premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is either tall or not calm then someone is not calm or not humble.
Everyone who is not wise or happy is both generous and tall and vice versa.
Everyone who is both not patient and not quiet is both funny and not tall.
Everyone who is not old is both not calm and curious.
If someone is not creative then someone is not strong.
If susan is both kind and quiet then someone is either not quiet or not tall.
If john is both rich and not calm then someone is both not quiet and not strong.
Everyone who is quiet is not strong and vice versa.
Everyone who is not kind is tall or kind and vice versa.
If mary is not quiet then mary is either rich or not old and vice versa.
Everyone who is either not humble or humble is either creative or strong.
Everyone who is brave or not calm is either quiet or tall.
If fred is both not strong and generous then someone is not happy.
If paul is not calm then someone is brave and vice versa.
Everyone who is either kind or not happy is not brave and vice versa.
If fred is curious or not patient then someone is creative or old.
Susan is both not old and not brave.
Someone is not brave or not generous.
Lucy is creative.
Fred is old or creative.
Someone is either not creative or not humble.
Someone is either happy or not kind. | Susan is not curious. | contradiction | ((?[X]:((tall(X)<~>~calm(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~wise(X)|happy(X))<=>(generous(X)&tall(X))))&
(![X]:((~patient(X)&~quiet(X))=>(funny(X)&~tall(X))))&
(![X]:(~old(X)=>(~calm(X)&curious(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~strong(X))))&
(((kind(susan)&quiet(susan)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(((rich(john)&~calm(john)))=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:(quiet(X)<=>~strong(X)))&
(![X]:(~kind(X)<=>(tall(X)|kind(X))))&
((~quiet(mary))<=>((rich(mary)<~>~old(mary))))&
(![X]:((~humble(X)<~>humble(X))=>(creative(X)<~>strong(X))))&
(![X]:((brave(X)|~calm(X))=>(quiet(X)<~>tall(X))))&
(((~strong(fred)&generous(fred)))=>(?[X]:(~happy(X))))&
((~calm(paul))<=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>~happy(X))<=>~brave(X)))&
(((curious(fred)|~patient(fred)))=>(?[X]:((creative(X)|old(X)))))&
((~old(susan)&~brave(susan)))&
(?[X]:((~brave(X)|~generous(X))))&
(creative(lucy))&
((old(fred)|creative(fred)))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:((happy(X)<~>~kind(X)))) | ~curious(susan) | [
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6505102058365231416672722
% SZS output start Proof for 6505102058365231416672722
4. ! [X0] : (~old(X0) => (curious(X0) & ~calm(X0))) [input p3]
17. ~brave(susan) & ~old(susan) [input p16]
23. ~curious(susan) [input hypothesis]
30. ! [X0] : ((curious(X0) & ~calm(X0)) | old(X0)) [ennf transformation 4]
86. curious(X0) | old(X0) [cnf transformation 30]
117. ~old(susan) [cnf transformation 17]
126. ~curious(susan) [cnf transformation 23]
285. old(susan) [resolution 86,126]
287. $false [subsumption resolution 285,117]
% SZS output end Proof for 6505102058365231416672722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is not creative or not brave is both creative and old.
Everyone who is calm or not creative is not generous and vice versa.
Everyone who is either calm or happy is both not curious and old and vice versa.
Everyone who is either not strong or creative is either creative or tall and vice versa.
If someone is either not funny or not old then john is wise.
Everyone who is not wise or calm is either brave or funny and vice versa.
If someone is both generous and not tall then mary is either creative or not rich and vice versa.
If someone is not quiet then mary is old or humble.
Everyone who is not humble or not calm is either generous or not funny and vice versa.
If alice is both wise and humble then someone is not old or not kind and vice versa.
Everyone who is not old is either funny or quiet and vice versa.
If susan is not kind or not calm then someone is strong.
Everyone who is either not funny or not strong is humble or not generous.
Everyone who is not wise is both rich and not quiet.
Everyone who is calm or not tall is both curious and tall.
Everyone who is either not wise or patient is strong.
Mary is not brave or calm.
Paul is generous or not brave.
Someone is not brave or funny.
Paul is tall.
Paul is happy or funny.
Someone is not brave. | Alice is not kind. | neutral | (![X]:((~creative(X)|~brave(X))=>(creative(X)&old(X))))&
(![X]:((calm(X)|~creative(X))<=>~generous(X)))&
(![X]:((calm(X)<~>happy(X))<=>(~curious(X)&old(X))))&
(![X]:((~strong(X)<~>creative(X))<=>(creative(X)<~>tall(X))))&
((?[X]:((~funny(X)<~>~old(X))))=>(wise(john)))&
(![X]:((~wise(X)|calm(X))<=>(brave(X)<~>funny(X))))&
((?[X]:((generous(X)&~tall(X))))<=>((creative(mary)<~>~rich(mary))))&
((?[X]:(~quiet(X)))=>((old(mary)|humble(mary))))&
(![X]:((~humble(X)|~calm(X))<=>(generous(X)<~>~funny(X))))&
(((wise(alice)&humble(alice)))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:(~old(X)<=>(funny(X)<~>quiet(X))))&
(((~kind(susan)|~calm(susan)))=>(?[X]:(strong(X))))&
(![X]:((~funny(X)<~>~strong(X))=>(humble(X)|~generous(X))))&
(![X]:(~wise(X)=>(rich(X)&~quiet(X))))&
(![X]:((calm(X)|~tall(X))=>(curious(X)&tall(X))))&
(![X]:((~wise(X)<~>patient(X))=>strong(X)))&
((~brave(mary)|calm(mary)))&
((generous(paul)|~brave(paul)))&
(?[X]:((~brave(X)|funny(X))))&
(tall(paul))&
((happy(paul)|funny(paul)))&
(?[X]:(~brave(X))) | ~kind(alice) | [] | null | 0 |
If someone is happy then john is both not kind and humble. Everyone who is both not generous and tall is both not creative and not tall. Everyone who is happy is not happy. If someone is both not generous and strong then paul is either not tall or tall. Everyone who is funny is patient and vice versa. If john is either kind or humble then someone is not old. If someone is not quiet or strong then alice is either happy or not rich. If someone is not happy or not generous then someone is not generous or not curious. If someone is not strong then someone is either not funny or happy and vice versa. Everyone who is old or patient is strong or not quiet and vice versa. Everyone who is either happy or generous is curious and vice versa. If someone is not funny then john is both not calm and brave and vice versa. Everyone who is either wise or not patient is generous or creative and vice versa. If alice is not old or not calm then someone is both not tall and not calm and vice versa. If someone is kind then someone is both rich and tall. Everyone who is either not calm or quiet is not rich and vice versa. Susan is either humble or brave. Lucy is funny. Someone is funny or not generous. Someone is both wise and kind. Someone is not funny or patient. Someone is either patient or generous. Susan is not funny. | Alice is old. | neutral | ((?[X]:(happy(X)))=>((~kind(john)&humble(john))))&
(![X]:((~generous(X)&tall(X))=>(~creative(X)&~tall(X))))&
(![X]:(happy(X)=>~happy(X)))&
((?[X]:((~generous(X)&strong(X))))=>((~tall(paul)<~>tall(paul))))&
(![X]:(funny(X)<=>patient(X)))&
(((kind(john)<~>humble(john)))=>(?[X]:(~old(X))))&
((?[X]:((~quiet(X)|strong(X))))=>((happy(alice)<~>~rich(alice))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(![X]:((old(X)|patient(X))<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)<~>generous(X))<=>curious(X)))&
((?[X]:(~funny(X)))<=>((~calm(john)&brave(john))))&
(![X]:((wise(X)<~>~patient(X))<=>(generous(X)|creative(X))))&
(((~old(alice)|~calm(alice)))<=>(?[X]:((~tall(X)&~calm(X)))))&
((?[X]:(kind(X)))=>(?[X]:((rich(X)&tall(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>~rich(X)))&
((humble(susan)<~>brave(susan)))&
(funny(lucy))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:((~funny(X)|patient(X))))&
(?[X]:((patient(X)<~>generous(X))))&
(~funny(susan)) | old(alice) | [] | null | 0 |
If someone is not funny then someone is both not patient and funny. Everyone who is both brave and happy is both not quiet and not curious and vice versa. Everyone who is funny is both not kind and not old and vice versa. If lucy is both strong and not old then someone is both funny and not funny and vice versa. If mary is rich or not tall then fred is brave and vice versa. Everyone who is brave or not humble is curious. Everyone who is either not kind or patient is tall or brave and vice versa. If someone is not funny or patient then fred is both not calm and strong. Everyone who is generous or not funny is either quiet or not kind. If someone is either not happy or not strong then someone is not generous. Everyone who is either not tall or patient is patient and vice versa. If someone is both not funny and not calm then alice is not humble and vice versa. Everyone who is either generous or happy is not wise or happy and vice versa. Everyone who is both not calm and funny is both not old and generous. Alice is not kind or calm. Someone is not happy. Someone is either calm or old. Someone is not old or calm. Someone is not quiet. Alice is both not creative and not wise. | Alice is not patient. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:((brave(X)&happy(X))<=>(~quiet(X)&~curious(X))))&
(![X]:(funny(X)<=>(~kind(X)&~old(X))))&
(((strong(lucy)&~old(lucy)))<=>(?[X]:((funny(X)&~funny(X)))))&
(((rich(mary)|~tall(mary)))<=>(brave(fred)))&
(![X]:((brave(X)|~humble(X))=>curious(X)))&
(![X]:((~kind(X)<~>patient(X))<=>(tall(X)|brave(X))))&
((?[X]:((~funny(X)|patient(X))))=>((~calm(fred)&strong(fred))))&
(![X]:((generous(X)|~funny(X))=>(quiet(X)<~>~kind(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~funny(X)&~calm(X))))<=>(~humble(alice)))&
(![X]:((generous(X)<~>happy(X))<=>(~wise(X)|happy(X))))&
(![X]:((~calm(X)&funny(X))=>(~old(X)&generous(X))))&
((~kind(alice)|calm(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:(~quiet(X)))&
((~creative(alice)&~wise(alice))) | ~patient(alice) | [] | null | 0 |
Everyone who is not rich or happy is kind and vice versa.
If someone is kind then lucy is either strong or tall.
If someone is not strong or funny then someone is not humble or not happy and vice versa.
Everyone who is strong or old is either not old or funny.
If someone is brave or not calm then someone is not quiet or happy.
Everyone who is humble or calm is not creative and vice versa.
Everyone who is strong is not old.
If someone is both patient and strong then someone is either brave or not humble.
Everyone who is not generous or not patient is not calm.
Everyone who is generous or not curious is both happy and not creative and vice versa.
If john is not happy or not brave then someone is tall or calm.
If alice is brave or curious then lucy is either not tall or calm.
Everyone who is either not calm or humble is not creative or creative and vice versa.
Everyone who is both tall and not strong is both tall and not generous.
Everyone who is both calm and rich is not old or generous and vice versa.
Everyone who is either kind or not wise is wise and vice versa.
Alice is both humble and patient.
Someone is not funny or creative.
Someone is creative or wise.
Alice is tall or not calm.
Someone is both rich and wise.
Someone is patient.
Someone is both not generous and funny. | John is rich. | neutral | (![X]:((~rich(X)|happy(X))<=>kind(X)))&
((?[X]:(kind(X)))=>((strong(lucy)<~>tall(lucy))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((strong(X)|old(X))=>(~old(X)<~>funny(X))))&
((?[X]:((brave(X)|~calm(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((humble(X)|calm(X))<=>~creative(X)))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:((brave(X)<~>~humble(X)))))&
(![X]:((~generous(X)|~patient(X))=>~calm(X)))&
(![X]:((generous(X)|~curious(X))<=>(happy(X)&~creative(X))))&
(((~happy(john)|~brave(john)))=>(?[X]:((tall(X)|calm(X)))))&
(((brave(alice)|curious(alice)))=>((~tall(lucy)<~>calm(lucy))))&
(![X]:((~calm(X)<~>humble(X))<=>(~creative(X)|creative(X))))&
(![X]:((tall(X)&~strong(X))=>(tall(X)&~generous(X))))&
(![X]:((calm(X)&rich(X))<=>(~old(X)|generous(X))))&
(![X]:((kind(X)<~>~wise(X))<=>wise(X)))&
((humble(alice)&patient(alice)))&
(?[X]:((~funny(X)|creative(X))))&
(?[X]:((creative(X)|wise(X))))&
((tall(alice)|~calm(alice)))&
(?[X]:((rich(X)&wise(X))))&
(?[X]:(patient(X)))&
(?[X]:((~generous(X)&funny(X)))) | rich(john) | [] | null | 0 |
Everyone who is both not quiet and not kind is not wise.
Everyone who is not quiet or not humble is either not old or quiet.
Everyone who is either not rich or old is brave and vice versa.
Everyone who is either funny or creative is either not happy or not generous.
If someone is not funny or curious then lucy is either creative or patient.
Everyone who is either tall or quiet is both not tall and quiet.
Everyone who is not generous or not funny is both not patient and old.
Everyone who is either old or not patient is both not brave and not happy and vice versa.
Everyone who is old is either wise or funny.
Everyone who is rich is both generous and brave and vice versa.
Everyone who is tall or not brave is not creative.
If lucy is happy then someone is either not brave or not strong and vice versa.
If someone is either old or not kind then someone is both not humble and not happy.
If susan is patient or not tall then lucy is not curious.
If someone is both humble and brave then lucy is both calm and generous.
If lucy is either not humble or brave then someone is both generous and tall.
Paul is not brave.
Alice is both not humble and not patient.
Fred is not calm or not creative.
Lucy is both not tall and not brave. | Lucy is wise. | contradiction | (![X]:((~quiet(X)&~kind(X))=>~wise(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~old(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>old(X))<=>brave(X)))&
(![X]:((funny(X)<~>creative(X))=>(~happy(X)<~>~generous(X))))&
((?[X]:((~funny(X)|curious(X))))=>((creative(lucy)<~>patient(lucy))))&
(![X]:((tall(X)<~>quiet(X))=>(~tall(X)&quiet(X))))&
(![X]:((~generous(X)|~funny(X))=>(~patient(X)&old(X))))&
(![X]:((old(X)<~>~patient(X))<=>(~brave(X)&~happy(X))))&
(![X]:(old(X)=>(wise(X)<~>funny(X))))&
(![X]:(rich(X)<=>(generous(X)&brave(X))))&
(![X]:((tall(X)|~brave(X))=>~creative(X)))&
((happy(lucy))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((old(X)<~>~kind(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(((patient(susan)|~tall(susan)))=>(~curious(lucy)))&
((?[X]:((humble(X)&brave(X))))=>((calm(lucy)&generous(lucy))))&
(((~humble(lucy)<~>brave(lucy)))=>(?[X]:((generous(X)&tall(X)))))&
(~brave(paul))&
((~humble(alice)&~patient(alice)))&
((~calm(fred)|~creative(fred)))&
((~tall(lucy)&~brave(lucy))) | wise(lucy) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5872780379822614619112201
% SZS output start Proof for 5872780379822614619112201
3. ! [X0] : ((~rich(X0) <~> old(X0)) <=> brave(X0)) [input p2]
5. ? [X0] : (curious(X0) | ~funny(X0)) => (creative(lucy) <~> patient(lucy)) [input p4]
7. ! [X0] : ((~funny(X0) | ~generous(X0)) => (old(X0) & ~patient(X0))) [input p6]
9. ! [X0] : (old(X0) => (wise(X0) <~> funny(X0))) [input p8]
10. ! [X0] : (rich(X0) <=> (brave(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~brave(X0) | tall(X0)) => ~creative(X0)) [input p10]
20. ~brave(lucy) & ~tall(lucy) [input p19]
21. wise(lucy) [input hypothesis]
24. ? [X0] : ~funny(X0) => (creative(lucy) <~> patient(lucy)) [pure predicate removal 5]
29. (creative(lucy) <~> patient(lucy)) | ! [X0] : funny(X0) [ennf transformation 24]
31. ! [X0] : ((old(X0) & ~patient(X0)) | (funny(X0) & generous(X0))) [ennf transformation 7]
32. ! [X0] : ((wise(X0) <~> funny(X0)) | ~old(X0)) [ennf transformation 9]
33. ! [X0] : (~creative(X0) | (brave(X0) & ~tall(X0))) [ennf transformation 11]
38. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | ~brave(X0)) & (brave(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [nnf transformation 3]
40. ((~patient(lucy) | ~creative(lucy)) & (patient(lucy) | creative(lucy))) | ! [X0] : funny(X0) [nnf transformation 29]
44. ! [X0] : (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~old(X0)) [nnf transformation 32]
45. ! [X0] : ((rich(X0) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | ~rich(X0))) [nnf transformation 10]
46. ! [X0] : ((rich(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | ~rich(X0))) [flattening 45]
63. brave(X0) | old(X0) | rich(X0) [cnf transformation 38]
71. patient(lucy) | creative(lucy) | funny(X0) [cnf transformation 40]
78. ~patient(X0) | funny(X0) [cnf transformation 31]
88. ~funny(X0) | ~wise(X0) | ~old(X0) [cnf transformation 44]
90. ~rich(X0) | brave(X0) [cnf transformation 46]
93. ~creative(X0) | brave(X0) [cnf transformation 33]
113. ~brave(lucy) [cnf transformation 20]
114. wise(lucy) [cnf transformation 21]
119. 1 <=> ! [X0] : funny(X0) [avatar definition]
120. funny(X0) <- (1) [avatar component clause 119]
122. 2 <=> creative(lucy) [avatar definition]
123. creative(lucy) <- (2) [avatar component clause 122]
126. 3 <=> patient(lucy) [avatar definition]
127. patient(lucy) <- (3) [avatar component clause 126]
130. 1 | 2 | 3 [avatar split clause 71,126,122,119]
186. 16 <=> brave(lucy) [avatar definition]
188. ~brave(lucy) <- (~16) [avatar component clause 186]
214. ~16 [avatar split clause 113,186]
215. brave(lucy) <- (2) [resolution 93,123]
216. $false <- (2, ~16) [subsumption resolution 215,188]
217. ~2 | 16 [avatar contradiction clause 216]
218. funny(lucy) <- (3) [resolution 127,78]
233. old(lucy) | rich(lucy) <- (~16) [resolution 63,188]
246. 26 <=> rich(lucy) [avatar definition]
248. rich(lucy) <- (26) [avatar component clause 246]
250. 27 <=> old(lucy) [avatar definition]
252. old(lucy) <- (27) [avatar component clause 250]
253. 26 | 27 | 16 [avatar split clause 233,186,250,246]
275. brave(lucy) <- (26) [resolution 248,90]
279. $false <- (~16, 26) [subsumption resolution 275,188]
280. 16 | ~26 [avatar contradiction clause 279]
290. ~wise(lucy) | ~old(lucy) <- (3) [resolution 88,218]
291. ~old(lucy) <- (3) [subsumption resolution 290,114]
292. $false <- (3, 27) [subsumption resolution 291,252]
293. ~3 | ~27 [avatar contradiction clause 292]
294. ~old(X0) | ~wise(X0) <- (1) [resolution 120,88]
299. ~wise(lucy) <- (1, 27) [resolution 294,252]
300. $false <- (1, 27) [subsumption resolution 299,114]
301. ~1 | ~27 [avatar contradiction clause 300]
302. $false [avatar sat refutation 130,214,217,253,280,293,301]
% SZS output end Proof for 5872780379822614619112201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and curious is not brave and vice versa.
If someone is either happy or kind then john is either not generous or not wise.
If lucy is either not humble or curious then mary is generous and vice versa.
If someone is both funny and tall then fred is calm or strong.
Everyone who is not rich or not funny is both not happy and not patient.
If lucy is not patient then someone is not wise and vice versa.
If someone is not tall or generous then someone is both not generous and kind and vice versa.
Everyone who is both not quiet and not calm is either not strong or generous.
Everyone who is either quiet or funny is not tall.
If someone is either generous or curious then lucy is curious and vice versa.
If someone is either old or not funny then someone is either not curious or not kind and vice versa.
Everyone who is either generous or not funny is old or not curious and vice versa.
Everyone who is either tall or not curious is both not old and funny.
Everyone who is patient or not happy is brave and vice versa.
Everyone who is both not generous and not patient is both not patient and rich and vice versa.
Everyone who is calm or not creative is tall and vice versa.
Someone is patient.
Someone is either humble or generous.
Mary is funny.
Susan is old.
Someone is not curious.
Someone is either not wise or happy. | Mary is wise. | neutral | (![X]:((~curious(X)&curious(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>kind(X))))=>((~generous(john)<~>~wise(john))))&
(((~humble(lucy)<~>curious(lucy)))<=>(generous(mary)))&
((?[X]:((funny(X)&tall(X))))=>((calm(fred)|strong(fred))))&
(![X]:((~rich(X)|~funny(X))=>(~happy(X)&~patient(X))))&
((~patient(lucy))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((~quiet(X)&~calm(X))=>(~strong(X)<~>generous(X))))&
(![X]:((quiet(X)<~>funny(X))=>~tall(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>(curious(lucy)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)|~curious(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((patient(X)|~happy(X))<=>brave(X)))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(![X]:((calm(X)|~creative(X))<=>tall(X)))&
(?[X]:(patient(X)))&
(?[X]:((humble(X)<~>generous(X))))&
(funny(mary))&
(old(susan))&
(?[X]:(~curious(X)))&
(?[X]:((~wise(X)<~>happy(X)))) | wise(mary) | [] | null | 0 |
If someone is both funny and strong then someone is both creative and not tall and vice versa.
If someone is not strong then john is creative and vice versa.
If paul is tall or not patient then someone is tall or not humble.
Everyone who is both humble and not wise is either creative or humble and vice versa.
If someone is not funny or funny then susan is either brave or creative.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
If someone is calm then someone is both strong and wise.
Everyone who is either funny or tall is either generous or not kind.
If someone is both happy and not curious then paul is humble.
Everyone who is either not tall or quiet is either not funny or patient and vice versa.
Everyone who is both brave and tall is both old and not funny.
John is both not curious and tall.
Someone is either not humble or not wise.
Susan is not rich.
Alice is happy or not rich.
Someone is either not funny or humble.
Alice is not tall. | Alice is not rich. | neutral | ((?[X]:((funny(X)&strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:(~strong(X)))<=>(creative(john)))&
(((tall(paul)|~patient(paul)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((humble(X)&~wise(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|funny(X))))=>((brave(susan)<~>creative(susan))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
((?[X]:(calm(X)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))=>(old(X)&~funny(X))))&
((~curious(john)&tall(john)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~rich(susan))&
((happy(alice)|~rich(alice)))&
(?[X]:((~funny(X)<~>humble(X))))&
(~tall(alice)) | ~rich(alice) | [] | null | 0 |
If john is not kind or not brave then someone is kind and vice versa. Everyone who is not rich is brave or not happy and vice versa. If someone is both not brave and not generous then mary is not old or patient and vice versa. Everyone who is both not rich and not humble is either brave or not creative and vice versa. If someone is not creative then alice is patient or kind. Everyone who is either brave or tall is both not brave and not patient. Everyone who is not humble is either creative or not kind. Everyone who is not wise or not patient is both wise and not patient and vice versa. Everyone who is not brave is both kind and old and vice versa. If fred is not generous then someone is both not creative and funny. If lucy is not wise or humble then john is not humble. Everyone who is quiet or not generous is both funny and not quiet. If mary is strong or not quiet then john is either not old or not calm. Everyone who is both strong and patient is both not creative and not tall. Everyone who is both rich and generous is not brave or humble and vice versa. Everyone who is either not creative or not quiet is both not strong and generous and vice versa. Fred is generous. Someone is either happy or not tall. Someone is humble or not patient. Someone is not calm or wise. Susan is funny. Someone is either funny or old. Someone is both kind and not quiet. Someone is both brave and not strong. | Alice is not strong. | entailment | (((~kind(john)|~brave(john)))<=>(?[X]:(kind(X))))&
(![X]:(~rich(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~brave(X)&~generous(X))))<=>((~old(mary)|patient(mary))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)<~>~creative(X))))&
((?[X]:(~creative(X)))=>((patient(alice)|kind(alice))))&
(![X]:((brave(X)<~>tall(X))=>(~brave(X)&~patient(X))))&
(![X]:(~humble(X)=>(creative(X)<~>~kind(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&~patient(X))))&
(![X]:(~brave(X)<=>(kind(X)&old(X))))&
((~generous(fred))=>(?[X]:((~creative(X)&funny(X)))))&
(((~wise(lucy)|humble(lucy)))=>(~humble(john)))&
(![X]:((quiet(X)|~generous(X))=>(funny(X)&~quiet(X))))&
(((strong(mary)|~quiet(mary)))=>((~old(john)<~>~calm(john))))&
(![X]:((strong(X)&patient(X))=>(~creative(X)&~tall(X))))&
(![X]:((rich(X)&generous(X))<=>(~brave(X)|humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(~strong(X)&generous(X))))&
(generous(fred))&
(?[X]:((happy(X)<~>~tall(X))))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~calm(X)|wise(X))))&
(funny(susan))&
(?[X]:((funny(X)<~>old(X))))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:((brave(X)&~strong(X)))) | ~strong(alice) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5490945976445012320288015
% SZS output start Proof for 5490945976445012320288015
2. ! [X0] : (~rich(X0) <=> (~happy(X0) | brave(X0))) [input p1]
4. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (brave(X0) <~> ~creative(X0))) [input p3]
5. ? [X0] : ~creative(X0) => (kind(alice) | patient(alice)) [input p4]
6. ! [X0] : ((brave(X0) <~> tall(X0)) => (~patient(X0) & ~brave(X0))) [input p5]
7. ! [X0] : (~humble(X0) => (creative(X0) <~> ~kind(X0))) [input p6]
9. ! [X0] : (~brave(X0) <=> (old(X0) & kind(X0))) [input p8]
12. ! [X0] : ((~generous(X0) | quiet(X0)) => (~quiet(X0) & funny(X0))) [input p11]
14. ! [X0] : ((patient(X0) & strong(X0)) => (~tall(X0) & ~creative(X0))) [input p13]
15. ! [X0] : ((generous(X0) & rich(X0)) <=> (humble(X0) | ~brave(X0))) [input p14]
16. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (generous(X0) & ~strong(X0))) [input p15]
25. strong(alice) [input hypothesis]
26. (kind(alice) | patient(alice)) | ! [X0] : creative(X0) [ennf transformation 5]
27. kind(alice) | patient(alice) | ! [X0] : creative(X0) [flattening 26]
28. ! [X0] : ((~patient(X0) & ~brave(X0)) | (brave(X0) <=> tall(X0))) [ennf transformation 6]
29. ! [X0] : ((creative(X0) <~> ~kind(X0)) | humble(X0)) [ennf transformation 7]
32. ! [X0] : ((~quiet(X0) & funny(X0)) | (generous(X0) & ~quiet(X0))) [ennf transformation 12]
34. ! [X0] : ((~tall(X0) & ~creative(X0)) | (~patient(X0) | ~strong(X0))) [ennf transformation 14]
35. ! [X0] : ((~tall(X0) & ~creative(X0)) | ~patient(X0) | ~strong(X0)) [flattening 34]
41. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | rich(X0))) [nnf transformation 2]
42. ! [X0] : ((~rich(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | rich(X0))) [flattening 41]
48. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (humble(X0) | rich(X0)))) [nnf transformation 4]
49. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | humble(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((~patient(X0) & ~brave(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0)))) [nnf transformation 28]
51. ! [X0] : (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | humble(X0)) [nnf transformation 29]
54. ! [X0] : ((~brave(X0) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | brave(X0))) [nnf transformation 9]
55. ! [X0] : ((~brave(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | brave(X0))) [flattening 54]
59. ! [X0] : (((generous(X0) & rich(X0)) | (~humble(X0) & brave(X0))) & ((humble(X0) | ~brave(X0)) | (~generous(X0) | ~rich(X0)))) [nnf transformation 15]
60. ! [X0] : (((generous(X0) & rich(X0)) | (~humble(X0) & brave(X0))) & (humble(X0) | ~brave(X0) | ~generous(X0) | ~rich(X0))) [flattening 59]
61. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~generous(X0) | strong(X0))) & ((generous(X0) & ~strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 16]
62. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~generous(X0) | strong(X0)) & ((generous(X0) & ~strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 61]
81. ~rich(X0) | ~brave(X0) [cnf transformation 42]
91. ~rich(X0) | brave(X0) | creative(X0) [cnf transformation 49]
94. kind(alice) | patient(alice) | creative(X0) [cnf transformation 27]
95. ~brave(X0) | tall(X0) | ~brave(X0) [cnf transformation 50]
99. ~kind(X0) | creative(X0) | humble(X0) [cnf transformation 51]
106. brave(X0) | kind(X0) [cnf transformation 55]
115. ~quiet(X0) | ~quiet(X0) [cnf transformation 32]
122. ~strong(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 35]
124. rich(X0) | brave(X0) [cnf transformation 60]
125. ~humble(X0) | rich(X0) [cnf transformation 60]
129. ~strong(X0) | ~creative(X0) | quiet(X0) [cnf transformation 62]
146. strong(alice) [cnf transformation 25]
147. ~quiet(X0) [duplicate literal removal 115]
150. ~brave(X0) | tall(X0) [duplicate literal removal 95]
193. ~rich(X0) | creative(X0) [subsumption resolution 91,81]
196. 10 <=> ! [X0] : creative(X0) [avatar definition]
197. creative(X0) <- (10) [avatar component clause 196]
199. 11 <=> patient(alice) [avatar definition]
201. patient(alice) <- (11) [avatar component clause 199]
203. 12 <=> kind(alice) [avatar definition]
205. kind(alice) <- (12) [avatar component clause 203]
206. 10 | 11 | 12 [avatar split clause 94,203,199,196]
252. ~strong(X0) | ~creative(X0) [subsumption resolution 129,147]
290. tall(X0) | kind(X0) [resolution 150,106]
297. creative(X0) | brave(X0) [resolution 193,124]
302. ~creative(alice) [resolution 252,146]
373. ~patient(alice) | ~tall(alice) [resolution 122,146]
374. ~tall(alice) <- (11) [subsumption resolution 373,201]
375. kind(alice) <- (11) [resolution 374,290]
376. 12 | ~11 [avatar split clause 375,199,203]
377. creative(alice) | humble(alice) <- (12) [resolution 205,99]
378. humble(alice) <- (12) [subsumption resolution 377,302]
381. rich(alice) <- (12) [resolution 378,125]
462. brave(alice) [resolution 297,302]
502. ~brave(alice) <- (12) [resolution 381,81]
505. $false <- (12) [subsumption resolution 502,462]
506. ~12 [avatar contradiction clause 505]
516. $false <- (10) [resolution 197,302]
517. ~10 [avatar contradiction clause 516]
518. $false [avatar sat refutation 206,376,506,517]
% SZS output end Proof for 5490945976445012320288015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not strong then someone is either not happy or not creative and vice versa.
Everyone who is not strong is creative and vice versa.
Everyone who is not calm is humble.
If someone is not generous then paul is either not rich or rich and vice versa.
If mary is not tall then someone is either patient or not funny and vice versa.
Everyone who is rich or not kind is not tall.
If alice is both not calm and humble then someone is either not tall or not generous.
Everyone who is calm or wise is not humble and vice versa.
Everyone who is creative is not kind and vice versa.
If john is either rich or brave then someone is creative.
Everyone who is not old is both not rich and not wise.
If someone is both wise and patient then lucy is both humble and not creative and vice versa.
Everyone who is not humble is not patient and vice versa.
Everyone who is either tall or strong is not rich or kind.
If someone is not curious then someone is both humble and not happy.
Everyone who is either old or creative is curious and vice versa.
Someone is brave or not generous.
Someone is kind.
Paul is not quiet.
Someone is either old or not patient.
Someone is not kind.
Someone is both not humble and funny.
Susan is both patient and tall. | Mary is not happy. | neutral | ((?[X]:((strong(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(![X]:(~strong(X)<=>creative(X)))&
(![X]:(~calm(X)=>humble(X)))&
((?[X]:(~generous(X)))<=>((~rich(paul)<~>rich(paul))))&
((~tall(mary))<=>(?[X]:((patient(X)<~>~funny(X)))))&
(![X]:((rich(X)|~kind(X))=>~tall(X)))&
(((~calm(alice)&humble(alice)))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((calm(X)|wise(X))<=>~humble(X)))&
(![X]:(creative(X)<=>~kind(X)))&
(((rich(john)<~>brave(john)))=>(?[X]:(creative(X))))&
(![X]:(~old(X)=>(~rich(X)&~wise(X))))&
((?[X]:((wise(X)&patient(X))))<=>((humble(lucy)&~creative(lucy))))&
(![X]:(~humble(X)<=>~patient(X)))&
(![X]:((tall(X)<~>strong(X))=>(~rich(X)|kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:((old(X)<~>creative(X))<=>curious(X)))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:(kind(X)))&
(~quiet(paul))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~humble(X)&funny(X))))&
((patient(susan)&tall(susan))) | ~happy(mary) | [] | null | 0 |
Everyone who is both generous and not funny is not tall or not calm and vice versa. If someone is either brave or not creative then paul is wise and vice versa. If someone is curious then alice is both brave and not happy. If someone is not generous or not old then alice is calm or not calm. Everyone who is both not rich and rich is old and vice versa. Everyone who is both old and kind is either tall or not wise and vice versa. If john is either not wise or not curious then fred is either not happy or not old. Everyone who is funny or not wise is not tall. Everyone who is either not wise or not rich is both not kind and patient. If someone is tall or strong then mary is either not generous or calm and vice versa. If alice is not strong then someone is both not creative and not quiet and vice versa. If john is either not rich or not patient then someone is either not creative or not wise and vice versa. Everyone who is either not happy or curious is not creative or kind. If someone is old or generous then fred is either not rich or not happy and vice versa. Everyone who is either not generous or old is both not brave and not strong. Someone is either not old or not brave. Susan is either old or not old. Someone is tall or brave. Someone is both not old and happy. Susan is either happy or not quiet. Someone is not wise or not quiet. Someone is not strong. Paul is patient or creative. | Fred is tall. | contradiction | (![X]:((generous(X)&~funny(X))<=>(~tall(X)|~calm(X))))&
((?[X]:((brave(X)<~>~creative(X))))<=>(wise(paul)))&
((?[X]:(curious(X)))=>((brave(alice)&~happy(alice))))&
((?[X]:((~generous(X)|~old(X))))=>((calm(alice)|~calm(alice))))&
(![X]:((~rich(X)&rich(X))<=>old(X)))&
(![X]:((old(X)&kind(X))<=>(tall(X)<~>~wise(X))))&
(((~wise(john)<~>~curious(john)))=>((~happy(fred)<~>~old(fred))))&
(![X]:((funny(X)|~wise(X))=>~tall(X)))&
(![X]:((~wise(X)<~>~rich(X))=>(~kind(X)&patient(X))))&
((?[X]:((tall(X)|strong(X))))<=>((~generous(mary)<~>calm(mary))))&
((~strong(alice))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(((~rich(john)<~>~patient(john)))<=>(?[X]:((~creative(X)<~>~wise(X)))))&
(![X]:((~happy(X)<~>curious(X))=>(~creative(X)|kind(X))))&
((?[X]:((old(X)|generous(X))))<=>((~rich(fred)<~>~happy(fred))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
((old(susan)<~>~old(susan)))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((~old(X)&happy(X))))&
((happy(susan)<~>~quiet(susan)))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:(~strong(X)))&
((patient(paul)|creative(paul))) | tall(fred) | [
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2112176260169756495888395
% SZS output start Proof for 2112176260169756495888395
5. ! [X0] : ((rich(X0) & ~rich(X0)) <=> old(X0)) [input p4]
6. ! [X0] : ((kind(X0) & old(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | funny(X0)) => ~tall(X0)) [input p7]
24. tall(fred) [input hypothesis]
29. ! [X0] : (~tall(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 8]
40. ! [X0] : (((rich(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | (~rich(X0) | rich(X0)))) [nnf transformation 5]
41. ! [X0] : (((rich(X0) & ~rich(X0)) | ~old(X0)) & (old(X0) | ~rich(X0) | rich(X0))) [flattening 40]
42. ! [X0] : (((kind(X0) & old(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 6]
43. ! [X0] : (((kind(X0) & old(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | ~kind(X0) | ~old(X0))) [flattening 42]
91. ~rich(X0) | ~old(X0) [cnf transformation 41]
92. ~old(X0) | rich(X0) [cnf transformation 41]
95. old(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 43]
96. old(X0) | tall(X0) | wise(X0) [cnf transformation 43]
104. ~tall(X0) | wise(X0) [cnf transformation 29]
150. tall(fred) [cnf transformation 24]
186. ~old(X0) [subsumption resolution 91,92]
187. wise(X0) | tall(X0) [subsumption resolution 96,186]
188. ~wise(X0) | ~tall(X0) [subsumption resolution 95,186]
205. wise(X0) [subsumption resolution 104,187]
233. 17 <=> ! [X1] : ~tall(X1) [avatar definition]
234. ~tall(X1) <- (17) [avatar component clause 233]
342. ~tall(X1) [resolution 188,205]
343. 17 [avatar split clause 342,233]
345. $false <- (17) [resolution 234,150]
350. ~17 [avatar contradiction clause 345]
351. $false [avatar sat refutation 343,350]
% SZS output end Proof for 2112176260169756495888395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not happy is either not calm or brave and vice versa.
Everyone who is not kind or generous is not generous and vice versa.
If someone is either tall or not calm then lucy is both not old and not creative.
If alice is both not strong and funny then someone is creative or generous and vice versa.
If someone is both not strong and not happy then lucy is both not quiet and not brave.
If someone is both strong and not patient then alice is both not curious and funny.
Everyone who is either not creative or not humble is patient or kind.
Everyone who is either not quiet or creative is either patient or happy.
Everyone who is not kind or not old is either not humble or not old.
Everyone who is either kind or old is not humble or not calm.
Everyone who is calm or not quiet is strong or patient and vice versa.
If alice is curious or not humble then someone is strong or not patient and vice versa.
Everyone who is both not patient and quiet is not rich or not wise and vice versa.
Everyone who is either not rich or not funny is both calm and not funny and vice versa.
If someone is either rich or calm then fred is happy and vice versa.
Everyone who is both not generous and not rich is curious and vice versa.
Susan is either not tall or quiet.
Fred is rich.
Someone is both not funny and not humble.
John is patient.
John is strong or quiet.
Someone is patient.
Someone is both creative and calm. | Susan is not curious. | neutral | (![X]:((quiet(X)&~happy(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((~kind(X)|generous(X))<=>~generous(X)))&
((?[X]:((tall(X)<~>~calm(X))))=>((~old(lucy)&~creative(lucy))))&
(((~strong(alice)&funny(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:((~strong(X)&~happy(X))))=>((~quiet(lucy)&~brave(lucy))))&
((?[X]:((strong(X)&~patient(X))))=>((~curious(alice)&funny(alice))))&
(![X]:((~creative(X)<~>~humble(X))=>(patient(X)|kind(X))))&
(![X]:((~quiet(X)<~>creative(X))=>(patient(X)<~>happy(X))))&
(![X]:((~kind(X)|~old(X))=>(~humble(X)<~>~old(X))))&
(![X]:((kind(X)<~>old(X))=>(~humble(X)|~calm(X))))&
(![X]:((calm(X)|~quiet(X))<=>(strong(X)|patient(X))))&
(((curious(alice)|~humble(alice)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~patient(X)&quiet(X))<=>(~rich(X)|~wise(X))))&
(![X]:((~rich(X)<~>~funny(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)<~>calm(X))))<=>(happy(fred)))&
(![X]:((~generous(X)&~rich(X))<=>curious(X)))&
((~tall(susan)<~>quiet(susan)))&
(rich(fred))&
(?[X]:((~funny(X)&~humble(X))))&
(patient(john))&
((strong(john)|quiet(john)))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)&calm(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is both not strong and happy is both calm and not kind and vice versa.
Everyone who is humble or not curious is creative or not tall and vice versa.
Everyone who is calm is happy or not curious.
If fred is either not quiet or strong then someone is both not patient and happy.
Everyone who is humble or happy is generous and vice versa.
Everyone who is either curious or not brave is happy or not rich.
If someone is either kind or rich then fred is rich and vice versa.
Everyone who is not tall is strong.
If mary is both not wise and not generous then someone is either not rich or kind.
Everyone who is either not strong or quiet is both not rich and strong and vice versa.
If someone is brave or rich then susan is either curious or not calm.
Everyone who is humble or strong is either curious or not rich.
Everyone who is not happy is not curious or old.
Everyone who is both rich and wise is either not tall or not humble and vice versa.
If fred is curious then someone is both not creative and not happy.
If susan is both curious and not old then john is not funny.
Someone is quiet.
Someone is tall or funny.
Someone is both wise and funny.
Someone is not old or not tall.
Someone is not rich.
Someone is not old or brave.
Fred is either not curious or tall.
Susan is not tall or old. | Fred is patient. | neutral | (![X]:((~strong(X)&happy(X))<=>(calm(X)&~kind(X))))&
(![X]:((humble(X)|~curious(X))<=>(creative(X)|~tall(X))))&
(![X]:(calm(X)=>(happy(X)|~curious(X))))&
(((~quiet(fred)<~>strong(fred)))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:((humble(X)|happy(X))<=>generous(X)))&
(![X]:((curious(X)<~>~brave(X))=>(happy(X)|~rich(X))))&
((?[X]:((kind(X)<~>rich(X))))<=>(rich(fred)))&
(![X]:(~tall(X)=>strong(X)))&
(((~wise(mary)&~generous(mary)))=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~rich(X)&strong(X))))&
((?[X]:((brave(X)|rich(X))))=>((curious(susan)<~>~calm(susan))))&
(![X]:((humble(X)|strong(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~curious(X)|old(X))))&
(![X]:((rich(X)&wise(X))<=>(~tall(X)<~>~humble(X))))&
((curious(fred))=>(?[X]:((~creative(X)&~happy(X)))))&
(((curious(susan)&~old(susan)))=>(~funny(john)))&
(?[X]:(quiet(X)))&
(?[X]:((tall(X)|funny(X))))&
(?[X]:((wise(X)&funny(X))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~old(X)|brave(X))))&
((~curious(fred)<~>tall(fred)))&
((~tall(susan)|old(susan))) | patient(fred) | [] | null | 0 |
Everyone who is not old is patient. If alice is either old or not patient then someone is not strong and vice versa. If someone is either not patient or not rich then someone is not rich and vice versa. Everyone who is either not quiet or not funny is both not creative and humble. Everyone who is either tall or calm is not wise or not funny. Everyone who is both not funny and kind is not quiet. Everyone who is kind or patient is both happy and not humble. Everyone who is patient or not strong is not tall or quiet and vice versa. Everyone who is either not happy or not old is both happy and not strong and vice versa. If alice is either calm or creative then someone is not creative and vice versa. Everyone who is not kind or rich is both old and not creative. If paul is both calm and not patient then someone is both curious and not rich and vice versa. Everyone who is either not wise or not humble is rich and vice versa. If someone is either creative or not strong then susan is either not humble or humble. Everyone who is either not happy or brave is not kind. Someone is both strong and happy. Susan is either not creative or curious. Someone is both old and brave. Mary is both not kind and not quiet. Someone is both strong and not generous. Someone is quiet. | Alice is happy. | entailment | (![X]:(~old(X)=>patient(X)))&
(((old(alice)<~>~patient(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~quiet(X)<~>~funny(X))=>(~creative(X)&humble(X))))&
(![X]:((tall(X)<~>calm(X))=>(~wise(X)|~funny(X))))&
(![X]:((~funny(X)&kind(X))=>~quiet(X)))&
(![X]:((kind(X)|patient(X))=>(happy(X)&~humble(X))))&
(![X]:((patient(X)|~strong(X))<=>(~tall(X)|quiet(X))))&
(![X]:((~happy(X)<~>~old(X))<=>(happy(X)&~strong(X))))&
(((calm(alice)<~>creative(alice)))<=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)|rich(X))=>(old(X)&~creative(X))))&
(((calm(paul)&~patient(paul)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((~wise(X)<~>~humble(X))<=>rich(X)))&
((?[X]:((creative(X)<~>~strong(X))))=>((~humble(susan)<~>humble(susan))))&
(![X]:((~happy(X)<~>brave(X))=>~kind(X)))&
(?[X]:((strong(X)&happy(X))))&
((~creative(susan)<~>curious(susan)))&
(?[X]:((old(X)&brave(X))))&
((~kind(mary)&~quiet(mary)))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:(quiet(X))) | happy(alice) | [
"p0",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6697164253802863034665040
% SZS output start Proof for 6697164253802863034665040
1. ! [X0] : (~old(X0) => patient(X0)) [input p0]
7. ! [X0] : ((patient(X0) | kind(X0)) => (~humble(X0) & happy(X0))) [input p6]
9. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> (~strong(X0) & happy(X0))) [input p8]
22. ~happy(alice) [input hypothesis]
25. ! [X0] : (patient(X0) | old(X0)) [ennf transformation 1]
31. ! [X0] : ((~humble(X0) & happy(X0)) | (~patient(X0) & ~kind(X0))) [ennf transformation 7]
48. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (strong(X0) | ~happy(X0))) & ((~strong(X0) & happy(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 9]
49. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | strong(X0) | ~happy(X0)) & ((~strong(X0) & happy(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [flattening 48]
71. patient(X0) | old(X0) [cnf transformation 25]
88. ~patient(X0) | happy(X0) [cnf transformation 31]
95. happy(X0) | ~old(X0) | happy(X0) [cnf transformation 49]
133. ~happy(alice) [cnf transformation 22]
134. happy(X0) | ~old(X0) [duplicate literal removal 95]
240. happy(X0) | old(X0) [resolution 88,71]
244. happy(X0) [subsumption resolution 240,134]
251. $false [resolution 244,133]
% SZS output end Proof for 6697164253802863034665040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If susan is humble then someone is not quiet or not humble and vice versa. If someone is either generous or funny then john is funny and vice versa. Everyone who is either not kind or not happy is patient and vice versa. If someone is strong or not happy then someone is generous or patient and vice versa. If mary is old then someone is both not brave and not humble and vice versa. If someone is quiet then someone is either tall or brave. Everyone who is both not patient and calm is either not calm or brave and vice versa. Everyone who is both humble and not rich is not creative and vice versa. Everyone who is not tall or not quiet is not old and vice versa. If someone is both quiet and funny then alice is either happy or not funny. If someone is not quiet then someone is either not quiet or not wise and vice versa. Everyone who is both not patient and calm is either happy or not creative. Everyone who is generous or not quiet is either tall or not kind. Everyone who is not patient or not tall is not brave and vice versa. Everyone who is not rich is both not creative and not humble and vice versa. If john is brave then someone is either kind or not humble and vice versa. Susan is both not old and curious. Susan is both tall and brave. Mary is either curious or humble. Someone is both curious and not wise. Someone is not brave. John is not happy or generous. Mary is calm or not wise. | Alice is brave. | neutral | ((humble(susan))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((generous(X)<~>funny(X))))<=>(funny(john)))&
(![X]:((~kind(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((strong(X)|~happy(X))))<=>(?[X]:((generous(X)|patient(X)))))&
((old(mary))<=>(?[X]:((~brave(X)&~humble(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:((~patient(X)&calm(X))<=>(~calm(X)<~>brave(X))))&
(![X]:((humble(X)&~rich(X))<=>~creative(X)))&
(![X]:((~tall(X)|~quiet(X))<=>~old(X)))&
((?[X]:((quiet(X)&funny(X))))=>((happy(alice)<~>~funny(alice))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((~patient(X)&calm(X))=>(happy(X)<~>~creative(X))))&
(![X]:((generous(X)|~quiet(X))=>(tall(X)<~>~kind(X))))&
(![X]:((~patient(X)|~tall(X))<=>~brave(X)))&
(![X]:(~rich(X)<=>(~creative(X)&~humble(X))))&
((brave(john))<=>(?[X]:((kind(X)<~>~humble(X)))))&
((~old(susan)&curious(susan)))&
((tall(susan)&brave(susan)))&
((curious(mary)<~>humble(mary)))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(~brave(X)))&
((~happy(john)|generous(john)))&
((calm(mary)|~wise(mary))) | brave(alice) | [] | null | 0 |
If lucy is both humble and funny then someone is both not creative and not kind.
If john is quiet then paul is creative and vice versa.
If paul is old or rich then someone is not brave or happy.
Everyone who is rich or not curious is both kind and calm and vice versa.
Everyone who is not funny or curious is strong and vice versa.
If alice is either generous or not happy then lucy is rich.
If someone is not rich or not funny then john is both happy and not kind and vice versa.
Everyone who is both not tall and kind is either calm or creative.
If john is both funny and generous then someone is both kind and tall.
Everyone who is curious or not brave is not calm or creative.
Everyone who is not wise is both brave and curious and vice versa.
If someone is not strong or not humble then someone is both quiet and generous and vice versa.
If alice is not quiet or not wise then alice is not calm or generous.
If lucy is not rich then mary is brave or creative and vice versa.
If someone is both not humble and tall then someone is not creative and vice versa.
If lucy is happy then paul is both happy and not rich and vice versa.
Someone is rich.
Alice is not creative.
Someone is not old.
John is either wise or strong.
Someone is calm or tall.
Mary is both wise and calm.
Someone is not strong or brave.
Mary is not tall. | John is wise. | contradiction | (((humble(lucy)&funny(lucy)))=>(?[X]:((~creative(X)&~kind(X)))))&
((quiet(john))<=>(creative(paul)))&
(((old(paul)|rich(paul)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((rich(X)|~curious(X))<=>(kind(X)&calm(X))))&
(![X]:((~funny(X)|curious(X))<=>strong(X)))&
(((generous(alice)<~>~happy(alice)))=>(rich(lucy)))&
((?[X]:((~rich(X)|~funny(X))))<=>((happy(john)&~kind(john))))&
(![X]:((~tall(X)&kind(X))=>(calm(X)<~>creative(X))))&
(((funny(john)&generous(john)))=>(?[X]:((kind(X)&tall(X)))))&
(![X]:((curious(X)|~brave(X))=>(~calm(X)|creative(X))))&
(![X]:(~wise(X)<=>(brave(X)&curious(X))))&
((?[X]:((~strong(X)|~humble(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
(((~quiet(alice)|~wise(alice)))=>((~calm(alice)|generous(alice))))&
((~rich(lucy))<=>((brave(mary)|creative(mary))))&
((?[X]:((~humble(X)&tall(X))))<=>(?[X]:(~creative(X))))&
((happy(lucy))<=>((happy(paul)&~rich(paul))))&
(?[X]:(rich(X)))&
(~creative(alice))&
(?[X]:(~old(X)))&
((wise(john)<~>strong(john)))&
(?[X]:((calm(X)|tall(X))))&
((wise(mary)&calm(mary)))&
(?[X]:((~strong(X)|brave(X))))&
(~tall(mary)) | wise(john) | [
"p3",
"p4",
"p6",
"p9",
"p13",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7625885664226295440360037
% SZS output start Proof for 7625885664226295440360037
4. ! [X0] : ((~curious(X0) | rich(X0)) <=> (calm(X0) & kind(X0))) [input p3]
5. ! [X0] : ((curious(X0) | ~funny(X0)) <=> strong(X0)) [input p4]
7. ? [X0] : (~funny(X0) | ~rich(X0)) <=> (~kind(john) & happy(john)) [input p6]
10. ! [X0] : ((~brave(X0) | curious(X0)) => (creative(X0) | ~calm(X0))) [input p9]
14. ~rich(lucy) <=> (creative(mary) | brave(mary)) [input p13]
20. wise(john) <~> strong(john) [input p19]
22. calm(mary) & wise(mary) [input p21]
25. wise(john) [input hypothesis]
38. ! [X0] : ((creative(X0) | ~calm(X0)) | (brave(X0) & ~curious(X0))) [ennf transformation 10]
39. ! [X0] : (creative(X0) | ~calm(X0) | (brave(X0) & ~curious(X0))) [flattening 38]
47. ! [X0] : (((~curious(X0) | rich(X0)) | (~calm(X0) | ~kind(X0))) & ((calm(X0) & kind(X0)) | (curious(X0) & ~rich(X0)))) [nnf transformation 4]
48. ! [X0] : ((~curious(X0) | rich(X0) | ~calm(X0) | ~kind(X0)) & ((calm(X0) & kind(X0)) | (curious(X0) & ~rich(X0)))) [flattening 47]
49. ! [X0] : (((curious(X0) | ~funny(X0)) | ~strong(X0)) & (strong(X0) | (~curious(X0) & funny(X0)))) [nnf transformation 5]
50. ! [X0] : ((curious(X0) | ~funny(X0) | ~strong(X0)) & (strong(X0) | (~curious(X0) & funny(X0)))) [flattening 49]
52. (? [X0] : (~funny(X0) | ~rich(X0)) | (kind(john) | ~happy(john))) & ((~kind(john) & happy(john)) | ! [X0] : (funny(X0) & rich(X0))) [nnf transformation 7]
53. (? [X0] : (~funny(X0) | ~rich(X0)) | kind(john) | ~happy(john)) & ((~kind(john) & happy(john)) | ! [X0] : (funny(X0) & rich(X0))) [flattening 52]
54. (? [X0] : (~funny(X0) | ~rich(X0)) | kind(john) | ~happy(john)) & ((~kind(john) & happy(john)) | ! [X1] : (funny(X1) & rich(X1))) [rectify 53]
55. ? [X0] : (~funny(X0) | ~rich(X0)) => (~funny(sK2) | ~rich(sK2)) [choice axiom]
56. ((~funny(sK2) | ~rich(sK2)) | kind(john) | ~happy(john)) & ((~kind(john) & happy(john)) | ! [X1] : (funny(X1) & rich(X1))) [skolemisation 54,55]
67. (~rich(lucy) | (~creative(mary) & ~brave(mary))) & ((creative(mary) | brave(mary)) | rich(lucy)) [nnf transformation 14]
68. (~rich(lucy) | (~creative(mary) & ~brave(mary))) & (creative(mary) | brave(mary) | rich(lucy)) [flattening 67]
78. (~strong(john) | ~wise(john)) & (strong(john) | wise(john)) [nnf transformation 20]
89. curious(X0) | kind(X0) [cnf transformation 48]
94. ~curious(X0) | strong(X0) [cnf transformation 50]
100. ~kind(john) | rich(X1) [cnf transformation 56]
108. ~calm(X0) | creative(X0) | brave(X0) [cnf transformation 39]
120. ~rich(lucy) | ~brave(mary) [cnf transformation 68]
121. ~rich(lucy) | ~creative(mary) [cnf transformation 68]
131. ~strong(john) | ~wise(john) [cnf transformation 78]
134. calm(mary) [cnf transformation 22]
137. wise(john) [cnf transformation 25]
188. 12 <=> rich(lucy) [avatar definition]
189. ~rich(lucy) <- (~12) [avatar component clause 188]
198. 14 <=> kind(john) [avatar definition]
215. 18 <=> ! [X1] : rich(X1) [avatar definition]
216. rich(X1) <- (18) [avatar component clause 215]
217. 18 | ~14 [avatar split clause 100,198,215]
283. 33 <=> creative(mary) [avatar definition]
286. ~33 | ~12 [avatar split clause 121,188,283]
288. 34 <=> brave(mary) [avatar definition]
290. ~brave(mary) <- (~34) [avatar component clause 288]
291. ~34 | ~12 [avatar split clause 120,188,288]
326. 42 <=> wise(john) [avatar definition]
330. 43 <=> strong(john) [avatar definition]
332. ~strong(john) <- (~43) [avatar component clause 330]
333. ~42 | ~43 [avatar split clause 131,330,326]
353. 42 [avatar split clause 137,326]
374. strong(X0) | kind(X0) [resolution 94,89]
412. creative(mary) | brave(mary) [resolution 108,134]
467. kind(john) <- (~43) [resolution 374,332]
472. 14 | 43 [avatar split clause 467,330,198]
491. $false <- (~12, 18) [resolution 216,189]
496. 12 | ~18 [avatar contradiction clause 491]
497. creative(mary) <- (~34) [subsumption resolution 412,290]
498. 33 | 34 [avatar split clause 497,288,283]
500. $false [avatar sat refutation 217,286,291,333,353,472,496,498]
% SZS output end Proof for 7625885664226295440360037
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not calm and curious then someone is not brave or not creative and vice versa.
Everyone who is either curious or brave is quiet and vice versa.
If someone is quiet then john is not brave and vice versa.
If alice is either patient or strong then mary is both not creative and not tall.
Everyone who is not strong is both tall and not creative.
If someone is kind then someone is not patient.
If someone is generous or not patient then someone is not creative or not funny.
Everyone who is happy or not strong is either not tall or calm.
Everyone who is not generous is both not kind and creative and vice versa.
Everyone who is tall is both not old and funny.
Everyone who is quiet is both tall and calm.
Everyone who is both generous and not happy is funny or not tall.
If someone is either curious or generous then susan is either patient or not brave and vice versa.
Everyone who is either brave or not tall is either strong or not curious and vice versa.
If lucy is not patient then lucy is brave or patient.
John is either funny or not brave.
Someone is either old or curious.
Someone is not humble.
Someone is not old.
Mary is kind or quiet.
Mary is strong.
Alice is happy. | Lucy is not tall. | contradiction | (((~calm(susan)&curious(susan)))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((curious(X)<~>brave(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(((patient(alice)<~>strong(alice)))=>((~creative(mary)&~tall(mary))))&
(![X]:(~strong(X)=>(tall(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:(~patient(X))))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((happy(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:(~generous(X)<=>(~kind(X)&creative(X))))&
(![X]:(tall(X)=>(~old(X)&funny(X))))&
(![X]:(quiet(X)=>(tall(X)&calm(X))))&
(![X]:((generous(X)&~happy(X))=>(funny(X)|~tall(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((brave(X)<~>~tall(X))<=>(strong(X)<~>~curious(X))))&
((~patient(lucy))=>((brave(lucy)|patient(lucy))))&
((funny(john)<~>~brave(john)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
((kind(mary)|quiet(mary)))&
(strong(mary))&
(happy(alice)) | ~tall(lucy) | [
"p1",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 114205192852620950800959
% SZS output start Proof for 114205192852620950800959
2. ! [X0] : ((curious(X0) <~> brave(X0)) <=> quiet(X0)) [input p1]
5. ! [X0] : (~strong(X0) => (~creative(X0) & tall(X0))) [input p4]
11. ! [X0] : (quiet(X0) => (calm(X0) & tall(X0))) [input p10]
14. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p13]
23. ~tall(lucy) [input hypothesis]
28. ! [X0] : ((~creative(X0) & tall(X0)) | strong(X0)) [ennf transformation 5]
33. ! [X0] : ((calm(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 11]
43. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ~quiet(X0)) & (quiet(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 2]
62. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 14]
74. ~curious(X0) | brave(X0) | quiet(X0) [cnf transformation 43]
75. ~brave(X0) | curious(X0) | quiet(X0) [cnf transformation 43]
84. tall(X0) | strong(X0) [cnf transformation 28]
98. ~quiet(X0) | tall(X0) [cnf transformation 33]
112. curious(X0) | ~strong(X0) | brave(X0) | tall(X0) [cnf transformation 62]
115. tall(X0) | ~brave(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 62]
126. ~tall(lucy) [cnf transformation 23]
243. ~brave(X0) | tall(X0) | ~curious(X0) [subsumption resolution 115,84]
245. tall(X0) | brave(X0) | curious(X0) [subsumption resolution 112,84]
248. 26 <=> brave(lucy) [avatar definition]
249. ~brave(lucy) <- (~26) [avatar component clause 248]
250. brave(lucy) <- (26) [avatar component clause 248]
326. curious(lucy) | quiet(lucy) <- (26) [resolution 75,250]
329. 35 <=> quiet(lucy) [avatar definition]
330. ~quiet(lucy) <- (~35) [avatar component clause 329]
331. quiet(lucy) <- (35) [avatar component clause 329]
333. 36 <=> curious(lucy) [avatar definition]
334. ~curious(lucy) <- (~36) [avatar component clause 333]
335. curious(lucy) <- (36) [avatar component clause 333]
336. 35 | 36 | ~26 [avatar split clause 326,248,333,329]
360. tall(lucy) <- (35) [resolution 331,98]
363. $false <- (35) [subsumption resolution 360,126]
364. ~35 [avatar contradiction clause 363]
369. brave(lucy) | quiet(lucy) <- (36) [resolution 335,74]
382. tall(lucy) | ~curious(lucy) <- (26) [resolution 243,250]
384. ~curious(lucy) <- (26) [subsumption resolution 382,126]
385. $false <- (26, 36) [subsumption resolution 384,335]
386. ~26 | ~36 [avatar contradiction clause 385]
388. brave(lucy) <- (~35, 36) [subsumption resolution 369,330]
389. 26 | 35 | ~36 [avatar split clause 388,333,329,248]
402. brave(lucy) | curious(lucy) [resolution 245,126]
405. curious(lucy) <- (~26) [subsumption resolution 402,249]
406. $false <- (~26, ~36) [subsumption resolution 405,334]
407. 26 | 36 [avatar contradiction clause 406]
409. $false [avatar sat refutation 336,364,386,389,407]
% SZS output end Proof for 114205192852620950800959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or brave is either not rich or not quiet. If susan is not patient then someone is not calm or not kind. Everyone who is either brave or not generous is not generous. If alice is both not kind and not happy then someone is generous or not old. Everyone who is both not humble and not kind is wise. Everyone who is calm or not rich is not calm. If someone is either calm or generous then susan is either funny or not kind. Everyone who is both rich and not calm is not creative or quiet and vice versa. If someone is not kind or happy then someone is not wise and vice versa. Everyone who is either not rich or creative is either wise or creative and vice versa. Everyone who is both not patient and not calm is not kind. Everyone who is brave is not patient or generous and vice versa. If john is not funny then someone is either not brave or not happy. Everyone who is not kind or calm is not curious or humble. Everyone who is not patient is not tall or not kind and vice versa. If someone is both not patient and kind then someone is both not curious and funny and vice versa. John is either not happy or old. Someone is both not calm and happy. Someone is not curious. Mary is either not kind or not wise. Someone is both rich and old. Someone is not wise. Someone is either not happy or not curious. Someone is either creative or not tall. | Mary is not brave. | entailment | (![X]:((kind(X)<~>brave(X))=>(~rich(X)<~>~quiet(X))))&
((~patient(susan))=>(?[X]:((~calm(X)|~kind(X)))))&
(![X]:((brave(X)<~>~generous(X))=>~generous(X)))&
(((~kind(alice)&~happy(alice)))=>(?[X]:((generous(X)|~old(X)))))&
(![X]:((~humble(X)&~kind(X))=>wise(X)))&
(![X]:((calm(X)|~rich(X))=>~calm(X)))&
((?[X]:((calm(X)<~>generous(X))))=>((funny(susan)<~>~kind(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~creative(X)|quiet(X))))&
((?[X]:((~kind(X)|happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~calm(X))=>~kind(X)))&
(![X]:(brave(X)<=>(~patient(X)|generous(X))))&
((~funny(john))=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~kind(X)|calm(X))=>(~curious(X)|humble(X))))&
(![X]:(~patient(X)<=>(~tall(X)|~kind(X))))&
((?[X]:((~patient(X)&kind(X))))<=>(?[X]:((~curious(X)&funny(X)))))&
((~happy(john)<~>old(john)))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:(~curious(X)))&
((~kind(mary)<~>~wise(mary)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~happy(X)<~>~curious(X))))&
(?[X]:((creative(X)<~>~tall(X)))) | ~brave(mary) | [
"p0",
"p2",
"p5",
"p7",
"p9",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7905173124022009662702314
% SZS output start Proof for 7905173124022009662702314
1. ! [X0] : ((kind(X0) <~> brave(X0)) => (~rich(X0) <~> ~quiet(X0))) [input p0]
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => ~generous(X0)) [input p2]
6. ! [X0] : ((~rich(X0) | calm(X0)) => ~calm(X0)) [input p5]
8. ! [X0] : ((~calm(X0) & rich(X0)) <=> (quiet(X0) | ~creative(X0))) [input p7]
10. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (wise(X0) <~> creative(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & ~patient(X0)) => ~kind(X0)) [input p10]
12. ! [X0] : (brave(X0) <=> (generous(X0) | ~patient(X0))) [input p11]
20. ~kind(mary) <~> ~wise(mary) [input p19]
25. brave(mary) [input hypothesis]
30. ! [X0] : ((~rich(X0) <~> ~quiet(X0)) | (kind(X0) <=> brave(X0))) [ennf transformation 1]
32. ! [X0] : (~generous(X0) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
35. ! [X0] : (~calm(X0) | (rich(X0) & ~calm(X0))) [ennf transformation 6]
37. ! [X0] : (~kind(X0) | (calm(X0) | patient(X0))) [ennf transformation 11]
38. ! [X0] : (~kind(X0) | calm(X0) | patient(X0)) [flattening 37]
40. ! [X0] : (((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 30]
43. ! [X0] : (~generous(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 32]
47. ! [X0] : (((~calm(X0) & rich(X0)) | (~quiet(X0) & creative(X0))) & ((quiet(X0) | ~creative(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 8]
48. ! [X0] : (((~calm(X0) & rich(X0)) | (~quiet(X0) & creative(X0))) & (quiet(X0) | ~creative(X0) | calm(X0) | ~rich(X0))) [flattening 47]
54. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) & (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 10]
55. ! [X0] : ((brave(X0) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ~brave(X0))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ~brave(X0))) [flattening 55]
72. (wise(mary) | kind(mary)) & (~wise(mary) | ~kind(mary)) [nnf transformation 20]
86. ~brave(X0) | rich(X0) | kind(X0) | quiet(X0) [cnf transformation 40]
88. ~generous(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 43]
91. ~calm(X0) | ~calm(X0) [cnf transformation 35]
98. creative(X0) | rich(X0) [cnf transformation 48]
99. ~quiet(X0) | rich(X0) [cnf transformation 48]
108. ~creative(X0) | ~wise(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 54]
109. creative(X0) | ~rich(X0) | creative(X0) | ~wise(X0) [cnf transformation 54]
113. ~kind(X0) | calm(X0) | patient(X0) [cnf transformation 38]
114. generous(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 56]
132. wise(mary) | kind(mary) [cnf transformation 72]
140. brave(mary) [cnf transformation 25]
142. ~creative(X0) | ~wise(X0) | ~rich(X0) [duplicate literal removal 108]
143. creative(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 109]
145. ~calm(X0) [duplicate literal removal 91]
146. ~generous(X0) | ~brave(X0) [duplicate literal removal 88]
218. ~wise(X0) | creative(X0) [subsumption resolution 143,98]
219. ~wise(X0) | ~rich(X0) [subsumption resolution 142,218]
220. ~kind(X0) | patient(X0) [subsumption resolution 113,145]
223. ~patient(X0) | ~brave(X0) [subsumption resolution 114,146]
262. 25 <=> kind(mary) [avatar definition]
263. ~kind(mary) <- (~25) [avatar component clause 262]
264. kind(mary) <- (25) [avatar component clause 262]
266. 26 <=> wise(mary) [avatar definition]
268. wise(mary) <- (26) [avatar component clause 266]
269. 25 | 26 [avatar split clause 132,266,262]
299. patient(mary) <- (25) [resolution 220,264]
303. ~brave(mary) <- (25) [resolution 223,299]
304. $false <- (25) [subsumption resolution 303,140]
305. ~25 [avatar contradiction clause 304]
306. ~rich(mary) <- (26) [resolution 268,219]
312. rich(mary) | kind(mary) | quiet(mary) [resolution 86,140]
316. kind(mary) | quiet(mary) <- (26) [subsumption resolution 312,306]
317. quiet(mary) <- (~25, 26) [subsumption resolution 316,263]
321. rich(mary) <- (~25, 26) [resolution 317,99]
322. $false <- (~25, 26) [subsumption resolution 321,306]
323. 25 | ~26 [avatar contradiction clause 322]
324. $false [avatar sat refutation 269,305,323]
% SZS output end Proof for 7905173124022009662702314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is either brave or old and vice versa.
If someone is not creative then fred is both not rich and not curious.
If fred is both quiet and not humble then someone is either not generous or patient and vice versa.
If susan is both not happy and old then alice is patient and vice versa.
Everyone who is not rich or humble is either not humble or not quiet.
Everyone who is both generous and not strong is not old and vice versa.
Everyone who is not old is rich or strong and vice versa.
Everyone who is either not kind or not tall is strong or not happy.
Everyone who is either brave or not wise is not curious or brave and vice versa.
Everyone who is either strong or not creative is either not funny or rich and vice versa.
If someone is either not tall or calm then lucy is patient and vice versa.
Everyone who is generous is either not quiet or not creative and vice versa.
If someone is either tall or calm then someone is both tall and not strong and vice versa.
Everyone who is both not wise and not calm is funny or curious and vice versa.
Everyone who is not patient is either not rich or not funny and vice versa.
If susan is old or creative then someone is patient or wise.
Susan is both not generous and not strong.
Someone is creative or funny.
Lucy is rich.
Someone is not rich.
Mary is either calm or happy.
Someone is both not calm and patient.
Paul is both not happy and patient. | Paul is not quiet. | entailment | (![X]:((calm(X)|~old(X))<=>(brave(X)<~>old(X))))&
((?[X]:(~creative(X)))=>((~rich(fred)&~curious(fred))))&
(((quiet(fred)&~humble(fred)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~happy(susan)&old(susan)))<=>(patient(alice)))&
(![X]:((~rich(X)|humble(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((generous(X)&~strong(X))<=>~old(X)))&
(![X]:(~old(X)<=>(rich(X)|strong(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(strong(X)|~happy(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(~curious(X)|brave(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(patient(lucy)))&
(![X]:(generous(X)<=>(~quiet(X)<~>~creative(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:((~wise(X)&~calm(X))<=>(funny(X)|curious(X))))&
(![X]:(~patient(X)<=>(~rich(X)<~>~funny(X))))&
(((old(susan)|creative(susan)))=>(?[X]:((patient(X)|wise(X)))))&
((~generous(susan)&~strong(susan)))&
(?[X]:((creative(X)|funny(X))))&
(rich(lucy))&
(?[X]:(~rich(X)))&
((calm(mary)<~>happy(mary)))&
(?[X]:((~calm(X)&patient(X))))&
((~happy(paul)&patient(paul))) | ~quiet(paul) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"p11",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3057057528541268460815745
% SZS output start Proof for 3057057528541268460815745
1. ! [X0] : ((~old(X0) | calm(X0)) <=> (brave(X0) <~> old(X0))) [input p0]
6. ! [X0] : ((~strong(X0) & generous(X0)) <=> ~old(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> (strong(X0) | rich(X0))) [input p6]
9. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (brave(X0) | ~curious(X0))) [input p8]
10. ! [X0] : ((strong(X0) <~> ~creative(X0)) <=> (~funny(X0) <~> rich(X0))) [input p9]
12. ! [X0] : (generous(X0) <=> (~quiet(X0) <~> ~creative(X0))) [input p11]
14. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> (curious(X0) | funny(X0))) [input p13]
15. ! [X0] : (~patient(X0) <=> (~rich(X0) <~> ~funny(X0))) [input p14]
23. patient(paul) & ~happy(paul) [input p22]
24. quiet(paul) [input hypothesis]
31. ! [X0] : (((~old(X0) | calm(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (old(X0) & ~calm(X0)))) [nnf transformation 1]
32. ! [X0] : ((~old(X0) | calm(X0) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (old(X0) & ~calm(X0)))) [flattening 31]
41. ! [X0] : (((~strong(X0) & generous(X0)) | old(X0)) & (~old(X0) | (strong(X0) | ~generous(X0)))) [nnf transformation 6]
42. ! [X0] : (((~strong(X0) & generous(X0)) | old(X0)) & (~old(X0) | strong(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : ((~old(X0) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | old(X0))) [nnf transformation 7]
44. ! [X0] : ((~old(X0) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | old(X0))) [flattening 43]
46. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 9]
47. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [flattening 46]
48. ! [X0] : ((((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))))) [nnf transformation 10]
53. ! [X0] : ((generous(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~generous(X0))) [nnf transformation 12]
59. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (calm(X0) | wise(X0)))) [nnf transformation 14]
60. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | calm(X0) | wise(X0))) [flattening 59]
61. ! [X0] : ((~patient(X0) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | patient(X0))) [nnf transformation 15]
72. old(X0) | brave(X0) | old(X0) [cnf transformation 32]
92. ~generous(X0) | strong(X0) | ~old(X0) [cnf transformation 42]
93. generous(X0) | old(X0) [cnf transformation 42]
94. ~strong(X0) | old(X0) [cnf transformation 42]
95. strong(X0) | rich(X0) | old(X0) [cnf transformation 44]
96. ~rich(X0) | ~old(X0) [cnf transformation 44]
97. ~old(X0) | ~strong(X0) [cnf transformation 44]
105. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 47]
109. ~rich(X0) | funny(X0) | strong(X0) | creative(X0) [cnf transformation 48]
110. ~creative(X0) | strong(X0) | rich(X0) | funny(X0) [cnf transformation 48]
118. ~generous(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 53]
121. ~quiet(X0) | generous(X0) | creative(X0) [cnf transformation 53]
129. ~funny(X0) | ~wise(X0) [cnf transformation 60]
135. ~funny(X0) | ~patient(X0) | rich(X0) [cnf transformation 61]
136. ~patient(X0) | ~rich(X0) | funny(X0) [cnf transformation 61]
149. patient(paul) [cnf transformation 23]
150. quiet(paul) [cnf transformation 24]
152. ~brave(X0) | wise(X0) [duplicate literal removal 105]
154. brave(X0) | old(X0) [duplicate literal removal 72]
212. ~strong(X0) [subsumption resolution 97,94]
213. rich(X0) | old(X0) [subsumption resolution 95,212]
218. ~creative(X0) | rich(X0) | funny(X0) [subsumption resolution 110,212]
219. ~rich(X0) | funny(X0) | creative(X0) [subsumption resolution 109,212]
312. wise(X0) | old(X0) [resolution 154,152]
359. ~quiet(X0) | ~creative(X0) | old(X0) [resolution 118,93]
395. generous(paul) | creative(paul) [resolution 121,150]
419. ~rich(paul) | funny(paul) [resolution 136,149]
433. 39 <=> funny(paul) [avatar definition]
434. ~funny(paul) <- (~39) [avatar component clause 433]
435. funny(paul) <- (39) [avatar component clause 433]
437. 40 <=> rich(paul) [avatar definition]
438. rich(paul) <- (40) [avatar component clause 437]
439. ~rich(paul) <- (~40) [avatar component clause 437]
440. 39 | ~40 [avatar split clause 419,437,433]
580. funny(X0) | creative(X0) | old(X0) [resolution 219,213]
606. ~patient(paul) | rich(paul) <- (39) [resolution 435,135]
609. ~wise(paul) <- (39) [resolution 435,129]
610. rich(paul) <- (39) [subsumption resolution 606,149]
613. 40 | ~39 [avatar split clause 610,433,437]
630. ~old(paul) <- (40) [resolution 438,96]
686. ~creative(paul) | old(paul) [resolution 359,150]
719. creative(X5) | old(X5) | ~wise(X5) [resolution 580,129]
725. creative(X5) | old(X5) [subsumption resolution 719,312]
779. old(paul) <- (39) [resolution 609,312]
780. $false <- (39, 40) [subsumption resolution 779,630]
781. ~39 | ~40 [avatar contradiction clause 780]
782. old(paul) [subsumption resolution 686,725]
784. 72 <=> creative(paul) [avatar definition]
786. creative(paul) <- (72) [avatar component clause 784]
788. 73 <=> generous(paul) [avatar definition]
790. generous(paul) <- (73) [avatar component clause 788]
791. 72 | 73 [avatar split clause 395,788,784]
805. rich(paul) | funny(paul) <- (72) [resolution 786,218]
807. funny(paul) <- (~40, 72) [subsumption resolution 805,439]
808. $false <- (~39, ~40, 72) [subsumption resolution 807,434]
809. 39 | 40 | ~72 [avatar contradiction clause 808]
812. strong(paul) | ~old(paul) <- (73) [resolution 790,92]
813. ~old(paul) <- (73) [subsumption resolution 812,212]
814. $false <- (73) [subsumption resolution 813,782]
815. ~73 [avatar contradiction clause 814]
816. $false [avatar sat refutation 440,613,781,791,809,815]
% SZS output end Proof for 3057057528541268460815745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is old or wise is not kind or not humble and vice versa.
If someone is not old or old then someone is strong and vice versa.
If someone is not strong or tall then susan is both not wise and kind.
If fred is not kind then someone is either old or not curious.
Everyone who is both not curious and calm is not patient or not wise and vice versa.
If susan is either not calm or happy then mary is not curious or not kind.
Everyone who is not patient is not brave or not old and vice versa.
If alice is either not creative or funny then paul is both patient and not happy and vice versa.
If someone is not happy then someone is either strong or generous and vice versa.
Everyone who is both creative and kind is either not quiet or not wise.
Everyone who is both not patient and not brave is either not curious or not quiet and vice versa.
Everyone who is not funny or not rich is both curious and strong and vice versa.
If someone is not tall or strong then someone is either not kind or creative and vice versa.
Everyone who is both curious and kind is both calm and not kind and vice versa.
If someone is creative then fred is either strong or calm.
If lucy is calm or tall then fred is not humble.
Mary is curious.
Alice is not rich.
Susan is not brave.
Susan is both generous and rich.
Someone is happy or curious.
Mary is either wise or not old.
Someone is not wise.
Someone is both happy and not rich. | Susan is not kind. | contradiction | (![X]:((old(X)|wise(X))<=>(~kind(X)|~humble(X))))&
((?[X]:((~old(X)|old(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~strong(X)|tall(X))))=>((~wise(susan)&kind(susan))))&
((~kind(fred))=>(?[X]:((old(X)<~>~curious(X)))))&
(![X]:((~curious(X)&calm(X))<=>(~patient(X)|~wise(X))))&
(((~calm(susan)<~>happy(susan)))=>((~curious(mary)|~kind(mary))))&
(![X]:(~patient(X)<=>(~brave(X)|~old(X))))&
(((~creative(alice)<~>funny(alice)))<=>((patient(paul)&~happy(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)<~>generous(X)))))&
(![X]:((creative(X)&kind(X))=>(~quiet(X)<~>~wise(X))))&
(![X]:((~patient(X)&~brave(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((~funny(X)|~rich(X))<=>(curious(X)&strong(X))))&
((?[X]:((~tall(X)|strong(X))))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:((curious(X)&kind(X))<=>(calm(X)&~kind(X))))&
((?[X]:(creative(X)))=>((strong(fred)<~>calm(fred))))&
(((calm(lucy)|tall(lucy)))=>(~humble(fred)))&
(curious(mary))&
(~rich(alice))&
(~brave(susan))&
((generous(susan)&rich(susan)))&
(?[X]:((happy(X)|curious(X))))&
((wise(mary)<~>~old(mary)))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)&~rich(X)))) | ~kind(susan) | [
"p4",
"p6",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7276503455681375580135502
% SZS output start Proof for 7276503455681375580135502
5. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (~wise(X0) | ~patient(X0))) [input p4]
7. ! [X0] : (~patient(X0) <=> (~old(X0) | ~brave(X0))) [input p6]
14. ! [X0] : ((kind(X0) & curious(X0)) <=> (~kind(X0) & calm(X0))) [input p13]
19. ~brave(susan) [input p18]
25. ~kind(susan) [input hypothesis]
47. ! [X0] : (((calm(X0) & ~curious(X0)) | (wise(X0) & patient(X0))) & ((~wise(X0) | ~patient(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 5]
48. ! [X0] : (((calm(X0) & ~curious(X0)) | (wise(X0) & patient(X0))) & (~wise(X0) | ~patient(X0) | ~calm(X0) | curious(X0))) [flattening 47]
50. ! [X0] : ((~patient(X0) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | patient(X0))) [nnf transformation 7]
51. ! [X0] : ((~patient(X0) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | patient(X0))) [flattening 50]
69. ! [X0] : (((kind(X0) & curious(X0)) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | (~kind(X0) | ~curious(X0)))) [nnf transformation 14]
70. ! [X0] : (((kind(X0) & curious(X0)) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | ~kind(X0) | ~curious(X0))) [flattening 69]
95. patient(X0) | calm(X0) [cnf transformation 48]
100. ~patient(X0) | brave(X0) [cnf transformation 51]
134. kind(X0) | kind(X0) | ~calm(X0) [cnf transformation 70]
141. ~brave(susan) [cnf transformation 19]
150. ~kind(susan) [cnf transformation 25]
152. ~calm(X0) | kind(X0) [duplicate literal removal 134]
169. 5 <=> kind(susan) [avatar definition]
170. ~kind(susan) <- (~5) [avatar component clause 169]
202. 12 <=> calm(susan) [avatar definition]
203. calm(susan) <- (12) [avatar component clause 202]
346. ~5 [avatar split clause 150,169]
361. brave(X0) | calm(X0) [resolution 100,95]
470. calm(susan) [resolution 361,141]
473. 12 [avatar split clause 470,202]
474. kind(susan) <- (12) [resolution 203,152]
475. $false <- (~5, 12) [subsumption resolution 474,170]
476. 5 | ~12 [avatar contradiction clause 475]
477. $false [avatar sat refutation 346,473,476]
% SZS output end Proof for 7276503455681375580135502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or happy is both not happy and not wise and vice versa. Everyone who is either funny or not kind is either happy or wise and vice versa. Everyone who is curious or not happy is not curious or not generous and vice versa. If alice is not kind or not happy then someone is kind or not quiet and vice versa. Everyone who is both patient and quiet is generous or not humble. Everyone who is not calm is either not curious or calm and vice versa. If someone is rich or not old then alice is both patient and strong and vice versa. If someone is creative then someone is both not wise and happy. If susan is both tall and kind then susan is either not wise or strong and vice versa. If someone is not wise then someone is patient and vice versa. If john is brave then alice is either happy or kind and vice versa. Everyone who is calm or patient is not old. Everyone who is either funny or not brave is either not quiet or not kind and vice versa. Everyone who is rich or humble is patient or not tall. Everyone who is both patient and humble is not happy. If someone is not tall or not brave then someone is either not tall or not funny. Lucy is not wise or kind. Someone is either not patient or calm. Fred is both not calm and old. Someone is not rich. Someone is not old. Fred is wise or not brave. John is funny. John is happy or tall. | Lucy is not wise. | neutral | (![X]:((~wise(X)<~>happy(X))<=>(~happy(X)&~wise(X))))&
(![X]:((funny(X)<~>~kind(X))<=>(happy(X)<~>wise(X))))&
(![X]:((curious(X)|~happy(X))<=>(~curious(X)|~generous(X))))&
(((~kind(alice)|~happy(alice)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((patient(X)&quiet(X))=>(generous(X)|~humble(X))))&
(![X]:(~calm(X)<=>(~curious(X)<~>calm(X))))&
((?[X]:((rich(X)|~old(X))))<=>((patient(alice)&strong(alice))))&
((?[X]:(creative(X)))=>(?[X]:((~wise(X)&happy(X)))))&
(((tall(susan)&kind(susan)))<=>((~wise(susan)<~>strong(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:(patient(X))))&
((brave(john))<=>((happy(alice)<~>kind(alice))))&
(![X]:((calm(X)|patient(X))=>~old(X)))&
(![X]:((funny(X)<~>~brave(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((rich(X)|humble(X))=>(patient(X)|~tall(X))))&
(![X]:((patient(X)&humble(X))=>~happy(X)))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:((~tall(X)<~>~funny(X)))))&
((~wise(lucy)|kind(lucy)))&
(?[X]:((~patient(X)<~>calm(X))))&
((~calm(fred)&old(fred)))&
(?[X]:(~rich(X)))&
(?[X]:(~old(X)))&
((wise(fred)|~brave(fred)))&
(funny(john))&
((happy(john)|tall(john))) | ~wise(lucy) | [] | null | 0 |
If someone is not calm or not humble then someone is both kind and not rich and vice versa. Everyone who is both curious and brave is not brave or not tall and vice versa. If someone is both calm and not wise then someone is both not wise and not tall and vice versa. Everyone who is either not strong or not old is not rich or not strong. If fred is either not generous or not humble then john is not rich or rich. Everyone who is both not wise and funny is kind and vice versa. If someone is either curious or not curious then alice is either not patient or curious. If someone is either not quiet or not patient then someone is either curious or not brave and vice versa. If paul is wise or creative then lucy is either strong or generous and vice versa. Everyone who is calm is funny or not curious and vice versa. If fred is brave then fred is both rich and curious. Everyone who is either not patient or not kind is either quiet or curious. Everyone who is both not humble and rich is both humble and not quiet and vice versa. Everyone who is quiet or not humble is creative or not strong. Everyone who is not wise is both brave and not brave. Everyone who is both wise and not curious is creative or humble. Someone is not tall or not old. Someone is both tall and quiet. Mary is both not generous and patient. Mary is not funny or wise. Someone is either wise or creative. Alice is not happy or rich. | Lucy is not funny. | neutral | ((?[X]:((~calm(X)|~humble(X))))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((curious(X)&brave(X))<=>(~brave(X)|~tall(X))))&
((?[X]:((calm(X)&~wise(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
(![X]:((~strong(X)<~>~old(X))=>(~rich(X)|~strong(X))))&
(((~generous(fred)<~>~humble(fred)))=>((~rich(john)|rich(john))))&
(![X]:((~wise(X)&funny(X))<=>kind(X)))&
((?[X]:((curious(X)<~>~curious(X))))=>((~patient(alice)<~>curious(alice))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(((wise(paul)|creative(paul)))<=>((strong(lucy)<~>generous(lucy))))&
(![X]:(calm(X)<=>(funny(X)|~curious(X))))&
((brave(fred))=>((rich(fred)&curious(fred))))&
(![X]:((~patient(X)<~>~kind(X))=>(quiet(X)<~>curious(X))))&
(![X]:((~humble(X)&rich(X))<=>(humble(X)&~quiet(X))))&
(![X]:((quiet(X)|~humble(X))=>(creative(X)|~strong(X))))&
(![X]:(~wise(X)=>(brave(X)&~brave(X))))&
(![X]:((wise(X)&~curious(X))=>(creative(X)|humble(X))))&
(?[X]:((~tall(X)|~old(X))))&
(?[X]:((tall(X)&quiet(X))))&
((~generous(mary)&patient(mary)))&
((~funny(mary)|wise(mary)))&
(?[X]:((wise(X)<~>creative(X))))&
((~happy(alice)|rich(alice))) | ~funny(lucy) | [] | null | 0 |
Everyone who is funny is humble or not humble and vice versa.
If mary is funny or wise then mary is not patient.
If john is both not wise and creative then someone is not humble or not quiet and vice versa.
Everyone who is either not kind or creative is both old and humble.
If mary is rich or kind then john is either not kind or not curious and vice versa.
If paul is both not calm and strong then mary is both rich and not tall.
Everyone who is either not kind or not funny is either curious or not calm.
Everyone who is both generous and not patient is both tall and not strong.
Everyone who is kind or calm is not tall or tall and vice versa.
Everyone who is not strong is not tall or quiet and vice versa.
Everyone who is both calm and strong is rich.
Everyone who is brave or not creative is old and vice versa.
If susan is kind then someone is tall.
If alice is patient or not funny then someone is not old and vice versa.
Everyone who is not funny or not curious is not generous.
Everyone who is not old or rich is both not brave and not tall and vice versa.
Lucy is patient.
Someone is both brave and calm.
Paul is not quiet.
Paul is either not calm or rich.
Alice is either not humble or not generous.
Someone is quiet.
Someone is either not brave or not happy.
Someone is humble or wise. | Alice is patient. | neutral | (![X]:(funny(X)<=>(humble(X)|~humble(X))))&
(((funny(mary)|wise(mary)))=>(~patient(mary)))&
(((~wise(john)&creative(john)))<=>(?[X]:((~humble(X)|~quiet(X)))))&
(![X]:((~kind(X)<~>creative(X))=>(old(X)&humble(X))))&
(((rich(mary)|kind(mary)))<=>((~kind(john)<~>~curious(john))))&
(((~calm(paul)&strong(paul)))=>((rich(mary)&~tall(mary))))&
(![X]:((~kind(X)<~>~funny(X))=>(curious(X)<~>~calm(X))))&
(![X]:((generous(X)&~patient(X))=>(tall(X)&~strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~tall(X)|tall(X))))&
(![X]:(~strong(X)<=>(~tall(X)|quiet(X))))&
(![X]:((calm(X)&strong(X))=>rich(X)))&
(![X]:((brave(X)|~creative(X))<=>old(X)))&
((kind(susan))=>(?[X]:(tall(X))))&
(((patient(alice)|~funny(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~funny(X)|~curious(X))=>~generous(X)))&
(![X]:((~old(X)|rich(X))<=>(~brave(X)&~tall(X))))&
(patient(lucy))&
(?[X]:((brave(X)&calm(X))))&
(~quiet(paul))&
((~calm(paul)<~>rich(paul)))&
((~humble(alice)<~>~generous(alice)))&
(?[X]:(quiet(X)))&
(?[X]:((~brave(X)<~>~happy(X))))&
(?[X]:((humble(X)|wise(X)))) | patient(alice) | [] | null | 0 |
If fred is not calm then someone is funny or not strong and vice versa.
Everyone who is both rich and wise is not humble and vice versa.
Everyone who is curious is both patient and creative and vice versa.
If john is tall or not curious then someone is both not patient and quiet.
If someone is either not patient or calm then alice is either not funny or not happy and vice versa.
Everyone who is rich or humble is old and vice versa.
Everyone who is either not old or calm is both not brave and not tall.
If someone is either happy or calm then someone is either not generous or tall and vice versa.
If lucy is not happy then someone is either kind or curious.
Everyone who is wise or generous is both not happy and creative.
Everyone who is rich or not patient is wise.
Everyone who is happy or not humble is not patient and vice versa.
Everyone who is either not rich or funny is quiet.
If mary is not curious then someone is kind or curious and vice versa.
If someone is strong then someone is either patient or not kind and vice versa.
Everyone who is tall is patient or quiet.
Someone is either patient or not patient.
Someone is not funny.
Someone is generous or not curious.
Someone is either not curious or patient.
John is either not tall or creative.
Someone is not strong or not curious. | Lucy is not old. | contradiction | ((~calm(fred))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((rich(X)&wise(X))<=>~humble(X)))&
(![X]:(curious(X)<=>(patient(X)&creative(X))))&
(((tall(john)|~curious(john)))=>(?[X]:((~patient(X)&quiet(X)))))&
((?[X]:((~patient(X)<~>calm(X))))<=>((~funny(alice)<~>~happy(alice))))&
(![X]:((rich(X)|humble(X))<=>old(X)))&
(![X]:((~old(X)<~>calm(X))=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((~happy(lucy))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)&creative(X))))&
(![X]:((rich(X)|~patient(X))=>wise(X)))&
(![X]:((happy(X)|~humble(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>funny(X))=>quiet(X)))&
((~curious(mary))<=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~kind(X)))))&
(![X]:(tall(X)=>(patient(X)|quiet(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((~tall(john)<~>creative(john)))&
(?[X]:((~strong(X)|~curious(X)))) | ~old(lucy) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8385760941774896364433854
% SZS output start Proof for 8385760941774896364433854
2. ! [X0] : ((wise(X0) & rich(X0)) <=> ~humble(X0)) [input p1]
6. ! [X0] : ((humble(X0) | rich(X0)) <=> old(X0)) [input p5]
23. ~old(lucy) [input hypothesis]
39. ! [X0] : (((wise(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | (~wise(X0) | ~rich(X0)))) [nnf transformation 2]
40. ! [X0] : (((wise(X0) & rich(X0)) | humble(X0)) & (~humble(X0) | ~wise(X0) | ~rich(X0))) [flattening 39]
49. ! [X0] : (((humble(X0) | rich(X0)) | ~old(X0)) & (old(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 6]
50. ! [X0] : ((humble(X0) | rich(X0) | ~old(X0)) & (old(X0) | (~humble(X0) & ~rich(X0)))) [flattening 49]
88. humble(X0) | rich(X0) [cnf transformation 40]
103. ~rich(X0) | old(X0) [cnf transformation 50]
104. ~humble(X0) | old(X0) [cnf transformation 50]
143. ~old(lucy) [cnf transformation 23]
343. old(X1) | rich(X1) [resolution 104,88]
344. old(X1) [subsumption resolution 343,103]
348. $false [resolution 344,143]
% SZS output end Proof for 8385760941774896364433854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or tall then someone is old or calm and vice versa. Everyone who is either not tall or happy is both happy and not patient and vice versa. Everyone who is not generous is not happy. Everyone who is either creative or not calm is both not happy and happy. Everyone who is both quiet and calm is funny or not calm and vice versa. If someone is wise then someone is either creative or kind. If someone is not humble then someone is happy or funny. If mary is both kind and quiet then someone is either not patient or strong. Everyone who is both quiet and strong is either not creative or not happy. Everyone who is generous is not generous or patient and vice versa. Everyone who is strong is not generous. If someone is either humble or calm then paul is both not curious and old and vice versa. Everyone who is not strong or calm is not curious or not generous. Everyone who is not rich is both not curious and strong and vice versa. If paul is either old or not calm then someone is either not patient or strong. If lucy is both curious and not calm then fred is wise or not wise. Fred is funny or quiet. Someone is either not kind or creative. Someone is either kind or not wise. Mary is both not kind and humble. Fred is not quiet or not old. Lucy is either not wise or old. | Mary is not calm. | contradiction | ((?[X]:((~old(X)<~>tall(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&~patient(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:((creative(X)<~>~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((quiet(X)&calm(X))<=>(funny(X)|~calm(X))))&
((?[X]:(wise(X)))=>(?[X]:((creative(X)<~>kind(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((happy(X)|funny(X)))))&
(((kind(mary)&quiet(mary)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((quiet(X)&strong(X))=>(~creative(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(~generous(X)|patient(X))))&
(![X]:(strong(X)=>~generous(X)))&
((?[X]:((humble(X)<~>calm(X))))<=>((~curious(paul)&old(paul))))&
(![X]:((~strong(X)|calm(X))=>(~curious(X)|~generous(X))))&
(![X]:(~rich(X)<=>(~curious(X)&strong(X))))&
(((old(paul)<~>~calm(paul)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((curious(lucy)&~calm(lucy)))=>((wise(fred)|~wise(fred))))&
((funny(fred)|quiet(fred)))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
((~kind(mary)&humble(mary)))&
((~quiet(fred)|~old(fred)))&
((~wise(lucy)<~>old(lucy))) | ~calm(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 480044837887349151966689
% SZS output start Proof for 480044837887349151966689
5. ! [X0] : ((calm(X0) & quiet(X0)) <=> (~calm(X0) | funny(X0))) [input p4]
23. ~calm(mary) [input hypothesis]
49. ! [X0] : (((calm(X0) & quiet(X0)) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 5]
50. ! [X0] : (((calm(X0) & quiet(X0)) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~calm(X0) | ~quiet(X0))) [flattening 49]
100. calm(X0) | calm(X0) [cnf transformation 50]
135. ~calm(mary) [cnf transformation 23]
139. calm(X0) [duplicate literal removal 100]
289. $false [subsumption resolution 135,139]
% SZS output end Proof for 480044837887349151966689
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich is both not curious and not tall and vice versa. Everyone who is both quiet and not kind is not strong or brave and vice versa. Everyone who is both not curious and tall is not generous or curious and vice versa. Everyone who is both not brave and calm is both calm and not calm. Everyone who is both calm and not strong is both happy and creative. If someone is both not creative and funny then fred is either not strong or kind and vice versa. Everyone who is quiet is brave. If paul is both creative and not tall then someone is not brave. Everyone who is creative or brave is not brave and vice versa. Everyone who is not tall or wise is either tall or not strong and vice versa. Everyone who is both not quiet and not happy is both calm and not brave and vice versa. If someone is not creative then paul is not brave or not wise. Everyone who is both funny and not brave is patient or not rich and vice versa. If someone is either strong or funny then someone is either patient or not old and vice versa. Everyone who is both not curious and tall is curious or funny. Someone is creative or not tall. Fred is happy. Someone is both creative and patient. | Fred is funny. | entailment | (![X]:(~rich(X)<=>(~curious(X)&~tall(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~strong(X)|brave(X))))&
(![X]:((~curious(X)&tall(X))<=>(~generous(X)|curious(X))))&
(![X]:((~brave(X)&calm(X))=>(calm(X)&~calm(X))))&
(![X]:((calm(X)&~strong(X))=>(happy(X)&creative(X))))&
((?[X]:((~creative(X)&funny(X))))<=>((~strong(fred)<~>kind(fred))))&
(![X]:(quiet(X)=>brave(X)))&
(((creative(paul)&~tall(paul)))=>(?[X]:(~brave(X))))&
(![X]:((creative(X)|brave(X))<=>~brave(X)))&
(![X]:((~tall(X)|wise(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(calm(X)&~brave(X))))&
((?[X]:(~creative(X)))=>((~brave(paul)|~wise(paul))))&
(![X]:((funny(X)&~brave(X))<=>(patient(X)|~rich(X))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>~old(X)))))&
(![X]:((~curious(X)&tall(X))=>(curious(X)|funny(X))))&
(?[X]:((creative(X)|~tall(X))))&
(happy(fred))&
(?[X]:((creative(X)&patient(X)))) | funny(fred) | [
"p1",
"p2",
"p6",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1307751682297307990205609
% SZS output start Proof for 1307751682297307990205609
2. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (brave(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (curious(X0) | ~generous(X0))) [input p2]
7. ! [X0] : (quiet(X0) => brave(X0)) [input p6]
9. ! [X0] : ((brave(X0) | creative(X0)) <=> ~brave(X0)) [input p8]
10. ! [X0] : ((wise(X0) | ~tall(X0)) <=> (tall(X0) <~> ~strong(X0))) [input p9]
15. ! [X0] : ((tall(X0) & ~curious(X0)) => (funny(X0) | curious(X0))) [input p14]
19. ~funny(fred) [input hypothesis]
25. ! [X0] : (brave(X0) | ~quiet(X0)) [ennf transformation 7]
30. ! [X0] : ((funny(X0) | curious(X0)) | (~tall(X0) | curious(X0))) [ennf transformation 15]
31. ! [X0] : (funny(X0) | curious(X0) | ~tall(X0) | curious(X0)) [flattening 30]
34. ! [X0] : (((~kind(X0) & quiet(X0)) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | (kind(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((~kind(X0) & quiet(X0)) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | kind(X0) | ~quiet(X0))) [flattening 34]
36. ! [X0] : (((tall(X0) & ~curious(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 3]
37. ! [X0] : (((tall(X0) & ~curious(X0)) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | ~tall(X0) | curious(X0))) [flattening 36]
44. ! [X0] : (((brave(X0) | creative(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~creative(X0)))) [nnf transformation 9]
45. ! [X0] : ((brave(X0) | creative(X0) | brave(X0)) & (~brave(X0) | (~brave(X0) & ~creative(X0)))) [flattening 44]
46. ! [X0] : (((wise(X0) | ~tall(X0)) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) & (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | (~wise(X0) & tall(X0)))) [nnf transformation 10]
47. ! [X0] : ((wise(X0) | ~tall(X0) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) & (((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | (~wise(X0) & tall(X0)))) [flattening 46]
65. strong(X0) | quiet(X0) [cnf transformation 35]
71. ~curious(X0) | ~curious(X0) [cnf transformation 37]
84. ~quiet(X0) | brave(X0) [cnf transformation 25]
87. ~brave(X0) | ~brave(X0) [cnf transformation 45]
89. ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 47]
113. funny(X0) | curious(X0) | ~tall(X0) | curious(X0) [cnf transformation 31]
118. ~funny(fred) [cnf transformation 19]
119. funny(X0) | curious(X0) | ~tall(X0) [duplicate literal removal 113]
120. ~strong(X0) | tall(X0) [duplicate literal removal 89]
122. ~brave(X0) [duplicate literal removal 87]
126. ~curious(X0) [duplicate literal removal 71]
140. 3 <=> strong(fred) [avatar definition]
141. ~strong(fred) <- (~3) [avatar component clause 140]
142. strong(fred) <- (3) [avatar component clause 140]
206. ~tall(X0) | funny(X0) [subsumption resolution 119,126]
216. quiet(fred) <- (~3) [resolution 65,141]
217. brave(fred) <- (~3) [resolution 84,216]
218. $false <- (~3) [subsumption resolution 217,122]
219. 3 [avatar contradiction clause 218]
225. tall(fred) <- (3) [resolution 120,142]
236. funny(fred) <- (3) [resolution 206,225]
239. $false <- (3) [subsumption resolution 236,118]
240. ~3 [avatar contradiction clause 239]
241. $false [avatar sat refutation 219,240]
% SZS output end Proof for 1307751682297307990205609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not old is quiet or not humble.
Everyone who is humble is happy.
If susan is patient then alice is both quiet and curious and vice versa.
If fred is brave then paul is both not old and not rich and vice versa.
If someone is happy then fred is not calm or not wise.
If someone is not humble or not curious then john is not quiet or not happy and vice versa.
If paul is wise then mary is happy and vice versa.
If alice is both not rich and not brave then someone is tall or calm and vice versa.
Everyone who is wise is either not funny or calm.
Everyone who is either humble or happy is both not creative and patient and vice versa.
If someone is both not curious and creative then someone is not happy or funny.
Everyone who is not creative is funny or not humble and vice versa.
If someone is happy or brave then someone is both not generous and funny.
If susan is either creative or not humble then paul is not patient and vice versa.
Everyone who is either wise or patient is either not generous or not humble.
If susan is generous then susan is happy and vice versa.
Susan is both kind and not humble.
Fred is either not funny or creative.
Susan is not strong.
Susan is not brave.
Paul is humble.
Someone is either not tall or not rich.
Someone is not creative or creative.
Someone is either wise or not humble. | Fred is not creative. | entailment | (![X]:((~generous(X)|~old(X))=>(quiet(X)|~humble(X))))&
(![X]:(humble(X)=>happy(X)))&
((patient(susan))<=>((quiet(alice)&curious(alice))))&
((brave(fred))<=>((~old(paul)&~rich(paul))))&
((?[X]:(happy(X)))=>((~calm(fred)|~wise(fred))))&
((?[X]:((~humble(X)|~curious(X))))<=>((~quiet(john)|~happy(john))))&
((wise(paul))<=>(happy(mary)))&
(((~rich(alice)&~brave(alice)))<=>(?[X]:((tall(X)|calm(X)))))&
(![X]:(wise(X)=>(~funny(X)<~>calm(X))))&
(![X]:((humble(X)<~>happy(X))<=>(~creative(X)&patient(X))))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((kind(susan)&~humble(susan)))&
((~funny(fred)<~>creative(fred)))&
(~strong(susan))&
(~brave(susan))&
(humble(paul))&
(?[X]:((~tall(X)<~>~rich(X))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((wise(X)<~>~humble(X)))) | ~creative(fred) | [
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1466151936080287463541193
% SZS output start Proof for 1466151936080287463541193
12. ! [X0] : (~creative(X0) <=> (~humble(X0) | funny(X0))) [input p11]
18. ~funny(fred) <~> creative(fred) [input p17]
25. creative(fred) [input hypothesis]
60. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | creative(X0))) [nnf transformation 12]
61. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | creative(X0))) [flattening 60]
68. (~creative(fred) | funny(fred)) & (creative(fred) | ~funny(fred)) [nnf transformation 18]
108. ~creative(X0) | ~funny(X0) [cnf transformation 61]
126. ~creative(fred) | funny(fred) [cnf transformation 68]
134. creative(fred) [cnf transformation 25]
297. ~creative(fred) [subsumption resolution 126,108]
319. $false [subsumption resolution 134,297]
% SZS output end Proof for 1466151936080287463541193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not calm is either not funny or humble.
If someone is either not funny or not quiet then someone is either tall or brave and vice versa.
Everyone who is humble is not old or not tall.
Everyone who is strong or patient is either humble or not kind and vice versa.
If mary is tall then someone is funny.
Everyone who is either humble or curious is both not old and not brave and vice versa.
Everyone who is not tall or old is kind or strong and vice versa.
Everyone who is both not tall and not wise is patient or not rich and vice versa.
Everyone who is both curious and not calm is both not brave and brave and vice versa.
If someone is either not generous or not wise then someone is either tall or brave and vice versa.
Everyone who is curious is both not strong and not funny.
If fred is not strong or happy then john is happy or not kind and vice versa.
Everyone who is funny or generous is curious or rich.
If someone is wise then mary is both kind and strong.
If fred is either not patient or happy then alice is either brave or quiet.
Everyone who is curious is funny.
Someone is old or not rich.
Mary is not humble.
Someone is either brave or patient.
Someone is tall.
Mary is not wise or strong.
Someone is either humble or brave. | Alice is old. | neutral | (![X]:((curious(X)&~calm(X))=>(~funny(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>~quiet(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(humble(X)=>(~old(X)|~tall(X))))&
(![X]:((strong(X)|patient(X))<=>(humble(X)<~>~kind(X))))&
((tall(mary))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((~tall(X)|old(X))<=>(kind(X)|strong(X))))&
(![X]:((~tall(X)&~wise(X))<=>(patient(X)|~rich(X))))&
(![X]:((curious(X)&~calm(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(curious(X)=>(~strong(X)&~funny(X))))&
(((~strong(fred)|happy(fred)))<=>((happy(john)|~kind(john))))&
(![X]:((funny(X)|generous(X))=>(curious(X)|rich(X))))&
((?[X]:(wise(X)))=>((kind(mary)&strong(mary))))&
(((~patient(fred)<~>happy(fred)))=>((brave(alice)<~>quiet(alice))))&
(![X]:(curious(X)=>funny(X)))&
(?[X]:((old(X)|~rich(X))))&
(~humble(mary))&
(?[X]:((brave(X)<~>patient(X))))&
(?[X]:(tall(X)))&
((~wise(mary)|strong(mary)))&
(?[X]:((humble(X)<~>brave(X)))) | old(alice) | [] | null | 0 |
If lucy is both generous and patient then fred is creative.
If someone is happy then paul is not generous and vice versa.
Everyone who is brave or not strong is both generous and not humble and vice versa.
If john is not calm or happy then someone is either not kind or not generous and vice versa.
Everyone who is not wise or not brave is not old and vice versa.
Everyone who is both strong and humble is both not brave and wise.
If fred is either not humble or happy then paul is either creative or not generous.
Everyone who is tall is both generous and calm.
Everyone who is tall or curious is not generous or calm and vice versa.
Everyone who is not wise or creative is either not quiet or generous and vice versa.
Everyone who is kind is either not patient or not quiet and vice versa.
If mary is either not tall or not strong then mary is either generous or not rich.
Everyone who is not rich is rich or old.
If mary is not kind or wise then alice is creative.
If someone is not old then mary is either rich or not rich and vice versa.
If someone is not humble then john is either not brave or not generous and vice versa.
Someone is tall.
Susan is not creative or not tall.
Someone is creative or not strong.
Someone is both quiet and not generous.
Someone is patient or old.
Someone is either not creative or old.
John is not tall.
Paul is not tall. | Paul is not curious. | neutral | (((generous(lucy)&patient(lucy)))=>(creative(fred)))&
((?[X]:(happy(X)))<=>(~generous(paul)))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~humble(X))))&
(((~calm(john)|happy(john)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(![X]:((~wise(X)|~brave(X))<=>~old(X)))&
(![X]:((strong(X)&humble(X))=>(~brave(X)&wise(X))))&
(((~humble(fred)<~>happy(fred)))=>((creative(paul)<~>~generous(paul))))&
(![X]:(tall(X)=>(generous(X)&calm(X))))&
(![X]:((tall(X)|curious(X))<=>(~generous(X)|calm(X))))&
(![X]:((~wise(X)|creative(X))<=>(~quiet(X)<~>generous(X))))&
(![X]:(kind(X)<=>(~patient(X)<~>~quiet(X))))&
(((~tall(mary)<~>~strong(mary)))=>((generous(mary)<~>~rich(mary))))&
(![X]:(~rich(X)=>(rich(X)|old(X))))&
(((~kind(mary)|wise(mary)))=>(creative(alice)))&
((?[X]:(~old(X)))<=>((rich(mary)<~>~rich(mary))))&
((?[X]:(~humble(X)))<=>((~brave(john)<~>~generous(john))))&
(?[X]:(tall(X)))&
((~creative(susan)|~tall(susan)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~creative(X)<~>old(X))))&
(~tall(john))&
(~tall(paul)) | ~curious(paul) | [] | null | 0 |
If someone is not kind then mary is kind or old and vice versa.
Everyone who is not old is both patient and not tall.
Everyone who is not happy is both wise and not funny.
Everyone who is brave is wise or patient and vice versa.
If someone is either humble or funny then someone is patient or not brave.
If susan is brave or not rich then someone is not brave or not kind.
Everyone who is not strong or funny is not wise or happy and vice versa.
Everyone who is either not patient or not quiet is either quiet or happy and vice versa.
If susan is either not generous or not humble then someone is not wise and vice versa.
If someone is both patient and not tall then someone is not strong and vice versa.
If someone is either not tall or curious then someone is not old or strong and vice versa.
If paul is brave or generous then alice is either not curious or not humble.
Everyone who is both brave and strong is either funny or not creative and vice versa.
Everyone who is creative or not quiet is both old and not creative and vice versa.
If someone is not curious then someone is generous and vice versa.
Someone is both brave and not patient.
Lucy is either not humble or kind.
Someone is not brave or generous.
Someone is not kind.
Someone is not generous.
Alice is not creative. | Susan is brave. | entailment | ((?[X]:(~kind(X)))<=>((kind(mary)|old(mary))))&
(![X]:(~old(X)=>(patient(X)&~tall(X))))&
(![X]:(~happy(X)=>(wise(X)&~funny(X))))&
(![X]:(brave(X)<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)<~>funny(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((brave(susan)|~rich(susan)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)|funny(X))<=>(~wise(X)|happy(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(quiet(X)<~>happy(X))))&
(((~generous(susan)<~>~humble(susan)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)&~tall(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((~old(X)|strong(X)))))&
(((brave(paul)|generous(paul)))=>((~curious(alice)<~>~humble(alice))))&
(![X]:((brave(X)&strong(X))<=>(funny(X)<~>~creative(X))))&
(![X]:((creative(X)|~quiet(X))<=>(old(X)&~creative(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(generous(X))))&
(?[X]:((brave(X)&~patient(X))))&
((~humble(lucy)<~>kind(lucy)))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~generous(X)))&
(~creative(alice)) | brave(susan) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8951839792146294681584733
% SZS output start Proof for 8951839792146294681584733
3. ! [X0] : (~happy(X0) => (~funny(X0) & wise(X0))) [input p2]
4. ! [X0] : (brave(X0) <=> (patient(X0) | wise(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (quiet(X0) <~> happy(X0))) [input p7]
22. ~brave(susan) [input hypothesis]
29. ! [X0] : ((~funny(X0) & wise(X0)) | happy(X0)) [ennf transformation 3]
38. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ~brave(X0))) [nnf transformation 4]
39. ! [X0] : ((brave(X0) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~brave(X0))) [flattening 38]
48. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 8]
87. wise(X0) | happy(X0) [cnf transformation 29]
90. ~wise(X0) | brave(X0) [cnf transformation 39]
91. ~patient(X0) | brave(X0) [cnf transformation 39]
101. ~happy(X0) | ~quiet(X0) | ~quiet(X0) | patient(X0) [cnf transformation 48]
106. quiet(X0) | patient(X0) | quiet(X0) | ~happy(X0) [cnf transformation 48]
145. ~brave(susan) [cnf transformation 22]
149. ~happy(X0) | ~quiet(X0) | patient(X0) [duplicate literal removal 101]
151. ~happy(X0) | patient(X0) | quiet(X0) [duplicate literal removal 106]
187. 9 <=> brave(susan) [avatar definition]
189. ~brave(susan) <- (~9) [avatar component clause 187]
200. ~happy(X0) | patient(X0) [subsumption resolution 149,151]
331. ~9 [avatar split clause 145,187]
347. brave(X0) | happy(X0) [resolution 90,87]
373. happy(susan) <- (~9) [resolution 347,189]
378. patient(susan) <- (~9) [resolution 373,200]
410. brave(susan) <- (~9) [resolution 378,91]
411. $false <- (~9) [subsumption resolution 410,189]
412. 9 [avatar contradiction clause 411]
413. $false [avatar sat refutation 331,412]
% SZS output end Proof for 8951839792146294681584733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich then john is kind or not strong and vice versa. Everyone who is both rich and not generous is either kind or curious and vice versa. Everyone who is not calm is not creative or strong and vice versa. Everyone who is both not old and not patient is not funny and vice versa. Everyone who is both not brave and not curious is both curious and funny and vice versa. If john is not rich or not generous then someone is either not wise or not tall and vice versa. Everyone who is not rich or not creative is both not patient and not tall and vice versa. If john is both not patient and strong then paul is either kind or not brave. If someone is quiet or not funny then someone is creative and vice versa. If lucy is both not rich and generous then paul is both happy and not tall. If lucy is either not curious or brave then john is either not generous or not funny and vice versa. Everyone who is either not patient or generous is old or brave. If someone is wise then someone is both not happy and brave and vice versa. Everyone who is old is either not tall or generous. If fred is not tall then mary is creative or not quiet and vice versa. Everyone who is not brave is either not generous or strong. John is both not creative and not wise. Someone is both not kind and not strong. Alice is not old. Fred is not rich. Susan is not old. Susan is both humble and not patient. Paul is either curious or kind. Mary is either not curious or not rich. | Paul is not brave. | contradiction | ((?[X]:((~generous(X)|~rich(X))))<=>((kind(john)|~strong(john))))&
(![X]:((rich(X)&~generous(X))<=>(kind(X)<~>curious(X))))&
(![X]:(~calm(X)<=>(~creative(X)|strong(X))))&
(![X]:((~old(X)&~patient(X))<=>~funny(X)))&
(![X]:((~brave(X)&~curious(X))<=>(curious(X)&funny(X))))&
(((~rich(john)|~generous(john)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(~patient(X)&~tall(X))))&
(((~patient(john)&strong(john)))=>((kind(paul)<~>~brave(paul))))&
((?[X]:((quiet(X)|~funny(X))))<=>(?[X]:(creative(X))))&
(((~rich(lucy)&generous(lucy)))=>((happy(paul)&~tall(paul))))&
(((~curious(lucy)<~>brave(lucy)))<=>((~generous(john)<~>~funny(john))))&
(![X]:((~patient(X)<~>generous(X))=>(old(X)|brave(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)&brave(X)))))&
(![X]:(old(X)=>(~tall(X)<~>generous(X))))&
((~tall(fred))<=>((creative(mary)|~quiet(mary))))&
(![X]:(~brave(X)=>(~generous(X)<~>strong(X))))&
((~creative(john)&~wise(john)))&
(?[X]:((~kind(X)&~strong(X))))&
(~old(alice))&
(~rich(fred))&
(~old(susan))&
((humble(susan)&~patient(susan)))&
((curious(paul)<~>kind(paul)))&
((~curious(mary)<~>~rich(mary))) | ~brave(paul) | [
"p1",
"p3",
"p4",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1368698450539371559662294
% SZS output start Proof for 1368698450539371559662294
2. ! [X0] : ((~generous(X0) & rich(X0)) <=> (kind(X0) <~> curious(X0))) [input p1]
4. ! [X0] : ((~patient(X0) & ~old(X0)) <=> ~funny(X0)) [input p3]
5. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> (funny(X0) & curious(X0))) [input p4]
12. ! [X0] : ((~patient(X0) <~> generous(X0)) => (brave(X0) | old(X0))) [input p11]
23. curious(paul) <~> kind(paul) [input p22]
25. ~brave(paul) [input hypothesis]
33. ! [X0] : ((brave(X0) | old(X0)) | (~patient(X0) <=> generous(X0))) [ennf transformation 12]
34. ! [X0] : (brave(X0) | old(X0) | (~patient(X0) <=> generous(X0))) [flattening 33]
42. ! [X0] : (((~generous(X0) & rich(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) & (((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | (generous(X0) | ~rich(X0)))) [nnf transformation 2]
43. ! [X0] : (((~generous(X0) & rich(X0)) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0)))) & (((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | generous(X0) | ~rich(X0))) [flattening 42]
44. ! [X0] : (((~patient(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) | old(X0)))) [nnf transformation 4]
45. ! [X0] : (((~patient(X0) & ~old(X0)) | funny(X0)) & (~funny(X0) | patient(X0) | old(X0))) [flattening 44]
46. ! [X0] : (((~curious(X0) & ~brave(X0)) | (~funny(X0) | ~curious(X0))) & ((funny(X0) & curious(X0)) | (curious(X0) | brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((~curious(X0) & ~brave(X0)) | ~funny(X0) | ~curious(X0)) & ((funny(X0) & curious(X0)) | curious(X0) | brave(X0))) [flattening 46]
62. ! [X0] : (brave(X0) | old(X0) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0)))) [nnf transformation 34]
74. (~kind(paul) | ~curious(paul)) & (kind(paul) | curious(paul)) [nnf transformation 23]
85. ~curious(X0) | kind(X0) | ~generous(X0) [cnf transformation 43]
87. ~old(X0) | funny(X0) [cnf transformation 45]
88. ~patient(X0) | funny(X0) [cnf transformation 45]
89. curious(X0) | curious(X0) | brave(X0) [cnf transformation 47]
92. ~curious(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 47]
119. brave(X0) | old(X0) | generous(X0) | patient(X0) [cnf transformation 62]
140. ~kind(paul) | ~curious(paul) [cnf transformation 74]
143. ~brave(paul) [cnf transformation 25]
144. brave(X0) | curious(X0) [duplicate literal removal 89]
145. ~funny(X0) | ~curious(X0) [duplicate literal removal 92]
205. 14 <=> kind(paul) [avatar definition]
207. ~kind(paul) <- (~14) [avatar component clause 205]
209. 15 <=> brave(paul) [avatar definition]
210. ~brave(paul) <- (~15) [avatar component clause 209]
315. 37 <=> curious(paul) [avatar definition]
316. curious(paul) <- (37) [avatar component clause 315]
318. ~37 | ~14 [avatar split clause 140,205,315]
330. ~15 [avatar split clause 143,209]
335. curious(paul) <- (~15) [resolution 144,210]
338. 37 | 15 [avatar split clause 335,209,315]
347. kind(paul) | ~generous(paul) <- (37) [resolution 85,316]
348. ~generous(paul) <- (~14, 37) [subsumption resolution 347,207]
415. old(paul) | generous(paul) | patient(paul) <- (~15) [resolution 119,210]
417. old(paul) | patient(paul) <- (~14, ~15, 37) [subsumption resolution 415,348]
419. 48 <=> patient(paul) [avatar definition]
421. patient(paul) <- (48) [avatar component clause 419]
423. 49 <=> old(paul) [avatar definition]
425. old(paul) <- (49) [avatar component clause 423]
426. 48 | 49 | 14 | 15 | ~37 [avatar split clause 417,315,209,205,423,419]
430. funny(paul) <- (48) [resolution 421,88]
433. ~curious(paul) <- (48) [resolution 430,145]
434. $false <- (37, 48) [subsumption resolution 433,316]
435. ~37 | ~48 [avatar contradiction clause 434]
437. funny(paul) <- (49) [resolution 425,87]
439. ~curious(paul) <- (49) [resolution 437,145]
440. $false <- (37, 49) [subsumption resolution 439,316]
441. ~37 | ~49 [avatar contradiction clause 440]
442. $false [avatar sat refutation 318,330,338,426,435,441]
% SZS output end Proof for 1368698450539371559662294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not brave is happy and vice versa.
If paul is both not curious and strong then someone is both not humble and happy.
If paul is both calm and not old then someone is curious and vice versa.
Everyone who is not wise is not quiet.
If someone is quiet or not strong then someone is both not quiet and not calm and vice versa.
If paul is humble or not kind then someone is either funny or old and vice versa.
If someone is not calm then susan is not curious and vice versa.
Everyone who is both not wise and not happy is both not curious and curious and vice versa.
Everyone who is not patient is kind and vice versa.
If mary is kind or not quiet then someone is both creative and humble.
Everyone who is both rich and brave is both funny and not curious and vice versa.
Everyone who is either curious or not curious is both not generous and not happy and vice versa.
If lucy is generous or not rich then paul is either not humble or strong.
If lucy is both funny and not rich then mary is either kind or curious and vice versa.
If someone is both wise and not calm then someone is wise or curious and vice versa.
If lucy is either not happy or not rich then someone is both not wise and not generous.
Someone is kind.
Someone is both humble and creative.
Someone is not strong or not kind.
Someone is creative or not calm.
Someone is both quiet and calm.
Someone is old.
Mary is both not generous and not tall.
Mary is not quiet. | Paul is not rich. | entailment | (![X]:((~strong(X)|~brave(X))<=>happy(X)))&
(((~curious(paul)&strong(paul)))=>(?[X]:((~humble(X)&happy(X)))))&
(((calm(paul)&~old(paul)))<=>(?[X]:(curious(X))))&
(![X]:(~wise(X)=>~quiet(X)))&
((?[X]:((quiet(X)|~strong(X))))<=>(?[X]:((~quiet(X)&~calm(X)))))&
(((humble(paul)|~kind(paul)))<=>(?[X]:((funny(X)<~>old(X)))))&
((?[X]:(~calm(X)))<=>(~curious(susan)))&
(![X]:((~wise(X)&~happy(X))<=>(~curious(X)&curious(X))))&
(![X]:(~patient(X)<=>kind(X)))&
(((kind(mary)|~quiet(mary)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((rich(X)&brave(X))<=>(funny(X)&~curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~generous(X)&~happy(X))))&
(((generous(lucy)|~rich(lucy)))=>((~humble(paul)<~>strong(paul))))&
(((funny(lucy)&~rich(lucy)))<=>((kind(mary)<~>curious(mary))))&
((?[X]:((wise(X)&~calm(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(((~happy(lucy)<~>~rich(lucy)))=>(?[X]:((~wise(X)&~generous(X)))))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((~strong(X)|~kind(X))))&
(?[X]:((creative(X)|~calm(X))))&
(?[X]:((quiet(X)&calm(X))))&
(?[X]:(old(X)))&
((~generous(mary)&~tall(mary)))&
(~quiet(mary)) | ~rich(paul) | [
"p0",
"p1",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2680216162401406694841254
% SZS output start Proof for 2680216162401406694841254
1. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> happy(X0)) [input p0]
2. (strong(paul) & ~curious(paul)) => ? [X0] : (happy(X0) & ~humble(X0)) [input p1]
11. ! [X0] : ((brave(X0) & rich(X0)) <=> (~curious(X0) & funny(X0))) [input p10]
12. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~happy(X0) & ~generous(X0))) [input p11]
25. rich(paul) [input hypothesis]
32. ? [X0] : (happy(X0) & ~humble(X0)) | (~strong(paul) | curious(paul)) [ennf transformation 2]
33. ? [X0] : (happy(X0) & ~humble(X0)) | ~strong(paul) | curious(paul) [flattening 32]
38. ! [X0] : (((~brave(X0) | ~strong(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((~brave(X0) | ~strong(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & strong(X0)))) [flattening 38]
40. ? [X0] : (happy(X0) & ~humble(X0)) => (happy(sK0) & ~humble(sK0)) [choice axiom]
41. (happy(sK0) & ~humble(sK0)) | ~strong(paul) | curious(paul) [skolemisation 33,40]
65. ! [X0] : (((brave(X0) & rich(X0)) | (curious(X0) | ~funny(X0))) & ((~curious(X0) & funny(X0)) | (~brave(X0) | ~rich(X0)))) [nnf transformation 11]
66. ! [X0] : (((brave(X0) & rich(X0)) | curious(X0) | ~funny(X0)) & ((~curious(X0) & funny(X0)) | ~brave(X0) | ~rich(X0))) [flattening 65]
67. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (happy(X0) | generous(X0))) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 12]
68. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | happy(X0) | generous(X0)) & ((~happy(X0) & ~generous(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 67]
90. happy(X0) | strong(X0) [cnf transformation 39]
91. happy(X0) | brave(X0) [cnf transformation 39]
94. happy(sK0) | ~strong(paul) | curious(paul) [cnf transformation 41]
119. ~rich(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 66]
124. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 68]
125. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 68]
155. rich(paul) [cnf transformation 25]
158. ~happy(X0) | ~curious(X0) [duplicate literal removal 124]
159. ~happy(X0) | curious(X0) [duplicate literal removal 125]
161. 1 <=> curious(paul) [avatar definition]
165. 2 <=> strong(paul) [avatar definition]
167. ~strong(paul) <- (~2) [avatar component clause 165]
169. 3 <=> happy(sK0) [avatar definition]
171. happy(sK0) <- (3) [avatar component clause 169]
172. 1 | ~2 | 3 [avatar split clause 94,169,165,161]
209. 12 <=> ! [X3] : strong(X3) [avatar definition]
210. strong(X3) <- (12) [avatar component clause 209]
282. ~happy(X0) [subsumption resolution 158,159]
347. strong(X0) [resolution 90,282]
348. 12 [avatar split clause 347,209]
349. $false <- (~2, 12) [resolution 210,167]
354. 2 | ~12 [avatar contradiction clause 349]
359. brave(X0) [resolution 91,282]
388. ~brave(paul) | ~curious(paul) [resolution 119,155]
389. ~curious(paul) [subsumption resolution 388,359]
392. ~1 [avatar split clause 389,161]
393. $false <- (3) [subsumption resolution 171,282]
394. ~3 [avatar contradiction clause 393]
395. $false [avatar sat refutation 172,348,354,392,394]
% SZS output end Proof for 2680216162401406694841254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and rich then fred is both not funny and humble and vice versa. Everyone who is not old or not tall is both generous and not brave and vice versa. Everyone who is generous or not funny is not funny and vice versa. If someone is either not rich or not generous then mary is happy and vice versa. Everyone who is funny is either not rich or kind and vice versa. Everyone who is both funny and curious is both wise and not tall and vice versa. Everyone who is calm is not calm or not generous and vice versa. If someone is either not kind or not generous then fred is either not wise or not quiet and vice versa. Everyone who is both rich and not humble is both not creative and not brave. Everyone who is either curious or not tall is old. If john is happy or humble then paul is both happy and rich and vice versa. Everyone who is rich is old or wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. Everyone who is both humble and not wise is either not creative or not strong. Paul is either strong or not rich. Lucy is both not funny and old. Alice is either not humble or not quiet. John is not brave. John is both not strong and happy. Paul is both patient and humble. Someone is either not generous or curious. | Fred is patient. | entailment | ((?[X]:((curious(X)&rich(X))))<=>((~funny(fred)&humble(fred))))&
(![X]:((~old(X)|~tall(X))<=>(generous(X)&~brave(X))))&
(![X]:((generous(X)|~funny(X))<=>~funny(X)))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(happy(mary)))&
(![X]:(funny(X)<=>(~rich(X)<~>kind(X))))&
(![X]:((funny(X)&curious(X))<=>(wise(X)&~tall(X))))&
(![X]:(calm(X)<=>(~calm(X)|~generous(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((rich(X)&~humble(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~tall(X))=>old(X)))&
(((happy(john)|humble(john)))<=>((happy(paul)&rich(paul))))&
(![X]:(rich(X)=>(old(X)|wise(X))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)<~>~strong(X))))&
((strong(paul)<~>~rich(paul)))&
((~funny(lucy)&old(lucy)))&
((~humble(alice)<~>~quiet(alice)))&
(~brave(john))&
((~strong(john)&happy(john)))&
((patient(paul)&humble(paul)))&
(?[X]:((~generous(X)<~>curious(X)))) | patient(fred) | [
"p1",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8317449689450320140886614
% SZS output start Proof for 8317449689450320140886614
2. ! [X0] : ((~tall(X0) | ~old(X0)) <=> (~brave(X0) & generous(X0))) [input p1]
7. ! [X0] : (calm(X0) <=> (~generous(X0) | ~calm(X0))) [input p6]
15. ! [X0] : ((old(X0) | ~calm(X0)) => (patient(X0) <~> ~tall(X0))) [input p14]
24. ~patient(fred) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 15]
38. ! [X0] : (((~tall(X0) | ~old(X0)) | (brave(X0) | ~generous(X0))) & ((~brave(X0) & generous(X0)) | (tall(X0) & old(X0)))) [nnf transformation 2]
39. ! [X0] : ((~tall(X0) | ~old(X0) | brave(X0) | ~generous(X0)) & ((~brave(X0) & generous(X0)) | (tall(X0) & old(X0)))) [flattening 38]
49. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | ~calm(X0))) [nnf transformation 7]
50. ! [X0] : ((calm(X0) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ~calm(X0))) [flattening 49]
64. ! [X0] : (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 30]
75. generous(X0) | old(X0) [cnf transformation 39]
76. generous(X0) | tall(X0) [cnf transformation 39]
95. ~generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 50]
96. calm(X0) | calm(X0) [cnf transformation 50]
125. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 64]
143. ~patient(fred) [cnf transformation 24]
144. ~generous(X0) | ~calm(X0) [duplicate literal removal 95]
145. calm(X0) [duplicate literal removal 96]
191. ~generous(X0) [subsumption resolution 144,145]
277. old(X0) [resolution 75,191]
278. tall(X0) [resolution 76,191]
320. patient(X1) | ~old(X1) [resolution 125,278]
321. patient(X1) [subsumption resolution 320,277]
323. $false [resolution 321,143]
% SZS output end Proof for 8317449689450320140886614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and not brave then someone is both not tall and old.
If someone is not quiet or rich then susan is tall.
If someone is either not old or not creative then mary is either not happy or not quiet.
If susan is both not happy and funny then john is patient and vice versa.
If someone is not curious then someone is not wise.
Everyone who is either strong or not calm is either rich or not wise.
Everyone who is humble or rich is both wise and not quiet and vice versa.
If someone is either humble or generous then susan is not humble.
Everyone who is either not brave or patient is not old.
Everyone who is not creative or generous is not patient or patient and vice versa.
If john is not curious then someone is not creative or not generous.
If lucy is either not generous or not tall then susan is either funny or not humble and vice versa.
If someone is either not wise or tall then susan is not wise.
Everyone who is patient or not wise is both curious and rich.
If someone is both not patient and not wise then susan is both not generous and not kind and vice versa.
Everyone who is not old or not quiet is not generous and vice versa.
Someone is not old or curious.
Alice is funny.
Alice is both generous and old.
Someone is either not calm or not curious.
John is humble or curious.
Someone is not tall. | John is humble. | contradiction | ((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(tall(susan)))&
((?[X]:((~old(X)<~>~creative(X))))=>((~happy(mary)<~>~quiet(mary))))&
(((~happy(susan)&funny(susan)))<=>(patient(john)))&
((?[X]:(~curious(X)))=>(?[X]:(~wise(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>~wise(X))))&
(![X]:((humble(X)|rich(X))<=>(wise(X)&~quiet(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(~humble(susan)))&
(![X]:((~brave(X)<~>patient(X))=>~old(X)))&
(![X]:((~creative(X)|generous(X))<=>(~patient(X)|patient(X))))&
((~curious(john))=>(?[X]:((~creative(X)|~generous(X)))))&
(((~generous(lucy)<~>~tall(lucy)))<=>((funny(susan)<~>~humble(susan))))&
((?[X]:((~wise(X)<~>tall(X))))=>(~wise(susan)))&
(![X]:((patient(X)|~wise(X))=>(curious(X)&rich(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((~generous(susan)&~kind(susan))))&
(![X]:((~old(X)|~quiet(X))<=>~generous(X)))&
(?[X]:((~old(X)|curious(X))))&
(funny(alice))&
((generous(alice)&old(alice)))&
(?[X]:((~calm(X)<~>~curious(X))))&
((humble(john)|curious(john)))&
(?[X]:(~tall(X))) | humble(john) | [
"p1",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 479688112052027296832846
% SZS output start Proof for 479688112052027296832846
2. ? [X0] : (rich(X0) | ~quiet(X0)) => tall(susan) [input p1]
7. ! [X0] : ((rich(X0) | humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p6]
13. ? [X0] : (~wise(X0) <~> tall(X0)) => ~wise(susan) [input p12]
14. ! [X0] : ((~wise(X0) | patient(X0)) => (rich(X0) & curious(X0))) [input p13]
23. humble(john) [input hypothesis]
27. tall(susan) | ! [X0] : (~rich(X0) & quiet(X0)) [ennf transformation 2]
34. ~wise(susan) | ! [X0] : (~wise(X0) <=> tall(X0)) [ennf transformation 13]
35. ! [X0] : ((rich(X0) & curious(X0)) | (wise(X0) & ~patient(X0))) [ennf transformation 14]
46. ! [X0] : (((rich(X0) | humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | humble(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [flattening 46]
55. ~wise(susan) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))) [nnf transformation 34]
72. tall(susan) | quiet(X0) [cnf transformation 27]
87. ~rich(X0) | wise(X0) [cnf transformation 47]
88. ~humble(X0) | ~quiet(X0) [cnf transformation 47]
109. ~wise(susan) | ~wise(X0) | ~tall(X0) [cnf transformation 55]
113. rich(X0) | wise(X0) [cnf transformation 35]
129. humble(john) [cnf transformation 23]
147. 5 <=> tall(susan) [avatar definition]
149. tall(susan) <- (5) [avatar component clause 147]
152. 6 <=> ! [X0] : quiet(X0) [avatar definition]
153. quiet(X0) <- (6) [avatar component clause 152]
154. 6 | 5 [avatar split clause 72,147,152]
236. 23 <=> ! [X0] : (~wise(X0) | ~tall(X0)) [avatar definition]
237. ~wise(X0) | ~tall(X0) <- (23) [avatar component clause 236]
239. 24 <=> wise(susan) [avatar definition]
241. ~wise(susan) <- (~24) [avatar component clause 239]
242. 23 | ~24 [avatar split clause 109,239,236]
247. wise(X0) [subsumption resolution 113,87]
283. 33 <=> humble(john) [avatar definition]
285. humble(john) <- (33) [avatar component clause 283]
287. 33 [avatar split clause 129,283]
288. $false <- (~24) [subsumption resolution 241,247]
289. 24 [avatar contradiction clause 288]
292. ~tall(X0) <- (23) [subsumption resolution 237,247]
295. $false <- (5, 23) [resolution 292,149]
296. ~5 | ~23 [avatar contradiction clause 295]
300. ~quiet(john) <- (33) [resolution 88,285]
301. $false <- (6, 33) [subsumption resolution 300,153]
302. ~6 | ~33 [avatar contradiction clause 301]
303. $false [avatar sat refutation 154,242,287,289,296,302]
% SZS output end Proof for 479688112052027296832846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is tall or not quiet and vice versa.
Everyone who is both not quiet and not kind is happy.
If john is either not calm or tall then fred is both not humble and not patient and vice versa.
If lucy is not rich then someone is not humble.
Everyone who is not brave or strong is not patient or not strong and vice versa.
Everyone who is both not humble and generous is rich and vice versa.
If someone is curious then someone is not creative or not curious and vice versa.
Everyone who is curious or not curious is both not patient and not strong.
If someone is either not happy or tall then someone is not patient or not curious and vice versa.
Everyone who is either not calm or calm is curious or creative and vice versa.
Everyone who is both not rich and not calm is creative or calm.
Everyone who is both not humble and not strong is either not wise or not calm.
Everyone who is either creative or quiet is either not rich or humble and vice versa.
Everyone who is either curious or not funny is curious or not wise and vice versa.
Everyone who is happy is not happy or funny.
Everyone who is rich or not creative is either not tall or curious.
Someone is either not happy or patient.
Someone is both kind and tall.
Someone is both calm and not strong.
Susan is not humble or old.
Someone is not patient.
Someone is not calm or creative.
Mary is either happy or tall.
Fred is wise. | Lucy is not rich. | neutral | (![X]:(funny(X)<=>(tall(X)|~quiet(X))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(((~calm(john)<~>tall(john)))<=>((~humble(fred)&~patient(fred))))&
((~rich(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)|strong(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~humble(X)&generous(X))<=>rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~creative(X)|~curious(X)))))&
(![X]:((curious(X)|~curious(X))=>(~patient(X)&~strong(X))))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~curious(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(curious(X)|creative(X))))&
(![X]:((~rich(X)&~calm(X))=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
(![X]:(happy(X)=>(~happy(X)|funny(X))))&
(![X]:((rich(X)|~creative(X))=>(~tall(X)<~>curious(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((calm(X)&~strong(X))))&
((~humble(susan)|old(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)|creative(X))))&
((happy(mary)<~>tall(mary)))&
(wise(fred)) | ~rich(lucy) | [] | null | 0 |
If someone is both not humble and creative then someone is either curious or creative.
Everyone who is creative is rich or not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
If someone is either creative or wise then john is not tall or tall and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Everyone who is both rich and strong is tall or not tall and vice versa.
Everyone who is not humble is rich.
Someone is not calm or funny.
Mary is not patient or not tall.
Someone is either curious or not tall.
Paul is either not curious or strong.
Someone is both strong and humble.
Susan is either not patient or not happy. | Paul is humble. | entailment | ((?[X]:((~humble(X)&creative(X))))=>(?[X]:((curious(X)<~>creative(X)))))&
(![X]:(creative(X)<=>(rich(X)|~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
((?[X]:((creative(X)<~>wise(X))))<=>((~tall(john)|tall(john))))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
(![X]:(~humble(X)=>rich(X)))&
(?[X]:((~calm(X)|funny(X))))&
((~patient(mary)|~tall(mary)))&
(?[X]:((curious(X)<~>~tall(X))))&
((~curious(paul)<~>strong(paul)))&
(?[X]:((strong(X)&humble(X))))&
((~patient(susan)<~>~happy(susan))) | humble(paul) | [
"p0",
"p1",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4341373655366232752371822
% SZS output start Proof for 4341373655366232752371822
1. ? [X0] : (creative(X0) & ~humble(X0)) => ? [X0] : (curious(X0) <~> creative(X0)) [input p0]
2. ! [X0] : (creative(X0) <=> (~old(X0) | rich(X0))) [input p1]
11. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p10]
15. ! [X0] : ((strong(X0) & rich(X0)) <=> (~tall(X0) | tall(X0))) [input p14]
23. ~humble(paul) [input hypothesis]
24. ? [X0] : (creative(X0) & ~humble(X0)) => ? [X1] : (curious(X1) <~> creative(X1)) [rectify 1]
28. ? [X1] : (curious(X1) <~> creative(X1)) | ! [X0] : (~creative(X0) | humble(X0)) [ennf transformation 24]
34. ? [X1] : ((~creative(X1) | ~curious(X1)) & (creative(X1) | curious(X1))) | ! [X0] : (~creative(X0) | humble(X0)) [nnf transformation 28]
35. ? [X0] : ((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ! [X1] : (~creative(X1) | humble(X1)) [rectify 34]
36. ? [X0] : ((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) => ((~creative(sK0) | ~curious(sK0)) & (creative(sK0) | curious(sK0))) [choice axiom]
37. ((~creative(sK0) | ~curious(sK0)) & (creative(sK0) | curious(sK0))) | ! [X1] : (~creative(X1) | humble(X1)) [skolemisation 35,36]
38. ! [X0] : ((creative(X0) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | ~creative(X0))) [nnf transformation 2]
39. ! [X0] : ((creative(X0) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | ~creative(X0))) [flattening 38]
52. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 11]
53. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 52]
61. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 15]
62. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ~strong(X0) | ~rich(X0))) [flattening 61]
73. ~creative(sK0) | ~curious(sK0) | ~creative(X1) | humble(X1) [cnf transformation 37]
75. ~rich(X0) | creative(X0) [cnf transformation 39]
96. curious(X0) | curious(X0) [cnf transformation 53]
118. rich(X0) | ~tall(X0) [cnf transformation 62]
119. rich(X0) | tall(X0) [cnf transformation 62]
133. ~humble(paul) [cnf transformation 23]
134. curious(X0) [duplicate literal removal 96]
137. 1 <=> ! [X1] : (~creative(X1) | humble(X1)) [avatar definition]
138. ~creative(X1) | humble(X1) <- (1) [avatar component clause 137]
140. 2 <=> curious(sK0) [avatar definition]
142. ~curious(sK0) <- (~2) [avatar component clause 140]
144. 3 <=> creative(sK0) [avatar definition]
146. ~creative(sK0) <- (~3) [avatar component clause 144]
147. 1 | ~2 | ~3 [avatar split clause 73,144,140,137]
231. rich(X0) [subsumption resolution 118,119]
261. $false <- (~2) [subsumption resolution 142,134]
262. 2 [avatar contradiction clause 261]
263. creative(X0) [resolution 75,231]
265. $false <- (~3) [resolution 263,146]
268. 3 [avatar contradiction clause 265]
269. humble(X1) <- (1) [subsumption resolution 138,263]
270. $false <- (1) [resolution 269,133]
271. ~1 [avatar contradiction clause 270]
272. $false [avatar sat refutation 147,262,268,271]
% SZS output end Proof for 4341373655366232752371822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not tall and calm and vice versa.
If alice is not tall or brave then fred is not kind.
Everyone who is both funny and not happy is both not calm and not quiet.
If someone is not humble then lucy is either not patient or not brave and vice versa.
If someone is either not rich or not old then someone is both wise and curious.
Everyone who is wise is funny.
Everyone who is both not curious and not rich is both wise and not old and vice versa.
Everyone who is either happy or patient is curious or tall.
If alice is brave then lucy is not curious and vice versa.
Everyone who is patient or not tall is both funny and quiet and vice versa.
If lucy is either generous or not old then mary is either not creative or curious.
Everyone who is either curious or kind is both humble and not strong and vice versa.
Everyone who is either curious or not calm is not tall or funny.
Everyone who is not creative or old is both funny and not quiet and vice versa.
Everyone who is not happy is either not wise or calm.
Everyone who is both not wise and not kind is both not happy and not creative.
Mary is either not brave or humble.
Lucy is either tall or not calm.
Someone is either creative or funny.
Someone is either not patient or generous.
Someone is not quiet or curious.
Someone is both kind and creative.
Lucy is not humble or curious.
Fred is either not rich or tall. | Lucy is not happy. | contradiction | (![X]:(kind(X)<=>(~tall(X)&calm(X))))&
(((~tall(alice)|brave(alice)))=>(~kind(fred)))&
(![X]:((funny(X)&~happy(X))=>(~calm(X)&~quiet(X))))&
((?[X]:(~humble(X)))<=>((~patient(lucy)<~>~brave(lucy))))&
((?[X]:((~rich(X)<~>~old(X))))=>(?[X]:((wise(X)&curious(X)))))&
(![X]:(wise(X)=>funny(X)))&
(![X]:((~curious(X)&~rich(X))<=>(wise(X)&~old(X))))&
(![X]:((happy(X)<~>patient(X))=>(curious(X)|tall(X))))&
((brave(alice))<=>(~curious(lucy)))&
(![X]:((patient(X)|~tall(X))<=>(funny(X)&quiet(X))))&
(((generous(lucy)<~>~old(lucy)))=>((~creative(mary)<~>curious(mary))))&
(![X]:((curious(X)<~>kind(X))<=>(humble(X)&~strong(X))))&
(![X]:((curious(X)<~>~calm(X))=>(~tall(X)|funny(X))))&
(![X]:((~creative(X)|old(X))<=>(funny(X)&~quiet(X))))&
(![X]:(~happy(X)=>(~wise(X)<~>calm(X))))&
(![X]:((~wise(X)&~kind(X))=>(~happy(X)&~creative(X))))&
((~brave(mary)<~>humble(mary)))&
((tall(lucy)<~>~calm(lucy)))&
(?[X]:((creative(X)<~>funny(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((kind(X)&creative(X))))&
((~humble(lucy)|curious(lucy)))&
((~rich(fred)<~>tall(fred))) | ~happy(lucy) | [
"p2",
"p5",
"p9",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2896827652402342875661617
% SZS output start Proof for 2896827652402342875661617
3. ! [X0] : ((~happy(X0) & funny(X0)) => (~quiet(X0) & ~calm(X0))) [input p2]
6. ! [X0] : (wise(X0) => funny(X0)) [input p5]
10. ! [X0] : ((~tall(X0) | patient(X0)) <=> (quiet(X0) & funny(X0))) [input p9]
15. ! [X0] : (~happy(X0) => (~wise(X0) <~> calm(X0))) [input p14]
18. tall(lucy) <~> ~calm(lucy) [input p17]
25. ~happy(lucy) [input hypothesis]
28. ! [X0] : ((~quiet(X0) & ~calm(X0)) | (happy(X0) | ~funny(X0))) [ennf transformation 3]
29. ! [X0] : ((~quiet(X0) & ~calm(X0)) | happy(X0) | ~funny(X0)) [flattening 28]
31. ! [X0] : (funny(X0) | ~wise(X0)) [ennf transformation 6]
37. ! [X0] : ((~wise(X0) <~> calm(X0)) | happy(X0)) [ennf transformation 15]
54. ! [X0] : (((~tall(X0) | patient(X0)) | (~quiet(X0) | ~funny(X0))) & ((quiet(X0) & funny(X0)) | (tall(X0) & ~patient(X0)))) [nnf transformation 10]
55. ! [X0] : ((~tall(X0) | patient(X0) | ~quiet(X0) | ~funny(X0)) & ((quiet(X0) & funny(X0)) | (tall(X0) & ~patient(X0)))) [flattening 54]
62. ! [X0] : (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | happy(X0)) [nnf transformation 37]
64. (calm(lucy) | ~tall(lucy)) & (~calm(lucy) | tall(lucy)) [nnf transformation 18]
81. ~funny(X0) | happy(X0) | ~calm(X0) [cnf transformation 29]
82. ~quiet(X0) | happy(X0) | ~funny(X0) [cnf transformation 29]
91. ~wise(X0) | funny(X0) [cnf transformation 31]
101. funny(X0) | tall(X0) [cnf transformation 55]
103. quiet(X0) | tall(X0) [cnf transformation 55]
123. ~calm(X0) | wise(X0) | happy(X0) [cnf transformation 62]
129. calm(lucy) | ~tall(lucy) [cnf transformation 64]
140. ~happy(lucy) [cnf transformation 25]
231. 19 <=> tall(lucy) [avatar definition]
235. 20 <=> calm(lucy) [avatar definition]
237. calm(lucy) <- (20) [avatar component clause 235]
238. ~19 | 20 [avatar split clause 129,235,231]
304. happy(X0) | ~funny(X0) | tall(X0) [resolution 82,103]
305. happy(X0) | tall(X0) [subsumption resolution 304,101]
333. 35 <=> wise(lucy) [avatar definition]
334. wise(lucy) <- (35) [avatar component clause 333]
368. tall(lucy) [resolution 305,140]
371. 19 [avatar split clause 368,231]
376. wise(lucy) | happy(lucy) <- (20) [resolution 123,237]
389. wise(lucy) <- (20) [subsumption resolution 376,140]
390. 35 | ~20 [avatar split clause 389,235,333]
398. funny(lucy) <- (35) [resolution 334,91]
429. happy(lucy) | ~calm(lucy) <- (35) [resolution 398,81]
430. ~calm(lucy) <- (35) [subsumption resolution 429,140]
431. $false <- (20, 35) [subsumption resolution 430,237]
432. ~20 | ~35 [avatar contradiction clause 431]
433. $false [avatar sat refutation 238,371,390,432]
% SZS output end Proof for 2896827652402342875661617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not funny and not patient then someone is either tall or humble and vice versa. Everyone who is not strong or not happy is both humble and kind. Everyone who is not tall or kind is either not rich or quiet. Everyone who is both not curious and creative is either not happy or humble and vice versa. Everyone who is either tall or patient is both humble and wise. If someone is both happy and tall then alice is either creative or not funny and vice versa. Everyone who is either not rich or patient is rich or wise. If someone is either humble or generous then someone is kind. Everyone who is not tall or humble is patient and vice versa. If someone is generous or not tall then alice is either not creative or calm and vice versa. If someone is both not kind and not calm then someone is either happy or brave and vice versa. Everyone who is either tall or not old is kind. Everyone who is not generous is not calm and vice versa. If lucy is patient or rich then someone is old or not rich and vice versa. Everyone who is not quiet or not patient is both creative and not happy. If paul is both strong and not tall then someone is not creative or not generous and vice versa. Susan is either quiet or not tall. Lucy is not brave. Someone is funny. Fred is not humble or not funny. Someone is not strong or not funny. Mary is both generous and quiet. Someone is not curious. Someone is not strong or not wise. | Paul is not creative. | contradiction | (((~funny(fred)&~patient(fred)))<=>(?[X]:((tall(X)<~>humble(X)))))&
(![X]:((~strong(X)|~happy(X))=>(humble(X)&kind(X))))&
(![X]:((~tall(X)|kind(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((~curious(X)&creative(X))<=>(~happy(X)<~>humble(X))))&
(![X]:((tall(X)<~>patient(X))=>(humble(X)&wise(X))))&
((?[X]:((happy(X)&tall(X))))<=>((creative(alice)<~>~funny(alice))))&
(![X]:((~rich(X)<~>patient(X))=>(rich(X)|wise(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:((generous(X)|~tall(X))))<=>((~creative(alice)<~>calm(alice))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>kind(X)))&
(![X]:(~generous(X)<=>~calm(X)))&
(((patient(lucy)|rich(lucy)))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(creative(X)&~happy(X))))&
(((strong(paul)&~tall(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
((quiet(susan)<~>~tall(susan)))&
(~brave(lucy))&
(?[X]:(funny(X)))&
((~humble(fred)|~funny(fred)))&
(?[X]:((~strong(X)|~funny(X))))&
((generous(mary)&quiet(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)|~wise(X)))) | ~creative(paul) | [
"p0",
"p1",
"p4",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3762540747959583618929926
% SZS output start Proof for 3762540747959583618929926
1. (~patient(fred) & ~funny(fred)) <=> ? [X0] : (tall(X0) <~> humble(X0)) [input p0]
2. ! [X0] : ((~happy(X0) | ~strong(X0)) => (kind(X0) & humble(X0))) [input p1]
5. ! [X0] : ((tall(X0) <~> patient(X0)) => (wise(X0) & humble(X0))) [input p4]
9. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p8]
15. ! [X0] : ((~patient(X0) | ~quiet(X0)) => (~happy(X0) & creative(X0))) [input p14]
16. (~tall(paul) & strong(paul)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p15]
25. ~creative(paul) [input hypothesis]
28. ! [X0] : ((kind(X0) & humble(X0)) | (happy(X0) & strong(X0))) [ennf transformation 2]
30. ! [X0] : ((wise(X0) & humble(X0)) | (tall(X0) <=> patient(X0))) [ennf transformation 5]
35. ! [X0] : ((~happy(X0) & creative(X0)) | (patient(X0) & quiet(X0))) [ennf transformation 15]
36. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (patient(fred) | funny(fred))) [nnf transformation 1]
37. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X0] : ((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | patient(fred) | funny(fred)) [flattening 36]
38. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (? [X1] : ((~humble(X1) | ~tall(X1)) & (humble(X1) | tall(X1))) | patient(fred) | funny(fred)) [rectify 37]
39. ? [X1] : ((~humble(X1) | ~tall(X1)) & (humble(X1) | tall(X1))) => ((~humble(sK0) | ~tall(sK0)) & (humble(sK0) | tall(sK0))) [choice axiom]
40. ((~patient(fred) & ~funny(fred)) | ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(sK0) | ~tall(sK0)) & (humble(sK0) | tall(sK0))) | patient(fred) | funny(fred)) [skolemisation 38,39]
44. ! [X0] : ((wise(X0) & humble(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) [nnf transformation 30]
54. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 9]
55. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 54]
72. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | (tall(paul) | ~strong(paul))) [nnf transformation 16]
73. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | tall(paul) | ~strong(paul)) [flattening 72]
74. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | tall(paul) | ~strong(paul)) [rectify 73]
75. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK7) | ~creative(sK7)) [choice axiom]
76. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK7) | ~creative(sK7)) | tall(paul) | ~strong(paul)) [skolemisation 74,75]
91. ~patient(fred) | tall(X0) | ~humble(X0) [cnf transformation 40]
93. happy(X0) | humble(X0) [cnf transformation 28]
107. humble(X0) | tall(X0) | ~patient(X0) [cnf transformation 44]
121. ~humble(X0) | patient(X0) [cnf transformation 55]
122. humble(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 55]
146. ~happy(X0) | patient(X0) [cnf transformation 35]
150. ~tall(paul) | creative(X0) [cnf transformation 76]
162. ~creative(paul) [cnf transformation 25]
165. 1 <=> ! [X0] : (tall(X0) | ~humble(X0)) [avatar definition]
166. tall(X0) | ~humble(X0) <- (1) [avatar component clause 165]
168. 2 <=> patient(fred) [avatar definition]
170. ~patient(fred) <- (~2) [avatar component clause 168]
171. 1 | ~2 [avatar split clause 91,168,165]
231. ~patient(X0) | humble(X0) [subsumption resolution 122,107]
247. 18 <=> ! [X1] : tall(X1) [avatar definition]
248. tall(X1) <- (18) [avatar component clause 247]
317. 34 <=> tall(paul) [avatar definition]
319. ~tall(paul) <- (~34) [avatar component clause 317]
322. 35 <=> ! [X0] : creative(X0) [avatar definition]
323. creative(X0) <- (35) [avatar component clause 322]
324. 35 | ~34 [avatar split clause 150,317,322]
375. $false <- (35) [resolution 323,162]
376. ~35 [avatar contradiction clause 375]
398. patient(X0) | humble(X0) [resolution 146,93]
400. humble(X0) [subsumption resolution 398,231]
412. patient(X0) [resolution 400,121]
414. tall(X0) <- (1) [subsumption resolution 166,400]
415. 18 | ~1 [avatar split clause 414,165,247]
417. $false <- (18, ~34) [resolution 248,319]
420. ~18 | 34 [avatar contradiction clause 417]
422. $false <- (~2) [subsumption resolution 170,412]
423. 2 [avatar contradiction clause 422]
424. $false [avatar sat refutation 171,324,376,415,420,423]
% SZS output end Proof for 3762540747959583618929926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is brave or not tall then someone is brave or happy. Everyone who is not curious is patient and vice versa. Everyone who is not generous is curious and vice versa. Everyone who is not strong or old is both funny and not tall. Everyone who is not creative or not brave is both tall and curious and vice versa. Everyone who is both funny and not patient is either rich or not calm and vice versa. If someone is not generous or funny then someone is funny and vice versa. Everyone who is either not old or not calm is not strong or strong and vice versa. Everyone who is both curious and tall is both not patient and creative. Everyone who is either not quiet or generous is rich or creative and vice versa. Everyone who is either not patient or not rich is both quiet and calm. Everyone who is either not brave or not wise is either not funny or curious. Everyone who is funny is either not brave or wise and vice versa. Everyone who is both patient and strong is strong and vice versa. If someone is either not patient or not humble then someone is both creative and not creative. Everyone who is both patient and not funny is both not funny and funny and vice versa. Fred is not quiet or not strong. Lucy is either kind or funny. Susan is either not tall or not wise. Susan is not calm. Paul is creative or old. Someone is happy or tall. Someone is generous. | Paul is quiet. | neutral | (((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)&funny(X))))&
((~quiet(fred)|~strong(fred)))&
((kind(lucy)<~>funny(lucy)))&
((~tall(susan)<~>~wise(susan)))&
(~calm(susan))&
((creative(paul)|old(paul)))&
(?[X]:((happy(X)|tall(X))))&
(?[X]:(generous(X))) | quiet(paul) | [] | null | 0 |
If someone is not old or creative then someone is either funny or creative and vice versa.
Everyone who is either patient or not generous is both curious and not tall.
Everyone who is either not tall or rich is kind or not tall.
If someone is both brave and not quiet then lucy is both quiet and curious.
If someone is either not rich or not humble then someone is not old or humble and vice versa.
If someone is either strong or not tall then someone is both rich and not kind and vice versa.
If john is either kind or not tall then fred is both not humble and old and vice versa.
If someone is patient then someone is not creative or wise.
Everyone who is either not creative or calm is either humble or funny.
Everyone who is both not old and not creative is not curious or brave.
Everyone who is both not strong and funny is either tall or quiet.
Everyone who is funny or strong is both rich and not generous and vice versa.
Everyone who is either funny or not curious is generous or patient.
If someone is both kind and happy then fred is not generous and vice versa.
Everyone who is both not tall and not humble is either brave or not humble and vice versa.
Everyone who is not wise or not quiet is kind.
Someone is not quiet or patient.
John is both kind and strong.
Someone is kind.
Paul is both patient and tall.
Someone is curious or calm.
Paul is either not curious or not calm.
Alice is not happy.
Paul is both not humble and not calm. | Paul is not tall. | contradiction | ((?[X]:((~old(X)|creative(X))))<=>(?[X]:((funny(X)<~>creative(X)))))&
(![X]:((patient(X)<~>~generous(X))=>(curious(X)&~tall(X))))&
(![X]:((~tall(X)<~>rich(X))=>(kind(X)|~tall(X))))&
((?[X]:((brave(X)&~quiet(X))))=>((quiet(lucy)&curious(lucy))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((~old(X)|humble(X)))))&
((?[X]:((strong(X)<~>~tall(X))))<=>(?[X]:((rich(X)&~kind(X)))))&
(((kind(john)<~>~tall(john)))<=>((~humble(fred)&old(fred))))&
((?[X]:(patient(X)))=>(?[X]:((~creative(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))=>(humble(X)<~>funny(X))))&
(![X]:((~old(X)&~creative(X))=>(~curious(X)|brave(X))))&
(![X]:((~strong(X)&funny(X))=>(tall(X)<~>quiet(X))))&
(![X]:((funny(X)|strong(X))<=>(rich(X)&~generous(X))))&
(![X]:((funny(X)<~>~curious(X))=>(generous(X)|patient(X))))&
((?[X]:((kind(X)&happy(X))))<=>(~generous(fred)))&
(![X]:((~tall(X)&~humble(X))<=>(brave(X)<~>~humble(X))))&
(![X]:((~wise(X)|~quiet(X))=>kind(X)))&
(?[X]:((~quiet(X)|patient(X))))&
((kind(john)&strong(john)))&
(?[X]:(kind(X)))&
((patient(paul)&tall(paul)))&
(?[X]:((curious(X)|calm(X))))&
((~curious(paul)<~>~calm(paul)))&
(~happy(alice))&
((~humble(paul)&~calm(paul))) | ~tall(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8371762468619638371317624
% SZS output start Proof for 8371762468619638371317624
20. tall(paul) & patient(paul) [input p19]
25. ~tall(paul) [input hypothesis]
142. tall(paul) [cnf transformation 20]
149. ~tall(paul) [cnf transformation 25]
334. $false [subsumption resolution 149,142]
% SZS output end Proof for 8371762468619638371317624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not old then someone is not curious or happy.
Everyone who is both humble and not quiet is patient and vice versa.
Everyone who is both not patient and not happy is either creative or curious and vice versa.
If susan is either not patient or happy then someone is rich.
If someone is either generous or not strong then alice is kind and vice versa.
If someone is kind then john is either not creative or not curious.
Everyone who is not humble or not tall is not humble and vice versa.
If someone is both not strong and humble then someone is not wise or not old and vice versa.
If lucy is not creative or generous then someone is kind and vice versa.
If someone is patient then someone is not creative and vice versa.
Everyone who is either creative or not curious is happy and vice versa.
If john is kind then alice is rich or not strong.
Everyone who is either old or not rich is both not generous and not patient.
Everyone who is both quiet and curious is not calm.
Everyone who is either not generous or kind is both kind and not quiet and vice versa.
Everyone who is not wise or not tall is both not tall and not patient and vice versa.
Lucy is tall.
Alice is both not quiet and creative.
Someone is not patient.
Susan is either not strong or not patient.
John is not rich or calm.
Paul is not creative.
Someone is either creative or strong.
Paul is not curious or strong. | Paul is curious. | neutral | ((?[X]:((~kind(X)<~>~old(X))))=>(?[X]:((~curious(X)|happy(X)))))&
(![X]:((humble(X)&~quiet(X))<=>patient(X)))&
(![X]:((~patient(X)&~happy(X))<=>(creative(X)<~>curious(X))))&
(((~patient(susan)<~>happy(susan)))=>(?[X]:(rich(X))))&
((?[X]:((generous(X)<~>~strong(X))))<=>(kind(alice)))&
((?[X]:(kind(X)))=>((~creative(john)<~>~curious(john))))&
(![X]:((~humble(X)|~tall(X))<=>~humble(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~wise(X)|~old(X)))))&
(((~creative(lucy)|generous(lucy)))<=>(?[X]:(kind(X))))&
((?[X]:(patient(X)))<=>(?[X]:(~creative(X))))&
(![X]:((creative(X)<~>~curious(X))<=>happy(X)))&
((kind(john))=>((rich(alice)|~strong(alice))))&
(![X]:((old(X)<~>~rich(X))=>(~generous(X)&~patient(X))))&
(![X]:((quiet(X)&curious(X))=>~calm(X)))&
(![X]:((~generous(X)<~>kind(X))<=>(kind(X)&~quiet(X))))&
(![X]:((~wise(X)|~tall(X))<=>(~tall(X)&~patient(X))))&
(tall(lucy))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~patient(X)))&
((~strong(susan)<~>~patient(susan)))&
((~rich(john)|calm(john)))&
(~creative(paul))&
(?[X]:((creative(X)<~>strong(X))))&
((~curious(paul)|strong(paul))) | curious(paul) | [] | null | 0 |
Everyone who is quiet is both generous and rich.
Everyone who is not strong or not rich is either not funny or kind.
If lucy is humble or not strong then someone is either patient or creative and vice versa.
If john is both not curious and humble then someone is both not generous and not patient.
If someone is not creative or strong then john is both not generous and not rich and vice versa.
Everyone who is not rich is both calm and generous and vice versa.
Everyone who is quiet or humble is both patient and rich.
Everyone who is either not happy or not creative is both not humble and curious and vice versa.
If someone is either not funny or old then paul is funny.
Everyone who is either not wise or not funny is not creative or not tall.
If susan is tall or funny then someone is not curious and vice versa.
If someone is either strong or not quiet then someone is not kind or not funny and vice versa.
Everyone who is both calm and not calm is generous and vice versa.
Everyone who is both happy and not funny is either happy or not rich.
Everyone who is both old and strong is not happy or not calm and vice versa.
Everyone who is creative or not kind is not strong.
Someone is either old or not patient.
Someone is not generous.
Alice is wise or not humble.
Fred is tall.
Fred is either humble or quiet. | Lucy is not wise. | neutral | (![X]:(quiet(X)=>(generous(X)&rich(X))))&
(![X]:((~strong(X)|~rich(X))=>(~funny(X)<~>kind(X))))&
(((humble(lucy)|~strong(lucy)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(((~curious(john)&humble(john)))=>(?[X]:((~generous(X)&~patient(X)))))&
((?[X]:((~creative(X)|strong(X))))<=>((~generous(john)&~rich(john))))&
(![X]:(~rich(X)<=>(calm(X)&generous(X))))&
(![X]:((quiet(X)|humble(X))=>(patient(X)&rich(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~funny(X)<~>old(X))))=>(funny(paul)))&
(![X]:((~wise(X)<~>~funny(X))=>(~creative(X)|~tall(X))))&
(((tall(susan)|funny(susan)))<=>(?[X]:(~curious(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:((calm(X)&~calm(X))<=>generous(X)))&
(![X]:((happy(X)&~funny(X))=>(happy(X)<~>~rich(X))))&
(![X]:((old(X)&strong(X))<=>(~happy(X)|~calm(X))))&
(![X]:((creative(X)|~kind(X))=>~strong(X)))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:(~generous(X)))&
((wise(alice)|~humble(alice)))&
(tall(fred))&
((humble(fred)<~>quiet(fred))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either quiet or humble is strong.
Everyone who is funny or not happy is calm.
Everyone who is both humble and not old is humble and vice versa.
If someone is either humble or curious then someone is both not creative and humble and vice versa.
If john is not funny or old then susan is not curious or not generous.
If someone is both not tall and not happy then someone is not tall and vice versa.
Everyone who is either happy or patient is both not patient and old and vice versa.
Everyone who is not curious or happy is either not generous or wise.
Everyone who is not wise is either brave or wise.
Everyone who is both generous and not kind is both generous and not generous and vice versa.
Everyone who is either tall or not quiet is not old and vice versa.
Everyone who is not wise or not patient is rich or not calm and vice versa.
Everyone who is both not funny and not humble is funny.
If paul is not quiet then someone is both wise and not brave and vice versa.
Everyone who is not happy is not tall or not quiet.
If susan is either strong or not calm then someone is not humble and vice versa.
Someone is not funny or brave.
Someone is not creative.
Paul is not curious.
Paul is tall or not rich.
Mary is quiet or humble.
Paul is patient.
Someone is both happy and curious.
Mary is both strong and wise. | John is not kind. | neutral | (![X]:((quiet(X)<~>humble(X))=>strong(X)))&
(![X]:((funny(X)|~happy(X))=>calm(X)))&
(![X]:((humble(X)&~old(X))<=>humble(X)))&
((?[X]:((humble(X)<~>curious(X))))<=>(?[X]:((~creative(X)&humble(X)))))&
(((~funny(john)|old(john)))=>((~curious(susan)|~generous(susan))))&
((?[X]:((~tall(X)&~happy(X))))<=>(?[X]:(~tall(X))))&
(![X]:((happy(X)<~>patient(X))<=>(~patient(X)&old(X))))&
(![X]:((~curious(X)|happy(X))=>(~generous(X)<~>wise(X))))&
(![X]:(~wise(X)=>(brave(X)<~>wise(X))))&
(![X]:((generous(X)&~kind(X))<=>(generous(X)&~generous(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>~old(X)))&
(![X]:((~wise(X)|~patient(X))<=>(rich(X)|~calm(X))))&
(![X]:((~funny(X)&~humble(X))=>funny(X)))&
((~quiet(paul))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~happy(X)=>(~tall(X)|~quiet(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:(~humble(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:(~creative(X)))&
(~curious(paul))&
((tall(paul)|~rich(paul)))&
((quiet(mary)|humble(mary)))&
(patient(paul))&
(?[X]:((happy(X)&curious(X))))&
((strong(mary)&wise(mary))) | ~kind(john) | [] | null | 0 |
Everyone who is either happy or rich is both not old and calm and vice versa.
If someone is both not generous and not quiet then someone is either not brave or old.
Everyone who is both calm and not strong is calm or not humble.
Everyone who is curious or not patient is generous or not tall.
If alice is not creative or not tall then susan is either not generous or calm and vice versa.
Everyone who is funny is kind or not patient.
Everyone who is either tall or not happy is old or happy and vice versa.
Everyone who is patient is not tall or not brave.
Everyone who is either not humble or brave is both kind and strong.
If someone is not patient or not humble then paul is either wise or funny.
If someone is both wise and tall then alice is kind or humble and vice versa.
If someone is not patient or patient then mary is either quiet or old.
If lucy is not patient or happy then lucy is either not strong or wise and vice versa.
If alice is both not brave and not wise then someone is not tall or strong and vice versa.
Everyone who is both old and brave is generous.
Everyone who is either not creative or creative is rich or happy.
John is either brave or rich.
Alice is both not kind and not humble.
Someone is calm.
Susan is generous.
Alice is both not curious and not funny.
Someone is not creative. | Alice is not tall. | contradiction | (![X]:((happy(X)<~>rich(X))<=>(~old(X)&calm(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((~brave(X)<~>old(X)))))&
(![X]:((calm(X)&~strong(X))=>(calm(X)|~humble(X))))&
(![X]:((curious(X)|~patient(X))=>(generous(X)|~tall(X))))&
(((~creative(alice)|~tall(alice)))<=>((~generous(susan)<~>calm(susan))))&
(![X]:(funny(X)=>(kind(X)|~patient(X))))&
(![X]:((tall(X)<~>~happy(X))<=>(old(X)|happy(X))))&
(![X]:(patient(X)=>(~tall(X)|~brave(X))))&
(![X]:((~humble(X)<~>brave(X))=>(kind(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>((wise(paul)<~>funny(paul))))&
((?[X]:((wise(X)&tall(X))))<=>((kind(alice)|humble(alice))))&
((?[X]:((~patient(X)|patient(X))))=>((quiet(mary)<~>old(mary))))&
(((~patient(lucy)|happy(lucy)))<=>((~strong(lucy)<~>wise(lucy))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((old(X)&brave(X))=>generous(X)))&
(![X]:((~creative(X)<~>creative(X))=>(rich(X)|happy(X))))&
((brave(john)<~>rich(john)))&
((~kind(alice)&~humble(alice)))&
(?[X]:(calm(X)))&
(generous(susan))&
((~curious(alice)&~funny(alice)))&
(?[X]:(~creative(X))) | ~tall(alice) | [
"p0",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3190182105032851760496724
% SZS output start Proof for 3190182105032851760496724
1. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (calm(X0) & ~old(X0))) [input p0]
7. ! [X0] : ((tall(X0) <~> ~happy(X0)) <=> (happy(X0) | old(X0))) [input p6]
16. ! [X0] : ((~creative(X0) <~> creative(X0)) => (happy(X0) | rich(X0))) [input p15]
23. ~tall(alice) [input hypothesis]
41. ! [X0] : ((happy(X0) | rich(X0)) | (~creative(X0) <=> creative(X0))) [ennf transformation 16]
42. ! [X0] : (happy(X0) | rich(X0) | (~creative(X0) <=> creative(X0))) [flattening 41]
43. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 1]
44. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 43]
51. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [nnf transformation 7]
52. ! [X0] : ((((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))))) [flattening 51]
68. ! [X0] : (happy(X0) | rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 42]
74. ~old(X0) | rich(X0) | ~happy(X0) [cnf transformation 44]
75. ~old(X0) | happy(X0) | ~rich(X0) [cnf transformation 44]
92. happy(X0) | old(X0) | tall(X0) | happy(X0) [cnf transformation 52]
94. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 52]
127. happy(X0) | rich(X0) | creative(X0) | creative(X0) [cnf transformation 68]
128. happy(X0) | rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 68]
137. ~tall(alice) [cnf transformation 23]
138. happy(X0) | rich(X0) | creative(X0) [duplicate literal removal 127]
139. happy(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 128]
140. happy(X0) | old(X0) | tall(X0) [duplicate literal removal 92]
141. ~happy(X0) | tall(X0) [duplicate literal removal 94]
168. 7 <=> tall(alice) [avatar definition]
170. ~tall(alice) <- (~7) [avatar component clause 168]
177. tall(X0) | old(X0) [subsumption resolution 140,141]
284. rich(X0) | happy(X0) [subsumption resolution 138,139]
298. ~7 [avatar split clause 137,168]
305. old(alice) <- (~7) [resolution 177,170]
311. rich(alice) | ~happy(alice) <- (~7) [resolution 74,305]
313. rich(alice) <- (~7) [subsumption resolution 311,284]
316. happy(alice) | ~rich(alice) <- (~7) [resolution 75,305]
318. happy(alice) <- (~7) [subsumption resolution 316,313]
337. tall(alice) <- (~7) [resolution 318,141]
338. $false <- (~7) [subsumption resolution 337,170]
339. 7 [avatar contradiction clause 338]
340. $false [avatar sat refutation 298,339]
% SZS output end Proof for 3190182105032851760496724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not curious and creative then someone is both not curious and rich.
Everyone who is both not old and not kind is either not happy or not kind and vice versa.
Everyone who is both creative and not calm is either not strong or quiet and vice versa.
Everyone who is both generous and kind is not curious and vice versa.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not generous is both calm and not humble.
If someone is both curious and not old then alice is both funny and calm and vice versa.
Everyone who is both patient and not creative is not patient or rich and vice versa.
Everyone who is happy is not humble or patient.
Everyone who is curious or not happy is not funny and vice versa.
If someone is either quiet or brave then paul is both humble and tall.
Everyone who is either creative or not brave is both strong and curious and vice versa.
If someone is either tall or quiet then paul is kind or humble and vice versa.
If someone is not curious or not patient then someone is both patient and not strong and vice versa.
If alice is both tall and not wise then someone is both funny and not quiet and vice versa.
Lucy is brave or kind.
Someone is humble or brave.
Lucy is curious.
Fred is not wise or not brave. | Paul is creative. | neutral | (((~curious(alice)&creative(alice)))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&kind(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~humble(X))))&
((?[X]:((curious(X)&~old(X))))<=>((funny(alice)&calm(alice))))&
(![X]:((patient(X)&~creative(X))<=>(~patient(X)|rich(X))))&
(![X]:(happy(X)=>(~humble(X)|patient(X))))&
(![X]:((curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>((humble(paul)&tall(paul))))&
(![X]:((creative(X)<~>~brave(X))<=>(strong(X)&curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((kind(paul)|humble(paul))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:((patient(X)&~strong(X)))))&
(((tall(alice)&~wise(alice)))<=>(?[X]:((funny(X)&~quiet(X)))))&
((brave(lucy)|kind(lucy)))&
(?[X]:((humble(X)|brave(X))))&
(curious(lucy))&
((~wise(fred)|~brave(fred))) | creative(paul) | [] | null | 0 |
Everyone who is curious is either not creative or curious and vice versa.
If john is not curious or not wise then someone is either old or not funny.
If someone is both not patient and not calm then mary is curious or patient.
If someone is not strong then someone is both old and strong and vice versa.
Everyone who is either creative or kind is both creative and quiet and vice versa.
Everyone who is either not curious or wise is both happy and not funny and vice versa.
Everyone who is patient is both brave and not strong.
Everyone who is both strong and not happy is either generous or tall and vice versa.
Everyone who is happy or not calm is both brave and curious.
If fred is not kind or old then someone is quiet.
If someone is both tall and not strong then someone is not quiet or not wise.
Everyone who is either quiet or old is old or curious and vice versa.
Everyone who is both quiet and not old is both not creative and not humble.
Everyone who is either not brave or wise is either not rich or humble and vice versa.
Everyone who is rich or not curious is both humble and creative.
If someone is not quiet then alice is either not patient or not creative.
Someone is both funny and not tall.
Someone is funny or not creative.
Mary is not quiet.
Someone is patient or brave.
Lucy is not humble or tall.
Someone is patient or not creative.
John is both rich and not calm.
Paul is either kind or rich. | Mary is creative. | entailment | (![X]:(curious(X)<=>(~creative(X)<~>curious(X))))&
(((~curious(john)|~wise(john)))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~calm(X))))=>((curious(mary)|patient(mary))))&
((?[X]:(~strong(X)))<=>(?[X]:((old(X)&strong(X)))))&
(![X]:((creative(X)<~>kind(X))<=>(creative(X)&quiet(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(happy(X)&~funny(X))))&
(![X]:(patient(X)=>(brave(X)&~strong(X))))&
(![X]:((strong(X)&~happy(X))<=>(generous(X)<~>tall(X))))&
(![X]:((happy(X)|~calm(X))=>(brave(X)&curious(X))))&
(((~kind(fred)|old(fred)))=>(?[X]:(quiet(X))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((~quiet(X)|~wise(X)))))&
(![X]:((quiet(X)<~>old(X))<=>(old(X)|curious(X))))&
(![X]:((quiet(X)&~old(X))=>(~creative(X)&~humble(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((rich(X)|~curious(X))=>(humble(X)&creative(X))))&
((?[X]:(~quiet(X)))=>((~patient(alice)<~>~creative(alice))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:((funny(X)|~creative(X))))&
(~quiet(mary))&
(?[X]:((patient(X)|brave(X))))&
((~humble(lucy)|tall(lucy)))&
(?[X]:((patient(X)|~creative(X))))&
((rich(john)&~calm(john)))&
((kind(paul)<~>rich(paul))) | creative(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 71583979158785448653888
% SZS output start Proof for 71583979158785448653888
1. ! [X0] : (curious(X0) <=> (~creative(X0) <~> curious(X0))) [input p0]
25. ~creative(mary) [input hypothesis]
39. ! [X0] : ((curious(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ~curious(X0))) [nnf transformation 1]
73. ~curious(X0) | creative(X0) | ~curious(X0) [cnf transformation 39]
74. curious(X0) | curious(X0) | creative(X0) [cnf transformation 39]
144. ~creative(mary) [cnf transformation 25]
149. ~curious(X0) | creative(X0) [duplicate literal removal 73]
150. curious(X0) | creative(X0) [duplicate literal removal 74]
151. creative(X0) [subsumption resolution 149,150]
261. $false [subsumption resolution 144,151]
% SZS output end Proof for 71583979158785448653888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then susan is either not curious or curious. If someone is tall or not quiet then someone is quiet or strong. If someone is not rich or humble then someone is brave or not curious. If fred is rich then someone is both not happy and not strong and vice versa. Everyone who is both humble and not brave is not rich or funny. Everyone who is not wise or patient is either quiet or not tall. Everyone who is both curious and not funny is both wise and brave. Everyone who is both not rich and not strong is patient or strong and vice versa. If fred is not humble then someone is not patient or not creative and vice versa. Everyone who is not generous or not kind is either humble or not rich and vice versa. Everyone who is both old and not tall is not wise or curious and vice versa. If fred is not rich then susan is both not brave and generous. If fred is not creative or not funny then someone is either not patient or humble and vice versa. Everyone who is creative or rich is either curious or calm. Everyone who is either patient or not patient is not calm or not rich and vice versa. Everyone who is either calm or quiet is not creative and vice versa. Someone is not old. Someone is calm. Mary is both not brave and wise. Someone is both not generous and not curious. Someone is strong or not funny. Someone is both generous and not tall. Someone is either not rich or happy. Susan is both not wise and generous. | Susan is strong. | contradiction | ((?[X]:(happy(X)))=>((~curious(susan)<~>curious(susan))))&
((?[X]:((tall(X)|~quiet(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((~rich(X)|humble(X))))=>(?[X]:((brave(X)|~curious(X)))))&
((rich(fred))<=>(?[X]:((~happy(X)&~strong(X)))))&
(![X]:((humble(X)&~brave(X))=>(~rich(X)|funny(X))))&
(![X]:((~wise(X)|patient(X))=>(quiet(X)<~>~tall(X))))&
(![X]:((curious(X)&~funny(X))=>(wise(X)&brave(X))))&
(![X]:((~rich(X)&~strong(X))<=>(patient(X)|strong(X))))&
((~humble(fred))<=>(?[X]:((~patient(X)|~creative(X)))))&
(![X]:((~generous(X)|~kind(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((old(X)&~tall(X))<=>(~wise(X)|curious(X))))&
((~rich(fred))=>((~brave(susan)&generous(susan))))&
(((~creative(fred)|~funny(fred)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((creative(X)|rich(X))=>(curious(X)<~>calm(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~calm(X)|~rich(X))))&
(![X]:((calm(X)<~>quiet(X))<=>~creative(X)))&
(?[X]:(~old(X)))&
(?[X]:(calm(X)))&
((~brave(mary)&wise(mary)))&
(?[X]:((~generous(X)&~curious(X))))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((generous(X)&~tall(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
((~wise(susan)&generous(susan))) | strong(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8711612893198368189882022
% SZS output start Proof for 8711612893198368189882022
8. ! [X0] : ((~strong(X0) & ~rich(X0)) <=> (strong(X0) | patient(X0))) [input p7]
25. strong(susan) [input hypothesis]
50. ! [X0] : (((~strong(X0) & ~rich(X0)) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | (strong(X0) | rich(X0)))) [nnf transformation 8]
51. ! [X0] : (((~strong(X0) & ~rich(X0)) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | strong(X0) | rich(X0))) [flattening 50]
102. ~strong(X0) | ~strong(X0) [cnf transformation 51]
152. strong(susan) [cnf transformation 25]
156. ~strong(X0) [duplicate literal removal 102]
280. $false [subsumption resolution 152,156]
% SZS output end Proof for 8711612893198368189882022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not patient is either brave or tall and vice versa.
Everyone who is not humble is not tall and vice versa.
Everyone who is not strong or not happy is calm or not brave.
Everyone who is either curious or humble is both kind and not humble.
Everyone who is both rich and wise is either quiet or strong and vice versa.
If alice is both not tall and old then someone is not patient or kind.
Everyone who is not calm is both humble and not strong and vice versa.
Everyone who is wise is old.
Everyone who is not brave is not quiet or creative.
Everyone who is not quiet is either calm or not happy.
If fred is both calm and tall then someone is both rich and creative and vice versa.
Everyone who is quiet or not quiet is not funny and vice versa.
Everyone who is both creative and humble is both not quiet and humble.
Everyone who is either not creative or not quiet is not rich or calm and vice versa.
Everyone who is not creative is both not strong and curious.
Everyone who is not quiet is not rich and vice versa.
Paul is both creative and wise.
Someone is curious or not rich.
Someone is not patient.
Someone is rich or not kind.
Susan is not kind.
Someone is not generous. | Susan is quiet. | contradiction | (![X]:((~funny(X)<~>~patient(X))<=>(brave(X)<~>tall(X))))&
(![X]:(~humble(X)<=>~tall(X)))&
(![X]:((~strong(X)|~happy(X))=>(calm(X)|~brave(X))))&
(![X]:((curious(X)<~>humble(X))=>(kind(X)&~humble(X))))&
(![X]:((rich(X)&wise(X))<=>(quiet(X)<~>strong(X))))&
(((~tall(alice)&old(alice)))=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:(~calm(X)<=>(humble(X)&~strong(X))))&
(![X]:(wise(X)=>old(X)))&
(![X]:(~brave(X)=>(~quiet(X)|creative(X))))&
(![X]:(~quiet(X)=>(calm(X)<~>~happy(X))))&
(((calm(fred)&tall(fred)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((quiet(X)|~quiet(X))<=>~funny(X)))&
(![X]:((creative(X)&humble(X))=>(~quiet(X)&humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(~rich(X)|calm(X))))&
(![X]:(~creative(X)=>(~strong(X)&curious(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
((creative(paul)&wise(paul)))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|~kind(X))))&
(~kind(susan))&
(?[X]:(~generous(X))) | quiet(susan) | [
"p2",
"p3",
"p6",
"p8",
"p10",
"p12",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8967591337991173945832302
% SZS output start Proof for 8967591337991173945832302
3. ! [X0] : ((~happy(X0) | ~strong(X0)) => (~brave(X0) | calm(X0))) [input p2]
4. ! [X0] : ((curious(X0) <~> humble(X0)) => (~humble(X0) & kind(X0))) [input p3]
7. ! [X0] : (~calm(X0) <=> (~strong(X0) & humble(X0))) [input p6]
9. ! [X0] : (~brave(X0) => (creative(X0) | ~quiet(X0))) [input p8]
11. (tall(fred) & calm(fred)) <=> ? [X0] : (creative(X0) & rich(X0)) [input p10]
13. ! [X0] : ((humble(X0) & creative(X0)) => (humble(X0) & ~quiet(X0))) [input p12]
14. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (calm(X0) | ~rich(X0))) [input p13]
15. ! [X0] : (~creative(X0) => (curious(X0) & ~strong(X0))) [input p14]
16. ! [X0] : (~quiet(X0) <=> ~rich(X0)) [input p15]
21. ~kind(susan) [input p20]
23. quiet(susan) [input hypothesis]
25. ! [X0] : ((~brave(X0) | calm(X0)) | (happy(X0) & strong(X0))) [ennf transformation 3]
26. ! [X0] : (~brave(X0) | calm(X0) | (happy(X0) & strong(X0))) [flattening 25]
27. ! [X0] : ((~humble(X0) & kind(X0)) | (curious(X0) <=> humble(X0))) [ennf transformation 4]
31. ! [X0] : ((creative(X0) | ~quiet(X0)) | brave(X0)) [ennf transformation 9]
32. ! [X0] : (creative(X0) | ~quiet(X0) | brave(X0)) [flattening 31]
34. ! [X0] : ((humble(X0) & ~quiet(X0)) | (~humble(X0) | ~creative(X0))) [ennf transformation 13]
35. ! [X0] : ((humble(X0) & ~quiet(X0)) | ~humble(X0) | ~creative(X0)) [flattening 34]
36. ! [X0] : ((curious(X0) & ~strong(X0)) | creative(X0)) [ennf transformation 15]
39. ! [X0] : ((~humble(X0) & kind(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) [nnf transformation 27]
44. ! [X0] : ((~calm(X0) | (strong(X0) | ~humble(X0))) & ((~strong(X0) & humble(X0)) | calm(X0))) [nnf transformation 7]
45. ! [X0] : ((~calm(X0) | strong(X0) | ~humble(X0)) & ((~strong(X0) & humble(X0)) | calm(X0))) [flattening 44]
47. ((tall(fred) & calm(fred)) | ! [X0] : (~creative(X0) | ~rich(X0))) & (? [X0] : (creative(X0) & rich(X0)) | (~tall(fred) | ~calm(fred))) [nnf transformation 11]
48. ((tall(fred) & calm(fred)) | ! [X0] : (~creative(X0) | ~rich(X0))) & (? [X0] : (creative(X0) & rich(X0)) | ~tall(fred) | ~calm(fred)) [flattening 47]
49. ((tall(fred) & calm(fred)) | ! [X0] : (~creative(X0) | ~rich(X0))) & (? [X1] : (creative(X1) & rich(X1)) | ~tall(fred) | ~calm(fred)) [rectify 48]
50. ? [X1] : (creative(X1) & rich(X1)) => (creative(sK1) & rich(sK1)) [choice axiom]
51. ((tall(fred) & calm(fred)) | ! [X0] : (~creative(X0) | ~rich(X0))) & ((creative(sK1) & rich(sK1)) | ~tall(fred) | ~calm(fred)) [skolemisation 49,50]
54. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~calm(X0) & rich(X0))) & ((calm(X0) | ~rich(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 14]
55. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~calm(X0) & rich(X0))) & (calm(X0) | ~rich(X0) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 54]
56. ! [X0] : ((~quiet(X0) | rich(X0)) & (~rich(X0) | quiet(X0))) [nnf transformation 16]
73. ~brave(X0) | calm(X0) | strong(X0) [cnf transformation 26]
75. ~curious(X0) | humble(X0) | kind(X0) [cnf transformation 39]
86. calm(X0) | humble(X0) [cnf transformation 45]
87. ~strong(X0) | calm(X0) [cnf transformation 45]
88. ~calm(X0) | strong(X0) | ~humble(X0) [cnf transformation 45]
90. ~quiet(X0) | creative(X0) | brave(X0) [cnf transformation 32]
93. rich(sK1) | ~tall(fred) | ~calm(fred) [cnf transformation 51]
94. creative(sK1) | ~tall(fred) | ~calm(fred) [cnf transformation 51]
95. calm(fred) | ~creative(X0) | ~rich(X0) [cnf transformation 51]
96. tall(fred) | ~creative(X0) | ~rich(X0) [cnf transformation 51]
100. ~creative(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 35]
105. ~creative(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 55]
108. ~strong(X0) | creative(X0) [cnf transformation 36]
109. creative(X0) | curious(X0) [cnf transformation 36]
110. ~rich(X0) | quiet(X0) [cnf transformation 56]
111. ~quiet(X0) | rich(X0) [cnf transformation 56]
117. ~kind(susan) [cnf transformation 21]
118. quiet(susan) [cnf transformation 23]
138. 5 <=> ! [X0] : (~creative(X0) | ~rich(X0)) [avatar definition]
139. ~creative(X0) | ~rich(X0) <- (5) [avatar component clause 138]
141. 6 <=> tall(fred) [avatar definition]
144. 5 | 6 [avatar split clause 96,141,138]
146. 7 <=> calm(fred) [avatar definition]
149. 5 | 7 [avatar split clause 95,146,138]
151. 8 <=> creative(sK1) [avatar definition]
153. creative(sK1) <- (8) [avatar component clause 151]
154. ~7 | ~6 | 8 [avatar split clause 94,151,141,146]
156. 9 <=> rich(sK1) [avatar definition]
158. rich(sK1) <- (9) [avatar component clause 156]
159. ~7 | ~6 | 9 [avatar split clause 93,156,141,146]
180. rich(susan) [resolution 111,118]
183. ~rich(X0) | curious(X0) <- (5) [resolution 139,109]
184. curious(susan) <- (5) [resolution 183,180]
185. humble(susan) | kind(susan) <- (5) [resolution 75,184]
186. humble(susan) <- (5) [subsumption resolution 185,117]
197. 15 <=> strong(susan) [avatar definition]
199. strong(susan) <- (15) [avatar component clause 197]
203. creative(susan) | brave(susan) [resolution 90,118]
205. 16 <=> brave(susan) [avatar definition]
207. brave(susan) <- (16) [avatar component clause 205]
209. 17 <=> creative(susan) [avatar definition]
210. ~creative(susan) <- (~17) [avatar component clause 209]
211. creative(susan) <- (17) [avatar component clause 209]
212. 16 | 17 [avatar split clause 203,209,205]
214. calm(susan) | strong(susan) <- (16) [resolution 207,73]
220. 19 <=> calm(susan) [avatar definition]
222. calm(susan) <- (19) [avatar component clause 220]
224. calm(susan) <- (16) [subsumption resolution 214,87]
225. 19 | ~16 [avatar split clause 224,205,220]
227. ~rich(susan) <- (5, 17) [resolution 211,139]
228. $false <- (5, 17) [subsumption resolution 227,180]
229. ~5 | ~17 [avatar contradiction clause 228]
255. strong(susan) | ~humble(susan) <- (19) [resolution 222,88]
256. strong(susan) <- (5, 19) [subsumption resolution 255,186]
257. 15 | ~5 | ~19 [avatar split clause 256,220,138,197]
262. creative(susan) <- (15) [resolution 199,108]
264. $false <- (15, ~17) [subsumption resolution 262,210]
265. ~15 | 17 [avatar contradiction clause 264]
290. ~quiet(sK1) | ~calm(sK1) <- (8) [resolution 153,105]
292. ~humble(sK1) | ~quiet(sK1) <- (8) [resolution 153,100]
294. 26 <=> calm(sK1) [avatar definition]
296. ~calm(sK1) <- (~26) [avatar component clause 294]
298. 27 <=> quiet(sK1) [avatar definition]
301. ~26 | ~27 | ~8 [avatar split clause 290,151,298,294]
303. 28 <=> humble(sK1) [avatar definition]
305. ~humble(sK1) <- (~28) [avatar component clause 303]
306. ~27 | ~28 | ~8 [avatar split clause 292,151,303,298]
307. quiet(sK1) <- (9) [resolution 158,110]
310. 27 | ~9 [avatar split clause 307,156,298]
368. humble(sK1) <- (~26) [resolution 296,86]
369. $false <- (~26, ~28) [subsumption resolution 368,305]
370. 26 | 28 [avatar contradiction clause 369]
371. $false [avatar sat refutation 144,149,154,159,212,225,229,257,265,301,306,310,370]
% SZS output end Proof for 8967591337991173945832302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or quiet then mary is both not strong and not curious and vice versa.
If someone is creative or not quiet then someone is not curious or curious.
Everyone who is both brave and not generous is both rich and calm.
If lucy is either not tall or not creative then someone is either kind or funny.
Everyone who is not tall or not creative is not quiet or not creative and vice versa.
Everyone who is patient or not creative is either not rich or humble.
Everyone who is not patient or not calm is not calm.
If someone is both quiet and not kind then lucy is patient or strong.
Everyone who is both happy and tall is not brave and vice versa.
If alice is either brave or not quiet then someone is not rich.
If paul is not patient then someone is both kind and not humble.
If someone is generous then someone is both not humble and not old and vice versa.
Everyone who is not curious or not strong is both not calm and not wise.
Everyone who is patient or strong is generous.
Everyone who is not generous is either not funny or not humble.
If susan is quiet then someone is both strong and not old and vice versa.
Someone is either not old or quiet.
Someone is either brave or not strong.
Alice is patient.
Someone is not humble or not calm.
Someone is either rich or not kind.
Someone is not funny.
Someone is old or not happy.
Susan is either not calm or happy. | Susan is generous. | entailment | ((?[X]:((curious(X)<~>quiet(X))))<=>((~strong(mary)&~curious(mary))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:((brave(X)&~generous(X))=>(rich(X)&calm(X))))&
(((~tall(lucy)<~>~creative(lucy)))=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((~tall(X)|~creative(X))<=>(~quiet(X)|~creative(X))))&
(![X]:((patient(X)|~creative(X))=>(~rich(X)<~>humble(X))))&
(![X]:((~patient(X)|~calm(X))=>~calm(X)))&
((?[X]:((quiet(X)&~kind(X))))=>((patient(lucy)|strong(lucy))))&
(![X]:((happy(X)&tall(X))<=>~brave(X)))&
(((brave(alice)<~>~quiet(alice)))=>(?[X]:(~rich(X))))&
((~patient(paul))=>(?[X]:((kind(X)&~humble(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~old(X)))))&
(![X]:((~curious(X)|~strong(X))=>(~calm(X)&~wise(X))))&
(![X]:((patient(X)|strong(X))=>generous(X)))&
(![X]:(~generous(X)=>(~funny(X)<~>~humble(X))))&
((quiet(susan))<=>(?[X]:((strong(X)&~old(X)))))&
(?[X]:((~old(X)<~>quiet(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
(patient(alice))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
(?[X]:((old(X)|~happy(X))))&
((~calm(susan)<~>happy(susan))) | generous(susan) | [
"p2",
"p8",
"p12",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1776276387960727646220570
% SZS output start Proof for 1776276387960727646220570
3. ! [X0] : ((~generous(X0) & brave(X0)) => (calm(X0) & rich(X0))) [input p2]
9. ! [X0] : ((tall(X0) & happy(X0)) <=> ~brave(X0)) [input p8]
13. ! [X0] : ((~strong(X0) | ~curious(X0)) => (~wise(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((strong(X0) | patient(X0)) => generous(X0)) [input p13]
24. ~calm(susan) <~> happy(susan) [input p23]
25. ~generous(susan) [input hypothesis]
28. ! [X0] : ((~strong(X0) | ~curious(X0)) => ~calm(X0)) [pure predicate removal 13]
30. ! [X0] : ((calm(X0) & rich(X0)) | (generous(X0) | ~brave(X0))) [ennf transformation 3]
31. ! [X0] : ((calm(X0) & rich(X0)) | generous(X0) | ~brave(X0)) [flattening 30]
39. ! [X0] : (~calm(X0) | (strong(X0) & curious(X0))) [ennf transformation 28]
40. ! [X0] : (generous(X0) | (~strong(X0) & ~patient(X0))) [ennf transformation 14]
56. ! [X0] : (((tall(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | (~tall(X0) | ~happy(X0)))) [nnf transformation 9]
57. ! [X0] : (((tall(X0) & happy(X0)) | brave(X0)) & (~brave(X0) | ~tall(X0) | ~happy(X0))) [flattening 56]
88. (~happy(susan) | calm(susan)) & (happy(susan) | ~calm(susan)) [nnf transformation 24]
98. ~brave(X0) | generous(X0) | calm(X0) [cnf transformation 31]
115. happy(X0) | brave(X0) [cnf transformation 57]
125. ~calm(X0) | strong(X0) [cnf transformation 39]
127. ~strong(X0) | generous(X0) [cnf transformation 40]
144. ~happy(susan) | calm(susan) [cnf transformation 88]
145. ~generous(susan) [cnf transformation 25]
322. 39 <=> calm(susan) [avatar definition]
323. ~calm(susan) <- (~39) [avatar component clause 322]
324. calm(susan) <- (39) [avatar component clause 322]
326. 40 <=> happy(susan) [avatar definition]
328. ~happy(susan) <- (~40) [avatar component clause 326]
329. 39 | ~40 [avatar split clause 144,326,322]
332. brave(susan) <- (~40) [resolution 115,328]
362. generous(susan) | calm(susan) <- (~40) [resolution 98,332]
363. calm(susan) <- (~40) [subsumption resolution 362,145]
364. $false <- (~39, ~40) [subsumption resolution 363,323]
365. 39 | 40 [avatar contradiction clause 364]
366. strong(susan) <- (39) [resolution 324,125]
370. generous(susan) <- (39) [resolution 366,127]
371. $false <- (39) [subsumption resolution 370,145]
372. ~39 [avatar contradiction clause 371]
373. $false [avatar sat refutation 329,365,372]
% SZS output end Proof for 1776276387960727646220570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble or generous then john is generous or not quiet and vice versa.
If alice is either not wise or not happy then susan is either generous or not old.
Everyone who is tall is generous.
If someone is not calm or not wise then lucy is either humble or funny.
If someone is either not brave or not tall then someone is either not curious or quiet and vice versa.
If john is creative or not brave then someone is either brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
If someone is not creative or not tall then susan is not brave and vice versa.
Everyone who is creative or kind is both patient and not creative and vice versa.
Someone is not brave or not strong.
Someone is both not brave and not rich.
Someone is either not funny or not old.
Someone is either happy or humble.
Lucy is either patient or strong.
Someone is rich.
Fred is either generous or curious. | Susan is not creative. | entailment | ((?[X]:((~humble(X)<~>generous(X))))<=>((generous(john)|~quiet(john))))&
(((~wise(alice)<~>~happy(alice)))=>((generous(susan)<~>~old(susan))))&
(![X]:(tall(X)=>generous(X)))&
((?[X]:((~calm(X)|~wise(X))))=>((humble(lucy)<~>funny(lucy))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((creative(john)|~brave(john)))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>(~brave(susan)))&
(![X]:((creative(X)|kind(X))<=>(patient(X)&~creative(X))))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((~brave(X)&~rich(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((happy(X)<~>humble(X))))&
((patient(lucy)<~>strong(lucy)))&
(?[X]:(rich(X)))&
((generous(fred)<~>curious(fred))) | ~creative(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1554929913683382164949409
% SZS output start Proof for 1554929913683382164949409
16. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) & patient(X0))) [input p15]
24. creative(susan) [input hypothesis]
75. ! [X0] : (((kind(X0) | creative(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 16]
76. ! [X0] : ((kind(X0) | creative(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 75]
165. ~creative(X0) | ~creative(X0) [cnf transformation 76]
180. creative(susan) [cnf transformation 24]
181. ~creative(X0) [duplicate literal removal 165]
459. $false [subsumption resolution 180,181]
% SZS output end Proof for 1554929913683382164949409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or quiet is not tall or not brave and vice versa.
Everyone who is calm is not patient and vice versa.
If mary is either not strong or not tall then john is both old and not old.
Everyone who is both not creative and funny is strong or rich.
Everyone who is both wise and strong is not creative and vice versa.
Everyone who is either brave or happy is not rich.
Everyone who is creative or not kind is not strong.
If alice is not curious or quiet then someone is either wise or not brave.
If someone is both not tall and funny then someone is generous or calm and vice versa.
Everyone who is not creative or strong is not kind or not calm and vice versa.
Everyone who is humble is both kind and not tall.
Everyone who is not strong is both quiet and not humble.
If someone is wise or patient then someone is not humble and vice versa.
If paul is creative then john is not old and vice versa.
If paul is tall then paul is both old and patient.
Everyone who is not curious or tall is wise or patient.
Lucy is happy.
Fred is both happy and not tall.
Alice is not kind or happy.
Alice is either wise or not happy.
Lucy is either not old or calm.
John is both curious and not humble.
Someone is either not kind or funny.
Mary is both not curious and generous. | Fred is not calm. | entailment | (![X]:((calm(X)<~>quiet(X))<=>(~tall(X)|~brave(X))))&
(![X]:(calm(X)<=>~patient(X)))&
(((~strong(mary)<~>~tall(mary)))=>((old(john)&~old(john))))&
(![X]:((~creative(X)&funny(X))=>(strong(X)|rich(X))))&
(![X]:((wise(X)&strong(X))<=>~creative(X)))&
(![X]:((brave(X)<~>happy(X))=>~rich(X)))&
(![X]:((creative(X)|~kind(X))=>~strong(X)))&
(((~curious(alice)|quiet(alice)))=>(?[X]:((wise(X)<~>~brave(X)))))&
((?[X]:((~tall(X)&funny(X))))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~creative(X)|strong(X))<=>(~kind(X)|~calm(X))))&
(![X]:(humble(X)=>(kind(X)&~tall(X))))&
(![X]:(~strong(X)=>(quiet(X)&~humble(X))))&
((?[X]:((wise(X)|patient(X))))<=>(?[X]:(~humble(X))))&
((creative(paul))<=>(~old(john)))&
((tall(paul))=>((old(paul)&patient(paul))))&
(![X]:((~curious(X)|tall(X))=>(wise(X)|patient(X))))&
(happy(lucy))&
((happy(fred)&~tall(fred)))&
((~kind(alice)|happy(alice)))&
((wise(alice)<~>~happy(alice)))&
((~old(lucy)<~>calm(lucy)))&
((curious(john)&~humble(john)))&
(?[X]:((~kind(X)<~>funny(X))))&
((~curious(mary)&generous(mary))) | ~calm(fred) | [
"p0",
"p4",
"p6",
"p9",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7116727811164938426902017
% SZS output start Proof for 7116727811164938426902017
1. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> (~brave(X0) | ~tall(X0))) [input p0]
5. ! [X0] : ((strong(X0) & wise(X0)) <=> ~creative(X0)) [input p4]
7. ! [X0] : ((~kind(X0) | creative(X0)) => ~strong(X0)) [input p6]
10. ! [X0] : ((strong(X0) | ~creative(X0)) <=> (~calm(X0) | ~kind(X0))) [input p9]
12. ! [X0] : (~strong(X0) => (~humble(X0) & quiet(X0))) [input p11]
18. ~tall(fred) & happy(fred) [input p17]
25. calm(fred) [input hypothesis]
32. ! [X0] : (~strong(X0) | (kind(X0) & ~creative(X0))) [ennf transformation 7]
35. ! [X0] : ((~humble(X0) & quiet(X0)) | strong(X0)) [ennf transformation 12]
39. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (brave(X0) & tall(X0))) & ((~brave(X0) | ~tall(X0)) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 1]
40. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | (brave(X0) & tall(X0))) & (~brave(X0) | ~tall(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [flattening 39]
43. ! [X0] : (((strong(X0) & wise(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & wise(X0)) | creative(X0)) & (~creative(X0) | ~strong(X0) | ~wise(X0))) [flattening 43]
54. ! [X0] : (((strong(X0) | ~creative(X0)) | (calm(X0) & kind(X0))) & ((~calm(X0) | ~kind(X0)) | (~strong(X0) & creative(X0)))) [nnf transformation 10]
55. ! [X0] : ((strong(X0) | ~creative(X0) | (calm(X0) & kind(X0))) & (~calm(X0) | ~kind(X0) | (~strong(X0) & creative(X0)))) [flattening 54]
71. ~quiet(X0) | ~calm(X0) | tall(X0) [cnf transformation 40]
82. creative(X0) | strong(X0) [cnf transformation 44]
85. ~creative(X0) | ~strong(X0) [cnf transformation 32]
86. ~strong(X0) | kind(X0) [cnf transformation 32]
96. ~calm(X0) | ~kind(X0) | creative(X0) [cnf transformation 55]
98. strong(X0) | ~creative(X0) | kind(X0) [cnf transformation 55]
102. strong(X0) | quiet(X0) [cnf transformation 35]
115. ~tall(fred) [cnf transformation 18]
127. calm(fred) [cnf transformation 25]
195. strong(X0) | kind(X0) [subsumption resolution 98,82]
196. kind(X0) [subsumption resolution 195,86]
198. ~calm(X0) | creative(X0) [subsumption resolution 96,196]
281. creative(fred) [resolution 198,127]
283. ~strong(fred) [resolution 281,85]
392. quiet(fred) [resolution 283,102]
395. ~calm(fred) | tall(fred) [resolution 392,71]
398. tall(fred) [subsumption resolution 395,127]
399. $false [subsumption resolution 398,115]
% SZS output end Proof for 7116727811164938426902017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and happy is strong. If someone is both not patient and rich then lucy is funny or not brave and vice versa. If john is quiet then susan is both not brave and not tall. Everyone who is quiet or not patient is both not rich and quiet and vice versa. Everyone who is both quiet and happy is not kind and vice versa. Everyone who is both happy and kind is kind or not tall and vice versa. Everyone who is patient or not old is rich and vice versa. Everyone who is not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Lucy is both strong and generous. John is not quiet or old. Susan is both humble and rich. Paul is creative or not strong. Alice is strong or not quiet. Mary is either not calm or curious. | Alice is brave. | neutral | (![X]:((~happy(X)&happy(X))=>strong(X)))&
((?[X]:((~patient(X)&rich(X))))<=>((funny(lucy)|~brave(lucy))))&
((quiet(john))=>((~brave(susan)&~tall(susan))))&
(![X]:((quiet(X)|~patient(X))<=>(~rich(X)&quiet(X))))&
(![X]:((quiet(X)&happy(X))<=>~kind(X)))&
(![X]:((happy(X)&kind(X))<=>(kind(X)|~tall(X))))&
(![X]:((patient(X)|~old(X))<=>rich(X)))&
(![X]:(~creative(X)=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
((strong(lucy)&generous(lucy)))&
((~quiet(john)|old(john)))&
((humble(susan)&rich(susan)))&
((creative(paul)|~strong(paul)))&
((strong(alice)|~quiet(alice)))&
((~calm(mary)<~>curious(mary))) | brave(alice) | [] | null | 0 |
If mary is either humble or not funny then lucy is either not happy or not funny and vice versa.
If fred is wise or not creative then john is either funny or not creative and vice versa.
Everyone who is either brave or not humble is both not old and calm.
Everyone who is tall is not tall or not quiet and vice versa.
If someone is both brave and patient then someone is both happy and calm and vice versa.
Everyone who is strong or rich is not kind or not rich.
Everyone who is not rich or funny is either not curious or kind.
If alice is both patient and not happy then someone is either not curious or not old.
Everyone who is not wise or not old is both rich and not wise and vice versa.
If john is not brave or not kind then alice is either not humble or not kind.
Everyone who is humble or creative is either not humble or brave.
Everyone who is not creative or creative is funny.
If someone is patient then someone is both not curious and not generous and vice versa.
If someone is both brave and not old then someone is kind or not strong.
Everyone who is both not strong and not wise is both not wise and not calm.
Lucy is tall or not old.
Mary is either wise or not calm.
Susan is not patient or generous.
Lucy is not tall or not humble.
Mary is either not brave or generous.
Paul is old or rich.
John is happy. | Paul is funny. | entailment | (((humble(mary)<~>~funny(mary)))<=>((~happy(lucy)<~>~funny(lucy))))&
(((wise(fred)|~creative(fred)))<=>((funny(john)<~>~creative(john))))&
(![X]:((brave(X)<~>~humble(X))=>(~old(X)&calm(X))))&
(![X]:(tall(X)<=>(~tall(X)|~quiet(X))))&
((?[X]:((brave(X)&patient(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~curious(X)<~>kind(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
((tall(lucy)|~old(lucy)))&
((wise(mary)<~>~calm(mary)))&
((~patient(susan)|generous(susan)))&
((~tall(lucy)|~humble(lucy)))&
((~brave(mary)<~>generous(mary)))&
((old(paul)|rich(paul)))&
(happy(john)) | funny(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1291919630023320955523838
% SZS output start Proof for 1291919630023320955523838
12. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p11]
23. ~funny(paul) [input hypothesis]
35. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 12]
114. funny(X0) | creative(X0) [cnf transformation 35]
115. funny(X0) | ~creative(X0) [cnf transformation 35]
131. ~funny(paul) [cnf transformation 23]
248. funny(X0) [subsumption resolution 114,115]
312. $false [subsumption resolution 131,248]
% SZS output end Proof for 1291919630023320955523838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both curious and not wise. If someone is both not kind and not calm then alice is both patient and not patient. If mary is both funny and not brave then lucy is either not strong or patient and vice versa. If fred is humble then susan is both not rich and curious and vice versa. If someone is either brave or generous then someone is not happy. If someone is either rich or not brave then susan is either humble or wise and vice versa. Everyone who is either not funny or creative is not funny or not kind and vice versa. Everyone who is either not wise or patient is curious or not old. Everyone who is brave or not tall is generous. Everyone who is either not rich or wise is not patient and vice versa. If someone is both not funny and not curious then lucy is not kind and vice versa. Everyone who is either quiet or generous is quiet and vice versa. If someone is not curious or funny then someone is not kind or tall and vice versa. If someone is both old and funny then someone is calm and vice versa. Everyone who is both patient and creative is either brave or patient. Everyone who is tall or not old is wise. Mary is wise or not humble. Someone is funny. Someone is not quiet. Fred is funny or not curious. Someone is either quiet or kind. Someone is either not patient or strong. | Mary is not wise. | contradiction | (![X]:(~strong(X)=>(curious(X)&~wise(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((patient(alice)&~patient(alice))))&
(((funny(mary)&~brave(mary)))<=>((~strong(lucy)<~>patient(lucy))))&
((humble(fred))<=>((~rich(susan)&curious(susan))))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:(~happy(X))))&
((?[X]:((rich(X)<~>~brave(X))))<=>((humble(susan)<~>wise(susan))))&
(![X]:((~funny(X)<~>creative(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~wise(X)<~>patient(X))=>(curious(X)|~old(X))))&
(![X]:((brave(X)|~tall(X))=>generous(X)))&
(![X]:((~rich(X)<~>wise(X))<=>~patient(X)))&
((?[X]:((~funny(X)&~curious(X))))<=>(~kind(lucy)))&
(![X]:((quiet(X)<~>generous(X))<=>quiet(X)))&
((?[X]:((~curious(X)|funny(X))))<=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&creative(X))=>(brave(X)<~>patient(X))))&
(![X]:((tall(X)|~old(X))=>wise(X)))&
((wise(mary)|~humble(mary)))&
(?[X]:(funny(X)))&
(?[X]:(~quiet(X)))&
((funny(fred)|~curious(fred)))&
(?[X]:((quiet(X)<~>kind(X))))&
(?[X]:((~patient(X)<~>strong(X)))) | ~wise(mary) | [
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7134810798363429892549282
% SZS output start Proof for 7134810798363429892549282
9. ! [X0] : ((~tall(X0) | brave(X0)) => generous(X0)) [input p8]
12. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> quiet(X0)) [input p11]
16. ! [X0] : ((~old(X0) | tall(X0)) => wise(X0)) [input p15]
23. ~wise(mary) [input hypothesis]
32. ! [X0] : (generous(X0) | (tall(X0) & ~brave(X0))) [ennf transformation 9]
35. ! [X0] : (wise(X0) | (old(X0) & ~tall(X0))) [ennf transformation 16]
52. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 12]
104. tall(X0) | generous(X0) [cnf transformation 32]
113. quiet(X0) | quiet(X0) | ~generous(X0) [cnf transformation 52]
115. ~generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 52]
125. ~tall(X0) | wise(X0) [cnf transformation 35]
135. ~wise(mary) [cnf transformation 23]
137. quiet(X0) | ~generous(X0) [duplicate literal removal 113]
138. ~generous(X0) | ~quiet(X0) [duplicate literal removal 115]
236. ~generous(X0) [subsumption resolution 137,138]
291. 33 <=> wise(mary) [avatar definition]
292. ~wise(mary) <- (~33) [avatar component clause 291]
328. ~33 [avatar split clause 135,291]
343. wise(X0) | generous(X0) [resolution 125,104]
344. wise(X0) [subsumption resolution 343,236]
346. $false <- (~33) [resolution 344,292]
348. 33 [avatar contradiction clause 346]
349. $false [avatar sat refutation 328,348]
% SZS output end Proof for 7134810798363429892549282
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then mary is not patient and vice versa.
Everyone who is both calm and not kind is kind and vice versa.
If someone is old then fred is either not funny or not brave.
Everyone who is either funny or not happy is funny or quiet and vice versa.
Everyone who is both generous and not funny is not calm or old and vice versa.
If someone is not funny or not happy then lucy is creative.
If lucy is both funny and strong then someone is brave or not curious.
Everyone who is both happy and wise is both curious and old.
Everyone who is not calm is either not old or rich and vice versa.
If someone is both not quiet and wise then paul is both not kind and kind and vice versa.
If someone is either not tall or not calm then someone is creative or patient.
If lucy is rich then someone is tall or not generous.
Everyone who is kind is both not strong and not tall and vice versa.
Everyone who is humble is not strong or not humble.
If mary is either not curious or strong then fred is calm or strong and vice versa.
If someone is either not funny or not quiet then someone is not kind.
Paul is not creative.
Paul is both rich and old.
Mary is either not curious or not brave.
John is happy.
Someone is either curious or not curious.
John is either rich or not tall.
Susan is both not tall and not old.
Paul is not tall or tall. | John is not quiet. | entailment | ((?[X]:((creative(X)<~>happy(X))))<=>(~patient(mary)))&
(![X]:((calm(X)&~kind(X))<=>kind(X)))&
((?[X]:(old(X)))=>((~funny(fred)<~>~brave(fred))))&
(![X]:((funny(X)<~>~happy(X))<=>(funny(X)|quiet(X))))&
(![X]:((generous(X)&~funny(X))<=>(~calm(X)|old(X))))&
((?[X]:((~funny(X)|~happy(X))))=>(creative(lucy)))&
(((funny(lucy)&strong(lucy)))=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((happy(X)&wise(X))=>(curious(X)&old(X))))&
(![X]:(~calm(X)<=>(~old(X)<~>rich(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~kind(paul)&kind(paul))))&
((?[X]:((~tall(X)<~>~calm(X))))=>(?[X]:((creative(X)|patient(X)))))&
((rich(lucy))=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:(kind(X)<=>(~strong(X)&~tall(X))))&
(![X]:(humble(X)=>(~strong(X)|~humble(X))))&
(((~curious(mary)<~>strong(mary)))<=>((calm(fred)|strong(fred))))&
((?[X]:((~funny(X)<~>~quiet(X))))=>(?[X]:(~kind(X))))&
(~creative(paul))&
((rich(paul)&old(paul)))&
((~curious(mary)<~>~brave(mary)))&
(happy(john))&
(?[X]:((curious(X)<~>~curious(X))))&
((rich(john)<~>~tall(john)))&
((~tall(susan)&~old(susan)))&
((~tall(paul)|tall(paul))) | ~quiet(john) | [
"p1",
"p3",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4355654585279992874415304
% SZS output start Proof for 4355654585279992874415304
2. ! [X0] : ((~kind(X0) & calm(X0)) <=> kind(X0)) [input p1]
4. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (quiet(X0) | funny(X0))) [input p3]
5. ! [X0] : ((~funny(X0) & generous(X0)) <=> (old(X0) | ~calm(X0))) [input p4]
20. happy(john) [input p19]
25. quiet(john) [input hypothesis]
42. ! [X0] : (((~kind(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~calm(X0)))) [nnf transformation 2]
43. ! [X0] : (((~kind(X0) & calm(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~calm(X0))) [flattening 42]
45. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (~quiet(X0) & ~funny(X0))) & ((quiet(X0) | funny(X0)) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 4]
46. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (~quiet(X0) & ~funny(X0))) & (quiet(X0) | funny(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [flattening 45]
47. ! [X0] : (((~funny(X0) & generous(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (funny(X0) | ~generous(X0)))) [nnf transformation 5]
48. ! [X0] : (((~funny(X0) & generous(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | funny(X0) | ~generous(X0))) [flattening 47]
80. kind(X0) | kind(X0) | ~calm(X0) [cnf transformation 43]
82. ~kind(X0) | ~kind(X0) [cnf transformation 43]
88. ~quiet(X0) | funny(X0) | ~happy(X0) [cnf transformation 46]
94. ~funny(X0) | calm(X0) [cnf transformation 48]
128. happy(john) [cnf transformation 20]
136. quiet(john) [cnf transformation 25]
139. kind(X0) | ~calm(X0) [duplicate literal removal 80]
140. ~kind(X0) [duplicate literal removal 82]
163. ~calm(X0) [subsumption resolution 139,140]
178. ~funny(X0) [subsumption resolution 94,163]
261. funny(john) | ~happy(john) [resolution 88,136]
263. ~happy(john) [subsumption resolution 261,178]
264. $false [subsumption resolution 263,128]
% SZS output end Proof for 4355654585279992874415304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not patient is wise.
If lucy is either quiet or wise then mary is either creative or curious and vice versa.
Everyone who is wise is not strong or not brave.
Everyone who is either humble or brave is not brave and vice versa.
Everyone who is either not patient or not quiet is either not humble or curious and vice versa.
Everyone who is both humble and happy is either not tall or funny and vice versa.
If someone is not funny then fred is either not tall or not old.
If john is curious then john is not curious or calm.
If someone is either quiet or kind then lucy is both not generous and not wise.
Everyone who is humble is not happy or old.
Everyone who is tall or old is not tall or strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Someone is both creative and not calm.
Someone is not generous.
Alice is happy or funny.
Someone is not calm or strong.
Alice is not old or funny.
Alice is both not quiet and creative. | Fred is humble. | entailment | (![X]:((patient(X)|~patient(X))=>wise(X)))&
(((quiet(lucy)<~>wise(lucy)))<=>((creative(mary)<~>curious(mary))))&
(![X]:(wise(X)=>(~strong(X)|~brave(X))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~generous(X)))&
((happy(alice)|funny(alice)))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice))) | humble(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 220873039392676609350540
% SZS output start Proof for 220873039392676609350540
4. ! [X0] : ((humble(X0) <~> brave(X0)) <=> ~brave(X0)) [input p3]
23. ~humble(fred) [input hypothesis]
39. ! [X0] : ((((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | brave(X0)) & (~brave(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0))))) [nnf transformation 4]
75. ~brave(X0) | humble(X0) | ~brave(X0) [cnf transformation 39]
76. brave(X0) | humble(X0) | brave(X0) [cnf transformation 39]
130. ~humble(fred) [cnf transformation 23]
134. ~brave(X0) | humble(X0) [duplicate literal removal 75]
135. brave(X0) | humble(X0) [duplicate literal removal 76]
158. humble(X0) [subsumption resolution 134,135]
246. $false [subsumption resolution 130,158]
% SZS output end Proof for 220873039392676609350540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not humble is not wise and vice versa.
If someone is funny or not calm then someone is wise or not quiet and vice versa.
Everyone who is either happy or not old is happy or generous and vice versa.
Everyone who is both old and tall is not brave or calm and vice versa.
Everyone who is both curious and quiet is both not old and wise.
If someone is either not rich or funny then john is either not tall or curious.
Everyone who is old or patient is either not generous or not kind and vice versa.
Everyone who is either curious or not curious is not old or not funny.
Everyone who is both not curious and not old is not quiet and vice versa.
If someone is both not creative and not wise then paul is either not quiet or not creative.
If someone is patient or not creative then someone is both not rich and old and vice versa.
Everyone who is both not kind and calm is not funny or not kind and vice versa.
If someone is both calm and curious then someone is quiet or creative.
Everyone who is quiet or kind is not old or not happy.
If someone is both not quiet and not creative then someone is brave or creative.
If someone is either not generous or not strong then someone is both funny and not curious.
Someone is either not curious or not humble.
Alice is either not happy or strong.
Someone is both not patient and brave.
Someone is tall or not kind.
Fred is not wise. | John is patient. | contradiction | (![X]:((~rich(X)&~humble(X))<=>~wise(X)))&
((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((happy(X)<~>~old(X))<=>(happy(X)|generous(X))))&
(![X]:((old(X)&tall(X))<=>(~brave(X)|calm(X))))&
(![X]:((curious(X)&quiet(X))=>(~old(X)&wise(X))))&
((?[X]:((~rich(X)<~>funny(X))))=>((~tall(john)<~>curious(john))))&
(![X]:((old(X)|patient(X))<=>(~generous(X)<~>~kind(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~old(X)|~funny(X))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
((?[X]:((~creative(X)&~wise(X))))=>((~quiet(paul)<~>~creative(paul))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((~rich(X)&old(X)))))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)|~kind(X))))&
((?[X]:((calm(X)&curious(X))))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((quiet(X)|kind(X))=>(~old(X)|~happy(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>(?[X]:((brave(X)|creative(X)))))&
((?[X]:((~generous(X)<~>~strong(X))))=>(?[X]:((funny(X)&~curious(X)))))&
(?[X]:((~curious(X)<~>~humble(X))))&
((~happy(alice)<~>strong(alice)))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:((tall(X)|~kind(X))))&
(~wise(fred)) | patient(john) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 533102715417366181887306
% SZS output start Proof for 533102715417366181887306
3. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (generous(X0) | happy(X0))) [input p2]
4. ! [X0] : ((tall(X0) & old(X0)) <=> (calm(X0) | ~brave(X0))) [input p3]
7. ! [X0] : ((patient(X0) | old(X0)) <=> (~generous(X0) <~> ~kind(X0))) [input p6]
8. ! [X0] : ((curious(X0) <~> ~curious(X0)) => (~funny(X0) | ~old(X0))) [input p7]
9. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p8]
11. ? [X0] : (~creative(X0) | patient(X0)) <=> ? [X0] : (old(X0) & ~rich(X0)) [input p10]
12. ! [X0] : ((calm(X0) & ~kind(X0)) <=> (~kind(X0) | ~funny(X0))) [input p11]
14. ! [X0] : ((kind(X0) | quiet(X0)) => (~happy(X0) | ~old(X0))) [input p13]
22. patient(john) [input hypothesis]
24. ? [X0] : (~creative(X0) | patient(X0)) <=> ? [X1] : (old(X1) & ~rich(X1)) [rectify 11]
31. ! [X0] : ((~funny(X0) | ~old(X0)) | (curious(X0) <=> ~curious(X0))) [ennf transformation 8]
32. ! [X0] : (~funny(X0) | ~old(X0) | (curious(X0) <=> ~curious(X0))) [flattening 31]
35. ! [X0] : ((~happy(X0) | ~old(X0)) | (~kind(X0) & ~quiet(X0))) [ennf transformation 14]
36. ! [X0] : (~happy(X0) | ~old(X0) | (~kind(X0) & ~quiet(X0))) [flattening 35]
46. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 3]
47. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 46]
48. ! [X0] : (((tall(X0) & old(X0)) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | (~tall(X0) | ~old(X0)))) [nnf transformation 4]
49. ! [X0] : (((tall(X0) & old(X0)) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | ~tall(X0) | ~old(X0))) [flattening 48]
51. ! [X0] : (((patient(X0) | old(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~patient(X0) & ~old(X0)))) [nnf transformation 7]
52. ! [X0] : ((patient(X0) | old(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~patient(X0) & ~old(X0)))) [flattening 51]
53. ! [X0] : (~funny(X0) | ~old(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 32]
54. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 54]
57. (? [X0] : (~creative(X0) | patient(X0)) | ! [X1] : (~old(X1) | rich(X1))) & (? [X1] : (old(X1) & ~rich(X1)) | ! [X0] : (creative(X0) & ~patient(X0))) [nnf transformation 24]
58. (? [X0] : (~creative(X0) | patient(X0)) | ! [X1] : (~old(X1) | rich(X1))) & (? [X2] : (old(X2) & ~rich(X2)) | ! [X3] : (creative(X3) & ~patient(X3))) [rectify 57]
59. ? [X0] : (~creative(X0) | patient(X0)) => (~creative(sK2) | patient(sK2)) [choice axiom]
60. ? [X2] : (old(X2) & ~rich(X2)) => (old(sK3) & ~rich(sK3)) [choice axiom]
61. ((~creative(sK2) | patient(sK2)) | ! [X1] : (~old(X1) | rich(X1))) & ((old(sK3) & ~rich(sK3)) | ! [X3] : (creative(X3) & ~patient(X3))) [skolemisation 58,60,59]
62. ! [X0] : (((calm(X0) & ~kind(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~calm(X0) | kind(X0)))) [nnf transformation 12]
63. ! [X0] : (((calm(X0) & ~kind(X0)) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | ~calm(X0) | kind(X0))) [flattening 62]
90. generous(X0) | happy(X0) | happy(X0) | old(X0) [cnf transformation 47]
92. ~generous(X0) | happy(X0) | ~old(X0) [cnf transformation 47]
93. old(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 47]
97. ~calm(X0) | old(X0) [cnf transformation 49]
108. kind(X0) | generous(X0) | ~old(X0) [cnf transformation 52]
112. ~funny(X0) | ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 53]
113. ~funny(X0) | ~old(X0) | curious(X0) | curious(X0) [cnf transformation 53]
116. ~old(X0) | quiet(X0) [cnf transformation 55]
121. old(sK3) | ~patient(X3) [cnf transformation 61]
125. ~kind(X0) | funny(X0) [cnf transformation 63]
127. calm(X0) | funny(X0) [cnf transformation 63]
130. ~happy(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 36]
145. patient(john) [cnf transformation 22]
146. ~funny(X0) | ~old(X0) | ~curious(X0) [duplicate literal removal 112]
147. ~old(X0) | ~funny(X0) | curious(X0) [duplicate literal removal 113]
148. generous(X0) | happy(X0) | old(X0) [duplicate literal removal 90]
149. ~happy(X0) | old(X0) [duplicate literal removal 93]
182. generous(X0) | old(X0) [subsumption resolution 148,149]
202. kind(X0) | generous(X0) [subsumption resolution 108,182]
203. ~old(X0) | ~funny(X0) [subsumption resolution 146,147]
233. 20 <=> old(sK3) [avatar definition]
235. old(sK3) <- (20) [avatar component clause 233]
238. 21 <=> ! [X3] : ~patient(X3) [avatar definition]
239. ~patient(X3) <- (21) [avatar component clause 238]
240. 21 | 20 [avatar split clause 121,233,238]
260. ~happy(X0) | ~old(X0) [subsumption resolution 130,116]
261. ~happy(X0) [subsumption resolution 260,149]
316. old(X1) | funny(X1) [resolution 127,97]
332. generous(X0) | funny(X0) [resolution 202,125]
333. ~funny(sK3) <- (20) [resolution 203,235]
446. funny(X1) | happy(X1) | ~old(X1) [resolution 332,92]
448. funny(X1) | ~old(X1) [subsumption resolution 446,261]
449. funny(X1) [subsumption resolution 448,316]
452. $false <- (20) [resolution 449,333]
453. ~20 [avatar contradiction clause 452]
457. $false <- (21) [resolution 239,145]
458. ~21 [avatar contradiction clause 457]
459. $false [avatar sat refutation 240,453,458]
% SZS output end Proof for 533102715417366181887306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not rich then someone is calm and vice versa.
Everyone who is old or kind is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
If someone is not calm or tall then someone is either not humble or not strong and vice versa.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is either not generous or quiet.
Lucy is not funny or strong.
John is not kind or not funny. | Mary is generous. | contradiction | ((?[X]:((brave(X)<~>~rich(X))))<=>(?[X]:(calm(X))))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~funny(lucy)|strong(lucy)))&
((~kind(john)|~funny(john))) | generous(mary) | [
"p1",
"p4",
"p6",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8791471919283832938145357
% SZS output start Proof for 8791471919283832938145357
2. ! [X0] : ((kind(X0) | old(X0)) <=> old(X0)) [input p1]
5. ! [X0] : (funny(X0) <=> (generous(X0) & ~creative(X0))) [input p4]
7. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> rich(X0)) [input p6]
8. ? [X0] : (creative(X0) | ~strong(X0)) <=> ~rich(mary) [input p7]
13. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p12]
15. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p14]
24. generous(mary) [input hypothesis]
35. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 13]
42. ! [X0] : (((kind(X0) | old(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 2]
43. ! [X0] : ((kind(X0) | old(X0) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [flattening 42]
45. ! [X0] : ((funny(X0) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | ~funny(X0))) [nnf transformation 5]
46. ! [X0] : ((funny(X0) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | ~funny(X0))) [flattening 45]
49. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [nnf transformation 7]
50. ! [X0] : ((~humble(X0) | ~happy(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & happy(X0)))) [flattening 49]
51. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X0] : (~creative(X0) & strong(X0))) [nnf transformation 8]
52. (? [X0] : (creative(X0) | ~strong(X0)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [rectify 51]
53. ? [X0] : (creative(X0) | ~strong(X0)) => (creative(sK2) | ~strong(sK2)) [choice axiom]
54. ((creative(sK2) | ~strong(sK2)) | rich(mary)) & (~rich(mary) | ! [X1] : (~creative(X1) & strong(X1))) [skolemisation 52,53]
61. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 15]
62. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 61]
79. ~kind(X0) | old(X0) [cnf transformation 43]
86. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 46]
94. humble(X0) | rich(X0) [cnf transformation 50]
97. ~rich(mary) | ~creative(X1) [cnf transformation 54]
109. ~humble(X0) | ~old(X0) [cnf transformation 35]
110. ~funny(X0) | ~old(X0) [cnf transformation 35]
114. old(X0) | kind(X0) [cnf transformation 62]
130. generous(mary) [cnf transformation 24]
193. 14 <=> rich(mary) [avatar definition]
194. ~rich(mary) <- (~14) [avatar component clause 193]
206. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
207. ~creative(X1) <- (17) [avatar component clause 206]
208. 17 | ~14 [avatar split clause 97,193,206]
252. old(X0) [subsumption resolution 114,79]
329. ~old(X0) | rich(X0) [resolution 109,94]
332. rich(X0) [subsumption resolution 329,252]
336. $false <- (~14) [resolution 332,194]
337. 14 [avatar contradiction clause 336]
348. funny(mary) | creative(mary) [resolution 86,130]
349. funny(mary) <- (17) [subsumption resolution 348,207]
350. ~old(mary) <- (17) [resolution 349,110]
353. $false <- (17) [subsumption resolution 350,252]
354. ~17 [avatar contradiction clause 353]
355. $false [avatar sat refutation 208,337,354]
% SZS output end Proof for 8791471919283832938145357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both humble and not tall is either not tall or not curious.
If mary is either not old or happy then paul is both happy and creative.
Everyone who is both not creative and not kind is not old and vice versa.
If paul is either not calm or not tall then someone is either not strong or not brave and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either not generous or not humble is either not old or quiet and vice versa.
Everyone who is creative or happy is not humble and vice versa.
Everyone who is either not kind or curious is either creative or humble.
If someone is generous or brave then mary is not curious and vice versa.
Everyone who is brave is either humble or not rich and vice versa.
If someone is both not rich and not humble then someone is generous and vice versa.
If someone is both not wise and not creative then someone is either brave or creative.
If alice is either brave or not generous then someone is brave and vice versa.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
Susan is not kind or humble.
Mary is both not creative and not brave.
Someone is happy or not calm.
Someone is either happy or strong.
Alice is either not curious or not kind. | Paul is quiet. | entailment | (![X]:((humble(X)&~tall(X))=>(~tall(X)<~>~curious(X))))&
(((~old(mary)<~>happy(mary)))=>((happy(paul)&creative(paul))))&
(![X]:((~creative(X)&~kind(X))<=>~old(X)))&
(((~calm(paul)<~>~tall(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)|happy(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>(~curious(mary)))&
(![X]:(brave(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(((brave(alice)<~>~generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~kind(susan)|humble(susan)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)<~>strong(X))))&
((~curious(alice)<~>~kind(alice))) | quiet(paul) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 103369272189400096089621
% SZS output start Proof for 103369272189400096089621
2. (~old(mary) <~> happy(mary)) => (creative(paul) & happy(paul)) [input p1]
3. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~old(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : ((happy(X0) | creative(X0)) <=> ~humble(X0)) [input p6]
14. ! [X0] : ((old(X0) <~> humble(X0)) => generous(X0)) [input p13]
22. ~quiet(paul) [input hypothesis]
28. (creative(paul) & happy(paul)) | (~old(mary) <=> happy(mary)) [ennf transformation 2]
31. ! [X0] : (generous(X0) | (old(X0) <=> humble(X0))) [ennf transformation 14]
34. (creative(paul) & happy(paul)) | ((~old(mary) | ~happy(mary)) & (happy(mary) | old(mary))) [nnf transformation 28]
35. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | (kind(X0) | creative(X0)))) [nnf transformation 3]
36. ! [X0] : (((~kind(X0) & ~creative(X0)) | old(X0)) & (~old(X0) | kind(X0) | creative(X0))) [flattening 35]
41. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 5]
42. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0)))) & (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 6]
43. ! [X0] : (((happy(X0) | creative(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [nnf transformation 7]
44. ! [X0] : ((happy(X0) | creative(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & ~creative(X0)))) [flattening 43]
64. ! [X0] : (generous(X0) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) [nnf transformation 31]
76. creative(paul) | happy(mary) | old(mary) [cnf transformation 34]
77. creative(paul) | ~old(mary) | ~happy(mary) [cnf transformation 34]
79. ~creative(X0) | old(X0) [cnf transformation 36]
89. ~happy(X0) | old(X0) [cnf transformation 41]
90. ~old(X0) | happy(X0) [cnf transformation 41]
92. ~generous(X0) | ~old(X0) | quiet(X0) | humble(X0) [cnf transformation 42]
99. ~creative(X0) | ~humble(X0) [cnf transformation 44]
122. ~old(X0) | humble(X0) | generous(X0) [cnf transformation 64]
136. ~quiet(paul) [cnf transformation 22]
139. 1 <=> happy(mary) [avatar definition]
140. happy(mary) <- (1) [avatar component clause 139]
141. ~happy(mary) <- (~1) [avatar component clause 139]
143. 2 <=> old(mary) [avatar definition]
144. old(mary) <- (2) [avatar component clause 143]
145. ~old(mary) <- (~2) [avatar component clause 143]
147. 3 <=> creative(paul) [avatar definition]
149. creative(paul) <- (3) [avatar component clause 147]
150. ~1 | ~2 | 3 [avatar split clause 77,147,143,139]
151. 2 | 1 | 3 [avatar split clause 76,147,139,143]
300. happy(mary) <- (2) [resolution 90,144]
302. $false <- (~1, 2) [subsumption resolution 300,141]
303. 1 | ~2 [avatar contradiction clause 302]
304. old(mary) <- (1) [resolution 140,89]
305. $false <- (1, ~2) [subsumption resolution 304,145]
306. ~1 | 2 [avatar contradiction clause 305]
307. old(paul) <- (3) [resolution 149,79]
309. ~humble(paul) <- (3) [resolution 99,149]
394. humble(paul) | generous(paul) <- (3) [resolution 122,307]
398. generous(paul) <- (3) [subsumption resolution 394,309]
504. ~old(paul) | quiet(paul) | humble(paul) <- (3) [resolution 398,92]
505. quiet(paul) | humble(paul) <- (3) [subsumption resolution 504,307]
506. humble(paul) <- (3) [subsumption resolution 505,136]
507. $false <- (3) [subsumption resolution 506,309]
508. ~3 [avatar contradiction clause 507]
509. $false [avatar sat refutation 150,151,303,306,508]
% SZS output end Proof for 103369272189400096089621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or strong then fred is brave.
If someone is not humble or happy then someone is not brave or creative and vice versa.
Everyone who is generous or not tall is either kind or not strong.
If someone is not old then lucy is either not curious or not generous and vice versa.
Everyone who is either tall or kind is either kind or not kind and vice versa.
Everyone who is either patient or not strong is not patient or old and vice versa.
Everyone who is either calm or not strong is either kind or not brave and vice versa.
Everyone who is both not patient and not funny is both old and not quiet.
Everyone who is not quiet or wise is not strong or funny and vice versa.
If someone is either curious or tall then someone is either not calm or rich.
If lucy is creative then someone is not quiet.
Everyone who is creative or not brave is not funny or patient and vice versa.
Everyone who is either not calm or curious is both not tall and wise.
Everyone who is kind or not creative is either not curious or not quiet and vice versa.
Everyone who is wise or not humble is not creative or not calm and vice versa.
Everyone who is either calm or not quiet is not quiet or kind and vice versa.
Lucy is both tall and not patient.
Fred is not happy.
Someone is both not rich and not creative.
Alice is both brave and curious.
Mary is quiet or tall.
Someone is not kind.
Lucy is either happy or patient. | Fred is strong. | entailment | ((?[X]:((curious(X)|strong(X))))=>(brave(fred)))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:((generous(X)|~tall(X))=>(kind(X)<~>~strong(X))))&
((?[X]:(~old(X)))<=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
((creative(lucy))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|~brave(X))<=>(~funny(X)|patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~tall(X)&wise(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((wise(X)|~humble(X))<=>(~creative(X)|~calm(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)|kind(X))))&
((tall(lucy)&~patient(lucy)))&
(~happy(fred))&
(?[X]:((~rich(X)&~creative(X))))&
((brave(alice)&curious(alice)))&
((quiet(mary)|tall(mary)))&
(?[X]:(~kind(X)))&
((happy(lucy)<~>patient(lucy))) | strong(fred) | [
"p0",
"p2",
"p4",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3725216695902392789167274
% SZS output start Proof for 3725216695902392789167274
1. ? [X0] : (strong(X0) | curious(X0)) => brave(fred) [input p0]
3. ! [X0] : ((~tall(X0) | generous(X0)) => (kind(X0) <~> ~strong(X0))) [input p2]
5. ! [X0] : ((tall(X0) <~> kind(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4]
7. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p6]
16. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (kind(X0) | ~quiet(X0))) [input p15]
20. curious(alice) & brave(alice) [input p19]
24. ~strong(fred) [input hypothesis]
27. brave(fred) | ! [X0] : (~strong(X0) & ~curious(X0)) [ennf transformation 1]
28. ! [X0] : ((kind(X0) <~> ~strong(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 3]
39. ! [X0] : (((strong(X0) | ~kind(X0)) & (~strong(X0) | kind(X0))) | (tall(X0) & ~generous(X0))) [nnf transformation 28]
44. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 5]
47. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 7]
63. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 16]
64. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 63]
70. brave(fred) | ~curious(X0) [cnf transformation 27]
79. ~kind(X0) | strong(X0) | tall(X0) [cnf transformation 39]
89. kind(X0) | tall(X0) | kind(X0) | kind(X0) [cnf transformation 44]
90. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 44]
99. ~brave(X0) | kind(X0) | calm(X0) | strong(X0) [cnf transformation 47]
135. kind(X0) | ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 64]
139. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 64]
147. curious(alice) [cnf transformation 20]
152. ~strong(fred) [cnf transformation 24]
153. kind(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 135]
154. ~calm(X0) | quiet(X0) [duplicate literal removal 139]
162. kind(X0) | tall(X0) [duplicate literal removal 89]
163. ~kind(X0) | ~tall(X0) [duplicate literal removal 90]
169. 2 <=> brave(fred) [avatar definition]
171. brave(fred) <- (2) [avatar component clause 169]
174. 3 <=> ! [X0] : ~curious(X0) [avatar definition]
175. ~curious(X0) <- (3) [avatar component clause 174]
176. 3 | 2 [avatar split clause 70,169,174]
256. ~calm(X0) | kind(X0) [subsumption resolution 153,154]
280. strong(X0) | tall(X0) | tall(X0) [resolution 79,162]
281. tall(X0) | strong(X0) [duplicate literal removal 280]
316. $false <- (3) [resolution 175,147]
317. ~3 [avatar contradiction clause 316]
380. kind(fred) | calm(fred) | strong(fred) <- (2) [resolution 99,171]
383. kind(fred) | calm(fred) <- (2) [subsumption resolution 380,152]
384. kind(fred) <- (2) [subsumption resolution 383,256]
394. ~tall(fred) <- (2) [resolution 384,163]
532. strong(fred) <- (2) [resolution 394,281]
533. $false <- (2) [subsumption resolution 532,152]
534. ~2 [avatar contradiction clause 533]
535. $false [avatar sat refutation 176,317,534]
% SZS output end Proof for 3725216695902392789167274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is quiet and vice versa. Everyone who is strong is not generous. If someone is tall or patient then someone is old or not generous and vice versa. If john is generous then someone is either not tall or kind. Everyone who is either kind or not wise is either not funny or not curious. Everyone who is old is either generous or not generous and vice versa. Everyone who is both not kind and old is not curious and vice versa. If john is either not strong or not creative then mary is not tall or happy. If alice is both kind and brave then alice is not kind or happy. Everyone who is old or not generous is either kind or wise and vice versa. Everyone who is both not calm and creative is not old and vice versa. Everyone who is not curious is either not strong or not curious. If paul is not tall or not rich then paul is humble or not tall. If someone is either not creative or quiet then someone is not curious or kind. Everyone who is either calm or not happy is both old and not calm and vice versa. Everyone who is both wise and not rich is not wise or calm and vice versa. Someone is either not creative or wise. Someone is tall or brave. Someone is humble. Someone is not generous or not creative. Mary is not generous or not rich. | John is not rich. | neutral | (![X]:(~happy(X)<=>quiet(X)))&
(![X]:(strong(X)=>~generous(X)))&
((?[X]:((tall(X)|patient(X))))<=>(?[X]:((old(X)|~generous(X)))))&
((generous(john))=>(?[X]:((~tall(X)<~>kind(X)))))&
(![X]:((kind(X)<~>~wise(X))=>(~funny(X)<~>~curious(X))))&
(![X]:(old(X)<=>(generous(X)<~>~generous(X))))&
(![X]:((~kind(X)&old(X))<=>~curious(X)))&
(((~strong(john)<~>~creative(john)))=>((~tall(mary)|happy(mary))))&
(((kind(alice)&brave(alice)))=>((~kind(alice)|happy(alice))))&
(![X]:((old(X)|~generous(X))<=>(kind(X)<~>wise(X))))&
(![X]:((~calm(X)&creative(X))<=>~old(X)))&
(![X]:(~curious(X)=>(~strong(X)<~>~curious(X))))&
(((~tall(paul)|~rich(paul)))=>((humble(paul)|~tall(paul))))&
((?[X]:((~creative(X)<~>quiet(X))))=>(?[X]:((~curious(X)|kind(X)))))&
(![X]:((calm(X)<~>~happy(X))<=>(old(X)&~calm(X))))&
(![X]:((wise(X)&~rich(X))<=>(~wise(X)|calm(X))))&
(?[X]:((~creative(X)<~>wise(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((~generous(X)|~creative(X))))&
((~generous(mary)|~rich(mary))) | ~rich(john) | [] | null | 0 |
Everyone who is strong or not tall is both creative and wise.
If someone is not wise or old then someone is either quiet or calm.
Everyone who is happy is both not tall and funny and vice versa.
Everyone who is both not patient and not tall is either brave or strong.
Everyone who is humble or not quiet is brave.
Everyone who is happy is both wise and not calm and vice versa.
If someone is humble then lucy is not generous or not wise and vice versa.
If someone is either not patient or curious then someone is both curious and not generous and vice versa.
If someone is either humble or not happy then alice is either not rich or not happy and vice versa.
If someone is both happy and not kind then someone is both not calm and not humble.
Everyone who is not kind or rich is funny or not quiet.
If someone is both not old and not generous then john is funny or humble.
If alice is both kind and not tall then lucy is not kind and vice versa.
If someone is not creative or calm then fred is not curious or not tall and vice versa.
If susan is both not kind and not curious then someone is quiet and vice versa.
Everyone who is both curious and not strong is both not humble and wise and vice versa.
Someone is both generous and humble.
John is either not wise or wise.
John is either not kind or happy.
Someone is not old.
Mary is either not kind or old.
Someone is either kind or not creative.
Lucy is not funny.
Fred is patient. | Mary is not kind. | neutral | (![X]:((strong(X)|~tall(X))=>(creative(X)&wise(X))))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:(happy(X)<=>(~tall(X)&funny(X))))&
(![X]:((~patient(X)&~tall(X))=>(brave(X)<~>strong(X))))&
(![X]:((humble(X)|~quiet(X))=>brave(X)))&
(![X]:(happy(X)<=>(wise(X)&~calm(X))))&
((?[X]:(humble(X)))<=>((~generous(lucy)|~wise(lucy))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((curious(X)&~generous(X)))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~rich(alice)<~>~happy(alice))))&
((?[X]:((happy(X)&~kind(X))))=>(?[X]:((~calm(X)&~humble(X)))))&
(![X]:((~kind(X)|rich(X))=>(funny(X)|~quiet(X))))&
((?[X]:((~old(X)&~generous(X))))=>((funny(john)|humble(john))))&
(((kind(alice)&~tall(alice)))<=>(~kind(lucy)))&
((?[X]:((~creative(X)|calm(X))))<=>((~curious(fred)|~tall(fred))))&
(((~kind(susan)&~curious(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((curious(X)&~strong(X))<=>(~humble(X)&wise(X))))&
(?[X]:((generous(X)&humble(X))))&
((~wise(john)<~>wise(john)))&
((~kind(john)<~>happy(john)))&
(?[X]:(~old(X)))&
((~kind(mary)<~>old(mary)))&
(?[X]:((kind(X)<~>~creative(X))))&
(~funny(lucy))&
(patient(fred)) | ~kind(mary) | [] | null | 0 |
Everyone who is both calm and generous is not strong or not brave. Everyone who is both generous and not calm is both brave and happy and vice versa. Everyone who is quiet or not brave is either not wise or not brave. Everyone who is not tall or not brave is both not creative and kind and vice versa. Everyone who is wise or tall is not tall. If alice is not funny then someone is either quiet or not tall and vice versa. Everyone who is either not curious or old is both not humble and kind. If john is either not wise or patient then fred is both curious and generous. Everyone who is not happy is not wise or not brave. Everyone who is not tall is curious or brave. If alice is not kind then susan is not calm or not wise and vice versa. If fred is quiet then someone is old. Everyone who is generous is not creative and vice versa. If someone is not calm then someone is not patient and vice versa. Everyone who is both quiet and kind is humble or not generous and vice versa. If someone is not patient then john is not happy or not strong and vice versa. Someone is not humble. Someone is either not generous or not curious. Someone is not tall. Alice is not calm or old. Paul is both not calm and curious. Alice is either wise or brave. Someone is kind or generous. | Alice is wise. | neutral | (![X]:((calm(X)&generous(X))=>(~strong(X)|~brave(X))))&
(![X]:((generous(X)&~calm(X))<=>(brave(X)&happy(X))))&
(![X]:((quiet(X)|~brave(X))=>(~wise(X)<~>~brave(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~creative(X)&kind(X))))&
(![X]:((wise(X)|tall(X))=>~tall(X)))&
((~funny(alice))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:((~curious(X)<~>old(X))=>(~humble(X)&kind(X))))&
(((~wise(john)<~>patient(john)))=>((curious(fred)&generous(fred))))&
(![X]:(~happy(X)=>(~wise(X)|~brave(X))))&
(![X]:(~tall(X)=>(curious(X)|brave(X))))&
((~kind(alice))<=>((~calm(susan)|~wise(susan))))&
((quiet(fred))=>(?[X]:(old(X))))&
(![X]:(generous(X)<=>~creative(X)))&
((?[X]:(~calm(X)))<=>(?[X]:(~patient(X))))&
(![X]:((quiet(X)&kind(X))<=>(humble(X)|~generous(X))))&
((?[X]:(~patient(X)))<=>((~happy(john)|~strong(john))))&
(?[X]:(~humble(X)))&
(?[X]:((~generous(X)<~>~curious(X))))&
(?[X]:(~tall(X)))&
((~calm(alice)|old(alice)))&
((~calm(paul)&curious(paul)))&
((wise(alice)<~>brave(alice)))&
(?[X]:((kind(X)|generous(X)))) | wise(alice) | [] | null | 0 |
Everyone who is happy or not curious is both generous and not creative. Everyone who is not old is either not kind or rich. If fred is either not strong or not generous then someone is brave and vice versa. Everyone who is either strong or not creative is either not brave or patient. Everyone who is either not curious or strong is not generous. Everyone who is both strong and not quiet is not kind or generous and vice versa. Everyone who is brave or not generous is both calm and patient and vice versa. Everyone who is either not generous or happy is generous or calm and vice versa. Everyone who is patient or happy is funny or calm. If john is creative or old then fred is both not curious and not calm and vice versa. If mary is not calm or not wise then mary is not quiet. If john is humble then paul is both calm and not funny. Everyone who is not funny or not wise is humble or quiet and vice versa. If john is either not humble or not funny then someone is both tall and strong. Everyone who is wise or old is both not curious and humble and vice versa. Everyone who is not patient or creative is either curious or not curious. Someone is either humble or not curious. Someone is either not humble or not quiet. Susan is quiet. Fred is both funny and not calm. Someone is not calm or tall. Someone is not wise or not strong. Mary is not rich or not strong. Paul is either tall or not patient. | Susan is generous. | contradiction | (![X]:((happy(X)|~curious(X))=>(generous(X)&~creative(X))))&
(![X]:(~old(X)=>(~kind(X)<~>rich(X))))&
(((~strong(fred)<~>~generous(fred)))<=>(?[X]:(brave(X))))&
(![X]:((strong(X)<~>~creative(X))=>(~brave(X)<~>patient(X))))&
(![X]:((~curious(X)<~>strong(X))=>~generous(X)))&
(![X]:((strong(X)&~quiet(X))<=>(~kind(X)|generous(X))))&
(![X]:((brave(X)|~generous(X))<=>(calm(X)&patient(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(generous(X)|calm(X))))&
(![X]:((patient(X)|happy(X))=>(funny(X)|calm(X))))&
(((creative(john)|old(john)))<=>((~curious(fred)&~calm(fred))))&
(((~calm(mary)|~wise(mary)))=>(~quiet(mary)))&
((humble(john))=>((calm(paul)&~funny(paul))))&
(![X]:((~funny(X)|~wise(X))<=>(humble(X)|quiet(X))))&
(((~humble(john)<~>~funny(john)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((wise(X)|old(X))<=>(~curious(X)&humble(X))))&
(![X]:((~patient(X)|creative(X))=>(curious(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(quiet(susan))&
((funny(fred)&~calm(fred)))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((~wise(X)|~strong(X))))&
((~rich(mary)|~strong(mary)))&
((tall(paul)<~>~patient(paul))) | generous(susan) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2415087950774923941901323
% SZS output start Proof for 2415087950774923941901323
6. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (generous(X0) | ~kind(X0))) [input p5]
19. quiet(susan) [input p18]
25. generous(susan) [input hypothesis]
43. ! [X0] : (((~quiet(X0) & strong(X0)) | (~generous(X0) & kind(X0))) & ((generous(X0) | ~kind(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) & strong(X0)) | (~generous(X0) & kind(X0))) & (generous(X0) | ~kind(X0) | quiet(X0) | ~strong(X0))) [flattening 43]
90. ~quiet(X0) | ~generous(X0) [cnf transformation 44]
134. quiet(susan) [cnf transformation 19]
142. generous(susan) [cnf transformation 25]
293. ~generous(susan) [resolution 90,134]
294. $false [subsumption resolution 293,142]
% SZS output end Proof for 2415087950774923941901323
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either brave or creative and vice versa. Everyone who is happy or funny is patient or not wise and vice versa. If someone is tall then paul is strong or creative. Everyone who is both calm and quiet is either not brave or happy. Everyone who is both not quiet and not humble is not wise or not calm and vice versa. Everyone who is curious or wise is both not old and not kind and vice versa. If someone is either happy or not brave then paul is either tall or not quiet and vice versa. Everyone who is either funny or not funny is not wise and vice versa. Everyone who is either not funny or brave is either not patient or not quiet and vice versa. If alice is not wise then alice is both not creative and not patient and vice versa. Everyone who is not wise is not brave or not rich. If alice is funny then susan is not patient or rich and vice versa. Everyone who is kind or not generous is both old and not generous and vice versa. Everyone who is old or not funny is either old or not quiet and vice versa. If mary is both brave and not quiet then mary is either generous or not wise and vice versa. Lucy is not wise or not quiet. Fred is not funny. Lucy is not humble. Someone is either not creative or strong. Someone is not kind. Mary is not rich or patient. | Lucy is patient. | neutral | (![X]:(~calm(X)<=>(brave(X)<~>creative(X))))&
(![X]:((happy(X)|funny(X))<=>(patient(X)|~wise(X))))&
((?[X]:(tall(X)))=>((strong(paul)|creative(paul))))&
(![X]:((calm(X)&quiet(X))=>(~brave(X)<~>happy(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~wise(X)|~calm(X))))&
(![X]:((curious(X)|wise(X))<=>(~old(X)&~kind(X))))&
((?[X]:((happy(X)<~>~brave(X))))<=>((tall(paul)<~>~quiet(paul))))&
(![X]:((funny(X)<~>~funny(X))<=>~wise(X)))&
(![X]:((~funny(X)<~>brave(X))<=>(~patient(X)<~>~quiet(X))))&
((~wise(alice))<=>((~creative(alice)&~patient(alice))))&
(![X]:(~wise(X)=>(~brave(X)|~rich(X))))&
((funny(alice))<=>((~patient(susan)|rich(susan))))&
(![X]:((kind(X)|~generous(X))<=>(old(X)&~generous(X))))&
(![X]:((old(X)|~funny(X))<=>(old(X)<~>~quiet(X))))&
(((brave(mary)&~quiet(mary)))<=>((generous(mary)<~>~wise(mary))))&
((~wise(lucy)|~quiet(lucy)))&
(~funny(fred))&
(~humble(lucy))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:(~kind(X)))&
((~rich(mary)|patient(mary))) | patient(lucy) | [] | null | 0 |
Everyone who is both old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Alice is generous. | entailment | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | generous(alice) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2380172267255604730995016
% SZS output start Proof for 2380172267255604730995016
2. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X0] : (~happy(X0) <~> creative(X0)) [input p1]
3. ! [X0] : ((kind(X0) & funny(X0)) => ~strong(X0)) [input p2]
4. ! [X0] : ((calm(X0) | tall(X0)) <=> (creative(X0) & ~calm(X0))) [input p3]
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> (quiet(X0) & curious(X0))) [input p6]
12. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> strong(X0)) [input p11]
13. ! [X0] : ((wise(X0) | tall(X0)) <=> (happy(X0) | ~quiet(X0))) [input p12]
14. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p13]
15. ! [X0] : ((~brave(X0) & ~happy(X0)) => ~tall(X0)) [input p14]
22. ~generous(alice) [input hypothesis]
23. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X1] : (~happy(X1) <~> creative(X1)) [rectify 2]
27. ! [X0] : (~strong(X0) | (~kind(X0) | ~funny(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | ~kind(X0) | ~funny(X0)) [flattening 27]
33. ! [X0] : (~tall(X0) | (brave(X0) | happy(X0))) [ennf transformation 15]
34. ! [X0] : (~tall(X0) | brave(X0) | happy(X0)) [flattening 33]
35. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X1] : ((~creative(X1) | happy(X1)) & (creative(X1) | ~happy(X1))) | ! [X0] : (~curious(X0) | brave(X0))) [nnf transformation 23]
36. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) | ! [X3] : (~curious(X3) | brave(X3))) [rectify 35]
37. ? [X0] : (curious(X0) & ~brave(X0)) => (curious(sK0) & ~brave(sK0)) [choice axiom]
38. ? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) => ((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) [choice axiom]
39. ((curious(sK0) & ~brave(sK0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) | ! [X3] : (~curious(X3) | brave(X3))) [skolemisation 36,38,37]
40. ! [X0] : (((calm(X0) | tall(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : ((calm(X0) | tall(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [flattening 40]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
46. ! [X0] : (((~generous(X0) & brave(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | generous(X0) | ~brave(X0))) [flattening 46]
55. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~strong(X0)) & (strong(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 12]
56. ! [X0] : (((wise(X0) | tall(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~wise(X0) & ~tall(X0)))) [nnf transformation 13]
57. ! [X0] : ((wise(X0) | tall(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | (~wise(X0) & ~tall(X0)))) [flattening 56]
58. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 14]
59. ! [X0] : ((~creative(X0) | ~strong(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [flattening 58]
73. ~brave(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
75. curious(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
77. ~kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 28]
79. ~calm(X0) | ~calm(X0) [cnf transformation 41]
82. calm(X0) | tall(X0) | ~creative(X0) | calm(X0) [cnf transformation 41]
89. ~strong(X0) | funny(X0) [cnf transformation 45]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | happy(X0) | happy(X0) | strong(X0) [cnf transformation 45]
94. ~brave(X0) | generous(X0) | quiet(X0) [cnf transformation 47]
95. ~quiet(X0) | brave(X0) | ~curious(X0) [cnf transformation 47]
108. ~strong(X0) | kind(X0) | quiet(X0) [cnf transformation 55]
110. happy(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 57]
116. funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 59]
120. ~tall(X0) | brave(X0) | happy(X0) [cnf transformation 34]
134. ~generous(alice) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
136. ~funny(X0) | happy(X0) | strong(X0) [duplicate literal removal 92]
137. ~calm(X0) [duplicate literal removal 79]
138. ~creative(X0) | tall(X0) | calm(X0) [duplicate literal removal 82]
143. 2 <=> curious(sK0) [avatar definition]
145. curious(sK0) <- (2) [avatar component clause 143]
148. 3 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
149. creative(X1) | happy(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 75,143,148]
152. 4 <=> brave(sK0) [avatar definition]
154. ~brave(sK0) <- (~4) [avatar component clause 152]
156. 3 | ~4 [avatar split clause 73,152,148]
240. ~quiet(X0) | ~tall(X0) [subsumption resolution 110,135]
242. ~curious(X0) | funny(X0) [subsumption resolution 116,89]
243. ~tall(X0) | brave(X0) [subsumption resolution 120,135]
345. creative(X1) <- (3) [subsumption resolution 149,135]
380. tall(X0) | calm(X0) <- (3) [resolution 138,345]
382. tall(X0) <- (3) [subsumption resolution 380,137]
395. brave(X0) <- (3) [resolution 382,243]
455. quiet(X0) | generous(X0) <- (3) [resolution 395,94]
462. generous(X4) | ~tall(X4) <- (3) [resolution 455,240]
465. generous(X4) <- (3) [subsumption resolution 462,382]
467. $false <- (3) [resolution 465,134]
468. ~3 [avatar contradiction clause 467]
472. funny(sK0) <- (2) [resolution 145,242]
478. 43 <=> strong(sK0) [avatar definition]
479. strong(sK0) <- (43) [avatar component clause 478]
483. 44 <=> funny(sK0) [avatar definition]
485. funny(sK0) <- (44) [avatar component clause 483]
489. 44 | ~2 [avatar split clause 472,143,483]
497. happy(sK0) | strong(sK0) <- (44) [resolution 485,136]
500. strong(sK0) <- (44) [subsumption resolution 497,135]
501. 43 | ~44 [avatar split clause 500,483,478]
502. kind(sK0) | quiet(sK0) <- (43) [resolution 479,108]
505. 45 <=> quiet(sK0) [avatar definition]
507. quiet(sK0) <- (45) [avatar component clause 505]
509. 46 <=> kind(sK0) [avatar definition]
511. kind(sK0) <- (46) [avatar component clause 509]
512. 45 | 46 | ~43 [avatar split clause 502,478,509,505]
533. ~strong(sK0) | ~funny(sK0) <- (46) [resolution 511,77]
534. ~funny(sK0) <- (43, 46) [subsumption resolution 533,479]
535. $false <- (43, 44, 46) [subsumption resolution 534,485]
536. ~43 | ~44 | ~46 [avatar contradiction clause 535]
540. brave(sK0) | ~curious(sK0) <- (45) [resolution 507,95]
543. ~curious(sK0) <- (~4, 45) [subsumption resolution 540,154]
544. $false <- (2, ~4, 45) [subsumption resolution 543,145]
545. ~2 | 4 | ~45 [avatar contradiction clause 544]
546. $false [avatar sat refutation 150,156,468,489,501,512,536,545]
% SZS output end Proof for 2380172267255604730995016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or kind is kind and vice versa.
If someone is either happy or not old then someone is either not old or not brave and vice versa.
Everyone who is both not rich and tall is both kind and not quiet.
Everyone who is both wise and not happy is either curious or creative.
Everyone who is either rich or not happy is either not old or brave.
If someone is not wise then lucy is either kind or curious and vice versa.
If someone is both not funny and not happy then someone is not curious or quiet and vice versa.
Everyone who is not happy or not calm is not quiet and vice versa.
Everyone who is either funny or not old is both not tall and not quiet and vice versa.
If someone is either old or wise then alice is both wise and creative.
Everyone who is both strong and not brave is not strong and vice versa.
Everyone who is either not generous or calm is not generous and vice versa.
If someone is both rich and generous then lucy is not rich.
Everyone who is both not rich and not old is wise or humble.
Everyone who is not strong or not creative is not curious and vice versa.
If lucy is either calm or not quiet then susan is not generous and vice versa.
Susan is both curious and not humble.
Someone is either humble or kind.
Someone is either calm or not rich.
Someone is both not happy and not patient.
John is not wise. | Lucy is not rich. | neutral | (![X]:((funny(X)|kind(X))<=>kind(X)))&
((?[X]:((happy(X)<~>~old(X))))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:((~rich(X)&tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((wise(X)&~happy(X))=>(curious(X)<~>creative(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~old(X)<~>brave(X))))&
((?[X]:(~wise(X)))<=>((kind(lucy)<~>curious(lucy))))&
((?[X]:((~funny(X)&~happy(X))))<=>(?[X]:((~curious(X)|quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~old(X))<=>(~tall(X)&~quiet(X))))&
((?[X]:((old(X)<~>wise(X))))=>((wise(alice)&creative(alice))))&
(![X]:((strong(X)&~brave(X))<=>~strong(X)))&
(![X]:((~generous(X)<~>calm(X))<=>~generous(X)))&
((?[X]:((rich(X)&generous(X))))=>(~rich(lucy)))&
(![X]:((~rich(X)&~old(X))=>(wise(X)|humble(X))))&
(![X]:((~strong(X)|~creative(X))<=>~curious(X)))&
(((calm(lucy)<~>~quiet(lucy)))<=>(~generous(susan)))&
((curious(susan)&~humble(susan)))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
(?[X]:((~happy(X)&~patient(X))))&
(~wise(john)) | ~rich(lucy) | [] | null | 0 |
Everyone who is either not happy or creative is either not tall or happy.
Everyone who is both not calm and not tall is either not generous or old and vice versa.
Everyone who is both not brave and not wise is either not brave or funny and vice versa.
Everyone who is both calm and not funny is both not creative and not humble and vice versa.
If paul is not tall or not happy then someone is both quiet and not happy and vice versa.
If someone is both not wise and strong then someone is both not wise and quiet.
If fred is not old then someone is both creative and not brave and vice versa.
Everyone who is either strong or rich is either strong or not calm.
Everyone who is not rich is both not rich and quiet.
Everyone who is both not humble and calm is either creative or patient.
Everyone who is tall or not patient is humble.
Everyone who is both not wise and not humble is not tall or not creative and vice versa.
Everyone who is not happy is both wise and kind.
Everyone who is either not brave or not kind is rich or calm and vice versa.
Everyone who is quiet or not old is both funny and brave.
If fred is both not calm and funny then someone is curious and vice versa.
Someone is either not brave or wise.
Fred is either not strong or not creative.
Someone is not quiet. | Paul is not brave. | contradiction | (![X]:((~happy(X)<~>creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~calm(X)&~tall(X))<=>(~generous(X)<~>old(X))))&
(![X]:((~brave(X)&~wise(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((calm(X)&~funny(X))<=>(~creative(X)&~humble(X))))&
(((~tall(paul)|~happy(paul)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:((~wise(X)&quiet(X)))))&
((~old(fred))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((strong(X)<~>rich(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(~rich(X)&quiet(X))))&
(![X]:((~humble(X)&calm(X))=>(creative(X)<~>patient(X))))&
(![X]:((tall(X)|~patient(X))=>humble(X)))&
(![X]:((~wise(X)&~humble(X))<=>(~tall(X)|~creative(X))))&
(![X]:(~happy(X)=>(wise(X)&kind(X))))&
(![X]:((~brave(X)<~>~kind(X))<=>(rich(X)|calm(X))))&
(![X]:((quiet(X)|~old(X))=>(funny(X)&brave(X))))&
(((~calm(fred)&funny(fred)))<=>(?[X]:(curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
((~strong(fred)<~>~creative(fred)))&
(?[X]:(~quiet(X))) | ~brave(paul) | [
"p2",
"p4",
"p6",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6469697289219187621275409
% SZS output start Proof for 6469697289219187621275409
3. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> (~brave(X0) <~> funny(X0))) [input p2]
5. (~happy(paul) | ~tall(paul)) <=> ? [X0] : (~happy(X0) & quiet(X0)) [input p4]
7. ~old(fred) <=> ? [X0] : (~brave(X0) & creative(X0)) [input p6]
11. ! [X0] : ((~patient(X0) | tall(X0)) => humble(X0)) [input p10]
12. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (~creative(X0) | ~tall(X0))) [input p11]
15. ! [X0] : ((~old(X0) | quiet(X0)) => (brave(X0) & funny(X0))) [input p14]
20. ~brave(paul) [input hypothesis]
28. ! [X0] : (humble(X0) | (patient(X0) & ~tall(X0))) [ennf transformation 11]
30. ! [X0] : ((brave(X0) & funny(X0)) | (old(X0) & ~quiet(X0))) [ennf transformation 15]
34. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (wise(X0) | brave(X0)))) [nnf transformation 3]
35. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | wise(X0) | brave(X0))) [flattening 34]
38. ((~happy(paul) | ~tall(paul)) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X0] : (~happy(X0) & quiet(X0)) | (happy(paul) & tall(paul))) [nnf transformation 5]
39. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X0] : (~happy(X0) & quiet(X0)) | (happy(paul) & tall(paul))) [flattening 38]
40. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & (? [X1] : (~happy(X1) & quiet(X1)) | (happy(paul) & tall(paul))) [rectify 39]
41. ? [X1] : (~happy(X1) & quiet(X1)) => (~happy(sK0) & quiet(sK0)) [choice axiom]
42. (~happy(paul) | ~tall(paul) | ! [X0] : (happy(X0) | ~quiet(X0))) & ((~happy(sK0) & quiet(sK0)) | (happy(paul) & tall(paul))) [skolemisation 40,41]
46. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & (? [X0] : (~brave(X0) & creative(X0)) | old(fred)) [nnf transformation 7]
47. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & (? [X1] : (~brave(X1) & creative(X1)) | old(fred)) [rectify 46]
48. ? [X1] : (~brave(X1) & creative(X1)) => (~brave(sK2) & creative(sK2)) [choice axiom]
49. (~old(fred) | ! [X0] : (brave(X0) | ~creative(X0))) & ((~brave(sK2) & creative(sK2)) | old(fred)) [skolemisation 47,48]
52. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 12]
53. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | humble(X0) | wise(X0))) [flattening 52]
80. ~brave(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 35]
87. quiet(sK0) | tall(paul) [cnf transformation 42]
96. ~old(fred) | brave(X0) | ~creative(X0) [cnf transformation 49]
105. ~tall(X0) | humble(X0) [cnf transformation 28]
111. ~humble(X0) | creative(X0) [cnf transformation 53]
120. ~quiet(X0) | funny(X0) [cnf transformation 30]
121. funny(X0) | old(X0) [cnf transformation 30]
122. ~quiet(X0) | brave(X0) [cnf transformation 30]
123. brave(X0) | old(X0) [cnf transformation 30]
132. ~brave(paul) [cnf transformation 20]
136. ~funny(X0) | ~brave(X0) [duplicate literal removal 80]
144. 2 <=> tall(paul) [avatar definition]
145. tall(paul) <- (2) [avatar component clause 144]
159. 5 <=> quiet(sK0) [avatar definition]
161. quiet(sK0) <- (5) [avatar component clause 159]
163. 2 | 5 [avatar split clause 87,159,144]
178. 9 <=> ! [X0] : (brave(X0) | ~creative(X0)) [avatar definition]
179. ~creative(X0) | brave(X0) <- (9) [avatar component clause 178]
181. 10 <=> old(fred) [avatar definition]
183. ~old(fred) <- (~10) [avatar component clause 181]
184. 9 | ~10 [avatar split clause 96,181,178]
234. humble(paul) <- (2) [resolution 105,145]
236. creative(paul) <- (2) [resolution 111,234]
240. funny(sK0) <- (5) [resolution 120,161]
242. brave(sK0) <- (5) [resolution 122,161]
245. ~brave(sK0) <- (5) [resolution 136,240]
246. ~brave(X0) | old(X0) [resolution 136,121]
247. $false <- (5) [subsumption resolution 245,242]
248. ~5 [avatar contradiction clause 247]
249. old(X0) [subsumption resolution 246,123]
256. brave(paul) <- (2, 9) [resolution 179,236]
258. $false <- (2, 9) [subsumption resolution 256,132]
259. ~2 | ~9 [avatar contradiction clause 258]
260. $false <- (~10) [subsumption resolution 183,249]
261. 10 [avatar contradiction clause 260]
262. $false [avatar sat refutation 163,184,248,259,261]
% SZS output end Proof for 6469697289219187621275409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not funny then paul is patient or not wise. Everyone who is both not rich and curious is humble or quiet and vice versa. If fred is not patient or old then someone is old and vice versa. Everyone who is not quiet is either not curious or not patient and vice versa. If someone is both old and not curious then someone is not old and vice versa. Everyone who is not strong is wise or not patient and vice versa. Everyone who is both kind and not strong is not generous and vice versa. Everyone who is not kind or kind is both kind and strong and vice versa. Everyone who is both not rich and kind is funny or creative. If someone is curious or calm then alice is either kind or brave. Everyone who is both not brave and not strong is not quiet and vice versa. If someone is creative then lucy is either calm or quiet and vice versa. Everyone who is not quiet is humble or not curious and vice versa. If someone is happy or not happy then mary is creative. If lucy is not strong then fred is both humble and quiet and vice versa. If someone is either brave or not tall then someone is either not creative or not humble and vice versa. Someone is not patient or old. Fred is creative or not creative. Someone is funny or not happy. Susan is not tall or not creative. Someone is not rich or generous. Someone is either not brave or not curious. John is patient. | John is not old. | contradiction | ((?[X]:((~rich(X)<~>~funny(X))))=>((patient(paul)|~wise(paul))))&
(![X]:((~rich(X)&curious(X))<=>(humble(X)|quiet(X))))&
(((~patient(fred)|old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((kind(X)&~strong(X))<=>~generous(X)))&
(![X]:((~kind(X)|kind(X))<=>(kind(X)&strong(X))))&
(![X]:((~rich(X)&kind(X))=>(funny(X)|creative(X))))&
((?[X]:((curious(X)|calm(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~brave(X)&~strong(X))<=>~quiet(X)))&
((?[X]:(creative(X)))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:(~quiet(X)<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~happy(X))))=>(creative(mary)))&
((~strong(lucy))<=>((humble(fred)&quiet(fred))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(?[X]:((~patient(X)|old(X))))&
((creative(fred)|~creative(fred)))&
(?[X]:((funny(X)|~happy(X))))&
((~tall(susan)|~creative(susan)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((~brave(X)<~>~curious(X))))&
(patient(john)) | ~old(john) | [
"p1",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5429603135589715401973980
% SZS output start Proof for 5429603135589715401973980
2. ! [X0] : ((curious(X0) & ~rich(X0)) <=> (quiet(X0) | humble(X0))) [input p1]
5. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X0] : ~old(X0) [input p4]
8. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (strong(X0) & kind(X0))) [input p7]
11. ! [X0] : ((~strong(X0) & ~brave(X0)) <=> ~quiet(X0)) [input p10]
24. ~old(john) [input hypothesis]
25. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X1] : ~old(X1) [rectify 5]
37. ! [X0] : (((curious(X0) & ~rich(X0)) | (~quiet(X0) & ~humble(X0))) & ((quiet(X0) | humble(X0)) | (~curious(X0) | rich(X0)))) [nnf transformation 2]
38. ! [X0] : (((curious(X0) & ~rich(X0)) | (~quiet(X0) & ~humble(X0))) & (quiet(X0) | humble(X0) | ~curious(X0) | rich(X0))) [flattening 37]
45. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (curious(X0) | ~old(X0))) [nnf transformation 25]
46. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (curious(X3) | ~old(X3))) [rectify 45]
47. ? [X0] : (~curious(X0) & old(X0)) => (~curious(sK1) & old(sK1)) [choice axiom]
48. ? [X2] : ~old(X2) => ~old(sK2) [choice axiom]
49. ((~curious(sK1) & old(sK1)) | ! [X1] : old(X1)) & (~old(sK2) | ! [X3] : (curious(X3) | ~old(X3))) [skolemisation 46,48,47]
52. ! [X0] : (((kind(X0) | ~kind(X0)) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | ~kind(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [flattening 52]
55. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (strong(X0) | brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | strong(X0) | brave(X0))) [flattening 55]
85. ~quiet(X0) | curious(X0) [cnf transformation 38]
95. ~curious(sK1) | old(X1) [cnf transformation 49]
102. strong(X0) | kind(X0) [cnf transformation 53]
103. strong(X0) | ~kind(X0) [cnf transformation 53]
112. ~strong(X0) | quiet(X0) [cnf transformation 56]
141. ~old(john) [cnf transformation 24]
181. 9 <=> ! [X1] : old(X1) [avatar definition]
182. old(X1) <- (9) [avatar component clause 181]
184. 10 <=> curious(sK1) [avatar definition]
186. ~curious(sK1) <- (~10) [avatar component clause 184]
187. 9 | ~10 [avatar split clause 95,184,181]
201. strong(X0) [subsumption resolution 102,103]
217. quiet(X0) [subsumption resolution 112,201]
322. $false <- (9) [resolution 182,141]
323. ~9 [avatar contradiction clause 322]
325. curious(X0) [resolution 85,217]
326. $false <- (~10) [resolution 325,186]
329. 10 [avatar contradiction clause 326]
330. $false [avatar sat refutation 187,323,329]
% SZS output end Proof for 5429603135589715401973980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not old is both not generous and not curious and vice versa.
If susan is curious or happy then someone is both not strong and quiet and vice versa.
If lucy is both kind and not happy then someone is both not old and rich and vice versa.
If someone is not calm then someone is both not creative and kind and vice versa.
If someone is wise or not kind then someone is either not generous or not funny and vice versa.
Everyone who is happy or not wise is both brave and not happy.
If someone is not kind then alice is both not patient and not brave.
Everyone who is both funny and not happy is either not curious or not strong.
Everyone who is both strong and not old is not funny and vice versa.
If someone is rich or not patient then fred is either not patient or tall.
If john is both not kind and creative then someone is both kind and generous.
Everyone who is not patient is either not wise or not tall and vice versa.
Everyone who is curious is either kind or tall.
If someone is either kind or brave then someone is not generous and vice versa.
If someone is not funny or not creative then lucy is both curious and not funny and vice versa.
If someone is calm then someone is either not brave or creative and vice versa.
Someone is both brave and humble.
Someone is both calm and wise.
Alice is both old and not curious.
Paul is not curious or patient.
Someone is not patient.
Susan is not curious or not funny.
Paul is strong. | Lucy is generous. | neutral | (![X]:((brave(X)&~old(X))<=>(~generous(X)&~curious(X))))&
(((curious(susan)|happy(susan)))<=>(?[X]:((~strong(X)&quiet(X)))))&
(((kind(lucy)&~happy(lucy)))<=>(?[X]:((~old(X)&rich(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((wise(X)|~kind(X))))<=>(?[X]:((~generous(X)<~>~funny(X)))))&
(![X]:((happy(X)|~wise(X))=>(brave(X)&~happy(X))))&
((?[X]:(~kind(X)))=>((~patient(alice)&~brave(alice))))&
(![X]:((funny(X)&~happy(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((strong(X)&~old(X))<=>~funny(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~patient(fred)<~>tall(fred))))&
(((~kind(john)&creative(john)))=>(?[X]:((kind(X)&generous(X)))))&
(![X]:(~patient(X)<=>(~wise(X)<~>~tall(X))))&
(![X]:(curious(X)=>(kind(X)<~>tall(X))))&
((?[X]:((kind(X)<~>brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(lucy)&~funny(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>creative(X)))))&
(?[X]:((brave(X)&humble(X))))&
(?[X]:((calm(X)&wise(X))))&
((old(alice)&~curious(alice)))&
((~curious(paul)|patient(paul)))&
(?[X]:(~patient(X)))&
((~curious(susan)|~funny(susan)))&
(strong(paul)) | generous(lucy) | [] | null | 0 |
Everyone who is calm or not old is either brave or old and vice versa.
If someone is not creative then fred is both not rich and not curious.
If fred is both quiet and not humble then someone is either not generous or patient and vice versa.
If susan is both not happy and old then alice is patient and vice versa.
Everyone who is not rich or humble is either not humble or not quiet.
Everyone who is both generous and not strong is not old and vice versa.
Everyone who is not old is rich or strong and vice versa.
Everyone who is either not kind or not tall is strong or not happy.
Everyone who is either brave or not wise is not curious or brave and vice versa.
Everyone who is either strong or not creative is either not funny or rich and vice versa.
If someone is either not tall or calm then lucy is patient and vice versa.
Everyone who is generous is either not quiet or not creative and vice versa.
If someone is either tall or calm then someone is both tall and not strong and vice versa.
Everyone who is both not wise and not calm is funny or curious and vice versa.
Everyone who is not patient is either not rich or not funny and vice versa.
If susan is old or creative then someone is patient or wise.
Susan is both not generous and not strong.
Someone is creative or funny.
Lucy is rich.
Someone is not rich.
Mary is either calm or happy.
Someone is both not calm and patient.
Paul is both not happy and patient. | Paul is quiet. | contradiction | (![X]:((calm(X)|~old(X))<=>(brave(X)<~>old(X))))&
((?[X]:(~creative(X)))=>((~rich(fred)&~curious(fred))))&
(((quiet(fred)&~humble(fred)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~happy(susan)&old(susan)))<=>(patient(alice)))&
(![X]:((~rich(X)|humble(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((generous(X)&~strong(X))<=>~old(X)))&
(![X]:(~old(X)<=>(rich(X)|strong(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(strong(X)|~happy(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(~curious(X)|brave(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(patient(lucy)))&
(![X]:(generous(X)<=>(~quiet(X)<~>~creative(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:((~wise(X)&~calm(X))<=>(funny(X)|curious(X))))&
(![X]:(~patient(X)<=>(~rich(X)<~>~funny(X))))&
(((old(susan)|creative(susan)))=>(?[X]:((patient(X)|wise(X)))))&
((~generous(susan)&~strong(susan)))&
(?[X]:((creative(X)|funny(X))))&
(rich(lucy))&
(?[X]:(~rich(X)))&
((calm(mary)<~>happy(mary)))&
(?[X]:((~calm(X)&patient(X))))&
((~happy(paul)&patient(paul))) | quiet(paul) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"p11",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 763178763355186555790512
% SZS output start Proof for 763178763355186555790512
1. ! [X0] : ((~old(X0) | calm(X0)) <=> (brave(X0) <~> old(X0))) [input p0]
6. ! [X0] : ((~strong(X0) & generous(X0)) <=> ~old(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> (strong(X0) | rich(X0))) [input p6]
9. ! [X0] : ((brave(X0) <~> ~wise(X0)) <=> (brave(X0) | ~curious(X0))) [input p8]
10. ! [X0] : ((strong(X0) <~> ~creative(X0)) <=> (~funny(X0) <~> rich(X0))) [input p9]
12. ! [X0] : (generous(X0) <=> (~quiet(X0) <~> ~creative(X0))) [input p11]
14. ! [X0] : ((~calm(X0) & ~wise(X0)) <=> (curious(X0) | funny(X0))) [input p13]
15. ! [X0] : (~patient(X0) <=> (~rich(X0) <~> ~funny(X0))) [input p14]
23. patient(paul) & ~happy(paul) [input p22]
24. quiet(paul) [input hypothesis]
31. ! [X0] : (((~old(X0) | calm(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (old(X0) & ~calm(X0)))) [nnf transformation 1]
32. ! [X0] : ((~old(X0) | calm(X0) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (old(X0) & ~calm(X0)))) [flattening 31]
41. ! [X0] : (((~strong(X0) & generous(X0)) | old(X0)) & (~old(X0) | (strong(X0) | ~generous(X0)))) [nnf transformation 6]
42. ! [X0] : (((~strong(X0) & generous(X0)) | old(X0)) & (~old(X0) | strong(X0) | ~generous(X0))) [flattening 41]
43. ! [X0] : ((~old(X0) | (~strong(X0) & ~rich(X0))) & ((strong(X0) | rich(X0)) | old(X0))) [nnf transformation 7]
44. ! [X0] : ((~old(X0) | (~strong(X0) & ~rich(X0))) & (strong(X0) | rich(X0) | old(X0))) [flattening 43]
46. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~brave(X0) & curious(X0))) & ((brave(X0) | ~curious(X0)) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [nnf transformation 9]
47. ! [X0] : ((((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~brave(X0) & curious(X0))) & (brave(X0) | ~curious(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0))))) [flattening 46]
48. ! [X0] : ((((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))))) [nnf transformation 10]
53. ! [X0] : ((generous(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~generous(X0))) [nnf transformation 12]
59. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (calm(X0) | wise(X0)))) [nnf transformation 14]
60. ! [X0] : (((~calm(X0) & ~wise(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | calm(X0) | wise(X0))) [flattening 59]
61. ! [X0] : ((~patient(X0) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | patient(X0))) [nnf transformation 15]
72. old(X0) | brave(X0) | old(X0) [cnf transformation 32]
92. ~generous(X0) | strong(X0) | ~old(X0) [cnf transformation 42]
93. generous(X0) | old(X0) [cnf transformation 42]
94. ~strong(X0) | old(X0) [cnf transformation 42]
95. strong(X0) | rich(X0) | old(X0) [cnf transformation 44]
96. ~rich(X0) | ~old(X0) [cnf transformation 44]
97. ~old(X0) | ~strong(X0) [cnf transformation 44]
105. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 47]
109. ~rich(X0) | funny(X0) | strong(X0) | creative(X0) [cnf transformation 48]
110. ~creative(X0) | strong(X0) | rich(X0) | funny(X0) [cnf transformation 48]
118. ~generous(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 53]
121. ~quiet(X0) | generous(X0) | creative(X0) [cnf transformation 53]
129. ~funny(X0) | ~wise(X0) [cnf transformation 60]
135. ~funny(X0) | ~patient(X0) | rich(X0) [cnf transformation 61]
136. ~patient(X0) | ~rich(X0) | funny(X0) [cnf transformation 61]
149. patient(paul) [cnf transformation 23]
150. quiet(paul) [cnf transformation 24]
152. ~brave(X0) | wise(X0) [duplicate literal removal 105]
154. brave(X0) | old(X0) [duplicate literal removal 72]
212. ~strong(X0) [subsumption resolution 97,94]
213. rich(X0) | old(X0) [subsumption resolution 95,212]
218. ~creative(X0) | rich(X0) | funny(X0) [subsumption resolution 110,212]
219. ~rich(X0) | funny(X0) | creative(X0) [subsumption resolution 109,212]
312. wise(X0) | old(X0) [resolution 154,152]
359. ~quiet(X0) | ~creative(X0) | old(X0) [resolution 118,93]
395. generous(paul) | creative(paul) [resolution 121,150]
419. ~rich(paul) | funny(paul) [resolution 136,149]
433. 39 <=> funny(paul) [avatar definition]
434. ~funny(paul) <- (~39) [avatar component clause 433]
435. funny(paul) <- (39) [avatar component clause 433]
437. 40 <=> rich(paul) [avatar definition]
438. rich(paul) <- (40) [avatar component clause 437]
439. ~rich(paul) <- (~40) [avatar component clause 437]
440. 39 | ~40 [avatar split clause 419,437,433]
580. funny(X0) | creative(X0) | old(X0) [resolution 219,213]
606. ~patient(paul) | rich(paul) <- (39) [resolution 435,135]
609. ~wise(paul) <- (39) [resolution 435,129]
610. rich(paul) <- (39) [subsumption resolution 606,149]
613. 40 | ~39 [avatar split clause 610,433,437]
630. ~old(paul) <- (40) [resolution 438,96]
686. ~creative(paul) | old(paul) [resolution 359,150]
719. creative(X5) | old(X5) | ~wise(X5) [resolution 580,129]
725. creative(X5) | old(X5) [subsumption resolution 719,312]
779. old(paul) <- (39) [resolution 609,312]
780. $false <- (39, 40) [subsumption resolution 779,630]
781. ~39 | ~40 [avatar contradiction clause 780]
782. old(paul) [subsumption resolution 686,725]
784. 72 <=> creative(paul) [avatar definition]
786. creative(paul) <- (72) [avatar component clause 784]
788. 73 <=> generous(paul) [avatar definition]
790. generous(paul) <- (73) [avatar component clause 788]
791. 72 | 73 [avatar split clause 395,788,784]
805. rich(paul) | funny(paul) <- (72) [resolution 786,218]
807. funny(paul) <- (~40, 72) [subsumption resolution 805,439]
808. $false <- (~39, ~40, 72) [subsumption resolution 807,434]
809. 39 | 40 | ~72 [avatar contradiction clause 808]
812. strong(paul) | ~old(paul) <- (73) [resolution 790,92]
813. ~old(paul) <- (73) [subsumption resolution 812,212]
814. $false <- (73) [subsumption resolution 813,782]
815. ~73 [avatar contradiction clause 814]
816. $false [avatar sat refutation 440,613,781,791,809,815]
% SZS output end Proof for 763178763355186555790512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not happy or not strong then someone is patient.
Everyone who is wise or not happy is not brave or generous and vice versa.
Everyone who is both not generous and kind is rich or not happy.
Everyone who is not funny is wise or not wise.
Everyone who is both brave and not old is either not brave or calm.
If someone is both brave and not calm then john is either funny or tall and vice versa.
Everyone who is not humble is either quiet or not humble.
Everyone who is tall is either curious or not happy.
Everyone who is both not creative and not wise is both old and brave and vice versa.
If alice is either creative or not curious then someone is both not brave and not calm and vice versa.
Everyone who is calm or humble is both not generous and not old and vice versa.
If alice is not funny or curious then mary is rich or curious and vice versa.
Everyone who is either old or quiet is funny or not wise.
If someone is not patient then paul is not happy or old.
Everyone who is not kind is both not strong and not kind.
Everyone who is both humble and curious is either quiet or kind.
Susan is not kind.
Someone is calm.
Fred is patient.
Mary is generous or old.
Mary is either funny or old.
Someone is both not humble and not strong.
Someone is both patient and not calm.
Someone is not wise. | Alice is creative. | neutral | (((~happy(mary)<~>~strong(mary)))=>(?[X]:(patient(X))))&
(![X]:((wise(X)|~happy(X))<=>(~brave(X)|generous(X))))&
(![X]:((~generous(X)&kind(X))=>(rich(X)|~happy(X))))&
(![X]:(~funny(X)=>(wise(X)|~wise(X))))&
(![X]:((brave(X)&~old(X))=>(~brave(X)<~>calm(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((funny(john)<~>tall(john))))&
(![X]:(~humble(X)=>(quiet(X)<~>~humble(X))))&
(![X]:(tall(X)=>(curious(X)<~>~happy(X))))&
(![X]:((~creative(X)&~wise(X))<=>(old(X)&brave(X))))&
(((creative(alice)<~>~curious(alice)))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((calm(X)|humble(X))<=>(~generous(X)&~old(X))))&
(((~funny(alice)|curious(alice)))<=>((rich(mary)|curious(mary))))&
(![X]:((old(X)<~>quiet(X))=>(funny(X)|~wise(X))))&
((?[X]:(~patient(X)))=>((~happy(paul)|old(paul))))&
(![X]:(~kind(X)=>(~strong(X)&~kind(X))))&
(![X]:((humble(X)&curious(X))=>(quiet(X)<~>kind(X))))&
(~kind(susan))&
(?[X]:(calm(X)))&
(patient(fred))&
((generous(mary)|old(mary)))&
((funny(mary)<~>old(mary)))&
(?[X]:((~humble(X)&~strong(X))))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(~wise(X))) | creative(alice) | [] | null | 0 |
Everyone who is not rich is kind or quiet and vice versa.
Everyone who is both patient and humble is both not humble and humble and vice versa.
If john is kind then alice is either not kind or not patient and vice versa.
Everyone who is wise or brave is either not rich or old.
If someone is either not calm or not rich then fred is either wise or not tall and vice versa.
Everyone who is both generous and not patient is both tall and not happy and vice versa.
If someone is wise then fred is not happy.
Everyone who is wise or generous is not happy.
Everyone who is not wise or not happy is not kind or not funny.
Everyone who is either generous or not wise is either humble or not tall and vice versa.
If susan is both not strong and not brave then lucy is both not kind and brave and vice versa.
If mary is not rich or kind then someone is not funny or wise.
If someone is not humble or patient then lucy is tall or happy.
Everyone who is both creative and not old is creative and vice versa.
Everyone who is both funny and not generous is calm and vice versa.
If alice is funny then someone is rich and vice versa.
Lucy is not curious or humble.
John is either not generous or not patient.
Paul is not rich or wise.
Someone is both quiet and funny.
Someone is creative or brave.
Someone is not humble or wise.
Fred is not rich.
Paul is either not rich or happy. | John is old. | neutral | (![X]:(~rich(X)<=>(kind(X)|quiet(X))))&
(![X]:((patient(X)&humble(X))<=>(~humble(X)&humble(X))))&
((kind(john))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:((wise(X)|brave(X))=>(~rich(X)<~>old(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((wise(fred)<~>~tall(fred))))&
(![X]:((generous(X)&~patient(X))<=>(tall(X)&~happy(X))))&
((?[X]:(wise(X)))=>(~happy(fred)))&
(![X]:((wise(X)|generous(X))=>~happy(X)))&
(![X]:((~wise(X)|~happy(X))=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)<~>~tall(X))))&
(((~strong(susan)&~brave(susan)))<=>((~kind(lucy)&brave(lucy))))&
(((~rich(mary)|kind(mary)))=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>((tall(lucy)|happy(lucy))))&
(![X]:((creative(X)&~old(X))<=>creative(X)))&
(![X]:((funny(X)&~generous(X))<=>calm(X)))&
((funny(alice))<=>(?[X]:(rich(X))))&
((~curious(lucy)|humble(lucy)))&
((~generous(john)<~>~patient(john)))&
((~rich(paul)|wise(paul)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~humble(X)|wise(X))))&
(~rich(fred))&
((~rich(paul)<~>happy(paul))) | old(john) | [] | null | 0 |
If someone is curious then someone is either patient or old. If someone is both generous and not funny then mary is either humble or old. Everyone who is either funny or happy is not patient or creative and vice versa. If someone is both not funny and not brave then paul is either tall or funny and vice versa. Everyone who is generous or patient is both brave and not patient and vice versa. If someone is either wise or not quiet then lucy is not rich or not wise. If john is both not wise and not curious then someone is not strong and vice versa. Everyone who is not old is not funny and vice versa. If paul is either creative or patient then susan is either not old or curious and vice versa. If paul is either happy or creative then someone is funny or humble and vice versa. If someone is either not curious or not quiet then someone is not humble. Everyone who is either brave or quiet is not generous. If fred is both not creative and not funny then mary is either not brave or not creative and vice versa. Everyone who is not rich or happy is strong and vice versa. Everyone who is either not curious or humble is not brave. If someone is not patient then someone is curious or happy and vice versa. Someone is old or kind. Fred is both generous and not happy. Lucy is wise. Susan is either brave or quiet. Mary is both curious and wise. Someone is either old or not wise. | Mary is not curious. | contradiction | ((?[X]:(curious(X)))=>(?[X]:((patient(X)<~>old(X)))))&
((?[X]:((generous(X)&~funny(X))))=>((humble(mary)<~>old(mary))))&
(![X]:((funny(X)<~>happy(X))<=>(~patient(X)|creative(X))))&
((?[X]:((~funny(X)&~brave(X))))<=>((tall(paul)<~>funny(paul))))&
(![X]:((generous(X)|patient(X))<=>(brave(X)&~patient(X))))&
((?[X]:((wise(X)<~>~quiet(X))))=>((~rich(lucy)|~wise(lucy))))&
(((~wise(john)&~curious(john)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)<=>~funny(X)))&
(((creative(paul)<~>patient(paul)))<=>((~old(susan)<~>curious(susan))))&
(((happy(paul)<~>creative(paul)))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:(~humble(X))))&
(![X]:((brave(X)<~>quiet(X))=>~generous(X)))&
(((~creative(fred)&~funny(fred)))<=>((~brave(mary)<~>~creative(mary))))&
(![X]:((~rich(X)|happy(X))<=>strong(X)))&
(![X]:((~curious(X)<~>humble(X))=>~brave(X)))&
((?[X]:(~patient(X)))<=>(?[X]:((curious(X)|happy(X)))))&
(?[X]:((old(X)|kind(X))))&
((generous(fred)&~happy(fred)))&
(wise(lucy))&
((brave(susan)<~>quiet(susan)))&
((curious(mary)&wise(mary)))&
(?[X]:((old(X)<~>~wise(X)))) | ~curious(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4984458884332565757702928
% SZS output start Proof for 4984458884332565757702928
21. wise(mary) & curious(mary) [input p20]
23. ~curious(mary) [input hypothesis]
144. curious(mary) [cnf transformation 21]
148. ~curious(mary) [cnf transformation 23]
346. $false [subsumption resolution 148,144]
% SZS output end Proof for 4984458884332565757702928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both creative and not patient and vice versa. Everyone who is both not brave and humble is brave and vice versa. If someone is either funny or not patient then someone is both not patient and old and vice versa. Everyone who is both funny and not kind is both humble and strong. If lucy is either not brave or brave then mary is both curious and quiet and vice versa. Everyone who is generous is either not old or not tall. Everyone who is not creative or not happy is calm. Everyone who is creative or old is both kind and not rich and vice versa. Everyone who is both patient and not brave is both not happy and not patient and vice versa. If mary is kind or funny then mary is both patient and not calm and vice versa. Everyone who is both quiet and funny is both happy and patient and vice versa. If alice is strong then john is either patient or generous. Everyone who is tall is not kind and vice versa. If susan is not creative or quiet then someone is both happy and not curious and vice versa. Alice is not humble or not happy. Someone is both not wise and generous. John is either not generous or funny. Someone is both old and not tall. Someone is not rich. Fred is either not humble or tall. | Alice is not tall. | neutral | (![X]:(patient(X)<=>(creative(X)&~patient(X))))&
(![X]:((~brave(X)&humble(X))<=>brave(X)))&
((?[X]:((funny(X)<~>~patient(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((funny(X)&~kind(X))=>(humble(X)&strong(X))))&
(((~brave(lucy)<~>brave(lucy)))<=>((curious(mary)&quiet(mary))))&
(![X]:(generous(X)=>(~old(X)<~>~tall(X))))&
(![X]:((~creative(X)|~happy(X))=>calm(X)))&
(![X]:((creative(X)|old(X))<=>(kind(X)&~rich(X))))&
(![X]:((patient(X)&~brave(X))<=>(~happy(X)&~patient(X))))&
(((kind(mary)|funny(mary)))<=>((patient(mary)&~calm(mary))))&
(![X]:((quiet(X)&funny(X))<=>(happy(X)&patient(X))))&
((strong(alice))=>((patient(john)<~>generous(john))))&
(![X]:(tall(X)<=>~kind(X)))&
(((~creative(susan)|quiet(susan)))<=>(?[X]:((happy(X)&~curious(X)))))&
((~humble(alice)|~happy(alice)))&
(?[X]:((~wise(X)&generous(X))))&
((~generous(john)<~>funny(john)))&
(?[X]:((old(X)&~tall(X))))&
(?[X]:(~rich(X)))&
((~humble(fred)<~>tall(fred))) | ~tall(alice) | [] | null | 0 |
Everyone who is not rich is creative.
Everyone who is either tall or funny is not generous.
Everyone who is quiet is both patient and not rich and vice versa.
Everyone who is either quiet or not old is strong or not humble.
Everyone who is patient or curious is both curious and strong and vice versa.
Everyone who is not kind or not patient is not humble and vice versa.
Everyone who is not calm is not creative or wise.
If someone is either not calm or creative then susan is both tall and not humble.
Everyone who is either not creative or not funny is not strong.
If someone is both curious and not creative then fred is curious or not funny and vice versa.
Everyone who is patient or not rich is not creative.
Everyone who is rich is quiet or patient and vice versa.
Everyone who is both not old and not patient is both wise and not brave and vice versa.
If someone is not patient then someone is generous or not patient and vice versa.
If someone is either kind or not funny then someone is both patient and rich and vice versa.
If lucy is both not patient and patient then mary is not strong and vice versa.
Mary is either not calm or not curious.
Someone is both not old and not happy.
Mary is humble.
Someone is not happy.
Someone is either not tall or patient.
Alice is creative or tall.
Someone is kind or not funny. | Alice is not generous. | entailment | (![X]:(~rich(X)=>creative(X)))&
(![X]:((tall(X)<~>funny(X))=>~generous(X)))&
(![X]:(quiet(X)<=>(patient(X)&~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>(strong(X)|~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(curious(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>(~creative(X)|wise(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>((tall(susan)&~humble(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>~strong(X)))&
((?[X]:((curious(X)&~creative(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((patient(X)|~rich(X))=>~creative(X)))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(![X]:((~old(X)&~patient(X))<=>(wise(X)&~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((patient(X)&rich(X)))))&
(((~patient(lucy)&patient(lucy)))<=>(~strong(mary)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:((~old(X)&~happy(X))))&
(humble(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(alice)|tall(alice)))&
(?[X]:((kind(X)|~funny(X)))) | ~generous(alice) | [
"p0",
"p2",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1559091206334271547207132
% SZS output start Proof for 1559091206334271547207132
1. ! [X0] : (~rich(X0) => creative(X0)) [input p0]
3. ! [X0] : (quiet(X0) <=> (~rich(X0) & patient(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | patient(X0)) => ~creative(X0)) [input p10]
12. ! [X0] : (rich(X0) <=> (patient(X0) | quiet(X0))) [input p11]
14. ? [X0] : ~patient(X0) <=> ? [X0] : (~patient(X0) | generous(X0)) [input p13]
24. generous(alice) [input hypothesis]
25. ? [X0] : ~patient(X0) <=> ? [X1] : (~patient(X1) | generous(X1)) [rectify 14]
29. ! [X0] : (creative(X0) | rich(X0)) [ennf transformation 1]
37. ! [X0] : (~creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((quiet(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [flattening 39]
53. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | ~rich(X0))) [nnf transformation 12]
54. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~rich(X0))) [flattening 53]
57. (? [X0] : ~patient(X0) | ! [X1] : (patient(X1) & ~generous(X1))) & (? [X1] : (~patient(X1) | generous(X1)) | ! [X0] : patient(X0)) [nnf transformation 25]
58. (? [X0] : ~patient(X0) | ! [X1] : (patient(X1) & ~generous(X1))) & (? [X2] : (~patient(X2) | generous(X2)) | ! [X3] : patient(X3)) [rectify 57]
59. ? [X0] : ~patient(X0) => ~patient(sK1) [choice axiom]
60. ? [X2] : (~patient(X2) | generous(X2)) => (~patient(sK2) | generous(sK2)) [choice axiom]
61. (~patient(sK1) | ! [X1] : (patient(X1) & ~generous(X1))) & ((~patient(sK2) | generous(sK2)) | ! [X3] : patient(X3)) [skolemisation 58,60,59]
77. creative(X0) | rich(X0) [cnf transformation 29]
80. patient(X0) | ~quiet(X0) [cnf transformation 40]
106. ~creative(X0) | rich(X0) [cnf transformation 37]
107. patient(X0) | quiet(X0) | ~rich(X0) [cnf transformation 54]
115. ~patient(sK1) | ~generous(X1) [cnf transformation 61]
134. generous(alice) [cnf transformation 24]
177. rich(X0) [subsumption resolution 106,77]
178. patient(X0) | quiet(X0) [subsumption resolution 107,177]
179. patient(X0) [subsumption resolution 178,80]
181. ~generous(X1) [subsumption resolution 115,179]
226. $false [subsumption resolution 134,181]
% SZS output end Proof for 1559091206334271547207132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not calm is tall.
Everyone who is not tall is either not tall or not quiet and vice versa.
If fred is either not brave or not quiet then someone is both not old and not kind.
Everyone who is humble is not rich or wise and vice versa.
Everyone who is not rich or rich is happy or curious.
If someone is curious or not generous then someone is not brave and vice versa.
If alice is not wise or wise then someone is either generous or rich.
If someone is strong then john is either funny or not generous.
Everyone who is either humble or not brave is either humble or calm and vice versa.
Everyone who is either funny or not generous is both not calm and not curious and vice versa.
Everyone who is wise or quiet is not curious and vice versa.
Everyone who is not calm or tall is either not wise or not creative.
If alice is both kind and brave then paul is not generous and vice versa.
If someone is calm or strong then mary is both curious and tall and vice versa.
Everyone who is old is both not rich and kind.
Everyone who is not quiet or not creative is generous and vice versa.
Fred is curious or brave.
Someone is either not funny or old.
Someone is either curious or not curious.
Mary is brave.
Someone is both not patient and tall.
Susan is either not curious or not humble. | Fred is humble. | entailment | (![X]:((patient(X)<~>~calm(X))=>tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)<~>~quiet(X))))&
(((~brave(fred)<~>~quiet(fred)))=>(?[X]:((~old(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~rich(X)|wise(X))))&
(![X]:((~rich(X)|rich(X))=>(happy(X)|curious(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:(~brave(X))))&
(((~wise(alice)|wise(alice)))=>(?[X]:((generous(X)<~>rich(X)))))&
((?[X]:(strong(X)))=>((funny(john)<~>~generous(john))))&
(![X]:((humble(X)<~>~brave(X))<=>(humble(X)<~>calm(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~calm(X)&~curious(X))))&
(![X]:((wise(X)|quiet(X))<=>~curious(X)))&
(![X]:((~calm(X)|tall(X))=>(~wise(X)<~>~creative(X))))&
(((kind(alice)&brave(alice)))<=>(~generous(paul)))&
((?[X]:((calm(X)|strong(X))))<=>((curious(mary)&tall(mary))))&
(![X]:(old(X)=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)|~creative(X))<=>generous(X)))&
((curious(fred)|brave(fred)))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(brave(mary))&
(?[X]:((~patient(X)&tall(X))))&
((~curious(susan)<~>~humble(susan))) | humble(fred) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3951306107463031728601911
% SZS output start Proof for 3951306107463031728601911
2. ! [X0] : (~tall(X0) <=> (~tall(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : (humble(X0) <=> (wise(X0) | ~rich(X0))) [input p3]
6. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X0] : ~brave(X0) [input p5]
9. ! [X0] : ((humble(X0) <~> ~brave(X0)) <=> (humble(X0) <~> calm(X0))) [input p8]
11. ! [X0] : ((quiet(X0) | wise(X0)) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((tall(X0) | ~calm(X0)) => (~wise(X0) <~> ~creative(X0))) [input p11]
14. ? [X0] : (strong(X0) | calm(X0)) <=> (tall(mary) & curious(mary)) [input p13]
16. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> generous(X0)) [input p15]
23. ~humble(fred) [input hypothesis]
24. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X1] : ~brave(X1) [rectify 6]
30. ! [X0] : ((~wise(X0) <~> ~creative(X0)) | (~tall(X0) & calm(X0))) [ennf transformation 12]
33. ! [X0] : ((~tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | tall(X0))) [nnf transformation 2]
37. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ~humble(X0))) [nnf transformation 4]
38. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ~humble(X0))) [flattening 37]
39. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (generous(X0) & ~curious(X0))) [nnf transformation 24]
40. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (generous(X3) & ~curious(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) | curious(X0)) => (~generous(sK1) | curious(sK1)) [choice axiom]
42. ? [X2] : ~brave(X2) => ~brave(sK2) [choice axiom]
43. ((~generous(sK1) | curious(sK1)) | ! [X1] : brave(X1)) & (~brave(sK2) | ! [X3] : (generous(X3) & ~curious(X3))) [skolemisation 40,42,41]
48. ! [X0] : ((((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0))))) [nnf transformation 9]
51. ! [X0] : (((quiet(X0) | wise(X0)) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : ((quiet(X0) | wise(X0) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [flattening 51]
53. ! [X0] : (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~tall(X0) & calm(X0))) [nnf transformation 30]
56. (? [X0] : (strong(X0) | calm(X0)) | (~tall(mary) | ~curious(mary))) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [nnf transformation 14]
57. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [flattening 56]
58. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [rectify 57]
59. ? [X0] : (strong(X0) | calm(X0)) => (strong(sK4) | calm(sK4)) [choice axiom]
60. ((strong(sK4) | calm(sK4)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [skolemisation 58,59]
61. ! [X0] : (((~creative(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((~creative(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [flattening 61]
75. quiet(X0) | tall(X0) | tall(X0) [cnf transformation 33]
77. ~tall(X0) | ~tall(X0) | quiet(X0) [cnf transformation 33]
84. ~wise(X0) | humble(X0) [cnf transformation 38]
86. ~brave(sK2) | generous(X3) [cnf transformation 43]
95. calm(X0) | humble(X0) | humble(X0) | brave(X0) [cnf transformation 48]
100. brave(X0) | ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 48]
109. ~curious(X0) | ~quiet(X0) [cnf transformation 52]
113. creative(X0) | wise(X0) | calm(X0) [cnf transformation 53]
118. curious(mary) | ~calm(X1) [cnf transformation 60]
127. ~creative(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 62]
138. ~humble(fred) [cnf transformation 23]
139. calm(X0) | humble(X0) | brave(X0) [duplicate literal removal 95]
142. brave(X0) | ~humble(X0) | calm(X0) [duplicate literal removal 100]
143. quiet(X0) | tall(X0) [duplicate literal removal 75]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 77]
145. quiet(X0) [subsumption resolution 143,144]
175. 7 <=> ! [X3] : generous(X3) [avatar definition]
176. generous(X3) <- (7) [avatar component clause 175]
178. 8 <=> brave(sK2) [avatar definition]
180. ~brave(sK2) <- (~8) [avatar component clause 178]
181. 7 | ~8 [avatar split clause 86,178,175]
183. 9 <=> ! [X3] : ~curious(X3) [avatar definition]
184. ~curious(X3) <- (9) [avatar component clause 183]
216. brave(X0) | calm(X0) [subsumption resolution 139,142]
217. ~curious(X0) [subsumption resolution 109,145]
218. 9 [avatar split clause 217,183]
235. 19 <=> curious(mary) [avatar definition]
236. curious(mary) <- (19) [avatar component clause 235]
253. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
254. ~calm(X1) <- (23) [avatar component clause 253]
257. 23 | 19 [avatar split clause 118,235,253]
258. ~creative(X0) | ~generous(X0) [subsumption resolution 127,145]
284. $false <- (9, 19) [resolution 236,184]
285. ~9 | ~19 [avatar contradiction clause 284]
298. calm(sK2) <- (~8) [resolution 216,180]
300. $false <- (~8, 23) [subsumption resolution 298,254]
301. 8 | ~23 [avatar contradiction clause 300]
317. wise(X2) | calm(X2) | ~generous(X2) [resolution 113,258]
319. wise(X2) | ~generous(X2) <- (23) [subsumption resolution 317,254]
320. wise(X2) <- (7, 23) [subsumption resolution 319,176]
325. humble(X0) <- (7, 23) [resolution 320,84]
332. $false <- (7, 23) [resolution 325,138]
333. ~7 | ~23 [avatar contradiction clause 332]
334. $false [avatar sat refutation 181,218,257,285,301,333]
% SZS output end Proof for 3951306107463031728601911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or not creative is wise or not calm and vice versa.
Everyone who is either humble or wise is either not brave or creative and vice versa.
Everyone who is strong or not happy is quiet or not calm.
Everyone who is not kind or not old is not creative or not curious.
If someone is either quiet or tall then someone is not curious and vice versa.
Everyone who is not brave or not rich is not happy.
If someone is strong or creative then john is both patient and not brave.
If paul is not strong or not brave then someone is both not wise and not generous and vice versa.
Everyone who is either strong or not wise is either not old or tall and vice versa.
If someone is funny or creative then fred is not tall.
Everyone who is both not tall and not happy is kind.
If fred is both curious and quiet then someone is not tall or wise.
Everyone who is not strong or not rich is both kind and not happy and vice versa.
Everyone who is wise is either not curious or humble.
If mary is tall or not humble then someone is quiet or strong and vice versa.
If someone is either humble or not brave then john is both not funny and calm.
John is either not funny or not old.
Someone is both not strong and humble.
John is both quiet and not old.
Someone is calm.
Alice is either not calm or rich.
Someone is both not quiet and not strong.
Susan is either humble or brave.
Paul is either funny or not funny. | John is not happy. | entailment | (![X]:((~strong(X)<~>~creative(X))<=>(wise(X)|~calm(X))))&
(![X]:((humble(X)<~>wise(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((strong(X)|~happy(X))=>(quiet(X)|~calm(X))))&
(![X]:((~kind(X)|~old(X))=>(~creative(X)|~curious(X))))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:(~curious(X))))&
(![X]:((~brave(X)|~rich(X))=>~happy(X)))&
((?[X]:((strong(X)|creative(X))))=>((patient(john)&~brave(john))))&
(((~strong(paul)|~brave(paul)))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((strong(X)<~>~wise(X))<=>(~old(X)<~>tall(X))))&
((?[X]:((funny(X)|creative(X))))=>(~tall(fred)))&
(![X]:((~tall(X)&~happy(X))=>kind(X)))&
(((curious(fred)&quiet(fred)))=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((~strong(X)|~rich(X))<=>(kind(X)&~happy(X))))&
(![X]:(wise(X)=>(~curious(X)<~>humble(X))))&
(((tall(mary)|~humble(mary)))<=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((humble(X)<~>~brave(X))))=>((~funny(john)&calm(john))))&
((~funny(john)<~>~old(john)))&
(?[X]:((~strong(X)&humble(X))))&
((quiet(john)&~old(john)))&
(?[X]:(calm(X)))&
((~calm(alice)<~>rich(alice)))&
(?[X]:((~quiet(X)&~strong(X))))&
((humble(susan)<~>brave(susan)))&
((funny(paul)<~>~funny(paul))) | ~happy(john) | [
"p5",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3291231160170067348430470
% SZS output start Proof for 3291231160170067348430470
6. ! [X0] : ((~rich(X0) | ~brave(X0)) => ~happy(X0)) [input p5]
7. ? [X0] : (creative(X0) | strong(X0)) => (~brave(john) & patient(john)) [input p6]
13. ! [X0] : ((~rich(X0) | ~strong(X0)) <=> (~happy(X0) & kind(X0))) [input p12]
25. happy(john) [input hypothesis]
27. ? [X0] : (creative(X0) | strong(X0)) => ~brave(john) [pure predicate removal 7]
32. ! [X0] : (~happy(X0) | (rich(X0) & brave(X0))) [ennf transformation 6]
33. ~brave(john) | ! [X0] : (~creative(X0) & ~strong(X0)) [ennf transformation 27]
57. ! [X0] : (((~rich(X0) | ~strong(X0)) | (happy(X0) | ~kind(X0))) & ((~happy(X0) & kind(X0)) | (rich(X0) & strong(X0)))) [nnf transformation 13]
58. ! [X0] : ((~rich(X0) | ~strong(X0) | happy(X0) | ~kind(X0)) & ((~happy(X0) & kind(X0)) | (rich(X0) & strong(X0)))) [flattening 57]
98. ~happy(X0) | brave(X0) [cnf transformation 32]
100. ~brave(john) | ~strong(X0) [cnf transformation 33]
121. ~happy(X0) | strong(X0) [cnf transformation 58]
149. happy(john) [cnf transformation 25]
179. 8 <=> brave(john) [avatar definition]
184. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
185. ~strong(X0) <- (9) [avatar component clause 184]
186. 9 | ~8 [avatar split clause 100,179,184]
307. brave(john) [resolution 98,149]
310. 8 [avatar split clause 307,179]
313. strong(john) [resolution 121,149]
314. $false <- (9) [subsumption resolution 313,185]
315. ~9 [avatar contradiction clause 314]
316. $false [avatar sat refutation 186,310,315]
% SZS output end Proof for 3291231160170067348430470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is brave and vice versa. If someone is not kind or old then someone is creative. Everyone who is not creative is kind or funny. Everyone who is patient is curious. If someone is not creative then someone is patient. Everyone who is not creative is either not curious or not patient. If lucy is either curious or not funny then susan is not quiet. Everyone who is either not wise or not generous is either brave or not quiet. Everyone who is not wise or not happy is both quiet and humble and vice versa. If someone is not happy then susan is either not old or quiet. If paul is either quiet or not strong then paul is either happy or not quiet and vice versa. Everyone who is either quiet or curious is either not strong or happy and vice versa. Everyone who is both humble and curious is not humble or not patient and vice versa. If someone is both not wise and tall then someone is tall and vice versa. If lucy is creative or not creative then someone is either calm or not kind and vice versa. Lucy is both not funny and not kind. Alice is funny or old. John is both wise and funny. Someone is not happy. Paul is happy. Lucy is either not generous or patient. | Alice is not curious. | contradiction | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(kind(X)|funny(X))))&
(![X]:(patient(X)=>curious(X)))&
((?[X]:(~creative(X)))=>(?[X]:(patient(X))))&
(![X]:(~creative(X)=>(~curious(X)<~>~patient(X))))&
(((curious(lucy)<~>~funny(lucy)))=>(~quiet(susan)))&
(![X]:((~wise(X)<~>~generous(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~happy(X))<=>(quiet(X)&humble(X))))&
((?[X]:(~happy(X)))=>((~old(susan)<~>quiet(susan))))&
(((quiet(paul)<~>~strong(paul)))<=>((happy(paul)<~>~quiet(paul))))&
(![X]:((quiet(X)<~>curious(X))<=>(~strong(X)<~>happy(X))))&
(![X]:((humble(X)&curious(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
((~funny(lucy)&~kind(lucy)))&
((funny(alice)|old(alice)))&
((wise(john)&funny(john)))&
(?[X]:(~happy(X)))&
(happy(paul))&
((~generous(lucy)<~>patient(lucy))) | ~curious(alice) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6570537648970142923392926
% SZS output start Proof for 6570537648970142923392926
4. ! [X0] : (patient(X0) => curious(X0)) [input p3]
13. ! [X0] : ((curious(X0) & humble(X0)) <=> (~patient(X0) | ~humble(X0))) [input p12]
22. ~curious(alice) [input hypothesis]
29. ! [X0] : (curious(X0) | ~patient(X0)) [ennf transformation 4]
50. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 13]
51. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 50]
70. curious(X0) | ~patient(X0) [cnf transformation 29]
107. curious(X0) | patient(X0) [cnf transformation 51]
126. ~curious(alice) [cnf transformation 22]
199. curious(X0) [subsumption resolution 107,70]
251. $false [subsumption resolution 126,199]
% SZS output end Proof for 6570537648970142923392926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both happy and not happy.
If susan is both curious and patient then someone is either calm or not rich.
Everyone who is both not happy and curious is both not tall and rich.
Everyone who is brave or not patient is not funny and vice versa.
Everyone who is tall is both not generous and not quiet.
Everyone who is not creative is either kind or creative.
Everyone who is either not calm or not tall is either not strong or not tall and vice versa.
Everyone who is not brave or not patient is humble and vice versa.
Everyone who is not brave or patient is creative or humble.
Everyone who is either tall or not funny is either brave or funny and vice versa.
Everyone who is either kind or quiet is quiet and vice versa.
Everyone who is quiet or funny is not creative and vice versa.
Everyone who is both not wise and tall is both not curious and not patient and vice versa.
Everyone who is tall or not old is not quiet or not old.
Everyone who is both not kind and not old is either not humble or not rich and vice versa.
If someone is kind or humble then alice is quiet.
Someone is either curious or not brave.
Susan is happy.
Someone is both not rich and not curious.
Someone is not happy or tall.
Susan is both happy and calm.
Someone is not calm or patient. | Alice is rich. | neutral | (![X]:(~strong(X)=>(happy(X)&~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((quiet(X)|funny(X))<=>~creative(X)))&
(![X]:((~wise(X)&tall(X))<=>(~curious(X)&~patient(X))))&
(![X]:((tall(X)|~old(X))=>(~quiet(X)|~old(X))))&
(![X]:((~kind(X)&~old(X))<=>(~humble(X)<~>~rich(X))))&
((?[X]:((kind(X)|humble(X))))=>(quiet(alice)))&
(?[X]:((curious(X)<~>~brave(X))))&
(happy(susan))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~happy(X)|tall(X))))&
((happy(susan)&calm(susan)))&
(?[X]:((~calm(X)|patient(X)))) | rich(alice) | [] | null | 0 |
Everyone who is not quiet is curious and vice versa.
If fred is both not creative and strong then someone is both humble and not wise and vice versa.
Everyone who is either generous or not generous is either not generous or not happy.
Everyone who is not humble is not old or happy and vice versa.
Everyone who is not rich is either patient or not calm.
Everyone who is not strong is both not tall and happy and vice versa.
Everyone who is both not calm and not tall is funny and vice versa.
Everyone who is either not curious or not calm is not strong or generous.
Everyone who is not creative is either not old or wise and vice versa.
If paul is not kind or not tall then john is either quiet or not patient.
Everyone who is not brave is both not creative and wise.
Everyone who is either not creative or kind is not humble.
Everyone who is both not brave and calm is wise.
Everyone who is not strong is either not creative or not calm and vice versa.
Everyone who is wise is not quiet or not calm and vice versa.
If someone is both generous and creative then susan is either not humble or quiet.
Someone is not quiet.
Paul is not strong or not generous.
Someone is strong.
Someone is either wise or happy.
John is either generous or not funny.
Someone is either not generous or not rich.
Someone is either calm or not happy.
Paul is funny. | Fred is not creative. | neutral | (![X]:(~quiet(X)<=>curious(X)))&
(((~creative(fred)&strong(fred)))<=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:((generous(X)<~>~generous(X))=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)<=>(~old(X)|happy(X))))&
(![X]:(~rich(X)=>(patient(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(~tall(X)&happy(X))))&
(![X]:((~calm(X)&~tall(X))<=>funny(X)))&
(![X]:((~curious(X)<~>~calm(X))=>(~strong(X)|generous(X))))&
(![X]:(~creative(X)<=>(~old(X)<~>wise(X))))&
(((~kind(paul)|~tall(paul)))=>((quiet(john)<~>~patient(john))))&
(![X]:(~brave(X)=>(~creative(X)&wise(X))))&
(![X]:((~creative(X)<~>kind(X))=>~humble(X)))&
(![X]:((~brave(X)&calm(X))=>wise(X)))&
(![X]:(~strong(X)<=>(~creative(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(~quiet(X)|~calm(X))))&
((?[X]:((generous(X)&creative(X))))=>((~humble(susan)<~>quiet(susan))))&
(?[X]:(~quiet(X)))&
((~strong(paul)|~generous(paul)))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)<~>happy(X))))&
((generous(john)<~>~funny(john)))&
(?[X]:((~generous(X)<~>~rich(X))))&
(?[X]:((calm(X)<~>~happy(X))))&
(funny(paul)) | ~creative(fred) | [] | null | 0 |
If someone is both kind and quiet then someone is either not creative or not rich and vice versa.
If john is either old or not wise then someone is both not kind and not wise and vice versa.
Everyone who is creative or strong is either strong or not patient and vice versa.
Everyone who is both not quiet and brave is kind.
If mary is brave then someone is both brave and not strong.
If alice is generous then someone is both not humble and not creative and vice versa.
If someone is not funny then lucy is not wise or quiet.
Everyone who is humble or not calm is both tall and brave and vice versa.
Everyone who is creative or old is not creative and vice versa.
Everyone who is either tall or not patient is not strong or not old and vice versa.
If someone is generous or not brave then paul is happy or not calm.
If alice is not patient then fred is both rich and humble and vice versa.
If john is not creative or wise then someone is creative or not funny.
If susan is either calm or funny then lucy is either tall or old.
Everyone who is either old or wise is either tall or not funny.
Lucy is rich or not rich.
Someone is not strong.
Susan is both not rich and not calm.
Paul is both not tall and funny.
Alice is either brave or strong. | Paul is not humble. | entailment | ((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(((old(john)<~>~wise(john)))<=>(?[X]:((~kind(X)&~wise(X)))))&
(![X]:((creative(X)|strong(X))<=>(strong(X)<~>~patient(X))))&
(![X]:((~quiet(X)&brave(X))=>kind(X)))&
((brave(mary))=>(?[X]:((brave(X)&~strong(X)))))&
((generous(alice))<=>(?[X]:((~humble(X)&~creative(X)))))&
((?[X]:(~funny(X)))=>((~wise(lucy)|quiet(lucy))))&
(![X]:((humble(X)|~calm(X))<=>(tall(X)&brave(X))))&
(![X]:((creative(X)|old(X))<=>~creative(X)))&
(![X]:((tall(X)<~>~patient(X))<=>(~strong(X)|~old(X))))&
((?[X]:((generous(X)|~brave(X))))=>((happy(paul)|~calm(paul))))&
((~patient(alice))<=>((rich(fred)&humble(fred))))&
(((~creative(john)|wise(john)))=>(?[X]:((creative(X)|~funny(X)))))&
(((calm(susan)<~>funny(susan)))=>((tall(lucy)<~>old(lucy))))&
(![X]:((old(X)<~>wise(X))=>(tall(X)<~>~funny(X))))&
((rich(lucy)|~rich(lucy)))&
(?[X]:(~strong(X)))&
((~rich(susan)&~calm(susan)))&
((~tall(paul)&funny(paul)))&
((brave(alice)<~>strong(alice))) | ~humble(paul) | [
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 268944148172089238720752
% SZS output start Proof for 268944148172089238720752
8. ! [X0] : ((~calm(X0) | humble(X0)) <=> (brave(X0) & tall(X0))) [input p7]
19. funny(paul) & ~tall(paul) [input p18]
21. humble(paul) [input hypothesis]
49. ! [X0] : (((~calm(X0) | humble(X0)) | (~brave(X0) | ~tall(X0))) & ((brave(X0) & tall(X0)) | (calm(X0) & ~humble(X0)))) [nnf transformation 8]
50. ! [X0] : ((~calm(X0) | humble(X0) | ~brave(X0) | ~tall(X0)) & ((brave(X0) & tall(X0)) | (calm(X0) & ~humble(X0)))) [flattening 49]
89. ~humble(X0) | tall(X0) [cnf transformation 50]
120. ~tall(paul) [cnf transformation 19]
124. humble(paul) [cnf transformation 21]
287. tall(paul) [resolution 89,124]
290. $false [subsumption resolution 287,120]
% SZS output end Proof for 268944148172089238720752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both not rich and not generous.
Everyone who is old is both generous and not creative.
If fred is not funny then lucy is either old or curious.
Everyone who is not happy is either not humble or not quiet and vice versa.
Everyone who is either not humble or humble is both not wise and not happy and vice versa.
Everyone who is not patient is not creative or kind and vice versa.
Everyone who is not funny or not creative is curious and vice versa.
Everyone who is not rich or not happy is creative or not patient.
Everyone who is either not quiet or not calm is either not patient or calm and vice versa.
Everyone who is not happy or not curious is both not brave and generous.
Everyone who is both not creative and not happy is both not kind and funny and vice versa.
Everyone who is both funny and not brave is either not old or not strong.
If someone is not curious then someone is both quiet and patient.
If alice is both happy and funny then someone is patient.
Everyone who is either kind or not tall is rich and vice versa.
Everyone who is either not funny or brave is both not curious and not generous.
Someone is tall or not kind.
Someone is not brave.
Someone is either rich or wise.
Someone is not old.
Alice is either not tall or not patient. | Lucy is creative. | contradiction | (![X]:(~quiet(X)=>(~rich(X)&~generous(X))))&
(![X]:(old(X)=>(generous(X)&~creative(X))))&
((~funny(fred))=>((old(lucy)<~>curious(lucy))))&
(![X]:(~happy(X)<=>(~humble(X)<~>~quiet(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(~wise(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~creative(X)|kind(X))))&
(![X]:((~funny(X)|~creative(X))<=>curious(X)))&
(![X]:((~rich(X)|~happy(X))=>(creative(X)|~patient(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((~tall(alice)<~>~patient(alice))) | creative(lucy) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2721629111560175087438376
% SZS output start Proof for 2721629111560175087438376
1. ! [X0] : (~quiet(X0) => (~generous(X0) & ~rich(X0))) [input p0]
5. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~happy(X0) & ~wise(X0))) [input p4]
7. ! [X0] : ((~creative(X0) | ~funny(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p8]
10. ! [X0] : ((~curious(X0) | ~happy(X0)) => (generous(X0) & ~brave(X0))) [input p9]
13. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p12]
16. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~generous(X0) & ~curious(X0))) [input p15]
22. creative(lucy) [input hypothesis]
23. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 13]
24. ! [X0] : ((~generous(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 1]
29. ! [X0] : ((generous(X0) & ~brave(X0)) | (curious(X0) & happy(X0))) [ennf transformation 10]
32. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 23]
35. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 16]
38. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 38]
42. ! [X0] : (((~creative(X0) | ~funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [nnf transformation 7]
43. ! [X0] : ((~creative(X0) | ~funny(X0) | ~curious(X0)) & (curious(X0) | (creative(X0) & funny(X0)))) [flattening 42]
44. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 9]
48. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 32]
49. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK0) & quiet(sK0)) [choice axiom]
50. (patient(sK0) & quiet(sK0)) | ! [X1] : curious(X1) [skolemisation 48,49]
54. ! [X0] : ((~generous(X0) & ~curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 35]
66. ~generous(X0) | quiet(X0) [cnf transformation 24]
77. ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 39]
78. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 39]
86. ~curious(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 43]
90. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 44]
94. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 44]
97. ~brave(X0) | happy(X0) [cnf transformation 29]
99. generous(X0) | happy(X0) [cnf transformation 29]
108. patient(sK0) | curious(X1) [cnf transformation 50]
116. ~generous(X0) | brave(X0) | funny(X0) [cnf transformation 54]
125. creative(lucy) [cnf transformation 22]
126. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 90]
128. ~calm(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 94]
132. ~happy(X0) | humble(X0) [duplicate literal removal 77]
133. ~humble(X0) | ~happy(X0) [duplicate literal removal 78]
143. 3 <=> curious(lucy) [avatar definition]
144. curious(lucy) <- (3) [avatar component clause 143]
145. ~curious(lucy) <- (~3) [avatar component clause 143]
148. ~happy(X0) [subsumption resolution 132,133]
151. ~patient(X0) | ~quiet(X0) [subsumption resolution 126,128]
152. generous(X0) [subsumption resolution 99,148]
153. ~brave(X0) [subsumption resolution 97,148]
159. 4 <=> ! [X1] : curious(X1) [avatar definition]
160. curious(X1) <- (4) [avatar component clause 159]
162. 5 <=> patient(sK0) [avatar definition]
164. patient(sK0) <- (5) [avatar component clause 162]
165. 4 | 5 [avatar split clause 108,162,159]
171. brave(X0) | funny(X0) [subsumption resolution 116,152]
172. funny(X0) [subsumption resolution 171,153]
193. $false <- (~3, 4) [subsumption resolution 145,160]
194. 3 | ~4 [avatar contradiction clause 193]
196. quiet(X0) [resolution 66,152]
206. ~quiet(sK0) <- (5) [resolution 151,164]
210. $false <- (5) [subsumption resolution 206,196]
211. ~5 [avatar contradiction clause 210]
234. ~funny(lucy) | ~creative(lucy) <- (3) [resolution 86,144]
239. ~creative(lucy) <- (3) [subsumption resolution 234,172]
240. $false <- (3) [subsumption resolution 239,125]
241. ~3 [avatar contradiction clause 240]
243. $false [avatar sat refutation 165,194,211,241]
% SZS output end Proof for 2721629111560175087438376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not patient and not tall then paul is either not strong or not kind and vice versa. If someone is not calm or not creative then alice is either kind or not curious. Everyone who is either not happy or funny is both quiet and not calm and vice versa. If fred is either calm or wise then someone is both wise and funny and vice versa. If someone is both creative and happy then someone is not generous or not wise. Everyone who is happy or humble is both not brave and not calm and vice versa. If someone is not brave or not happy then someone is old or generous and vice versa. If lucy is not old then susan is not wise and vice versa. If someone is not curious then someone is both strong and generous and vice versa. If someone is not strong then paul is either creative or generous and vice versa. If someone is funny or not curious then alice is not generous. If someone is funny then mary is either not quiet or humble and vice versa. If susan is both curious and not old then susan is both not rich and calm and vice versa. If john is either not creative or creative then someone is either kind or strong. If paul is either not creative or not tall then fred is either creative or not patient. If someone is not brave or rich then lucy is either funny or not rich and vice versa. Someone is not happy. John is not rich or wise. Paul is either not humble or not patient. Susan is both humble and happy. Someone is not quiet. John is either strong or not tall. | Lucy is brave. | neutral | (((~patient(susan)&~tall(susan)))<=>((~strong(paul)<~>~kind(paul))))&
((?[X]:((~calm(X)|~creative(X))))=>((kind(alice)<~>~curious(alice))))&
(![X]:((~happy(X)<~>funny(X))<=>(quiet(X)&~calm(X))))&
(((calm(fred)<~>wise(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((happy(X)|humble(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~brave(X)|~happy(X))))<=>(?[X]:((old(X)|generous(X)))))&
((~old(lucy))<=>(~wise(susan)))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)&generous(X)))))&
((?[X]:(~strong(X)))<=>((creative(paul)<~>generous(paul))))&
((?[X]:((funny(X)|~curious(X))))=>(~generous(alice)))&
((?[X]:(funny(X)))<=>((~quiet(mary)<~>humble(mary))))&
(((curious(susan)&~old(susan)))<=>((~rich(susan)&calm(susan))))&
(((~creative(john)<~>creative(john)))=>(?[X]:((kind(X)<~>strong(X)))))&
(((~creative(paul)<~>~tall(paul)))=>((creative(fred)<~>~patient(fred))))&
((?[X]:((~brave(X)|rich(X))))<=>((funny(lucy)<~>~rich(lucy))))&
(?[X]:(~happy(X)))&
((~rich(john)|wise(john)))&
((~humble(paul)<~>~patient(paul)))&
((humble(susan)&happy(susan)))&
(?[X]:(~quiet(X)))&
((strong(john)<~>~tall(john))) | brave(lucy) | [] | null | 0 |
If someone is not rich then someone is not wise or not funny and vice versa.
Everyone who is not quiet is not humble and vice versa.
If mary is both not funny and strong then someone is either calm or not strong and vice versa.
Everyone who is happy or curious is not funny or happy.
If someone is old then susan is both generous and not generous.
Everyone who is not quiet is both not rich and humble and vice versa.
If someone is old then mary is either not old or not kind.
Everyone who is either not curious or not creative is both not strong and old.
If paul is curious or funny then mary is not curious or not strong.
Everyone who is wise or brave is both strong and funny.
Everyone who is both not generous and not patient is not humble and vice versa.
Everyone who is not calm is happy.
Everyone who is tall or rich is humble.
If someone is both not kind and not funny then mary is either kind or not tall.
If paul is kind or tall then paul is either tall or not wise and vice versa.
If someone is either humble or not generous then someone is either calm or not quiet.
Someone is both not calm and not kind.
Paul is both patient and not kind.
Someone is not happy or not kind.
Paul is strong.
Someone is curious or not quiet.
Someone is both strong and happy. | Susan is not calm. | entailment | ((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(~quiet(X)<=>~humble(X)))&
(((~funny(mary)&strong(mary)))<=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((happy(X)|curious(X))=>(~funny(X)|happy(X))))&
((?[X]:(old(X)))=>((generous(susan)&~generous(susan))))&
(![X]:(~quiet(X)<=>(~rich(X)&humble(X))))&
((?[X]:(old(X)))=>((~old(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~creative(X))=>(~strong(X)&old(X))))&
(((curious(paul)|funny(paul)))=>((~curious(mary)|~strong(mary))))&
(![X]:((wise(X)|brave(X))=>(strong(X)&funny(X))))&
(![X]:((~generous(X)&~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>happy(X)))&
(![X]:((tall(X)|rich(X))=>humble(X)))&
((?[X]:((~kind(X)&~funny(X))))=>((kind(mary)<~>~tall(mary))))&
(((kind(paul)|tall(paul)))<=>((tall(paul)<~>~wise(paul))))&
((?[X]:((humble(X)<~>~generous(X))))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(?[X]:((~calm(X)&~kind(X))))&
((patient(paul)&~kind(paul)))&
(?[X]:((~happy(X)|~kind(X))))&
(strong(paul))&
(?[X]:((curious(X)|~quiet(X))))&
(?[X]:((strong(X)&happy(X)))) | ~calm(susan) | [
"p0",
"p1",
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7944619271310180774515049
% SZS output start Proof for 7944619271310180774515049
1. ? [X0] : ~rich(X0) <=> ? [X0] : (~funny(X0) | ~wise(X0)) [input p0]
2. ! [X0] : (~quiet(X0) <=> ~humble(X0)) [input p1]
3. (strong(mary) & ~funny(mary)) <=> ? [X0] : (calm(X0) <~> ~strong(X0)) [input p2]
6. ! [X0] : (~quiet(X0) <=> (humble(X0) & ~rich(X0))) [input p5]
10. ! [X0] : ((brave(X0) | wise(X0)) => (funny(X0) & strong(X0))) [input p9]
23. calm(susan) [input hypothesis]
24. ? [X0] : ~rich(X0) <=> ? [X1] : (~funny(X1) | ~wise(X1)) [rectify 1]
26. ! [X0] : (wise(X0) => (funny(X0) & strong(X0))) [pure predicate removal 10]
34. ! [X0] : ((funny(X0) & strong(X0)) | ~wise(X0)) [ennf transformation 26]
39. (? [X0] : ~rich(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X1] : (~funny(X1) | ~wise(X1)) | ! [X0] : rich(X0)) [nnf transformation 24]
40. (? [X0] : ~rich(X0) | ! [X1] : (funny(X1) & wise(X1))) & (? [X2] : (~funny(X2) | ~wise(X2)) | ! [X3] : rich(X3)) [rectify 39]
41. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
42. ? [X2] : (~funny(X2) | ~wise(X2)) => (~funny(sK1) | ~wise(sK1)) [choice axiom]
43. (~rich(sK0) | ! [X1] : (funny(X1) & wise(X1))) & ((~funny(sK1) | ~wise(sK1)) | ! [X3] : rich(X3)) [skolemisation 40,42,41]
44. ! [X0] : ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0))) [nnf transformation 2]
45. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (~strong(mary) | funny(mary))) [nnf transformation 3]
46. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ~strong(mary) | funny(mary)) [flattening 45]
47. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (? [X1] : ((strong(X1) | ~calm(X1)) & (~strong(X1) | calm(X1))) | ~strong(mary) | funny(mary)) [rectify 46]
48. ? [X1] : ((strong(X1) | ~calm(X1)) & (~strong(X1) | calm(X1))) => ((strong(sK2) | ~calm(sK2)) & (~strong(sK2) | calm(sK2))) [choice axiom]
49. ((strong(mary) & ~funny(mary)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) & (((strong(sK2) | ~calm(sK2)) & (~strong(sK2) | calm(sK2))) | ~strong(mary) | funny(mary)) [skolemisation 47,48]
50. ! [X0] : ((~quiet(X0) | (~humble(X0) | rich(X0))) & ((humble(X0) & ~rich(X0)) | quiet(X0))) [nnf transformation 6]
51. ! [X0] : ((~quiet(X0) | ~humble(X0) | rich(X0)) & ((humble(X0) & ~rich(X0)) | quiet(X0))) [flattening 50]
72. ~rich(sK0) | wise(X1) [cnf transformation 43]
73. ~rich(sK0) | funny(X1) [cnf transformation 43]
74. ~humble(X0) | quiet(X0) [cnf transformation 44]
75. ~quiet(X0) | humble(X0) [cnf transformation 44]
78. ~funny(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 49]
87. humble(X0) | quiet(X0) [cnf transformation 51]
88. ~quiet(X0) | ~humble(X0) | rich(X0) [cnf transformation 51]
97. ~wise(X0) | strong(X0) [cnf transformation 34]
126. calm(susan) [cnf transformation 23]
130. 1 <=> ! [X1] : funny(X1) [avatar definition]
131. funny(X1) <- (1) [avatar component clause 130]
133. 2 <=> rich(sK0) [avatar definition]
135. ~rich(sK0) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 73,133,130]
138. 3 <=> ! [X1] : wise(X1) [avatar definition]
139. wise(X1) <- (3) [avatar component clause 138]
140. 3 | ~2 [avatar split clause 72,133,138]
142. 4 <=> ! [X3] : rich(X3) [avatar definition]
143. rich(X3) <- (4) [avatar component clause 142]
162. 9 <=> ! [X0] : (~strong(X0) | ~calm(X0)) [avatar definition]
163. ~calm(X0) | ~strong(X0) <- (9) [avatar component clause 162]
166. 10 <=> funny(mary) [avatar definition]
168. ~funny(mary) <- (~10) [avatar component clause 166]
170. 9 | ~10 [avatar split clause 78,166,162]
190. ~humble(X0) | rich(X0) [subsumption resolution 88,74]
191. humble(X0) [subsumption resolution 87,75]
285. rich(X0) [resolution 190,191]
286. 4 [avatar split clause 285,142]
287. $false <- (~2, 4) [resolution 143,135]
289. 2 | ~4 [avatar contradiction clause 287]
290. $false <- (1, ~10) [resolution 131,168]
291. ~1 | 10 [avatar contradiction clause 290]
294. strong(X1) <- (3) [resolution 139,97]
301. ~strong(susan) <- (9) [resolution 163,126]
303. $false <- (3, 9) [subsumption resolution 301,294]
304. ~3 | ~9 [avatar contradiction clause 303]
305. $false [avatar sat refutation 136,140,170,286,289,291,304]
% SZS output end Proof for 7944619271310180774515049
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is quiet then someone is not happy. Everyone who is kind is tall or not tall and vice versa. Everyone who is curious is both humble and not kind and vice versa. If someone is quiet or tall then someone is not creative and vice versa. Everyone who is either patient or not patient is not brave and vice versa. Everyone who is brave or strong is not calm. If someone is not wise or patient then someone is not rich. Everyone who is either old or brave is not funny. Everyone who is not rich or curious is wise or kind and vice versa. Everyone who is not happy or rich is not patient or rich and vice versa. Everyone who is happy or not strong is either not curious or not patient. If someone is both happy and brave then someone is not brave. Everyone who is wise is not creative and vice versa. If fred is both humble and brave then alice is either not creative or not curious and vice versa. Everyone who is either happy or curious is either old or strong. If someone is either strong or not quiet then someone is both humble and happy and vice versa. Someone is strong. Lucy is old. Someone is generous or brave. Someone is not wise or not calm. Someone is not humble or curious. Alice is quiet or creative. | Alice is generous. | neutral | ((quiet(mary))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)<=>(tall(X)|~tall(X))))&
(![X]:(curious(X)<=>(humble(X)&~kind(X))))&
((?[X]:((quiet(X)|tall(X))))<=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((brave(X)|strong(X))=>~calm(X)))&
((?[X]:((~wise(X)|patient(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)<~>brave(X))=>~funny(X)))&
(![X]:((~rich(X)|curious(X))<=>(wise(X)|kind(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((?[X]:((happy(X)&brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(wise(X)<=>~creative(X)))&
(((humble(fred)&brave(fred)))<=>((~creative(alice)<~>~curious(alice))))&
(![X]:((happy(X)<~>curious(X))=>(old(X)<~>strong(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>(?[X]:((humble(X)&happy(X)))))&
(?[X]:(strong(X)))&
(old(lucy))&
(?[X]:((generous(X)|brave(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~humble(X)|curious(X))))&
((quiet(alice)|creative(alice))) | generous(alice) | [] | null | 0 |
If someone is not kind or tall then mary is either not kind or rich.
Everyone who is not curious or not happy is not generous or funny.
If someone is either not rich or curious then lucy is both rich and tall and vice versa.
Everyone who is both brave and not generous is not creative.
If john is not old then someone is either humble or not brave.
If someone is calm or not tall then mary is not quiet or happy.
If fred is either not kind or not patient then paul is not calm.
If someone is old then someone is not patient or funny and vice versa.
If someone is both not kind and humble then alice is not quiet or not curious and vice versa.
Everyone who is either not old or not humble is humble and vice versa.
Everyone who is both quiet and curious is not curious or not patient and vice versa.
If someone is both calm and patient then lucy is not tall and vice versa.
Everyone who is either not happy or not curious is either kind or generous and vice versa.
Everyone who is humble is creative or calm and vice versa.
Everyone who is both not humble and creative is quiet.
Everyone who is old or not curious is both not old and not tall.
John is humble or old.
John is not generous.
Someone is both strong and not generous.
Mary is either curious or not generous.
John is both curious and not happy. | John is old. | contradiction | ((?[X]:((~kind(X)|tall(X))))=>((~kind(mary)<~>rich(mary))))&
(![X]:((~curious(X)|~happy(X))=>(~generous(X)|funny(X))))&
((?[X]:((~rich(X)<~>curious(X))))<=>((rich(lucy)&tall(lucy))))&
(![X]:((brave(X)&~generous(X))=>~creative(X)))&
((~old(john))=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:((calm(X)|~tall(X))))=>((~quiet(mary)|happy(mary))))&
(((~kind(fred)<~>~patient(fred)))=>(~calm(paul)))&
((?[X]:(old(X)))<=>(?[X]:((~patient(X)|funny(X)))))&
((?[X]:((~kind(X)&humble(X))))<=>((~quiet(alice)|~curious(alice))))&
(![X]:((~old(X)<~>~humble(X))<=>humble(X)))&
(![X]:((quiet(X)&curious(X))<=>(~curious(X)|~patient(X))))&
((?[X]:((calm(X)&patient(X))))<=>(~tall(lucy)))&
(![X]:((~happy(X)<~>~curious(X))<=>(kind(X)<~>generous(X))))&
(![X]:(humble(X)<=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&creative(X))=>quiet(X)))&
(![X]:((old(X)|~curious(X))=>(~old(X)&~tall(X))))&
((humble(john)|old(john)))&
(~generous(john))&
(?[X]:((strong(X)&~generous(X))))&
((curious(mary)<~>~generous(mary)))&
((curious(john)&~happy(john))) | old(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4347142457215656485653944
% SZS output start Proof for 4347142457215656485653944
16. ! [X0] : ((~curious(X0) | old(X0)) => (~tall(X0) & ~old(X0))) [input p15]
22. old(john) [input hypothesis]
36. ! [X0] : ((~tall(X0) & ~old(X0)) | (curious(X0) & ~old(X0))) [ennf transformation 16]
121. ~old(X0) | ~old(X0) [cnf transformation 36]
132. old(john) [cnf transformation 22]
133. ~old(X0) [duplicate literal removal 121]
185. 11 <=> old(john) [avatar definition]
187. old(john) <- (11) [avatar component clause 185]
241. 24 <=> ! [X3] : ~old(X3) [avatar definition]
242. ~old(X3) <- (24) [avatar component clause 241]
297. 24 [avatar split clause 133,241]
304. 11 [avatar split clause 132,185]
309. $false <- (11, 24) [subsumption resolution 187,242]
310. ~11 | ~24 [avatar contradiction clause 309]
312. $false [avatar sat refutation 297,304,310]
% SZS output end Proof for 4347142457215656485653944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and creative is old and vice versa.
Everyone who is humble is both funny and not patient and vice versa.
If someone is both funny and brave then alice is strong or not tall and vice versa.
Everyone who is not quiet is either humble or not humble.
Everyone who is brave is both patient and not old.
Everyone who is kind is tall.
If someone is wise or calm then someone is generous or strong.
Everyone who is generous or old is patient or not calm and vice versa.
Everyone who is happy or not old is either not brave or not calm.
Everyone who is either not patient or not creative is not strong and vice versa.
Everyone who is both not calm and kind is both not generous and not funny and vice versa.
Everyone who is not quiet or not strong is not generous.
If susan is not brave or not wise then someone is both not creative and not calm and vice versa.
Everyone who is both not brave and rich is both not brave and not kind and vice versa.
Everyone who is humble is either kind or not funny and vice versa.
If someone is not calm then john is not quiet and vice versa.
Someone is patient.
John is either generous or not kind.
Mary is either happy or not kind.
Someone is not kind or not rich.
Paul is not curious.
Someone is either not generous or old.
Someone is not humble.
Fred is not tall. | Mary is brave. | contradiction | (![X]:((~happy(X)&creative(X))<=>old(X)))&
(![X]:(humble(X)<=>(funny(X)&~patient(X))))&
((?[X]:((funny(X)&brave(X))))<=>((strong(alice)|~tall(alice))))&
(![X]:(~quiet(X)=>(humble(X)<~>~humble(X))))&
(![X]:(brave(X)=>(patient(X)&~old(X))))&
(![X]:(kind(X)=>tall(X)))&
((?[X]:((wise(X)|calm(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((generous(X)|old(X))<=>(patient(X)|~calm(X))))&
(![X]:((happy(X)|~old(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>~strong(X)))&
(![X]:((~calm(X)&kind(X))<=>(~generous(X)&~funny(X))))&
(![X]:((~quiet(X)|~strong(X))=>~generous(X)))&
(((~brave(susan)|~wise(susan)))<=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~brave(X)&rich(X))<=>(~brave(X)&~kind(X))))&
(![X]:(humble(X)<=>(kind(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(~quiet(john)))&
(?[X]:(patient(X)))&
((generous(john)<~>~kind(john)))&
((happy(mary)<~>~kind(mary)))&
(?[X]:((~kind(X)|~rich(X))))&
(~curious(paul))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:(~humble(X)))&
(~tall(fred)) | brave(mary) | [
"p0",
"p4",
"p7",
"p8",
"p9",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2169460092805570845742514
% SZS output start Proof for 2169460092805570845742514
1. ! [X0] : ((creative(X0) & ~happy(X0)) <=> old(X0)) [input p0]
5. ! [X0] : (brave(X0) => (~old(X0) & patient(X0))) [input p4]
8. ! [X0] : ((old(X0) | generous(X0)) <=> (~calm(X0) | patient(X0))) [input p7]
9. ! [X0] : ((~old(X0) | happy(X0)) => (~brave(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((~patient(X0) <~> ~creative(X0)) <=> ~strong(X0)) [input p9]
11. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (~funny(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((~strong(X0) | ~quiet(X0)) => ~generous(X0)) [input p11]
19. happy(mary) <~> ~kind(mary) [input p18]
25. brave(mary) [input hypothesis]
29. ! [X0] : ((~old(X0) & patient(X0)) | ~brave(X0)) [ennf transformation 5]
32. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (old(X0) & ~happy(X0))) [ennf transformation 9]
33. ! [X0] : (~generous(X0) | (strong(X0) & quiet(X0))) [ennf transformation 12]
34. ! [X0] : (((creative(X0) & ~happy(X0)) | ~old(X0)) & (old(X0) | (~creative(X0) | happy(X0)))) [nnf transformation 1]
35. ! [X0] : (((creative(X0) & ~happy(X0)) | ~old(X0)) & (old(X0) | ~creative(X0) | happy(X0))) [flattening 34]
47. ! [X0] : (((old(X0) | generous(X0)) | (calm(X0) & ~patient(X0))) & ((~calm(X0) | patient(X0)) | (~old(X0) & ~generous(X0)))) [nnf transformation 8]
48. ! [X0] : ((old(X0) | generous(X0) | (calm(X0) & ~patient(X0))) & (~calm(X0) | patient(X0) | (~old(X0) & ~generous(X0)))) [flattening 47]
49. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (old(X0) & ~happy(X0))) [nnf transformation 32]
50. ! [X0] : ((((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | strong(X0)) & (~strong(X0) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))))) [nnf transformation 10]
51. ! [X0] : (((kind(X0) & ~calm(X0)) | (funny(X0) | generous(X0))) & ((~funny(X0) & ~generous(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 11]
52. ! [X0] : (((kind(X0) & ~calm(X0)) | funny(X0) | generous(X0)) & ((~funny(X0) & ~generous(X0)) | ~kind(X0) | calm(X0))) [flattening 51]
68. (kind(mary) | ~happy(mary)) & (~kind(mary) | happy(mary)) [nnf transformation 19]
76. ~creative(X0) | old(X0) | happy(X0) [cnf transformation 35]
89. ~brave(X0) | patient(X0) [cnf transformation 29]
90. ~brave(X0) | ~old(X0) [cnf transformation 29]
96. ~patient(X0) | generous(X0) | old(X0) [cnf transformation 48]
99. ~calm(X0) | ~brave(X0) | old(X0) [cnf transformation 49]
103. ~strong(X0) | ~patient(X0) | creative(X0) [cnf transformation 50]
106. ~generous(X0) | ~kind(X0) | calm(X0) [cnf transformation 52]
111. ~generous(X0) | strong(X0) [cnf transformation 33]
131. kind(mary) | ~happy(mary) [cnf transformation 68]
137. brave(mary) [cnf transformation 25]
178. ~calm(X0) | ~brave(X0) [subsumption resolution 99,90]
229. 20 <=> happy(mary) [avatar definition]
233. 21 <=> kind(mary) [avatar definition]
236. ~20 | 21 [avatar split clause 131,233,229]
258. patient(mary) [resolution 89,137]
261. ~old(mary) [resolution 90,137]
323. generous(mary) | old(mary) [resolution 96,258]
334. generous(mary) [subsumption resolution 323,261]
406. 42 <=> strong(mary) [avatar definition]
408. strong(mary) <- (42) [avatar component clause 406]
410. 43 <=> creative(mary) [avatar definition]
411. creative(mary) <- (43) [avatar component clause 410]
508. ~kind(mary) | calm(mary) [resolution 334,106]
510. strong(mary) [resolution 334,111]
512. 42 [avatar split clause 510,406]
574. 58 <=> calm(mary) [avatar definition]
576. calm(mary) <- (58) [avatar component clause 574]
577. 58 | ~21 [avatar split clause 508,233,574]
604. ~patient(mary) | creative(mary) <- (42) [resolution 408,103]
606. creative(mary) <- (42) [subsumption resolution 604,258]
609. 43 | ~42 [avatar split clause 606,406,410]
610. old(mary) | happy(mary) <- (43) [resolution 411,76]
748. ~brave(mary) <- (58) [resolution 576,178]
749. $false <- (58) [subsumption resolution 748,137]
750. ~58 [avatar contradiction clause 749]
751. happy(mary) <- (43) [subsumption resolution 610,261]
752. 20 | ~43 [avatar split clause 751,410,229]
753. $false [avatar sat refutation 236,512,577,609,750,752]
% SZS output end Proof for 2169460092805570845742514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not kind is not wise.
Everyone who is not quiet or not humble is either not old or quiet.
Everyone who is either not rich or old is brave and vice versa.
Everyone who is either funny or creative is either not happy or not generous.
If someone is not funny or curious then lucy is either creative or patient.
Everyone who is either tall or quiet is both not tall and quiet.
Everyone who is not generous or not funny is both not patient and old.
Everyone who is either old or not patient is both not brave and not happy and vice versa.
Everyone who is old is either wise or funny.
Everyone who is rich is both generous and brave and vice versa.
Everyone who is tall or not brave is not creative.
If lucy is happy then someone is either not brave or not strong and vice versa.
If someone is either old or not kind then someone is both not humble and not happy.
If susan is patient or not tall then lucy is not curious.
If someone is both humble and brave then lucy is both calm and generous.
If lucy is either not humble or brave then someone is both generous and tall.
Paul is not brave.
Alice is both not humble and not patient.
Fred is not calm or not creative.
Lucy is both not tall and not brave. | Alice is not wise. | neutral | (![X]:((~quiet(X)&~kind(X))=>~wise(X)))&
(![X]:((~quiet(X)|~humble(X))=>(~old(X)<~>quiet(X))))&
(![X]:((~rich(X)<~>old(X))<=>brave(X)))&
(![X]:((funny(X)<~>creative(X))=>(~happy(X)<~>~generous(X))))&
((?[X]:((~funny(X)|curious(X))))=>((creative(lucy)<~>patient(lucy))))&
(![X]:((tall(X)<~>quiet(X))=>(~tall(X)&quiet(X))))&
(![X]:((~generous(X)|~funny(X))=>(~patient(X)&old(X))))&
(![X]:((old(X)<~>~patient(X))<=>(~brave(X)&~happy(X))))&
(![X]:(old(X)=>(wise(X)<~>funny(X))))&
(![X]:(rich(X)<=>(generous(X)&brave(X))))&
(![X]:((tall(X)|~brave(X))=>~creative(X)))&
((happy(lucy))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((old(X)<~>~kind(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(((patient(susan)|~tall(susan)))=>(~curious(lucy)))&
((?[X]:((humble(X)&brave(X))))=>((calm(lucy)&generous(lucy))))&
(((~humble(lucy)<~>brave(lucy)))=>(?[X]:((generous(X)&tall(X)))))&
(~brave(paul))&
((~humble(alice)&~patient(alice)))&
((~calm(fred)|~creative(fred)))&
((~tall(lucy)&~brave(lucy))) | ~wise(alice) | [] | null | 0 |
If lucy is old or not tall then paul is wise or curious.
Everyone who is humble is both not calm and not generous and vice versa.
Everyone who is quiet or not brave is rich and vice versa.
If paul is either creative or funny then paul is tall.
Everyone who is curious is not strong.
If lucy is not brave then lucy is either rich or not tall.
If mary is brave then paul is either humble or funny.
Everyone who is curious is not funny and vice versa.
If someone is tall or funny then someone is not funny or quiet and vice versa.
Everyone who is not old or not creative is either tall or not calm and vice versa.
Everyone who is not generous is not happy.
Everyone who is not old is not curious.
Everyone who is either not happy or strong is not tall.
If someone is both not old and happy then someone is funny.
If someone is not happy then someone is generous.
Everyone who is either old or not wise is not humble.
Someone is brave.
Lucy is not old or not rich.
Paul is not funny.
John is not old.
Someone is either rich or not patient.
Lucy is not happy.
John is rich or kind.
Paul is either not quiet or not tall. | Paul is not rich. | neutral | (((old(lucy)|~tall(lucy)))=>((wise(paul)|curious(paul))))&
(![X]:(humble(X)<=>(~calm(X)&~generous(X))))&
(![X]:((quiet(X)|~brave(X))<=>rich(X)))&
(((creative(paul)<~>funny(paul)))=>(tall(paul)))&
(![X]:(curious(X)=>~strong(X)))&
((~brave(lucy))=>((rich(lucy)<~>~tall(lucy))))&
((brave(mary))=>((humble(paul)<~>funny(paul))))&
(![X]:(curious(X)<=>~funny(X)))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~old(X)|~creative(X))<=>(tall(X)<~>~calm(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:(~old(X)=>~curious(X)))&
(![X]:((~happy(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((old(X)<~>~wise(X))=>~humble(X)))&
(?[X]:(brave(X)))&
((~old(lucy)|~rich(lucy)))&
(~funny(paul))&
(~old(john))&
(?[X]:((rich(X)<~>~patient(X))))&
(~happy(lucy))&
((rich(john)|kind(john)))&
((~quiet(paul)<~>~tall(paul))) | ~rich(paul) | [] | null | 0 |
Everyone who is both not strong and not kind is either not tall or not strong.
If mary is either creative or not strong then someone is either not humble or curious.
If lucy is both not happy and not brave then susan is calm.
Everyone who is both curious and old is quiet or not patient.
Everyone who is not wise is either not kind or not funny.
Everyone who is brave or tall is either rich or not curious.
Everyone who is either calm or tall is either rich or not wise and vice versa.
Everyone who is not wise is both not curious and not rich and vice versa.
Everyone who is either not generous or calm is either old or not happy and vice versa.
Everyone who is both patient and not calm is both not funny and not kind.
If paul is both quiet and not tall then someone is either kind or humble.
Everyone who is both not rich and not happy is either not strong or humble and vice versa.
Everyone who is generous or not happy is not happy.
If paul is wise then someone is either not kind or creative.
If alice is funny or wise then susan is not quiet or humble.
If alice is both not brave and not creative then paul is old.
Lucy is calm or not funny.
Mary is not happy or generous.
Someone is happy or not old.
Lucy is either quiet or not patient.
Paul is not tall or not wise.
Someone is either not calm or not quiet.
Alice is not wise. | Alice is creative. | neutral | (![X]:((~strong(X)&~kind(X))=>(~tall(X)<~>~strong(X))))&
(((creative(mary)<~>~strong(mary)))=>(?[X]:((~humble(X)<~>curious(X)))))&
(((~happy(lucy)&~brave(lucy)))=>(calm(susan)))&
(![X]:((curious(X)&old(X))=>(quiet(X)|~patient(X))))&
(![X]:(~wise(X)=>(~kind(X)<~>~funny(X))))&
(![X]:((brave(X)|tall(X))=>(rich(X)<~>~curious(X))))&
(![X]:((calm(X)<~>tall(X))<=>(rich(X)<~>~wise(X))))&
(![X]:(~wise(X)<=>(~curious(X)&~rich(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(old(X)<~>~happy(X))))&
(![X]:((patient(X)&~calm(X))=>(~funny(X)&~kind(X))))&
(((quiet(paul)&~tall(paul)))=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)|~happy(X))=>~happy(X)))&
((wise(paul))=>(?[X]:((~kind(X)<~>creative(X)))))&
(((funny(alice)|wise(alice)))=>((~quiet(susan)|humble(susan))))&
(((~brave(alice)&~creative(alice)))=>(old(paul)))&
((calm(lucy)|~funny(lucy)))&
((~happy(mary)|generous(mary)))&
(?[X]:((happy(X)|~old(X))))&
((quiet(lucy)<~>~patient(lucy)))&
((~tall(paul)|~wise(paul)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(~wise(alice)) | creative(alice) | [] | null | 0 |
Everyone who is not old or wise is strong or not brave and vice versa. If someone is not funny or calm then someone is either not generous or not curious. If someone is both humble and not curious then someone is not strong and vice versa. If someone is either funny or not kind then alice is curious and vice versa. Everyone who is both strong and not wise is wise and vice versa. If fred is patient then someone is both rich and wise. Everyone who is not rich or kind is not happy. Everyone who is not brave is not funny or not kind. If someone is either not humble or not old then susan is both tall and not humble. If alice is not generous then lucy is strong. If alice is either strong or not wise then someone is not calm or humble. Everyone who is funny or calm is both not brave and not calm. If someone is both not humble and brave then someone is happy. If paul is either not brave or not wise then susan is tall or not calm. Everyone who is either brave or curious is both not generous and not quiet and vice versa. Everyone who is curious is both wise and creative and vice versa. Someone is either patient or not generous. Someone is either wise or generous. Someone is either not tall or not old. Alice is not brave or not funny. Mary is creative or not brave. | Fred is creative. | neutral | (![X]:((~old(X)|wise(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)|calm(X))))=>(?[X]:((~generous(X)<~>~curious(X)))))&
((?[X]:((humble(X)&~curious(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>(curious(alice)))&
(![X]:((strong(X)&~wise(X))<=>wise(X)))&
((patient(fred))=>(?[X]:((rich(X)&wise(X)))))&
(![X]:((~rich(X)|kind(X))=>~happy(X)))&
(![X]:(~brave(X)=>(~funny(X)|~kind(X))))&
((?[X]:((~humble(X)<~>~old(X))))=>((tall(susan)&~humble(susan))))&
((~generous(alice))=>(strong(lucy)))&
(((strong(alice)<~>~wise(alice)))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((funny(X)|calm(X))=>(~brave(X)&~calm(X))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:(happy(X))))&
(((~brave(paul)<~>~wise(paul)))=>((tall(susan)|~calm(susan))))&
(![X]:((brave(X)<~>curious(X))<=>(~generous(X)&~quiet(X))))&
(![X]:(curious(X)<=>(wise(X)&creative(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~tall(X)<~>~old(X))))&
((~brave(alice)|~funny(alice)))&
((creative(mary)|~brave(mary))) | creative(fred) | [] | null | 0 |
Everyone who is not kind or calm is both kind and not rich. Everyone who is wise or not curious is either not creative or strong. Everyone who is not strong is strong or funny and vice versa. Everyone who is both wise and not tall is both strong and not wise. Everyone who is patient is happy or funny and vice versa. If someone is not happy or not humble then someone is both brave and funny and vice versa. Everyone who is both not brave and generous is both not old and brave. Everyone who is either funny or not brave is either curious or not calm and vice versa. If someone is both not tall and not generous then susan is not curious or tall. Everyone who is calm or not brave is either not calm or not funny and vice versa. If alice is either not tall or not old then alice is both not quiet and patient and vice versa. Everyone who is patient or not funny is not wise. Everyone who is not tall is wise and vice versa. If mary is not curious or not old then someone is either not kind or tall. If lucy is not calm or curious then someone is either not tall or curious and vice versa. Paul is either not curious or happy. Fred is both not creative and funny. Susan is rich or funny. Lucy is either not calm or old. Lucy is not curious or happy. | Paul is not funny. | contradiction | (![X]:((~kind(X)|calm(X))=>(kind(X)&~rich(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)<~>strong(X))))&
(![X]:(~strong(X)<=>(strong(X)|funny(X))))&
(![X]:((wise(X)&~tall(X))=>(strong(X)&~wise(X))))&
(![X]:(patient(X)<=>(happy(X)|funny(X))))&
((?[X]:((~happy(X)|~humble(X))))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((~brave(X)&generous(X))=>(~old(X)&brave(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(curious(X)<~>~calm(X))))&
((?[X]:((~tall(X)&~generous(X))))=>((~curious(susan)|tall(susan))))&
(![X]:((calm(X)|~brave(X))<=>(~calm(X)<~>~funny(X))))&
(((~tall(alice)<~>~old(alice)))<=>((~quiet(alice)&patient(alice))))&
(![X]:((patient(X)|~funny(X))=>~wise(X)))&
(![X]:(~tall(X)<=>wise(X)))&
(((~curious(mary)|~old(mary)))=>(?[X]:((~kind(X)<~>tall(X)))))&
(((~calm(lucy)|curious(lucy)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
((~curious(paul)<~>happy(paul)))&
((~creative(fred)&funny(fred)))&
((rich(susan)|funny(susan)))&
((~calm(lucy)<~>old(lucy)))&
((~curious(lucy)|happy(lucy))) | ~funny(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 8122307314510397784198230
% SZS output start Proof for 8122307314510397784198230
3. ! [X0] : (~strong(X0) <=> (funny(X0) | strong(X0))) [input p2]
21. ~funny(paul) [input hypothesis]
34. ! [X0] : ((~strong(X0) | (~funny(X0) & ~strong(X0))) & ((funny(X0) | strong(X0)) | strong(X0))) [nnf transformation 3]
35. ! [X0] : ((~strong(X0) | (~funny(X0) & ~strong(X0))) & (funny(X0) | strong(X0) | strong(X0))) [flattening 34]
67. funny(X0) | strong(X0) | strong(X0) [cnf transformation 35]
68. ~strong(X0) | ~strong(X0) [cnf transformation 35]
125. ~funny(paul) [cnf transformation 21]
130. funny(X0) | strong(X0) [duplicate literal removal 67]
131. ~strong(X0) [duplicate literal removal 68]
133. funny(X0) [subsumption resolution 130,131]
228. $false [subsumption resolution 125,133]
% SZS output end Proof for 8122307314510397784198230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is generous then someone is both not rich and rich.
If susan is either not calm or not curious then someone is not curious or not kind and vice versa.
Everyone who is both brave and not humble is either creative or old and vice versa.
If mary is both not strong and rich then someone is not calm and vice versa.
Everyone who is not rich is either kind or not kind.
If susan is either not rich or curious then someone is either rich or not tall and vice versa.
Everyone who is either not happy or not kind is not quiet.
If someone is not creative or not wise then fred is both wise and not rich and vice versa.
If someone is not generous then someone is funny and vice versa.
Everyone who is funny is either quiet or funny.
If john is not humble then john is curious or not curious and vice versa.
Everyone who is either old or strong is both not curious and not patient and vice versa.
Everyone who is either quiet or not wise is not rich and vice versa.
Everyone who is not calm is both generous and funny.
If mary is not tall or not funny then someone is quiet or tall and vice versa.
If someone is not funny or not rich then fred is both not happy and not creative and vice versa.
Lucy is either not old or wise.
Someone is either not wise or tall.
Alice is both happy and not tall.
Paul is both tall and not calm.
Someone is not humble or not patient.
Mary is not quiet or happy.
Alice is both wise and funny.
John is either brave or not rich. | Paul is old. | neutral | ((generous(lucy))=>(?[X]:((~rich(X)&rich(X)))))&
(((~calm(susan)<~>~curious(susan)))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((brave(X)&~humble(X))<=>(creative(X)<~>old(X))))&
(((~strong(mary)&rich(mary)))<=>(?[X]:(~calm(X))))&
(![X]:(~rich(X)=>(kind(X)<~>~kind(X))))&
(((~rich(susan)<~>curious(susan)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>~quiet(X)))&
((?[X]:((~creative(X)|~wise(X))))<=>((wise(fred)&~rich(fred))))&
((?[X]:(~generous(X)))<=>(?[X]:(funny(X))))&
(![X]:(funny(X)=>(quiet(X)<~>funny(X))))&
((~humble(john))<=>((curious(john)|~curious(john))))&
(![X]:((old(X)<~>strong(X))<=>(~curious(X)&~patient(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>~rich(X)))&
(![X]:(~calm(X)=>(generous(X)&funny(X))))&
(((~tall(mary)|~funny(mary)))<=>(?[X]:((quiet(X)|tall(X)))))&
((?[X]:((~funny(X)|~rich(X))))<=>((~happy(fred)&~creative(fred))))&
((~old(lucy)<~>wise(lucy)))&
(?[X]:((~wise(X)<~>tall(X))))&
((happy(alice)&~tall(alice)))&
((tall(paul)&~calm(paul)))&
(?[X]:((~humble(X)|~patient(X))))&
((~quiet(mary)|happy(mary)))&
((wise(alice)&funny(alice)))&
((brave(john)<~>~rich(john))) | old(paul) | [] | null | 0 |
If john is not quiet then alice is both not kind and not generous and vice versa.
If someone is both kind and patient then someone is not funny or wise and vice versa.
Everyone who is not strong is both not old and patient and vice versa.
Everyone who is not strong is calm and vice versa.
If alice is both not brave and not tall then someone is creative or brave.
Everyone who is either humble or generous is old.
If john is both old and not calm then mary is both not funny and not old and vice versa.
If alice is rich or not rich then alice is both humble and not quiet.
Everyone who is either brave or not strong is both calm and brave and vice versa.
Everyone who is either patient or quiet is not humble or not tall and vice versa.
Everyone who is either not creative or not happy is either quiet or not creative.
Everyone who is humble or patient is either rich or not brave.
If alice is not old then fred is not kind or tall.
If john is not patient or brave then mary is not funny and vice versa.
Everyone who is not funny is creative or not kind and vice versa.
If someone is quiet then someone is not calm or old.
Fred is both rich and not kind.
Mary is both curious and happy.
Susan is not curious.
Paul is either not quiet or not tall.
John is both quiet and kind.
Mary is curious or brave. | Fred is quiet. | entailment | ((~quiet(john))<=>((~kind(alice)&~generous(alice))))&
((?[X]:((kind(X)&patient(X))))<=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(~strong(X)<=>(~old(X)&patient(X))))&
(![X]:(~strong(X)<=>calm(X)))&
(((~brave(alice)&~tall(alice)))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((humble(X)<~>generous(X))=>old(X)))&
(((old(john)&~calm(john)))<=>((~funny(mary)&~old(mary))))&
(((rich(alice)|~rich(alice)))=>((humble(alice)&~quiet(alice))))&
(![X]:((brave(X)<~>~strong(X))<=>(calm(X)&brave(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~humble(X)|~tall(X))))&
(![X]:((~creative(X)<~>~happy(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((humble(X)|patient(X))=>(rich(X)<~>~brave(X))))&
((~old(alice))=>((~kind(fred)|tall(fred))))&
(((~patient(john)|brave(john)))<=>(~funny(mary)))&
(![X]:(~funny(X)<=>(creative(X)|~kind(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|old(X)))))&
((rich(fred)&~kind(fred)))&
((curious(mary)&happy(mary)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul)))&
((quiet(john)&kind(john)))&
((curious(mary)|brave(mary))) | quiet(fred) | [
"p3",
"p8",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6228706282057589050653853
% SZS output start Proof for 6228706282057589050653853
4. ! [X0] : (~strong(X0) <=> calm(X0)) [input p3]
9. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) & calm(X0))) [input p8]
10. ! [X0] : ((patient(X0) <~> quiet(X0)) <=> (~tall(X0) | ~humble(X0))) [input p9]
12. ! [X0] : ((patient(X0) | humble(X0)) => (rich(X0) <~> ~brave(X0))) [input p11]
17. ~kind(fred) & rich(fred) [input p16]
23. ~quiet(fred) [input hypothesis]
31. ! [X0] : ((rich(X0) <~> ~brave(X0)) | (~patient(X0) & ~humble(X0))) [ennf transformation 12]
44. ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))) [nnf transformation 4]
50. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 9]
51. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 50]
52. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0))))) [flattening 52]
55. ! [X0] : (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | (~patient(X0) & ~humble(X0))) [nnf transformation 31]
75. calm(X0) | strong(X0) [cnf transformation 44]
76. ~calm(X0) | ~strong(X0) [cnf transformation 44]
88. calm(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 51]
93. strong(X0) | ~brave(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 51]
96. humble(X0) | patient(X0) | quiet(X0) [cnf transformation 53]
106. brave(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 55]
107. brave(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 55]
116. rich(fred) [cnf transformation 17]
126. ~quiet(fred) [cnf transformation 23]
130. strong(X0) | ~brave(X0) | ~calm(X0) [duplicate literal removal 93]
229. ~brave(X0) | ~calm(X0) [subsumption resolution 130,76]
230. calm(X0) | ~brave(X0) [subsumption resolution 88,75]
231. ~brave(X0) [subsumption resolution 230,229]
232. ~rich(X0) | ~patient(X0) [subsumption resolution 107,231]
233. ~rich(X0) | ~humble(X0) [subsumption resolution 106,231]
287. ~patient(fred) [resolution 232,116]
288. ~humble(fred) [resolution 233,116]
297. patient(fred) | quiet(fred) [resolution 96,288]
299. quiet(fred) [subsumption resolution 297,287]
300. $false [subsumption resolution 299,126]
% SZS output end Proof for 6228706282057589050653853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not patient or patient then someone is not tall.
Everyone who is happy or wise is not rich and vice versa.
Everyone who is not funny or not wise is not strong and vice versa.
Everyone who is not wise is not humble or wise.
If someone is both curious and not kind then someone is either calm or funny and vice versa.
Everyone who is not quiet is both not brave and brave.
Everyone who is brave is either not generous or brave.
If john is strong then someone is not funny.
Everyone who is both rich and kind is not strong or generous and vice versa.
If john is both funny and strong then john is both not rich and not wise.
Everyone who is both not brave and not happy is not rich.
If fred is both not wise and strong then someone is both not curious and not kind.
Everyone who is calm is funny or not humble and vice versa.
Everyone who is not calm is not patient and vice versa.
Everyone who is either old or funny is curious or not wise and vice versa.
Everyone who is both old and curious is either not generous or humble and vice versa.
Alice is both not humble and brave.
Lucy is either strong or patient.
Someone is both curious and humble.
Fred is both not happy and not strong.
Someone is not tall.
Paul is either brave or humble.
Someone is either not funny or funny.
Mary is both quiet and old. | Paul is patient. | entailment | (((~patient(mary)<~>patient(mary)))=>(?[X]:(~tall(X))))&
(![X]:((happy(X)|wise(X))<=>~rich(X)))&
(![X]:((~funny(X)|~wise(X))<=>~strong(X)))&
(![X]:(~wise(X)=>(~humble(X)|wise(X))))&
((?[X]:((curious(X)&~kind(X))))<=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&brave(X))))&
(![X]:(brave(X)=>(~generous(X)<~>brave(X))))&
((strong(john))=>(?[X]:(~funny(X))))&
(![X]:((rich(X)&kind(X))<=>(~strong(X)|generous(X))))&
(((funny(john)&strong(john)))=>((~rich(john)&~wise(john))))&
(![X]:((~brave(X)&~happy(X))=>~rich(X)))&
(((~wise(fred)&strong(fred)))=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:(calm(X)<=>(funny(X)|~humble(X))))&
(![X]:(~calm(X)<=>~patient(X)))&
(![X]:((old(X)<~>funny(X))<=>(curious(X)|~wise(X))))&
(![X]:((old(X)&curious(X))<=>(~generous(X)<~>humble(X))))&
((~humble(alice)&brave(alice)))&
((strong(lucy)<~>patient(lucy)))&
(?[X]:((curious(X)&humble(X))))&
((~happy(fred)&~strong(fred)))&
(?[X]:(~tall(X)))&
((brave(paul)<~>humble(paul)))&
(?[X]:((~funny(X)<~>funny(X))))&
((quiet(mary)&old(mary))) | patient(paul) | [
"p1",
"p2",
"p3",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8903332915532762757339670
% SZS output start Proof for 8903332915532762757339670
2. ! [X0] : ((wise(X0) | happy(X0)) <=> ~rich(X0)) [input p1]
3. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> ~strong(X0)) [input p2]
4. ! [X0] : (~wise(X0) => (wise(X0) | ~humble(X0))) [input p3]
9. ! [X0] : ((kind(X0) & rich(X0)) <=> (generous(X0) | ~strong(X0))) [input p8]
13. ! [X0] : (calm(X0) <=> (~humble(X0) | funny(X0))) [input p12]
14. ! [X0] : (~calm(X0) <=> ~patient(X0)) [input p13]
25. ~patient(paul) [input hypothesis]
31. ! [X0] : ((wise(X0) | ~humble(X0)) | wise(X0)) [ennf transformation 4]
32. ! [X0] : (wise(X0) | ~humble(X0) | wise(X0)) [flattening 31]
41. ! [X0] : (((wise(X0) | happy(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~happy(X0)))) [nnf transformation 2]
42. ! [X0] : ((wise(X0) | happy(X0) | rich(X0)) & (~rich(X0) | (~wise(X0) & ~happy(X0)))) [flattening 41]
43. ! [X0] : (((~wise(X0) | ~funny(X0)) | strong(X0)) & (~strong(X0) | (wise(X0) & funny(X0)))) [nnf transformation 3]
44. ! [X0] : ((~wise(X0) | ~funny(X0) | strong(X0)) & (~strong(X0) | (wise(X0) & funny(X0)))) [flattening 43]
53. ! [X0] : (((kind(X0) & rich(X0)) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | (~kind(X0) | ~rich(X0)))) [nnf transformation 9]
54. ! [X0] : (((kind(X0) & rich(X0)) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | ~kind(X0) | ~rich(X0))) [flattening 53]
57. ! [X0] : ((calm(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | ~calm(X0))) [nnf transformation 13]
58. ! [X0] : ((calm(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | ~calm(X0))) [flattening 57]
59. ! [X0] : ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))) [nnf transformation 14]
72. ~rich(X0) | ~wise(X0) [cnf transformation 42]
74. ~strong(X0) | funny(X0) [cnf transformation 44]
77. wise(X0) | ~humble(X0) | wise(X0) [cnf transformation 32]
88. strong(X0) | rich(X0) [cnf transformation 54]
98. calm(X0) | ~funny(X0) [cnf transformation 58]
99. calm(X0) | humble(X0) [cnf transformation 58]
101. ~calm(X0) | patient(X0) [cnf transformation 59]
127. ~patient(paul) [cnf transformation 25]
129. ~humble(X0) | wise(X0) [duplicate literal removal 77]
131. 1 <=> ! [X1] : (calm(X1) | ~funny(X1)) [avatar definition]
132. ~funny(X1) | calm(X1) <- (1) [avatar component clause 131]
180. 1 [avatar split clause 98,131]
206. funny(X1) | rich(X1) [resolution 88,74]
212. humble(X0) | patient(X0) [resolution 101,99]
359. calm(X2) | rich(X2) <- (1) [resolution 206,132]
367. wise(X0) | patient(X0) [resolution 212,129]
419. rich(X2) | patient(X2) <- (1) [resolution 359,101]
610. patient(X1) | ~wise(X1) <- (1) [resolution 419,72]
613. patient(X1) <- (1) [subsumption resolution 610,367]
638. $false <- (1) [resolution 613,127]
640. ~1 [avatar contradiction clause 638]
641. $false [avatar sat refutation 180,640]
% SZS output end Proof for 8903332915532762757339670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not brave is either not tall or not old.
If john is both not generous and quiet then someone is patient or tall and vice versa.
If susan is either not kind or tall then susan is tall or not quiet and vice versa.
Everyone who is either not calm or not happy is either humble or kind.
Everyone who is not kind is strong or curious and vice versa.
If someone is not quiet then fred is both rich and not patient and vice versa.
If paul is not calm then mary is not patient or patient.
If susan is both generous and not calm then john is both rich and strong and vice versa.
If lucy is funny then someone is wise or strong and vice versa.
If someone is not happy then someone is both funny and not calm.
If someone is not brave then someone is rich or not strong and vice versa.
Everyone who is patient is either not humble or not generous.
Everyone who is either not calm or tall is both not old and not kind 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.
Someone is both not tall and not strong.
Someone is either not wise or not brave.
Someone is not calm.
Alice is happy.
Someone is either not patient or quiet.
Someone is both not wise and not curious.
Mary is both funny and not curious. | Alice is strong. | contradiction | (![X]:((tall(X)|~brave(X))=>(~tall(X)<~>~old(X))))&
(((~generous(john)&quiet(john)))<=>(?[X]:((patient(X)|tall(X)))))&
(((~kind(susan)<~>tall(susan)))<=>((tall(susan)|~quiet(susan))))&
(![X]:((~calm(X)<~>~happy(X))=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(strong(X)|curious(X))))&
((?[X]:(~quiet(X)))<=>((rich(fred)&~patient(fred))))&
((~calm(paul))=>((~patient(mary)|patient(mary))))&
(((generous(susan)&~calm(susan)))<=>((rich(john)&strong(john))))&
((funny(lucy))<=>(?[X]:((wise(X)|strong(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)&~calm(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(patient(X)=>(~humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>tall(X))<=>(~old(X)&~kind(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]:((~tall(X)&~strong(X))))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:(~calm(X)))&
(happy(alice))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((~wise(X)&~curious(X))))&
((funny(mary)&~curious(mary))) | strong(alice) | [
"p0",
"p5",
"p12",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4886476863736500595328436
% SZS output start Proof for 4886476863736500595328436
1. ! [X0] : ((~brave(X0) | tall(X0)) => (~tall(X0) <~> ~old(X0))) [input p0]
6. ? [X0] : ~quiet(X0) <=> (~patient(fred) & rich(fred)) [input p5]
13. ! [X0] : ((~calm(X0) <~> tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p12]
14. ! [X0] : ((generous(X0) | brave(X0)) <=> (strong(X0) <~> quiet(X0))) [input p13]
15. ! [X0] : ((quiet(X0) & tall(X0)) => (rich(X0) & ~happy(X0))) [input p14]
16. ! [X0] : ((~calm(X0) & patient(X0)) <=> (~happy(X0) | happy(X0))) [input p15]
20. happy(alice) [input p19]
24. strong(alice) [input hypothesis]
27. ! [X0] : ((~tall(X0) <~> ~old(X0)) | (brave(X0) & ~tall(X0))) [ennf transformation 1]
33. ! [X0] : ((rich(X0) & ~happy(X0)) | (~quiet(X0) | ~tall(X0))) [ennf transformation 15]
34. ! [X0] : ((rich(X0) & ~happy(X0)) | ~quiet(X0) | ~tall(X0)) [flattening 33]
35. ! [X0] : (((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | (brave(X0) & ~tall(X0))) [nnf transformation 27]
46. (? [X0] : ~quiet(X0) | (patient(fred) | ~rich(fred))) & ((~patient(fred) & rich(fred)) | ! [X0] : quiet(X0)) [nnf transformation 6]
47. (? [X0] : ~quiet(X0) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X0] : quiet(X0)) [flattening 46]
48. (? [X0] : ~quiet(X0) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X1] : quiet(X1)) [rectify 47]
49. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
50. (~quiet(sK1) | patient(fred) | ~rich(fred)) & ((~patient(fred) & rich(fred)) | ! [X1] : quiet(X1)) [skolemisation 48,49]
66. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | ((~calm(X0) | ~tall(X0)) & (tall(X0) | calm(X0))))) [flattening 66]
68. ! [X0] : (((generous(X0) | brave(X0)) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | (~generous(X0) & ~brave(X0)))) [nnf transformation 14]
69. ! [X0] : ((generous(X0) | brave(X0) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | (~generous(X0) & ~brave(X0)))) [flattening 68]
70. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | (calm(X0) | ~patient(X0)))) [nnf transformation 16]
71. ! [X0] : (((~calm(X0) & patient(X0)) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | calm(X0) | ~patient(X0))) [flattening 70]
84. ~old(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 35]
87. old(X0) | tall(X0) | brave(X0) [cnf transformation 35]
107. ~patient(fred) | quiet(X1) [cnf transformation 50]
124. ~old(X0) | tall(X0) | calm(X0) [cnf transformation 67]
132. ~strong(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 69]
136. ~happy(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 34]
139. patient(X0) | ~happy(X0) [cnf transformation 71]
140. happy(X0) | patient(X0) [cnf transformation 71]
141. ~calm(X0) | ~happy(X0) [cnf transformation 71]
142. ~calm(X0) | happy(X0) [cnf transformation 71]
148. happy(alice) [cnf transformation 20]
155. strong(alice) [cnf transformation 24]
158. ~old(X0) | ~tall(X0) [duplicate literal removal 84]
207. 11 <=> patient(fred) [avatar definition]
208. ~patient(fred) <- (~11) [avatar component clause 207]
216. 13 <=> ! [X1] : quiet(X1) [avatar definition]
217. quiet(X1) <- (13) [avatar component clause 216]
218. 13 | ~11 [avatar split clause 107,207,216]
299. ~old(X0) | calm(X0) [subsumption resolution 124,158]
300. ~calm(X0) [subsumption resolution 141,142]
301. patient(X0) [subsumption resolution 139,140]
313. $false <- (~11) [subsumption resolution 208,301]
314. 11 [avatar contradiction clause 313]
325. tall(X1) | brave(X1) | calm(X1) [resolution 87,299]
328. brave(X1) | tall(X1) [subsumption resolution 325,300]
364. ~quiet(alice) | ~brave(alice) [resolution 132,155]
365. ~brave(alice) <- (13) [subsumption resolution 364,217]
366. tall(alice) <- (13) [resolution 365,328]
369. ~quiet(alice) | ~tall(alice) [resolution 136,148]
372. ~tall(alice) <- (13) [subsumption resolution 369,217]
373. $false <- (13) [subsumption resolution 372,366]
374. ~13 [avatar contradiction clause 373]
377. $false [avatar sat refutation 218,314,374]
% SZS output end Proof for 4886476863736500595328436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not happy or not wise then someone is either tall or quiet and vice versa.
If lucy is not calm or not funny then someone is curious and vice versa.
If someone is both not funny and funny then someone is happy and vice versa.
Everyone who is not kind or not tall is old or creative and vice versa.
Everyone who is either not happy or happy is not generous and vice versa.
Everyone who is not rich or not generous is brave and vice versa.
Everyone who is either curious or not quiet is either not old or tall.
If someone is both curious and not curious then susan is not calm or strong.
Everyone who is either not strong or happy is both not generous and not old and vice versa.
Everyone who is not quiet is either not kind or tall.
If lucy is not brave then someone is both rich and not calm.
Everyone who is both not strong and not funny is both curious and patient.
If lucy is either tall or creative then susan is brave.
Everyone who is not calm is either not patient or not tall and vice versa.
Everyone who is either not kind or not brave is curious and vice versa.
Everyone who is generous or not strong is not brave.
Someone is not creative.
Paul is both not rich and humble.
Someone is either not tall or tall.
Paul is both not curious and funny.
Fred is either calm or not creative.
Mary is curious.
Someone is either old or not wise. | Paul is not old. | contradiction | (((~happy(alice)|~wise(alice)))<=>(?[X]:((tall(X)<~>quiet(X)))))&
(((~calm(lucy)|~funny(lucy)))<=>(?[X]:(curious(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~kind(X)|~tall(X))<=>(old(X)|creative(X))))&
(![X]:((~happy(X)<~>happy(X))<=>~generous(X)))&
(![X]:((~rich(X)|~generous(X))<=>brave(X)))&
(![X]:((curious(X)<~>~quiet(X))=>(~old(X)<~>tall(X))))&
((?[X]:((curious(X)&~curious(X))))=>((~calm(susan)|strong(susan))))&
(![X]:((~strong(X)<~>happy(X))<=>(~generous(X)&~old(X))))&
(![X]:(~quiet(X)=>(~kind(X)<~>tall(X))))&
((~brave(lucy))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~strong(X)&~funny(X))=>(curious(X)&patient(X))))&
(((tall(lucy)<~>creative(lucy)))=>(brave(susan)))&
(![X]:(~calm(X)<=>(~patient(X)<~>~tall(X))))&
(![X]:((~kind(X)<~>~brave(X))<=>curious(X)))&
(![X]:((generous(X)|~strong(X))=>~brave(X)))&
(?[X]:(~creative(X)))&
((~rich(paul)&humble(paul)))&
(?[X]:((~tall(X)<~>tall(X))))&
((~curious(paul)&funny(paul)))&
((calm(fred)<~>~creative(fred)))&
(curious(mary))&
(?[X]:((old(X)<~>~wise(X)))) | ~old(paul) | [
"p2",
"p4",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7414026378403931631570768
% SZS output start Proof for 7414026378403931631570768
3. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X0] : happy(X0) [input p2]
5. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> ~generous(X0)) [input p4]
6. ! [X0] : ((~generous(X0) | ~rich(X0)) <=> brave(X0)) [input p5]
9. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~old(X0) & ~generous(X0))) [input p8]
16. ! [X0] : ((~strong(X0) | generous(X0)) => ~brave(X0)) [input p15]
24. ~old(paul) [input hypothesis]
25. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X1] : happy(X1) [rectify 3]
35. ! [X0] : (~brave(X0) | (strong(X0) & ~generous(X0))) [ennf transformation 16]
46. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (~funny(X0) | funny(X0))) [nnf transformation 25]
47. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (~funny(X3) | funny(X3))) [rectify 46]
48. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK2) & ~funny(sK2)) [choice axiom]
49. ? [X2] : happy(X2) => happy(sK3) [choice axiom]
50. ((funny(sK2) & ~funny(sK2)) | ! [X1] : ~happy(X1)) & (happy(sK3) | ! [X3] : (~funny(X3) | funny(X3))) [skolemisation 47,49,48]
53. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | generous(X0)) & (~generous(X0) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 5]
54. ! [X0] : (((~generous(X0) | ~rich(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) & rich(X0)))) [nnf transformation 6]
55. ! [X0] : ((~generous(X0) | ~rich(X0) | ~brave(X0)) & (brave(X0) | (generous(X0) & rich(X0)))) [flattening 54]
57. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 57]
84. ~funny(sK2) | ~happy(X1) [cnf transformation 50]
85. funny(sK2) | ~happy(X1) [cnf transformation 50]
90. ~generous(X0) | happy(X0) | happy(X0) [cnf transformation 53]
91. ~generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 53]
95. brave(X0) | generous(X0) [cnf transformation 55]
106. happy(X0) | ~strong(X0) | old(X0) | generous(X0) [cnf transformation 58]
125. ~brave(X0) | strong(X0) [cnf transformation 35]
137. ~old(paul) [cnf transformation 24]
138. ~generous(X0) | happy(X0) [duplicate literal removal 90]
139. ~generous(X0) | ~happy(X0) [duplicate literal removal 91]
187. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
188. ~happy(X1) <- (11) [avatar component clause 187]
190. 12 <=> funny(sK2) [avatar definition]
193. 11 | 12 [avatar split clause 85,190,187]
194. 11 | ~12 [avatar split clause 84,190,187]
195. ~generous(X0) [subsumption resolution 138,139]
196. brave(X0) [subsumption resolution 95,195]
198. ~strong(X0) | happy(X0) | old(X0) [subsumption resolution 106,195]
201. strong(X0) [subsumption resolution 125,196]
291. happy(X1) | old(X1) [resolution 198,201]
293. old(X1) <- (11) [subsumption resolution 291,188]
301. $false <- (11) [resolution 293,137]
307. ~11 [avatar contradiction clause 301]
308. $false [avatar sat refutation 193,194,307]
% SZS output end Proof for 7414026378403931631570768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.017 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and generous is generous and vice versa. If someone is both not quiet and not curious then someone is not happy or not brave and vice versa. Everyone who is rich is either creative or curious. Everyone who is both wise and funny is not generous or not humble and vice versa. Everyone who is either not patient or patient is either generous or not wise and vice versa. Everyone who is either not wise or humble is funny or not happy and vice versa. Everyone who is kind or not funny is not patient and vice versa. Everyone who is either not rich or old is happy or kind. If someone is either funny or creative then someone is both not happy and not kind. Everyone who is both humble and not kind is strong. If someone is both old and not curious then john is either not calm or not curious. Everyone who is not old or rich is either not tall or generous. Everyone who is both tall and not rich is not tall. Everyone who is not wise or not happy is either not generous or not happy. If mary is calm or creative then fred is strong or patient. Everyone who is not generous is either old or funny and vice versa. Someone is kind. Someone is not patient. Someone is not brave or not calm. Someone is not calm or strong. Someone is either not calm or kind. Someone is either rich or calm. Someone is either kind or brave. | John is not patient. | entailment | (![X]:((~old(X)&generous(X))<=>generous(X)))&
((?[X]:((~quiet(X)&~curious(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:(rich(X)=>(creative(X)<~>curious(X))))&
(![X]:((wise(X)&funny(X))<=>(~generous(X)|~humble(X))))&
(![X]:((~patient(X)<~>patient(X))<=>(generous(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>humble(X))<=>(funny(X)|~happy(X))))&
(![X]:((kind(X)|~funny(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>old(X))=>(happy(X)|kind(X))))&
((?[X]:((funny(X)<~>creative(X))))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((humble(X)&~kind(X))=>strong(X)))&
((?[X]:((old(X)&~curious(X))))=>((~calm(john)<~>~curious(john))))&
(![X]:((~old(X)|rich(X))=>(~tall(X)<~>generous(X))))&
(![X]:((tall(X)&~rich(X))=>~tall(X)))&
(![X]:((~wise(X)|~happy(X))=>(~generous(X)<~>~happy(X))))&
(((calm(mary)|creative(mary)))=>((strong(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(old(X)<~>funny(X))))&
(?[X]:(kind(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~brave(X)|~calm(X))))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~calm(X)<~>kind(X))))&
(?[X]:((rich(X)<~>calm(X))))&
(?[X]:((kind(X)<~>brave(X)))) | ~patient(john) | [
"p0",
"p3",
"p4",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7816274274481409731746785
% SZS output start Proof for 7816274274481409731746785
1. ! [X0] : ((generous(X0) & ~old(X0)) <=> generous(X0)) [input p0]
4. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) | ~generous(X0))) [input p3]
5. ! [X0] : ((~patient(X0) <~> patient(X0)) <=> (generous(X0) <~> ~wise(X0))) [input p4]
7. ! [X0] : ((~funny(X0) | kind(X0)) <=> ~patient(X0)) [input p6]
16. ! [X0] : (~generous(X0) <=> (old(X0) <~> funny(X0))) [input p15]
24. patient(john) [input hypothesis]
39. ! [X0] : (((generous(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | (~generous(X0) | old(X0)))) [nnf transformation 1]
40. ! [X0] : (((generous(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | ~generous(X0) | old(X0))) [flattening 39]
47. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 4]
48. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ~funny(X0) | ~wise(X0))) [flattening 47]
49. ! [X0] : ((((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0))))) [nnf transformation 5]
52. ! [X0] : (((~funny(X0) | kind(X0)) | patient(X0)) & (~patient(X0) | (funny(X0) & ~kind(X0)))) [nnf transformation 7]
53. ! [X0] : ((~funny(X0) | kind(X0) | patient(X0)) & (~patient(X0) | (funny(X0) & ~kind(X0)))) [flattening 52]
62. ! [X0] : ((~generous(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) & (((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | generous(X0))) [nnf transformation 16]
79. ~generous(X0) | ~old(X0) [cnf transformation 40]
89. wise(X0) | generous(X0) [cnf transformation 48]
93. ~wise(X0) | generous(X0) | patient(X0) | patient(X0) [cnf transformation 49]
94. ~wise(X0) | generous(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 49]
95. wise(X0) | ~generous(X0) | patient(X0) | patient(X0) [cnf transformation 49]
96. wise(X0) | ~generous(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 49]
108. ~patient(X0) | funny(X0) [cnf transformation 53]
130. ~generous(X0) | old(X0) | ~funny(X0) [cnf transformation 62]
140. patient(john) [cnf transformation 24]
143. ~wise(X0) | generous(X0) | patient(X0) [duplicate literal removal 93]
144. ~wise(X0) | generous(X0) | ~patient(X0) [duplicate literal removal 94]
145. wise(X0) | ~generous(X0) | patient(X0) [duplicate literal removal 95]
146. wise(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 96]
177. ~patient(X0) | wise(X0) [subsumption resolution 146,89]
178. wise(X0) | patient(X0) [subsumption resolution 145,89]
179. wise(X0) [subsumption resolution 178,177]
180. ~patient(X0) | generous(X0) [subsumption resolution 144,179]
181. generous(X0) | patient(X0) [subsumption resolution 143,179]
182. generous(X0) [subsumption resolution 181,180]
221. ~funny(X0) | old(X0) [subsumption resolution 130,182]
261. ~old(X0) [resolution 79,182]
264. funny(john) [resolution 108,140]
273. old(john) [resolution 221,264]
274. $false [subsumption resolution 273,261]
% SZS output end Proof for 7816274274481409731746785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not tall is either calm or not happy. If someone is either not brave or quiet then someone is both happy and not tall and vice versa. Everyone who is not funny or curious is not strong or not old and vice versa. If someone is either strong or creative then someone is funny or not kind. If paul is happy or not patient then susan is either creative or happy. Everyone who is not creative or generous is either not tall or old. If lucy is not humble then someone is both generous and creative. If someone is either tall or kind then fred is not humble or patient. Everyone who is either not creative or curious is not wise. If john is wise then someone is not happy or not curious. If mary is old or not calm then someone is not patient or not happy and vice versa. Everyone who is either not funny or not calm is tall or generous and vice versa. If someone is not strong or curious then alice is both old and not patient and vice versa. Everyone who is both quiet and calm is both not brave and not happy. Everyone who is either creative or old is not old. Everyone who is both not creative and curious is either humble or not curious and vice versa. Alice is not wise or not humble. Fred is not creative. Paul is either humble or not calm. Someone is not curious. Someone is creative. Mary is both not brave and funny. Someone is either funny or not rich. Susan is patient. | Fred is tall. | contradiction | (![X]:((~quiet(X)<~>~tall(X))=>(calm(X)<~>~happy(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~funny(X)|curious(X))<=>(~strong(X)|~old(X))))&
((?[X]:((strong(X)<~>creative(X))))=>(?[X]:((funny(X)|~kind(X)))))&
(((happy(paul)|~patient(paul)))=>((creative(susan)<~>happy(susan))))&
(![X]:((~creative(X)|generous(X))=>(~tall(X)<~>old(X))))&
((~humble(lucy))=>(?[X]:((generous(X)&creative(X)))))&
((?[X]:((tall(X)<~>kind(X))))=>((~humble(fred)|patient(fred))))&
(![X]:((~creative(X)<~>curious(X))=>~wise(X)))&
((wise(john))=>(?[X]:((~happy(X)|~curious(X)))))&
(((old(mary)|~calm(mary)))<=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(tall(X)|generous(X))))&
((?[X]:((~strong(X)|curious(X))))<=>((old(alice)&~patient(alice))))&
(![X]:((quiet(X)&calm(X))=>(~brave(X)&~happy(X))))&
(![X]:((creative(X)<~>old(X))=>~old(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)<~>~curious(X))))&
((~wise(alice)|~humble(alice)))&
(~creative(fred))&
((humble(paul)<~>~calm(paul)))&
(?[X]:(~curious(X)))&
(?[X]:(creative(X)))&
((~brave(mary)&funny(mary)))&
(?[X]:((funny(X)<~>~rich(X))))&
(patient(susan)) | tall(fred) | [
"p5",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9068434798195968276868948
% SZS output start Proof for 9068434798195968276868948
6. ! [X0] : ((generous(X0) | ~creative(X0)) => (~tall(X0) <~> old(X0))) [input p5]
15. ! [X0] : ((creative(X0) <~> old(X0)) => ~old(X0)) [input p14]
18. ~creative(fred) [input p17]
25. tall(fred) [input hypothesis]
34. ! [X0] : ((~tall(X0) <~> old(X0)) | (~generous(X0) & creative(X0))) [ennf transformation 6]
40. ! [X0] : (~old(X0) | (creative(X0) <=> old(X0))) [ennf transformation 15]
54. ! [X0] : (((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | (~generous(X0) & creative(X0))) [nnf transformation 34]
70. ! [X0] : (~old(X0) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0)))) [nnf transformation 40]
101. ~tall(X0) | old(X0) | creative(X0) [cnf transformation 54]
127. ~old(X0) | creative(X0) | ~old(X0) [cnf transformation 70]
134. ~creative(fred) [cnf transformation 18]
144. tall(fred) [cnf transformation 25]
147. ~old(X0) | creative(X0) [duplicate literal removal 127]
359. old(fred) | creative(fred) [resolution 101,144]
360. old(fred) [subsumption resolution 359,134]
366. creative(fred) [resolution 360,147]
381. $false [subsumption resolution 366,134]
% SZS output end Proof for 9068434798195968276868948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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