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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is wise then susan is either strong or wise and vice versa.
Everyone who is not wise is humble and vice versa.
If lucy is both humble and not patient then someone is generous or not curious.
Everyone who is both not happy and not calm is both not wise and rich.
Everyone who is brave is creative or patient and vice versa.
If lucy is either not brave or generous then lucy is both curious and calm and vice versa.
Everyone who is not old or not generous is either funny or curious and vice versa.
If someone is either not tall or not wise then susan is tall or rich.
Everyone who is brave is tall and vice versa.
Everyone who is old is both tall and not old and vice versa.
If alice is either not calm or wise then someone is either not kind or kind.
Everyone who is quiet is kind.
Everyone who is not funny or generous is not happy or not strong and vice versa.
Everyone who is generous or curious is creative or not happy.
Everyone who is either kind or not kind is not curious and vice versa.
Lucy is either not humble or not strong.
Someone is either rich or strong.
Someone is either not strong or not creative.
Someone is either happy or not funny.
Mary is happy.
Mary is funny.
Mary is not calm.
|
Alice is not quiet.
|
neutral
|
((?[X]:(wise(X)))<=>((strong(susan)<~>wise(susan))))&
(![X]:(~wise(X)<=>humble(X)))&
(((humble(lucy)&~patient(lucy)))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~wise(X)&rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
(((~brave(lucy)<~>generous(lucy)))<=>((curious(lucy)&calm(lucy))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)<~>curious(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>((tall(susan)|rich(susan))))&
(![X]:(brave(X)<=>tall(X)))&
(![X]:(old(X)<=>(tall(X)&~old(X))))&
(((~calm(alice)<~>wise(alice)))=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((~funny(X)|generous(X))<=>(~happy(X)|~strong(X))))&
(![X]:((generous(X)|curious(X))=>(creative(X)|~happy(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~curious(X)))&
((~humble(lucy)<~>~strong(lucy)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(?[X]:((happy(X)<~>~funny(X))))&
(happy(mary))&
(funny(mary))&
(~calm(mary))
|
~quiet(alice)
|
[] | null | 0 |
Everyone who is either strong or generous is both not curious and not wise.
If someone is not happy then someone is both not patient and not calm and vice versa.
Everyone who is not funny is both humble and funny and vice versa.
If fred is either old or not calm then fred is curious or funny.
Everyone who is generous is wise.
If lucy is either not kind or not generous then john is not happy or not funny and vice versa.
Everyone who is either not creative or old is either not humble or patient and vice versa.
Everyone who is curious or calm is brave.
If mary is either not calm or not rich then someone is either old or not quiet.
Everyone who is either not happy or not generous is either happy or strong and vice versa.
Everyone who is either kind or not happy is both not quiet and not calm and vice versa.
If mary is either not rich or not quiet then john is not funny or quiet.
If someone is not generous or strong then someone is generous or not generous and vice versa.
Everyone who is old or quiet is both not rich and not happy and vice versa.
Everyone who is not strong is both strong and kind and vice versa.
Everyone who is not rich is both brave and not creative.
Someone is either kind or not creative.
Alice is either not old or not tall.
Someone is not patient.
Someone is happy.
Someone is not quiet.
|
Alice is generous.
|
entailment
|
(![X]:((strong(X)<~>generous(X))=>(~curious(X)&~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:(~funny(X)<=>(humble(X)&funny(X))))&
(((old(fred)<~>~calm(fred)))=>((curious(fred)|funny(fred))))&
(![X]:(generous(X)=>wise(X)))&
(((~kind(lucy)<~>~generous(lucy)))<=>((~happy(john)|~funny(john))))&
(![X]:((~creative(X)<~>old(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((curious(X)|calm(X))=>brave(X)))&
(((~calm(mary)<~>~rich(mary)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>(happy(X)<~>strong(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~quiet(X)&~calm(X))))&
(((~rich(mary)<~>~quiet(mary)))=>((~funny(john)|quiet(john))))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((old(X)|quiet(X))<=>(~rich(X)&~happy(X))))&
(![X]:(~strong(X)<=>(strong(X)&kind(X))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(?[X]:((kind(X)<~>~creative(X))))&
((~old(alice)<~>~tall(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(happy(X)))&
(?[X]:(~quiet(X)))
|
generous(alice)
|
[
"p9",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 10134532052309424976729
% SZS output start Proof for 10134532052309424976729
10. ! [X0] : ((~happy(X0) <~> ~generous(X0)) <=> (happy(X0) <~> strong(X0))) [input p9]
15. ! [X0] : (~strong(X0) <=> (kind(X0) & strong(X0))) [input p14]
22. ~generous(alice) [input hypothesis]
50. ! [X0] : ((((generous(X0) | happy(X0)) & (~generous(X0) | ~happy(X0))) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))))) [nnf transformation 10]
61. ! [X0] : ((~strong(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | strong(X0))) [nnf transformation 15]
62. ! [X0] : ((~strong(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | strong(X0))) [flattening 61]
107. ~strong(X0) | ~happy(X0) | ~happy(X0) | generous(X0) [cnf transformation 50]
111. generous(X0) | happy(X0) | happy(X0) | ~strong(X0) [cnf transformation 50]
129. strong(X0) | strong(X0) [cnf transformation 62]
140. ~generous(alice) [cnf transformation 22]
141. strong(X0) [duplicate literal removal 129]
144. ~strong(X0) | ~happy(X0) | generous(X0) [duplicate literal removal 107]
146. generous(X0) | happy(X0) | ~strong(X0) [duplicate literal removal 111]
208. ~strong(X0) | generous(X0) [subsumption resolution 144,146]
246. generous(X0) [resolution 208,141]
247. $false [resolution 246,140]
% SZS output end Proof for 10134532052309424976729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not patient or not old then susan is both not brave and not kind.
Everyone who is both not funny and not rich is both happy and funny.
Everyone who is not wise is both not tall and not rich.
Everyone who is both calm and creative is brave and vice versa.
Everyone who is both not brave and curious is both curious and not quiet.
Everyone who is quiet is wise or not patient and vice versa.
Everyone who is tall is not generous and vice versa.
Everyone who is both brave and not generous is both not curious and funny.
If john is not old or not funny then mary is both wise and not wise.
If someone is either rich or not calm then susan is not creative or not tall.
Everyone who is not tall is quiet or not patient and vice versa.
If mary is not old then someone is either not strong or calm.
Everyone who is both not strong and brave is both generous and creative and vice versa.
Everyone who is not generous is both not patient and humble and vice versa.
If paul is not rich or old then fred is either strong or wise.
Everyone who is either not strong or quiet is not creative.
Paul is creative or patient.
John is both not kind and not strong.
Someone is either brave or humble.
Someone is either humble or strong.
John is not kind.
John is either not brave or kind.
Susan is either not creative or creative.
|
Susan is quiet.
|
entailment
|
(((~patient(lucy)<~>~old(lucy)))=>((~brave(susan)&~kind(susan))))&
(![X]:((~funny(X)&~rich(X))=>(happy(X)&funny(X))))&
(![X]:(~wise(X)=>(~tall(X)&~rich(X))))&
(![X]:((calm(X)&creative(X))<=>brave(X)))&
(![X]:((~brave(X)&curious(X))=>(curious(X)&~quiet(X))))&
(![X]:(quiet(X)<=>(wise(X)|~patient(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((brave(X)&~generous(X))=>(~curious(X)&funny(X))))&
(((~old(john)|~funny(john)))=>((wise(mary)&~wise(mary))))&
((?[X]:((rich(X)<~>~calm(X))))=>((~creative(susan)|~tall(susan))))&
(![X]:(~tall(X)<=>(quiet(X)|~patient(X))))&
((~old(mary))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((~strong(X)&brave(X))<=>(generous(X)&creative(X))))&
(![X]:(~generous(X)<=>(~patient(X)&humble(X))))&
(((~rich(paul)|old(paul)))=>((strong(fred)<~>wise(fred))))&
(![X]:((~strong(X)<~>quiet(X))=>~creative(X)))&
((creative(paul)|patient(paul)))&
((~kind(john)&~strong(john)))&
(?[X]:((brave(X)<~>humble(X))))&
(?[X]:((humble(X)<~>strong(X))))&
(~kind(john))&
((~brave(john)<~>kind(john)))&
((~creative(susan)<~>creative(susan)))
|
quiet(susan)
|
[
"p5",
"p6",
"p10",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 9102643148106635440921154
% SZS output start Proof for 9102643148106635440921154
6. ! [X0] : (quiet(X0) <=> (~patient(X0) | wise(X0))) [input p5]
7. ! [X0] : (tall(X0) <=> ~generous(X0)) [input p6]
11. ! [X0] : (~tall(X0) <=> (~patient(X0) | quiet(X0))) [input p10]
14. ! [X0] : (~generous(X0) <=> (humble(X0) & ~patient(X0))) [input p13]
24. ~quiet(susan) [input hypothesis]
44. ! [X0] : ((quiet(X0) | (patient(X0) & ~wise(X0))) & ((~patient(X0) | wise(X0)) | ~quiet(X0))) [nnf transformation 6]
45. ! [X0] : ((quiet(X0) | (patient(X0) & ~wise(X0))) & (~patient(X0) | wise(X0) | ~quiet(X0))) [flattening 44]
46. ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))) [nnf transformation 7]
48. ! [X0] : ((~tall(X0) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | tall(X0))) [nnf transformation 11]
49. ! [X0] : ((~tall(X0) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | tall(X0))) [flattening 48]
55. ! [X0] : ((~generous(X0) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | generous(X0))) [nnf transformation 14]
56. ! [X0] : ((~generous(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | generous(X0))) [flattening 55]
80. quiet(X0) | patient(X0) [cnf transformation 45]
81. ~generous(X0) | ~tall(X0) [cnf transformation 46]
88. ~patient(X0) | quiet(X0) | tall(X0) [cnf transformation 49]
97. ~patient(X0) | generous(X0) [cnf transformation 56]
118. ~quiet(susan) [cnf transformation 24]
157. 9 <=> tall(susan) [avatar definition]
165. quiet(X0) | tall(X0) [subsumption resolution 88,80]
232. patient(susan) [resolution 80,118]
235. generous(susan) [resolution 97,232]
236. ~tall(susan) [resolution 235,81]
239. tall(susan) [resolution 165,118]
243. 9 [avatar split clause 239,157]
244. ~9 [avatar split clause 236,157]
245. $false [avatar sat refutation 243,244]
% SZS output end Proof for 9102643148106635440921154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or humble then fred is rich and vice versa.
If alice is not wise or calm then mary is both not calm and not funny and vice versa.
Everyone who is either not generous or wise is kind and vice versa.
If susan is both not humble and creative then fred is not humble or generous.
If paul is both quiet and rich then lucy is generous or rich.
Everyone who is either rich or strong is both tall and not creative.
Everyone who is both not generous and not strong is both not tall and not humble and vice versa.
Everyone who is strong or not funny is either humble or generous and vice versa.
If someone is either not kind or rich then fred is either not funny or not strong and vice versa.
Everyone who is either humble or not funny is patient or not calm and vice versa.
Everyone who is both not creative and not strong is either not curious or old and vice versa.
If someone is not strong or not calm then susan is either not kind or patient and vice versa.
Everyone who is not curious or not patient is both not humble and rich.
Everyone who is either not humble or curious is both old and not tall and vice versa.
If someone is both not curious and funny then fred is either calm or not funny.
If someone is not humble then someone is either humble or rich and vice versa.
Paul is both humble and not brave.
Someone is curious or kind.
Fred is either not rich or curious.
Susan is both brave and wise.
Someone is not rich.
Susan is either rich or not humble.
John is kind.
|
Paul is strong.
|
contradiction
|
((?[X]:((~generous(X)|humble(X))))<=>(rich(fred)))&
(((~wise(alice)|calm(alice)))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>kind(X)))&
(((~humble(susan)&creative(susan)))=>((~humble(fred)|generous(fred))))&
(((quiet(paul)&rich(paul)))=>((generous(lucy)|rich(lucy))))&
(![X]:((rich(X)<~>strong(X))=>(tall(X)&~creative(X))))&
(![X]:((~generous(X)&~strong(X))<=>(~tall(X)&~humble(X))))&
(![X]:((strong(X)|~funny(X))<=>(humble(X)<~>generous(X))))&
((?[X]:((~kind(X)<~>rich(X))))<=>((~funny(fred)<~>~strong(fred))))&
(![X]:((humble(X)<~>~funny(X))<=>(patient(X)|~calm(X))))&
(![X]:((~creative(X)&~strong(X))<=>(~curious(X)<~>old(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~kind(susan)<~>patient(susan))))&
(![X]:((~curious(X)|~patient(X))=>(~humble(X)&rich(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(old(X)&~tall(X))))&
((?[X]:((~curious(X)&funny(X))))=>((calm(fred)<~>~funny(fred))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)<~>rich(X)))))&
((humble(paul)&~brave(paul)))&
(?[X]:((curious(X)|kind(X))))&
((~rich(fred)<~>curious(fred)))&
((brave(susan)&wise(susan)))&
(?[X]:(~rich(X)))&
((rich(susan)<~>~humble(susan)))&
(kind(john))
|
strong(paul)
|
[
"p10",
"p12",
"p13",
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 3274838305813764796239043
% SZS output start Proof for 3274838305813764796239043
11. ! [X0] : ((~strong(X0) & ~creative(X0)) <=> (~curious(X0) <~> old(X0))) [input p10]
13. ! [X0] : ((~patient(X0) | ~curious(X0)) => (rich(X0) & ~humble(X0))) [input p12]
14. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (~tall(X0) & old(X0))) [input p13]
17. ~brave(paul) & humble(paul) [input p16]
24. strong(paul) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~humble(X0)) | (patient(X0) & curious(X0))) [ennf transformation 13]
50. ! [X0] : (((~strong(X0) & ~creative(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (strong(X0) | creative(X0)))) [nnf transformation 11]
51. ! [X0] : (((~strong(X0) & ~creative(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | strong(X0) | creative(X0))) [flattening 50]
56. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (tall(X0) | ~old(X0))) & ((~tall(X0) & old(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 14]
57. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | tall(X0) | ~old(X0)) & ((~tall(X0) & old(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [flattening 56]
116. ~old(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 51]
123. ~humble(X0) | curious(X0) [cnf transformation 30]
128. old(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 57]
139. humble(paul) [cnf transformation 17]
150. strong(paul) [cnf transformation 24]
270. ~humble(X0) | old(X0) [subsumption resolution 128,123]
330. curious(paul) [resolution 123,139]
337. old(paul) [resolution 270,139]
574. ~curious(paul) | ~strong(paul) [resolution 116,337]
576. ~strong(paul) [subsumption resolution 574,330]
577. $false [subsumption resolution 576,150]
% SZS output end Proof for 3274838305813764796239043
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not quiet is either not kind or not curious and vice versa.
Everyone who is both curious and not curious is either generous or quiet and vice versa.
Everyone who is not happy is both not calm and not tall.
If john is either not wise or not humble then someone is strong or not calm.
If alice is both not funny and humble then lucy is both old and not tall and vice versa.
Everyone who is either not patient or brave is both humble and not happy and vice versa.
Everyone who is tall or not creative is either not brave or not creative.
Everyone who is not quiet or not curious is happy and vice versa.
If paul is both funny and rich then fred is not rich.
Everyone who is both not strong and happy is both not creative and not kind and vice versa.
Everyone who is funny or creative is not wise and vice versa.
Everyone who is brave or funny is rich or not tall and vice versa.
Everyone who is either not creative or not quiet is either happy or not kind and vice versa.
Everyone who is not funny is either not humble or not strong and vice versa.
If paul is calm then mary is humble or kind.
Everyone who is funny or not humble is either happy or not brave and vice versa.
Mary is either not happy or wise.
Someone is not strong or not quiet.
Someone is either brave or not kind.
John is either generous or not happy.
Someone is both not old and not strong.
Someone is either generous or not kind.
Fred is not happy or not creative.
|
Paul is curious.
|
neutral
|
(![X]:((old(X)&~quiet(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((curious(X)&~curious(X))<=>(generous(X)<~>quiet(X))))&
(![X]:(~happy(X)=>(~calm(X)&~tall(X))))&
(((~wise(john)<~>~humble(john)))=>(?[X]:((strong(X)|~calm(X)))))&
(((~funny(alice)&humble(alice)))<=>((old(lucy)&~tall(lucy))))&
(![X]:((~patient(X)<~>brave(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)|~creative(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~curious(X))<=>happy(X)))&
(((funny(paul)&rich(paul)))=>(~rich(fred)))&
(![X]:((~strong(X)&happy(X))<=>(~creative(X)&~kind(X))))&
(![X]:((funny(X)|creative(X))<=>~wise(X)))&
(![X]:((brave(X)|funny(X))<=>(rich(X)|~tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(happy(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(~humble(X)<~>~strong(X))))&
((calm(paul))=>((humble(mary)|kind(mary))))&
(![X]:((funny(X)|~humble(X))<=>(happy(X)<~>~brave(X))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((generous(john)<~>~happy(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:((generous(X)<~>~kind(X))))&
((~happy(fred)|~creative(fred)))
|
curious(paul)
|
[] | null | 0 |
If someone is not old or curious then lucy is not creative or curious. If someone is both not rich and not quiet then john is brave and vice versa. Everyone who is strong or not creative is brave. Everyone who is both not brave and old is either not kind or quiet and vice versa. Everyone who is either not rich or not happy is not brave or tall and vice versa. If someone is not humble or not calm then someone is both brave and strong and vice versa. Everyone who is not quiet or creative is not strong or not patient. Everyone who is both not creative and not curious is either creative or not funny and vice versa. If susan is either not happy or not old then john is either not rich or not old. If alice is both not wise and curious then someone is either creative or wise. If paul is not strong or not calm then someone is kind or old. Everyone who is not rich or kind is either old or wise. If susan is not funny then someone is rich and vice versa. If someone is both not quiet and kind then someone is not brave and vice versa. If susan is wise or quiet then susan is not brave or not wise and vice versa. Everyone who is either wise or rich is creative or not generous. Paul is not calm or not kind. Someone is not brave or not rich. Lucy is not patient or not brave. Susan is calm. Fred is not strong or calm. Paul is not tall. Paul is both not wise and not tall. Someone is patient or not curious.
|
John is not kind.
|
neutral
|
((?[X]:((~old(X)|curious(X))))=>((~creative(lucy)|curious(lucy))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(brave(john)))&
(![X]:((strong(X)|~creative(X))=>brave(X)))&
(![X]:((~brave(X)&old(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(~brave(X)|tall(X))))&
((?[X]:((~humble(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((~quiet(X)|creative(X))=>(~strong(X)|~patient(X))))&
(![X]:((~creative(X)&~curious(X))<=>(creative(X)<~>~funny(X))))&
(((~happy(susan)<~>~old(susan)))=>((~rich(john)<~>~old(john))))&
(((~wise(alice)&curious(alice)))=>(?[X]:((creative(X)<~>wise(X)))))&
(((~strong(paul)|~calm(paul)))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((~rich(X)|kind(X))=>(old(X)<~>wise(X))))&
((~funny(susan))<=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&kind(X))))<=>(?[X]:(~brave(X))))&
(((wise(susan)|quiet(susan)))<=>((~brave(susan)|~wise(susan))))&
(![X]:((wise(X)<~>rich(X))=>(creative(X)|~generous(X))))&
((~calm(paul)|~kind(paul)))&
(?[X]:((~brave(X)|~rich(X))))&
((~patient(lucy)|~brave(lucy)))&
(calm(susan))&
((~strong(fred)|calm(fred)))&
(~tall(paul))&
((~wise(paul)&~tall(paul)))&
(?[X]:((patient(X)|~curious(X))))
|
~kind(john)
|
[] | null | 0 |
Everyone who is not humble or brave is both not rich and not happy and vice versa.
If mary is tall then someone is not strong and vice versa.
If alice is either brave or not calm then someone is either old or not strong and vice versa.
Everyone who is not curious or calm is not calm and vice versa.
If mary is not calm then someone is not creative.
Everyone who is either patient or old is either curious or not curious.
Everyone who is happy is both wise and not quiet.
If mary is old or curious then someone is rich or kind.
Everyone who is not brave or not wise is either creative or not humble.
Everyone who is either not kind or not funny is calm and vice versa.
If someone is both patient and not creative then someone is either wise or tall and vice versa.
Everyone who is either not rich or patient is either kind or wise and vice versa.
Everyone who is both not happy and not brave is either not humble or happy and vice versa.
If paul is tall then someone is not generous and vice versa.
If paul is wise then someone is both not curious and generous and vice versa.
If someone is either not patient or not humble then someone is patient and vice versa.
Someone is either not old or calm.
Someone is either not patient or not generous.
Someone is both not tall and not quiet.
Someone is either old or strong.
Fred is either calm or patient.
Lucy is calm or not curious.
|
Paul is not calm.
|
entailment
|
(![X]:((~humble(X)|brave(X))<=>(~rich(X)&~happy(X))))&
((tall(mary))<=>(?[X]:(~strong(X))))&
(((brave(alice)<~>~calm(alice)))<=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((~curious(X)|calm(X))<=>~calm(X)))&
((~calm(mary))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>old(X))=>(curious(X)<~>~curious(X))))&
(![X]:(happy(X)=>(wise(X)&~quiet(X))))&
(((old(mary)|curious(mary)))=>(?[X]:((rich(X)|kind(X)))))&
(![X]:((~brave(X)|~wise(X))=>(creative(X)<~>~humble(X))))&
(![X]:((~kind(X)<~>~funny(X))<=>calm(X)))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(kind(X)<~>wise(X))))&
(![X]:((~happy(X)&~brave(X))<=>(~humble(X)<~>happy(X))))&
((tall(paul))<=>(?[X]:(~generous(X))))&
((wise(paul))<=>(?[X]:((~curious(X)&generous(X)))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
(?[X]:((~old(X)<~>calm(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((old(X)<~>strong(X))))&
((calm(fred)<~>patient(fred)))&
((calm(lucy)|~curious(lucy)))
|
~calm(paul)
|
[
"p3",
"hypothesis"
] |
% SZS status Unsatisfiable for 2890511922920262123559144
% SZS output start Proof for 2890511922920262123559144
4. ! [X0] : ((calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p3]
23. calm(paul) [input hypothesis]
43. ! [X0] : (((calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) & curious(X0)))) [nnf transformation 4]
44. ! [X0] : ((calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (~calm(X0) & curious(X0)))) [flattening 43]
101. ~calm(X0) | ~calm(X0) [cnf transformation 44]
158. calm(paul) [cnf transformation 23]
161. ~calm(X0) [duplicate literal removal 101]
339. $false [subsumption resolution 158,161]
% SZS output end Proof for 2890511922920262123559144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is not creative.
Everyone who is both tall and not creative is both not calm and not creative.
Everyone who is not curious is strong and vice versa.
If someone is both not brave and not calm then lucy is not humble or not tall and vice versa.
Everyone who is either not quiet or calm is quiet.
If someone is not generous or not quiet then someone is curious and vice versa.
Everyone who is either strong or creative is wise or not strong.
Everyone who is not humble or not generous is either not old or brave and vice versa.
Everyone who is both curious and not happy is either not calm or creative and vice versa.
Everyone who is calm is rich or quiet and vice versa.
If someone is kind or brave then someone is either old or not funny.
Everyone who is either not kind or not tall is both not wise and not humble and vice versa.
If someone is curious then susan is tall.
If someone is both curious and not generous then mary is kind or calm and vice versa.
If susan is happy or funny then someone is either generous or curious and vice versa.
If mary is either quiet or not happy then lucy is either wise or creative.
Someone is not wise.
Mary is not happy.
John is both generous and not wise.
John is creative or not wise.
Someone is both not generous and not strong.
Someone is either generous or kind.
Mary is either not wise or calm.
Someone is both not kind and not quiet.
|
Lucy is not calm.
|
contradiction
|
(![X]:((~old(X)|generous(X))=>~creative(X)))&
(![X]:((tall(X)&~creative(X))=>(~calm(X)&~creative(X))))&
(![X]:(~curious(X)<=>strong(X)))&
((?[X]:((~brave(X)&~calm(X))))<=>((~humble(lucy)|~tall(lucy))))&
(![X]:((~quiet(X)<~>calm(X))=>quiet(X)))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:(curious(X))))&
(![X]:((strong(X)<~>creative(X))=>(wise(X)|~strong(X))))&
(![X]:((~humble(X)|~generous(X))<=>(~old(X)<~>brave(X))))&
(![X]:((curious(X)&~happy(X))<=>(~calm(X)<~>creative(X))))&
(![X]:(calm(X)<=>(rich(X)|quiet(X))))&
((?[X]:((kind(X)|brave(X))))=>(?[X]:((old(X)<~>~funny(X)))))&
(![X]:((~kind(X)<~>~tall(X))<=>(~wise(X)&~humble(X))))&
((?[X]:(curious(X)))=>(tall(susan)))&
((?[X]:((curious(X)&~generous(X))))<=>((kind(mary)|calm(mary))))&
(((happy(susan)|funny(susan)))<=>(?[X]:((generous(X)<~>curious(X)))))&
(((quiet(mary)<~>~happy(mary)))=>((wise(lucy)<~>creative(lucy))))&
(?[X]:(~wise(X)))&
(~happy(mary))&
((generous(john)&~wise(john)))&
((creative(john)|~wise(john)))&
(?[X]:((~generous(X)&~strong(X))))&
(?[X]:((generous(X)<~>kind(X))))&
((~wise(mary)<~>calm(mary)))&
(?[X]:((~kind(X)&~quiet(X))))
|
~calm(lucy)
|
[
"p4",
"p9",
"hypothesis"
] |
% SZS status Unsatisfiable for 4563202712939504117531917
% SZS output start Proof for 4563202712939504117531917
5. ! [X0] : ((~quiet(X0) <~> calm(X0)) => quiet(X0)) [input p4]
10. ! [X0] : (calm(X0) <=> (quiet(X0) | rich(X0))) [input p9]
25. ~calm(lucy) [input hypothesis]
31. ! [X0] : (quiet(X0) | (~quiet(X0) <=> calm(X0))) [ennf transformation 5]
43. ! [X0] : (quiet(X0) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0)))) [nnf transformation 31]
54. ! [X0] : ((calm(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~calm(X0))) [nnf transformation 10]
55. ! [X0] : ((calm(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~calm(X0))) [flattening 54]
94. quiet(X0) | calm(X0) | quiet(X0) [cnf transformation 43]
115. calm(X0) | ~quiet(X0) [cnf transformation 55]
155. ~calm(lucy) [cnf transformation 25]
157. quiet(X0) | calm(X0) [duplicate literal removal 94]
206. calm(X0) [subsumption resolution 115,157]
293. $false [subsumption resolution 155,206]
% SZS output end Proof for 4563202712939504117531917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or funny then someone is not tall or not generous and vice versa.
Everyone who is either humble or not curious is both patient and curious and vice versa.
Everyone who is both not creative and not old is either not rich or not quiet.
Everyone who is funny or kind is both rich and old.
If someone is both not calm and brave then someone is both not calm and not strong.
Everyone who is both not strong and not patient is brave or tall.
Everyone who is either not kind or not humble is not old and vice versa.
Everyone who is rich or not tall is not generous and vice versa.
Everyone who is brave or not calm is either patient or generous and vice versa.
Everyone who is both not strong and not rich is either strong or funny and vice versa.
If lucy is not wise then someone is both not kind and not patient.
If someone is funny or calm then alice is either not generous or calm.
Everyone who is not brave or not kind is not old or curious.
If paul is either rich or not patient then someone is either not calm or quiet.
Everyone who is both strong and wise is rich or patient and vice versa.
Everyone who is both patient and not calm is tall or patient.
Someone is happy or calm.
Someone is not happy or not quiet.
Someone is tall or strong.
Someone is either not creative or rich.
Someone is wise.
Susan is either not brave or old.
Someone is not curious or strong.
|
Lucy is funny.
|
entailment
|
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((humble(X)<~>~curious(X))<=>(patient(X)&curious(X))))&
(![X]:((~creative(X)&~old(X))=>(~rich(X)<~>~quiet(X))))&
(![X]:((funny(X)|kind(X))=>(rich(X)&old(X))))&
((?[X]:((~calm(X)&brave(X))))=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((~strong(X)&~patient(X))=>(brave(X)|tall(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>~old(X)))&
(![X]:((rich(X)|~tall(X))<=>~generous(X)))&
(![X]:((brave(X)|~calm(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~strong(X)&~rich(X))<=>(strong(X)<~>funny(X))))&
((~wise(lucy))=>(?[X]:((~kind(X)&~patient(X)))))&
((?[X]:((funny(X)|calm(X))))=>((~generous(alice)<~>calm(alice))))&
(![X]:((~brave(X)|~kind(X))=>(~old(X)|curious(X))))&
(((rich(paul)<~>~patient(paul)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:((strong(X)&wise(X))<=>(rich(X)|patient(X))))&
(![X]:((patient(X)&~calm(X))=>(tall(X)|patient(X))))&
(?[X]:((happy(X)|calm(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((tall(X)|strong(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
(?[X]:(wise(X)))&
((~brave(susan)<~>old(susan)))&
(?[X]:((~curious(X)|strong(X))))
|
funny(lucy)
|
[
"p3",
"p9",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 500269017783439429660335
% SZS output start Proof for 500269017783439429660335
4. ! [X0] : ((kind(X0) | funny(X0)) => (old(X0) & rich(X0))) [input p3]
10. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> (strong(X0) <~> funny(X0))) [input p9]
15. ! [X0] : ((wise(X0) & strong(X0)) <=> (patient(X0) | rich(X0))) [input p14]
24. ~funny(lucy) [input hypothesis]
29. ! [X0] : ((old(X0) & rich(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 4]
56. ! [X0] : (((~rich(X0) & ~strong(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | (rich(X0) | strong(X0)))) [nnf transformation 10]
57. ! [X0] : (((~rich(X0) & ~strong(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | rich(X0) | strong(X0))) [flattening 56]
64. ! [X0] : (((wise(X0) & strong(X0)) | (~patient(X0) & ~rich(X0))) & ((patient(X0) | rich(X0)) | (~wise(X0) | ~strong(X0)))) [nnf transformation 15]
65. ! [X0] : (((wise(X0) & strong(X0)) | (~patient(X0) & ~rich(X0))) & (patient(X0) | rich(X0) | ~wise(X0) | ~strong(X0))) [flattening 64]
94. ~funny(X0) | rich(X0) [cnf transformation 29]
114. funny(X0) | strong(X0) | rich(X0) | strong(X0) [cnf transformation 57]
116. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 57]
133. strong(X0) | ~rich(X0) [cnf transformation 65]
147. ~funny(lucy) [cnf transformation 24]
148. funny(X0) | strong(X0) | rich(X0) [duplicate literal removal 114]
149. ~strong(X0) | funny(X0) [duplicate literal removal 116]
167. 4 <=> ! [X3] : funny(X3) [avatar definition]
168. funny(X3) <- (4) [avatar component clause 167]
186. strong(X0) | rich(X0) [subsumption resolution 148,94]
236. strong(X0) [subsumption resolution 133,186]
278. funny(X0) [resolution 149,236]
279. 4 [avatar split clause 278,167]
280. $false <- (4) [resolution 168,147]
283. ~4 [avatar contradiction clause 280]
284. $false [avatar sat refutation 279,283]
% SZS output end Proof for 500269017783439429660335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and calm then someone is patient. Everyone who is not patient is either patient or old. If someone is kind or old then fred is either not generous or not happy and vice versa. If mary is both kind and not rich then someone is both rich and not tall and vice versa. If someone is both creative and tall then susan is tall and vice versa. Everyone who is both not calm and not old is patient and vice versa. Everyone who is both patient and not curious is either happy or not quiet and vice versa. If someone is funny or quiet then someone is both rich and creative and vice versa. Everyone who is not patient is either not strong or not creative. If john is either creative or quiet then someone is not creative and vice versa. Everyone who is strong is not old or not kind and vice versa. Everyone who is either not humble or rich is both wise and not funny. Everyone who is generous or old is both not rich and not humble and vice versa. If fred is both quiet and humble then mary is old or not humble. Everyone who is creative is not kind and vice versa. If someone is not humble then paul is either not humble or curious. Someone is curious or not funny. Someone is patient or not creative. Someone is either creative or calm. Someone is both not happy and not funny. Fred is not brave. Someone is not calm. Someone is either not humble or creative.
|
Susan is not strong.
|
contradiction
|
((?[X]:((~humble(X)&calm(X))))=>(?[X]:(patient(X))))&
(![X]:(~patient(X)=>(patient(X)<~>old(X))))&
((?[X]:((kind(X)|old(X))))<=>((~generous(fred)<~>~happy(fred))))&
(((kind(mary)&~rich(mary)))<=>(?[X]:((rich(X)&~tall(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(tall(susan)))&
(![X]:((~calm(X)&~old(X))<=>patient(X)))&
(![X]:((patient(X)&~curious(X))<=>(happy(X)<~>~quiet(X))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~patient(X)=>(~strong(X)<~>~creative(X))))&
(((creative(john)<~>quiet(john)))<=>(?[X]:(~creative(X))))&
(![X]:(strong(X)<=>(~old(X)|~kind(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)&~funny(X))))&
(![X]:((generous(X)|old(X))<=>(~rich(X)&~humble(X))))&
(((quiet(fred)&humble(fred)))=>((old(mary)|~humble(mary))))&
(![X]:(creative(X)<=>~kind(X)))&
((?[X]:(~humble(X)))=>((~humble(paul)<~>curious(paul))))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((patient(X)|~creative(X))))&
(?[X]:((creative(X)<~>calm(X))))&
(?[X]:((~happy(X)&~funny(X))))&
(~brave(fred))&
(?[X]:(~calm(X)))&
(?[X]:((~humble(X)<~>creative(X))))
|
~strong(susan)
|
[
"p5",
"p8",
"p10",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 7692578078509427157783203
% SZS output start Proof for 7692578078509427157783203
6. ! [X0] : ((~old(X0) & ~calm(X0)) <=> patient(X0)) [input p5]
9. ! [X0] : (~patient(X0) => (~strong(X0) <~> ~creative(X0))) [input p8]
11. ! [X0] : (strong(X0) <=> (~kind(X0) | ~old(X0))) [input p10]
15. ! [X0] : (creative(X0) <=> ~kind(X0)) [input p14]
24. ~strong(susan) [input hypothesis]
31. ! [X0] : ((~strong(X0) <~> ~creative(X0)) | patient(X0)) [ennf transformation 9]
53. ! [X0] : (((~old(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | (old(X0) | calm(X0)))) [nnf transformation 6]
54. ! [X0] : (((~old(X0) & ~calm(X0)) | ~patient(X0)) & (patient(X0) | old(X0) | calm(X0))) [flattening 53]
62. ! [X0] : (((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | patient(X0)) [nnf transformation 31]
67. ! [X0] : ((strong(X0) | (kind(X0) & old(X0))) & ((~kind(X0) | ~old(X0)) | ~strong(X0))) [nnf transformation 11]
68. ! [X0] : ((strong(X0) | (kind(X0) & old(X0))) & (~kind(X0) | ~old(X0) | ~strong(X0))) [flattening 67]
72. ! [X0] : ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0))) [nnf transformation 15]
106. ~old(X0) | ~patient(X0) [cnf transformation 54]
119. strong(X0) | creative(X0) | patient(X0) [cnf transformation 62]
125. strong(X0) | old(X0) [cnf transformation 68]
126. strong(X0) | kind(X0) [cnf transformation 68]
135. ~creative(X0) | ~kind(X0) [cnf transformation 72]
148. ~strong(susan) [cnf transformation 24]
358. old(susan) [resolution 125,148]
359. kind(susan) [resolution 126,148]
360. ~patient(susan) [resolution 358,106]
409. creative(susan) | patient(susan) [resolution 119,148]
412. creative(susan) [subsumption resolution 409,360]
419. ~kind(susan) [resolution 412,135]
420. $false [subsumption resolution 419,359]
% SZS output end Proof for 7692578078509427157783203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not quiet is both brave and not generous and vice versa.
Everyone who is not happy is not funny.
If john is kind or creative then someone is both patient and creative and vice versa.
Everyone who is either generous or quiet is either brave or old and vice versa.
If someone is both kind and not quiet then lucy is rich or not strong.
Everyone who is not old is either not kind or generous.
Everyone who is both kind and not strong is both creative and calm.
Everyone who is either not patient or rich is both not curious and not humble and vice versa.
Everyone who is both generous and calm is both wise and creative and vice versa.
If someone is not quiet then someone is not kind and vice versa.
If alice is both not kind and creative then someone is not funny.
If susan is tall then lucy is not curious or humble.
Everyone who is both not humble and old is strong or not brave and vice versa.
Everyone who is either rich or not creative is not humble.
Everyone who is either not rich or not generous is not creative and vice versa.
Everyone who is not generous or not tall is humble and vice versa.
Mary is kind or not brave.
Someone is both wise and not happy.
Someone is either not patient or happy.
Susan is not curious or tall.
Lucy is not quiet.
John is not kind or strong.
|
John is not curious.
|
neutral
|
(![X]:((strong(X)|~quiet(X))<=>(brave(X)&~generous(X))))&
(![X]:(~happy(X)=>~funny(X)))&
(((kind(john)|creative(john)))<=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>(brave(X)<~>old(X))))&
((?[X]:((kind(X)&~quiet(X))))=>((rich(lucy)|~strong(lucy))))&
(![X]:(~old(X)=>(~kind(X)<~>generous(X))))&
(![X]:((kind(X)&~strong(X))=>(creative(X)&calm(X))))&
(![X]:((~patient(X)<~>rich(X))<=>(~curious(X)&~humble(X))))&
(![X]:((generous(X)&calm(X))<=>(wise(X)&creative(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~kind(X))))&
(((~kind(alice)&creative(alice)))=>(?[X]:(~funny(X))))&
((tall(susan))=>((~curious(lucy)|humble(lucy))))&
(![X]:((~humble(X)&old(X))<=>(strong(X)|~brave(X))))&
(![X]:((rich(X)<~>~creative(X))=>~humble(X)))&
(![X]:((~rich(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~generous(X)|~tall(X))<=>humble(X)))&
((kind(mary)|~brave(mary)))&
(?[X]:((wise(X)&~happy(X))))&
(?[X]:((~patient(X)<~>happy(X))))&
((~curious(susan)|tall(susan)))&
(~quiet(lucy))&
((~kind(john)|strong(john)))
|
~curious(john)
|
[] | null | 0 |
Everyone who is either tall or calm is either quiet or not humble.
If john is both not kind and creative then someone is both not creative and not kind and vice versa.
Everyone who is brave or wise is old or curious and vice versa.
If someone is both not calm and not humble then alice is creative and vice versa.
Everyone who is curious is not rich and vice versa.
If fred is either not wise or not quiet then john is either quiet or not calm and vice versa.
Everyone who is either not tall or happy is either brave or generous.
Everyone who is not funny or not wise is kind.
Everyone who is both not creative and not tall is both rich and patient and vice versa.
Everyone who is not happy or generous is rich or happy and vice versa.
If someone is strong then lucy is funny.
Everyone who is either not quiet or not humble is humble.
If alice is either not tall or not humble then john is both not patient and old.
Everyone who is not quiet is both tall and not happy and vice versa.
If someone is both tall and not strong then john is either old or not tall and vice versa.
If someone is curious then susan is both creative and not quiet and vice versa.
Mary is either old or curious.
Someone is generous or calm.
Lucy is either not calm or not curious.
Susan is either not brave or tall.
Someone is either patient or not tall.
Fred is patient.
Someone is either patient or not kind.
|
John is not creative.
|
neutral
|
(![X]:((tall(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
(((~kind(john)&creative(john)))<=>(?[X]:((~creative(X)&~kind(X)))))&
(![X]:((brave(X)|wise(X))<=>(old(X)|curious(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>(creative(alice)))&
(![X]:(curious(X)<=>~rich(X)))&
(((~wise(fred)<~>~quiet(fred)))<=>((quiet(john)<~>~calm(john))))&
(![X]:((~tall(X)<~>happy(X))=>(brave(X)<~>generous(X))))&
(![X]:((~funny(X)|~wise(X))=>kind(X)))&
(![X]:((~creative(X)&~tall(X))<=>(rich(X)&patient(X))))&
(![X]:((~happy(X)|generous(X))<=>(rich(X)|happy(X))))&
((?[X]:(strong(X)))=>(funny(lucy)))&
(![X]:((~quiet(X)<~>~humble(X))=>humble(X)))&
(((~tall(alice)<~>~humble(alice)))=>((~patient(john)&old(john))))&
(![X]:(~quiet(X)<=>(tall(X)&~happy(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((old(john)<~>~tall(john))))&
((?[X]:(curious(X)))<=>((creative(susan)&~quiet(susan))))&
((old(mary)<~>curious(mary)))&
(?[X]:((generous(X)|calm(X))))&
((~calm(lucy)<~>~curious(lucy)))&
((~brave(susan)<~>tall(susan)))&
(?[X]:((patient(X)<~>~tall(X))))&
(patient(fred))&
(?[X]:((patient(X)<~>~kind(X))))
|
~creative(john)
|
[] | null | 0 |
If someone is both creative and not wise then someone is old or not generous.
Everyone who is both quiet and creative is both brave and generous and vice versa.
If susan is generous then someone is either not creative or quiet.
If fred is either humble or not rich then lucy is both not curious and happy.
If alice is patient or not strong then fred is tall.
If someone is not calm or calm then someone is quiet and vice versa.
If someone is either generous or kind then someone is calm and vice versa.
If john is either not rich or not old then paul is not creative.
Everyone who is wise or not humble is not wise and vice versa.
If alice is both generous and rich then alice is both calm and not humble and vice versa.
Everyone who is curious or patient is both funny and not old and vice versa.
If paul is patient then someone is either patient or humble and vice versa.
If someone is either not wise or humble then lucy is tall.
If someone is both humble and creative then lucy is not happy or quiet.
Everyone who is not kind is either funny or brave.
Everyone who is tall or not rich is not tall or not generous and vice versa.
Someone is both happy and not strong.
Someone is both not generous and not creative.
Lucy is not generous.
Someone is calm or curious.
Someone is both not curious and patient.
Paul is wise or happy.
John is both funny and not generous.
Lucy is creative.
|
Lucy is quiet.
|
contradiction
|
((?[X]:((creative(X)&~wise(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((quiet(X)&creative(X))<=>(brave(X)&generous(X))))&
((generous(susan))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(((humble(fred)<~>~rich(fred)))=>((~curious(lucy)&happy(lucy))))&
(((patient(alice)|~strong(alice)))=>(tall(fred)))&
((?[X]:((~calm(X)|calm(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((generous(X)<~>kind(X))))<=>(?[X]:(calm(X))))&
(((~rich(john)<~>~old(john)))=>(~creative(paul)))&
(![X]:((wise(X)|~humble(X))<=>~wise(X)))&
(((generous(alice)&rich(alice)))<=>((calm(alice)&~humble(alice))))&
(![X]:((curious(X)|patient(X))<=>(funny(X)&~old(X))))&
((patient(paul))<=>(?[X]:((patient(X)<~>humble(X)))))&
((?[X]:((~wise(X)<~>humble(X))))=>(tall(lucy)))&
((?[X]:((humble(X)&creative(X))))=>((~happy(lucy)|quiet(lucy))))&
(![X]:(~kind(X)=>(funny(X)<~>brave(X))))&
(![X]:((tall(X)|~rich(X))<=>(~tall(X)|~generous(X))))&
(?[X]:((happy(X)&~strong(X))))&
(?[X]:((~generous(X)&~creative(X))))&
(~generous(lucy))&
(?[X]:((calm(X)|curious(X))))&
(?[X]:((~curious(X)&patient(X))))&
((wise(paul)|happy(paul)))&
((funny(john)&~generous(john)))&
(creative(lucy))
|
quiet(lucy)
|
[
"p1",
"p18",
"p23",
"hypothesis"
] |
% SZS status Unsatisfiable for 8435287857966853253553846
% SZS output start Proof for 8435287857966853253553846
2. ! [X0] : ((creative(X0) & quiet(X0)) <=> (generous(X0) & brave(X0))) [input p1]
19. ~generous(lucy) [input p18]
24. creative(lucy) [input p23]
25. quiet(lucy) [input hypothesis]
41. ! [X0] : (((creative(X0) & quiet(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~creative(X0) | ~quiet(X0)))) [nnf transformation 2]
42. ! [X0] : (((creative(X0) & quiet(X0)) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | ~creative(X0) | ~quiet(X0))) [flattening 41]
82. ~quiet(X0) | ~creative(X0) | generous(X0) [cnf transformation 42]
131. ~generous(lucy) [cnf transformation 19]
138. creative(lucy) [cnf transformation 24]
139. quiet(lucy) [cnf transformation 25]
307. 37 <=> quiet(lucy) [avatar definition]
309. quiet(lucy) <- (37) [avatar component clause 307]
321. 37 [avatar split clause 139,307]
375. ~creative(lucy) | generous(lucy) <- (37) [resolution 82,309]
376. generous(lucy) <- (37) [subsumption resolution 375,138]
377. $false <- (37) [subsumption resolution 376,131]
378. ~37 [avatar contradiction clause 377]
379. $false [avatar sat refutation 321,378]
% SZS output end Proof for 8435287857966853253553846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not happy then someone is either not patient or rich.
If someone is both happy and not quiet then fred is not quiet.
Everyone who is curious is either patient or happy.
Everyone who is happy is not wise or patient.
Everyone who is not patient is either strong or not creative.
Everyone who is not humble or quiet is not strong or old and vice versa.
Everyone who is either patient or not calm is both kind and not curious.
If mary is both wise and rich then mary is either humble or not quiet and vice versa.
If lucy is kind or old then someone is either not calm or not quiet.
If someone is either old or patient then john is either not strong or not calm and vice versa.
If someone is quiet or kind then mary is humble or not calm and vice versa.
If mary is not rich or not calm then someone is both not curious and rich and vice versa.
Everyone who is patient or brave is both not happy and strong and vice versa.
If someone is both happy and quiet then someone is not quiet.
Everyone who is humble is not strong or not old and vice versa.
Everyone who is not brave or rich is either quiet or not strong.
John is both not generous and not curious.
Alice is not generous or funny.
Paul is either tall or rich.
Someone is not brave.
Someone is not humble or not funny.
Someone is either quiet or not happy.
Lucy is either calm or not patient.
|
Fred is not strong.
|
contradiction
|
((?[X]:((generous(X)|~happy(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((happy(X)&~quiet(X))))=>(~quiet(fred)))&
(![X]:(curious(X)=>(patient(X)<~>happy(X))))&
(![X]:(happy(X)=>(~wise(X)|patient(X))))&
(![X]:(~patient(X)=>(strong(X)<~>~creative(X))))&
(![X]:((~humble(X)|quiet(X))<=>(~strong(X)|old(X))))&
(![X]:((patient(X)<~>~calm(X))=>(kind(X)&~curious(X))))&
(((wise(mary)&rich(mary)))<=>((humble(mary)<~>~quiet(mary))))&
(((kind(lucy)|old(lucy)))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
((?[X]:((old(X)<~>patient(X))))<=>((~strong(john)<~>~calm(john))))&
((?[X]:((quiet(X)|kind(X))))<=>((humble(mary)|~calm(mary))))&
(((~rich(mary)|~calm(mary)))<=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((patient(X)|brave(X))<=>(~happy(X)&strong(X))))&
((?[X]:((happy(X)&quiet(X))))=>(?[X]:(~quiet(X))))&
(![X]:(humble(X)<=>(~strong(X)|~old(X))))&
(![X]:((~brave(X)|rich(X))=>(quiet(X)<~>~strong(X))))&
((~generous(john)&~curious(john)))&
((~generous(alice)|funny(alice)))&
((tall(paul)<~>rich(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((~humble(X)|~funny(X))))&
(?[X]:((quiet(X)<~>~happy(X))))&
((calm(lucy)<~>~patient(lucy)))
|
~strong(fred)
|
[
"p5",
"p12",
"p14",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 2757806461132298596700555
% SZS output start Proof for 2757806461132298596700555
6. ! [X0] : ((quiet(X0) | ~humble(X0)) <=> (old(X0) | ~strong(X0))) [input p5]
13. ! [X0] : ((brave(X0) | patient(X0)) <=> (strong(X0) & ~happy(X0))) [input p12]
15. ! [X0] : (humble(X0) <=> (~old(X0) | ~strong(X0))) [input p14]
16. ! [X0] : ((rich(X0) | ~brave(X0)) => (quiet(X0) <~> ~strong(X0))) [input p15]
24. ~strong(fred) [input hypothesis]
40. ! [X0] : ((quiet(X0) <~> ~strong(X0)) | (~rich(X0) & brave(X0))) [ennf transformation 16]
47. ! [X0] : (((quiet(X0) | ~humble(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (~quiet(X0) & humble(X0)))) [nnf transformation 6]
48. ! [X0] : ((quiet(X0) | ~humble(X0) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | (~quiet(X0) & humble(X0)))) [flattening 47]
69. ! [X0] : (((brave(X0) | patient(X0)) | (~strong(X0) | happy(X0))) & ((strong(X0) & ~happy(X0)) | (~brave(X0) & ~patient(X0)))) [nnf transformation 13]
70. ! [X0] : ((brave(X0) | patient(X0) | ~strong(X0) | happy(X0)) & ((strong(X0) & ~happy(X0)) | (~brave(X0) & ~patient(X0)))) [flattening 69]
74. ! [X0] : ((humble(X0) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | ~humble(X0))) [nnf transformation 15]
75. ! [X0] : ((humble(X0) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ~humble(X0))) [flattening 74]
76. ! [X0] : (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (~rich(X0) & brave(X0))) [nnf transformation 40]
94. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 48]
130. ~brave(X0) | strong(X0) [cnf transformation 70]
134. humble(X0) | strong(X0) [cnf transformation 75]
138. strong(X0) | ~quiet(X0) | brave(X0) [cnf transformation 76]
148. ~strong(fred) [cnf transformation 24]
288. ~quiet(X0) | strong(X0) [subsumption resolution 138,130]
355. quiet(X0) | strong(X0) | strong(X0) [resolution 94,134]
357. quiet(X0) | strong(X0) [duplicate literal removal 355]
358. strong(X0) [subsumption resolution 357,288]
359. $false [resolution 358,148]
% SZS output end Proof for 2757806461132298596700555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not tall or curious then fred is both wise and patient and vice versa.
If alice is not funny then someone is both not happy and funny.
Everyone who is not funny is not tall.
If susan is not funny or tall then paul is not humble or strong and vice versa.
Everyone who is either not humble or not funny is not tall and vice versa.
Everyone who is not kind is either not strong or wise.
If someone is wise or funny then someone is creative or kind.
If alice is not patient then alice is both not strong and creative.
If fred is both not wise and not brave then someone is either happy or not curious and vice versa.
Everyone who is either not strong or not brave is not tall.
If fred is either generous or not creative then someone is both humble and not kind.
Everyone who is not curious or not rich is old or not funny.
Everyone who is either not quiet or quiet is both not calm and tall.
If mary is calm then someone is either strong or humble and vice versa.
Everyone who is not wise is both not wise and not humble.
If john is both curious and not creative then someone is either creative or not kind.
Someone is either wise or not wise.
Fred is either not tall or not calm.
John is either creative or not curious.
Someone is not creative or curious.
Someone is not tall or patient.
Mary is either not strong or generous.
|
John is not brave.
|
contradiction
|
(((~tall(lucy)|curious(lucy)))<=>((wise(fred)&patient(fred))))&
((~funny(alice))=>(?[X]:((~happy(X)&funny(X)))))&
(![X]:(~funny(X)=>~tall(X)))&
(((~funny(susan)|tall(susan)))<=>((~humble(paul)|strong(paul))))&
(![X]:((~humble(X)<~>~funny(X))<=>~tall(X)))&
(![X]:(~kind(X)=>(~strong(X)<~>wise(X))))&
((?[X]:((wise(X)|funny(X))))=>(?[X]:((creative(X)|kind(X)))))&
((~patient(alice))=>((~strong(alice)&creative(alice))))&
(((~wise(fred)&~brave(fred)))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(![X]:((~strong(X)<~>~brave(X))=>~tall(X)))&
(((generous(fred)<~>~creative(fred)))=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:((~curious(X)|~rich(X))=>(old(X)|~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))=>(~calm(X)&tall(X))))&
((calm(mary))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:(~wise(X)=>(~wise(X)&~humble(X))))&
(((curious(john)&~creative(john)))=>(?[X]:((creative(X)<~>~kind(X)))))&
(?[X]:((wise(X)<~>~wise(X))))&
((~tall(fred)<~>~calm(fred)))&
((creative(john)<~>~curious(john)))&
(?[X]:((~creative(X)|curious(X))))&
(?[X]:((~tall(X)|patient(X))))&
((~strong(mary)<~>generous(mary)))
|
~brave(john)
|
[
"p2",
"p4",
"p9",
"p12",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 6943907274299322120733275
% SZS output start Proof for 6943907274299322120733275
3. ! [X0] : (~funny(X0) => ~tall(X0)) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p4]
10. ! [X0] : ((~strong(X0) <~> ~brave(X0)) => ~tall(X0)) [input p9]
13. ! [X0] : ((~quiet(X0) <~> quiet(X0)) => (tall(X0) & ~calm(X0))) [input p12]
14. calm(mary) <=> ? [X0] : (strong(X0) <~> humble(X0)) [input p13]
23. ~brave(john) [input hypothesis]
27. ! [X0] : (~tall(X0) | funny(X0)) [ennf transformation 3]
31. ! [X0] : (~tall(X0) | (~strong(X0) <=> ~brave(X0))) [ennf transformation 10]
33. ! [X0] : ((tall(X0) & ~calm(X0)) | (~quiet(X0) <=> quiet(X0))) [ennf transformation 13]
43. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | tall(X0)) & (~tall(X0) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 5]
53. ! [X0] : (~tall(X0) | ((~strong(X0) | brave(X0)) & (~brave(X0) | strong(X0)))) [nnf transformation 31]
57. ! [X0] : ((tall(X0) & ~calm(X0)) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0)))) [nnf transformation 33]
58. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X0] : ((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | ~calm(mary)) [nnf transformation 14]
59. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) | ~calm(mary)) [rectify 58]
60. ? [X1] : ((~humble(X1) | ~strong(X1)) & (humble(X1) | strong(X1))) => ((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) [choice axiom]
61. (calm(mary) | ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) & (((~humble(sK4) | ~strong(sK4)) & (humble(sK4) | strong(sK4))) | ~calm(mary)) [skolemisation 59,60]
82. ~tall(X0) | funny(X0) [cnf transformation 27]
87. ~tall(X0) | ~funny(X0) | humble(X0) [cnf transformation 43]
90. funny(X0) | humble(X0) | tall(X0) [cnf transformation 43]
104. ~strong(X0) | ~tall(X0) | brave(X0) [cnf transformation 53]
109. ~calm(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
110. ~calm(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
111. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
112. tall(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 57]
116. calm(mary) | strong(X0) | ~humble(X0) [cnf transformation 61]
131. ~brave(john) [cnf transformation 23]
132. ~calm(X0) | quiet(X0) [duplicate literal removal 109]
133. ~calm(X0) | ~quiet(X0) [duplicate literal removal 110]
134. tall(X0) | quiet(X0) [duplicate literal removal 111]
135. ~quiet(X0) | tall(X0) [duplicate literal removal 112]
191. humble(X0) | funny(X0) [subsumption resolution 90,82]
192. ~tall(X0) | humble(X0) [subsumption resolution 87,191]
267. tall(X0) [subsumption resolution 134,135]
268. ~calm(X0) [subsumption resolution 132,133]
269. ~humble(X0) | strong(X0) [subsumption resolution 116,268]
316. humble(X0) [resolution 192,267]
327. strong(X0) [resolution 269,316]
339. ~tall(X0) | brave(X0) [resolution 104,327]
341. brave(X0) [subsumption resolution 339,267]
343. $false [resolution 341,131]
% SZS output end Proof for 6943907274299322120733275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or quiet is not strong or not happy and vice versa.
Everyone who is not brave is both happy and generous and vice versa.
Everyone who is either not generous or not creative is both humble and tall.
Everyone who is either not funny or brave is curious or not curious and vice versa.
Everyone who is not strong or generous is not humble or not curious.
Everyone who is either not quiet or calm is both old and calm and vice versa.
If someone is either humble or brave then mary is humble or not kind.
Everyone who is both not rich and calm is strong or not rich and vice versa.
If mary is not patient or not kind then mary is not generous.
Everyone who is both not humble and not old is both not calm and brave.
Everyone who is tall is not brave or happy.
If mary is both curious and not quiet then lucy is not wise or not creative.
Everyone who is either rich or not creative is generous and vice versa.
If john is generous then someone is both not calm and patient and vice versa.
Everyone who is not funny or tall is not calm or rich and vice versa.
If paul is not rich then someone is both not kind and not generous and vice versa.
Someone is brave.
Alice is creative.
Someone is happy or not calm.
Someone is not curious or not patient.
Someone is either not creative or rich.
Mary is both patient and not humble.
Someone is not quiet or not wise.
Fred is strong or not funny.
|
Fred is funny.
|
contradiction
|
(![X]:((humble(X)<~>quiet(X))<=>(~strong(X)|~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)&generous(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(humble(X)&tall(X))))&
(![X]:((~funny(X)<~>brave(X))<=>(curious(X)|~curious(X))))&
(![X]:((~strong(X)|generous(X))=>(~humble(X)|~curious(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(old(X)&calm(X))))&
((?[X]:((humble(X)<~>brave(X))))=>((humble(mary)|~kind(mary))))&
(![X]:((~rich(X)&calm(X))<=>(strong(X)|~rich(X))))&
(((~patient(mary)|~kind(mary)))=>(~generous(mary)))&
(![X]:((~humble(X)&~old(X))=>(~calm(X)&brave(X))))&
(![X]:(tall(X)=>(~brave(X)|happy(X))))&
(((curious(mary)&~quiet(mary)))=>((~wise(lucy)|~creative(lucy))))&
(![X]:((rich(X)<~>~creative(X))<=>generous(X)))&
((generous(john))<=>(?[X]:((~calm(X)&patient(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~calm(X)|rich(X))))&
((~rich(paul))<=>(?[X]:((~kind(X)&~generous(X)))))&
(?[X]:(brave(X)))&
(creative(alice))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((~creative(X)<~>rich(X))))&
((patient(mary)&~humble(mary)))&
(?[X]:((~quiet(X)|~wise(X))))&
((strong(fred)|~funny(fred)))
|
funny(fred)
|
[
"p1",
"p2",
"p3",
"p7",
"p10",
"p12",
"p14",
"p23",
"hypothesis"
] |
% SZS status Unsatisfiable for 344585762428791324895785
% SZS output start Proof for 344585762428791324895785
2. ! [X0] : (~brave(X0) <=> (generous(X0) & happy(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> ~creative(X0)) => (tall(X0) & humble(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> (~curious(X0) | curious(X0))) [input p3]
8. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (~rich(X0) | strong(X0))) [input p7]
11. ! [X0] : (tall(X0) => (happy(X0) | ~brave(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> generous(X0)) [input p12]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
24. ~funny(fred) | strong(fred) [input p23]
25. funny(fred) [input hypothesis]
28. ! [X0] : ((tall(X0) & humble(X0)) | (~generous(X0) <=> ~creative(X0))) [ennf transformation 3]
36. ! [X0] : ((happy(X0) | ~brave(X0)) | ~tall(X0)) [ennf transformation 11]
37. ! [X0] : (happy(X0) | ~brave(X0) | ~tall(X0)) [flattening 36]
40. ! [X0] : ((~brave(X0) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | brave(X0))) [nnf transformation 2]
41. ! [X0] : ((~brave(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | brave(X0))) [flattening 40]
42. ! [X0] : ((tall(X0) & humble(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) [nnf transformation 28]
43. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [flattening 43]
48. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((calm(X0) & ~rich(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | ~generous(X0)) & (generous(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : (((tall(X0) | ~funny(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
56. ! [X0] : ((tall(X0) | ~funny(X0) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | (~tall(X0) & funny(X0)))) [flattening 55]
76. brave(X0) | happy(X0) [cnf transformation 41]
78. ~generous(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 41]
81. ~creative(X0) | tall(X0) | generous(X0) [cnf transformation 42]
82. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 42]
85. brave(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 44]
86. ~funny(X0) | brave(X0) | curious(X0) [cnf transformation 44]
87. ~brave(X0) | funny(X0) | ~curious(X0) [cnf transformation 44]
88. ~brave(X0) | funny(X0) | curious(X0) [cnf transformation 44]
100. ~rich(X0) | ~strong(X0) [cnf transformation 49]
103. rich(X0) | calm(X0) [cnf transformation 49]
108. happy(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 37]
110. rich(X0) | generous(X0) | creative(X0) [cnf transformation 50]
111. ~creative(X0) | rich(X0) | ~generous(X0) [cnf transformation 50]
117. rich(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 56]
119. ~rich(X0) | ~funny(X0) | tall(X0) [cnf transformation 56]
131. ~funny(fred) | strong(fred) [cnf transformation 24]
132. funny(fred) [cnf transformation 25]
135. ~brave(X0) | funny(X0) [subsumption resolution 87,88]
136. ~funny(X0) | brave(X0) [subsumption resolution 85,86]
163. ~tall(X0) | happy(X0) [subsumption resolution 108,76]
182. ~tall(X0) | rich(X0) [subsumption resolution 117,103]
233. 21 <=> strong(fred) [avatar definition]
235. strong(fred) <- (21) [avatar component clause 233]
237. 22 <=> funny(fred) [avatar definition]
238. funny(fred) <- (22) [avatar component clause 237]
240. 21 | ~22 [avatar split clause 131,237,233]
241. 22 [avatar split clause 132,237]
250. funny(X0) | happy(X0) [resolution 135,76]
255. brave(fred) <- (22) [resolution 136,238]
469. ~strong(X1) | creative(X1) | generous(X1) [resolution 110,100]
604. ~funny(X0) | tall(X0) | generous(X0) | creative(X0) [resolution 119,110]
609. ~funny(X0) | tall(X0) | creative(X0) [subsumption resolution 604,82]
766. creative(fred) | generous(fred) <- (21) [resolution 469,235]
769. 77 <=> generous(fred) [avatar definition]
771. generous(fred) <- (77) [avatar component clause 769]
773. 78 <=> creative(fred) [avatar definition]
774. ~creative(fred) <- (~78) [avatar component clause 773]
775. creative(fred) <- (78) [avatar component clause 773]
776. 77 | 78 | ~21 [avatar split clause 766,233,773,769]
794. tall(X0) | creative(X0) | happy(X0) [resolution 609,250]
797. creative(X0) | happy(X0) [subsumption resolution 794,163]
894. rich(fred) | ~generous(fred) <- (78) [resolution 775,111]
895. tall(fred) | generous(fred) <- (78) [resolution 775,81]
898. 84 <=> rich(fred) [avatar definition]
900. rich(fred) <- (84) [avatar component clause 898]
901. ~77 | 84 | ~78 [avatar split clause 894,773,898,769]
903. 85 <=> tall(fred) [avatar definition]
905. tall(fred) <- (85) [avatar component clause 903]
906. 77 | 85 | ~78 [avatar split clause 895,773,903,769]
1027. rich(fred) <- (85) [resolution 905,182]
1029. 84 | ~85 [avatar split clause 1027,903,898]
1034. ~brave(fred) | ~happy(fred) <- (77) [resolution 771,78]
1035. ~happy(fred) <- (22, 77) [subsumption resolution 1034,255]
1036. happy(fred) <- (~78) [resolution 774,797]
1038. $false <- (22, 77, ~78) [subsumption resolution 1036,1035]
1039. ~22 | ~77 | 78 [avatar contradiction clause 1038]
1048. ~strong(fred) <- (84) [resolution 900,100]
1052. $false <- (21, 84) [subsumption resolution 1048,235]
1053. ~21 | ~84 [avatar contradiction clause 1052]
1054. $false [avatar sat refutation 240,241,776,901,906,1029,1039,1053]
% SZS output end Proof for 344585762428791324895785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and old then someone is either patient or old and vice versa. Everyone who is not wise or not humble is generous. Everyone who is kind or humble is either quiet or not brave and vice versa. Everyone who is either not strong or not patient is funny or not strong. If someone is either not quiet or kind then someone is both not rich and tall. Everyone who is both brave and not quiet is not generous or patient and vice versa. Everyone who is not quiet is either curious or not funny. If someone is both tall and not brave then someone is creative and vice versa. Everyone who is not rich is not old or not curious. If someone is either not wise or not kind then alice is brave and vice versa. Everyone who is both funny and not brave is either not kind or not strong and vice versa. If someone is calm then paul is both wise and not strong. Everyone who is not calm or tall is not humble or not quiet. If someone is kind then someone is rich and vice versa. If paul is either kind or wise then someone is funny and vice versa. Everyone who is funny is both brave and not wise. Paul is either patient or not quiet. Mary is generous or kind. Someone is curious. Mary is calm or generous. Lucy is patient. Susan is both not quiet and curious. Someone is either not creative or generous.
|
Paul is strong.
|
contradiction
|
((?[X]:((generous(X)&old(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
(![X]:((~wise(X)|~humble(X))=>generous(X)))&
(![X]:((kind(X)|humble(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(funny(X)|~strong(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((brave(X)&~quiet(X))<=>(~generous(X)|patient(X))))&
(![X]:(~quiet(X)=>(curious(X)<~>~funny(X))))&
((?[X]:((tall(X)&~brave(X))))<=>(?[X]:(creative(X))))&
(![X]:(~rich(X)=>(~old(X)|~curious(X))))&
((?[X]:((~wise(X)<~>~kind(X))))<=>(brave(alice)))&
(![X]:((funny(X)&~brave(X))<=>(~kind(X)<~>~strong(X))))&
((?[X]:(calm(X)))=>((wise(paul)&~strong(paul))))&
(![X]:((~calm(X)|tall(X))=>(~humble(X)|~quiet(X))))&
((?[X]:(kind(X)))<=>(?[X]:(rich(X))))&
(((kind(paul)<~>wise(paul)))<=>(?[X]:(funny(X))))&
(![X]:(funny(X)=>(brave(X)&~wise(X))))&
((patient(paul)<~>~quiet(paul)))&
((generous(mary)|kind(mary)))&
(?[X]:(curious(X)))&
((calm(mary)|generous(mary)))&
(patient(lucy))&
((~quiet(susan)&curious(susan)))&
(?[X]:((~creative(X)<~>generous(X))))
|
strong(paul)
|
[
"p2",
"p3",
"p5",
"p10",
"p15",
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 129762655730295961765710
% SZS output start Proof for 129762655730295961765710
3. ! [X0] : ((humble(X0) | kind(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p2]
4. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (~strong(X0) | funny(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) & brave(X0)) <=> (patient(X0) | ~generous(X0))) [input p5]
11. ! [X0] : ((~brave(X0) & funny(X0)) <=> (~kind(X0) <~> ~strong(X0))) [input p10]
16. ! [X0] : (funny(X0) => (~wise(X0) & brave(X0))) [input p15]
17. patient(paul) <~> ~quiet(paul) [input p16]
24. strong(paul) [input hypothesis]
30. ! [X0] : ((~strong(X0) | funny(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 4]
31. ! [X0] : (~strong(X0) | funny(X0) | (~strong(X0) <=> ~patient(X0))) [flattening 30]
39. ! [X0] : ((~wise(X0) & brave(X0)) | ~funny(X0)) [ennf transformation 16]
45. ! [X0] : (((humble(X0) | kind(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (~humble(X0) & ~kind(X0)))) [nnf transformation 3]
46. ! [X0] : ((humble(X0) | kind(X0) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (~humble(X0) & ~kind(X0)))) [flattening 45]
47. ! [X0] : (~strong(X0) | funny(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 31]
52. ! [X0] : (((~quiet(X0) & brave(X0)) | (~patient(X0) & generous(X0))) & ((patient(X0) | ~generous(X0)) | (quiet(X0) | ~brave(X0)))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) & brave(X0)) | (~patient(X0) & generous(X0))) & (patient(X0) | ~generous(X0) | quiet(X0) | ~brave(X0))) [flattening 52]
64. ! [X0] : (((~brave(X0) & funny(X0)) | ((~kind(X0) | strong(X0)) & (~strong(X0) | kind(X0)))) & (((strong(X0) | kind(X0)) & (~strong(X0) | ~kind(X0))) | (brave(X0) | ~funny(X0)))) [nnf transformation 11]
65. ! [X0] : (((~brave(X0) & funny(X0)) | ((~kind(X0) | strong(X0)) & (~strong(X0) | kind(X0)))) & (((strong(X0) | kind(X0)) & (~strong(X0) | ~kind(X0))) | brave(X0) | ~funny(X0))) [flattening 64]
75. (quiet(paul) | ~patient(paul)) & (~quiet(paul) | patient(paul)) [nnf transformation 17]
89. ~brave(X0) | quiet(X0) | ~kind(X0) [cnf transformation 46]
96. ~strong(X0) | funny(X0) | ~strong(X0) | patient(X0) [cnf transformation 47]
105. ~quiet(X0) | ~patient(X0) [cnf transformation 53]
116. ~funny(X0) | ~kind(X0) | brave(X0) | ~strong(X0) [cnf transformation 65]
118. ~strong(X0) | funny(X0) | kind(X0) [cnf transformation 65]
120. ~strong(X0) | ~brave(X0) | kind(X0) [cnf transformation 65]
132. ~funny(X0) | brave(X0) [cnf transformation 39]
134. ~quiet(paul) | patient(paul) [cnf transformation 75]
135. quiet(paul) | ~patient(paul) [cnf transformation 75]
144. strong(paul) [cnf transformation 24]
145. ~strong(X0) | funny(X0) | patient(X0) [duplicate literal removal 96]
242. 23 <=> strong(paul) [avatar definition]
243. strong(paul) <- (23) [avatar component clause 242]
271. 30 <=> kind(paul) [avatar definition]
272. kind(paul) <- (30) [avatar component clause 271]
273. ~kind(paul) <- (~30) [avatar component clause 271]
282. ~patient(paul) [subsumption resolution 135,105]
283. ~quiet(paul) [subsumption resolution 134,282]
308. 23 [avatar split clause 144,242]
413. funny(paul) | kind(paul) <- (23) [resolution 118,243]
414. funny(paul) <- (23, ~30) [subsumption resolution 413,273]
423. ~brave(paul) | kind(paul) <- (23) [resolution 120,243]
424. ~brave(paul) <- (23, ~30) [subsumption resolution 423,273]
446. brave(paul) <- (23, ~30) [resolution 414,132]
450. $false <- (23, ~30) [subsumption resolution 446,424]
451. ~23 | 30 [avatar contradiction clause 450]
537. funny(paul) | patient(paul) <- (23) [resolution 145,243]
538. funny(paul) <- (23) [subsumption resolution 537,282]
622. ~kind(paul) | brave(paul) | ~strong(paul) <- (23) [resolution 538,116]
626. brave(paul) | ~strong(paul) <- (23, 30) [subsumption resolution 622,272]
627. brave(paul) <- (23, 30) [subsumption resolution 626,243]
731. quiet(paul) | ~kind(paul) <- (23, 30) [resolution 627,89]
737. ~kind(paul) <- (23, 30) [subsumption resolution 731,283]
738. $false <- (23, 30) [subsumption resolution 737,272]
739. ~23 | ~30 [avatar contradiction clause 738]
740. $false [avatar sat refutation 308,451,739]
% SZS output end Proof for 129762655730295961765710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not rich then alice is not quiet.
Everyone who is not quiet is not generous.
Everyone who is not calm or not curious is both wise and not wise.
If mary is either not rich or curious then someone is either brave or happy.
Everyone who is either not brave or curious is both strong and kind.
Everyone who is not curious is both quiet and tall and vice versa.
If john is both brave and calm then someone is generous or not brave.
Everyone who is not patient or not creative is both not curious and kind and vice versa.
If paul is patient then someone is both strong and not quiet.
Everyone who is either rich or not tall is either generous or not rich and vice versa.
If mary is not wise then someone is either not rich or wise.
If someone is not humble then someone is both not tall and not rich and vice versa.
Everyone who is not quiet or generous is brave or humble and vice versa.
Everyone who is funny or generous is either strong or old.
Everyone who is either not humble or funny is kind or curious and vice versa.
Everyone who is either not tall or not humble is brave or creative and vice versa.
Mary is not quiet or not curious.
Lucy is either curious or not brave.
Susan is either creative or kind.
Susan is both funny and not quiet.
Someone is not tall or not generous.
|
John is not humble.
|
contradiction
|
((~rich(john))=>(~quiet(alice)))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((~calm(X)|~curious(X))=>(wise(X)&~wise(X))))&
(((~rich(mary)<~>curious(mary)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:((~brave(X)<~>curious(X))=>(strong(X)&kind(X))))&
(![X]:(~curious(X)<=>(quiet(X)&tall(X))))&
(((brave(john)&calm(john)))=>(?[X]:((generous(X)|~brave(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~curious(X)&kind(X))))&
((patient(paul))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~tall(X))<=>(generous(X)<~>~rich(X))))&
((~wise(mary))=>(?[X]:((~rich(X)<~>wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((~tall(X)&~rich(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(brave(X)|humble(X))))&
(![X]:((funny(X)|generous(X))=>(strong(X)<~>old(X))))&
(![X]:((~humble(X)<~>funny(X))<=>(kind(X)|curious(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(brave(X)|creative(X))))&
((~quiet(mary)|~curious(mary)))&
((curious(lucy)<~>~brave(lucy)))&
((creative(susan)<~>kind(susan)))&
((funny(susan)&~quiet(susan)))&
(?[X]:((~tall(X)|~generous(X))))
|
~humble(john)
|
[
"p1",
"p2",
"p5",
"p7",
"p9",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 3729903880663095540722098
% SZS output start Proof for 3729903880663095540722098
2. ! [X0] : (~quiet(X0) => ~generous(X0)) [input p1]
3. ! [X0] : ((~curious(X0) | ~calm(X0)) => (~wise(X0) & wise(X0))) [input p2]
6. ! [X0] : (~curious(X0) <=> (tall(X0) & quiet(X0))) [input p5]
8. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (kind(X0) & ~curious(X0))) [input p7]
10. ! [X0] : ((rich(X0) <~> ~tall(X0)) <=> (generous(X0) <~> ~rich(X0))) [input p9]
16. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (creative(X0) | brave(X0))) [input p15]
22. ~humble(john) [input hypothesis]
25. ! [X0] : (~generous(X0) | quiet(X0)) [ennf transformation 2]
26. ! [X0] : ((~wise(X0) & wise(X0)) | (curious(X0) & calm(X0))) [ennf transformation 3]
38. ! [X0] : ((~curious(X0) | (~tall(X0) | ~quiet(X0))) & ((tall(X0) & quiet(X0)) | curious(X0))) [nnf transformation 6]
39. ! [X0] : ((~curious(X0) | ~tall(X0) | ~quiet(X0)) & ((tall(X0) & quiet(X0)) | curious(X0))) [flattening 38]
42. ! [X0] : (((~creative(X0) | ~patient(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 8]
43. ! [X0] : ((~creative(X0) | ~patient(X0) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | (creative(X0) & patient(X0)))) [flattening 42]
46. ! [X0] : ((((tall(X0) | ~rich(X0)) & (~tall(X0) | rich(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0)))) & (((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))))) [nnf transformation 10]
60. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~creative(X0) & ~brave(X0))) & ((creative(X0) | brave(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 16]
61. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~creative(X0) & ~brave(X0))) & (creative(X0) | brave(X0) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [flattening 60]
67. ~generous(X0) | quiet(X0) [cnf transformation 25]
69. wise(X0) | curious(X0) [cnf transformation 26]
71. ~wise(X0) | curious(X0) [cnf transformation 26]
82. ~curious(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 39]
85. ~curious(X0) | creative(X0) [cnf transformation 43]
91. ~rich(X0) | generous(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 46]
96. ~tall(X0) | rich(X0) | generous(X0) | rich(X0) [cnf transformation 46]
123. humble(X0) | tall(X0) | ~creative(X0) [cnf transformation 61]
132. ~humble(john) [cnf transformation 22]
133. ~rich(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 91]
135. ~tall(X0) | rich(X0) | generous(X0) [duplicate literal removal 96]
146. curious(X0) [subsumption resolution 69,71]
166. ~tall(X0) | ~quiet(X0) [subsumption resolution 82,146]
181. creative(X0) [subsumption resolution 85,146]
186. ~tall(X0) | generous(X0) [subsumption resolution 133,135]
224. humble(X0) | tall(X0) [subsumption resolution 123,181]
234. tall(john) [resolution 224,132]
239. generous(john) [resolution 234,186]
240. ~quiet(john) [resolution 234,166]
331. quiet(john) [resolution 239,67]
332. $false [subsumption resolution 331,240]
% SZS output end Proof for 3729903880663095540722098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not strong or not rich then alice is both generous and happy and vice versa. Everyone who is not brave or funny is both not patient and wise and vice versa. Everyone who is either quiet or not creative is quiet and vice versa. If someone is curious then mary is old. If someone is either quiet or rich then fred is not quiet or not rich. If susan is both not strong and not humble then mary is either not humble or kind and vice versa. If someone is quiet then fred is either not tall or not generous. Everyone who is either calm or funny is both strong and not brave. If someone is kind then someone is either patient or happy. If someone is both not happy and funny then mary is brave or not generous and vice versa. Everyone who is not rich or generous is either humble or not quiet and vice versa. Everyone who is not quiet or creative is both brave and quiet. Everyone who is not brave is both not quiet and not patient and vice versa. Everyone who is old or wise is old and vice versa. If john is both old and not quiet then someone is either not creative or not rich and vice versa. If mary is either quiet or strong then alice is happy or not creative and vice versa. Mary is wise or not creative. John is not calm or strong. Lucy is not funny. Paul is either funny or old. Lucy is either funny or tall. Susan is both old and wise.
|
Alice is not strong.
|
neutral
|
(((~strong(fred)|~rich(fred)))<=>((generous(alice)&happy(alice))))&
(![X]:((~brave(X)|funny(X))<=>(~patient(X)&wise(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>quiet(X)))&
((?[X]:(curious(X)))=>(old(mary)))&
((?[X]:((quiet(X)<~>rich(X))))=>((~quiet(fred)|~rich(fred))))&
(((~strong(susan)&~humble(susan)))<=>((~humble(mary)<~>kind(mary))))&
((?[X]:(quiet(X)))=>((~tall(fred)<~>~generous(fred))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((brave(mary)|~generous(mary))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|creative(X))=>(brave(X)&quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)&~patient(X))))&
(![X]:((old(X)|wise(X))<=>old(X)))&
(((old(john)&~quiet(john)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(((quiet(mary)<~>strong(mary)))<=>((happy(alice)|~creative(alice))))&
((wise(mary)|~creative(mary)))&
((~calm(john)|strong(john)))&
(~funny(lucy))&
((funny(paul)<~>old(paul)))&
((funny(lucy)<~>tall(lucy)))&
((old(susan)&wise(susan)))
|
~strong(alice)
|
[] | null | 0 |
If fred is not humble or wise then someone is not old or not rich.
If lucy is either not happy or brave then fred is either quiet or not wise.
Everyone who is not rich or not tall is not happy.
Everyone who is either wise or curious is creative.
If someone is both not humble and old then someone is both not happy and calm and vice versa.
If someone is either not kind or brave then someone is not brave and vice versa.
Everyone who is both not generous and humble is brave.
Everyone who is not kind is happy or patient.
Everyone who is either not strong or not tall is both old and not curious.
Everyone who is curious is either quiet or old and vice versa.
If mary is either not tall or wise then someone is not humble or patient.
Everyone who is not old or not humble is curious or quiet and vice versa.
Everyone who is both not tall and curious is tall and vice versa.
Everyone who is patient or not humble is not funny and vice versa.
If john is both not old and rich then someone is either humble or not happy.
If john is rich or tall then someone is either not humble or not funny and vice versa.
Someone is funny or not funny.
Someone is both generous and not kind.
Mary is either not happy or patient.
Someone is either brave or kind.
Mary is either kind or strong.
Someone is kind.
|
Mary is not humble.
|
entailment
|
(((~humble(fred)|wise(fred)))=>(?[X]:((~old(X)|~rich(X)))))&
(((~happy(lucy)<~>brave(lucy)))=>((quiet(fred)<~>~wise(fred))))&
(![X]:((~rich(X)|~tall(X))=>~happy(X)))&
(![X]:((wise(X)<~>curious(X))=>creative(X)))&
((?[X]:((~humble(X)&old(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
((?[X]:((~kind(X)<~>brave(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)&humble(X))=>brave(X)))&
(![X]:(~kind(X)=>(happy(X)|patient(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(old(X)&~curious(X))))&
(![X]:(curious(X)<=>(quiet(X)<~>old(X))))&
(((~tall(mary)<~>wise(mary)))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((~old(X)|~humble(X))<=>(curious(X)|quiet(X))))&
(![X]:((~tall(X)&curious(X))<=>tall(X)))&
(![X]:((patient(X)|~humble(X))<=>~funny(X)))&
(((~old(john)&rich(john)))=>(?[X]:((humble(X)<~>~happy(X)))))&
(((rich(john)|tall(john)))<=>(?[X]:((~humble(X)<~>~funny(X)))))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((generous(X)&~kind(X))))&
((~happy(mary)<~>patient(mary)))&
(?[X]:((brave(X)<~>kind(X))))&
((kind(mary)<~>strong(mary)))&
(?[X]:(kind(X)))
|
~humble(mary)
|
[
"p9",
"p11",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 3300131351557351607114095
% SZS output start Proof for 3300131351557351607114095
10. ! [X0] : (curious(X0) <=> (quiet(X0) <~> old(X0))) [input p9]
12. ! [X0] : ((~humble(X0) | ~old(X0)) <=> (quiet(X0) | curious(X0))) [input p11]
13. ! [X0] : ((curious(X0) & ~tall(X0)) <=> tall(X0)) [input p12]
23. humble(mary) [input hypothesis]
52. ! [X0] : ((curious(X0) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) & (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | ~curious(X0))) [nnf transformation 10]
56. ! [X0] : (((~humble(X0) | ~old(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (humble(X0) & old(X0)))) [nnf transformation 12]
57. ! [X0] : ((~humble(X0) | ~old(X0) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | (humble(X0) & old(X0)))) [flattening 56]
58. ! [X0] : (((curious(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | (~curious(X0) | tall(X0)))) [nnf transformation 13]
59. ! [X0] : (((curious(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | ~curious(X0) | tall(X0))) [flattening 58]
104. ~quiet(X0) | old(X0) | curious(X0) [cnf transformation 52]
105. ~old(X0) | quiet(X0) | curious(X0) [cnf transformation 52]
108. quiet(X0) | curious(X0) | old(X0) [cnf transformation 57]
111. ~quiet(X0) | ~old(X0) | ~humble(X0) [cnf transformation 57]
112. tall(X0) | ~curious(X0) | tall(X0) [cnf transformation 59]
113. ~tall(X0) | ~tall(X0) [cnf transformation 59]
135. humble(mary) [cnf transformation 23]
136. tall(X0) | ~curious(X0) [duplicate literal removal 112]
137. ~tall(X0) [duplicate literal removal 113]
241. curious(X0) | quiet(X0) [subsumption resolution 108,105]
242. ~curious(X0) [subsumption resolution 136,137]
308. quiet(X0) [resolution 241,242]
319. old(X0) | curious(X0) [resolution 104,308]
320. old(X0) [subsumption resolution 319,242]
338. ~old(X0) | ~humble(X0) [resolution 111,308]
339. ~humble(X0) [subsumption resolution 338,320]
340. $false [resolution 339,135]
% SZS output end Proof for 3300131351557351607114095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either brave or not kind.
If susan is both rich and not humble then someone is calm.
Everyone who is patient is not happy and vice versa.
If susan is not strong then fred is both not old and quiet.
If someone is both funny and not brave then someone is brave or not quiet and vice versa.
Everyone who is both quiet and not quiet is not kind or happy.
Everyone who is both not happy and humble is quiet or not rich and vice versa.
Everyone who is funny or not brave is either kind or not humble and vice versa.
If alice is either tall or not kind then fred is either wise or not creative.
If fred is either not generous or tall then alice is wise.
Everyone who is both curious and wise is funny.
Everyone who is not brave is happy.
Everyone who is not tall is not creative or happy and vice versa.
If someone is creative or quiet then paul is humble and vice versa.
Everyone who is tall or patient is either not wise or kind.
Everyone who is funny is either not creative or not strong and vice versa.
Susan is both creative and funny.
Lucy is rich or curious.
Someone is calm or funny.
Susan is happy.
John is both not patient and not tall.
Lucy is either not brave or not rich.
Someone is either quiet or calm.
Lucy is happy.
|
Susan is not happy.
|
contradiction
|
(![X]:(~quiet(X)=>(brave(X)<~>~kind(X))))&
(((rich(susan)&~humble(susan)))=>(?[X]:(calm(X))))&
(![X]:(patient(X)<=>~happy(X)))&
((~strong(susan))=>((~old(fred)&quiet(fred))))&
((?[X]:((funny(X)&~brave(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((quiet(X)&~quiet(X))=>(~kind(X)|happy(X))))&
(![X]:((~happy(X)&humble(X))<=>(quiet(X)|~rich(X))))&
(![X]:((funny(X)|~brave(X))<=>(kind(X)<~>~humble(X))))&
(((tall(alice)<~>~kind(alice)))=>((wise(fred)<~>~creative(fred))))&
(((~generous(fred)<~>tall(fred)))=>(wise(alice)))&
(![X]:((curious(X)&wise(X))=>funny(X)))&
(![X]:(~brave(X)=>happy(X)))&
(![X]:(~tall(X)<=>(~creative(X)|happy(X))))&
((?[X]:((creative(X)|quiet(X))))<=>(humble(paul)))&
(![X]:((tall(X)|patient(X))=>(~wise(X)<~>kind(X))))&
(![X]:(funny(X)<=>(~creative(X)<~>~strong(X))))&
((creative(susan)&funny(susan)))&
((rich(lucy)|curious(lucy)))&
(?[X]:((calm(X)|funny(X))))&
(happy(susan))&
((~patient(john)&~tall(john)))&
((~brave(lucy)<~>~rich(lucy)))&
(?[X]:((quiet(X)<~>calm(X))))&
(happy(lucy))
|
~happy(susan)
|
[
"p19",
"hypothesis"
] |
% SZS status Unsatisfiable for 7507518346432038402995606
% SZS output start Proof for 7507518346432038402995606
20. happy(susan) [input p19]
25. ~happy(susan) [input hypothesis]
118. happy(susan) [cnf transformation 20]
126. ~happy(susan) [cnf transformation 25]
268. $false [subsumption resolution 126,118]
% SZS output end Proof for 7507518346432038402995606
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or patient then lucy is happy and vice versa.
If lucy is funny then lucy is either not funny or tall.
If john is not patient or humble then someone is not humble.
If alice is both generous and not wise then lucy is not quiet and vice versa.
Everyone who is not tall is not calm and vice versa.
If paul is both not humble and not patient then someone is strong or not quiet and vice versa.
Everyone who is either rich or not funny is both not calm and calm and vice versa.
If someone is both not strong and tall then someone is old.
Everyone who is quiet or wise is patient or not curious.
Everyone who is not happy or not calm is generous or creative and vice versa.
Everyone who is both not happy and rich is humble or not funny.
Everyone who is patient is not wise or curious and vice versa.
Everyone who is funny is tall or generous.
If lucy is both creative and not strong then mary is kind and vice versa.
Everyone who is both curious and strong is either strong or not curious.
Everyone who is not funny or not rich is both not wise and brave and vice versa.
John is either not creative or not calm.
Paul is either not patient or not creative.
John is not old.
Someone is not curious.
Susan is not curious.
|
Lucy is not quiet.
|
contradiction
|
((?[X]:((~quiet(X)|patient(X))))<=>(happy(lucy)))&
((funny(lucy))=>((~funny(lucy)<~>tall(lucy))))&
(((~patient(john)|humble(john)))=>(?[X]:(~humble(X))))&
(((generous(alice)&~wise(alice)))<=>(~quiet(lucy)))&
(![X]:(~tall(X)<=>~calm(X)))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:(old(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~curious(X))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|creative(X))))&
(![X]:((~happy(X)&rich(X))=>(humble(X)|~funny(X))))&
(![X]:(patient(X)<=>(~wise(X)|curious(X))))&
(![X]:(funny(X)=>(tall(X)|generous(X))))&
(((creative(lucy)&~strong(lucy)))<=>(kind(mary)))&
(![X]:((curious(X)&strong(X))=>(strong(X)<~>~curious(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~wise(X)&brave(X))))&
((~creative(john)<~>~calm(john)))&
((~patient(paul)<~>~creative(paul)))&
(~old(john))&
(?[X]:(~curious(X)))&
(~curious(susan))
|
~quiet(lucy)
|
[
"p5",
"p6",
"p11",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 3237797003949062728988937
% SZS output start Proof for 3237797003949062728988937
6. (~patient(paul) & ~humble(paul)) <=> ? [X0] : (~quiet(X0) | strong(X0)) [input p5]
7. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (calm(X0) & ~calm(X0))) [input p6]
12. ! [X0] : (patient(X0) <=> (curious(X0) | ~wise(X0))) [input p11]
16. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (brave(X0) & ~wise(X0))) [input p15]
22. ~quiet(lucy) [input hypothesis]
45. ((~patient(paul) & ~humble(paul)) | ! [X0] : (quiet(X0) & ~strong(X0))) & (? [X0] : (~quiet(X0) | strong(X0)) | (patient(paul) | humble(paul))) [nnf transformation 6]
46. ((~patient(paul) & ~humble(paul)) | ! [X0] : (quiet(X0) & ~strong(X0))) & (? [X0] : (~quiet(X0) | strong(X0)) | patient(paul) | humble(paul)) [flattening 45]
47. ((~patient(paul) & ~humble(paul)) | ! [X0] : (quiet(X0) & ~strong(X0))) & (? [X1] : (~quiet(X1) | strong(X1)) | patient(paul) | humble(paul)) [rectify 46]
48. ? [X1] : (~quiet(X1) | strong(X1)) => (~quiet(sK2) | strong(sK2)) [choice axiom]
49. ((~patient(paul) & ~humble(paul)) | ! [X0] : (quiet(X0) & ~strong(X0))) & ((~quiet(sK2) | strong(sK2)) | patient(paul) | humble(paul)) [skolemisation 47,48]
50. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 7]
51. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [flattening 50]
57. ! [X0] : ((patient(X0) | (~curious(X0) & wise(X0))) & ((curious(X0) | ~wise(X0)) | ~patient(X0))) [nnf transformation 12]
58. ! [X0] : ((patient(X0) | (~curious(X0) & wise(X0))) & (curious(X0) | ~wise(X0) | ~patient(X0))) [flattening 57]
62. ! [X0] : (((~rich(X0) | ~funny(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (rich(X0) & funny(X0)))) [nnf transformation 16]
63. ! [X0] : ((~rich(X0) | ~funny(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | (rich(X0) & funny(X0)))) [flattening 62]
84. ~patient(paul) | quiet(X0) [cnf transformation 49]
85. ~calm(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 51]
87. ~rich(X0) | ~funny(X0) | calm(X0) [cnf transformation 51]
100. wise(X0) | patient(X0) [cnf transformation 58]
108. ~wise(X0) | funny(X0) [cnf transformation 63]
109. ~wise(X0) | rich(X0) [cnf transformation 63]
120. ~quiet(lucy) [cnf transformation 22]
142. 5 <=> ! [X1] : quiet(X1) [avatar definition]
143. quiet(X1) <- (5) [avatar component clause 142]
169. 11 <=> quiet(lucy) [avatar definition]
170. ~quiet(lucy) <- (~11) [avatar component clause 169]
184. 14 <=> patient(paul) [avatar definition]
186. ~patient(paul) <- (~14) [avatar component clause 184]
187. 5 | ~14 [avatar split clause 84,184,142]
208. ~rich(X0) | ~funny(X0) [subsumption resolution 85,87]
248. ~11 [avatar split clause 120,169]
254. funny(X0) | patient(X0) [resolution 108,100]
255. rich(X0) | patient(X0) [resolution 109,100]
263. patient(X1) | ~funny(X1) [resolution 255,208]
265. patient(X1) [subsumption resolution 263,254]
266. $false <- (~14) [resolution 265,186]
267. 14 [avatar contradiction clause 266]
269. $false <- (5, ~11) [resolution 143,170]
270. ~5 | 11 [avatar contradiction clause 269]
272. $false [avatar sat refutation 187,248,267,270]
% SZS output end Proof for 3237797003949062728988937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or generous then someone is not strong and vice versa.
Everyone who is either tall or not generous is curious.
If alice is both not tall and old then lucy is both not old and happy.
If someone is either not happy or not strong then someone is either rich or not brave and vice versa.
Everyone who is both not funny and not strong is both brave and not kind and vice versa.
Everyone who is funny is wise or humble.
If john is either not calm or not creative then someone is humble or not tall.
Everyone who is both patient and not rich is either not strong or humble and vice versa.
Everyone who is not curious is both creative and not happy and vice versa.
Everyone who is both brave and not wise is both calm and not calm and vice versa.
If someone is not curious or not tall then someone is humble or quiet.
If someone is patient then someone is both not brave and not quiet and vice versa.
If someone is not calm then fred is both quiet and not creative.
Everyone who is either not old or not kind is both not quiet and old.
Everyone who is both not curious and not quiet is both not curious and not strong and vice versa.
If susan is either not old or not happy then lucy is both patient and strong.
Paul is either not kind or curious.
Someone is not generous or curious.
Someone is generous.
Someone is both not wise and old.
Someone is either old or not calm.
Someone is both not generous and funny.
Someone is both not brave and wise.
|
John is happy.
|
neutral
|
(((tall(john)<~>generous(john)))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)<~>~generous(X))=>curious(X)))&
(((~tall(alice)&old(alice)))=>((~old(lucy)&happy(lucy))))&
((?[X]:((~happy(X)<~>~strong(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((~funny(X)&~strong(X))<=>(brave(X)&~kind(X))))&
(![X]:(funny(X)=>(wise(X)|humble(X))))&
(((~calm(john)<~>~creative(john)))=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((patient(X)&~rich(X))<=>(~strong(X)<~>humble(X))))&
(![X]:(~curious(X)<=>(creative(X)&~happy(X))))&
(![X]:((brave(X)&~wise(X))<=>(calm(X)&~calm(X))))&
((?[X]:((~curious(X)|~tall(X))))=>(?[X]:((humble(X)|quiet(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~calm(X)))=>((quiet(fred)&~creative(fred))))&
(![X]:((~old(X)<~>~kind(X))=>(~quiet(X)&old(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~curious(X)&~strong(X))))&
(((~old(susan)<~>~happy(susan)))=>((patient(lucy)&strong(lucy))))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&old(X))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:((~brave(X)&wise(X))))
|
happy(john)
|
[] | null | 0 |
Everyone who is both happy and not humble is either not creative or not humble and vice versa.
Everyone who is happy is either funny or wise and vice versa.
Everyone who is not old is generous.
If paul is both not happy and not calm then someone is both tall and not happy.
Everyone who is old or not funny is either rich or happy and vice versa.
If fred is tall or old then someone is either quiet or not quiet.
Everyone who is either not wise or happy is not brave and vice versa.
If susan is not quiet then someone is either old or strong.
If someone is either tall or generous then alice is both not humble and not tall.
Everyone who is generous or not tall is kind and vice versa.
Everyone who is either not patient or not funny is both not tall and patient and vice versa.
If someone is either rich or patient then someone is either happy or not funny and vice versa.
Everyone who is not creative or old is both wise and funny.
If someone is funny or tall then lucy is both not tall and old.
Everyone who is both not calm and kind is tall.
Everyone who is both rich and not wise is not creative.
Someone is happy or not old.
John is humble.
Fred is generous or not quiet.
Someone is either generous or not kind.
|
Alice is happy.
|
entailment
|
(![X]:((happy(X)&~humble(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:(happy(X)<=>(funny(X)<~>wise(X))))&
(![X]:(~old(X)=>generous(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((old(X)|~funny(X))<=>(rich(X)<~>happy(X))))&
(((tall(fred)|old(fred)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>happy(X))<=>~brave(X)))&
((~quiet(susan))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((tall(X)<~>generous(X))))=>((~humble(alice)&~tall(alice))))&
(![X]:((generous(X)|~tall(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:((~creative(X)|old(X))=>(wise(X)&funny(X))))&
((?[X]:((funny(X)|tall(X))))=>((~tall(lucy)&old(lucy))))&
(![X]:((~calm(X)&kind(X))=>tall(X)))&
(![X]:((rich(X)&~wise(X))=>~creative(X)))&
(?[X]:((happy(X)|~old(X))))&
(humble(john))&
((generous(fred)|~quiet(fred)))&
(?[X]:((generous(X)<~>~kind(X))))
|
happy(alice)
|
[
"p1",
"p4",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 6616590659469084880858734
% SZS output start Proof for 6616590659469084880858734
2. ! [X0] : (happy(X0) <=> (funny(X0) <~> wise(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | old(X0)) <=> (rich(X0) <~> happy(X0))) [input p4]
11. ! [X0] : ((~patient(X0) <~> ~funny(X0)) <=> (patient(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((old(X0) | ~creative(X0)) => (funny(X0) & wise(X0))) [input p12]
14. ? [X0] : (tall(X0) | funny(X0)) => (old(lucy) & ~tall(lucy)) [input p13]
16. ! [X0] : ((~wise(X0) & rich(X0)) => ~creative(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
29. ! [X0] : ((funny(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 13]
30. (old(lucy) & ~tall(lucy)) | ! [X0] : (~tall(X0) & ~funny(X0)) [ennf transformation 14]
31. ! [X0] : (~creative(X0) | (wise(X0) | ~rich(X0))) [ennf transformation 16]
32. ! [X0] : (~creative(X0) | wise(X0) | ~rich(X0)) [flattening 31]
35. ! [X0] : ((happy(X0) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) & (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ~happy(X0))) [nnf transformation 2]
36. ! [X0] : (((~funny(X0) | old(X0)) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [nnf transformation 5]
37. ! [X0] : ((~funny(X0) | old(X0) | ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | (funny(X0) & ~old(X0)))) [flattening 36]
47. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | (~patient(X0) | tall(X0))) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [nnf transformation 11]
48. ! [X0] : ((((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ~patient(X0) | tall(X0)) & ((patient(X0) & ~tall(X0)) | ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))))) [flattening 47]
65. ~happy(X0) | funny(X0) | wise(X0) [cnf transformation 35]
68. ~wise(X0) | funny(X0) | happy(X0) [cnf transformation 35]
71. rich(X0) | happy(X0) | funny(X0) [cnf transformation 37]
91. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 48]
93. ~funny(X0) | ~patient(X0) | ~patient(X0) | tall(X0) [cnf transformation 48]
103. wise(X0) | creative(X0) [cnf transformation 29]
106. ~old(X0) | funny(X0) [cnf transformation 29]
107. ~tall(lucy) | ~funny(X0) [cnf transformation 30]
109. old(lucy) | ~funny(X0) [cnf transformation 30]
111. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 32]
117. ~happy(alice) [cnf transformation 21]
118. ~funny(X0) | patient(X0) [duplicate literal removal 91]
119. ~patient(X0) | ~funny(X0) | tall(X0) [duplicate literal removal 93]
195. 17 <=> old(lucy) [avatar definition]
197. old(lucy) <- (17) [avatar component clause 195]
200. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
201. ~funny(X0) <- (18) [avatar component clause 200]
202. 18 | 17 [avatar split clause 109,195,200]
204. 19 <=> tall(lucy) [avatar definition]
206. ~tall(lucy) <- (~19) [avatar component clause 204]
208. 18 | ~19 [avatar split clause 107,204,200]
209. ~rich(X0) | wise(X0) [subsumption resolution 111,103]
243. funny(lucy) <- (17) [resolution 106,197]
247. patient(lucy) <- (17) [resolution 243,118]
282. happy(X0) | funny(X0) | wise(X0) [resolution 71,209]
284. wise(X0) | funny(X0) [subsumption resolution 282,65]
309. ~funny(lucy) | tall(lucy) <- (17) [resolution 119,247]
312. tall(lucy) <- (17) [subsumption resolution 309,243]
313. $false <- (17, ~19) [subsumption resolution 312,206]
314. ~17 | 19 [avatar contradiction clause 313]
334. funny(X0) | funny(X0) | happy(X0) [resolution 284,68]
336. funny(X0) | happy(X0) [duplicate literal removal 334]
337. happy(X0) <- (18) [subsumption resolution 336,201]
340. $false <- (18) [resolution 337,117]
343. ~18 [avatar contradiction clause 340]
344. $false [avatar sat refutation 202,208,314,343]
% SZS output end Proof for 6616590659469084880858734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not brave is kind or old and vice versa.
Everyone who is generous or not generous is both not curious and funny.
Everyone who is curious is humble or not tall and vice versa.
If mary is not strong or not funny then susan is either not kind or not brave and vice versa.
Everyone who is both not old and old is not old and vice versa.
Everyone who is both quiet and generous is humble.
Everyone who is not kind or not generous is not tall and vice versa.
If paul is happy then susan is either not generous or not strong.
If someone is tall then someone is both not humble and old.
If john is not patient or funny then susan is either not old or rich.
Everyone who is both brave and not patient is kind and vice versa.
If someone is either not kind or not humble then paul is either not happy or not kind.
If mary is both funny and creative then lucy is not strong or not humble and vice versa.
If someone is both not kind and not calm then mary is both funny and not creative.
Someone is not calm.
John is not kind or not quiet.
Someone is funny.
Someone is old.
Someone is generous.
|
Mary is patient.
|
contradiction
|
(![X]:((wise(X)<~>~brave(X))<=>(kind(X)|old(X))))&
(![X]:((generous(X)|~generous(X))=>(~curious(X)&funny(X))))&
(![X]:(curious(X)<=>(humble(X)|~tall(X))))&
(((~strong(mary)|~funny(mary)))<=>((~kind(susan)<~>~brave(susan))))&
(![X]:((~old(X)&old(X))<=>~old(X)))&
(![X]:((quiet(X)&generous(X))=>humble(X)))&
(![X]:((~kind(X)|~generous(X))<=>~tall(X)))&
((happy(paul))=>((~generous(susan)<~>~strong(susan))))&
((?[X]:(tall(X)))=>(?[X]:((~humble(X)&old(X)))))&
(((~patient(john)|funny(john)))=>((~old(susan)<~>rich(susan))))&
(![X]:((brave(X)&~patient(X))<=>kind(X)))&
((?[X]:((~kind(X)<~>~humble(X))))=>((~happy(paul)<~>~kind(paul))))&
(((funny(mary)&creative(mary)))<=>((~strong(lucy)|~humble(lucy))))&
((?[X]:((~kind(X)&~calm(X))))=>((funny(mary)&~creative(mary))))&
(?[X]:(~calm(X)))&
((~kind(john)|~quiet(john)))&
(?[X]:(funny(X)))&
(?[X]:(old(X)))&
(?[X]:(generous(X)))
|
patient(mary)
|
[
"p1",
"p2",
"p6",
"p10",
"hypothesis"
] |
% SZS status Unsatisfiable for 284711314691895782172299
% SZS output start Proof for 284711314691895782172299
2. ! [X0] : ((~generous(X0) | generous(X0)) => (funny(X0) & ~curious(X0))) [input p1]
3. ! [X0] : (curious(X0) <=> (~tall(X0) | humble(X0))) [input p2]
7. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> ~tall(X0)) [input p6]
11. ! [X0] : ((~patient(X0) & brave(X0)) <=> kind(X0)) [input p10]
20. patient(mary) [input hypothesis]
22. ! [X0] : ((~tall(X0) | humble(X0)) => curious(X0)) [unused predicate definition removal 3]
25. ! [X0] : ((funny(X0) & ~curious(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 2]
26. ! [X0] : (curious(X0) | (tall(X0) & ~humble(X0))) [ennf transformation 22]
38. ! [X0] : (((~generous(X0) | ~kind(X0)) | tall(X0)) & (~tall(X0) | (generous(X0) & kind(X0)))) [nnf transformation 7]
39. ! [X0] : ((~generous(X0) | ~kind(X0) | tall(X0)) & (~tall(X0) | (generous(X0) & kind(X0)))) [flattening 38]
45. ! [X0] : (((~patient(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (patient(X0) | ~brave(X0)))) [nnf transformation 11]
46. ! [X0] : (((~patient(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | patient(X0) | ~brave(X0))) [flattening 45]
64. ~curious(X0) | ~generous(X0) [cnf transformation 25]
65. ~curious(X0) | generous(X0) [cnf transformation 25]
69. curious(X0) | tall(X0) [cnf transformation 26]
79. ~tall(X0) | kind(X0) [cnf transformation 39]
92. ~patient(X0) | ~kind(X0) [cnf transformation 46]
108. patient(mary) [cnf transformation 20]
112. ~curious(X0) [subsumption resolution 64,65]
113. tall(X0) [subsumption resolution 69,112]
134. kind(X0) [subsumption resolution 79,113]
147. ~patient(X0) [subsumption resolution 92,134]
154. $false [subsumption resolution 108,147]
% SZS output end Proof for 284711314691895782172299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then susan is both kind and funny and vice versa.
If someone is not brave then john is quiet or not tall.
If susan is either quiet or humble then john is not humble and vice versa.
Everyone who is both not quiet and funny is not kind or funny.
Everyone who is creative or old is not humble or strong.
Everyone who is funny is both not tall and not kind.
Everyone who is funny is either humble or not tall.
Everyone who is both not brave and not quiet is either not brave or brave.
Everyone who is not strong or calm is both not tall and not generous and vice versa.
If someone is brave or curious then someone is wise.
If fred is both curious and not creative then alice is both not funny and not old and vice versa.
If someone is either not rich or not tall then someone is brave or not old and vice versa.
Everyone who is both not funny and not quiet is not happy or not kind and vice versa.
If fred is both old and generous then lucy is either curious or strong and vice versa.
If alice is not happy or patient then paul is both humble and tall.
Everyone who is both tall and old is both quiet and generous.
Someone is either happy or not wise.
John is both not rich and not curious.
Susan is either generous or strong.
Someone is either brave or not wise.
Fred is not curious.
Alice is not generous.
Susan is not humble.
Fred is both kind and brave.
|
Alice is happy.
|
neutral
|
((?[X]:(~creative(X)))<=>((kind(susan)&funny(susan))))&
((?[X]:(~brave(X)))=>((quiet(john)|~tall(john))))&
(((quiet(susan)<~>humble(susan)))<=>(~humble(john)))&
(![X]:((~quiet(X)&funny(X))=>(~kind(X)|funny(X))))&
(![X]:((creative(X)|old(X))=>(~humble(X)|strong(X))))&
(![X]:(funny(X)=>(~tall(X)&~kind(X))))&
(![X]:(funny(X)=>(humble(X)<~>~tall(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)<~>brave(X))))&
(![X]:((~strong(X)|calm(X))<=>(~tall(X)&~generous(X))))&
((?[X]:((brave(X)|curious(X))))=>(?[X]:(wise(X))))&
(((curious(fred)&~creative(fred)))<=>((~funny(alice)&~old(alice))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(~happy(X)|~kind(X))))&
(((old(fred)&generous(fred)))<=>((curious(lucy)<~>strong(lucy))))&
(((~happy(alice)|patient(alice)))=>((humble(paul)&tall(paul))))&
(![X]:((tall(X)&old(X))=>(quiet(X)&generous(X))))&
(?[X]:((happy(X)<~>~wise(X))))&
((~rich(john)&~curious(john)))&
((generous(susan)<~>strong(susan)))&
(?[X]:((brave(X)<~>~wise(X))))&
(~curious(fred))&
(~generous(alice))&
(~humble(susan))&
((kind(fred)&brave(fred)))
|
happy(alice)
|
[] | null | 0 |
Everyone who is either humble or not strong is both not humble and funny and vice versa. Everyone who is both wise and not tall is not old or not generous. Everyone who is either not creative or humble is generous or not strong and vice versa. If john is either calm or not strong then someone is either wise or old. If someone is not strong or not curious then mary is not strong. If someone is both not happy and not old then someone is creative and vice versa. Everyone who is either not tall or not wise is either not generous or not funny and vice versa. If john is either rich or strong then lucy is calm and vice versa. If someone is tall or humble then someone is either not kind or old. If someone is not humble or strong then someone is either not wise or humble. Everyone who is not funny or not tall is either not strong or strong. Everyone who is not generous or not patient is patient and vice versa. Everyone who is not tall is kind and vice versa. Everyone who is either not tall or quiet is not kind or patient and vice versa. Everyone who is not brave is both funny and not old. If someone is curious or generous then alice is both not humble and not brave. Paul is both brave and rich. Susan is not tall or patient. Someone is not humble or tall. Fred is either not calm or not happy. Someone is either not kind or not brave. John is either brave or not brave.
|
Susan is not happy.
|
neutral
|
(![X]:((humble(X)<~>~strong(X))<=>(~humble(X)&funny(X))))&
(![X]:((wise(X)&~tall(X))=>(~old(X)|~generous(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)|~strong(X))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((~strong(X)|~curious(X))))=>(~strong(mary)))&
((?[X]:((~happy(X)&~old(X))))<=>(?[X]:(creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~generous(X)<~>~funny(X))))&
(((rich(john)<~>strong(john)))<=>(calm(lucy)))&
((?[X]:((tall(X)|humble(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((~humble(X)|strong(X))))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~funny(X)|~tall(X))=>(~strong(X)<~>strong(X))))&
(![X]:((~generous(X)|~patient(X))<=>patient(X)))&
(![X]:(~tall(X)<=>kind(X)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|patient(X))))&
(![X]:(~brave(X)=>(funny(X)&~old(X))))&
((?[X]:((curious(X)|generous(X))))=>((~humble(alice)&~brave(alice))))&
((brave(paul)&rich(paul)))&
((~tall(susan)|patient(susan)))&
(?[X]:((~humble(X)|tall(X))))&
((~calm(fred)<~>~happy(fred)))&
(?[X]:((~kind(X)<~>~brave(X))))&
((brave(john)<~>~brave(john)))
|
~happy(susan)
|
[] | null | 0 |
If paul is curious or not happy then someone is either not old or humble.
Everyone who is curious is both old and happy.
Everyone who is both not tall and quiet is either not quiet or quiet.
If someone is either rich or not rich then someone is patient.
If someone is humble or not patient then john is both generous and not brave.
Everyone who is humble is tall or not old and vice versa.
If alice is either funny or rich then john is either not quiet or calm.
If someone is not old or not tall then john is happy.
Everyone who is either not brave or not old is both brave and not funny and vice versa.
If someone is both strong and happy then paul is quiet.
Everyone who is both not humble and curious is both not calm and not patient and vice versa.
Everyone who is not happy is either rich or not strong and vice versa.
Everyone who is wise or creative is either not creative or not curious.
If someone is funny or patient then someone is strong or happy.
If alice is both not generous and brave then someone is both not kind and curious.
Everyone who is either not generous or not creative is either strong or kind.
Someone is not tall or patient.
John is either generous or humble.
Someone is either not old or quiet.
Lucy is either kind or strong.
Someone is both not wise and not humble.
John is wise.
Susan is not curious or not calm.
|
Paul is not patient.
|
contradiction
|
(((curious(paul)|~happy(paul)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:(curious(X)=>(old(X)&happy(X))))&
(![X]:((~tall(X)&quiet(X))=>(~quiet(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>(?[X]:(patient(X))))&
((?[X]:((humble(X)|~patient(X))))=>((generous(john)&~brave(john))))&
(![X]:(humble(X)<=>(tall(X)|~old(X))))&
(((funny(alice)<~>rich(alice)))=>((~quiet(john)<~>calm(john))))&
((?[X]:((~old(X)|~tall(X))))=>(happy(john)))&
(![X]:((~brave(X)<~>~old(X))<=>(brave(X)&~funny(X))))&
((?[X]:((strong(X)&happy(X))))=>(quiet(paul)))&
(![X]:((~humble(X)&curious(X))<=>(~calm(X)&~patient(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>~strong(X))))&
(![X]:((wise(X)|creative(X))=>(~creative(X)<~>~curious(X))))&
((?[X]:((funny(X)|patient(X))))=>(?[X]:((strong(X)|happy(X)))))&
(((~generous(alice)&brave(alice)))=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((~generous(X)<~>~creative(X))=>(strong(X)<~>kind(X))))&
(?[X]:((~tall(X)|patient(X))))&
((generous(john)<~>humble(john)))&
(?[X]:((~old(X)<~>quiet(X))))&
((kind(lucy)<~>strong(lucy)))&
(?[X]:((~wise(X)&~humble(X))))&
(wise(john))&
((~curious(susan)|~calm(susan)))
|
~patient(paul)
|
[
"p4",
"p5",
"p8",
"p17",
"hypothesis"
] |
% SZS status Unsatisfiable for 802515903793153705017467
% SZS output start Proof for 802515903793153705017467
5. ? [X0] : (~patient(X0) | humble(X0)) => (~brave(john) & generous(john)) [input p4]
6. ! [X0] : (humble(X0) <=> (~old(X0) | tall(X0))) [input p5]
9. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (~funny(X0) & brave(X0))) [input p8]
18. generous(john) <~> humble(john) [input p17]
24. ~patient(paul) [input hypothesis]
32. (~brave(john) & generous(john)) | ! [X0] : (patient(X0) & ~humble(X0)) [ennf transformation 5]
49. ! [X0] : ((humble(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~humble(X0))) [nnf transformation 6]
50. ! [X0] : ((humble(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~humble(X0))) [flattening 49]
52. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (funny(X0) | ~brave(X0))) & ((~funny(X0) & brave(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 9]
53. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | funny(X0) | ~brave(X0)) & ((~funny(X0) & brave(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 52]
66. (~humble(john) | ~generous(john)) & (humble(john) | generous(john)) [nnf transformation 18]
84. generous(john) | patient(X0) [cnf transformation 32]
86. ~brave(john) | patient(X0) [cnf transformation 32]
89. humble(X0) | old(X0) [cnf transformation 50]
96. brave(X0) | ~old(X0) | brave(X0) [cnf transformation 53]
125. ~humble(john) | ~generous(john) [cnf transformation 66]
134. ~patient(paul) [cnf transformation 24]
136. ~old(X0) | brave(X0) [duplicate literal removal 96]
175. 8 <=> ! [X0] : patient(X0) [avatar definition]
176. patient(X0) <- (8) [avatar component clause 175]
178. 9 <=> brave(john) [avatar definition]
181. 8 | ~9 [avatar split clause 86,178,175]
187. 11 <=> generous(john) [avatar definition]
190. 8 | 11 [avatar split clause 84,187,175]
276. 31 <=> humble(john) [avatar definition]
278. ~humble(john) <- (~31) [avatar component clause 276]
279. ~11 | ~31 [avatar split clause 125,276,187]
312. old(john) <- (~31) [resolution 89,278]
316. brave(john) <- (~31) [resolution 136,312]
319. 9 | 31 [avatar split clause 316,276,178]
320. $false <- (8) [resolution 176,134]
321. ~8 [avatar contradiction clause 320]
322. $false [avatar sat refutation 181,190,279,319,321]
% SZS output end Proof for 802515903793153705017467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is not brave then john is not kind or happy and vice versa.
Everyone who is kind or not tall is not strong or funny and vice versa.
Everyone who is both humble and not kind is kind and vice versa.
Everyone who is patient is creative or not generous.
Everyone who is brave or old is either not brave or not rich and vice versa.
Everyone who is not kind is both not funny and not old and vice versa.
Everyone who is not quiet is not patient or not kind.
Everyone who is both not calm and not brave is both wise and rich and vice versa.
Everyone who is both wise and happy is not creative.
Everyone who is either strong or not old is either brave or strong.
Everyone who is tall is not creative or wise.
Everyone who is not happy or creative is not curious or wise.
Everyone who is either not creative or calm is either patient or not generous and vice versa.
If fred is not generous or creative then alice is old and vice versa.
Everyone who is either generous or rich is rich or generous.
Someone is either not patient or not kind.
Lucy is either rich or not curious.
Fred is not curious or not creative.
Someone is not funny or brave.
Someone is either not quiet or not calm.
Someone is quiet.
|
Fred is not calm.
|
contradiction
|
((~brave(john))<=>((~kind(john)|happy(john))))&
(![X]:((kind(X)|~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
(![X]:((generous(X)<~>rich(X))=>(rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
((rich(lucy)<~>~curious(lucy)))&
((~curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:(quiet(X)))
|
~calm(fred)
|
[
"p2",
"p3",
"p5",
"p12",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 2645015462851616713143298
% SZS output start Proof for 2645015462851616713143298
3. ! [X0] : ((~kind(X0) & humble(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : (patient(X0) => (~generous(X0) | creative(X0))) [input p3]
6. ! [X0] : (~kind(X0) <=> (~old(X0) & ~funny(X0))) [input p5]
13. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p12]
14. (creative(fred) | ~generous(fred)) <=> old(alice) [input p13]
22. ~calm(fred) [input hypothesis]
23. ! [X0] : ((~generous(X0) | creative(X0)) | ~patient(X0)) [ennf transformation 4]
24. ! [X0] : (~generous(X0) | creative(X0) | ~patient(X0)) [flattening 23]
40. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~humble(X0))) [flattening 40]
44. ! [X0] : ((~kind(X0) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 6]
45. ! [X0] : ((~kind(X0) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | kind(X0))) [flattening 44]
49. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 13]
50. ((creative(fred) | ~generous(fred)) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [nnf transformation 14]
51. (creative(fred) | ~generous(fred) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [flattening 50]
73. ~kind(X0) | ~kind(X0) [cnf transformation 41]
74. ~generous(X0) | creative(X0) | ~patient(X0) [cnf transformation 24]
82. ~old(X0) | kind(X0) [cnf transformation 45]
97. ~generous(X0) | patient(X0) | calm(X0) | creative(X0) [cnf transformation 49]
101. calm(X0) | ~creative(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 49]
105. old(alice) | generous(fred) [cnf transformation 51]
106. old(alice) | ~creative(fred) [cnf transformation 51]
119. ~calm(fred) [cnf transformation 22]
127. ~kind(X0) [duplicate literal removal 73]
144. ~old(X0) [subsumption resolution 82,127]
147. ~generous(X0) | calm(X0) | ~patient(X0) [subsumption resolution 101,74]
149. ~generous(X0) | calm(X0) | creative(X0) [subsumption resolution 97,147]
150. ~creative(fred) [subsumption resolution 106,144]
151. generous(fred) [subsumption resolution 105,144]
219. calm(fred) | creative(fred) [resolution 149,151]
220. creative(fred) [subsumption resolution 219,119]
221. $false [subsumption resolution 220,150]
% SZS output end Proof for 2645015462851616713143298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is old then fred is creative or not generous and vice versa. If someone is both curious and not funny then fred is either not wise or not old and vice versa. If lucy is either not humble or kind then someone is both generous and wise. Everyone who is quiet or wise is both not happy and not generous. Everyone who is either not wise or not creative is both humble and not creative and vice versa. If someone is brave or calm then mary is old and vice versa. Everyone who is either not funny or not curious is tall and vice versa. Everyone who is tall is not tall. If alice is either not strong or curious then someone is curious or not old and vice versa. Everyone who is both not wise and not patient is both funny and tall. Everyone who is both brave and kind is not brave. Everyone who is either not calm or generous is both creative and not calm and vice versa. Everyone who is either funny or rich is either calm or strong and vice versa. If lucy is both patient and not old then someone is both generous and not creative. If susan is either not wise or not generous then someone is both not curious and not happy. Everyone who is either rich or not generous is not quiet and vice versa. Alice is generous. Someone is rich. Someone is either not quiet or kind. Someone is calm. Alice is curious or not creative. Someone is kind. Someone is both calm and humble. Fred is either wise or brave.
|
Lucy is old.
|
entailment
|
((old(john))<=>((creative(fred)|~generous(fred))))&
((?[X]:((curious(X)&~funny(X))))<=>((~wise(fred)<~>~old(fred))))&
(((~humble(lucy)<~>kind(lucy)))=>(?[X]:((generous(X)&wise(X)))))&
(![X]:((quiet(X)|wise(X))=>(~happy(X)&~generous(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>(humble(X)&~creative(X))))&
((?[X]:((brave(X)|calm(X))))<=>(old(mary)))&
(![X]:((~funny(X)<~>~curious(X))<=>tall(X)))&
(![X]:(tall(X)=>~tall(X)))&
(((~strong(alice)<~>curious(alice)))<=>(?[X]:((curious(X)|~old(X)))))&
(![X]:((~wise(X)&~patient(X))=>(funny(X)&tall(X))))&
(![X]:((brave(X)&kind(X))=>~brave(X)))&
(![X]:((~calm(X)<~>generous(X))<=>(creative(X)&~calm(X))))&
(![X]:((funny(X)<~>rich(X))<=>(calm(X)<~>strong(X))))&
(((patient(lucy)&~old(lucy)))=>(?[X]:((generous(X)&~creative(X)))))&
(((~wise(susan)<~>~generous(susan)))=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((rich(X)<~>~generous(X))<=>~quiet(X)))&
(generous(alice))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:(calm(X)))&
((curious(alice)|~creative(alice)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)&humble(X))))&
((wise(fred)<~>brave(fred)))
|
old(lucy)
|
[
"p3",
"p6",
"p7",
"p8",
"p11",
"p12",
"p15",
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 6422744342266263570985302
% SZS output start Proof for 6422744342266263570985302
4. ! [X0] : ((wise(X0) | quiet(X0)) => (~generous(X0) & ~happy(X0))) [input p3]
7. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> tall(X0)) [input p6]
8. ! [X0] : (tall(X0) => ~tall(X0)) [input p7]
9. (~strong(alice) <~> curious(alice)) <=> ? [X0] : (~old(X0) | curious(X0)) [input p8]
12. ! [X0] : ((~calm(X0) <~> generous(X0)) <=> (~calm(X0) & creative(X0))) [input p11]
13. ! [X0] : ((funny(X0) <~> rich(X0)) <=> (calm(X0) <~> strong(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> ~generous(X0)) <=> ~quiet(X0)) [input p15]
17. generous(alice) [input p16]
25. ~old(lucy) [input hypothesis]
26. ! [X0] : ((wise(X0) | quiet(X0)) => ~generous(X0)) [pure predicate removal 4]
29. ! [X0] : (~generous(X0) | (~wise(X0) & ~quiet(X0))) [ennf transformation 26]
30. ! [X0] : (~tall(X0) | ~tall(X0)) [ennf transformation 8]
53. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | ~tall(X0)) & (tall(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 7]
54. (((~curious(alice) | strong(alice)) & (curious(alice) | ~strong(alice))) | ! [X0] : (old(X0) & ~curious(X0))) & (? [X0] : (~old(X0) | curious(X0)) | ((~strong(alice) | ~curious(alice)) & (curious(alice) | strong(alice)))) [nnf transformation 9]
55. (((~curious(alice) | strong(alice)) & (curious(alice) | ~strong(alice))) | ! [X0] : (old(X0) & ~curious(X0))) & (? [X1] : (~old(X1) | curious(X1)) | ((~strong(alice) | ~curious(alice)) & (curious(alice) | strong(alice)))) [rectify 54]
56. ? [X1] : (~old(X1) | curious(X1)) => (~old(sK3) | curious(sK3)) [choice axiom]
57. (((~curious(alice) | strong(alice)) & (curious(alice) | ~strong(alice))) | ! [X0] : (old(X0) & ~curious(X0))) & ((~old(sK3) | curious(sK3)) | ((~strong(alice) | ~curious(alice)) & (curious(alice) | strong(alice)))) [skolemisation 55,56]
58. ! [X0] : ((((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | (calm(X0) | ~creative(X0))) & ((~calm(X0) & creative(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))))) [nnf transformation 12]
59. ! [X0] : ((((~generous(X0) | calm(X0)) & (generous(X0) | ~calm(X0))) | calm(X0) | ~creative(X0)) & ((~calm(X0) & creative(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))))) [flattening 58]
60. ! [X0] : ((((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | ((calm(X0) | ~strong(X0)) & (strong(X0) | ~calm(X0)))) & (((~strong(X0) | ~calm(X0)) & (strong(X0) | calm(X0))) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))))) [nnf transformation 13]
66. ! [X0] : ((((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | quiet(X0)) & (~quiet(X0) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0))))) [nnf transformation 16]
92. ~quiet(X0) | ~generous(X0) [cnf transformation 29]
103. ~curious(X0) | tall(X0) | funny(X0) [cnf transformation 53]
104. ~funny(X0) | tall(X0) | curious(X0) [cnf transformation 53]
107. ~tall(X0) | ~tall(X0) [cnf transformation 30]
111. curious(alice) | ~strong(alice) | old(X0) [cnf transformation 57]
112. ~curious(alice) | strong(alice) | ~curious(X0) [cnf transformation 57]
120. ~calm(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 59]
124. ~rich(X0) | calm(X0) | funny(X0) | strong(X0) [cnf transformation 60]
130. ~rich(X0) | ~funny(X0) | calm(X0) | ~strong(X0) [cnf transformation 60]
137. ~generous(X0) | rich(X0) | quiet(X0) [cnf transformation 66]
139. generous(alice) [cnf transformation 17]
150. ~old(lucy) [cnf transformation 25]
151. ~calm(X0) | ~generous(X0) [duplicate literal removal 120]
154. ~tall(X0) [duplicate literal removal 107]
239. 18 <=> ! [X0] : old(X0) [avatar definition]
240. old(X0) <- (18) [avatar component clause 239]
242. 19 <=> strong(alice) [avatar definition]
244. strong(alice) <- (19) [avatar component clause 242]
246. 20 <=> curious(alice) [avatar definition]
247. curious(alice) <- (20) [avatar component clause 246]
251. 21 <=> ! [X0] : ~curious(X0) [avatar definition]
252. ~curious(X0) <- (21) [avatar component clause 251]
253. 21 | 19 | ~20 [avatar split clause 112,246,242,251]
254. 18 | ~19 | 20 [avatar split clause 111,246,242,239]
272. 25 <=> old(lucy) [avatar definition]
273. ~old(lucy) <- (~25) [avatar component clause 272]
301. ~generous(X0) | rich(X0) [subsumption resolution 137,92]
324. ~25 [avatar split clause 150,272]
331. rich(alice) [resolution 301,139]
384. calm(alice) | funny(alice) | strong(alice) [resolution 124,331]
400. 44 <=> funny(alice) [avatar definition]
402. funny(alice) <- (44) [avatar component clause 400]
404. 45 <=> calm(alice) [avatar definition]
406. calm(alice) <- (45) [avatar component clause 404]
408. 19 | 44 | 45 [avatar split clause 384,404,400,242]
410. tall(alice) | funny(alice) <- (20) [resolution 247,103]
412. funny(alice) <- (20) [subsumption resolution 410,154]
413. 44 | ~20 [avatar split clause 412,246,400]
414. $false <- (18, ~25) [resolution 240,273]
419. ~18 | 25 [avatar contradiction clause 414]
422. tall(alice) | curious(alice) <- (44) [resolution 402,104]
423. curious(alice) <- (44) [subsumption resolution 422,154]
424. $false <- (21, 44) [subsumption resolution 423,252]
425. ~21 | ~44 [avatar contradiction clause 424]
426. 20 | ~44 [avatar split clause 423,400,246]
481. ~funny(alice) | calm(alice) | ~strong(alice) [resolution 130,331]
486. calm(alice) | ~strong(alice) <- (44) [subsumption resolution 481,402]
487. calm(alice) <- (19, 44) [subsumption resolution 486,244]
488. 45 | ~19 | ~44 [avatar split clause 487,400,242,404]
500. ~generous(alice) <- (45) [resolution 406,151]
501. $false <- (45) [subsumption resolution 500,139]
502. ~45 [avatar contradiction clause 501]
503. $false [avatar sat refutation 253,254,324,408,413,419,425,426,488,502]
% SZS output end Proof for 6422744342266263570985302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is not tall or strong and vice versa. Everyone who is not brave or rich is not patient or not creative. If paul is both tall and rich then john is either not old or not tall. Everyone who is humble is either not calm or not quiet and vice versa. If someone is either not brave or not calm then someone is both humble and not strong and vice versa. If lucy is not brave or humble then someone is not generous. If mary is not happy then john is both not happy and quiet and vice versa. If paul is either generous or not quiet then alice is either not wise or wise. Everyone who is curious or patient is both humble and not rich. Everyone who is both not calm and humble is not curious or tall and vice versa. Everyone who is not old or not curious is strong and vice versa. If someone is either not curious or not creative then someone is both tall and creative and vice versa. Everyone who is both not strong and funny is either not old or kind and vice versa. Everyone who is not rich is both curious and tall and vice versa. Everyone who is not tall is not brave or not strong and vice versa. If someone is both funny and not humble then alice is both not creative and creative. Someone is both strong and funny. Someone is quiet or not happy. Mary is not brave. Someone is tall or generous. Someone is either old or not patient.
|
John is kind.
|
neutral
|
(![X]:((~old(X)|~creative(X))<=>(~tall(X)|strong(X))))&
(![X]:((~brave(X)|rich(X))=>(~patient(X)|~creative(X))))&
(((tall(paul)&rich(paul)))=>((~old(john)<~>~tall(john))))&
(![X]:(humble(X)<=>(~calm(X)<~>~quiet(X))))&
((?[X]:((~brave(X)<~>~calm(X))))<=>(?[X]:((humble(X)&~strong(X)))))&
(((~brave(lucy)|humble(lucy)))=>(?[X]:(~generous(X))))&
((~happy(mary))<=>((~happy(john)&quiet(john))))&
(((generous(paul)<~>~quiet(paul)))=>((~wise(alice)<~>wise(alice))))&
(![X]:((curious(X)|patient(X))=>(humble(X)&~rich(X))))&
(![X]:((~calm(X)&humble(X))<=>(~curious(X)|tall(X))))&
(![X]:((~old(X)|~curious(X))<=>strong(X)))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((tall(X)&creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)<~>kind(X))))&
(![X]:(~rich(X)<=>(curious(X)&tall(X))))&
(![X]:(~tall(X)<=>(~brave(X)|~strong(X))))&
((?[X]:((funny(X)&~humble(X))))=>((~creative(alice)&creative(alice))))&
(?[X]:((strong(X)&funny(X))))&
(?[X]:((quiet(X)|~happy(X))))&
(~brave(mary))&
(?[X]:((tall(X)|generous(X))))&
(?[X]:((old(X)<~>~patient(X))))
|
kind(john)
|
[] | null | 0 |
Everyone who is not tall or not curious is both not patient and calm and vice versa.
If someone is both not brave and not old then someone is either curious or not wise and vice versa.
If alice is not strong or not brave then someone is both rich and old.
If someone is not wise then fred is either old or strong.
Everyone who is quiet or not brave is not old or not rich and vice versa.
If someone is not strong or not happy then someone is calm or not patient.
If someone is both not generous and humble then mary is either rich or happy.
Everyone who is not wise is not humble or not kind and vice versa.
Everyone who is both creative and not funny is both not patient and not happy and vice versa.
Everyone who is both not quiet and not wise is both funny and not tall.
If susan is either humble or not humble then alice is quiet.
Everyone who is both kind and not quiet is kind.
Everyone who is both brave and not strong is calm or not kind and vice versa.
If someone is both not tall and happy then someone is generous and vice versa.
If mary is both humble and strong then someone is not quiet and vice versa.
Everyone who is brave or quiet is either tall or rich and vice versa.
Someone is either happy or not generous.
Someone is not happy.
Mary is patient.
Fred is both generous and not brave.
Someone is both tall and rich.
Someone is both tall and not patient.
Susan is generous.
Someone is not quiet.
|
Mary is not wise.
|
contradiction
|
(![X]:((~tall(X)|~curious(X))<=>(~patient(X)&calm(X))))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~strong(alice)|~brave(alice)))=>(?[X]:((rich(X)&old(X)))))&
((?[X]:(~wise(X)))=>((old(fred)<~>strong(fred))))&
(![X]:((quiet(X)|~brave(X))<=>(~old(X)|~rich(X))))&
((?[X]:((~strong(X)|~happy(X))))=>(?[X]:((calm(X)|~patient(X)))))&
((?[X]:((~generous(X)&humble(X))))=>((rich(mary)<~>happy(mary))))&
(![X]:(~wise(X)<=>(~humble(X)|~kind(X))))&
(![X]:((creative(X)&~funny(X))<=>(~patient(X)&~happy(X))))&
(![X]:((~quiet(X)&~wise(X))=>(funny(X)&~tall(X))))&
(((humble(susan)<~>~humble(susan)))=>(quiet(alice)))&
(![X]:((kind(X)&~quiet(X))=>kind(X)))&
(![X]:((brave(X)&~strong(X))<=>(calm(X)|~kind(X))))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:(generous(X))))&
(((humble(mary)&strong(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|quiet(X))<=>(tall(X)<~>rich(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(patient(mary))&
((generous(fred)&~brave(fred)))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((tall(X)&~patient(X))))&
(generous(susan))&
(?[X]:(~quiet(X)))
|
~wise(mary)
|
[
"p7",
"p12",
"p14",
"p23",
"hypothesis"
] |
% SZS status Unsatisfiable for 4036827837930668671493112
% SZS output start Proof for 4036827837930668671493112
8. ! [X0] : (~wise(X0) <=> (~kind(X0) | ~humble(X0))) [input p7]
13. ! [X0] : ((~strong(X0) & brave(X0)) <=> (~kind(X0) | calm(X0))) [input p12]
15. (strong(mary) & humble(mary)) <=> ? [X0] : ~quiet(X0) [input p14]
24. ? [X0] : ~quiet(X0) [input p23]
25. ~wise(mary) [input hypothesis]
54. ! [X0] : ((~wise(X0) | (kind(X0) & humble(X0))) & ((~kind(X0) | ~humble(X0)) | wise(X0))) [nnf transformation 8]
55. ! [X0] : ((~wise(X0) | (kind(X0) & humble(X0))) & (~kind(X0) | ~humble(X0) | wise(X0))) [flattening 54]
59. ! [X0] : (((~strong(X0) & brave(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & brave(X0)) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | strong(X0) | ~brave(X0))) [flattening 59]
66. ((strong(mary) & humble(mary)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (~strong(mary) | ~humble(mary))) [nnf transformation 15]
67. ((strong(mary) & humble(mary)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | ~strong(mary) | ~humble(mary)) [flattening 66]
68. ((strong(mary) & humble(mary)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | ~strong(mary) | ~humble(mary)) [rectify 67]
69. ? [X1] : ~quiet(X1) => ~quiet(sK6) [choice axiom]
70. ((strong(mary) & humble(mary)) | ! [X0] : quiet(X0)) & (~quiet(sK6) | ~strong(mary) | ~humble(mary)) [skolemisation 68,69]
82. ? [X0] : ~quiet(X0) => ~quiet(sK11) [choice axiom]
83. ~quiet(sK11) [skolemisation 24,82]
109. ~kind(X0) | ~humble(X0) | wise(X0) [cnf transformation 55]
125. ~strong(X0) | kind(X0) [cnf transformation 60]
130. humble(mary) | quiet(X0) [cnf transformation 70]
131. strong(mary) | quiet(X0) [cnf transformation 70]
149. ~quiet(sK11) [cnf transformation 83]
150. ~wise(mary) [cnf transformation 25]
278. 29 <=> ! [X0] : quiet(X0) [avatar definition]
279. quiet(X0) <- (29) [avatar component clause 278]
281. 30 <=> strong(mary) [avatar definition]
283. strong(mary) <- (30) [avatar component clause 281]
284. 29 | 30 [avatar split clause 131,281,278]
286. 31 <=> humble(mary) [avatar definition]
288. humble(mary) <- (31) [avatar component clause 286]
289. 29 | 31 [avatar split clause 130,286,278]
315. $false <- (29) [resolution 279,149]
316. ~29 [avatar contradiction clause 315]
328. kind(mary) <- (30) [resolution 125,283]
360. ~humble(mary) | wise(mary) <- (30) [resolution 109,328]
371. wise(mary) <- (30, 31) [subsumption resolution 360,288]
372. $false <- (30, 31) [subsumption resolution 371,150]
373. ~30 | ~31 [avatar contradiction clause 372]
374. $false [avatar sat refutation 284,289,316,373]
% SZS output end Proof for 4036827837930668671493112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either humble or not creative and vice versa. Everyone who is either not quiet or strong is both not calm and patient and vice versa. Everyone who is not wise or strong is not patient. Everyone who is funny is either creative or not old. Everyone who is not old or creative is either not humble or not brave. Everyone who is both happy and not calm is generous and vice versa. If mary is kind or patient then someone is not patient or not brave. If someone is either curious or not funny then mary is both not generous and not old. If someone is either creative or not generous then susan is either curious or not funny. If lucy is either calm or patient then someone is brave. Everyone who is either not funny or curious is generous or not rich and vice versa. If fred is not happy or not wise then someone is not quiet and vice versa. Everyone who is not strong is not quiet. If paul is both not curious and kind then fred is strong and vice versa. Everyone who is both brave and kind is both not generous and not old. If someone is both old and not wise then alice is either generous or not calm. Someone is not creative or strong. Someone is not funny. Someone is humble. John is not old. Paul is either patient or not generous. Fred is strong or not wise. Paul is both calm and rich. Paul is kind.
|
Lucy is not quiet.
|
entailment
|
(![X]:(~tall(X)<=>(humble(X)<~>~creative(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>(~calm(X)&patient(X))))&
(![X]:((~wise(X)|strong(X))=>~patient(X)))&
(![X]:(funny(X)=>(creative(X)<~>~old(X))))&
(![X]:((~old(X)|creative(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((happy(X)&~calm(X))<=>generous(X)))&
(((kind(mary)|patient(mary)))=>(?[X]:((~patient(X)|~brave(X)))))&
((?[X]:((curious(X)<~>~funny(X))))=>((~generous(mary)&~old(mary))))&
((?[X]:((creative(X)<~>~generous(X))))=>((curious(susan)<~>~funny(susan))))&
(((calm(lucy)<~>patient(lucy)))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
(((~happy(fred)|~wise(fred)))<=>(?[X]:(~quiet(X))))&
(![X]:(~strong(X)=>~quiet(X)))&
(((~curious(paul)&kind(paul)))<=>(strong(fred)))&
(![X]:((brave(X)&kind(X))=>(~generous(X)&~old(X))))&
((?[X]:((old(X)&~wise(X))))=>((generous(alice)<~>~calm(alice))))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:(humble(X)))&
(~old(john))&
((patient(paul)<~>~generous(paul)))&
((strong(fred)|~wise(fred)))&
((calm(paul)&rich(paul)))&
(kind(paul))
|
~quiet(lucy)
|
[
"p1",
"p2",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 6377148897967961403261637
% SZS output start Proof for 6377148897967961403261637
2. ! [X0] : ((~quiet(X0) <~> strong(X0)) <=> (patient(X0) & ~calm(X0))) [input p1]
3. ! [X0] : ((strong(X0) | ~wise(X0)) => ~patient(X0)) [input p2]
13. ! [X0] : (~strong(X0) => ~quiet(X0)) [input p12]
25. quiet(lucy) [input hypothesis]
26. ! [X0] : (~patient(X0) | (~strong(X0) & wise(X0))) [ennf transformation 3]
33. ! [X0] : (~quiet(X0) | strong(X0)) [ennf transformation 13]
37. ! [X0] : ((((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0))))) [flattening 37]
70. ~strong(X0) | ~quiet(X0) | patient(X0) [cnf transformation 38]
74. ~patient(X0) | ~strong(X0) [cnf transformation 26]
105. ~quiet(X0) | strong(X0) [cnf transformation 33]
123. quiet(lucy) [cnf transformation 25]
179. 13 <=> patient(lucy) [avatar definition]
180. patient(lucy) <- (13) [avatar component clause 179]
261. strong(lucy) [resolution 105,123]
273. ~quiet(lucy) | patient(lucy) [resolution 70,261]
277. patient(lucy) [subsumption resolution 273,123]
290. 13 [avatar split clause 277,179]
291. ~strong(lucy) <- (13) [resolution 180,74]
293. $false <- (13) [subsumption resolution 291,261]
294. ~13 [avatar contradiction clause 293]
295. $false [avatar sat refutation 290,294]
% SZS output end Proof for 6377148897967961403261637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is humble and vice versa. If someone is not rich or not humble then someone is humble or not kind and vice versa. Everyone who is both not strong and not brave is not tall and vice versa. Everyone who is wise or humble is patient or creative. Everyone who is quiet or not quiet is both not calm and not wise and vice versa. Everyone who is not tall is both not strong and creative and vice versa. If someone is happy or not brave then someone is strong or not wise and vice versa. If someone is wise or not happy then someone is both brave and not happy. If mary is either kind or not strong then mary is not funny or old. If fred is both not generous and creative then someone is either not wise or not kind. Everyone who is not patient or not creative is both not humble and humble and vice versa. Everyone who is either kind or humble is both not funny and generous. Everyone who is both creative and not old is either not wise or not patient. If someone is not tall then alice is both not wise and not happy. Everyone who is not curious is either not generous or not happy. Everyone who is not humble is either not creative or strong. Someone is both not generous and strong. Someone is not quiet. Someone is both happy and not curious. Someone is curious. Someone is both not brave and funny. Someone is not tall.
|
Fred is rich.
|
neutral
|
((?[X]:(creative(X)))<=>(?[X]:(humble(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~strong(X)&~brave(X))<=>~tall(X)))&
(![X]:((wise(X)|humble(X))=>(patient(X)|creative(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:(~tall(X)<=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((kind(mary)<~>~strong(mary)))=>((~funny(mary)|old(mary))))&
(((~generous(fred)&creative(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(~funny(X)&generous(X))))&
(![X]:((creative(X)&~old(X))=>(~wise(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>((~wise(alice)&~happy(alice))))&
(![X]:(~curious(X)=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>strong(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:(~tall(X)))
|
rich(fred)
|
[] | null | 0 |
Everyone who is either wise or quiet is either not curious or not kind and vice versa.
Everyone who is either curious or old is rich and vice versa.
If susan is either not funny or not patient then someone is not generous.
If paul is both not creative and wise then fred is not calm.
If someone is creative then fred is either generous or not creative and vice versa.
Everyone who is not old is both kind and patient.
Everyone who is old or curious is happy or not patient and vice versa.
If someone is either strong or tall then someone is not creative or old and vice versa.
Everyone who is not kind is calm or happy and vice versa.
If someone is either wise or funny then alice is both not strong and not humble.
If susan is not quiet or patient then someone is either not generous or not old.
Everyone who is both patient and creative is not calm and vice versa.
If paul is strong or quiet then john is either rich or tall and vice versa.
If someone is both kind and not kind then susan is either kind or generous.
Everyone who is both rich and not wise is creative.
Lucy is both not curious and not patient.
Someone is not rich or quiet.
Paul is both wise and not brave.
Someone is curious or humble.
Someone is not wise or not patient.
Someone is not tall.
Lucy is either rich or funny.
|
Paul is not wise.
|
contradiction
|
(![X]:((wise(X)<~>quiet(X))<=>(~curious(X)<~>~kind(X))))&
(![X]:((curious(X)<~>old(X))<=>rich(X)))&
(((~funny(susan)<~>~patient(susan)))=>(?[X]:(~generous(X))))&
(((~creative(paul)&wise(paul)))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>((generous(fred)<~>~creative(fred))))&
(![X]:(~old(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|curious(X))<=>(happy(X)|~patient(X))))&
((?[X]:((strong(X)<~>tall(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:(~kind(X)<=>(calm(X)|happy(X))))&
((?[X]:((wise(X)<~>funny(X))))=>((~strong(alice)&~humble(alice))))&
(((~quiet(susan)|patient(susan)))=>(?[X]:((~generous(X)<~>~old(X)))))&
(![X]:((patient(X)&creative(X))<=>~calm(X)))&
(((strong(paul)|quiet(paul)))<=>((rich(john)<~>tall(john))))&
((?[X]:((kind(X)&~kind(X))))=>((kind(susan)<~>generous(susan))))&
(![X]:((rich(X)&~wise(X))=>creative(X)))&
((~curious(lucy)&~patient(lucy)))&
(?[X]:((~rich(X)|quiet(X))))&
((wise(paul)&~brave(paul)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((~wise(X)|~patient(X))))&
(?[X]:(~tall(X)))&
((rich(lucy)<~>funny(lucy)))
|
~wise(paul)
|
[
"p17",
"hypothesis"
] |
% SZS status Unsatisfiable for 1101998864528605978629935
% SZS output start Proof for 1101998864528605978629935
18. ~brave(paul) & wise(paul) [input p17]
23. ~wise(paul) [input hypothesis]
25. wise(paul) [pure predicate removal 18]
128. wise(paul) [cnf transformation 25]
134. ~wise(paul) [cnf transformation 23]
154. 5 <=> wise(paul) [avatar definition]
280. 5 [avatar split clause 128,154]
309. ~5 [avatar split clause 134,154]
310. $false [avatar sat refutation 280,309]
% SZS output end Proof for 1101998864528605978629935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then alice is not calm or strong and vice versa.
Everyone who is both creative and not rich is creative and vice versa.
Everyone who is rich is not brave.
Everyone who is both old and not patient is both not humble and old and vice versa.
Everyone who is both generous and strong is either not patient or kind.
Everyone who is both humble and not humble is both not happy and not brave and vice versa.
Everyone who is generous or not humble is either patient or kind.
If someone is not humble then someone is not patient or not brave.
Everyone who is both generous and not strong is happy.
If john is strong or not happy then someone is not generous or humble and vice versa.
Everyone who is not calm is either not calm or not wise and vice versa.
If someone is either tall or wise then someone is funny and vice versa.
Everyone who is either quiet or old is kind or not old.
Everyone who is not funny or old is not kind and vice versa.
If someone is either calm or kind then someone is not strong or wise.
If john is curious or rich then someone is generous or brave.
Someone is both not calm and not patient.
Susan is both not creative and brave.
Alice is old.
Someone is rich.
Someone is either not humble or not tall.
Someone is both humble and patient.
Paul is not funny.
Someone is humble.
|
Alice is tall.
|
neutral
|
((?[X]:(generous(X)))<=>((~calm(alice)|strong(alice))))&
(![X]:((creative(X)&~rich(X))<=>creative(X)))&
(![X]:(rich(X)=>~brave(X)))&
(![X]:((old(X)&~patient(X))<=>(~humble(X)&old(X))))&
(![X]:((generous(X)&strong(X))=>(~patient(X)<~>kind(X))))&
(![X]:((humble(X)&~humble(X))<=>(~happy(X)&~brave(X))))&
(![X]:((generous(X)|~humble(X))=>(patient(X)<~>kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((generous(X)&~strong(X))=>happy(X)))&
(((strong(john)|~happy(john)))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:(~calm(X)<=>(~calm(X)<~>~wise(X))))&
((?[X]:((tall(X)<~>wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((quiet(X)<~>old(X))=>(kind(X)|~old(X))))&
(![X]:((~funny(X)|old(X))<=>~kind(X)))&
((?[X]:((calm(X)<~>kind(X))))=>(?[X]:((~strong(X)|wise(X)))))&
(((curious(john)|rich(john)))=>(?[X]:((generous(X)|brave(X)))))&
(?[X]:((~calm(X)&~patient(X))))&
((~creative(susan)&brave(susan)))&
(old(alice))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((humble(X)&patient(X))))&
(~funny(paul))&
(?[X]:(humble(X)))
|
tall(alice)
|
[] | null | 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa.
Everyone who is rich or strong is both not calm and calm and vice versa.
Everyone who is either patient or happy is either not curious or not humble.
If susan is both humble and quiet then mary is creative or kind and vice versa.
Everyone who is either brave or not brave is both not strong and generous.
Everyone who is both not old and not curious is not happy or curious and vice versa.
Everyone who is either happy or generous is either funny or not patient.
If someone is either not kind or brave then susan is either humble or creative.
Everyone who is both funny and not creative is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
Everyone who is not calm is old.
If alice is both not humble and funny then someone is not curious and vice versa.
Fred is brave or not humble.
Paul is not curious.
Paul is humble.
Someone is either calm or brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave.
|
Alice is not curious.
|
entailment
|
(![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(~calm(X)&calm(X))))&
(![X]:((patient(X)<~>happy(X))=>(~curious(X)<~>~humble(X))))&
(((humble(susan)&quiet(susan)))<=>((creative(mary)|kind(mary))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((brave(fred)|~humble(fred)))&
(~curious(paul))&
(humble(paul))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))
|
~curious(alice)
|
[
"p5",
"hypothesis"
] |
% SZS status Unsatisfiable for 664660542684522511928578
% SZS output start Proof for 664660542684522511928578
6. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p5]
24. curious(alice) [input hypothesis]
41. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 6]
42. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 41]
103. ~curious(X0) | ~curious(X0) [cnf transformation 42]
148. curious(alice) [cnf transformation 24]
150. ~curious(X0) [duplicate literal removal 103]
287. $false [subsumption resolution 148,150]
% SZS output end Proof for 664660542684522511928578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is curious and vice versa.
Everyone who is not curious or wise is both not creative and not calm.
If mary is either patient or not quiet then lucy is generous or not brave and vice versa.
Everyone who is either calm or quiet is not curious and vice versa.
Everyone who is not rich is old.
Everyone who is not quiet or not strong is both not patient and not curious and vice versa.
If lucy is either humble or not humble then lucy is either not wise or not rich.
If someone is not wise or not quiet then someone is not curious and vice versa.
If someone is wise or humble then lucy is either not kind or tall and vice versa.
Everyone who is both old and wise is either not strong or humble and vice versa.
Everyone who is not old or tall is both humble and not old.
If someone is either quiet or patient then susan is either not humble or tall.
Everyone who is happy is either not curious or creative.
Everyone who is either not kind or wise is not humble or not kind.
If alice is quiet then someone is both rich and not patient.
Someone is either not happy or not curious.
Someone is either not brave or wise.
Someone is not generous.
Mary is either not old or funny.
John is both not kind and patient.
Someone is not calm.
Paul is either not creative or creative.
Someone is either quiet or not quiet.
|
Mary is humble.
|
contradiction
|
(![X]:(humble(X)<=>curious(X)))&
(![X]:((~curious(X)|wise(X))=>(~creative(X)&~calm(X))))&
(((patient(mary)<~>~quiet(mary)))<=>((generous(lucy)|~brave(lucy))))&
(![X]:((calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((~quiet(X)|~strong(X))<=>(~patient(X)&~curious(X))))&
(((humble(lucy)<~>~humble(lucy)))=>((~wise(lucy)<~>~rich(lucy))))&
((?[X]:((~wise(X)|~quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((wise(X)|humble(X))))<=>((~kind(lucy)<~>tall(lucy))))&
(![X]:((old(X)&wise(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((~old(X)|tall(X))=>(humble(X)&~old(X))))&
((?[X]:((quiet(X)<~>patient(X))))=>((~humble(susan)<~>tall(susan))))&
(![X]:(happy(X)=>(~curious(X)<~>creative(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~humble(X)|~kind(X))))&
((quiet(alice))=>(?[X]:((rich(X)&~patient(X)))))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(~generous(X)))&
((~old(mary)<~>funny(mary)))&
((~kind(john)&patient(john)))&
(?[X]:(~calm(X)))&
((~creative(paul)<~>creative(paul)))&
(?[X]:((quiet(X)<~>~quiet(X))))
|
humble(mary)
|
[
"p0",
"p1",
"p3",
"p5",
"p9",
"hypothesis"
] |
% SZS status Unsatisfiable for 8523269374012617524708525
% SZS output start Proof for 8523269374012617524708525
1. ! [X0] : (humble(X0) <=> curious(X0)) [input p0]
2. ! [X0] : ((wise(X0) | ~curious(X0)) => (~calm(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> ~curious(X0)) [input p3]
6. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> (~curious(X0) & ~patient(X0))) [input p5]
10. ! [X0] : ((wise(X0) & old(X0)) <=> (~strong(X0) <~> humble(X0))) [input p9]
24. humble(mary) [input hypothesis]
26. ! [X0] : ((~calm(X0) & ~creative(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 2]
35. ! [X0] : ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))) [nnf transformation 1]
38. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) | ~quiet(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [nnf transformation 6]
40. ! [X0] : ((~strong(X0) | ~quiet(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (strong(X0) & quiet(X0)))) [flattening 39]
51. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~wise(X0) | ~old(X0)))) [nnf transformation 10]
52. ! [X0] : (((wise(X0) & old(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~wise(X0) | ~old(X0))) [flattening 51]
73. ~humble(X0) | curious(X0) [cnf transformation 35]
77. ~calm(X0) | curious(X0) [cnf transformation 26]
78. ~calm(X0) | ~wise(X0) [cnf transformation 26]
86. ~quiet(X0) | calm(X0) | ~curious(X0) [cnf transformation 38]
87. quiet(X0) | calm(X0) | curious(X0) [cnf transformation 38]
92. ~curious(X0) | quiet(X0) [cnf transformation 40]
93. ~curious(X0) | strong(X0) [cnf transformation 40]
113. ~strong(X0) | wise(X0) | ~humble(X0) [cnf transformation 52]
142. humble(mary) [cnf transformation 24]
170. quiet(X0) | curious(X0) [subsumption resolution 87,77]
173. quiet(X0) [subsumption resolution 92,170]
282. curious(mary) [resolution 73,142]
287. strong(mary) [resolution 93,282]
290. ~curious(X1) | calm(X1) [resolution 86,173]
291. calm(mary) [resolution 290,282]
293. ~wise(mary) [resolution 291,78]
324. wise(mary) | ~humble(mary) [resolution 287,113]
326. ~humble(mary) [subsumption resolution 324,293]
327. $false [subsumption resolution 326,142]
% SZS output end Proof for 8523269374012617524708525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and creative is creative or not patient and vice versa.
If someone is not happy or brave then someone is both wise and not tall and vice versa.
If someone is patient or not curious then someone is either curious or strong.
Everyone who is humble or wise is either tall or not rich.
Everyone who is either humble or not humble is either not funny or calm.
Everyone who is both old and not tall is not strong or calm and vice versa.
Everyone who is not calm is not funny and vice versa.
If susan is tall or not calm then someone is strong or not strong.
Everyone who is either not funny or patient is both not curious and strong.
If someone is not brave or not creative then mary is either not kind or generous.
Everyone who is both kind and funny is not brave or creative and vice versa.
Everyone who is not tall or not happy is funny or creative.
If someone is not strong then someone is either strong or not calm and vice versa.
If fred is both kind and calm then susan is funny and vice versa.
Everyone who is either not curious or generous is not calm.
If mary is old or not rich then someone is either not wise or humble and vice versa.
Someone is kind.
Alice is either wise or not old.
Fred is both wise and funny.
Lucy is either old or calm.
Someone is both not generous and not quiet.
Paul is both generous and wise.
Someone is either brave or funny.
Paul is both humble and not rich.
|
Lucy is old.
|
entailment
|
(![X]:((~patient(X)&creative(X))<=>(creative(X)|~patient(X))))&
((?[X]:((~happy(X)|brave(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:((curious(X)<~>strong(X)))))&
(![X]:((humble(X)|wise(X))=>(tall(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~humble(X))=>(~funny(X)<~>calm(X))))&
(![X]:((old(X)&~tall(X))<=>(~strong(X)|calm(X))))&
(![X]:(~calm(X)<=>~funny(X)))&
(((tall(susan)|~calm(susan)))=>(?[X]:((strong(X)|~strong(X)))))&
(![X]:((~funny(X)<~>patient(X))=>(~curious(X)&strong(X))))&
((?[X]:((~brave(X)|~creative(X))))=>((~kind(mary)<~>generous(mary))))&
(![X]:((kind(X)&funny(X))<=>(~brave(X)|creative(X))))&
(![X]:((~tall(X)|~happy(X))=>(funny(X)|creative(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(((kind(fred)&calm(fred)))<=>(funny(susan)))&
(![X]:((~curious(X)<~>generous(X))=>~calm(X)))&
(((old(mary)|~rich(mary)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(?[X]:(kind(X)))&
((wise(alice)<~>~old(alice)))&
((wise(fred)&funny(fred)))&
((old(lucy)<~>calm(lucy)))&
(?[X]:((~generous(X)&~quiet(X))))&
((generous(paul)&wise(paul)))&
(?[X]:((brave(X)<~>funny(X))))&
((humble(paul)&~rich(paul)))
|
old(lucy)
|
[
"p5",
"p19",
"hypothesis"
] |
% SZS status Unsatisfiable for 1672446046788076493614300
% SZS output start Proof for 1672446046788076493614300
6. ! [X0] : ((~tall(X0) & old(X0)) <=> (calm(X0) | ~strong(X0))) [input p5]
20. old(lucy) <~> calm(lucy) [input p19]
25. ~old(lucy) [input hypothesis]
52. ! [X0] : (((~tall(X0) & old(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (tall(X0) | ~old(X0)))) [nnf transformation 6]
53. ! [X0] : (((~tall(X0) & old(X0)) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | tall(X0) | ~old(X0))) [flattening 52]
77. (~calm(lucy) | ~old(lucy)) & (calm(lucy) | old(lucy)) [nnf transformation 20]
107. old(X0) | ~calm(X0) [cnf transformation 53]
149. calm(lucy) | old(lucy) [cnf transformation 77]
150. ~calm(lucy) | ~old(lucy) [cnf transformation 77]
158. ~old(lucy) [cnf transformation 25]
311. ~calm(lucy) [subsumption resolution 150,107]
312. old(lucy) [subsumption resolution 149,311]
322. $false [subsumption resolution 158,312]
% SZS output end Proof for 1672446046788076493614300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not calm then paul is not tall and vice versa.
If someone is either not quiet or not generous then someone is both quiet and not old and vice versa.
Everyone who is either not tall or not quiet is tall and vice versa.
Everyone who is patient or tall is not happy and vice versa.
Everyone who is not tall is quiet and vice versa.
Everyone who is not generous or calm is either not patient or happy and vice versa.
Everyone who is both not brave and not tall is quiet or not creative and vice versa.
Everyone who is tall is both not funny and not generous.
If lucy is both not wise and not quiet then susan is not curious and vice versa.
If paul is not rich or curious then someone is both not calm and not curious.
Everyone who is brave or not curious is not wise or not brave.
If paul is both rich and not calm then lucy is not rich or not tall and vice versa.
If someone is both not strong and rich then john is both funny and happy.
Everyone who is both brave and not wise is not old.
Mary is tall.
Susan is not curious or calm.
Lucy is either not brave or not happy.
Someone is either kind or not old.
Someone is either not old or wise.
Someone is both not kind and calm.
Susan is both not quiet and not strong.
Susan is not old or not funny.
|
Paul is rich.
|
entailment
|
((?[X]:((generous(X)|~calm(X))))<=>(~tall(paul)))&
((?[X]:((~quiet(X)<~>~generous(X))))<=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>tall(X)))&
(![X]:((patient(X)|tall(X))<=>~happy(X)))&
(![X]:(~tall(X)<=>quiet(X)))&
(![X]:((~generous(X)|calm(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~brave(X)&~tall(X))<=>(quiet(X)|~creative(X))))&
(![X]:(tall(X)=>(~funny(X)&~generous(X))))&
(((~wise(lucy)&~quiet(lucy)))<=>(~curious(susan)))&
(((~rich(paul)|curious(paul)))=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((brave(X)|~curious(X))=>(~wise(X)|~brave(X))))&
(((rich(paul)&~calm(paul)))<=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((~strong(X)&rich(X))))=>((funny(john)&happy(john))))&
(![X]:((brave(X)&~wise(X))=>~old(X)))&
(tall(mary))&
((~curious(susan)|calm(susan)))&
((~brave(lucy)<~>~happy(lucy)))&
(?[X]:((kind(X)<~>~old(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((~kind(X)&calm(X))))&
((~quiet(susan)&~strong(susan)))&
((~old(susan)|~funny(susan)))
|
rich(paul)
|
[
"p0",
"p2",
"p4",
"p9",
"hypothesis"
] |
% SZS status Unsatisfiable for 3054926416067635609124610
% SZS output start Proof for 3054926416067635609124610
1. ? [X0] : (~calm(X0) | generous(X0)) <=> ~tall(paul) [input p0]
3. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> tall(X0)) [input p2]
5. ! [X0] : (~tall(X0) <=> quiet(X0)) [input p4]
10. (curious(paul) | ~rich(paul)) => ? [X0] : (~curious(X0) & ~calm(X0)) [input p9]
23. ~rich(paul) [input hypothesis]
26. ? [X0] : (~curious(X0) & ~calm(X0)) | (~curious(paul) & rich(paul)) [ennf transformation 10]
32. (? [X0] : (~calm(X0) | generous(X0)) | tall(paul)) & (~tall(paul) | ! [X0] : (calm(X0) & ~generous(X0))) [nnf transformation 1]
33. (? [X0] : (~calm(X0) | generous(X0)) | tall(paul)) & (~tall(paul) | ! [X1] : (calm(X1) & ~generous(X1))) [rectify 32]
34. ? [X0] : (~calm(X0) | generous(X0)) => (~calm(sK0) | generous(sK0)) [choice axiom]
35. ((~calm(sK0) | generous(sK0)) | tall(paul)) & (~tall(paul) | ! [X1] : (calm(X1) & ~generous(X1))) [skolemisation 33,34]
41. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~tall(X0)) & (tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 3]
44. ! [X0] : ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))) [nnf transformation 5]
51. ? [X0] : (~curious(X0) & ~calm(X0)) => (~curious(sK3) & ~calm(sK3)) [choice axiom]
52. (~curious(sK3) & ~calm(sK3)) | (~curious(paul) & rich(paul)) [skolemisation 26,51]
65. ~tall(paul) | calm(X1) [cnf transformation 35]
73. tall(X0) | ~quiet(X0) | tall(X0) [cnf transformation 41]
75. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 41]
80. quiet(X0) | tall(X0) [cnf transformation 44]
98. ~calm(sK3) | rich(paul) [cnf transformation 52]
125. ~rich(paul) [cnf transformation 23]
127. tall(X0) | ~quiet(X0) [duplicate literal removal 73]
128. ~quiet(X0) | ~tall(X0) [duplicate literal removal 75]
130. 1 <=> tall(paul) [avatar definition]
131. ~tall(paul) <- (~1) [avatar component clause 130]
143. 4 <=> ! [X1] : calm(X1) [avatar definition]
144. calm(X1) <- (4) [avatar component clause 143]
145. 4 | ~1 [avatar split clause 65,130,143]
181. ~quiet(X0) [subsumption resolution 127,128]
182. tall(X0) [subsumption resolution 80,181]
212. 17 <=> rich(paul) [avatar definition]
217. 18 <=> calm(sK3) [avatar definition]
219. ~calm(sK3) <- (~18) [avatar component clause 217]
221. 17 | ~18 [avatar split clause 98,217,212]
280. ~17 [avatar split clause 125,212]
283. $false <- (~1) [subsumption resolution 131,182]
284. 1 [avatar contradiction clause 283]
287. $false <- (4, ~18) [resolution 219,144]
288. ~4 | 18 [avatar contradiction clause 287]
289. $false [avatar sat refutation 145,221,280,284,288]
% SZS output end Proof for 3054926416067635609124610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either tall or not generous then someone is either not humble or not old and vice versa.
If fred is both brave and rich then alice is quiet.
Everyone who is both happy and calm is either happy or quiet.
If someone is not wise then john is not funny or quiet.
If paul is both not patient and wise then mary is either strong or brave.
Everyone who is not wise is not curious and vice versa.
Everyone who is not curious or quiet is both not rich and curious and vice versa.
Everyone who is both not generous and not humble is creative or not happy.
Everyone who is both brave and not wise is both calm and not calm and vice versa.
If someone is not curious or not tall then someone is humble or quiet.
If someone is patient then someone is both not brave and not quiet and vice versa.
If someone is not calm then fred is both quiet and not creative.
Everyone who is either not old or not kind is both not quiet and old.
Everyone who is both not curious and not quiet is both not curious and not strong and vice versa.
If susan is either not old or not happy then lucy is both patient and strong.
If someone is both rich and brave then someone is either not generous or not calm and vice versa.
Someone is strong or brave.
Mary is not creative or not generous.
Someone is not brave or tall.
Someone is kind or not brave.
Paul is either humble or not brave.
Someone is not funny or generous.
John is not brave.
|
Susan is humble.
|
neutral
|
(((tall(john)<~>~generous(john)))<=>(?[X]:((~humble(X)<~>~old(X)))))&
(((brave(fred)&rich(fred)))=>(quiet(alice)))&
(![X]:((happy(X)&calm(X))=>(happy(X)<~>quiet(X))))&
((?[X]:(~wise(X)))=>((~funny(john)|quiet(john))))&
(((~patient(paul)&wise(paul)))=>((strong(mary)<~>brave(mary))))&
(![X]:(~wise(X)<=>~curious(X)))&
(![X]:((~curious(X)|quiet(X))<=>(~rich(X)&curious(X))))&
(![X]:((~generous(X)&~humble(X))=>(creative(X)|~happy(X))))&
(![X]:((brave(X)&~wise(X))<=>(calm(X)&~calm(X))))&
((?[X]:((~curious(X)|~tall(X))))=>(?[X]:((humble(X)|quiet(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:(~calm(X)))=>((quiet(fred)&~creative(fred))))&
(![X]:((~old(X)<~>~kind(X))=>(~quiet(X)&old(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~curious(X)&~strong(X))))&
(((~old(susan)<~>~happy(susan)))=>((patient(lucy)&strong(lucy))))&
((?[X]:((rich(X)&brave(X))))<=>(?[X]:((~generous(X)<~>~calm(X)))))&
(?[X]:((strong(X)|brave(X))))&
((~creative(mary)|~generous(mary)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((kind(X)|~brave(X))))&
((humble(paul)<~>~brave(paul)))&
(?[X]:((~funny(X)|generous(X))))&
(~brave(john))
|
humble(susan)
|
[] | null | 0 |
If someone is either not generous or funny then mary is not creative or tall. If someone is either quiet or not rich then someone is both curious and old. If someone is either strong or quiet then paul is both kind and not calm and vice versa. If someone is not old or not tall then someone is not happy and vice versa. If lucy is not wise or not humble then paul is happy. If fred is not calm or wise then someone is brave or wise. Everyone who is either rich or kind is either happy or funny. If mary is both curious and calm then someone is not humble or patient. Everyone who is not funny or not old is both not tall and tall and vice versa. Everyone who is not calm or brave is not curious. If lucy is not strong then someone is either not funny or not kind. If fred is either wise or generous then mary is both not kind and not generous and vice versa. If someone is both rich and strong then mary is either curious or quiet. Everyone who is rich or tall is both not quiet and calm and vice versa. Everyone who is both calm and strong is humble or not humble and vice versa. Everyone who is either not curious or not rich is either not generous or humble and vice versa. Susan is not brave or creative. Someone is calm. Mary is both not curious and not rich. Someone is both not curious and funny. Someone is not old or not kind. Someone is not generous.
|
Paul is funny.
|
entailment
|
((?[X]:((~generous(X)<~>funny(X))))=>((~creative(mary)|tall(mary))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(?[X]:((curious(X)&old(X)))))&
((?[X]:((strong(X)<~>quiet(X))))<=>((kind(paul)&~calm(paul))))&
((?[X]:((~old(X)|~tall(X))))<=>(?[X]:(~happy(X))))&
(((~wise(lucy)|~humble(lucy)))=>(happy(paul)))&
(((~calm(fred)|wise(fred)))=>(?[X]:((brave(X)|wise(X)))))&
(![X]:((rich(X)<~>kind(X))=>(happy(X)<~>funny(X))))&
(((curious(mary)&calm(mary)))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((~funny(X)|~old(X))<=>(~tall(X)&tall(X))))&
(![X]:((~calm(X)|brave(X))=>~curious(X)))&
((~strong(lucy))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(((wise(fred)<~>generous(fred)))<=>((~kind(mary)&~generous(mary))))&
((?[X]:((rich(X)&strong(X))))=>((curious(mary)<~>quiet(mary))))&
(![X]:((rich(X)|tall(X))<=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&strong(X))<=>(humble(X)|~humble(X))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~generous(X)<~>humble(X))))&
((~brave(susan)|creative(susan)))&
(?[X]:(calm(X)))&
((~curious(mary)&~rich(mary)))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:(~generous(X)))
|
funny(paul)
|
[
"p8",
"hypothesis"
] |
% SZS status Unsatisfiable for 8555758058602564986653839
% SZS output start Proof for 8555758058602564986653839
9. ! [X0] : ((~old(X0) | ~funny(X0)) <=> (tall(X0) & ~tall(X0))) [input p8]
23. ~funny(paul) [input hypothesis]
54. ! [X0] : (((~old(X0) | ~funny(X0)) | (~tall(X0) | tall(X0))) & ((tall(X0) & ~tall(X0)) | (old(X0) & funny(X0)))) [nnf transformation 9]
55. ! [X0] : ((~old(X0) | ~funny(X0) | ~tall(X0) | tall(X0)) & ((tall(X0) & ~tall(X0)) | (old(X0) & funny(X0)))) [flattening 54]
98. ~tall(X0) | funny(X0) [cnf transformation 55]
100. tall(X0) | funny(X0) [cnf transformation 55]
141. ~funny(paul) [cnf transformation 23]
262. funny(X0) [subsumption resolution 98,100]
326. $false [subsumption resolution 141,262]
% SZS output end Proof for 8555758058602564986653839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious or not funny is not calm or happy.
Everyone who is not quiet or not humble is not brave or old and vice versa.
If someone is both humble and old then john is tall and vice versa.
Everyone who is not humble is not happy.
Everyone who is either not wise or not brave is both tall and not tall and vice versa.
Everyone who is funny is not humble or not old and vice versa.
If someone is humble or not old then john is either brave or calm.
Everyone who is both quiet and calm is either funny or not old.
Everyone who is either brave or not tall is both not tall and brave and vice versa.
Everyone who is both patient and creative is brave or not brave.
Everyone who is tall or strong is calm or patient and vice versa.
Everyone who is not creative is generous or humble and vice versa.
Everyone who is not curious or happy is either quiet or kind and vice versa.
If fred is either generous or not tall then john is either wise or funny.
Everyone who is either humble or creative is not quiet.
Everyone who is quiet is not creative or not generous.
Alice is both creative and not patient.
Someone is old.
Paul is either wise or calm.
Alice is not quiet.
Someone is both tall and humble.
Lucy is both strong and not calm.
Someone is patient or not humble.
|
Lucy is not brave.
|
entailment
|
(![X]:((~curious(X)|~funny(X))=>(~calm(X)|happy(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~brave(X)|old(X))))&
((?[X]:((humble(X)&old(X))))<=>(tall(john)))&
(![X]:(~humble(X)=>~happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(tall(X)&~tall(X))))&
(![X]:(funny(X)<=>(~humble(X)|~old(X))))&
((?[X]:((humble(X)|~old(X))))=>((brave(john)<~>calm(john))))&
(![X]:((quiet(X)&calm(X))=>(funny(X)<~>~old(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~tall(X)&brave(X))))&
(![X]:((patient(X)&creative(X))=>(brave(X)|~brave(X))))&
(![X]:((tall(X)|strong(X))<=>(calm(X)|patient(X))))&
(![X]:(~creative(X)<=>(generous(X)|humble(X))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)<~>kind(X))))&
(((generous(fred)<~>~tall(fred)))=>((wise(john)<~>funny(john))))&
(![X]:((humble(X)<~>creative(X))=>~quiet(X)))&
(![X]:(quiet(X)=>(~creative(X)|~generous(X))))&
((creative(alice)&~patient(alice)))&
(?[X]:(old(X)))&
((wise(paul)<~>calm(paul)))&
(~quiet(alice))&
(?[X]:((tall(X)&humble(X))))&
((strong(lucy)&~calm(lucy)))&
(?[X]:((patient(X)|~humble(X))))
|
~brave(lucy)
|
[
"p8",
"hypothesis"
] |
% SZS status Unsatisfiable for 638948523792716800818302
% SZS output start Proof for 638948523792716800818302
9. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (brave(X0) & ~tall(X0))) [input p8]
24. brave(lucy) [input hypothesis]
49. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 9]
50. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [flattening 49]
91. ~tall(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 50]
94. brave(X0) | brave(X0) | tall(X0) [cnf transformation 50]
96. tall(X0) | ~brave(X0) | ~brave(X0) | tall(X0) [cnf transformation 50]
129. brave(lucy) [cnf transformation 24]
130. ~tall(X0) | ~brave(X0) [duplicate literal removal 91]
131. brave(X0) | tall(X0) [duplicate literal removal 94]
132. tall(X0) | ~brave(X0) [duplicate literal removal 96]
173. tall(X0) [subsumption resolution 131,132]
174. ~brave(X0) [subsumption resolution 130,173]
213. $false [subsumption resolution 129,174]
% SZS output end Proof for 638948523792716800818302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious or wise then someone is not funny or happy.
If alice is rich or creative then someone is rich or not curious and vice versa.
If alice is both not calm and not quiet then lucy is not patient and vice versa.
Everyone who is wise is not quiet and vice versa.
If lucy is creative or not kind then alice is both not kind and tall.
Everyone who is both generous and kind is old or not wise and vice versa.
Everyone who is both happy and not patient is funny or curious.
Everyone who is both curious and not kind is kind or quiet and vice versa.
Everyone who is either curious or not wise is both not patient and happy.
If someone is either strong or not funny then fred is brave and vice versa.
If susan is either creative or not kind then someone is not rich.
Everyone who is humble is both not kind and creative.
If someone is both tall and patient then someone is not kind.
If someone is not curious then someone is either kind or not happy.
Everyone who is both brave and funny is happy or not patient and vice versa.
Everyone who is either not creative or quiet is both not funny and patient.
Paul is not generous or patient.
Susan is either not tall or strong.
Fred is not curious or old.
Mary is either not old or tall.
Someone is either not happy or brave.
Susan is not funny.
Someone is either kind or generous.
|
Paul is not curious.
|
entailment
|
(((~curious(lucy)|wise(lucy)))=>(?[X]:((~funny(X)|happy(X)))))&
(((rich(alice)|creative(alice)))<=>(?[X]:((rich(X)|~curious(X)))))&
(((~calm(alice)&~quiet(alice)))<=>(~patient(lucy)))&
(![X]:(wise(X)<=>~quiet(X)))&
(((creative(lucy)|~kind(lucy)))=>((~kind(alice)&tall(alice))))&
(![X]:((generous(X)&kind(X))<=>(old(X)|~wise(X))))&
(![X]:((happy(X)&~patient(X))=>(funny(X)|curious(X))))&
(![X]:((curious(X)&~kind(X))<=>(kind(X)|quiet(X))))&
(![X]:((curious(X)<~>~wise(X))=>(~patient(X)&happy(X))))&
((?[X]:((strong(X)<~>~funny(X))))<=>(brave(fred)))&
(((creative(susan)<~>~kind(susan)))=>(?[X]:(~rich(X))))&
(![X]:(humble(X)=>(~kind(X)&creative(X))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((brave(X)&funny(X))<=>(happy(X)|~patient(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(~funny(X)&patient(X))))&
((~generous(paul)|patient(paul)))&
((~tall(susan)<~>strong(susan)))&
((~curious(fred)|old(fred)))&
((~old(mary)<~>tall(mary)))&
(?[X]:((~happy(X)<~>brave(X))))&
(~funny(susan))&
(?[X]:((kind(X)<~>generous(X))))
|
~curious(paul)
|
[
"p3",
"p5",
"p7",
"hypothesis"
] |
% SZS status Unsatisfiable for 5073178571978244934604720
% SZS output start Proof for 5073178571978244934604720
4. ! [X0] : (wise(X0) <=> ~quiet(X0)) [input p3]
6. ! [X0] : ((kind(X0) & generous(X0)) <=> (~wise(X0) | old(X0))) [input p5]
8. ! [X0] : ((~kind(X0) & curious(X0)) <=> (quiet(X0) | kind(X0))) [input p7]
24. curious(paul) [input hypothesis]
46. ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0))) [nnf transformation 4]
47. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | (~kind(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((kind(X0) & generous(X0)) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | ~kind(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & ((quiet(X0) | kind(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 8]
50. ! [X0] : (((~kind(X0) & curious(X0)) | (~quiet(X0) & ~kind(X0))) & (quiet(X0) | kind(X0) | kind(X0) | ~curious(X0))) [flattening 49]
86. ~quiet(X0) | ~wise(X0) [cnf transformation 46]
96. kind(X0) | wise(X0) [cnf transformation 48]
98. quiet(X0) | kind(X0) | kind(X0) | ~curious(X0) [cnf transformation 50]
101. ~kind(X0) | ~kind(X0) [cnf transformation 50]
136. curious(paul) [cnf transformation 24]
137. quiet(X0) | kind(X0) | ~curious(X0) [duplicate literal removal 98]
138. ~kind(X0) [duplicate literal removal 101]
218. ~curious(X0) | quiet(X0) [subsumption resolution 137,138]
310. wise(X0) [resolution 96,138]
315. quiet(paul) [resolution 218,136]
317. ~wise(paul) [resolution 315,86]
320. $false [subsumption resolution 317,310]
% SZS output end Proof for 5073178571978244934604720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then lucy is old or not humble and vice versa.
If john is either quiet or curious then mary is both not funny and generous.
Everyone who is either not tall or old is happy.
If someone is either brave or curious then paul is either curious or generous and vice versa.
If someone is both creative and old then lucy is not kind.
Everyone who is not curious is both not funny and quiet.
Everyone who is quiet or tall is both brave and creative.
If someone is either happy or not calm then someone is brave or not creative.
If someone is not happy or not calm then someone is both brave and strong and vice versa.
If mary is not wise or not calm then someone is either not wise or old.
Everyone who is either generous or strong is both not patient and not quiet.
If someone is either funny or quiet then someone is both tall and not creative and vice versa.
Everyone who is both kind and curious is both not curious and not creative.
If someone is either curious or old then someone is either old or humble.
Everyone who is happy is either not curious or not kind.
If susan is either not curious or creative then mary is not creative.
Paul is not happy or not generous.
Mary is both strong and funny.
Someone is both not old and strong.
Someone is old or not quiet.
Lucy is tall.
Susan is not curious or not quiet.
Someone is not humble or quiet.
Someone is wise or patient.
|
Lucy is curious.
|
entailment
|
((?[X]:(~calm(X)))<=>((old(lucy)|~humble(lucy))))&
(((quiet(john)<~>curious(john)))=>((~funny(mary)&generous(mary))))&
(![X]:((~tall(X)<~>old(X))=>happy(X)))&
((?[X]:((brave(X)<~>curious(X))))<=>((curious(paul)<~>generous(paul))))&
((?[X]:((creative(X)&old(X))))=>(~kind(lucy)))&
(![X]:(~curious(X)=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)|tall(X))=>(brave(X)&creative(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((brave(X)|~creative(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>(?[X]:((brave(X)&strong(X)))))&
(((~wise(mary)|~calm(mary)))=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:((generous(X)<~>strong(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((funny(X)<~>quiet(X))))<=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((kind(X)&curious(X))=>(~curious(X)&~creative(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:(happy(X)=>(~curious(X)<~>~kind(X))))&
(((~curious(susan)<~>creative(susan)))=>(~creative(mary)))&
((~happy(paul)|~generous(paul)))&
((strong(mary)&funny(mary)))&
(?[X]:((~old(X)&strong(X))))&
(?[X]:((old(X)|~quiet(X))))&
(tall(lucy))&
((~curious(susan)|~quiet(susan)))&
(?[X]:((~humble(X)|quiet(X))))&
(?[X]:((wise(X)|patient(X))))
|
curious(lucy)
|
[
"p5",
"p6",
"p11",
"hypothesis"
] |
% SZS status Unsatisfiable for 2469696646934460175429576
% SZS output start Proof for 2469696646934460175429576
6. ! [X0] : (~curious(X0) => (quiet(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((tall(X0) | quiet(X0)) => (creative(X0) & brave(X0))) [input p6]
12. ? [X0] : (funny(X0) <~> quiet(X0)) <=> ? [X0] : (~creative(X0) & tall(X0)) [input p11]
25. ~curious(lucy) [input hypothesis]
28. ? [X0] : (funny(X0) <~> quiet(X0)) <=> ? [X1] : (~creative(X1) & tall(X1)) [rectify 12]
33. ! [X0] : ((quiet(X0) & ~funny(X0)) | curious(X0)) [ennf transformation 6]
34. ! [X0] : ((creative(X0) & brave(X0)) | (~tall(X0) & ~quiet(X0))) [ennf transformation 7]
67. (? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X1] : (~creative(X1) & tall(X1)) | ! [X0] : ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) [nnf transformation 28]
68. (? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | ! [X1] : (creative(X1) | ~tall(X1))) & (? [X2] : (~creative(X2) & tall(X2)) | ! [X3] : ((funny(X3) | ~quiet(X3)) & (quiet(X3) | ~funny(X3)))) [rectify 67]
69. ? [X0] : ((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) => ((~quiet(sK6) | ~funny(sK6)) & (quiet(sK6) | funny(sK6))) [choice axiom]
70. ? [X2] : (~creative(X2) & tall(X2)) => (~creative(sK7) & tall(sK7)) [choice axiom]
71. (((~quiet(sK6) | ~funny(sK6)) & (quiet(sK6) | funny(sK6))) | ! [X1] : (creative(X1) | ~tall(X1))) & ((~creative(sK7) & tall(sK7)) | ! [X3] : ((funny(X3) | ~quiet(X3)) & (quiet(X3) | ~funny(X3)))) [skolemisation 68,70,69]
104. ~funny(X0) | curious(X0) [cnf transformation 33]
105. curious(X0) | quiet(X0) [cnf transformation 33]
109. ~tall(X0) | creative(X0) [cnf transformation 34]
126. tall(sK7) | funny(X3) | ~quiet(X3) [cnf transformation 71]
128. ~creative(sK7) | funny(X3) | ~quiet(X3) [cnf transformation 71]
151. ~curious(lucy) [cnf transformation 25]
293. 31 <=> ! [X3] : (funny(X3) | ~quiet(X3)) [avatar definition]
294. ~quiet(X3) | funny(X3) <- (31) [avatar component clause 293]
296. 32 <=> creative(sK7) [avatar definition]
298. ~creative(sK7) <- (~32) [avatar component clause 296]
299. 31 | ~32 [avatar split clause 128,296,293]
305. 34 <=> tall(sK7) [avatar definition]
307. tall(sK7) <- (34) [avatar component clause 305]
308. 31 | 34 [avatar split clause 126,305,293]
389. quiet(lucy) [resolution 105,151]
410. funny(lucy) <- (31) [resolution 294,389]
422. creative(sK7) <- (34) [resolution 307,109]
424. $false <- (~32, 34) [subsumption resolution 422,298]
425. 32 | ~34 [avatar contradiction clause 424]
499. curious(lucy) <- (31) [resolution 410,104]
500. $false <- (31) [subsumption resolution 499,151]
501. ~31 [avatar contradiction clause 500]
502. $false [avatar sat refutation 299,308,425,501]
% SZS output end Proof for 2469696646934460175429576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either brave or not rich and vice versa.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is not humble or not strong.
|
Paul is not humble.
|
neutral
|
(![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~humble(X)|~strong(X))))
|
~humble(paul)
|
[] | null | 0 |
Everyone who is strong or generous is either not happy or tall and vice versa.
Everyone who is either strong or patient is brave or humble.
Everyone who is either curious or funny is either funny or not old and vice versa.
Everyone who is either rich or curious is not creative or not kind.
If someone is not calm then paul is either not humble or not generous and vice versa.
Everyone who is both not humble and not rich is not wise.
Everyone who is not calm or curious is happy and vice versa.
If mary is both wise and not brave then mary is both rich and old and vice versa.
Everyone who is strong is either quiet or not old and vice versa.
Everyone who is not creative or generous is quiet.
If alice is tall then alice is both kind and not happy and vice versa.
Everyone who is not happy or not humble is either old or kind and vice versa.
Everyone who is either generous or tall is either not tall or calm and vice versa.
If susan is both quiet and not happy then mary is both brave and kind.
If fred is not strong then susan is either not rich or strong.
Everyone who is either wise or not rich is either not brave or happy and vice versa.
Someone is quiet.
Someone is not patient or not tall.
Mary is both not quiet and not rich.
Someone is either generous or not old.
Someone is tall or not creative.
Someone is either happy or wise.
Someone is either brave or old.
Paul is either happy or wise.
|
Alice is not generous.
|
entailment
|
(![X]:((strong(X)|generous(X))<=>(~happy(X)<~>tall(X))))&
(![X]:((strong(X)<~>patient(X))=>(brave(X)|humble(X))))&
(![X]:((curious(X)<~>funny(X))<=>(funny(X)<~>~old(X))))&
(![X]:((rich(X)<~>curious(X))=>(~creative(X)|~kind(X))))&
((?[X]:(~calm(X)))<=>((~humble(paul)<~>~generous(paul))))&
(![X]:((~humble(X)&~rich(X))=>~wise(X)))&
(![X]:((~calm(X)|curious(X))<=>happy(X)))&
(((wise(mary)&~brave(mary)))<=>((rich(mary)&old(mary))))&
(![X]:(strong(X)<=>(quiet(X)<~>~old(X))))&
(![X]:((~creative(X)|generous(X))=>quiet(X)))&
((tall(alice))<=>((kind(alice)&~happy(alice))))&
(![X]:((~happy(X)|~humble(X))<=>(old(X)<~>kind(X))))&
(![X]:((generous(X)<~>tall(X))<=>(~tall(X)<~>calm(X))))&
(((quiet(susan)&~happy(susan)))=>((brave(mary)&kind(mary))))&
((~strong(fred))=>((~rich(susan)<~>strong(susan))))&
(![X]:((wise(X)<~>~rich(X))<=>(~brave(X)<~>happy(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~patient(X)|~tall(X))))&
((~quiet(mary)&~rich(mary)))&
(?[X]:((generous(X)<~>~old(X))))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:((brave(X)<~>old(X))))&
((happy(paul)<~>wise(paul)))
|
~generous(alice)
|
[
"p0",
"p6",
"p10",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 5376523880137122396170886
% SZS output start Proof for 5376523880137122396170886
1. ! [X0] : ((generous(X0) | strong(X0)) <=> (~happy(X0) <~> tall(X0))) [input p0]
7. ! [X0] : ((curious(X0) | ~calm(X0)) <=> happy(X0)) [input p6]
11. tall(alice) <=> (~happy(alice) & kind(alice)) [input p10]
13. ! [X0] : ((generous(X0) <~> tall(X0)) <=> (~tall(X0) <~> calm(X0))) [input p12]
25. generous(alice) [input hypothesis]
36. ! [X0] : (((generous(X0) | strong(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~generous(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((generous(X0) | strong(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (~generous(X0) & ~strong(X0)))) [flattening 36]
45. ! [X0] : (((curious(X0) | ~calm(X0)) | ~happy(X0)) & (happy(X0) | (~curious(X0) & calm(X0)))) [nnf transformation 7]
46. ! [X0] : ((curious(X0) | ~calm(X0) | ~happy(X0)) & (happy(X0) | (~curious(X0) & calm(X0)))) [flattening 45]
50. (tall(alice) | (happy(alice) | ~kind(alice))) & ((~happy(alice) & kind(alice)) | ~tall(alice)) [nnf transformation 11]
51. (tall(alice) | happy(alice) | ~kind(alice)) & ((~happy(alice) & kind(alice)) | ~tall(alice)) [flattening 50]
54. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0)))) & (((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 13]
74. ~happy(X0) | tall(X0) | ~generous(X0) [cnf transformation 37]
96. calm(X0) | happy(X0) [cnf transformation 46]
110. ~happy(alice) | ~tall(alice) [cnf transformation 51]
120. ~calm(X0) | tall(X0) | tall(X0) | ~generous(X0) [cnf transformation 54]
125. ~tall(X0) | ~generous(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 54]
151. generous(alice) [cnf transformation 25]
153. ~calm(X0) | tall(X0) | ~generous(X0) [duplicate literal removal 120]
155. ~calm(X0) | ~generous(X0) | ~tall(X0) [duplicate literal removal 125]
206. 10 <=> happy(alice) [avatar definition]
208. happy(alice) <- (10) [avatar component clause 206]
210. 11 <=> tall(alice) [avatar definition]
211. ~tall(alice) <- (~11) [avatar component clause 210]
214. ~11 | ~10 [avatar split clause 110,206,210]
216. ~calm(X0) | ~generous(X0) [subsumption resolution 153,155]
312. ~generous(X0) | happy(X0) [resolution 216,96]
681. happy(alice) [resolution 312,151]
687. 10 [avatar split clause 681,206]
700. tall(alice) | ~generous(alice) <- (10) [resolution 208,74]
708. ~generous(alice) <- (10, ~11) [subsumption resolution 700,211]
709. $false <- (10, ~11) [subsumption resolution 708,151]
710. ~10 | 11 [avatar contradiction clause 709]
714. $false [avatar sat refutation 214,687,710]
% SZS output end Proof for 5376523880137122396170886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not wise then someone is both not generous and not brave and vice versa.
Everyone who is either not patient or not rich is both not tall and not happy.
Everyone who is tall is both not happy and generous and vice versa.
If someone is either calm or not kind then lucy is not brave or patient.
If someone is not humble or patient then paul is both curious and not patient and vice versa.
Everyone who is not funny is both brave and not curious.
If someone is calm then someone is either not old or funny and vice versa.
Everyone who is either creative or not happy is both humble and not old.
Everyone who is both not funny and happy is not kind or happy.
Everyone who is both not wise and curious is either not creative or creative and vice versa.
Everyone who is creative is either not patient or not brave and vice versa.
Everyone who is either not kind or not old is either kind or brave and vice versa.
Everyone who is not humble is funny or calm.
Everyone who is quiet or not rich is both not patient and not generous.
Everyone who is patient is not brave and vice versa.
If lucy is curious or patient then paul is not humble or rich.
Susan is not humble or rich.
Lucy is strong.
Mary is old or wise.
Someone is either generous or kind.
Someone is humble or curious.
Someone is both rich and quiet.
Someone is not old.
Paul is either creative or not kind.
|
Paul is old.
|
entailment
|
((?[X]:((rich(X)|~wise(X))))<=>(?[X]:((~generous(X)&~brave(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>(~tall(X)&~happy(X))))&
(![X]:(tall(X)<=>(~happy(X)&generous(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~brave(lucy)|patient(lucy))))&
((?[X]:((~humble(X)|patient(X))))<=>((curious(paul)&~patient(paul))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(![X]:((~wise(X)&curious(X))<=>(~creative(X)<~>creative(X))))&
(![X]:(creative(X)<=>(~patient(X)<~>~brave(X))))&
(![X]:((~kind(X)<~>~old(X))<=>(kind(X)<~>brave(X))))&
(![X]:(~humble(X)=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((curious(lucy)|patient(lucy)))=>((~humble(paul)|rich(paul))))&
((~humble(susan)|rich(susan)))&
(strong(lucy))&
((old(mary)|wise(mary)))&
(?[X]:((generous(X)<~>kind(X))))&
(?[X]:((humble(X)|curious(X))))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:(~old(X)))&
((creative(paul)<~>~kind(paul)))
|
old(paul)
|
[
"p4",
"p11",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 9129779428067750949860113
% SZS output start Proof for 9129779428067750949860113
5. ? [X0] : (patient(X0) | ~humble(X0)) <=> (~patient(paul) & curious(paul)) [input p4]
12. ! [X0] : ((~kind(X0) <~> ~old(X0)) <=> (kind(X0) <~> brave(X0))) [input p11]
15. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p14]
25. ~old(paul) [input hypothesis]
51. (? [X0] : (patient(X0) | ~humble(X0)) | (patient(paul) | ~curious(paul))) & ((~patient(paul) & curious(paul)) | ! [X0] : (~patient(X0) & humble(X0))) [nnf transformation 5]
52. (? [X0] : (patient(X0) | ~humble(X0)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X0] : (~patient(X0) & humble(X0))) [flattening 51]
53. (? [X0] : (patient(X0) | ~humble(X0)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X1] : (~patient(X1) & humble(X1))) [rectify 52]
54. ? [X0] : (patient(X0) | ~humble(X0)) => (patient(sK2) | ~humble(sK2)) [choice axiom]
55. ((patient(sK2) | ~humble(sK2)) | patient(paul) | ~curious(paul)) & ((~patient(paul) & curious(paul)) | ! [X1] : (~patient(X1) & humble(X1))) [skolemisation 53,54]
65. ! [X0] : ((((old(X0) | kind(X0)) & (~old(X0) | ~kind(X0))) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))))) [nnf transformation 12]
66. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 15]
92. ~patient(paul) | ~patient(X1) [cnf transformation 55]
118. ~brave(X0) | ~kind(X0) | ~kind(X0) | old(X0) [cnf transformation 65]
122. old(X0) | kind(X0) | kind(X0) | ~brave(X0) [cnf transformation 65]
129. patient(X0) | brave(X0) [cnf transformation 66]
142. ~old(paul) [cnf transformation 25]
144. ~brave(X0) | ~kind(X0) | old(X0) [duplicate literal removal 118]
146. old(X0) | kind(X0) | ~brave(X0) [duplicate literal removal 122]
202. 13 <=> patient(paul) [avatar definition]
203. ~patient(paul) <- (~13) [avatar component clause 202]
204. patient(paul) <- (13) [avatar component clause 202]
215. 16 <=> ! [X1] : ~patient(X1) [avatar definition]
216. ~patient(X1) <- (16) [avatar component clause 215]
217. 16 | ~13 [avatar split clause 92,202,215]
251. ~brave(X0) | old(X0) [subsumption resolution 144,146]
306. brave(paul) <- (~13) [resolution 129,203]
310. old(paul) <- (~13) [resolution 251,306]
312. $false <- (~13) [subsumption resolution 310,142]
313. 13 [avatar contradiction clause 312]
314. $false <- (13, 16) [subsumption resolution 204,216]
315. ~13 | ~16 [avatar contradiction clause 314]
316. $false [avatar sat refutation 217,313,315]
% SZS output end Proof for 9129779428067750949860113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is creative or not kind then john is wise or not patient and vice versa.
Everyone who is not curious is either not brave or tall and vice versa.
If someone is rich then alice is either not creative or not humble and vice versa.
Everyone who is not tall or not curious is either not strong or not calm.
Everyone who is not wise is generous.
Everyone who is both not rich and rich is humble and vice versa.
Everyone who is both not curious and not quiet is not calm and vice versa.
If someone is both happy and creative then susan is not funny or not curious.
If paul is old then someone is both strong and kind.
If alice is both not kind and not creative then someone is not old or not wise.
Everyone who is quiet is either not old or not humble and vice versa.
Everyone who is both not happy and not kind is either not calm or not brave and vice versa.
If mary is either humble or not kind then lucy is not strong or curious and vice versa.
Everyone who is both not funny and not calm is rich and vice versa.
Everyone who is either not funny or generous is not strong.
If someone is calm or not quiet then someone is not brave or curious and vice versa.
John is either not creative or generous.
Someone is quiet or not strong.
Mary is either tall or not patient.
Fred is both patient and not funny.
Someone is either not rich or brave.
Lucy is strong or not curious.
Someone is both wise and not rich.
Susan is not old or kind.
|
Susan is generous.
|
neutral
|
(((creative(john)|~kind(john)))<=>((wise(john)|~patient(john))))&
(![X]:(~curious(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:(rich(X)))<=>((~creative(alice)<~>~humble(alice))))&
(![X]:((~tall(X)|~curious(X))=>(~strong(X)<~>~calm(X))))&
(![X]:(~wise(X)=>generous(X)))&
(![X]:((~rich(X)&rich(X))<=>humble(X)))&
(![X]:((~curious(X)&~quiet(X))<=>~calm(X)))&
((?[X]:((happy(X)&creative(X))))=>((~funny(susan)|~curious(susan))))&
((old(paul))=>(?[X]:((strong(X)&kind(X)))))&
(((~kind(alice)&~creative(alice)))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(quiet(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~happy(X)&~kind(X))<=>(~calm(X)<~>~brave(X))))&
(((humble(mary)<~>~kind(mary)))<=>((~strong(lucy)|curious(lucy))))&
(![X]:((~funny(X)&~calm(X))<=>rich(X)))&
(![X]:((~funny(X)<~>generous(X))=>~strong(X)))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:((~brave(X)|curious(X)))))&
((~creative(john)<~>generous(john)))&
(?[X]:((quiet(X)|~strong(X))))&
((tall(mary)<~>~patient(mary)))&
((patient(fred)&~funny(fred)))&
(?[X]:((~rich(X)<~>brave(X))))&
((strong(lucy)|~curious(lucy)))&
(?[X]:((wise(X)&~rich(X))))&
((~old(susan)|kind(susan)))
|
generous(susan)
|
[] | null | 0 |
Everyone who is either not creative or brave is both not tall and strong.
Everyone who is both not wise and curious is not quiet and vice versa.
Everyone who is either old or not rich is both not old and calm and vice versa.
Everyone who is both not happy and kind is either not generous or not funny.
If someone is rich then lucy is quiet and vice versa.
Everyone who is not strong or not creative is not tall and vice versa.
If someone is both strong and brave then someone is not funny and vice versa.
If someone is both funny and creative then mary is both not funny and not old and vice versa.
Everyone who is not curious or old is both curious and happy.
If someone is curious then mary is patient.
Everyone who is humble or old is not strong.
If someone is not strong then fred is funny and vice versa.
Everyone who is both rich and not calm is not strong or not wise and vice versa.
If someone is either not funny or quiet then someone is either not rich or creative and vice versa.
If someone is not generous then fred is either rich or kind and vice versa.
If mary is not happy or humble then someone is not happy or not generous and vice versa.
Someone is both not humble and not generous.
Someone is generous.
Lucy is both tall and kind.
Paul is both not funny and rich.
Mary is either generous or not old.
Someone is not old.
Someone is not funny or not brave.
|
Lucy is rich.
|
contradiction
|
(![X]:((~creative(X)<~>brave(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)&curious(X))<=>~quiet(X)))&
(![X]:((old(X)<~>~rich(X))<=>(~old(X)&calm(X))))&
(![X]:((~happy(X)&kind(X))=>(~generous(X)<~>~funny(X))))&
((?[X]:(rich(X)))<=>(quiet(lucy)))&
(![X]:((~strong(X)|~creative(X))<=>~tall(X)))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((funny(X)&creative(X))))<=>((~funny(mary)&~old(mary))))&
(![X]:((~curious(X)|old(X))=>(curious(X)&happy(X))))&
((?[X]:(curious(X)))=>(patient(mary)))&
(![X]:((humble(X)|old(X))=>~strong(X)))&
((?[X]:(~strong(X)))<=>(funny(fred)))&
(![X]:((rich(X)&~calm(X))<=>(~strong(X)|~wise(X))))&
((?[X]:((~funny(X)<~>quiet(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
((?[X]:(~generous(X)))<=>((rich(fred)<~>kind(fred))))&
(((~happy(mary)|humble(mary)))<=>(?[X]:((~happy(X)|~generous(X)))))&
(?[X]:((~humble(X)&~generous(X))))&
(?[X]:(generous(X)))&
((tall(lucy)&kind(lucy)))&
((~funny(paul)&rich(paul)))&
((generous(mary)<~>~old(mary)))&
(?[X]:(~old(X)))&
(?[X]:((~funny(X)|~brave(X))))
|
rich(lucy)
|
[
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p12",
"p18",
"p19",
"hypothesis"
] |
% SZS status Unsatisfiable for 69239517002735280720080
% SZS output start Proof for 69239517002735280720080
2. ! [X0] : ((curious(X0) & ~wise(X0)) <=> ~quiet(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (calm(X0) & ~old(X0))) [input p2]
5. ? [X0] : rich(X0) <=> quiet(lucy) [input p4]
6. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> ~tall(X0)) [input p5]
9. ! [X0] : ((old(X0) | ~curious(X0)) => (happy(X0) & curious(X0))) [input p8]
11. ! [X0] : ((old(X0) | humble(X0)) => ~strong(X0)) [input p10]
13. ! [X0] : ((~calm(X0) & rich(X0)) <=> (~wise(X0) | ~strong(X0))) [input p12]
19. kind(lucy) & tall(lucy) [input p18]
20. rich(paul) & ~funny(paul) [input p19]
24. rich(lucy) [input hypothesis]
31. ! [X0] : ((happy(X0) & curious(X0)) | (~old(X0) & curious(X0))) [ennf transformation 9]
32. ! [X0] : (~strong(X0) | (~old(X0) & ~humble(X0))) [ennf transformation 11]
34. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | (~curious(X0) | wise(X0)))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) & ~wise(X0)) | quiet(X0)) & (~quiet(X0) | ~curious(X0) | wise(X0))) [flattening 34]
36. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 3]
37. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [flattening 36]
39. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X0] : ~rich(X0)) [nnf transformation 5]
40. (? [X0] : rich(X0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [rectify 39]
41. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
42. (rich(sK0) | ~quiet(lucy)) & (quiet(lucy) | ! [X1] : ~rich(X1)) [skolemisation 40,41]
43. ! [X0] : (((~creative(X0) | ~strong(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [nnf transformation 6]
44. ! [X0] : ((~creative(X0) | ~strong(X0) | tall(X0)) & (~tall(X0) | (creative(X0) & strong(X0)))) [flattening 43]
59. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((~calm(X0) & rich(X0)) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | calm(X0) | ~rich(X0))) [flattening 59]
88. ~quiet(X0) | ~curious(X0) | wise(X0) [cnf transformation 35]
91. ~old(X0) | ~rich(X0) | ~old(X0) [cnf transformation 37]
95. ~rich(X0) | old(X0) | ~calm(X0) | old(X0) [cnf transformation 37]
99. quiet(lucy) | ~rich(X1) [cnf transformation 42]
101. ~tall(X0) | strong(X0) [cnf transformation 44]
111. curious(X0) | curious(X0) [cnf transformation 31]
116. ~old(X0) | ~strong(X0) [cnf transformation 32]
119. ~rich(X0) | ~strong(X0) | calm(X0) | ~wise(X0) [cnf transformation 60]
120. rich(X0) | strong(X0) [cnf transformation 60]
143. tall(lucy) [cnf transformation 19]
146. rich(paul) [cnf transformation 20]
151. rich(lucy) [cnf transformation 24]
152. curious(X0) [duplicate literal removal 111]
153. ~rich(X0) | ~old(X0) [duplicate literal removal 91]
154. ~calm(X0) | old(X0) | ~rich(X0) [duplicate literal removal 95]
156. 1 <=> quiet(lucy) [avatar definition]
157. quiet(lucy) <- (1) [avatar component clause 156]
165. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
166. ~rich(X1) <- (3) [avatar component clause 165]
167. 3 | 1 [avatar split clause 99,156,165]
318. $false <- (3) [resolution 166,146]
321. ~3 [avatar contradiction clause 318]
325. strong(lucy) [resolution 101,143]
335. ~old(X1) | strong(X1) [resolution 153,120]
339. ~old(X1) [subsumption resolution 335,116]
356. ~curious(lucy) | wise(lucy) <- (1) [resolution 88,157]
359. wise(lucy) <- (1) [subsumption resolution 356,152]
421. ~strong(lucy) | calm(lucy) | ~wise(lucy) [resolution 119,151]
425. calm(lucy) | ~wise(lucy) [subsumption resolution 421,325]
426. calm(lucy) <- (1) [subsumption resolution 425,359]
457. old(lucy) | ~rich(lucy) <- (1) [resolution 426,154]
460. ~rich(lucy) <- (1) [subsumption resolution 457,339]
461. $false <- (1) [subsumption resolution 460,151]
462. ~1 [avatar contradiction clause 461]
463. $false [avatar sat refutation 167,321,462]
% SZS output end Proof for 69239517002735280720080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then john is rich or curious.
If fred is either not old or not happy then someone is not patient and vice versa.
If someone is either creative or strong then someone is not strong or patient.
Everyone who is both not kind and kind is either patient or creative.
Everyone who is not kind is not rich.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
Everyone who is calm is both curious and humble.
If someone is brave then paul is not patient and vice versa.
If someone is funny or not quiet then someone is kind or brave.
John is tall or funny.
Mary is both not patient and brave.
Someone is either quiet or humble.
Alice is either kind or curious.
Mary is kind.
Fred is not humble.
Fred is both quiet and not patient.
Fred is both not patient and funny.
|
Mary is happy.
|
entailment
|
((?[X]:(~quiet(X)))=>((rich(john)|curious(john))))&
(((~old(fred)<~>~happy(fred)))<=>(?[X]:(~patient(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(?[X]:((~strong(X)|patient(X)))))&
(![X]:((~kind(X)&kind(X))=>(patient(X)<~>creative(X))))&
(![X]:(~kind(X)=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
(![X]:(calm(X)=>(curious(X)&humble(X))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((kind(X)|brave(X)))))&
((tall(john)|funny(john)))&
((~patient(mary)&brave(mary)))&
(?[X]:((quiet(X)<~>humble(X))))&
((kind(alice)<~>curious(alice)))&
(kind(mary))&
(~humble(fred))&
((quiet(fred)&~patient(fred)))&
((~patient(fred)&funny(fred)))
|
happy(mary)
|
[
"p5",
"p9",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 2867407379811380304506211
% SZS output start Proof for 2867407379811380304506211
6. ! [X0] : ((~old(X0) & happy(X0)) <=> ~calm(X0)) [input p5]
10. ! [X0] : (~happy(X0) => (~calm(X0) <~> ~humble(X0))) [input p9]
14. ! [X0] : (calm(X0) => (humble(X0) & curious(X0))) [input p13]
25. ~happy(mary) [input hypothesis]
35. ! [X0] : ((~calm(X0) <~> ~humble(X0)) | happy(X0)) [ennf transformation 10]
37. ! [X0] : ((humble(X0) & curious(X0)) | ~calm(X0)) [ennf transformation 14]
48. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | (old(X0) | ~happy(X0)))) [nnf transformation 6]
49. ! [X0] : (((~old(X0) & happy(X0)) | calm(X0)) & (~calm(X0) | old(X0) | ~happy(X0))) [flattening 48]
58. ! [X0] : (((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | happy(X0)) [nnf transformation 35]
84. calm(X0) | happy(X0) [cnf transformation 49]
97. ~humble(X0) | ~calm(X0) | happy(X0) [cnf transformation 58]
108. ~calm(X0) | humble(X0) [cnf transformation 37]
126. ~happy(mary) [cnf transformation 25]
195. ~humble(X0) | happy(X0) [subsumption resolution 97,84]
285. humble(X0) | happy(X0) [resolution 108,84]
287. happy(X0) [subsumption resolution 285,195]
293. $false [resolution 287,126]
% SZS output end Proof for 2867407379811380304506211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not quiet is both not curious and generous.
Everyone who is both generous and not patient is not calm or not old.
Everyone who is either brave or creative is either not brave or not generous and vice versa.
If someone is either tall or quiet then someone is not wise or kind and vice versa.
If someone is either curious or not calm then someone is brave and vice versa.
If susan is either not quiet or not brave then lucy is either not kind or not rich and vice versa.
If alice is generous or not strong then someone is both old and happy and vice versa.
Everyone who is not rich or humble is either tall or humble.
Everyone who is not rich or not quiet is not patient and vice versa.
Everyone who is not happy is generous and vice versa.
Everyone who is either quiet or old is both happy and rich and vice versa.
Everyone who is both not calm and not rich is either not brave or calm and vice versa.
If paul is not tall or not calm then someone is either kind or not happy and vice versa.
Everyone who is brave or curious is curious and vice versa.
If someone is not calm then someone is either happy or generous and vice versa.
If alice is generous then lucy is both kind and calm.
Lucy is creative or not creative.
Someone is brave or not wise.
Someone is both not wise and creative.
Susan is either calm or brave.
John is both not brave and rich.
Paul is either not old or curious.
John is wise.
|
Susan is generous.
|
neutral
|
(![X]:((~happy(X)|~quiet(X))=>(~curious(X)&generous(X))))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|~old(X))))&
(![X]:((brave(X)<~>creative(X))<=>(~brave(X)<~>~generous(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>(?[X]:((~wise(X)|kind(X)))))&
((?[X]:((curious(X)<~>~calm(X))))<=>(?[X]:(brave(X))))&
(((~quiet(susan)<~>~brave(susan)))<=>((~kind(lucy)<~>~rich(lucy))))&
(((generous(alice)|~strong(alice)))<=>(?[X]:((old(X)&happy(X)))))&
(![X]:((~rich(X)|humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((~rich(X)|~quiet(X))<=>~patient(X)))&
(![X]:(~happy(X)<=>generous(X)))&
(![X]:((quiet(X)<~>old(X))<=>(happy(X)&rich(X))))&
(![X]:((~calm(X)&~rich(X))<=>(~brave(X)<~>calm(X))))&
(((~tall(paul)|~calm(paul)))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((brave(X)|curious(X))<=>curious(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((happy(X)<~>generous(X)))))&
((generous(alice))=>((kind(lucy)&calm(lucy))))&
((creative(lucy)|~creative(lucy)))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((~wise(X)&creative(X))))&
((calm(susan)<~>brave(susan)))&
((~brave(john)&rich(john)))&
((~old(paul)<~>curious(paul)))&
(wise(john))
|
generous(susan)
|
[] | null | 0 |
Everyone who is not strong is not brave or wise and vice versa.
Everyone who is either happy or funny is both curious and humble and vice versa.
If someone is patient or not creative then lucy is creative or not rich and vice versa.
Everyone who is not happy is either not curious or kind.
Everyone who is both curious and not tall is either quiet or not brave.
If paul is not old or not calm then lucy is either not tall or funny and vice versa.
Everyone who is not generous or calm is both old and not strong and vice versa.
If someone is funny or not quiet then john is not humble.
If someone is not tall or not humble then lucy is not rich.
If paul is both calm and humble then alice is strong or not happy and vice versa.
If someone is not wise or not curious then someone is not funny.
Everyone who is not brave or tall is tall or not quiet.
Everyone who is calm is either not generous or not patient and vice versa.
Everyone who is either not creative or calm is both not happy and not creative and vice versa.
Everyone who is wise is not funny or not wise and vice versa.
Everyone who is tall or kind is old.
Someone is both humble and not old.
Someone is not happy or funny.
Lucy is not calm or not generous.
Someone is not brave.
Susan is not calm.
Mary is tall or quiet.
Susan is brave.
|
Lucy is not quiet.
|
neutral
|
(![X]:(~strong(X)<=>(~brave(X)|wise(X))))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)&humble(X))))&
((?[X]:((patient(X)|~creative(X))))<=>((creative(lucy)|~rich(lucy))))&
(![X]:(~happy(X)=>(~curious(X)<~>kind(X))))&
(![X]:((curious(X)&~tall(X))=>(quiet(X)<~>~brave(X))))&
(((~old(paul)|~calm(paul)))<=>((~tall(lucy)<~>funny(lucy))))&
(![X]:((~generous(X)|calm(X))<=>(old(X)&~strong(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(~humble(john)))&
((?[X]:((~tall(X)|~humble(X))))=>(~rich(lucy)))&
(((calm(paul)&humble(paul)))<=>((strong(alice)|~happy(alice))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)|tall(X))=>(tall(X)|~quiet(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>~patient(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&~creative(X))))&
(![X]:(wise(X)<=>(~funny(X)|~wise(X))))&
(![X]:((tall(X)|kind(X))=>old(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((~happy(X)|funny(X))))&
((~calm(lucy)|~generous(lucy)))&
(?[X]:(~brave(X)))&
(~calm(susan))&
((tall(mary)|quiet(mary)))&
(brave(susan))
|
~quiet(lucy)
|
[] | null | 0 |
Everyone who is both rich and wise is either not creative or not quiet.
Everyone who is both not rich and patient is either curious or generous.
If john is either not wise or not old then fred is both calm and funny.
If fred is quiet then someone is not old or not quiet.
If lucy is either not patient or tall then paul is brave and vice versa.
If someone is quiet then mary is either not wise or not creative and vice versa.
If someone is not patient or calm then someone is not curious or not calm.
Everyone who is not tall or not rich is both not generous and creative and vice versa.
If someone is brave then someone is either not humble or patient and vice versa.
Everyone who is either funny or strong is both not strong and generous and vice versa.
If mary is either not tall or not humble then someone is either not kind or not generous and vice versa.
If someone is either not brave or patient then someone is generous or not wise.
If someone is not strong or funny then someone is creative or not happy and vice versa.
If paul is not patient or rich then alice is either quiet or not quiet.
If alice is both quiet and not brave then alice is not tall or rich.
Everyone who is either calm or rich is wise and vice versa.
John is both not happy and not funny.
Susan is not calm.
Paul is both not brave and not tall.
Paul is not kind or brave.
Mary is curious.
John is both curious and quiet.
Someone is either not creative or not humble.
Someone is both strong and funny.
|
John is happy.
|
contradiction
|
(![X]:((rich(X)&wise(X))=>(~creative(X)<~>~quiet(X))))&
(![X]:((~rich(X)&patient(X))=>(curious(X)<~>generous(X))))&
(((~wise(john)<~>~old(john)))=>((calm(fred)&funny(fred))))&
((quiet(fred))=>(?[X]:((~old(X)|~quiet(X)))))&
(((~patient(lucy)<~>tall(lucy)))<=>(brave(paul)))&
((?[X]:(quiet(X)))<=>((~wise(mary)<~>~creative(mary))))&
((?[X]:((~patient(X)|calm(X))))=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((~tall(X)|~rich(X))<=>(~generous(X)&creative(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((funny(X)<~>strong(X))<=>(~strong(X)&generous(X))))&
(((~tall(mary)<~>~humble(mary)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
((?[X]:((~brave(X)<~>patient(X))))=>(?[X]:((generous(X)|~wise(X)))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((creative(X)|~happy(X)))))&
(((~patient(paul)|rich(paul)))=>((quiet(alice)<~>~quiet(alice))))&
(((quiet(alice)&~brave(alice)))=>((~tall(alice)|rich(alice))))&
(![X]:((calm(X)<~>rich(X))<=>wise(X)))&
((~happy(john)&~funny(john)))&
(~calm(susan))&
((~brave(paul)&~tall(paul)))&
((~kind(paul)|brave(paul)))&
(curious(mary))&
((curious(john)&quiet(john)))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:((strong(X)&funny(X))))
|
happy(john)
|
[
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 2658313553756958451980600
% SZS output start Proof for 2658313553756958451980600
17. ~funny(john) & ~happy(john) [input p16]
25. happy(john) [input hypothesis]
140. ~happy(john) [cnf transformation 17]
153. happy(john) [cnf transformation 25]
360. $false [subsumption resolution 153,140]
% SZS output end Proof for 2658313553756958451980600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not rich then susan is not patient or curious. Everyone who is not creative or not strong is both not brave and not strong and vice versa. If someone is not tall or curious then someone is both not happy and generous and vice versa. Everyone who is wise or not quiet is either not brave or strong. Everyone who is either not curious or tall is both not patient and not calm and vice versa. If paul is curious or not humble then someone is not brave or funny and vice versa. If someone is not calm then fred is both wise and happy. If someone is not rich then paul is old and vice versa. Everyone who is not kind is not patient or not generous. If someone is kind or not creative then someone is either not happy or not patient and vice versa. Everyone who is not quiet or generous is either patient or curious and vice versa. Everyone who is quiet or humble is either not humble or not brave and vice versa. If someone is not brave then paul is either quiet or curious and vice versa. If someone is either not curious or not calm then someone is both not strong and not brave. Everyone who is not kind or not curious is either not happy or not tall. If mary is generous or not brave then someone is either not strong or not rich and vice versa. Paul is wise or not generous. Someone is both wise and patient. Lucy is happy or kind. Lucy is strong. John is either not kind or rich. Paul is either not calm or not strong. John is either kind or not humble.
|
John is not quiet.
|
neutral
|
((?[X]:((wise(X)|~rich(X))))=>((~patient(susan)|curious(susan))))&
(![X]:((~creative(X)|~strong(X))<=>(~brave(X)&~strong(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~brave(X)<~>strong(X))))&
(![X]:((~curious(X)<~>tall(X))<=>(~patient(X)&~calm(X))))&
(((curious(paul)|~humble(paul)))<=>(?[X]:((~brave(X)|funny(X)))))&
((?[X]:(~calm(X)))=>((wise(fred)&happy(fred))))&
((?[X]:(~rich(X)))<=>(old(paul)))&
(![X]:(~kind(X)=>(~patient(X)|~generous(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(patient(X)<~>curious(X))))&
(![X]:((quiet(X)|humble(X))<=>(~humble(X)<~>~brave(X))))&
((?[X]:(~brave(X)))<=>((quiet(paul)<~>curious(paul))))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~tall(X))))&
(((generous(mary)|~brave(mary)))<=>(?[X]:((~strong(X)<~>~rich(X)))))&
((wise(paul)|~generous(paul)))&
(?[X]:((wise(X)&patient(X))))&
((happy(lucy)|kind(lucy)))&
(strong(lucy))&
((~kind(john)<~>rich(john)))&
((~calm(paul)<~>~strong(paul)))&
((kind(john)<~>~humble(john)))
|
~quiet(john)
|
[] | null | 0 |
Everyone who is not quiet is not funny.
If someone is both quiet and not happy then lucy is either not generous or not humble and vice versa.
If someone is creative then mary is both not happy and not funny and vice versa.
If susan is both not rich and not patient then someone is either not funny or not strong.
Everyone who is not kind is either not patient or brave.
Everyone who is either not generous or not funny is both not funny and not kind and vice versa.
Everyone who is funny is either not calm or not funny and vice versa.
If susan is calm or not funny then paul is both old and not rich and vice versa.
If someone is not funny then paul is both happy and brave.
If someone is both not kind and tall then someone is either not kind or calm.
Everyone who is either not quiet or not kind is either strong or not strong.
If someone is tall then mary is either calm or not funny and vice versa.
Everyone who is brave is either not quiet or not wise and vice versa.
If someone is either not calm or humble then someone is not brave and vice versa.
Everyone who is either not creative or calm is patient or not rich.
Everyone who is either happy or curious is kind.
Paul is either kind or curious.
Someone is either not creative or kind.
Someone is either happy or not patient.
Someone is both not creative and not calm.
Someone is brave or creative.
Paul is either not curious or creative.
Someone is either brave or not happy.
Lucy is tall.
|
Paul is not brave.
|
contradiction
|
(![X]:(~quiet(X)=>~funny(X)))&
((?[X]:((quiet(X)&~happy(X))))<=>((~generous(lucy)<~>~humble(lucy))))&
((?[X]:(creative(X)))<=>((~happy(mary)&~funny(mary))))&
(((~rich(susan)&~patient(susan)))=>(?[X]:((~funny(X)<~>~strong(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>brave(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>(~funny(X)&~kind(X))))&
(![X]:(funny(X)<=>(~calm(X)<~>~funny(X))))&
(((calm(susan)|~funny(susan)))<=>((old(paul)&~rich(paul))))&
((?[X]:(~funny(X)))=>((happy(paul)&brave(paul))))&
((?[X]:((~kind(X)&tall(X))))=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~quiet(X)<~>~kind(X))=>(strong(X)<~>~strong(X))))&
((?[X]:(tall(X)))<=>((calm(mary)<~>~funny(mary))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>humble(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~creative(X)<~>calm(X))=>(patient(X)|~rich(X))))&
(![X]:((happy(X)<~>curious(X))=>kind(X)))&
((kind(paul)<~>curious(paul)))&
(?[X]:((~creative(X)<~>kind(X))))&
(?[X]:((happy(X)<~>~patient(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((brave(X)|creative(X))))&
((~curious(paul)<~>creative(paul)))&
(?[X]:((brave(X)<~>~happy(X))))&
(tall(lucy))
|
~brave(paul)
|
[
"p6",
"p8",
"p11",
"p23",
"hypothesis"
] |
% SZS status Unsatisfiable for 4948829412689438332479558
% SZS output start Proof for 4948829412689438332479558
7. ! [X0] : (funny(X0) <=> (~calm(X0) <~> ~funny(X0))) [input p6]
9. ? [X0] : ~funny(X0) => (brave(paul) & happy(paul)) [input p8]
12. ? [X0] : tall(X0) <=> (calm(mary) <~> ~funny(mary)) [input p11]
24. tall(lucy) [input p23]
25. ~brave(paul) [input hypothesis]
32. (brave(paul) & happy(paul)) | ! [X0] : funny(X0) [ennf transformation 9]
53. ! [X0] : ((funny(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) & (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | ~funny(X0))) [nnf transformation 7]
61. (? [X0] : tall(X0) | ((calm(mary) | funny(mary)) & (~funny(mary) | ~calm(mary)))) & (((funny(mary) | ~calm(mary)) & (~funny(mary) | calm(mary))) | ! [X0] : ~tall(X0)) [nnf transformation 12]
62. (? [X0] : tall(X0) | ((calm(mary) | funny(mary)) & (~funny(mary) | ~calm(mary)))) & (((funny(mary) | ~calm(mary)) & (~funny(mary) | calm(mary))) | ! [X1] : ~tall(X1)) [rectify 61]
63. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
64. (tall(sK4) | ((calm(mary) | funny(mary)) & (~funny(mary) | ~calm(mary)))) & (((funny(mary) | ~calm(mary)) & (~funny(mary) | calm(mary))) | ! [X1] : ~tall(X1)) [skolemisation 62,63]
108. ~funny(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 53]
111. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 53]
118. brave(paul) | funny(X0) [cnf transformation 32]
125. ~funny(mary) | calm(mary) | ~tall(X1) [cnf transformation 64]
154. tall(lucy) [cnf transformation 24]
155. ~brave(paul) [cnf transformation 25]
156. ~funny(X0) | ~calm(X0) [duplicate literal removal 108]
157. funny(X0) | ~calm(X0) [duplicate literal removal 111]
190. 7 <=> funny(mary) [avatar definition]
191. ~funny(mary) <- (~7) [avatar component clause 190]
221. ~calm(X0) [subsumption resolution 156,157]
239. 17 <=> ! [X0] : funny(X0) [avatar definition]
240. funny(X0) <- (17) [avatar component clause 239]
242. 18 <=> brave(paul) [avatar definition]
245. 17 | 18 [avatar split clause 118,242,239]
266. ~funny(mary) | ~tall(X1) [subsumption resolution 125,221]
268. 23 <=> ! [X1] : ~tall(X1) [avatar definition]
269. ~tall(X1) <- (23) [avatar component clause 268]
270. 23 | ~7 [avatar split clause 266,190,268]
345. ~18 [avatar split clause 155,242]
348. $false <- (~7, 17) [subsumption resolution 191,240]
349. 7 | ~17 [avatar contradiction clause 348]
352. $false <- (23) [resolution 269,154]
355. ~23 [avatar contradiction clause 352]
356. $false [avatar sat refutation 245,270,345,349,355]
% SZS output end Proof for 4948829412689438332479558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not patient and not happy then fred is both not creative and generous. Everyone who is not patient is both calm and tall. Everyone who is kind is both old and not happy and vice versa. If lucy is not patient or tall then someone is funny. If someone is either quiet or curious then someone is either not old or creative and vice versa. If someone is not tall then someone is both creative and humble. Everyone who is not old is not creative and vice versa. If someone is patient then alice is not brave and vice versa. Everyone who is kind or patient is both not quiet and calm and vice versa. Everyone who is not old is either patient or wise. If someone is either rich or curious then someone is patient or tall. Everyone who is both quiet and strong is either not happy or quiet and vice versa. If someone is humble or not rich then mary is both not brave and not strong and vice versa. Everyone who is rich is both rich and not patient. Everyone who is either not generous or not strong is curious or quiet. If someone is tall then someone is humble. Someone is not calm or not creative. Someone is not rich or creative. Lucy is wise or not creative. Lucy is either tall or not brave. Someone is not generous or not kind. Someone is both not generous and not rich.
|
Alice is not calm.
|
contradiction
|
(((~patient(fred)&~happy(fred)))=>((~creative(fred)&generous(fred))))&
(![X]:(~patient(X)=>(calm(X)&tall(X))))&
(![X]:(kind(X)<=>(old(X)&~happy(X))))&
(((~patient(lucy)|tall(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((~old(X)<~>creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:(~old(X)<=>~creative(X)))&
((?[X]:(patient(X)))<=>(~brave(alice)))&
(![X]:((kind(X)|patient(X))<=>(~quiet(X)&calm(X))))&
(![X]:(~old(X)=>(patient(X)<~>wise(X))))&
((?[X]:((rich(X)<~>curious(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)<~>quiet(X))))&
((?[X]:((humble(X)|~rich(X))))<=>((~brave(mary)&~strong(mary))))&
(![X]:(rich(X)=>(rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(curious(X)|quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:(humble(X))))&
(?[X]:((~calm(X)|~creative(X))))&
(?[X]:((~rich(X)|creative(X))))&
((wise(lucy)|~creative(lucy)))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:((~generous(X)|~kind(X))))&
(?[X]:((~generous(X)&~rich(X))))
|
~calm(alice)
|
[
"p1",
"p8",
"hypothesis"
] |
% SZS status Unsatisfiable for 6914812470905777780638359
% SZS output start Proof for 6914812470905777780638359
2. ! [X0] : (~patient(X0) => (tall(X0) & calm(X0))) [input p1]
9. ! [X0] : ((patient(X0) | kind(X0)) <=> (calm(X0) & ~quiet(X0))) [input p8]
23. ~calm(alice) [input hypothesis]
31. ! [X0] : ((tall(X0) & calm(X0)) | patient(X0)) [ennf transformation 2]
54. ! [X0] : (((patient(X0) | kind(X0)) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | (~patient(X0) & ~kind(X0)))) [nnf transformation 9]
55. ! [X0] : ((patient(X0) | kind(X0) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | (~patient(X0) & ~kind(X0)))) [flattening 54]
83. calm(X0) | patient(X0) [cnf transformation 31]
105. calm(X0) | ~patient(X0) [cnf transformation 55]
135. ~calm(alice) [cnf transformation 23]
219. calm(X0) [subsumption resolution 105,83]
294. $false [subsumption resolution 135,219]
% SZS output end Proof for 6914812470905777780638359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not humble is both creative and patient.
Everyone who is calm or rich is both not calm and creative.
If lucy is not funny then someone is old.
If someone is rich then john is not creative or happy and vice versa.
Everyone who is either calm or not rich is not old or funny and vice versa.
Everyone who is either not brave or not funny is either kind or not calm.
Everyone who is not tall or kind is either not generous or brave.
Everyone who is not wise or brave is not funny and vice versa.
Everyone who is not tall is either kind or not quiet.
Everyone who is not tall or old is funny.
If someone is both rich and not humble then alice is either curious or not quiet and vice versa.
Everyone who is generous or not patient is not creative.
Everyone who is both not creative and not brave is brave and vice versa.
Everyone who is either wise or humble is both not curious and generous.
If fred is not tall or tall then someone is brave or humble.
If lucy is both not wise and not old then fred is either calm or not humble and vice versa.
Lucy is wise or old.
Someone is both not brave and creative.
John is either not patient or quiet.
Fred is not happy.
Someone is either funny or not strong.
Someone is not wise.
|
Fred is kind.
|
contradiction
|
(![X]:((humble(X)<~>~humble(X))=>(creative(X)&patient(X))))&
(![X]:((calm(X)|rich(X))=>(~calm(X)&creative(X))))&
((~funny(lucy))=>(?[X]:(old(X))))&
((?[X]:(rich(X)))<=>((~creative(john)|happy(john))))&
(![X]:((calm(X)<~>~rich(X))<=>(~old(X)|funny(X))))&
(![X]:((~brave(X)<~>~funny(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~tall(X)|kind(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~wise(X)|brave(X))<=>~funny(X)))&
(![X]:(~tall(X)=>(kind(X)<~>~quiet(X))))&
(![X]:((~tall(X)|old(X))=>funny(X)))&
((?[X]:((rich(X)&~humble(X))))<=>((curious(alice)<~>~quiet(alice))))&
(![X]:((generous(X)|~patient(X))=>~creative(X)))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
(![X]:((wise(X)<~>humble(X))=>(~curious(X)&generous(X))))&
(((~tall(fred)|tall(fred)))=>(?[X]:((brave(X)|humble(X)))))&
(((~wise(lucy)&~old(lucy)))<=>((calm(fred)<~>~humble(fred))))&
((wise(lucy)|old(lucy)))&
(?[X]:((~brave(X)&creative(X))))&
((~patient(john)<~>quiet(john)))&
(~happy(fred))&
(?[X]:((funny(X)<~>~strong(X))))&
(?[X]:(~wise(X)))
|
kind(fred)
|
[
"p0",
"p1",
"p5",
"p7",
"p9",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 1436455101973465438833236
% SZS output start Proof for 1436455101973465438833236
1. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (patient(X0) & creative(X0))) [input p0]
2. ! [X0] : ((rich(X0) | calm(X0)) => (creative(X0) & ~calm(X0))) [input p1]
6. ! [X0] : ((~brave(X0) <~> ~funny(X0)) => (kind(X0) <~> ~calm(X0))) [input p5]
8. ! [X0] : ((brave(X0) | ~wise(X0)) <=> ~funny(X0)) [input p7]
10. ! [X0] : ((old(X0) | ~tall(X0)) => funny(X0)) [input p9]
12. ! [X0] : ((~patient(X0) | generous(X0)) => ~creative(X0)) [input p11]
13. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> brave(X0)) [input p12]
14. ! [X0] : ((wise(X0) <~> humble(X0)) => (generous(X0) & ~curious(X0))) [input p13]
16. (~old(lucy) & ~wise(lucy)) <=> (calm(fred) <~> ~humble(fred)) [input p15]
17. old(lucy) | wise(lucy) [input p16]
23. kind(fred) [input hypothesis]
24. ! [X0] : ((patient(X0) & creative(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 1]
25. ! [X0] : ((creative(X0) & ~calm(X0)) | (~rich(X0) & ~calm(X0))) [ennf transformation 2]
27. ! [X0] : ((kind(X0) <~> ~calm(X0)) | (~brave(X0) <=> ~funny(X0))) [ennf transformation 6]
30. ! [X0] : (funny(X0) | (~old(X0) & tall(X0))) [ennf transformation 10]
31. ! [X0] : (~creative(X0) | (patient(X0) & ~generous(X0))) [ennf transformation 12]
32. ! [X0] : ((generous(X0) & ~curious(X0)) | (wise(X0) <=> humble(X0))) [ennf transformation 14]
34. ! [X0] : ((patient(X0) & creative(X0)) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 24]
44. ! [X0] : (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) [nnf transformation 27]
46. ! [X0] : (((brave(X0) | ~wise(X0)) | funny(X0)) & (~funny(X0) | (~brave(X0) & wise(X0)))) [nnf transformation 8]
47. ! [X0] : ((brave(X0) | ~wise(X0) | funny(X0)) & (~funny(X0) | (~brave(X0) & wise(X0)))) [flattening 46]
53. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | creative(X0)))) [nnf transformation 13]
54. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | creative(X0))) [flattening 53]
55. ! [X0] : ((generous(X0) & ~curious(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) [nnf transformation 32]
58. ((~old(lucy) & ~wise(lucy)) | ((calm(fred) | humble(fred)) & (~humble(fred) | ~calm(fred)))) & (((humble(fred) | ~calm(fred)) & (~humble(fred) | calm(fred))) | (old(lucy) | wise(lucy))) [nnf transformation 16]
59. ((~old(lucy) & ~wise(lucy)) | ((calm(fred) | humble(fred)) & (~humble(fred) | ~calm(fred)))) & (((humble(fred) | ~calm(fred)) & (~humble(fred) | calm(fred))) | old(lucy) | wise(lucy)) [flattening 58]
68. creative(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
69. creative(X0) | humble(X0) | humble(X0) [cnf transformation 34]
72. ~calm(X0) | ~calm(X0) [cnf transformation 25]
88. calm(X0) | ~kind(X0) | ~funny(X0) | brave(X0) [cnf transformation 44]
94. ~funny(X0) | wise(X0) [cnf transformation 47]
96. ~wise(X0) | brave(X0) | funny(X0) [cnf transformation 47]
100. ~old(X0) | funny(X0) [cnf transformation 30]
107. ~creative(X0) | ~generous(X0) [cnf transformation 31]
111. ~brave(X0) | ~brave(X0) [cnf transformation 54]
115. generous(X0) | wise(X0) | ~humble(X0) [cnf transformation 55]
121. ~wise(lucy) | calm(fred) | humble(fred) [cnf transformation 59]
124. old(lucy) | wise(lucy) [cnf transformation 17]
133. kind(fred) [cnf transformation 23]
135. ~brave(X0) [duplicate literal removal 111]
136. ~calm(X0) [duplicate literal removal 72]
137. creative(X0) | ~humble(X0) [duplicate literal removal 68]
138. creative(X0) | humble(X0) [duplicate literal removal 69]
142. creative(X0) [subsumption resolution 137,138]
144. 1 <=> funny(lucy) [avatar definition]
146. funny(lucy) <- (1) [avatar component clause 144]
170. ~kind(X0) | ~funny(X0) | brave(X0) [subsumption resolution 88,136]
196. ~generous(X0) [subsumption resolution 107,142]
197. ~humble(X0) | wise(X0) [subsumption resolution 115,196]
213. 13 <=> humble(fred) [avatar definition]
215. humble(fred) <- (13) [avatar component clause 213]
217. 14 <=> old(lucy) [avatar definition]
218. old(lucy) <- (14) [avatar component clause 217]
221. ~wise(lucy) | humble(fred) [subsumption resolution 121,136]
223. 15 <=> wise(lucy) [avatar definition]
226. 13 | ~15 [avatar split clause 221,223,213]
229. 15 | 14 [avatar split clause 124,217,223]
244. funny(lucy) <- (14) [resolution 100,218]
245. 1 | ~14 [avatar split clause 244,217,144]
246. wise(lucy) <- (1) [resolution 146,94]
247. 15 | ~1 [avatar split clause 246,144,223]
254. wise(fred) <- (13) [resolution 197,215]
264. brave(fred) | funny(fred) <- (13) [resolution 96,254]
267. funny(fred) <- (13) [subsumption resolution 264,135]
300. ~funny(fred) | brave(fred) [resolution 170,133]
301. brave(fred) <- (13) [subsumption resolution 300,267]
302. $false <- (13) [subsumption resolution 301,135]
303. ~13 [avatar contradiction clause 302]
304. $false [avatar sat refutation 226,229,245,247,303]
% SZS output end Proof for 1436455101973465438833236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not quiet is humble or wise and vice versa. If mary is both calm and not rich then someone is curious or calm and vice versa. Everyone who is both not generous and generous is either not curious or not calm. Everyone who is not calm is both not humble and quiet and vice versa. Everyone who is both not calm and not humble is not old and vice versa. If someone is either not funny or generous then someone is both curious and not humble and vice versa. Everyone who is humble or not creative is old and vice versa. Everyone who is not calm or not funny is either not wise or humble. If susan is not generous or not patient then someone is both happy and quiet and vice versa. Everyone who is not funny or generous is either strong or not strong. Everyone who is both not curious and generous is both not rich and not happy. If someone is generous or patient then someone is funny or not strong and vice versa. If lucy is not calm then fred is either wise or not old and vice versa. Everyone who is not humble is both not strong and humble. Everyone who is wise or not old is either not happy or not old. If someone is humble then alice is wise or not patient. Someone is not tall or happy. Lucy is either quiet or not happy. Alice is either not strong or brave. Someone is not calm or creative. Mary is either not strong or not humble. Lucy is not creative. Paul is both patient and old. Someone is tall.
|
Mary is quiet.
|
contradiction
|
(![X]:((rich(X)<~>~quiet(X))<=>(humble(X)|wise(X))))&
(((calm(mary)&~rich(mary)))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((~generous(X)&generous(X))=>(~curious(X)<~>~calm(X))))&
(![X]:(~calm(X)<=>(~humble(X)&quiet(X))))&
(![X]:((~calm(X)&~humble(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>generous(X))))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((humble(X)|~creative(X))<=>old(X)))&
(![X]:((~calm(X)|~funny(X))=>(~wise(X)<~>humble(X))))&
(((~generous(susan)|~patient(susan)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|generous(X))=>(strong(X)<~>~strong(X))))&
(![X]:((~curious(X)&generous(X))=>(~rich(X)&~happy(X))))&
((?[X]:((generous(X)|patient(X))))<=>(?[X]:((funny(X)|~strong(X)))))&
((~calm(lucy))<=>((wise(fred)<~>~old(fred))))&
(![X]:(~humble(X)=>(~strong(X)&humble(X))))&
(![X]:((wise(X)|~old(X))=>(~happy(X)<~>~old(X))))&
((?[X]:(humble(X)))=>((wise(alice)|~patient(alice))))&
(?[X]:((~tall(X)|happy(X))))&
((quiet(lucy)<~>~happy(lucy)))&
((~strong(alice)<~>brave(alice)))&
(?[X]:((~calm(X)|creative(X))))&
((~strong(mary)<~>~humble(mary)))&
(~creative(lucy))&
((patient(paul)&old(paul)))&
(?[X]:(tall(X)))
|
quiet(mary)
|
[
"p0",
"p1",
"p3",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 391819591828090594436871
% SZS output start Proof for 391819591828090594436871
1. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (wise(X0) | humble(X0))) [input p0]
2. (~rich(mary) & calm(mary)) <=> ? [X0] : (calm(X0) | curious(X0)) [input p1]
4. ! [X0] : (~calm(X0) <=> (quiet(X0) & ~humble(X0))) [input p3]
14. ! [X0] : (~humble(X0) => (humble(X0) & ~strong(X0))) [input p13]
25. quiet(mary) [input hypothesis]
34. ! [X0] : ((humble(X0) & ~strong(X0)) | humble(X0)) [ennf transformation 14]
38. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 1]
39. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [flattening 38]
40. ((~rich(mary) & calm(mary)) | ! [X0] : (~calm(X0) & ~curious(X0))) & (? [X0] : (calm(X0) | curious(X0)) | (rich(mary) | ~calm(mary))) [nnf transformation 2]
41. ((~rich(mary) & calm(mary)) | ! [X0] : (~calm(X0) & ~curious(X0))) & (? [X0] : (calm(X0) | curious(X0)) | rich(mary) | ~calm(mary)) [flattening 40]
42. ((~rich(mary) & calm(mary)) | ! [X0] : (~calm(X0) & ~curious(X0))) & (? [X1] : (calm(X1) | curious(X1)) | rich(mary) | ~calm(mary)) [rectify 41]
43. ? [X1] : (calm(X1) | curious(X1)) => (calm(sK0) | curious(sK0)) [choice axiom]
44. ((~rich(mary) & calm(mary)) | ! [X0] : (~calm(X0) & ~curious(X0))) & ((calm(sK0) | curious(sK0)) | rich(mary) | ~calm(mary)) [skolemisation 42,43]
46. ! [X0] : ((~calm(X0) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | calm(X0))) [nnf transformation 4]
47. ! [X0] : ((~calm(X0) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | calm(X0))) [flattening 46]
82. ~humble(X0) | rich(X0) | ~quiet(X0) [cnf transformation 39]
90. ~rich(mary) | ~calm(X0) [cnf transformation 44]
93. ~humble(X0) | calm(X0) [cnf transformation 47]
132. humble(X0) | humble(X0) [cnf transformation 34]
150. quiet(mary) [cnf transformation 25]
152. humble(X0) [duplicate literal removal 132]
154. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
155. ~calm(X0) <- (1) [avatar component clause 154]
157. 2 <=> rich(mary) [avatar definition]
160. 1 | ~2 [avatar split clause 90,157,154]
334. calm(X0) [resolution 93,152]
357. ~quiet(X0) | rich(X0) [resolution 82,152]
359. rich(mary) [resolution 357,150]
362. 2 [avatar split clause 359,157]
363. $false <- (1) [subsumption resolution 155,334]
364. ~1 [avatar contradiction clause 363]
365. $false [avatar sat refutation 160,362,364]
% SZS output end Proof for 391819591828090594436871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not humble is patient or not wise. If someone is not patient or funny then lucy is both not funny and creative. If someone is happy or humble then fred is either strong or tall and vice versa. Everyone who is both funny and not funny is either not humble or funny and vice versa. Everyone who is either wise or not wise is both not creative and not rich and vice versa. Everyone who is not creative is happy and vice versa. If lucy is patient then fred is not creative or not happy and vice versa. If someone is not tall or not strong then fred is either happy or not calm. If someone is rich then someone is both old and rich and vice versa. If someone is either not tall or not curious then someone is either not generous or kind and vice versa. Everyone who is both not humble and brave is both creative and funny and vice versa. Everyone who is not curious or not quiet is not wise or curious and vice versa. Everyone who is both not wise and not kind is not tall and vice versa. Everyone who is both funny and kind is patient. Everyone who is both old and not rich is not creative or not generous. If someone is not brave then john is both funny and not wise. Alice is not calm or not old. Fred is not quiet. Paul is either brave or kind. Someone is not generous. Someone is both generous and tall. Someone is not strong. Susan is both humble and not generous. John is either not kind or happy.
|
Fred is calm.
|
entailment
|
(![X]:((~kind(X)&~humble(X))=>(patient(X)|~wise(X))))&
((?[X]:((~patient(X)|funny(X))))=>((~funny(lucy)&creative(lucy))))&
((?[X]:((happy(X)|humble(X))))<=>((strong(fred)<~>tall(fred))))&
(![X]:((funny(X)&~funny(X))<=>(~humble(X)<~>funny(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(~creative(X)&~rich(X))))&
(![X]:(~creative(X)<=>happy(X)))&
((patient(lucy))<=>((~creative(fred)|~happy(fred))))&
((?[X]:((~tall(X)|~strong(X))))=>((happy(fred)<~>~calm(fred))))&
((?[X]:(rich(X)))<=>(?[X]:((old(X)&rich(X)))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(![X]:((~humble(X)&brave(X))<=>(creative(X)&funny(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(~wise(X)|curious(X))))&
(![X]:((~wise(X)&~kind(X))<=>~tall(X)))&
(![X]:((funny(X)&kind(X))=>patient(X)))&
(![X]:((old(X)&~rich(X))=>(~creative(X)|~generous(X))))&
((?[X]:(~brave(X)))=>((funny(john)&~wise(john))))&
((~calm(alice)|~old(alice)))&
(~quiet(fred))&
((brave(paul)<~>kind(paul)))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)&tall(X))))&
(?[X]:(~strong(X)))&
((humble(susan)&~generous(susan)))&
((~kind(john)<~>happy(john)))
|
calm(fred)
|
[
"p2",
"p4",
"p5",
"p7",
"hypothesis"
] |
% SZS status Unsatisfiable for 675103769177040952888153
% SZS output start Proof for 675103769177040952888153
3. ? [X0] : (humble(X0) | happy(X0)) <=> (strong(fred) <~> tall(fred)) [input p2]
5. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~rich(X0) & ~creative(X0))) [input p4]
6. ! [X0] : (~creative(X0) <=> happy(X0)) [input p5]
8. ? [X0] : (~strong(X0) | ~tall(X0)) => (happy(fred) <~> ~calm(fred)) [input p7]
25. ~calm(fred) [input hypothesis]
31. (happy(fred) <~> ~calm(fred)) | ! [X0] : (strong(X0) & tall(X0)) [ennf transformation 8]
37. (? [X0] : (humble(X0) | happy(X0)) | ((strong(fred) | ~tall(fred)) & (tall(fred) | ~strong(fred)))) & (((~tall(fred) | ~strong(fred)) & (tall(fred) | strong(fred))) | ! [X0] : (~humble(X0) & ~happy(X0))) [nnf transformation 3]
38. (? [X0] : (humble(X0) | happy(X0)) | ((strong(fred) | ~tall(fred)) & (tall(fred) | ~strong(fred)))) & (((~tall(fred) | ~strong(fred)) & (tall(fred) | strong(fred))) | ! [X1] : (~humble(X1) & ~happy(X1))) [rectify 37]
39. ? [X0] : (humble(X0) | happy(X0)) => (humble(sK0) | happy(sK0)) [choice axiom]
40. ((humble(sK0) | happy(sK0)) | ((strong(fred) | ~tall(fred)) & (tall(fred) | ~strong(fred)))) & (((~tall(fred) | ~strong(fred)) & (tall(fred) | strong(fred))) | ! [X1] : (~humble(X1) & ~happy(X1))) [skolemisation 38,39]
43. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (rich(X0) | creative(X0))) & ((~rich(X0) & ~creative(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 5]
44. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | rich(X0) | creative(X0)) & ((~rich(X0) & ~creative(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [flattening 43]
45. ! [X0] : ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))) [nnf transformation 6]
48. ((calm(fred) | ~happy(fred)) & (~calm(fred) | happy(fred))) | ! [X0] : (strong(X0) & tall(X0)) [nnf transformation 31]
80. ~tall(fred) | ~strong(fred) | ~happy(X1) [cnf transformation 40]
90. ~creative(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 44]
91. ~creative(X0) | wise(X0) | wise(X0) [cnf transformation 44]
96. happy(X0) | creative(X0) [cnf transformation 45]
103. calm(fred) | ~happy(fred) | tall(X0) [cnf transformation 48]
104. calm(fred) | ~happy(fred) | strong(X0) [cnf transformation 48]
143. ~calm(fred) [cnf transformation 25]
146. ~creative(X0) | ~wise(X0) [duplicate literal removal 90]
147. ~creative(X0) | wise(X0) [duplicate literal removal 91]
173. 5 <=> tall(fred) [avatar definition]
175. ~tall(fred) <- (~5) [avatar component clause 173]
177. 6 <=> strong(fred) [avatar definition]
178. ~strong(fred) <- (~6) [avatar component clause 177]
195. 10 <=> ! [X1] : ~happy(X1) [avatar definition]
196. ~happy(X1) <- (10) [avatar component clause 195]
197. 10 | ~6 | ~5 [avatar split clause 80,173,177,195]
201. ~creative(X0) [subsumption resolution 146,147]
202. happy(X0) [subsumption resolution 96,201]
204. calm(fred) | strong(X0) [subsumption resolution 104,202]
206. 11 <=> ! [X0] : strong(X0) [avatar definition]
207. strong(X0) <- (11) [avatar component clause 206]
209. 12 <=> calm(fred) [avatar definition]
212. 11 | 12 [avatar split clause 204,209,206]
213. calm(fred) | tall(X0) [subsumption resolution 103,202]
215. 13 <=> ! [X0] : tall(X0) [avatar definition]
216. tall(X0) <- (13) [avatar component clause 215]
217. 13 | 12 [avatar split clause 213,209,215]
288. ~12 [avatar split clause 143,209]
289. $false <- (~6, 11) [subsumption resolution 178,207]
290. 6 | ~11 [avatar contradiction clause 289]
293. $false <- (10) [subsumption resolution 196,202]
294. ~10 [avatar contradiction clause 293]
295. $false <- (~5, 13) [subsumption resolution 175,216]
296. 5 | ~13 [avatar contradiction clause 295]
297. $false [avatar sat refutation 197,212,217,288,290,294,296]
% SZS output end Proof for 675103769177040952888153
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not humble is either generous or rich. Everyone who is both generous and quiet is not brave. Everyone who is both kind and not humble is both not brave and not calm and vice versa. Everyone who is not generous or not funny is both calm and not wise. If someone is both not tall and not strong then someone is either not brave or not rich. If someone is both wise and happy then someone is humble and vice versa. If someone is funny then someone is calm or not tall. Everyone who is either quiet or not rich is not wise. If someone is not patient or strong then lucy is either quiet or calm and vice versa. Everyone who is either funny or not kind is not brave or strong. Everyone who is either wise or not brave is either creative or strong and vice versa. If someone is both not funny and not curious then john is curious and vice versa. Everyone who is both brave and not patient is both not happy and wise. Everyone who is either strong or not patient is not rich. If someone is not tall then alice is not wise. If someone is both not kind and curious then alice is not humble and vice versa. Alice is not rich. Mary is not funny. Paul is either not humble or brave. Lucy is not old. Fred is both brave and rich. Someone is both strong and generous. Someone is both rich and funny. Paul is both not curious and not tall.
|
Mary is tall.
|
neutral
|
(![X]:((generous(X)&~humble(X))=>(generous(X)<~>rich(X))))&
(![X]:((generous(X)&quiet(X))=>~brave(X)))&
(![X]:((kind(X)&~humble(X))<=>(~brave(X)&~calm(X))))&
(![X]:((~generous(X)|~funny(X))=>(calm(X)&~wise(X))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((wise(X)&happy(X))))<=>(?[X]:(humble(X))))&
((?[X]:(funny(X)))=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((quiet(X)<~>~rich(X))=>~wise(X)))&
((?[X]:((~patient(X)|strong(X))))<=>((quiet(lucy)<~>calm(lucy))))&
(![X]:((funny(X)<~>~kind(X))=>(~brave(X)|strong(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(creative(X)<~>strong(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(curious(john)))&
(![X]:((brave(X)&~patient(X))=>(~happy(X)&wise(X))))&
(![X]:((strong(X)<~>~patient(X))=>~rich(X)))&
((?[X]:(~tall(X)))=>(~wise(alice)))&
((?[X]:((~kind(X)&curious(X))))<=>(~humble(alice)))&
(~rich(alice))&
(~funny(mary))&
((~humble(paul)<~>brave(paul)))&
(~old(lucy))&
((brave(fred)&rich(fred)))&
(?[X]:((strong(X)&generous(X))))&
(?[X]:((rich(X)&funny(X))))&
((~curious(paul)&~tall(paul)))
|
tall(mary)
|
[] | null | 0 |
Everyone who is not patient or tall is not generous and vice versa. Everyone who is not quiet or not happy is either not happy or tall. If someone is creative then susan is old and vice versa. If paul is generous then mary is tall and vice versa. Everyone who is quiet or not tall is kind. Everyone who is both rich and not curious is both old and not old and vice versa. Everyone who is kind or old is happy. Everyone who is both not curious and not calm is either not happy or brave and vice versa. Everyone who is strong or tall is both humble and brave. If lucy is either generous or not strong then someone is old or not calm and vice versa. Everyone who is generous is rich or not happy and vice versa. Everyone who is either not calm or curious is not quiet or humble. Everyone who is not kind or funny is not brave. Everyone who is either not creative or tall is either calm or not generous and vice versa. Everyone who is either not wise or quiet is either not generous or wise. Paul is either not brave or tall. Someone is strong. Someone is not tall or not generous. Fred is not tall or not old. Lucy is either humble or old. Someone is not curious or not patient. Mary is either not creative or tall.
|
Mary is patient.
|
neutral
|
(![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>(old(susan)))&
((generous(paul))<=>(tall(mary)))&
(![X]:((quiet(X)|~tall(X))=>kind(X)))&
(![X]:((rich(X)&~curious(X))<=>(old(X)&~old(X))))&
(![X]:((kind(X)|old(X))=>happy(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
((~brave(paul)<~>tall(paul)))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)|~generous(X))))&
((~tall(fred)|~old(fred)))&
((humble(lucy)<~>old(lucy)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))
|
patient(mary)
|
[] | null | 0 |
Everyone who is not humble or happy is not humble and vice versa.
Everyone who is wise or not kind is tall and vice versa.
Everyone who is kind or not old is both calm and old and vice versa.
Everyone who is both funny and strong is not kind or happy.
Everyone who is not rich is not calm or not curious.
Everyone who is either calm or not old is both not quiet and not patient and vice versa.
If john is either quiet or humble then someone is calm or generous and vice versa.
Everyone who is both not calm and happy is not brave.
Everyone who is not calm is not strong.
If someone is wise or tall then someone is both old and creative.
Everyone who is both rich and calm is not generous or old and vice versa.
Everyone who is both creative and quiet is either not patient or patient.
If someone is either old or generous then susan is both not rich and not quiet and vice versa.
Everyone who is both not patient and brave is both not quiet and old.
Everyone who is either not wise or not generous is either kind or not rich.
John is generous.
Someone is not calm or not tall.
Alice is either strong or happy.
Someone is tall or calm.
|
Susan is generous.
|
entailment
|
(![X]:((~humble(X)|happy(X))<=>~humble(X)))&
(![X]:((wise(X)|~kind(X))<=>tall(X)))&
(![X]:((kind(X)|~old(X))<=>(calm(X)&old(X))))&
(![X]:((funny(X)&strong(X))=>(~kind(X)|happy(X))))&
(![X]:(~rich(X)=>(~calm(X)|~curious(X))))&
(![X]:((calm(X)<~>~old(X))<=>(~quiet(X)&~patient(X))))&
(((quiet(john)<~>humble(john)))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~calm(X)&happy(X))=>~brave(X)))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((wise(X)|tall(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((rich(X)&calm(X))<=>(~generous(X)|old(X))))&
(![X]:((creative(X)&quiet(X))=>(~patient(X)<~>patient(X))))&
((?[X]:((old(X)<~>generous(X))))<=>((~rich(susan)&~quiet(susan))))&
(![X]:((~patient(X)&brave(X))=>(~quiet(X)&old(X))))&
(![X]:((~wise(X)<~>~generous(X))=>(kind(X)<~>~rich(X))))&
(generous(john))&
(?[X]:((~calm(X)|~tall(X))))&
((strong(alice)<~>happy(alice)))&
(?[X]:((tall(X)|calm(X))))
|
generous(susan)
|
[
"p2",
"p10",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 6580718762548510836950578
% SZS output start Proof for 6580718762548510836950578
3. ! [X0] : ((~old(X0) | kind(X0)) <=> (old(X0) & calm(X0))) [input p2]
11. ! [X0] : ((calm(X0) & rich(X0)) <=> (old(X0) | ~generous(X0))) [input p10]
13. ? [X0] : (old(X0) <~> generous(X0)) <=> (~quiet(susan) & ~rich(susan)) [input p12]
20. ~generous(susan) [input hypothesis]
35. ! [X0] : (((~old(X0) | kind(X0)) | (~old(X0) | ~calm(X0))) & ((old(X0) & calm(X0)) | (old(X0) & ~kind(X0)))) [nnf transformation 3]
36. ! [X0] : ((~old(X0) | kind(X0) | ~old(X0) | ~calm(X0)) & ((old(X0) & calm(X0)) | (old(X0) & ~kind(X0)))) [flattening 35]
46. ! [X0] : (((calm(X0) & rich(X0)) | (~old(X0) & generous(X0))) & ((old(X0) | ~generous(X0)) | (~calm(X0) | ~rich(X0)))) [nnf transformation 11]
47. ! [X0] : (((calm(X0) & rich(X0)) | (~old(X0) & generous(X0))) & (old(X0) | ~generous(X0) | ~calm(X0) | ~rich(X0))) [flattening 46]
49. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | (quiet(susan) | rich(susan))) & ((~quiet(susan) & ~rich(susan)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 13]
50. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | quiet(susan) | rich(susan)) & ((~quiet(susan) & ~rich(susan)) | ! [X0] : ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [flattening 49]
51. (? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) | quiet(susan) | rich(susan)) & ((~quiet(susan) & ~rich(susan)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [rectify 50]
52. ? [X0] : ((~generous(X0) | ~old(X0)) & (generous(X0) | old(X0))) => ((~generous(sK2) | ~old(sK2)) & (generous(sK2) | old(sK2))) [choice axiom]
53. (((~generous(sK2) | ~old(sK2)) & (generous(sK2) | old(sK2))) | quiet(susan) | rich(susan)) & ((~quiet(susan) & ~rich(susan)) | ! [X1] : ((old(X1) | ~generous(X1)) & (generous(X1) | ~old(X1)))) [skolemisation 51,52]
69. old(X0) | old(X0) [cnf transformation 36]
90. rich(X0) | ~old(X0) [cnf transformation 47]
95. ~rich(susan) | generous(X1) | ~old(X1) [cnf transformation 53]
110. ~generous(susan) [cnf transformation 20]
111. old(X0) [duplicate literal removal 69]
157. rich(X0) [subsumption resolution 90,111]
160. 10 <=> ! [X1] : generous(X1) [avatar definition]
161. generous(X1) <- (10) [avatar component clause 160]
167. generous(X1) | ~old(X1) [subsumption resolution 95,157]
168. generous(X1) [subsumption resolution 167,111]
169. 10 [avatar split clause 168,160]
183. $false <- (10) [resolution 161,110]
184. ~10 [avatar contradiction clause 183]
185. $false [avatar sat refutation 169,184]
% SZS output end Proof for 6580718762548510836950578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and strong then john is either wise or creative and vice versa.
Everyone who is either not kind or creative is both tall and not patient.
Everyone who is strong is either creative or not curious and vice versa.
If someone is not wise or not kind then someone is not calm or wise.
Everyone who is calm or not humble is creative and vice versa.
If someone is not rich then someone is either not old or tall.
If someone is both not tall and calm then fred is either creative or not old.
Everyone who is brave or generous is either kind or not strong and vice versa.
If someone is not happy or not kind then susan is either old or creative and vice versa.
If fred is both old and not kind then john is kind and vice versa.
Everyone who is not strong is not calm or not tall.
Everyone who is generous is not wise.
Everyone who is either not calm or tall is creative or old and vice versa.
If someone is both not strong and brave then someone is either wise or brave and vice versa.
Everyone who is not quiet is not kind and vice versa.
Everyone who is either not generous or not strong is brave and vice versa.
John is both not generous and not humble.
Someone is tall or generous.
Someone is not creative.
Someone is strong or not quiet.
Alice is either not calm or quiet.
Someone is either not strong or quiet.
Someone is curious or kind.
Paul is not tall or tall.
|
Fred is not kind.
|
entailment
|
((?[X]:((brave(X)&strong(X))))<=>((wise(john)<~>creative(john))))&
(![X]:((~kind(X)<~>creative(X))=>(tall(X)&~patient(X))))&
(![X]:(strong(X)<=>(creative(X)<~>~curious(X))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((~calm(X)|wise(X)))))&
(![X]:((calm(X)|~humble(X))<=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((~old(X)<~>tall(X)))))&
((?[X]:((~tall(X)&calm(X))))=>((creative(fred)<~>~old(fred))))&
(![X]:((brave(X)|generous(X))<=>(kind(X)<~>~strong(X))))&
((?[X]:((~happy(X)|~kind(X))))<=>((old(susan)<~>creative(susan))))&
(((old(fred)&~kind(fred)))<=>(kind(john)))&
(![X]:(~strong(X)=>(~calm(X)|~tall(X))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:((~calm(X)<~>tall(X))<=>(creative(X)|old(X))))&
((?[X]:((~strong(X)&brave(X))))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:(~quiet(X)<=>~kind(X)))&
(![X]:((~generous(X)<~>~strong(X))<=>brave(X)))&
((~generous(john)&~humble(john)))&
(?[X]:((tall(X)|generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)|~quiet(X))))&
((~calm(alice)<~>quiet(alice)))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:((curious(X)|kind(X))))&
((~tall(paul)|tall(paul)))
|
~kind(fred)
|
[
"p7",
"p9",
"p15",
"p16",
"hypothesis"
] |
% SZS status Unsatisfiable for 4538886628228014783295796
% SZS output start Proof for 4538886628228014783295796
8. ! [X0] : ((generous(X0) | brave(X0)) <=> (kind(X0) <~> ~strong(X0))) [input p7]
10. (~kind(fred) & old(fred)) <=> kind(john) [input p9]
16. ! [X0] : ((~generous(X0) <~> ~strong(X0)) <=> brave(X0)) [input p15]
17. ~humble(john) & ~generous(john) [input p16]
25. kind(fred) [input hypothesis]
49. ! [X0] : (((generous(X0) | brave(X0)) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (~generous(X0) & ~brave(X0)))) [nnf transformation 8]
50. ! [X0] : ((generous(X0) | brave(X0) | ((kind(X0) | strong(X0)) & (~strong(X0) | ~kind(X0)))) & (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (~generous(X0) & ~brave(X0)))) [flattening 49]
55. ((~kind(fred) & old(fred)) | ~kind(john)) & (kind(john) | (kind(fred) | ~old(fred))) [nnf transformation 10]
56. ((~kind(fred) & old(fred)) | ~kind(john)) & (kind(john) | kind(fred) | ~old(fred)) [flattening 55]
65. ! [X0] : ((((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | ~brave(X0)) & (brave(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))))) [nnf transformation 16]
97. ~strong(X0) | kind(X0) | ~brave(X0) [cnf transformation 50]
102. generous(X0) | brave(X0) | kind(X0) | strong(X0) [cnf transformation 50]
111. ~kind(fred) | ~kind(john) [cnf transformation 56]
128. ~strong(X0) | brave(X0) | generous(X0) [cnf transformation 65]
131. ~brave(X0) | generous(X0) | strong(X0) [cnf transformation 65]
132. ~generous(john) [cnf transformation 17]
143. kind(fred) [cnf transformation 25]
224. 18 <=> kind(john) [avatar definition]
226. ~kind(john) <- (~18) [avatar component clause 224]
228. 19 <=> kind(fred) [avatar definition]
231. ~18 | ~19 [avatar split clause 111,228,224]
315. 19 [avatar split clause 143,228]
356. 42 <=> strong(john) [avatar definition]
357. strong(john) <- (42) [avatar component clause 356]
358. ~strong(john) <- (~42) [avatar component clause 356]
407. brave(john) | kind(john) | strong(john) [resolution 102,132]
416. brave(john) | strong(john) <- (~18) [subsumption resolution 407,226]
417. brave(john) <- (~18, ~42) [subsumption resolution 416,358]
419. generous(john) | strong(john) <- (~18, ~42) [resolution 417,131]
422. strong(john) <- (~18, ~42) [subsumption resolution 419,132]
423. $false <- (~18, ~42) [subsumption resolution 422,358]
424. 18 | 42 [avatar contradiction clause 423]
431. brave(john) | generous(john) <- (42) [resolution 357,128]
432. kind(john) | ~brave(john) <- (42) [resolution 357,97]
433. brave(john) <- (42) [subsumption resolution 431,132]
434. ~brave(john) <- (~18, 42) [subsumption resolution 432,226]
435. $false <- (~18, 42) [subsumption resolution 434,433]
436. 18 | ~42 [avatar contradiction clause 435]
437. $false [avatar sat refutation 231,315,424,436]
% SZS output end Proof for 4538886628228014783295796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is rich or wise and vice versa.
Everyone who is not kind is either not generous or wise.
Everyone who is patient is either not wise or strong.
Everyone who is rich or patient is both wise and not patient and vice versa.
Everyone who is both humble and happy is wise or happy and vice versa.
Everyone who is not strong or not generous is either tall or not curious and vice versa.
If someone is either not quiet or not curious then someone is both not old and funny.
Everyone who is patient or not kind is not strong or happy and vice versa.
Everyone who is not old or not happy is curious and vice versa.
Everyone who is either creative or not patient is either not quiet or not tall and vice versa.
Everyone who is either not calm or old is either not quiet or not kind.
Everyone who is not strong is either strong or generous.
If paul is either curious or quiet then alice is rich or wise.
Everyone who is not humble is not generous or not quiet and vice versa.
John is not happy or tall.
Someone is either not funny or not curious.
Someone is not creative or rich.
Fred is calm.
Someone is either not kind or not funny.
|
Alice is funny.
|
neutral
|
(![X]:(~generous(X)<=>(rich(X)|wise(X))))&
(![X]:(~kind(X)=>(~generous(X)<~>wise(X))))&
(![X]:(patient(X)=>(~wise(X)<~>strong(X))))&
(![X]:((rich(X)|patient(X))<=>(wise(X)&~patient(X))))&
(![X]:((humble(X)&happy(X))<=>(wise(X)|happy(X))))&
(![X]:((~strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
((?[X]:((~quiet(X)<~>~curious(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((patient(X)|~kind(X))<=>(~strong(X)|happy(X))))&
(![X]:((~old(X)|~happy(X))<=>curious(X)))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~calm(X)<~>old(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(~strong(X)=>(strong(X)<~>generous(X))))&
(((curious(paul)<~>quiet(paul)))=>((rich(alice)|wise(alice))))&
(![X]:(~humble(X)<=>(~generous(X)|~quiet(X))))&
((~happy(john)|tall(john)))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~creative(X)|rich(X))))&
(calm(fred))&
(?[X]:((~kind(X)<~>~funny(X))))
|
funny(alice)
|
[] | null | 0 |
Everyone who is rich or curious is either calm or funny. Everyone who is both patient and not quiet is not curious and vice versa. Everyone who is wise is not rich or not calm and vice versa. If someone is both rich and not curious then john is both brave and creative. If john is either generous or not happy then lucy is both old and happy and vice versa. Everyone who is rich or generous is humble or not generous and vice versa. If someone is not wise or not curious then someone is not curious. Everyone who is either kind or not generous is both not wise and creative and vice versa. Everyone who is either brave or curious is brave. Everyone who is rich is not rich or rich and vice versa. If someone is not funny then someone is either tall or old and vice versa. If john is tall then john is either generous or not generous and vice versa. If susan is not wise then alice is kind. Everyone who is either creative or wise is not humble or funny and vice versa. If someone is both not patient and curious then paul is curious and vice versa. Someone is not funny. Mary is both funny and not tall. Lucy is both brave and not humble. Someone is either not funny or quiet. Someone is not patient. Alice is not calm.
|
John is wise.
|
contradiction
|
(![X]:((rich(X)|curious(X))=>(calm(X)<~>funny(X))))&
(![X]:((patient(X)&~quiet(X))<=>~curious(X)))&
(![X]:(wise(X)<=>(~rich(X)|~calm(X))))&
((?[X]:((rich(X)&~curious(X))))=>((brave(john)&creative(john))))&
(((generous(john)<~>~happy(john)))<=>((old(lucy)&happy(lucy))))&
(![X]:((rich(X)|generous(X))<=>(humble(X)|~generous(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~wise(X)&creative(X))))&
(![X]:((brave(X)<~>curious(X))=>brave(X)))&
(![X]:(rich(X)<=>(~rich(X)|rich(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((tall(X)<~>old(X)))))&
((tall(john))<=>((generous(john)<~>~generous(john))))&
((~wise(susan))=>(kind(alice)))&
(![X]:((creative(X)<~>wise(X))<=>(~humble(X)|funny(X))))&
((?[X]:((~patient(X)&curious(X))))<=>(curious(paul)))&
(?[X]:(~funny(X)))&
((funny(mary)&~tall(mary)))&
((brave(lucy)&~humble(lucy)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:(~patient(X)))&
(~calm(alice))
|
wise(john)
|
[
"p0",
"p2",
"p3",
"p6",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 9025351647159083188378242
% SZS output start Proof for 9025351647159083188378242
1. ! [X0] : ((curious(X0) | rich(X0)) => (calm(X0) <~> funny(X0))) [input p0]
3. ! [X0] : (wise(X0) <=> (~calm(X0) | ~rich(X0))) [input p2]
4. ? [X0] : (~curious(X0) & rich(X0)) => (creative(john) & brave(john)) [input p3]
7. ? [X0] : (~curious(X0) | ~wise(X0)) => ? [X0] : ~curious(X0) [input p6]
10. ! [X0] : (rich(X0) <=> (rich(X0) | ~rich(X0))) [input p9]
11. ? [X0] : ~funny(X0) <=> ? [X0] : (tall(X0) <~> old(X0)) [input p10]
14. ! [X0] : ((creative(X0) <~> wise(X0)) <=> (funny(X0) | ~humble(X0))) [input p13]
16. ? [X0] : ~funny(X0) [input p15]
22. wise(john) [input hypothesis]
23. ? [X0] : (~curious(X0) | ~wise(X0)) => ? [X1] : ~curious(X1) [rectify 7]
24. ? [X0] : ~funny(X0) <=> ? [X1] : (tall(X1) <~> old(X1)) [rectify 11]
25. ! [X0] : ((calm(X0) <~> funny(X0)) | (~curious(X0) & ~rich(X0))) [ennf transformation 1]
26. (creative(john) & brave(john)) | ! [X0] : (curious(X0) | ~rich(X0)) [ennf transformation 4]
27. ? [X1] : ~curious(X1) | ! [X0] : (curious(X0) & wise(X0)) [ennf transformation 23]
30. ! [X0] : (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (~curious(X0) & ~rich(X0))) [nnf transformation 25]
33. ! [X0] : ((wise(X0) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | ~wise(X0))) [nnf transformation 3]
34. ! [X0] : ((wise(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | ~wise(X0))) [flattening 33]
39. ? [X0] : ~curious(X0) | ! [X1] : (curious(X1) & wise(X1)) [rectify 27]
40. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
41. ~curious(sK0) | ! [X1] : (curious(X1) & wise(X1)) [skolemisation 39,40]
45. ! [X0] : ((rich(X0) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | ~rich(X0))) [nnf transformation 10]
46. ! [X0] : ((rich(X0) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | ~rich(X0))) [flattening 45]
47. (? [X0] : ~funny(X0) | ! [X1] : ((tall(X1) | ~old(X1)) & (old(X1) | ~tall(X1)))) & (? [X1] : ((~old(X1) | ~tall(X1)) & (old(X1) | tall(X1))) | ! [X0] : funny(X0)) [nnf transformation 24]
48. (? [X0] : ~funny(X0) | ! [X1] : ((tall(X1) | ~old(X1)) & (old(X1) | ~tall(X1)))) & (? [X2] : ((~old(X2) | ~tall(X2)) & (old(X2) | tall(X2))) | ! [X3] : funny(X3)) [rectify 47]
49. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
50. ? [X2] : ((~old(X2) | ~tall(X2)) & (old(X2) | tall(X2))) => ((~old(sK2) | ~tall(sK2)) & (old(sK2) | tall(sK2))) [choice axiom]
51. (~funny(sK1) | ! [X1] : ((tall(X1) | ~old(X1)) & (old(X1) | ~tall(X1)))) & (((~old(sK2) | ~tall(sK2)) & (old(sK2) | tall(sK2))) | ! [X3] : funny(X3)) [skolemisation 48,50,49]
53. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~funny(X0) & humble(X0))) & ((funny(X0) | ~humble(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~funny(X0) & humble(X0))) & (funny(X0) | ~humble(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0))))) [flattening 53]
59. ? [X0] : ~funny(X0) => ~funny(sK4) [choice axiom]
60. ~funny(sK4) [skolemisation 16,59]
66. ~rich(X0) | calm(X0) | funny(X0) [cnf transformation 30]
73. ~wise(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 34]
77. creative(john) | curious(X0) | ~rich(X0) [cnf transformation 26]
88. ~curious(sK0) | wise(X1) [cnf transformation 41]
99. rich(X0) | rich(X0) [cnf transformation 46]
101. old(sK2) | tall(sK2) | funny(X3) [cnf transformation 51]
102. ~old(sK2) | ~tall(sK2) | funny(X3) [cnf transformation 51]
103. ~funny(sK1) | old(X1) | ~tall(X1) [cnf transformation 51]
104. ~funny(sK1) | tall(X1) | ~old(X1) [cnf transformation 51]
115. ~creative(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 54]
119. ~funny(sK4) [cnf transformation 60]
128. wise(john) [cnf transformation 22]
132. rich(X0) [duplicate literal removal 99]
137. 1 <=> ! [X0] : (curious(X0) | ~rich(X0)) [avatar definition]
138. curious(X0) | ~rich(X0) <- (1) [avatar component clause 137]
140. 2 <=> creative(john) [avatar definition]
142. creative(john) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 77,140,137]
172. 8 <=> ! [X1] : curious(X1) [avatar definition]
173. curious(X1) <- (8) [avatar component clause 172]
175. 9 <=> curious(sK0) [avatar definition]
177. ~curious(sK0) <- (~9) [avatar component clause 175]
180. 10 <=> ! [X1] : wise(X1) [avatar definition]
181. wise(X1) <- (10) [avatar component clause 180]
182. 10 | ~9 [avatar split clause 88,175,180]
184. 11 <=> ! [X1] : (tall(X1) | ~old(X1)) [avatar definition]
185. ~old(X1) | tall(X1) <- (11) [avatar component clause 184]
187. 12 <=> funny(sK1) [avatar definition]
189. ~funny(sK1) <- (~12) [avatar component clause 187]
190. 11 | ~12 [avatar split clause 104,187,184]
192. 13 <=> ! [X1] : (old(X1) | ~tall(X1)) [avatar definition]
193. ~tall(X1) | old(X1) <- (13) [avatar component clause 192]
194. 13 | ~12 [avatar split clause 103,187,192]
196. 14 <=> ! [X3] : funny(X3) [avatar definition]
197. funny(X3) <- (14) [avatar component clause 196]
199. 15 <=> tall(sK2) [avatar definition]
200. tall(sK2) <- (15) [avatar component clause 199]
201. ~tall(sK2) <- (~15) [avatar component clause 199]
203. 16 <=> old(sK2) [avatar definition]
204. old(sK2) <- (16) [avatar component clause 203]
205. ~old(sK2) <- (~16) [avatar component clause 203]
206. 14 | ~15 | ~16 [avatar split clause 102,203,199,196]
207. 14 | 15 | 16 [avatar split clause 101,203,199,196]
259. funny(X0) | calm(X0) [resolution 66,132]
268. calm(sK1) <- (~12) [resolution 259,189]
272. ~rich(john) | ~calm(john) [resolution 73,128]
276. ~calm(john) [subsumption resolution 272,132]
355. ~wise(john) | ~funny(john) <- (2) [resolution 115,142]
356. ~funny(john) <- (2) [subsumption resolution 355,128]
393. calm(john) <- (2) [resolution 356,259]
394. $false <- (2) [subsumption resolution 393,276]
395. ~2 [avatar contradiction clause 394]
402. curious(X0) <- (1) [subsumption resolution 138,132]
403. 8 | ~1 [avatar split clause 402,137,172]
404. $false <- (8, ~9) [resolution 173,177]
407. ~8 | 9 [avatar contradiction clause 404]
409. ~rich(X1) | ~calm(X1) <- (10) [resolution 181,73]
414. ~calm(X1) <- (10) [subsumption resolution 409,132]
421. $false <- (10, ~12) [resolution 414,268]
422. ~10 | 12 [avatar contradiction clause 421]
426. tall(sK2) <- (11, 16) [resolution 185,204]
427. $false <- (11, ~15, 16) [subsumption resolution 426,201]
428. ~11 | 15 | ~16 [avatar contradiction clause 427]
432. $false <- (14) [resolution 197,119]
435. ~14 [avatar contradiction clause 432]
437. old(sK2) <- (13, 15) [resolution 193,200]
438. $false <- (13, 15, ~16) [subsumption resolution 437,205]
439. ~13 | ~15 | 16 [avatar contradiction clause 438]
440. $false [avatar sat refutation 143,182,190,194,206,207,395,403,407,422,428,435,439]
% SZS output end Proof for 9025351647159083188378242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or quiet is generous and vice versa. If someone is both not creative and brave then mary is patient. If lucy is either not old or kind then susan is both not rich and humble and vice versa. Everyone who is happy is not funny and vice versa. Everyone who is both strong and curious is both calm and not wise. If alice is either generous or not rich then susan is not curious or patient and vice versa. Everyone who is either calm or patient is not quiet or not strong and vice versa. Everyone who is both quiet and not patient is both not curious and calm and vice versa. If someone is both not calm and not kind then someone is either funny or not patient and vice versa. If lucy is happy then someone is not generous or rich. Everyone who is both quiet and curious is generous or humble and vice versa. Everyone who is either strong or not patient is not generous or wise. Everyone who is both patient and wise is either not happy or generous and vice versa. If someone is either quiet or tall then someone is either wise or strong. Everyone who is either not old or not wise is generous or brave and vice versa. Someone is not old or funny. Fred is patient. Susan is either creative or curious. Paul is not happy or old. Lucy is either tall or not patient.
|
Alice is generous.
|
contradiction
|
(![X]:((curious(X)<~>quiet(X))<=>generous(X)))&
((?[X]:((~creative(X)&brave(X))))=>(patient(mary)))&
(((~old(lucy)<~>kind(lucy)))<=>((~rich(susan)&humble(susan))))&
(![X]:(happy(X)<=>~funny(X)))&
(![X]:((strong(X)&curious(X))=>(calm(X)&~wise(X))))&
(((generous(alice)<~>~rich(alice)))<=>((~curious(susan)|patient(susan))))&
(![X]:((calm(X)<~>patient(X))<=>(~quiet(X)|~strong(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~curious(X)&calm(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:((funny(X)<~>~patient(X)))))&
((happy(lucy))=>(?[X]:((~generous(X)|rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>(generous(X)|humble(X))))&
(![X]:((strong(X)<~>~patient(X))=>(~generous(X)|wise(X))))&
(![X]:((patient(X)&wise(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((quiet(X)<~>tall(X))))=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(generous(X)|brave(X))))&
(?[X]:((~old(X)|funny(X))))&
(patient(fred))&
((creative(susan)<~>curious(susan)))&
((~happy(paul)|old(paul)))&
((tall(lucy)<~>~patient(lucy)))
|
generous(alice)
|
[
"p0",
"p10",
"hypothesis"
] |
% SZS status Unsatisfiable for 2731293904723063333385422
% SZS output start Proof for 2731293904723063333385422
1. ! [X0] : ((curious(X0) <~> quiet(X0)) <=> generous(X0)) [input p0]
11. ! [X0] : ((curious(X0) & quiet(X0)) <=> (humble(X0) | generous(X0))) [input p10]
21. generous(alice) [input hypothesis]
31. ! [X0] : ((((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | ~generous(X0)) & (generous(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0))))) [nnf transformation 1]
48. ! [X0] : (((curious(X0) & quiet(X0)) | (~humble(X0) & ~generous(X0))) & ((humble(X0) | generous(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 11]
49. ! [X0] : (((curious(X0) & quiet(X0)) | (~humble(X0) & ~generous(X0))) & (humble(X0) | generous(X0) | ~curious(X0) | ~quiet(X0))) [flattening 48]
66. ~generous(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 31]
102. ~generous(X0) | quiet(X0) [cnf transformation 49]
104. ~generous(X0) | curious(X0) [cnf transformation 49]
131. generous(alice) [cnf transformation 21]
167. 8 <=> generous(alice) [avatar definition]
168. generous(alice) <- (8) [avatar component clause 167]
282. 8 [avatar split clause 131,167]
285. quiet(alice) <- (8) [resolution 102,168]
287. curious(alice) <- (8) [resolution 104,168]
295. ~curious(alice) | ~quiet(alice) <- (8) [resolution 66,168]
296. ~quiet(alice) <- (8) [subsumption resolution 295,287]
297. $false <- (8) [subsumption resolution 296,285]
298. ~8 [avatar contradiction clause 297]
299. $false [avatar sat refutation 282,298]
% SZS output end Proof for 2731293904723063333385422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either curious or not rich then lucy is both kind and funny and vice versa.
Everyone who is not calm is rich or old.
Everyone who is either not strong or strong is both calm and not humble.
If someone is not tall then susan is not tall.
Everyone who is both quiet and not strong is not strong or not tall.
If someone is wise or generous then susan is funny or not tall.
Everyone who is humble or wise is funny.
Everyone who is not happy is calm or not calm and vice versa.
If someone is quiet or funny then someone is both wise and kind.
If susan is either wise or not strong then someone is both not calm and creative.
Everyone who is either humble or rich is wise or not rich.
Everyone who is not generous or funny is not funny and vice versa.
If someone is both calm and not curious then someone is both happy and not kind.
Everyone who is tall is either patient or old and vice versa.
If mary is either quiet or not old then someone is either curious or not wise and vice versa.
Someone is either not quiet or rich.
Someone is either not calm or not patient.
Alice is not old or not patient.
John is either not brave or generous.
Someone is tall or not humble.
Lucy is either not happy or kind.
|
Lucy is not curious.
|
contradiction
|
(((curious(lucy)<~>~rich(lucy)))<=>((kind(lucy)&funny(lucy))))&
(![X]:(~calm(X)=>(rich(X)|old(X))))&
(![X]:((~strong(X)<~>strong(X))=>(calm(X)&~humble(X))))&
((?[X]:(~tall(X)))=>(~tall(susan)))&
(![X]:((quiet(X)&~strong(X))=>(~strong(X)|~tall(X))))&
((?[X]:((wise(X)|generous(X))))=>((funny(susan)|~tall(susan))))&
(![X]:((humble(X)|wise(X))=>funny(X)))&
(![X]:(~happy(X)<=>(calm(X)|~calm(X))))&
((?[X]:((quiet(X)|funny(X))))=>(?[X]:((wise(X)&kind(X)))))&
(((wise(susan)<~>~strong(susan)))=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((humble(X)<~>rich(X))=>(wise(X)|~rich(X))))&
(![X]:((~generous(X)|funny(X))<=>~funny(X)))&
((?[X]:((calm(X)&~curious(X))))=>(?[X]:((happy(X)&~kind(X)))))&
(![X]:(tall(X)<=>(patient(X)<~>old(X))))&
(((quiet(mary)<~>~old(mary)))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
((~old(alice)|~patient(alice)))&
((~brave(john)<~>generous(john)))&
(?[X]:((tall(X)|~humble(X))))&
((~happy(lucy)<~>kind(lucy)))
|
~curious(lucy)
|
[
"p2",
"p7",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 1386458328638892927737756
% SZS output start Proof for 1386458328638892927737756
3. ! [X0] : ((~strong(X0) <~> strong(X0)) => (~humble(X0) & calm(X0))) [input p2]
8. ! [X0] : (~happy(X0) <=> (~calm(X0) | calm(X0))) [input p7]
13. ? [X0] : (~curious(X0) & calm(X0)) => ? [X0] : (~kind(X0) & happy(X0)) [input p12]
22. ~curious(lucy) [input hypothesis]
24. ? [X0] : (~curious(X0) & calm(X0)) => ? [X1] : (~kind(X1) & happy(X1)) [rectify 13]
28. ! [X0] : ((~humble(X0) & calm(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 3]
39. ? [X1] : (~kind(X1) & happy(X1)) | ! [X0] : (curious(X0) | ~calm(X0)) [ennf transformation 24]
42. ! [X0] : ((~humble(X0) & calm(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 28]
43. ! [X0] : ((~happy(X0) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | happy(X0))) [nnf transformation 8]
44. ! [X0] : ((~happy(X0) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | happy(X0))) [flattening 43]
54. ? [X0] : (~kind(X0) & happy(X0)) | ! [X1] : (curious(X1) | ~calm(X1)) [rectify 39]
55. ? [X0] : (~kind(X0) & happy(X0)) => (~kind(sK2) & happy(sK2)) [choice axiom]
56. (~kind(sK2) & happy(sK2)) | ! [X1] : (curious(X1) | ~calm(X1)) [skolemisation 54,55]
79. calm(X0) | strong(X0) | strong(X0) [cnf transformation 42]
80. calm(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 42]
90. ~happy(X0) | ~calm(X0) [cnf transformation 44]
103. happy(sK2) | curious(X1) | ~calm(X1) [cnf transformation 56]
127. ~curious(lucy) [cnf transformation 22]
131. calm(X0) | strong(X0) [duplicate literal removal 79]
132. calm(X0) | ~strong(X0) [duplicate literal removal 80]
144. 3 <=> curious(lucy) [avatar definition]
146. ~curious(lucy) <- (~3) [avatar component clause 144]
158. calm(X0) [subsumption resolution 131,132]
179. ~happy(X0) [subsumption resolution 90,158]
214. 16 <=> ! [X1] : curious(X1) [avatar definition]
215. curious(X1) <- (16) [avatar component clause 214]
221. curious(X1) | ~calm(X1) [subsumption resolution 103,179]
222. curious(X1) [subsumption resolution 221,158]
223. 16 [avatar split clause 222,214]
286. ~3 [avatar split clause 127,144]
287. $false <- (~3, 16) [subsumption resolution 146,215]
288. 3 | ~16 [avatar contradiction clause 287]
289. $false [avatar sat refutation 223,286,288]
% SZS output end Proof for 1386458328638892927737756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and rich is either not calm or not curious.
If alice is not happy then someone is either funny or curious.
Everyone who is either not quiet or not tall is not old.
Everyone who is either not generous or generous is not tall or not wise.
Everyone who is creative is either happy or kind.
Everyone who is either not old or old is not quiet and vice versa.
If someone is patient or not kind then someone is brave or happy.
If someone is not tall then susan is not old or not generous.
Everyone who is either humble or tall is both not generous and not strong and vice versa.
Everyone who is not humble is not brave and vice versa.
If someone is both not patient and not humble then someone is both not quiet and tall and vice versa.
Everyone who is rich is not generous.
Everyone who is both kind and not brave is not kind or not strong.
If john is not creative or not funny then someone is both not tall and kind.
Everyone who is not happy or brave is not patient and vice versa.
If mary is curious or not rich then fred is either not calm or humble and vice versa.
Someone is not patient.
Fred is not calm.
Someone is not brave.
Lucy is either not funny or strong.
Someone is both not quiet and not old.
Someone is funny or not wise.
Paul is both generous and not tall.
|
Alice is quiet.
|
contradiction
|
(![X]:((~quiet(X)&rich(X))=>(~calm(X)<~>~curious(X))))&
((~happy(alice))=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((~quiet(X)<~>~tall(X))=>~old(X)))&
(![X]:((~generous(X)<~>generous(X))=>(~tall(X)|~wise(X))))&
(![X]:(creative(X)=>(happy(X)<~>kind(X))))&
(![X]:((~old(X)<~>old(X))<=>~quiet(X)))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((brave(X)|happy(X)))))&
((?[X]:(~tall(X)))=>((~old(susan)|~generous(susan))))&
(![X]:((humble(X)<~>tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~humble(X)<=>~brave(X)))&
((?[X]:((~patient(X)&~humble(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:(rich(X)=>~generous(X)))&
(![X]:((kind(X)&~brave(X))=>(~kind(X)|~strong(X))))&
(((~creative(john)|~funny(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:((~happy(X)|brave(X))<=>~patient(X)))&
(((curious(mary)|~rich(mary)))<=>((~calm(fred)<~>humble(fred))))&
(?[X]:(~patient(X)))&
(~calm(fred))&
(?[X]:(~brave(X)))&
((~funny(lucy)<~>strong(lucy)))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((funny(X)|~wise(X))))&
((generous(paul)&~tall(paul)))
|
quiet(alice)
|
[
"p5",
"hypothesis"
] |
% SZS status Unsatisfiable for 6313554277002660874734546
% SZS output start Proof for 6313554277002660874734546
6. ! [X0] : ((~old(X0) <~> old(X0)) <=> ~quiet(X0)) [input p5]
24. quiet(alice) [input hypothesis]
47. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | quiet(X0)) & (~quiet(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 6]
80. ~quiet(X0) | old(X0) | old(X0) [cnf transformation 47]
81. ~quiet(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
123. quiet(alice) [cnf transformation 24]
125. ~quiet(X0) | old(X0) [duplicate literal removal 80]
126. ~quiet(X0) | ~old(X0) [duplicate literal removal 81]
141. ~quiet(X0) [subsumption resolution 125,126]
246. $false [subsumption resolution 123,141]
% SZS output end Proof for 6313554277002660874734546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then paul is both not rich and creative.
Everyone who is not patient is either not wise or calm and vice versa.
If susan is both not old and not creative then someone is funny and vice versa.
Everyone who is funny or tall is either brave or not rich.
Everyone who is patient or old is either not happy or generous.
If alice is rich then lucy is either not generous or not curious.
If susan is both old and rich then someone is strong and vice versa.
If someone is generous then someone is either wise or rich and vice versa.
If someone is wise then paul is both not strong and kind and vice versa.
Everyone who is happy is either not rich or creative.
If mary is both not generous and brave then paul is either calm or happy.
Everyone who is not generous or rich is either not patient or patient and vice versa.
If someone is not quiet then someone is not old.
If someone is both tall and brave then paul is both quiet and not strong and vice versa.
Everyone who is brave is not funny and vice versa.
Everyone who is both humble and not wise is not creative or not wise.
Paul is either wise or tall.
Mary is either not old or humble.
Someone is not humble or brave.
Paul is not tall or not funny.
Someone is old.
Someone is both not humble and tall.
Lucy is not rich or not quiet.
Someone is both funny and not old.
|
Susan is not old.
|
entailment
|
((rich(fred))=>((~rich(paul)&creative(paul))))&
(![X]:(~patient(X)<=>(~wise(X)<~>calm(X))))&
(((~old(susan)&~creative(susan)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)|tall(X))=>(brave(X)<~>~rich(X))))&
(![X]:((patient(X)|old(X))=>(~happy(X)<~>generous(X))))&
((rich(alice))=>((~generous(lucy)<~>~curious(lucy))))&
(((old(susan)&rich(susan)))<=>(?[X]:(strong(X))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(wise(X)))<=>((~strong(paul)&kind(paul))))&
(![X]:(happy(X)=>(~rich(X)<~>creative(X))))&
(((~generous(mary)&brave(mary)))=>((calm(paul)<~>happy(paul))))&
(![X]:((~generous(X)|rich(X))<=>(~patient(X)<~>patient(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(~old(X))))&
((?[X]:((tall(X)&brave(X))))<=>((quiet(paul)&~strong(paul))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)|~wise(X))))&
((wise(paul)<~>tall(paul)))&
((~old(mary)<~>humble(mary)))&
(?[X]:((~humble(X)|brave(X))))&
((~tall(paul)|~funny(paul)))&
(?[X]:(old(X)))&
(?[X]:((~humble(X)&tall(X))))&
((~rich(lucy)|~quiet(lucy)))&
(?[X]:((funny(X)&~old(X))))
|
~old(susan)
|
[
"p2",
"p23",
"hypothesis"
] |
% SZS status Unsatisfiable for 5553458206840089419963111
% SZS output start Proof for 5553458206840089419963111
3. (~creative(susan) & ~old(susan)) <=> ? [X0] : funny(X0) [input p2]
24. ? [X0] : (~old(X0) & funny(X0)) [input p23]
25. old(susan) [input hypothesis]
39. ((~creative(susan) & ~old(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (creative(susan) | old(susan))) [nnf transformation 3]
40. ((~creative(susan) & ~old(susan)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | creative(susan) | old(susan)) [flattening 39]
41. ((~creative(susan) & ~old(susan)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | creative(susan) | old(susan)) [rectify 40]
42. ? [X1] : funny(X1) => funny(sK0) [choice axiom]
43. ((~creative(susan) & ~old(susan)) | ! [X0] : ~funny(X0)) & (funny(sK0) | creative(susan) | old(susan)) [skolemisation 41,42]
83. ? [X0] : (~old(X0) & funny(X0)) => (~old(sK10) & funny(sK10)) [choice axiom]
84. ~old(sK10) & funny(sK10) [skolemisation 24,83]
92. ~old(susan) | ~funny(X0) [cnf transformation 43]
142. funny(sK10) [cnf transformation 84]
144. old(susan) [cnf transformation 25]
162. 4 <=> ! [X0] : ~funny(X0) [avatar definition]
163. ~funny(X0) <- (4) [avatar component clause 162]
170. 6 <=> old(susan) [avatar definition]
173. 4 | ~6 [avatar split clause 92,170,162]
339. 6 [avatar split clause 144,170]
342. $false <- (4) [resolution 163,142]
343. ~4 [avatar contradiction clause 342]
344. $false [avatar sat refutation 173,339,343]
% SZS output end Proof for 5553458206840089419963111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not humble is not kind and vice versa.
If someone is not rich then fred is old or not curious and vice versa.
If someone is both not kind and not patient then john is either funny or brave.
If someone is either not curious or happy then fred is both not curious and not strong and vice versa.
Everyone who is both not wise and rich is either brave or creative.
If someone is not rich then someone is both creative and quiet and vice versa.
If alice is both not tall and not creative then lucy is not funny and vice versa.
Everyone who is either old or funny is either not old or not tall and vice versa.
If susan is both wise and not tall then someone is strong and vice versa.
Everyone who is either strong or calm is either calm or old and vice versa.
If someone is either not funny or not patient then lucy is both not rich and rich and vice versa.
Everyone who is both not patient and quiet is not kind and vice versa.
If someone is strong or kind then paul is not brave or humble.
If someone is both not rich and patient then fred is not curious.
Everyone who is not old or not brave is not brave or not happy and vice versa.
If someone is kind or creative then paul is not creative or funny and vice versa.
Lucy is both strong and not patient.
Susan is calm or funny.
Alice is happy or kind.
Someone is wise.
Mary is either not generous or not happy.
Lucy is both calm and not wise.
Someone is both quiet and calm.
Lucy is humble.
|
Susan is not calm.
|
contradiction
|
(![X]:((~strong(X)<~>~humble(X))<=>~kind(X)))&
((?[X]:(~rich(X)))<=>((old(fred)|~curious(fred))))&
((?[X]:((~kind(X)&~patient(X))))=>((funny(john)<~>brave(john))))&
((?[X]:((~curious(X)<~>happy(X))))<=>((~curious(fred)&~strong(fred))))&
(![X]:((~wise(X)&rich(X))=>(brave(X)<~>creative(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((creative(X)&quiet(X)))))&
(((~tall(alice)&~creative(alice)))<=>(~funny(lucy)))&
(![X]:((old(X)<~>funny(X))<=>(~old(X)<~>~tall(X))))&
(((wise(susan)&~tall(susan)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)<~>calm(X))<=>(calm(X)<~>old(X))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>((~rich(lucy)&rich(lucy))))&
(![X]:((~patient(X)&quiet(X))<=>~kind(X)))&
((?[X]:((strong(X)|kind(X))))=>((~brave(paul)|humble(paul))))&
((?[X]:((~rich(X)&patient(X))))=>(~curious(fred)))&
(![X]:((~old(X)|~brave(X))<=>(~brave(X)|~happy(X))))&
((?[X]:((kind(X)|creative(X))))<=>((~creative(paul)|funny(paul))))&
((strong(lucy)&~patient(lucy)))&
((calm(susan)|funny(susan)))&
((happy(alice)|kind(alice)))&
(?[X]:(wise(X)))&
((~generous(mary)<~>~happy(mary)))&
((calm(lucy)&~wise(lucy)))&
(?[X]:((quiet(X)&calm(X))))&
(humble(lucy))
|
~calm(susan)
|
[
"p7",
"p8",
"p16",
"p17",
"hypothesis"
] |
% SZS status Unsatisfiable for 2914903435703983671608374
% SZS output start Proof for 2914903435703983671608374
8. ! [X0] : ((old(X0) <~> funny(X0)) <=> (~old(X0) <~> ~tall(X0))) [input p7]
9. (~tall(susan) & wise(susan)) <=> ? [X0] : strong(X0) [input p8]
17. ~patient(lucy) & strong(lucy) [input p16]
18. funny(susan) | calm(susan) [input p17]
25. ~calm(susan) [input hypothesis]
53. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) & (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 8]
54. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (tall(susan) | ~wise(susan))) [nnf transformation 9]
55. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | tall(susan) | ~wise(susan)) [flattening 54]
56. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | tall(susan) | ~wise(susan)) [rectify 55]
57. ? [X1] : strong(X1) => strong(sK4) [choice axiom]
58. ((~tall(susan) & wise(susan)) | ! [X0] : ~strong(X0)) & (strong(sK4) | tall(susan) | ~wise(susan)) [skolemisation 56,57]
105. tall(X0) | old(X0) | old(X0) | ~funny(X0) [cnf transformation 53]
109. ~funny(X0) | ~old(X0) | ~old(X0) | tall(X0) [cnf transformation 53]
112. ~tall(susan) | ~strong(X0) [cnf transformation 58]
141. strong(lucy) [cnf transformation 17]
143. funny(susan) | calm(susan) [cnf transformation 18]
153. ~calm(susan) [cnf transformation 25]
159. tall(X0) | old(X0) | ~funny(X0) [duplicate literal removal 105]
161. ~funny(X0) | ~old(X0) | tall(X0) [duplicate literal removal 109]
250. ~funny(X0) | tall(X0) [subsumption resolution 159,161]
253. 20 <=> ! [X0] : ~strong(X0) [avatar definition]
254. ~strong(X0) <- (20) [avatar component clause 253]
256. 21 <=> tall(susan) [avatar definition]
258. ~tall(susan) <- (~21) [avatar component clause 256]
259. 20 | ~21 [avatar split clause 112,256,253]
327. 36 <=> calm(susan) [avatar definition]
331. 37 <=> funny(susan) [avatar definition]
333. funny(susan) <- (37) [avatar component clause 331]
334. 36 | 37 [avatar split clause 143,331,327]
354. ~36 [avatar split clause 153,327]
358. $false <- (20) [resolution 254,141]
359. ~20 [avatar contradiction clause 358]
360. tall(susan) <- (37) [resolution 250,333]
361. $false <- (~21, 37) [subsumption resolution 360,258]
362. 21 | ~37 [avatar contradiction clause 361]
363. $false [avatar sat refutation 259,334,354,359,362]
% SZS output end Proof for 2914903435703983671608374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not generous is either not tall or not generous and vice versa.
Everyone who is brave is both humble and patient and vice versa.
Everyone who is both not tall and not wise is not happy or old.
If someone is rich then lucy is either quiet or not funny and vice versa.
If paul is both tall and not happy then someone is both not humble and not calm.
Everyone who is not brave or patient is both kind and brave.
If fred is not tall or not funny then fred is either not strong or strong.
If mary is humble or creative then lucy is either not tall or generous.
Everyone who is either tall or brave is not rich.
If john is not old then fred is not old and vice versa.
If someone is not kind or patient then someone is either not strong or not funny and vice versa.
Everyone who is generous is not brave.
If someone is not calm then lucy is not calm and vice versa.
If john is not generous then paul is either not patient or patient.
Everyone who is both kind and old is both kind and funny.
Mary is old or not curious.
Paul is humble or not creative.
Someone is quiet.
Someone is either rich or generous.
Someone is both not curious and patient.
Someone is either old or rich.
|
Lucy is not generous.
|
entailment
|
(![X]:((~funny(X)<~>~generous(X))<=>(~tall(X)<~>~generous(X))))&
(![X]:(brave(X)<=>(humble(X)&patient(X))))&
(![X]:((~tall(X)&~wise(X))=>(~happy(X)|old(X))))&
((?[X]:(rich(X)))<=>((quiet(lucy)<~>~funny(lucy))))&
(((tall(paul)&~happy(paul)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((~brave(X)|patient(X))=>(kind(X)&brave(X))))&
(((~tall(fred)|~funny(fred)))=>((~strong(fred)<~>strong(fred))))&
(((humble(mary)|creative(mary)))=>((~tall(lucy)<~>generous(lucy))))&
(![X]:((tall(X)<~>brave(X))=>~rich(X)))&
((~old(john))<=>(~old(fred)))&
((?[X]:((~kind(X)|patient(X))))<=>(?[X]:((~strong(X)<~>~funny(X)))))&
(![X]:(generous(X)=>~brave(X)))&
((?[X]:(~calm(X)))<=>(~calm(lucy)))&
((~generous(john))=>((~patient(paul)<~>patient(paul))))&
(![X]:((kind(X)&old(X))=>(kind(X)&funny(X))))&
((old(mary)|~curious(mary)))&
((humble(paul)|~creative(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~curious(X)&patient(X))))&
(?[X]:((old(X)<~>rich(X))))
|
~generous(lucy)
|
[
"p5",
"p11",
"hypothesis"
] |
% SZS status Unsatisfiable for 1463511495476443989131608
% SZS output start Proof for 1463511495476443989131608
6. ! [X0] : ((patient(X0) | ~brave(X0)) => (brave(X0) & kind(X0))) [input p5]
12. ! [X0] : (generous(X0) => ~brave(X0)) [input p11]
22. generous(lucy) [input hypothesis]
30. ! [X0] : ((brave(X0) & kind(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 6]
34. ! [X0] : (~brave(X0) | ~generous(X0)) [ennf transformation 12]
86. brave(X0) | brave(X0) [cnf transformation 30]
104. ~brave(X0) | ~generous(X0) [cnf transformation 34]
117. generous(lucy) [cnf transformation 22]
118. brave(X0) [duplicate literal removal 86]
203. ~generous(X0) [subsumption resolution 104,118]
228. $false [subsumption resolution 117,203]
% SZS output end Proof for 1463511495476443989131608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both creative and tall then alice is both funny and generous.
If fred is rich or not calm then mary is either kind or not kind and vice versa.
Everyone who is either not curious or not rich is either not wise or wise and vice versa.
If paul is either happy or not wise then someone is both happy and rich.
If someone is patient or old then mary is both not quiet and funny and vice versa.
If someone is either wise or not strong then mary is rich or old.
Everyone who is both not calm and quiet is not old or funny and vice versa.
Everyone who is not kind is both not tall and humble and vice versa.
Everyone who is kind is both funny and calm and vice versa.
Everyone who is not creative is both happy and brave and vice versa.
Everyone who is either patient or not generous is not strong and vice versa.
Everyone who is creative or wise is not old and vice versa.
Everyone who is curious or not funny is not creative.
Everyone who is either not creative or calm is kind and vice versa.
If someone is either not rich or not wise then fred is both patient and not tall.
If lucy is both strong and not rich then lucy is either curious or quiet.
Someone is quiet.
Fred is brave or not curious.
Someone is generous or not happy.
Susan is not wise or not happy.
Susan is not patient or not creative.
|
Paul is not funny.
|
contradiction
|
(((creative(lucy)&tall(lucy)))=>((funny(alice)&generous(alice))))&
(((rich(fred)|~calm(fred)))<=>((kind(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~wise(X)<~>wise(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((patient(X)|old(X))))<=>((~quiet(mary)&funny(mary))))&
((?[X]:((wise(X)<~>~strong(X))))=>((rich(mary)|old(mary))))&
(![X]:((~calm(X)&quiet(X))<=>(~old(X)|funny(X))))&
(![X]:(~kind(X)<=>(~tall(X)&humble(X))))&
(![X]:(kind(X)<=>(funny(X)&calm(X))))&
(![X]:(~creative(X)<=>(happy(X)&brave(X))))&
(![X]:((patient(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((creative(X)|wise(X))<=>~old(X)))&
(![X]:((curious(X)|~funny(X))=>~creative(X)))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
((?[X]:((~rich(X)<~>~wise(X))))=>((patient(fred)&~tall(fred))))&
(((strong(lucy)&~rich(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(?[X]:(quiet(X)))&
((brave(fred)|~curious(fred)))&
(?[X]:((generous(X)|~happy(X))))&
((~wise(susan)|~happy(susan)))&
((~patient(susan)|~creative(susan)))
|
~funny(paul)
|
[
"p4",
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 8980092226108794984344659
% SZS output start Proof for 8980092226108794984344659
5. ? [X0] : (old(X0) | patient(X0)) <=> (funny(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (funny(X0) | ~old(X0))) [input p6]
9. ! [X0] : (kind(X0) <=> (calm(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~funny(X0) | curious(X0)) => ~creative(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> kind(X0)) [input p13]
22. ~funny(paul) [input hypothesis]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~curious(X0))) [ennf transformation 13]
38. (? [X0] : (old(X0) | patient(X0)) | (~funny(mary) | quiet(mary))) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 5]
39. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 38]
40. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 39]
41. ? [X0] : (old(X0) | patient(X0)) => (old(sK1) | patient(sK1)) [choice axiom]
42. ((old(sK1) | patient(sK1)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 40,41]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
48. ! [X0] : ((kind(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~kind(X0))) [flattening 48]
55. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
83. ~quiet(mary) | ~old(X1) [cnf transformation 42]
85. funny(mary) | ~old(X1) [cnf transformation 42]
90. ~calm(X0) | old(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 45]
98. ~kind(X0) | calm(X0) [cnf transformation 49]
111. ~creative(X0) | funny(X0) [cnf transformation 28]
112. kind(X0) | calm(X0) | creative(X0) [cnf transformation 55]
115. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 55]
127. ~funny(paul) [cnf transformation 22]
189. 12 <=> quiet(mary) [avatar definition]
193. 13 <=> funny(mary) [avatar definition]
194. funny(mary) <- (13) [avatar component clause 193]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 13 [avatar split clause 85,193,206]
213. 16 | ~12 [avatar split clause 83,189,206]
231. ~kind(X0) | creative(X0) [subsumption resolution 115,98]
232. calm(X0) | creative(X0) [subsumption resolution 112,231]
305. quiet(mary) <- (13) [resolution 93,194]
322. old(X1) | creative(X1) [resolution 232,90]
332. 12 | ~13 [avatar split clause 305,193,189]
402. creative(X0) <- (16) [resolution 322,207]
406. funny(X1) <- (16) [resolution 402,111]
412. $false <- (16) [resolution 406,127]
417. ~16 [avatar contradiction clause 412]
418. $false [avatar sat refutation 208,213,332,417]
% SZS output end Proof for 8980092226108794984344659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or generous then someone is not happy.
Everyone who is both not wise and calm is old.
If alice is either not strong or not brave then someone is funny and vice versa.
Everyone who is not tall or creative is either creative or not calm.
If fred is old or not strong then someone is old or kind and vice versa.
Everyone who is both not creative and happy is both patient and not generous.
If alice is both brave and not funny then someone is rich and vice versa.
Everyone who is not happy is either not creative or quiet and vice versa.
Everyone who is either funny or creative is both wise and creative.
Everyone who is either quiet or generous is either not strong or not wise and vice versa.
Everyone who is both not curious and old is either not kind or tall.
If susan is either not brave or tall then someone is tall or curious and vice versa.
Everyone who is quiet is strong or not quiet and vice versa.
Everyone who is wise is not strong or curious and vice versa.
If someone is both not strong and old then mary is not wise or not generous and vice versa.
If someone is generous or quiet then someone is not patient or not old.
Paul is either curious or quiet.
Susan is both funny and not kind.
Someone is not humble.
Someone is calm or funny.
Someone is both curious and old.
Alice is either not wise or not strong.
Someone is not wise or wise.
Someone is both patient and not curious.
|
Mary is not creative.
|
contradiction
|
(((calm(john)|generous(john)))=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&calm(X))=>old(X)))&
(((~strong(alice)<~>~brave(alice)))<=>(?[X]:(funny(X))))&
(![X]:((~tall(X)|creative(X))=>(creative(X)<~>~calm(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~creative(X)&happy(X))=>(patient(X)&~generous(X))))&
(((brave(alice)&~funny(alice)))<=>(?[X]:(rich(X))))&
(![X]:(~happy(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((funny(X)<~>creative(X))=>(wise(X)&creative(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((~curious(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~brave(susan)<~>tall(susan)))<=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(quiet(X)<=>(strong(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~strong(X)|curious(X))))&
((?[X]:((~strong(X)&old(X))))<=>((~wise(mary)|~generous(mary))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~patient(X)|~old(X)))))&
((curious(paul)<~>quiet(paul)))&
((funny(susan)&~kind(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((curious(X)&old(X))))&
((~wise(alice)<~>~strong(alice)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((patient(X)&~curious(X))))
|
~creative(mary)
|
[
"p5",
"p7",
"p12",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 837088987977804101036703
% SZS output start Proof for 837088987977804101036703
6. ! [X0] : ((happy(X0) & ~creative(X0)) => (~generous(X0) & patient(X0))) [input p5]
8. ! [X0] : (~happy(X0) <=> (~creative(X0) <~> quiet(X0))) [input p7]
13. ! [X0] : (quiet(X0) <=> (~quiet(X0) | strong(X0))) [input p12]
15. ? [X0] : (old(X0) & ~strong(X0)) <=> (~generous(mary) | ~wise(mary)) [input p14]
25. ~creative(mary) [input hypothesis]
27. ! [X0] : (~happy(X0) => (~creative(X0) <~> quiet(X0))) [unused predicate definition removal 8]
33. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) | creative(X0))) [ennf transformation 6]
34. ! [X0] : ((~generous(X0) & patient(X0)) | ~happy(X0) | creative(X0)) [flattening 33]
35. ! [X0] : ((~creative(X0) <~> quiet(X0)) | happy(X0)) [ennf transformation 27]
57. ! [X0] : (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | happy(X0)) [nnf transformation 35]
65. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 13]
66. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~quiet(X0))) [flattening 65]
69. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & ((~generous(mary) | ~wise(mary)) | ! [X0] : (~old(X0) | strong(X0))) [nnf transformation 15]
70. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X0] : (~old(X0) | strong(X0))) [flattening 69]
71. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [rectify 70]
72. ? [X0] : (old(X0) & ~strong(X0)) => (old(sK5) & ~strong(sK5)) [choice axiom]
73. ((old(sK5) & ~strong(sK5)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [skolemisation 71,72]
103. ~happy(X0) | ~generous(X0) | creative(X0) [cnf transformation 34]
108. ~quiet(X0) | creative(X0) | happy(X0) [cnf transformation 57]
129. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 66]
131. quiet(X0) | quiet(X0) [cnf transformation 66]
137. ~strong(sK5) | generous(mary) [cnf transformation 73]
154. ~creative(mary) [cnf transformation 25]
155. ~quiet(X0) | strong(X0) [duplicate literal removal 129]
156. quiet(X0) [duplicate literal removal 131]
260. strong(X0) [subsumption resolution 155,156]
263. 23 <=> generous(mary) [avatar definition]
265. generous(mary) <- (23) [avatar component clause 263]
276. generous(mary) [subsumption resolution 137,260]
277. 23 [avatar split clause 276,263]
369. creative(X0) | happy(X0) [resolution 108,156]
392. happy(mary) [resolution 369,154]
402. ~generous(mary) | creative(mary) [resolution 392,103]
404. creative(mary) <- (23) [subsumption resolution 402,265]
405. $false <- (23) [subsumption resolution 404,154]
406. ~23 [avatar contradiction clause 405]
408. $false [avatar sat refutation 277,406]
% SZS output end Proof for 837088987977804101036703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind.
|
Susan is tall.
|
entailment
|
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice)))
|
tall(susan)
|
[
"p0",
"p1",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] |
% SZS status Unsatisfiable for 6771143683534931390447879
% SZS output start Proof for 6771143683534931390447879
1. ? [X0] : (rich(X0) | brave(X0)) => (~happy(john) & ~funny(john)) [input p0]
2. ! [X0] : (tall(X0) <=> ~brave(X0)) [input p1]
6. ! [X0] : (~curious(X0) <=> (~kind(X0) & old(X0))) [input p5]
7. ! [X0] : (humble(X0) => (~wise(X0) & happy(X0))) [input p6]
11. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> ~kind(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & ~humble(X0)) => (~brave(X0) & funny(X0))) [input p11]
22. ~tall(susan) [input hypothesis]
23. (~happy(john) & ~funny(john)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 1]
24. ! [X0] : ((~wise(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 7]
27. ! [X0] : ((~brave(X0) & funny(X0)) | (kind(X0) | humble(X0))) [ennf transformation 12]
28. ! [X0] : ((~brave(X0) & funny(X0)) | kind(X0) | humble(X0)) [flattening 27]
29. ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))) [nnf transformation 2]
35. ! [X0] : ((~curious(X0) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | curious(X0))) [nnf transformation 6]
36. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | curious(X0))) [flattening 35]
43. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 11]
57. ~funny(john) | ~brave(X0) [cnf transformation 23]
59. ~happy(john) | ~brave(X0) [cnf transformation 23]
62. tall(X0) | brave(X0) [cnf transformation 29]
78. ~kind(X0) | curious(X0) [cnf transformation 36]
80. ~humble(X0) | happy(X0) [cnf transformation 24]
95. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 43]
98. kind(X0) | funny(X0) | humble(X0) [cnf transformation 28]
121. ~tall(susan) [cnf transformation 22]
132. 2 <=> happy(john) [avatar definition]
134. ~happy(john) <- (~2) [avatar component clause 132]
137. 3 <=> ! [X0] : ~brave(X0) [avatar definition]
138. ~brave(X0) <- (3) [avatar component clause 137]
139. 3 | ~2 [avatar split clause 59,132,137]
141. 4 <=> funny(john) [avatar definition]
143. ~funny(john) <- (~4) [avatar component clause 141]
145. 3 | ~4 [avatar split clause 57,141,137]
189. ~kind(X0) | happy(X0) [subsumption resolution 95,78]
283. 32 <=> brave(susan) [avatar definition]
284. brave(susan) <- (32) [avatar component clause 283]
285. ~brave(susan) <- (~32) [avatar component clause 283]
298. brave(susan) [resolution 62,121]
301. $false <- (~32) [subsumption resolution 298,285]
302. 32 [avatar contradiction clause 301]
354. funny(X0) | humble(X0) | happy(X0) [resolution 98,189]
389. happy(X0) | funny(X0) [subsumption resolution 354,80]
450. funny(john) <- (~2) [resolution 389,134]
451. $false <- (~2, ~4) [subsumption resolution 450,143]
452. 2 | 4 [avatar contradiction clause 451]
455. $false <- (3, 32) [resolution 138,284]
456. ~3 | ~32 [avatar contradiction clause 455]
459. $false [avatar sat refutation 139,145,302,452,456]
% SZS output end Proof for 6771143683534931390447879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous or not funny then someone is quiet or happy and vice versa.
Everyone who is not happy or funny is calm or old.
Everyone who is not humble is old or not strong and vice versa.
If john is creative then someone is both not funny and calm and vice versa.
If someone is funny then someone is both creative and not quiet and vice versa.
Everyone who is not rich is rich or not rich.
Everyone who is not brave or not strong is either not rich or funny.
Everyone who is tall or old is both humble and quiet and vice versa.
Everyone who is either not quiet or not calm is humble.
If someone is not kind or not generous then someone is both rich and patient and vice versa.
Everyone who is both old and creative is old or wise.
Everyone who is brave is both wise and creative and vice versa.
If someone is either not tall or not rich then someone is not old.
Everyone who is both humble and not strong is humble and vice versa.
Everyone who is not curious is either not kind or not strong.
If john is humble then susan is not funny or not calm and vice versa.
Paul is either not humble or not funny.
Lucy is patient.
Mary is not old.
Lucy is either tall or brave.
Someone is not wise.
Paul is either funny or not happy.
|
Paul is tall.
|
contradiction
|
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((~happy(X)|funny(X))=>(calm(X)|old(X))))&
(![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((creative(john))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~brave(X)|~strong(X))=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)|old(X))<=>(humble(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>humble(X)))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((old(X)&creative(X))=>(old(X)|wise(X))))&
(![X]:(brave(X)<=>(wise(X)&creative(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(~old(X))))&
(![X]:((humble(X)&~strong(X))<=>humble(X)))&
(![X]:(~curious(X)=>(~kind(X)<~>~strong(X))))&
((humble(john))<=>((~funny(susan)|~calm(susan))))&
((~humble(paul)<~>~funny(paul)))&
(patient(lucy))&
(~old(mary))&
((tall(lucy)<~>brave(lucy)))&
(?[X]:(~wise(X)))&
((funny(paul)<~>~happy(paul)))
|
tall(paul)
|
[
"p2",
"p7",
"p13",
"hypothesis"
] |
% SZS status Unsatisfiable for 1072469136093215467312528
% SZS output start Proof for 1072469136093215467312528
3. ! [X0] : (~humble(X0) <=> (~strong(X0) | old(X0))) [input p2]
8. ! [X0] : ((old(X0) | tall(X0)) <=> (quiet(X0) & humble(X0))) [input p7]
14. ! [X0] : ((~strong(X0) & humble(X0)) <=> humble(X0)) [input p13]
23. tall(paul) [input hypothesis]
43. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | humble(X0))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | humble(X0))) [flattening 43]
55. ! [X0] : (((old(X0) | tall(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 8]
56. ! [X0] : ((old(X0) | tall(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [flattening 55]
69. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) | ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | strong(X0) | ~humble(X0))) [flattening 69]
86. ~humble(X0) | strong(X0) [cnf transformation 44]
98. ~tall(X0) | humble(X0) [cnf transformation 56]
118. ~strong(X0) | ~humble(X0) [cnf transformation 70]
131. tall(paul) [cnf transformation 23]
233. ~humble(X0) [subsumption resolution 118,86]
257. humble(paul) [resolution 98,131]
259. $false [subsumption resolution 257,233]
% SZS output end Proof for 1072469136093215467312528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not old then someone is both not happy and brave and vice versa. If someone is either not calm or creative then paul is both calm and not quiet. Everyone who is not curious is not happy. If someone is both old and not calm then someone is curious or calm. If someone is both brave and tall then someone is not generous and vice versa. Everyone who is calm or not happy is not generous or not quiet and vice versa. If lucy is either not old or not creative then alice is calm or quiet. Everyone who is both not happy and not funny is not creative. If alice is not strong then someone is either not happy or not patient and vice versa. Everyone who is both not funny and not quiet is both humble and not creative and vice versa. Everyone who is both not generous and kind is either strong or not patient. If paul is not rich then someone is not calm or not tall. If someone is not happy then someone is both tall and not tall. Everyone who is both not old and rich is not brave and vice versa. Everyone who is not tall or not kind is not calm or not kind. Everyone who is calm is not generous and vice versa. John is not patient or kind. Lucy is either not quiet or not curious. Someone is both not humble and not brave. Mary is calm or not funny. Someone is creative or not kind. Mary is not strong.
|
Mary is not funny.
|
neutral
|
((?[X]:((~kind(X)&~old(X))))<=>(?[X]:((~happy(X)&brave(X)))))&
((?[X]:((~calm(X)<~>creative(X))))=>((calm(paul)&~quiet(paul))))&
(![X]:(~curious(X)=>~happy(X)))&
((?[X]:((old(X)&~calm(X))))=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:(~generous(X))))&
(![X]:((calm(X)|~happy(X))<=>(~generous(X)|~quiet(X))))&
(((~old(lucy)<~>~creative(lucy)))=>((calm(alice)|quiet(alice))))&
(![X]:((~happy(X)&~funny(X))=>~creative(X)))&
((~strong(alice))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>(humble(X)&~creative(X))))&
(![X]:((~generous(X)&kind(X))=>(strong(X)<~>~patient(X))))&
((~rich(paul))=>(?[X]:((~calm(X)|~tall(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((tall(X)&~tall(X)))))&
(![X]:((~old(X)&rich(X))<=>~brave(X)))&
(![X]:((~tall(X)|~kind(X))=>(~calm(X)|~kind(X))))&
(![X]:(calm(X)<=>~generous(X)))&
((~patient(john)|kind(john)))&
((~quiet(lucy)<~>~curious(lucy)))&
(?[X]:((~humble(X)&~brave(X))))&
((calm(mary)|~funny(mary)))&
(?[X]:((creative(X)|~kind(X))))&
(~strong(mary))
|
~funny(mary)
|
[] | null | 0 |
If someone is old then john is either kind or not kind and vice versa. Everyone who is brave is not brave or not humble. Everyone who is both not kind and happy is funny or wise. If susan is wise then alice is funny or curious. Everyone who is wise or quiet is brave or not brave. Everyone who is either not strong or not rich is not strong or patient and vice versa. Everyone who is either funny or not curious is either generous or happy. Everyone who is either not happy or not funny is both wise and rich and vice versa. If fred is either rich or funny then someone is calm. Everyone who is not generous or not creative is both creative and not humble and vice versa. Everyone who is tall is old or not funny and vice versa. If someone is either not curious or brave then john is patient and vice versa. If someone is humble then someone is funny. If someone is patient or funny then fred is not strong and vice versa. Everyone who is both old and not happy is either rich or calm. Someone is not tall. Someone is not happy or not humble. Someone is not strong or not wise. Alice is either curious or not creative. Someone is either not humble or not tall. Someone is either funny or creative. Someone is either not strong or quiet. Alice is not kind or not strong.
|
Susan is not curious.
|
neutral
|
((?[X]:(old(X)))<=>((kind(john)<~>~kind(john))))&
(![X]:(brave(X)=>(~brave(X)|~humble(X))))&
(![X]:((~kind(X)&happy(X))=>(funny(X)|wise(X))))&
((wise(susan))=>((funny(alice)|curious(alice))))&
(![X]:((wise(X)|quiet(X))=>(brave(X)|~brave(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~strong(X)|patient(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(wise(X)&rich(X))))&
(((rich(fred)<~>funny(fred)))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)|~creative(X))<=>(creative(X)&~humble(X))))&
(![X]:(tall(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>(patient(john)))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((~strong(X)|~wise(X))))&
((curious(alice)<~>~creative(alice)))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~kind(alice)|~strong(alice)))
|
~curious(susan)
|
[] | null | 0 |
Everyone who is both curious and not old is both not humble and humble.
Everyone who is either not creative or wise is not funny and vice versa.
If john is not patient or not kind then someone is not rich or creative and vice versa.
If someone is wise then lucy is humble and vice versa.
Everyone who is curious or not funny is either tall or generous and vice versa.
Everyone who is not funny is wise or strong.
If paul is calm then someone is not humble and vice versa.
Everyone who is not humble or not curious is rich or old and vice versa.
If someone is either generous or brave then fred is not wise or wise and vice versa.
Everyone who is not rich is either patient or brave.
If someone is calm or brave then someone is not rich and vice versa.
If lucy is both brave and not generous then someone is either not brave or not kind.
Everyone who is not calm is not humble and vice versa.
Everyone who is wise or not rich is either quiet or not quiet and vice versa.
Everyone who is either not creative or generous is either brave or generous.
If someone is not calm then paul is not creative or humble and vice versa.
Someone is not generous or kind.
Susan is not calm.
John is both not old and not calm.
Mary is wise or not tall.
Someone is both not generous and kind.
Someone is either not quiet or rich.
Alice is both not brave and not tall.
John is either not brave or not curious.
|
Lucy is humble.
|
entailment
|
(![X]:((curious(X)&~old(X))=>(~humble(X)&humble(X))))&
(![X]:((~creative(X)<~>wise(X))<=>~funny(X)))&
(((~patient(john)|~kind(john)))<=>(?[X]:((~rich(X)|creative(X)))))&
((?[X]:(wise(X)))<=>(humble(lucy)))&
(![X]:((curious(X)|~funny(X))<=>(tall(X)<~>generous(X))))&
(![X]:(~funny(X)=>(wise(X)|strong(X))))&
((calm(paul))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|~curious(X))<=>(rich(X)|old(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((~wise(fred)|wise(fred))))&
(![X]:(~rich(X)=>(patient(X)<~>brave(X))))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:(~rich(X))))&
(((brave(lucy)&~generous(lucy)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
(![X]:((wise(X)|~rich(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>generous(X))=>(brave(X)<~>generous(X))))&
((?[X]:(~calm(X)))<=>((~creative(paul)|humble(paul))))&
(?[X]:((~generous(X)|kind(X))))&
(~calm(susan))&
((~old(john)&~calm(john)))&
((wise(mary)|~tall(mary)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((~quiet(X)<~>rich(X))))&
((~brave(alice)&~tall(alice)))&
((~brave(john)<~>~curious(john)))
|
humble(lucy)
|
[
"p0",
"p3",
"p7",
"p13",
"p18",
"hypothesis"
] |
% SZS status Unsatisfiable for 3965774839558968656726436
% SZS output start Proof for 3965774839558968656726436
1. ! [X0] : ((~old(X0) & curious(X0)) => (humble(X0) & ~humble(X0))) [input p0]
4. ? [X0] : wise(X0) <=> humble(lucy) [input p3]
8. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (old(X0) | rich(X0))) [input p7]
14. ! [X0] : ((~rich(X0) | wise(X0)) <=> (quiet(X0) <~> ~quiet(X0))) [input p13]
19. ~calm(john) & ~old(john) [input p18]
25. ~humble(lucy) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~humble(X0)) | (old(X0) | ~curious(X0))) [ennf transformation 1]
29. ! [X0] : ((humble(X0) & ~humble(X0)) | old(X0) | ~curious(X0)) [flattening 28]
40. (? [X0] : wise(X0) | ~humble(lucy)) & (humble(lucy) | ! [X0] : ~wise(X0)) [nnf transformation 4]
41. (? [X0] : wise(X0) | ~humble(lucy)) & (humble(lucy) | ! [X1] : ~wise(X1)) [rectify 40]
42. ? [X0] : wise(X0) => wise(sK1) [choice axiom]
43. (wise(sK1) | ~humble(lucy)) & (humble(lucy) | ! [X1] : ~wise(X1)) [skolemisation 41,42]
50. ! [X0] : (((~curious(X0) | ~humble(X0)) | (~old(X0) & ~rich(X0))) & ((old(X0) | rich(X0)) | (curious(X0) & humble(X0)))) [nnf transformation 8]
51. ! [X0] : ((~curious(X0) | ~humble(X0) | (~old(X0) & ~rich(X0))) & (old(X0) | rich(X0) | (curious(X0) & humble(X0)))) [flattening 50]
67. ! [X0] : (((~rich(X0) | wise(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (rich(X0) & ~wise(X0)))) [nnf transformation 14]
68. ! [X0] : ((~rich(X0) | wise(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) & (((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | (rich(X0) & ~wise(X0)))) [flattening 67]
83. ~humble(X0) | old(X0) | ~curious(X0) [cnf transformation 29]
84. ~curious(X0) | old(X0) | humble(X0) [cnf transformation 29]
93. humble(lucy) | ~wise(X1) [cnf transformation 43]
104. old(X0) | rich(X0) | curious(X0) [cnf transformation 51]
126. ~rich(X0) | wise(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 68]
127. ~rich(X0) | wise(X0) | quiet(X0) | quiet(X0) [cnf transformation 68]
137. ~old(john) [cnf transformation 19]
148. ~humble(lucy) [cnf transformation 25]
151. ~rich(X0) | wise(X0) | ~quiet(X0) [duplicate literal removal 126]
152. ~rich(X0) | wise(X0) | quiet(X0) [duplicate literal removal 127]
153. ~curious(X0) | old(X0) [subsumption resolution 83,84]
181. 7 <=> humble(lucy) [avatar definition]
190. 9 <=> ! [X1] : ~wise(X1) [avatar definition]
191. ~wise(X1) <- (9) [avatar component clause 190]
192. 9 | 7 [avatar split clause 93,181,190]
207. rich(X0) | old(X0) [subsumption resolution 104,153]
263. ~rich(X0) | wise(X0) [subsumption resolution 151,152]
320. ~7 [avatar split clause 148,181]
337. wise(X0) | old(X0) [resolution 263,207]
340. old(X0) <- (9) [subsumption resolution 337,191]
342. $false <- (9) [resolution 340,137]
343. ~9 [avatar contradiction clause 342]
344. $false [avatar sat refutation 192,320,343]
% SZS output end Proof for 3965774839558968656726436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is both curious and not brave. Everyone who is funny or quiet is not quiet and vice versa. If alice is curious then someone is calm and vice versa. Everyone who is both not humble and curious is either not funny or not calm and vice versa. If mary is either not wise or not creative then someone is rich. Everyone who is either happy or funny is not tall and vice versa. If someone is not creative or humble then john is not generous and vice versa. If susan is not happy then lucy is both not happy and happy. Everyone who is wise or generous is either not humble or not brave and vice versa. If alice is quiet then john is either quiet or brave and vice versa. If someone is not curious then lucy is quiet. If someone is old then someone is both patient and calm and vice versa. If paul is either not happy or not funny then someone is strong. Everyone who is not brave or not rich is tall or not old and vice versa. If susan is patient or strong then someone is not strong and vice versa. Everyone who is either not old or not funny is either not humble or funny. Someone is generous. Paul is either not funny or not generous. Someone is both tall and wise. Someone is either humble or not creative. Someone is creative. Someone is not happy or not quiet. Someone is either wise or creative. Someone is creative or not calm.
|
Mary is brave.
|
contradiction
|
(![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((funny(X)|quiet(X))<=>~quiet(X)))&
((curious(alice))<=>(?[X]:(calm(X))))&
(![X]:((~humble(X)&curious(X))<=>(~funny(X)<~>~calm(X))))&
(((~wise(mary)<~>~creative(mary)))=>(?[X]:(rich(X))))&
(![X]:((happy(X)<~>funny(X))<=>~tall(X)))&
((?[X]:((~creative(X)|humble(X))))<=>(~generous(john)))&
((~happy(susan))=>((~happy(lucy)&happy(lucy))))&
(![X]:((wise(X)|generous(X))<=>(~humble(X)<~>~brave(X))))&
((quiet(alice))<=>((quiet(john)<~>brave(john))))&
((?[X]:(~curious(X)))=>(quiet(lucy)))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&calm(X)))))&
(((~happy(paul)<~>~funny(paul)))=>(?[X]:(strong(X))))&
(![X]:((~brave(X)|~rich(X))<=>(tall(X)|~old(X))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(?[X]:(generous(X)))&
((~funny(paul)<~>~generous(paul)))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X))))
|
brave(mary)
|
[
"p0",
"p1",
"p10",
"hypothesis"
] |
% SZS status Unsatisfiable for 2595244782005303969529502
% SZS output start Proof for 2595244782005303969529502
1. ! [X0] : ((kind(X0) | curious(X0)) => (~brave(X0) & curious(X0))) [input p0]
2. ! [X0] : ((quiet(X0) | funny(X0)) <=> ~quiet(X0)) [input p1]
11. ? [X0] : ~curious(X0) => quiet(lucy) [input p10]
25. brave(mary) [input hypothesis]
27. ! [X0] : (curious(X0) => (~brave(X0) & curious(X0))) [pure predicate removal 1]
28. ! [X0] : ((~brave(X0) & curious(X0)) | ~curious(X0)) [ennf transformation 27]
31. quiet(lucy) | ! [X0] : curious(X0) [ennf transformation 11]
34. ! [X0] : (((quiet(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 2]
35. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 34]
87. ~brave(X0) | ~curious(X0) [cnf transformation 28]
89. ~quiet(X0) | ~quiet(X0) [cnf transformation 35]
120. quiet(lucy) | curious(X0) [cnf transformation 31]
149. brave(mary) [cnf transformation 25]
152. ~quiet(X0) [duplicate literal removal 89]
214. curious(X0) [subsumption resolution 120,152]
305. ~curious(mary) [resolution 87,149]
306. $false [subsumption resolution 305,214]
% SZS output end Proof for 2595244782005303969529502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and quiet is both not generous and patient and vice versa.
If john is curious or not generous then alice is either quiet or calm and vice versa.
If someone is either wise or brave then lucy is both not generous and not creative.
If alice is either old or not strong then someone is not generous.
If someone is not humble then someone is not creative or tall.
Everyone who is both quiet and patient is not generous.
Everyone who is either not strong or strong is both generous and creative.
If someone is both funny and not quiet then someone is both generous and kind.
If lucy is either not wise or calm then john is patient.
If john is not wise then lucy is brave.
Everyone who is generous or strong is brave and vice versa.
Everyone who is not humble is both quiet and not humble.
Everyone who is either quiet or wise is both rich and not wise and vice versa.
If someone is both creative and rich then someone is both tall and not funny.
Everyone who is not old is either not happy or generous.
If someone is not creative then mary is funny or tall.
Someone is not humble.
Fred is both rich and not old.
Paul is not rich or calm.
John is either not patient or not kind.
Someone is rich.
Someone is creative.
Someone is both funny and brave.
|
Fred is quiet.
|
entailment
|
(![X]:((humble(X)&quiet(X))<=>(~generous(X)&patient(X))))&
(((curious(john)|~generous(john)))<=>((quiet(alice)<~>calm(alice))))&
((?[X]:((wise(X)<~>brave(X))))=>((~generous(lucy)&~creative(lucy))))&
(((old(alice)<~>~strong(alice)))=>(?[X]:(~generous(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:((quiet(X)&patient(X))=>~generous(X)))&
(![X]:((~strong(X)<~>strong(X))=>(generous(X)&creative(X))))&
((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((generous(X)&kind(X)))))&
(((~wise(lucy)<~>calm(lucy)))=>(patient(john)))&
((~wise(john))=>(brave(lucy)))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:(~humble(X)=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(rich(X)&~wise(X))))&
((?[X]:((creative(X)&rich(X))))=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(~old(X)=>(~happy(X)<~>generous(X))))&
((?[X]:(~creative(X)))=>((funny(mary)|tall(mary))))&
(?[X]:(~humble(X)))&
((rich(fred)&~old(fred)))&
((~rich(paul)|calm(paul)))&
((~patient(john)<~>~kind(john)))&
(?[X]:(rich(X)))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)&brave(X))))
|
quiet(fred)
|
[
"p2",
"p6",
"p10",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 9211332816841883705189704
% SZS output start Proof for 9211332816841883705189704
3. ? [X0] : (wise(X0) <~> brave(X0)) => (~creative(lucy) & ~generous(lucy)) [input p2]
7. ! [X0] : ((~strong(X0) <~> strong(X0)) => (creative(X0) & generous(X0))) [input p6]
11. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p10]
13. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~wise(X0) & rich(X0))) [input p12]
24. ~quiet(fred) [input hypothesis]
31. (~creative(lucy) & ~generous(lucy)) | ! [X0] : (wise(X0) <=> brave(X0)) [ennf transformation 3]
35. ! [X0] : ((creative(X0) & generous(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 7]
46. (~creative(lucy) & ~generous(lucy)) | ! [X0] : ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))) [nnf transformation 31]
50. ! [X0] : ((creative(X0) & generous(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 35]
55. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 11]
56. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 55]
57. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 13]
58. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 57]
83. ~generous(lucy) | wise(X0) | ~brave(X0) [cnf transformation 46]
89. generous(X0) | strong(X0) | strong(X0) [cnf transformation 50]
90. generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 50]
98. brave(X0) | ~generous(X0) [cnf transformation 56]
106. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 58]
122. ~quiet(fred) [cnf transformation 24]
123. ~wise(X0) | quiet(X0) [duplicate literal removal 106]
125. generous(X0) | strong(X0) [duplicate literal removal 89]
126. ~strong(X0) | generous(X0) [duplicate literal removal 90]
152. 5 <=> ! [X0] : (wise(X0) | ~brave(X0)) [avatar definition]
153. wise(X0) | ~brave(X0) <- (5) [avatar component clause 152]
164. 8 <=> generous(lucy) [avatar definition]
166. ~generous(lucy) <- (~8) [avatar component clause 164]
167. 5 | ~8 [avatar split clause 83,164,152]
184. generous(X0) [subsumption resolution 125,126]
216. brave(X0) [subsumption resolution 98,184]
244. $false <- (~8) [subsumption resolution 166,184]
245. 8 [avatar contradiction clause 244]
250. wise(X0) <- (5) [subsumption resolution 153,216]
255. quiet(X0) <- (5) [resolution 123,250]
258. $false <- (5) [resolution 255,122]
261. ~5 [avatar contradiction clause 258]
262. $false [avatar sat refutation 167,245,261]
% SZS output end Proof for 9211332816841883705189704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is creative then paul is both strong and not patient and vice versa. Everyone who is patient is both rich and brave and vice versa. If someone is quiet then paul is strong or not happy. Everyone who is either not kind or old is both not humble and happy and vice versa. If paul is either not old or not generous then mary is not rich and vice versa. If someone is either creative or brave then someone is both patient and not brave. If someone is creative then someone is curious or not creative and vice versa. Everyone who is both brave and not rich is quiet. Everyone who is either rich or creative is both kind and not curious and vice versa. If someone is both curious and kind then someone is humble or patient and vice versa. Everyone who is both quiet and tall is both not curious and old. If fred is not happy or not generous then someone is either strong or not generous and vice versa. Everyone who is either not brave or not strong is both not kind and happy and vice versa. Everyone who is quiet or not happy is both not strong and humble and vice versa. If someone is either funny or brave then someone is not kind. If susan is both not calm and not strong then someone is both not humble and brave. Lucy is rich. Susan is either calm or not generous. Someone is wise or funny. Fred is both not rich and funny. Someone is either curious or humble. Susan is both not strong and happy. Alice is not curious or brave. Alice is not wise.
|
John is curious.
|
neutral
|
((creative(john))<=>((strong(paul)&~patient(paul))))&
(![X]:(patient(X)<=>(rich(X)&brave(X))))&
((?[X]:(quiet(X)))=>((strong(paul)|~happy(paul))))&
(![X]:((~kind(X)<~>old(X))<=>(~humble(X)&happy(X))))&
(((~old(paul)<~>~generous(paul)))<=>(~rich(mary)))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((patient(X)&~brave(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:((brave(X)&~rich(X))=>quiet(X)))&
(![X]:((rich(X)<~>creative(X))<=>(kind(X)&~curious(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((quiet(X)&tall(X))=>(~curious(X)&old(X))))&
(((~happy(fred)|~generous(fred)))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((~brave(X)<~>~strong(X))<=>(~kind(X)&happy(X))))&
(![X]:((quiet(X)|~happy(X))<=>(~strong(X)&humble(X))))&
((?[X]:((funny(X)<~>brave(X))))=>(?[X]:(~kind(X))))&
(((~calm(susan)&~strong(susan)))=>(?[X]:((~humble(X)&brave(X)))))&
(rich(lucy))&
((calm(susan)<~>~generous(susan)))&
(?[X]:((wise(X)|funny(X))))&
((~rich(fred)&funny(fred)))&
(?[X]:((curious(X)<~>humble(X))))&
((~strong(susan)&happy(susan)))&
((~curious(alice)|brave(alice)))&
(~wise(alice))
|
curious(john)
|
[] | null | 0 |
If john is not rich or not brave then fred is both not funny and not strong.
Everyone who is brave is either calm or funny.
If someone is not happy then someone is both not kind and not calm and vice versa.
If someone is either creative or not calm then someone is wise and vice versa.
Everyone who is strong is either happy or brave and vice versa.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
If someone is creative or not patient then someone is both rich and not rich and vice versa.
Everyone who is funny or curious is either not rich or not tall and vice versa.
Everyone who is both strong and not patient is both not kind and not curious.
If susan is either patient or curious then someone is strong or brave.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Someone is not kind or strong.
Someone is both not curious and quiet.
Fred is not curious or brave.
Fred is not patient or humble.
Someone is both wise and not rich.
Someone is not strong.
Susan is both funny and not humble.
|
Lucy is creative.
|
contradiction
|
(((~rich(john)|~brave(john)))=>((~funny(fred)&~strong(fred))))&
(![X]:(brave(X)=>(calm(X)<~>funny(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~kind(X)&~calm(X)))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(happy(X)<~>brave(X))))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((funny(X)|curious(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:((strong(X)&~patient(X))=>(~kind(X)&~curious(X))))&
(((patient(susan)<~>curious(susan)))=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~curious(X)&quiet(X))))&
((~curious(fred)|brave(fred)))&
((~patient(fred)|humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
(?[X]:(~strong(X)))&
((funny(susan)&~humble(susan)))
|
creative(lucy)
|
[
"p7",
"hypothesis"
] |
% SZS status Unsatisfiable for 3739443623464952798396997
% SZS output start Proof for 3739443623464952798396997
8. ? [X0] : (~patient(X0) | creative(X0)) <=> ? [X0] : (~rich(X0) & rich(X0)) [input p7]
23. creative(lucy) [input hypothesis]
26. ? [X0] : (~patient(X0) | creative(X0)) <=> ? [X1] : (~rich(X1) & rich(X1)) [rectify 8]
51. (? [X0] : (~patient(X0) | creative(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X1] : (~rich(X1) & rich(X1)) | ! [X0] : (patient(X0) & ~creative(X0))) [nnf transformation 26]
52. (? [X0] : (~patient(X0) | creative(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X2] : (~rich(X2) & rich(X2)) | ! [X3] : (patient(X3) & ~creative(X3))) [rectify 51]
53. ? [X0] : (~patient(X0) | creative(X0)) => (~patient(sK4) | creative(sK4)) [choice axiom]
54. ? [X2] : (~rich(X2) & rich(X2)) => (~rich(sK5) & rich(sK5)) [choice axiom]
55. ((~patient(sK4) | creative(sK4)) | ! [X1] : (rich(X1) | ~rich(X1))) & ((~rich(sK5) & rich(sK5)) | ! [X3] : (patient(X3) & ~creative(X3))) [skolemisation 52,54,53]
107. rich(sK5) | ~creative(X3) [cnf transformation 55]
109. ~rich(sK5) | ~creative(X3) [cnf transformation 55]
148. creative(lucy) [cnf transformation 23]
219. 17 <=> rich(sK5) [avatar definition]
224. 18 <=> ! [X3] : ~creative(X3) [avatar definition]
225. ~creative(X3) <- (18) [avatar component clause 224]
226. 18 | ~17 [avatar split clause 109,219,224]
228. 18 | 17 [avatar split clause 107,219,224]
366. $false <- (18) [resolution 225,148]
367. ~18 [avatar contradiction clause 366]
368. $false [avatar sat refutation 226,228,367]
% SZS output end Proof for 3739443623464952798396997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not happy is tall.
If lucy is both tall and not quiet then paul is both wise and strong.
Everyone who is both quiet and not humble is either tall or calm.
Everyone who is either not generous or not old is wise or rich and vice versa.
Everyone who is happy is either humble or not tall and vice versa.
Everyone who is kind or not humble is either wise or not humble and vice versa.
If john is both strong and not happy then someone is not strong or tall and vice versa.
Everyone who is either not kind or not patient is not kind or quiet.
Everyone who is both not generous and creative is both patient and tall.
If someone is curious then fred is funny and vice versa.
Everyone who is not rich is both not humble and not curious and vice versa.
Everyone who is brave or generous is either strong or quiet and vice versa.
Everyone who is both tall and quiet is both not happy and rich.
Everyone who is both patient and not calm is happy or not happy and vice versa.
Everyone who is both rich and not strong is not wise.
Everyone who is not calm or patient is not happy or kind.
Someone is either not humble or not creative.
Someone is quiet.
Lucy is both not kind and not tall.
Someone is both funny and tall.
Someone is happy or not generous.
John is not wise.
Paul is not funny or brave.
Someone is both kind and quiet.
|
Lucy is not wise.
|
entailment
|
(![X]:((calm(X)&~happy(X))=>tall(X)))&
(((tall(lucy)&~quiet(lucy)))=>((wise(paul)&strong(paul))))&
(![X]:((quiet(X)&~humble(X))=>(tall(X)<~>calm(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(wise(X)|rich(X))))&
(![X]:(happy(X)<=>(humble(X)<~>~tall(X))))&
(![X]:((kind(X)|~humble(X))<=>(wise(X)<~>~humble(X))))&
(((strong(john)&~happy(john)))<=>(?[X]:((~strong(X)|tall(X)))))&
(![X]:((~kind(X)<~>~patient(X))=>(~kind(X)|quiet(X))))&
(![X]:((~generous(X)&creative(X))=>(patient(X)&tall(X))))&
((?[X]:(curious(X)))<=>(funny(fred)))&
(![X]:(~rich(X)<=>(~humble(X)&~curious(X))))&
(![X]:((brave(X)|generous(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)&quiet(X))=>(~happy(X)&rich(X))))&
(![X]:((patient(X)&~calm(X))<=>(happy(X)|~happy(X))))&
(![X]:((rich(X)&~strong(X))=>~wise(X)))&
(![X]:((~calm(X)|patient(X))=>(~happy(X)|kind(X))))&
(?[X]:((~humble(X)<~>~creative(X))))&
(?[X]:(quiet(X)))&
((~kind(lucy)&~tall(lucy)))&
(?[X]:((funny(X)&tall(X))))&
(?[X]:((happy(X)|~generous(X))))&
(~wise(john))&
((~funny(paul)|brave(paul)))&
(?[X]:((kind(X)&quiet(X))))
|
~wise(lucy)
|
[
"p5",
"p18",
"hypothesis"
] |
% SZS status Unsatisfiable for 9133461379535888778729042
% SZS output start Proof for 9133461379535888778729042
6. ! [X0] : ((~humble(X0) | kind(X0)) <=> (wise(X0) <~> ~humble(X0))) [input p5]
19. ~tall(lucy) & ~kind(lucy) [input p18]
25. wise(lucy) [input hypothesis]
46. ! [X0] : (((~humble(X0) | kind(X0)) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (humble(X0) & ~kind(X0)))) [nnf transformation 6]
47. ! [X0] : ((~humble(X0) | kind(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (humble(X0) & ~kind(X0)))) [flattening 46]
93. humble(X0) | ~wise(X0) | humble(X0) [cnf transformation 47]
94. ~humble(X0) | kind(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 47]
129. ~kind(lucy) [cnf transformation 19]
138. wise(lucy) [cnf transformation 25]
140. ~wise(X0) | humble(X0) [duplicate literal removal 93]
141. ~humble(X0) | kind(X0) | ~wise(X0) [duplicate literal removal 94]
238. humble(lucy) [resolution 140,138]
399. kind(lucy) | ~wise(lucy) [resolution 141,238]
402. ~wise(lucy) [subsumption resolution 399,129]
403. $false [subsumption resolution 402,138]
% SZS output end Proof for 9133461379535888778729042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not tall then paul is not old or funny and vice versa.
Everyone who is not rich or brave is both curious and not happy.
If paul is kind or not wise then someone is happy or not funny and vice versa.
Everyone who is both not humble and not tall is either calm or funny and vice versa.
If mary is both happy and not generous then john is humble and vice versa.
Everyone who is both not humble and kind is either not happy or strong.
Everyone who is both not old and happy is both not tall and not creative.
Everyone who is either not humble or generous is either not generous or quiet.
If paul is both not kind and not humble then someone is not rich or patient and vice versa.
Everyone who is either kind or not quiet is both not old and not curious.
If someone is both not humble and quiet then someone is wise or not funny and vice versa.
If someone is tall then susan is either patient or calm and vice versa.
If someone is creative or calm then someone is both tall and not wise.
If susan is either quiet or not wise then mary is curious or not old.
If paul is either not kind or not humble then susan is curious or tall.
Everyone who is not tall is both not calm and rich.
Alice is both generous and creative.
Alice is quiet.
Someone is both not strong and funny.
Susan is not curious or not patient.
John is humble.
Someone is either quiet or creative.
Susan is both generous and not patient.
|
Paul is funny.
|
neutral
|
((?[X]:((creative(X)<~>~tall(X))))<=>((~old(paul)|funny(paul))))&
(![X]:((~rich(X)|brave(X))=>(curious(X)&~happy(X))))&
(((kind(paul)|~wise(paul)))<=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)<~>funny(X))))&
(((happy(mary)&~generous(mary)))<=>(humble(john)))&
(![X]:((~humble(X)&kind(X))=>(~happy(X)<~>strong(X))))&
(![X]:((~old(X)&happy(X))=>(~tall(X)&~creative(X))))&
(![X]:((~humble(X)<~>generous(X))=>(~generous(X)<~>quiet(X))))&
(((~kind(paul)&~humble(paul)))<=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((kind(X)<~>~quiet(X))=>(~old(X)&~curious(X))))&
((?[X]:((~humble(X)&quiet(X))))<=>(?[X]:((wise(X)|~funny(X)))))&
((?[X]:(tall(X)))<=>((patient(susan)<~>calm(susan))))&
((?[X]:((creative(X)|calm(X))))=>(?[X]:((tall(X)&~wise(X)))))&
(((quiet(susan)<~>~wise(susan)))=>((curious(mary)|~old(mary))))&
(((~kind(paul)<~>~humble(paul)))=>((curious(susan)|tall(susan))))&
(![X]:(~tall(X)=>(~calm(X)&rich(X))))&
((generous(alice)&creative(alice)))&
(quiet(alice))&
(?[X]:((~strong(X)&funny(X))))&
((~curious(susan)|~patient(susan)))&
(humble(john))&
(?[X]:((quiet(X)<~>creative(X))))&
((generous(susan)&~patient(susan)))
|
funny(paul)
|
[] | null | 0 |
If someone is both not humble and kind then someone is both not kind and wise and vice versa.
If fred is either not rich or strong then someone is both not creative and not calm and vice versa.
If susan is not tall then someone is calm or rich.
Everyone who is either funny or patient is not rich and vice versa.
Everyone who is brave or calm is not old and vice versa.
If mary is both brave and not patient then someone is not funny.
If lucy is both curious and not happy then alice is kind and vice versa.
If lucy is curious or generous then someone is both not wise and not curious.
Everyone who is brave or not brave is both patient and happy.
If someone is not happy or quiet then someone is both not kind and patient.
If someone is tall then someone is both not kind and not tall and vice versa.
If alice is both not humble and happy then someone is not creative or humble.
If someone is both not kind and curious then fred is not rich or not humble and vice versa.
If john is not rich then someone is not curious.
Everyone who is not strong or calm is either not happy or not rich and vice versa.
Everyone who is rich is not kind and vice versa.
Lucy is both rich and strong.
Someone is calm or not brave.
Someone is not strong.
Mary is either not wise or not old.
Someone is both not brave and not creative.
Someone is either brave or not kind.
Someone is either not strong or brave.
John is generous or old.
|
Alice is strong.
|
entailment
|
((?[X]:((~humble(X)&kind(X))))<=>(?[X]:((~kind(X)&wise(X)))))&
(((~rich(fred)<~>strong(fred)))<=>(?[X]:((~creative(X)&~calm(X)))))&
((~tall(susan))=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((funny(X)<~>patient(X))<=>~rich(X)))&
(![X]:((brave(X)|calm(X))<=>~old(X)))&
(((brave(mary)&~patient(mary)))=>(?[X]:(~funny(X))))&
(((curious(lucy)&~happy(lucy)))<=>(kind(alice)))&
(((curious(lucy)|generous(lucy)))=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|~brave(X))=>(patient(X)&happy(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:((~kind(X)&patient(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)&~tall(X)))))&
(((~humble(alice)&happy(alice)))=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:((~kind(X)&curious(X))))<=>((~rich(fred)|~humble(fred))))&
((~rich(john))=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)|calm(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(rich(X)<=>~kind(X)))&
((rich(lucy)&strong(lucy)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:(~strong(X)))&
((~wise(mary)<~>~old(mary)))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((~strong(X)<~>brave(X))))&
((generous(john)|old(john)))
|
strong(alice)
|
[
"p6",
"p8",
"p14",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 721155604933567510220692
% SZS output start Proof for 721155604933567510220692
7. (~happy(lucy) & curious(lucy)) <=> kind(alice) [input p6]
9. ! [X0] : ((~brave(X0) | brave(X0)) => (happy(X0) & patient(X0))) [input p8]
15. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~happy(X0) <~> ~rich(X0))) [input p14]
16. ! [X0] : (rich(X0) <=> ~kind(X0)) [input p15]
25. ~strong(alice) [input hypothesis]
34. ! [X0] : ((happy(X0) & patient(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 9]
55. ((~happy(lucy) & curious(lucy)) | ~kind(alice)) & (kind(alice) | (happy(lucy) | ~curious(lucy))) [nnf transformation 7]
56. ((~happy(lucy) & curious(lucy)) | ~kind(alice)) & (kind(alice) | happy(lucy) | ~curious(lucy)) [flattening 55]
76. ! [X0] : (((calm(X0) | ~strong(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (~calm(X0) & strong(X0)))) [nnf transformation 15]
77. ! [X0] : ((calm(X0) | ~strong(X0) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (~calm(X0) & strong(X0)))) [flattening 76]
78. ! [X0] : ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))) [nnf transformation 16]
113. ~happy(lucy) | ~kind(alice) [cnf transformation 56]
120. happy(X0) | ~brave(X0) [cnf transformation 34]
121. happy(X0) | brave(X0) [cnf transformation 34]
134. ~rich(X0) | ~happy(X0) | strong(X0) [cnf transformation 77]
141. rich(X0) | kind(X0) [cnf transformation 78]
155. ~strong(alice) [cnf transformation 25]
234. 18 <=> kind(alice) [avatar definition]
238. 19 <=> happy(lucy) [avatar definition]
240. ~happy(lucy) <- (~19) [avatar component clause 238]
241. ~18 | ~19 [avatar split clause 113,238,234]
264. happy(X0) [subsumption resolution 120,121]
332. ~rich(X0) | strong(X0) [subsumption resolution 134,264]
394. strong(X0) | kind(X0) [resolution 332,141]
401. kind(alice) [resolution 394,155]
406. 18 [avatar split clause 401,234]
407. $false <- (~19) [subsumption resolution 240,264]
408. 19 [avatar contradiction clause 407]
409. $false [avatar sat refutation 241,406,408]
% SZS output end Proof for 721155604933567510220692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not generous is not funny or humble.
Everyone who is both not old and generous is funny or quiet and vice versa.
Everyone who is not tall is patient or wise.
Everyone who is both not tall and calm is not curious or not generous and vice versa.
Everyone who is both strong and not calm is either humble or brave and vice versa.
Everyone who is not tall or strong is not curious or not brave and vice versa.
If fred is not kind then someone is humble and vice versa.
If someone is wise or happy then fred is funny.
Everyone who is either not happy or not funny is both not generous and curious.
Everyone who is not happy is either not tall or not rich.
Everyone who is creative or kind is both not kind and rich and vice versa.
If someone is both calm and not strong then alice is both not curious and kind.
If someone is not tall then paul is both wise and rich.
If someone is either not quiet or old then someone is creative or quiet and vice versa.
Everyone who is either not brave or not curious is both curious and creative and vice versa.
If someone is both happy and quiet then someone is either quiet or not kind and vice versa.
Someone is either brave or not old.
Someone is both calm and old.
Someone is not rich or kind.
Fred is both not quiet and not patient.
Paul is either not generous or brave.
Someone is both quiet and not strong.
|
Fred is not happy.
|
contradiction
|
(![X]:((rich(X)<~>~generous(X))=>(~funny(X)|humble(X))))&
(![X]:((~old(X)&generous(X))<=>(funny(X)|quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|wise(X))))&
(![X]:((~tall(X)&calm(X))<=>(~curious(X)|~generous(X))))&
(![X]:((strong(X)&~calm(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~tall(X)|strong(X))<=>(~curious(X)|~brave(X))))&
((~kind(fred))<=>(?[X]:(humble(X))))&
((?[X]:((wise(X)|happy(X))))=>(funny(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(![X]:(~happy(X)=>(~tall(X)<~>~rich(X))))&
(![X]:((creative(X)|kind(X))<=>(~kind(X)&rich(X))))&
((?[X]:((calm(X)&~strong(X))))=>((~curious(alice)&kind(alice))))&
((?[X]:(~tall(X)))=>((wise(paul)&rich(paul))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>(curious(X)&creative(X))))&
((?[X]:((happy(X)&quiet(X))))<=>(?[X]:((quiet(X)<~>~kind(X)))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:((calm(X)&old(X))))&
(?[X]:((~rich(X)|kind(X))))&
((~quiet(fred)&~patient(fred)))&
((~generous(paul)<~>brave(paul)))&
(?[X]:((quiet(X)&~strong(X))))
|
~happy(fred)
|
[
"p1",
"p7",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 70067835558946509164962
% SZS output start Proof for 70067835558946509164962
2. ! [X0] : ((generous(X0) & ~old(X0)) <=> (quiet(X0) | funny(X0))) [input p1]
8. ? [X0] : (happy(X0) | wise(X0)) => funny(fred) [input p7]
9. ! [X0] : ((~happy(X0) <~> ~funny(X0)) => (curious(X0) & ~generous(X0))) [input p8]
11. ! [X0] : ((kind(X0) | creative(X0)) <=> (rich(X0) & ~kind(X0))) [input p10]
14. ? [X0] : (~quiet(X0) <~> old(X0)) <=> ? [X0] : (quiet(X0) | creative(X0)) [input p13]
16. ? [X0] : (quiet(X0) & happy(X0)) <=> ? [X0] : (quiet(X0) <~> ~kind(X0)) [input p15]
23. ~happy(fred) [input hypothesis]
24. ? [X0] : (~quiet(X0) <~> old(X0)) <=> ? [X1] : (quiet(X1) | creative(X1)) [rectify 14]
25. ? [X0] : (quiet(X0) & happy(X0)) <=> ? [X1] : (quiet(X1) <~> ~kind(X1)) [rectify 16]
30. funny(fred) | ! [X0] : (~happy(X0) & ~wise(X0)) [ennf transformation 8]
31. ! [X0] : ((curious(X0) & ~generous(X0)) | (~happy(X0) <=> ~funny(X0))) [ennf transformation 9]
36. ! [X0] : (((generous(X0) & ~old(X0)) | (~quiet(X0) & ~funny(X0))) & ((quiet(X0) | funny(X0)) | (~generous(X0) | old(X0)))) [nnf transformation 2]
37. ! [X0] : (((generous(X0) & ~old(X0)) | (~quiet(X0) & ~funny(X0))) & (quiet(X0) | funny(X0) | ~generous(X0) | old(X0))) [flattening 36]
48. ! [X0] : ((curious(X0) & ~generous(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) [nnf transformation 31]
50. ! [X0] : (((kind(X0) | creative(X0)) | (~rich(X0) | kind(X0))) & ((rich(X0) & ~kind(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 11]
51. ! [X0] : ((kind(X0) | creative(X0) | ~rich(X0) | kind(X0)) & ((rich(X0) & ~kind(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 50]
52. (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ! [X1] : (~quiet(X1) & ~creative(X1))) & (? [X1] : (quiet(X1) | creative(X1)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) [nnf transformation 24]
53. (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ! [X1] : (~quiet(X1) & ~creative(X1))) & (? [X2] : (quiet(X2) | creative(X2)) | ! [X3] : ((~quiet(X3) | ~old(X3)) & (old(X3) | quiet(X3)))) [rectify 52]
54. ? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) => ((~old(sK1) | quiet(sK1)) & (old(sK1) | ~quiet(sK1))) [choice axiom]
55. ? [X2] : (quiet(X2) | creative(X2)) => (quiet(sK2) | creative(sK2)) [choice axiom]
56. (((~old(sK1) | quiet(sK1)) & (old(sK1) | ~quiet(sK1))) | ! [X1] : (~quiet(X1) & ~creative(X1))) & ((quiet(sK2) | creative(sK2)) | ! [X3] : ((~quiet(X3) | ~old(X3)) & (old(X3) | quiet(X3)))) [skolemisation 53,55,54]
59. (? [X0] : (quiet(X0) & happy(X0)) | ! [X1] : ((quiet(X1) | kind(X1)) & (~kind(X1) | ~quiet(X1)))) & (? [X1] : ((kind(X1) | ~quiet(X1)) & (~kind(X1) | quiet(X1))) | ! [X0] : (~quiet(X0) | ~happy(X0))) [nnf transformation 25]
60. (? [X0] : (quiet(X0) & happy(X0)) | ! [X1] : ((quiet(X1) | kind(X1)) & (~kind(X1) | ~quiet(X1)))) & (? [X2] : ((kind(X2) | ~quiet(X2)) & (~kind(X2) | quiet(X2))) | ! [X3] : (~quiet(X3) | ~happy(X3))) [rectify 59]
61. ? [X0] : (quiet(X0) & happy(X0)) => (quiet(sK3) & happy(sK3)) [choice axiom]
62. ? [X2] : ((kind(X2) | ~quiet(X2)) & (~kind(X2) | quiet(X2))) => ((kind(sK4) | ~quiet(sK4)) & (~kind(sK4) | quiet(sK4))) [choice axiom]
63. ((quiet(sK3) & happy(sK3)) | ! [X1] : ((quiet(X1) | kind(X1)) & (~kind(X1) | ~quiet(X1)))) & (((kind(sK4) | ~quiet(sK4)) & (~kind(sK4) | quiet(sK4))) | ! [X3] : (~quiet(X3) | ~happy(X3))) [skolemisation 60,62,61]
78. ~quiet(X0) | ~old(X0) [cnf transformation 37]
79. ~funny(X0) | generous(X0) [cnf transformation 37]
100. funny(fred) | ~happy(X0) [cnf transformation 30]
101. ~generous(X0) | ~funny(X0) | happy(X0) [cnf transformation 48]
108. ~kind(X0) | ~kind(X0) [cnf transformation 51]
119. old(sK1) | ~quiet(sK1) | ~quiet(X1) [cnf transformation 56]
131. happy(sK3) | quiet(X1) | kind(X1) [cnf transformation 63]
145. ~happy(fred) [cnf transformation 23]
148. ~kind(X0) [duplicate literal removal 108]
164. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
165. ~happy(X0) <- (4) [avatar component clause 164]
167. 5 <=> funny(fred) [avatar definition]
169. funny(fred) <- (5) [avatar component clause 167]
170. 4 | 5 [avatar split clause 100,167,164]
175. ~funny(X0) | happy(X0) [subsumption resolution 101,79]
192. 10 <=> ! [X1] : ~quiet(X1) [avatar definition]
193. ~quiet(X1) <- (10) [avatar component clause 192]
204. ~quiet(sK1) | ~quiet(X1) [subsumption resolution 119,78]
206. 13 <=> quiet(sK1) [avatar definition]
208. ~quiet(sK1) <- (~13) [avatar component clause 206]
209. 10 | ~13 [avatar split clause 204,206,192]
226. 17 <=> ! [X1] : quiet(X1) [avatar definition]
227. quiet(X1) <- (17) [avatar component clause 226]
233. happy(sK3) | quiet(X1) [subsumption resolution 131,148]
235. 19 <=> happy(sK3) [avatar definition]
237. happy(sK3) <- (19) [avatar component clause 235]
238. 17 | 19 [avatar split clause 233,235,226]
269. $false <- (~13, 17) [subsumption resolution 208,227]
270. 13 | ~17 [avatar contradiction clause 269]
271. $false <- (10, 17) [subsumption resolution 193,227]
272. ~10 | ~17 [avatar contradiction clause 271]
283. happy(fred) <- (5) [resolution 175,169]
284. $false <- (5) [subsumption resolution 283,145]
285. ~5 [avatar contradiction clause 284]
286. $false <- (4, 19) [resolution 165,237]
287. ~4 | ~19 [avatar contradiction clause 286]
288. $false [avatar sat refutation 170,209,238,270,272,285,287]
% SZS output end Proof for 70067835558946509164962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not strong then someone is both not happy and kind and vice versa.
Everyone who is both calm and strong is either not wise or old.
If someone is tall or not humble then someone is either creative or generous.
Everyone who is not tall or not rich is both old and not curious.
If john is either not funny or creative then paul is humble or curious and vice versa.
Everyone who is wise is old or strong.
Everyone who is not funny or brave is curious and vice versa.
Everyone who is humble is both not curious and not kind and vice versa.
Everyone who is either not tall or old is both not creative and patient.
If someone is kind then someone is curious and vice versa.
Everyone who is not kind is humble or not generous.
Everyone who is either not generous or calm is not quiet or not tall and vice versa.
Everyone who is both brave and not happy is old or not creative and vice versa.
Everyone who is not old is curious.
Everyone who is happy or old is not old and vice versa.
Someone is both generous and curious.
Mary is rich or curious.
John is creative or not curious.
Someone is rich or strong.
Mary is both generous and not brave.
Someone is either kind or not funny.
|
Mary is funny.
|
contradiction
|
(((patient(lucy)|~strong(lucy)))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:(curious(X))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((brave(X)&~happy(X))<=>(old(X)|~creative(X))))&
(![X]:(~old(X)=>curious(X)))&
(![X]:((happy(X)|old(X))<=>~old(X)))&
(?[X]:((generous(X)&curious(X))))&
((rich(mary)|curious(mary)))&
((creative(john)|~curious(john)))&
(?[X]:((rich(X)|strong(X))))&
((generous(mary)&~brave(mary)))&
(?[X]:((kind(X)<~>~funny(X))))
|
funny(mary)
|
[
"p6",
"p13",
"p14",
"p19",
"hypothesis"
] |
% SZS status Unsatisfiable for 2250427071802593412894556
% SZS output start Proof for 2250427071802593412894556
7. ! [X0] : ((brave(X0) | ~funny(X0)) <=> curious(X0)) [input p6]
14. ! [X0] : (~old(X0) => curious(X0)) [input p13]
15. ! [X0] : ((old(X0) | happy(X0)) <=> ~old(X0)) [input p14]
20. ~brave(mary) & generous(mary) [input p19]
22. funny(mary) [input hypothesis]
37. ! [X0] : (curious(X0) | old(X0)) [ennf transformation 14]
50. ! [X0] : (((brave(X0) | ~funny(X0)) | ~curious(X0)) & (curious(X0) | (~brave(X0) & funny(X0)))) [nnf transformation 7]
51. ! [X0] : ((brave(X0) | ~funny(X0) | ~curious(X0)) & (curious(X0) | (~brave(X0) & funny(X0)))) [flattening 50]
64. ! [X0] : (((old(X0) | happy(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [nnf transformation 15]
65. ! [X0] : ((old(X0) | happy(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~happy(X0)))) [flattening 64]
93. ~funny(X0) | brave(X0) | ~curious(X0) [cnf transformation 51]
115. curious(X0) | old(X0) [cnf transformation 37]
117. ~old(X0) | ~old(X0) [cnf transformation 65]
123. ~brave(mary) [cnf transformation 20]
126. funny(mary) [cnf transformation 22]
127. ~old(X0) [duplicate literal removal 117]
258. brave(mary) | ~curious(mary) [resolution 93,126]
261. ~curious(mary) [subsumption resolution 258,123]
270. old(mary) [resolution 261,115]
272. $false [subsumption resolution 270,127]
% SZS output end Proof for 2250427071802593412894556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is not humble or funny is both not curious and tall.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
Everyone who is creative is both strong and not creative.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Everyone who is either humble or not humble is not humble.
Someone is not brave or patient.
Someone is either not old or tall.
Susan is not brave.
Fred is both funny and not creative.
Susan is either old or kind.
|
Fred is not quiet.
|
entailment
|
(![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((~humble(X)|funny(X))=>(~curious(X)&tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>(strong(X)&~creative(X))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
(![X]:((humble(X)<~>~humble(X))=>~humble(X)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~old(X)<~>tall(X))))&
(~brave(susan))&
((funny(fred)&~creative(fred)))&
((old(susan)<~>kind(susan)))
|
~quiet(fred)
|
[
"p2",
"p3",
"p7",
"p8",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] |
% SZS status Unsatisfiable for 3429978134566582842523877
% SZS output start Proof for 3429978134566582842523877
3. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p2]
4. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p3]
8. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p7]
9. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p8]
12. ? [X0] : ~wise(X0) <=> ? [X0] : (~calm(X0) <~> ~quiet(X0)) [input p11]
13. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
20. ~creative(fred) & funny(fred) [input p19]
22. quiet(fred) [input hypothesis]
23. ? [X0] : ~wise(X0) <=> ? [X1] : (~calm(X1) <~> ~quiet(X1)) [rectify 12]
25. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 3]
32. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 13]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 4]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 8]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
45. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 9]
46. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 45]
55. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X1] : ((quiet(X1) | calm(X1)) & (~quiet(X1) | ~calm(X1))) | ! [X0] : wise(X0)) [nnf transformation 23]
56. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) | ! [X3] : wise(X3)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. ? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) => ((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) [choice axiom]
59. (~wise(sK3) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) | ! [X3] : wise(X3)) [skolemisation 56,58,57]
63. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 63]
80. ~rich(X0) | happy(X0) [cnf transformation 25]
84. ~happy(X0) | creative(X0) | patient(X0) [cnf transformation 36]
93. ~funny(fred) | wise(X1) [cnf transformation 44]
96. ~patient(fred) | creative(alice) [cnf transformation 46]
109. ~wise(sK3) | ~quiet(X1) | calm(X1) [cnf transformation 59]
112. ~creative(X0) | ~creative(X0) [cnf transformation 32]
117. rich(X0) | ~calm(X0) | rich(X0) | happy(X0) [cnf transformation 64]
129. funny(fred) [cnf transformation 20]
133. quiet(fred) [cnf transformation 22]
136. rich(X0) | ~calm(X0) | happy(X0) [duplicate literal removal 117]
138. ~creative(X0) [duplicate literal removal 112]
144. 2 <=> funny(fred) [avatar definition]
153. 4 <=> ! [X1] : wise(X1) [avatar definition]
154. wise(X1) <- (4) [avatar component clause 153]
155. 4 | ~2 [avatar split clause 93,144,153]
158. 5 <=> patient(fred) [avatar definition]
170. 8 <=> creative(alice) [avatar definition]
171. creative(alice) <- (8) [avatar component clause 170]
176. 8 | ~5 [avatar split clause 96,158,170]
216. 17 <=> wise(sK3) [avatar definition]
218. ~wise(sK3) <- (~17) [avatar component clause 216]
221. 18 <=> ! [X1] : (~quiet(X1) | calm(X1)) [avatar definition]
222. ~quiet(X1) | calm(X1) <- (18) [avatar component clause 221]
223. 18 | ~17 [avatar split clause 109,216,221]
248. ~calm(X0) | happy(X0) [subsumption resolution 136,80]
268. 2 [avatar split clause 129,144]
279. $false <- (4, ~17) [resolution 218,154]
280. ~4 | 17 [avatar contradiction clause 279]
292. calm(fred) <- (18) [resolution 222,133]
294. happy(fred) <- (18) [resolution 248,292]
307. creative(fred) | patient(fred) <- (18) [resolution 84,294]
309. patient(fred) <- (18) [subsumption resolution 307,138]
312. 5 | ~18 [avatar split clause 309,221,158]
313. $false <- (8) [subsumption resolution 171,138]
314. ~8 [avatar contradiction clause 313]
315. $false [avatar sat refutation 155,176,223,268,280,312,314]
% SZS output end Proof for 3429978134566582842523877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is tall or not patient then paul is not kind or happy and vice versa. Everyone who is quiet is kind. Everyone who is either rich or funny is either strong or generous and vice versa. Everyone who is either tall or creative is quiet or not strong. Everyone who is both not tall and wise is not curious and vice versa. Everyone who is generous is brave or old and vice versa. Everyone who is not rich or brave is either brave or not old and vice versa. Everyone who is not humble is kind. If alice is either not quiet or humble then someone is both tall and old and vice versa. Everyone who is creative is either not curious or not funny. Everyone who is both kind and generous is not brave or tall and vice versa. If fred is kind then susan is not curious. If someone is either strong or not quiet then someone is either brave or not rich. If someone is not creative or quiet then john is not generous and vice versa. Everyone who is both creative and not rich is both not wise and not curious and vice versa. If john is either funny or happy then someone is not humble and vice versa. Alice is either not patient or strong. Lucy is either not tall or not curious. Someone is not strong or generous. Alice is either not funny or funny. Someone is old.
|
Paul is not curious.
|
contradiction
|
(((tall(fred)|~patient(fred)))<=>((~kind(paul)|happy(paul))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((rich(X)<~>funny(X))<=>(strong(X)<~>generous(X))))&
(![X]:((tall(X)<~>creative(X))=>(quiet(X)|~strong(X))))&
(![X]:((~tall(X)&wise(X))<=>~curious(X)))&
(![X]:(generous(X)<=>(brave(X)|old(X))))&
(![X]:((~rich(X)|brave(X))<=>(brave(X)<~>~old(X))))&
(![X]:(~humble(X)=>kind(X)))&
(((~quiet(alice)<~>humble(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:(creative(X)=>(~curious(X)<~>~funny(X))))&
(![X]:((kind(X)&generous(X))<=>(~brave(X)|tall(X))))&
((kind(fred))=>(~curious(susan)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
((?[X]:((~creative(X)|quiet(X))))<=>(~generous(john)))&
(![X]:((creative(X)&~rich(X))<=>(~wise(X)&~curious(X))))&
(((funny(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
((~patient(alice)<~>strong(alice)))&
((~tall(lucy)<~>~curious(lucy)))&
(?[X]:((~strong(X)|generous(X))))&
((~funny(alice)<~>funny(alice)))&
(?[X]:(old(X)))
|
~curious(paul)
|
[
"p2",
"p3",
"p4",
"p5",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 5798737951297405755563856
% SZS output start Proof for 5798737951297405755563856
3. ! [X0] : ((rich(X0) <~> funny(X0)) <=> (strong(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((tall(X0) <~> creative(X0)) => (~strong(X0) | quiet(X0))) [input p3]
5. ! [X0] : ((wise(X0) & ~tall(X0)) <=> ~curious(X0)) [input p4]
6. ! [X0] : (generous(X0) <=> (old(X0) | brave(X0))) [input p5]
10. ! [X0] : (creative(X0) => (~curious(X0) <~> ~funny(X0))) [input p9]
11. ! [X0] : ((generous(X0) & kind(X0)) <=> (tall(X0) | ~brave(X0))) [input p10]
14. ? [X0] : (quiet(X0) | ~creative(X0)) <=> ~generous(john) [input p13]
15. ! [X0] : ((~rich(X0) & creative(X0)) <=> (~curious(X0) & ~wise(X0))) [input p14]
22. ~curious(paul) [input hypothesis]
25. ! [X0] : ((~strong(X0) | quiet(X0)) | (tall(X0) <=> creative(X0))) [ennf transformation 4]
26. ! [X0] : (~strong(X0) | quiet(X0) | (tall(X0) <=> creative(X0))) [flattening 25]
28. ! [X0] : ((~curious(X0) <~> ~funny(X0)) | ~creative(X0)) [ennf transformation 10]
33. ! [X0] : ((((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0)))) & (((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0))))) [nnf transformation 3]
34. ! [X0] : (~strong(X0) | quiet(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) [nnf transformation 26]
35. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | (~wise(X0) | tall(X0)))) [nnf transformation 5]
36. ! [X0] : (((wise(X0) & ~tall(X0)) | curious(X0)) & (~curious(X0) | ~wise(X0) | tall(X0))) [flattening 35]
37. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & ((old(X0) | brave(X0)) | ~generous(X0))) [nnf transformation 6]
38. ! [X0] : ((generous(X0) | (~old(X0) & ~brave(X0))) & (old(X0) | brave(X0) | ~generous(X0))) [flattening 37]
45. ! [X0] : (((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | ~creative(X0)) [nnf transformation 28]
46. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (~generous(X0) | ~kind(X0)))) [nnf transformation 11]
47. ! [X0] : (((generous(X0) & kind(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | ~generous(X0) | ~kind(X0))) [flattening 46]
52. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 14]
53. (? [X0] : (quiet(X0) | ~creative(X0)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK2) | ~creative(sK2)) [choice axiom]
55. ((quiet(sK2) | ~creative(sK2)) | generous(john)) & (~generous(john) | ! [X1] : (~quiet(X1) & creative(X1))) [skolemisation 53,54]
56. ! [X0] : (((~rich(X0) & creative(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 15]
57. ! [X0] : (((~rich(X0) & creative(X0)) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | rich(X0) | ~creative(X0))) [flattening 56]
81. ~generous(X0) | ~rich(X0) | strong(X0) | ~funny(X0) [cnf transformation 33]
83. ~creative(X0) | quiet(X0) | tall(X0) | ~strong(X0) [cnf transformation 34]
85. ~tall(X0) | curious(X0) [cnf transformation 36]
86. curious(X0) | wise(X0) [cnf transformation 36]
88. ~brave(X0) | generous(X0) [cnf transformation 38]
104. ~creative(X0) | curious(X0) | funny(X0) [cnf transformation 45]
108. generous(X0) | brave(X0) [cnf transformation 47]
115. ~generous(john) | creative(X1) [cnf transformation 55]
116. ~generous(john) | ~quiet(X1) [cnf transformation 55]
118. ~wise(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
119. ~curious(X0) | rich(X0) | ~creative(X0) [cnf transformation 57]
134. ~curious(paul) [cnf transformation 22]
182. generous(X0) [subsumption resolution 108,88]
211. ~quiet(X1) [subsumption resolution 116,182]
212. creative(X1) [subsumption resolution 115,182]
213. ~curious(X0) | rich(X0) [subsumption resolution 119,212]
214. ~wise(X0) | rich(X0) [subsumption resolution 118,212]
260. rich(X0) | wise(X0) [resolution 213,86]
261. rich(X0) [subsumption resolution 260,214]
283. curious(X0) | funny(X0) [resolution 104,212]
300. funny(paul) [resolution 283,134]
310. ~rich(X0) | strong(X0) | ~funny(X0) [resolution 81,182]
311. ~funny(X0) | strong(X0) [subsumption resolution 310,261]
313. strong(paul) [resolution 311,300]
318. quiet(X0) | tall(X0) | ~strong(X0) [resolution 83,212]
319. ~strong(X0) | tall(X0) [subsumption resolution 318,211]
343. tall(paul) [resolution 313,319]
353. curious(paul) [resolution 343,85]
356. $false [subsumption resolution 353,134]
% SZS output end Proof for 5798737951297405755563856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not old is either not creative or quiet and vice versa.
If lucy is generous then alice is either quiet or not happy and vice versa.
If john is either quiet or patient then someone is both not wise and old and vice versa.
Everyone who is tall is curious and vice versa.
If john is both not old and happy then someone is patient or generous.
If mary is not kind then someone is not wise or funny.
If someone is both not wise and not creative then someone is either not kind or old.
If someone is either tall or not happy then fred is wise and vice versa.
Everyone who is both not brave and old is brave and vice versa.
Everyone who is either kind or not wise is not kind or quiet.
If someone is quiet then lucy is not wise or generous and vice versa.
If mary is either old or happy then lucy is funny or quiet and vice versa.
If someone is not happy then paul is rich and vice versa.
If fred is generous or rich then fred is either not rich or not creative and vice versa.
If lucy is tall then fred is either not brave or not wise and vice versa.
Everyone who is not strong is either not wise or creative.
Someone is both not wise and not humble.
Someone is tall.
Someone is either not generous or wise.
Paul is not strong or humble.
Someone is not tall.
Paul is old or not wise.
Alice is either not patient or tall.
|
Lucy is not wise.
|
neutral
|
(![X]:((~brave(X)|~old(X))<=>(~creative(X)<~>quiet(X))))&
((generous(lucy))<=>((quiet(alice)<~>~happy(alice))))&
(((quiet(john)<~>patient(john)))<=>(?[X]:((~wise(X)&old(X)))))&
(![X]:(tall(X)<=>curious(X)))&
(((~old(john)&happy(john)))=>(?[X]:((patient(X)|generous(X)))))&
((~kind(mary))=>(?[X]:((~wise(X)|funny(X)))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>(wise(fred)))&
(![X]:((~brave(X)&old(X))<=>brave(X)))&
(![X]:((kind(X)<~>~wise(X))=>(~kind(X)|quiet(X))))&
((?[X]:(quiet(X)))<=>((~wise(lucy)|generous(lucy))))&
(((old(mary)<~>happy(mary)))<=>((funny(lucy)|quiet(lucy))))&
((?[X]:(~happy(X)))<=>(rich(paul)))&
(((generous(fred)|rich(fred)))<=>((~rich(fred)<~>~creative(fred))))&
((tall(lucy))<=>((~brave(fred)<~>~wise(fred))))&
(![X]:(~strong(X)=>(~wise(X)<~>creative(X))))&
(?[X]:((~wise(X)&~humble(X))))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)<~>wise(X))))&
((~strong(paul)|humble(paul)))&
(?[X]:(~tall(X)))&
((old(paul)|~wise(paul)))&
((~patient(alice)<~>tall(alice)))
|
~wise(lucy)
|
[] | null | 0 |
Everyone who is both not generous and not rich is both rich and not creative and vice versa.
Everyone who is not calm is not patient or strong and vice versa.
Everyone who is either not humble or calm is not calm or creative.
Everyone who is not calm is old or not rich and vice versa.
If lucy is curious or not humble then lucy is not humble or not strong and vice versa.
If someone is both not calm and not rich then alice is either not creative or not humble and vice versa.
Everyone who is not strong is curious and vice versa.
Everyone who is not funny is kind or not creative.
If someone is not strong then someone is both not brave and humble and vice versa.
Everyone who is not tall or calm is happy or not calm and vice versa.
If mary is not kind then susan is either not rich or generous and vice versa.
If mary is not calm then paul is not quiet or not tall.
Everyone who is kind is both strong and not humble and vice versa.
Everyone who is either not brave or brave is not old or generous.
Everyone who is old or not calm is both patient and curious.
If someone is both kind and quiet then mary is both tall and not happy.
Someone is not quiet or not happy.
Someone is not brave or humble.
Alice is rich.
Someone is tall.
Someone is either not kind or not rich.
Someone is either not creative or not generous.
|
Mary is not old.
|
entailment
|
(![X]:((~generous(X)&~rich(X))<=>(rich(X)&~creative(X))))&
(![X]:(~calm(X)<=>(~patient(X)|strong(X))))&
(![X]:((~humble(X)<~>calm(X))=>(~calm(X)|creative(X))))&
(![X]:(~calm(X)<=>(old(X)|~rich(X))))&
(((curious(lucy)|~humble(lucy)))<=>((~humble(lucy)|~strong(lucy))))&
((?[X]:((~calm(X)&~rich(X))))<=>((~creative(alice)<~>~humble(alice))))&
(![X]:(~strong(X)<=>curious(X)))&
(![X]:(~funny(X)=>(kind(X)|~creative(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~tall(X)|calm(X))<=>(happy(X)|~calm(X))))&
((~kind(mary))<=>((~rich(susan)<~>generous(susan))))&
((~calm(mary))=>((~quiet(paul)|~tall(paul))))&
(![X]:(kind(X)<=>(strong(X)&~humble(X))))&
(![X]:((~brave(X)<~>brave(X))=>(~old(X)|generous(X))))&
(![X]:((old(X)|~calm(X))=>(patient(X)&curious(X))))&
((?[X]:((kind(X)&quiet(X))))=>((tall(mary)&~happy(mary))))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((~brave(X)|humble(X))))&
(rich(alice))&
(?[X]:(tall(X)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((~creative(X)<~>~generous(X))))
|
~old(mary)
|
[
"p1",
"p3",
"p6",
"p14",
"hypothesis"
] |
% SZS status Unsatisfiable for 6788314090755755839476756
% SZS output start Proof for 6788314090755755839476756
2. ! [X0] : (~calm(X0) <=> (strong(X0) | ~patient(X0))) [input p1]
4. ! [X0] : (~calm(X0) <=> (~rich(X0) | old(X0))) [input p3]
7. ! [X0] : (~strong(X0) <=> curious(X0)) [input p6]
15. ! [X0] : ((~calm(X0) | old(X0)) => (curious(X0) & patient(X0))) [input p14]
23. old(mary) [input hypothesis]
33. ! [X0] : ((curious(X0) & patient(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 15]
36. ! [X0] : ((~calm(X0) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | calm(X0))) [nnf transformation 2]
37. ! [X0] : ((~calm(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | calm(X0))) [flattening 36]
39. ! [X0] : ((~calm(X0) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | calm(X0))) [nnf transformation 4]
40. ! [X0] : ((~calm(X0) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | calm(X0))) [flattening 39]
47. ! [X0] : ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0))) [nnf transformation 7]
73. ~patient(X0) | strong(X0) | calm(X0) [cnf transformation 37]
74. ~calm(X0) | patient(X0) [cnf transformation 37]
75. ~strong(X0) | ~calm(X0) [cnf transformation 37]
79. ~old(X0) | ~calm(X0) [cnf transformation 40]
92. ~curious(X0) | ~strong(X0) [cnf transformation 47]
110. patient(X0) | calm(X0) [cnf transformation 33]
112. curious(X0) | calm(X0) [cnf transformation 33]
120. old(mary) [cnf transformation 23]
208. patient(X0) [subsumption resolution 110,74]
241. ~calm(mary) [resolution 79,120]
246. calm(X0) | ~strong(X0) [resolution 112,92]
250. ~strong(X0) [subsumption resolution 246,75]
281. strong(X0) | calm(X0) [resolution 73,208]
282. calm(X0) [subsumption resolution 281,250]
287. $false [resolution 282,241]
% SZS output end Proof for 6788314090755755839476756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either brave or not rich then someone is both quiet and not strong and vice versa.
If someone is kind or not creative then mary is not quiet or old and vice versa.
If someone is both not humble and not strong then paul is not quiet and vice versa.
Everyone who is both not quiet and happy is both generous and not quiet and vice versa.
If someone is not rich then paul is both not calm and not old.
Everyone who is old or patient is humble or not patient and vice versa.
If fred is either calm or patient then someone is brave or not old.
Everyone who is both curious and not curious is both brave and not humble and vice versa.
If someone is creative or not patient then someone is not humble or patient.
Everyone who is either funny or not happy is rich or old and vice versa.
If paul is either not strong or not old then lucy is either not rich or not old.
If someone is both calm and creative then paul is either calm or humble and vice versa.
Everyone who is either not funny or not patient is not humble and vice versa.
Everyone who is generous is both calm and kind and vice versa.
Everyone who is not creative or old is both old and not happy and vice versa.
Everyone who is either not brave or kind is either kind or curious and vice versa.
Mary is not rich.
Susan is humble or curious.
John is either humble or not generous.
Someone is either strong or patient.
Mary is kind or not patient.
Paul is not brave or not strong.
Someone is both calm and humble.
|
Paul is curious.
|
neutral
|
((?[X]:((brave(X)<~>~rich(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((kind(X)|~creative(X))))<=>((~quiet(mary)|old(mary))))&
((?[X]:((~humble(X)&~strong(X))))<=>(~quiet(paul)))&
(![X]:((~quiet(X)&happy(X))<=>(generous(X)&~quiet(X))))&
((?[X]:(~rich(X)))=>((~calm(paul)&~old(paul))))&
(![X]:((old(X)|patient(X))<=>(humble(X)|~patient(X))))&
(((calm(fred)<~>patient(fred)))=>(?[X]:((brave(X)|~old(X)))))&
(![X]:((curious(X)&~curious(X))<=>(brave(X)&~humble(X))))&
((?[X]:((creative(X)|~patient(X))))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((funny(X)<~>~happy(X))<=>(rich(X)|old(X))))&
(((~strong(paul)<~>~old(paul)))=>((~rich(lucy)<~>~old(lucy))))&
((?[X]:((calm(X)&creative(X))))<=>((calm(paul)<~>humble(paul))))&
(![X]:((~funny(X)<~>~patient(X))<=>~humble(X)))&
(![X]:(generous(X)<=>(calm(X)&kind(X))))&
(![X]:((~creative(X)|old(X))<=>(old(X)&~happy(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(kind(X)<~>curious(X))))&
(~rich(mary))&
((humble(susan)|curious(susan)))&
((humble(john)<~>~generous(john)))&
(?[X]:((strong(X)<~>patient(X))))&
((kind(mary)|~patient(mary)))&
((~brave(paul)|~strong(paul)))&
(?[X]:((calm(X)&humble(X))))
|
curious(paul)
|
[] | null | 0 |
If mary is not generous or strong then someone is either not creative or not brave and vice versa.
Everyone who is either generous or not curious is either not generous or strong.
Everyone who is either not wise or strong is not tall and vice versa.
If fred is either not humble or not rich then fred is not old or tall and vice versa.
If john is both not creative and not curious then someone is not calm or patient.
Everyone who is both not curious and not patient is old and vice versa.
Everyone who is humble or not funny is both wise and funny.
If someone is not calm then someone is not tall and vice versa.
If someone is not curious or not happy then someone is either not tall or not kind and vice versa.
Everyone who is curious is not strong and vice versa.
If fred is not kind then susan is not wise.
If susan is both not old and not generous then paul is patient or not patient and vice versa.
If someone is either wise or not generous then someone is both not rich and creative and vice versa.
Everyone who is generous is both not calm and not brave and vice versa.
If someone is both creative and not creative then paul is not creative or calm.
Everyone who is both calm and not calm is not funny or quiet and vice versa.
Someone is not rich.
Someone is either not wise or not happy.
Someone is not calm.
Fred is not tall.
Someone is either rich or creative.
John is not generous or old.
|
Mary is not humble.
|
neutral
|
(((~generous(mary)|strong(mary)))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((generous(X)<~>~curious(X))=>(~generous(X)<~>strong(X))))&
(![X]:((~wise(X)<~>strong(X))<=>~tall(X)))&
(((~humble(fred)<~>~rich(fred)))<=>((~old(fred)|tall(fred))))&
(((~creative(john)&~curious(john)))=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~curious(X)&~patient(X))<=>old(X)))&
(![X]:((humble(X)|~funny(X))=>(wise(X)&funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~curious(X)|~happy(X))))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
(![X]:(curious(X)<=>~strong(X)))&
((~kind(fred))=>(~wise(susan)))&
(((~old(susan)&~generous(susan)))<=>((patient(paul)|~patient(paul))))&
((?[X]:((wise(X)<~>~generous(X))))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:(generous(X)<=>(~calm(X)&~brave(X))))&
((?[X]:((creative(X)&~creative(X))))=>((~creative(paul)|calm(paul))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|quiet(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~wise(X)<~>~happy(X))))&
(?[X]:(~calm(X)))&
(~tall(fred))&
(?[X]:((rich(X)<~>creative(X))))&
((~generous(john)|old(john)))
|
~humble(mary)
|
[] | null | 0 |
Everyone who is either happy or not strong is both not funny and brave.
If mary is funny then someone is not kind and vice versa.
Everyone who is kind or not quiet is both tall and creative and vice versa.
Everyone who is either calm or not funny is both generous and not wise and vice versa.
Everyone who is quiet or happy is both wise and generous and vice versa.
Everyone who is both generous and not quiet is either not kind or generous.
If someone is not patient or not strong then mary is either happy or not wise.
Everyone who is either strong or rich is both not brave and strong.
If lucy is either funny or not brave then fred is not funny or not creative and vice versa.
Everyone who is strong is both brave and not tall and vice versa.
If someone is curious or not old then someone is either not funny or rich and vice versa.
If someone is either patient or generous then lucy is brave and vice versa.
If susan is creative or not quiet then john is not kind and vice versa.
If mary is not creative then someone is not patient.
Everyone who is either strong or not brave is not patient.
Everyone who is either patient or not brave is rich and vice versa.
Someone is not quiet.
Someone is not wise or not humble.
Someone is either not rich or not creative.
Someone is both not kind and old.
Paul is humble.
Paul is not old or not generous.
Fred is not curious or calm.
Lucy is curious or not wise.
|
Lucy is curious.
|
neutral
|
(![X]:((happy(X)<~>~strong(X))=>(~funny(X)&brave(X))))&
((funny(mary))<=>(?[X]:(~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(tall(X)&creative(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(generous(X)&~wise(X))))&
(![X]:((quiet(X)|happy(X))<=>(wise(X)&generous(X))))&
(![X]:((generous(X)&~quiet(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((~patient(X)|~strong(X))))=>((happy(mary)<~>~wise(mary))))&
(![X]:((strong(X)<~>rich(X))=>(~brave(X)&strong(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((~funny(fred)|~creative(fred))))&
(![X]:(strong(X)<=>(brave(X)&~tall(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((patient(X)<~>generous(X))))<=>(brave(lucy)))&
(((creative(susan)|~quiet(susan)))<=>(~kind(john)))&
((~creative(mary))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)<~>~brave(X))=>~patient(X)))&
(![X]:((patient(X)<~>~brave(X))<=>rich(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
(?[X]:((~kind(X)&old(X))))&
(humble(paul))&
((~old(paul)|~generous(paul)))&
((~curious(fred)|calm(fred)))&
((curious(lucy)|~wise(lucy)))
|
curious(lucy)
|
[] | null | 0 |
Everyone who is tall is either not happy or not rich and vice versa. If john is generous then someone is either rich or not generous and vice versa. Everyone who is not tall or funny is old or not calm and vice versa. If paul is both creative and quiet then someone is either not curious or rich. If someone is both rich and calm then lucy is both old and not wise. Everyone who is not generous or creative is not funny. Everyone who is either not strong or generous is either curious or not strong. Everyone who is either not wise or not brave is either not brave or happy and vice versa. If someone is either not tall or strong then someone is either not strong or not creative and vice versa. Everyone who is not calm is old or kind and vice versa. Everyone who is both quiet and happy is curious or creative. If someone is not happy then someone is patient or not humble and vice versa. If mary is strong then susan is both calm and not generous and vice versa. Everyone who is both funny and not wise is not creative or generous and vice versa. Everyone who is either not brave or happy is either curious or strong and vice versa. Everyone who is not generous or kind is both tall and not calm and vice versa. Fred is not wise or tall. John is not kind or funny. Someone is either rich or not calm. Someone is not kind. Someone is not funny or brave. Someone is kind. Someone is either kind or not brave. Paul is either happy or not old.
|
Mary is calm.
|
contradiction
|
(![X]:(tall(X)<=>(~happy(X)<~>~rich(X))))&
((generous(john))<=>(?[X]:((rich(X)<~>~generous(X)))))&
(![X]:((~tall(X)|funny(X))<=>(old(X)|~calm(X))))&
(((creative(paul)&quiet(paul)))=>(?[X]:((~curious(X)<~>rich(X)))))&
((?[X]:((rich(X)&calm(X))))=>((old(lucy)&~wise(lucy))))&
(![X]:((~generous(X)|creative(X))=>~funny(X)))&
(![X]:((~strong(X)<~>generous(X))=>(curious(X)<~>~strong(X))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~brave(X)<~>happy(X))))&
((?[X]:((~tall(X)<~>strong(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:(~calm(X)<=>(old(X)|kind(X))))&
(![X]:((quiet(X)&happy(X))=>(curious(X)|creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|~humble(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(curious(X)<~>strong(X))))&
(![X]:((~generous(X)|kind(X))<=>(tall(X)&~calm(X))))&
((~wise(fred)|tall(fred)))&
((~kind(john)|funny(john)))&
(?[X]:((rich(X)<~>~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:(kind(X)))&
(?[X]:((kind(X)<~>~brave(X))))&
((happy(paul)<~>~old(paul)))
|
calm(mary)
|
[
"p2",
"p9",
"p13",
"p15",
"hypothesis"
] |
% SZS status Unsatisfiable for 7456953814057107946194322
% SZS output start Proof for 7456953814057107946194322
3. ! [X0] : ((funny(X0) | ~tall(X0)) <=> (~calm(X0) | old(X0))) [input p2]
10. ! [X0] : (~calm(X0) <=> (kind(X0) | old(X0))) [input p9]
14. ! [X0] : ((~wise(X0) & funny(X0)) <=> (generous(X0) | ~creative(X0))) [input p13]
16. ! [X0] : ((kind(X0) | ~generous(X0)) <=> (~calm(X0) & tall(X0))) [input p15]
25. calm(mary) [input hypothesis]
38. ! [X0] : (((funny(X0) | ~tall(X0)) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | (~funny(X0) & tall(X0)))) [nnf transformation 3]
39. ! [X0] : ((funny(X0) | ~tall(X0) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | (~funny(X0) & tall(X0)))) [flattening 38]
47. ! [X0] : ((~calm(X0) | (~kind(X0) & ~old(X0))) & ((kind(X0) | old(X0)) | calm(X0))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | (~kind(X0) & ~old(X0))) & (kind(X0) | old(X0) | calm(X0))) [flattening 47]
56. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & ((generous(X0) | ~creative(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 14]
57. ! [X0] : (((~wise(X0) & funny(X0)) | (~generous(X0) & creative(X0))) & (generous(X0) | ~creative(X0) | wise(X0) | ~funny(X0))) [flattening 56]
59. ! [X0] : (((kind(X0) | ~generous(X0)) | (calm(X0) | ~tall(X0))) & ((~calm(X0) & tall(X0)) | (~kind(X0) & generous(X0)))) [nnf transformation 16]
60. ! [X0] : ((kind(X0) | ~generous(X0) | calm(X0) | ~tall(X0)) & ((~calm(X0) & tall(X0)) | (~kind(X0) & generous(X0)))) [flattening 59]
83. ~calm(X0) | old(X0) | ~funny(X0) [cnf transformation 39]
111. ~calm(X0) | ~old(X0) [cnf transformation 48]
121. ~generous(X0) | funny(X0) [cnf transformation 57]
134. ~calm(X0) | generous(X0) [cnf transformation 60]
148. calm(mary) [cnf transformation 25]
324. ~old(mary) [resolution 111,148]
336. generous(mary) [resolution 134,148]
338. funny(mary) [resolution 336,121]
372. old(mary) | ~funny(mary) [resolution 83,148]
373. ~funny(mary) [subsumption resolution 372,324]
374. $false [subsumption resolution 373,338]
% SZS output end Proof for 7456953814057107946194322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is creative is not old or quiet and vice versa.
Everyone who is either wise or not wise is kind or not funny.
If mary is funny or wise then fred is both humble and patient.
If someone is not humble then fred is either wise or patient.
If someone is not generous or old then fred is either brave or not kind and vice versa.
Everyone who is not humble or calm is either not funny or not creative.
If someone is both funny and not strong then susan is either not humble or curious.
Everyone who is funny is not quiet or not tall and vice versa.
Everyone who is both not kind and funny is either not old or quiet.
Everyone who is quiet is either not funny or not rich.
If someone is not strong or not curious then someone is either kind or not quiet and vice versa.
Everyone who is calm or quiet is both not patient and patient and vice versa.
If lucy is either curious or not strong then fred is not creative and vice versa.
Everyone who is calm or tall is old or generous.
If alice is both not patient and not brave then someone is either funny or not strong.
If someone is not patient or patient then someone is either strong or not tall.
Someone is either happy or old.
Mary is patient.
Susan is not happy or not brave.
John is both strong and rich.
Someone is either quiet or not generous.
Susan is both brave and not quiet.
Susan is both not old and rich.
|
Fred is old.
|
entailment
|
(![X]:(creative(X)<=>(~old(X)|quiet(X))))&
(![X]:((wise(X)<~>~wise(X))=>(kind(X)|~funny(X))))&
(((funny(mary)|wise(mary)))=>((humble(fred)&patient(fred))))&
((?[X]:(~humble(X)))=>((wise(fred)<~>patient(fred))))&
((?[X]:((~generous(X)|old(X))))<=>((brave(fred)<~>~kind(fred))))&
(![X]:((~humble(X)|calm(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((funny(X)&~strong(X))))=>((~humble(susan)<~>curious(susan))))&
(![X]:(funny(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((~kind(X)&funny(X))=>(~old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>(~funny(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&patient(X))))&
(((curious(lucy)<~>~strong(lucy)))<=>(~creative(fred)))&
(![X]:((calm(X)|tall(X))=>(old(X)|generous(X))))&
(((~patient(alice)&~brave(alice)))=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)|patient(X))))=>(?[X]:((strong(X)<~>~tall(X)))))&
(?[X]:((happy(X)<~>old(X))))&
(patient(mary))&
((~happy(susan)|~brave(susan)))&
((strong(john)&rich(john)))&
(?[X]:((quiet(X)<~>~generous(X))))&
((brave(susan)&~quiet(susan)))&
((~old(susan)&rich(susan)))
|
old(fred)
|
[
"p0",
"p1",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] |
% SZS status Unsatisfiable for 1962802234963072078174709
% SZS output start Proof for 1962802234963072078174709
1. ! [X0] : (creative(X0) <=> (quiet(X0) | ~old(X0))) [input p0]
2. ! [X0] : ((wise(X0) <~> ~wise(X0)) => (~funny(X0) | kind(X0))) [input p1]
8. ! [X0] : (funny(X0) <=> (~tall(X0) | ~quiet(X0))) [input p7]
11. ? [X0] : (~curious(X0) | ~strong(X0)) <=> ? [X0] : (kind(X0) <~> ~quiet(X0)) [input p10]
12. ! [X0] : ((quiet(X0) | calm(X0)) <=> (patient(X0) & ~patient(X0))) [input p11]
13. (curious(lucy) <~> ~strong(lucy)) <=> ~creative(fred) [input p12]
24. ~old(fred) [input hypothesis]
25. ? [X0] : (~curious(X0) | ~strong(X0)) <=> ? [X1] : (kind(X1) <~> ~quiet(X1)) [rectify 11]
27. ! [X0] : ((~funny(X0) | kind(X0)) | (wise(X0) <=> ~wise(X0))) [ennf transformation 2]
28. ! [X0] : (~funny(X0) | kind(X0) | (wise(X0) <=> ~wise(X0))) [flattening 27]
41. ! [X0] : ((creative(X0) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | ~creative(X0))) [nnf transformation 1]
42. ! [X0] : ((creative(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | ~creative(X0))) [flattening 41]
43. ! [X0] : (~funny(X0) | kind(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 28]
51. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ~funny(X0))) [flattening 51]
55. (? [X0] : (~curious(X0) | ~strong(X0)) | ! [X1] : ((kind(X1) | quiet(X1)) & (~quiet(X1) | ~kind(X1)))) & (? [X1] : ((quiet(X1) | ~kind(X1)) & (~quiet(X1) | kind(X1))) | ! [X0] : (curious(X0) & strong(X0))) [nnf transformation 25]
56. (? [X0] : (~curious(X0) | ~strong(X0)) | ! [X1] : ((kind(X1) | quiet(X1)) & (~quiet(X1) | ~kind(X1)))) & (? [X2] : ((quiet(X2) | ~kind(X2)) & (~quiet(X2) | kind(X2))) | ! [X3] : (curious(X3) & strong(X3))) [rectify 55]
57. ? [X0] : (~curious(X0) | ~strong(X0)) => (~curious(sK1) | ~strong(sK1)) [choice axiom]
58. ? [X2] : ((quiet(X2) | ~kind(X2)) & (~quiet(X2) | kind(X2))) => ((quiet(sK2) | ~kind(sK2)) & (~quiet(sK2) | kind(sK2))) [choice axiom]
59. ((~curious(sK1) | ~strong(sK1)) | ! [X1] : ((kind(X1) | quiet(X1)) & (~quiet(X1) | ~kind(X1)))) & (((quiet(sK2) | ~kind(sK2)) & (~quiet(sK2) | kind(sK2))) | ! [X3] : (curious(X3) & strong(X3))) [skolemisation 56,58,57]
60. ! [X0] : (((quiet(X0) | calm(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 12]
61. ! [X0] : ((quiet(X0) | calm(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 60]
62. (((strong(lucy) | ~curious(lucy)) & (~strong(lucy) | curious(lucy))) | creative(fred)) & (~creative(fred) | ((curious(lucy) | strong(lucy)) & (~strong(lucy) | ~curious(lucy)))) [nnf transformation 13]
77. old(X0) | creative(X0) [cnf transformation 42]
79. ~funny(X0) | kind(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
80. ~funny(X0) | kind(X0) | wise(X0) | wise(X0) [cnf transformation 43]
100. funny(X0) | quiet(X0) [cnf transformation 52]
108. quiet(sK2) | ~kind(sK2) | strong(X3) [cnf transformation 59]
109. quiet(sK2) | ~kind(sK2) | curious(X3) [cnf transformation 59]
113. ~patient(X0) | ~quiet(X0) [cnf transformation 61]
115. ~quiet(X0) | patient(X0) [cnf transformation 61]
117. ~creative(fred) | ~strong(lucy) | ~curious(lucy) [cnf transformation 62]
141. ~old(fred) [cnf transformation 24]
142. ~funny(X0) | kind(X0) | ~wise(X0) [duplicate literal removal 79]
143. ~funny(X0) | kind(X0) | wise(X0) [duplicate literal removal 80]
144. ~funny(X0) | kind(X0) [subsumption resolution 142,143]
233. 20 <=> ! [X3] : curious(X3) [avatar definition]
234. curious(X3) <- (20) [avatar component clause 233]
236. 21 <=> kind(sK2) [avatar definition]
238. ~kind(sK2) <- (~21) [avatar component clause 236]
240. 22 <=> quiet(sK2) [avatar definition]
242. quiet(sK2) <- (22) [avatar component clause 240]
243. 20 | ~21 | 22 [avatar split clause 109,240,236,233]
245. 23 <=> ! [X3] : strong(X3) [avatar definition]
246. strong(X3) <- (23) [avatar component clause 245]
247. 23 | ~21 | 22 [avatar split clause 108,240,236,245]
250. ~quiet(X0) [subsumption resolution 113,115]
253. 24 <=> creative(fred) [avatar definition]
257. 25 <=> curious(lucy) [avatar definition]
259. ~curious(lucy) <- (~25) [avatar component clause 257]
261. 26 <=> strong(lucy) [avatar definition]
262. ~strong(lucy) <- (~26) [avatar component clause 261]
267. ~25 | ~26 | ~24 [avatar split clause 117,253,261,257]
326. creative(fred) [resolution 77,141]
330. 24 [avatar split clause 326,253]
338. kind(X0) | quiet(X0) [resolution 144,100]
342. kind(X0) [subsumption resolution 338,250]
344. $false <- (~21) [resolution 342,238]
345. 21 [avatar contradiction clause 344]
347. $false <- (22) [subsumption resolution 242,250]
348. ~22 [avatar contradiction clause 347]
351. $false <- (23, ~26) [resolution 246,262]
358. ~23 | 26 [avatar contradiction clause 351]
359. $false <- (20, ~25) [subsumption resolution 259,234]
360. ~20 | 25 [avatar contradiction clause 359]
363. $false [avatar sat refutation 243,247,267,330,345,348,358,360]
% SZS output end Proof for 1962802234963072078174709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not funny and happy then paul is creative and vice versa.
Everyone who is either creative or not quiet is either not brave or not curious and vice versa.
Everyone who is not generous is wise or creative and vice versa.
Everyone who is not wise or not humble is not funny and vice versa.
If someone is kind then someone is not tall or generous.
Everyone who is not funny or not humble is not generous or humble.
Everyone who is not quiet or generous is either tall or old.
Everyone who is either curious or not curious is not rich or generous.
Everyone who is not creative is not happy or tall.
Everyone who is old or not humble is not old or creative and vice versa.
If someone is not calm or quiet then someone is not strong or funny and vice versa.
If alice is tall or not patient then someone is both not rich and not quiet and vice versa.
If someone is happy or not funny then susan is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
Someone is both not creative and not funny.
Susan is both curious and tall.
Someone is not patient.
Someone is rich or tall.
Someone is either patient or curious.
Lucy is calm or not generous.
Someone is both tall and not wise.
|
Lucy is humble.
|
neutral
|
((?[X]:((~funny(X)&happy(X))))<=>(creative(paul)))&
(![X]:((creative(X)<~>~quiet(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(~generous(X)<=>(wise(X)|creative(X))))&
(![X]:((~wise(X)|~humble(X))<=>~funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((~funny(X)|~humble(X))=>(~generous(X)|humble(X))))&
(![X]:((~quiet(X)|generous(X))=>(tall(X)<~>old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~rich(X)|generous(X))))&
(![X]:(~creative(X)=>(~happy(X)|tall(X))))&
(![X]:((old(X)|~humble(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((~rich(X)&~quiet(X)))))&
((?[X]:((happy(X)|~funny(X))))<=>((~wise(susan)<~>happy(susan))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(?[X]:((~creative(X)&~funny(X))))&
((curious(susan)&tall(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|tall(X))))&
(?[X]:((patient(X)<~>curious(X))))&
((calm(lucy)|~generous(lucy)))&
(?[X]:((tall(X)&~wise(X))))
|
humble(lucy)
|
[] | null | 0 |
Everyone who is both not tall and happy is creative or rich.
If someone is not creative then someone is both humble and not kind.
If someone is either rich or not wise then susan is rich or not wise and vice versa.
If someone is wise or not generous then someone is both not rich and patient and vice versa.
Everyone who is both calm and curious is both not humble and wise and vice versa.
Everyone who is not funny or not patient is not calm and vice versa.
If mary is not creative or not tall then susan is both patient and not kind and vice versa.
Everyone who is not rich is either wise or not tall.
Everyone who is both not funny and funny is patient.
If someone is humble or not creative then someone is not wise.
Everyone who is not wise is either not kind or humble and vice versa.
If someone is both funny and not rich then mary is both humble and not happy.
Everyone who is generous is either humble or quiet and vice versa.
Everyone who is not strong or curious is not wise and vice versa.
If john is either not funny or not quiet then mary is happy and vice versa.
Everyone who is patient or not calm is creative and vice versa.
Alice is not generous.
Alice is either humble or old.
Someone is either not patient or creative.
Mary is curious or not curious.
Lucy is kind.
Mary is not generous.
Someone is funny or creative.
Someone is either not wise or creative.
|
Alice is humble.
|
neutral
|
(![X]:((~tall(X)&happy(X))=>(creative(X)|rich(X))))&
((?[X]:(~creative(X)))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((rich(X)<~>~wise(X))))<=>((rich(susan)|~wise(susan))))&
((?[X]:((wise(X)|~generous(X))))<=>(?[X]:((~rich(X)&patient(X)))))&
(![X]:((calm(X)&curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((~funny(X)|~patient(X))<=>~calm(X)))&
(((~creative(mary)|~tall(mary)))<=>((patient(susan)&~kind(susan))))&
(![X]:(~rich(X)=>(wise(X)<~>~tall(X))))&
(![X]:((~funny(X)&funny(X))=>patient(X)))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:(~wise(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>humble(X))))&
((?[X]:((funny(X)&~rich(X))))=>((humble(mary)&~happy(mary))))&
(![X]:(generous(X)<=>(humble(X)<~>quiet(X))))&
(![X]:((~strong(X)|curious(X))<=>~wise(X)))&
(((~funny(john)<~>~quiet(john)))<=>(happy(mary)))&
(![X]:((patient(X)|~calm(X))<=>creative(X)))&
(~generous(alice))&
((humble(alice)<~>old(alice)))&
(?[X]:((~patient(X)<~>creative(X))))&
((curious(mary)|~curious(mary)))&
(kind(lucy))&
(~generous(mary))&
(?[X]:((funny(X)|creative(X))))&
(?[X]:((~wise(X)<~>creative(X))))
|
humble(alice)
|
[] | null | 0 |
Everyone who is either not old or not happy is either not creative or not humble.
If paul is wise then someone is not strong.
Everyone who is not calm is kind.
If someone is either quiet or brave then alice is quiet or not rich and vice versa.
Everyone who is not strong is not rich.
Everyone who is curious is quiet.
Everyone who is not creative is either curious or quiet and vice versa.
Everyone who is happy is both strong and generous and vice versa.
If someone is curious or wise then someone is not wise or not generous.
Everyone who is both not curious and not tall is either not patient or kind and vice versa.
If fred is curious or calm then lucy is wise or not curious.
Everyone who is patient is both not wise and kind and vice versa.
Everyone who is kind or not generous is both not funny and not happy and vice versa.
Everyone who is not patient is patient.
If susan is strong or old then alice is both not kind and curious.
Everyone who is both not old and not wise is either funny or kind and vice versa.
Someone is both not humble and kind.
Someone is both not rich and calm.
Someone is not generous.
Someone is both not tall and calm.
Mary is brave.
Someone is humble or creative.
|
Alice is not humble.
|
neutral
|
(![X]:((~old(X)<~>~happy(X))=>(~creative(X)<~>~humble(X))))&
((wise(paul))=>(?[X]:(~strong(X))))&
(![X]:(~calm(X)=>kind(X)))&
((?[X]:((quiet(X)<~>brave(X))))<=>((quiet(alice)|~rich(alice))))&
(![X]:(~strong(X)=>~rich(X)))&
(![X]:(curious(X)=>quiet(X)))&
(![X]:(~creative(X)<=>(curious(X)<~>quiet(X))))&
(![X]:(happy(X)<=>(strong(X)&generous(X))))&
((?[X]:((curious(X)|wise(X))))=>(?[X]:((~wise(X)|~generous(X)))))&
(![X]:((~curious(X)&~tall(X))<=>(~patient(X)<~>kind(X))))&
(((curious(fred)|calm(fred)))=>((wise(lucy)|~curious(lucy))))&
(![X]:(patient(X)<=>(~wise(X)&kind(X))))&
(![X]:((kind(X)|~generous(X))<=>(~funny(X)&~happy(X))))&
(![X]:(~patient(X)=>patient(X)))&
(((strong(susan)|old(susan)))=>((~kind(alice)&curious(alice))))&
(![X]:((~old(X)&~wise(X))<=>(funny(X)<~>kind(X))))&
(?[X]:((~humble(X)&kind(X))))&
(?[X]:((~rich(X)&calm(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~tall(X)&calm(X))))&
(brave(mary))&
(?[X]:((humble(X)|creative(X))))
|
~humble(alice)
|
[] | null | 0 |
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