich(lucy)))) & (((old(lucy) | rich(lucy)) & (~old(lucy) | ~rich(lucy))) | ! [X1] : brave(X1)) [skolemisation 55,56]
74. ~strong(X0) | ~humble(X0) | old(X0) [cnf transformation 37]
78. ~tall(X0) | strong(X0) [cnf transformation 39]
81. ~brave(X0) | ~curious(X0) [cnf transformation 39]
86. ~patient(X0) | ~tall(X0) | funny(X0) [cnf transformation 41]
100. creative(paul) | ~kind(X0) [cnf transformation 26]
111. ~funny(X0) | ~creative(X0) | curious(X0) [cnf transformation 31]
112. funny(X0) | tall(X0) | funny(X0) [cnf transformation 53]
118. ~old(lucy) | ~rich(lucy) | brave(X1) [cnf transformation 57]
122. ~old(X0) | kind(X0) [cnf transformation 32]
139. rich(lucy) [cnf transformation 22]
141. humble(lucy) [cnf transformation 23]
142. ~funny(lucy) [cnf transformation 23]
143. patient(paul) [cnf transformation 24]
144. funny(X0) | tall(X0) [duplicate literal removal 112]
171. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
172. ~kind(X0) <- (6) [avatar component clause 171]
174. 7 <=> creative(paul) [avatar definition]
176. creative(paul) <- (7) [avatar component clause 174]
177. 6 | 7 [avatar split clause 100,174,171]
179. 8 <=> old(lucy) [avatar definition]
181. old(lucy) <- (8) [avatar component clause 179]
183. 9 <=> rich(lucy) [avatar definition]
193. 11 <=> ! [X1] : brave(X1) [avatar definition]
194. brave(X1) <- (11) [avatar component clause 193]
196. 11 | ~9 | ~8 [avatar split clause 118,179,183,193]
206. 14 <=> humble(lucy) [avatar definition]
207. humble(lucy) <- (14) [avatar component clause 206]
250. 9 [avatar split clause 139,183]
251. 14 [avatar split clause 141,206]
254. tall(lucy) [resolution 144,142]
258. strong(lucy) [resolution 254,78]
261. ~humble(lucy) | old(lucy) [resolution 258,74]
262. old(lucy) <- (14) [subsumption resolution 261,207]
265. 8 | ~14 [avatar split clause 262,206,179]
266. kind(lucy) <- (8) [resolution 181,122]
267. $false <- (6, 8) [subsumption resolution 266,172]
268. ~6 | ~8 [avatar contradiction clause 267]
270. ~curious(X0) <- (11) [resolution 194,81]
288. ~tall(paul) | funny(paul) [resolution 86,143]
289. funny(paul) [subsumption resolution 288,144]
373. ~creative(paul) | curious(paul) [resolution 111,289]
377. curious(paul) <- (7) [subsumption resolution 373,176]
378. $false <- (7, 11) [subsumption resolution 377,270]
379. ~7 | ~11 [avatar contradiction clause 378]
380. $false [avatar sat refutation 177,196,250,251,265,268,379]
% SZS output end Proof for 4503761443785148275797296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is generous or not kind then lucy is not quiet and vice versa.
Everyone who is either not quiet or not brave is not curious and vice versa.
If someone is not wise or not patient then someone is both not funny and not kind and vice versa.
If someone is either not curious or old then someone is both quiet and not creative.
Everyone who is either not creative or old is not creative and vice versa.
If someone is either humble or old then alice is not tall or not old.
Everyone who is either rich or not wise is funny and vice versa.
If someone is either not happy or not tall then someone is either not old or not generous and vice versa.
If someone is either humble or not quiet then someone is not generous or curious.
Everyone who is either not creative or happy is both happy and tall and vice versa.
Everyone who is both not happy and not creative is not kind or not tall.
If someone is old then susan is funny and vice versa.
If someone is either not rich or tall then paul is not funny or not humble.
Everyone who is generous or not old is creative and vice versa.
Everyone who is rich or tall is not rich.
Everyone who is both not creative and not funny is either not tall or not curious.
Fred is strong or not quiet.
Someone is not creative or not funny.
Mary is not funny.
Mary is either not curious or not calm.
Someone is humble.
Someone is not strong or calm. | Lucy is not happy. | neutral | (((generous(john)|~kind(john)))<=>(~quiet(lucy)))&
(![X]:((~quiet(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~wise(X)|~patient(X))))<=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~curious(X)<~>old(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~creative(X)<~>old(X))<=>~creative(X)))&
((?[X]:((humble(X)<~>old(X))))=>((~tall(alice)|~old(alice))))&
(![X]:((rich(X)<~>~wise(X))<=>funny(X)))&
((?[X]:((~happy(X)<~>~tall(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~creative(X)<~>happy(X))<=>(happy(X)&tall(X))))&
(![X]:((~happy(X)&~creative(X))=>(~kind(X)|~tall(X))))&
((?[X]:(old(X)))<=>(funny(susan)))&
((?[X]:((~rich(X)<~>tall(X))))=>((~funny(paul)|~humble(paul))))&
(![X]:((generous(X)|~old(X))<=>creative(X)))&
(![X]:((rich(X)|tall(X))=>~rich(X)))&
(![X]:((~creative(X)&~funny(X))=>(~tall(X)<~>~curious(X))))&
((strong(fred)|~quiet(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(~funny(mary))&
((~curious(mary)<~>~calm(mary)))&
(?[X]:(humble(X)))&
(?[X]:((~strong(X)|calm(X)))) | ~happy(lucy) | [] | null | 0 |
If someone is old then paul is both not old and creative. If someone is either not funny or patient then paul is not funny. If someone is creative or not curious then paul is not creative or not tall. Everyone who is not tall is quiet or not calm. If someone is not strong or humble then someone is happy or patient. If someone is both not humble and not funny then paul is either not quiet or not patient and vice versa. If someone is humble or not kind then mary is either not strong or patient and vice versa. If mary is either not happy or wise then someone is both not humble and happy. Everyone who is either humble or kind is either not generous or quiet and vice versa. If susan is not humble or happy then someone is both rich and not quiet. Everyone who is not tall is both humble and funny and vice versa. Everyone who is either kind or generous is not old. Everyone who is not tall is either kind or not humble and vice versa. Everyone who is either patient or wise is curious. Everyone who is both not quiet and not tall is old or calm and vice versa. If susan is rich then someone is happy or not curious and vice versa. Someone is not rich. Paul is either not strong or not tall. Alice is not happy or not strong. Someone is both curious and old. Someone is not curious. Alice is either quiet or not quiet. Alice is either not tall or brave. Someone is not quiet or creative. | Paul is patient. | contradiction | ((?[X]:(old(X)))=>((~old(paul)&creative(paul))))&
((?[X]:((~funny(X)<~>patient(X))))=>(~funny(paul)))&
((?[X]:((creative(X)|~curious(X))))=>((~creative(paul)|~tall(paul))))&
(![X]:(~tall(X)=>(quiet(X)|~calm(X))))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~humble(X)&~funny(X))))<=>((~quiet(paul)<~>~patient(paul))))&
((?[X]:((humble(X)|~kind(X))))<=>((~strong(mary)<~>patient(mary))))&
(((~happy(mary)<~>wise(mary)))=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:((humble(X)<~>kind(X))<=>(~generous(X)<~>quiet(X))))&
(((~humble(susan)|happy(susan)))=>(?[X]:((rich(X)&~quiet(X)))))&
(![X]:(~tall(X)<=>(humble(X)&funny(X))))&
(![X]:((kind(X)<~>generous(X))=>~old(X)))&
(![X]:(~tall(X)<=>(kind(X)<~>~humble(X))))&
(![X]:((patient(X)<~>wise(X))=>curious(X)))&
(![X]:((~quiet(X)&~tall(X))<=>(old(X)|calm(X))))&
((rich(susan))<=>(?[X]:((happy(X)|~curious(X)))))&
(?[X]:(~rich(X)))&
((~strong(paul)<~>~tall(paul)))&
((~happy(alice)|~strong(alice)))&
(?[X]:((curious(X)&old(X))))&
(?[X]:(~curious(X)))&
((quiet(alice)<~>~quiet(alice)))&
((~tall(alice)<~>brave(alice)))&
(?[X]:((~quiet(X)|creative(X)))) | patient(paul) | [
"p0",
"p1",
"p2",
"p10",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1025270551253241856307545
% SZS output start Proof for 1025270551253241856307545
1. ? [X0] : old(X0) => (creative(paul) & ~old(paul)) [input p0]
2. ? [X0] : (~funny(X0) <~> patient(X0)) => ~funny(paul) [input p1]
3. ? [X0] : (~curious(X0) | creative(X0)) => (~tall(paul) | ~creative(paul)) [input p2]
11. ! [X0] : (~tall(X0) <=> (funny(X0) & humble(X0))) [input p10]
20. ? [X0] : (old(X0) & curious(X0)) [input p19]
21. ? [X0] : ~curious(X0) [input p20]
25. patient(paul) [input hypothesis]
27. (creative(paul) & ~old(paul)) | ! [X0] : ~old(X0) [ennf transformation 1]
28. ~funny(paul) | ! [X0] : (~funny(X0) <=> patient(X0)) [ennf transformation 2]
29. (~tall(paul) | ~creative(paul)) | ! [X0] : (curious(X0) & ~creative(X0)) [ennf transformation 3]
30. ~tall(paul) | ~creative(paul) | ! [X0] : (curious(X0) & ~creative(X0)) [flattening 29]
38. ~funny(paul) | ! [X0] : ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))) [nnf transformation 28]
56. ! [X0] : ((~tall(X0) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | tall(X0))) [nnf transformation 11]
57. ! [X0] : ((~tall(X0) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | tall(X0))) [flattening 56]
70. ? [X0] : (old(X0) & curious(X0)) => (old(sK7) & curious(sK7)) [choice axiom]
71. old(sK7) & curious(sK7) [skolemisation 20,70]
72. ? [X0] : ~curious(X0) => ~curious(sK8) [choice axiom]
73. ~curious(sK8) [skolemisation 21,72]
79. creative(paul) | ~old(X0) [cnf transformation 27]
81. ~funny(paul) | ~funny(X0) | ~patient(X0) [cnf transformation 38]
83. ~tall(paul) | ~creative(paul) | curious(X0) [cnf transformation 30]
116. tall(X0) | funny(X0) [cnf transformation 57]
139. old(sK7) [cnf transformation 71]
140. ~curious(sK8) [cnf transformation 73]
146. patient(paul) [cnf transformation 25]
148. 1 <=> ! [X0] : ~old(X0) [avatar definition]
149. ~old(X0) <- (1) [avatar component clause 148]
151. 2 <=> creative(paul) [avatar definition]
154. 1 | 2 [avatar split clause 79,151,148]
161. 4 <=> ! [X0] : (~funny(X0) | ~patient(X0)) [avatar definition]
162. ~patient(X0) | ~funny(X0) <- (4) [avatar component clause 161]
164. 5 <=> funny(paul) [avatar definition]
167. 4 | ~5 [avatar split clause 81,164,161]
173. 7 <=> ! [X0] : curious(X0) [avatar definition]
174. curious(X0) <- (7) [avatar component clause 173]
176. 8 <=> tall(paul) [avatar definition]
178. ~tall(paul) <- (~8) [avatar component clause 176]
179. 7 | ~2 | ~8 [avatar split clause 83,176,151,173]
201. 14 <=> patient(paul) [avatar definition]
203. patient(paul) <- (14) [avatar component clause 201]
345. 14 [avatar split clause 146,201]
348. $false <- (7) [resolution 174,140]
349. ~7 [avatar contradiction clause 348]
352. funny(paul) <- (~8) [resolution 116,178]
356. 5 | 8 [avatar split clause 352,176,164]
360. ~funny(paul) <- (4, 14) [resolution 162,203]
363. ~5 | ~4 | ~14 [avatar split clause 360,201,161,164]
364. $false <- (1) [resolution 149,139]
365. ~1 [avatar contradiction clause 364]
366. $false [avatar sat refutation 154,167,179,345,349,356,363,365]
% SZS output end Proof for 1025270551253241856307545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or not quiet is both not tall and old and vice versa.
Everyone who is both rich and not quiet is tall or not happy and vice versa.
Everyone who is not creative is both not creative and patient.
If mary is not quiet then alice is not tall.
If someone is either rich or calm then someone is either not humble or funny.
Everyone who is both not generous and not happy is both patient and strong and vice versa.
If someone is creative then someone is wise or old.
Everyone who is not patient or not generous is humble or patient and vice versa.
If susan is calm or not curious then john is both not humble and creative.
If someone is not quiet or tall then lucy is either not quiet or not funny and vice versa.
Everyone who is generous is both not humble and not tall.
If susan is old then john is either old or not calm.
Everyone who is quiet or wise is not kind and vice versa.
If someone is either not rich or not curious then someone is both generous and brave.
If mary is either not happy or creative then lucy is patient.
Everyone who is funny or not quiet is not patient and vice versa.
Someone is not humble or not strong.
Lucy is not quiet or funny.
Lucy is strong.
Someone is either not wise or curious.
Someone is both not kind and not tall.
Someone is both creative and not patient.
John is both not strong and not funny. | Susan is happy. | entailment | (![X]:((brave(X)<~>~quiet(X))<=>(~tall(X)&old(X))))&
(![X]:((rich(X)&~quiet(X))<=>(tall(X)|~happy(X))))&
(![X]:(~creative(X)=>(~creative(X)&patient(X))))&
((~quiet(mary))=>(~tall(alice)))&
((?[X]:((rich(X)<~>calm(X))))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~generous(X)&~happy(X))<=>(patient(X)&strong(X))))&
((?[X]:(creative(X)))=>(?[X]:((wise(X)|old(X)))))&
(![X]:((~patient(X)|~generous(X))<=>(humble(X)|patient(X))))&
(((calm(susan)|~curious(susan)))=>((~humble(john)&creative(john))))&
((?[X]:((~quiet(X)|tall(X))))<=>((~quiet(lucy)<~>~funny(lucy))))&
(![X]:(generous(X)=>(~humble(X)&~tall(X))))&
((old(susan))=>((old(john)<~>~calm(john))))&
(![X]:((quiet(X)|wise(X))<=>~kind(X)))&
((?[X]:((~rich(X)<~>~curious(X))))=>(?[X]:((generous(X)&brave(X)))))&
(((~happy(mary)<~>creative(mary)))=>(patient(lucy)))&
(![X]:((funny(X)|~quiet(X))<=>~patient(X)))&
(?[X]:((~humble(X)|~strong(X))))&
((~quiet(lucy)|funny(lucy)))&
(strong(lucy))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((creative(X)&~patient(X))))&
((~strong(john)&~funny(john))) | happy(susan) | [
"p1",
"p5",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7016104958646984523142211
% SZS output start Proof for 7016104958646984523142211
2. ! [X0] : ((~quiet(X0) & rich(X0)) <=> (~happy(X0) | tall(X0))) [input p1]
6. ! [X0] : ((~happy(X0) & ~generous(X0)) <=> (strong(X0) & patient(X0))) [input p5]
8. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (patient(X0) | humble(X0))) [input p7]
11. ! [X0] : (generous(X0) => (~tall(X0) & ~humble(X0))) [input p10]
16. ! [X0] : ((~quiet(X0) | funny(X0)) <=> ~patient(X0)) [input p15]
24. ~happy(susan) [input hypothesis]
34. ! [X0] : ((~tall(X0) & ~humble(X0)) | ~generous(X0)) [ennf transformation 11]
42. ! [X0] : (((~quiet(X0) & rich(X0)) | (happy(X0) & ~tall(X0))) & ((~happy(X0) | tall(X0)) | (quiet(X0) | ~rich(X0)))) [nnf transformation 2]
43. ! [X0] : (((~quiet(X0) & rich(X0)) | (happy(X0) & ~tall(X0))) & (~happy(X0) | tall(X0) | quiet(X0) | ~rich(X0))) [flattening 42]
48. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~strong(X0) | ~patient(X0))) & ((strong(X0) & patient(X0)) | (happy(X0) | generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((~happy(X0) & ~generous(X0)) | ~strong(X0) | ~patient(X0)) & ((strong(X0) & patient(X0)) | happy(X0) | generous(X0))) [flattening 48]
53. ! [X0] : (((~generous(X0) | ~patient(X0)) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 8]
54. ! [X0] : ((~generous(X0) | ~patient(X0) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | (generous(X0) & patient(X0)))) [flattening 53]
65. ! [X0] : (((~quiet(X0) | funny(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~funny(X0)))) [nnf transformation 16]
66. ! [X0] : ((~quiet(X0) | funny(X0) | patient(X0)) & (~patient(X0) | (quiet(X0) & ~funny(X0)))) [flattening 65]
86. ~quiet(X0) | happy(X0) [cnf transformation 43]
94. generous(X0) | happy(X0) | patient(X0) [cnf transformation 49]
99. patient(X0) | humble(X0) | patient(X0) [cnf transformation 54]
113. ~generous(X0) | ~humble(X0) [cnf transformation 34]
125. ~patient(X0) | quiet(X0) [cnf transformation 66]
138. ~happy(susan) [cnf transformation 24]
139. humble(X0) | patient(X0) [duplicate literal removal 99]
353. happy(X2) | patient(X2) | ~humble(X2) [resolution 94,113]
354. patient(X2) | happy(X2) [subsumption resolution 353,139]
427. happy(X0) | quiet(X0) [resolution 354,125]
428. happy(X0) [subsumption resolution 427,86]
454. $false [resolution 428,138]
% SZS output end Proof for 7016104958646984523142211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then fred is both not rich and brave. If alice is either not patient or not old then someone is not tall. Everyone who is not rich or old is both kind and tall and vice versa. Everyone who is not wise or generous is wise. If someone is either patient or not tall then someone is both curious and not happy and vice versa. Everyone who is not old or wise is either wise or curious. If paul is creative or calm then paul is either not quiet or tall and vice versa. If lucy is not brave or wise then fred is quiet. If alice is either not rich or wise then someone is both not old and funny. If someone is both tall and patient then paul is not brave or rich. Everyone who is both happy and not strong is both not creative and not wise and vice versa. If alice is not old or tall then someone is not brave or not quiet. Everyone who is kind or not humble is brave or not curious and vice versa. Everyone who is not funny is tall or rich and vice versa. Everyone who is not kind or not generous is creative or not happy and vice versa. Everyone who is not creative is brave or happy. Someone is both not kind and strong. Someone is strong or calm. Someone is either humble or not rich. Someone is kind or not strong. Someone is either not wise or quiet. Someone is not creative or not humble. Someone is not funny. Susan is brave or not calm. | Lucy is wise. | entailment | ((?[X]:(~happy(X)))=>((~rich(fred)&brave(fred))))&
(((~patient(alice)<~>~old(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|old(X))<=>(kind(X)&tall(X))))&
(![X]:((~wise(X)|generous(X))=>wise(X)))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~old(X)|wise(X))=>(wise(X)<~>curious(X))))&
(((creative(paul)|calm(paul)))<=>((~quiet(paul)<~>tall(paul))))&
(((~brave(lucy)|wise(lucy)))=>(quiet(fred)))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((tall(X)&patient(X))))=>((~brave(paul)|rich(paul))))&
(![X]:((happy(X)&~strong(X))<=>(~creative(X)&~wise(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|~curious(X))))&
(![X]:(~funny(X)<=>(tall(X)|rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:(~creative(X)=>(brave(X)|happy(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:(~funny(X)))&
((brave(susan)|~calm(susan))) | wise(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6119436223112089851676750
% SZS output start Proof for 6119436223112089851676750
4. ! [X0] : ((generous(X0) | ~wise(X0)) => wise(X0)) [input p3]
25. ~wise(lucy) [input hypothesis]
29. ! [X0] : (wise(X0) | (~generous(X0) & wise(X0))) [ennf transformation 4]
89. wise(X0) | wise(X0) [cnf transformation 29]
143. ~wise(lucy) [cnf transformation 25]
145. wise(X0) [duplicate literal removal 89]
316. $false [subsumption resolution 143,145]
% SZS output end Proof for 6119436223112089851676750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Mary is wise. | 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))) | wise(mary) | [
"p0",
"p1",
"p2",
"p6",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1433333892182723311724524
% SZS output start Proof for 1433333892182723311724524
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. ~wise(mary) [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]
103. ~rich(mary) | ~happy(X1) [cnf transformation 56]
130. calm(sK6) | wise(sK6) [cnf transformation 72]
140. ~wise(mary) [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]
149. happy(john) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 83,147,144]
169. 7 <=> ! [X1] : ~happy(X1) [avatar definition]
170. ~happy(X1) <- (7) [avatar component clause 169]
188. 11 <=> rich(mary) [avatar definition]
189. ~rich(mary) <- (~11) [avatar component clause 188]
200. 7 | ~11 [avatar split clause 103,188,169]
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]
388. $false <- (1, 26) [subsumption resolution 263,145]
389. ~1 | ~26 [avatar contradiction clause 388]
469. $false <- (2, 7) [resolution 170,149]
470. ~2 | ~7 [avatar contradiction clause 469]
472. tall(mary) <- (~11) [resolution 189,98]
482. wise(mary) | calm(mary) <- (~11) [resolution 472,142]
483. calm(mary) <- (~11) [subsumption resolution 482,140]
588. rich(mary) <- (~11) [resolution 483,80]
589. $false <- (~11) [subsumption resolution 588,189]
590. 11 [avatar contradiction clause 589]
605. ~calm(X1) <- (14) [resolution 203,81]
611. $false <- (14, 27) [resolution 605,267]
612. ~14 | ~27 [avatar contradiction clause 611]
615. $false [avatar sat refutation 150,200,204,270,389,470,590,612]
% SZS output end Proof for 1433333892182723311724524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is not tall and vice versa. Everyone who is either not tall or brave is not calm or not generous. If fred is both wise and kind then someone is both creative and not funny and vice versa. Everyone who is not quiet is not strong or strong. If someone is both not strong and generous then someone is both wise and not old. If lucy is both not quiet and not rich then fred is not funny and vice versa. Everyone who is patient or not generous is both not humble and not curious. If mary is both not strong and creative then fred is happy. Everyone who is either not curious or happy is both generous and not strong and vice versa. Everyone who is happy or not calm is both not tall and not brave. If someone is not creative then someone is calm. Everyone who is brave is curious. Everyone who is funny is quiet or curious. Everyone who is either not happy or not brave is rich and vice versa. Everyone who is quiet or curious is either quiet or generous and vice versa. Everyone who is both not humble and not brave is not kind. Someone is wise or not old. Paul is either not patient or wise. Someone is both humble and not brave. Paul is either not humble or kind. Someone is not calm. Susan is both not curious and old. John is generous. Paul is either not happy or not rich. | Susan is tall. | contradiction | (![X]:(~creative(X)<=>~tall(X)))&
(![X]:((~tall(X)<~>brave(X))=>(~calm(X)|~generous(X))))&
(((wise(fred)&kind(fred)))<=>(?[X]:((creative(X)&~funny(X)))))&
(![X]:(~quiet(X)=>(~strong(X)|strong(X))))&
((?[X]:((~strong(X)&generous(X))))=>(?[X]:((wise(X)&~old(X)))))&
(((~quiet(lucy)&~rich(lucy)))<=>(~funny(fred)))&
(![X]:((patient(X)|~generous(X))=>(~humble(X)&~curious(X))))&
(((~strong(mary)&creative(mary)))=>(happy(fred)))&
(![X]:((~curious(X)<~>happy(X))<=>(generous(X)&~strong(X))))&
(![X]:((happy(X)|~calm(X))=>(~tall(X)&~brave(X))))&
((?[X]:(~creative(X)))=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:(funny(X)=>(quiet(X)|curious(X))))&
(![X]:((~happy(X)<~>~brave(X))<=>rich(X)))&
(![X]:((quiet(X)|curious(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((~humble(X)&~brave(X))=>~kind(X)))&
(?[X]:((wise(X)|~old(X))))&
((~patient(paul)<~>wise(paul)))&
(?[X]:((humble(X)&~brave(X))))&
((~humble(paul)<~>kind(paul)))&
(?[X]:(~calm(X)))&
((~curious(susan)&old(susan)))&
(generous(john))&
((~happy(paul)<~>~rich(paul))) | tall(susan) | [
"p6",
"p8",
"p9",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6787932876160167084542398
% SZS output start Proof for 6787932876160167084542398
7. ! [X0] : ((~generous(X0) | patient(X0)) => (~curious(X0) & ~humble(X0))) [input p6]
9. ! [X0] : ((~curious(X0) <~> happy(X0)) <=> (~strong(X0) & generous(X0))) [input p8]
10. ! [X0] : ((~calm(X0) | happy(X0)) => (~brave(X0) & ~tall(X0))) [input p9]
15. ! [X0] : ((curious(X0) | quiet(X0)) <=> (quiet(X0) <~> generous(X0))) [input p14]
22. old(susan) & ~curious(susan) [input p21]
25. tall(susan) [input hypothesis]
33. ! [X0] : ((~curious(X0) & ~humble(X0)) | (generous(X0) & ~patient(X0))) [ennf transformation 7]
36. ! [X0] : ((~brave(X0) & ~tall(X0)) | (calm(X0) & ~happy(X0))) [ennf transformation 10]
55. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0))))) [flattening 55]
61. ! [X0] : (((curious(X0) | quiet(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) & (((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (~curious(X0) & ~quiet(X0)))) [nnf transformation 15]
62. ! [X0] : ((curious(X0) | quiet(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) & (((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (~curious(X0) & ~quiet(X0)))) [flattening 61]
89. ~curious(X0) | generous(X0) [cnf transformation 33]
91. generous(X0) | happy(X0) | curious(X0) [cnf transformation 56]
97. ~happy(X0) | ~tall(X0) [cnf transformation 36]
110. ~generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 62]
113. curious(X0) | quiet(X0) | quiet(X0) | ~generous(X0) [cnf transformation 62]
123. ~curious(susan) [cnf transformation 22]
128. tall(susan) [cnf transformation 25]
129. ~quiet(X0) | ~generous(X0) [duplicate literal removal 110]
130. ~generous(X0) | quiet(X0) | curious(X0) [duplicate literal removal 113]
196. happy(X0) | generous(X0) [subsumption resolution 91,89]
261. ~tall(X1) | generous(X1) [resolution 196,97]
295. generous(susan) [resolution 261,128]
318. quiet(susan) | curious(susan) [resolution 130,295]
321. quiet(susan) [subsumption resolution 318,123]
432. ~generous(susan) [resolution 321,129]
433. $false [subsumption resolution 432,295]
% SZS output end Proof for 6787932876160167084542398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not patient is rich and vice versa. Everyone who is not wise or not strong is not strong. If someone is rich or kind then paul is not kind or happy. Everyone who is happy is both not calm and humble and vice versa. If someone is not brave then mary is either not happy or tall. If fred is old or not creative then susan is not old. If someone is not generous or not funny then someone is humble and vice versa. Everyone who is either quiet or not generous is strong and vice versa. Everyone who is calm is both not calm and rich and vice versa. If mary is both not happy and not creative then someone is curious or calm and vice versa. If susan is either not generous or curious then someone is quiet or not calm and vice versa. If fred is rich or kind then someone is either wise or funny and vice versa. Everyone who is either not strong or tall is either not brave or humble. Everyone who is not tall is both not happy and creative. Everyone who is kind or not happy is both not funny and funny. If someone is not kind then susan is tall and vice versa. Someone is not creative or rich. Fred is old. Paul is either creative or not patient. Alice is funny. Someone is not generous. Susan is either kind or brave. | Alice is not kind. | entailment | (![X]:((~brave(X)&~patient(X))<=>rich(X)))&
(![X]:((~wise(X)|~strong(X))=>~strong(X)))&
((?[X]:((rich(X)|kind(X))))=>((~kind(paul)|happy(paul))))&
(![X]:(happy(X)<=>(~calm(X)&humble(X))))&
((?[X]:(~brave(X)))=>((~happy(mary)<~>tall(mary))))&
(((old(fred)|~creative(fred)))=>(~old(susan)))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:(humble(X))))&
(![X]:((quiet(X)<~>~generous(X))<=>strong(X)))&
(![X]:(calm(X)<=>(~calm(X)&rich(X))))&
(((~happy(mary)&~creative(mary)))<=>(?[X]:((curious(X)|calm(X)))))&
(((~generous(susan)<~>curious(susan)))<=>(?[X]:((quiet(X)|~calm(X)))))&
(((rich(fred)|kind(fred)))<=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(~brave(X)<~>humble(X))))&
(![X]:(~tall(X)=>(~happy(X)&creative(X))))&
(![X]:((kind(X)|~happy(X))=>(~funny(X)&funny(X))))&
((?[X]:(~kind(X)))<=>(tall(susan)))&
(?[X]:((~creative(X)|rich(X))))&
(old(fred))&
((creative(paul)<~>~patient(paul)))&
(funny(alice))&
(?[X]:(~generous(X)))&
((kind(susan)<~>brave(susan))) | ~kind(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 273170167567358126776239
% SZS output start Proof for 273170167567358126776239
15. ! [X0] : ((~happy(X0) | kind(X0)) => (funny(X0) & ~funny(X0))) [input p14]
23. kind(alice) [input hypothesis]
32. ! [X0] : ((funny(X0) & ~funny(X0)) | (happy(X0) & ~kind(X0))) [ennf transformation 15]
118. ~funny(X0) | ~kind(X0) [cnf transformation 32]
120. funny(X0) | ~kind(X0) [cnf transformation 32]
132. kind(alice) [cnf transformation 23]
136. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
137. ~kind(X0) <- (1) [avatar component clause 136]
263. ~kind(X0) [subsumption resolution 118,120]
264. 1 [avatar split clause 263,136]
308. $false <- (1) [resolution 137,132]
309. ~1 [avatar contradiction clause 308]
310. $false [avatar sat refutation 264,309]
% SZS output end Proof for 273170167567358126776239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or humble is not strong or not patient and vice versa.
Everyone who is either patient or kind is either strong or happy.
Everyone who is either wise or happy is happy.
If someone is not rich or kind then lucy is curious and vice versa.
Everyone who is either not strong or not quiet is not rich and vice versa.
If someone is curious or not wise then someone is not rich.
Everyone who is not curious is creative or not patient and vice versa.
Everyone who is old or not quiet is either not creative or not curious and vice versa.
If someone is both not generous and not funny then someone is not quiet.
Everyone who is quiet or not curious is both not funny and generous and vice versa.
If fred is both humble and not creative then someone is brave or not curious and vice versa.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Someone is calm or not happy.
Someone is both wise and not kind.
Someone is calm or wise.
John is generous or not humble.
Alice is both creative and not quiet.
John is either calm or patient.
Someone is either wise or not humble.
Someone is old. | John is creative. | contradiction | (![X]:((~creative(X)<~>humble(X))<=>(~strong(X)|~patient(X))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>(creative(X)|~patient(X))))&
(![X]:((old(X)|~quiet(X))<=>(~creative(X)<~>~curious(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~funny(X)&generous(X))))&
(((humble(fred)&~creative(fred)))<=>(?[X]:((brave(X)|~curious(X)))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(?[X]:((calm(X)|~happy(X))))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((calm(X)|wise(X))))&
((generous(john)|~humble(john)))&
((creative(alice)&~quiet(alice)))&
((calm(john)<~>patient(john)))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:(old(X))) | creative(john) | [
"p6",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4411178025064473913653329
% SZS output start Proof for 4411178025064473913653329
7. ! [X0] : (~curious(X0) <=> (~patient(X0) | creative(X0))) [input p6]
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (generous(X0) & ~funny(X0))) [input p9]
12. generous(fred) <=> funny(john) [input p11]
13. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p12]
15. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p14]
25. creative(john) [input hypothesis]
47. ! [X0] : ((~curious(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | curious(X0))) [nnf transformation 7]
48. ! [X0] : ((~curious(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | curious(X0))) [flattening 47]
54. ! [X0] : (((~curious(X0) | quiet(X0)) | (~generous(X0) | funny(X0))) & ((generous(X0) & ~funny(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
55. ! [X0] : ((~curious(X0) | quiet(X0) | ~generous(X0) | funny(X0)) & ((generous(X0) & ~funny(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 54]
61. (generous(fred) | ~funny(john)) & (funny(john) | ~generous(fred)) [nnf transformation 12]
62. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 13]
63. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 62]
65. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 15]
66. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 65]
101. ~curious(X0) | ~creative(X0) [cnf transformation 48]
111. ~funny(X0) | curious(X0) [cnf transformation 55]
120. funny(john) | ~generous(fred) [cnf transformation 61]
124. ~strong(X0) | generous(X0) [cnf transformation 63]
129. strong(X0) | generous(X0) [cnf transformation 66]
145. creative(john) [cnf transformation 25]
218. 17 <=> funny(john) [avatar definition]
219. funny(john) <- (17) [avatar component clause 218]
222. 18 <=> generous(fred) [avatar definition]
223. ~generous(fred) <- (~18) [avatar component clause 222]
226. ~18 | 17 [avatar split clause 120,218,222]
239. generous(X0) [subsumption resolution 129,124]
279. $false <- (~18) [subsumption resolution 223,239]
280. 18 [avatar contradiction clause 279]
288. curious(john) <- (17) [resolution 111,219]
290. ~creative(john) <- (17) [resolution 288,101]
293. $false <- (17) [subsumption resolution 290,145]
294. ~17 [avatar contradiction clause 293]
295. $false [avatar sat refutation 226,280,294]
% SZS output end Proof for 4411178025064473913653329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not generous then paul is either creative or not happy and vice versa. If susan is both creative and not wise then someone is either patient or strong. Everyone who is either not old or not strong is not quiet or not happy. If lucy is strong or curious then paul is not creative and vice versa. Everyone who is old or not tall is not strong. Everyone who is quiet or not curious is generous or not rich and vice versa. Everyone who is both curious and not creative is either not brave or not calm. If someone is not creative or generous then someone is humble or happy. If someone is either humble or rich then lucy is not wise and vice versa. Everyone who is both old and humble is not rich or calm and vice versa. If someone is not strong then someone is humble or curious and vice versa. Everyone who is both not old and calm is both not humble and not quiet and vice versa. Everyone who is happy is either not brave or not humble and vice versa. If someone is quiet or brave then lucy is both old and wise and vice versa. Everyone who is both not quiet and happy is either not wise or not curious and vice versa. Everyone who is patient is calm or not curious. Someone is either not rich or curious. Alice is either not funny or not curious. Lucy is kind. Someone is either wise or not patient. Lucy is not curious. Someone is either not kind or tall. Mary is either strong or not calm. John is either kind or not strong. | Susan is not rich. | contradiction | ((?[X]:((happy(X)<~>~generous(X))))<=>((creative(paul)<~>~happy(paul))))&
(((creative(susan)&~wise(susan)))=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~strong(X))=>(~quiet(X)|~happy(X))))&
(((strong(lucy)|curious(lucy)))<=>(~creative(paul)))&
(![X]:((old(X)|~tall(X))=>~strong(X)))&
(![X]:((quiet(X)|~curious(X))<=>(generous(X)|~rich(X))))&
(![X]:((curious(X)&~creative(X))=>(~brave(X)<~>~calm(X))))&
((?[X]:((~creative(X)|generous(X))))=>(?[X]:((humble(X)|happy(X)))))&
((?[X]:((humble(X)<~>rich(X))))<=>(~wise(lucy)))&
(![X]:((old(X)&humble(X))<=>(~rich(X)|calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((humble(X)|curious(X)))))&
(![X]:((~old(X)&calm(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(happy(X)<=>(~brave(X)<~>~humble(X))))&
((?[X]:((quiet(X)|brave(X))))<=>((old(lucy)&wise(lucy))))&
(![X]:((~quiet(X)&happy(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:(patient(X)=>(calm(X)|~curious(X))))&
(?[X]:((~rich(X)<~>curious(X))))&
((~funny(alice)<~>~curious(alice)))&
(kind(lucy))&
(?[X]:((wise(X)<~>~patient(X))))&
(~curious(lucy))&
(?[X]:((~kind(X)<~>tall(X))))&
((strong(mary)<~>~calm(mary)))&
((kind(john)<~>~strong(john))) | ~rich(susan) | [
"p8",
"p9",
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1946562784601692435379132
% SZS output start Proof for 1946562784601692435379132
9. ? [X0] : (humble(X0) <~> rich(X0)) <=> ~wise(lucy) [input p8]
10. ! [X0] : ((humble(X0) & old(X0)) <=> (calm(X0) | ~rich(X0))) [input p9]
12. ! [X0] : ((calm(X0) & ~old(X0)) <=> (~quiet(X0) & ~humble(X0))) [input p11]
13. ! [X0] : (happy(X0) <=> (~brave(X0) <~> ~humble(X0))) [input p12]
14. ? [X0] : (brave(X0) | quiet(X0)) <=> (wise(lucy) & old(lucy)) [input p13]
15. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> (~wise(X0) <~> ~curious(X0))) [input p14]
21. ~curious(lucy) [input p20]
25. ~rich(susan) [input hypothesis]
54. (? [X0] : ((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | wise(lucy)) & (~wise(lucy) | ! [X0] : ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) [nnf transformation 9]
55. (? [X0] : ((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | wise(lucy)) & (~wise(lucy) | ! [X1] : ((humble(X1) | ~rich(X1)) & (rich(X1) | ~humble(X1)))) [rectify 54]
56. ? [X0] : ((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) => ((~rich(sK3) | ~humble(sK3)) & (rich(sK3) | humble(sK3))) [choice axiom]
57. (((~rich(sK3) | ~humble(sK3)) & (rich(sK3) | humble(sK3))) | wise(lucy)) & (~wise(lucy) | ! [X1] : ((humble(X1) | ~rich(X1)) & (rich(X1) | ~humble(X1)))) [skolemisation 55,56]
58. ! [X0] : (((humble(X0) & old(X0)) | (~calm(X0) & rich(X0))) & ((calm(X0) | ~rich(X0)) | (~humble(X0) | ~old(X0)))) [nnf transformation 10]
59. ! [X0] : (((humble(X0) & old(X0)) | (~calm(X0) & rich(X0))) & (calm(X0) | ~rich(X0) | ~humble(X0) | ~old(X0))) [flattening 58]
65. ! [X0] : (((calm(X0) & ~old(X0)) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | (~calm(X0) | old(X0)))) [nnf transformation 12]
66. ! [X0] : (((calm(X0) & ~old(X0)) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | ~calm(X0) | old(X0))) [flattening 65]
67. ! [X0] : ((happy(X0) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | ~happy(X0))) [nnf transformation 13]
68. (? [X0] : (brave(X0) | quiet(X0)) | (~wise(lucy) | ~old(lucy))) & ((wise(lucy) & old(lucy)) | ! [X0] : (~brave(X0) & ~quiet(X0))) [nnf transformation 14]
69. (? [X0] : (brave(X0) | quiet(X0)) | ~wise(lucy) | ~old(lucy)) & ((wise(lucy) & old(lucy)) | ! [X0] : (~brave(X0) & ~quiet(X0))) [flattening 68]
70. (? [X0] : (brave(X0) | quiet(X0)) | ~wise(lucy) | ~old(lucy)) & ((wise(lucy) & old(lucy)) | ! [X1] : (~brave(X1) & ~quiet(X1))) [rectify 69]
71. ? [X0] : (brave(X0) | quiet(X0)) => (brave(sK6) | quiet(sK6)) [choice axiom]
72. ((brave(sK6) | quiet(sK6)) | ~wise(lucy) | ~old(lucy)) & ((wise(lucy) & old(lucy)) | ! [X1] : (~brave(X1) & ~quiet(X1))) [skolemisation 70,71]
73. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~happy(X0) | quiet(X0)))) [nnf transformation 15]
74. ! [X0] : (((happy(X0) & ~quiet(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ~happy(X0) | quiet(X0))) [flattening 73]
112. ~wise(lucy) | rich(X1) | ~humble(X1) [cnf transformation 57]
119. humble(X0) | rich(X0) [cnf transformation 59]
120. ~calm(X0) | humble(X0) [cnf transformation 59]
127. calm(X0) | quiet(X0) | humble(X0) [cnf transformation 66]
130. ~humble(X0) | happy(X0) | brave(X0) [cnf transformation 67]
134. wise(lucy) | ~quiet(X1) [cnf transformation 72]
135. wise(lucy) | ~brave(X1) [cnf transformation 72]
138. ~happy(X0) | wise(X0) | curious(X0) | quiet(X0) [cnf transformation 74]
151. ~curious(lucy) [cnf transformation 21]
158. ~rich(susan) [cnf transformation 25]
212. 12 <=> curious(lucy) [avatar definition]
213. ~curious(lucy) <- (~12) [avatar component clause 212]
235. 17 <=> wise(lucy) [avatar definition]
236. ~wise(lucy) <- (~17) [avatar component clause 235]
253. 21 <=> ! [X1] : (rich(X1) | ~humble(X1)) [avatar definition]
254. rich(X1) | ~humble(X1) <- (21) [avatar component clause 253]
255. 21 | ~17 [avatar split clause 112,235,253]
280. humble(X0) | quiet(X0) [subsumption resolution 127,120]
295. 31 <=> ! [X1] : ~brave(X1) [avatar definition]
296. ~brave(X1) <- (31) [avatar component clause 295]
297. 31 | 17 [avatar split clause 135,235,295]
299. 32 <=> ! [X1] : ~quiet(X1) [avatar definition]
300. ~quiet(X1) <- (32) [avatar component clause 299]
301. 32 | 17 [avatar split clause 134,235,299]
334. ~12 [avatar split clause 151,212]
367. rich(X1) <- (21) [subsumption resolution 254,119]
373. $false <- (21) [resolution 367,158]
376. ~21 [avatar contradiction clause 373]
406. happy(X0) | brave(X0) | quiet(X0) [resolution 130,280]
412. happy(X0) | quiet(X0) <- (31) [subsumption resolution 406,296]
413. happy(X0) <- (31, 32) [subsumption resolution 412,300]
458. wise(X0) | curious(X0) | quiet(X0) <- (31, 32) [resolution 138,413]
479. curious(X0) | wise(X0) <- (31, 32) [subsumption resolution 458,300]
512. wise(lucy) <- (~12, 31, 32) [resolution 479,213]
520. $false <- (~12, ~17, 31, 32) [subsumption resolution 512,236]
521. 12 | 17 | ~31 | ~32 [avatar contradiction clause 520]
522. $false [avatar sat refutation 255,297,301,334,376,521]
% SZS output end Proof for 1946562784601692435379132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or not happy then someone is both not creative and funny.
If fred is either brave or not calm then fred is not generous or happy.
Everyone who is happy or not quiet is either not strong or rich.
Everyone who is either generous or not curious is not funny and vice versa.
Everyone who is both not quiet and funny is both happy and funny.
If someone is both not rich and not strong then fred is not tall and vice versa.
If mary is wise then lucy is not brave and vice versa.
Everyone who is both not kind and strong is kind and vice versa.
Everyone who is both not tall and not kind is both calm and not brave.
Everyone who is either not funny or not generous is either not brave or calm and vice versa.
If someone is funny then someone is not calm and vice versa.
Everyone who is both not kind and not brave is patient or kind and vice versa.
Everyone who is either not creative or not calm is both wise and curious.
Everyone who is both not tall and not brave is quiet and vice versa.
If mary is rich or strong then alice is patient.
If paul is either rich or not calm then mary is either calm or kind.
Someone is patient.
John is not creative.
Alice is not wise.
Someone is happy.
Lucy is either curious or not humble.
Someone is not happy or strong.
Someone is both not wise and funny. | Lucy is not humble. | neutral | ((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(((brave(fred)<~>~calm(fred)))=>((~generous(fred)|happy(fred))))&
(![X]:((happy(X)|~quiet(X))=>(~strong(X)<~>rich(X))))&
(![X]:((generous(X)<~>~curious(X))<=>~funny(X)))&
(![X]:((~quiet(X)&funny(X))=>(happy(X)&funny(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(~tall(fred)))&
((wise(mary))<=>(~brave(lucy)))&
(![X]:((~kind(X)&strong(X))<=>kind(X)))&
(![X]:((~tall(X)&~kind(X))=>(calm(X)&~brave(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(~brave(X)<~>calm(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)&~brave(X))<=>(patient(X)|kind(X))))&
(![X]:((~creative(X)<~>~calm(X))=>(wise(X)&curious(X))))&
(![X]:((~tall(X)&~brave(X))<=>quiet(X)))&
(((rich(mary)|strong(mary)))=>(patient(alice)))&
(((rich(paul)<~>~calm(paul)))=>((calm(mary)<~>kind(mary))))&
(?[X]:(patient(X)))&
(~creative(john))&
(~wise(alice))&
(?[X]:(happy(X)))&
((curious(lucy)<~>~humble(lucy)))&
(?[X]:((~happy(X)|strong(X))))&
(?[X]:((~wise(X)&funny(X)))) | ~humble(lucy) | [] | null | 0 |
If someone is calm then someone is not curious and vice versa.
Everyone who is wise is either curious or rich and vice versa.
If someone is either not calm or calm then fred is both funny and not old and vice versa.
If someone is rich or not calm then someone is either quiet or funny and vice versa.
If someone is either generous or funny then someone is not tall.
Everyone who is not brave is both quiet and happy.
Everyone who is both not brave and not happy is either not wise or creative and vice versa.
If mary is old then alice is curious and vice versa.
Everyone who is brave is either not patient or curious.
If someone is not funny then someone is both generous and not patient and vice versa.
If someone is either not generous or not old then someone is either not creative or not brave.
Everyone who is both not old and generous is not patient and vice versa.
If someone is not kind or not quiet then someone is not old and vice versa.
Everyone who is old or humble is tall and vice versa.
Everyone who is calm is both calm and not tall and vice versa.
Everyone who is both strong and brave is either creative or not calm.
Someone is generous.
Someone is not humble.
John is creative.
Someone is strong or not kind.
John is old.
Someone is either rich or not calm.
Someone is both kind and not creative.
Someone is not funny. | John is not tall. | contradiction | ((?[X]:(calm(X)))<=>(?[X]:(~curious(X))))&
(![X]:(wise(X)<=>(curious(X)<~>rich(X))))&
((?[X]:((~calm(X)<~>calm(X))))<=>((funny(fred)&~old(fred))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((quiet(X)<~>funny(X)))))&
((?[X]:((generous(X)<~>funny(X))))=>(?[X]:(~tall(X))))&
(![X]:(~brave(X)=>(quiet(X)&happy(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~wise(X)<~>creative(X))))&
((old(mary))<=>(curious(alice)))&
(![X]:(brave(X)=>(~patient(X)<~>curious(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((generous(X)&~patient(X)))))&
((?[X]:((~generous(X)<~>~old(X))))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((~old(X)&generous(X))<=>~patient(X)))&
((?[X]:((~kind(X)|~quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((old(X)|humble(X))<=>tall(X)))&
(![X]:(calm(X)<=>(calm(X)&~tall(X))))&
(![X]:((strong(X)&brave(X))=>(creative(X)<~>~calm(X))))&
(?[X]:(generous(X)))&
(?[X]:(~humble(X)))&
(creative(john))&
(?[X]:((strong(X)|~kind(X))))&
(old(john))&
(?[X]:((rich(X)<~>~calm(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~funny(X))) | ~tall(john) | [
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5352613653099093081234740
% SZS output start Proof for 5352613653099093081234740
14. ! [X0] : ((humble(X0) | old(X0)) <=> tall(X0)) [input p13]
21. old(john) [input p20]
25. ~tall(john) [input hypothesis]
78. ! [X0] : (((humble(X0) | old(X0)) | ~tall(X0)) & (tall(X0) | (~humble(X0) & ~old(X0)))) [nnf transformation 14]
79. ! [X0] : ((humble(X0) | old(X0) | ~tall(X0)) & (tall(X0) | (~humble(X0) & ~old(X0)))) [flattening 78]
141. ~old(X0) | tall(X0) [cnf transformation 79]
153. old(john) [cnf transformation 21]
159. ~tall(john) [cnf transformation 25]
349. tall(john) [resolution 141,153]
351. $false [subsumption resolution 349,159]
% SZS output end Proof for 5352613653099093081234740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not tall or not rich then someone is generous and vice versa.
Everyone who is either not quiet or not curious is either not generous or patient and vice versa.
Everyone who is quiet or not curious is not calm or wise.
Everyone who is not curious is both generous and tall.
If someone is either quiet or not generous then someone is creative.
Everyone who is both tall and not wise is either not funny or happy.
Everyone who is either not generous or creative is calm and vice versa.
Everyone who is kind is not funny and vice versa.
Everyone who is either brave or not humble is both creative and quiet and vice versa.
If someone is either creative or not happy then someone is either generous or not rich and vice versa.
Everyone who is either not creative or not generous is quiet or kind.
Everyone who is either rich or not calm is either not tall or not wise.
Everyone who is patient or not quiet is not rich or not strong and vice versa.
If someone is creative or strong then someone is not happy.
Everyone who is both not generous and curious is either patient or tall.
Everyone who is not quiet is either funny or not strong.
Lucy is not rich or not creative.
Someone is both not strong and curious.
Lucy is strong.
John is both not strong and not brave.
Someone is generous.
Someone is both funny and not strong.
John is both patient and not brave.
Fred is both not curious and not brave. | Fred is rich. | contradiction | (((~tall(fred)<~>~rich(fred)))<=>(?[X]:(generous(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~generous(X)<~>patient(X))))&
(![X]:((quiet(X)|~curious(X))=>(~calm(X)|wise(X))))&
(![X]:(~curious(X)=>(generous(X)&tall(X))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:(creative(X))))&
(![X]:((tall(X)&~wise(X))=>(~funny(X)<~>happy(X))))&
(![X]:((~generous(X)<~>creative(X))<=>calm(X)))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((brave(X)<~>~humble(X))<=>(creative(X)&quiet(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(quiet(X)|kind(X))))&
(![X]:((rich(X)<~>~calm(X))=>(~tall(X)<~>~wise(X))))&
(![X]:((patient(X)|~quiet(X))<=>(~rich(X)|~strong(X))))&
((?[X]:((creative(X)|strong(X))))=>(?[X]:(~happy(X))))&
(![X]:((~generous(X)&curious(X))=>(patient(X)<~>tall(X))))&
(![X]:(~quiet(X)=>(funny(X)<~>~strong(X))))&
((~rich(lucy)|~creative(lucy)))&
(?[X]:((~strong(X)&curious(X))))&
(strong(lucy))&
((~strong(john)&~brave(john)))&
(?[X]:(generous(X)))&
(?[X]:((funny(X)&~strong(X))))&
((patient(john)&~brave(john)))&
((~curious(fred)&~brave(fred))) | rich(fred) | [
"p0",
"p3",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5630937880914756814123341
% SZS output start Proof for 5630937880914756814123341
1. (~tall(fred) <~> ~rich(fred)) <=> ? [X0] : generous(X0) [input p0]
4. ! [X0] : (~curious(X0) => (tall(X0) & generous(X0))) [input p3]
21. ? [X0] : generous(X0) [input p20]
24. ~brave(fred) & ~curious(fred) [input p23]
25. rich(fred) [input hypothesis]
32. ! [X0] : ((tall(X0) & generous(X0)) | curious(X0)) [ennf transformation 4]
44. (((rich(fred) | tall(fred)) & (~rich(fred) | ~tall(fred))) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ((~tall(fred) | rich(fred)) & (~rich(fred) | tall(fred)))) [nnf transformation 1]
45. (((rich(fred) | tall(fred)) & (~rich(fred) | ~tall(fred))) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ((~tall(fred) | rich(fred)) & (~rich(fred) | tall(fred)))) [rectify 44]
46. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
47. (((rich(fred) | tall(fred)) & (~rich(fred) | ~tall(fred))) | ! [X0] : ~generous(X0)) & (generous(sK0) | ((~tall(fred) | rich(fred)) & (~rich(fred) | tall(fred)))) [skolemisation 45,46]
73. ? [X0] : generous(X0) => generous(sK6) [choice axiom]
74. generous(sK6) [skolemisation 21,73]
79. ~rich(fred) | ~tall(fred) | ~generous(X0) [cnf transformation 47]
92. curious(X0) | tall(X0) [cnf transformation 32]
138. generous(sK6) [cnf transformation 74]
143. ~curious(fred) [cnf transformation 24]
145. rich(fred) [cnf transformation 25]
147. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
148. ~generous(X0) <- (1) [avatar component clause 147]
150. 2 <=> tall(fred) [avatar definition]
154. 3 <=> rich(fred) [avatar definition]
158. 1 | ~2 | ~3 [avatar split clause 79,154,150,147]
236. 3 [avatar split clause 145,154]
238. tall(fred) [resolution 92,143]
241. 2 [avatar split clause 238,150]
242. $false <- (1) [resolution 148,138]
247. ~1 [avatar contradiction clause 242]
248. $false [avatar sat refutation 158,236,241,247]
% SZS output end Proof for 5630937880914756814123341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not strong or not generous then someone is not funny. If lucy is generous or quiet then paul is both not creative and rich. Everyone who is either humble or calm is creative or not calm and vice versa. Everyone who is both humble and wise is not strong. If lucy is not creative or not humble then someone is either not creative or humble. Everyone who is both rich and not strong is both generous and not old. Everyone who is not kind is calm and vice versa. If mary is both not generous and not rich then paul is not creative or not old and vice versa. Everyone who is both brave and not happy is both tall and curious and vice versa. Everyone who is either not patient or curious is both strong and quiet. If someone is tall then someone is not quiet. If someone is calm or generous then john is not curious or old and vice versa. If fred is curious or not rich then someone is rich or not old and vice versa. Everyone who is strong is not quiet or kind. If someone is not patient or not strong then someone is funny. Everyone who is strong is kind and vice versa. Lucy is both curious and quiet. John is rich. Lucy is not strong. Susan is either not generous or not quiet. Someone is not brave or generous. Lucy is strong or calm. Susan is either not generous or humble. | Lucy is quiet. | entailment | (((~strong(mary)<~>~generous(mary)))=>(?[X]:(~funny(X))))&
(((generous(lucy)|quiet(lucy)))=>((~creative(paul)&rich(paul))))&
(![X]:((humble(X)<~>calm(X))<=>(creative(X)|~calm(X))))&
(![X]:((humble(X)&wise(X))=>~strong(X)))&
(((~creative(lucy)|~humble(lucy)))=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((rich(X)&~strong(X))=>(generous(X)&~old(X))))&
(![X]:(~kind(X)<=>calm(X)))&
(((~generous(mary)&~rich(mary)))<=>((~creative(paul)|~old(paul))))&
(![X]:((brave(X)&~happy(X))<=>(tall(X)&curious(X))))&
(![X]:((~patient(X)<~>curious(X))=>(strong(X)&quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((calm(X)|generous(X))))<=>((~curious(john)|old(john))))&
(((curious(fred)|~rich(fred)))<=>(?[X]:((rich(X)|~old(X)))))&
(![X]:(strong(X)=>(~quiet(X)|kind(X))))&
((?[X]:((~patient(X)|~strong(X))))=>(?[X]:(funny(X))))&
(![X]:(strong(X)<=>kind(X)))&
((curious(lucy)&quiet(lucy)))&
(rich(john))&
(~strong(lucy))&
((~generous(susan)<~>~quiet(susan)))&
(?[X]:((~brave(X)|generous(X))))&
((strong(lucy)|calm(lucy)))&
((~generous(susan)<~>humble(susan))) | quiet(lucy) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1697192744515082006165756
% SZS output start Proof for 1697192744515082006165756
17. quiet(lucy) & curious(lucy) [input p16]
24. ~quiet(lucy) [input hypothesis]
121. quiet(lucy) [cnf transformation 17]
130. ~quiet(lucy) [cnf transformation 24]
148. 4 <=> quiet(lucy) [avatar definition]
277. 4 [avatar split clause 121,148]
304. ~4 [avatar split clause 130,148]
305. $false [avatar sat refutation 277,304]
% SZS output end Proof for 1697192744515082006165756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not patient is not generous or not rich and vice versa.
Everyone who is either not brave or not old is either not funny or not kind and vice versa.
If someone is either not generous or not happy then someone is either not calm or not strong and vice versa.
Everyone who is humble or not quiet is both patient and tall and vice versa.
Everyone who is creative or kind is both wise and strong.
If someone is both creative and not curious then someone is both funny and not humble.
If alice is either happy or quiet then someone is not strong or patient and vice versa.
Everyone who is not old is either not strong or not happy.
Everyone who is not old is either happy or humble.
Everyone who is not generous or not rich is quiet and vice versa.
Everyone who is quiet or not creative is either not creative or happy and vice versa.
If someone is not patient or not creative then someone is not rich or not kind.
Everyone who is quiet or not brave is either brave or patient and vice versa.
If lucy is either kind or not kind then someone is either quiet or funny.
Everyone who is either not happy or not strong is patient and vice versa.
Everyone who is happy or old is either calm or not curious and vice versa.
Someone is quiet or not creative.
Someone is creative or not brave.
Someone is both calm and not rich.
Paul is funny. | Lucy is not patient. | entailment | (![X]:((creative(X)&~patient(X))<=>(~generous(X)|~rich(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:((humble(X)|~quiet(X))<=>(patient(X)&tall(X))))&
(![X]:((creative(X)|kind(X))=>(wise(X)&strong(X))))&
((?[X]:((creative(X)&~curious(X))))=>(?[X]:((funny(X)&~humble(X)))))&
(((happy(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~creative(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((calm(X)&~rich(X))))&
(funny(paul)) | ~patient(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1398645942497028584957960
% SZS output start Proof for 1398645942497028584957960
1. ! [X0] : ((~patient(X0) & creative(X0)) <=> (~rich(X0) | ~generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | humble(X0)) <=> (tall(X0) & patient(X0))) [input p3]
5. ! [X0] : ((kind(X0) | creative(X0)) => (strong(X0) & wise(X0))) [input p4]
7. (happy(alice) <~> quiet(alice)) <=> ? [X0] : (patient(X0) | ~strong(X0)) [input p6]
10. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> quiet(X0)) [input p9]
11. ! [X0] : ((~creative(X0) | quiet(X0)) <=> (~creative(X0) <~> happy(X0))) [input p10]
15. ! [X0] : ((~happy(X0) <~> ~strong(X0)) <=> patient(X0)) [input p14]
21. patient(lucy) [input hypothesis]
25. ! [X0] : ((kind(X0) | creative(X0)) => strong(X0)) [pure predicate removal 5]
26. ! [X0] : (strong(X0) | (~kind(X0) & ~creative(X0))) [ennf transformation 25]
32. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & ((~rich(X0) | ~generous(X0)) | (patient(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((~patient(X0) & creative(X0)) | (rich(X0) & generous(X0))) & (~rich(X0) | ~generous(X0) | patient(X0) | ~creative(X0))) [flattening 32]
40. ! [X0] : (((~quiet(X0) | humble(X0)) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [nnf transformation 4]
41. ! [X0] : ((~quiet(X0) | humble(X0) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | (quiet(X0) & ~humble(X0)))) [flattening 40]
45. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X0] : (patient(X0) | ~strong(X0)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [nnf transformation 7]
46. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & (? [X1] : (patient(X1) | ~strong(X1)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [rectify 45]
47. ? [X1] : (patient(X1) | ~strong(X1)) => (patient(sK3) | ~strong(sK3)) [choice axiom]
48. (((~quiet(alice) | ~happy(alice)) & (quiet(alice) | happy(alice))) | ! [X0] : (~patient(X0) & strong(X0))) & ((patient(sK3) | ~strong(sK3)) | ((happy(alice) | ~quiet(alice)) & (quiet(alice) | ~happy(alice)))) [skolemisation 46,47]
51. ! [X0] : (((~rich(X0) | ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~rich(X0) | ~generous(X0) | ~quiet(X0)) & (quiet(X0) | (rich(X0) & generous(X0)))) [flattening 51]
53. ! [X0] : (((~creative(X0) | quiet(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((~creative(X0) | quiet(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) & (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (creative(X0) & ~quiet(X0)))) [flattening 53]
63. ! [X0] : ((((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~patient(X0)) & (patient(X0) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))))) [nnf transformation 15]
73. generous(X0) | creative(X0) [cnf transformation 33]
74. rich(X0) | creative(X0) [cnf transformation 33]
94. quiet(X0) | patient(X0) [cnf transformation 41]
98. ~creative(X0) | strong(X0) [cnf transformation 26]
105. quiet(alice) | happy(alice) | ~patient(X0) [cnf transformation 48]
107. ~quiet(alice) | ~happy(alice) | ~patient(X0) [cnf transformation 48]
114. ~quiet(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 52]
115. ~quiet(X0) | ~creative(X0) | happy(X0) [cnf transformation 54]
118. ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 54]
135. ~strong(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 63]
148. patient(lucy) [cnf transformation 21]
155. ~happy(X0) | creative(X0) [duplicate literal removal 118]
207. 12 <=> ! [X0] : ~patient(X0) [avatar definition]
208. ~patient(X0) <- (12) [avatar component clause 207]
210. 13 <=> happy(alice) [avatar definition]
211. happy(alice) <- (13) [avatar component clause 210]
212. ~happy(alice) <- (~13) [avatar component clause 210]
214. 14 <=> quiet(alice) [avatar definition]
215. quiet(alice) <- (14) [avatar component clause 214]
216. ~quiet(alice) <- (~14) [avatar component clause 214]
217. 12 | ~13 | ~14 [avatar split clause 107,214,210,207]
222. 12 | 13 | 14 [avatar split clause 105,214,210,207]
289. patient(alice) <- (~14) [resolution 94,216]
301. creative(alice) <- (13) [resolution 155,211]
302. strong(alice) <- (13) [resolution 301,98]
468. ~happy(alice) | ~patient(alice) <- (13) [resolution 302,135]
471. ~patient(alice) <- (13) [subsumption resolution 468,211]
472. $false <- (13, ~14) [subsumption resolution 471,289]
473. ~13 | 14 [avatar contradiction clause 472]
476. ~creative(alice) | happy(alice) <- (14) [resolution 215,115]
477. ~generous(alice) | ~rich(alice) <- (14) [resolution 215,114]
487. ~creative(alice) <- (~13, 14) [subsumption resolution 476,212]
489. 50 <=> rich(alice) [avatar definition]
491. ~rich(alice) <- (~50) [avatar component clause 489]
493. 51 <=> generous(alice) [avatar definition]
495. ~generous(alice) <- (~51) [avatar component clause 493]
496. ~50 | ~51 | ~14 [avatar split clause 477,214,493,489]
507. creative(alice) <- (~51) [resolution 495,73]
508. $false <- (~13, 14, ~51) [subsumption resolution 507,487]
509. 13 | ~14 | 51 [avatar contradiction clause 508]
513. creative(alice) <- (~50) [resolution 491,74]
514. $false <- (~13, 14, ~50) [subsumption resolution 513,487]
515. 13 | ~14 | 50 [avatar contradiction clause 514]
516. $false <- (12) [resolution 208,148]
521. ~12 [avatar contradiction clause 516]
522. $false [avatar sat refutation 217,222,473,496,509,515,521]
% SZS output end Proof for 1398645942497028584957960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not creative is both not strong and generous and vice versa.
Everyone who is either quiet or not quiet is rich or not quiet.
Everyone who is both kind and not old is both not kind and not rich.
If lucy is both quiet and wise then someone is either not funny or not creative.
Everyone who is both not strong and funny is both not curious and not calm and vice versa.
Everyone who is either not calm or strong is patient or rich and vice versa.
If john is not patient then john is tall or not patient.
Everyone who is not quiet or humble is both not funny and patient.
Everyone who is both not creative and not quiet is either generous or humble and vice versa.
Everyone who is either strong or not patient is patient.
Everyone who is either not strong or not brave is either not kind or not rich and vice versa.
Everyone who is both curious and kind is either not funny or not wise.
Everyone who is not kind or wise is either not humble or not curious and vice versa.
Everyone who is not old or kind is generous or tall and vice versa.
If someone is not patient or creative then mary is not tall or not wise.
Everyone who is either not strong or not rich is not strong or tall.
John is both quiet and brave.
Fred is strong or patient.
Someone is either patient or tall.
Mary is both tall and funny.
Fred is not patient or not old.
Someone is patient or not generous.
Someone is wise. | Mary is rich. | entailment | (![X]:((~tall(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(rich(X)|~quiet(X))))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&~rich(X))))&
(((quiet(lucy)&wise(lucy)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(patient(X)|rich(X))))&
((~patient(john))=>((tall(john)|~patient(john))))&
(![X]:((~quiet(X)|humble(X))=>(~funny(X)&patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)<~>humble(X))))&
(![X]:((strong(X)<~>~patient(X))=>patient(X)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((curious(X)&kind(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~old(X)|kind(X))<=>(generous(X)|tall(X))))&
((?[X]:((~patient(X)|creative(X))))=>((~tall(mary)|~wise(mary))))&
(![X]:((~strong(X)<~>~rich(X))=>(~strong(X)|tall(X))))&
((quiet(john)&brave(john)))&
((strong(fred)|patient(fred)))&
(?[X]:((patient(X)<~>tall(X))))&
((tall(mary)&funny(mary)))&
((~patient(fred)|~old(fred)))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:(wise(X))) | rich(mary) | [
"p1",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9096255237752081898665388
% SZS output start Proof for 9096255237752081898665388
2. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (~quiet(X0) | rich(X0))) [input p1]
8. ! [X0] : ((humble(X0) | ~quiet(X0)) => (patient(X0) & ~funny(X0))) [input p7]
20. funny(mary) & tall(mary) [input p19]
24. ~rich(mary) [input hypothesis]
25. ! [X0] : ((~quiet(X0) | rich(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 2]
26. ! [X0] : (~quiet(X0) | rich(X0) | (quiet(X0) <=> ~quiet(X0))) [flattening 25]
33. ! [X0] : ((patient(X0) & ~funny(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 8]
43. ! [X0] : (~quiet(X0) | rich(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 26]
73. ~quiet(X0) | rich(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 43]
90. ~funny(X0) | quiet(X0) [cnf transformation 33]
132. funny(mary) [cnf transformation 20]
136. ~rich(mary) [cnf transformation 24]
140. ~quiet(X0) | rich(X0) [duplicate literal removal 73]
209. quiet(mary) [resolution 90,132]
215. rich(mary) [resolution 140,209]
217. $false [subsumption resolution 215,136]
% SZS output end Proof for 9096255237752081898665388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and not wise is brave or not patient and vice versa.
If alice is generous then someone is either curious or not creative and vice versa.
If alice is either humble or not curious then lucy is not patient or not rich.
If someone is strong or curious then susan is both not kind and not wise.
Everyone who is happy or not curious is either creative or wise and vice versa.
If paul is either curious or wise then paul is either not tall or funny and vice versa.
Everyone who is wise or creative is both humble and not generous and vice versa.
If someone is either not patient or calm then lucy is curious or not curious.
If someone is funny or patient then susan is both not funny and not humble.
If john is either not funny or funny then john is either calm or not rich and vice versa.
Everyone who is humble or wise is either not brave or rich and vice versa.
If lucy is both old and patient then someone is either quiet or rich and vice versa.
If john is both curious and not wise then paul is either creative or not tall and vice versa.
Everyone who is not rich or not generous is both brave and quiet.
Everyone who is not quiet is curious or not kind.
Everyone who is quiet or humble is patient or generous and vice versa.
Someone is quiet or not quiet.
Someone is not wise or not old.
Someone is either not humble or curious.
Alice is strong or curious.
Someone is calm.
Someone is not tall or not calm.
Someone is not generous or not funny. | Susan is not creative. | entailment | (![X]:((happy(X)&~wise(X))<=>(brave(X)|~patient(X))))&
((generous(alice))<=>(?[X]:((curious(X)<~>~creative(X)))))&
(((humble(alice)<~>~curious(alice)))=>((~patient(lucy)|~rich(lucy))))&
((?[X]:((strong(X)|curious(X))))=>((~kind(susan)&~wise(susan))))&
(![X]:((happy(X)|~curious(X))<=>(creative(X)<~>wise(X))))&
(((curious(paul)<~>wise(paul)))<=>((~tall(paul)<~>funny(paul))))&
(![X]:((wise(X)|creative(X))<=>(humble(X)&~generous(X))))&
((?[X]:((~patient(X)<~>calm(X))))=>((curious(lucy)|~curious(lucy))))&
((?[X]:((funny(X)|patient(X))))=>((~funny(susan)&~humble(susan))))&
(((~funny(john)<~>funny(john)))<=>((calm(john)<~>~rich(john))))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>rich(X))))&
(((old(lucy)&patient(lucy)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(((curious(john)&~wise(john)))<=>((creative(paul)<~>~tall(paul))))&
(![X]:((~rich(X)|~generous(X))=>(brave(X)&quiet(X))))&
(![X]:(~quiet(X)=>(curious(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))<=>(patient(X)|generous(X))))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:((~humble(X)<~>curious(X))))&
((strong(alice)|curious(alice)))&
(?[X]:(calm(X)))&
(?[X]:((~tall(X)|~calm(X))))&
(?[X]:((~generous(X)|~funny(X)))) | ~creative(susan) | [
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1481078130357693093276449
% SZS output start Proof for 1481078130357693093276449
7. ! [X0] : ((creative(X0) | wise(X0)) <=> (~generous(X0) & humble(X0))) [input p6]
9. ? [X0] : (patient(X0) | funny(X0)) => (~humble(susan) & ~funny(susan)) [input p8]
14. ! [X0] : ((~generous(X0) | ~rich(X0)) => (quiet(X0) & brave(X0))) [input p13]
16. ! [X0] : ((humble(X0) | quiet(X0)) <=> (generous(X0) | patient(X0))) [input p15]
24. creative(susan) [input hypothesis]
32. (~humble(susan) & ~funny(susan)) | ! [X0] : (~patient(X0) & ~funny(X0)) [ennf transformation 9]
33. ! [X0] : ((quiet(X0) & brave(X0)) | (generous(X0) & rich(X0))) [ennf transformation 14]
44. ! [X0] : (((creative(X0) | wise(X0)) | (generous(X0) | ~humble(X0))) & ((~generous(X0) & humble(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 7]
45. ! [X0] : ((creative(X0) | wise(X0) | generous(X0) | ~humble(X0)) & ((~generous(X0) & humble(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 44]
57. ! [X0] : (((humble(X0) | quiet(X0)) | (~generous(X0) & ~patient(X0))) & ((generous(X0) | patient(X0)) | (~humble(X0) & ~quiet(X0)))) [nnf transformation 16]
58. ! [X0] : ((humble(X0) | quiet(X0) | (~generous(X0) & ~patient(X0))) & (generous(X0) | patient(X0) | (~humble(X0) & ~quiet(X0)))) [flattening 57]
100. ~creative(X0) | humble(X0) [cnf transformation 45]
102. ~creative(X0) | ~generous(X0) [cnf transformation 45]
109. ~humble(susan) | ~patient(X0) [cnf transformation 32]
139. quiet(X0) | generous(X0) [cnf transformation 33]
140. generous(X0) | patient(X0) | ~quiet(X0) [cnf transformation 58]
152. creative(susan) [cnf transformation 24]
234. 17 <=> ! [X0] : ~patient(X0) [avatar definition]
235. ~patient(X0) <- (17) [avatar component clause 234]
237. 18 <=> humble(susan) [avatar definition]
240. 17 | ~18 [avatar split clause 109,237,234]
313. generous(X0) | patient(X0) [subsumption resolution 140,139]
361. humble(susan) [resolution 100,152]
364. 18 [avatar split clause 361,237]
367. ~generous(susan) [resolution 102,152]
380. patient(susan) [resolution 313,367]
383. $false <- (17) [subsumption resolution 380,235]
384. ~17 [avatar contradiction clause 383]
385. $false [avatar sat refutation 240,364,384]
% SZS output end Proof for 1481078130357693093276449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then john is happy.
Everyone who is not rich or strong is not curious or not calm.
If susan is strong then alice is both kind and not humble.
If someone is either calm or creative then someone is quiet and vice versa.
Everyone who is not creative is either not creative or not tall and vice versa.
Everyone who is either not rich or not humble is tall.
Everyone who is both not patient and not creative is curious.
If someone is quiet then someone is not curious.
If paul is both not humble and calm then john is old.
If someone is old then alice is not strong.
Everyone who is both calm and not happy is either not funny or calm.
Everyone who is either not tall or patient is not humble and vice versa.
If someone is not tall then someone is either not tall or old and vice versa.
Everyone who is either not strong or brave is not old.
If someone is both quiet and not quiet then someone is both strong and not humble.
Everyone who is both not curious and wise is happy or not old.
Someone is either tall or not tall.
John is both strong and not old.
Someone is tall.
Someone is either calm or happy.
Lucy is not rich or brave.
Someone is both strong and happy.
John is not rich. | Paul is funny. | neutral | ((?[X]:(happy(X)))=>(happy(john)))&
(![X]:((~rich(X)|strong(X))=>(~curious(X)|~calm(X))))&
((strong(susan))=>((kind(alice)&~humble(alice))))&
((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>~humble(X))=>tall(X)))&
(![X]:((~patient(X)&~creative(X))=>curious(X)))&
((?[X]:(quiet(X)))=>(?[X]:(~curious(X))))&
(((~humble(paul)&calm(paul)))=>(old(john)))&
((?[X]:(old(X)))=>(~strong(alice)))&
(![X]:((calm(X)&~happy(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~tall(X)<~>patient(X))<=>~humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:((~strong(X)<~>brave(X))=>~old(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:((~curious(X)&wise(X))=>(happy(X)|~old(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((strong(john)&~old(john)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)<~>happy(X))))&
((~rich(lucy)|brave(lucy)))&
(?[X]:((strong(X)&happy(X))))&
(~rich(john)) | funny(paul) | [] | null | 0 |
Everyone who is either old or not brave is humble and vice versa. Everyone who is both not tall and not happy is generous. If paul is not rich then someone is both not curious and tall and vice versa. Everyone who is both curious and not kind is not happy and vice versa. If fred is not kind or tall then someone is not kind or not patient and vice versa. If someone is both kind and tall then paul is not happy or not strong. If someone is not tall or curious then someone is not generous and vice versa. If someone is both humble and not old then fred is humble or brave. Everyone who is both not brave and humble is both not wise and not tall. If mary is both happy and not generous then fred is humble or not curious. Everyone who is either not brave or quiet is not humble. Everyone who is kind is both strong and not old and vice versa. Everyone who is both strong and quiet is calm or not calm. If paul is old or happy then fred is generous. If john is either tall or not quiet then lucy is both patient and calm and vice versa. If john is either happy or not creative then someone is both not creative and generous. Someone is not funny or not generous. Someone is kind or funny. Someone is either funny or not creative. Alice is both not patient and funny. Someone is not rich or kind. Someone is both brave and not humble. Fred is both not generous and tall. | John is not wise. | neutral | (![X]:((old(X)<~>~brave(X))<=>humble(X)))&
(![X]:((~tall(X)&~happy(X))=>generous(X)))&
((~rich(paul))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((curious(X)&~kind(X))<=>~happy(X)))&
(((~kind(fred)|tall(fred)))<=>(?[X]:((~kind(X)|~patient(X)))))&
((?[X]:((kind(X)&tall(X))))=>((~happy(paul)|~strong(paul))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((humble(X)&~old(X))))=>((humble(fred)|brave(fred))))&
(![X]:((~brave(X)&humble(X))=>(~wise(X)&~tall(X))))&
(((happy(mary)&~generous(mary)))=>((humble(fred)|~curious(fred))))&
(![X]:((~brave(X)<~>quiet(X))=>~humble(X)))&
(![X]:(kind(X)<=>(strong(X)&~old(X))))&
(![X]:((strong(X)&quiet(X))=>(calm(X)|~calm(X))))&
(((old(paul)|happy(paul)))=>(generous(fred)))&
(((tall(john)<~>~quiet(john)))<=>((patient(lucy)&calm(lucy))))&
(((happy(john)<~>~creative(john)))=>(?[X]:((~creative(X)&generous(X)))))&
(?[X]:((~funny(X)|~generous(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((funny(X)<~>~creative(X))))&
((~patient(alice)&funny(alice)))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((brave(X)&~humble(X))))&
((~generous(fred)&tall(fred))) | ~wise(john) | [] | null | 0 |
If paul is both quiet and curious then paul is either not strong or rich and vice versa. If someone is not brave or patient then someone is funny and vice versa. Everyone who is both not wise and wise is either not patient or wise and vice versa. Everyone who is tall is not brave or wise and vice versa. Everyone who is happy or not humble is creative and vice versa. If someone is rich then someone is either not patient or not kind. Everyone who is both quiet and not tall is either not calm or not humble. If someone is both not brave and tall then someone is either brave or not rich and vice versa. Everyone who is humble is either calm or rich. Everyone who is not calm is either not funny or patient and vice versa. Everyone who is either not funny or not calm is not tall or curious and vice versa. If someone is rich then alice is not happy or strong. If someone is old then someone is either wise or not generous and vice versa. If someone is not quiet or not calm then someone is not calm or happy and vice versa. Everyone who is either not brave or calm is old or not curious and vice versa. If someone is not strong then alice is strong or calm and vice versa. Someone is calm. John is not kind or tall. Mary is both patient and not curious. Susan is not rich or tall. John is either curious or not old. Mary is quiet. Someone is generous. Lucy is not creative. | Lucy is not humble. | contradiction | (((quiet(paul)&curious(paul)))<=>((~strong(paul)<~>rich(paul))))&
((?[X]:((~brave(X)|patient(X))))<=>(?[X]:(funny(X))))&
(![X]:((~wise(X)&wise(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(tall(X)<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)|~humble(X))<=>creative(X)))&
((?[X]:(rich(X)))=>(?[X]:((~patient(X)<~>~kind(X)))))&
(![X]:((quiet(X)&~tall(X))=>(~calm(X)<~>~humble(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(humble(X)=>(calm(X)<~>rich(X))))&
(![X]:(~calm(X)<=>(~funny(X)<~>patient(X))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~tall(X)|curious(X))))&
((?[X]:(rich(X)))=>((~happy(alice)|strong(alice))))&
((?[X]:(old(X)))<=>(?[X]:((wise(X)<~>~generous(X)))))&
((?[X]:((~quiet(X)|~calm(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(old(X)|~curious(X))))&
((?[X]:(~strong(X)))<=>((strong(alice)|calm(alice))))&
(?[X]:(calm(X)))&
((~kind(john)|tall(john)))&
((patient(mary)&~curious(mary)))&
((~rich(susan)|tall(susan)))&
((curious(john)<~>~old(john)))&
(quiet(mary))&
(?[X]:(generous(X)))&
(~creative(lucy)) | ~humble(lucy) | [
"p4",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4217914667296949463814021
% SZS output start Proof for 4217914667296949463814021
5. ! [X0] : ((~humble(X0) | happy(X0)) <=> creative(X0)) [input p4]
24. ~creative(lucy) [input p23]
25. ~humble(lucy) [input hypothesis]
31. ! [X0] : ((~humble(X0) | happy(X0)) => creative(X0)) [unused predicate definition removal 5]
32. ! [X0] : (creative(X0) | (humble(X0) & ~happy(X0))) [ennf transformation 31]
105. creative(X0) | humble(X0) [cnf transformation 32]
155. ~creative(lucy) [cnf transformation 24]
156. ~humble(lucy) [cnf transformation 25]
355. humble(lucy) [resolution 105,155]
356. $false [subsumption resolution 355,156]
% SZS output end Proof for 4217914667296949463814021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is not strong or curious and vice versa.
If john is either patient or old then someone is both not wise and rich.
If someone is funny then fred is either not old or wise and vice versa.
Everyone who is not calm or creative is rich and vice versa.
Everyone who is not kind is not calm and vice versa.
If mary is either not humble or not funny then someone is not tall and vice versa.
Everyone who is either not generous or not curious is either brave or not brave and vice versa.
If fred is either tall or patient then someone is not strong or not brave.
Everyone who is either not strong or generous is either funny or generous.
Everyone who is either kind or not generous is both kind and rich.
If paul is either not humble or funny then someone is not creative or patient and vice versa.
Everyone who is either patient or not wise is either tall or not brave.
Everyone who is either not wise or kind is both not brave and not quiet.
Everyone who is either brave or strong is tall or not kind and vice versa.
Everyone who is either not calm or not happy is both kind and not kind and vice versa.
If someone is either calm or not generous then someone is either not creative or generous and vice versa.
Mary is either funny or patient.
Someone is curious or not creative.
Lucy is brave.
Someone is both curious and not creative.
Someone is either funny or not strong.
Mary is not happy.
Someone is either not happy or calm.
Susan is both creative and calm. | Lucy is brave. | entailment | (![X]:(funny(X)<=>(~strong(X)|curious(X))))&
(((patient(john)<~>old(john)))=>(?[X]:((~wise(X)&rich(X)))))&
((?[X]:(funny(X)))<=>((~old(fred)<~>wise(fred))))&
(![X]:((~calm(X)|creative(X))<=>rich(X)))&
(![X]:(~kind(X)<=>~calm(X)))&
(((~humble(mary)<~>~funny(mary)))<=>(?[X]:(~tall(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(brave(X)<~>~brave(X))))&
(((tall(fred)<~>patient(fred)))=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((~strong(X)<~>generous(X))=>(funny(X)<~>generous(X))))&
(![X]:((kind(X)<~>~generous(X))=>(kind(X)&rich(X))))&
(((~humble(paul)<~>funny(paul)))<=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:((patient(X)<~>~wise(X))=>(tall(X)<~>~brave(X))))&
(![X]:((~wise(X)<~>kind(X))=>(~brave(X)&~quiet(X))))&
(![X]:((brave(X)<~>strong(X))<=>(tall(X)|~kind(X))))&
(![X]:((~calm(X)<~>~happy(X))<=>(kind(X)&~kind(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
((funny(mary)<~>patient(mary)))&
(?[X]:((curious(X)|~creative(X))))&
(brave(lucy))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:((funny(X)<~>~strong(X))))&
(~happy(mary))&
(?[X]:((~happy(X)<~>calm(X))))&
((creative(susan)&calm(susan))) | brave(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3772495540126233465211816
% SZS output start Proof for 3772495540126233465211816
19. brave(lucy) [input p18]
25. ~brave(lucy) [input hypothesis]
154. brave(lucy) [cnf transformation 19]
164. ~brave(lucy) [cnf transformation 25]
343. $false [subsumption resolution 164,154]
% SZS output end Proof for 3772495540126233465211816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not brave or not strong then someone is either not old or generous. If susan is generous then someone is either not quiet or not wise and vice versa. If john is not patient or kind then someone is creative or kind and vice versa. Everyone who is not tall is creative. If mary is quiet or funny then fred is generous and vice versa. If fred is funny then someone is kind and vice versa. If someone is either tall or not kind then someone is not tall or not old. Everyone who is not calm is either not old or not quiet. If someone is happy or creative then someone is not old or not creative and vice versa. Everyone who is either not rich or patient is not humble or not generous. If someone is both not humble and not calm then someone is either not happy or tall and vice versa. Everyone who is not strong is not creative or not patient. Everyone who is wise or not happy is happy or not calm and vice versa. If alice is not funny then someone is either not strong or not curious and vice versa. Everyone who is not rich or not generous is either humble or creative. If susan is either not strong or not brave then susan is either not strong or not patient. John is both not brave and not generous. Someone is either strong or old. Someone is not old. Someone is not generous or not quiet. Fred is either brave or patient. John is not humble or not generous. Someone is both not patient and not tall. | Mary is not calm. | neutral | (((~brave(lucy)<~>~strong(lucy)))=>(?[X]:((~old(X)<~>generous(X)))))&
((generous(susan))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(((~patient(john)|kind(john)))<=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~tall(X)=>creative(X)))&
(((quiet(mary)|funny(mary)))<=>(generous(fred)))&
((funny(fred))<=>(?[X]:(kind(X))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(~calm(X)=>(~old(X)<~>~quiet(X))))&
((?[X]:((happy(X)|creative(X))))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(~humble(X)|~generous(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:(~strong(X)=>(~creative(X)|~patient(X))))&
(![X]:((wise(X)|~happy(X))<=>(happy(X)|~calm(X))))&
((~funny(alice))<=>(?[X]:((~strong(X)<~>~curious(X)))))&
(![X]:((~rich(X)|~generous(X))=>(humble(X)<~>creative(X))))&
(((~strong(susan)<~>~brave(susan)))=>((~strong(susan)<~>~patient(susan))))&
((~brave(john)&~generous(john)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:(~old(X)))&
(?[X]:((~generous(X)|~quiet(X))))&
((brave(fred)<~>patient(fred)))&
((~humble(john)|~generous(john)))&
(?[X]:((~patient(X)&~tall(X)))) | ~calm(mary) | [] | null | 0 |
If someone is both not strong and not creative then someone is both not humble and brave and vice versa.
If someone is either generous or not creative then john is not happy and vice versa.
Everyone who is generous is either not creative or old and vice versa.
If someone is not kind or not tall then someone is not rich or old.
If alice is both not generous and kind then alice is both not brave and humble and vice versa.
Everyone who is old is either not creative or rich and vice versa.
If susan is brave then susan is either not kind or not strong and vice versa.
If someone is either not wise or wise then alice is both not kind and not old and vice versa.
If someone is not funny or happy then lucy is kind and vice versa.
Everyone who is both generous and not humble is either not curious or patient.
Everyone who is either strong or tall is curious or not strong and vice versa.
Everyone who is either funny or not wise is both not funny and strong and vice versa.
If someone is both kind and not curious then paul is creative or not brave and vice versa.
Everyone who is brave is both not creative and generous and vice versa.
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is either kind or not curious.
Alice is not tall or patient.
Someone is calm.
Someone is either old or not rich.
Someone is either not rich or not wise.
Someone is rich.
Someone is not strong.
John is not rich.
Someone is not happy. | Susan is happy. | neutral | ((?[X]:((~strong(X)&~creative(X))))<=>(?[X]:((~humble(X)&brave(X)))))&
((?[X]:((generous(X)<~>~creative(X))))<=>(~happy(john)))&
(![X]:(generous(X)<=>(~creative(X)<~>old(X))))&
((?[X]:((~kind(X)|~tall(X))))=>(?[X]:((~rich(X)|old(X)))))&
(((~generous(alice)&kind(alice)))<=>((~brave(alice)&humble(alice))))&
(![X]:(old(X)<=>(~creative(X)<~>rich(X))))&
((brave(susan))<=>((~kind(susan)<~>~strong(susan))))&
((?[X]:((~wise(X)<~>wise(X))))<=>((~kind(alice)&~old(alice))))&
((?[X]:((~funny(X)|happy(X))))<=>(kind(lucy)))&
(![X]:((generous(X)&~humble(X))=>(~curious(X)<~>patient(X))))&
(![X]:((strong(X)<~>tall(X))<=>(curious(X)|~strong(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(~funny(X)&strong(X))))&
((?[X]:((kind(X)&~curious(X))))<=>((creative(paul)|~brave(paul))))&
(![X]:(brave(X)<=>(~creative(X)&generous(X))))&
(![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)<~>~curious(X))))&
((~tall(alice)|patient(alice)))&
(?[X]:(calm(X)))&
(?[X]:((old(X)<~>~rich(X))))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(rich(X)))&
(?[X]:(~strong(X)))&
(~rich(john))&
(?[X]:(~happy(X))) | happy(susan) | [] | null | 0 |
Everyone who is either not creative or not patient is both brave and funny. Everyone who is not patient is not strong and vice versa. If susan is not funny or brave then someone is not strong or humble and vice versa. Everyone who is kind is not kind or happy. If fred is not curious or wise then someone is both not generous and not rich. Everyone who is either rich or not rich is either calm or not brave and vice versa. If someone is creative or old then someone is both kind and not kind and vice versa. Everyone who is not strong is both not humble and not kind. Everyone who is brave or not quiet is not old and vice versa. If fred is not curious then mary is both curious and quiet. Everyone who is rich or humble is rich and vice versa. Everyone who is both not happy and humble is both strong and not old and vice versa. Everyone who is either generous or not wise is calm. Everyone who is either not wise or not creative is both strong and creative. If someone is both calm and wise then someone is both curious and not calm and vice versa. If mary is both creative and not creative then someone is either not strong or calm and vice versa. Someone is both not rich and not humble. Someone is not wise. Alice is either not wise or patient. Someone is calm. John is not patient. | Mary is not calm. | contradiction | (![X]:((~creative(X)<~>~patient(X))=>(brave(X)&funny(X))))&
(![X]:(~patient(X)<=>~strong(X)))&
(((~funny(susan)|brave(susan)))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:(kind(X)=>(~kind(X)|happy(X))))&
(((~curious(fred)|wise(fred)))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((rich(X)<~>~rich(X))<=>(calm(X)<~>~brave(X))))&
((?[X]:((creative(X)|old(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:(~strong(X)=>(~humble(X)&~kind(X))))&
(![X]:((brave(X)|~quiet(X))<=>~old(X)))&
((~curious(fred))=>((curious(mary)&quiet(mary))))&
(![X]:((rich(X)|humble(X))<=>rich(X)))&
(![X]:((~happy(X)&humble(X))<=>(strong(X)&~old(X))))&
(![X]:((generous(X)<~>~wise(X))=>calm(X)))&
(![X]:((~wise(X)<~>~creative(X))=>(strong(X)&creative(X))))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(?[X]:((~rich(X)&~humble(X))))&
(?[X]:(~wise(X)))&
((~wise(alice)<~>patient(alice)))&
(?[X]:(calm(X)))&
(~patient(john)) | ~calm(mary) | [
"p0",
"p1",
"p5",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7698050283978660324527203
% SZS output start Proof for 7698050283978660324527203
1. ! [X0] : ((~creative(X0) <~> ~patient(X0)) => (funny(X0) & brave(X0))) [input p0]
2. ! [X0] : (~patient(X0) <=> ~strong(X0)) [input p1]
6. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p5]
7. ? [X0] : (old(X0) | creative(X0)) <=> ? [X0] : (~kind(X0) & kind(X0)) [input p6]
16. (~creative(mary) & creative(mary)) <=> ? [X0] : (~strong(X0) <~> calm(X0)) [input p15]
22. ~calm(mary) [input hypothesis]
23. ? [X0] : (old(X0) | creative(X0)) <=> ? [X1] : (~kind(X1) & kind(X1)) [rectify 7]
25. ! [X0] : ((funny(X0) & brave(X0)) | (~creative(X0) <=> ~patient(X0))) [ennf transformation 1]
33. ! [X0] : ((funny(X0) & brave(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) [nnf transformation 25]
34. ! [X0] : ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0))) [nnf transformation 2]
42. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 6]
43. (? [X0] : (old(X0) | creative(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~old(X0) & ~creative(X0))) [nnf transformation 23]
44. (? [X0] : (old(X0) | creative(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X2] : (~kind(X2) & kind(X2)) | ! [X3] : (~old(X3) & ~creative(X3))) [rectify 43]
45. ? [X0] : (old(X0) | creative(X0)) => (old(sK2) | creative(sK2)) [choice axiom]
46. ? [X2] : (~kind(X2) & kind(X2)) => (~kind(sK3) & kind(sK3)) [choice axiom]
47. ((old(sK2) | creative(sK2)) | ! [X1] : (kind(X1) | ~kind(X1))) & ((~kind(sK3) & kind(sK3)) | ! [X3] : (~old(X3) & ~creative(X3))) [skolemisation 44,46,45]
61. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (creative(mary) | ~creative(mary))) [nnf transformation 16]
62. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | creative(mary) | ~creative(mary)) [flattening 61]
63. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) | creative(mary) | ~creative(mary)) [rectify 62]
64. ? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) => ((~calm(sK6) | strong(sK6)) & (calm(sK6) | ~strong(sK6))) [choice axiom]
65. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(sK6) | strong(sK6)) & (calm(sK6) | ~strong(sK6))) | creative(mary) | ~creative(mary)) [skolemisation 63,64]
73. ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 33]
77. ~strong(X0) | patient(X0) [cnf transformation 34]
88. ~brave(X0) | calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 42]
89. ~brave(X0) | calm(X0) | rich(X0) | rich(X0) [cnf transformation 42]
96. kind(sK3) | ~creative(X3) [cnf transformation 47]
98. ~kind(sK3) | ~creative(X3) [cnf transformation 47]
127. creative(mary) | calm(X0) | strong(X0) [cnf transformation 65]
129. ~creative(mary) | calm(X0) | strong(X0) [cnf transformation 65]
138. ~calm(mary) [cnf transformation 22]
140. ~brave(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 88]
141. ~brave(X0) | calm(X0) | rich(X0) [duplicate literal removal 89]
192. ~brave(X0) | calm(X0) [subsumption resolution 140,141]
197. 12 <=> kind(sK3) [avatar definition]
202. 13 <=> ! [X3] : ~creative(X3) [avatar definition]
203. ~creative(X3) <- (13) [avatar component clause 202]
204. 13 | ~12 [avatar split clause 98,197,202]
206. 13 | 12 [avatar split clause 96,197,202]
247. 23 <=> creative(mary) [avatar definition]
252. 24 <=> ! [X0] : (calm(X0) | strong(X0)) [avatar definition]
253. calm(X0) | strong(X0) <- (24) [avatar component clause 252]
254. 24 | ~23 [avatar split clause 129,247,252]
256. 24 | 23 [avatar split clause 127,247,252]
275. strong(mary) <- (24) [resolution 253,138]
279. patient(mary) <- (24) [resolution 275,77]
282. brave(mary) | creative(mary) <- (24) [resolution 279,73]
285. brave(mary) <- (13, 24) [subsumption resolution 282,203]
286. calm(mary) <- (13, 24) [resolution 285,192]
287. $false <- (13, 24) [subsumption resolution 286,138]
288. ~13 | ~24 [avatar contradiction clause 287]
289. $false [avatar sat refutation 204,206,254,256,288]
% SZS output end Proof for 7698050283978660324527203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not wise is both not rich and wise.
If susan is not old then someone is curious and vice versa.
Everyone who is not happy is either strong or not brave and vice versa.
Everyone who is both humble and not humble is either happy or curious and vice versa.
If someone is either quiet or not tall then someone is either rich or not strong and vice versa.
If someone is not kind then someone is both creative and generous.
If someone is not funny or not calm then lucy is both not strong and not funny and vice versa.
Everyone who is not quiet or not brave is both not calm and generous and vice versa.
Everyone who is both not creative and strong is kind or wise.
If mary is creative or kind then fred is not strong.
If someone is not quiet or not funny then fred is calm.
If someone is patient or brave then someone is not curious or humble.
Everyone who is strong or not tall is both strong and funny and vice versa.
Everyone who is curious is both not patient and creative.
If someone is not patient then someone is creative and vice versa.
Everyone who is quiet or humble is not strong or not tall.
John is both not wise and not curious.
Paul is not humble or not curious.
Susan is curious.
Someone is both not generous and funny.
Someone is not old.
Someone is either not rich or patient.
Someone is funny.
Someone is not brave or patient. | Susan is old. | contradiction | (![X]:((~quiet(X)&~wise(X))=>(~rich(X)&wise(X))))&
((~old(susan))<=>(?[X]:(curious(X))))&
(![X]:(~happy(X)<=>(strong(X)<~>~brave(X))))&
(![X]:((humble(X)&~humble(X))<=>(happy(X)<~>curious(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((rich(X)<~>~strong(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((creative(X)&generous(X)))))&
((?[X]:((~funny(X)|~calm(X))))<=>((~strong(lucy)&~funny(lucy))))&
(![X]:((~quiet(X)|~brave(X))<=>(~calm(X)&generous(X))))&
(![X]:((~creative(X)&strong(X))=>(kind(X)|wise(X))))&
(((creative(mary)|kind(mary)))=>(~strong(fred)))&
((?[X]:((~quiet(X)|~funny(X))))=>(calm(fred)))&
((?[X]:((patient(X)|brave(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((strong(X)|~tall(X))<=>(strong(X)&funny(X))))&
(![X]:(curious(X)=>(~patient(X)&creative(X))))&
((?[X]:(~patient(X)))<=>(?[X]:(creative(X))))&
(![X]:((quiet(X)|humble(X))=>(~strong(X)|~tall(X))))&
((~wise(john)&~curious(john)))&
((~humble(paul)|~curious(paul)))&
(curious(susan))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)|patient(X)))) | old(susan) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9114566607793351604986138
% SZS output start Proof for 9114566607793351604986138
2. ~old(susan) <=> ? [X0] : curious(X0) [input p1]
19. curious(susan) [input p18]
25. old(susan) [input hypothesis]
41. (~old(susan) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | old(susan)) [nnf transformation 2]
42. (~old(susan) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | old(susan)) [rectify 41]
43. ? [X1] : curious(X1) => curious(sK0) [choice axiom]
44. (~old(susan) | ! [X0] : ~curious(X0)) & (curious(sK0) | old(susan)) [skolemisation 42,43]
87. ~old(susan) | ~curious(X0) [cnf transformation 44]
139. curious(susan) [cnf transformation 19]
147. old(susan) [cnf transformation 25]
150. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
151. ~curious(X0) <- (1) [avatar component clause 150]
153. 2 <=> old(susan) [avatar definition]
156. 1 | ~2 [avatar split clause 87,153,150]
323. 2 [avatar split clause 147,153]
326. $false <- (1) [resolution 151,139]
327. ~1 [avatar contradiction clause 326]
328. $false [avatar sat refutation 156,323,327]
% SZS output end Proof for 9114566607793351604986138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and kind is not strong or tall.
Everyone who is funny or creative is both not strong and tall.
Everyone who is not brave or not patient is not funny.
Everyone who is happy or not tall is either not generous or generous and vice versa.
Everyone who is happy or brave is rich and vice versa.
Everyone who is curious or kind is both not old and not curious.
If paul is either strong or humble then lucy is not rich or curious.
If paul is generous or not kind then susan is creative and vice versa.
If someone is calm or kind then someone is patient or old and vice versa.
Everyone who is quiet or not funny is either not calm or curious.
Everyone who is rich is not quiet or funny.
If someone is not rich then someone is either not old or calm and vice versa.
Everyone who is not strong or not calm is either curious or quiet and vice versa.
If lucy is either humble or not curious then someone is both old and generous.
Someone is generous or funny.
Someone is both not funny and not brave.
John is not funny or rich.
Someone is not funny. | Paul is not creative. | neutral | (![X]:((~curious(X)&kind(X))=>(~strong(X)|tall(X))))&
(![X]:((funny(X)|creative(X))=>(~strong(X)&tall(X))))&
(![X]:((~brave(X)|~patient(X))=>~funny(X)))&
(![X]:((happy(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((happy(X)|brave(X))<=>rich(X)))&
(![X]:((curious(X)|kind(X))=>(~old(X)&~curious(X))))&
(((strong(paul)<~>humble(paul)))=>((~rich(lucy)|curious(lucy))))&
(((generous(paul)|~kind(paul)))<=>(creative(susan)))&
((?[X]:((calm(X)|kind(X))))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((quiet(X)|~funny(X))=>(~calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~quiet(X)|funny(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)<~>quiet(X))))&
(((humble(lucy)<~>~curious(lucy)))=>(?[X]:((old(X)&generous(X)))))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((~funny(X)&~brave(X))))&
((~funny(john)|rich(john)))&
(?[X]:(~funny(X))) | ~creative(paul) | [] | null | 0 |
Everyone who is both humble and curious is wise. Everyone who is generous is not funny or rich and vice versa. If someone is either not calm or curious then someone is not tall. If someone is not generous or kind then paul is patient or brave. Everyone who is not wise or curious is tall or patient and vice versa. If someone is not humble then someone is either generous or funny. If someone is not happy or not old then someone is not old or old and vice versa. Everyone who is rich or funny is generous and vice versa. If alice is tall or not wise then lucy is either not funny or not patient. Everyone who is not curious is either not curious or not creative. If fred is not rich or quiet then fred is either curious or not quiet and vice versa. Everyone who is either not happy or brave is not humble or not old and vice versa. Everyone who is both not humble and generous is not brave. Everyone who is both not strong and not wise is not creative or not kind. If john is humble or not rich then someone is either not humble or rich and vice versa. Everyone who is humble or not generous is curious and vice versa. Lucy is rich. Fred is not tall. John is humble or quiet. Someone is both rich and curious. Lucy is either not humble or creative. Paul is either not calm or not tall. | John is humble. | entailment | (![X]:((humble(X)&curious(X))=>wise(X)))&
(![X]:(generous(X)<=>(~funny(X)|rich(X))))&
((?[X]:((~calm(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)|kind(X))))=>((patient(paul)|brave(paul))))&
(![X]:((~wise(X)|curious(X))<=>(tall(X)|patient(X))))&
((?[X]:(~humble(X)))=>(?[X]:((generous(X)<~>funny(X)))))&
((?[X]:((~happy(X)|~old(X))))<=>(?[X]:((~old(X)|old(X)))))&
(![X]:((rich(X)|funny(X))<=>generous(X)))&
(((tall(alice)|~wise(alice)))=>((~funny(lucy)<~>~patient(lucy))))&
(![X]:(~curious(X)=>(~curious(X)<~>~creative(X))))&
(((~rich(fred)|quiet(fred)))<=>((curious(fred)<~>~quiet(fred))))&
(![X]:((~happy(X)<~>brave(X))<=>(~humble(X)|~old(X))))&
(![X]:((~humble(X)&generous(X))=>~brave(X)))&
(![X]:((~strong(X)&~wise(X))=>(~creative(X)|~kind(X))))&
(((humble(john)|~rich(john)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((humble(X)|~generous(X))<=>curious(X)))&
(rich(lucy))&
(~tall(fred))&
((humble(john)|quiet(john)))&
(?[X]:((rich(X)&curious(X))))&
((~humble(lucy)<~>creative(lucy)))&
((~calm(paul)<~>~tall(paul))) | humble(john) | [
"p1",
"p7",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3062959129404421101782562
% SZS output start Proof for 3062959129404421101782562
2. ! [X0] : (generous(X0) <=> (rich(X0) | ~funny(X0))) [input p1]
8. ! [X0] : ((funny(X0) | rich(X0)) <=> generous(X0)) [input p7]
15. (~rich(john) | humble(john)) <=> ? [X0] : (~humble(X0) <~> rich(X0)) [input p14]
16. ! [X0] : ((~generous(X0) | humble(X0)) <=> curious(X0)) [input p15]
20. ? [X0] : (curious(X0) & rich(X0)) [input p19]
23. ~humble(john) [input hypothesis]
39. ! [X0] : ((generous(X0) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | ~generous(X0))) [nnf transformation 2]
40. ! [X0] : ((generous(X0) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ~generous(X0))) [flattening 39]
56. ! [X0] : (((funny(X0) | rich(X0)) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~rich(X0)))) [nnf transformation 8]
57. ! [X0] : ((funny(X0) | rich(X0) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~rich(X0)))) [flattening 56]
64. ((~rich(john) | humble(john)) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X0] : ((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (rich(john) & ~humble(john))) [nnf transformation 15]
65. (~rich(john) | humble(john) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X0] : ((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (rich(john) & ~humble(john))) [flattening 64]
66. (~rich(john) | humble(john) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X1] : ((~rich(X1) | humble(X1)) & (rich(X1) | ~humble(X1))) | (rich(john) & ~humble(john))) [rectify 65]
67. ? [X1] : ((~rich(X1) | humble(X1)) & (rich(X1) | ~humble(X1))) => ((~rich(sK4) | humble(sK4)) & (rich(sK4) | ~humble(sK4))) [choice axiom]
68. (~rich(john) | humble(john) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(sK4) | humble(sK4)) & (rich(sK4) | ~humble(sK4))) | (rich(john) & ~humble(john))) [skolemisation 66,67]
69. ! [X0] : (((~generous(X0) | humble(X0)) | ~curious(X0)) & (curious(X0) | (generous(X0) & ~humble(X0)))) [nnf transformation 16]
70. ! [X0] : ((~generous(X0) | humble(X0) | ~curious(X0)) & (curious(X0) | (generous(X0) & ~humble(X0)))) [flattening 69]
71. ? [X0] : (curious(X0) & rich(X0)) => (curious(sK5) & rich(sK5)) [choice axiom]
72. curious(sK5) & rich(sK5) [skolemisation 20,71]
76. ~funny(X0) | rich(X0) | ~generous(X0) [cnf transformation 40]
77. funny(X0) | generous(X0) [cnf transformation 40]
93. generous(X0) | ~funny(X0) [cnf transformation 57]
94. funny(X0) | rich(X0) | ~generous(X0) [cnf transformation 57]
119. ~rich(john) | humble(john) | ~humble(X0) | ~rich(X0) [cnf transformation 68]
122. ~generous(X0) | humble(X0) | ~curious(X0) [cnf transformation 70]
127. curious(sK5) [cnf transformation 72]
132. ~humble(john) [cnf transformation 23]
149. 4 <=> ! [X0] : generous(X0) [avatar definition]
150. generous(X0) <- (4) [avatar component clause 149]
188. ~generous(X0) | rich(X0) [subsumption resolution 94,76]
189. generous(X0) [subsumption resolution 93,77]
190. 4 [avatar split clause 189,149]
228. 21 <=> ! [X0] : (~humble(X0) | ~rich(X0)) [avatar definition]
229. ~humble(X0) | ~rich(X0) <- (21) [avatar component clause 228]
231. 22 <=> humble(john) [avatar definition]
235. 23 <=> rich(john) [avatar definition]
237. ~rich(john) <- (~23) [avatar component clause 235]
238. 21 | 22 | ~23 [avatar split clause 119,235,231,228]
280. ~22 [avatar split clause 132,231]
286. rich(X1) <- (4) [resolution 188,150]
289. $false <- (4, ~23) [resolution 286,237]
292. ~4 | 23 [avatar contradiction clause 289]
294. ~humble(X0) <- (4, 21) [subsumption resolution 229,286]
328. humble(X1) | ~curious(X1) <- (4) [resolution 122,150]
329. ~curious(X1) <- (4, 21) [subsumption resolution 328,294]
330. $false <- (4, 21) [resolution 329,127]
335. ~4 | ~21 [avatar contradiction clause 330]
336. $false [avatar sat refutation 190,238,280,292,335]
% SZS output end Proof for 3062959129404421101782562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is old or not humble and vice versa. If alice is not wise or tall then someone is old or not strong and vice versa. Everyone who is rich or patient is not old or curious and vice versa. If someone is either tall or wise then someone is either not old or generous and vice versa. Everyone who is both brave and humble is calm or not curious and vice versa. If john is strong or quiet then john is not kind and vice versa. If john is not creative then someone is either strong or not strong and vice versa. Everyone who is both not generous and not funny is not creative and vice versa. If someone is both kind and not patient then someone is old and vice versa. Everyone who is both creative and patient is not old and vice versa. If someone is either not generous or not creative then paul is either quiet or calm and vice versa. If someone is generous then someone is quiet or not curious and vice versa. If lucy is brave or not tall then fred is either rich or not patient. Everyone who is not kind is creative or funny. If someone is either creative or not wise then someone is generous and vice versa. If paul is not wise then fred is both tall and kind. Someone is both strong and quiet. Someone is not generous or brave. Lucy is not rich or not creative. Someone is both not strong and brave. Someone is not humble. Someone is both not calm and patient. Lucy is both rich and strong. Someone is either not tall or quiet. | Lucy is calm. | contradiction | (![X]:((~calm(X)<~>creative(X))<=>(old(X)|~humble(X))))&
(((~wise(alice)|tall(alice)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((rich(X)|patient(X))<=>(~old(X)|curious(X))))&
((?[X]:((tall(X)<~>wise(X))))<=>(?[X]:((~old(X)<~>generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(calm(X)|~curious(X))))&
(((strong(john)|quiet(john)))<=>(~kind(john)))&
((~creative(john))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((~generous(X)&~funny(X))<=>~creative(X)))&
((?[X]:((kind(X)&~patient(X))))<=>(?[X]:(old(X))))&
(![X]:((creative(X)&patient(X))<=>~old(X)))&
((?[X]:((~generous(X)<~>~creative(X))))<=>((quiet(paul)<~>calm(paul))))&
((?[X]:(generous(X)))<=>(?[X]:((quiet(X)|~curious(X)))))&
(((brave(lucy)|~tall(lucy)))=>((rich(fred)<~>~patient(fred))))&
(![X]:(~kind(X)=>(creative(X)|funny(X))))&
((?[X]:((creative(X)<~>~wise(X))))<=>(?[X]:(generous(X))))&
((~wise(paul))=>((tall(fred)&kind(fred))))&
(?[X]:((strong(X)&quiet(X))))&
(?[X]:((~generous(X)|brave(X))))&
((~rich(lucy)|~creative(lucy)))&
(?[X]:((~strong(X)&brave(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~calm(X)&patient(X))))&
((rich(lucy)&strong(lucy)))&
(?[X]:((~tall(X)<~>quiet(X)))) | calm(lucy) | [
"p0",
"p9",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 701329362987795682665576
% SZS output start Proof for 701329362987795682665576
1. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~humble(X0) | old(X0))) [input p0]
10. ! [X0] : ((patient(X0) & creative(X0)) <=> ~old(X0)) [input p9]
19. ~creative(lucy) | ~rich(lucy) [input p18]
23. strong(lucy) & rich(lucy) [input p22]
25. calm(lucy) [input hypothesis]
34. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (humble(X0) & ~old(X0))) & ((~humble(X0) | old(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 1]
35. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (humble(X0) & ~old(X0))) & (~humble(X0) | old(X0) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [flattening 34]
63. ! [X0] : (((patient(X0) & creative(X0)) | old(X0)) & (~old(X0) | (~patient(X0) | ~creative(X0)))) [nnf transformation 10]
64. ! [X0] : (((patient(X0) & creative(X0)) | old(X0)) & (~old(X0) | ~patient(X0) | ~creative(X0))) [flattening 63]
95. ~old(X0) | ~calm(X0) | creative(X0) [cnf transformation 35]
134. old(X0) | creative(X0) [cnf transformation 64]
161. ~creative(lucy) | ~rich(lucy) [cnf transformation 19]
167. rich(lucy) [cnf transformation 23]
171. calm(lucy) [cnf transformation 25]
398. 49 <=> rich(lucy) [avatar definition]
402. 50 <=> creative(lucy) [avatar definition]
404. ~creative(lucy) <- (~50) [avatar component clause 402]
405. ~49 | ~50 [avatar split clause 161,402,398]
406. 49 [avatar split clause 167,398]
435. ~calm(X0) | creative(X0) | creative(X0) [resolution 95,134]
438. ~calm(X0) | creative(X0) [duplicate literal removal 435]
442. creative(lucy) [resolution 438,171]
444. $false <- (~50) [subsumption resolution 442,404]
445. 50 [avatar contradiction clause 444]
446. $false [avatar sat refutation 405,406,445]
% SZS output end Proof for 701329362987795682665576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not quiet is either old or calm and vice versa.
If someone is not calm or curious then john is not tall or quiet and vice versa.
If alice is both not happy and quiet then someone is either old or funny.
Everyone who is not creative or not quiet is tall and vice versa.
Everyone who is not calm or not strong is generous.
If someone is not kind then fred is both not funny and old.
Everyone who is either calm or not humble is both not quiet and not strong.
If paul is not tall or not humble then someone is both not tall and tall.
If someone is not creative then lucy is either not wise or not humble and vice versa.
Everyone who is both not calm and not curious is either wise or calm and vice versa.
If someone is old then fred is either not tall or not strong.
Everyone who is both not patient and strong is old.
Everyone who is both old and not funny is not wise or humble.
If susan is not humble or not brave then someone is creative and vice versa.
John is either not quiet or not happy.
John is funny.
Mary is either not strong or happy.
Someone is generous or calm.
Lucy is curious or not calm.
John is not rich or calm. | Fred is generous. | neutral | (![X]:((~patient(X)|~quiet(X))<=>(old(X)<~>calm(X))))&
((?[X]:((~calm(X)|curious(X))))<=>((~tall(john)|quiet(john))))&
(((~happy(alice)&quiet(alice)))=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~creative(X)|~quiet(X))<=>tall(X)))&
(![X]:((~calm(X)|~strong(X))=>generous(X)))&
((?[X]:(~kind(X)))=>((~funny(fred)&old(fred))))&
(![X]:((calm(X)<~>~humble(X))=>(~quiet(X)&~strong(X))))&
(((~tall(paul)|~humble(paul)))=>(?[X]:((~tall(X)&tall(X)))))&
((?[X]:(~creative(X)))<=>((~wise(lucy)<~>~humble(lucy))))&
(![X]:((~calm(X)&~curious(X))<=>(wise(X)<~>calm(X))))&
((?[X]:(old(X)))=>((~tall(fred)<~>~strong(fred))))&
(![X]:((~patient(X)&strong(X))=>old(X)))&
(![X]:((old(X)&~funny(X))=>(~wise(X)|humble(X))))&
(((~humble(susan)|~brave(susan)))<=>(?[X]:(creative(X))))&
((~quiet(john)<~>~happy(john)))&
(funny(john))&
((~strong(mary)<~>happy(mary)))&
(?[X]:((generous(X)|calm(X))))&
((curious(lucy)|~calm(lucy)))&
((~rich(john)|calm(john))) | generous(fred) | [] | null | 0 |
Everyone who is creative is both humble and brave. If someone is both not strong and old then susan is not creative. Everyone who is not strong or quiet is either curious or old. Everyone who is both old and generous is not kind or not rich and vice versa. If alice is tall then someone is either not generous or not rich and vice versa. If fred is both funny and not quiet then lucy is either not generous or not wise. Everyone who is not quiet or old is either not calm or not creative and vice versa. Everyone who is both not old and curious is not wise or not brave and vice versa. Everyone who is wise or patient is both not generous and patient and vice versa. If someone is both not happy and not old then fred is strong or not curious. Everyone who is tall or not generous is brave. Everyone who is both not brave and kind is quiet or humble. If someone is not curious or curious then someone is not rich or not curious. Everyone who is both generous and patient is not humble and vice versa. If someone is both quiet and not old then someone is not happy or not kind. Everyone who is not funny or not patient is both not rich and kind and vice versa. Someone is either not wise or not generous. Someone is either not creative or not curious. Someone is either not quiet or calm. Someone is either quiet or not rich. | Susan is wise. | neutral | (![X]:(creative(X)=>(humble(X)&brave(X))))&
((?[X]:((~strong(X)&old(X))))=>(~creative(susan)))&
(![X]:((~strong(X)|quiet(X))=>(curious(X)<~>old(X))))&
(![X]:((old(X)&generous(X))<=>(~kind(X)|~rich(X))))&
((tall(alice))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
(((funny(fred)&~quiet(fred)))=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:((~quiet(X)|old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~old(X)&curious(X))<=>(~wise(X)|~brave(X))))&
(![X]:((wise(X)|patient(X))<=>(~generous(X)&patient(X))))&
((?[X]:((~happy(X)&~old(X))))=>((strong(fred)|~curious(fred))))&
(![X]:((tall(X)|~generous(X))=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((?[X]:((quiet(X)&~old(X))))=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(~rich(X)&kind(X))))&
(?[X]:((~wise(X)<~>~generous(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
(?[X]:((quiet(X)<~>~rich(X)))) | wise(susan) | [] | null | 0 |
Everyone who is humble is strong or quiet and vice versa. Everyone who is quiet or tall is both creative and not quiet. Everyone who is both not happy and not calm is either calm or not creative and vice versa. Everyone who is both rich and not tall is either not curious or wise. Everyone who is either happy or not funny is not humble and vice versa. Everyone who is both humble and creative is not quiet or funny. Everyone who is not calm or quiet is generous and vice versa. If someone is either curious or not old then someone is not patient or calm and vice versa. If someone is both calm and not quiet then someone is not rich and vice versa. If mary is either kind or not kind then someone is not patient or creative and vice versa. If someone is either not old or rich then susan is either rich or happy. Everyone who is either not curious or old is either quiet or not old. If paul is either tall or not calm then someone is humble or not quiet. Everyone who is both generous and strong is both not humble and not happy. Everyone who is not rich or strong is funny. Everyone who is both not rich and brave is tall and vice versa. Someone is strong. Mary is either happy or not quiet. Paul is either not happy or rich. Alice is both strong and not old. Lucy is both rich and not tall. Someone is both generous and rich. Paul is kind. Susan is both not happy and not calm. | Susan is generous. | entailment | (![X]:(humble(X)<=>(strong(X)|quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(creative(X)&~quiet(X))))&
(![X]:((~happy(X)&~calm(X))<=>(calm(X)<~>~creative(X))))&
(![X]:((rich(X)&~tall(X))=>(~curious(X)<~>wise(X))))&
(![X]:((happy(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)|funny(X))))&
(![X]:((~calm(X)|quiet(X))<=>generous(X)))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:(~rich(X))))&
(((kind(mary)<~>~kind(mary)))<=>(?[X]:((~patient(X)|creative(X)))))&
((?[X]:((~old(X)<~>rich(X))))=>((rich(susan)<~>happy(susan))))&
(![X]:((~curious(X)<~>old(X))=>(quiet(X)<~>~old(X))))&
(((tall(paul)<~>~calm(paul)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)|strong(X))=>funny(X)))&
(![X]:((~rich(X)&brave(X))<=>tall(X)))&
(?[X]:(strong(X)))&
((happy(mary)<~>~quiet(mary)))&
((~happy(paul)<~>rich(paul)))&
((strong(alice)&~old(alice)))&
((rich(lucy)&~tall(lucy)))&
(?[X]:((generous(X)&rich(X))))&
(kind(paul))&
((~happy(susan)&~calm(susan))) | generous(susan) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1744997995199266442830443
% SZS output start Proof for 1744997995199266442830443
7. ! [X0] : ((quiet(X0) | ~calm(X0)) <=> generous(X0)) [input p6]
24. ~calm(susan) & ~happy(susan) [input p23]
25. ~generous(susan) [input hypothesis]
45. ! [X0] : (((quiet(X0) | ~calm(X0)) | ~generous(X0)) & (generous(X0) | (~quiet(X0) & calm(X0)))) [nnf transformation 7]
46. ! [X0] : ((quiet(X0) | ~calm(X0) | ~generous(X0)) & (generous(X0) | (~quiet(X0) & calm(X0)))) [flattening 45]
94. generous(X0) | calm(X0) [cnf transformation 46]
142. ~calm(susan) [cnf transformation 24]
143. ~generous(susan) [cnf transformation 25]
252. calm(susan) [resolution 94,143]
253. $false [subsumption resolution 252,142]
% SZS output end Proof for 1744997995199266442830443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not strong and not happy.
Everyone who is both wise and not kind is either old or not creative and vice versa.
If someone is not strong or not wise then john is kind or not calm and vice versa.
Everyone who is not tall or quiet is not quiet.
If someone is either not strong or kind then someone is both funny and brave and vice versa.
Everyone who is either not wise or not strong is either not happy or quiet and vice versa.
If fred is generous or happy then susan is not rich or calm and vice versa.
If someone is not patient or curious then someone is happy or creative.
If alice is not wise then susan is either quiet or not brave.
If someone is either wise or not curious then alice is both not happy and strong and vice versa.
If someone is both not creative and kind then susan is not rich.
Everyone who is both not funny and not calm is both wise and not happy and vice versa.
If susan is not calm then lucy is not patient.
Everyone who is both curious and not creative is calm and vice versa.
Everyone who is not funny or not humble is either quiet or calm.
Someone is both old and patient.
Someone is both brave and not funny.
Someone is both curious and generous.
Someone is strong or quiet.
Alice is rich.
Susan is not rich or not tall.
Someone is either not rich or not calm. | John is not kind. | contradiction | (![X]:(funny(X)=>(~strong(X)&~happy(X))))&
(![X]:((wise(X)&~kind(X))<=>(old(X)<~>~creative(X))))&
((?[X]:((~strong(X)|~wise(X))))<=>((kind(john)|~calm(john))))&
(![X]:((~tall(X)|quiet(X))=>~quiet(X)))&
((?[X]:((~strong(X)<~>kind(X))))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~happy(X)<~>quiet(X))))&
(((generous(fred)|happy(fred)))<=>((~rich(susan)|calm(susan))))&
((?[X]:((~patient(X)|curious(X))))=>(?[X]:((happy(X)|creative(X)))))&
((~wise(alice))=>((quiet(susan)<~>~brave(susan))))&
((?[X]:((wise(X)<~>~curious(X))))<=>((~happy(alice)&strong(alice))))&
((?[X]:((~creative(X)&kind(X))))=>(~rich(susan)))&
(![X]:((~funny(X)&~calm(X))<=>(wise(X)&~happy(X))))&
((~calm(susan))=>(~patient(lucy)))&
(![X]:((curious(X)&~creative(X))<=>calm(X)))&
(![X]:((~funny(X)|~humble(X))=>(quiet(X)<~>calm(X))))&
(?[X]:((old(X)&patient(X))))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((curious(X)&generous(X))))&
(?[X]:((strong(X)|quiet(X))))&
(rich(alice))&
((~rich(susan)|~tall(susan)))&
(?[X]:((~rich(X)<~>~calm(X)))) | ~kind(john) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2238260358159411124703247
% SZS output start Proof for 2238260358159411124703247
1. ! [X0] : (funny(X0) => (~happy(X0) & ~strong(X0))) [input p0]
3. ? [X0] : (~wise(X0) | ~strong(X0)) <=> (~calm(john) | kind(john)) [input p2]
4. ! [X0] : ((quiet(X0) | ~tall(X0)) => ~quiet(X0)) [input p3]
6. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~happy(X0) <~> quiet(X0))) [input p5]
10. ? [X0] : (wise(X0) <~> ~curious(X0)) <=> (strong(alice) & ~happy(alice)) [input p9]
12. ! [X0] : ((~calm(X0) & ~funny(X0)) <=> (~happy(X0) & wise(X0))) [input p11]
14. ! [X0] : ((~creative(X0) & curious(X0)) <=> calm(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | ~funny(X0)) => (quiet(X0) <~> calm(X0))) [input p14]
23. ~kind(john) [input hypothesis]
26. ! [X0] : (~funny(X0) => (quiet(X0) <~> calm(X0))) [pure predicate removal 15]
27. ! [X0] : ((~happy(X0) & ~strong(X0)) | ~funny(X0)) [ennf transformation 1]
28. ! [X0] : (~quiet(X0) | (~quiet(X0) & tall(X0))) [ennf transformation 4]
33. ! [X0] : ((quiet(X0) <~> calm(X0)) | funny(X0)) [ennf transformation 26]
36. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & ((~calm(john) | kind(john)) | ! [X0] : (wise(X0) & strong(X0))) [nnf transformation 3]
37. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X0] : (wise(X0) & strong(X0))) [flattening 36]
38. (? [X0] : (~wise(X0) | ~strong(X0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X1] : (wise(X1) & strong(X1))) [rectify 37]
39. ? [X0] : (~wise(X0) | ~strong(X0)) => (~wise(sK0) | ~strong(sK0)) [choice axiom]
40. ((~wise(sK0) | ~strong(sK0)) | (calm(john) & ~kind(john))) & (~calm(john) | kind(john) | ! [X1] : (wise(X1) & strong(X1))) [skolemisation 38,39]
46. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 6]
53. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | (~strong(alice) | happy(alice))) & ((strong(alice) & ~happy(alice)) | ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [nnf transformation 10]
54. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X0] : ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [flattening 53]
55. (? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X1] : ((wise(X1) | curious(X1)) & (~curious(X1) | ~wise(X1)))) [rectify 54]
56. ? [X0] : ((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) => ((curious(sK4) | ~wise(sK4)) & (~curious(sK4) | wise(sK4))) [choice axiom]
57. (((curious(sK4) | ~wise(sK4)) & (~curious(sK4) | wise(sK4))) | ~strong(alice) | happy(alice)) & ((strong(alice) & ~happy(alice)) | ! [X1] : ((wise(X1) | curious(X1)) & (~curious(X1) | ~wise(X1)))) [skolemisation 55,56]
58. ! [X0] : (((~calm(X0) & ~funny(X0)) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | (calm(X0) | funny(X0)))) [nnf transformation 12]
59. ! [X0] : (((~calm(X0) & ~funny(X0)) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | calm(X0) | funny(X0))) [flattening 58]
60. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) | ~curious(X0)))) [nnf transformation 14]
61. ! [X0] : (((~creative(X0) & curious(X0)) | ~calm(X0)) & (calm(X0) | creative(X0) | ~curious(X0))) [flattening 60]
62. ! [X0] : (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | funny(X0)) [nnf transformation 33]
74. ~strong(X0) | ~funny(X0) [cnf transformation 27]
75. ~happy(X0) | ~funny(X0) [cnf transformation 27]
83. ~calm(john) | kind(john) | wise(X1) [cnf transformation 40]
87. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
100. strong(X0) | wise(X0) | quiet(X0) | happy(X0) [cnf transformation 46]
110. ~happy(alice) | ~curious(X1) | ~wise(X1) [cnf transformation 57]
119. ~funny(X0) | happy(X0) | ~wise(X0) [cnf transformation 59]
120. ~calm(X0) | happy(X0) | ~wise(X0) [cnf transformation 59]
123. ~calm(X0) | curious(X0) [cnf transformation 61]
125. calm(X0) | quiet(X0) | funny(X0) [cnf transformation 62]
138. ~kind(john) [cnf transformation 23]
139. ~quiet(X0) [duplicate literal removal 87]
141. 1 <=> calm(john) [avatar definition]
142. ~calm(john) <- (~1) [avatar component clause 141]
143. calm(john) <- (1) [avatar component clause 141]
154. 4 <=> kind(john) [avatar definition]
159. 5 <=> ! [X1] : wise(X1) [avatar definition]
160. wise(X1) <- (5) [avatar component clause 159]
161. 5 | 4 | ~1 [avatar split clause 83,141,154,159]
197. wise(X0) | strong(X0) | happy(X0) [subsumption resolution 100,139]
222. 18 <=> ! [X1] : ~curious(X1) [avatar definition]
223. ~curious(X1) <- (18) [avatar component clause 222]
248. 24 <=> happy(alice) [avatar definition]
249. ~happy(alice) <- (~24) [avatar component clause 248]
270. 29 <=> ! [X1] : (~curious(X1) | ~wise(X1)) [avatar definition]
271. ~curious(X1) | ~wise(X1) <- (29) [avatar component clause 270]
274. 29 | ~24 [avatar split clause 110,248,270]
279. ~wise(X0) | ~funny(X0) [subsumption resolution 119,75]
286. calm(X0) | funny(X0) [subsumption resolution 125,139]
303. ~4 [avatar split clause 138,154]
330. curious(john) <- (1) [resolution 143,123]
332. ~funny(X0) <- (5) [resolution 160,279]
356. happy(X1) | ~wise(X1) | funny(X1) [resolution 120,286]
360. happy(X1) | funny(X1) <- (5) [subsumption resolution 356,160]
361. happy(X1) <- (5) [subsumption resolution 360,332]
362. $false <- (5, ~24) [resolution 361,249]
365. ~5 | 24 [avatar contradiction clause 362]
366. ~curious(X1) <- (5, 29) [subsumption resolution 271,160]
367. 18 | ~5 | ~29 [avatar split clause 366,270,159,222]
368. $false <- (1, 18) [resolution 223,330]
375. ~1 | ~18 [avatar contradiction clause 368]
405. funny(john) <- (~1) [resolution 142,286]
407. 40 <=> funny(john) [avatar definition]
409. funny(john) <- (40) [avatar component clause 407]
415. 40 | 1 [avatar split clause 405,141,407]
450. strong(X0) | happy(X0) | ~funny(X0) [resolution 197,279]
453. strong(X0) | ~funny(X0) [subsumption resolution 450,75]
454. ~funny(X0) [subsumption resolution 453,74]
485. $false <- (40) [resolution 454,409]
488. ~40 [avatar contradiction clause 485]
490. $false [avatar sat refutation 161,274,303,365,367,375,415,488]
% SZS output end Proof for 2238260358159411124703247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and wise is not kind.
If fred is not old then susan is either not old or not funny and vice versa.
If lucy is both not patient and wise then mary is not old or rich.
Everyone who is not generous or humble is not funny or creative and vice versa.
If someone is either not creative or brave then someone is not curious or not humble.
If someone is not creative then fred is either not kind or not generous.
Everyone who is both not humble and not creative is not creative or calm.
Everyone who is quiet is not calm and vice versa.
If paul is either not strong or quiet then someone is not happy or not tall.
Everyone who is not tall or not strong is both patient and not kind.
Everyone who is brave or rich is happy and vice versa.
Everyone who is patient is not rich or not creative.
If lucy is either not kind or not funny then someone is both not old and brave and vice versa.
Everyone who is not curious is either not happy or funny and vice versa.
If lucy is either not patient or not rich then someone is both brave and not tall and vice versa.
Everyone who is tall or not tall is not quiet.
Someone is not wise or quiet.
Alice is not curious or not wise.
Paul is both kind and strong.
Paul is either not old or not funny.
Mary is not happy or not patient.
Mary is funny or not strong.
Someone is funny.
Someone is either strong or generous. | Alice is wise. | neutral | (![X]:((~calm(X)&wise(X))=>~kind(X)))&
((~old(fred))<=>((~old(susan)<~>~funny(susan))))&
(((~patient(lucy)&wise(lucy)))=>((~old(mary)|rich(mary))))&
(![X]:((~generous(X)|humble(X))<=>(~funny(X)|creative(X))))&
((?[X]:((~creative(X)<~>brave(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
((?[X]:(~creative(X)))=>((~kind(fred)<~>~generous(fred))))&
(![X]:((~humble(X)&~creative(X))=>(~creative(X)|calm(X))))&
(![X]:(quiet(X)<=>~calm(X)))&
(((~strong(paul)<~>quiet(paul)))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~tall(X)|~strong(X))=>(patient(X)&~kind(X))))&
(![X]:((brave(X)|rich(X))<=>happy(X)))&
(![X]:(patient(X)=>(~rich(X)|~creative(X))))&
(((~kind(lucy)<~>~funny(lucy)))<=>(?[X]:((~old(X)&brave(X)))))&
(![X]:(~curious(X)<=>(~happy(X)<~>funny(X))))&
(((~patient(lucy)<~>~rich(lucy)))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((tall(X)|~tall(X))=>~quiet(X)))&
(?[X]:((~wise(X)|quiet(X))))&
((~curious(alice)|~wise(alice)))&
((kind(paul)&strong(paul)))&
((~old(paul)<~>~funny(paul)))&
((~happy(mary)|~patient(mary)))&
((funny(mary)|~strong(mary)))&
(?[X]:(funny(X)))&
(?[X]:((strong(X)<~>generous(X)))) | wise(alice) | [] | null | 0 |
Everyone who is not quiet or not patient is not happy and vice versa. Everyone who is not curious or not calm is not brave. Everyone who is either humble or not patient is both not rich and old. If someone is both not quiet and rich then someone is humble and vice versa. Everyone who is both not kind and not brave is rich. If someone is either brave or patient then someone is not curious. Everyone who is both funny and not kind is both tall and creative and vice versa. Everyone who is patient is brave or wise. Everyone who is kind is either kind or calm. Everyone who is not happy or funny is both not creative and not tall. If mary is both tall and calm then paul is either old or not wise. If john is generous then someone is both not creative and old and vice versa. If someone is both tall and not quiet then someone is brave or calm. Everyone who is both not tall and happy is both brave and rich and vice versa. Everyone who is both not brave and patient is not tall and vice versa. Everyone who is either brave or not humble is quiet or calm. Fred is both not quiet and kind. Someone is either not strong or not generous. Susan is brave or quiet. Alice is not old. Someone is both not calm and not funny. Someone is humble. John is kind or not old. Mary is not happy or happy. | Mary is not creative. | entailment | (![X]:((~quiet(X)|~patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)&old(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(tall(X)&creative(X))))&
(![X]:(patient(X)=>(brave(X)|wise(X))))&
(![X]:(kind(X)=>(kind(X)<~>calm(X))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)&~tall(X))))&
(((tall(mary)&calm(mary)))=>((old(paul)<~>~wise(paul))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((~quiet(fred)&kind(fred)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(susan)|quiet(susan)))&
(~old(alice))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:(humble(X)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary))) | ~creative(mary) | [
"p6",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 902409725629422577462923
% SZS output start Proof for 902409725629422577462923
7. ! [X0] : ((~kind(X0) & funny(X0)) <=> (creative(X0) & tall(X0))) [input p6]
10. ! [X0] : ((funny(X0) | ~happy(X0)) => (~tall(X0) & ~creative(X0))) [input p9]
14. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (rich(X0) & brave(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p14]
25. creative(mary) [input hypothesis]
37. ! [X0] : ((~tall(X0) & ~creative(X0)) | (~funny(X0) & happy(X0))) [ennf transformation 10]
55. ! [X0] : (((~kind(X0) & funny(X0)) | (~creative(X0) | ~tall(X0))) & ((creative(X0) & tall(X0)) | (kind(X0) | ~funny(X0)))) [nnf transformation 7]
56. ! [X0] : (((~kind(X0) & funny(X0)) | ~creative(X0) | ~tall(X0)) & ((creative(X0) & tall(X0)) | kind(X0) | ~funny(X0))) [flattening 55]
66. ! [X0] : (((happy(X0) & ~tall(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 14]
67. ! [X0] : (((happy(X0) & ~tall(X0)) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | ~happy(X0) | tall(X0))) [flattening 66]
68. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 15]
69. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 68]
95. ~creative(X0) | funny(X0) | ~tall(X0) [cnf transformation 56]
100. ~creative(X0) | happy(X0) [cnf transformation 37]
101. ~creative(X0) | ~funny(X0) [cnf transformation 37]
110. ~happy(X0) | brave(X0) | tall(X0) [cnf transformation 67]
115. ~brave(X0) | tall(X0) [cnf transformation 69]
130. creative(mary) [cnf transformation 25]
166. 9 <=> tall(mary) [avatar definition]
241. happy(mary) [resolution 100,130]
242. ~funny(mary) [resolution 101,130]
283. funny(mary) | ~tall(mary) [resolution 95,130]
306. brave(mary) | tall(mary) [resolution 110,241]
314. tall(mary) [subsumption resolution 306,115]
315. 9 [avatar split clause 314,166]
321. ~tall(mary) [subsumption resolution 283,242]
322. ~9 [avatar split clause 321,166]
323. $false [avatar sat refutation 315,322]
% SZS output end Proof for 902409725629422577462923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not generous then someone is both curious and not rich and vice versa.
If paul is either not curious or quiet then susan is both not wise and not curious.
Everyone who is either curious or funny is funny and vice versa.
If alice is either quiet or wise then someone is both curious and not rich and vice versa.
Everyone who is not wise is both brave and generous and vice versa.
If john is not kind or not quiet then someone is not wise or not kind.
If someone is either not calm or not happy then someone is kind or rich and vice versa.
Everyone who is both brave and creative is either tall or generous.
If susan is not creative or kind then paul is happy and vice versa.
If someone is both patient and not curious then paul is brave.
If someone is not rich or wise then paul is strong or not tall.
Everyone who is either not brave or not happy is creative or brave and vice versa.
If someone is wise or happy then someone is not tall and vice versa.
If someone is not creative or not strong then paul is either strong or kind and vice versa.
If mary is both not humble and curious then someone is not brave or creative.
If someone is calm then someone is humble.
Mary is either not wise or curious.
Someone is not generous.
Someone is either curious or quiet.
Susan is either brave or strong.
Someone is both tall and wise.
Paul is both not quiet and rich.
Someone is both not happy and calm.
Someone is not humble. | Mary is not generous. | contradiction | ((?[X]:((~tall(X)&~generous(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(((~curious(paul)<~>quiet(paul)))=>((~wise(susan)&~curious(susan))))&
(![X]:((curious(X)<~>funny(X))<=>funny(X)))&
(((quiet(alice)<~>wise(alice)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~wise(X)<=>(brave(X)&generous(X))))&
(((~kind(john)|~quiet(john)))=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&creative(X))=>(tall(X)<~>generous(X))))&
(((~creative(susan)|kind(susan)))<=>(happy(paul)))&
((?[X]:((patient(X)&~curious(X))))=>(brave(paul)))&
((?[X]:((~rich(X)|wise(X))))=>((strong(paul)|~tall(paul))))&
(![X]:((~brave(X)<~>~happy(X))<=>(creative(X)|brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((strong(paul)<~>kind(paul))))&
(((~humble(mary)&curious(mary)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:(calm(X)))=>(?[X]:(humble(X))))&
((~wise(mary)<~>curious(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>quiet(X))))&
((brave(susan)<~>strong(susan)))&
(?[X]:((tall(X)&wise(X))))&
((~quiet(paul)&rich(paul)))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:(~humble(X))) | ~generous(mary) | [
"p2",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1353877747712883240519875
% SZS output start Proof for 1353877747712883240519875
3. ! [X0] : ((curious(X0) <~> funny(X0)) <=> funny(X0)) [input p2]
5. ! [X0] : (~wise(X0) <=> (generous(X0) & brave(X0))) [input p4]
17. ~wise(mary) <~> curious(mary) [input p16]
25. ~generous(mary) [input hypothesis]
46. ! [X0] : ((((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | ~funny(X0)) & (funny(X0) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0))))) [nnf transformation 3]
51. ! [X0] : ((~wise(X0) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | wise(X0))) [nnf transformation 5]
52. ! [X0] : ((~wise(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | wise(X0))) [flattening 51]
79. (~curious(mary) | wise(mary)) & (curious(mary) | ~wise(mary)) [nnf transformation 17]
100. funny(X0) | funny(X0) | ~curious(X0) [cnf transformation 46]
103. ~funny(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 46]
111. wise(X0) | generous(X0) [cnf transformation 52]
145. curious(mary) | ~wise(mary) [cnf transformation 79]
159. ~generous(mary) [cnf transformation 25]
162. funny(X0) | ~curious(X0) [duplicate literal removal 100]
163. ~funny(X0) | ~curious(X0) [duplicate literal removal 103]
210. ~curious(X0) [subsumption resolution 162,163]
366. ~wise(mary) [subsumption resolution 145,210]
387. generous(mary) [resolution 111,366]
389. $false [subsumption resolution 387,159]
% SZS output end Proof for 1353877747712883240519875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not creative is both calm and curious and vice versa. If someone is happy then someone is both not curious and old and vice versa. If someone is either generous or funny then lucy is happy. If lucy is brave or not brave then someone is not wise and vice versa. If alice is both patient and strong then alice is creative or not brave and vice versa. Everyone who is both not creative and not quiet is both calm and not rich. If susan is not wise then paul is not kind. Everyone who is both not creative and funny is old or wise and vice versa. Everyone who is either not kind or kind is not generous or not quiet. Everyone who is not calm is both not rich and kind. Everyone who is tall or quiet is not happy and vice versa. If someone is generous then someone is either wise or not creative and vice versa. Everyone who is creative is both happy and calm and vice versa. Everyone who is kind or not patient is not happy. If fred is not calm or wise then susan is both not brave and not curious and vice versa. Someone is either old or not humble. Someone is either not generous or brave. Someone is either not rich or curious. Someone is both not patient and rich. Paul is not strong. Mary is patient or calm. | Alice is happy. | contradiction | (![X]:((~kind(X)|~creative(X))<=>(calm(X)&curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)&old(X)))))&
((?[X]:((generous(X)<~>funny(X))))=>(happy(lucy)))&
(((brave(lucy)|~brave(lucy)))<=>(?[X]:(~wise(X))))&
(((patient(alice)&strong(alice)))<=>((creative(alice)|~brave(alice))))&
(![X]:((~creative(X)&~quiet(X))=>(calm(X)&~rich(X))))&
((~wise(susan))=>(~kind(paul)))&
(![X]:((~creative(X)&funny(X))<=>(old(X)|wise(X))))&
(![X]:((~kind(X)<~>kind(X))=>(~generous(X)|~quiet(X))))&
(![X]:(~calm(X)=>(~rich(X)&kind(X))))&
(![X]:((tall(X)|quiet(X))<=>~happy(X)))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(![X]:(creative(X)<=>(happy(X)&calm(X))))&
(![X]:((kind(X)|~patient(X))=>~happy(X)))&
(((~calm(fred)|wise(fred)))<=>((~brave(susan)&~curious(susan))))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:((~patient(X)&rich(X))))&
(~strong(paul))&
((patient(mary)|calm(mary))) | happy(alice) | [
"p0",
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6034882977243221449140389
% SZS output start Proof for 6034882977243221449140389
1. ! [X0] : ((~creative(X0) | ~kind(X0)) <=> (curious(X0) & calm(X0))) [input p0]
2. ? [X0] : happy(X0) <=> ? [X0] : (old(X0) & ~curious(X0)) [input p1]
8. ! [X0] : ((funny(X0) & ~creative(X0)) <=> (wise(X0) | old(X0))) [input p7]
22. happy(alice) [input hypothesis]
23. ? [X0] : happy(X0) <=> ? [X1] : (old(X1) & ~curious(X1)) [rectify 2]
33. ! [X0] : (((~creative(X0) | ~kind(X0)) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | (creative(X0) & kind(X0)))) [nnf transformation 1]
34. ! [X0] : ((~creative(X0) | ~kind(X0) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | (creative(X0) & kind(X0)))) [flattening 33]
35. (? [X0] : happy(X0) | ! [X1] : (~old(X1) | curious(X1))) & (? [X1] : (old(X1) & ~curious(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 23]
36. (? [X0] : happy(X0) | ! [X1] : (~old(X1) | curious(X1))) & (? [X2] : (old(X2) & ~curious(X2)) | ! [X3] : ~happy(X3)) [rectify 35]
37. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
38. ? [X2] : (old(X2) & ~curious(X2)) => (old(sK1) & ~curious(sK1)) [choice axiom]
39. (happy(sK0) | ! [X1] : (~old(X1) | curious(X1))) & ((old(sK1) & ~curious(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 36,38,37]
48. ! [X0] : (((funny(X0) & ~creative(X0)) | (~wise(X0) & ~old(X0))) & ((wise(X0) | old(X0)) | (~funny(X0) | creative(X0)))) [nnf transformation 8]
49. ! [X0] : (((funny(X0) & ~creative(X0)) | (~wise(X0) & ~old(X0))) & (wise(X0) | old(X0) | ~funny(X0) | creative(X0))) [flattening 48]
76. curious(X0) | creative(X0) [cnf transformation 34]
78. ~curious(sK1) | ~happy(X3) [cnf transformation 39]
79. old(sK1) | ~happy(X3) [cnf transformation 39]
95. ~old(X0) | ~creative(X0) [cnf transformation 49]
130. happy(alice) [cnf transformation 22]
142. 3 <=> ! [X3] : ~happy(X3) [avatar definition]
143. ~happy(X3) <- (3) [avatar component clause 142]
145. 4 <=> old(sK1) [avatar definition]
147. old(sK1) <- (4) [avatar component clause 145]
148. 3 | 4 [avatar split clause 79,145,142]
150. 5 <=> curious(sK1) [avatar definition]
152. ~curious(sK1) <- (~5) [avatar component clause 150]
153. 3 | ~5 [avatar split clause 78,150,142]
280. $false <- (3) [resolution 143,130]
281. ~3 [avatar contradiction clause 280]
284. creative(sK1) <- (~5) [resolution 76,152]
286. ~creative(sK1) <- (4) [resolution 95,147]
287. $false <- (4, ~5) [subsumption resolution 286,284]
288. ~4 | 5 [avatar contradiction clause 287]
289. $false [avatar sat refutation 148,153,281,288]
% SZS output end Proof for 6034882977243221449140389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either humble or funny then alice is both not patient and not humble and vice versa.
If susan is both not rich and not strong then mary is either not happy or quiet and vice versa.
Everyone who is not calm is not creative or not old and vice versa.
If someone is both creative and not quiet then paul is curious or not curious.
Everyone who is both not rich and generous is both happy and generous and vice versa.
Everyone who is either not strong or not old is both funny and not old and vice versa.
Everyone who is funny or not funny is both strong and kind and vice versa.
Everyone who is not quiet or generous is not brave and vice versa.
If alice is both creative and strong then alice is either old or not old.
If mary is calm then someone is calm and vice versa.
Everyone who is happy or not tall is quiet or not calm and vice versa.
Everyone who is patient is either not tall or rich and vice versa.
Everyone who is tall or brave is either not old or rich and vice versa.
If mary is not rich or not strong then mary is not calm or old and vice versa.
Everyone who is not kind is either happy or not old and vice versa.
Everyone who is either not humble or rich is both humble and brave.
Fred is both generous and wise.
Mary is not quiet or not wise.
Paul is not patient or happy.
Someone is not humble or not kind.
Someone is not creative.
Someone is either not humble or curious.
Susan is not calm or not strong. | Mary is not calm. | entailment | (((humble(alice)<~>funny(alice)))<=>((~patient(alice)&~humble(alice))))&
(((~rich(susan)&~strong(susan)))<=>((~happy(mary)<~>quiet(mary))))&
(![X]:(~calm(X)<=>(~creative(X)|~old(X))))&
((?[X]:((creative(X)&~quiet(X))))=>((curious(paul)|~curious(paul))))&
(![X]:((~rich(X)&generous(X))<=>(happy(X)&generous(X))))&
(![X]:((~strong(X)<~>~old(X))<=>(funny(X)&~old(X))))&
(![X]:((funny(X)|~funny(X))<=>(strong(X)&kind(X))))&
(![X]:((~quiet(X)|generous(X))<=>~brave(X)))&
(((creative(alice)&strong(alice)))=>((old(alice)<~>~old(alice))))&
((calm(mary))<=>(?[X]:(calm(X))))&
(![X]:((happy(X)|~tall(X))<=>(quiet(X)|~calm(X))))&
(![X]:(patient(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((tall(X)|brave(X))<=>(~old(X)<~>rich(X))))&
(((~rich(mary)|~strong(mary)))<=>((~calm(mary)|old(mary))))&
(![X]:(~kind(X)<=>(happy(X)<~>~old(X))))&
(![X]:((~humble(X)<~>rich(X))=>(humble(X)&brave(X))))&
((generous(fred)&wise(fred)))&
((~quiet(mary)|~wise(mary)))&
((~patient(paul)|happy(paul)))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)<~>curious(X))))&
((~calm(susan)|~strong(susan))) | ~calm(mary) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5280906078525545423128329
% SZS output start Proof for 5280906078525545423128329
2. (~strong(susan) & ~rich(susan)) <=> (~happy(mary) <~> quiet(mary)) [input p1]
3. ! [X0] : (~calm(X0) <=> (~old(X0) | ~creative(X0))) [input p2]
5. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (generous(X0) & happy(X0))) [input p4]
7. ! [X0] : ((~funny(X0) | funny(X0)) <=> (kind(X0) & strong(X0))) [input p6]
8. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> ~brave(X0)) [input p7]
13. ! [X0] : ((brave(X0) | tall(X0)) <=> (~old(X0) <~> rich(X0))) [input p12]
14. (~strong(mary) | ~rich(mary)) <=> (old(mary) | ~calm(mary)) [input p13]
15. ! [X0] : (~kind(X0) <=> (happy(X0) <~> ~old(X0))) [input p14]
24. calm(mary) [input hypothesis]
32. ((~strong(susan) & ~rich(susan)) | ((~happy(mary) | ~quiet(mary)) & (quiet(mary) | happy(mary)))) & (((~quiet(mary) | happy(mary)) & (quiet(mary) | ~happy(mary))) | (strong(susan) | rich(susan))) [nnf transformation 2]
33. ((~strong(susan) & ~rich(susan)) | ((~happy(mary) | ~quiet(mary)) & (quiet(mary) | happy(mary)))) & (((~quiet(mary) | happy(mary)) & (quiet(mary) | ~happy(mary))) | strong(susan) | rich(susan)) [flattening 32]
34. ! [X0] : ((~calm(X0) | (old(X0) & creative(X0))) & ((~old(X0) | ~creative(X0)) | calm(X0))) [nnf transformation 3]
35. ! [X0] : ((~calm(X0) | (old(X0) & creative(X0))) & (~old(X0) | ~creative(X0) | calm(X0))) [flattening 34]
36. ! [X0] : (((generous(X0) & ~rich(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 5]
37. ! [X0] : (((generous(X0) & ~rich(X0)) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | ~generous(X0) | rich(X0))) [flattening 36]
40. ! [X0] : (((~funny(X0) | funny(X0)) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | (funny(X0) & ~funny(X0)))) [nnf transformation 7]
41. ! [X0] : ((~funny(X0) | funny(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | (funny(X0) & ~funny(X0)))) [flattening 40]
42. ! [X0] : (((generous(X0) | ~quiet(X0)) | brave(X0)) & (~brave(X0) | (~generous(X0) & quiet(X0)))) [nnf transformation 8]
43. ! [X0] : ((generous(X0) | ~quiet(X0) | brave(X0)) & (~brave(X0) | (~generous(X0) & quiet(X0)))) [flattening 42]
52. ! [X0] : (((brave(X0) | tall(X0)) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 13]
53. ! [X0] : ((brave(X0) | tall(X0) | ((~old(X0) | ~rich(X0)) & (rich(X0) | old(X0)))) & (((~rich(X0) | old(X0)) & (rich(X0) | ~old(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 52]
54. ((~strong(mary) | ~rich(mary)) | (~old(mary) & calm(mary))) & ((old(mary) | ~calm(mary)) | (strong(mary) & rich(mary))) [nnf transformation 14]
55. (~strong(mary) | ~rich(mary) | (~old(mary) & calm(mary))) & (old(mary) | ~calm(mary) | (strong(mary) & rich(mary))) [flattening 54]
56. ! [X0] : ((~kind(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | kind(X0))) [nnf transformation 15]
75. ~strong(susan) | quiet(mary) | happy(mary) [cnf transformation 33]
79. ~calm(X0) | old(X0) [cnf transformation 35]
81. ~generous(X0) | happy(X0) | rich(X0) [cnf transformation 37]
91. strong(X0) | ~funny(X0) [cnf transformation 41]
92. strong(X0) | funny(X0) [cnf transformation 41]
93. kind(X0) | ~funny(X0) [cnf transformation 41]
94. kind(X0) | funny(X0) [cnf transformation 41]
98. ~quiet(X0) | generous(X0) | brave(X0) [cnf transformation 43]
112. ~brave(X0) | ~old(X0) | rich(X0) [cnf transformation 53]
120. ~strong(mary) | ~rich(mary) | ~old(mary) [cnf transformation 55]
123. ~kind(X0) | ~old(X0) | ~happy(X0) [cnf transformation 56]
138. calm(mary) [cnf transformation 24]
161. 4 <=> quiet(mary) [avatar definition]
162. quiet(mary) <- (4) [avatar component clause 161]
165. 5 <=> happy(mary) [avatar definition]
167. ~happy(mary) <- (~5) [avatar component clause 165]
169. 6 <=> strong(susan) [avatar definition]
171. ~strong(susan) <- (~6) [avatar component clause 169]
173. 5 | 4 | ~6 [avatar split clause 75,169,161,165]
182. kind(X0) [subsumption resolution 93,94]
183. strong(X0) [subsumption resolution 91,92]
188. 9 <=> calm(mary) [avatar definition]
190. calm(mary) <- (9) [avatar component clause 188]
197. ~rich(mary) | ~old(mary) [subsumption resolution 120,183]
199. 11 <=> old(mary) [avatar definition]
200. old(mary) <- (11) [avatar component clause 199]
203. 12 <=> rich(mary) [avatar definition]
205. ~rich(mary) <- (~12) [avatar component clause 203]
206. ~11 | ~12 [avatar split clause 197,203,199]
210. ~old(X0) | ~happy(X0) [subsumption resolution 123,182]
237. 9 [avatar split clause 138,188]
238. $false <- (~6) [subsumption resolution 171,183]
239. 6 [avatar contradiction clause 238]
242. old(mary) <- (9) [resolution 79,190]
246. 11 | ~9 [avatar split clause 242,188,199]
252. ~happy(mary) <- (11) [resolution 210,200]
257. ~5 | ~11 [avatar split clause 252,199,165]
277. generous(mary) | brave(mary) <- (4) [resolution 98,162]
279. 20 <=> brave(mary) [avatar definition]
281. brave(mary) <- (20) [avatar component clause 279]
283. 21 <=> generous(mary) [avatar definition]
285. generous(mary) <- (21) [avatar component clause 283]
286. 20 | 21 | ~4 [avatar split clause 277,161,283,279]
352. ~old(mary) | rich(mary) <- (20) [resolution 112,281]
353. rich(mary) <- (11, 20) [subsumption resolution 352,200]
354. $false <- (11, ~12, 20) [subsumption resolution 353,205]
355. ~11 | 12 | ~20 [avatar contradiction clause 354]
358. happy(mary) | rich(mary) <- (21) [resolution 285,81]
359. rich(mary) <- (~5, 21) [subsumption resolution 358,167]
360. $false <- (~5, ~12, 21) [subsumption resolution 359,205]
361. 5 | 12 | ~21 [avatar contradiction clause 360]
362. $false [avatar sat refutation 173,206,237,239,246,257,286,355,361]
% SZS output end Proof for 5280906078525545423128329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not curious is kind and vice versa.
Everyone who is not strong is wise and vice versa.
If someone is not happy or not patient then someone is not creative.
If someone is brave then lucy is either happy or not kind.
If someone is both creative and not brave then someone is old or strong.
Everyone who is either funny or curious is both happy and rich and vice versa.
Everyone who is either not funny or not old is either strong or not strong and vice versa.
Everyone who is rich is both kind and funny and vice versa.
If mary is creative then mary is quiet or curious.
Everyone who is calm is not creative or wise.
Everyone who is both not kind and funny is not brave or not old and vice versa.
Everyone who is either calm or not humble is both not quiet and strong and vice versa.
If someone is not strong or calm then fred is both not happy and funny.
Everyone who is not calm or wise is both happy and not wise and vice versa.
If alice is both funny and tall then someone is either happy or not strong.
Someone is not happy or creative.
Someone is either generous or not patient.
Susan is brave or not funny.
John is not creative.
Someone is tall.
John is humble.
Someone is either happy or not generous. | John is quiet. | entailment | (![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:(~strong(X)<=>wise(X)))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:(brave(X)))=>((happy(lucy)<~>~kind(lucy))))&
((?[X]:((creative(X)&~brave(X))))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(happy(X)&rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(rich(X)<=>(kind(X)&funny(X))))&
((creative(mary))=>((quiet(mary)|curious(mary))))&
(![X]:(calm(X)=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)&funny(X))<=>(~brave(X)|~old(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~strong(X)|calm(X))))=>((~happy(fred)&funny(fred))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~wise(X))))&
(((funny(alice)&tall(alice)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
((brave(susan)|~funny(susan)))&
(~creative(john))&
(?[X]:(tall(X)))&
(humble(john))&
(?[X]:((happy(X)<~>~generous(X)))) | quiet(john) | [
"p0",
"p1",
"p6",
"p10",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2783057124490947346376154
% SZS output start Proof for 2783057124490947346376154
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p0]
2. ! [X0] : (~strong(X0) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p6]
11. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (~old(X0) | ~brave(X0))) [input p10]
12. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (strong(X0) & ~quiet(X0))) [input p11]
13. ? [X0] : (calm(X0) | ~strong(X0)) => (funny(fred) & ~happy(fred)) [input p12]
14. ! [X0] : ((wise(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
21. humble(john) [input p20]
23. ~quiet(john) [input hypothesis]
33. (funny(fred) & ~happy(fred)) | ! [X0] : (~calm(X0) & strong(X0)) [ennf transformation 13]
36. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 36]
38. ! [X0] : ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))) [nnf transformation 2]
48. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 7]
51. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | (~funny(X0) | kind(X0)))) [nnf transformation 11]
52. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ~funny(X0) | kind(X0))) [flattening 51]
53. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 12]
54. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 53]
55. ! [X0] : (((wise(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [flattening 55]
70. ~strong(X0) | kind(X0) [cnf transformation 37]
73. wise(X0) | strong(X0) [cnf transformation 38]
90. ~old(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
91. ~old(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 48]
101. ~kind(X0) | old(X0) [cnf transformation 52]
108. ~humble(X0) | calm(X0) | ~strong(X0) | quiet(X0) [cnf transformation 54]
113. funny(fred) | ~calm(X0) [cnf transformation 33]
117. ~wise(X0) | ~wise(X0) [cnf transformation 56]
127. humble(john) [cnf transformation 21]
130. ~quiet(john) [cnf transformation 23]
131. ~wise(X0) [duplicate literal removal 117]
133. ~old(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 90]
134. ~funny(X0) | ~old(X0) | strong(X0) [duplicate literal removal 91]
175. ~funny(X0) | ~old(X0) [subsumption resolution 133,134]
190. 13 <=> ! [X0] : ~calm(X0) [avatar definition]
191. ~calm(X0) <- (13) [avatar component clause 190]
193. 14 <=> funny(fred) [avatar definition]
195. funny(fred) <- (14) [avatar component clause 193]
196. 13 | 14 [avatar split clause 113,193,190]
198. 15 <=> ! [X0] : strong(X0) [avatar definition]
199. strong(X0) <- (15) [avatar component clause 198]
256. strong(X0) [resolution 73,131]
257. 15 [avatar split clause 256,198]
258. kind(X0) <- (15) [resolution 199,70]
266. old(X0) <- (15) [resolution 101,258]
270. ~old(fred) <- (14) [resolution 175,195]
273. $false <- (14, 15) [subsumption resolution 270,266]
274. ~14 | ~15 [avatar contradiction clause 273]
311. calm(john) | ~strong(john) | quiet(john) [resolution 108,127]
314. ~strong(john) | quiet(john) <- (13) [subsumption resolution 311,191]
315. quiet(john) <- (13, 15) [subsumption resolution 314,199]
316. $false <- (13, 15) [subsumption resolution 315,130]
317. ~13 | ~15 [avatar contradiction clause 316]
318. $false [avatar sat refutation 196,257,274,317]
% SZS output end Proof for 2783057124490947346376154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then paul is both patient and quiet.
If paul is both not wise and old then someone is not humble.
Everyone who is either not rich or kind is not strong or not happy and vice versa.
If someone is either not kind or old then someone is either not wise or not brave and vice versa.
Everyone who is both not creative and strong is both not rich and calm.
If someone is both happy and strong then john is either not old or not brave.
Everyone who is not patient or strong is not old or wise and vice versa.
Everyone who is either not generous or not rich is funny.
If lucy is both brave and not humble then someone is both tall and not creative and vice versa.
Everyone who is either patient or not curious is either not happy or quiet.
If someone is either funny or happy then lucy is both not curious and humble.
Everyone who is both not old and not kind is either wise or not brave.
Everyone who is not patient is either quiet or kind and vice versa.
Everyone who is both not quiet and not curious is brave.
If someone is generous or not tall then someone is not tall or creative and vice versa.
If someone is either not quiet or funny then john is both not old and not wise and vice versa.
John is not strong.
Mary is not curious.
Someone is either not rich or creative.
Someone is both not tall and not curious.
Someone is both not brave and happy.
Fred is both not rich and not funny.
Someone is either not rich or generous. | Lucy is funny. | neutral | ((?[X]:(~kind(X)))=>((patient(paul)&quiet(paul))))&
(((~wise(paul)&old(paul)))=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>kind(X))<=>(~strong(X)|~happy(X))))&
((?[X]:((~kind(X)<~>old(X))))<=>(?[X]:((~wise(X)<~>~brave(X)))))&
(![X]:((~creative(X)&strong(X))=>(~rich(X)&calm(X))))&
((?[X]:((happy(X)&strong(X))))=>((~old(john)<~>~brave(john))))&
(![X]:((~patient(X)|strong(X))<=>(~old(X)|wise(X))))&
(![X]:((~generous(X)<~>~rich(X))=>funny(X)))&
(((brave(lucy)&~humble(lucy)))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((patient(X)<~>~curious(X))=>(~happy(X)<~>quiet(X))))&
((?[X]:((funny(X)<~>happy(X))))=>((~curious(lucy)&humble(lucy))))&
(![X]:((~old(X)&~kind(X))=>(wise(X)<~>~brave(X))))&
(![X]:(~patient(X)<=>(quiet(X)<~>kind(X))))&
(![X]:((~quiet(X)&~curious(X))=>brave(X)))&
((?[X]:((generous(X)|~tall(X))))<=>(?[X]:((~tall(X)|creative(X)))))&
((?[X]:((~quiet(X)<~>funny(X))))<=>((~old(john)&~wise(john))))&
(~strong(john))&
(~curious(mary))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((~tall(X)&~curious(X))))&
(?[X]:((~brave(X)&happy(X))))&
((~rich(fred)&~funny(fred)))&
(?[X]:((~rich(X)<~>generous(X)))) | funny(lucy) | [] | null | 0 |
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