premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is either patient or not patient then someone is not calm or brave and vice versa. Everyone who is either calm or not wise is not kind or not old and vice versa. Everyone who is both creative and calm is not patient or patient. Everyone who is both not funny and not calm is both not funny and not curious and vice versa. Everyone who is not patient or humble is not creative and vice versa. Everyone who is both not happy and not old is either calm or not rich and vice versa. Everyone who is both quiet and rich is both strong and not funny and vice versa. Everyone who is both not curious and not tall is strong and vice versa. If mary is both not old and not tall then someone is both not funny and generous. Everyone who is both wise and old is either not creative or not rich and vice versa. Everyone who is both calm and not rich is not wise. Everyone who is either strong or kind is not calm or not happy and vice versa. If someone is both humble and not brave then lucy is brave or kind and vice versa. Everyone who is either strong or not kind is patient and vice versa. Everyone who is either not tall or not creative is happy and vice versa. Everyone who is happy or not rich is both not patient and not curious. Paul is patient or humble. Someone is tall or not strong. Someone is not humble or not rich. Susan is both not strong and not tall. Someone is either not humble or strong. Someone is either generous or strong. Someone is curious. | Paul is generous. | neutral | ((?[X]:((patient(X)<~>~patient(X))))<=>(?[X]:((~calm(X)|brave(X)))))&
(![X]:((calm(X)<~>~wise(X))<=>(~kind(X)|~old(X))))&
(![X]:((creative(X)&calm(X))=>(~patient(X)|patient(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~funny(X)&~curious(X))))&
(![X]:((~patient(X)|humble(X))<=>~creative(X)))&
(![X]:((~happy(X)&~old(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((quiet(X)&rich(X))<=>(strong(X)&~funny(X))))&
(![X]:((~curious(X)&~tall(X))<=>strong(X)))&
(((~old(mary)&~tall(mary)))=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((wise(X)&old(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((calm(X)&~rich(X))=>~wise(X)))&
(![X]:((strong(X)<~>kind(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((humble(X)&~brave(X))))<=>((brave(lucy)|kind(lucy))))&
(![X]:((strong(X)<~>~kind(X))<=>patient(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>happy(X)))&
(![X]:((happy(X)|~rich(X))=>(~patient(X)&~curious(X))))&
((patient(paul)|humble(paul)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((~humble(X)|~rich(X))))&
((~strong(susan)&~tall(susan)))&
(?[X]:((~humble(X)<~>strong(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(?[X]:(curious(X))) | generous(paul) | [] | null | 0 |
Everyone who is rich or strong is not tall or not creative.
Everyone who is strong is generous or not creative and vice versa.
Everyone who is either not strong or patient is both humble and brave and vice versa.
If susan is not kind or patient then someone is both not old and funny and vice versa.
Everyone who is both humble and creative is either not quiet or not old.
Everyone who is not patient or not creative is both rich and not humble.
Everyone who is both rich and kind is quiet.
Everyone who is both kind and tall is patient and vice versa.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
If someone is either not patient or not creative then john is not funny.
If fred is creative then john is not tall or strong.
Everyone who is either not generous or not kind is humble or not old.
Everyone who is strong is either old or creative and vice versa.
Everyone who is wise or not brave is wise or not old.
Everyone who is either not brave or not happy is funny.
Someone is not old.
Alice is both patient and calm.
Susan is quiet or strong.
Someone is both funny and not patient.
Someone is not quiet.
Someone is not wise.
Mary is either curious or kind.
Someone is both rich and not calm. | Alice is not rich. | entailment | (![X]:((rich(X)|strong(X))=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(generous(X)|~creative(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)&brave(X))))&
(((~kind(susan)|patient(susan)))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:((rich(X)&kind(X))=>quiet(X)))&
(![X]:((kind(X)&tall(X))<=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~patient(X)<~>~creative(X))))=>(~funny(john)))&
((creative(fred))=>((~tall(john)|strong(john))))&
(![X]:((~generous(X)<~>~kind(X))=>(humble(X)|~old(X))))&
(![X]:(strong(X)<=>(old(X)<~>creative(X))))&
(![X]:((wise(X)|~brave(X))=>(wise(X)|~old(X))))&
(![X]:((~brave(X)<~>~happy(X))=>funny(X)))&
(?[X]:(~old(X)))&
((patient(alice)&calm(alice)))&
((quiet(susan)|strong(susan)))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(~wise(X)))&
((curious(mary)<~>kind(mary)))&
(?[X]:((rich(X)&~calm(X)))) | ~rich(alice) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8968027115681088907435595
% SZS output start Proof for 8968027115681088907435595
1. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) | ~tall(X0))) [input p0]
2. ! [X0] : (strong(X0) <=> (~creative(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (brave(X0) & humble(X0))) [input p2]
6. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~humble(X0) & rich(X0))) [input p5]
8. ! [X0] : ((tall(X0) & kind(X0)) <=> patient(X0)) [input p7]
18. calm(alice) & patient(alice) [input p17]
25. rich(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 1]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (~strong(X0) & ~rich(X0))) [flattening 27]
31. ! [X0] : ((~humble(X0) & rich(X0)) | (creative(X0) & patient(X0))) [ennf transformation 6]
44. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 2]
45. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | ~strong(X0))) [flattening 44]
46. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [nnf transformation 3]
47. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [flattening 46]
54. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) | ~kind(X0)))) [nnf transformation 8]
55. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~tall(X0) | ~kind(X0))) [flattening 54]
76. ~creative(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 28]
80. creative(X0) | strong(X0) [cnf transformation 45]
82. ~patient(X0) | ~strong(X0) | humble(X0) [cnf transformation 47]
97. ~humble(X0) | creative(X0) [cnf transformation 31]
101. ~patient(X0) | tall(X0) [cnf transformation 55]
120. patient(alice) [cnf transformation 18]
131. rich(alice) [cnf transformation 25]
230. tall(alice) [resolution 101,120]
238. ~tall(X1) | ~rich(X1) | strong(X1) [resolution 76,80]
257. ~strong(alice) | humble(alice) [resolution 82,120]
261. 22 <=> humble(alice) [avatar definition]
263. humble(alice) <- (22) [avatar component clause 261]
265. 23 <=> strong(alice) [avatar definition]
268. 22 | ~23 [avatar split clause 257,265,261]
380. ~rich(alice) | strong(alice) [resolution 238,230]
383. strong(alice) [subsumption resolution 380,131]
387. 23 [avatar split clause 383,265]
394. creative(alice) <- (22) [resolution 263,97]
427. ~tall(alice) | ~rich(alice) <- (22) [resolution 394,76]
432. ~rich(alice) <- (22) [subsumption resolution 427,230]
433. $false <- (22) [subsumption resolution 432,131]
434. ~22 [avatar contradiction clause 433]
435. $false [avatar sat refutation 268,387,434]
% SZS output end Proof for 8968027115681088907435595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and happy is curious. If someone is both not calm and curious then paul is either funny or not calm. Everyone who is happy is not happy or not funny and vice versa. If lucy is either curious or not funny then paul is either not wise or not patient. Everyone who is not generous is quiet. Everyone who is patient or wise is both curious and rich. If lucy is quiet then susan is not creative or not strong. Everyone who is not calm is not patient or not generous. If someone is either curious or not generous then someone is not curious. If john is either rich or not calm then someone is either tall or not funny. Everyone who is either not rich or not patient is either not brave or not generous. If someone is funny then fred is both happy and not old and vice versa. If alice is not rich then alice is both humble and not old. Everyone who is either strong or not wise is both not patient and calm. If susan is either not wise or calm then paul is both strong and calm and vice versa. Someone is either patient or humble. Someone is brave. Alice is not wise. Susan is wise. Someone is both not rich and calm. Lucy is brave. Someone is both not wise and not generous. | Fred is not happy. | contradiction | (![X]:((brave(X)&happy(X))=>curious(X)))&
((?[X]:((~calm(X)&curious(X))))=>((funny(paul)<~>~calm(paul))))&
(![X]:(happy(X)<=>(~happy(X)|~funny(X))))&
(((curious(lucy)<~>~funny(lucy)))=>((~wise(paul)<~>~patient(paul))))&
(![X]:(~generous(X)=>quiet(X)))&
(![X]:((patient(X)|wise(X))=>(curious(X)&rich(X))))&
((quiet(lucy))=>((~creative(susan)|~strong(susan))))&
(![X]:(~calm(X)=>(~patient(X)|~generous(X))))&
((?[X]:((curious(X)<~>~generous(X))))=>(?[X]:(~curious(X))))&
(((rich(john)<~>~calm(john)))=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))=>(~brave(X)<~>~generous(X))))&
((?[X]:(funny(X)))<=>((happy(fred)&~old(fred))))&
((~rich(alice))=>((humble(alice)&~old(alice))))&
(![X]:((strong(X)<~>~wise(X))=>(~patient(X)&calm(X))))&
(((~wise(susan)<~>calm(susan)))<=>((strong(paul)&calm(paul))))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:(brave(X)))&
(~wise(alice))&
(wise(susan))&
(?[X]:((~rich(X)&calm(X))))&
(brave(lucy))&
(?[X]:((~wise(X)&~generous(X)))) | ~happy(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7628622512087120425238638
% SZS output start Proof for 7628622512087120425238638
3. ! [X0] : (happy(X0) <=> (~funny(X0) | ~happy(X0))) [input p2]
23. ~happy(fred) [input hypothesis]
40. ! [X0] : ((happy(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 3]
41. ! [X0] : ((happy(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | ~happy(X0))) [flattening 40]
72. happy(X0) | happy(X0) [cnf transformation 41]
118. ~happy(fred) [cnf transformation 23]
120. happy(X0) [duplicate literal removal 72]
224. $false [subsumption resolution 118,120]
% SZS output end Proof for 7628622512087120425238638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or wise is not old or curious and vice versa.
Everyone who is both not old and tall is both old and kind and vice versa.
If alice is not quiet or not funny then fred is either humble or patient.
If john is either not curious or not generous then someone is both brave and wise and vice versa.
Everyone who is either not quiet or not happy is patient and vice versa.
If someone is not funny or not generous then fred is quiet.
Everyone who is both kind and not quiet is happy.
Everyone who is not generous or quiet is either not wise or not curious and vice versa.
If someone is either not patient or strong then someone is not kind.
If john is either patient or quiet then lucy is both funny and kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Everyone who is not creative is either not creative or creative and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Mary is wise.
John is both not kind and generous.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | John is not generous. | contradiction | (![X]:((~calm(X)<~>wise(X))<=>(~old(X)|curious(X))))&
(![X]:((~old(X)&tall(X))<=>(old(X)&kind(X))))&
(((~quiet(alice)|~funny(alice)))=>((humble(fred)<~>patient(fred))))&
(((~curious(john)<~>~generous(john)))<=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((~quiet(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((~funny(X)|~generous(X))))=>(quiet(fred)))&
(![X]:((kind(X)&~quiet(X))=>happy(X)))&
(![X]:((~generous(X)|quiet(X))<=>(~wise(X)<~>~curious(X))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
(((patient(john)<~>quiet(john)))<=>((funny(lucy)&kind(lucy))))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>creative(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
((~kind(john)&generous(john)))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | ~generous(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8113939486004136649731386
% SZS output start Proof for 8113939486004136649731386
21. generous(john) & ~kind(john) [input p20]
25. ~generous(john) [input hypothesis]
153. generous(john) [cnf transformation 21]
157. ~generous(john) [cnf transformation 25]
192. 7 <=> generous(john) [avatar definition]
320. 7 [avatar split clause 153,192]
348. ~7 [avatar split clause 157,192]
349. $false [avatar sat refutation 320,348]
% SZS output end Proof for 8113939486004136649731386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either kind or humble and vice versa.
Everyone who is both quiet and generous is either creative or not brave.
Everyone who is wise is not old or brave and vice versa.
Everyone who is either not quiet or not kind is not calm and vice versa.
If fred is both not humble and rich then someone is either not strong or not generous and vice versa.
If lucy is either curious or rich then someone is not kind or not wise.
If someone is both creative and quiet then fred is funny or rich and vice versa.
Everyone who is either not creative or creative is not old.
If someone is happy or quiet then someone is happy and vice versa.
If alice is either quiet or tall then susan is not kind or rich.
If john is humble then someone is not quiet.
If paul is both not funny and tall then fred is not curious.
If alice is either not happy or patient then someone is either not curious or tall and vice versa.
Everyone who is not kind or not curious is either not happy or funny and vice versa.
Everyone who is not tall or not brave is both not patient and tall and vice versa.
Everyone who is brave or not tall is both not brave and not quiet and vice versa.
Lucy is kind.
Someone is either generous or not humble.
Someone is both kind and rich.
Susan is either not quiet or not creative.
Someone is not rich or not humble.
Someone is quiet.
Someone is either kind or wise. | Paul is not humble. | entailment | (![X]:(kind(X)<=>(kind(X)<~>humble(X))))&
(![X]:((quiet(X)&generous(X))=>(creative(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~old(X)|brave(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>~calm(X)))&
(((~humble(fred)&rich(fred)))<=>(?[X]:((~strong(X)<~>~generous(X)))))&
(((curious(lucy)<~>rich(lucy)))=>(?[X]:((~kind(X)|~wise(X)))))&
((?[X]:((creative(X)&quiet(X))))<=>((funny(fred)|rich(fred))))&
(![X]:((~creative(X)<~>creative(X))=>~old(X)))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:(happy(X))))&
(((quiet(alice)<~>tall(alice)))=>((~kind(susan)|rich(susan))))&
((humble(john))=>(?[X]:(~quiet(X))))&
(((~funny(paul)&tall(paul)))=>(~curious(fred)))&
(((~happy(alice)<~>patient(alice)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)&tall(X))))&
(![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))&
(kind(lucy))&
(?[X]:((generous(X)<~>~humble(X))))&
(?[X]:((kind(X)&rich(X))))&
((~quiet(susan)<~>~creative(susan)))&
(?[X]:((~rich(X)|~humble(X))))&
(?[X]:(quiet(X)))&
(?[X]:((kind(X)<~>wise(X)))) | ~humble(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 797818720452600317148945
% SZS output start Proof for 797818720452600317148945
1. ! [X0] : (kind(X0) <=> (kind(X0) <~> humble(X0))) [input p0]
24. humble(paul) [input hypothesis]
35. ! [X0] : ((kind(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 1]
85. ~humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 35]
87. kind(X0) | kind(X0) | ~humble(X0) [cnf transformation 35]
150. humble(paul) [cnf transformation 24]
157. ~humble(X0) | ~kind(X0) [duplicate literal removal 85]
158. kind(X0) | ~humble(X0) [duplicate literal removal 87]
159. ~humble(X0) [subsumption resolution 157,158]
327. $false [subsumption resolution 150,159]
% SZS output end Proof for 797818720452600317148945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not creative is not happy or not old and vice versa.
Everyone who is either not calm or not wise is not strong.
Everyone who is both not calm and strong is both not quiet and not rich.
If john is both not funny and not happy then someone is tall or not funny.
Everyone who is happy is both creative and curious.
If fred is funny then susan is either not quiet or tall and vice versa.
Everyone who is not creative or funny is kind.
Everyone who is both quiet and not tall is either not patient or not old.
If fred is curious then lucy is old or wise.
If someone is not tall then alice is either not funny or not old and vice versa.
If fred is either not generous or brave then someone is brave or not rich and vice versa.
If someone is both quiet and not strong then someone is kind and vice versa.
Everyone who is both not wise and patient is either not rich or strong and vice versa.
Everyone who is both not patient and not tall is happy or humble and vice versa.
Everyone who is rich or not wise is either quiet or not funny and vice versa.
Everyone who is either not strong or generous is wise or not patient and vice versa.
Someone is both not funny and humble.
Someone is both not funny and not quiet.
Fred is both not curious and calm.
Someone is both not happy and tall.
Someone is either quiet or kind.
Susan is not curious or not strong.
Alice is both not strong and funny.
Mary is not rich. | Susan is not tall. | neutral | (![X]:((~humble(X)&~creative(X))<=>(~happy(X)|~old(X))))&
(![X]:((~calm(X)<~>~wise(X))=>~strong(X)))&
(![X]:((~calm(X)&strong(X))=>(~quiet(X)&~rich(X))))&
(((~funny(john)&~happy(john)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:(happy(X)=>(creative(X)&curious(X))))&
((funny(fred))<=>((~quiet(susan)<~>tall(susan))))&
(![X]:((~creative(X)|funny(X))=>kind(X)))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>~old(X))))&
((curious(fred))=>((old(lucy)|wise(lucy))))&
((?[X]:(~tall(X)))<=>((~funny(alice)<~>~old(alice))))&
(((~generous(fred)<~>brave(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)&patient(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~patient(X)&~tall(X))<=>(happy(X)|humble(X))))&
(![X]:((rich(X)|~wise(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(wise(X)|~patient(X))))&
(?[X]:((~funny(X)&humble(X))))&
(?[X]:((~funny(X)&~quiet(X))))&
((~curious(fred)&calm(fred)))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
((~curious(susan)|~strong(susan)))&
((~strong(alice)&funny(alice)))&
(~rich(mary)) | ~tall(susan) | [] | null | 0 |
If someone is curious then someone is patient and vice versa. If alice is either tall or not tall then someone is kind or happy and vice versa. If paul is either not humble or not rich then someone is both not tall and not generous and vice versa. Everyone who is either not calm or brave is not tall. If someone is either not calm or not creative then someone is not curious or wise. Everyone who is either not patient or funny is tall or quiet and vice versa. Everyone who is curious is not creative or not quiet. Everyone who is either not rich or curious is not calm or not generous. Everyone who is not funny or funny is either not rich or not wise. If someone is not creative then lucy is both not quiet and not strong. Everyone who is not tall is not wise or tall and vice versa. Everyone who is either kind or not patient is both rich and happy and vice versa. Everyone who is either not kind or brave is humble and vice versa. If alice is not curious then someone is not rich and vice versa. Everyone who is both not wise and not happy is either not patient or not quiet. If lucy is not brave or not humble then someone is not generous or not calm. Someone is both generous and not quiet. Someone is not calm or curious. Someone is both funny and not humble. Someone is both not wise and kind. Someone is both generous and not strong. John is not kind or not patient. Someone is either not happy or not funny. | Lucy is calm. | neutral | ((?[X]:(curious(X)))<=>(?[X]:(patient(X))))&
(((tall(alice)<~>~tall(alice)))<=>(?[X]:((kind(X)|happy(X)))))&
(((~humble(paul)<~>~rich(paul)))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~calm(X)<~>brave(X))=>~tall(X)))&
((?[X]:((~calm(X)<~>~creative(X))))=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((~patient(X)<~>funny(X))<=>(tall(X)|quiet(X))))&
(![X]:(curious(X)=>(~creative(X)|~quiet(X))))&
(![X]:((~rich(X)<~>curious(X))=>(~calm(X)|~generous(X))))&
(![X]:((~funny(X)|funny(X))=>(~rich(X)<~>~wise(X))))&
((?[X]:(~creative(X)))=>((~quiet(lucy)&~strong(lucy))))&
(![X]:(~tall(X)<=>(~wise(X)|tall(X))))&
(![X]:((kind(X)<~>~patient(X))<=>(rich(X)&happy(X))))&
(![X]:((~kind(X)<~>brave(X))<=>humble(X)))&
((~curious(alice))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(~patient(X)<~>~quiet(X))))&
(((~brave(lucy)|~humble(lucy)))=>(?[X]:((~generous(X)|~calm(X)))))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((~calm(X)|curious(X))))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((generous(X)&~strong(X))))&
((~kind(john)|~patient(john)))&
(?[X]:((~happy(X)<~>~funny(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not generous is both not humble and not patient and vice versa.
If someone is both not kind and humble then fred is either wise or rich and vice versa.
Everyone who is both not old and not generous is both strong and kind.
If someone is happy then lucy is kind and vice versa.
Everyone who is generous or not creative is both curious and strong and vice versa.
Everyone who is both not strong and quiet is both rich and funny.
Everyone who is both not funny and not kind is both calm and kind and vice versa.
Everyone who is both tall and not funny is not curious or tall and vice versa.
If alice is not generous or not kind then someone is quiet or patient and vice versa.
Everyone who is either not old or not funny is either calm or old and vice versa.
Everyone who is either kind or wise is tall and vice versa.
If someone is either not humble or not generous then mary is either creative or not old.
If paul is both not patient and wise then mary is not happy.
If someone is wise then someone is both not tall and kind and vice versa.
Paul is either happy or not old.
Alice is both not rich and creative.
Someone is either old or rich.
Paul is not generous or humble.
Someone is either not strong or old.
Susan is both not funny and not rich. | Paul is not generous. | neutral | (![X]:(~generous(X)<=>(~humble(X)&~patient(X))))&
((?[X]:((~kind(X)&humble(X))))<=>((wise(fred)<~>rich(fred))))&
(![X]:((~old(X)&~generous(X))=>(strong(X)&kind(X))))&
((?[X]:(happy(X)))<=>(kind(lucy)))&
(![X]:((generous(X)|~creative(X))<=>(curious(X)&strong(X))))&
(![X]:((~strong(X)&quiet(X))=>(rich(X)&funny(X))))&
(![X]:((~funny(X)&~kind(X))<=>(calm(X)&kind(X))))&
(![X]:((tall(X)&~funny(X))<=>(~curious(X)|tall(X))))&
(((~generous(alice)|~kind(alice)))<=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:((~old(X)<~>~funny(X))<=>(calm(X)<~>old(X))))&
(![X]:((kind(X)<~>wise(X))<=>tall(X)))&
((?[X]:((~humble(X)<~>~generous(X))))=>((creative(mary)<~>~old(mary))))&
(((~patient(paul)&wise(paul)))=>(~happy(mary)))&
((?[X]:(wise(X)))<=>(?[X]:((~tall(X)&kind(X)))))&
((happy(paul)<~>~old(paul)))&
((~rich(alice)&creative(alice)))&
(?[X]:((old(X)<~>rich(X))))&
((~generous(paul)|humble(paul)))&
(?[X]:((~strong(X)<~>old(X))))&
((~funny(susan)&~rich(susan))) | ~generous(paul) | [] | null | 0 |
If mary is both rich and wise then someone is both tall and not patient and vice versa.
If someone is calm then alice is not curious or strong and vice versa.
If alice is both not funny and patient then fred is creative.
If someone is either creative or not quiet then someone is either wise or not kind and vice versa.
Everyone who is strong or curious is either kind or not kind and vice versa.
Everyone who is both calm and creative is not happy.
Everyone who is not tall is both kind and not curious.
Everyone who is either humble or calm is rich or not rich.
If someone is not patient or humble then someone is both not rich and not generous.
If lucy is both quiet and creative then mary is either quiet or not kind.
If fred is not patient or creative then someone is both old and funny and vice versa.
If someone is either calm or not old then susan is funny or quiet.
If someone is either creative or old then someone is not curious or quiet.
If alice is either tall or humble then susan is tall and vice versa.
Everyone who is either not wise or not humble is both not rich and not generous.
If someone is curious then someone is both calm and not calm and vice versa.
Someone is strong.
Someone is both not happy and quiet.
John is not calm.
Someone is not tall or old.
Someone is both not happy and not brave.
Lucy is both not quiet and not patient.
Someone is either old or strong.
Susan is not calm. | Alice is not strong. | contradiction | (((rich(mary)&wise(mary)))<=>(?[X]:((tall(X)&~patient(X)))))&
((?[X]:(calm(X)))<=>((~curious(alice)|strong(alice))))&
(((~funny(alice)&patient(alice)))=>(creative(fred)))&
((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((strong(X)|curious(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((calm(X)&creative(X))=>~happy(X)))&
(![X]:(~tall(X)=>(kind(X)&~curious(X))))&
(![X]:((humble(X)<~>calm(X))=>(rich(X)|~rich(X))))&
((?[X]:((~patient(X)|humble(X))))=>(?[X]:((~rich(X)&~generous(X)))))&
(((quiet(lucy)&creative(lucy)))=>((quiet(mary)<~>~kind(mary))))&
(((~patient(fred)|creative(fred)))<=>(?[X]:((old(X)&funny(X)))))&
((?[X]:((calm(X)<~>~old(X))))=>((funny(susan)|quiet(susan))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((~curious(X)|quiet(X)))))&
(((tall(alice)<~>humble(alice)))<=>(tall(susan)))&
(![X]:((~wise(X)<~>~humble(X))=>(~rich(X)&~generous(X))))&
((?[X]:(curious(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)&quiet(X))))&
(~calm(john))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((~happy(X)&~brave(X))))&
((~quiet(lucy)&~patient(lucy)))&
(?[X]:((old(X)<~>strong(X))))&
(~calm(susan)) | ~strong(alice) | [
"p4",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4200048882192102546156739
% SZS output start Proof for 4200048882192102546156739
5. ! [X0] : ((curious(X0) | strong(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p4]
16. ? [X0] : curious(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p15]
25. ~strong(alice) [input hypothesis]
29. ? [X0] : curious(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 16]
63. ! [X0] : (((curious(X0) | strong(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~curious(X0) & ~strong(X0)))) [nnf transformation 5]
64. ! [X0] : ((curious(X0) | strong(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~curious(X0) & ~strong(X0)))) [flattening 63]
82. (? [X0] : curious(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : ~curious(X0)) [nnf transformation 29]
83. (? [X0] : curious(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : ~curious(X3)) [rectify 82]
84. ? [X0] : curious(X0) => curious(sK7) [choice axiom]
85. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK8) & calm(sK8)) [choice axiom]
86. (curious(sK7) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK8) & calm(sK8)) | ! [X3] : ~curious(X3)) [skolemisation 83,85,84]
116. curious(X0) | strong(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 64]
117. curious(X0) | strong(X0) | kind(X0) | kind(X0) [cnf transformation 64]
141. calm(sK8) | ~curious(X3) [cnf transformation 86]
142. ~calm(sK8) | ~curious(X3) [cnf transformation 86]
153. ~strong(alice) [cnf transformation 25]
154. curious(X0) | strong(X0) | ~kind(X0) [duplicate literal removal 116]
155. curious(X0) | strong(X0) | kind(X0) [duplicate literal removal 117]
180. 6 <=> strong(alice) [avatar definition]
182. ~strong(alice) <- (~6) [avatar component clause 180]
246. strong(X0) | curious(X0) [subsumption resolution 154,155]
346. 43 <=> ! [X3] : ~curious(X3) [avatar definition]
347. ~curious(X3) <- (43) [avatar component clause 346]
349. 44 <=> calm(sK8) [avatar definition]
352. 43 | ~44 [avatar split clause 142,349,346]
353. 43 | 44 [avatar split clause 141,349,346]
374. ~6 [avatar split clause 153,180]
376. curious(alice) <- (~6) [resolution 246,182]
378. $false <- (~6, 43) [subsumption resolution 376,347]
379. 6 | ~43 [avatar contradiction clause 378]
382. $false [avatar sat refutation 352,353,374,379]
% SZS output end Proof for 4200048882192102546156739
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. If someone is both not calm and not happy then john is not curious. Someone is both not happy and old. Paul is brave or not curious. Someone is either patient or creative. Someone is either calm or happy. Someone is either not brave or not generous. Someone is kind. John is rich. Someone is not curious or not rich. | Mary is not kind. | neutral | (![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((?[X]:((~calm(X)&~happy(X))))=>(~curious(john)))&
(?[X]:((~happy(X)&old(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(rich(john))&
(?[X]:((~curious(X)|~rich(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is humble or generous is either happy or not creative.
If susan is both not old and not rich then someone is both not humble and not strong and vice versa.
If fred is either not humble or patient then someone is either calm or brave and vice versa.
Everyone who is both not tall and funny is not humble or patient and vice versa.
Everyone who is both not kind and patient is not kind or not happy and vice versa.
Everyone who is not tall is both not humble and curious.
Everyone who is not rich is old or happy and vice versa.
If someone is not calm then lucy is not old or not tall and vice versa.
If someone is either creative or patient then someone is not creative or not kind and vice versa.
If mary is either quiet or not brave then fred is both not curious and not rich.
If paul is creative or patient then fred is not rich and vice versa.
Everyone who is strong or quiet is tall or quiet and vice versa.
If someone is both not strong and not brave then someone is not strong and vice versa.
If fred is not creative then fred is not humble or not kind and vice versa.
Everyone who is not old or humble is not patient.
Everyone who is both not brave and funny is not strong.
Alice is both happy and not creative.
Susan is both not rich and funny.
Someone is old.
Mary is old or curious.
Someone is both not rich and not kind.
Someone is not kind.
Paul is either not old or curious.
Someone is both not generous and not kind. | Paul is rich. | contradiction | (![X]:((humble(X)|generous(X))=>(happy(X)<~>~creative(X))))&
(((~old(susan)&~rich(susan)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(((~humble(fred)<~>patient(fred)))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((~tall(X)&funny(X))<=>(~humble(X)|patient(X))))&
(![X]:((~kind(X)&patient(X))<=>(~kind(X)|~happy(X))))&
(![X]:(~tall(X)=>(~humble(X)&curious(X))))&
(![X]:(~rich(X)<=>(old(X)|happy(X))))&
((?[X]:(~calm(X)))<=>((~old(lucy)|~tall(lucy))))&
((?[X]:((creative(X)<~>patient(X))))<=>(?[X]:((~creative(X)|~kind(X)))))&
(((quiet(mary)<~>~brave(mary)))=>((~curious(fred)&~rich(fred))))&
(((creative(paul)|patient(paul)))<=>(~rich(fred)))&
(![X]:((strong(X)|quiet(X))<=>(tall(X)|quiet(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>(?[X]:(~strong(X))))&
((~creative(fred))<=>((~humble(fred)|~kind(fred))))&
(![X]:((~old(X)|humble(X))=>~patient(X)))&
(![X]:((~brave(X)&funny(X))=>~strong(X)))&
((happy(alice)&~creative(alice)))&
((~rich(susan)&funny(susan)))&
(?[X]:(old(X)))&
((old(mary)|curious(mary)))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:(~kind(X)))&
((~old(paul)<~>curious(paul)))&
(?[X]:((~generous(X)&~kind(X)))) | rich(paul) | [
"p4",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2914120935386738501649246
% SZS output start Proof for 2914120935386738501649246
5. ! [X0] : ((patient(X0) & ~kind(X0)) <=> (~happy(X0) | ~kind(X0))) [input p4]
7. ! [X0] : (~rich(X0) <=> (happy(X0) | old(X0))) [input p6]
15. ! [X0] : ((humble(X0) | ~old(X0)) => ~patient(X0)) [input p14]
25. rich(paul) [input hypothesis]
33. ! [X0] : (~patient(X0) | (~humble(X0) & old(X0))) [ennf transformation 15]
48. ! [X0] : (((patient(X0) & ~kind(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~patient(X0) | kind(X0)))) [nnf transformation 5]
49. ! [X0] : (((patient(X0) & ~kind(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~patient(X0) | kind(X0))) [flattening 48]
50. ! [X0] : ((~rich(X0) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | rich(X0))) [nnf transformation 7]
51. ! [X0] : ((~rich(X0) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | rich(X0))) [flattening 50]
106. patient(X0) | happy(X0) [cnf transformation 49]
110. ~rich(X0) | ~old(X0) [cnf transformation 51]
111. ~rich(X0) | ~happy(X0) [cnf transformation 51]
138. ~patient(X0) | old(X0) [cnf transformation 33]
153. rich(paul) [cnf transformation 25]
284. 29 <=> patient(paul) [avatar definition]
285. ~patient(paul) <- (~29) [avatar component clause 284]
286. patient(paul) <- (29) [avatar component clause 284]
333. 39 <=> old(paul) [avatar definition]
353. happy(paul) <- (~29) [resolution 106,285]
360. ~old(paul) [resolution 110,153]
363. ~happy(paul) [resolution 111,153]
365. $false <- (~29) [subsumption resolution 363,353]
366. 29 [avatar contradiction clause 365]
371. old(paul) <- (29) [resolution 138,286]
378. 39 | ~29 [avatar split clause 371,284,333]
379. ~39 [avatar split clause 360,333]
380. $false [avatar sat refutation 366,378,379]
% SZS output end Proof for 2914120935386738501649246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not curious is not creative.
If someone is tall or not old then paul is both brave and not tall and vice versa.
Everyone who is either not wise or creative is both funny and not calm.
If susan is both not humble and not funny then someone is either brave or not generous.
Everyone who is quiet or brave is either wise or patient.
If paul is not wise then alice is either tall or happy.
If someone is both not old and not creative then someone is either not happy or not quiet and vice versa.
If someone is both brave and humble then someone is both not kind and patient.
Everyone who is both humble and not brave is not creative or not curious.
Everyone who is not calm is curious and vice versa.
Everyone who is curious or patient is either happy or brave.
Everyone who is not generous is kind or not calm and vice versa.
If paul is both not wise and not kind then someone is either curious or not rich.
Everyone who is not brave or not humble is not strong.
If john is funny or old then someone is either not patient or not funny.
If alice is generous or strong then someone is either funny or brave and vice versa.
Someone is either wise or not strong.
Someone is not funny.
Someone is not patient.
Someone is brave or not creative.
Someone is either calm or brave.
Mary is both not rich and not funny.
Susan is not curious.
Paul is both not tall and not brave. | Susan is not patient. | entailment | (![X]:((patient(X)&~curious(X))=>~creative(X)))&
((?[X]:((tall(X)|~old(X))))<=>((brave(paul)&~tall(paul))))&
(![X]:((~wise(X)<~>creative(X))=>(funny(X)&~calm(X))))&
(((~humble(susan)&~funny(susan)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((quiet(X)|brave(X))=>(wise(X)<~>patient(X))))&
((~wise(paul))=>((tall(alice)<~>happy(alice))))&
((?[X]:((~old(X)&~creative(X))))<=>(?[X]:((~happy(X)<~>~quiet(X)))))&
((?[X]:((brave(X)&humble(X))))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:((humble(X)&~brave(X))=>(~creative(X)|~curious(X))))&
(![X]:(~calm(X)<=>curious(X)))&
(![X]:((curious(X)|patient(X))=>(happy(X)<~>brave(X))))&
(![X]:(~generous(X)<=>(kind(X)|~calm(X))))&
(((~wise(paul)&~kind(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((~brave(X)|~humble(X))=>~strong(X)))&
(((funny(john)|old(john)))=>(?[X]:((~patient(X)<~>~funny(X)))))&
(((generous(alice)|strong(alice)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(?[X]:((wise(X)<~>~strong(X))))&
(?[X]:(~funny(X)))&
(?[X]:(~patient(X)))&
(?[X]:((brave(X)|~creative(X))))&
(?[X]:((calm(X)<~>brave(X))))&
((~rich(mary)&~funny(mary)))&
(~curious(susan))&
((~tall(paul)&~brave(paul))) | ~patient(susan) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p9",
"p10",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1923680143406185467664779
% SZS output start Proof for 1923680143406185467664779
1. ! [X0] : ((~curious(X0) & patient(X0)) => ~creative(X0)) [input p0]
2. ? [X0] : (~old(X0) | tall(X0)) <=> (~tall(paul) & brave(paul)) [input p1]
3. ! [X0] : ((~wise(X0) <~> creative(X0)) => (~calm(X0) & funny(X0))) [input p2]
5. ! [X0] : ((brave(X0) | quiet(X0)) => (wise(X0) <~> patient(X0))) [input p4]
7. ? [X0] : (~creative(X0) & ~old(X0)) <=> ? [X0] : (~happy(X0) <~> ~quiet(X0)) [input p6]
10. ! [X0] : (~calm(X0) <=> curious(X0)) [input p9]
11. ! [X0] : ((patient(X0) | curious(X0)) => (happy(X0) <~> brave(X0))) [input p10]
23. ~curious(susan) [input p22]
24. ~brave(paul) & ~tall(paul) [input p23]
25. patient(susan) [input hypothesis]
26. ? [X0] : (~creative(X0) & ~old(X0)) <=> ? [X1] : (~happy(X1) <~> ~quiet(X1)) [rectify 7]
28. ! [X0] : (~creative(X0) | (curious(X0) | ~patient(X0))) [ennf transformation 1]
29. ! [X0] : (~creative(X0) | curious(X0) | ~patient(X0)) [flattening 28]
30. ! [X0] : ((~calm(X0) & funny(X0)) | (~wise(X0) <=> creative(X0))) [ennf transformation 3]
33. ! [X0] : ((wise(X0) <~> patient(X0)) | (~brave(X0) & ~quiet(X0))) [ennf transformation 5]
38. ! [X0] : ((happy(X0) <~> brave(X0)) | (~patient(X0) & ~curious(X0))) [ennf transformation 11]
43. (? [X0] : (~old(X0) | tall(X0)) | (tall(paul) | ~brave(paul))) & ((~tall(paul) & brave(paul)) | ! [X0] : (old(X0) & ~tall(X0))) [nnf transformation 2]
44. (? [X0] : (~old(X0) | tall(X0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X0] : (old(X0) & ~tall(X0))) [flattening 43]
45. (? [X0] : (~old(X0) | tall(X0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X1] : (old(X1) & ~tall(X1))) [rectify 44]
46. ? [X0] : (~old(X0) | tall(X0)) => (~old(sK0) | tall(sK0)) [choice axiom]
47. ((~old(sK0) | tall(sK0)) | tall(paul) | ~brave(paul)) & ((~tall(paul) & brave(paul)) | ! [X1] : (old(X1) & ~tall(X1))) [skolemisation 45,46]
48. ! [X0] : ((~calm(X0) & funny(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0)))) [nnf transformation 30]
52. ! [X0] : (((~patient(X0) | ~wise(X0)) & (patient(X0) | wise(X0))) | (~brave(X0) & ~quiet(X0))) [nnf transformation 33]
54. (? [X0] : (~creative(X0) & ~old(X0)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (? [X1] : ((quiet(X1) | happy(X1)) & (~quiet(X1) | ~happy(X1))) | ! [X0] : (creative(X0) | old(X0))) [nnf transformation 26]
55. (? [X0] : (~creative(X0) & ~old(X0)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (? [X2] : ((quiet(X2) | happy(X2)) & (~quiet(X2) | ~happy(X2))) | ! [X3] : (creative(X3) | old(X3))) [rectify 54]
56. ? [X0] : (~creative(X0) & ~old(X0)) => (~creative(sK2) & ~old(sK2)) [choice axiom]
57. ? [X2] : ((quiet(X2) | happy(X2)) & (~quiet(X2) | ~happy(X2))) => ((quiet(sK3) | happy(sK3)) & (~quiet(sK3) | ~happy(sK3))) [choice axiom]
58. ((~creative(sK2) & ~old(sK2)) | ! [X1] : ((~happy(X1) | quiet(X1)) & (~quiet(X1) | happy(X1)))) & (((quiet(sK3) | happy(sK3)) & (~quiet(sK3) | ~happy(sK3))) | ! [X3] : (creative(X3) | old(X3))) [skolemisation 55,57,56]
62. ! [X0] : ((~calm(X0) | ~curious(X0)) & (curious(X0) | calm(X0))) [nnf transformation 10]
63. ! [X0] : (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | (~patient(X0) & ~curious(X0))) [nnf transformation 38]
89. ~creative(X0) | curious(X0) | ~patient(X0) [cnf transformation 29]
91. brave(paul) | old(X1) [cnf transformation 47]
97. ~calm(X0) | creative(X0) | wise(X0) [cnf transformation 48]
103. ~quiet(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 52]
104. ~wise(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 52]
110. ~old(sK2) | ~happy(X1) | quiet(X1) [cnf transformation 58]
116. calm(X0) | curious(X0) [cnf transformation 62]
119. ~patient(X0) | happy(X0) | brave(X0) [cnf transformation 63]
148. ~curious(susan) [cnf transformation 23]
150. ~brave(paul) [cnf transformation 24]
151. patient(susan) [cnf transformation 25]
153. 1 <=> brave(paul) [avatar definition]
170. 5 <=> ! [X1] : old(X1) [avatar definition]
171. old(X1) <- (5) [avatar component clause 170]
177. 5 | 1 [avatar split clause 91,153,170]
212. 14 <=> ! [X1] : (~happy(X1) | quiet(X1)) [avatar definition]
213. ~happy(X1) | quiet(X1) <- (14) [avatar component clause 212]
224. 17 <=> old(sK2) [avatar definition]
226. ~old(sK2) <- (~17) [avatar component clause 224]
227. 14 | ~17 [avatar split clause 110,224,212]
346. ~1 [avatar split clause 150,153]
348. $false <- (5, ~17) [resolution 226,171]
349. ~5 | 17 [avatar contradiction clause 348]
411. wise(X0) | creative(X0) | curious(X0) [resolution 97,116]
467. happy(susan) | brave(susan) [resolution 119,151]
469. 60 <=> brave(susan) [avatar definition]
471. brave(susan) <- (60) [avatar component clause 469]
473. 61 <=> happy(susan) [avatar definition]
475. happy(susan) <- (61) [avatar component clause 473]
476. 60 | 61 [avatar split clause 467,473,469]
520. creative(X0) | curious(X0) | ~patient(X0) | ~brave(X0) [resolution 411,104]
531. ~brave(X0) | ~patient(X0) | curious(X0) [subsumption resolution 520,89]
576. ~patient(susan) | curious(susan) <- (60) [resolution 531,471]
578. curious(susan) <- (60) [subsumption resolution 576,151]
579. $false <- (60) [subsumption resolution 578,148]
580. ~60 [avatar contradiction clause 579]
585. quiet(susan) <- (14, 61) [resolution 475,213]
587. ~wise(susan) | ~patient(susan) <- (14, 61) [resolution 585,103]
590. ~wise(susan) <- (14, 61) [subsumption resolution 587,151]
607. creative(susan) | curious(susan) <- (14, 61) [resolution 590,411]
608. creative(susan) <- (14, 61) [subsumption resolution 607,148]
609. curious(susan) | ~patient(susan) <- (14, 61) [resolution 608,89]
610. ~patient(susan) <- (14, 61) [subsumption resolution 609,148]
611. $false <- (14, 61) [subsumption resolution 610,151]
612. ~14 | ~61 [avatar contradiction clause 611]
613. $false [avatar sat refutation 177,227,346,349,476,580,612]
% SZS output end Proof for 1923680143406185467664779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not creative then fred is both creative and wise.
Everyone who is curious is not tall or not rich and vice versa.
Everyone who is quiet or not strong is both not patient and not creative.
Everyone who is both rich and not creative is both not happy and not quiet.
If someone is both brave and happy then someone is both not brave and not rich and vice versa.
Everyone who is not wise or funny is both funny and not creative.
Everyone who is not wise is either old or not curious.
If someone is funny or not quiet then alice is both calm and not brave.
Everyone who is not quiet or brave is both calm and not creative.
If mary is either not rich or not curious then someone is both rich and strong and vice versa.
Everyone who is not kind or humble is old or not generous and vice versa.
If someone is not calm then someone is not creative.
Everyone who is not wise is both not curious and not calm and vice versa.
If paul is creative or not brave then paul is not happy and vice versa.
If someone is either old or patient then someone is happy.
If lucy is not calm or not kind then someone is not old or brave and vice versa.
Susan is not strong.
Someone is wise or not generous.
Someone is not creative.
Someone is either not kind or not funny.
Paul is not brave or not creative.
Someone is both calm and not kind.
Someone is both not happy and not funny. | Mary is not creative. | entailment | ((?[X]:((strong(X)&~creative(X))))=>((creative(fred)&wise(fred))))&
(![X]:(curious(X)<=>(~tall(X)|~rich(X))))&
(![X]:((quiet(X)|~strong(X))=>(~patient(X)&~creative(X))))&
(![X]:((rich(X)&~creative(X))=>(~happy(X)&~quiet(X))))&
((?[X]:((brave(X)&happy(X))))<=>(?[X]:((~brave(X)&~rich(X)))))&
(![X]:((~wise(X)|funny(X))=>(funny(X)&~creative(X))))&
(![X]:(~wise(X)=>(old(X)<~>~curious(X))))&
((?[X]:((funny(X)|~quiet(X))))=>((calm(alice)&~brave(alice))))&
(![X]:((~quiet(X)|brave(X))=>(calm(X)&~creative(X))))&
(((~rich(mary)<~>~curious(mary)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~kind(X)|humble(X))<=>(old(X)|~generous(X))))&
((?[X]:(~calm(X)))=>(?[X]:(~creative(X))))&
(![X]:(~wise(X)<=>(~curious(X)&~calm(X))))&
(((creative(paul)|~brave(paul)))<=>(~happy(paul)))&
((?[X]:((old(X)<~>patient(X))))=>(?[X]:(happy(X))))&
(((~calm(lucy)|~kind(lucy)))<=>(?[X]:((~old(X)|brave(X)))))&
(~strong(susan))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~kind(X)<~>~funny(X))))&
((~brave(paul)|~creative(paul)))&
(?[X]:((calm(X)&~kind(X))))&
(?[X]:((~happy(X)&~funny(X)))) | ~creative(mary) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6068760549523989124903604
% SZS output start Proof for 6068760549523989124903604
3. ! [X0] : ((~strong(X0) | quiet(X0)) => (~creative(X0) & ~patient(X0))) [input p2]
9. ! [X0] : ((brave(X0) | ~quiet(X0)) => (~creative(X0) & calm(X0))) [input p8]
24. creative(mary) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~patient(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 3]
36. ! [X0] : ((~creative(X0) & calm(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 9]
87. ~creative(X0) | ~quiet(X0) [cnf transformation 30]
107. ~creative(X0) | quiet(X0) [cnf transformation 36]
140. creative(mary) [cnf transformation 24]
199. ~creative(X0) [subsumption resolution 107,87]
296. $false [subsumption resolution 140,199]
% SZS output end Proof for 6068760549523989124903604
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not curious then someone is both curious and happy.
If someone is both strong and generous then someone is either brave or happy and vice versa.
If someone is not happy then susan is both not wise and curious.
Everyone who is kind is both not calm and calm and vice versa.
Everyone who is both tall and brave is both wise and not tall and vice versa.
Everyone who is creative is not calm or wise and vice versa.
If someone is either not generous or generous then someone is both not curious and not patient.
If someone is creative or not quiet then mary is funny and vice versa.
Everyone who is either not brave or quiet is both calm and happy and vice versa.
Everyone who is both not wise and funny is both not generous and not calm and vice versa.
If someone is patient then mary is either strong or generous and vice versa.
Everyone who is not funny is not rich.
If someone is not tall or quiet then someone is either not wise or calm.
Everyone who is not generous or funny is strong.
Everyone who is both not rich and funny is both not calm and patient.
If susan is both generous and not creative then mary is not rich or quiet.
Lucy is either strong or not patient.
John is not curious.
Someone is tall or humble.
Someone is either wise or creative.
Lucy is either not brave or not calm.
Fred is either not tall or not old.
John is quiet or funny.
Alice is not patient. | Lucy is not calm. | neutral | ((?[X]:((~humble(X)&~curious(X))))=>(?[X]:((curious(X)&happy(X)))))&
((?[X]:((strong(X)&generous(X))))<=>(?[X]:((brave(X)<~>happy(X)))))&
((?[X]:(~happy(X)))=>((~wise(susan)&curious(susan))))&
(![X]:(kind(X)<=>(~calm(X)&calm(X))))&
(![X]:((tall(X)&brave(X))<=>(wise(X)&~tall(X))))&
(![X]:(creative(X)<=>(~calm(X)|wise(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>(?[X]:((~curious(X)&~patient(X)))))&
((?[X]:((creative(X)|~quiet(X))))<=>(funny(mary)))&
(![X]:((~brave(X)<~>quiet(X))<=>(calm(X)&happy(X))))&
(![X]:((~wise(X)&funny(X))<=>(~generous(X)&~calm(X))))&
((?[X]:(patient(X)))<=>((strong(mary)<~>generous(mary))))&
(![X]:(~funny(X)=>~rich(X)))&
((?[X]:((~tall(X)|quiet(X))))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((~generous(X)|funny(X))=>strong(X)))&
(![X]:((~rich(X)&funny(X))=>(~calm(X)&patient(X))))&
(((generous(susan)&~creative(susan)))=>((~rich(mary)|quiet(mary))))&
((strong(lucy)<~>~patient(lucy)))&
(~curious(john))&
(?[X]:((tall(X)|humble(X))))&
(?[X]:((wise(X)<~>creative(X))))&
((~brave(lucy)<~>~calm(lucy)))&
((~tall(fred)<~>~old(fred)))&
((quiet(john)|funny(john)))&
(~patient(alice)) | ~calm(lucy) | [] | null | 0 |
Everyone who is both not old and not curious is either rich or not happy and vice versa.
Everyone who is either patient or not old is patient and vice versa.
If susan is not calm then someone is not old and vice versa.
Everyone who is both not curious and rich is not quiet.
If paul is funny or calm then mary is both not generous and tall and vice versa.
If someone is either not creative or not humble then someone is not creative and vice versa.
If john is kind then alice is happy or humble and vice versa.
If john is quiet then susan is not quiet.
Everyone who is both not creative and quiet is both not kind and wise and vice versa.
If lucy is either not rich or not brave then someone is curious.
Everyone who is either not happy or quiet is creative or not happy.
If paul is both not quiet and old then someone is not wise or rich and vice versa.
Everyone who is strong is both wise and curious.
Everyone who is either not creative or not brave is quiet.
If someone is brave then paul is either not curious or not quiet and vice versa.
If someone is brave or not kind then someone is strong and vice versa.
Someone is not brave.
Lucy is both not happy and calm.
Paul is either quiet or not curious.
Someone is either kind or quiet.
Someone is both kind and not curious. | John is brave. | contradiction | (![X]:((~old(X)&~curious(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((patient(X)<~>~old(X))<=>patient(X)))&
((~calm(susan))<=>(?[X]:(~old(X))))&
(![X]:((~curious(X)&rich(X))=>~quiet(X)))&
(((funny(paul)|calm(paul)))<=>((~generous(mary)&tall(mary))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:(~creative(X))))&
((kind(john))<=>((happy(alice)|humble(alice))))&
((quiet(john))=>(~quiet(susan)))&
(![X]:((~creative(X)&quiet(X))<=>(~kind(X)&wise(X))))&
(((~rich(lucy)<~>~brave(lucy)))=>(?[X]:(curious(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(creative(X)|~happy(X))))&
(((~quiet(paul)&old(paul)))<=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(strong(X)=>(wise(X)&curious(X))))&
(![X]:((~creative(X)<~>~brave(X))=>quiet(X)))&
((?[X]:(brave(X)))<=>((~curious(paul)<~>~quiet(paul))))&
((?[X]:((brave(X)|~kind(X))))<=>(?[X]:(strong(X))))&
(?[X]:(~brave(X)))&
((~happy(lucy)&calm(lucy)))&
((quiet(paul)<~>~curious(paul)))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((kind(X)&~curious(X)))) | brave(john) | [
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6467285720145573546607445
% SZS output start Proof for 6467285720145573546607445
15. ? [X0] : brave(X0) <=> (~curious(paul) <~> ~quiet(paul)) [input p14]
19. quiet(paul) <~> ~curious(paul) [input p18]
22. brave(john) [input hypothesis]
61. (? [X0] : brave(X0) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X0] : ~brave(X0)) [nnf transformation 15]
62. (? [X0] : brave(X0) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X1] : ~brave(X1)) [rectify 61]
63. ? [X0] : brave(X0) => brave(sK5) [choice axiom]
64. (brave(sK5) | ((~curious(paul) | quiet(paul)) & (~quiet(paul) | curious(paul)))) & (((quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul))) | ! [X1] : ~brave(X1)) [skolemisation 62,63]
72. (curious(paul) | ~quiet(paul)) & (~curious(paul) | quiet(paul)) [nnf transformation 19]
121. ~quiet(paul) | ~curious(paul) | ~brave(X1) [cnf transformation 64]
122. quiet(paul) | curious(paul) | ~brave(X1) [cnf transformation 64]
131. ~curious(paul) | quiet(paul) [cnf transformation 72]
132. curious(paul) | ~quiet(paul) [cnf transformation 72]
137. brave(john) [cnf transformation 22]
231. 20 <=> quiet(paul) [avatar definition]
250. 24 <=> curious(paul) [avatar definition]
260. 26 <=> ! [X1] : ~brave(X1) [avatar definition]
261. ~brave(X1) <- (26) [avatar component clause 260]
262. 26 | 24 | 20 [avatar split clause 122,231,250,260]
263. 26 | ~24 | ~20 [avatar split clause 121,231,250,260]
285. ~20 | 24 [avatar split clause 132,250,231]
286. 20 | ~24 [avatar split clause 131,250,231]
304. $false <- (26) [resolution 261,137]
305. ~26 [avatar contradiction clause 304]
306. $false [avatar sat refutation 262,263,285,286,305]
% SZS output end Proof for 6467285720145573546607445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either humble or not curious then lucy is not rich or old and vice versa.
If someone is not brave or not humble then someone is not creative or rich and vice versa.
Everyone who is either not patient or humble is either old or curious and vice versa.
If john is both not brave and not funny then alice is either funny or patient and vice versa.
If someone is calm or wise then someone is not strong or calm.
Everyone who is both not happy and creative is wise or brave and vice versa.
Everyone who is either brave or not patient is either brave or wise.
Everyone who is happy or not wise is both brave and not brave and vice versa.
Everyone who is either funny or not kind is kind and vice versa.
Everyone who is not generous or quiet is both strong and not tall.
Everyone who is not rich or not tall is quiet or patient and vice versa.
If john is not generous then paul is both quiet and old and vice versa.
If someone is both funny and not humble then alice is both not quiet and tall and vice versa.
If susan is both happy and brave then someone is either calm or happy.
John is not happy.
Paul is either not quiet or old.
John is not calm or quiet.
Someone is not curious or generous.
Someone is either brave or strong.
Susan is either not kind or quiet. | Susan is not wise. | contradiction | (((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))&
(((happy(susan)&brave(susan)))=>(?[X]:((calm(X)<~>happy(X)))))&
(~happy(john))&
((~quiet(paul)<~>old(paul)))&
((~calm(john)|quiet(john)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((~kind(susan)<~>quiet(susan))) | ~wise(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1974743911365613093208578
% SZS output start Proof for 1974743911365613093208578
8. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p7]
21. ~wise(susan) [input hypothesis]
45. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 8]
46. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 45]
103. brave(X0) | wise(X0) [cnf transformation 46]
105. ~brave(X0) | wise(X0) [cnf transformation 46]
137. ~wise(susan) [cnf transformation 21]
234. wise(X0) [subsumption resolution 103,105]
310. $false [subsumption resolution 137,234]
% SZS output end Proof for 1974743911365613093208578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or quiet is both not brave and not funny.
If someone is not patient or not old then someone is not old and vice versa.
Everyone who is not old is brave.
If someone is both wise and not happy then john is either humble or quiet.
Everyone who is strong or wise is both not curious and rich.
Everyone who is not curious is either not happy or not rich.
Everyone who is either creative or not happy is not humble or kind.
If someone is not brave then lucy is old.
Everyone who is not strong or generous is both wise and curious and vice versa.
If someone is not tall then john is happy or not calm and vice versa.
Everyone who is not calm is wise and vice versa.
Everyone who is not brave or not quiet is calm or not kind.
Everyone who is both not humble and tall is not brave.
If mary is both calm and not humble then someone is both patient and not calm and vice versa.
Everyone who is not calm or wise is both tall and not creative and vice versa.
If someone is funny or kind then fred is either not generous or not humble and vice versa.
John is either not funny or wise.
Mary is kind or not quiet.
Someone is either old or not brave.
Someone is curious or patient.
Someone is not kind.
John is both not funny and not happy.
Someone is wise or old. | Lucy is patient. | neutral | (![X]:((~funny(X)<~>quiet(X))=>(~brave(X)&~funny(X))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:(~old(X))))&
(![X]:(~old(X)=>brave(X)))&
((?[X]:((wise(X)&~happy(X))))=>((humble(john)<~>quiet(john))))&
(![X]:((strong(X)|wise(X))=>(~curious(X)&rich(X))))&
(![X]:(~curious(X)=>(~happy(X)<~>~rich(X))))&
(![X]:((creative(X)<~>~happy(X))=>(~humble(X)|kind(X))))&
((?[X]:(~brave(X)))=>(old(lucy)))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((happy(john)|~calm(john))))&
(![X]:(~calm(X)<=>wise(X)))&
(![X]:((~brave(X)|~quiet(X))=>(calm(X)|~kind(X))))&
(![X]:((~humble(X)&tall(X))=>~brave(X)))&
(((calm(mary)&~humble(mary)))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:((~calm(X)|wise(X))<=>(tall(X)&~creative(X))))&
((?[X]:((funny(X)|kind(X))))<=>((~generous(fred)<~>~humble(fred))))&
((~funny(john)<~>wise(john)))&
((kind(mary)|~quiet(mary)))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:(~kind(X)))&
((~funny(john)&~happy(john)))&
(?[X]:((wise(X)|old(X)))) | patient(lucy) | [] | null | 0 |
Everyone who is not quiet or generous is either strong or not humble. Everyone who is both old and brave is funny or brave. Everyone who is not wise or quiet is both not tall and not patient. Everyone who is either kind or not kind is funny and vice versa. If john is generous or not brave then someone is not brave and vice versa. Everyone who is wise is both not funny and curious. Everyone who is either not wise or not happy is either not brave or not creative. Everyone who is not kind or creative is both funny and wise. Everyone who is both tall and not funny is not wise. Everyone who is both kind and curious is not curious or not wise. Everyone who is either funny or happy is either not curious or not generous. Everyone who is either calm or quiet is both creative and old and vice versa. If susan is either patient or wise then alice is not rich and vice versa. If susan is patient or generous then fred is funny. If someone is either curious or not old then someone is either not strong or strong and vice versa. Someone is not generous. Someone is either not kind or not happy. Alice is wise or not happy. Someone is not quiet. Someone is old or kind. John is funny or not tall. | John is not creative. | entailment | (![X]:((~quiet(X)|generous(X))=>(strong(X)<~>~humble(X))))&
(![X]:((old(X)&brave(X))=>(funny(X)|brave(X))))&
(![X]:((~wise(X)|quiet(X))=>(~tall(X)&~patient(X))))&
(![X]:((kind(X)<~>~kind(X))<=>funny(X)))&
(((generous(john)|~brave(john)))<=>(?[X]:(~brave(X))))&
(![X]:(wise(X)=>(~funny(X)&curious(X))))&
(![X]:((~wise(X)<~>~happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~kind(X)|creative(X))=>(funny(X)&wise(X))))&
(![X]:((tall(X)&~funny(X))=>~wise(X)))&
(![X]:((kind(X)&curious(X))=>(~curious(X)|~wise(X))))&
(![X]:((funny(X)<~>happy(X))=>(~curious(X)<~>~generous(X))))&
(![X]:((calm(X)<~>quiet(X))<=>(creative(X)&old(X))))&
(((patient(susan)<~>wise(susan)))<=>(~rich(alice)))&
(((patient(susan)|generous(susan)))=>(funny(fred)))&
((?[X]:((curious(X)<~>~old(X))))<=>(?[X]:((~strong(X)<~>strong(X)))))&
(?[X]:(~generous(X)))&
(?[X]:((~kind(X)<~>~happy(X))))&
((wise(alice)|~happy(alice)))&
(?[X]:(~quiet(X)))&
(?[X]:((old(X)|kind(X))))&
((funny(john)|~tall(john))) | ~creative(john) | [
"p3",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5226273394300146600211918
% SZS output start Proof for 5226273394300146600211918
4. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> funny(X0)) [input p3]
6. ! [X0] : (wise(X0) => (curious(X0) & ~funny(X0))) [input p5]
8. ! [X0] : ((creative(X0) | ~kind(X0)) => (wise(X0) & funny(X0))) [input p7]
22. creative(john) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~funny(X0)) | ~wise(X0)) [ennf transformation 6]
33. ! [X0] : ((wise(X0) & funny(X0)) | (~creative(X0) & kind(X0))) [ennf transformation 8]
39. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~funny(X0)) & (funny(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 4]
71. funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39]
72. funny(X0) | kind(X0) | kind(X0) [cnf transformation 39]
78. ~funny(X0) | ~wise(X0) [cnf transformation 31]
87. wise(X0) | ~creative(X0) [cnf transformation 33]
119. creative(john) [cnf transformation 22]
125. funny(X0) | ~kind(X0) [duplicate literal removal 71]
126. funny(X0) | kind(X0) [duplicate literal removal 72]
127. funny(X0) [subsumption resolution 125,126]
146. ~wise(X0) [subsumption resolution 78,127]
149. ~creative(X0) [subsumption resolution 87,146]
185. $false [subsumption resolution 119,149]
% SZS output end Proof for 5226273394300146600211918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either not wise or not kind and vice versa. If someone is not brave or funny then someone is not brave. If mary is not strong or strong then john is calm or generous. Everyone who is both not happy and tall is either not humble or not old. If mary is not rich then someone is both not happy and old. Everyone who is generous is both strong and not patient. Everyone who is quiet or kind is happy or funny and vice versa. Everyone who is both generous and wise is not humble and vice versa. If someone is both not tall and not old then someone is brave or not generous and vice versa. If susan is kind then someone is both funny and patient and vice versa. Everyone who is not quiet is both creative and funny and vice versa. Everyone who is not kind or not humble is not generous or not curious. If john is not curious then someone is wise or not rich. If someone is kind then someone is both curious and not kind. Everyone who is kind or quiet is both strong and patient and vice versa. Everyone who is both kind and calm is quiet. Someone is either creative or not curious. Susan is either generous or not curious. Paul is both creative and wise. Someone is either funny or not happy. Someone is rich. Lucy is either quiet or humble. Lucy is not patient or humble. | Lucy is humble. | entailment | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~curious(X))))&
((generous(susan)<~>~curious(susan)))&
((creative(paul)&wise(paul)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:(rich(X)))&
((quiet(lucy)<~>humble(lucy)))&
((~patient(lucy)|humble(lucy))) | humble(lucy) | [
"p14",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1701857695690504564674912
% SZS output start Proof for 1701857695690504564674912
15. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p14]
22. quiet(lucy) <~> humble(lucy) [input p21]
23. humble(lucy) | ~patient(lucy) [input p22]
24. ~humble(lucy) [input hypothesis]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 15]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
79. (~humble(lucy) | ~quiet(lucy)) & (humble(lucy) | quiet(lucy)) [nnf transformation 22]
120. ~quiet(X0) | patient(X0) [cnf transformation 69]
132. humble(lucy) | quiet(lucy) [cnf transformation 79]
134. humble(lucy) | ~patient(lucy) [cnf transformation 23]
135. ~humble(lucy) [cnf transformation 24]
282. 33 <=> quiet(lucy) [avatar definition]
283. quiet(lucy) <- (33) [avatar component clause 282]
286. 34 <=> humble(lucy) [avatar definition]
290. 33 | 34 [avatar split clause 132,286,282]
292. 35 <=> patient(lucy) [avatar definition]
294. ~patient(lucy) <- (~35) [avatar component clause 292]
295. ~35 | 34 [avatar split clause 134,286,292]
296. ~34 [avatar split clause 135,286]
304. patient(lucy) <- (33) [resolution 120,283]
307. $false <- (33, ~35) [subsumption resolution 304,294]
308. ~33 | 35 [avatar contradiction clause 307]
309. $false [avatar sat refutation 290,295,296,308]
% SZS output end Proof for 1701857695690504564674912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then alice is either calm or not happy and vice versa. Everyone who is both calm and rich is either not wise or not brave and vice versa. Everyone who is either humble or not brave is both not curious and not creative and vice versa. If someone is either not tall or not curious then john is not old or rich and vice versa. Everyone who is either quiet or funny is funny or strong. Everyone who is both curious and not strong is quiet. If someone is either not calm or humble then susan is either brave or not generous. If susan is kind then someone is either not patient or happy and vice versa. If someone is either not wise or not patient then someone is either kind or not humble and vice versa. Everyone who is not calm is not strong. If someone is both not wise and quiet then lucy is generous. Everyone who is creative is either not funny or not strong and vice versa. If alice is both not happy and not calm then paul is kind and vice versa. Everyone who is tall is not humble or humble and vice versa. If someone is wise then susan is either rich or curious and vice versa. If paul is either funny or old then someone is either not quiet or not creative and vice versa. John is either calm or curious. Someone is old. Someone is either not curious or creative. John is either not curious or humble. Susan is either brave or happy. Someone is brave. Someone is not brave. | Paul is not kind. | neutral | ((?[X]:(creative(X)))<=>((calm(alice)<~>~happy(alice))))&
(![X]:((calm(X)&rich(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:((humble(X)<~>~brave(X))<=>(~curious(X)&~creative(X))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>((~old(john)|rich(john))))&
(![X]:((quiet(X)<~>funny(X))=>(funny(X)|strong(X))))&
(![X]:((curious(X)&~strong(X))=>quiet(X)))&
((?[X]:((~calm(X)<~>humble(X))))=>((brave(susan)<~>~generous(susan))))&
((kind(susan))<=>(?[X]:((~patient(X)<~>happy(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(?[X]:((kind(X)<~>~humble(X)))))&
(![X]:(~calm(X)=>~strong(X)))&
((?[X]:((~wise(X)&quiet(X))))=>(generous(lucy)))&
(![X]:(creative(X)<=>(~funny(X)<~>~strong(X))))&
(((~happy(alice)&~calm(alice)))<=>(kind(paul)))&
(![X]:(tall(X)<=>(~humble(X)|humble(X))))&
((?[X]:(wise(X)))<=>((rich(susan)<~>curious(susan))))&
(((funny(paul)<~>old(paul)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
((calm(john)<~>curious(john)))&
(?[X]:(old(X)))&
(?[X]:((~curious(X)<~>creative(X))))&
((~curious(john)<~>humble(john)))&
((brave(susan)<~>happy(susan)))&
(?[X]:(brave(X)))&
(?[X]:(~brave(X))) | ~kind(paul) | [] | null | 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. | John is funny. | 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))) | funny(john) | [] | null | 0 |
If someone is old or curious then someone is both patient and calm.
If alice is both not curious and wise then fred is not strong and vice versa.
If fred is quiet or patient then someone is not curious or old.
If alice is not curious then someone is both tall and not strong.
Everyone who is both not tall and old is both not kind and curious and vice versa.
Everyone who is both strong and curious is not rich or not humble and vice versa.
Everyone who is rich or calm is either not kind or funny.
Everyone who is either humble or tall is both generous and wise and vice versa.
Everyone who is both not curious and not funny is rich or funny and vice versa.
Everyone who is generous or old is both not old and not creative and vice versa.
Everyone who is both brave and tall is not quiet and vice versa.
Everyone who is either not quiet or not tall is not curious.
Everyone who is funny or happy is not calm or strong.
Everyone who is either rich or calm is old and vice versa.
If someone is kind then paul is either generous or not old and vice versa.
If someone is both not funny and creative then mary is not happy or not kind.
Lucy is both not quiet and not old.
Someone is both generous and not kind.
John is not rich.
John is both not rich and strong.
Someone is not calm or not rich.
Fred is either not patient or humble.
John is either not rich or brave. | Paul is not brave. | neutral | ((?[X]:((old(X)|curious(X))))=>(?[X]:((patient(X)&calm(X)))))&
(((~curious(alice)&wise(alice)))<=>(~strong(fred)))&
(((quiet(fred)|patient(fred)))=>(?[X]:((~curious(X)|old(X)))))&
((~curious(alice))=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:((~tall(X)&old(X))<=>(~kind(X)&curious(X))))&
(![X]:((strong(X)&curious(X))<=>(~rich(X)|~humble(X))))&
(![X]:((rich(X)|calm(X))=>(~kind(X)<~>funny(X))))&
(![X]:((humble(X)<~>tall(X))<=>(generous(X)&wise(X))))&
(![X]:((~curious(X)&~funny(X))<=>(rich(X)|funny(X))))&
(![X]:((generous(X)|old(X))<=>(~old(X)&~creative(X))))&
(![X]:((brave(X)&tall(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~tall(X))=>~curious(X)))&
(![X]:((funny(X)|happy(X))=>(~calm(X)|strong(X))))&
(![X]:((rich(X)<~>calm(X))<=>old(X)))&
((?[X]:(kind(X)))<=>((generous(paul)<~>~old(paul))))&
((?[X]:((~funny(X)&creative(X))))=>((~happy(mary)|~kind(mary))))&
((~quiet(lucy)&~old(lucy)))&
(?[X]:((generous(X)&~kind(X))))&
(~rich(john))&
((~rich(john)&strong(john)))&
(?[X]:((~calm(X)|~rich(X))))&
((~patient(fred)<~>humble(fred)))&
((~rich(john)<~>brave(john))) | ~brave(paul) | [] | null | 0 |
If someone is patient or not kind then someone is old.
If susan is both rich and not old then someone is both happy and creative.
Everyone who is not brave or not humble is both tall and not wise.
Everyone who is humble or not humble is creative or not happy and vice versa.
If someone is funny then someone is either rich or not rich.
Everyone who is either strong or not curious is either creative or strong.
Everyone who is calm or not old is either brave or not brave.
Everyone who is not patient or not rich is not generous or curious.
Everyone who is either not happy or humble is quiet or happy and vice versa.
If someone is both creative and not creative then john is old.
If someone is both humble and funny then someone is either not rich or not kind and vice versa.
Everyone who is either not quiet or quiet is rich and vice versa.
Everyone who is creative is tall and vice versa.
Everyone who is either not old or brave is both not funny and funny and vice versa.
Everyone who is funny or strong is both not happy and not brave.
Everyone who is both strong and rich is both strong and brave and vice versa.
Someone is both humble and not brave.
Someone is creative or not funny.
Paul is humble or creative.
Someone is not wise or brave.
Someone is kind or not happy.
John is not creative or not strong.
Someone is either tall or generous.
Someone is not happy or not old. | John is old. | neutral | ((?[X]:((patient(X)|~kind(X))))=>(?[X]:(old(X))))&
(((rich(susan)&~old(susan)))=>(?[X]:((happy(X)&creative(X)))))&
(![X]:((~brave(X)|~humble(X))=>(tall(X)&~wise(X))))&
(![X]:((humble(X)|~humble(X))<=>(creative(X)|~happy(X))))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(![X]:((strong(X)<~>~curious(X))=>(creative(X)<~>strong(X))))&
(![X]:((calm(X)|~old(X))=>(brave(X)<~>~brave(X))))&
(![X]:((~patient(X)|~rich(X))=>(~generous(X)|curious(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(quiet(X)|happy(X))))&
((?[X]:((creative(X)&~creative(X))))=>(old(john)))&
((?[X]:((humble(X)&funny(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>rich(X)))&
(![X]:(creative(X)<=>tall(X)))&
(![X]:((~old(X)<~>brave(X))<=>(~funny(X)&funny(X))))&
(![X]:((funny(X)|strong(X))=>(~happy(X)&~brave(X))))&
(![X]:((strong(X)&rich(X))<=>(strong(X)&brave(X))))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:((creative(X)|~funny(X))))&
((humble(paul)|creative(paul)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((kind(X)|~happy(X))))&
((~creative(john)|~strong(john)))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((~happy(X)|~old(X)))) | old(john) | [] | null | 0 |
If someone is kind or quiet then someone is happy.
Everyone who is both not tall and not generous is either curious or not curious and vice versa.
If susan is tall then someone is humble.
Everyone who is not strong is tall or not strong.
Everyone who is not patient is funny or quiet.
Everyone who is old or not happy is creative or calm.
If someone is either not brave or quiet then mary is both curious and humble and vice versa.
Everyone who is either calm or kind is not generous or not kind and vice versa.
Everyone who is not calm or happy is either strong or quiet and vice versa.
Everyone who is either tall or strong is strong or not brave and vice versa.
Everyone who is patient is either not brave or not strong and vice versa.
Everyone who is both not calm and calm is funny and vice versa.
Everyone who is old is both not funny and patient and vice versa.
If fred is both not creative and calm then mary is kind and vice versa.
If someone is not old or not strong then lucy is old.
Everyone who is both not creative and generous is strong.
Someone is both brave and calm.
Someone is either not kind or curious.
Alice is either brave or not tall.
Fred is not rich or not strong.
John is both creative and happy.
Someone is both not kind and not curious.
Someone is creative. | Mary is rich. | neutral | ((?[X]:((kind(X)|quiet(X))))=>(?[X]:(happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>(curious(X)<~>~curious(X))))&
((tall(susan))=>(?[X]:(humble(X))))&
(![X]:(~strong(X)=>(tall(X)|~strong(X))))&
(![X]:(~patient(X)=>(funny(X)|quiet(X))))&
(![X]:((old(X)|~happy(X))=>(creative(X)|calm(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((curious(mary)&humble(mary))))&
(![X]:((calm(X)<~>kind(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~calm(X)|happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)<~>strong(X))<=>(strong(X)|~brave(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&calm(X))<=>funny(X)))&
(![X]:(old(X)<=>(~funny(X)&patient(X))))&
(((~creative(fred)&calm(fred)))<=>(kind(mary)))&
((?[X]:((~old(X)|~strong(X))))=>(old(lucy)))&
(![X]:((~creative(X)&generous(X))=>strong(X)))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((brave(alice)<~>~tall(alice)))&
((~rich(fred)|~strong(fred)))&
((creative(john)&happy(john)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(creative(X))) | rich(mary) | [] | null | 0 |
If someone is old or not rich then someone is not patient and vice versa. Everyone who is both not generous and tall is both not funny and humble and vice versa. Everyone who is either not old or patient is not generous and vice versa. Everyone who is both not brave and not patient is either not patient or not wise and vice versa. Everyone who is either calm or funny is both not kind and not happy and vice versa. Everyone who is either not funny or happy is generous or rich and vice versa. If paul is patient or not happy then someone is either quiet or not rich. If someone is both not kind and generous then fred is humble or not quiet. Everyone who is either not tall or happy is quiet and vice versa. Everyone who is both not quiet and not generous is both not generous and funny. Everyone who is both wise and tall is either curious or generous. If someone is either generous or funny then someone is both kind and not strong and vice versa. If someone is both not strong and old then paul is both not generous and curious. Everyone who is not quiet is either patient or calm. Everyone who is funny is brave and vice versa. Everyone who is not humble or happy is either not patient or not wise. John is either curious or not kind. John is both wise and not curious. Someone is both happy and tall. Someone is not old. Someone is both not generous and not rich. Someone is curious. Someone is not rich or quiet. Someone is not curious. | Paul is calm. | neutral | ((?[X]:((old(X)|~rich(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~generous(X)&tall(X))<=>(~funny(X)&humble(X))))&
(![X]:((~old(X)<~>patient(X))<=>~generous(X)))&
(![X]:((~brave(X)&~patient(X))<=>(~patient(X)<~>~wise(X))))&
(![X]:((calm(X)<~>funny(X))<=>(~kind(X)&~happy(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(generous(X)|rich(X))))&
(((patient(paul)|~happy(paul)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~kind(X)&generous(X))))=>((humble(fred)|~quiet(fred))))&
(![X]:((~tall(X)<~>happy(X))<=>quiet(X)))&
(![X]:((~quiet(X)&~generous(X))=>(~generous(X)&funny(X))))&
(![X]:((wise(X)&tall(X))=>(curious(X)<~>generous(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((~strong(X)&old(X))))=>((~generous(paul)&curious(paul))))&
(![X]:(~quiet(X)=>(patient(X)<~>calm(X))))&
(![X]:(funny(X)<=>brave(X)))&
(![X]:((~humble(X)|happy(X))=>(~patient(X)<~>~wise(X))))&
((curious(john)<~>~kind(john)))&
((wise(john)&~curious(john)))&
(?[X]:((happy(X)&tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:(~curious(X))) | calm(paul) | [] | null | 0 |
Everyone who is either not quiet or kind is both creative and funny.
If lucy is both not generous and patient then someone is kind or not old.
If lucy is creative or not quiet then someone is wise or brave.
Everyone who is either not humble or rich is not generous or not funny.
If susan is calm then someone is either not creative or not tall.
Everyone who is both happy and wise is not curious or not rich.
If someone is either not creative or humble then someone is both not kind and rich and vice versa.
Everyone who is not old is both not quiet and humble.
Everyone who is both humble and not happy is not happy.
If someone is curious then mary is curious or creative and vice versa.
If someone is patient then someone is not kind or old.
Everyone who is not patient is not rich or humble and vice versa.
Everyone who is either quiet or not creative is patient or rich.
Everyone who is either not brave or not happy is strong or not wise.
If someone is not happy then someone is both kind and quiet and vice versa.
Everyone who is strong is both not curious and tall.
Fred is either humble or not old.
Lucy is either not strong or patient.
Fred is not brave or patient.
Mary is not rich or not calm.
Someone is not patient or not kind.
Someone is not patient or not tall.
Someone is either rich or brave.
Paul is both calm and strong. | Paul is calm. | entailment | (![X]:((~quiet(X)<~>kind(X))=>(creative(X)&funny(X))))&
(((~generous(lucy)&patient(lucy)))=>(?[X]:((kind(X)|~old(X)))))&
(((creative(lucy)|~quiet(lucy)))=>(?[X]:((wise(X)|brave(X)))))&
(![X]:((~humble(X)<~>rich(X))=>(~generous(X)|~funny(X))))&
((calm(susan))=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((happy(X)&wise(X))=>(~curious(X)|~rich(X))))&
((?[X]:((~creative(X)<~>humble(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~old(X)=>(~quiet(X)&humble(X))))&
(![X]:((humble(X)&~happy(X))=>~happy(X)))&
((?[X]:(curious(X)))<=>((curious(mary)|creative(mary))))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:(~patient(X)<=>(~rich(X)|humble(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(patient(X)|rich(X))))&
(![X]:((~brave(X)<~>~happy(X))=>(strong(X)|~wise(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:(strong(X)=>(~curious(X)&tall(X))))&
((humble(fred)<~>~old(fred)))&
((~strong(lucy)<~>patient(lucy)))&
((~brave(fred)|patient(fred)))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((calm(paul)&strong(paul))) | calm(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7497727590349227656594655
% SZS output start Proof for 7497727590349227656594655
24. strong(paul) & calm(paul) [input p23]
25. ~calm(paul) [input hypothesis]
134. calm(paul) [cnf transformation 24]
136. ~calm(paul) [cnf transformation 25]
324. $false [subsumption resolution 136,134]
% SZS output end Proof for 7497727590349227656594655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not creative is old or curious.
If someone is either strong or not quiet then alice is both creative and not patient and vice versa.
Everyone who is creative is generous.
If fred is either not kind or strong then someone is either happy or old and vice versa.
Everyone who is kind or humble is either curious or strong and vice versa.
Everyone who is either not creative or funny is brave or not humble and vice versa.
If alice is both kind and not calm then lucy is not kind or not funny.
Everyone who is either not old or rich is not happy or not patient and vice versa.
If lucy is both kind and funny then someone is not calm or not old and vice versa.
If lucy is tall then someone is not strong and vice versa.
If someone is not old then fred is both wise and curious and vice versa.
If alice is old or wise then mary is not rich and vice versa.
If someone is both funny and kind then someone is humble or patient.
Everyone who is both not funny and strong is rich or strong and vice versa.
Everyone who is both kind and creative is not calm or not happy.
If john is either generous or humble then someone is not curious or not calm and vice versa.
Someone is either tall or not calm.
Someone is rich or not creative.
Susan is either happy or not curious.
Someone is not calm.
Someone is either wise or not calm.
Someone is both not wise and not rich.
Someone is humble or calm.
Lucy is not strong. | Susan is strong. | neutral | (![X]:((~curious(X)<~>~creative(X))=>(old(X)|curious(X))))&
((?[X]:((strong(X)<~>~quiet(X))))<=>((creative(alice)&~patient(alice))))&
(![X]:(creative(X)=>generous(X)))&
(((~kind(fred)<~>strong(fred)))<=>(?[X]:((happy(X)<~>old(X)))))&
(![X]:((kind(X)|humble(X))<=>(curious(X)<~>strong(X))))&
(![X]:((~creative(X)<~>funny(X))<=>(brave(X)|~humble(X))))&
(((kind(alice)&~calm(alice)))=>((~kind(lucy)|~funny(lucy))))&
(![X]:((~old(X)<~>rich(X))<=>(~happy(X)|~patient(X))))&
(((kind(lucy)&funny(lucy)))<=>(?[X]:((~calm(X)|~old(X)))))&
((tall(lucy))<=>(?[X]:(~strong(X))))&
((?[X]:(~old(X)))<=>((wise(fred)&curious(fred))))&
(((old(alice)|wise(alice)))<=>(~rich(mary)))&
((?[X]:((funny(X)&kind(X))))=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((~funny(X)&strong(X))<=>(rich(X)|strong(X))))&
(![X]:((kind(X)&creative(X))=>(~calm(X)|~happy(X))))&
(((generous(john)<~>humble(john)))<=>(?[X]:((~curious(X)|~calm(X)))))&
(?[X]:((tall(X)<~>~calm(X))))&
(?[X]:((rich(X)|~creative(X))))&
((happy(susan)<~>~curious(susan)))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>~calm(X))))&
(?[X]:((~wise(X)&~rich(X))))&
(?[X]:((humble(X)|calm(X))))&
(~strong(lucy)) | strong(susan) | [] | null | 0 |
Everyone who is either not calm or not curious is either funny or creative and vice versa.
If lucy is kind or not generous then someone is both wise and not brave and vice versa.
Everyone who is not curious is funny and vice versa.
Everyone who is both generous and kind is both not wise and not old and vice versa.
If mary is either tall or quiet then someone is both not old and not quiet.
Everyone who is either curious or not curious is not old or kind and vice versa.
Everyone who is not brave or curious is not curious and vice versa.
If someone is curious or humble then john is creative.
If someone is either not kind or not happy then alice is both funny and not humble and vice versa.
Everyone who is both generous and not generous is generous.
Everyone who is both brave and not patient is either wise or not quiet.
Everyone who is either tall or patient is both not quiet and not creative.
Everyone who is either not funny or not kind is curious or not patient and vice versa.
If someone is either creative or brave then someone is wise or kind.
Everyone who is both creative and strong is patient or old and vice versa.
If someone is quiet or not strong then fred is both quiet and not strong and vice versa.
Someone is not calm or tall.
Paul is either curious or not rich.
Someone is both calm and not brave.
Paul is not tall or creative.
Alice is both not calm and kind.
Someone is either tall or not strong.
Someone is either not creative or kind. | Alice is not strong. | contradiction | (![X]:((~calm(X)<~>~curious(X))<=>(funny(X)<~>creative(X))))&
(((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(?[X]:((~calm(X)|tall(X))))&
((curious(paul)<~>~rich(paul)))&
(?[X]:((calm(X)&~brave(X))))&
((~tall(paul)|creative(paul)))&
((~calm(alice)&kind(alice)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~creative(X)<~>kind(X)))) | ~strong(alice) | [
"p2",
"p6",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9189583969832499308612483
% SZS output start Proof for 9189583969832499308612483
3. ! [X0] : (~curious(X0) <=> funny(X0)) [input p2]
7. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p6]
13. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> (~patient(X0) | curious(X0))) [input p12]
15. ! [X0] : ((strong(X0) & creative(X0)) <=> (old(X0) | patient(X0))) [input p14]
21. kind(alice) & ~calm(alice) [input p20]
24. ~strong(alice) [input hypothesis]
40. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 3]
48. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 7]
49. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 48]
57. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 13]
58. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [flattening 57]
63. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 15]
64. ! [X0] : (((strong(X0) & creative(X0)) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ~strong(X0) | ~creative(X0))) [flattening 63]
94. funny(X0) | curious(X0) [cnf transformation 40]
111. ~curious(X0) | ~curious(X0) [cnf transformation 49]
131. ~kind(X0) | ~funny(X0) | patient(X0) [cnf transformation 58]
139. ~patient(X0) | strong(X0) [cnf transformation 64]
153. kind(alice) [cnf transformation 21]
158. ~strong(alice) [cnf transformation 24]
160. ~curious(X0) [duplicate literal removal 111]
218. 12 <=> funny(alice) [avatar definition]
219. funny(alice) <- (12) [avatar component clause 218]
220. ~funny(alice) <- (~12) [avatar component clause 218]
383. ~funny(alice) | patient(alice) [resolution 131,153]
385. patient(alice) <- (12) [subsumption resolution 383,219]
401. strong(alice) <- (12) [resolution 385,139]
417. $false <- (12) [subsumption resolution 401,158]
418. ~12 [avatar contradiction clause 417]
425. curious(alice) <- (~12) [resolution 220,94]
426. $false <- (~12) [subsumption resolution 425,160]
427. 12 [avatar contradiction clause 426]
428. $false [avatar sat refutation 418,427]
% SZS output end Proof for 9189583969832499308612483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then fred is either creative or generous. Everyone who is not kind or not old is wise and vice versa. Everyone who is kind is funny or not rich. If paul is not funny or calm then paul is not generous or humble and vice versa. Everyone who is both happy and not curious is not happy or curious. Everyone who is not curious is both not generous and not humble. If someone is either patient or funny then someone is either brave or wise and vice versa. Everyone who is not creative is not patient. If someone is not old then someone is both not brave and not tall. Everyone who is both calm and not old is either brave or not tall. Everyone who is both not generous and not rich is either not creative or rich and vice versa. Everyone who is both not quiet and kind is creative or not generous. If someone is old or not tall then alice is both patient and calm and vice versa. Everyone who is either tall or calm is not tall or not rich and vice versa. Everyone who is humble or not funny is either not tall or not kind and vice versa. If someone is both creative and generous then someone is either calm or rich and vice versa. Fred is either not wise or wise. Someone is both curious and rich. Someone is not funny. Paul is brave. Paul is either kind or not funny. Fred is either happy or creative. John is either funny or tall. Alice is funny. | Fred is wise. | neutral | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>wise(X)))&
(![X]:(kind(X)=>(funny(X)|~rich(X))))&
(((~funny(paul)|calm(paul)))<=>((~generous(paul)|humble(paul))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | wise(fred) | [] | null | 0 |
Everyone who is funny is either not wise or calm and vice versa.
Everyone who is both happy and brave is either not brave or not curious and vice versa.
If susan is either not generous or not rich then alice is both not kind and humble and vice versa.
If someone is either creative or not patient then john is generous and vice versa.
If someone is not quiet then paul is both quiet and not rich and vice versa.
If someone is tall then someone is both not wise and generous and vice versa.
If someone is either not wise or not humble then someone is wise.
If someone is not wise then someone is not rich or humble and vice versa.
Everyone who is patient is either brave or not patient and vice versa.
If paul is funny then fred is strong and vice versa.
Everyone who is either not humble or not rich is not strong or not humble and vice versa.
Everyone who is rich or not old is both tall and old.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
Someone is not kind.
Someone is both not wise and not creative.
John is either tall or generous.
Someone is quiet or not kind.
Paul is either wise or funny.
Lucy is both not creative and not generous.
Alice is not funny.
Someone is not humble. | Alice is brave. | entailment | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~brave(X)<~>~curious(X))))&
(((~generous(susan)<~>~rich(susan)))<=>((~kind(alice)&humble(alice))))&
((?[X]:((creative(X)<~>~patient(X))))<=>(generous(john)))&
((?[X]:(~quiet(X)))<=>((quiet(paul)&~rich(paul))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X))))&
((wise(paul)<~>funny(paul)))&
((~creative(lucy)&~generous(lucy)))&
(~funny(alice))&
(?[X]:(~humble(X))) | brave(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5961892176560407980450497
% SZS output start Proof for 5961892176560407980450497
9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8]
25. ~brave(alice) [input hypothesis]
66. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9]
117. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 66]
120. patient(X0) | brave(X0) | patient(X0) [cnf transformation 66]
149. ~brave(alice) [cnf transformation 25]
152. ~patient(X0) | brave(X0) [duplicate literal removal 117]
153. patient(X0) | brave(X0) [duplicate literal removal 120]
276. brave(X0) [subsumption resolution 152,153]
338. $false [subsumption resolution 149,276]
% SZS output end Proof for 5961892176560407980450497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both creative and generous then someone is not kind or not creative.
Everyone who is not old or not strong is both kind and old and vice versa.
Everyone who is quiet or not curious is both brave and not wise.
Everyone who is both happy and kind is calm and vice versa.
Everyone who is not generous or calm is either not happy or not old and vice versa.
Everyone who is both happy and not kind is both humble and not calm.
Everyone who is quiet is not humble or humble.
If someone is not generous or not patient then someone is happy or curious and vice versa.
If alice is both not kind and not funny then fred is funny or strong and vice versa.
If someone is either kind or not kind then someone is both not patient and generous.
Everyone who is not funny is calm or not calm and vice versa.
Everyone who is either not old or brave is either not happy or not humble.
If fred is both not wise and not patient then someone is quiet.
If john is either creative or not strong then susan is happy or not curious.
Everyone who is either kind or calm is either patient or kind and vice versa.
Everyone who is tall is not funny.
Susan is either not brave or rich.
Someone is both wise and not creative.
Alice is both happy and not calm.
Lucy is either not quiet or not generous.
Alice is creative.
Someone is not curious. | Alice is not generous. | contradiction | ((?[X]:((creative(X)&generous(X))))=>(?[X]:((~kind(X)|~creative(X)))))&
(![X]:((~old(X)|~strong(X))<=>(kind(X)&old(X))))&
(![X]:((quiet(X)|~curious(X))=>(brave(X)&~wise(X))))&
(![X]:((happy(X)&kind(X))<=>calm(X)))&
(![X]:((~generous(X)|calm(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((happy(X)&~kind(X))=>(humble(X)&~calm(X))))&
(![X]:(quiet(X)=>(~humble(X)|humble(X))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((happy(X)|curious(X)))))&
(((~kind(alice)&~funny(alice)))<=>((funny(fred)|strong(fred))))&
((?[X]:((kind(X)<~>~kind(X))))=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:(~funny(X)<=>(calm(X)|~calm(X))))&
(![X]:((~old(X)<~>brave(X))=>(~happy(X)<~>~humble(X))))&
(((~wise(fred)&~patient(fred)))=>(?[X]:(quiet(X))))&
(((creative(john)<~>~strong(john)))=>((happy(susan)|~curious(susan))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)<~>kind(X))))&
(![X]:(tall(X)=>~funny(X)))&
((~brave(susan)<~>rich(susan)))&
(?[X]:((wise(X)&~creative(X))))&
((happy(alice)&~calm(alice)))&
((~quiet(lucy)<~>~generous(lucy)))&
(creative(alice))&
(?[X]:(~curious(X))) | ~generous(alice) | [
"p1",
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4386282711082501853716136
% SZS output start Proof for 4386282711082501853716136
2. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (old(X0) & kind(X0))) [input p1]
5. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~happy(X0) <~> ~old(X0))) [input p4]
19. ~calm(alice) & happy(alice) [input p18]
23. ~generous(alice) [input hypothesis]
43. ! [X0] : (((~strong(X0) | ~old(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [nnf transformation 2]
44. ! [X0] : ((~strong(X0) | ~old(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [flattening 43]
47. ! [X0] : (((calm(X0) | ~generous(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 5]
48. ! [X0] : ((calm(X0) | ~generous(X0) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 47]
76. old(X0) | old(X0) [cnf transformation 44]
86. ~old(X0) | ~happy(X0) | generous(X0) [cnf transformation 48]
130. happy(alice) [cnf transformation 19]
136. ~generous(alice) [cnf transformation 23]
145. old(X0) [duplicate literal removal 76]
163. ~happy(X0) | generous(X0) [subsumption resolution 86,145]
302. generous(alice) [resolution 163,130]
305. $false [subsumption resolution 302,136]
% SZS output end Proof for 4386282711082501853716136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not brave then someone is both tall and rich and vice versa.
If someone is either wise or not strong then paul is both happy and not curious.
If someone is happy then someone is patient or happy.
If someone is both old and creative then someone is both kind and not generous and vice versa.
If someone is either not humble or curious then susan is rich.
If mary is not calm then someone is not happy and vice versa.
If mary is both funny and happy then lucy is both old and wise and vice versa.
If fred is both not creative and not funny then someone is both curious and not kind.
Everyone who is either not wise or funny is happy or rich and vice versa.
If john is creative or not funny then someone is both not tall and funny.
Everyone who is not curious or not kind is rich or happy and vice versa.
Everyone who is either not old or not kind is either calm or not patient and vice versa.
Everyone who is not generous or not humble is rich.
If lucy is either not tall or wise then lucy is either not rich or quiet.
Everyone who is curious is not curious or creative and vice versa.
If alice is either not strong or curious then someone is either kind or wise.
Lucy is either not curious or kind.
Mary is not brave.
Alice is both tall and not brave.
Susan is either not quiet or not happy.
Someone is either not kind or old.
Paul is kind.
Lucy is strong. | Lucy is not funny. | contradiction | ((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((wise(X)<~>~strong(X))))=>((happy(paul)&~curious(paul))))&
((?[X]:(happy(X)))=>(?[X]:((patient(X)|happy(X)))))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((kind(X)&~generous(X)))))&
((?[X]:((~humble(X)<~>curious(X))))=>(rich(susan)))&
((~calm(mary))<=>(?[X]:(~happy(X))))&
(((funny(mary)&happy(mary)))<=>((old(lucy)&wise(lucy))))&
(((~creative(fred)&~funny(fred)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~wise(X)<~>funny(X))<=>(happy(X)|rich(X))))&
(((creative(john)|~funny(john)))=>(?[X]:((~tall(X)&funny(X)))))&
(![X]:((~curious(X)|~kind(X))<=>(rich(X)|happy(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(calm(X)<~>~patient(X))))&
(![X]:((~generous(X)|~humble(X))=>rich(X)))&
(((~tall(lucy)<~>wise(lucy)))=>((~rich(lucy)<~>quiet(lucy))))&
(![X]:(curious(X)<=>(~curious(X)|creative(X))))&
(((~strong(alice)<~>curious(alice)))=>(?[X]:((kind(X)<~>wise(X)))))&
((~curious(lucy)<~>kind(lucy)))&
(~brave(mary))&
((tall(alice)&~brave(alice)))&
((~quiet(susan)<~>~happy(susan)))&
(?[X]:((~kind(X)<~>old(X))))&
(kind(paul))&
(strong(lucy)) | ~funny(lucy) | [
"p1",
"p8",
"p10",
"p14",
"p16",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1012832541534290596709467
% SZS output start Proof for 1012832541534290596709467
2. ? [X0] : (wise(X0) <~> ~strong(X0)) => (~curious(paul) & happy(paul)) [input p1]
9. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> (rich(X0) | happy(X0))) [input p8]
11. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (happy(X0) | rich(X0))) [input p10]
15. ! [X0] : (curious(X0) <=> (creative(X0) | ~curious(X0))) [input p14]
17. ~curious(lucy) <~> kind(lucy) [input p16]
22. kind(paul) [input p21]
23. strong(lucy) [input p22]
24. ~funny(lucy) [input hypothesis]
28. (~curious(paul) & happy(paul)) | ! [X0] : (wise(X0) <=> ~strong(X0)) [ennf transformation 2]
42. (~curious(paul) & happy(paul)) | ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 28]
60. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 9]
61. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [flattening 60]
64. ! [X0] : (((~kind(X0) | ~curious(X0)) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | (kind(X0) & curious(X0)))) [nnf transformation 11]
65. ! [X0] : ((~kind(X0) | ~curious(X0) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | (kind(X0) & curious(X0)))) [flattening 64]
68. ! [X0] : ((curious(X0) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ~curious(X0))) [nnf transformation 15]
69. ! [X0] : ((curious(X0) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ~curious(X0))) [flattening 68]
73. (~kind(lucy) | curious(lucy)) & (kind(lucy) | ~curious(lucy)) [nnf transformation 17]
84. happy(paul) | ~strong(X0) | ~wise(X0) [cnf transformation 42]
103. funny(X0) | happy(X0) | rich(X0) | wise(X0) [cnf transformation 61]
115. ~kind(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 65]
116. ~kind(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 65]
132. curious(X0) | curious(X0) [cnf transformation 69]
138. kind(lucy) | ~curious(lucy) [cnf transformation 73]
147. kind(paul) [cnf transformation 22]
148. strong(lucy) [cnf transformation 23]
149. ~funny(lucy) [cnf transformation 24]
151. curious(X0) [duplicate literal removal 132]
192. 10 <=> ! [X0] : (~strong(X0) | ~wise(X0)) [avatar definition]
193. ~strong(X0) | ~wise(X0) <- (10) [avatar component clause 192]
196. 11 <=> happy(paul) [avatar definition]
200. 10 | 11 [avatar split clause 84,196,192]
269. 28 <=> wise(lucy) [avatar definition]
327. 40 <=> rich(lucy) [avatar definition]
355. kind(lucy) [subsumption resolution 138,151]
384. ~wise(lucy) <- (10) [resolution 193,148]
424. ~curious(lucy) | ~rich(lucy) [resolution 115,355]
427. ~curious(paul) | ~happy(paul) [resolution 116,147]
428. ~curious(lucy) | ~happy(lucy) [resolution 116,355]
430. happy(lucy) | rich(lucy) | wise(lucy) [resolution 103,149]
441. ~happy(lucy) [subsumption resolution 428,151]
444. ~happy(paul) [subsumption resolution 427,151]
445. ~11 [avatar split clause 444,196]
467. ~28 | ~10 [avatar split clause 384,192,269]
470. rich(lucy) | wise(lucy) [subsumption resolution 430,441]
471. 28 | 40 [avatar split clause 470,327,269]
472. ~rich(lucy) [subsumption resolution 424,151]
473. ~40 [avatar split clause 472,327]
474. $false [avatar sat refutation 200,445,467,471,473]
% SZS output end Proof for 1012832541534290596709467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 then someone is not curious and vice versa.
If someone is either not patient or not brave then someone is either not funny or old and vice versa.
Everyone who is both not calm and humble is calm or not brave and vice versa.
If someone is either old or tall then someone is both not creative and brave.
Everyone who is wise or tall is both not generous and not humble.
If lucy is not generous then someone is both humble and rich and vice versa.
Everyone who is not humble is not strong.
Everyone who is not humble or not tall is not brave or not happy.
If someone is strong or not funny then someone is patient.
Everyone who is both old and generous is both generous and kind and vice versa.
Everyone who is either patient or not rich is not generous.
Everyone who is strong or generous is not curious and vice versa.
Everyone who is both strong and not wise is either not brave or not curious.
Everyone who is either creative or humble is curious and vice versa.
If john is old or kind then someone is calm and vice versa.
Everyone who is both not happy and not strong is not rich.
Someone is not generous or calm.
Susan is not creative or not wise.
Alice is either brave or not wise.
Susan is either brave or not funny.
Fred is happy.
Someone is either not generous or old.
Susan is either not curious or kind. | John is kind. | contradiction | ((?[X]:(curious(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~patient(X)<~>~brave(X))))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)|~brave(X))))&
((?[X]:((old(X)<~>tall(X))))=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:((wise(X)|tall(X))=>(~generous(X)&~humble(X))))&
((~generous(lucy))<=>(?[X]:((humble(X)&rich(X)))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((~humble(X)|~tall(X))=>(~brave(X)|~happy(X))))&
((?[X]:((strong(X)|~funny(X))))=>(?[X]:(patient(X))))&
(![X]:((old(X)&generous(X))<=>(generous(X)&kind(X))))&
(![X]:((patient(X)<~>~rich(X))=>~generous(X)))&
(![X]:((strong(X)|generous(X))<=>~curious(X)))&
(![X]:((strong(X)&~wise(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((creative(X)<~>humble(X))<=>curious(X)))&
(((old(john)|kind(john)))<=>(?[X]:(calm(X))))&
(![X]:((~happy(X)&~strong(X))=>~rich(X)))&
(?[X]:((~generous(X)|calm(X))))&
((~creative(susan)|~wise(susan)))&
((brave(alice)<~>~wise(alice)))&
((brave(susan)<~>~funny(susan)))&
(happy(fred))&
(?[X]:((~generous(X)<~>old(X))))&
((~curious(susan)<~>kind(susan))) | kind(john) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2238777355607420785563599
% SZS output start Proof for 2238777355607420785563599
3. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (~brave(X0) | calm(X0))) [input p2]
15. (kind(john) | old(john)) <=> ? [X0] : calm(X0) [input p14]
24. kind(john) [input hypothesis]
50. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | (~humble(X0) | calm(X0)))) [nnf transformation 3]
51. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ~humble(X0) | calm(X0))) [flattening 50]
70. ((kind(john) | old(john)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~kind(john) & ~old(john))) [nnf transformation 15]
71. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~kind(john) & ~old(john))) [flattening 70]
72. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | (~kind(john) & ~old(john))) [rectify 71]
73. ? [X1] : calm(X1) => calm(sK7) [choice axiom]
74. (kind(john) | old(john) | ! [X0] : ~calm(X0)) & (calm(sK7) | (~kind(john) & ~old(john))) [skolemisation 72,73]
94. ~calm(X0) | ~calm(X0) [cnf transformation 51]
130. calm(sK7) | ~kind(john) [cnf transformation 74]
144. kind(john) [cnf transformation 24]
146. ~calm(X0) [duplicate literal removal 94]
250. ~kind(john) [subsumption resolution 130,146]
302. $false [subsumption resolution 144,250]
% SZS output end Proof for 2238777355607420785563599
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not humble or not quiet.
Everyone who is both quiet and not humble is kind and vice versa.
Everyone who is either not funny or not creative is both not generous and tall and vice versa.
If mary is curious then someone is quiet and vice versa.
Everyone who is not rich is not humble and vice versa.
If john is patient then lucy is either brave or not rich.
Everyone who is both patient and wise is patient or not patient and vice versa.
Everyone who is curious or happy is wise and vice versa.
Everyone who is both not funny and humble is brave or curious and vice versa.
Everyone who is funny is either not wise or not strong and vice versa.
If paul is strong then someone is not wise or wise.
If fred is not funny then susan is both not wise and curious and vice versa.
Everyone who is wise is not old.
Everyone who is either brave or patient is either old or not kind.
If alice is either curious or brave then someone is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Someone is not happy or not wise.
Someone is not funny or brave.
Someone is either curious or rich.
Lucy is happy.
Someone is both tall and brave.
John is not funny.
Someone is not calm or curious. | Susan is not generous. | neutral | (![X]:(strong(X)=>(~humble(X)<~>~quiet(X))))&
(![X]:((quiet(X)&~humble(X))<=>kind(X)))&
(![X]:((~funny(X)<~>~creative(X))<=>(~generous(X)&tall(X))))&
((curious(mary))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
((patient(john))=>((brave(lucy)<~>~rich(lucy))))&
(![X]:((patient(X)&wise(X))<=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|happy(X))<=>wise(X)))&
(![X]:((~funny(X)&humble(X))<=>(brave(X)|curious(X))))&
(![X]:(funny(X)<=>(~wise(X)<~>~strong(X))))&
((strong(paul))=>(?[X]:((~wise(X)|wise(X)))))&
((~funny(fred))<=>((~wise(susan)&curious(susan))))&
(![X]:(wise(X)=>~old(X)))&
(![X]:((brave(X)<~>patient(X))=>(old(X)<~>~kind(X))))&
(((curious(alice)<~>brave(alice)))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((curious(X)<~>rich(X))))&
(happy(lucy))&
(?[X]:((tall(X)&brave(X))))&
(~funny(john))&
(?[X]:((~calm(X)|curious(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is happy or brave is tall or not creative and vice versa.
Everyone who is either not patient or funny is tall or generous.
If someone is either not creative or not quiet then someone is both generous and not brave.
If paul is either calm or tall then someone is not happy or old.
Everyone who is either curious or humble is both not calm and not funny and vice versa.
Everyone who is either not kind or not humble is not happy or not patient.
Everyone who is both calm and not calm is creative or not happy and vice versa.
Everyone who is both not creative and brave is both not strong and not quiet.
Everyone who is either not quiet or generous is old.
If someone is either old or generous then someone is either not calm or wise.
Everyone who is both not patient and strong is not humble or curious and vice versa.
If susan is creative or not curious then someone is happy or curious.
Everyone who is not happy is either not old or happy.
Everyone who is not curious or not kind is either not kind or generous and vice versa.
Everyone who is either not funny or not tall is not kind or not quiet.
Everyone who is not patient is either not creative or strong.
Alice is both patient and not brave.
Someone is not old.
Alice is not calm.
Paul is not humble or not generous.
John is either quiet or wise. | John is not calm. | entailment | (![X]:((happy(X)|brave(X))<=>(tall(X)|~creative(X))))&
(![X]:((~patient(X)<~>funny(X))=>(tall(X)|generous(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:((generous(X)&~brave(X)))))&
(((calm(paul)<~>tall(paul)))=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((curious(X)<~>humble(X))<=>(~calm(X)&~funny(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(~happy(X)|~patient(X))))&
(![X]:((calm(X)&~calm(X))<=>(creative(X)|~happy(X))))&
(![X]:((~creative(X)&brave(X))=>(~strong(X)&~quiet(X))))&
(![X]:((~quiet(X)<~>generous(X))=>old(X)))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((~patient(X)&strong(X))<=>(~humble(X)|curious(X))))&
(((creative(susan)|~curious(susan)))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~happy(X)=>(~old(X)<~>happy(X))))&
(![X]:((~curious(X)|~kind(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((~funny(X)<~>~tall(X))=>(~kind(X)|~quiet(X))))&
(![X]:(~patient(X)=>(~creative(X)<~>strong(X))))&
((patient(alice)&~brave(alice)))&
(?[X]:(~old(X)))&
(~calm(alice))&
((~humble(paul)|~generous(paul)))&
((quiet(john)<~>wise(john))) | ~calm(john) | [
"p4",
"p6",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7875960783566261374589635
% SZS output start Proof for 7875960783566261374589635
5. ! [X0] : ((curious(X0) <~> humble(X0)) <=> (~funny(X0) & ~calm(X0))) [input p4]
7. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~happy(X0) | creative(X0))) [input p6]
11. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (curious(X0) | ~humble(X0))) [input p10]
16. ! [X0] : (~patient(X0) => (~creative(X0) <~> strong(X0))) [input p15]
22. calm(john) [input hypothesis]
39. ! [X0] : ((~creative(X0) <~> strong(X0)) | patient(X0)) [ennf transformation 16]
50. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [nnf transformation 5]
51. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [flattening 50]
53. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 7]
54. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | calm(X0) | ~calm(X0))) [flattening 53]
60. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 11]
61. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ~strong(X0) | patient(X0))) [flattening 60]
68. ! [X0] : (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | patient(X0)) [nnf transformation 39]
85. ~humble(X0) | curious(X0) | ~calm(X0) [cnf transformation 51]
93. calm(X0) | ~creative(X0) [cnf transformation 54]
95. ~calm(X0) | ~creative(X0) [cnf transformation 54]
106. ~patient(X0) | humble(X0) [cnf transformation 61]
107. ~curious(X0) | ~patient(X0) [cnf transformation 61]
108. strong(X0) | humble(X0) [cnf transformation 61]
109. ~curious(X0) | strong(X0) [cnf transformation 61]
123. ~strong(X0) | creative(X0) | patient(X0) [cnf transformation 68]
131. calm(john) [cnf transformation 22]
172. ~creative(X0) [subsumption resolution 93,95]
193. ~strong(X0) | patient(X0) [subsumption resolution 123,172]
221. patient(X0) | humble(X0) [resolution 193,108]
222. humble(X0) [subsumption resolution 221,106]
229. ~calm(X0) | curious(X0) [resolution 85,222]
230. curious(john) [resolution 229,131]
233. strong(john) [resolution 230,109]
234. ~patient(john) [resolution 230,107]
405. patient(john) [resolution 233,193]
407. $false [subsumption resolution 405,234]
% SZS output end Proof for 7875960783566261374589635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not brave is not wise or patient and vice versa.
Everyone who is tall is both rich and creative.
Everyone who is not rich or creative is both curious and not calm.
If paul is brave then someone is happy or not generous.
If someone is not tall then someone is either quiet or not calm.
If paul is either curious or not brave then lucy is either rich or not quiet and vice versa.
If someone is not calm or generous then paul is both not strong and funny.
If mary is either not brave or not curious then paul is not brave or not rich.
Everyone who is happy or not rich is both not humble and generous and vice versa.
Everyone who is not happy is both not wise and patient and vice versa.
If fred is happy then alice is both quiet and kind.
Everyone who is either not patient or not curious is either rich or not curious and vice versa.
If fred is old then someone is not patient.
If someone is not rich or not generous then john is either not happy or happy.
If fred is not old or tall then fred is both wise and not quiet.
Everyone who is both patient and kind is either brave or strong and vice versa.
Someone is humble or kind.
Mary is either not rich or not quiet.
Someone is not creative.
Someone is curious or not rich.
Someone is calm.
John is either humble or curious.
Paul is both not strong and not rich.
John is either happy or not generous. | Fred is humble. | contradiction | (![X]:((~humble(X)|~brave(X))<=>(~wise(X)|patient(X))))&
(![X]:(tall(X)=>(rich(X)&creative(X))))&
(![X]:((~rich(X)|creative(X))=>(curious(X)&~calm(X))))&
((brave(paul))=>(?[X]:((happy(X)|~generous(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(((curious(paul)<~>~brave(paul)))<=>((rich(lucy)<~>~quiet(lucy))))&
((?[X]:((~calm(X)|generous(X))))=>((~strong(paul)&funny(paul))))&
(((~brave(mary)<~>~curious(mary)))=>((~brave(paul)|~rich(paul))))&
(![X]:((happy(X)|~rich(X))<=>(~humble(X)&generous(X))))&
(![X]:(~happy(X)<=>(~wise(X)&patient(X))))&
((happy(fred))=>((quiet(alice)&kind(alice))))&
(![X]:((~patient(X)<~>~curious(X))<=>(rich(X)<~>~curious(X))))&
((old(fred))=>(?[X]:(~patient(X))))&
((?[X]:((~rich(X)|~generous(X))))=>((~happy(john)<~>happy(john))))&
(((~old(fred)|tall(fred)))=>((wise(fred)&~quiet(fred))))&
(![X]:((patient(X)&kind(X))<=>(brave(X)<~>strong(X))))&
(?[X]:((humble(X)|kind(X))))&
((~rich(mary)<~>~quiet(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:(calm(X)))&
((humble(john)<~>curious(john)))&
((~strong(paul)&~rich(paul)))&
((happy(john)<~>~generous(john))) | humble(fred) | [
"p2",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 19143516303203230976535
% SZS output start Proof for 19143516303203230976535
3. ! [X0] : ((creative(X0) | ~rich(X0)) => (~calm(X0) & curious(X0))) [input p2]
9. ! [X0] : ((~rich(X0) | happy(X0)) <=> (generous(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (~happy(X0) <=> (patient(X0) & ~wise(X0))) [input p9]
12. ! [X0] : ((~patient(X0) <~> ~curious(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p11]
25. humble(fred) [input hypothesis]
29. ! [X0] : ((~calm(X0) & curious(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 3]
49. ! [X0] : (((~rich(X0) | happy(X0)) | (~generous(X0) | humble(X0))) & ((generous(X0) & ~humble(X0)) | (rich(X0) & ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : ((~rich(X0) | happy(X0) | ~generous(X0) | humble(X0)) & ((generous(X0) & ~humble(X0)) | (rich(X0) & ~happy(X0)))) [flattening 49]
51. ! [X0] : ((~happy(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | happy(X0))) [nnf transformation 10]
52. ! [X0] : ((~happy(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | happy(X0))) [flattening 51]
53. ! [X0] : ((((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0))))) [nnf transformation 12]
76. curious(X0) | rich(X0) [cnf transformation 29]
95. ~happy(X0) | ~humble(X0) [cnf transformation 50]
96. ~humble(X0) | rich(X0) [cnf transformation 50]
101. happy(X0) | patient(X0) [cnf transformation 52]
108. curious(X0) | ~rich(X0) | ~patient(X0) | curious(X0) [cnf transformation 53]
109. ~curious(X0) | ~patient(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 53]
140. humble(fred) [cnf transformation 25]
142. curious(X0) | ~rich(X0) | ~patient(X0) [duplicate literal removal 108]
143. ~curious(X0) | ~patient(X0) | ~rich(X0) [duplicate literal removal 109]
218. 16 <=> happy(fred) [avatar definition]
219. happy(fred) <- (16) [avatar component clause 218]
220. ~happy(fred) <- (~16) [avatar component clause 218]
231. ~patient(X0) | curious(X0) [subsumption resolution 142,76]
305. rich(fred) [resolution 96,140]
309. patient(fred) <- (~16) [resolution 101,220]
312. curious(fred) <- (~16) [resolution 309,231]
348. ~patient(fred) | ~rich(fred) <- (~16) [resolution 143,312]
351. ~rich(fred) <- (~16) [subsumption resolution 348,309]
352. $false <- (~16) [subsumption resolution 351,305]
353. 16 [avatar contradiction clause 352]
377. ~humble(fred) <- (16) [resolution 219,95]
380. $false <- (16) [subsumption resolution 377,140]
381. ~16 [avatar contradiction clause 380]
382. $false [avatar sat refutation 353,381]
% SZS output end Proof for 19143516303203230976535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is kind or brave.
Everyone who is both not strong and brave is either not creative or not patient and vice versa.
If someone is creative or curious then alice is both quiet and not strong and vice versa.
Everyone who is both not calm and happy is old or not patient and vice versa.
Everyone who is either humble or not quiet is patient and vice versa.
If someone is tall then someone is not rich or rich and vice versa.
If mary is either old or curious then someone is kind or not old.
If someone is both not strong and creative then mary is not patient or not humble.
Everyone who is funny is both creative and strong.
If someone is both not quiet and not generous then someone is not generous and vice versa.
Everyone who is both happy and quiet is wise or funny and vice versa.
If susan is calm then alice is not tall or tall and vice versa.
Everyone who is both tall and rich is brave.
Everyone who is either kind or not funny is either not wise or wise.
Everyone who is not brave is humble and vice versa.
If fred is humble or curious then paul is either not patient or not old.
Someone is both not kind and not curious.
Someone is not quiet.
Someone is wise or happy.
Someone is both tall and brave.
Someone is calm.
Susan is both not curious and not kind.
Lucy is either happy or not quiet. | Lucy is patient. | neutral | (![X]:((calm(X)|~old(X))=>(kind(X)|brave(X))))&
(![X]:((~strong(X)&brave(X))<=>(~creative(X)<~>~patient(X))))&
((?[X]:((creative(X)|curious(X))))<=>((quiet(alice)&~strong(alice))))&
(![X]:((~calm(X)&happy(X))<=>(old(X)|~patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|rich(X)))))&
(((old(mary)<~>curious(mary)))=>(?[X]:((kind(X)|~old(X)))))&
((?[X]:((~strong(X)&creative(X))))=>((~patient(mary)|~humble(mary))))&
(![X]:(funny(X)=>(creative(X)&strong(X))))&
((?[X]:((~quiet(X)&~generous(X))))<=>(?[X]:(~generous(X))))&
(![X]:((happy(X)&quiet(X))<=>(wise(X)|funny(X))))&
((calm(susan))<=>((~tall(alice)|tall(alice))))&
(![X]:((tall(X)&rich(X))=>brave(X)))&
(![X]:((kind(X)<~>~funny(X))=>(~wise(X)<~>wise(X))))&
(![X]:(~brave(X)<=>humble(X)))&
(((humble(fred)|curious(fred)))=>((~patient(paul)<~>~old(paul))))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:((tall(X)&brave(X))))&
(?[X]:(calm(X)))&
((~curious(susan)&~kind(susan)))&
((happy(lucy)<~>~quiet(lucy))) | patient(lucy) | [] | null | 0 |
Everyone who is not patient is either creative or not curious.
Everyone who is both not happy and not patient is either quiet or happy.
Everyone who is not creative is both not generous and not wise and vice versa.
If someone is both not curious and funny then lucy is not quiet and vice versa.
Everyone who is curious is generous or not quiet and vice versa.
If someone is both not brave and kind then someone is not brave or not quiet and vice versa.
If john is quiet then mary is either kind or not quiet.
Everyone who is brave or not funny is not funny or not kind.
Everyone who is not humble or not kind is either not quiet or not kind.
Everyone who is not kind is not funny or rich.
If someone is either not wise or old then someone is calm.
Everyone who is not strong is not creative or not patient.
Everyone who is humble is either not happy or not humble.
Everyone who is either rich or wise is not rich or quiet.
If mary is not humble then someone is creative or not strong and vice versa.
Everyone who is both strong and old is not strong or kind.
Mary is either old or not generous.
Lucy is either not humble or not wise.
Paul is either not curious or strong.
Paul is both happy and not generous.
Someone is funny or not generous.
Someone is not rich or not funny.
Someone is funny or not kind.
Someone is either not wise or rich. | Mary is not kind. | neutral | (![X]:(~patient(X)=>(creative(X)<~>~curious(X))))&
(![X]:((~happy(X)&~patient(X))=>(quiet(X)<~>happy(X))))&
(![X]:(~creative(X)<=>(~generous(X)&~wise(X))))&
((?[X]:((~curious(X)&funny(X))))<=>(~quiet(lucy)))&
(![X]:(curious(X)<=>(generous(X)|~quiet(X))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
((quiet(john))=>((kind(mary)<~>~quiet(mary))))&
(![X]:((brave(X)|~funny(X))=>(~funny(X)|~kind(X))))&
(![X]:((~humble(X)|~kind(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(~kind(X)=>(~funny(X)|rich(X))))&
((?[X]:((~wise(X)<~>old(X))))=>(?[X]:(calm(X))))&
(![X]:(~strong(X)=>(~creative(X)|~patient(X))))&
(![X]:(humble(X)=>(~happy(X)<~>~humble(X))))&
(![X]:((rich(X)<~>wise(X))=>(~rich(X)|quiet(X))))&
((~humble(mary))<=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((strong(X)&old(X))=>(~strong(X)|kind(X))))&
((old(mary)<~>~generous(mary)))&
((~humble(lucy)<~>~wise(lucy)))&
((~curious(paul)<~>strong(paul)))&
((happy(paul)&~generous(paul)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:((funny(X)|~kind(X))))&
(?[X]:((~wise(X)<~>rich(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is not humble is humble or happy.
Everyone who is both creative and not kind is both strong and not calm and vice versa.
Everyone who is strong is patient or calm.
If susan is both not old and not rich then mary is both not wise and not happy and vice versa.
If someone is not happy or not humble then someone is calm or not humble and vice versa.
Everyone who is not patient or calm is both wise and creative.
Everyone who is not calm is both generous and not rich.
Everyone who is both not brave and calm is both brave and not humble.
If someone is both brave and not kind then john is wise or not tall.
Everyone who is kind is rich and vice versa.
If fred is either not happy or tall then someone is both funny and happy.
Everyone who is calm or not old is calm and vice versa.
If susan is both not brave and patient then john is not wise.
Everyone who is either wise or not calm is not tall or not old.
If someone is either patient or not strong then someone is either not funny or not brave and vice versa.
Everyone who is calm or not rich is kind or not generous.
Someone is kind or not humble.
Someone is brave or not calm.
Lucy is curious.
Someone is both not tall and happy.
Fred is calm.
Someone is either happy or not patient.
Susan is either not kind or quiet. | John is kind. | entailment | (![X]:(~humble(X)=>(humble(X)|happy(X))))&
(![X]:((creative(X)&~kind(X))<=>(strong(X)&~calm(X))))&
(![X]:(strong(X)=>(patient(X)|calm(X))))&
(((~old(susan)&~rich(susan)))<=>((~wise(mary)&~happy(mary))))&
((?[X]:((~happy(X)|~humble(X))))<=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((~patient(X)|calm(X))=>(wise(X)&creative(X))))&
(![X]:(~calm(X)=>(generous(X)&~rich(X))))&
(![X]:((~brave(X)&calm(X))=>(brave(X)&~humble(X))))&
((?[X]:((brave(X)&~kind(X))))=>((wise(john)|~tall(john))))&
(![X]:(kind(X)<=>rich(X)))&
(((~happy(fred)<~>tall(fred)))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:((calm(X)|~old(X))<=>calm(X)))&
(((~brave(susan)&patient(susan)))=>(~wise(john)))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|~old(X))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((calm(X)|~rich(X))=>(kind(X)|~generous(X))))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:((brave(X)|~calm(X))))&
(curious(lucy))&
(?[X]:((~tall(X)&happy(X))))&
(calm(fred))&
(?[X]:((happy(X)<~>~patient(X))))&
((~kind(susan)<~>quiet(susan))) | kind(john) | [
"p1",
"p5",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6920771965652146994595
% SZS output start Proof for 6920771965652146994595
2. ! [X0] : ((~kind(X0) & creative(X0)) <=> (~calm(X0) & strong(X0))) [input p1]
6. ! [X0] : ((calm(X0) | ~patient(X0)) => (creative(X0) & wise(X0))) [input p5]
7. ! [X0] : (~calm(X0) => (~rich(X0) & generous(X0))) [input p6]
10. ! [X0] : (kind(X0) <=> rich(X0)) [input p9]
16. ! [X0] : ((~rich(X0) | calm(X0)) => (~generous(X0) | kind(X0))) [input p15]
24. ~kind(john) [input hypothesis]
32. ! [X0] : ((creative(X0) & wise(X0)) | (~calm(X0) & patient(X0))) [ennf transformation 6]
33. ! [X0] : ((~rich(X0) & generous(X0)) | calm(X0)) [ennf transformation 7]
43. ! [X0] : ((~generous(X0) | kind(X0)) | (rich(X0) & ~calm(X0))) [ennf transformation 16]
44. ! [X0] : (~generous(X0) | kind(X0) | (rich(X0) & ~calm(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) & creative(X0)) | (calm(X0) | ~strong(X0))) & ((~calm(X0) & strong(X0)) | (kind(X0) | ~creative(X0)))) [nnf transformation 2]
46. ! [X0] : (((~kind(X0) & creative(X0)) | calm(X0) | ~strong(X0)) & ((~calm(X0) & strong(X0)) | kind(X0) | ~creative(X0))) [flattening 45]
54. ! [X0] : ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0))) [nnf transformation 10]
78. ~calm(X0) | kind(X0) | ~creative(X0) [cnf transformation 46]
93. ~calm(X0) | creative(X0) [cnf transformation 32]
94. generous(X0) | calm(X0) [cnf transformation 33]
95. ~rich(X0) | calm(X0) [cnf transformation 33]
99. ~kind(X0) | rich(X0) [cnf transformation 54]
120. ~generous(X0) | kind(X0) | rich(X0) [cnf transformation 44]
130. ~kind(john) [cnf transformation 24]
261. ~generous(X0) | rich(X0) [subsumption resolution 120,99]
308. rich(X0) | calm(X0) [resolution 261,94]
309. calm(X0) [subsumption resolution 308,95]
339. ~creative(X0) | kind(X0) [resolution 309,78]
341. creative(X2) [resolution 309,93]
366. kind(X0) [resolution 339,341]
369. $false [resolution 366,130]
% SZS output end Proof for 6920771965652146994595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then lucy is not old and vice versa.
If someone is both wise and kind then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Everyone who is either quiet or patient is quiet or tall.
Everyone who is curious or happy is not happy or quiet.
If lucy is not patient or wise then someone is both brave and generous and vice versa.
If paul is either generous or not creative then someone is not curious and vice versa.
Mary is not funny.
Alice is not quiet.
Fred is happy or curious.
Someone is both creative and generous.
Susan is rich.
Someone is either patient or old.
Someone is strong or not generous.
Mary is not happy or strong. | Fred is curious. | entailment | ((?[X]:(kind(X)))<=>(~old(lucy)))&
((?[X]:((wise(X)&kind(X))))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
(![X]:((quiet(X)<~>patient(X))=>(quiet(X)|tall(X))))&
(![X]:((curious(X)|happy(X))=>(~happy(X)|quiet(X))))&
(((~patient(lucy)|wise(lucy)))<=>(?[X]:((brave(X)&generous(X)))))&
(((generous(paul)<~>~creative(paul)))<=>(?[X]:(~curious(X))))&
(~funny(mary))&
(~quiet(alice))&
((happy(fred)|curious(fred)))&
(?[X]:((creative(X)&generous(X))))&
(rich(susan))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:((strong(X)|~generous(X))))&
((~happy(mary)|strong(mary))) | curious(fred) | [
"p8",
"p10",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1483762946380957315318181
% SZS output start Proof for 1483762946380957315318181
9. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (wise(X0) | ~creative(X0))) [input p8]
11. ! [X0] : ((kind(X0) | quiet(X0)) => generous(X0)) [input p10]
12. ! [X0] : ((~calm(X0) | ~wise(X0)) => ~quiet(X0)) [input p11]
14. ! [X0] : ((happy(X0) | curious(X0)) => (quiet(X0) | ~happy(X0))) [input p13]
19. curious(fred) | happy(fred) [input p18]
25. ~curious(fred) [input hypothesis]
36. ! [X0] : (generous(X0) | (~kind(X0) & ~quiet(X0))) [ennf transformation 11]
37. ! [X0] : (~quiet(X0) | (calm(X0) & wise(X0))) [ennf transformation 12]
40. ! [X0] : ((quiet(X0) | ~happy(X0)) | (~happy(X0) & ~curious(X0))) [ennf transformation 14]
41. ! [X0] : (quiet(X0) | ~happy(X0) | (~happy(X0) & ~curious(X0))) [flattening 40]
63. ! [X0] : (((~generous(X0) | ~quiet(X0)) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | (generous(X0) & quiet(X0)))) [nnf transformation 9]
64. ! [X0] : ((~generous(X0) | ~quiet(X0) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | (generous(X0) & quiet(X0)))) [flattening 63]
115. ~quiet(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 64]
120. ~quiet(X0) | generous(X0) [cnf transformation 36]
122. ~quiet(X0) | wise(X0) [cnf transformation 37]
127. quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 41]
139. curious(fred) | happy(fred) [cnf transformation 19]
147. ~curious(fred) [cnf transformation 25]
148. ~happy(X0) | quiet(X0) [duplicate literal removal 127]
291. 31 <=> happy(fred) [avatar definition]
293. happy(fred) <- (31) [avatar component clause 291]
295. 32 <=> curious(fred) [avatar definition]
298. 31 | 32 [avatar split clause 139,295,291]
327. ~32 [avatar split clause 147,295]
329. quiet(fred) <- (31) [resolution 148,293]
331. wise(fred) <- (31) [resolution 329,122]
332. generous(fred) <- (31) [resolution 329,120]
362. ~generous(fred) | ~wise(fred) <- (31) [resolution 115,329]
363. ~wise(fred) <- (31) [subsumption resolution 362,332]
364. $false <- (31) [subsumption resolution 363,331]
365. ~31 [avatar contradiction clause 364]
366. $false [avatar sat refutation 298,327,365]
% SZS output end Proof for 1483762946380957315318181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or rich is both not wise and not calm.
If someone is not happy or not generous then paul is either humble or not curious and vice versa.
If alice is either funny or not patient then lucy is rich and vice versa.
Everyone who is either creative or not curious is kind.
If someone is either creative or calm then john is both patient and not funny and vice versa.
Everyone who is not calm or not humble is not happy or generous and vice versa.
Everyone who is both generous and not brave is not patient or not quiet and vice versa.
Everyone who is not quiet is not curious or patient and vice versa.
Everyone who is both not generous and brave is either not funny or not calm.
If john is either not calm or strong then john is tall and vice versa.
Everyone who is both wise and not rich is either not creative or rich.
Everyone who is not wise is funny and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Mary is both not happy and funny.
Lucy is either not tall or patient.
Paul is either not humble or curious.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet. | Mary is creative. | contradiction | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>((humble(paul)<~>~curious(paul))))&
(((funny(alice)<~>~patient(alice)))<=>(rich(lucy)))&
(![X]:((creative(X)<~>~curious(X))=>kind(X)))&
((?[X]:((creative(X)<~>calm(X))))<=>((patient(john)&~funny(john))))&
(![X]:((~calm(X)|~humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((generous(X)&~brave(X))<=>(~patient(X)|~quiet(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|patient(X))))&
(![X]:((~generous(X)&brave(X))=>(~funny(X)<~>~calm(X))))&
(((~calm(john)<~>strong(john)))<=>(tall(john)))&
(![X]:((wise(X)&~rich(X))=>(~creative(X)<~>rich(X))))&
(![X]:(~wise(X)<=>funny(X)))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
((~happy(mary)&funny(mary)))&
((~tall(lucy)<~>patient(lucy)))&
((~humble(paul)<~>curious(paul)))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john))) | creative(mary) | [
"p0",
"p4",
"p7",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 299744695652001325923463
% SZS output start Proof for 299744695652001325923463
1. ! [X0] : ((rich(X0) | generous(X0)) => (~calm(X0) & ~wise(X0))) [input p0]
5. ? [X0] : (creative(X0) <~> calm(X0)) <=> (~funny(john) & patient(john)) [input p4]
8. ! [X0] : (~quiet(X0) <=> (patient(X0) | ~curious(X0))) [input p7]
21. rich(mary) [input p20]
23. quiet(john) & tall(john) [input p22]
24. creative(mary) [input hypothesis]
28. ! [X0] : ((~calm(X0) & ~wise(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 1]
39. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | (funny(john) | ~patient(john))) & ((~funny(john) & patient(john)) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 5]
40. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [flattening 39]
41. (? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1)))) [rectify 40]
42. ? [X0] : ((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) => ((~calm(sK1) | ~creative(sK1)) & (calm(sK1) | creative(sK1))) [choice axiom]
43. (((~calm(sK1) | ~creative(sK1)) & (calm(sK1) | creative(sK1))) | funny(john) | ~patient(john)) & ((~funny(john) & patient(john)) | ! [X1] : ((creative(X1) | ~calm(X1)) & (calm(X1) | ~creative(X1)))) [skolemisation 41,42]
48. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | quiet(X0))) [nnf transformation 8]
49. ! [X0] : ((~quiet(X0) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | quiet(X0))) [flattening 48]
76. ~calm(X0) | ~rich(X0) [cnf transformation 28]
87. patient(john) | calm(X1) | ~creative(X1) [cnf transformation 43]
104. ~quiet(X0) | ~patient(X0) [cnf transformation 49]
132. rich(mary) [cnf transformation 21]
136. quiet(john) [cnf transformation 23]
137. creative(mary) [cnf transformation 24]
184. 10 <=> patient(john) [avatar definition]
206. 15 <=> ! [X1] : (calm(X1) | ~creative(X1)) [avatar definition]
207. ~creative(X1) | calm(X1) <- (15) [avatar component clause 206]
210. 15 | 10 [avatar split clause 87,184,206]
311. ~patient(john) [resolution 104,136]
317. ~10 [avatar split clause 311,184]
341. calm(mary) <- (15) [resolution 207,137]
351. ~rich(mary) <- (15) [resolution 341,76]
353. $false <- (15) [subsumption resolution 351,132]
354. ~15 [avatar contradiction clause 353]
357. $false [avatar sat refutation 210,317,354]
% SZS output end Proof for 299744695652001325923463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich then someone is both quiet and generous and vice versa. If fred is either tall or not wise then alice is both old and not generous and vice versa. Everyone who is not patient is not creative. Everyone who is either not quiet or quiet is generous and vice versa. If someone is either not wise or happy then fred is not curious or old. If someone is not happy then someone is strong. Everyone who is either quiet or not happy is brave or not tall. Everyone who is not happy is either curious or not rich. If someone is both quiet and humble then susan is kind or funny. Everyone who is either funny or strong is either not old or not wise and vice versa. If fred is not curious then paul is both not wise and not quiet. If someone is both not kind and creative then someone is either not calm or not curious and vice versa. If alice is brave or not generous then alice is either not funny or not strong. If fred is both happy and strong then someone is both calm and not generous and vice versa. If someone is tall then susan is either brave or not tall. If mary is not calm or creative then someone is happy or quiet and vice versa. Paul is not creative or not calm. Someone is kind. Someone is not wise or not creative. Alice is both calm and kind. Paul is both not patient and wise. Someone is tall. Someone is not calm. Lucy is quiet or happy. | Fred is not curious. | contradiction | ((~rich(lucy))<=>(?[X]:((quiet(X)&generous(X)))))&
(((tall(fred)<~>~wise(fred)))<=>((old(alice)&~generous(alice))))&
(![X]:(~patient(X)=>~creative(X)))&
(![X]:((~quiet(X)<~>quiet(X))<=>generous(X)))&
((?[X]:((~wise(X)<~>happy(X))))=>((~curious(fred)|old(fred))))&
((?[X]:(~happy(X)))=>(?[X]:(strong(X))))&
(![X]:((quiet(X)<~>~happy(X))=>(brave(X)|~tall(X))))&
(![X]:(~happy(X)=>(curious(X)<~>~rich(X))))&
((?[X]:((quiet(X)&humble(X))))=>((kind(susan)|funny(susan))))&
(![X]:((funny(X)<~>strong(X))<=>(~old(X)<~>~wise(X))))&
((~curious(fred))=>((~wise(paul)&~quiet(paul))))&
((?[X]:((~kind(X)&creative(X))))<=>(?[X]:((~calm(X)<~>~curious(X)))))&
(((brave(alice)|~generous(alice)))=>((~funny(alice)<~>~strong(alice))))&
(((happy(fred)&strong(fred)))<=>(?[X]:((calm(X)&~generous(X)))))&
((?[X]:(tall(X)))=>((brave(susan)<~>~tall(susan))))&
(((~calm(mary)|creative(mary)))<=>(?[X]:((happy(X)|quiet(X)))))&
((~creative(paul)|~calm(paul)))&
(?[X]:(kind(X)))&
(?[X]:((~wise(X)|~creative(X))))&
((calm(alice)&kind(alice)))&
((~patient(paul)&wise(paul)))&
(?[X]:(tall(X)))&
(?[X]:(~calm(X)))&
((quiet(lucy)|happy(lucy))) | ~curious(fred) | [
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9066198627986126663945854
% SZS output start Proof for 9066198627986126663945854
11. ~curious(fred) => (~quiet(paul) & ~wise(paul)) [input p10]
21. wise(paul) & ~patient(paul) [input p20]
25. ~curious(fred) [input hypothesis]
36. (~quiet(paul) & ~wise(paul)) | curious(fred) [ennf transformation 11]
107. ~wise(paul) | curious(fred) [cnf transformation 36]
135. wise(paul) [cnf transformation 21]
139. ~curious(fred) [cnf transformation 25]
187. 10 <=> curious(fred) [avatar definition]
213. 16 <=> wise(paul) [avatar definition]
216. 10 | ~16 [avatar split clause 107,213,187]
334. 16 [avatar split clause 135,213]
344. ~10 [avatar split clause 139,187]
345. $false [avatar sat refutation 216,334,344]
% SZS output end Proof for 9066198627986126663945854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or curious is both brave and not patient.
Everyone who is not happy is either not strong or not funny and vice versa.
Everyone who is kind or not rich is not strong and vice versa.
Everyone who is both curious and not curious is quiet or not funny.
If someone is not patient then mary is not patient and vice versa.
If john is strong then mary is generous or creative and vice versa.
If lucy is tall then paul is both not patient and brave and vice versa.
If someone is not creative then paul is both not curious and wise.
Everyone who is wise or not curious is both not rich and generous and vice versa.
If someone is either not kind or not patient then someone is either not funny or not calm and vice versa.
If fred is not tall or not humble then someone is creative or quiet and vice versa.
If lucy is not kind or happy then someone is both funny and brave and vice versa.
Everyone who is not happy is kind and vice versa.
If john is calm or not tall then someone is either not curious or not creative and vice versa.
Everyone who is either not wise or wise is not tall and vice versa.
If john is both not curious and not humble then john is tall or humble and vice versa.
Someone is either not patient or not curious.
Someone is not calm.
Lucy is kind.
Fred is either not kind or not quiet.
Lucy is either creative or patient.
Someone is humble.
Fred is both generous and quiet. | Mary is rich. | contradiction | (![X]:((quiet(X)|curious(X))=>(brave(X)&~patient(X))))&
(![X]:(~happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((kind(X)|~rich(X))<=>~strong(X)))&
(![X]:((curious(X)&~curious(X))=>(quiet(X)|~funny(X))))&
((?[X]:(~patient(X)))<=>(~patient(mary)))&
((strong(john))<=>((generous(mary)|creative(mary))))&
((tall(lucy))<=>((~patient(paul)&brave(paul))))&
((?[X]:(~creative(X)))=>((~curious(paul)&wise(paul))))&
(![X]:((wise(X)|~curious(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)<~>~patient(X))))<=>(?[X]:((~funny(X)<~>~calm(X)))))&
(((~tall(fred)|~humble(fred)))<=>(?[X]:((creative(X)|quiet(X)))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(~happy(X)<=>kind(X)))&
(((calm(john)|~tall(john)))<=>(?[X]:((~curious(X)<~>~creative(X)))))&
(![X]:((~wise(X)<~>wise(X))<=>~tall(X)))&
(((~curious(john)&~humble(john)))<=>((tall(john)|humble(john))))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
((~kind(fred)<~>~quiet(fred)))&
((creative(lucy)<~>patient(lucy)))&
(?[X]:(humble(X)))&
((generous(fred)&quiet(fred))) | rich(mary) | [
"p0",
"p1",
"p2",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7890532133196430497818876
% SZS output start Proof for 7890532133196430497818876
1. ! [X0] : ((curious(X0) | quiet(X0)) => (~patient(X0) & brave(X0))) [input p0]
2. ! [X0] : (~happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | kind(X0)) <=> ~strong(X0)) [input p2]
9. ! [X0] : ((~curious(X0) | wise(X0)) <=> (generous(X0) & ~rich(X0))) [input p8]
12. (happy(lucy) | ~kind(lucy)) <=> ? [X0] : (brave(X0) & funny(X0)) [input p11]
13. ! [X0] : (~happy(X0) <=> kind(X0)) [input p12]
19. kind(lucy) [input p18]
24. rich(mary) [input hypothesis]
26. ! [X0] : ((~patient(X0) & brave(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 1]
30. ! [X0] : ((~happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | happy(X0))) [nnf transformation 2]
31. ! [X0] : (((~rich(X0) | kind(X0)) | strong(X0)) & (~strong(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 3]
32. ! [X0] : ((~rich(X0) | kind(X0) | strong(X0)) & (~strong(X0) | (rich(X0) & ~kind(X0)))) [flattening 31]
41. ! [X0] : (((~curious(X0) | wise(X0)) | (~generous(X0) | rich(X0))) & ((generous(X0) & ~rich(X0)) | (curious(X0) & ~wise(X0)))) [nnf transformation 9]
42. ! [X0] : ((~curious(X0) | wise(X0) | ~generous(X0) | rich(X0)) & ((generous(X0) & ~rich(X0)) | (curious(X0) & ~wise(X0)))) [flattening 41]
53. ((happy(lucy) | ~kind(lucy)) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [nnf transformation 12]
54. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X0] : (brave(X0) & funny(X0)) | (~happy(lucy) & kind(lucy))) [flattening 53]
55. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & (? [X1] : (brave(X1) & funny(X1)) | (~happy(lucy) & kind(lucy))) [rectify 54]
56. ? [X1] : (brave(X1) & funny(X1)) => (brave(sK4) & funny(sK4)) [choice axiom]
57. (happy(lucy) | ~kind(lucy) | ! [X0] : (~brave(X0) | ~funny(X0))) & ((brave(sK4) & funny(sK4)) | (~happy(lucy) & kind(lucy))) [skolemisation 55,56]
58. ! [X0] : ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))) [nnf transformation 13]
77. ~curious(X0) | brave(X0) [cnf transformation 26]
81. funny(X0) | strong(X0) | happy(X0) [cnf transformation 30]
83. ~strong(X0) | ~happy(X0) | funny(X0) [cnf transformation 30]
84. ~kind(X0) | ~strong(X0) [cnf transformation 32]
86. ~rich(X0) | kind(X0) | strong(X0) [cnf transformation 32]
99. ~rich(X0) | curious(X0) [cnf transformation 42]
119. happy(lucy) | ~kind(lucy) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. kind(X0) | happy(X0) [cnf transformation 58]
121. ~kind(X0) | ~happy(X0) [cnf transformation 58]
140. kind(lucy) [cnf transformation 19]
148. rich(mary) [cnf transformation 24]
272. 27 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition]
273. ~funny(X0) | ~brave(X0) <- (27) [avatar component clause 272]
275. 28 <=> kind(lucy) [avatar definition]
276. kind(lucy) <- (28) [avatar component clause 275]
279. 29 <=> happy(lucy) [avatar definition]
282. 27 | ~28 | 29 [avatar split clause 119,279,275,272]
335. 28 [avatar split clause 140,275]
376. curious(mary) [resolution 99,148]
379. brave(mary) [resolution 376,77]
381. ~strong(X0) | happy(X0) [resolution 120,84]
383. ~happy(lucy) <- (28) [resolution 121,276]
400. strong(X1) | happy(X1) | ~brave(X1) <- (27) [resolution 81,273]
402. ~brave(X1) | happy(X1) <- (27) [subsumption resolution 400,381]
415. kind(mary) | strong(mary) [resolution 86,148]
417. 46 <=> strong(mary) [avatar definition]
419. strong(mary) <- (46) [avatar component clause 417]
421. 47 <=> kind(mary) [avatar definition]
423. kind(mary) <- (47) [avatar component clause 421]
424. 46 | 47 [avatar split clause 415,421,417]
425. ~happy(mary) | funny(mary) <- (46) [resolution 419,83]
428. 48 <=> funny(mary) [avatar definition]
430. funny(mary) <- (48) [avatar component clause 428]
432. 49 <=> happy(mary) [avatar definition]
434. ~happy(mary) <- (~49) [avatar component clause 432]
435. 48 | ~49 | ~46 [avatar split clause 425,417,432,428]
455. ~happy(mary) <- (47) [resolution 423,121]
457. happy(mary) <- (27) [resolution 402,379]
463. $false <- (27, ~49) [subsumption resolution 457,434]
464. ~27 | 49 [avatar contradiction clause 463]
467. ~29 | ~28 [avatar split clause 383,275,279]
468. ~49 | ~47 [avatar split clause 455,421,432]
495. ~brave(mary) <- (27, 48) [resolution 430,273]
498. $false <- (27, 48) [subsumption resolution 495,379]
499. ~27 | ~48 [avatar contradiction clause 498]
500. $false [avatar sat refutation 282,335,424,435,464,467,468,499]
% SZS output end Proof for 7890532133196430497818876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not generous is both quiet and brave and vice versa. If someone is either not generous or calm then mary is generous. Everyone who is not humble or not kind is funny. If fred is either tall or not patient then alice is both not happy and strong. If someone is both not generous and not old then someone is either not brave or brave and vice versa. If someone is both patient and tall then someone is both creative and kind and vice versa. Everyone who is not humble or funny is both not humble and not funny. Everyone who is either tall or not creative is not rich and vice versa. If mary is either not curious or curious then someone is either not funny or funny. If alice is quiet then paul is not patient or not rich. Everyone who is quiet or not quiet is either funny or quiet. If someone is either old or humble then fred is calm or rich and vice versa. Everyone who is quiet is creative and vice versa. Everyone who is both not curious and funny is either tall or not curious and vice versa. If alice is old or happy then john is humble and vice versa. Everyone who is quiet or creative is brave or kind. Susan is not strong. Paul is either wise or rich. Someone is both wise and tall. Lucy is creative or not tall. John is both wise and not curious. | Fred is tall. | neutral | (![X]:((calm(X)|~generous(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~generous(X)<~>calm(X))))=>(generous(mary)))&
(![X]:((~humble(X)|~kind(X))=>funny(X)))&
(((tall(fred)<~>~patient(fred)))=>((~happy(alice)&strong(alice))))&
((?[X]:((~generous(X)&~old(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
((?[X]:((patient(X)&tall(X))))<=>(?[X]:((creative(X)&kind(X)))))&
(![X]:((~humble(X)|funny(X))=>(~humble(X)&~funny(X))))&
(![X]:((tall(X)<~>~creative(X))<=>~rich(X)))&
(((~curious(mary)<~>curious(mary)))=>(?[X]:((~funny(X)<~>funny(X)))))&
((quiet(alice))=>((~patient(paul)|~rich(paul))))&
(![X]:((quiet(X)|~quiet(X))=>(funny(X)<~>quiet(X))))&
((?[X]:((old(X)<~>humble(X))))<=>((calm(fred)|rich(fred))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:((~curious(X)&funny(X))<=>(tall(X)<~>~curious(X))))&
(((old(alice)|happy(alice)))<=>(humble(john)))&
(![X]:((quiet(X)|creative(X))=>(brave(X)|kind(X))))&
(~strong(susan))&
((wise(paul)<~>rich(paul)))&
(?[X]:((wise(X)&tall(X))))&
((creative(lucy)|~tall(lucy)))&
((wise(john)&~curious(john))) | tall(fred) | [] | null | 0 |
If lucy is either not old or wise then susan is generous. Everyone who is either not creative or not curious is calm and vice versa. If someone is tall or not old then paul is both not happy and not patient. Everyone who is both funny and curious is either not happy or creative and vice versa. Everyone who is both kind and not happy is either rich or not creative and vice versa. If someone is not happy or not creative then alice is not old or creative. Everyone who is either generous or not brave is not humble and vice versa. If someone is either not creative or kind then fred is both not happy and strong. If someone is strong or creative then someone is humble and vice versa. Everyone who is both generous and wise is both creative and not old and vice versa. Everyone who is not happy is not generous and vice versa. Everyone who is not quiet is happy and vice versa. Everyone who is either not curious or creative is either humble or quiet and vice versa. Everyone who is both not curious and curious is not happy or funny. If paul is brave or rich then susan is both not generous and not funny and vice versa. Everyone who is either brave or not tall is both calm and curious. Someone is not curious or funny. Someone is either not wise or rich. Someone is curious or happy. Someone is brave or not happy. Someone is not happy. Someone is not wise or brave. Someone is not brave or tall. Someone is not kind. | Paul is not happy. | entailment | (((~old(lucy)<~>wise(lucy)))=>(generous(susan)))&
(![X]:((~creative(X)<~>~curious(X))<=>calm(X)))&
((?[X]:((tall(X)|~old(X))))=>((~happy(paul)&~patient(paul))))&
(![X]:((funny(X)&curious(X))<=>(~happy(X)<~>creative(X))))&
(![X]:((kind(X)&~happy(X))<=>(rich(X)<~>~creative(X))))&
((?[X]:((~happy(X)|~creative(X))))=>((~old(alice)|creative(alice))))&
(![X]:((generous(X)<~>~brave(X))<=>~humble(X)))&
((?[X]:((~creative(X)<~>kind(X))))=>((~happy(fred)&strong(fred))))&
((?[X]:((strong(X)|creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((generous(X)&wise(X))<=>(creative(X)&~old(X))))&
(![X]:(~happy(X)<=>~generous(X)))&
(![X]:(~quiet(X)<=>happy(X)))&
(![X]:((~curious(X)<~>creative(X))<=>(humble(X)<~>quiet(X))))&
(![X]:((~curious(X)&curious(X))=>(~happy(X)|funny(X))))&
(((brave(paul)|rich(paul)))<=>((~generous(susan)&~funny(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(calm(X)&curious(X))))&
(?[X]:((~curious(X)|funny(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:(~kind(X))) | ~happy(paul) | [
"p1",
"p2",
"p3",
"p6",
"p10",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3597430228050107919515635
% SZS output start Proof for 3597430228050107919515635
2. ! [X0] : ((~creative(X0) <~> ~curious(X0)) <=> calm(X0)) [input p1]
3. ? [X0] : (~old(X0) | tall(X0)) => (~patient(paul) & ~happy(paul)) [input p2]
4. ! [X0] : ((curious(X0) & funny(X0)) <=> (~happy(X0) <~> creative(X0))) [input p3]
7. ! [X0] : ((generous(X0) <~> ~brave(X0)) <=> ~humble(X0)) [input p6]
11. ! [X0] : (~happy(X0) <=> ~generous(X0)) [input p10]
12. ! [X0] : (~quiet(X0) <=> happy(X0)) [input p11]
13. ! [X0] : ((~curious(X0) <~> creative(X0)) <=> (humble(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (curious(X0) & calm(X0))) [input p15]
23. ? [X0] : (tall(X0) | ~brave(X0)) [input p22]
25. happy(paul) [input hypothesis]
27. ! [X0] : (calm(X0) => (~creative(X0) <~> ~curious(X0))) [unused predicate definition removal 2]
28. ? [X0] : (~old(X0) | tall(X0)) => ~happy(paul) [pure predicate removal 3]
30. ! [X0] : ((~creative(X0) <~> ~curious(X0)) | ~calm(X0)) [ennf transformation 27]
31. ~happy(paul) | ! [X0] : (old(X0) & ~tall(X0)) [ennf transformation 28]
37. ! [X0] : ((curious(X0) & calm(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 16]
39. ! [X0] : (((curious(X0) | creative(X0)) & (~curious(X0) | ~creative(X0))) | ~calm(X0)) [nnf transformation 30]
40. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | (~curious(X0) | ~funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & funny(X0)) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) & (((~creative(X0) | happy(X0)) & (creative(X0) | ~happy(X0))) | ~curious(X0) | ~funny(X0))) [flattening 40]
44. ! [X0] : ((((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | humble(X0)) & (~humble(X0) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))))) [nnf transformation 7]
53. ! [X0] : ((~happy(X0) | generous(X0)) & (~generous(X0) | happy(X0))) [nnf transformation 11]
54. ! [X0] : ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0))) [nnf transformation 12]
55. ! [X0] : ((((~creative(X0) | curious(X0)) & (creative(X0) | ~curious(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) & (((~quiet(X0) | ~humble(X0)) & (quiet(X0) | humble(X0))) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0))))) [nnf transformation 13]
58. ! [X0] : ((curious(X0) & calm(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 37]
72. ? [X0] : (tall(X0) | ~brave(X0)) => (tall(sK8) | ~brave(sK8)) [choice axiom]
73. tall(sK8) | ~brave(sK8) [skolemisation 23,72]
78. ~calm(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 39]
80. ~happy(paul) | ~tall(X0) [cnf transformation 31]
86. happy(X0) | creative(X0) | curious(X0) [cnf transformation 41]
97. ~humble(X0) | generous(X0) | brave(X0) [cnf transformation 44]
99. ~generous(X0) | brave(X0) | humble(X0) [cnf transformation 44]
111. ~generous(X0) | happy(X0) [cnf transformation 53]
112. ~happy(X0) | generous(X0) [cnf transformation 53]
113. quiet(X0) | happy(X0) [cnf transformation 54]
114. ~quiet(X0) | ~happy(X0) [cnf transformation 54]
119. ~humble(X0) | ~curious(X0) | quiet(X0) | creative(X0) [cnf transformation 55]
120. ~quiet(X0) | ~curious(X0) | humble(X0) | creative(X0) [cnf transformation 55]
130. brave(X0) | calm(X0) | tall(X0) [cnf transformation 58]
132. brave(X0) | curious(X0) | tall(X0) [cnf transformation 58]
140. tall(sK8) | ~brave(sK8) [cnf transformation 73]
142. happy(paul) [cnf transformation 25]
161. 5 <=> happy(paul) [avatar definition]
166. 6 <=> ! [X0] : ~tall(X0) [avatar definition]
167. ~tall(X0) <- (6) [avatar component clause 166]
168. 6 | ~5 [avatar split clause 80,161,166]
291. 34 <=> brave(sK8) [avatar definition]
293. ~brave(sK8) <- (~34) [avatar component clause 291]
295. 35 <=> tall(sK8) [avatar definition]
297. tall(sK8) <- (35) [avatar component clause 295]
298. ~34 | 35 [avatar split clause 140,295,291]
299. 5 [avatar split clause 142,161]
606. ~curious(X1) | humble(X1) | creative(X1) | happy(X1) [resolution 120,113]
608. humble(X1) | creative(X1) | happy(X1) [subsumption resolution 606,86]
685. $false <- (6, 35) [subsumption resolution 297,167]
686. ~6 | ~35 [avatar contradiction clause 685]
719. curious(sK8) | tall(sK8) <- (~34) [resolution 293,132]
720. calm(sK8) | tall(sK8) <- (~34) [resolution 293,130]
721. curious(sK8) <- (6, ~34) [subsumption resolution 719,167]
722. calm(sK8) <- (6, ~34) [subsumption resolution 720,167]
766. 74 <=> creative(sK8) [avatar definition]
768. ~creative(sK8) <- (~74) [avatar component clause 766]
770. 75 <=> quiet(sK8) [avatar definition]
772. quiet(sK8) <- (75) [avatar component clause 770]
774. 76 <=> humble(sK8) [avatar definition]
776. humble(sK8) <- (76) [avatar component clause 774]
779. ~creative(sK8) | ~curious(sK8) <- (6, ~34) [resolution 722,78]
846. creative(X2) | happy(X2) | generous(X2) | brave(X2) [resolution 608,97]
850. brave(X2) | generous(X2) | creative(X2) [subsumption resolution 846,112]
1207. generous(sK8) | creative(sK8) <- (~34) [resolution 850,293]
1209. generous(sK8) <- (~34, ~74) [subsumption resolution 1207,768]
1261. brave(sK8) | humble(sK8) <- (~34, ~74) [resolution 1209,99]
1264. humble(sK8) <- (~34, ~74) [subsumption resolution 1261,293]
1265. 76 | 34 | 74 [avatar split clause 1264,766,291,774]
1267. 98 <=> generous(sK8) [avatar definition]
1269. generous(sK8) <- (98) [avatar component clause 1267]
1271. 74 | 98 | 34 [avatar split clause 1207,291,1267,766]
1272. ~creative(sK8) <- (6, ~34) [subsumption resolution 779,721]
1273. ~74 | ~6 | 34 [avatar split clause 1272,291,166,766]
1278. ~happy(sK8) <- (75) [resolution 772,114]
1281. ~curious(sK8) | quiet(sK8) | creative(sK8) <- (76) [resolution 776,119]
1287. happy(sK8) <- (98) [resolution 1269,111]
1289. $false <- (75, 98) [subsumption resolution 1287,1278]
1290. ~75 | ~98 [avatar contradiction clause 1289]
1291. quiet(sK8) | creative(sK8) <- (6, ~34, 76) [subsumption resolution 1281,721]
1292. quiet(sK8) <- (6, ~34, ~74, 76) [subsumption resolution 1291,768]
1293. 75 | ~6 | 34 | 74 | ~76 [avatar split clause 1292,774,766,291,166,770]
1294. $false [avatar sat refutation 168,298,299,686,1265,1271,1273,1290,1293]
% SZS output end Proof for 3597430228050107919515635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or brave is either funny or tall and vice versa.
Everyone who is both patient and strong is both not brave and rich.
If lucy is quiet then someone is not strong and vice versa.
Everyone who is funny or kind is not patient or not quiet and vice versa.
If someone is either humble or rich then someone is not curious or rich.
Everyone who is not calm is not tall and vice versa.
If someone is either patient or generous then someone is both wise and humble and vice versa.
If alice is not wise then someone is curious or not kind and vice versa.
Everyone who is either quiet or not humble is not patient.
Everyone who is both not old and happy is either curious or not happy and vice versa.
Everyone who is both wise and not old is happy.
If someone is not wise or strong then john is either tall or not wise and vice versa.
Everyone who is not curious is brave or curious and vice versa.
If fred is either funny or calm then someone is either not calm or brave and vice versa.
Everyone who is not strong is not curious or not quiet.
Someone is both not strong and not kind.
Paul is not wise or old.
Someone is quiet.
Susan is not happy or not strong.
Someone is both not humble and not quiet.
Lucy is not curious or not happy.
Someone is rich.
Fred is kind or patient. | John is not generous. | neutral | (![X]:((patient(X)<~>brave(X))<=>(funny(X)<~>tall(X))))&
(![X]:((patient(X)&strong(X))=>(~brave(X)&rich(X))))&
((quiet(lucy))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|kind(X))<=>(~patient(X)|~quiet(X))))&
((?[X]:((humble(X)<~>rich(X))))=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:(~calm(X)<=>~tall(X)))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((wise(X)&humble(X)))))&
((~wise(alice))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((quiet(X)<~>~humble(X))=>~patient(X)))&
(![X]:((~old(X)&happy(X))<=>(curious(X)<~>~happy(X))))&
(![X]:((wise(X)&~old(X))=>happy(X)))&
((?[X]:((~wise(X)|strong(X))))<=>((tall(john)<~>~wise(john))))&
(![X]:(~curious(X)<=>(brave(X)|curious(X))))&
(((funny(fred)<~>calm(fred)))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:(~strong(X)=>(~curious(X)|~quiet(X))))&
(?[X]:((~strong(X)&~kind(X))))&
((~wise(paul)|old(paul)))&
(?[X]:(quiet(X)))&
((~happy(susan)|~strong(susan)))&
(?[X]:((~humble(X)&~quiet(X))))&
((~curious(lucy)|~happy(lucy)))&
(?[X]:(rich(X)))&
((kind(fred)|patient(fred))) | ~generous(john) | [] | null | 0 |
Everyone who is either not tall or funny is rich or curious and vice versa.
Everyone who is both not calm and not generous is both not kind and not tall.
If someone is not generous then someone is calm or rich and vice versa.
Everyone who is either not wise or not patient is either not wise or not calm and vice versa.
Everyone who is happy or not strong is not tall or not happy and vice versa.
Everyone who is both not old and not patient is creative or generous.
If john is not patient then someone is kind or not strong.
Everyone who is creative is not curious.
Everyone who is both not brave and not happy is not wise or wise and vice versa.
Everyone who is not happy or not old is not wise or not patient.
Everyone who is either not strong or not humble is creative and vice versa.
Everyone who is not curious is both not tall and not humble and vice versa.
Everyone who is brave or not tall is both not generous and calm and vice versa.
Everyone who is either humble or not tall is either wise or creative.
If alice is either kind or creative then susan is humble and vice versa.
Everyone who is not calm is either patient or not strong and vice versa.
Someone is either not quiet or not happy.
Someone is not calm or not happy.
Someone is happy or not wise.
Fred is generous.
Someone is patient or not humble.
John is either humble or not humble.
Someone is happy or generous.
Someone is either generous or not tall. | Alice is tall. | entailment | (![X]:((~tall(X)<~>funny(X))<=>(rich(X)|curious(X))))&
(![X]:((~calm(X)&~generous(X))=>(~kind(X)&~tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~wise(X)<~>~calm(X))))&
(![X]:((happy(X)|~strong(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~old(X)&~patient(X))=>(creative(X)|generous(X))))&
((~patient(john))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:(creative(X)=>~curious(X)))&
(![X]:((~brave(X)&~happy(X))<=>(~wise(X)|wise(X))))&
(![X]:((~happy(X)|~old(X))=>(~wise(X)|~patient(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>creative(X)))&
(![X]:(~curious(X)<=>(~tall(X)&~humble(X))))&
(![X]:((brave(X)|~tall(X))<=>(~generous(X)&calm(X))))&
(![X]:((humble(X)<~>~tall(X))=>(wise(X)<~>creative(X))))&
(((kind(alice)<~>creative(alice)))<=>(humble(susan)))&
(![X]:(~calm(X)<=>(patient(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:((happy(X)|~wise(X))))&
(generous(fred))&
(?[X]:((patient(X)|~humble(X))))&
((humble(john)<~>~humble(john)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((generous(X)<~>~tall(X)))) | tall(alice) | [
"p3",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3965711501142324810453695
% SZS output start Proof for 3965711501142324810453695
4. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> (~wise(X0) <~> ~calm(X0))) [input p3]
8. ! [X0] : (creative(X0) => ~curious(X0)) [input p7]
9. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (wise(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((~old(X0) | ~happy(X0)) => (~patient(X0) | ~wise(X0))) [input p9]
11. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : (~curious(X0) <=> (~humble(X0) & ~tall(X0))) [input p11]
13. ! [X0] : ((~tall(X0) | brave(X0)) <=> (calm(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (wise(X0) <~> creative(X0))) [input p13]
16. ! [X0] : (~calm(X0) <=> (patient(X0) <~> ~strong(X0))) [input p15]
25. ~tall(alice) [input hypothesis]
27. ! [X0] : (~happy(X0) => (~patient(X0) | ~wise(X0))) [pure predicate removal 10]
32. ! [X0] : (~curious(X0) | ~creative(X0)) [ennf transformation 8]
33. ! [X0] : ((~patient(X0) | ~wise(X0)) | happy(X0)) [ennf transformation 27]
34. ! [X0] : (~patient(X0) | ~wise(X0) | happy(X0)) [flattening 33]
35. ! [X0] : ((wise(X0) <~> creative(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 14]
43. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 4]
48. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & ((wise(X0) | ~wise(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((~happy(X0) & ~brave(X0)) | (~wise(X0) & wise(X0))) & (wise(X0) | ~wise(X0) | happy(X0) | brave(X0))) [flattening 48]
50. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~creative(X0)) & (creative(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 11]
51. ! [X0] : ((~curious(X0) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [nnf transformation 12]
52. ! [X0] : ((~curious(X0) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [flattening 51]
53. ! [X0] : (((~tall(X0) | brave(X0)) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 13]
54. ! [X0] : ((~tall(X0) | brave(X0) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | (tall(X0) & ~brave(X0)))) [flattening 53]
55. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 35]
57. ! [X0] : ((~calm(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | calm(X0))) [nnf transformation 16]
85. ~calm(X0) | ~wise(X0) | ~wise(X0) | patient(X0) [cnf transformation 43]
86. calm(X0) | wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
89. ~patient(X0) | ~wise(X0) | ~wise(X0) | calm(X0) [cnf transformation 43]
90. patient(X0) | wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 43]
97. ~creative(X0) | ~curious(X0) [cnf transformation 32]
101. ~happy(X0) | wise(X0) [cnf transformation 49]
102. ~happy(X0) | ~wise(X0) [cnf transformation 49]
103. ~patient(X0) | ~wise(X0) | happy(X0) [cnf transformation 34]
104. ~humble(X0) | creative(X0) | strong(X0) [cnf transformation 50]
107. ~creative(X0) | strong(X0) | humble(X0) [cnf transformation 50]
109. ~humble(X0) | curious(X0) [cnf transformation 52]
114. calm(X0) | tall(X0) [cnf transformation 54]
117. humble(X0) | wise(X0) | creative(X0) | tall(X0) [cnf transformation 55]
124. ~strong(X0) | patient(X0) | calm(X0) [cnf transformation 57]
126. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57]
139. ~tall(alice) [cnf transformation 25]
142. ~calm(X0) | ~wise(X0) | patient(X0) [duplicate literal removal 85]
143. calm(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 86]
144. ~patient(X0) | ~wise(X0) | calm(X0) [duplicate literal removal 89]
145. ~calm(X0) | wise(X0) | patient(X0) [duplicate literal removal 90]
170. ~patient(X0) | calm(X0) [subsumption resolution 143,144]
171. ~calm(X0) | patient(X0) [subsumption resolution 142,145]
185. ~happy(X0) [subsumption resolution 101,102]
187. ~patient(X0) | ~wise(X0) [subsumption resolution 103,185]
199. 12 <=> creative(alice) [avatar definition]
200. creative(alice) <- (12) [avatar component clause 199]
201. ~creative(alice) <- (~12) [avatar component clause 199]
206. ~strong(X0) | ~patient(X0) [subsumption resolution 126,170]
207. ~strong(X0) | patient(X0) [subsumption resolution 124,171]
208. ~strong(X0) [subsumption resolution 207,206]
228. patient(X0) | tall(X0) [resolution 171,114]
233. ~wise(X0) | tall(X0) [resolution 228,187]
261. wise(X2) | creative(X2) | tall(X2) | creative(X2) | strong(X2) [resolution 117,104]
263. wise(X2) | creative(X2) | tall(X2) | strong(X2) [duplicate literal removal 261]
285. wise(X2) | creative(X2) | tall(X2) [subsumption resolution 263,208]
286. creative(X2) | tall(X2) [subsumption resolution 285,233]
377. tall(alice) <- (~12) [resolution 286,201]
382. $false <- (~12) [subsumption resolution 377,139]
383. 12 [avatar contradiction clause 382]
395. strong(alice) | humble(alice) <- (12) [resolution 200,107]
396. ~curious(alice) <- (12) [resolution 200,97]
397. humble(alice) <- (12) [subsumption resolution 395,208]
425. curious(alice) <- (12) [resolution 397,109]
426. $false <- (12) [subsumption resolution 425,396]
427. ~12 [avatar contradiction clause 426]
428. $false [avatar sat refutation 383,427]
% SZS output end Proof for 3965711501142324810453695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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