premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not kind is either not calm or kind and vice versa. Everyone who is quiet or not happy is not calm. Everyone who is either quiet or not generous is both happy and wise and vice versa. Everyone who is not happy or curious is not creative or generous and vice versa. If fred is not patient then lucy is not wise and vice versa. Everyone who is both happy and funny is either rich or generous and vice versa. If alice is either not kind or not creative then someone is not brave or wise. Everyone who is either not creative or calm is either strong or tall and vice versa. Everyone who is not patient is humble. Everyone who is not quiet is not rich and vice versa. Everyone who is wise or patient is humble and vice versa. Everyone who is not happy is not curious or not calm. If someone is not humble or patient then susan is both not funny and wise and vice versa. Everyone who is both not humble and calm is either tall or not humble. Everyone who is both brave and not wise is both not kind and brave. Someone is old. Alice is either tall or not wise. Lucy is both not quiet and not generous. Someone is quiet. Mary is both not old and generous. Someone is either humble or kind. Lucy is generous or not curious. | Lucy is not strong. | neutral | (![X]:(~kind(X)<=>(~calm(X)<~>kind(X))))&
(![X]:((quiet(X)|~happy(X))=>~calm(X)))&
(![X]:((quiet(X)<~>~generous(X))<=>(happy(X)&wise(X))))&
(![X]:((~happy(X)|curious(X))<=>(~creative(X)|generous(X))))&
((~patient(fred))<=>(~wise(lucy)))&
(![X]:((happy(X)&funny(X))<=>(rich(X)<~>generous(X))))&
(((~kind(alice)<~>~creative(alice)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(strong(X)<~>tall(X))))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:((wise(X)|patient(X))<=>humble(X)))&
(![X]:(~happy(X)=>(~curious(X)|~calm(X))))&
((?[X]:((~humble(X)|patient(X))))<=>((~funny(susan)&wise(susan))))&
(![X]:((~humble(X)&calm(X))=>(tall(X)<~>~humble(X))))&
(![X]:((brave(X)&~wise(X))=>(~kind(X)&brave(X))))&
(?[X]:(old(X)))&
((tall(alice)<~>~wise(alice)))&
((~quiet(lucy)&~generous(lucy)))&
(?[X]:(quiet(X)))&
((~old(mary)&generous(mary)))&
(?[X]:((humble(X)<~>kind(X))))&
((generous(lucy)|~curious(lucy))) | ~strong(lucy) | [] | null | 0 |
If someone is not humble then alice is either not kind or wise and vice versa.
Everyone who is both old and happy is quiet or wise.
If someone is not creative then someone is old and vice versa.
If alice is both kind and not strong then someone is both not strong and rich and vice versa.
If someone is not curious then someone is patient or brave.
If mary is both happy and rich then someone is both not wise and not generous and vice versa.
If someone is not kind or not curious then someone is brave and vice versa.
Everyone who is not strong or not tall is either not curious or kind and vice versa.
If someone is either humble or tall then someone is kind.
If someone is brave then someone is either brave or not funny and vice versa.
Everyone who is brave or old is not wise or not brave and vice versa.
If mary is not creative or not kind then john is humble or funny and vice versa.
If someone is both humble and not humble then susan is both not patient and not curious and vice versa.
Everyone who is not quiet is both not curious and not generous.
Everyone who is not wise is either generous or wise.
Everyone who is either not old or old is not generous.
John is not brave or not tall.
John is not kind or not rich.
Alice is both rich and quiet.
Susan is not creative or not kind.
Someone is both old and rich. | Mary is strong. | neutral | ((?[X]:(~humble(X)))<=>((~kind(alice)<~>wise(alice))))&
(![X]:((old(X)&happy(X))=>(quiet(X)|wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(old(X))))&
(((kind(alice)&~strong(alice)))<=>(?[X]:((~strong(X)&rich(X)))))&
((?[X]:(~curious(X)))=>(?[X]:((patient(X)|brave(X)))))&
(((happy(mary)&rich(mary)))<=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:(brave(X))))&
(![X]:((~strong(X)|~tall(X))<=>(~curious(X)<~>kind(X))))&
((?[X]:((humble(X)<~>tall(X))))=>(?[X]:(kind(X))))&
((?[X]:(brave(X)))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((brave(X)|old(X))<=>(~wise(X)|~brave(X))))&
(((~creative(mary)|~kind(mary)))<=>((humble(john)|funny(john))))&
((?[X]:((humble(X)&~humble(X))))<=>((~patient(susan)&~curious(susan))))&
(![X]:(~quiet(X)=>(~curious(X)&~generous(X))))&
(![X]:(~wise(X)=>(generous(X)<~>wise(X))))&
(![X]:((~old(X)<~>old(X))=>~generous(X)))&
((~brave(john)|~tall(john)))&
((~kind(john)|~rich(john)))&
((rich(alice)&quiet(alice)))&
((~creative(susan)|~kind(susan)))&
(?[X]:((old(X)&rich(X)))) | strong(mary) | [] | null | 0 |
If alice is either not happy or not humble then alice is not wise or humble.
Everyone who is either quiet or not happy is either not rich or not creative and vice versa.
If john is kind then fred is calm.
Everyone who is both not humble and not rich is either not patient or not old.
Everyone who is not wise or not kind is humble.
Everyone who is either not creative or not curious is not generous.
If alice is brave then lucy is both tall and not creative and vice versa.
Everyone who is both creative and not happy is curious or strong.
If fred is either not tall or patient then someone is either wise or not humble.
Everyone who is not happy or not brave is happy and vice versa.
Everyone who is both strong and kind is not creative.
If paul is either not humble or not creative then someone is both not patient and not kind.
If john is not brave or funny then someone is strong or curious and vice versa.
If someone is brave then mary is both old and patient.
Everyone who is not happy is either funny or not brave and vice versa.
Everyone who is both not creative and not curious is not patient or not old.
Someone is not patient or quiet.
Mary is wise or kind.
Lucy is funny.
Paul is tall or generous.
Someone is not strong or generous.
Mary is either old or not generous. | Mary is not brave. | entailment | (((~happy(alice)<~>~humble(alice)))=>((~wise(alice)|humble(alice))))&
(![X]:((quiet(X)<~>~happy(X))<=>(~rich(X)<~>~creative(X))))&
((kind(john))=>(calm(fred)))&
(![X]:((~humble(X)&~rich(X))=>(~patient(X)<~>~old(X))))&
(![X]:((~wise(X)|~kind(X))=>humble(X)))&
(![X]:((~creative(X)<~>~curious(X))=>~generous(X)))&
((brave(alice))<=>((tall(lucy)&~creative(lucy))))&
(![X]:((creative(X)&~happy(X))=>(curious(X)|strong(X))))&
(((~tall(fred)<~>patient(fred)))=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((~happy(X)|~brave(X))<=>happy(X)))&
(![X]:((strong(X)&kind(X))=>~creative(X)))&
(((~humble(paul)<~>~creative(paul)))=>(?[X]:((~patient(X)&~kind(X)))))&
(((~brave(john)|funny(john)))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:(brave(X)))=>((old(mary)&patient(mary))))&
(![X]:(~happy(X)<=>(funny(X)<~>~brave(X))))&
(![X]:((~creative(X)&~curious(X))=>(~patient(X)|~old(X))))&
(?[X]:((~patient(X)|quiet(X))))&
((wise(mary)|kind(mary)))&
(funny(lucy))&
((tall(paul)|generous(paul)))&
(?[X]:((~strong(X)|generous(X))))&
((old(mary)<~>~generous(mary))) | ~brave(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 83739525502537920829944
% SZS output start Proof for 83739525502537920829944
10. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> happy(X0)) [input p9]
23. brave(mary) [input hypothesis]
49. ! [X0] : (((~brave(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [nnf transformation 10]
50. ! [X0] : ((~brave(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [flattening 49]
89. happy(X0) | happy(X0) [cnf transformation 50]
91. ~brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 50]
115. brave(mary) [cnf transformation 23]
116. happy(X0) [duplicate literal removal 89]
117. ~brave(X0) | ~happy(X0) [duplicate literal removal 91]
283. ~happy(mary) [resolution 117,115]
285. $false [subsumption resolution 283,116]
% SZS output end Proof for 83739525502537920829944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or brave is not humble and vice versa. If someone is both curious and not rich then mary is calm and vice versa. If fred is both not old and not calm then paul is either wise or not rich. If someone is humble or not creative then lucy is either curious or calm. If someone is kind or patient then fred is either wise or not kind. If mary is brave then someone is both not quiet and not old. If someone is either not rich or creative then someone is creative. Everyone who is brave is not kind. If john is not wise or not calm then susan is either creative or not creative and vice versa. Everyone who is both not generous and not rich is rich or wise. If john is either not happy or wise then susan is not calm or patient and vice versa. Everyone who is both not curious and strong is both old and not wise. Everyone who is both not tall and brave is not brave or not happy and vice versa. If someone is brave then paul is kind or happy. If susan is not old or patient then someone is either not generous or kind and vice versa. Someone is generous or not kind. Someone is both not funny and not kind. Someone is not tall. Someone is generous. Alice is either not wise or not creative. | Paul is old. | neutral | (![X]:((kind(X)|brave(X))<=>~humble(X)))&
((?[X]:((curious(X)&~rich(X))))<=>(calm(mary)))&
(((~old(fred)&~calm(fred)))=>((wise(paul)<~>~rich(paul))))&
((?[X]:((humble(X)|~creative(X))))=>((curious(lucy)<~>calm(lucy))))&
((?[X]:((kind(X)|patient(X))))=>((wise(fred)<~>~kind(fred))))&
((brave(mary))=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:(creative(X))))&
(![X]:(brave(X)=>~kind(X)))&
(((~wise(john)|~calm(john)))<=>((creative(susan)<~>~creative(susan))))&
(![X]:((~generous(X)&~rich(X))=>(rich(X)|wise(X))))&
(((~happy(john)<~>wise(john)))<=>((~calm(susan)|patient(susan))))&
(![X]:((~curious(X)&strong(X))=>(old(X)&~wise(X))))&
(![X]:((~tall(X)&brave(X))<=>(~brave(X)|~happy(X))))&
((?[X]:(brave(X)))=>((kind(paul)|happy(paul))))&
(((~old(susan)|patient(susan)))<=>(?[X]:((~generous(X)<~>kind(X)))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((~funny(X)&~kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:(generous(X)))&
((~wise(alice)<~>~creative(alice))) | old(paul) | [] | null | 0 |
If lucy is either not tall or tall then alice is not kind and vice versa. Everyone who is happy is humble and vice versa. Everyone who is either not old or not quiet is curious or not creative and vice versa. Everyone who is strong or brave is not patient. Everyone who is either not generous or not funny is both not creative and not patient and vice versa. Everyone who is humble or not strong is both patient and not brave and vice versa. Everyone who is not quiet or not generous is humble or kind and vice versa. If someone is curious then someone is both generous and not rich. If alice is both old and not happy then john is not strong and vice versa. Everyone who is not happy is both brave and not kind and vice versa. If someone is not creative then mary is both not patient and quiet and vice versa. Everyone who is not curious is both not humble and tall. If someone is generous then someone is wise. Everyone who is either patient or creative is both not old and not quiet. If paul is happy then someone is not patient or generous. If someone is not quiet then someone is curious or strong. Someone is wise or patient. Someone is not quiet. Susan is both calm and not patient. Paul is not humble. Fred is either happy or not humble. Mary is kind or not calm. Susan is strong. | Mary is not calm. | entailment | (((~tall(lucy)<~>tall(lucy)))<=>(~kind(alice)))&
(![X]:(happy(X)<=>humble(X)))&
(![X]:((~old(X)<~>~quiet(X))<=>(curious(X)|~creative(X))))&
(![X]:((strong(X)|brave(X))=>~patient(X)))&
(![X]:((~generous(X)<~>~funny(X))<=>(~creative(X)&~patient(X))))&
(![X]:((humble(X)|~strong(X))<=>(patient(X)&~brave(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(humble(X)|kind(X))))&
((?[X]:(curious(X)))=>(?[X]:((generous(X)&~rich(X)))))&
(((old(alice)&~happy(alice)))<=>(~strong(john)))&
(![X]:(~happy(X)<=>(brave(X)&~kind(X))))&
((?[X]:(~creative(X)))<=>((~patient(mary)&quiet(mary))))&
(![X]:(~curious(X)=>(~humble(X)&tall(X))))&
((?[X]:(generous(X)))=>(?[X]:(wise(X))))&
(![X]:((patient(X)<~>creative(X))=>(~old(X)&~quiet(X))))&
((happy(paul))=>(?[X]:((~patient(X)|generous(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((curious(X)|strong(X)))))&
(?[X]:((wise(X)|patient(X))))&
(?[X]:(~quiet(X)))&
((calm(susan)&~patient(susan)))&
(~humble(paul))&
((happy(fred)<~>~humble(fred)))&
((kind(mary)|~calm(mary)))&
(strong(susan)) | ~calm(mary) | [
"p1",
"p5",
"p6",
"p9",
"p10",
"p13",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4555410213166646369912555
% SZS output start Proof for 4555410213166646369912555
2. ! [X0] : (happy(X0) <=> humble(X0)) [input p1]
6. ! [X0] : ((~strong(X0) | humble(X0)) <=> (~brave(X0) & patient(X0))) [input p5]
7. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (kind(X0) | humble(X0))) [input p6]
10. ! [X0] : (~happy(X0) <=> (~kind(X0) & brave(X0))) [input p9]
11. ? [X0] : ~creative(X0) <=> (quiet(mary) & ~patient(mary)) [input p10]
14. ! [X0] : ((patient(X0) <~> creative(X0)) => (~quiet(X0) & ~old(X0))) [input p13]
19. ~patient(susan) & calm(susan) [input p18]
22. ~calm(mary) | kind(mary) [input p21]
24. calm(mary) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & ~old(X0)) | (patient(X0) <=> creative(X0))) [ennf transformation 14]
38. ! [X0] : ((happy(X0) | ~humble(X0)) & (humble(X0) | ~happy(X0))) [nnf transformation 2]
43. ! [X0] : (((~strong(X0) | humble(X0)) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | (strong(X0) & ~humble(X0)))) [nnf transformation 6]
44. ! [X0] : ((~strong(X0) | humble(X0) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | (strong(X0) & ~humble(X0)))) [flattening 43]
45. ! [X0] : (((~generous(X0) | ~quiet(X0)) | (~kind(X0) & ~humble(X0))) & ((kind(X0) | humble(X0)) | (generous(X0) & quiet(X0)))) [nnf transformation 7]
46. ! [X0] : ((~generous(X0) | ~quiet(X0) | (~kind(X0) & ~humble(X0))) & (kind(X0) | humble(X0) | (generous(X0) & quiet(X0)))) [flattening 45]
52. ! [X0] : ((~happy(X0) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | happy(X0))) [nnf transformation 10]
53. ! [X0] : ((~happy(X0) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | happy(X0))) [flattening 52]
54. (? [X0] : ~creative(X0) | (~quiet(mary) | patient(mary))) & ((quiet(mary) & ~patient(mary)) | ! [X0] : creative(X0)) [nnf transformation 11]
55. (? [X0] : ~creative(X0) | ~quiet(mary) | patient(mary)) & ((quiet(mary) & ~patient(mary)) | ! [X0] : creative(X0)) [flattening 54]
56. (? [X0] : ~creative(X0) | ~quiet(mary) | patient(mary)) & ((quiet(mary) & ~patient(mary)) | ! [X1] : creative(X1)) [rectify 55]
57. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
58. (~creative(sK1) | ~quiet(mary) | patient(mary)) & ((quiet(mary) & ~patient(mary)) | ! [X1] : creative(X1)) [skolemisation 56,57]
59. ! [X0] : ((~quiet(X0) & ~old(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0)))) [nnf transformation 34]
72. ~happy(X0) | humble(X0) [cnf transformation 38]
88. ~humble(X0) | patient(X0) [cnf transformation 44]
93. quiet(X0) | humble(X0) | kind(X0) [cnf transformation 46]
102. ~kind(X0) | happy(X0) [cnf transformation 53]
104. ~patient(mary) | creative(X1) [cnf transformation 58]
112. ~creative(X0) | patient(X0) | ~quiet(X0) [cnf transformation 59]
117. ~patient(susan) [cnf transformation 19]
121. ~calm(mary) | kind(mary) [cnf transformation 22]
123. calm(mary) [cnf transformation 24]
160. 8 <=> patient(mary) [avatar definition]
173. 11 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (11) [avatar component clause 173]
176. 11 | ~8 [avatar split clause 104,160,173]
203. 18 <=> kind(mary) [avatar definition]
205. kind(mary) <- (18) [avatar component clause 203]
207. 19 <=> calm(mary) [avatar definition]
210. 18 | ~19 [avatar split clause 121,207,203]
211. 19 [avatar split clause 123,207]
223. happy(mary) <- (18) [resolution 102,205]
224. humble(mary) <- (18) [resolution 223,72]
226. patient(mary) <- (18) [resolution 224,88]
230. 8 | ~18 [avatar split clause 226,203,160]
326. ~quiet(X1) | patient(X1) <- (11) [resolution 112,174]
357. patient(X0) | humble(X0) | kind(X0) <- (11) [resolution 326,93]
359. patient(X0) | kind(X0) <- (11) [subsumption resolution 357,88]
409. kind(susan) <- (11) [resolution 359,117]
430. happy(susan) <- (11) [resolution 409,102]
455. humble(susan) <- (11) [resolution 430,72]
480. patient(susan) <- (11) [resolution 455,88]
482. $false <- (11) [subsumption resolution 480,117]
483. ~11 [avatar contradiction clause 482]
484. $false [avatar sat refutation 176,210,211,230,483]
% SZS output end Proof for 4555410213166646369912555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or happy is not old or not quiet and vice versa.
If lucy is both not funny and not kind then fred is either rich or humble and vice versa.
Everyone who is tall or kind is both not humble and not calm and vice versa.
Everyone who is either not generous or not strong is both not creative and not wise.
Everyone who is not wise is either quiet or not generous and vice versa.
If someone is both kind and not calm then someone is not tall or not wise and vice versa.
If paul is funny or not brave then someone is either not rich or not curious and vice versa.
If someone is not humble then mary is not tall and vice versa.
If someone is patient or not calm then fred is either old or not patient and vice versa.
Everyone who is either happy or wise is both not creative and creative and vice versa.
If someone is both not happy and not creative then someone is either quiet or not patient.
Everyone who is either not creative or humble is both quiet and not calm and vice versa.
If someone is tall or not curious then alice is either old or not rich and vice versa.
Everyone who is both tall and not brave is creative or not humble.
If fred is both not wise and generous then paul is not calm.
Everyone who is either not wise or not tall is either old or kind.
Paul is both old and not quiet.
John is either not old or not curious.
Mary is both not quiet and happy.
John is not strong or not kind.
Susan is both old and strong.
Someone is creative or kind.
Someone is either not quiet or happy. | Paul is wise. | neutral | (![X]:((humble(X)|happy(X))<=>(~old(X)|~quiet(X))))&
(((~funny(lucy)&~kind(lucy)))<=>((rich(fred)<~>humble(fred))))&
(![X]:((tall(X)|kind(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(~creative(X)&~wise(X))))&
(![X]:(~wise(X)<=>(quiet(X)<~>~generous(X))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(((funny(paul)|~brave(paul)))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:(~humble(X)))<=>(~tall(mary)))&
((?[X]:((patient(X)|~calm(X))))<=>((old(fred)<~>~patient(fred))))&
(![X]:((happy(X)<~>wise(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~happy(X)&~creative(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((old(alice)<~>~rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(creative(X)|~humble(X))))&
(((~wise(fred)&generous(fred)))=>(~calm(paul)))&
(![X]:((~wise(X)<~>~tall(X))=>(old(X)<~>kind(X))))&
((old(paul)&~quiet(paul)))&
((~old(john)<~>~curious(john)))&
((~quiet(mary)&happy(mary)))&
((~strong(john)|~kind(john)))&
((old(susan)&strong(susan)))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:((~quiet(X)<~>happy(X)))) | wise(paul) | [] | null | 0 |
Everyone who is not tall is both not brave and tall and vice versa.
If fred is either brave or not patient then someone is brave or not patient.
Everyone who is brave or not kind is not patient and vice versa.
Everyone who is either not generous or not curious is not tall or not strong.
If someone is not brave or patient then someone is not rich or not generous.
If someone is either brave or not kind then paul is both not creative and not funny and vice versa.
If someone is not wise then fred is either kind or not strong.
If fred is either old or not tall then someone is wise or not old and vice versa.
Everyone who is both not brave and humble is either generous or strong and vice versa.
Everyone who is either quiet or rich is not tall.
If someone is either not strong or not wise then someone is either not strong or not patient and vice versa.
If alice is either not patient or wise then someone is not creative or not brave.
Everyone who is either not kind or creative is both happy and not wise and vice versa.
If someone is either not rich or funny then someone is either patient or not curious and vice versa.
Everyone who is calm is not strong.
If john is calm then mary is rich and vice versa.
Susan is both not humble and funny.
Someone is not humble.
John is rich.
Someone is either patient or quiet.
Someone is both curious and not creative.
Someone is rich.
John is either wise or creative. | John is not patient. | entailment | (![X]:(~tall(X)<=>(~brave(X)&tall(X))))&
(((brave(fred)<~>~patient(fred)))=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:((brave(X)|~kind(X))<=>~patient(X)))&
(![X]:((~generous(X)<~>~curious(X))=>(~tall(X)|~strong(X))))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~rich(X)|~generous(X)))))&
((?[X]:((brave(X)<~>~kind(X))))<=>((~creative(paul)&~funny(paul))))&
((?[X]:(~wise(X)))=>((kind(fred)<~>~strong(fred))))&
(((old(fred)<~>~tall(fred)))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~brave(X)&humble(X))<=>(generous(X)<~>strong(X))))&
(![X]:((quiet(X)<~>rich(X))=>~tall(X)))&
((?[X]:((~strong(X)<~>~wise(X))))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
(((~patient(alice)<~>wise(alice)))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((~kind(X)<~>creative(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:(calm(X)=>~strong(X)))&
((calm(john))<=>(rich(mary)))&
((~humble(susan)&funny(susan)))&
(?[X]:(~humble(X)))&
(rich(john))&
(?[X]:((patient(X)<~>quiet(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:(rich(X)))&
((wise(john)<~>creative(john))) | ~patient(john) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7090686130536018680658502
% SZS output start Proof for 7090686130536018680658502
1. ! [X0] : (~tall(X0) <=> (tall(X0) & ~brave(X0))) [input p0]
3. ! [X0] : ((~kind(X0) | brave(X0)) <=> ~patient(X0)) [input p2]
24. patient(john) [input hypothesis]
36. ! [X0] : ((~tall(X0) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | tall(X0))) [nnf transformation 1]
37. ! [X0] : ((~tall(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | tall(X0))) [flattening 36]
41. ! [X0] : (((~kind(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [nnf transformation 3]
42. ! [X0] : ((~kind(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (kind(X0) & ~brave(X0)))) [flattening 41]
87. tall(X0) | tall(X0) [cnf transformation 37]
88. ~tall(X0) | ~tall(X0) | brave(X0) [cnf transformation 37]
91. ~patient(X0) | ~brave(X0) [cnf transformation 42]
158. patient(john) [cnf transformation 24]
159. tall(X0) [duplicate literal removal 87]
160. ~tall(X0) | brave(X0) [duplicate literal removal 88]
194. 8 <=> ! [X1] : brave(X1) [avatar definition]
195. brave(X1) <- (8) [avatar component clause 194]
384. ~brave(john) [resolution 91,158]
388. brave(X0) [resolution 160,159]
389. 8 [avatar split clause 388,194]
391. $false <- (8) [resolution 195,384]
394. ~8 [avatar contradiction clause 391]
396. $false [avatar sat refutation 389,394]
% SZS output end Proof for 7090686130536018680658502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or funny then mary is either not brave or not curious. If alice is either not generous or old then someone is not happy and vice versa. Everyone who is either calm or funny is both curious and not wise. If someone is either not strong or calm then fred is not brave and vice versa. Everyone who is rich or not calm is either not humble or humble and vice versa. Everyone who is not rich or not happy is brave. Everyone who is both curious and brave is calm or not happy. If fred is either not patient or not kind then someone is tall and vice versa. Everyone who is calm is rich and vice versa. If lucy is both brave and not curious then mary is both not brave and patient. Everyone who is creative or not calm is old or rich and vice versa. If someone is not generous or not wise then someone is rich or not kind. If paul is curious or happy then someone is either not rich or not happy and vice versa. If someone is creative then alice is old or calm. Everyone who is either not patient or not old is patient and vice versa. If someone is either not old or calm then fred is both funny and not generous and vice versa. Lucy is not curious or not creative. Someone is both curious and not tall. Susan is calm. Alice is either brave or not kind. John is creative or old. Fred is strong or not humble. Someone is either not rich or not patient. | Lucy is funny. | entailment | ((?[X]:((~calm(X)|funny(X))))=>((~brave(mary)<~>~curious(mary))))&
(((~generous(alice)<~>old(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((calm(X)<~>funny(X))=>(curious(X)&~wise(X))))&
((?[X]:((~strong(X)<~>calm(X))))<=>(~brave(fred)))&
(![X]:((rich(X)|~calm(X))<=>(~humble(X)<~>humble(X))))&
(![X]:((~rich(X)|~happy(X))=>brave(X)))&
(![X]:((curious(X)&brave(X))=>(calm(X)|~happy(X))))&
(((~patient(fred)<~>~kind(fred)))<=>(?[X]:(tall(X))))&
(![X]:(calm(X)<=>rich(X)))&
(((brave(lucy)&~curious(lucy)))=>((~brave(mary)&patient(mary))))&
(![X]:((creative(X)|~calm(X))<=>(old(X)|rich(X))))&
((?[X]:((~generous(X)|~wise(X))))=>(?[X]:((rich(X)|~kind(X)))))&
(((curious(paul)|happy(paul)))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
((?[X]:(creative(X)))=>((old(alice)|calm(alice))))&
(![X]:((~patient(X)<~>~old(X))<=>patient(X)))&
((?[X]:((~old(X)<~>calm(X))))<=>((funny(fred)&~generous(fred))))&
((~curious(lucy)|~creative(lucy)))&
(?[X]:((curious(X)&~tall(X))))&
(calm(susan))&
((brave(alice)<~>~kind(alice)))&
((creative(john)|old(john)))&
((strong(fred)|~humble(fred)))&
(?[X]:((~rich(X)<~>~patient(X)))) | funny(lucy) | [
"p2",
"p4",
"p8",
"p10",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1081848808993445406642011
% SZS output start Proof for 1081848808993445406642011
3. ! [X0] : ((calm(X0) <~> funny(X0)) => (~wise(X0) & curious(X0))) [input p2]
5. ! [X0] : ((~calm(X0) | rich(X0)) <=> (~humble(X0) <~> humble(X0))) [input p4]
9. ! [X0] : (calm(X0) <=> rich(X0)) [input p8]
11. ! [X0] : ((~calm(X0) | creative(X0)) <=> (rich(X0) | old(X0))) [input p10]
15. ! [X0] : ((~patient(X0) <~> ~old(X0)) <=> patient(X0)) [input p14]
17. ~creative(lucy) | ~curious(lucy) [input p16]
24. ~funny(lucy) [input hypothesis]
27. ! [X0] : ((~wise(X0) & curious(X0)) | (calm(X0) <=> funny(X0))) [ennf transformation 3]
41. ! [X0] : ((~wise(X0) & curious(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) [nnf transformation 27]
46. ! [X0] : (((~calm(X0) | rich(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (calm(X0) & ~rich(X0)))) [nnf transformation 5]
47. ! [X0] : ((~calm(X0) | rich(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (calm(X0) & ~rich(X0)))) [flattening 46]
52. ! [X0] : ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0))) [nnf transformation 9]
53. ! [X0] : (((~calm(X0) | creative(X0)) | (~rich(X0) & ~old(X0))) & ((rich(X0) | old(X0)) | (calm(X0) & ~creative(X0)))) [nnf transformation 11]
54. ! [X0] : ((~calm(X0) | creative(X0) | (~rich(X0) & ~old(X0))) & (rich(X0) | old(X0) | (calm(X0) & ~creative(X0)))) [flattening 53]
63. ! [X0] : ((((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0))))) [nnf transformation 15]
83. ~calm(X0) | funny(X0) | curious(X0) [cnf transformation 41]
95. ~calm(X0) | rich(X0) | humble(X0) | humble(X0) [cnf transformation 47]
96. ~calm(X0) | rich(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
105. ~rich(X0) | calm(X0) [cnf transformation 52]
109. rich(X0) | old(X0) | calm(X0) [cnf transformation 54]
111. ~calm(X0) | creative(X0) | ~rich(X0) [cnf transformation 54]
121. patient(X0) | ~old(X0) | patient(X0) [cnf transformation 63]
123. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 63]
131. ~creative(lucy) | ~curious(lucy) [cnf transformation 17]
141. ~funny(lucy) [cnf transformation 24]
142. patient(X0) | ~old(X0) [duplicate literal removal 121]
143. ~patient(X0) | ~old(X0) [duplicate literal removal 123]
144. ~calm(X0) | rich(X0) | humble(X0) [duplicate literal removal 95]
145. ~humble(X0) | rich(X0) | ~calm(X0) [duplicate literal removal 96]
159. 4 <=> ! [X0] : calm(X0) [avatar definition]
160. calm(X0) <- (4) [avatar component clause 159]
205. ~calm(X0) | rich(X0) [subsumption resolution 144,145]
230. 19 <=> curious(lucy) [avatar definition]
231. ~curious(lucy) <- (~19) [avatar component clause 230]
239. ~rich(X0) | creative(X0) [subsumption resolution 111,105]
240. rich(X0) | old(X0) [subsumption resolution 109,205]
293. ~old(X0) [subsumption resolution 142,143]
313. 36 <=> creative(lucy) [avatar definition]
315. ~creative(lucy) <- (~36) [avatar component clause 313]
316. ~19 | ~36 [avatar split clause 131,313,230]
369. old(X0) | creative(X0) [resolution 240,239]
370. old(X1) | calm(X1) [resolution 240,105]
384. calm(X1) [subsumption resolution 370,293]
385. 4 [avatar split clause 384,159]
386. creative(X0) [subsumption resolution 369,293]
398. curious(X0) | funny(X0) <- (4) [resolution 83,160]
403. $false <- (~36) [resolution 386,315]
404. 36 [avatar contradiction clause 403]
412. funny(lucy) <- (4, ~19) [resolution 398,231]
413. $false <- (4, ~19) [subsumption resolution 412,141]
414. ~4 | 19 [avatar contradiction clause 413]
415. $false [avatar sat refutation 316,385,404,414]
% SZS output end Proof for 1081848808993445406642011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or calm then mary is either not curious or not rich and vice versa.
If someone is both brave and strong then lucy is both not quiet and quiet.
If lucy is either tall or not curious then someone is either not calm or rich and vice versa.
If john is not patient then someone is curious or not rich.
Everyone who is patient or not brave is not old or strong.
Everyone who is not calm or not brave is both not funny and funny and vice versa.
Everyone who is either not brave or happy is both not tall and not generous.
Everyone who is either not strong or not calm is patient or not funny.
Everyone who is kind is not calm or not happy.
If lucy is both creative and rich then paul is not calm or not wise.
Everyone who is either strong or generous is both not generous and curious and vice versa.
Everyone who is not rich is kind or curious and vice versa.
Everyone who is generous or happy is both patient and not kind.
If someone is both not curious and not old then mary is creative.
If someone is either not funny or not old then susan is both strong and funny and vice versa.
Lucy is happy or strong.
Paul is old or not kind.
Someone is either creative or quiet.
Someone is not strong.
Someone is both brave and not creative.
Someone is both quiet and not kind.
Fred is rich or not generous.
Someone is both kind and brave. | Mary is generous. | contradiction | ((?[X]:((quiet(X)<~>calm(X))))<=>((~curious(mary)<~>~rich(mary))))&
((?[X]:((brave(X)&strong(X))))=>((~quiet(lucy)&quiet(lucy))))&
(((tall(lucy)<~>~curious(lucy)))<=>(?[X]:((~calm(X)<~>rich(X)))))&
((~patient(john))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((patient(X)|~brave(X))=>(~old(X)|strong(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~funny(X)&funny(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~tall(X)&~generous(X))))&
(![X]:((~strong(X)<~>~calm(X))=>(patient(X)|~funny(X))))&
(![X]:(kind(X)=>(~calm(X)|~happy(X))))&
(((creative(lucy)&rich(lucy)))=>((~calm(paul)|~wise(paul))))&
(![X]:((strong(X)<~>generous(X))<=>(~generous(X)&curious(X))))&
(![X]:(~rich(X)<=>(kind(X)|curious(X))))&
(![X]:((generous(X)|happy(X))=>(patient(X)&~kind(X))))&
((?[X]:((~curious(X)&~old(X))))=>(creative(mary)))&
((?[X]:((~funny(X)<~>~old(X))))<=>((strong(susan)&funny(susan))))&
((happy(lucy)|strong(lucy)))&
((old(paul)|~kind(paul)))&
(?[X]:((creative(X)<~>quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:((brave(X)&~creative(X))))&
(?[X]:((quiet(X)&~kind(X))))&
((rich(fred)|~generous(fred)))&
(?[X]:((kind(X)&brave(X)))) | generous(mary) | [
"p1",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6023515443994158956616915
% SZS output start Proof for 6023515443994158956616915
2. ? [X0] : (strong(X0) & brave(X0)) => (quiet(lucy) & ~quiet(lucy)) [input p1]
6. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (funny(X0) & ~funny(X0))) [input p5]
11. ! [X0] : ((strong(X0) <~> generous(X0)) <=> (curious(X0) & ~generous(X0))) [input p10]
24. generous(mary) [input hypothesis]
26. (quiet(lucy) & ~quiet(lucy)) | ! [X0] : (~strong(X0) | ~brave(X0)) [ennf transformation 2]
47. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 6]
48. ! [X0] : ((~brave(X0) | ~calm(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (brave(X0) & calm(X0)))) [flattening 47]
51. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~curious(X0) | generous(X0))) & ((curious(X0) & ~generous(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 11]
52. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | ~curious(X0) | generous(X0)) & ((curious(X0) & ~generous(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [flattening 51]
79. ~quiet(lucy) | ~strong(X0) | ~brave(X0) [cnf transformation 26]
80. quiet(lucy) | ~strong(X0) | ~brave(X0) [cnf transformation 26]
93. ~funny(X0) | brave(X0) [cnf transformation 48]
95. funny(X0) | brave(X0) [cnf transformation 48]
105. ~generous(X0) | strong(X0) | ~generous(X0) [cnf transformation 52]
136. generous(mary) [cnf transformation 24]
137. ~generous(X0) | strong(X0) [duplicate literal removal 105]
170. 7 <=> ! [X0] : (~strong(X0) | ~brave(X0)) [avatar definition]
171. ~strong(X0) | ~brave(X0) <- (7) [avatar component clause 170]
173. 8 <=> quiet(lucy) [avatar definition]
176. 7 | 8 [avatar split clause 80,173,170]
177. 7 | ~8 [avatar split clause 79,173,170]
221. brave(X0) [subsumption resolution 93,95]
302. ~strong(X0) <- (7) [subsumption resolution 171,221]
315. strong(mary) [resolution 137,136]
316. $false <- (7) [subsumption resolution 315,302]
317. ~7 [avatar contradiction clause 316]
318. $false [avatar sat refutation 176,177,317]
% SZS output end Proof for 6023515443994158956616915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or old is patient or rich and vice versa.
If someone is calm or quiet then someone is humble or tall and vice versa.
Everyone who is not curious or calm is both quiet and happy.
Everyone who is either patient or not happy is not generous or strong and vice versa.
Everyone who is either funny or not humble is rich.
If someone is not strong then someone is not quiet or old and vice versa.
If john is either not strong or rich then someone is old and vice versa.
Everyone who is both generous and not old is both not humble and not generous and vice versa.
If paul is both calm and not calm then someone is not calm.
If someone is either generous or not quiet then susan is creative.
If lucy is not quiet or not generous then someone is not funny or not humble.
If fred is either strong or quiet then someone is either not strong or not patient.
If someone is both funny and not humble then someone is either humble or generous.
If lucy is generous then someone is both calm and funny.
Everyone who is not strong is strong.
If someone is tall or not calm then susan is not patient or old and vice versa.
Someone is not patient or patient.
Someone is both not curious and not old.
Lucy is not patient or creative.
Susan is not rich.
Someone is both not generous and not brave.
Someone is either patient or rich.
Someone is not funny or not strong. | Fred is not happy. | contradiction | (![X]:((humble(X)<~>old(X))<=>(patient(X)|rich(X))))&
((?[X]:((calm(X)|quiet(X))))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~curious(X)|calm(X))=>(quiet(X)&happy(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(~generous(X)|strong(X))))&
(![X]:((funny(X)<~>~humble(X))=>rich(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~quiet(X)|old(X)))))&
(((~strong(john)<~>rich(john)))<=>(?[X]:(old(X))))&
(![X]:((generous(X)&~old(X))<=>(~humble(X)&~generous(X))))&
(((calm(paul)&~calm(paul)))=>(?[X]:(~calm(X))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(creative(susan)))&
(((~quiet(lucy)|~generous(lucy)))=>(?[X]:((~funny(X)|~humble(X)))))&
(((strong(fred)<~>quiet(fred)))=>(?[X]:((~strong(X)<~>~patient(X)))))&
((?[X]:((funny(X)&~humble(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((generous(lucy))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:(~strong(X)=>strong(X)))&
((?[X]:((tall(X)|~calm(X))))<=>((~patient(susan)|old(susan))))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:((~curious(X)&~old(X))))&
((~patient(lucy)|creative(lucy)))&
(~rich(susan))&
(?[X]:((~generous(X)&~brave(X))))&
(?[X]:((patient(X)<~>rich(X))))&
(?[X]:((~funny(X)|~strong(X)))) | ~happy(fred) | [
"p0",
"p2",
"p5",
"p7",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7262968602926735147962713
% SZS output start Proof for 7262968602926735147962713
1. ! [X0] : ((humble(X0) <~> old(X0)) <=> (rich(X0) | patient(X0))) [input p0]
3. ! [X0] : ((calm(X0) | ~curious(X0)) => (happy(X0) & quiet(X0))) [input p2]
6. ? [X0] : ~strong(X0) <=> ? [X0] : (old(X0) | ~quiet(X0)) [input p5]
8. ! [X0] : ((~old(X0) & generous(X0)) <=> (~generous(X0) & ~humble(X0))) [input p7]
15. ! [X0] : (~strong(X0) => strong(X0)) [input p14]
16. ? [X0] : (~calm(X0) | tall(X0)) <=> (old(susan) | ~patient(susan)) [input p15]
20. ~rich(susan) [input p19]
24. ~happy(fred) [input hypothesis]
26. ? [X0] : ~strong(X0) <=> ? [X1] : (old(X1) | ~quiet(X1)) [rectify 6]
31. ! [X0] : ((happy(X0) & quiet(X0)) | (~calm(X0) & curious(X0))) [ennf transformation 3]
39. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 15]
40. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 40]
50. (? [X0] : ~strong(X0) | ! [X1] : (~old(X1) & quiet(X1))) & (? [X1] : (old(X1) | ~quiet(X1)) | ! [X0] : strong(X0)) [nnf transformation 26]
51. (? [X0] : ~strong(X0) | ! [X1] : (~old(X1) & quiet(X1))) & (? [X2] : (old(X2) | ~quiet(X2)) | ! [X3] : strong(X3)) [rectify 50]
52. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
53. ? [X2] : (old(X2) | ~quiet(X2)) => (old(sK3) | ~quiet(sK3)) [choice axiom]
54. (~strong(sK2) | ! [X1] : (~old(X1) & quiet(X1))) & ((old(sK3) | ~quiet(sK3)) | ! [X3] : strong(X3)) [skolemisation 51,53,52]
59. ! [X0] : (((~old(X0) & generous(X0)) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | (old(X0) | ~generous(X0)))) [nnf transformation 8]
60. ! [X0] : (((~old(X0) & generous(X0)) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | old(X0) | ~generous(X0))) [flattening 59]
74. (? [X0] : (~calm(X0) | tall(X0)) | (~old(susan) & patient(susan))) & ((old(susan) | ~patient(susan)) | ! [X0] : (calm(X0) & ~tall(X0))) [nnf transformation 16]
75. (? [X0] : (~calm(X0) | tall(X0)) | (~old(susan) & patient(susan))) & (old(susan) | ~patient(susan) | ! [X0] : (calm(X0) & ~tall(X0))) [flattening 74]
76. (? [X0] : (~calm(X0) | tall(X0)) | (~old(susan) & patient(susan))) & (old(susan) | ~patient(susan) | ! [X1] : (calm(X1) & ~tall(X1))) [rectify 75]
77. ? [X0] : (~calm(X0) | tall(X0)) => (~calm(sK10) | tall(sK10)) [choice axiom]
78. ((~calm(sK10) | tall(sK10)) | (~old(susan) & patient(susan))) & (old(susan) | ~patient(susan) | ! [X1] : (calm(X1) & ~tall(X1))) [skolemisation 76,77]
90. ~humble(X0) | patient(X0) | old(X0) | rich(X0) [cnf transformation 41]
103. ~calm(X0) | happy(X0) [cnf transformation 31]
114. ~strong(sK2) | ~old(X1) [cnf transformation 54]
120. ~generous(X0) | old(X0) | ~generous(X0) [cnf transformation 60]
121. generous(X0) | generous(X0) | humble(X0) [cnf transformation 60]
134. strong(X0) | strong(X0) [cnf transformation 39]
136. old(susan) | ~patient(susan) | calm(X1) [cnf transformation 78]
142. ~rich(susan) [cnf transformation 20]
147. ~happy(fred) [cnf transformation 24]
148. strong(X0) [duplicate literal removal 134]
149. ~generous(X0) | old(X0) [duplicate literal removal 120]
150. generous(X0) | humble(X0) [duplicate literal removal 121]
184. 9 <=> ! [X1] : ~old(X1) [avatar definition]
185. ~old(X1) <- (9) [avatar component clause 184]
187. 10 <=> strong(sK2) [avatar definition]
189. ~strong(sK2) <- (~10) [avatar component clause 187]
190. 9 | ~10 [avatar split clause 114,187,184]
196. 12 <=> ! [X3] : strong(X3) [avatar definition]
197. strong(X3) <- (12) [avatar component clause 196]
283. 12 [avatar split clause 148,196]
285. 31 <=> old(susan) [avatar definition]
286. old(susan) <- (31) [avatar component clause 285]
298. 34 <=> patient(susan) [avatar definition]
303. 35 <=> ! [X1] : calm(X1) [avatar definition]
304. calm(X1) <- (35) [avatar component clause 303]
305. 35 | ~34 | 31 [avatar split clause 136,285,298,303]
326. $false <- (~10, 12) [subsumption resolution 189,197]
327. 10 | ~12 [avatar contradiction clause 326]
336. humble(X0) | old(X0) [resolution 150,149]
340. humble(X0) <- (9) [subsumption resolution 336,185]
395. patient(X0) | old(X0) | rich(X0) <- (9) [resolution 90,340]
406. rich(X0) | patient(X0) <- (9) [subsumption resolution 395,185]
417. patient(susan) <- (9) [resolution 406,142]
420. 34 | ~9 [avatar split clause 417,184,298]
421. $false <- (9, 31) [subsumption resolution 286,185]
422. ~9 | ~31 [avatar contradiction clause 421]
430. happy(X0) <- (35) [resolution 304,103]
435. $false <- (35) [resolution 430,147]
438. ~35 [avatar contradiction clause 435]
439. $false [avatar sat refutation 190,283,305,327,420,422,438]
% SZS output end Proof for 7262968602926735147962713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both kind and calm.
Everyone who is both not rich and rich is old or tall.
Everyone who is not funny is both curious and not patient and vice versa.
Everyone who is not humble or patient is wise and vice versa.
Everyone who is not kind is both wise and patient and vice versa.
Everyone who is not funny is either not brave or brave and vice versa.
If someone is both kind and wise then fred is both not humble and not wise.
If someone is both not rich and generous then someone is happy or old and vice versa.
If someone is not old then alice is not kind or quiet and vice versa.
Everyone who is funny is both humble and creative.
Everyone who is kind is not quiet and vice versa.
Everyone who is either rich or not brave is either wise or not quiet and vice versa.
Someone is kind.
Fred is both happy and not tall.
Alice is not strong or not kind.
Someone is either tall or not brave.
Fred is either not funny or not curious.
Someone is not curious or curious.
John is not creative or rich. | Alice is happy. | neutral | (![X]:(calm(X)=>(kind(X)&calm(X))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(wise(X)<~>~quiet(X))))&
(?[X]:(kind(X)))&
((happy(fred)&~tall(fred)))&
((~strong(alice)|~kind(alice)))&
(?[X]:((tall(X)<~>~brave(X))))&
((~funny(fred)<~>~curious(fred)))&
(?[X]:((~curious(X)|curious(X))))&
((~creative(john)|rich(john))) | happy(alice) | [] | null | 0 |
Everyone who is both not creative and calm is both wise and not calm and vice versa. If mary is both quiet and calm then fred is happy or not rich and vice versa. If john is both strong and humble then someone is calm and vice versa. Everyone who is not kind is not humble or not patient and vice versa. Everyone who is either not strong or not funny is quiet and vice versa. If john is either curious or not patient then someone is patient and vice versa. Everyone who is both not kind and not creative is not patient or humble and vice versa. If someone is both quiet and not patient then someone is not old or not patient. Everyone who is not strong or not old is not strong or brave and vice versa. If someone is not tall then someone is both brave and old and vice versa. If someone is both not curious and strong then someone is both not quiet and not calm. If someone is either patient or not creative then someone is not curious or not tall. Everyone who is not creative or not humble is either not wise or brave and vice versa. Everyone who is either brave or not kind is both not happy and tall and vice versa. Everyone who is both not tall and not creative is either wise or not patient and vice versa. Someone is either not kind or not creative. Paul is not rich. Someone is brave or strong. Someone is both not calm and old. | Paul is not patient. | contradiction | (![X]:((~creative(X)&calm(X))<=>(wise(X)&~calm(X))))&
(((quiet(mary)&calm(mary)))<=>((happy(fred)|~rich(fred))))&
(((strong(john)&humble(john)))<=>(?[X]:(calm(X))))&
(![X]:(~kind(X)<=>(~humble(X)|~patient(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>quiet(X)))&
(((curious(john)<~>~patient(john)))<=>(?[X]:(patient(X))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)|humble(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~strong(X)|~old(X))<=>(~strong(X)|brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((~quiet(X)&~calm(X)))))&
((?[X]:((patient(X)<~>~creative(X))))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((~creative(X)|~humble(X))<=>(~wise(X)<~>brave(X))))&
(![X]:((brave(X)<~>~kind(X))<=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~creative(X))<=>(wise(X)<~>~patient(X))))&
(?[X]:((~kind(X)<~>~creative(X))))&
(~rich(paul))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((~calm(X)&old(X)))) | ~patient(paul) | [
"p0",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8960388991078148228429895
% SZS output start Proof for 8960388991078148228429895
1. ! [X0] : ((calm(X0) & ~creative(X0)) <=> (~calm(X0) & wise(X0))) [input p0]
7. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (humble(X0) | ~patient(X0))) [input p6]
10. ? [X0] : ~tall(X0) <=> ? [X0] : (old(X0) & brave(X0)) [input p9]
13. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> (~wise(X0) <~> brave(X0))) [input p12]
15. ! [X0] : ((~creative(X0) & ~tall(X0)) <=> (wise(X0) <~> ~patient(X0))) [input p14]
20. ~patient(paul) [input hypothesis]
22. ? [X0] : ~tall(X0) <=> ? [X1] : (old(X1) & brave(X1)) [rectify 10]
28. ! [X0] : (((calm(X0) & ~creative(X0)) | (calm(X0) | ~wise(X0))) & ((~calm(X0) & wise(X0)) | (~calm(X0) | creative(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & ~creative(X0)) | calm(X0) | ~wise(X0)) & ((~calm(X0) & wise(X0)) | ~calm(X0) | creative(X0))) [flattening 28]
44. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (creative(X0) | kind(X0)))) [nnf transformation 7]
45. ! [X0] : (((~creative(X0) & ~kind(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | creative(X0) | kind(X0))) [flattening 44]
51. (? [X0] : ~tall(X0) | ! [X1] : (~old(X1) | ~brave(X1))) & (? [X1] : (old(X1) & brave(X1)) | ! [X0] : tall(X0)) [nnf transformation 22]
52. (? [X0] : ~tall(X0) | ! [X1] : (~old(X1) | ~brave(X1))) & (? [X2] : (old(X2) & brave(X2)) | ! [X3] : tall(X3)) [rectify 51]
53. ? [X0] : ~tall(X0) => ~tall(sK3) [choice axiom]
54. ? [X2] : (old(X2) & brave(X2)) => (old(sK4) & brave(sK4)) [choice axiom]
55. (~tall(sK3) | ! [X1] : (~old(X1) | ~brave(X1))) & ((old(sK4) & brave(sK4)) | ! [X3] : tall(X3)) [skolemisation 52,54,53]
63. ! [X0] : (((~humble(X0) | ~creative(X0)) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | (humble(X0) & creative(X0)))) [nnf transformation 13]
64. ! [X0] : ((~humble(X0) | ~creative(X0) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0)))) & (((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | (humble(X0) & creative(X0)))) [flattening 63]
67. ! [X0] : (((~creative(X0) & ~tall(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | (creative(X0) | tall(X0)))) [nnf transformation 15]
68. ! [X0] : (((~creative(X0) & ~tall(X0)) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) & (((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | creative(X0) | tall(X0))) [flattening 67]
77. ~calm(X0) | ~calm(X0) | creative(X0) [cnf transformation 29]
79. calm(X0) | calm(X0) | ~wise(X0) [cnf transformation 29]
102. ~creative(X0) | patient(X0) [cnf transformation 45]
103. ~humble(X0) | ~creative(X0) [cnf transformation 45]
109. brave(sK4) | tall(X3) [cnf transformation 55]
118. ~brave(X0) | wise(X0) | creative(X0) [cnf transformation 64]
119. ~brave(X0) | wise(X0) | humble(X0) [cnf transformation 64]
131. ~tall(X0) | wise(X0) | patient(X0) [cnf transformation 68]
132. ~creative(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 68]
140. ~patient(paul) [cnf transformation 20]
141. ~calm(X0) | creative(X0) [duplicate literal removal 77]
142. ~wise(X0) | calm(X0) [duplicate literal removal 79]
224. 18 <=> ! [X3] : tall(X3) [avatar definition]
225. tall(X3) <- (18) [avatar component clause 224]
232. 20 <=> brave(sK4) [avatar definition]
234. brave(sK4) <- (20) [avatar component clause 232]
235. 18 | 20 [avatar split clause 109,232,224]
270. ~wise(X0) | ~creative(X0) [subsumption resolution 132,102]
354. wise(sK4) | creative(sK4) <- (20) [resolution 118,234]
358. 36 <=> creative(sK4) [avatar definition]
362. 37 <=> wise(sK4) [avatar definition]
364. wise(sK4) <- (37) [avatar component clause 362]
365. 36 | 37 | ~20 [avatar split clause 354,232,362,358]
377. wise(sK4) | humble(sK4) <- (20) [resolution 119,234]
381. 40 <=> humble(sK4) [avatar definition]
383. humble(sK4) <- (40) [avatar component clause 381]
384. 40 | 37 | ~20 [avatar split clause 377,232,362,381]
413. patient(X1) | wise(X1) <- (18) [resolution 131,225]
422. ~creative(sK4) <- (40) [resolution 383,103]
425. ~36 | ~40 [avatar split clause 422,381,358]
443. ~creative(sK4) <- (37) [resolution 364,270]
444. calm(sK4) <- (37) [resolution 364,142]
505. wise(paul) <- (18) [resolution 413,140]
533. creative(sK4) <- (37) [resolution 444,141]
536. 36 | ~37 [avatar split clause 533,362,358]
537. ~36 | ~37 [avatar split clause 443,362,358]
570. ~creative(paul) <- (18) [resolution 505,270]
571. calm(paul) <- (18) [resolution 505,142]
582. 54 <=> creative(paul) [avatar definition]
583. ~creative(paul) <- (~54) [avatar component clause 582]
586. ~54 | ~18 [avatar split clause 570,224,582]
675. creative(paul) <- (18) [resolution 571,141]
677. $false <- (18, ~54) [subsumption resolution 675,583]
678. ~18 | 54 [avatar contradiction clause 677]
679. $false [avatar sat refutation 235,365,384,425,536,537,586,678]
% SZS output end Proof for 8960388991078148228429895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong then alice is not rich or not curious.
If paul is not tall or not old then someone is both not wise and tall and vice versa.
If fred is either not wise or not happy then someone is either funny or not quiet.
Everyone who is both strong and funny is not tall or happy and vice versa.
Everyone who is either not funny or old is both not calm and brave.
Everyone who is both not happy and not kind is either patient or tall and vice versa.
Everyone who is either not rich or quiet is either curious or calm.
If fred is both brave and happy then fred is not humble.
Everyone who is funny or wise is curious.
Everyone who is both not patient and not old is not kind and vice versa.
If someone is either rich or not old then someone is wise or humble and vice versa.
Everyone who is funny or creative is patient.
Everyone who is both not brave and curious is both curious and creative and vice versa.
Everyone who is both creative and not curious is not kind or wise.
If paul is kind then someone is both not rich and not strong and vice versa.
Everyone who is creative or not generous is not funny and vice versa.
Fred is not old or not funny.
Lucy is wise.
Paul is not wise or strong.
John is either curious or not humble.
Someone is both old and not quiet.
Someone is calm or quiet.
Someone is both creative and not strong. | Lucy is tall. | entailment | ((strong(john))=>((~rich(alice)|~curious(alice))))&
(((~tall(paul)|~old(paul)))<=>(?[X]:((~wise(X)&tall(X)))))&
(((~wise(fred)<~>~happy(fred)))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)|happy(X))))&
(![X]:((~funny(X)<~>old(X))=>(~calm(X)&brave(X))))&
(![X]:((~happy(X)&~kind(X))<=>(patient(X)<~>tall(X))))&
(![X]:((~rich(X)<~>quiet(X))=>(curious(X)<~>calm(X))))&
(((brave(fred)&happy(fred)))=>(~humble(fred)))&
(![X]:((funny(X)|wise(X))=>curious(X)))&
(![X]:((~patient(X)&~old(X))<=>~kind(X)))&
((?[X]:((rich(X)<~>~old(X))))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((funny(X)|creative(X))=>patient(X)))&
(![X]:((~brave(X)&curious(X))<=>(curious(X)&creative(X))))&
(![X]:((creative(X)&~curious(X))=>(~kind(X)|wise(X))))&
((kind(paul))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((creative(X)|~generous(X))<=>~funny(X)))&
((~old(fred)|~funny(fred)))&
(wise(lucy))&
((~wise(paul)|strong(paul)))&
((curious(john)<~>~humble(john)))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((calm(X)|quiet(X))))&
(?[X]:((creative(X)&~strong(X)))) | tall(lucy) | [
"p3",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 368045615897788798724383
% SZS output start Proof for 368045615897788798724383
4. ! [X0] : ((funny(X0) & strong(X0)) <=> (happy(X0) | ~tall(X0))) [input p3]
6. ! [X0] : ((~kind(X0) & ~happy(X0)) <=> (patient(X0) <~> tall(X0))) [input p5]
10. ! [X0] : ((~old(X0) & ~patient(X0)) <=> ~kind(X0)) [input p9]
12. ! [X0] : ((creative(X0) | funny(X0)) => patient(X0)) [input p11]
24. ~tall(lucy) [input hypothesis]
34. ! [X0] : (patient(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 12]
45. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0)))) [nnf transformation 4]
46. ! [X0] : (((funny(X0) & strong(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0))) [flattening 45]
48. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (kind(X0) | happy(X0)))) [nnf transformation 6]
49. ! [X0] : (((~kind(X0) & ~happy(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | kind(X0) | happy(X0))) [flattening 48]
51. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | (old(X0) | patient(X0)))) [nnf transformation 10]
52. ! [X0] : (((~old(X0) & ~patient(X0)) | kind(X0)) & (~kind(X0) | old(X0) | patient(X0))) [flattening 51]
86. funny(X0) | tall(X0) [cnf transformation 46]
96. ~patient(X0) | tall(X0) | ~kind(X0) [cnf transformation 49]
106. ~patient(X0) | kind(X0) [cnf transformation 52]
114. ~funny(X0) | patient(X0) [cnf transformation 34]
137. ~tall(lucy) [cnf transformation 24]
302. patient(X0) | tall(X0) [resolution 114,86]
327. kind(X0) | tall(X0) [resolution 302,106]
334. tall(X0) | ~kind(X0) | tall(X0) [resolution 96,302]
335. tall(X0) | ~kind(X0) [duplicate literal removal 334]
336. tall(X0) [subsumption resolution 335,327]
337. $false [resolution 336,137]
% SZS output end Proof for 368045615897788798724383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then paul is strong.
Everyone who is either rich or generous is either not tall or wise.
If someone is not rich then someone is not creative or happy and vice versa.
If susan is not wise then paul is rich and vice versa.
If alice is both calm and not wise then someone is not wise or not humble.
Everyone who is patient or creative is brave.
Everyone who is not curious is both tall and wise.
Everyone who is either not quiet or tall is not quiet or not old.
Everyone who is both creative and wise is either creative or not generous and vice versa.
Everyone who is generous or curious is both humble and not tall.
Everyone who is not tall or humble is funny or humble and vice versa.
Everyone who is both happy and humble is either quiet or not old and vice versa.
If someone is both not humble and not old then someone is both not calm and brave and vice versa.
If someone is generous or quiet then someone is both not generous and happy and vice versa.
Everyone who is humble is kind or not creative.
If fred is both old and not patient then lucy is not strong or happy.
Someone is not tall.
Paul is happy or not funny.
Someone is both wise and not funny.
Someone is strong or not old.
Mary is either not strong or patient.
Lucy is not generous.
Someone is not quiet. | Alice is humble. | entailment | ((?[X]:(~old(X)))=>(strong(paul)))&
(![X]:((rich(X)<~>generous(X))=>(~tall(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)|happy(X)))))&
((~wise(susan))<=>(rich(paul)))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((patient(X)|creative(X))=>brave(X)))&
(![X]:(~curious(X)=>(tall(X)&wise(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~tall(X)|humble(X))<=>(funny(X)|humble(X))))&
(![X]:((happy(X)&humble(X))<=>(quiet(X)<~>~old(X))))&
((?[X]:((~humble(X)&~old(X))))<=>(?[X]:((~calm(X)&brave(X)))))&
((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:(humble(X)=>(kind(X)|~creative(X))))&
(((old(fred)&~patient(fred)))=>((~strong(lucy)|happy(lucy))))&
(?[X]:(~tall(X)))&
((happy(paul)|~funny(paul)))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:((strong(X)|~old(X))))&
((~strong(mary)<~>patient(mary)))&
(~generous(lucy))&
(?[X]:(~quiet(X))) | humble(alice) | [
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1746054703467458434425218
% SZS output start Proof for 1746054703467458434425218
7. ! [X0] : (~curious(X0) => (wise(X0) & tall(X0))) [input p6]
9. ! [X0] : ((wise(X0) & creative(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p8]
10. ! [X0] : ((curious(X0) | generous(X0)) => (~tall(X0) & humble(X0))) [input p9]
24. ~humble(alice) [input hypothesis]
34. ! [X0] : ((wise(X0) & tall(X0)) | curious(X0)) [ennf transformation 7]
37. ! [X0] : ((~tall(X0) & humble(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 10]
50. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (~wise(X0) | ~creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ~wise(X0) | ~creative(X0))) [flattening 50]
89. curious(X0) | wise(X0) [cnf transformation 34]
93. generous(X0) | ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 51]
95. creative(X0) | creative(X0) | generous(X0) [cnf transformation 51]
98. ~generous(X0) | humble(X0) [cnf transformation 37]
99. ~curious(X0) | humble(X0) [cnf transformation 37]
131. ~humble(alice) [cnf transformation 24]
132. generous(X0) | ~creative(X0) | ~wise(X0) [duplicate literal removal 93]
133. creative(X0) | generous(X0) [duplicate literal removal 95]
182. 12 <=> wise(alice) [avatar definition]
184. wise(alice) <- (12) [avatar component clause 182]
194. ~wise(X0) | generous(X0) [subsumption resolution 132,133]
296. humble(X0) | wise(X0) [resolution 99,89]
323. wise(alice) [resolution 296,131]
325. 12 [avatar split clause 323,182]
326. generous(alice) <- (12) [resolution 184,194]
327. humble(alice) <- (12) [resolution 326,98]
328. $false <- (12) [subsumption resolution 327,131]
329. ~12 [avatar contradiction clause 328]
330. $false [avatar sat refutation 325,329]
% SZS output end Proof for 1746054703467458434425218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not kind is not rich.
Everyone who is humble is brave.
If paul is not funny or not creative then fred is not patient.
Everyone who is curious or funny is both not funny and not happy.
Everyone who is both not creative and calm is both not rich and kind and vice versa.
Everyone who is either creative or not brave is either not happy or not rich and vice versa.
If john is not tall or not quiet then alice is creative or tall.
Everyone who is either curious or not rich is either not creative or not humble.
Everyone who is patient or not humble is both kind and funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
Someone is both not patient and brave.
Fred is not funny.
Susan is not humble or not strong.
Someone is not kind.
John is both not quiet and brave.
Mary is not generous or strong.
Paul is not patient. | John is not rich. | contradiction | (![X]:((~strong(X)<~>~kind(X))=>~rich(X)))&
(![X]:(humble(X)=>brave(X)))&
(((~funny(paul)|~creative(paul)))=>(~patient(fred)))&
(![X]:((curious(X)|funny(X))=>(~funny(X)&~happy(X))))&
(![X]:((~creative(X)&calm(X))<=>(~rich(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~happy(X)<~>~rich(X))))&
(((~tall(john)|~quiet(john)))=>((creative(alice)|tall(alice))))&
(![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(?[X]:((~patient(X)&brave(X))))&
(~funny(fred))&
((~humble(susan)|~strong(susan)))&
(?[X]:(~kind(X)))&
((~quiet(john)&brave(john)))&
((~generous(mary)|strong(mary)))&
(~patient(paul)) | ~rich(john) | [
"p1",
"p3",
"p5",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6316379410237868867358774
% SZS output start Proof for 6316379410237868867358774
2. ! [X0] : (humble(X0) => brave(X0)) [input p1]
4. ! [X0] : ((funny(X0) | curious(X0)) => (~happy(X0) & ~funny(X0))) [input p3]
6. ! [X0] : ((creative(X0) <~> ~brave(X0)) <=> (~happy(X0) <~> ~rich(X0))) [input p5]
8. ! [X0] : ((curious(X0) <~> ~rich(X0)) => (~creative(X0) <~> ~humble(X0))) [input p7]
9. ! [X0] : ((~humble(X0) | patient(X0)) => (funny(X0) & kind(X0))) [input p8]
14. ! [X0] : ((humble(X0) | wise(X0)) <=> creative(X0)) [input p13]
24. ~rich(john) [input hypothesis]
28. ! [X0] : (brave(X0) | ~humble(X0)) [ennf transformation 2]
30. ! [X0] : ((~happy(X0) & ~funny(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 4]
33. ! [X0] : ((~creative(X0) <~> ~humble(X0)) | (curious(X0) <=> ~rich(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) & kind(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 9]
40. ! [X0] : ((((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))))) [nnf transformation 6]
41. ! [X0] : (((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 33]
57. ! [X0] : (((humble(X0) | wise(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) & ~wise(X0)))) [nnf transformation 14]
58. ! [X0] : ((humble(X0) | wise(X0) | ~creative(X0)) & (creative(X0) | (~humble(X0) & ~wise(X0)))) [flattening 57]
66. ~humble(X0) | brave(X0) [cnf transformation 28]
70. ~funny(X0) | ~funny(X0) [cnf transformation 30]
71. ~happy(X0) | ~curious(X0) [cnf transformation 30]
79. ~creative(X0) | happy(X0) | ~brave(X0) | rich(X0) [cnf transformation 40]
88. ~creative(X0) | ~humble(X0) | curious(X0) | rich(X0) [cnf transformation 41]
94. funny(X0) | humble(X0) [cnf transformation 34]
110. creative(X0) | ~humble(X0) [cnf transformation 58]
128. ~rich(john) [cnf transformation 24]
129. ~funny(X0) [duplicate literal removal 70]
162. humble(X0) [subsumption resolution 94,129]
165. 8 <=> ! [X1] : creative(X1) [avatar definition]
166. creative(X1) <- (8) [avatar component clause 165]
203. creative(X0) [subsumption resolution 110,162]
204. 8 [avatar split clause 203,165]
218. brave(X0) [resolution 66,162]
238. happy(X0) | ~brave(X0) | rich(X0) <- (8) [resolution 79,166]
240. happy(X0) | rich(X0) <- (8) [subsumption resolution 238,218]
249. ~curious(X3) | rich(X3) <- (8) [resolution 240,71]
266. ~humble(X0) | curious(X0) | rich(X0) <- (8) [resolution 88,166]
268. curious(X0) | rich(X0) <- (8) [subsumption resolution 266,162]
269. rich(X0) <- (8) [subsumption resolution 268,249]
270. $false <- (8) [resolution 269,128]
273. ~8 [avatar contradiction clause 270]
274. $false [avatar sat refutation 204,273]
% SZS output end Proof for 6316379410237868867358774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or patient is not brave.
Everyone who is both not tall and happy is not old and vice versa.
If someone is either generous or not strong then paul is generous or not funny.
If someone is patient or old then alice is both not old and creative and vice versa.
Everyone who is not quiet is not kind.
Everyone who is both not generous and not patient is tall or not old and vice versa.
If mary is both not wise and not happy then john is either tall or not brave and vice versa.
If someone is happy then someone is not quiet or happy and vice versa.
Everyone who is not kind or wise is generous and vice versa.
If someone is wise then lucy is both not wise and humble and vice versa.
If paul is either funny or not wise then someone is both old and not old and vice versa.
Everyone who is funny is either not quiet or happy and vice versa.
If someone is not rich then someone is either kind or old and vice versa.
If someone is not brave then someone is not quiet.
If someone is both curious and wise then someone is not generous or funny and vice versa.
Lucy is either not brave or generous.
Fred is not kind or funny.
Someone is either humble or curious.
Fred is either strong or creative.
Someone is both not brave and not patient.
Someone is not patient. | Alice is patient. | contradiction | (![X]:((brave(X)<~>patient(X))=>~brave(X)))&
(![X]:((~tall(X)&happy(X))<=>~old(X)))&
((?[X]:((generous(X)<~>~strong(X))))=>((generous(paul)|~funny(paul))))&
((?[X]:((patient(X)|old(X))))<=>((~old(alice)&creative(alice))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((~generous(X)&~patient(X))<=>(tall(X)|~old(X))))&
(((~wise(mary)&~happy(mary)))<=>((tall(john)<~>~brave(john))))&
((?[X]:(happy(X)))<=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:((~kind(X)|wise(X))<=>generous(X)))&
((?[X]:(wise(X)))<=>((~wise(lucy)&humble(lucy))))&
(((funny(paul)<~>~wise(paul)))<=>(?[X]:((old(X)&~old(X)))))&
(![X]:(funny(X)<=>(~quiet(X)<~>happy(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:((~generous(X)|funny(X)))))&
((~brave(lucy)<~>generous(lucy)))&
((~kind(fred)|funny(fred)))&
(?[X]:((humble(X)<~>curious(X))))&
((strong(fred)<~>creative(fred)))&
(?[X]:((~brave(X)&~patient(X))))&
(?[X]:(~patient(X))) | patient(alice) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6659921505626716115715671
% SZS output start Proof for 6659921505626716115715671
4. ? [X0] : (old(X0) | patient(X0)) <=> (creative(alice) & ~old(alice)) [input p3]
6. ! [X0] : ((~patient(X0) & ~generous(X0)) <=> (~old(X0) | tall(X0))) [input p5]
22. patient(alice) [input hypothesis]
36. (? [X0] : (old(X0) | patient(X0)) | (~creative(alice) | old(alice))) & ((creative(alice) & ~old(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 4]
37. (? [X0] : (old(X0) | patient(X0)) | ~creative(alice) | old(alice)) & ((creative(alice) & ~old(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 36]
38. (? [X0] : (old(X0) | patient(X0)) | ~creative(alice) | old(alice)) & ((creative(alice) & ~old(alice)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 37]
39. ? [X0] : (old(X0) | patient(X0)) => (old(sK0) | patient(sK0)) [choice axiom]
40. ((old(sK0) | patient(sK0)) | ~creative(alice) | old(alice)) & ((creative(alice) & ~old(alice)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 38,39]
41. ! [X0] : (((~patient(X0) & ~generous(X0)) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | (patient(X0) | generous(X0)))) [nnf transformation 6]
42. ! [X0] : (((~patient(X0) & ~generous(X0)) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | patient(X0) | generous(X0))) [flattening 41]
92. ~old(alice) | ~old(X1) [cnf transformation 40]
101. ~patient(X0) | old(X0) [cnf transformation 42]
147. patient(alice) [cnf transformation 22]
166. 5 <=> old(alice) [avatar definition]
168. old(alice) <- (5) [avatar component clause 166]
183. 9 <=> ! [X1] : ~old(X1) [avatar definition]
184. ~old(X1) <- (9) [avatar component clause 183]
190. 9 | ~5 [avatar split clause 92,166,183]
376. old(alice) [resolution 101,147]
381. 5 [avatar split clause 376,166]
382. $false <- (5, 9) [subsumption resolution 168,184]
383. ~5 | ~9 [avatar contradiction clause 382]
384. $false [avatar sat refutation 190,381,383]
% SZS output end Proof for 6659921505626716115715671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and creative is either not curious or kind and vice versa. Everyone who is not brave is kind and vice versa. If someone is both not old and curious then someone is both calm and kind. If fred is both not old and not humble then someone is both wise and not calm. If fred is both not happy and not curious then someone is not brave or not tall and vice versa. Everyone who is not quiet or not wise is funny. If alice is quiet or not humble then someone is happy and vice versa. Everyone who is not calm or strong is both not creative and not happy and vice versa. If someone is humble or not calm then someone is both generous and not humble. Everyone who is either not strong or not curious is tall and vice versa. If someone is not calm or old then john is both brave and not wise and vice versa. Everyone who is not funny or brave is not creative. If john is both not generous and not rich then lucy is rich. If someone is both not calm and old then someone is both not patient and not curious and vice versa. If paul is either not kind or wise then john is both not kind and funny. Everyone who is tall is not strong and vice versa. Someone is either not brave or not wise. Fred is not curious or quiet. Someone is not generous or not curious. Someone is not calm or not kind. Susan is either not brave or curious. Mary is not brave or not creative. | Mary is not brave. | contradiction | (![X]:((kind(X)&creative(X))<=>(~curious(X)<~>kind(X))))&
(![X]:(~brave(X)<=>kind(X)))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((calm(X)&kind(X)))))&
(((~old(fred)&~humble(fred)))=>(?[X]:((wise(X)&~calm(X)))))&
(((~happy(fred)&~curious(fred)))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~quiet(X)|~wise(X))=>funny(X)))&
(((quiet(alice)|~humble(alice)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)|strong(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((humble(X)|~calm(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((~calm(X)|old(X))))<=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|brave(X))=>~creative(X)))&
(((~generous(john)&~rich(john)))=>(rich(lucy)))&
((?[X]:((~calm(X)&old(X))))<=>(?[X]:((~patient(X)&~curious(X)))))&
(((~kind(paul)<~>wise(paul)))=>((~kind(john)&funny(john))))&
(![X]:(tall(X)<=>~strong(X)))&
(?[X]:((~brave(X)<~>~wise(X))))&
((~curious(fred)|quiet(fred)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((~calm(X)|~kind(X))))&
((~brave(susan)<~>curious(susan)))&
((~brave(mary)|~creative(mary))) | ~brave(mary) | [
"p4",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4290327303749568162567364
% SZS output start Proof for 4290327303749568162567364
5. (~curious(fred) & ~happy(fred)) <=> ? [X0] : (~tall(X0) | ~brave(X0)) [input p4]
10. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> tall(X0)) [input p9]
16. ! [X0] : (tall(X0) <=> ~strong(X0)) [input p15]
23. ~brave(mary) [input hypothesis]
45. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | (curious(fred) | happy(fred))) [nnf transformation 5]
46. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | curious(fred) | happy(fred)) [flattening 45]
47. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X1] : (~tall(X1) | ~brave(X1)) | curious(fred) | happy(fred)) [rectify 46]
48. ? [X1] : (~tall(X1) | ~brave(X1)) => (~tall(sK2) | ~brave(sK2)) [choice axiom]
49. ((~curious(fred) & ~happy(fred)) | ! [X0] : (tall(X0) & brave(X0))) & ((~tall(sK2) | ~brave(sK2)) | curious(fred) | happy(fred)) [skolemisation 47,48]
60. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | ~tall(X0)) & (tall(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 10]
72. ! [X0] : ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0))) [nnf transformation 16]
96. ~curious(fred) | brave(X0) [cnf transformation 49]
111. ~strong(X0) | tall(X0) | curious(X0) [cnf transformation 60]
113. ~tall(X0) | strong(X0) | curious(X0) [cnf transformation 60]
126. ~strong(X0) | ~tall(X0) [cnf transformation 72]
127. strong(X0) | tall(X0) [cnf transformation 72]
136. ~brave(mary) [cnf transformation 23]
175. 9 <=> curious(fred) [avatar definition]
177. ~curious(fred) <- (~9) [avatar component clause 175]
180. 10 <=> ! [X0] : brave(X0) [avatar definition]
181. brave(X0) <- (10) [avatar component clause 180]
182. 10 | ~9 [avatar split clause 96,175,180]
374. tall(X0) | curious(X0) | tall(X0) [resolution 111,127]
375. tall(X0) | curious(X0) [duplicate literal removal 374]
390. strong(X0) | curious(X0) | curious(X0) [resolution 113,375]
391. strong(X0) | curious(X0) [duplicate literal removal 390]
418. curious(X2) | ~tall(X2) [resolution 391,126]
422. curious(X2) [subsumption resolution 418,375]
426. $false <- (~9) [resolution 422,177]
431. 9 [avatar contradiction clause 426]
437. $false <- (10) [resolution 181,136]
440. ~10 [avatar contradiction clause 437]
441. $false [avatar sat refutation 182,431,440]
% SZS output end Proof for 4290327303749568162567364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not funny then someone is both not rich and old.
If alice is not creative then susan is wise and vice versa.
If someone is not tall then alice is either kind or not brave and vice versa.
Everyone who is both not old and calm is both not funny and not wise and vice versa.
If someone is not generous then lucy is not brave and vice versa.
If someone is not old then someone is either rich or funny and vice versa.
If someone is curious then someone is not humble or quiet.
Everyone who is rich is calm or not calm.
Everyone who is not wise is both not generous and not curious.
If paul is happy then alice is calm or curious and vice versa.
If someone is either not curious or kind then someone is either curious or calm.
Everyone who is both not quiet and rich is both happy and kind.
Everyone who is happy or old is both not quiet and not strong and vice versa.
Everyone who is either not happy or not kind is funny and vice versa.
If paul is either tall or not curious then paul is both brave and not strong and vice versa.
Everyone who is both not happy and curious is generous or curious and vice versa.
Someone is both not strong and curious.
Mary is brave.
Someone is either strong or not old.
Susan is both not generous and tall.
Someone is happy.
Someone is not patient.
Someone is both quiet and funny.
John is both not strong and happy. | John is generous. | contradiction | ((?[X]:((~rich(X)|~funny(X))))=>(?[X]:((~rich(X)&old(X)))))&
((~creative(alice))<=>(wise(susan)))&
((?[X]:(~tall(X)))<=>((kind(alice)<~>~brave(alice))))&
(![X]:((~old(X)&calm(X))<=>(~funny(X)&~wise(X))))&
((?[X]:(~generous(X)))<=>(~brave(lucy)))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>funny(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:(rich(X)=>(calm(X)|~calm(X))))&
(![X]:(~wise(X)=>(~generous(X)&~curious(X))))&
((happy(paul))<=>((calm(alice)|curious(alice))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((~quiet(X)&rich(X))=>(happy(X)&kind(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)&~strong(X))))&
(![X]:((~happy(X)<~>~kind(X))<=>funny(X)))&
(((tall(paul)<~>~curious(paul)))<=>((brave(paul)&~strong(paul))))&
(![X]:((~happy(X)&curious(X))<=>(generous(X)|curious(X))))&
(?[X]:((~strong(X)&curious(X))))&
(brave(mary))&
(?[X]:((strong(X)<~>~old(X))))&
((~generous(susan)&tall(susan)))&
(?[X]:(happy(X)))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)&funny(X))))&
((~strong(john)&happy(john))) | generous(john) | [
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3830609743237763767951530
% SZS output start Proof for 3830609743237763767951530
16. ! [X0] : ((curious(X0) & ~happy(X0)) <=> (curious(X0) | generous(X0))) [input p15]
24. happy(john) & ~strong(john) [input p23]
25. generous(john) [input hypothesis]
69. ! [X0] : (((curious(X0) & ~happy(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (~curious(X0) | happy(X0)))) [nnf transformation 16]
70. ! [X0] : (((curious(X0) & ~happy(X0)) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | ~curious(X0) | happy(X0))) [flattening 69]
128. ~happy(X0) | ~generous(X0) [cnf transformation 70]
143. happy(john) [cnf transformation 24]
144. generous(john) [cnf transformation 25]
298. ~generous(john) [resolution 128,143]
299. $false [subsumption resolution 298,144]
% SZS output end Proof for 3830609743237763767951530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both funny and not patient.
Everyone who is either humble or rich is quiet and vice versa.
If fred is both rich and curious then mary is not old or calm and vice versa.
Everyone who is old is either not strong or wise and vice versa.
Everyone who is patient or generous is funny or rich and vice versa.
Everyone who is not wise is either not quiet or humble and vice versa.
Everyone who is both happy and not old is not funny or generous.
If someone is not patient or not creative then someone is calm and vice versa.
If someone is both not creative and generous then someone is wise.
Everyone who is either generous or rich is either not tall or not generous and vice versa.
If paul is either not kind or wise then someone is not funny and vice versa.
Everyone who is not rich or not wise is curious and vice versa.
If someone is both not funny and not humble then lucy is both strong and not calm and vice versa.
Everyone who is either calm or old is old and vice versa.
If john is either tall or funny then john is not patient or strong.
If someone is not creative or humble then john is creative or not strong.
Someone is not quiet.
Someone is kind or generous.
Someone is brave.
Someone is both creative and generous.
Someone is not wise or not strong.
Someone is not generous. | John is not calm. | entailment | (![X]:(~kind(X)=>(funny(X)&~patient(X))))&
(![X]:((humble(X)<~>rich(X))<=>quiet(X)))&
(((rich(fred)&curious(fred)))<=>((~old(mary)|calm(mary))))&
(![X]:(old(X)<=>(~strong(X)<~>wise(X))))&
(![X]:((patient(X)|generous(X))<=>(funny(X)|rich(X))))&
(![X]:(~wise(X)<=>(~quiet(X)<~>humble(X))))&
(![X]:((happy(X)&~old(X))=>(~funny(X)|generous(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~creative(X)&generous(X))))=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>rich(X))<=>(~tall(X)<~>~generous(X))))&
(((~kind(paul)<~>wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)|~wise(X))<=>curious(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>((strong(lucy)&~calm(lucy))))&
(![X]:((calm(X)<~>old(X))<=>old(X)))&
(((tall(john)<~>funny(john)))=>((~patient(john)|strong(john))))&
((?[X]:((~creative(X)|humble(X))))=>((creative(john)|~strong(john))))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:(~generous(X))) | ~calm(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 241666804892026052772546
% SZS output start Proof for 241666804892026052772546
14. ! [X0] : ((calm(X0) <~> old(X0)) <=> old(X0)) [input p13]
23. calm(john) [input hypothesis]
61. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | ~old(X0)) & (old(X0) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 14]
119. old(X0) | old(X0) | ~calm(X0) [cnf transformation 61]
122. ~old(X0) | ~calm(X0) | ~old(X0) [cnf transformation 61]
133. calm(john) [cnf transformation 23]
134. old(X0) | ~calm(X0) [duplicate literal removal 119]
135. ~old(X0) | ~calm(X0) [duplicate literal removal 122]
162. 5 <=> ! [X1] : ~calm(X1) [avatar definition]
163. ~calm(X1) <- (5) [avatar component clause 162]
237. ~calm(X0) [subsumption resolution 134,135]
238. 5 [avatar split clause 237,162]
284. $false <- (5) [resolution 163,133]
285. ~5 [avatar contradiction clause 284]
286. $false [avatar sat refutation 238,285]
% SZS output end Proof for 241666804892026052772546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not brave and brave then paul is both not brave and not curious and vice versa.
Everyone who is not kind or creative is both old and patient and vice versa.
If someone is both not happy and not funny then lucy is happy.
If lucy is curious or kind then fred is both tall and happy and vice versa.
Everyone who is both not curious and generous is either curious or not old and vice versa.
Everyone who is funny is either not patient or funny.
If fred is either brave or not strong then john is patient or not patient and vice versa.
If susan is both not quiet and brave then someone is either patient or funny and vice versa.
Everyone who is generous or curious is either curious or not happy.
If john is either strong or wise then someone is both patient and not rich.
If someone is not curious or not funny then alice is curious.
Everyone who is not generous or happy is either not wise or not curious and vice versa.
If someone is both not generous and wise then alice is either not quiet or not tall.
If someone is brave or not humble then paul is both old and not creative and vice versa.
If someone is generous then someone is either not wise or old and vice versa.
John is tall or not old.
Paul is both not patient and quiet.
Susan is humble or calm.
Fred is funny.
Someone is both tall and not calm.
Someone is both not curious and happy.
Mary is both not creative and wise.
Someone is brave or not wise. | Mary is not generous. | entailment | (((~brave(paul)&brave(paul)))<=>((~brave(paul)&~curious(paul))))&
(![X]:((~kind(X)|creative(X))<=>(old(X)&patient(X))))&
((?[X]:((~happy(X)&~funny(X))))=>(happy(lucy)))&
(((curious(lucy)|kind(lucy)))<=>((tall(fred)&happy(fred))))&
(![X]:((~curious(X)&generous(X))<=>(curious(X)<~>~old(X))))&
(![X]:(funny(X)=>(~patient(X)<~>funny(X))))&
(((brave(fred)<~>~strong(fred)))<=>((patient(john)|~patient(john))))&
(((~quiet(susan)&brave(susan)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(![X]:((generous(X)|curious(X))=>(curious(X)<~>~happy(X))))&
(((strong(john)<~>wise(john)))=>(?[X]:((patient(X)&~rich(X)))))&
((?[X]:((~curious(X)|~funny(X))))=>(curious(alice)))&
(![X]:((~generous(X)|happy(X))<=>(~wise(X)<~>~curious(X))))&
((?[X]:((~generous(X)&wise(X))))=>((~quiet(alice)<~>~tall(alice))))&
((?[X]:((brave(X)|~humble(X))))<=>((old(paul)&~creative(paul))))&
((?[X]:(generous(X)))<=>(?[X]:((~wise(X)<~>old(X)))))&
((tall(john)|~old(john)))&
((~patient(paul)&quiet(paul)))&
((humble(susan)|calm(susan)))&
(funny(fred))&
(?[X]:((tall(X)&~calm(X))))&
(?[X]:((~curious(X)&happy(X))))&
((~creative(mary)&wise(mary)))&
(?[X]:((brave(X)|~wise(X)))) | ~generous(mary) | [
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 46601394466186502366773
% SZS output start Proof for 46601394466186502366773
9. ! [X0] : ((curious(X0) | generous(X0)) => (curious(X0) <~> ~happy(X0))) [input p8]
12. ! [X0] : ((happy(X0) | ~generous(X0)) <=> (~wise(X0) <~> ~curious(X0))) [input p11]
22. wise(mary) & ~creative(mary) [input p21]
24. generous(mary) [input hypothesis]
29. ! [X0] : ((curious(X0) <~> ~happy(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 9]
49. ! [X0] : (((happy(X0) | ~curious(X0)) & (~happy(X0) | curious(X0))) | (~curious(X0) & ~generous(X0))) [nnf transformation 29]
53. ! [X0] : (((happy(X0) | ~generous(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~happy(X0) & generous(X0)))) [nnf transformation 12]
54. ! [X0] : ((happy(X0) | ~generous(X0) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~happy(X0) & generous(X0)))) [flattening 53]
107. ~generous(X0) | curious(X0) | ~happy(X0) [cnf transformation 49]
110. happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 49]
116. ~curious(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 54]
120. happy(X0) | ~generous(X0) | ~wise(X0) | curious(X0) [cnf transformation 54]
142. wise(mary) [cnf transformation 22]
144. generous(mary) [cnf transformation 24]
145. ~curious(X0) | happy(X0) [duplicate literal removal 110]
257. ~wise(X0) | ~generous(X0) | curious(X0) [subsumption resolution 120,107]
258. ~wise(X0) | ~curious(X0) [subsumption resolution 116,145]
366. ~curious(mary) [resolution 258,142]
397. ~generous(mary) | curious(mary) [resolution 257,142]
401. curious(mary) [subsumption resolution 397,144]
402. $false [subsumption resolution 401,366]
% SZS output end Proof for 46601394466186502366773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not happy is old.
If someone is both not humble and funny then paul is either not calm or not wise.
Everyone who is brave or rich is not humble and vice versa.
If someone is rich or not calm then someone is not patient or not generous.
Everyone who is both tall and not rich is not creative or not funny and vice versa.
Everyone who is humble or not generous is both rich and not kind and vice versa.
If paul is kind or not quiet then paul is quiet and vice versa.
If someone is brave or quiet then alice is not kind or curious and vice versa.
If someone is either not kind or strong then someone is not kind.
If mary is generous then alice is either not brave or tall.
If paul is generous or not generous then fred is both not patient and not old.
Everyone who is both humble and wise is curious or funny and vice versa.
If someone is tall or strong then someone is not creative and vice versa.
Everyone who is not strong is either not creative or not curious.
Everyone who is both strong and tall is either not rich or not wise.
Everyone who is not strong or kind is kind or strong.
Someone is not happy.
Paul is brave or patient.
Someone is either strong or old.
Someone is either curious or not old.
Someone is either quiet or old. | Alice is not tall. | contradiction | (![X]:((~creative(X)|~happy(X))=>old(X)))&
((?[X]:((~humble(X)&funny(X))))=>((~calm(paul)<~>~wise(paul))))&
(![X]:((brave(X)|rich(X))<=>~humble(X)))&
((?[X]:((rich(X)|~calm(X))))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((tall(X)&~rich(X))<=>(~creative(X)|~funny(X))))&
(![X]:((humble(X)|~generous(X))<=>(rich(X)&~kind(X))))&
(((kind(paul)|~quiet(paul)))<=>(quiet(paul)))&
((?[X]:((brave(X)|quiet(X))))<=>((~kind(alice)|curious(alice))))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
((generous(mary))=>((~brave(alice)<~>tall(alice))))&
(((generous(paul)|~generous(paul)))=>((~patient(fred)&~old(fred))))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|funny(X))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>~curious(X))))&
(![X]:((strong(X)&tall(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((~strong(X)|kind(X))=>(kind(X)|strong(X))))&
(?[X]:(~happy(X)))&
((brave(paul)|patient(paul)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((quiet(X)<~>old(X)))) | ~tall(alice) | [
"p2",
"p4",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2472884988435101388500918
% SZS output start Proof for 2472884988435101388500918
3. ! [X0] : ((rich(X0) | brave(X0)) <=> ~humble(X0)) [input p2]
5. ! [X0] : ((~rich(X0) & tall(X0)) <=> (~funny(X0) | ~creative(X0))) [input p4]
6. ! [X0] : ((~generous(X0) | humble(X0)) <=> (~kind(X0) & rich(X0))) [input p5]
12. ! [X0] : ((wise(X0) & humble(X0)) <=> (funny(X0) | curious(X0))) [input p11]
22. ~tall(alice) [input hypothesis]
38. ! [X0] : (((rich(X0) | brave(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) & ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : ((rich(X0) | brave(X0) | humble(X0)) & (~humble(X0) | (~rich(X0) & ~brave(X0)))) [flattening 38]
43. ! [X0] : (((~rich(X0) & tall(X0)) | (funny(X0) & creative(X0))) & ((~funny(X0) | ~creative(X0)) | (rich(X0) | ~tall(X0)))) [nnf transformation 5]
44. ! [X0] : (((~rich(X0) & tall(X0)) | (funny(X0) & creative(X0))) & (~funny(X0) | ~creative(X0) | rich(X0) | ~tall(X0))) [flattening 43]
45. ! [X0] : (((~generous(X0) | humble(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (generous(X0) & ~humble(X0)))) [nnf transformation 6]
46. ! [X0] : ((~generous(X0) | humble(X0) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | (generous(X0) & ~humble(X0)))) [flattening 45]
59. ! [X0] : (((wise(X0) & humble(X0)) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | (~wise(X0) | ~humble(X0)))) [nnf transformation 12]
60. ! [X0] : (((wise(X0) & humble(X0)) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | ~wise(X0) | ~humble(X0))) [flattening 59]
84. ~rich(X0) | ~humble(X0) [cnf transformation 39]
90. tall(X0) | funny(X0) [cnf transformation 44]
93. rich(X0) | ~humble(X0) [cnf transformation 46]
115. humble(X0) | ~funny(X0) [cnf transformation 60]
135. ~tall(alice) [cnf transformation 22]
169. ~humble(X0) [subsumption resolution 93,84]
228. 21 <=> tall(alice) [avatar definition]
230. ~tall(alice) <- (~21) [avatar component clause 228]
249. ~funny(X0) [subsumption resolution 115,169]
307. ~21 [avatar split clause 135,228]
321. funny(alice) <- (~21) [resolution 90,230]
322. $false <- (~21) [subsumption resolution 321,249]
323. 21 [avatar contradiction clause 322]
324. $false [avatar sat refutation 307,323]
% SZS output end Proof for 2472884988435101388500918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not strong is kind or not patient and vice versa.
Everyone who is quiet or patient is both curious and generous and vice versa.
Everyone who is not curious or not happy is happy.
Everyone who is both not funny and not humble is both humble and strong.
If john is both kind and brave then someone is brave or not quiet and vice versa.
Everyone who is both not wise and old is both calm and rich.
Everyone who is either not rich or not brave is both happy and not strong.
Everyone who is both strong and kind is old and vice versa.
Everyone who is generous or not funny is both creative and not kind and vice versa.
Everyone who is both not generous and not kind is not kind or not old.
Everyone who is humble or tall is patient and vice versa.
If john is calm then mary is not creative and vice versa.
Everyone who is not funny or wise is both rich and not kind and vice versa.
If lucy is not creative or patient then someone is both funny and quiet and vice versa.
If someone is creative then fred is both wise and humble.
If mary is patient then john is both old and calm and vice versa.
Someone is brave.
Alice is either humble or patient.
Someone is both generous and rich.
Someone is not old.
Someone is either humble or patient.
Someone is not brave.
Someone is quiet or not old.
Paul is strong or curious. | Fred is not tall. | neutral | (![X]:((patient(X)<~>~strong(X))<=>(kind(X)|~patient(X))))&
(![X]:((quiet(X)|patient(X))<=>(curious(X)&generous(X))))&
(![X]:((~curious(X)|~happy(X))=>happy(X)))&
(![X]:((~funny(X)&~humble(X))=>(humble(X)&strong(X))))&
(((kind(john)&brave(john)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((~wise(X)&old(X))=>(calm(X)&rich(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(happy(X)&~strong(X))))&
(![X]:((strong(X)&kind(X))<=>old(X)))&
(![X]:((generous(X)|~funny(X))<=>(creative(X)&~kind(X))))&
(![X]:((~generous(X)&~kind(X))=>(~kind(X)|~old(X))))&
(![X]:((humble(X)|tall(X))<=>patient(X)))&
((calm(john))<=>(~creative(mary)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)&~kind(X))))&
(((~creative(lucy)|patient(lucy)))<=>(?[X]:((funny(X)&quiet(X)))))&
((?[X]:(creative(X)))=>((wise(fred)&humble(fred))))&
((patient(mary))<=>((old(john)&calm(john))))&
(?[X]:(brave(X)))&
((humble(alice)<~>patient(alice)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:(~old(X)))&
(?[X]:((humble(X)<~>patient(X))))&
(?[X]:(~brave(X)))&
(?[X]:((quiet(X)|~old(X))))&
((strong(paul)|curious(paul))) | ~tall(fred) | [] | null | 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa.
If john is rich then lucy is tall or not brave and vice versa.
Everyone who is both not calm and wise is both not strong and curious and vice versa.
If alice is both strong and old then susan is calm.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Someone is not patient or tall.
Someone is either brave or calm.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny.
Alice is both not rich and not wise. | Paul is calm. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
((rich(john))<=>((tall(lucy)|~brave(lucy))))&
(![X]:((~calm(X)&wise(X))<=>(~strong(X)&curious(X))))&
(((strong(alice)&old(alice)))=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice))) | calm(paul) | [
"p0",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2798177867082351255972033
% SZS output start Proof for 2798177867082351255972033
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
10. ! [X0] : (~quiet(X0) => (~calm(X0) | ~wise(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> tall(X0)) => (~quiet(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p12]
25. calm(paul) [input hypothesis]
35. ! [X0] : ((~calm(X0) | ~wise(X0)) | quiet(X0)) [ennf transformation 10]
36. ! [X0] : (~calm(X0) | ~wise(X0) | quiet(X0)) [flattening 35]
37. ! [X0] : ((~quiet(X0) & ~rich(X0)) | (~wise(X0) <=> tall(X0))) [ennf transformation 11]
39. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 13]
42. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
43. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 42]
50. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
51. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 50]
52. ! [X0] : ((~quiet(X0) & ~rich(X0)) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) [nnf transformation 37]
53. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 39]
76. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
79. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 43]
105. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 51]
107. tall(X0) | patient(X0) | tall(X0) [cnf transformation 51]
110. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 36]
114. ~quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 52]
119. ~strong(X0) | wise(X0) | ~calm(X0) [cnf transformation 53]
141. calm(paul) [cnf transformation 25]
142. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 105]
143. tall(X0) | patient(X0) [duplicate literal removal 107]
148. ~patient(X0) | wise(X0) [duplicate literal removal 76]
149. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 79]
216. strong(X0) | patient(X0) [subsumption resolution 142,143]
360. ~wise(paul) | quiet(paul) [resolution 110,141]
362. 40 <=> quiet(paul) [avatar definition]
364. quiet(paul) <- (40) [avatar component clause 362]
366. 41 <=> wise(paul) [avatar definition]
367. wise(paul) <- (41) [avatar component clause 366]
369. 40 | ~41 [avatar split clause 360,366,362]
405. wise(X0) | ~calm(X0) | patient(X0) [resolution 119,216]
407. ~calm(X0) | wise(X0) [subsumption resolution 405,148]
432. ~patient(paul) | ~wise(paul) [resolution 149,141]
509. wise(paul) [resolution 407,141]
513. 41 [avatar split clause 509,366]
514. ~patient(paul) [subsumption resolution 432,148]
515. ~wise(paul) | ~tall(paul) <- (40) [resolution 364,114]
517. ~tall(paul) <- (40, 41) [subsumption resolution 515,367]
553. patient(paul) <- (40, 41) [resolution 517,143]
554. $false <- (40, 41) [subsumption resolution 553,514]
555. ~40 | ~41 [avatar contradiction clause 554]
556. $false [avatar sat refutation 369,513,555]
% SZS output end Proof for 2798177867082351255972033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or not brave then alice is both not quiet and not curious and vice versa.
Everyone who is either quiet or not tall is either generous or not rich and vice versa.
Everyone who is funny is either not happy or kind and vice versa.
Everyone who is not old or old is either patient or happy.
Everyone who is not humble or not strong is quiet or old and vice versa.
If someone is funny or quiet then susan is not brave.
If someone is not curious or rich then someone is either not generous or not strong and vice versa.
Everyone who is either creative or old is not calm or not curious and vice versa.
Everyone who is either wise or not quiet is brave.
Everyone who is not patient is either old or not funny.
If someone is both not strong and not tall then lucy is not generous or not creative and vice versa.
If mary is both not old and not humble then someone is wise and vice versa.
If someone is both not humble and not curious then someone is both kind and not wise and vice versa.
If alice is both strong and not tall then susan is quiet or not creative.
Everyone who is both funny and kind is both patient and humble and vice versa.
Everyone who is either not strong or funny is either curious or humble and vice versa.
Someone is not humble.
Someone is either not happy or not strong.
Someone is both kind and rich.
Paul is either curious or tall.
Alice is either not quiet or not funny.
John is happy or strong.
Paul is not creative.
John is either not tall or rich. | Alice is old. | entailment | ((?[X]:((old(X)|~brave(X))))<=>((~quiet(alice)&~curious(alice))))&
(![X]:((quiet(X)<~>~tall(X))<=>(generous(X)<~>~rich(X))))&
(![X]:(funny(X)<=>(~happy(X)<~>kind(X))))&
(![X]:((~old(X)|old(X))=>(patient(X)<~>happy(X))))&
(![X]:((~humble(X)|~strong(X))<=>(quiet(X)|old(X))))&
((?[X]:((funny(X)|quiet(X))))=>(~brave(susan)))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~calm(X)|~curious(X))))&
(![X]:((wise(X)<~>~quiet(X))=>brave(X)))&
(![X]:(~patient(X)=>(old(X)<~>~funny(X))))&
((?[X]:((~strong(X)&~tall(X))))<=>((~generous(lucy)|~creative(lucy))))&
(((~old(mary)&~humble(mary)))<=>(?[X]:(wise(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>(?[X]:((kind(X)&~wise(X)))))&
(((strong(alice)&~tall(alice)))=>((quiet(susan)|~creative(susan))))&
(![X]:((funny(X)&kind(X))<=>(patient(X)&humble(X))))&
(![X]:((~strong(X)<~>funny(X))<=>(curious(X)<~>humble(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((kind(X)&rich(X))))&
((curious(paul)<~>tall(paul)))&
((~quiet(alice)<~>~funny(alice)))&
((happy(john)|strong(john)))&
(~creative(paul))&
((~tall(john)<~>rich(john))) | old(alice) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p9",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6384240830387267504776374
% SZS output start Proof for 6384240830387267504776374
1. ? [X0] : (~brave(X0) | old(X0)) <=> (~curious(alice) & ~quiet(alice)) [input p0]
3. ! [X0] : (funny(X0) <=> (~happy(X0) <~> kind(X0))) [input p2]
4. ! [X0] : ((old(X0) | ~old(X0)) => (patient(X0) <~> happy(X0))) [input p3]
5. ! [X0] : ((~strong(X0) | ~humble(X0)) <=> (old(X0) | quiet(X0))) [input p4]
6. ? [X0] : (quiet(X0) | funny(X0)) => ~brave(susan) [input p5]
10. ! [X0] : (~patient(X0) => (old(X0) <~> ~funny(X0))) [input p9]
15. ! [X0] : ((kind(X0) & funny(X0)) <=> (humble(X0) & patient(X0))) [input p14]
21. ~quiet(alice) <~> ~funny(alice) [input p20]
25. ~old(alice) [input hypothesis]
28. ! [X0] : ((patient(X0) <~> happy(X0)) | (~old(X0) & old(X0))) [ennf transformation 4]
29. ~brave(susan) | ! [X0] : (~quiet(X0) & ~funny(X0)) [ennf transformation 6]
31. ! [X0] : ((old(X0) <~> ~funny(X0)) | patient(X0)) [ennf transformation 10]
34. (? [X0] : (~brave(X0) | old(X0)) | (curious(alice) | quiet(alice))) & ((~curious(alice) & ~quiet(alice)) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 1]
35. (? [X0] : (~brave(X0) | old(X0)) | curious(alice) | quiet(alice)) & ((~curious(alice) & ~quiet(alice)) | ! [X0] : (brave(X0) & ~old(X0))) [flattening 34]
36. (? [X0] : (~brave(X0) | old(X0)) | curious(alice) | quiet(alice)) & ((~curious(alice) & ~quiet(alice)) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 35]
37. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK0) | old(sK0)) [choice axiom]
38. ((~brave(sK0) | old(sK0)) | curious(alice) | quiet(alice)) & ((~curious(alice) & ~quiet(alice)) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 36,37]
40. ! [X0] : ((funny(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~funny(X0))) [nnf transformation 3]
41. ! [X0] : (((~happy(X0) | ~patient(X0)) & (happy(X0) | patient(X0))) | (~old(X0) & old(X0))) [nnf transformation 28]
42. ! [X0] : (((~strong(X0) | ~humble(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (strong(X0) & humble(X0)))) [nnf transformation 5]
43. ! [X0] : ((~strong(X0) | ~humble(X0) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | (strong(X0) & humble(X0)))) [flattening 42]
52. ! [X0] : (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | patient(X0)) [nnf transformation 31]
68. ! [X0] : (((kind(X0) & funny(X0)) | (~humble(X0) | ~patient(X0))) & ((humble(X0) & patient(X0)) | (~kind(X0) | ~funny(X0)))) [nnf transformation 15]
69. ! [X0] : (((kind(X0) & funny(X0)) | ~humble(X0) | ~patient(X0)) & ((humble(X0) & patient(X0)) | ~kind(X0) | ~funny(X0))) [flattening 68]
79. (funny(alice) | quiet(alice)) & (~funny(alice) | ~quiet(alice)) [nnf transformation 21]
82. ~quiet(alice) | brave(X1) [cnf transformation 38]
95. ~kind(X0) | happy(X0) | ~funny(X0) [cnf transformation 40]
100. ~happy(X0) | ~patient(X0) | old(X0) [cnf transformation 41]
101. ~patient(X0) | ~happy(X0) | ~old(X0) [cnf transformation 41]
102. humble(X0) | quiet(X0) | old(X0) [cnf transformation 43]
107. ~brave(susan) | ~quiet(X0) [cnf transformation 29]
122. ~funny(X0) | old(X0) | patient(X0) [cnf transformation 52]
140. ~humble(X0) | kind(X0) | ~patient(X0) [cnf transformation 69]
157. funny(alice) | quiet(alice) [cnf transformation 79]
162. ~old(alice) [cnf transformation 25]
164. 1 <=> quiet(alice) [avatar definition]
165. ~quiet(alice) <- (~1) [avatar component clause 164]
166. quiet(alice) <- (1) [avatar component clause 164]
181. 5 <=> ! [X1] : brave(X1) [avatar definition]
182. brave(X1) <- (5) [avatar component clause 181]
188. 5 | ~1 [avatar split clause 82,164,181]
190. ~patient(X0) | ~happy(X0) [subsumption resolution 100,101]
193. 7 <=> ! [X0] : ~quiet(X0) [avatar definition]
194. ~quiet(X0) <- (7) [avatar component clause 193]
196. 8 <=> brave(susan) [avatar definition]
198. ~brave(susan) <- (~8) [avatar component clause 196]
199. 7 | ~8 [avatar split clause 107,196,193]
344. 41 <=> funny(alice) [avatar definition]
346. funny(alice) <- (41) [avatar component clause 344]
347. 1 | 41 [avatar split clause 157,344,164]
565. old(alice) | patient(alice) <- (41) [resolution 122,346]
566. patient(alice) <- (41) [subsumption resolution 565,162]
605. ~patient(X0) | kind(X0) | quiet(X0) | old(X0) [resolution 140,102]
609. ~happy(alice) <- (41) [resolution 566,190]
921. kind(alice) | quiet(alice) | old(alice) <- (41) [resolution 605,566]
1007. kind(alice) | old(alice) <- (~1, 41) [subsumption resolution 921,165]
1008. kind(alice) <- (~1, 41) [subsumption resolution 1007,162]
1126. happy(alice) | ~funny(alice) <- (~1, 41) [resolution 1008,95]
1127. ~funny(alice) <- (~1, 41) [subsumption resolution 1126,609]
1128. $false <- (~1, 41) [subsumption resolution 1127,346]
1129. 1 | ~41 [avatar contradiction clause 1128]
1143. $false <- (5, ~8) [resolution 182,198]
1144. ~5 | 8 [avatar contradiction clause 1143]
1162. $false <- (1, 7) [resolution 194,166]
1175. ~1 | ~7 [avatar contradiction clause 1162]
1176. $false [avatar sat refutation 188,199,347,1129,1144,1175]
% SZS output end Proof for 6384240830387267504776374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or funny then fred is not quiet or not funny and vice versa.
If someone is quiet or not funny then someone is either strong or brave.
If lucy is not humble or generous then someone is either not creative or not wise.
If paul is wise or kind then someone is humble or old and vice versa.
Everyone who is not wise or generous is both not strong and quiet and vice versa.
Everyone who is both kind and humble is either humble or not old and vice versa.
If someone is either kind or old then mary is tall or not kind.
Everyone who is not calm or not happy is both strong and not tall.
Everyone who is calm is curious or strong.
If alice is both not humble and brave then someone is both not happy and calm.
Everyone who is patient is either not quiet or strong and vice versa.
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Someone is not patient or brave.
Alice is wise or not quiet.
Someone is not creative.
Susan is funny or not rich.
Lucy is not creative or not funny.
Paul is not kind.
Someone is kind.
John is either curious or not brave. | Susan is old. | entailment | ((?[X]:((happy(X)<~>funny(X))))<=>((~quiet(fred)|~funny(fred))))&
((?[X]:((quiet(X)|~funny(X))))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~humble(lucy)|generous(lucy)))=>(?[X]:((~creative(X)<~>~wise(X)))))&
(((wise(paul)|kind(paul)))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(?[X]:((~patient(X)|brave(X))))&
((wise(alice)|~quiet(alice)))&
(?[X]:(~creative(X)))&
((funny(susan)|~rich(susan)))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john))) | old(susan) | [
"p4",
"p7",
"p11",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4805852047553528971557258
% SZS output start Proof for 4805852047553528971557258
5. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p4]
8. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~tall(X0) & strong(X0))) [input p7]
12. ! [X0] : ((wise(X0) | funny(X0)) => happy(X0)) [input p11]
13. ! [X0] : ((rich(X0) & patient(X0)) <=> ~funny(X0)) [input p12]
14. (happy(lucy) | ~humble(lucy)) <=> (~wise(susan) <~> happy(susan)) [input p13]
16. ! [X0] : ((old(X0) <~> wise(X0)) <=> (~funny(X0) & ~creative(X0))) [input p15]
20. ~rich(susan) | funny(susan) [input p19]
25. ~old(susan) [input hypothesis]
31. ! [X0] : ((~tall(X0) & strong(X0)) | (happy(X0) & calm(X0))) [ennf transformation 8]
36. ! [X0] : (happy(X0) | (~wise(X0) & ~funny(X0))) [ennf transformation 12]
55. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 5]
56. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 55]
63. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | ~patient(X0)))) [nnf transformation 13]
64. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | ~patient(X0))) [flattening 63]
65. ((happy(lucy) | ~humble(lucy)) | ((~wise(susan) | ~happy(susan)) & (happy(susan) | wise(susan)))) & (((~happy(susan) | wise(susan)) & (happy(susan) | ~wise(susan))) | (~happy(lucy) & humble(lucy))) [nnf transformation 14]
66. (happy(lucy) | ~humble(lucy) | ((~wise(susan) | ~happy(susan)) & (happy(susan) | wise(susan)))) & (((~happy(susan) | wise(susan)) & (happy(susan) | ~wise(susan))) | (~happy(lucy) & humble(lucy))) [flattening 65]
68. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 16]
69. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [flattening 68]
95. ~strong(X0) | wise(X0) [cnf transformation 56]
109. strong(X0) | happy(X0) [cnf transformation 31]
120. ~wise(X0) | happy(X0) [cnf transformation 36]
123. rich(X0) | funny(X0) [cnf transformation 64]
127. ~happy(susan) | wise(susan) | ~happy(lucy) [cnf transformation 66]
137. ~wise(X0) | old(X0) | ~funny(X0) [cnf transformation 69]
143. ~rich(susan) | funny(susan) [cnf transformation 20]
149. ~old(susan) [cnf transformation 25]
279. 28 <=> wise(susan) [avatar definition]
280. wise(susan) <- (28) [avatar component clause 279]
283. 29 <=> happy(lucy) [avatar definition]
284. ~happy(lucy) <- (~29) [avatar component clause 283]
289. 30 <=> happy(susan) [avatar definition]
290. ~happy(susan) <- (~30) [avatar component clause 289]
293. ~29 | 28 | ~30 [avatar split clause 127,289,279,283]
323. funny(susan) [subsumption resolution 143,123]
347. happy(X0) | wise(X0) [resolution 109,95]
348. happy(X0) [subsumption resolution 347,120]
349. $false <- (~30) [resolution 348,290]
350. 30 [avatar contradiction clause 349]
491. old(susan) | ~funny(susan) <- (28) [resolution 137,280]
504. ~funny(susan) <- (28) [subsumption resolution 491,149]
505. $false <- (28) [subsumption resolution 504,323]
506. ~28 [avatar contradiction clause 505]
517. $false <- (~29) [subsumption resolution 284,348]
518. 29 [avatar contradiction clause 517]
519. $false [avatar sat refutation 293,350,506,518]
% SZS output end Proof for 4805852047553528971557258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not calm and not kind.
Everyone who is both not funny and not humble is both patient and humble and vice versa.
If john is not brave or kind then john is funny and vice versa.
Everyone who is either not kind or not patient is quiet.
Everyone who is funny or not kind is both rich and not patient and vice versa.
If someone is patient or tall then someone is not happy and vice versa.
If susan is not generous then someone is brave.
If fred is not rich then someone is both not calm and creative and vice versa.
Everyone who is not humble or not brave is both not generous and quiet and vice versa.
If lucy is either patient or not humble then someone is either calm or not funny.
Everyone who is creative is both not generous and not happy and vice versa.
If paul is not brave then paul is either not quiet or rich and vice versa.
Everyone who is both quiet and not humble is both brave and patient.
If someone is both not calm and not creative then alice is tall or calm.
If someone is rich then someone is both not brave and not kind.
John is not strong.
Lucy is wise.
Mary is old.
Someone is quiet.
Paul is not curious or not funny.
John is both generous and kind.
Susan is both happy and brave. | Susan is not creative. | entailment | (![X]:(calm(X)=>(~calm(X)&~kind(X))))&
(![X]:((~funny(X)&~humble(X))<=>(patient(X)&humble(X))))&
(((~brave(john)|kind(john)))<=>(funny(john)))&
(![X]:((~kind(X)<~>~patient(X))=>quiet(X)))&
(![X]:((funny(X)|~kind(X))<=>(rich(X)&~patient(X))))&
((?[X]:((patient(X)|tall(X))))<=>(?[X]:(~happy(X))))&
((~generous(susan))=>(?[X]:(brave(X))))&
((~rich(fred))<=>(?[X]:((~calm(X)&creative(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~generous(X)&quiet(X))))&
(((patient(lucy)<~>~humble(lucy)))=>(?[X]:((calm(X)<~>~funny(X)))))&
(![X]:(creative(X)<=>(~generous(X)&~happy(X))))&
((~brave(paul))<=>((~quiet(paul)<~>rich(paul))))&
(![X]:((quiet(X)&~humble(X))=>(brave(X)&patient(X))))&
((?[X]:((~calm(X)&~creative(X))))=>((tall(alice)|calm(alice))))&
((?[X]:(rich(X)))=>(?[X]:((~brave(X)&~kind(X)))))&
(~strong(john))&
(wise(lucy))&
(old(mary))&
(?[X]:(quiet(X)))&
((~curious(paul)|~funny(paul)))&
((generous(john)&kind(john)))&
((happy(susan)&brave(susan))) | ~creative(susan) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1085279284145173545566971
% SZS output start Proof for 1085279284145173545566971
11. ! [X0] : (creative(X0) <=> (~happy(X0) & ~generous(X0))) [input p10]
22. brave(susan) & happy(susan) [input p21]
23. creative(susan) [input hypothesis]
62. ! [X0] : ((creative(X0) | (happy(X0) | generous(X0))) & ((~happy(X0) & ~generous(X0)) | ~creative(X0))) [nnf transformation 11]
63. ! [X0] : ((creative(X0) | happy(X0) | generous(X0)) & ((~happy(X0) & ~generous(X0)) | ~creative(X0))) [flattening 62]
103. ~creative(X0) | ~happy(X0) [cnf transformation 63]
117. happy(susan) [cnf transformation 22]
119. creative(susan) [cnf transformation 23]
264. ~happy(susan) [resolution 103,119]
266. $false [subsumption resolution 264,117]
% SZS output end Proof for 1085279284145173545566971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or curious then someone is either not creative or quiet and vice versa.
Everyone who is not curious is wise.
If paul is both kind and generous then someone is both wise and rich and vice versa.
Everyone who is both curious and strong is not strong or quiet and vice versa.
Everyone who is either not happy or creative is old or generous.
Everyone who is quiet or rich is either patient or not kind.
Everyone who is either generous or not rich is not calm or not brave.
If someone is either creative or calm then someone is either wise or calm and vice versa.
Everyone who is both tall and funny is either not happy or not humble and vice versa.
Everyone who is either happy or humble is either quiet or not curious and vice versa.
Everyone who is not rich or not calm is old or not old.
If someone is either generous or rich then paul is both generous and not curious.
Everyone who is not quiet is either not curious or not creative.
Everyone who is both curious and not humble is not brave or old and vice versa.
Everyone who is kind is both not patient and not creative.
Everyone who is calm is both not humble and not rich.
Paul is either not patient or not generous.
Someone is strong.
Someone is calm or not brave.
Someone is either not patient or not quiet.
Someone is either not curious or funny. | Paul is not old. | neutral | ((?[X]:((calm(X)|curious(X))))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:(~curious(X)=>wise(X)))&
(((kind(paul)&generous(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((curious(X)&strong(X))<=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)<~>creative(X))=>(old(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(patient(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~rich(X))=>(~calm(X)|~brave(X))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((tall(X)&funny(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((happy(X)<~>humble(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)|~calm(X))=>(old(X)|~old(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((generous(paul)&~curious(paul))))&
(![X]:(~quiet(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((curious(X)&~humble(X))<=>(~brave(X)|old(X))))&
(![X]:(kind(X)=>(~patient(X)&~creative(X))))&
(![X]:(calm(X)=>(~humble(X)&~rich(X))))&
((~patient(paul)<~>~generous(paul)))&
(?[X]:(strong(X)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~curious(X)<~>funny(X)))) | ~old(paul) | [] | null | 0 |
If mary is not quiet or quiet then mary is either not tall or strong.
Everyone who is either funny or humble is not creative.
Everyone who is curious is humble or not old.
If paul is both generous and not generous then alice is not humble.
Everyone who is both old and curious is old or not old and vice versa.
If someone is curious or not humble then someone is humble and vice versa.
Everyone who is not funny or kind is generous or strong.
If susan is either old or quiet then someone is rich.
Everyone who is both not old and humble is calm and vice versa.
Everyone who is either wise or not curious is both tall and not curious and vice versa.
If susan is either not rich or strong then someone is both calm and not humble and vice versa.
If someone is curious then mary is kind.
Everyone who is either tall or not patient is either patient or creative.
Everyone who is not humble is both happy and not strong.
If someone is not curious then susan is not creative.
Everyone who is both not calm and not funny is tall.
Someone is not creative.
Someone is humble or not rich.
Someone is happy or not wise.
Someone is not brave or not generous.
Mary is not creative or strong.
Someone is either rich or not tall. | Paul is not old. | contradiction | (((~quiet(mary)|quiet(mary)))=>((~tall(mary)<~>strong(mary))))&
(![X]:((funny(X)<~>humble(X))=>~creative(X)))&
(![X]:(curious(X)=>(humble(X)|~old(X))))&
(((generous(paul)&~generous(paul)))=>(~humble(alice)))&
(![X]:((old(X)&curious(X))<=>(old(X)|~old(X))))&
((?[X]:((curious(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|kind(X))=>(generous(X)|strong(X))))&
(((old(susan)<~>quiet(susan)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)&humble(X))<=>calm(X)))&
(![X]:((wise(X)<~>~curious(X))<=>(tall(X)&~curious(X))))&
(((~rich(susan)<~>strong(susan)))<=>(?[X]:((calm(X)&~humble(X)))))&
((?[X]:(curious(X)))=>(kind(mary)))&
(![X]:((tall(X)<~>~patient(X))=>(patient(X)<~>creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~strong(X))))&
((?[X]:(~curious(X)))=>(~creative(susan)))&
(![X]:((~calm(X)&~funny(X))=>tall(X)))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:((happy(X)|~wise(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((~creative(mary)|strong(mary)))&
(?[X]:((rich(X)<~>~tall(X)))) | ~old(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8119808352434128456207647
% SZS output start Proof for 8119808352434128456207647
5. ! [X0] : ((curious(X0) & old(X0)) <=> (~old(X0) | old(X0))) [input p4]
23. ~old(paul) [input hypothesis]
45. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 5]
46. ! [X0] : (((curious(X0) & old(X0)) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~curious(X0) | ~old(X0))) [flattening 45]
81. old(X0) | old(X0) [cnf transformation 46]
119. ~old(paul) [cnf transformation 23]
125. old(X0) [duplicate literal removal 81]
209. $false [subsumption resolution 119,125]
% SZS output end Proof for 8119808352434128456207647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is either patient or not wise.
Everyone who is either not funny or calm is either kind or not generous and vice versa.
Everyone who is both calm and not brave is both not humble and happy.
Everyone who is not humble is both not tall and old and vice versa.
Everyone who is not calm or not rich is both not humble and not funny.
If mary is not generous then mary is kind or wise and vice versa.
If alice is both not creative and not generous then someone is humble or wise and vice versa.
Everyone who is not old is both old and wise and vice versa.
If someone is strong then someone is both not creative and curious and vice versa.
Everyone who is not brave is not happy and vice versa.
If someone is both old and creative then someone is not creative or happy and vice versa.
If lucy is either generous or curious then someone is creative.
If someone is not kind then alice is kind.
Everyone who is either funny or not brave is not kind.
If someone is not kind then someone is not tall and vice versa.
Fred is generous or brave.
Someone is not wise or not happy.
Fred is either not creative or quiet.
Mary is either not humble or humble.
Someone is either humble or curious. | Mary is creative. | neutral | (![X]:((wise(X)|~strong(X))=>(patient(X)<~>~wise(X))))&
(![X]:((~funny(X)<~>calm(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((calm(X)&~brave(X))=>(~humble(X)&happy(X))))&
(![X]:(~humble(X)<=>(~tall(X)&old(X))))&
(![X]:((~calm(X)|~rich(X))=>(~humble(X)&~funny(X))))&
((~generous(mary))<=>((kind(mary)|wise(mary))))&
(((~creative(alice)&~generous(alice)))<=>(?[X]:((humble(X)|wise(X)))))&
(![X]:(~old(X)<=>(old(X)&wise(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:(~brave(X)<=>~happy(X)))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~creative(X)|happy(X)))))&
(((generous(lucy)<~>curious(lucy)))=>(?[X]:(creative(X))))&
((?[X]:(~kind(X)))=>(kind(alice)))&
(![X]:((funny(X)<~>~brave(X))=>~kind(X)))&
((?[X]:(~kind(X)))<=>(?[X]:(~tall(X))))&
((generous(fred)|brave(fred)))&
(?[X]:((~wise(X)|~happy(X))))&
((~creative(fred)<~>quiet(fred)))&
((~humble(mary)<~>humble(mary)))&
(?[X]:((humble(X)<~>curious(X)))) | creative(mary) | [] | null | 0 |
If mary is both rich and patient then alice is both not strong and not tall.
Everyone who is rich or happy is either not quiet or strong and vice versa.
If mary is both tall and happy then someone is not calm.
If someone is not tall then mary is either not curious or not funny.
If lucy is either not humble or generous then someone is both not strong and rich.
Everyone who is not rich or curious is both not generous and creative and vice versa.
If someone is both tall and not curious then someone is either quiet or patient.
Everyone who is rich or not kind is not humble.
Everyone who is either brave or not quiet is calm.
If lucy is both generous and not generous then susan is not patient or not generous and vice versa.
Everyone who is kind or wise is both not happy and happy.
Everyone who is either not quiet or not humble is not patient and vice versa.
Everyone who is kind is curious or rich.
If someone is either not patient or happy then lucy is not calm or tall and vice versa.
If someone is either funny or not old then susan is either not old or tall and vice versa.
Everyone who is both not rich and curious is either not brave or not creative.
Mary is not happy.
Someone is kind or not generous.
John is both tall and not quiet.
Alice is either not creative or not generous.
Someone is either happy or not patient.
Lucy is both rich and funny.
Someone is not rich or calm. | Alice is not kind. | entailment | (((rich(mary)&patient(mary)))=>((~strong(alice)&~tall(alice))))&
(![X]:((rich(X)|happy(X))<=>(~quiet(X)<~>strong(X))))&
(((tall(mary)&happy(mary)))=>(?[X]:(~calm(X))))&
((?[X]:(~tall(X)))=>((~curious(mary)<~>~funny(mary))))&
(((~humble(lucy)<~>generous(lucy)))=>(?[X]:((~strong(X)&rich(X)))))&
(![X]:((~rich(X)|curious(X))<=>(~generous(X)&creative(X))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((rich(X)|~kind(X))=>~humble(X)))&
(![X]:((brave(X)<~>~quiet(X))=>calm(X)))&
(((generous(lucy)&~generous(lucy)))<=>((~patient(susan)|~generous(susan))))&
(![X]:((kind(X)|wise(X))=>(~happy(X)&happy(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>~patient(X)))&
(![X]:(kind(X)=>(curious(X)|rich(X))))&
((?[X]:((~patient(X)<~>happy(X))))<=>((~calm(lucy)|tall(lucy))))&
((?[X]:((funny(X)<~>~old(X))))<=>((~old(susan)<~>tall(susan))))&
(![X]:((~rich(X)&curious(X))=>(~brave(X)<~>~creative(X))))&
(~happy(mary))&
(?[X]:((kind(X)|~generous(X))))&
((tall(john)&~quiet(john)))&
((~creative(alice)<~>~generous(alice)))&
(?[X]:((happy(X)<~>~patient(X))))&
((rich(lucy)&funny(lucy)))&
(?[X]:((~rich(X)|calm(X)))) | ~kind(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7132261082814817224335430
% SZS output start Proof for 7132261082814817224335430
11. ! [X0] : ((wise(X0) | kind(X0)) => (happy(X0) & ~happy(X0))) [input p10]
24. kind(alice) [input hypothesis]
26. ! [X0] : (kind(X0) => (happy(X0) & ~happy(X0))) [pure predicate removal 11]
36. ! [X0] : ((happy(X0) & ~happy(X0)) | ~kind(X0)) [ennf transformation 26]
108. ~happy(X0) | ~kind(X0) [cnf transformation 36]
109. happy(X0) | ~kind(X0) [cnf transformation 36]
142. kind(alice) [cnf transformation 24]
232. ~kind(X0) [subsumption resolution 108,109]
323. $false [subsumption resolution 142,232]
% SZS output end Proof for 7132261082814817224335430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is either not old or curious and vice versa.
If john is humble then someone is not humble or not strong.
If someone is not quiet then someone is both kind and wise and vice versa.
If susan is not patient or not curious then someone is either not happy or strong and vice versa.
Everyone who is quiet or strong is funny or humble and vice versa.
If alice is both calm and not kind then susan is either not humble or happy and vice versa.
Everyone who is either creative or generous is either not patient or not strong and vice versa.
If mary is both tall and not patient then paul is both not patient and not wise and vice versa.
If alice is both not quiet and generous then someone is either rich or not rich.
Everyone who is not calm or not kind is not old and vice versa.
Everyone who is both patient and not happy is either old or generous.
If someone is quiet then alice is both not tall and generous.
Everyone who is not wise is both happy and funny and vice versa.
If mary is both patient and not funny then someone is either generous or calm.
Everyone who is happy or rich is both not quiet and not kind and vice versa.
Everyone who is humble or not quiet is either not quiet or rich.
Susan is both humble and not curious.
Alice is either not strong or not creative.
Someone is either funny or rich.
Fred is both not strong and calm.
Paul is humble.
Alice is curious or humble.
Fred is not humble or not kind.
Someone is either humble or not wise. | Susan is humble. | entailment | (![X]:(~calm(X)<=>(~old(X)<~>curious(X))))&
((humble(john))=>(?[X]:((~humble(X)|~strong(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~patient(susan)|~curious(susan)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((quiet(X)|strong(X))<=>(funny(X)|humble(X))))&
(((calm(alice)&~kind(alice)))<=>((~humble(susan)<~>happy(susan))))&
(![X]:((creative(X)<~>generous(X))<=>(~patient(X)<~>~strong(X))))&
(((tall(mary)&~patient(mary)))<=>((~patient(paul)&~wise(paul))))&
(((~quiet(alice)&generous(alice)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(old(X)<~>generous(X))))&
((?[X]:(quiet(X)))=>((~tall(alice)&generous(alice))))&
(![X]:(~wise(X)<=>(happy(X)&funny(X))))&
(((patient(mary)&~funny(mary)))=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((happy(X)|rich(X))<=>(~quiet(X)&~kind(X))))&
(![X]:((humble(X)|~quiet(X))=>(~quiet(X)<~>rich(X))))&
((humble(susan)&~curious(susan)))&
((~strong(alice)<~>~creative(alice)))&
(?[X]:((funny(X)<~>rich(X))))&
((~strong(fred)&calm(fred)))&
(humble(paul))&
((curious(alice)|humble(alice)))&
((~humble(fred)|~kind(fred)))&
(?[X]:((humble(X)<~>~wise(X)))) | humble(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1720274550138657341533211
% SZS output start Proof for 1720274550138657341533211
17. ~curious(susan) & humble(susan) [input p16]
25. ~humble(susan) [input hypothesis]
136. humble(susan) [cnf transformation 17]
149. ~humble(susan) [cnf transformation 25]
218. 16 <=> humble(susan) [avatar definition]
285. 16 [avatar split clause 136,218]
325. ~16 [avatar split clause 149,218]
326. $false [avatar sat refutation 285,325]
% SZS output end Proof for 1720274550138657341533211
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is patient or funny and vice versa. Everyone who is both strong and creative is brave or not happy and vice versa. Everyone who is both not funny and funny is not tall and vice versa. Everyone who is not tall is quiet or not humble. If mary is not tall then someone is not rich or not brave and vice versa. If john is either calm or not strong then someone is not wise or quiet. If someone is not curious or not wise then someone is curious or not creative. Everyone who is quiet is either creative or quiet. Everyone who is either rich or not humble is not patient and vice versa. Everyone who is either strong or not brave is creative and vice versa. Everyone who is either strong or humble is either generous or calm and vice versa. Everyone who is either not happy or not curious is either brave or strong. If someone is curious then paul is not happy or generous. Everyone who is either creative or not kind is humble and vice versa. Everyone who is not curious or not kind is both not tall and rich. If paul is either strong or generous then someone is patient and vice versa. Someone is either old or happy. Alice is either humble or quiet. Someone is either not happy or generous. Lucy is not quiet or creative. Someone is creative. Someone is either not curious or generous. Alice is either not patient or calm. Lucy is calm. | Paul is not quiet. | entailment | (![X]:(wise(X)<=>(patient(X)|funny(X))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)|~happy(X))))&
(![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~curious(X)|~kind(X))=>(~tall(X)&rich(X))))&
(((strong(paul)<~>generous(paul)))<=>(?[X]:(patient(X))))&
(?[X]:((old(X)<~>happy(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~patient(alice)<~>calm(alice)))&
(calm(lucy)) | ~quiet(paul) | [
"p1",
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4450933489490854821407940
% SZS output start Proof for 4450933489490854821407940
2. ! [X0] : ((creative(X0) & strong(X0)) <=> (~happy(X0) | brave(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p2]
5. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p4]
8. ! [X0] : (quiet(X0) => (creative(X0) <~> quiet(X0))) [input p7]
25. quiet(paul) [input hypothesis]
31. ! [X0] : ((creative(X0) <~> quiet(X0)) | ~quiet(X0)) [ennf transformation 8]
38. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (~creative(X0) | ~strong(X0)))) [nnf transformation 2]
39. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ~creative(X0) | ~strong(X0))) [flattening 38]
40. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 3]
41. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 40]
42. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 5]
43. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 42]
44. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK0) | ~rich(sK0)) [choice axiom]
45. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK0) | ~rich(sK0)) | tall(mary)) [skolemisation 43,44]
52. ! [X0] : (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~quiet(X0)) [nnf transformation 31]
81. ~brave(X0) | creative(X0) [cnf transformation 39]
84. ~funny(X0) | tall(X0) [cnf transformation 41]
85. tall(X0) | funny(X0) [cnf transformation 41]
89. ~tall(mary) | brave(X0) [cnf transformation 45]
95. ~quiet(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 52]
142. quiet(paul) [cnf transformation 25]
143. ~quiet(X0) | ~creative(X0) [duplicate literal removal 95]
144. tall(X0) [subsumption resolution 84,85]
145. brave(X0) [subsumption resolution 89,144]
275. creative(X0) [resolution 81,145]
285. ~creative(paul) [resolution 143,142]
287. $false [subsumption resolution 285,275]
% SZS output end Proof for 4450933489490854821407940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either old or generous then someone is both not strong and not creative and vice versa.
If paul is wise or curious then lucy is either curious or tall.
Everyone who is either humble or not funny is either not happy or calm.
Everyone who is either not brave or rich is calm or generous and vice versa.
If someone is patient or not brave then lucy is both kind and not funny and vice versa.
Everyone who is both funny and not humble is both not quiet and not old.
If alice is calm then someone is funny or not strong.
If someone is both humble and not wise then mary is not wise and vice versa.
If paul is both strong and not funny then fred is not wise or not humble and vice versa.
Everyone who is not old is tall and vice versa.
If paul is both patient and not strong then someone is either tall or not tall and vice versa.
If someone is not happy then fred is either strong or not rich.
Everyone who is not strong is patient or wise and vice versa.
If paul is either strong or not rich then mary is curious.
If someone is not old or not happy then lucy is not tall or wise and vice versa.
Everyone who is either happy or tall is not happy or not rich and vice versa.
Someone is both not creative and funny.
Paul is both not tall and not humble.
Someone is both generous and not calm.
Lucy is either not kind or not brave.
Mary is calm or brave.
Someone is either wise or not curious.
Alice is not curious or not calm.
Someone is both not creative and old. | Paul is old. | entailment | (((old(fred)<~>generous(fred)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(((wise(paul)|curious(paul)))=>((curious(lucy)<~>tall(lucy))))&
(![X]:((humble(X)<~>~funny(X))=>(~happy(X)<~>calm(X))))&
(![X]:((~brave(X)<~>rich(X))<=>(calm(X)|generous(X))))&
((?[X]:((patient(X)|~brave(X))))<=>((kind(lucy)&~funny(lucy))))&
(![X]:((funny(X)&~humble(X))=>(~quiet(X)&~old(X))))&
((calm(alice))=>(?[X]:((funny(X)|~strong(X)))))&
((?[X]:((humble(X)&~wise(X))))<=>(~wise(mary)))&
(((strong(paul)&~funny(paul)))<=>((~wise(fred)|~humble(fred))))&
(![X]:(~old(X)<=>tall(X)))&
(((patient(paul)&~strong(paul)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
((?[X]:(~happy(X)))=>((strong(fred)<~>~rich(fred))))&
(![X]:(~strong(X)<=>(patient(X)|wise(X))))&
(((strong(paul)<~>~rich(paul)))=>(curious(mary)))&
((?[X]:((~old(X)|~happy(X))))<=>((~tall(lucy)|wise(lucy))))&
(![X]:((happy(X)<~>tall(X))<=>(~happy(X)|~rich(X))))&
(?[X]:((~creative(X)&funny(X))))&
((~tall(paul)&~humble(paul)))&
(?[X]:((generous(X)&~calm(X))))&
((~kind(lucy)<~>~brave(lucy)))&
((calm(mary)|brave(mary)))&
(?[X]:((wise(X)<~>~curious(X))))&
((~curious(alice)|~calm(alice)))&
(?[X]:((~creative(X)&old(X)))) | old(paul) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3980140432303585929665769
% SZS output start Proof for 3980140432303585929665769
10. ! [X0] : (~old(X0) <=> tall(X0)) [input p9]
18. ~humble(paul) & ~tall(paul) [input p17]
25. ~old(paul) [input hypothesis]
55. ! [X0] : ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0))) [nnf transformation 10]
117. tall(X0) | old(X0) [cnf transformation 55]
144. ~tall(paul) [cnf transformation 18]
156. ~old(paul) [cnf transformation 25]
376. old(paul) [resolution 117,144]
378. $false [subsumption resolution 376,156]
% SZS output end Proof for 3980140432303585929665769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not brave is both rich and not brave and vice versa.
If someone is not tall or curious then someone is not funny.
Everyone who is not funny is either not tall or generous and vice versa.
If john is either old or generous then someone is both brave and humble and vice versa.
Everyone who is both strong and not strong is either not old or happy.
Everyone who is either generous or patient is quiet or not rich and vice versa.
If someone is either not happy or curious then paul is not generous or wise and vice versa.
If lucy is not calm then john is not generous or curious and vice versa.
Everyone who is not calm or not happy is either not kind or quiet and vice versa.
Everyone who is both not strong and quiet is strong and vice versa.
Everyone who is not rich is both not creative and not quiet and vice versa.
Everyone who is both not tall and strong is generous or not wise and vice versa.
If alice is wise then someone is either old or not patient.
If susan is both brave and not quiet then someone is old or calm and vice versa.
Everyone who is either rich or funny is creative and vice versa.
Everyone who is both strong and not generous is either not wise or not curious and vice versa.
Someone is either not calm or not happy.
Someone is not tall.
Someone is both humble and rich.
Fred is quiet or not quiet.
Someone is both not strong and calm.
Someone is both wise and not tall. | John is tall. | contradiction | (![X]:((quiet(X)|~brave(X))<=>(rich(X)&~brave(X))))&
((?[X]:((~tall(X)|curious(X))))=>(?[X]:(~funny(X))))&
(![X]:(~funny(X)<=>(~tall(X)<~>generous(X))))&
(((old(john)<~>generous(john)))<=>(?[X]:((brave(X)&humble(X)))))&
(![X]:((strong(X)&~strong(X))=>(~old(X)<~>happy(X))))&
(![X]:((generous(X)<~>patient(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((~happy(X)<~>curious(X))))<=>((~generous(paul)|wise(paul))))&
((~calm(lucy))<=>((~generous(john)|curious(john))))&
(![X]:((~calm(X)|~happy(X))<=>(~kind(X)<~>quiet(X))))&
(![X]:((~strong(X)&quiet(X))<=>strong(X)))&
(![X]:(~rich(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((~tall(X)&strong(X))<=>(generous(X)|~wise(X))))&
((wise(alice))=>(?[X]:((old(X)<~>~patient(X)))))&
(((brave(susan)&~quiet(susan)))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((rich(X)<~>funny(X))<=>creative(X)))&
(![X]:((strong(X)&~generous(X))<=>(~wise(X)<~>~curious(X))))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((humble(X)&rich(X))))&
((quiet(fred)|~quiet(fred)))&
(?[X]:((~strong(X)&calm(X))))&
(?[X]:((wise(X)&~tall(X)))) | tall(john) | [
"p2",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2153276443529738345239855
% SZS output start Proof for 2153276443529738345239855
3. ! [X0] : (~funny(X0) <=> (~tall(X0) <~> generous(X0))) [input p2]
10. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : (~rich(X0) <=> (~quiet(X0) & ~creative(X0))) [input p10]
12. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~wise(X0) | generous(X0))) [input p11]
15. ! [X0] : ((rich(X0) <~> funny(X0)) <=> creative(X0)) [input p14]
23. tall(john) [input hypothesis]
34. ! [X0] : ((~funny(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | funny(X0))) [nnf transformation 3]
51. ! [X0] : (((quiet(X0) & ~strong(X0)) | ~strong(X0)) & (strong(X0) | (~quiet(X0) | strong(X0)))) [nnf transformation 10]
52. ! [X0] : (((quiet(X0) & ~strong(X0)) | ~strong(X0)) & (strong(X0) | ~quiet(X0) | strong(X0))) [flattening 51]
53. ! [X0] : ((~rich(X0) | (quiet(X0) | creative(X0))) & ((~quiet(X0) & ~creative(X0)) | rich(X0))) [nnf transformation 11]
54. ! [X0] : ((~rich(X0) | quiet(X0) | creative(X0)) & ((~quiet(X0) & ~creative(X0)) | rich(X0))) [flattening 53]
55. ! [X0] : (((strong(X0) & ~tall(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 12]
56. ! [X0] : (((strong(X0) & ~tall(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | ~strong(X0) | tall(X0))) [flattening 55]
65. ! [X0] : ((((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ~creative(X0)) & (creative(X0) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0))))) [nnf transformation 15]
86. ~tall(X0) | generous(X0) | funny(X0) [cnf transformation 34]
119. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 52]
120. ~strong(X0) | ~strong(X0) [cnf transformation 52]
122. ~creative(X0) | rich(X0) [cnf transformation 54]
124. ~rich(X0) | quiet(X0) | creative(X0) [cnf transformation 54]
128. strong(X0) | ~generous(X0) [cnf transformation 56]
138. creative(X0) | rich(X0) | ~funny(X0) [cnf transformation 65]
140. ~funny(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 65]
157. tall(john) [cnf transformation 23]
158. strong(X0) | ~quiet(X0) [duplicate literal removal 119]
159. ~strong(X0) [duplicate literal removal 120]
236. ~quiet(X0) [subsumption resolution 158,159]
237. ~rich(X0) | creative(X0) [subsumption resolution 124,236]
239. ~generous(X0) [subsumption resolution 128,159]
274. ~creative(X0) | ~funny(X0) [subsumption resolution 140,122]
275. creative(X0) | ~funny(X0) [subsumption resolution 138,237]
276. ~funny(X0) [subsumption resolution 275,274]
305. generous(john) | funny(john) [resolution 86,157]
306. funny(john) [subsumption resolution 305,239]
307. $false [subsumption resolution 306,276]
% SZS output end Proof for 2153276443529738345239855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and strong is either not brave or quiet and vice versa.
Everyone who is both not generous and old is not brave.
Everyone who is either creative or kind is creative or not patient.
Everyone who is not kind is both quiet and not quiet.
If someone is not funny or not curious then paul is not wise.
Everyone who is not generous or not tall is either curious or not calm.
If someone is both brave and not strong then lucy is not creative and vice versa.
Everyone who is not tall or tall is not strong.
Everyone who is both wise and not happy is not quiet or wise and vice versa.
If someone is either not wise or kind then susan is brave and vice versa.
Everyone who is not funny is either not generous or not tall and vice versa.
Everyone who is patient or creative is not brave or not funny and vice versa.
Everyone who is not funny is not humble and vice versa.
Everyone who is both not patient and not curious is not brave or not curious and vice versa.
If paul is either humble or old then someone is either not quiet or happy.
Everyone who is not strong or happy is both not creative and not quiet and vice versa.
Fred is not old or generous.
Fred is patient or not patient.
John is generous or patient.
Someone is tall.
Fred is not kind or not patient. | Susan is generous. | neutral | (![X]:((~rich(X)&strong(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:((~generous(X)&old(X))=>~brave(X)))&
(![X]:((creative(X)<~>kind(X))=>(creative(X)|~patient(X))))&
(![X]:(~kind(X)=>(quiet(X)&~quiet(X))))&
((?[X]:((~funny(X)|~curious(X))))=>(~wise(paul)))&
(![X]:((~generous(X)|~tall(X))=>(curious(X)<~>~calm(X))))&
((?[X]:((brave(X)&~strong(X))))<=>(~creative(lucy)))&
(![X]:((~tall(X)|tall(X))=>~strong(X)))&
(![X]:((wise(X)&~happy(X))<=>(~quiet(X)|wise(X))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(brave(susan)))&
(![X]:(~funny(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((patient(X)|creative(X))<=>(~brave(X)|~funny(X))))&
(![X]:(~funny(X)<=>~humble(X)))&
(![X]:((~patient(X)&~curious(X))<=>(~brave(X)|~curious(X))))&
(((humble(paul)<~>old(paul)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((~strong(X)|happy(X))<=>(~creative(X)&~quiet(X))))&
((~old(fred)|generous(fred)))&
((patient(fred)|~patient(fred)))&
((generous(john)|patient(john)))&
(?[X]:(tall(X)))&
((~kind(fred)|~patient(fred))) | generous(susan) | [] | null | 0 |
Everyone who is not strong is either patient or not brave. Everyone who is not calm is strong. Everyone who is both not creative and not rich is both funny and not wise. Everyone who is both not calm and not humble is both brave and old and vice versa. Everyone who is both not creative and not rich is either patient or humble and vice versa. Everyone who is old is quiet and vice versa. Everyone who is either not creative or calm is both tall and not wise and vice versa. Everyone who is kind or old is not wise or calm and vice versa. Everyone who is both not humble and strong is not creative or not generous. Everyone who is rich or kind is rich or patient. Everyone who is not humble is humble or calm. Everyone who is not funny or strong is either patient or quiet and vice versa. If alice is curious or humble then mary is wise or quiet and vice versa. Everyone who is both tall and not brave is not creative or happy. If someone is not calm or not quiet then fred is both not curious and curious and vice versa. Everyone who is not patient is wise and vice versa. Susan is either not curious or rich. Alice is brave or not patient. Someone is either not patient or curious. Someone is rich. Someone is not happy or not tall. Someone is both not tall and funny. Someone is either not funny or brave. | Susan is not funny. | neutral | (![X]:(~strong(X)=>(patient(X)<~>~brave(X))))&
(![X]:(~calm(X)=>strong(X)))&
(![X]:((~creative(X)&~rich(X))=>(funny(X)&~wise(X))))&
(![X]:((~calm(X)&~humble(X))<=>(brave(X)&old(X))))&
(![X]:((~creative(X)&~rich(X))<=>(patient(X)<~>humble(X))))&
(![X]:(old(X)<=>quiet(X)))&
(![X]:((~creative(X)<~>calm(X))<=>(tall(X)&~wise(X))))&
(![X]:((kind(X)|old(X))<=>(~wise(X)|calm(X))))&
(![X]:((~humble(X)&strong(X))=>(~creative(X)|~generous(X))))&
(![X]:((rich(X)|kind(X))=>(rich(X)|patient(X))))&
(![X]:(~humble(X)=>(humble(X)|calm(X))))&
(![X]:((~funny(X)|strong(X))<=>(patient(X)<~>quiet(X))))&
(((curious(alice)|humble(alice)))<=>((wise(mary)|quiet(mary))))&
(![X]:((tall(X)&~brave(X))=>(~creative(X)|happy(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~curious(fred)&curious(fred))))&
(![X]:(~patient(X)<=>wise(X)))&
((~curious(susan)<~>rich(susan)))&
((brave(alice)|~patient(alice)))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((~happy(X)|~tall(X))))&
(?[X]:((~tall(X)&funny(X))))&
(?[X]:((~funny(X)<~>brave(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is quiet is either funny or not rich. Everyone who is not brave is patient and vice versa. If john is either not generous or not tall then fred is old or not kind and vice versa. Everyone who is quiet is not quiet or not creative. If someone is either patient or curious then someone is both happy and not funny and vice versa. If mary is humble or not brave then someone is quiet and vice versa. If susan is quiet then someone is quiet or calm and vice versa. Everyone who is rich or not quiet is humble or not old and vice versa. Everyone who is not quiet or not tall is creative. If someone is not kind or not wise then fred is either patient or not tall. Everyone who is either not creative or creative is either curious or creative. If someone is either not wise or not patient then someone is both not tall and creative. Everyone who is either calm or not quiet is both generous and not quiet. Everyone who is both quiet and not tall is happy and vice versa. If mary is patient or not wise then someone is either rich or old. Everyone who is both not creative and not humble is either generous or wise. Someone is not kind or creative. Fred is both generous and quiet. Lucy is both wise and not tall. Someone is tall. Fred is both not rich and patient. | Susan is not old. | neutral | (![X]:(quiet(X)=>(funny(X)<~>~rich(X))))&
(![X]:(~brave(X)<=>patient(X)))&
(((~generous(john)<~>~tall(john)))<=>((old(fred)|~kind(fred))))&
(![X]:(quiet(X)=>(~quiet(X)|~creative(X))))&
((?[X]:((patient(X)<~>curious(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(((humble(mary)|~brave(mary)))<=>(?[X]:(quiet(X))))&
((quiet(susan))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((rich(X)|~quiet(X))<=>(humble(X)|~old(X))))&
(![X]:((~quiet(X)|~tall(X))=>creative(X)))&
((?[X]:((~kind(X)|~wise(X))))=>((patient(fred)<~>~tall(fred))))&
(![X]:((~creative(X)<~>creative(X))=>(curious(X)<~>creative(X))))&
((?[X]:((~wise(X)<~>~patient(X))))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:((calm(X)<~>~quiet(X))=>(generous(X)&~quiet(X))))&
(![X]:((quiet(X)&~tall(X))<=>happy(X)))&
(((patient(mary)|~wise(mary)))=>(?[X]:((rich(X)<~>old(X)))))&
(![X]:((~creative(X)&~humble(X))=>(generous(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((generous(fred)&quiet(fred)))&
((wise(lucy)&~tall(lucy)))&
(?[X]:(tall(X)))&
((~rich(fred)&patient(fred))) | ~old(susan) | [] | null | 0 |
Everyone who is either not patient or not kind is either tall or happy and vice versa. Everyone who is happy or not creative is either calm or not happy and vice versa. Everyone who is both rich and creative is both not old and calm and vice versa. If paul is not calm or patient then someone is happy and vice versa. Everyone who is either not funny or not creative is both not rich and not patient and vice versa. If mary is not tall or not curious then fred is both not brave and not creative. Everyone who is calm or curious is either not funny or not brave and vice versa. If someone is not curious then fred is rich or not funny and vice versa. If fred is tall or wise then someone is either not kind or kind and vice versa. If susan is curious or not brave then fred is either creative or not generous. If susan is both tall and not brave then someone is funny. Everyone who is both not generous and not quiet is not brave or not generous. Everyone who is not generous or rich is not funny. If mary is both not funny and not generous then someone is both not curious and not wise. If someone is either not wise or not curious then someone is rich and vice versa. If someone is not calm then someone is not calm or funny and vice versa. Susan is not patient. Fred is funny or brave. Susan is not wise. Someone is both not calm and strong. Someone is not generous or not quiet. Someone is not happy. Someone is strong or not patient. Lucy is either quiet or not curious. | Lucy is old. | neutral | (![X]:((~patient(X)<~>~kind(X))<=>(tall(X)<~>happy(X))))&
(![X]:((happy(X)|~creative(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((rich(X)&creative(X))<=>(~old(X)&calm(X))))&
(((~calm(paul)|patient(paul)))<=>(?[X]:(happy(X))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~rich(X)&~patient(X))))&
(((~tall(mary)|~curious(mary)))=>((~brave(fred)&~creative(fred))))&
(![X]:((calm(X)|curious(X))<=>(~funny(X)<~>~brave(X))))&
((?[X]:(~curious(X)))<=>((rich(fred)|~funny(fred))))&
(((tall(fred)|wise(fred)))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(((curious(susan)|~brave(susan)))=>((creative(fred)<~>~generous(fred))))&
(((tall(susan)&~brave(susan)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)|rich(X))=>~funny(X)))&
(((~funny(mary)&~generous(mary)))=>(?[X]:((~curious(X)&~wise(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(~patient(susan))&
((funny(fred)|brave(fred)))&
(~wise(susan))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(~happy(X)))&
(?[X]:((strong(X)|~patient(X))))&
((quiet(lucy)<~>~curious(lucy))) | old(lucy) | [] | null | 0 |
If someone is quiet then john is not rich or not wise.
If someone is either happy or not old then paul is both calm and not humble.
Everyone who is strong or not patient is brave and vice versa.
Everyone who is both rich and creative is old and vice versa.
Everyone who is patient or brave is either kind or not humble.
If paul is not patient or humble then john is either calm or funny and vice versa.
If someone is both quiet and not brave then someone is either not wise or tall and vice versa.
If someone is not creative then paul is either old or kind and vice versa.
Everyone who is not brave or strong is humble or not brave.
If paul is not quiet or not tall then fred is not creative or not brave.
If mary is both kind and brave then john is both kind and wise.
Everyone who is tall or not calm is not curious.
If susan is old or kind then someone is both not kind and not happy and vice versa.
Everyone who is not curious is both not patient and patient.
Everyone who is either not humble or kind is either not calm or not brave and vice versa.
If alice is both not funny and not quiet then fred is either not brave or old.
Someone is not creative.
Alice is both generous and not happy.
Lucy is quiet.
Someone is either patient or not wise.
Someone is either funny or not patient.
Someone is either old or not quiet.
Mary is not generous or not kind. | Alice is patient. | entailment | ((?[X]:(quiet(X)))=>((~rich(john)|~wise(john))))&
((?[X]:((happy(X)<~>~old(X))))=>((calm(paul)&~humble(paul))))&
(![X]:((strong(X)|~patient(X))<=>brave(X)))&
(![X]:((rich(X)&creative(X))<=>old(X)))&
(![X]:((patient(X)|brave(X))=>(kind(X)<~>~humble(X))))&
(((~patient(paul)|humble(paul)))<=>((calm(john)<~>funny(john))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~creative(X)))<=>((old(paul)<~>kind(paul))))&
(![X]:((~brave(X)|strong(X))=>(humble(X)|~brave(X))))&
(((~quiet(paul)|~tall(paul)))=>((~creative(fred)|~brave(fred))))&
(((kind(mary)&brave(mary)))=>((kind(john)&wise(john))))&
(![X]:((tall(X)|~calm(X))=>~curious(X)))&
(((old(susan)|kind(susan)))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(~curious(X)=>(~patient(X)&patient(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(~calm(X)<~>~brave(X))))&
(((~funny(alice)&~quiet(alice)))=>((~brave(fred)<~>old(fred))))&
(?[X]:(~creative(X)))&
((generous(alice)&~happy(alice)))&
(quiet(lucy))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((old(X)<~>~quiet(X))))&
((~generous(mary)|~kind(mary))) | patient(alice) | [
"p2",
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4138396205831202413291273
% SZS output start Proof for 4138396205831202413291273
3. ! [X0] : ((~patient(X0) | strong(X0)) <=> brave(X0)) [input p2]
5. ! [X0] : ((brave(X0) | patient(X0)) => (kind(X0) <~> ~humble(X0))) [input p4]
12. ! [X0] : ((~calm(X0) | tall(X0)) => ~curious(X0)) [input p11]
14. ! [X0] : (~curious(X0) => (patient(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~humble(X0) <~> kind(X0)) <=> (~calm(X0) <~> ~brave(X0))) [input p14]
24. ~patient(alice) [input hypothesis]
29. ! [X0] : ((kind(X0) <~> ~humble(X0)) | (~brave(X0) & ~patient(X0))) [ennf transformation 5]
36. ! [X0] : (~curious(X0) | (calm(X0) & ~tall(X0))) [ennf transformation 12]
37. ! [X0] : ((patient(X0) & ~patient(X0)) | curious(X0)) [ennf transformation 14]
41. ! [X0] : (((~patient(X0) | strong(X0)) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((~patient(X0) | strong(X0) | ~brave(X0)) & (brave(X0) | (patient(X0) & ~strong(X0)))) [flattening 41]
45. ! [X0] : (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | (~brave(X0) & ~patient(X0))) [nnf transformation 29]
62. ! [X0] : ((((~kind(X0) | humble(X0)) & (kind(X0) | ~humble(X0))) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ((~humble(X0) | ~kind(X0)) & (kind(X0) | humble(X0))))) [nnf transformation 15]
81. brave(X0) | patient(X0) [cnf transformation 42]
87. ~humble(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
89. humble(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 45]
113. ~curious(X0) | calm(X0) [cnf transformation 36]
119. ~patient(X0) | curious(X0) [cnf transformation 37]
120. curious(X0) | patient(X0) [cnf transformation 37]
121. ~brave(X0) | ~calm(X0) | kind(X0) | humble(X0) [cnf transformation 62]
122. ~brave(X0) | ~calm(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 62]
126. kind(X0) | ~humble(X0) | ~calm(X0) | brave(X0) [cnf transformation 62]
142. ~patient(alice) [cnf transformation 24]
298. curious(X0) [subsumption resolution 119,120]
300. kind(X0) | ~humble(X0) | ~calm(X0) [subsumption resolution 126,87]
301. ~brave(X0) | ~calm(X0) | ~kind(X0) [subsumption resolution 122,89]
302. ~brave(X0) | ~calm(X0) | kind(X0) [subsumption resolution 121,300]
303. ~brave(X0) | ~calm(X0) [subsumption resolution 302,301]
355. calm(X0) [resolution 113,298]
375. ~calm(X0) | patient(X0) [resolution 303,81]
376. patient(X0) [subsumption resolution 375,355]
379. $false [resolution 376,142]
% SZS output end Proof for 4138396205831202413291273
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not happy is patient and vice versa.
Everyone who is both brave and not calm is both not old and humble.
If someone is patient or wise then fred is tall or calm.
If someone is not funny or rich then alice is both not funny and tall and vice versa.
Everyone who is not rich is both not calm and not creative.
Everyone who is not old is old or not rich.
Everyone who is either rich or not patient is not old or not quiet and vice versa.
If someone is both not humble and not generous then someone is either brave or not generous and vice versa.
Everyone who is either not curious or not patient is either calm or not creative and vice versa.
If someone is not kind then someone is funny or patient and vice versa.
Everyone who is both wise and quiet is either not quiet or calm and vice versa.
If someone is not old or curious then lucy is either not kind or old and vice versa.
Everyone who is happy is not happy.
Everyone who is not calm or not generous is either calm or not happy and vice versa.
Everyone who is not tall or not rich is not humble or tall and vice versa.
If someone is quiet or kind then fred is calm and vice versa.
Someone is curious.
John is either not creative or not quiet.
Someone is either not tall or not kind.
Someone is both humble and not kind.
Susan is either generous or rich.
Someone is not brave or brave. | Fred is not humble. | entailment | (![X]:((strong(X)|~happy(X))<=>patient(X)))&
(![X]:((brave(X)&~calm(X))=>(~old(X)&humble(X))))&
((?[X]:((patient(X)|wise(X))))=>((tall(fred)|calm(fred))))&
((?[X]:((~funny(X)|rich(X))))<=>((~funny(alice)&tall(alice))))&
(![X]:(~rich(X)=>(~calm(X)&~creative(X))))&
(![X]:(~old(X)=>(old(X)|~rich(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~old(X)|~quiet(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~curious(X)<~>~patient(X))<=>(calm(X)<~>~creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((wise(X)&quiet(X))<=>(~quiet(X)<~>calm(X))))&
((?[X]:((~old(X)|curious(X))))<=>((~kind(lucy)<~>old(lucy))))&
(![X]:(happy(X)=>~happy(X)))&
(![X]:((~calm(X)|~generous(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~rich(X))<=>(~humble(X)|tall(X))))&
((?[X]:((quiet(X)|kind(X))))<=>(calm(fred)))&
(?[X]:(curious(X)))&
((~creative(john)<~>~quiet(john)))&
(?[X]:((~tall(X)<~>~kind(X))))&
(?[X]:((humble(X)&~kind(X))))&
((generous(susan)<~>rich(susan)))&
(?[X]:((~brave(X)|brave(X)))) | ~humble(fred) | [
"p0",
"p4",
"p5",
"p6",
"p11",
"p12",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 245828620524569035957455
% SZS output start Proof for 245828620524569035957455
1. ! [X0] : ((~happy(X0) | strong(X0)) <=> patient(X0)) [input p0]
5. ! [X0] : (~rich(X0) => (~creative(X0) & ~calm(X0))) [input p4]
6. ! [X0] : (~old(X0) => (~rich(X0) | old(X0))) [input p5]
7. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> (~quiet(X0) | ~old(X0))) [input p6]
12. ? [X0] : (curious(X0) | ~old(X0)) <=> (~kind(lucy) <~> old(lucy)) [input p11]
13. ! [X0] : (happy(X0) => ~happy(X0)) [input p12]
15. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> (tall(X0) | ~humble(X0))) [input p14]
16. ? [X0] : (kind(X0) | quiet(X0)) <=> calm(fred) [input p15]
17. ? [X0] : curious(X0) [input p16]
23. humble(fred) [input hypothesis]
30. ! [X0] : ((~creative(X0) & ~calm(X0)) | rich(X0)) [ennf transformation 5]
31. ! [X0] : ((~rich(X0) | old(X0)) | old(X0)) [ennf transformation 6]
32. ! [X0] : (~rich(X0) | old(X0) | old(X0)) [flattening 31]
33. ! [X0] : (~happy(X0) | ~happy(X0)) [ennf transformation 13]
34. ! [X0] : (((~happy(X0) | strong(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : ((~happy(X0) | strong(X0) | ~patient(X0)) & (patient(X0) | (happy(X0) & ~strong(X0)))) [flattening 34]
41. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 7]
42. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [flattening 41]
56. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X0] : (~curious(X0) & old(X0))) [nnf transformation 12]
57. (? [X0] : (curious(X0) | ~old(X0)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [rectify 56]
58. ? [X0] : (curious(X0) | ~old(X0)) => (curious(sK5) | ~old(sK5)) [choice axiom]
59. ((curious(sK5) | ~old(sK5)) | ((~kind(lucy) | ~old(lucy)) & (old(lucy) | kind(lucy)))) & (((~old(lucy) | kind(lucy)) & (old(lucy) | ~kind(lucy))) | ! [X1] : (~curious(X1) & old(X1))) [skolemisation 57,58]
62. ! [X0] : (((~rich(X0) | ~tall(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (rich(X0) & tall(X0)))) [nnf transformation 15]
63. ! [X0] : ((~rich(X0) | ~tall(X0) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | (rich(X0) & tall(X0)))) [flattening 62]
64. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X0] : (~kind(X0) & ~quiet(X0))) [nnf transformation 16]
65. (? [X0] : (kind(X0) | quiet(X0)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [rectify 64]
66. ? [X0] : (kind(X0) | quiet(X0)) => (kind(sK6) | quiet(sK6)) [choice axiom]
67. ((kind(sK6) | quiet(sK6)) | ~calm(fred)) & (calm(fred) | ! [X1] : (~kind(X1) & ~quiet(X1))) [skolemisation 65,66]
68. ? [X0] : curious(X0) => curious(sK7) [choice axiom]
69. curious(sK7) [skolemisation 17,68]
80. patient(X0) | happy(X0) [cnf transformation 35]
91. ~calm(X0) | rich(X0) [cnf transformation 30]
93. ~rich(X0) | old(X0) | old(X0) [cnf transformation 32]
96. ~patient(X0) | rich(X0) | old(X0) [cnf transformation 42]
126. ~old(lucy) | kind(lucy) | ~curious(X1) [cnf transformation 59]
129. ~happy(X0) | ~happy(X0) [cnf transformation 33]
136. tall(X0) | ~humble(X0) | tall(X0) [cnf transformation 63]
139. ~rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 63]
141. calm(fred) | ~kind(X1) [cnf transformation 67]
143. curious(sK7) [cnf transformation 69]
153. humble(fred) [cnf transformation 23]
154. ~humble(X0) | tall(X0) [duplicate literal removal 136]
155. ~rich(X0) | ~tall(X0) [duplicate literal removal 139]
158. ~happy(X0) [duplicate literal removal 129]
161. ~rich(X0) | old(X0) [duplicate literal removal 93]
166. 2 <=> tall(fred) [avatar definition]
168. tall(fred) <- (2) [avatar component clause 166]
170. 3 <=> calm(fred) [avatar definition]
172. calm(fred) <- (3) [avatar component clause 170]
205. ~patient(X0) | old(X0) [subsumption resolution 96,161]
261. 23 <=> old(lucy) [avatar definition]
263. ~old(lucy) <- (~23) [avatar component clause 261]
265. 24 <=> kind(lucy) [avatar definition]
266. kind(lucy) <- (24) [avatar component clause 265]
279. 27 <=> ! [X1] : ~curious(X1) [avatar definition]
280. ~curious(X1) <- (27) [avatar component clause 279]
281. 27 | 24 | ~23 [avatar split clause 126,261,265,279]
283. 28 <=> ! [X1] : old(X1) [avatar definition]
284. old(X1) <- (28) [avatar component clause 283]
299. 31 <=> ! [X1] : ~kind(X1) [avatar definition]
300. ~kind(X1) <- (31) [avatar component clause 299]
301. 31 | 3 [avatar split clause 141,170,299]
345. rich(fred) <- (3) [resolution 91,172]
348. tall(fred) [resolution 154,153]
349. 2 [avatar split clause 348,166]
350. ~tall(fred) <- (3) [resolution 155,345]
351. $false <- (2, 3) [subsumption resolution 350,168]
352. ~2 | ~3 [avatar contradiction clause 351]
359. old(X0) | happy(X0) [resolution 205,80]
360. old(X0) [subsumption resolution 359,158]
361. 28 [avatar split clause 360,283]
362. $false <- (~23, 28) [resolution 284,263]
365. 23 | ~28 [avatar contradiction clause 362]
366. $false <- (24, 31) [subsumption resolution 266,300]
367. ~24 | ~31 [avatar contradiction clause 366]
368. $false <- (27) [resolution 280,143]
371. ~27 [avatar contradiction clause 368]
372. $false [avatar sat refutation 281,301,349,352,361,365,367,371]
% SZS output end Proof for 245828620524569035957455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not strong or brave then paul is quiet or not quiet.
If mary is both calm and kind then alice is not old or not wise and vice versa.
Everyone who is both curious and quiet is either not generous or not brave.
Everyone who is both old and not happy is not wise or not patient and vice versa.
Everyone who is both wise and calm is generous or quiet.
Everyone who is either not curious or not wise is not rich.
Everyone who is not generous is happy or not kind and vice versa.
Everyone who is both wise and tall is both brave and rich and vice versa.
Everyone who is either humble or wise is either not strong or not curious.
Everyone who is not humble or not rich is kind.
Everyone who is either generous or not brave is both wise and creative and vice versa.
Everyone who is both not old and not quiet is either kind or not rich and vice versa.
Everyone who is brave or not humble is not brave.
If mary is not brave or humble then someone is happy and vice versa.
If someone is rich then susan is quiet and vice versa.
Everyone who is not funny or patient is either not brave or kind and vice versa.
Someone is generous or calm.
Alice is curious or not rich.
Susan is not wise or not strong.
Fred is not kind or quiet.
Lucy is tall.
Mary is either not funny or not humble. | Lucy is not happy. | entailment | (((~strong(lucy)|brave(lucy)))=>((quiet(paul)|~quiet(paul))))&
(((calm(mary)&kind(mary)))<=>((~old(alice)|~wise(alice))))&
(![X]:((curious(X)&quiet(X))=>(~generous(X)<~>~brave(X))))&
(![X]:((old(X)&~happy(X))<=>(~wise(X)|~patient(X))))&
(![X]:((wise(X)&calm(X))=>(generous(X)|quiet(X))))&
(![X]:((~curious(X)<~>~wise(X))=>~rich(X)))&
(![X]:(~generous(X)<=>(happy(X)|~kind(X))))&
(![X]:((wise(X)&tall(X))<=>(brave(X)&rich(X))))&
(![X]:((humble(X)<~>wise(X))=>(~strong(X)<~>~curious(X))))&
(![X]:((~humble(X)|~rich(X))=>kind(X)))&
(![X]:((generous(X)<~>~brave(X))<=>(wise(X)&creative(X))))&
(![X]:((~old(X)&~quiet(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)|~humble(X))=>~brave(X)))&
(((~brave(mary)|humble(mary)))<=>(?[X]:(happy(X))))&
((?[X]:(rich(X)))<=>(quiet(susan)))&
(![X]:((~funny(X)|patient(X))<=>(~brave(X)<~>kind(X))))&
(?[X]:((generous(X)|calm(X))))&
((curious(alice)|~rich(alice)))&
((~wise(susan)|~strong(susan)))&
((~kind(fred)|quiet(fred)))&
(tall(lucy))&
((~funny(mary)<~>~humble(mary))) | ~happy(lucy) | [
"p3",
"p7",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 383447409408722831824460
% SZS output start Proof for 383447409408722831824460
4. ! [X0] : ((~happy(X0) & old(X0)) <=> (~patient(X0) | ~wise(X0))) [input p3]
8. ! [X0] : ((tall(X0) & wise(X0)) <=> (rich(X0) & brave(X0))) [input p7]
13. ! [X0] : ((~humble(X0) | brave(X0)) => ~brave(X0)) [input p12]
21. tall(lucy) [input p20]
23. happy(lucy) [input hypothesis]
33. ! [X0] : (~brave(X0) | (humble(X0) & ~brave(X0))) [ennf transformation 13]
37. ! [X0] : (((~happy(X0) & old(X0)) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 4]
38. ! [X0] : (((~happy(X0) & old(X0)) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | happy(X0) | ~old(X0))) [flattening 37]
42. ! [X0] : (((tall(X0) & wise(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 8]
43. ! [X0] : (((tall(X0) & wise(X0)) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | ~tall(X0) | ~wise(X0))) [flattening 42]
75. ~happy(X0) | wise(X0) [cnf transformation 38]
83. ~tall(X0) | brave(X0) | ~wise(X0) [cnf transformation 43]
105. ~brave(X0) | ~brave(X0) [cnf transformation 33]
122. tall(lucy) [cnf transformation 21]
125. happy(lucy) [cnf transformation 23]
126. ~brave(X0) [duplicate literal removal 105]
221. wise(lucy) [resolution 75,125]
279. brave(lucy) | ~wise(lucy) [resolution 83,122]
280. ~wise(lucy) [subsumption resolution 279,126]
281. $false [subsumption resolution 280,221]
% SZS output end Proof for 383447409408722831824460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or brave is curious or generous.
Everyone who is both not brave and generous is not rich and vice versa.
If someone is either not quiet or creative then someone is patient and vice versa.
Everyone who is not funny or strong is strong or not generous and vice versa.
If someone is not quiet or curious then lucy is humble or happy.
Everyone who is either humble or curious is not humble.
Everyone who is calm or strong is both strong and not strong.
Everyone who is both brave and not funny is not strong or creative and vice versa.
Everyone who is wise is rich.
Everyone who is either creative or old is patient or not creative and vice versa.
Everyone who is both not strong and not old is either rich or creative and vice versa.
If paul is both not kind and brave then paul is either strong or not patient.
If mary is not happy or not calm then someone is kind.
Everyone who is not rich is both not calm and kind.
If paul is curious then susan is calm or old.
If someone is wise then mary is happy.
Someone is both not wise and humble.
Someone is either old or not kind.
Someone is both not humble and curious.
Someone is not wise or not humble.
Someone is both not happy and not kind. | Mary is curious. | entailment | (![X]:((~quiet(X)|brave(X))=>(curious(X)|generous(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~quiet(X)|curious(X))))=>((humble(lucy)|happy(lucy))))&
(![X]:((humble(X)<~>curious(X))=>~humble(X)))&
(![X]:((calm(X)|strong(X))=>(strong(X)&~strong(X))))&
(![X]:((brave(X)&~funny(X))<=>(~strong(X)|creative(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((creative(X)<~>old(X))<=>(patient(X)|~creative(X))))&
(![X]:((~strong(X)&~old(X))<=>(rich(X)<~>creative(X))))&
(((~kind(paul)&brave(paul)))=>((strong(paul)<~>~patient(paul))))&
(((~happy(mary)|~calm(mary)))=>(?[X]:(kind(X))))&
(![X]:(~rich(X)=>(~calm(X)&kind(X))))&
((curious(paul))=>((calm(susan)|old(susan))))&
((?[X]:(wise(X)))=>(happy(mary)))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~happy(X)&~kind(X)))) | curious(mary) | [
"p0",
"p3",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 88803480339941152822227
% SZS output start Proof for 88803480339941152822227
1. ! [X0] : ((brave(X0) | ~quiet(X0)) => (generous(X0) | curious(X0))) [input p0]
4. ! [X0] : ((strong(X0) | ~funny(X0)) <=> (~generous(X0) | strong(X0))) [input p3]
7. ! [X0] : ((strong(X0) | calm(X0)) => (~strong(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & brave(X0)) <=> (creative(X0) | ~strong(X0))) [input p7]
22. ~curious(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) | curious(X0)) | (~brave(X0) & quiet(X0))) [ennf transformation 1]
29. ! [X0] : (generous(X0) | curious(X0) | (~brave(X0) & quiet(X0))) [flattening 28]
33. ! [X0] : ((~strong(X0) & strong(X0)) | (~strong(X0) & ~calm(X0))) [ennf transformation 7]
47. ! [X0] : (((strong(X0) | ~funny(X0)) | (generous(X0) & ~strong(X0))) & ((~generous(X0) | strong(X0)) | (~strong(X0) & funny(X0)))) [nnf transformation 4]
48. ! [X0] : ((strong(X0) | ~funny(X0) | (generous(X0) & ~strong(X0))) & (~generous(X0) | strong(X0) | (~strong(X0) & funny(X0)))) [flattening 47]
50. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | funny(X0) | ~brave(X0))) [flattening 50]
69. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 29]
77. ~generous(X0) | strong(X0) | funny(X0) [cnf transformation 48]
88. ~strong(X0) | ~strong(X0) [cnf transformation 33]
90. brave(X0) | strong(X0) [cnf transformation 51]
92. ~funny(X0) | strong(X0) [cnf transformation 51]
120. ~curious(mary) [cnf transformation 22]
123. ~strong(X0) [duplicate literal removal 88]
167. ~funny(X0) [subsumption resolution 92,123]
168. brave(X0) [subsumption resolution 90,123]
226. generous(X0) | curious(X0) [resolution 69,168]
229. strong(X0) | funny(X0) | curious(X0) [resolution 77,226]
231. funny(X0) | curious(X0) [subsumption resolution 229,123]
232. curious(X0) [subsumption resolution 231,167]
233. $false [resolution 232,120]
% SZS output end Proof for 88803480339941152822227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not wise is not kind or quiet and vice versa.
If fred is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Everyone who is both calm and happy is either kind or humble and vice versa.
Everyone who is either not creative or not strong is patient and vice versa.
If alice is both not calm and not kind then someone is quiet and vice versa.
If lucy is both generous and happy then mary is curious.
Everyone who is both not quiet and not rich is strong or wise and vice versa.
If paul is either not patient or not creative then someone is kind or curious.
Everyone who is quiet is not creative.
If someone is either happy or curious then someone is either not old or quiet and vice versa.
Everyone who is either curious or funny is not humble or not calm and vice versa.
Susan is either not old or not humble.
Someone is not calm or not strong.
Someone is not wise or brave.
Someone is humble.
Someone is brave or not wise.
Someone is not curious or not creative. | Alice is not patient. | entailment | (![X]:((~old(X)|~wise(X))<=>(~kind(X)|quiet(X))))&
(((~brave(fred)&~old(fred)))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((calm(X)&happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>patient(X)))&
(((~calm(alice)&~kind(alice)))<=>(?[X]:(quiet(X))))&
(((generous(lucy)&happy(lucy)))=>(curious(mary)))&
(![X]:((~quiet(X)&~rich(X))<=>(strong(X)|wise(X))))&
(((~patient(paul)<~>~creative(paul)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(quiet(X)=>~creative(X)))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((~old(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))<=>(~humble(X)|~calm(X))))&
((~old(susan)<~>~humble(susan)))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((~curious(X)|~creative(X)))) | ~patient(alice) | [
"p2",
"p3",
"p4",
"p6",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2320299004708461282258839
% SZS output start Proof for 2320299004708461282258839
3. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p2]
4. ? [X0] : (~quiet(X0) | curious(X0)) => (~calm(alice) & old(alice)) [input p3]
5. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~old(X0) <~> curious(X0))) [input p4]
7. ! [X0] : ((wise(X0) & tall(X0)) => (~quiet(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : ((~creative(X0) <~> ~strong(X0)) <=> patient(X0)) [input p8]
12. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> (wise(X0) | strong(X0))) [input p11]
14. ! [X0] : (quiet(X0) => ~creative(X0)) [input p13]
23. patient(alice) [input hypothesis]
25. (~calm(alice) & old(alice)) | ! [X0] : (quiet(X0) & ~curious(X0)) [ennf transformation 4]
27. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | (~wise(X0) | ~tall(X0))) [ennf transformation 7]
28. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | ~wise(X0) | ~tall(X0)) [flattening 27]
32. ! [X0] : (~creative(X0) | ~quiet(X0)) [ennf transformation 14]
40. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 3]
41. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~tall(X0) | curious(X0))) [flattening 40]
42. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (wise(X0) | ~patient(X0)))) [nnf transformation 5]
43. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | wise(X0) | ~patient(X0))) [flattening 42]
44. ! [X0] : (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~wise(X0) | ~tall(X0)) [nnf transformation 28]
47. ! [X0] : ((((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ~patient(X0)) & (patient(X0) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))))) [nnf transformation 9]
53. ! [X0] : (((~rich(X0) & ~quiet(X0)) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | (rich(X0) | quiet(X0)))) [nnf transformation 12]
54. ! [X0] : (((~rich(X0) & ~quiet(X0)) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | rich(X0) | quiet(X0))) [flattening 53]
85. ~curious(X0) | quiet(X0) [cnf transformation 41]
87. tall(X0) | quiet(X0) [cnf transformation 41]
90. old(alice) | quiet(X0) [cnf transformation 25]
92. ~calm(alice) | quiet(X0) [cnf transformation 25]
93. ~patient(X0) | ~old(X0) | wise(X0) | curious(X0) [cnf transformation 43]
102. calm(X0) | quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 44]
112. ~patient(X0) | creative(X0) | strong(X0) [cnf transformation 47]
118. ~strong(X0) | ~quiet(X0) [cnf transformation 54]
124. ~creative(X0) | ~quiet(X0) [cnf transformation 32]
146. patient(alice) [cnf transformation 23]
171. 6 <=> ! [X0] : quiet(X0) [avatar definition]
172. quiet(X0) <- (6) [avatar component clause 171]
174. 7 <=> calm(alice) [avatar definition]
176. ~calm(alice) <- (~7) [avatar component clause 174]
177. 6 | ~7 [avatar split clause 92,174,171]
183. 9 <=> old(alice) [avatar definition]
186. 6 | 9 [avatar split clause 90,183,171]
204. ~wise(X0) | quiet(X0) | calm(X0) [subsumption resolution 102,87]
361. creative(alice) | strong(alice) [resolution 112,146]
365. 44 <=> strong(alice) [avatar definition]
367. strong(alice) <- (44) [avatar component clause 365]
369. 45 <=> creative(alice) [avatar definition]
371. creative(alice) <- (45) [avatar component clause 369]
372. 44 | 45 [avatar split clause 361,369,365]
375. ~quiet(alice) <- (44) [resolution 367,118]
378. $false <- (6, 44) [subsumption resolution 375,172]
379. ~6 | ~44 [avatar contradiction clause 378]
431. ~old(alice) | wise(alice) | curious(alice) [resolution 93,146]
447. 53 <=> curious(alice) [avatar definition]
449. curious(alice) <- (53) [avatar component clause 447]
451. 54 <=> wise(alice) [avatar definition]
453. wise(alice) <- (54) [avatar component clause 451]
455. 53 | 54 | ~9 [avatar split clause 431,183,451,447]
461. 56 <=> quiet(alice) [avatar definition]
462. quiet(alice) <- (56) [avatar component clause 461]
463. ~quiet(alice) <- (~56) [avatar component clause 461]
469. ~quiet(alice) <- (45) [resolution 371,124]
470. $false <- (6, 45) [subsumption resolution 469,172]
471. ~6 | ~45 [avatar contradiction clause 470]
472. ~56 | ~45 [avatar split clause 469,369,461]
476. quiet(alice) <- (53) [resolution 449,85]
479. $false <- (53, ~56) [subsumption resolution 476,463]
480. ~53 | 56 [avatar contradiction clause 479]
497. quiet(alice) | calm(alice) <- (54) [resolution 453,204]
507. quiet(alice) <- (~7, 54) [subsumption resolution 497,176]
508. 56 | 7 | ~54 [avatar split clause 507,451,174,461]
533. ~quiet(alice) <- (44) [resolution 367,118]
560. $false <- (44, 56) [subsumption resolution 533,462]
561. ~44 | ~56 [avatar contradiction clause 560]
564. $false [avatar sat refutation 177,186,372,379,455,471,472,480,508,561]
% SZS output end Proof for 2320299004708461282258839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not strong is both not creative and curious and vice versa. If fred is both not funny and not wise then someone is patient and vice versa. If someone is both not happy and not wise then someone is not wise or curious and vice versa. If someone is either tall or not kind then paul is either curious or calm. If mary is not wise then paul is both not curious and calm. Everyone who is both kind and not tall is either kind or not strong and vice versa. If someone is strong or quiet then someone is both wise and not curious and vice versa. If paul is strong or patient then someone is either calm or creative. Everyone who is both curious and brave is either tall or not humble. If someone is both old and strong then lucy is both patient and not generous and vice versa. Everyone who is not tall or not strong is not generous or humble and vice versa. Everyone who is not funny or not generous is both not quiet and wise. If someone is either calm or not curious then someone is not wise or funny and vice versa. Everyone who is not curious or not generous is not creative or not wise and vice versa. If someone is not humble then someone is both not old and strong. Everyone who is not patient is brave or not calm. Alice is not strong or not brave. Someone is not generous. Someone is either not strong or old. Someone is not curious or brave. Someone is either not humble or not old. Someone is either generous or not calm. Lucy is both not humble and not kind. Susan is both creative and quiet. | Susan is rich. | entailment | (![X]:((~rich(X)|~strong(X))<=>(~creative(X)&curious(X))))&
(((~funny(fred)&~wise(fred)))<=>(?[X]:(patient(X))))&
((?[X]:((~happy(X)&~wise(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>((curious(paul)<~>calm(paul))))&
((~wise(mary))=>((~curious(paul)&calm(paul))))&
(![X]:((kind(X)&~tall(X))<=>(kind(X)<~>~strong(X))))&
((?[X]:((strong(X)|quiet(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(paul)|patient(paul)))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((curious(X)&brave(X))=>(tall(X)<~>~humble(X))))&
((?[X]:((old(X)&strong(X))))<=>((patient(lucy)&~generous(lucy))))&
(![X]:((~tall(X)|~strong(X))<=>(~generous(X)|humble(X))))&
(![X]:((~funny(X)|~generous(X))=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((~strong(alice)|~brave(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
((~humble(lucy)&~kind(lucy)))&
((creative(susan)&quiet(susan))) | rich(susan) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5837950669508354047567213
% SZS output start Proof for 5837950669508354047567213
1. ! [X0] : ((~strong(X0) | ~rich(X0)) <=> (curious(X0) & ~creative(X0))) [input p0]
24. quiet(susan) & creative(susan) [input p23]
25. ~rich(susan) [input hypothesis]
39. ! [X0] : (((~strong(X0) | ~rich(X0)) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | (strong(X0) & rich(X0)))) [nnf transformation 1]
40. ! [X0] : ((~strong(X0) | ~rich(X0) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | (strong(X0) & rich(X0)))) [flattening 39]
93. ~creative(X0) | rich(X0) [cnf transformation 40]
165. creative(susan) [cnf transformation 24]
167. ~rich(susan) [cnf transformation 25]
414. rich(susan) [resolution 93,165]
415. $false [subsumption resolution 414,167]
% SZS output end Proof for 5837950669508354047567213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is both not funny and calm. If paul is both not wise and generous then fred is humble and vice versa. Everyone who is brave or not tall is either strong or not humble and vice versa. Everyone who is either not kind or calm is brave or tall and vice versa. If susan is either not kind or humble then someone is not creative or old and vice versa. Everyone who is rich or not strong is both not quiet and not kind. Everyone who is either not humble or not patient is both strong and not patient. Everyone who is both curious and generous is either happy or rich. If john is brave then mary is either not happy or wise. If someone is both brave and not happy then lucy is not strong. Everyone who is either calm or not creative is not generous or not funny. If someone is both humble and quiet then mary is not quiet or happy and vice versa. Everyone who is not patient or not happy is either quiet or wise and vice versa. Everyone who is either patient or calm is either not calm or not funny. Everyone who is either patient or rich is not strong and vice versa. Everyone who is kind or wise is funny and vice versa. Mary is creative or curious. Someone is curious or humble. Someone is old. Fred is not calm. Paul is either wise or tall. | John is not brave. | entailment | (![X]:(funny(X)=>(~funny(X)&calm(X))))&
(((~wise(paul)&generous(paul)))<=>(humble(fred)))&
(![X]:((brave(X)|~tall(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(brave(X)|tall(X))))&
(((~kind(susan)<~>humble(susan)))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((rich(X)|~strong(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~humble(X)<~>~patient(X))=>(strong(X)&~patient(X))))&
(![X]:((curious(X)&generous(X))=>(happy(X)<~>rich(X))))&
((brave(john))=>((~happy(mary)<~>wise(mary))))&
((?[X]:((brave(X)&~happy(X))))=>(~strong(lucy)))&
(![X]:((calm(X)<~>~creative(X))=>(~generous(X)|~funny(X))))&
((?[X]:((humble(X)&quiet(X))))<=>((~quiet(mary)|happy(mary))))&
(![X]:((~patient(X)|~happy(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((patient(X)<~>calm(X))=>(~calm(X)<~>~funny(X))))&
(![X]:((patient(X)<~>rich(X))<=>~strong(X)))&
(![X]:((kind(X)|wise(X))<=>funny(X)))&
((creative(mary)|curious(mary)))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:(old(X)))&
(~calm(fred))&
((wise(paul)<~>tall(paul))) | ~brave(john) | [
"p0",
"p2",
"p3",
"p5",
"p8",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2350467616531786222306616
% SZS output start Proof for 2350467616531786222306616
1. ! [X0] : (funny(X0) => (calm(X0) & ~funny(X0))) [input p0]
3. ! [X0] : ((~tall(X0) | brave(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p2]
4. ! [X0] : ((~kind(X0) <~> calm(X0)) <=> (tall(X0) | brave(X0))) [input p3]
6. ! [X0] : ((~strong(X0) | rich(X0)) => (~kind(X0) & ~quiet(X0))) [input p5]
9. brave(john) => (~happy(mary) <~> wise(mary)) [input p8]
12. ? [X0] : (quiet(X0) & humble(X0)) <=> (happy(mary) | ~quiet(mary)) [input p11]
13. ! [X0] : ((~happy(X0) | ~patient(X0)) <=> (quiet(X0) <~> wise(X0))) [input p12]
14. ! [X0] : ((patient(X0) <~> calm(X0)) => (~calm(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : ((wise(X0) | kind(X0)) <=> funny(X0)) [input p15]
22. brave(john) [input hypothesis]
23. ! [X0] : ((calm(X0) & ~funny(X0)) | ~funny(X0)) [ennf transformation 1]
24. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (strong(X0) & ~rich(X0))) [ennf transformation 6]
28. (~happy(mary) <~> wise(mary)) | ~brave(john) [ennf transformation 9]
32. ! [X0] : ((~calm(X0) <~> ~funny(X0)) | (patient(X0) <=> calm(X0))) [ennf transformation 14]
35. ! [X0] : (((~tall(X0) | brave(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (tall(X0) & ~brave(X0)))) [nnf transformation 3]
36. ! [X0] : ((~tall(X0) | brave(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (tall(X0) & ~brave(X0)))) [flattening 35]
37. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~tall(X0) & ~brave(X0))) & ((tall(X0) | brave(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~tall(X0) & ~brave(X0))) & (tall(X0) | brave(X0) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [flattening 37]
45. ((~wise(mary) | happy(mary)) & (wise(mary) | ~happy(mary))) | ~brave(john) [nnf transformation 28]
47. (? [X0] : (quiet(X0) & humble(X0)) | (~happy(mary) & quiet(mary))) & ((happy(mary) | ~quiet(mary)) | ! [X0] : (~quiet(X0) | ~humble(X0))) [nnf transformation 12]
48. (? [X0] : (quiet(X0) & humble(X0)) | (~happy(mary) & quiet(mary))) & (happy(mary) | ~quiet(mary) | ! [X0] : (~quiet(X0) | ~humble(X0))) [flattening 47]
49. (? [X0] : (quiet(X0) & humble(X0)) | (~happy(mary) & quiet(mary))) & (happy(mary) | ~quiet(mary) | ! [X1] : (~quiet(X1) | ~humble(X1))) [rectify 48]
50. ? [X0] : (quiet(X0) & humble(X0)) => (quiet(sK1) & humble(sK1)) [choice axiom]
51. ((quiet(sK1) & humble(sK1)) | (~happy(mary) & quiet(mary))) & (happy(mary) | ~quiet(mary) | ! [X1] : (~quiet(X1) | ~humble(X1))) [skolemisation 49,50]
52. ! [X0] : (((~happy(X0) | ~patient(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (happy(X0) & patient(X0)))) [nnf transformation 13]
53. ! [X0] : ((~happy(X0) | ~patient(X0) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (happy(X0) & patient(X0)))) [flattening 52]
54. ! [X0] : (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | ((patient(X0) | ~calm(X0)) & (calm(X0) | ~patient(X0)))) [nnf transformation 32]
56. ! [X0] : (((wise(X0) | kind(X0)) | ~funny(X0)) & (funny(X0) | (~wise(X0) & ~kind(X0)))) [nnf transformation 16]
57. ! [X0] : ((wise(X0) | kind(X0) | ~funny(X0)) & (funny(X0) | (~wise(X0) & ~kind(X0)))) [flattening 56]
63. ~funny(X0) | ~funny(X0) [cnf transformation 23]
70. ~strong(X0) | humble(X0) | ~brave(X0) [cnf transformation 36]
78. ~brave(X0) | kind(X0) | ~calm(X0) [cnf transformation 38]
87. ~quiet(X0) | strong(X0) [cnf transformation 24]
96. wise(mary) | ~happy(mary) | ~brave(john) [cnf transformation 45]
101. happy(mary) | ~quiet(mary) | ~quiet(X1) | ~humble(X1) [cnf transformation 51]
106. patient(X0) | quiet(X0) | wise(X0) [cnf transformation 53]
107. happy(X0) | quiet(X0) | wise(X0) [cnf transformation 53]
114. funny(X0) | calm(X0) | calm(X0) | ~patient(X0) [cnf transformation 54]
120. funny(X0) | ~kind(X0) [cnf transformation 57]
121. funny(X0) | ~wise(X0) [cnf transformation 57]
129. brave(john) [cnf transformation 22]
131. funny(X0) | calm(X0) | ~patient(X0) [duplicate literal removal 114]
133. ~funny(X0) [duplicate literal removal 63]
178. 10 <=> brave(john) [avatar definition]
179. brave(john) <- (10) [avatar component clause 178]
182. 11 <=> happy(mary) [avatar definition]
183. ~happy(mary) <- (~11) [avatar component clause 182]
186. 12 <=> wise(mary) [avatar definition]
187. wise(mary) <- (12) [avatar component clause 186]
190. ~10 | ~11 | 12 [avatar split clause 96,186,182,178]
205. 16 <=> quiet(mary) [avatar definition]
216. 18 <=> ! [X1] : (~quiet(X1) | ~humble(X1)) [avatar definition]
217. ~quiet(X1) | ~humble(X1) <- (18) [avatar component clause 216]
218. 18 | ~16 | 11 [avatar split clause 101,182,205,216]
219. ~patient(X0) | calm(X0) [subsumption resolution 131,133]
220. ~wise(X0) [subsumption resolution 121,133]
221. ~kind(X0) [subsumption resolution 120,133]
241. 10 [avatar split clause 129,178]
242. $false <- (12) [subsumption resolution 187,220]
243. ~12 [avatar contradiction clause 242]
259. kind(john) | ~calm(john) <- (10) [resolution 78,179]
260. ~calm(john) <- (10) [subsumption resolution 259,221]
264. quiet(X0) | wise(X0) | calm(X0) [resolution 106,219]
266. quiet(X0) | calm(X0) [subsumption resolution 264,220]
269. strong(X0) | calm(X0) [resolution 266,87]
271. quiet(mary) | wise(mary) <- (~11) [resolution 107,183]
275. quiet(mary) <- (~11) [subsumption resolution 271,220]
276. 16 | 11 [avatar split clause 275,182,205]
280. ~humble(X0) | calm(X0) <- (18) [resolution 217,266]
398. calm(X2) | humble(X2) | ~brave(X2) [resolution 269,70]
400. ~brave(X2) | calm(X2) <- (18) [subsumption resolution 398,280]
486. calm(john) <- (10, 18) [resolution 400,179]
487. $false <- (10, 18) [subsumption resolution 486,260]
488. ~10 | ~18 [avatar contradiction clause 487]
489. $false [avatar sat refutation 190,218,241,243,276,488]
% SZS output end Proof for 2350467616531786222306616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not humble is both not creative and happy. Everyone who is both not funny and not brave is either brave or quiet and vice versa. Everyone who is happy or generous is either not generous or not tall and vice versa. Everyone who is both not strong and not kind is either not creative or wise and vice versa. If someone is either rich or tall then paul is wise or not strong and vice versa. If someone is not patient or not humble then lucy is not tall or strong and vice versa. If someone is both not rich and humble then someone is brave. If someone is not strong or not calm then alice is not humble or patient. If alice is not humble then someone is not strong. If someone is both not creative and not humble then someone is either not creative or humble and vice versa. Everyone who is kind or not funny is creative or not patient and vice versa. If fred is humble or wise then someone is not wise or not humble. Everyone who is not generous is either curious or not kind and vice versa. Everyone who is either not quiet or tall is not patient or not curious and vice versa. Everyone who is funny or rich is either strong or not old and vice versa. If john is either patient or not humble then someone is curious. Paul is either not funny or not old. Someone is kind. Paul is both tall and kind. Paul is either not kind or brave. Someone is either not rich or funny. Someone is not old or rich. Someone is both quiet and generous. Someone is not curious or not quiet. | Paul is not patient. | entailment | (![X]:((generous(X)&~humble(X))=>(~creative(X)&happy(X))))&
(![X]:((~funny(X)&~brave(X))<=>(brave(X)<~>quiet(X))))&
(![X]:((happy(X)|generous(X))<=>(~generous(X)<~>~tall(X))))&
(![X]:((~strong(X)&~kind(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:((rich(X)<~>tall(X))))<=>((wise(paul)|~strong(paul))))&
((?[X]:((~patient(X)|~humble(X))))<=>((~tall(lucy)|strong(lucy))))&
((?[X]:((~rich(X)&humble(X))))=>(?[X]:(brave(X))))&
((?[X]:((~strong(X)|~calm(X))))=>((~humble(alice)|patient(alice))))&
((~humble(alice))=>(?[X]:(~strong(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((~creative(X)<~>humble(X)))))&
(![X]:((kind(X)|~funny(X))<=>(creative(X)|~patient(X))))&
(((humble(fred)|wise(fred)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:(~generous(X)<=>(curious(X)<~>~kind(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(~patient(X)|~curious(X))))&
(![X]:((funny(X)|rich(X))<=>(strong(X)<~>~old(X))))&
(((patient(john)<~>~humble(john)))=>(?[X]:(curious(X))))&
((~funny(paul)<~>~old(paul)))&
(?[X]:(kind(X)))&
((tall(paul)&kind(paul)))&
((~kind(paul)<~>brave(paul)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:((~old(X)|rich(X))))&
(?[X]:((quiet(X)&generous(X))))&
(?[X]:((~curious(X)|~quiet(X)))) | ~patient(paul) | [
"p1",
"p2",
"p12",
"p13",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5277393047894632733950679
% SZS output start Proof for 5277393047894632733950679
2. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (brave(X0) <~> quiet(X0))) [input p1]
3. ! [X0] : ((generous(X0) | happy(X0)) <=> (~generous(X0) <~> ~tall(X0))) [input p2]
13. ! [X0] : (~generous(X0) <=> (curious(X0) <~> ~kind(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) <~> tall(X0)) <=> (~curious(X0) | ~patient(X0))) [input p13]
19. kind(paul) & tall(paul) [input p18]
20. ~kind(paul) <~> brave(paul) [input p19]
25. patient(paul) [input hypothesis]
37. ! [X0] : (((~brave(X0) & ~funny(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | (brave(X0) | funny(X0)))) [nnf transformation 2]
38. ! [X0] : (((~brave(X0) & ~funny(X0)) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0)))) & (((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | brave(X0) | funny(X0))) [flattening 37]
39. ! [X0] : (((generous(X0) | happy(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~generous(X0) & ~happy(X0)))) [nnf transformation 3]
40. ! [X0] : ((generous(X0) | happy(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~generous(X0) & ~happy(X0)))) [flattening 39]
67. ! [X0] : ((~generous(X0) | ((curious(X0) | kind(X0)) & (~kind(X0) | ~curious(X0)))) & (((kind(X0) | ~curious(X0)) & (~kind(X0) | curious(X0))) | generous(X0))) [nnf transformation 13]
68. ! [X0] : ((((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | (curious(X0) & patient(X0))) & ((~curious(X0) | ~patient(X0)) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0))))) [nnf transformation 14]
69. ! [X0] : ((((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | (curious(X0) & patient(X0))) & (~curious(X0) | ~patient(X0) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0))))) [flattening 68]
78. (~brave(paul) | kind(paul)) & (brave(paul) | ~kind(paul)) [nnf transformation 20]
94. ~brave(X0) | quiet(X0) | ~brave(X0) [cnf transformation 38]
97. ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 40]
133. ~kind(X0) | curious(X0) | generous(X0) [cnf transformation 67]
138. ~curious(X0) | ~patient(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 69]
154. tall(paul) [cnf transformation 19]
155. kind(paul) [cnf transformation 19]
156. brave(paul) | ~kind(paul) [cnf transformation 78]
164. patient(paul) [cnf transformation 25]
165. ~tall(X0) | ~generous(X0) [duplicate literal removal 97]
168. ~brave(X0) | quiet(X0) [duplicate literal removal 94]
319. brave(paul) [subsumption resolution 156,155]
348. ~generous(paul) [resolution 165,154]
349. quiet(paul) [resolution 168,319]
415. curious(paul) | generous(paul) [resolution 133,155]
417. curious(paul) [subsumption resolution 415,348]
514. ~patient(paul) | ~quiet(paul) | ~tall(paul) [resolution 138,417]
516. ~quiet(paul) | ~tall(paul) [subsumption resolution 514,164]
517. ~tall(paul) [subsumption resolution 516,349]
518. $false [subsumption resolution 517,154]
% SZS output end Proof for 5277393047894632733950679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not patient is patient.
Everyone who is patient is either not creative or tall.
Everyone who is both kind and old is not generous or not rich.
Everyone who is either quiet or wise is tall or not happy and vice versa.
If lucy is not creative then someone is both old and not creative and vice versa.
Everyone who is not brave or generous is not calm or tall and vice versa.
If someone is either not old or old then someone is not curious.
Everyone who is happy is quiet.
If someone is both brave and not curious then someone is both creative and humble and vice versa.
Everyone who is either strong or wise is quiet and vice versa.
Everyone who is both patient and not patient is not humble.
If someone is either not happy or quiet then john is old or not happy.
If someone is quiet then paul is either not rich or not humble and vice versa.
If paul is funny or not curious then someone is not patient or not kind and vice versa.
Everyone who is not happy or not curious is either brave or kind and vice versa.
If mary is not happy or not tall then lucy is either humble or not wise and vice versa.
Someone is either creative or brave.
Lucy is not quiet or not brave.
Someone is calm or humble.
Lucy is not funny.
Someone is not quiet.
Paul is either not tall or generous.
Someone is either not happy or quiet. | Lucy is patient. | neutral | (![X]:((brave(X)&~patient(X))=>patient(X)))&
(![X]:(patient(X)=>(~creative(X)<~>tall(X))))&
(![X]:((kind(X)&old(X))=>(~generous(X)|~rich(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(tall(X)|~happy(X))))&
((~creative(lucy))<=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~calm(X)|tall(X))))&
((?[X]:((~old(X)<~>old(X))))=>(?[X]:(~curious(X))))&
(![X]:(happy(X)=>quiet(X)))&
((?[X]:((brave(X)&~curious(X))))<=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((strong(X)<~>wise(X))<=>quiet(X)))&
(![X]:((patient(X)&~patient(X))=>~humble(X)))&
((?[X]:((~happy(X)<~>quiet(X))))=>((old(john)|~happy(john))))&
((?[X]:(quiet(X)))<=>((~rich(paul)<~>~humble(paul))))&
(((funny(paul)|~curious(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(brave(X)<~>kind(X))))&
(((~happy(mary)|~tall(mary)))<=>((humble(lucy)<~>~wise(lucy))))&
(?[X]:((creative(X)<~>brave(X))))&
((~quiet(lucy)|~brave(lucy)))&
(?[X]:((calm(X)|humble(X))))&
(~funny(lucy))&
(?[X]:(~quiet(X)))&
((~tall(paul)<~>generous(paul)))&
(?[X]:((~happy(X)<~>quiet(X)))) | patient(lucy) | [] | null | 0 |
Everyone who is not tall or curious is not brave or kind and vice versa.
Everyone who is both not wise and not generous is both not wise and not happy.
Everyone who is either generous or not funny is either kind or not humble.
Everyone who is humble or brave is happy.
Everyone who is both not kind and not brave is both creative and calm and vice versa.
If someone is creative then mary is not curious or not strong.
Everyone who is both patient and funny is both not wise and rich.
If someone is either creative or happy then someone is humble.
If john is not funny or not creative then someone is rich and vice versa.
Everyone who is either not creative or funny is both kind and not kind and vice versa.
Everyone who is both quiet and not rich is calm or generous.
Everyone who is wise is not kind and vice versa.
If someone is either not calm or quiet then mary is both patient and not kind and vice versa.
Everyone who is wise or not tall is both creative and brave.
Everyone who is creative or wise is both calm and not creative and vice versa.
If susan is kind or not wise then susan is not curious or not old and vice versa.
Someone is not generous.
Someone is either generous or wise.
Someone is not creative or generous.
Someone is both quiet and not creative.
Fred is either not curious or not wise. | John is tall. | entailment | (![X]:((~tall(X)|curious(X))<=>(~brave(X)|kind(X))))&
(![X]:((~wise(X)&~generous(X))=>(~wise(X)&~happy(X))))&
(![X]:((generous(X)<~>~funny(X))=>(kind(X)<~>~humble(X))))&
(![X]:((humble(X)|brave(X))=>happy(X)))&
(![X]:((~kind(X)&~brave(X))<=>(creative(X)&calm(X))))&
((?[X]:(creative(X)))=>((~curious(mary)|~strong(mary))))&
(![X]:((patient(X)&funny(X))=>(~wise(X)&rich(X))))&
((?[X]:((creative(X)<~>happy(X))))=>(?[X]:(humble(X))))&
(((~funny(john)|~creative(john)))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)<~>funny(X))<=>(kind(X)&~kind(X))))&
(![X]:((quiet(X)&~rich(X))=>(calm(X)|generous(X))))&
(![X]:(wise(X)<=>~kind(X)))&
((?[X]:((~calm(X)<~>quiet(X))))<=>((patient(mary)&~kind(mary))))&
(![X]:((wise(X)|~tall(X))=>(creative(X)&brave(X))))&
(![X]:((creative(X)|wise(X))<=>(calm(X)&~creative(X))))&
(((kind(susan)|~wise(susan)))<=>((~curious(susan)|~old(susan))))&
(?[X]:(~generous(X)))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:((quiet(X)&~creative(X))))&
((~curious(fred)<~>~wise(fred))) | tall(john) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8004786294035637655465607
% SZS output start Proof for 8004786294035637655465607
14. ! [X0] : ((~tall(X0) | wise(X0)) => (brave(X0) & creative(X0))) [input p13]
15. ! [X0] : ((wise(X0) | creative(X0)) <=> (~creative(X0) & calm(X0))) [input p14]
22. ~tall(john) [input hypothesis]
34. ! [X0] : ((brave(X0) & creative(X0)) | (tall(X0) & ~wise(X0))) [ennf transformation 14]
57. ! [X0] : (((wise(X0) | creative(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 15]
58. ! [X0] : ((wise(X0) | creative(X0) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | (~wise(X0) & ~creative(X0)))) [flattening 57]
110. creative(X0) | tall(X0) [cnf transformation 34]
115. ~creative(X0) | ~creative(X0) [cnf transformation 58]
130. ~tall(john) [cnf transformation 22]
131. ~creative(X0) [duplicate literal removal 115]
222. tall(X0) [resolution 110,131]
224. $false [resolution 222,130]
% SZS output end Proof for 8004786294035637655465607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is creative then someone is not brave or kind.
If susan is patient or not funny then someone is both tall and brave.
If someone is either funny or not creative then lucy is not wise or not strong and vice versa.
If john is both not happy and humble then paul is not rich.
If john is both tall and not old then someone is both not funny and calm and vice versa.
If someone is generous or not happy then someone is both not creative and not humble and vice versa.
Everyone who is curious or not rich is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
Everyone who is either brave or wise is both not humble and not funny and vice versa.
If someone is either curious or creative then someone is not quiet or old.
Someone is either brave or wise.
Someone is both not kind and not strong.
Someone is both not wise and not kind.
Mary is either generous or not brave.
Someone is not tall or creative.
Alice is either not quiet or not happy.
Someone is either tall or calm.
Someone is not funny or quiet. | Fred is strong. | neutral | ((creative(paul))=>(?[X]:((~brave(X)|kind(X)))))&
(((patient(susan)|~funny(susan)))=>(?[X]:((tall(X)&brave(X)))))&
((?[X]:((funny(X)<~>~creative(X))))<=>((~wise(lucy)|~strong(lucy))))&
(((~happy(john)&humble(john)))=>(~rich(paul)))&
(((tall(john)&~old(john)))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((generous(X)|~happy(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((generous(mary)<~>~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~funny(X)|quiet(X)))) | strong(fred) | [] | null | 0 |
Everyone who is not wise is wise or calm. Everyone who is not kind is not curious or not creative. Everyone who is not quiet or not strong is funny. If john is either strong or not calm then someone is not tall or patient and vice versa. If someone is both not generous and not wise then someone is both not rich and not calm. If someone is both not patient and not creative then alice is patient or quiet. Everyone who is kind or not happy is either humble or not generous and vice versa. If john is both not rich and not quiet then alice is both strong and happy. If someone is brave then alice is humble or not quiet. If someone is not old then someone is both humble and kind. Everyone who is either tall or old is not humble. If someone is both happy and not tall then fred is quiet. Everyone who is either strong or not curious is either not curious or not calm and vice versa. Everyone who is both not rich and not strong is not happy. If someone is creative or funny then paul is not creative. If someone is either humble or quiet then someone is brave or strong. Fred is both not generous and not brave. Someone is not wise or not creative. Paul is both kind and not funny. Fred is either kind or creative. Alice is either not funny or not quiet. Mary is both brave and kind. Fred is both tall and happy. | Alice is old. | entailment | (![X]:(~wise(X)=>(wise(X)|calm(X))))&
(![X]:(~kind(X)=>(~curious(X)|~creative(X))))&
(![X]:((~quiet(X)|~strong(X))=>funny(X)))&
(((strong(john)<~>~calm(john)))<=>(?[X]:((~tall(X)|patient(X)))))&
((?[X]:((~generous(X)&~wise(X))))=>(?[X]:((~rich(X)&~calm(X)))))&
((?[X]:((~patient(X)&~creative(X))))=>((patient(alice)|quiet(alice))))&
(![X]:((kind(X)|~happy(X))<=>(humble(X)<~>~generous(X))))&
(((~rich(john)&~quiet(john)))=>((strong(alice)&happy(alice))))&
((?[X]:(brave(X)))=>((humble(alice)|~quiet(alice))))&
((?[X]:(~old(X)))=>(?[X]:((humble(X)&kind(X)))))&
(![X]:((tall(X)<~>old(X))=>~humble(X)))&
((?[X]:((happy(X)&~tall(X))))=>(quiet(fred)))&
(![X]:((strong(X)<~>~curious(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:((~rich(X)&~strong(X))=>~happy(X)))&
((?[X]:((creative(X)|funny(X))))=>(~creative(paul)))&
((?[X]:((humble(X)<~>quiet(X))))=>(?[X]:((brave(X)|strong(X)))))&
((~generous(fred)&~brave(fred)))&
(?[X]:((~wise(X)|~creative(X))))&
((kind(paul)&~funny(paul)))&
((kind(fred)<~>creative(fred)))&
((~funny(alice)<~>~quiet(alice)))&
((brave(mary)&kind(mary)))&
((tall(fred)&happy(fred))) | old(alice) | [
"p3",
"p5",
"p8",
"p10",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4622643944377224865705471
% SZS output start Proof for 4622643944377224865705471
4. (strong(john) <~> ~calm(john)) <=> ? [X0] : (patient(X0) | ~tall(X0)) [input p3]
6. ? [X0] : (~creative(X0) & ~patient(X0)) => (quiet(alice) | patient(alice)) [input p5]
9. ? [X0] : brave(X0) => (~quiet(alice) | humble(alice)) [input p8]
11. ! [X0] : ((tall(X0) <~> old(X0)) => ~humble(X0)) [input p10]
13. ! [X0] : ((strong(X0) <~> ~curious(X0)) <=> (~curious(X0) <~> ~calm(X0))) [input p12]
15. ? [X0] : (funny(X0) | creative(X0)) => ~creative(paul) [input p14]
22. kind(mary) & brave(mary) [input p21]
24. ~old(alice) [input hypothesis]
34. (quiet(alice) | patient(alice)) | ! [X0] : (creative(X0) | patient(X0)) [ennf transformation 6]
35. quiet(alice) | patient(alice) | ! [X0] : (creative(X0) | patient(X0)) [flattening 34]
38. (~quiet(alice) | humble(alice)) | ! [X0] : ~brave(X0) [ennf transformation 9]
39. ~quiet(alice) | humble(alice) | ! [X0] : ~brave(X0) [flattening 38]
41. ! [X0] : (~humble(X0) | (tall(X0) <=> old(X0))) [ennf transformation 11]
45. ~creative(paul) | ! [X0] : (~funny(X0) & ~creative(X0)) [ennf transformation 15]
47. (((calm(john) | ~strong(john)) & (~calm(john) | strong(john))) | ! [X0] : (~patient(X0) & tall(X0))) & (? [X0] : (patient(X0) | ~tall(X0)) | ((strong(john) | calm(john)) & (~calm(john) | ~strong(john)))) [nnf transformation 4]
48. (((calm(john) | ~strong(john)) & (~calm(john) | strong(john))) | ! [X0] : (~patient(X0) & tall(X0))) & (? [X1] : (patient(X1) | ~tall(X1)) | ((strong(john) | calm(john)) & (~calm(john) | ~strong(john)))) [rectify 47]
49. ? [X1] : (patient(X1) | ~tall(X1)) => (patient(sK0) | ~tall(sK0)) [choice axiom]
50. (((calm(john) | ~strong(john)) & (~calm(john) | strong(john))) | ! [X0] : (~patient(X0) & tall(X0))) & ((patient(sK0) | ~tall(sK0)) | ((strong(john) | calm(john)) & (~calm(john) | ~strong(john)))) [skolemisation 48,49]
59. ! [X0] : (~humble(X0) | ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0)))) [nnf transformation 41]
60. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0)))) & (((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [nnf transformation 13]
75. ~calm(john) | strong(john) | tall(X0) [cnf transformation 50]
76. ~calm(john) | strong(john) | ~patient(X0) [cnf transformation 50]
77. calm(john) | ~strong(john) | tall(X0) [cnf transformation 50]
78. calm(john) | ~strong(john) | ~patient(X0) [cnf transformation 50]
81. quiet(alice) | patient(alice) | creative(X0) | patient(X0) [cnf transformation 35]
90. ~quiet(alice) | humble(alice) | ~brave(X0) [cnf transformation 39]
93. ~humble(X0) | old(X0) | ~tall(X0) [cnf transformation 59]
96. ~calm(X0) | ~curious(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 60]
99. calm(X0) | curious(X0) | strong(X0) | curious(X0) [cnf transformation 60]
101. ~curious(X0) | strong(X0) | ~curious(X0) | calm(X0) [cnf transformation 60]
102. curious(X0) | ~strong(X0) | ~calm(X0) | curious(X0) [cnf transformation 60]
105. ~creative(paul) | ~creative(X0) [cnf transformation 45]
118. brave(mary) [cnf transformation 22]
122. ~old(alice) [cnf transformation 24]
123. ~calm(X0) | ~curious(X0) | ~strong(X0) [duplicate literal removal 96]
124. calm(X0) | curious(X0) | strong(X0) [duplicate literal removal 99]
125. ~curious(X0) | strong(X0) | calm(X0) [duplicate literal removal 101]
126. curious(X0) | ~strong(X0) | ~calm(X0) [duplicate literal removal 102]
129. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
130. ~patient(X0) <- (1) [avatar component clause 129]
132. 2 <=> strong(john) [avatar definition]
133. strong(john) <- (2) [avatar component clause 132]
134. ~strong(john) <- (~2) [avatar component clause 132]
136. 3 <=> calm(john) [avatar definition]
137. ~calm(john) <- (~3) [avatar component clause 136]
139. 1 | ~2 | 3 [avatar split clause 78,136,132,129]
141. 4 <=> ! [X0] : tall(X0) [avatar definition]
142. tall(X0) <- (4) [avatar component clause 141]
143. 4 | ~2 | 3 [avatar split clause 77,136,132,141]
144. 1 | 2 | ~3 [avatar split clause 76,136,132,129]
145. 4 | 2 | ~3 [avatar split clause 75,136,132,141]
170. 10 <=> ! [X0] : (creative(X0) | patient(X0)) [avatar definition]
171. patient(X0) | creative(X0) <- (10) [avatar component clause 170]
173. 11 <=> patient(alice) [avatar definition]
175. patient(alice) <- (11) [avatar component clause 173]
177. 12 <=> quiet(alice) [avatar definition]
180. 10 | 11 | 12 [avatar split clause 81,177,173,170]
200. 17 <=> ! [X0] : ~brave(X0) [avatar definition]
201. ~brave(X0) <- (17) [avatar component clause 200]
203. 18 <=> humble(alice) [avatar definition]
205. humble(alice) <- (18) [avatar component clause 203]
206. 17 | 18 | ~12 [avatar split clause 90,177,203,200]
228. strong(X0) | calm(X0) [subsumption resolution 124,125]
229. ~strong(X0) | ~calm(X0) [subsumption resolution 123,126]
234. 25 <=> creative(paul) [avatar definition]
236. ~creative(paul) <- (~25) [avatar component clause 234]
239. 26 <=> ! [X0] : ~creative(X0) [avatar definition]
240. ~creative(X0) <- (26) [avatar component clause 239]
241. 26 | ~25 [avatar split clause 105,234,239]
289. calm(john) <- (~2) [resolution 228,134]
290. $false <- (~2, ~3) [subsumption resolution 289,137]
291. 2 | 3 [avatar contradiction clause 290]
294. ~calm(john) <- (2) [resolution 229,133]
297. ~3 | ~2 [avatar split clause 294,132,136]
298. creative(X0) <- (1, 10) [resolution 130,171]
302. $false <- (1, 10, ~25) [resolution 298,236]
307. ~1 | ~10 | 25 [avatar contradiction clause 302]
308. $false <- (17) [resolution 201,118]
311. ~17 [avatar contradiction clause 308]
312. $false <- (1, 11) [subsumption resolution 175,130]
313. ~1 | ~11 [avatar contradiction clause 312]
338. old(alice) | ~tall(alice) <- (18) [resolution 93,205]
340. ~tall(alice) <- (18) [subsumption resolution 338,122]
341. $false <- (4, 18) [subsumption resolution 340,142]
342. ~4 | ~18 [avatar contradiction clause 341]
346. creative(X0) <- (1, 10) [subsumption resolution 171,130]
347. $false <- (1, 10, 26) [subsumption resolution 346,240]
348. ~1 | ~10 | ~26 [avatar contradiction clause 347]
349. $false [avatar sat refutation 139,143,144,145,180,206,241,291,297,307,311,313,342,348]
% SZS output end Proof for 4622643944377224865705471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or not rich is either happy or patient and vice versa.
If someone is patient or humble then paul is not rich.
Everyone who is either tall or not generous is both strong and not patient and vice versa.
Everyone who is old is both not happy and strong.
If john is both patient and not patient then fred is brave and vice versa.
If someone is old or not old then susan is both not curious and not kind.
If alice is creative then someone is not happy or not humble.
Everyone who is not strong is both old and not humble.
Everyone who is either not brave or not humble is quiet or not quiet and vice versa.
If john is either not strong or not kind then someone is funny or not patient.
If alice is curious or not curious then alice is either not wise or rich.
Everyone who is either not curious or brave is either not rich or calm.
Everyone who is old is not kind or not generous.
Everyone who is not happy or not calm is not happy or old.
If someone is not humble then someone is old and vice versa.
If susan is both patient and kind then someone is brave or calm and vice versa.
Someone is both not calm and rich.
John is either not patient or not brave.
Someone is either rich or not quiet.
Someone is both curious and funny.
Mary is both not kind and creative. | Alice is not rich. | neutral | (![X]:((wise(X)<~>~rich(X))<=>(happy(X)<~>patient(X))))&
((?[X]:((patient(X)|humble(X))))=>(~rich(paul)))&
(![X]:((tall(X)<~>~generous(X))<=>(strong(X)&~patient(X))))&
(![X]:(old(X)=>(~happy(X)&strong(X))))&
(((patient(john)&~patient(john)))<=>(brave(fred)))&
((?[X]:((old(X)|~old(X))))=>((~curious(susan)&~kind(susan))))&
((creative(alice))=>(?[X]:((~happy(X)|~humble(X)))))&
(![X]:(~strong(X)=>(old(X)&~humble(X))))&
(![X]:((~brave(X)<~>~humble(X))<=>(quiet(X)|~quiet(X))))&
(((~strong(john)<~>~kind(john)))=>(?[X]:((funny(X)|~patient(X)))))&
(((curious(alice)|~curious(alice)))=>((~wise(alice)<~>rich(alice))))&
(![X]:((~curious(X)<~>brave(X))=>(~rich(X)<~>calm(X))))&
(![X]:(old(X)=>(~kind(X)|~generous(X))))&
(![X]:((~happy(X)|~calm(X))=>(~happy(X)|old(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(old(X))))&
(((patient(susan)&kind(susan)))<=>(?[X]:((brave(X)|calm(X)))))&
(?[X]:((~calm(X)&rich(X))))&
((~patient(john)<~>~brave(john)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:((curious(X)&funny(X))))&
((~kind(mary)&creative(mary))) | ~rich(alice) | [] | null | 0 |
If someone is brave then someone is strong or rich. If susan is either calm or quiet then alice is either not rich or calm and vice versa. Everyone who is either not brave or not generous is both old and not creative and vice versa. Everyone who is wise or generous is both not funny and not curious. If john is either not rich or strong then someone is kind. Everyone who is either not funny or strong is either not curious or patient and vice versa. If paul is not quiet or not funny then someone is kind or old and vice versa. If someone is not generous then someone is both not creative and not quiet. If someone is not patient or not rich then paul is not humble or old and vice versa. Everyone who is not wise or calm is either strong or generous and vice versa. Everyone who is tall or calm is not wise. Everyone who is both happy and not generous is either not happy or not tall. If someone is both not curious and not old then someone is not patient or tall and vice versa. Everyone who is both humble and patient is either calm or funny. Everyone who is either curious or not tall is both strong and tall. If lucy is either not happy or not brave then mary is quiet or not generous. Someone is both not creative and not quiet. Someone is both quiet and creative. Someone is not generous. Someone is not funny. Someone is not rich. Alice is not funny or humble. Paul is either not patient or not humble. | John is strong. | neutral | ((?[X]:(brave(X)))=>(?[X]:((strong(X)|rich(X)))))&
(((calm(susan)<~>quiet(susan)))<=>((~rich(alice)<~>calm(alice))))&
(![X]:((~brave(X)<~>~generous(X))<=>(old(X)&~creative(X))))&
(![X]:((wise(X)|generous(X))=>(~funny(X)&~curious(X))))&
(((~rich(john)<~>strong(john)))=>(?[X]:(kind(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(~curious(X)<~>patient(X))))&
(((~quiet(paul)|~funny(paul)))<=>(?[X]:((kind(X)|old(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((~creative(X)&~quiet(X)))))&
((?[X]:((~patient(X)|~rich(X))))<=>((~humble(paul)|old(paul))))&
(![X]:((~wise(X)|calm(X))<=>(strong(X)<~>generous(X))))&
(![X]:((tall(X)|calm(X))=>~wise(X)))&
(![X]:((happy(X)&~generous(X))=>(~happy(X)<~>~tall(X))))&
((?[X]:((~curious(X)&~old(X))))<=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((humble(X)&patient(X))=>(calm(X)<~>funny(X))))&
(![X]:((curious(X)<~>~tall(X))=>(strong(X)&tall(X))))&
(((~happy(lucy)<~>~brave(lucy)))=>((quiet(mary)|~generous(mary))))&
(?[X]:((~creative(X)&~quiet(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~funny(X)))&
(?[X]:(~rich(X)))&
((~funny(alice)|humble(alice)))&
((~patient(paul)<~>~humble(paul))) | strong(john) | [] | null | 0 |
If susan is both not curious and not generous then fred is not creative. Everyone who is both humble and calm is either kind or not quiet. If fred is both calm and not humble then someone is wise or not generous and vice versa. If alice is both not happy and not creative then lucy is curious or rich and vice versa. Everyone who is tall or curious is not kind. Everyone who is either quiet or not rich is not happy and vice versa. Everyone who is either not generous or not humble is not brave or kind. If someone is curious or not patient then mary is either not happy or not humble. Everyone who is either not humble or not generous is either not strong or not humble and vice versa. If someone is humble then susan is either not rich or patient. Everyone who is both not tall and not funny is brave or patient. Everyone who is either not happy or happy is not generous or tall and vice versa. Everyone who is both creative and kind is not quiet or quiet. Everyone who is tall or old is not wise or funny and vice versa. If mary is not happy then someone is either calm or patient and vice versa. Everyone who is not strong is strong. Someone is patient. Fred is not brave or tall. Lucy is both not calm and humble. Someone is humble or generous. John is either not creative or curious. John is both not humble and not curious. | Alice is not rich. | neutral | (((~curious(susan)&~generous(susan)))=>(~creative(fred)))&
(![X]:((humble(X)&calm(X))=>(kind(X)<~>~quiet(X))))&
(((calm(fred)&~humble(fred)))<=>(?[X]:((wise(X)|~generous(X)))))&
(((~happy(alice)&~creative(alice)))<=>((curious(lucy)|rich(lucy))))&
(![X]:((tall(X)|curious(X))=>~kind(X)))&
(![X]:((quiet(X)<~>~rich(X))<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))=>(~brave(X)|kind(X))))&
((?[X]:((curious(X)|~patient(X))))=>((~happy(mary)<~>~humble(mary))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~strong(X)<~>~humble(X))))&
((?[X]:(humble(X)))=>((~rich(susan)<~>patient(susan))))&
(![X]:((~tall(X)&~funny(X))=>(brave(X)|patient(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~generous(X)|tall(X))))&
(![X]:((creative(X)&kind(X))=>(~quiet(X)|quiet(X))))&
(![X]:((tall(X)|old(X))<=>(~wise(X)|funny(X))))&
((~happy(mary))<=>(?[X]:((calm(X)<~>patient(X)))))&
(![X]:(~strong(X)=>strong(X)))&
(?[X]:(patient(X)))&
((~brave(fred)|tall(fred)))&
((~calm(lucy)&humble(lucy)))&
(?[X]:((humble(X)|generous(X))))&
((~creative(john)<~>curious(john)))&
((~humble(john)&~curious(john))) | ~rich(alice) | [] | null | 0 |
If fred is both happy and not tall then someone is either not funny or quiet and vice versa. If lucy is not wise then someone is either funny or not quiet and vice versa. If mary is brave or not patient then mary is both not patient and old and vice versa. Everyone who is not patient or curious is both not calm and quiet and vice versa. Everyone who is calm or not kind is both not calm and kind. If paul is not old then lucy is both happy and not funny. Everyone who is either brave or not rich is both humble and funny. Everyone who is both not funny and generous is funny or happy and vice versa. If someone is not quiet then fred is both funny and calm. If alice is both tall and not generous then someone is both not wise and strong and vice versa. If susan is humble then lucy is brave and vice versa. Everyone who is either humble or not happy is calm and vice versa. Everyone who is creative or not creative is either not calm or not wise. If someone is strong then fred is not curious and vice versa. Everyone who is either not wise or patient is either funny or not humble. Everyone who is creative is either quiet or not tall and vice versa. Lucy is rich. Someone is both tall and rich. Someone is generous or not kind. Someone is not generous or quiet. Mary is rich or not humble. John is both rich and not happy. | Susan is strong. | neutral | (((happy(fred)&~tall(fred)))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
((~wise(lucy))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(((brave(mary)|~patient(mary)))<=>((~patient(mary)&old(mary))))&
(![X]:((~patient(X)|curious(X))<=>(~calm(X)&quiet(X))))&
(![X]:((calm(X)|~kind(X))=>(~calm(X)&kind(X))))&
((~old(paul))=>((happy(lucy)&~funny(lucy))))&
(![X]:((brave(X)<~>~rich(X))=>(humble(X)&funny(X))))&
(![X]:((~funny(X)&generous(X))<=>(funny(X)|happy(X))))&
((?[X]:(~quiet(X)))=>((funny(fred)&calm(fred))))&
(((tall(alice)&~generous(alice)))<=>(?[X]:((~wise(X)&strong(X)))))&
((humble(susan))<=>(brave(lucy)))&
(![X]:((humble(X)<~>~happy(X))<=>calm(X)))&
(![X]:((creative(X)|~creative(X))=>(~calm(X)<~>~wise(X))))&
((?[X]:(strong(X)))<=>(~curious(fred)))&
(![X]:((~wise(X)<~>patient(X))=>(funny(X)<~>~humble(X))))&
(![X]:(creative(X)<=>(quiet(X)<~>~tall(X))))&
(rich(lucy))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((~generous(X)|quiet(X))))&
((rich(mary)|~humble(mary)))&
((rich(john)&~happy(john))) | strong(susan) | [] | null | 0 |
If lucy is both brave and rich then someone is not wise or not humble.
Everyone who is both not kind and wise is both kind and old and vice versa.
Everyone who is not patient or not curious is not patient or strong and vice versa.
Everyone who is either old or happy is not quiet and vice versa.
Everyone who is both not kind and calm is strong and vice versa.
If someone is both not kind and not old then someone is both strong and happy.
If someone is either creative or not curious then someone is not strong or not generous and vice versa.
Everyone who is funny or tall is both quiet and curious and vice versa.
If fred is not wise or rich then john is both not tall and not patient and vice versa.
If fred is not brave or humble then paul is kind and vice versa.
Everyone who is either kind or curious is both rich and funny.
Everyone who is not quiet is both not quiet and not patient.
If fred is calm or kind then someone is humble.
Everyone who is wise is not happy or not calm and vice versa.
Everyone who is either rich or not patient is rich and vice versa.
If someone is either happy or curious then someone is not brave or generous.
Fred is not tall or funny.
Someone is old or not funny.
John is either not curious or not quiet.
Someone is not calm or creative.
Alice is both not old and brave.
Alice is both calm and not tall.
Someone is both rich and not funny. | Fred is wise. | entailment | (((brave(lucy)&rich(lucy)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~kind(X)&wise(X))<=>(kind(X)&old(X))))&
(![X]:((~patient(X)|~curious(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)<~>happy(X))<=>~quiet(X)))&
(![X]:((~kind(X)&calm(X))<=>strong(X)))&
((?[X]:((~kind(X)&~old(X))))=>(?[X]:((strong(X)&happy(X)))))&
((?[X]:((creative(X)<~>~curious(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((funny(X)|tall(X))<=>(quiet(X)&curious(X))))&
(((~wise(fred)|rich(fred)))<=>((~tall(john)&~patient(john))))&
(((~brave(fred)|humble(fred)))<=>(kind(paul)))&
(![X]:((kind(X)<~>curious(X))=>(rich(X)&funny(X))))&
(![X]:(~quiet(X)=>(~quiet(X)&~patient(X))))&
(((calm(fred)|kind(fred)))=>(?[X]:(humble(X))))&
(![X]:(wise(X)<=>(~happy(X)|~calm(X))))&
(![X]:((rich(X)<~>~patient(X))<=>rich(X)))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((~brave(X)|generous(X)))))&
((~tall(fred)|funny(fred)))&
(?[X]:((old(X)|~funny(X))))&
((~curious(john)<~>~quiet(john)))&
(?[X]:((~calm(X)|creative(X))))&
((~old(alice)&brave(alice)))&
((calm(alice)&~tall(alice)))&
(?[X]:((rich(X)&~funny(X)))) | wise(fred) | [
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2567976467093079298978707
% SZS output start Proof for 2567976467093079298978707
9. (rich(fred) | ~wise(fred)) <=> (~patient(john) & ~tall(john)) [input p8]
15. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> rich(X0)) [input p14]
24. ~wise(fred) [input hypothesis]
54. ((rich(fred) | ~wise(fred)) | (patient(john) | tall(john))) & ((~patient(john) & ~tall(john)) | (~rich(fred) & wise(fred))) [nnf transformation 9]
55. (rich(fred) | ~wise(fred) | patient(john) | tall(john)) & ((~patient(john) & ~tall(john)) | (~rich(fred) & wise(fred))) [flattening 54]
63. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ~rich(X0)) & (rich(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 15]
106. ~patient(john) | wise(fred) [cnf transformation 55]
124. rich(X0) | rich(X0) | patient(X0) [cnf transformation 63]
126. patient(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
140. ~wise(fred) [cnf transformation 24]
141. rich(X0) | patient(X0) [duplicate literal removal 124]
142. patient(X0) | ~rich(X0) [duplicate literal removal 126]
214. 17 <=> patient(john) [avatar definition]
215. ~patient(john) <- (~17) [avatar component clause 214]
218. 18 <=> wise(fred) [avatar definition]
227. 18 | ~17 [avatar split clause 106,214,218]
260. patient(X0) [subsumption resolution 141,142]
314. ~18 [avatar split clause 140,218]
315. $false <- (~17) [subsumption resolution 215,260]
316. 17 [avatar contradiction clause 315]
317. $false [avatar sat refutation 227,314,316]
% SZS output end Proof for 2567976467093079298978707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not tall or calm and vice versa.
If fred is either not generous or tall then someone is not creative.
Everyone who is either not kind or funny is not funny.
Everyone who is not patient or old is not brave or quiet and vice versa.
If someone is creative or generous then someone is either not strong or not creative and vice versa.
Everyone who is not happy or not curious is either generous or not old and vice versa.
Everyone who is old is not tall or not generous.
Everyone who is creative or not strong is either not curious or brave and vice versa.
If paul is not curious then john is both old and creative.
Everyone who is not strong is both not wise and tall and vice versa.
Everyone who is not kind is both not tall and not wise and vice versa.
Everyone who is either not happy or patient is not creative and vice versa.
If alice is not brave then john is either quiet or calm.
Everyone who is both happy and generous is wise or happy and vice versa.
Everyone who is both wise and curious is not patient or humble and vice versa.
Alice is either not patient or not wise.
Someone is either not old or rich.
Someone is creative.
Paul is not tall or curious.
Someone is humble or creative.
Susan is either kind or happy. | Susan is generous. | contradiction | (![X]:(~old(X)<=>(~tall(X)|calm(X))))&
(((~generous(fred)<~>tall(fred)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>funny(X))=>~funny(X)))&
(![X]:((~patient(X)|old(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)=>(~tall(X)|~generous(X))))&
(![X]:((creative(X)|~strong(X))<=>(~curious(X)<~>brave(X))))&
((~curious(paul))=>((old(john)&creative(john))))&
(![X]:(~strong(X)<=>(~wise(X)&tall(X))))&
(![X]:(~kind(X)<=>(~tall(X)&~wise(X))))&
(![X]:((~happy(X)<~>patient(X))<=>~creative(X)))&
((~brave(alice))=>((quiet(john)<~>calm(john))))&
(![X]:((happy(X)&generous(X))<=>(wise(X)|happy(X))))&
(![X]:((wise(X)&curious(X))<=>(~patient(X)|humble(X))))&
((~patient(alice)<~>~wise(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(creative(X)))&
((~tall(paul)|curious(paul)))&
(?[X]:((humble(X)|creative(X))))&
((kind(susan)<~>happy(susan))) | generous(susan) | [
"p0",
"p3",
"p5",
"p6",
"p7",
"p9",
"p10",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6707205796090697915907414
% SZS output start Proof for 6707205796090697915907414
1. ! [X0] : (~old(X0) <=> (calm(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((old(X0) | ~patient(X0)) <=> (quiet(X0) | ~brave(X0))) [input p3]
6. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (generous(X0) <~> ~old(X0))) [input p5]
7. ! [X0] : (old(X0) => (~generous(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~curious(X0) <~> brave(X0))) [input p7]
10. ! [X0] : (~strong(X0) <=> (tall(X0) & ~wise(X0))) [input p9]
11. ! [X0] : (~kind(X0) <=> (~wise(X0) & ~tall(X0))) [input p10]
12. ! [X0] : ((~happy(X0) <~> patient(X0)) <=> ~creative(X0)) [input p11]
15. ! [X0] : ((curious(X0) & wise(X0)) <=> (humble(X0) | ~patient(X0))) [input p14]
21. kind(susan) <~> happy(susan) [input p20]
22. generous(susan) [input hypothesis]
26. ! [X0] : ((~generous(X0) | ~tall(X0)) | ~old(X0)) [ennf transformation 7]
27. ! [X0] : (~generous(X0) | ~tall(X0) | ~old(X0)) [flattening 26]
30. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | old(X0))) [nnf transformation 1]
31. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | old(X0))) [flattening 30]
36. ! [X0] : (((old(X0) | ~patient(X0)) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | (~old(X0) & patient(X0)))) [nnf transformation 4]
37. ! [X0] : ((old(X0) | ~patient(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | (~old(X0) & patient(X0)))) [flattening 36]
43. ! [X0] : (((~curious(X0) | ~happy(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [nnf transformation 6]
44. ! [X0] : ((~curious(X0) | ~happy(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [flattening 43]
45. ! [X0] : (((~strong(X0) | creative(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [nnf transformation 8]
46. ! [X0] : ((~strong(X0) | creative(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [flattening 45]
47. ! [X0] : ((~strong(X0) | (~tall(X0) | wise(X0))) & ((tall(X0) & ~wise(X0)) | strong(X0))) [nnf transformation 10]
48. ! [X0] : ((~strong(X0) | ~tall(X0) | wise(X0)) & ((tall(X0) & ~wise(X0)) | strong(X0))) [flattening 47]
49. ! [X0] : ((~kind(X0) | (wise(X0) | tall(X0))) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [nnf transformation 11]
50. ! [X0] : ((~kind(X0) | wise(X0) | tall(X0)) & ((~wise(X0) & ~tall(X0)) | kind(X0))) [flattening 49]
51. ! [X0] : ((((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | creative(X0)) & (~creative(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))))) [nnf transformation 12]
55. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~curious(X0) | ~wise(X0)))) [nnf transformation 15]
56. ! [X0] : (((curious(X0) & wise(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~curious(X0) | ~wise(X0))) [flattening 55]
65. (~happy(susan) | ~kind(susan)) & (happy(susan) | kind(susan)) [nnf transformation 21]
67. ~old(X0) | tall(X0) [cnf transformation 31]
75. ~patient(X0) | old(X0) | brave(X0) [cnf transformation 37]
85. ~generous(X0) | old(X0) | happy(X0) [cnf transformation 44]
86. ~generous(X0) | old(X0) | curious(X0) [cnf transformation 44]
89. ~generous(X0) | ~tall(X0) | ~old(X0) [cnf transformation 27]
95. ~curious(X0) | creative(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 46]
99. strong(X0) | tall(X0) [cnf transformation 48]
101. ~tall(X0) | kind(X0) [cnf transformation 50]
102. ~wise(X0) | kind(X0) [cnf transformation 50]
105. ~happy(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 51]
116. wise(X0) | patient(X0) [cnf transformation 56]
128. ~happy(susan) | ~kind(susan) [cnf transformation 65]
129. generous(susan) [cnf transformation 22]
179. ~generous(X0) | ~old(X0) [subsumption resolution 89,67]
242. 25 <=> kind(susan) [avatar definition]
244. ~kind(susan) <- (~25) [avatar component clause 242]
246. 26 <=> happy(susan) [avatar definition]
247. happy(susan) <- (26) [avatar component clause 246]
249. ~25 | ~26 [avatar split clause 128,246,242]
253. patient(X2) | kind(X2) [resolution 116,102]
261. ~old(susan) [resolution 179,129]
271. old(susan) | happy(susan) [resolution 85,129]
274. happy(susan) [subsumption resolution 271,261]
278. 26 [avatar split clause 274,246]
280. old(susan) | curious(susan) [resolution 86,129]
283. curious(susan) [subsumption resolution 280,261]
299. 29 <=> creative(susan) [avatar definition]
301. ~creative(susan) <- (~29) [avatar component clause 299]
303. 30 <=> brave(susan) [avatar definition]
322. 33 <=> strong(susan) [avatar definition]
323. ~strong(susan) <- (~33) [avatar component clause 322]
381. ~creative(susan) | ~patient(susan) <- (26) [resolution 105,247]
387. 41 <=> patient(susan) [avatar definition]
388. ~patient(susan) <- (~41) [avatar component clause 387]
389. patient(susan) <- (41) [avatar component clause 387]
401. ~41 | ~29 | ~26 [avatar split clause 381,246,299,387]
419. 44 <=> tall(susan) [avatar definition]
420. tall(susan) <- (44) [avatar component clause 419]
452. creative(susan) | ~strong(susan) | ~brave(susan) [resolution 95,283]
484. kind(susan) <- (~41) [resolution 388,253]
486. $false <- (~25, ~41) [subsumption resolution 484,244]
487. 25 | 41 [avatar contradiction clause 486]
491. ~strong(susan) | ~brave(susan) <- (~29) [subsumption resolution 452,301]
664. tall(susan) <- (~33) [resolution 323,99]
804. old(susan) | brave(susan) <- (41) [resolution 389,75]
827. kind(susan) <- (44) [resolution 420,101]
829. $false <- (~25, 44) [subsumption resolution 827,244]
830. 25 | ~44 [avatar contradiction clause 829]
831. 44 | 33 [avatar split clause 664,322,419]
832. brave(susan) <- (41) [subsumption resolution 804,261]
833. 30 | ~41 [avatar split clause 832,387,303]
834. ~30 | ~33 | 29 [avatar split clause 491,299,322,303]
835. $false [avatar sat refutation 249,278,401,487,830,831,833,834]
% SZS output end Proof for 6707205796090697915907414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either funny or not tall and vice versa. If someone is either not brave or not curious then someone is not calm. If lucy is either wise or humble then someone is either humble or not curious. If someone is not quiet then someone is generous. 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. | Fred is not brave. | contradiction | (![X]:(funny(X)<=>(funny(X)<~>~tall(X))))&
((?[X]:((~brave(X)<~>~curious(X))))=>(?[X]:(~calm(X))))&
(((wise(lucy)<~>humble(lucy)))=>(?[X]:((humble(X)<~>~curious(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:(generous(X))))&
((?[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(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8391918805547631135886772
% SZS output start Proof for 8391918805547631135886772
9. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p8]
25. ~brave(fred) [input hypothesis]
69. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 9]
109. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 69]
112. patient(X0) | brave(X0) | patient(X0) [cnf transformation 69]
137. ~brave(fred) [cnf transformation 25]
140. ~patient(X0) | brave(X0) [duplicate literal removal 109]
141. patient(X0) | brave(X0) [duplicate literal removal 112]
226. brave(X0) [subsumption resolution 140,141]
275. $false [subsumption resolution 137,226]
% SZS output end Proof for 8391918805547631135886772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or brave is strong or humble and vice versa. Everyone who is both not happy and curious is both curious and happy and vice versa. Everyone who is not humble or creative is generous. If someone is either not curious or calm then someone is tall or not wise and vice versa. If someone is curious then someone is both not strong and kind. If lucy is either not rich or creative then alice is rich or not quiet. If someone is not strong then someone is both not generous and not old. If alice is either not kind or creative then john is not brave. If mary is either calm or kind then fred is either strong or not old and vice versa. Everyone who is both not calm and not brave is either strong or funny and vice versa. Everyone who is both not funny and not tall is either happy or old and vice versa. Everyone who is both curious and not happy is happy and vice versa. If someone is both not patient and not humble then someone is either not old or happy. If john is old then someone is either not calm or strong and vice versa. Everyone who is both not quiet and patient is quiet. If fred is both brave and creative then lucy is calm. Fred is either patient or not calm. Susan is either not wise or not patient. Someone is both not generous and quiet. Someone is not old. Someone is kind. Someone is patient or not curious. Mary is strong or curious. | John is happy. | contradiction | (![X]:((~quiet(X)<~>brave(X))<=>(strong(X)|humble(X))))&
(![X]:((~happy(X)&curious(X))<=>(curious(X)&happy(X))))&
(![X]:((~humble(X)|creative(X))=>generous(X)))&
((?[X]:((~curious(X)<~>calm(X))))<=>(?[X]:((tall(X)|~wise(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((~rich(lucy)<~>creative(lucy)))=>((rich(alice)|~quiet(alice))))&
((?[X]:(~strong(X)))=>(?[X]:((~generous(X)&~old(X)))))&
(((~kind(alice)<~>creative(alice)))=>(~brave(john)))&
(((calm(mary)<~>kind(mary)))<=>((strong(fred)<~>~old(fred))))&
(![X]:((~calm(X)&~brave(X))<=>(strong(X)<~>funny(X))))&
(![X]:((~funny(X)&~tall(X))<=>(happy(X)<~>old(X))))&
(![X]:((curious(X)&~happy(X))<=>happy(X)))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:((~old(X)<~>happy(X)))))&
((old(john))<=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((~quiet(X)&patient(X))=>quiet(X)))&
(((brave(fred)&creative(fred)))=>(calm(lucy)))&
((patient(fred)<~>~calm(fred)))&
((~wise(susan)<~>~patient(susan)))&
(?[X]:((~generous(X)&quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:(kind(X)))&
(?[X]:((patient(X)|~curious(X))))&
((strong(mary)|curious(mary))) | happy(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4808808239408308647515626
% SZS output start Proof for 4808808239408308647515626
12. ! [X0] : ((~happy(X0) & curious(X0)) <=> happy(X0)) [input p11]
24. happy(john) [input hypothesis]
62. ! [X0] : (((~happy(X0) & curious(X0)) | ~happy(X0)) & (happy(X0) | (happy(X0) | ~curious(X0)))) [nnf transformation 12]
63. ! [X0] : (((~happy(X0) & curious(X0)) | ~happy(X0)) & (happy(X0) | happy(X0) | ~curious(X0))) [flattening 62]
130. ~happy(X0) | ~happy(X0) [cnf transformation 63]
149. happy(john) [cnf transformation 24]
152. ~happy(X0) [duplicate literal removal 130]
317. $false [subsumption resolution 149,152]
% SZS output end Proof for 4808808239408308647515626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is kind or funny then john is wise.
Everyone who is tall is strong or calm and vice versa.
If someone is not strong or not calm then lucy is both humble and quiet.
Everyone who is either not happy or not humble is both funny and calm and vice versa.
If someone is not rich then alice is not funny or generous.
If someone is not tall or tall then someone is old or not curious.
If john is quiet then someone is calm and vice versa.
If paul is not funny or wise then someone is both not funny and not wise.
Everyone who is either not humble or quiet is old and vice versa.
If someone is not curious or happy then lucy is both not wise and creative and vice versa.
Everyone who is both rich and curious is not strong or happy.
If someone is either not rich or not calm then someone is not calm or not tall and vice versa.
If john is both strong and funny then someone is funny.
Everyone who is not creative or not kind is kind or rich.
If someone is happy then john is not wise and vice versa.
Everyone who is humble or not strong is not rich or calm.
Susan is curious or tall.
Alice is both wise and kind.
Alice is not strong or calm.
Alice is not quiet.
Someone is not tall.
Someone is not tall or curious.
Someone is either kind or strong. | Paul is not old. | neutral | (((kind(lucy)|funny(lucy)))=>(wise(john)))&
(![X]:(tall(X)<=>(strong(X)|calm(X))))&
((?[X]:((~strong(X)|~calm(X))))=>((humble(lucy)&quiet(lucy))))&
(![X]:((~happy(X)<~>~humble(X))<=>(funny(X)&calm(X))))&
((?[X]:(~rich(X)))=>((~funny(alice)|generous(alice))))&
((?[X]:((~tall(X)|tall(X))))=>(?[X]:((old(X)|~curious(X)))))&
((quiet(john))<=>(?[X]:(calm(X))))&
(((~funny(paul)|wise(paul)))=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~humble(X)<~>quiet(X))<=>old(X)))&
((?[X]:((~curious(X)|happy(X))))<=>((~wise(lucy)&creative(lucy))))&
(![X]:((rich(X)&curious(X))=>(~strong(X)|happy(X))))&
((?[X]:((~rich(X)<~>~calm(X))))<=>(?[X]:((~calm(X)|~tall(X)))))&
(((strong(john)&funny(john)))=>(?[X]:(funny(X))))&
(![X]:((~creative(X)|~kind(X))=>(kind(X)|rich(X))))&
((?[X]:(happy(X)))<=>(~wise(john)))&
(![X]:((humble(X)|~strong(X))=>(~rich(X)|calm(X))))&
((curious(susan)|tall(susan)))&
((wise(alice)&kind(alice)))&
((~strong(alice)|calm(alice)))&
(~quiet(alice))&
(?[X]:(~tall(X)))&
(?[X]:((~tall(X)|curious(X))))&
(?[X]:((kind(X)<~>strong(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is either not creative or quiet is both not tall and not humble.
Everyone who is both old and not calm is both old and not humble and vice versa.
If someone is both patient and not strong then john is either strong or not kind and vice versa.
If someone is not kind then someone is both not funny and not kind and vice versa.
If someone is wise or not calm then someone is brave or not strong and vice versa.
Everyone who is not kind or old is either wise or not kind.
If lucy is either not tall or quiet then someone is funny.
If someone is kind then susan is old and vice versa.
If someone is not kind or not humble then paul is both old and not curious.
Everyone who is both rich and tall is not patient or creative and vice versa.
Everyone who is not humble is not generous and vice versa.
If mary is wise then someone is either old or happy.
Everyone who is both not kind and wise is not calm and vice versa.
If someone is either brave or not strong then someone is either rich or not calm.
If alice is both tall and not brave then john is not creative or calm and vice versa.
If someone is not patient then someone is not funny or strong and vice versa.
Someone is calm or strong.
Someone is kind.
Someone is either not curious or not old.
Paul is either not creative or not curious.
Someone is not brave or not humble.
Someone is curious.
Susan is both wise and not brave.
Paul is not quiet or brave. | Mary is calm. | entailment | (![X]:((~creative(X)<~>quiet(X))=>(~tall(X)&~humble(X))))&
(![X]:((old(X)&~calm(X))<=>(old(X)&~humble(X))))&
((?[X]:((patient(X)&~strong(X))))<=>((strong(john)<~>~kind(john))))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:((brave(X)|~strong(X)))))&
(![X]:((~kind(X)|old(X))=>(wise(X)<~>~kind(X))))&
(((~tall(lucy)<~>quiet(lucy)))=>(?[X]:(funny(X))))&
((?[X]:(kind(X)))<=>(old(susan)))&
((?[X]:((~kind(X)|~humble(X))))=>((old(paul)&~curious(paul))))&
(![X]:((rich(X)&tall(X))<=>(~patient(X)|creative(X))))&
(![X]:(~humble(X)<=>~generous(X)))&
((wise(mary))=>(?[X]:((old(X)<~>happy(X)))))&
(![X]:((~kind(X)&wise(X))<=>~calm(X)))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((tall(alice)&~brave(alice)))<=>((~creative(john)|calm(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((~funny(X)|strong(X)))))&
(?[X]:((calm(X)|strong(X))))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)<~>~old(X))))&
((~creative(paul)<~>~curious(paul)))&
(?[X]:((~brave(X)|~humble(X))))&
(?[X]:(curious(X)))&
((wise(susan)&~brave(susan)))&
((~quiet(paul)|brave(paul))) | calm(mary) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2928034300261939114184277
% SZS output start Proof for 2928034300261939114184277
6. ! [X0] : ((old(X0) | ~kind(X0)) => (wise(X0) <~> ~kind(X0))) [input p5]
13. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~calm(X0)) [input p12]
25. ~calm(mary) [input hypothesis]
31. ! [X0] : ((wise(X0) <~> ~kind(X0)) | (~old(X0) & kind(X0))) [ennf transformation 6]
53. ! [X0] : (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | (~old(X0) & kind(X0))) [nnf transformation 31]
67. ! [X0] : (((wise(X0) & ~kind(X0)) | calm(X0)) & (~calm(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 13]
68. ! [X0] : (((wise(X0) & ~kind(X0)) | calm(X0)) & (~calm(X0) | ~wise(X0) | kind(X0))) [flattening 67]
115. kind(X0) | ~wise(X0) | kind(X0) [cnf transformation 53]
135. ~kind(X0) | calm(X0) [cnf transformation 68]
136. wise(X0) | calm(X0) [cnf transformation 68]
160. ~calm(mary) [cnf transformation 25]
161. ~wise(X0) | kind(X0) [duplicate literal removal 115]
225. 15 <=> ! [X3] : calm(X3) [avatar definition]
226. calm(X3) <- (15) [avatar component clause 225]
420. kind(X0) | calm(X0) [resolution 161,136]
422. calm(X0) [subsumption resolution 420,135]
423. 15 [avatar split clause 422,225]
425. $false <- (15) [resolution 226,160]
430. ~15 [avatar contradiction clause 425]
432. $false [avatar sat refutation 423,430]
% SZS output end Proof for 2928034300261939114184277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not tall is curious and vice versa. Everyone who is funny or not strong is both not generous and not humble. Everyone who is both happy and not tall is not brave. If someone is strong then paul is calm. If john is both happy and not funny then someone is happy and vice versa. If someone is not calm then mary is creative. Everyone who is not old or creative is both calm and not brave and vice versa. Everyone who is creative or not happy is strong. If alice is both not patient and quiet then someone is either not quiet or not generous and vice versa. Everyone who is not rich or not curious is not tall and vice versa. If someone is both rich and generous then someone is both generous and not funny and vice versa. If susan is both strong and old then mary is tall or not strong. Everyone who is not wise is happy or humble. Everyone who is not tall is both not creative and not happy. If someone is both funny and not humble then someone is both not happy and generous and vice versa. If john is either not happy or not kind then someone is not old or quiet and vice versa. Someone is either creative or not tall. Susan is either not generous or not wise. Lucy is not happy or not brave. Mary is strong. Someone is brave. Alice is either old or not old. Someone is wise or calm. | John is not calm. | contradiction | (![X]:((~strong(X)<~>~tall(X))<=>curious(X)))&
(![X]:((funny(X)|~strong(X))=>(~generous(X)&~humble(X))))&
(![X]:((happy(X)&~tall(X))=>~brave(X)))&
((?[X]:(strong(X)))=>(calm(paul)))&
(((happy(john)&~funny(john)))<=>(?[X]:(happy(X))))&
((?[X]:(~calm(X)))=>(creative(mary)))&
(![X]:((~old(X)|creative(X))<=>(calm(X)&~brave(X))))&
(![X]:((creative(X)|~happy(X))=>strong(X)))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~rich(X)|~curious(X))<=>~tall(X)))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
(((strong(susan)&old(susan)))=>((tall(mary)|~strong(mary))))&
(![X]:(~wise(X)=>(happy(X)|humble(X))))&
(![X]:(~tall(X)=>(~creative(X)&~happy(X))))&
((?[X]:((funny(X)&~humble(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(((~happy(john)<~>~kind(john)))<=>(?[X]:((~old(X)|quiet(X)))))&
(?[X]:((creative(X)<~>~tall(X))))&
((~generous(susan)<~>~wise(susan)))&
((~happy(lucy)|~brave(lucy)))&
(strong(mary))&
(?[X]:(brave(X)))&
((old(alice)<~>~old(alice)))&
(?[X]:((wise(X)|calm(X)))) | ~calm(john) | [
"p0",
"p5",
"p9",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5887764702263814390427431
% SZS output start Proof for 5887764702263814390427431
1. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> curious(X0)) [input p0]
6. ? [X0] : ~calm(X0) => creative(mary) [input p5]
10. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> ~tall(X0)) [input p9]
14. ! [X0] : (~tall(X0) => (~happy(X0) & ~creative(X0))) [input p13]
20. strong(mary) [input p19]
24. ~calm(john) [input hypothesis]
31. creative(mary) | ! [X0] : calm(X0) [ennf transformation 6]
37. ! [X0] : ((~happy(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 14]
38. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ~curious(X0)) & (curious(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 1]
51. ! [X0] : (((~curious(X0) | ~rich(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) & rich(X0)))) [nnf transformation 10]
52. ! [X0] : ((~curious(X0) | ~rich(X0) | tall(X0)) & (~tall(X0) | (curious(X0) & rich(X0)))) [flattening 51]
78. ~curious(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 38]
89. creative(mary) | calm(X0) [cnf transformation 31]
104. ~tall(X0) | curious(X0) [cnf transformation 52]
112. ~creative(X0) | tall(X0) [cnf transformation 37]
129. strong(mary) [cnf transformation 20]
134. ~calm(john) [cnf transformation 24]
162. 7 <=> ! [X0] : calm(X0) [avatar definition]
163. calm(X0) <- (7) [avatar component clause 162]
165. 8 <=> creative(mary) [avatar definition]
167. creative(mary) <- (8) [avatar component clause 165]
168. 7 | 8 [avatar split clause 89,165,162]
234. 23 <=> tall(mary) [avatar definition]
236. tall(mary) <- (23) [avatar component clause 234]
238. 24 <=> strong(mary) [avatar definition]
239. strong(mary) <- (24) [avatar component clause 238]
322. 24 [avatar split clause 129,238]
342. $false <- (7) [resolution 163,134]
343. ~7 [avatar contradiction clause 342]
358. tall(mary) <- (8) [resolution 112,167]
359. 23 | ~8 [avatar split clause 358,165,234]
360. curious(mary) <- (23) [resolution 236,104]
391. ~strong(mary) | ~tall(mary) <- (23) [resolution 78,360]
392. ~tall(mary) <- (23, 24) [subsumption resolution 391,239]
393. $false <- (23, 24) [subsumption resolution 392,236]
394. ~23 | ~24 [avatar contradiction clause 393]
395. $false [avatar sat refutation 168,322,343,359,394]
% SZS output end Proof for 5887764702263814390427431
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy or funny then someone is brave and vice versa. Everyone who is curious or strong is not funny. If someone is both tall and humble then someone is not rich or wise. If susan is calm then someone is both not calm and curious and vice versa. Everyone who is generous is kind or not generous and vice versa. Everyone who is either not rich or not tall is not rich. If alice is both not funny and not quiet then someone is kind and vice versa. Everyone who is curious or rich is not curious or not calm. Everyone who is generous or not humble is not brave. Everyone who is curious is either not patient or not funny and vice versa. If someone is humble then someone is not generous or not old and vice versa. Everyone who is either tall or kind is creative or tall. If fred is tall or creative then someone is brave or not patient and vice versa. If someone is either not brave or funny then someone is generous and vice versa. Everyone who is either not generous or tall is either calm or not funny and vice versa. Everyone who is humble or not strong is brave and vice versa. Someone is either curious or not rich. Someone is both strong and calm. Mary is either kind or brave. Someone is not strong or not rich. Alice is not wise. Someone is both not humble and curious. Paul is wise or not patient. | Alice is humble. | contradiction | (((happy(mary)|funny(mary)))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)|strong(X))=>~funny(X)))&
((?[X]:((tall(X)&humble(X))))=>(?[X]:((~rich(X)|wise(X)))))&
((calm(susan))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(generous(X)<=>(kind(X)|~generous(X))))&
(![X]:((~rich(X)<~>~tall(X))=>~rich(X)))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:(kind(X))))&
(![X]:((curious(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((generous(X)|~humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>(~patient(X)<~>~funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((tall(X)<~>kind(X))=>(creative(X)|tall(X))))&
(((tall(fred)|creative(fred)))<=>(?[X]:((brave(X)|~patient(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(generous(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((humble(X)|~strong(X))<=>brave(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((strong(X)&calm(X))))&
((kind(mary)<~>brave(mary)))&
(?[X]:((~strong(X)|~rich(X))))&
(~wise(alice))&
(?[X]:((~humble(X)&curious(X))))&
((wise(paul)|~patient(paul))) | humble(alice) | [
"p4",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9150872679833201683802954
% SZS output start Proof for 9150872679833201683802954
5. ! [X0] : (generous(X0) <=> (~generous(X0) | kind(X0))) [input p4]
9. ! [X0] : ((~humble(X0) | generous(X0)) => ~brave(X0)) [input p8]
16. ! [X0] : ((~strong(X0) | humble(X0)) <=> brave(X0)) [input p15]
24. humble(alice) [input hypothesis]
33. ! [X0] : (~brave(X0) | (humble(X0) & ~generous(X0))) [ennf transformation 9]
48. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((generous(X0) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | ~generous(X0))) [flattening 48]
74. ! [X0] : (((~strong(X0) | humble(X0)) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [nnf transformation 16]
75. ! [X0] : ((~strong(X0) | humble(X0) | ~brave(X0)) & (brave(X0) | (strong(X0) & ~humble(X0)))) [flattening 74]
97. generous(X0) | generous(X0) [cnf transformation 49]
105. ~brave(X0) | ~generous(X0) [cnf transformation 33]
132. ~humble(X0) | brave(X0) [cnf transformation 75]
146. humble(alice) [cnf transformation 24]
151. generous(X0) [duplicate literal removal 97]
153. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
154. ~brave(X0) <- (1) [avatar component clause 153]
203. ~brave(X0) [subsumption resolution 105,151]
204. 1 [avatar split clause 203,153]
296. brave(alice) [resolution 132,146]
298. $false <- (1) [subsumption resolution 296,154]
299. ~1 [avatar contradiction clause 298]
302. $false [avatar sat refutation 204,299]
% SZS output end Proof for 9150872679833201683802954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and quiet is both funny and wise and vice versa. Everyone who is either not calm or creative is either not tall or kind and vice versa. Everyone who is either kind or not wise is tall. Everyone who is not kind is rich or wise. Everyone who is funny is not old or not happy and vice versa. Everyone who is both calm and not strong is creative or not humble. Everyone who is curious or not happy is strong or not brave and vice versa. Everyone who is both not wise and not old is either old or patient and vice versa. Everyone who is not calm or old is not strong or quiet and vice versa. If paul is either rich or not generous then someone is patient or tall and vice versa. Everyone who is not quiet is either not happy or quiet and vice versa. If susan is happy or rich then paul is tall and vice versa. If someone is not brave or not creative then paul is humble and vice versa. If someone is not quiet or creative then paul is both kind and not curious and vice versa. Everyone who is both kind and patient is either not happy or not rich. Everyone who is either curious or old is both not brave and happy. Someone is not patient. Someone is either humble or not patient. Lucy is rich. Mary is either creative or funny. Alice is strong. Alice is both not creative and not wise. | Paul is rich. | entailment | (![X]:((creative(X)&quiet(X))<=>(funny(X)&wise(X))))&
(![X]:((~calm(X)<~>creative(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((kind(X)<~>~wise(X))=>tall(X)))&
(![X]:(~kind(X)=>(rich(X)|wise(X))))&
(![X]:(funny(X)<=>(~old(X)|~happy(X))))&
(![X]:((calm(X)&~strong(X))=>(creative(X)|~humble(X))))&
(![X]:((curious(X)|~happy(X))<=>(strong(X)|~brave(X))))&
(![X]:((~wise(X)&~old(X))<=>(old(X)<~>patient(X))))&
(![X]:((~calm(X)|old(X))<=>(~strong(X)|quiet(X))))&
(((rich(paul)<~>~generous(paul)))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>quiet(X))))&
(((happy(susan)|rich(susan)))<=>(tall(paul)))&
((?[X]:((~brave(X)|~creative(X))))<=>(humble(paul)))&
((?[X]:((~quiet(X)|creative(X))))<=>((kind(paul)&~curious(paul))))&
(![X]:((kind(X)&patient(X))=>(~happy(X)<~>~rich(X))))&
(![X]:((curious(X)<~>old(X))=>(~brave(X)&happy(X))))&
(?[X]:(~patient(X)))&
(?[X]:((humble(X)<~>~patient(X))))&
(rich(lucy))&
((creative(mary)<~>funny(mary)))&
(strong(alice))&
((~creative(alice)&~wise(alice))) | rich(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p7",
"p8",
"p10",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3422451856213444138728459
% SZS output start Proof for 3422451856213444138728459
1. ! [X0] : ((quiet(X0) & creative(X0)) <=> (wise(X0) & funny(X0))) [input p0]
2. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~tall(X0) <~> kind(X0))) [input p1]
3. ! [X0] : ((kind(X0) <~> ~wise(X0)) => tall(X0)) [input p2]
4. ! [X0] : (~kind(X0) => (wise(X0) | rich(X0))) [input p3]
5. ! [X0] : (funny(X0) <=> (~happy(X0) | ~old(X0))) [input p4]
8. ! [X0] : ((~old(X0) & ~wise(X0)) <=> (old(X0) <~> patient(X0))) [input p7]
9. ! [X0] : ((old(X0) | ~calm(X0)) <=> (quiet(X0) | ~strong(X0))) [input p8]
11. ! [X0] : (~quiet(X0) <=> (~happy(X0) <~> quiet(X0))) [input p10]
14. ? [X0] : (creative(X0) | ~quiet(X0)) <=> (~curious(paul) & kind(paul)) [input p13]
15. ! [X0] : ((patient(X0) & kind(X0)) => (~happy(X0) <~> ~rich(X0))) [input p14]
16. ! [X0] : ((curious(X0) <~> old(X0)) => (happy(X0) & ~brave(X0))) [input p15]
17. ? [X0] : ~patient(X0) [input p16]
23. ~rich(paul) [input hypothesis]
24. ! [X0] : (tall(X0) | (kind(X0) <=> ~wise(X0))) [ennf transformation 3]
25. ! [X0] : ((wise(X0) | rich(X0)) | kind(X0)) [ennf transformation 4]
26. ! [X0] : (wise(X0) | rich(X0) | kind(X0)) [flattening 25]
29. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | (~patient(X0) | ~kind(X0))) [ennf transformation 15]
30. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | ~patient(X0) | ~kind(X0)) [flattening 29]
31. ! [X0] : ((happy(X0) & ~brave(X0)) | (curious(X0) <=> old(X0))) [ennf transformation 16]
32. ! [X0] : (((quiet(X0) & creative(X0)) | (~wise(X0) | ~funny(X0))) & ((wise(X0) & funny(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((quiet(X0) & creative(X0)) | ~wise(X0) | ~funny(X0)) & ((wise(X0) & funny(X0)) | ~quiet(X0) | ~creative(X0))) [flattening 32]
34. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 2]
35. ! [X0] : (tall(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0)))) [nnf transformation 24]
36. ! [X0] : ((funny(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | ~funny(X0))) [nnf transformation 5]
37. ! [X0] : ((funny(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | ~funny(X0))) [flattening 36]
40. ! [X0] : (((~old(X0) & ~wise(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | (old(X0) | wise(X0)))) [nnf transformation 8]
41. ! [X0] : (((~old(X0) & ~wise(X0)) | ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0)))) & (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | old(X0) | wise(X0))) [flattening 40]
42. ! [X0] : (((old(X0) | ~calm(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (~old(X0) & calm(X0)))) [nnf transformation 9]
43. ! [X0] : ((old(X0) | ~calm(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | (~old(X0) & calm(X0)))) [flattening 42]
48. ! [X0] : ((~quiet(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0)))) & (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | quiet(X0))) [nnf transformation 11]
55. (? [X0] : (creative(X0) | ~quiet(X0)) | (curious(paul) | ~kind(paul))) & ((~curious(paul) & kind(paul)) | ! [X0] : (~creative(X0) & quiet(X0))) [nnf transformation 14]
56. (? [X0] : (creative(X0) | ~quiet(X0)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X0] : (~creative(X0) & quiet(X0))) [flattening 55]
57. (? [X0] : (creative(X0) | ~quiet(X0)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X1] : (~creative(X1) & quiet(X1))) [rectify 56]
58. ? [X0] : (creative(X0) | ~quiet(X0)) => (creative(sK2) | ~quiet(sK2)) [choice axiom]
59. ((creative(sK2) | ~quiet(sK2)) | curious(paul) | ~kind(paul)) & ((~curious(paul) & kind(paul)) | ! [X1] : (~creative(X1) & quiet(X1))) [skolemisation 57,58]
60. ! [X0] : (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ~patient(X0) | ~kind(X0)) [nnf transformation 30]
61. ! [X0] : ((happy(X0) & ~brave(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0)))) [nnf transformation 31]
62. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
63. ~patient(sK3) [skolemisation 17,62]
70. ~wise(X0) | creative(X0) | ~funny(X0) [cnf transformation 33]
71. ~wise(X0) | quiet(X0) | ~funny(X0) [cnf transformation 33]
79. ~kind(X0) | calm(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 34]
80. ~kind(X0) | ~wise(X0) | tall(X0) [cnf transformation 35]
82. rich(X0) | wise(X0) | kind(X0) [cnf transformation 26]
85. happy(X0) | funny(X0) [cnf transformation 37]
91. patient(X0) | old(X0) | old(X0) | wise(X0) [cnf transformation 41]
95. ~old(X0) | patient(X0) | ~old(X0) [cnf transformation 41]
100. ~calm(X0) | old(X0) | ~quiet(X0) [cnf transformation 43]
107. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 48]
110. ~quiet(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 48]
118. kind(paul) | ~creative(X1) [cnf transformation 59]
120. ~curious(paul) | ~creative(X1) [cnf transformation 59]
123. rich(X0) | happy(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 60]
127. happy(X0) | curious(X0) | ~old(X0) [cnf transformation 61]
128. ~patient(sK3) [cnf transformation 63]
137. ~rich(paul) [cnf transformation 23]
138. quiet(X0) | ~happy(X0) [duplicate literal removal 107]
139. ~happy(X0) | ~quiet(X0) [duplicate literal removal 110]
140. patient(X0) | old(X0) | wise(X0) [duplicate literal removal 91]
141. ~old(X0) | patient(X0) [duplicate literal removal 95]
142. patient(X0) | wise(X0) [subsumption resolution 140,141]
147. 2 <=> rich(paul) [avatar definition]
149. ~rich(paul) <- (~2) [avatar component clause 147]
171. ~happy(X0) [subsumption resolution 138,139]
174. 7 <=> tall(paul) [avatar definition]
175. tall(paul) <- (7) [avatar component clause 174]
205. 14 <=> kind(paul) [avatar definition]
206. kind(paul) <- (14) [avatar component clause 205]
209. 15 <=> curious(paul) [avatar definition]
210. ~curious(paul) <- (~15) [avatar component clause 209]
222. 18 <=> ! [X1] : ~creative(X1) [avatar definition]
223. ~creative(X1) <- (18) [avatar component clause 222]
224. 18 | ~15 [avatar split clause 120,209,222]
229. 18 | 14 [avatar split clause 118,205,222]
231. ~patient(X0) | rich(X0) | ~kind(X0) [subsumption resolution 123,171]
232. ~old(X0) | curious(X0) [subsumption resolution 127,171]
254. ~2 [avatar split clause 137,147]
255. funny(X0) [resolution 85,171]
260. wise(sK3) [resolution 142,128]
263. creative(sK3) | ~funny(sK3) [resolution 70,260]
265. creative(sK3) [subsumption resolution 263,255]
271. ~wise(paul) | tall(paul) <- (14) [resolution 80,206]
289. 26 <=> wise(paul) [avatar definition]
290. wise(paul) <- (26) [avatar component clause 289]
292. 7 | ~26 | ~14 [avatar split clause 271,205,289,174]
331. rich(X0) | ~kind(X0) | wise(X0) [resolution 231,142]
341. rich(X0) | wise(X0) [subsumption resolution 331,82]
377. 36 <=> creative(paul) [avatar definition]
381. 37 <=> calm(paul) [avatar definition]
382. calm(paul) <- (37) [avatar component clause 381]
383. ~calm(paul) <- (~37) [avatar component clause 381]
443. calm(paul) | ~tall(paul) | ~creative(paul) <- (14) [resolution 79,206]
445. ~tall(paul) | ~creative(paul) <- (14, ~37) [subsumption resolution 443,383]
446. ~creative(paul) <- (7, 14, ~37) [subsumption resolution 445,175]
447. ~36 | ~7 | ~14 | 37 [avatar split clause 446,381,205,174,377]
460. wise(paul) <- (~2) [resolution 341,149]
461. 26 | 2 [avatar split clause 460,147,289]
462. quiet(paul) | ~funny(paul) <- (26) [resolution 290,71]
463. creative(paul) | ~funny(paul) <- (26) [resolution 290,70]
464. quiet(paul) <- (26) [subsumption resolution 462,255]
470. creative(paul) <- (26) [subsumption resolution 463,255]
471. 36 | ~26 [avatar split clause 470,289,377]
473. $false <- (18) [resolution 223,265]
476. ~18 [avatar contradiction clause 473]
490. old(paul) | ~quiet(paul) <- (37) [resolution 382,100]
492. old(paul) <- (26, 37) [subsumption resolution 490,464]
499. curious(paul) <- (26, 37) [resolution 492,232]
501. $false <- (~15, 26, 37) [subsumption resolution 499,210]
502. 15 | ~26 | ~37 [avatar contradiction clause 501]
503. $false [avatar sat refutation 224,229,254,292,447,461,471,476,502]
% SZS output end Proof for 3422451856213444138728459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or not strong then someone is both patient and wise.
If fred is not curious or tall then someone is humble or old.
If john is either rich or not calm then someone is not calm or not generous.
Everyone who is both not calm and not funny is generous.
Everyone who is not calm is not generous or not kind.
If someone is brave or curious then john is quiet and vice versa.
If john is both not rich and not strong then lucy is either strong or wise and vice versa.
Everyone who is either not tall or wise is both quiet and not generous.
Everyone who is both quiet and not old is both not strong and funny.
If john is either not brave or not curious then someone is not brave.
Everyone who is not old or humble is both generous and not old.
Everyone who is either generous or not kind is not calm and vice versa.
If someone is quiet then john is not generous.
Everyone who is either not tall or not curious is both humble and not brave.
Everyone who is quiet is tall and vice versa.
Everyone who is strong is not old and vice versa.
Fred is not kind or not creative.
Someone is both humble and not tall.
Someone is either tall or not tall.
Someone is patient.
John is not happy or not calm.
Someone is not happy. | John is not kind. | neutral | ((?[X]:((~kind(X)|~strong(X))))=>(?[X]:((patient(X)&wise(X)))))&
(((~curious(fred)|tall(fred)))=>(?[X]:((humble(X)|old(X)))))&
(((rich(john)<~>~calm(john)))=>(?[X]:((~calm(X)|~generous(X)))))&
(![X]:((~calm(X)&~funny(X))=>generous(X)))&
(![X]:(~calm(X)=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)|curious(X))))<=>(quiet(john)))&
(((~rich(john)&~strong(john)))<=>((strong(lucy)<~>wise(lucy))))&
(![X]:((~tall(X)<~>wise(X))=>(quiet(X)&~generous(X))))&
(![X]:((quiet(X)&~old(X))=>(~strong(X)&funny(X))))&
(((~brave(john)<~>~curious(john)))=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|humble(X))=>(generous(X)&~old(X))))&
(![X]:((generous(X)<~>~kind(X))<=>~calm(X)))&
((?[X]:(quiet(X)))=>(~generous(john)))&
(![X]:((~tall(X)<~>~curious(X))=>(humble(X)&~brave(X))))&
(![X]:(quiet(X)<=>tall(X)))&
(![X]:(strong(X)<=>~old(X)))&
((~kind(fred)|~creative(fred)))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
(?[X]:(patient(X)))&
((~happy(john)|~calm(john)))&
(?[X]:(~happy(X))) | ~kind(john) | [] | null | 0 |
Everyone who is humble or happy is either not old or kind and vice versa. If someone is either curious or quiet then someone is quiet or generous and vice versa. Everyone who is either not kind or not calm is patient and vice versa. If alice is not happy or brave then someone is creative. If someone is both generous and quiet then someone is either not kind or calm and vice versa. Everyone who is not brave or old is both not funny and quiet. Everyone who is both patient and kind is generous and vice versa. Everyone who is either curious or patient is curious or not quiet and vice versa. Everyone who is wise is either calm or funny and vice versa. If someone is either brave or not old then lucy is strong. If john is both not strong and not curious then someone is both not generous and not tall. Everyone who is both quiet and curious is wise or happy and vice versa. If alice is either brave or not humble then someone is brave or not strong and vice versa. Lucy is either tall or not creative. Susan is patient or not tall. Someone is brave. Someone is not happy or not curious. Alice is either funny or wise. Someone is either not quiet or not funny. | John is not quiet. | entailment | (![X]:((humble(X)|happy(X))<=>(~old(X)<~>kind(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>patient(X)))&
(((~happy(alice)|brave(alice)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~brave(X)|old(X))=>(~funny(X)&quiet(X))))&
(![X]:((patient(X)&kind(X))<=>generous(X)))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)|~quiet(X))))&
(![X]:(wise(X)<=>(calm(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~old(X))))=>(strong(lucy)))&
(((~strong(john)&~curious(john)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|happy(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((brave(X)|~strong(X)))))&
((tall(lucy)<~>~creative(lucy)))&
((patient(susan)|~tall(susan)))&
(?[X]:(brave(X)))&
(?[X]:((~happy(X)|~curious(X))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | ~quiet(john) | [
"p2",
"p4",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 704812518310636151485761
% SZS output start Proof for 704812518310636151485761
3. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> patient(X0)) [input p2]
5. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X0] : (~kind(X0) <~> calm(X0)) [input p4]
7. ! [X0] : ((kind(X0) & patient(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (~quiet(X0) | curious(X0))) [input p7]
20. quiet(john) [input hypothesis]
22. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X1] : (~kind(X1) <~> calm(X1)) [rectify 5]
35. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~patient(X0)) & (patient(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 3]
38. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X1] : ((~calm(X1) | kind(X1)) & (calm(X1) | ~kind(X1))) | ! [X0] : (~quiet(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (quiet(X0) & generous(X0)) => (quiet(sK3) & generous(sK3)) [choice axiom]
41. ? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) => ((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) [choice axiom]
42. ((quiet(sK3) & generous(sK3)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | ~kind(X0) | ~patient(X0))) [flattening 43]
45. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 45]
78. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 35]
79. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 35]
86. generous(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
87. generous(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
88. quiet(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
89. quiet(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
95. ~generous(X0) | patient(X0) [cnf transformation 44]
98. ~quiet(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 46]
101. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
131. quiet(john) [cnf transformation 20]
132. ~quiet(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 98]
133. ~patient(X0) | ~curious(X0) [duplicate literal removal 101]
183. 12 <=> ! [X1] : (~kind(X1) | ~calm(X1)) [avatar definition]
184. ~calm(X1) | ~kind(X1) <- (12) [avatar component clause 183]
186. 13 <=> quiet(sK3) [avatar definition]
188. quiet(sK3) <- (13) [avatar component clause 186]
189. 12 | 13 [avatar split clause 89,186,183]
191. 14 <=> ! [X1] : (calm(X1) | kind(X1)) [avatar definition]
192. calm(X1) | kind(X1) <- (14) [avatar component clause 191]
193. 14 | 13 [avatar split clause 88,186,191]
195. 15 <=> generous(sK3) [avatar definition]
197. generous(sK3) <- (15) [avatar component clause 195]
198. 12 | 15 [avatar split clause 87,195,183]
199. 14 | 15 [avatar split clause 86,195,191]
213. ~patient(X0) | ~quiet(X0) [subsumption resolution 132,133]
318. patient(sK3) <- (15) [resolution 197,95]
319. ~quiet(sK3) <- (15) [resolution 318,213]
321. $false <- (13, 15) [subsumption resolution 319,188]
322. ~13 | ~15 [avatar contradiction clause 321]
341. patient(X0) | kind(X0) | kind(X0) <- (14) [resolution 78,192]
342. patient(X0) | kind(X0) <- (14) [duplicate literal removal 341]
343. ~quiet(X0) | kind(X0) <- (14) [resolution 342,213]
365. kind(john) <- (14) [resolution 343,131]
373. patient(john) | calm(john) <- (14) [resolution 365,79]
377. 42 <=> calm(john) [avatar definition]
379. calm(john) <- (42) [avatar component clause 377]
381. 43 <=> patient(john) [avatar definition]
383. patient(john) <- (43) [avatar component clause 381]
384. 42 | 43 | ~14 [avatar split clause 373,191,381,377]
620. ~kind(john) <- (12, 42) [resolution 379,184]
621. $false <- (12, 14, 42) [subsumption resolution 620,365]
622. ~12 | ~14 | ~42 [avatar contradiction clause 621]
650. ~quiet(john) <- (43) [resolution 383,213]
653. $false <- (43) [subsumption resolution 650,131]
654. ~43 [avatar contradiction clause 653]
655. $false [avatar sat refutation 189,193,198,199,322,384,622,654]
% SZS output end Proof for 704812518310636151485761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is either generous or not creative.
Everyone who is both happy and wise is curious or not old and vice versa.
If fred is either not strong or not quiet then john is either curious or humble.
Everyone who is curious or calm is both not kind and not quiet.
If someone is patient then someone is both brave and curious and vice versa.
If someone is either not happy or wise then someone is funny or strong.
If paul is not wise or not calm then someone is either not old or old and vice versa.
If someone is both quiet and rich then fred is both not patient and kind and vice versa.
Everyone who is not calm is not wise.
If someone is not patient then someone is generous or happy.
Everyone who is both not creative and rich is calm and vice versa.
Everyone who is both not brave and not generous is rich or curious and vice versa.
If someone is brave or not humble then someone is not humble or not calm.
Everyone who is both not wise and happy is either not wise or not humble and vice versa.
If alice is not rich then someone is old or creative and vice versa.
If someone is both kind and quiet then susan is strong or tall and vice versa.
Someone is wise.
Someone is not generous.
Someone is calm or not curious.
Mary is both not old and wise.
Someone is both happy and quiet.
Someone is either rich or not happy.
Someone is either not humble or not tall.
Someone is strong. | Alice is rich. | contradiction | (![X]:(funny(X)=>(generous(X)<~>~creative(X))))&
(![X]:((happy(X)&wise(X))<=>(curious(X)|~old(X))))&
(((~strong(fred)<~>~quiet(fred)))=>((curious(john)<~>humble(john))))&
(![X]:((curious(X)|calm(X))=>(~kind(X)&~quiet(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((funny(X)|strong(X)))))&
(((~wise(paul)|~calm(paul)))<=>(?[X]:((~old(X)<~>old(X)))))&
((?[X]:((quiet(X)&rich(X))))<=>((~patient(fred)&kind(fred))))&
(![X]:(~calm(X)=>~wise(X)))&
((?[X]:(~patient(X)))=>(?[X]:((generous(X)|happy(X)))))&
(![X]:((~creative(X)&rich(X))<=>calm(X)))&
(![X]:((~brave(X)&~generous(X))<=>(rich(X)|curious(X))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((~wise(X)&happy(X))<=>(~wise(X)<~>~humble(X))))&
((~rich(alice))<=>(?[X]:((old(X)|creative(X)))))&
((?[X]:((kind(X)&quiet(X))))<=>((strong(susan)|tall(susan))))&
(?[X]:(wise(X)))&
(?[X]:(~generous(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~old(mary)&wise(mary)))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:((rich(X)<~>~happy(X))))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:(strong(X))) | rich(alice) | [
"p1",
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1073427614206026904759162
% SZS output start Proof for 1073427614206026904759162
2. ! [X0] : ((wise(X0) & happy(X0)) <=> (~old(X0) | curious(X0))) [input p1]
7. (~calm(paul) | ~wise(paul)) <=> ? [X0] : (~old(X0) <~> old(X0)) [input p6]
9. ! [X0] : (~calm(X0) => ~wise(X0)) [input p8]
15. ~rich(alice) <=> ? [X0] : (creative(X0) | old(X0)) [input p14]
25. rich(alice) [input hypothesis]
34. ! [X0] : (~wise(X0) | calm(X0)) [ennf transformation 9]
38. ! [X0] : (((wise(X0) & happy(X0)) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | (~wise(X0) | ~happy(X0)))) [nnf transformation 2]
39. ! [X0] : (((wise(X0) & happy(X0)) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ~wise(X0) | ~happy(X0))) [flattening 38]
50. ((~calm(paul) | ~wise(paul)) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (calm(paul) & wise(paul))) [nnf transformation 7]
51. (~calm(paul) | ~wise(paul) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (? [X0] : ((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (calm(paul) & wise(paul))) [flattening 50]
52. (~calm(paul) | ~wise(paul) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (? [X1] : ((~old(X1) | old(X1)) & (old(X1) | ~old(X1))) | (calm(paul) & wise(paul))) [rectify 51]
53. ? [X1] : ((~old(X1) | old(X1)) & (old(X1) | ~old(X1))) => ((~old(sK3) | old(sK3)) & (old(sK3) | ~old(sK3))) [choice axiom]
54. (~calm(paul) | ~wise(paul) | ! [X0] : ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(sK3) | old(sK3)) & (old(sK3) | ~old(sK3))) | (calm(paul) & wise(paul))) [skolemisation 52,53]
72. (~rich(alice) | ! [X0] : (~creative(X0) & ~old(X0))) & (? [X0] : (creative(X0) | old(X0)) | rich(alice)) [nnf transformation 15]
73. (~rich(alice) | ! [X0] : (~creative(X0) & ~old(X0))) & (? [X1] : (creative(X1) | old(X1)) | rich(alice)) [rectify 72]
74. ? [X1] : (creative(X1) | old(X1)) => (creative(sK7) | old(sK7)) [choice axiom]
75. (~rich(alice) | ! [X0] : (~creative(X0) & ~old(X0))) & ((creative(sK7) | old(sK7)) | rich(alice)) [skolemisation 73,74]
103. old(X0) | wise(X0) [cnf transformation 39]
121. ~calm(paul) | ~wise(paul) | old(X0) | old(X0) [cnf transformation 54]
127. ~wise(X0) | calm(X0) [cnf transformation 34]
146. ~rich(alice) | ~old(X0) [cnf transformation 75]
165. rich(alice) [cnf transformation 25]
168. ~calm(paul) | ~wise(paul) | old(X0) [duplicate literal removal 121]
228. 14 <=> ! [X0] : ~old(X0) [avatar definition]
229. ~old(X0) <- (14) [avatar component clause 228]
231. 15 <=> wise(paul) [avatar definition]
233. ~wise(paul) <- (~15) [avatar component clause 231]
235. 16 <=> calm(paul) [avatar definition]
237. ~calm(paul) <- (~16) [avatar component clause 235]
240. 17 <=> ! [X0] : old(X0) [avatar definition]
241. old(X0) <- (17) [avatar component clause 240]
242. 17 | ~15 | ~16 [avatar split clause 168,235,231,240]
300. 31 <=> rich(alice) [avatar definition]
304. 14 | ~31 [avatar split clause 146,300,228]
367. 31 [avatar split clause 165,300]
377. wise(X0) <- (14) [resolution 103,229]
387. calm(X0) <- (14) [resolution 127,377]
429. $false <- (14, ~16) [resolution 387,237]
432. ~14 | 16 [avatar contradiction clause 429]
434. $false <- (14, ~15) [subsumption resolution 233,377]
435. ~14 | 15 [avatar contradiction clause 434]
436. $false <- (14, 17) [subsumption resolution 241,229]
437. ~14 | ~17 [avatar contradiction clause 436]
438. $false [avatar sat refutation 242,304,367,432,435,437]
% SZS output end Proof for 1073427614206026904759162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or not creative then fred is not tall or not happy and vice versa. If someone is brave then someone is calm and vice versa. If alice is both not wise and not quiet then someone is both calm and not old and vice versa. Everyone who is wise or not patient is either not happy or rich and vice versa. Everyone who is not kind is either wise or creative. Everyone who is calm is not old and vice versa. Everyone who is both wise and not humble is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Everyone who is not rich is not old or curious and vice versa. Everyone who is not wise or creative is both not curious and quiet. If lucy is kind or not kind then mary is not funny and vice versa. Everyone who is both kind and funny is both funny and not happy. Someone is both not quiet and not happy. John is not calm. Lucy is either creative or not tall. Someone is not calm. Someone is not rich or not funny. John is both not tall and not creative. Someone is either wise or funny. | Paul is old. | entailment | ((?[X]:((rich(X)<~>~creative(X))))<=>((~tall(fred)|~happy(fred))))&
((?[X]:(brave(X)))<=>(?[X]:(calm(X))))&
(((~wise(alice)&~quiet(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(~kind(X)=>(wise(X)<~>creative(X))))&
(![X]:(calm(X)<=>~old(X)))&
(![X]:((wise(X)&~humble(X))=>(~quiet(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
(![X]:(~rich(X)<=>(~old(X)|curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~curious(X)&quiet(X))))&
(((kind(lucy)|~kind(lucy)))<=>(~funny(mary)))&
(![X]:((kind(X)&funny(X))=>(funny(X)&~happy(X))))&
(?[X]:((~quiet(X)&~happy(X))))&
(~calm(john))&
((creative(lucy)<~>~tall(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)|~funny(X))))&
((~tall(john)&~creative(john)))&
(?[X]:((wise(X)<~>funny(X)))) | old(paul) | [
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 908058366515598797318826
% SZS output start Proof for 908058366515598797318826
3. (~quiet(alice) & ~wise(alice)) <=> ? [X0] : (~old(X0) & calm(X0)) [input p2]
6. ! [X0] : (calm(X0) <=> ~old(X0)) [input p5]
14. ! [X0] : ((creative(X0) | ~wise(X0)) => (quiet(X0) & ~curious(X0))) [input p13]
24. ~old(paul) [input hypothesis]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 14]
48. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | (quiet(alice) | wise(alice))) [nnf transformation 3]
49. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | quiet(alice) | wise(alice)) [flattening 48]
50. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X1] : (~old(X1) & calm(X1)) | quiet(alice) | wise(alice)) [rectify 49]
51. ? [X1] : (~old(X1) & calm(X1)) => (~old(sK3) & calm(sK3)) [choice axiom]
52. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & ((~old(sK3) & calm(sK3)) | quiet(alice) | wise(alice)) [skolemisation 50,51]
56. ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))) [nnf transformation 6]
89. ~wise(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
90. ~quiet(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
99. ~old(X0) | ~calm(X0) [cnf transformation 56]
100. old(X0) | calm(X0) [cnf transformation 56]
115. quiet(X0) | wise(X0) [cnf transformation 35]
133. ~old(paul) [cnf transformation 24]
163. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
164. ~calm(X1) <- (7) [avatar component clause 163]
179. 11 <=> ! [X0] : (old(X0) | ~calm(X0)) [avatar definition]
180. old(X0) | ~calm(X0) <- (11) [avatar component clause 179]
182. 12 <=> quiet(alice) [avatar definition]
184. ~quiet(alice) <- (~12) [avatar component clause 182]
185. 11 | ~12 [avatar split clause 90,182,179]
187. 13 <=> wise(alice) [avatar definition]
189. ~wise(alice) <- (~13) [avatar component clause 187]
190. 11 | ~13 [avatar split clause 89,187,179]
268. ~calm(X0) <- (11) [subsumption resolution 180,99]
269. 7 | ~11 [avatar split clause 268,179,163]
270. calm(paul) [resolution 100,133]
272. $false <- (7) [subsumption resolution 270,164]
273. ~7 [avatar contradiction clause 272]
278. wise(alice) <- (~12) [resolution 115,184]
279. $false <- (~12, ~13) [subsumption resolution 278,189]
280. 12 | 13 [avatar contradiction clause 279]
281. $false [avatar sat refutation 185,190,269,273,280]
% SZS output end Proof for 908058366515598797318826
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then susan is both not quiet and not old and vice versa.
Everyone who is not curious or not humble is quiet and vice versa.
If someone is either wise or not tall then someone is generous or not quiet and vice versa.
Everyone who is both not curious and not wise is curious or not quiet and vice versa.
If someone is either not strong or tall then mary is humble or not happy and vice versa.
If someone is either not quiet or not curious then someone is either strong or quiet and vice versa.
Everyone who is curious or not old is wise or calm and vice versa.
Everyone who is both strong and tall is either not patient or quiet and vice versa.
If fred is humble then lucy is not wise and vice versa.
If john is either not generous or not rich then susan is not rich and vice versa.
Everyone who is either humble or happy is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
If fred is not wise or kind then someone is rich or patient.
Everyone who is humble is both not quiet and not patient.
John is not quiet or happy.
Someone is not patient.
Someone is either creative or rich.
Lucy is calm or not generous.
Paul is not patient or not creative.
John is either not generous or calm. | Fred is not curious. | entailment | ((?[X]:(~generous(X)))<=>((~quiet(susan)&~old(susan))))&
(![X]:((~curious(X)|~humble(X))<=>quiet(X)))&
((?[X]:((wise(X)<~>~tall(X))))<=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(curious(X)|~quiet(X))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((humble(mary)|~happy(mary))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((curious(X)|~old(X))<=>(wise(X)|calm(X))))&
(![X]:((strong(X)&tall(X))<=>(~patient(X)<~>quiet(X))))&
((humble(fred))<=>(~wise(lucy)))&
(((~generous(john)<~>~rich(john)))<=>(~rich(susan)))&
(![X]:((humble(X)<~>happy(X))<=>(~wise(X)<~>happy(X))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(humble(X)=>(~quiet(X)&~patient(X))))&
((~quiet(john)|happy(john)))&
(?[X]:(~patient(X)))&
(?[X]:((creative(X)<~>rich(X))))&
((calm(lucy)|~generous(lucy)))&
((~patient(paul)|~creative(paul)))&
((~generous(john)<~>calm(john))) | ~curious(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6930191870787159333726750
% SZS output start Proof for 6930191870787159333726750
4. ! [X0] : ((~wise(X0) & ~curious(X0)) <=> (~quiet(X0) | curious(X0))) [input p3]
23. curious(fred) [input hypothesis]
43. ! [X0] : (((~wise(X0) & ~curious(X0)) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | (wise(X0) | curious(X0)))) [nnf transformation 4]
44. ! [X0] : (((~wise(X0) & ~curious(X0)) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | wise(X0) | curious(X0))) [flattening 43]
90. ~curious(X0) | ~curious(X0) [cnf transformation 44]
152. curious(fred) [cnf transformation 23]
158. ~curious(X0) [duplicate literal removal 90]
359. $false [subsumption resolution 152,158]
% SZS output end Proof for 6930191870787159333726750
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is curious then someone is either creative or not brave.
If someone is not patient or generous then someone is not old.
Everyone who is not happy is both not humble and curious.
If mary is quiet then fred is generous.
Everyone who is both not rich and happy is curious and vice versa.
Everyone who is strong is both funny and strong and vice versa.
If fred is either not tall or not creative then fred is not rich or not funny.
Everyone who is not brave or funny is not tall and vice versa.
If someone is either not kind or curious then paul is both not quiet and not generous.
Everyone who is happy or not calm is not brave.
Everyone who is either not wise or not curious is not patient and vice versa.
Everyone who is both not brave and not old is both not calm and tall.
If lucy is both curious and not brave then alice is both rich and patient and vice versa.
If someone is either not patient or rich then fred is either not strong or tall.
If lucy is both not humble and rich then lucy is not patient or rich.
Everyone who is both happy and not curious is both patient and funny.
Susan is not calm.
Lucy is either old or strong.
John is not curious.
Someone is strong or humble.
Lucy is not tall or old.
Someone is not tall. | Paul is not tall. | entailment | ((curious(mary))=>(?[X]:((creative(X)<~>~brave(X)))))&
((?[X]:((~patient(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:(~happy(X)=>(~humble(X)&curious(X))))&
((quiet(mary))=>(generous(fred)))&
(![X]:((~rich(X)&happy(X))<=>curious(X)))&
(![X]:(strong(X)<=>(funny(X)&strong(X))))&
(((~tall(fred)<~>~creative(fred)))=>((~rich(fred)|~funny(fred))))&
(![X]:((~brave(X)|funny(X))<=>~tall(X)))&
((?[X]:((~kind(X)<~>curious(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:((happy(X)|~calm(X))=>~brave(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>~patient(X)))&
(![X]:((~brave(X)&~old(X))=>(~calm(X)&tall(X))))&
(((curious(lucy)&~brave(lucy)))<=>((rich(alice)&patient(alice))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~strong(fred)<~>tall(fred))))&
(((~humble(lucy)&rich(lucy)))=>((~patient(lucy)|rich(lucy))))&
(![X]:((happy(X)&~curious(X))=>(patient(X)&funny(X))))&
(~calm(susan))&
((old(lucy)<~>strong(lucy)))&
(~curious(john))&
(?[X]:((strong(X)|humble(X))))&
((~tall(lucy)|old(lucy)))&
(?[X]:(~tall(X))) | ~tall(paul) | [
"p2",
"p4",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2899012657076680585283923
% SZS output start Proof for 2899012657076680585283923
3. ! [X0] : (~happy(X0) => (curious(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((happy(X0) & ~rich(X0)) <=> curious(X0)) [input p4]
8. ! [X0] : ((funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p7]
10. ! [X0] : ((~calm(X0) | happy(X0)) => ~brave(X0)) [input p9]
23. tall(paul) [input hypothesis]
31. ! [X0] : ((curious(X0) & ~humble(X0)) | happy(X0)) [ennf transformation 3]
34. ! [X0] : (~brave(X0) | (calm(X0) & ~happy(X0))) [ennf transformation 10]
48. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | (~happy(X0) | rich(X0)))) [nnf transformation 5]
49. ! [X0] : (((happy(X0) & ~rich(X0)) | ~curious(X0)) & (curious(X0) | ~happy(X0) | rich(X0))) [flattening 48]
53. ! [X0] : (((funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 8]
54. ! [X0] : ((funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [flattening 53]
68. happy(X0) | curious(X0) [cnf transformation 31]
71. happy(X0) | ~curious(X0) [cnf transformation 49]
77. ~tall(X0) | brave(X0) [cnf transformation 54]
80. ~brave(X0) | ~happy(X0) [cnf transformation 34]
106. tall(paul) [cnf transformation 23]
129. happy(X0) [subsumption resolution 71,68]
149. ~brave(X0) [subsumption resolution 80,129]
207. brave(paul) [resolution 77,106]
208. $false [subsumption resolution 207,149]
% SZS output end Proof for 2899012657076680585283923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not humble or not kind then someone is not generous and vice versa. Everyone who is not generous or calm is either curious or not funny. Everyone who is either strong or not calm is both not tall and not creative. Everyone who is not humble or brave is either not rich or happy and vice versa. Everyone who is not rich or not strong is both not generous and not humble. Everyone who is not funny is either wise or not creative. If paul is both not calm and not happy then someone is not kind and vice versa. If john is humble or patient then someone is not kind or not rich. If mary is either not calm or not wise then susan is both not tall and not creative and vice versa. If someone is both not tall and not old then mary is not wise and vice versa. Everyone who is both happy and generous is not patient or not humble and vice versa. Everyone who is not strong is either humble or patient. If someone is either creative or patient then lucy is either humble or not creative. If someone is both not old and brave then someone is either quiet or not generous and vice versa. Everyone who is either not humble or not calm is kind and vice versa. If someone is either not tall or not funny then fred is quiet or calm. Someone is both funny and curious. Susan is either not calm or not wise. Susan is both not old and not creative. Someone is either funny or generous. John is either generous or rich. John is not creative or patient. John is both rich and not curious. | Paul is rich. | entailment | (((~humble(lucy)|~kind(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)|calm(X))=>(curious(X)<~>~funny(X))))&
(![X]:((strong(X)<~>~calm(X))=>(~tall(X)&~creative(X))))&
(![X]:((~humble(X)|brave(X))<=>(~rich(X)<~>happy(X))))&
(![X]:((~rich(X)|~strong(X))=>(~generous(X)&~humble(X))))&
(![X]:(~funny(X)=>(wise(X)<~>~creative(X))))&
(((~calm(paul)&~happy(paul)))<=>(?[X]:(~kind(X))))&
(((humble(john)|patient(john)))=>(?[X]:((~kind(X)|~rich(X)))))&
(((~calm(mary)<~>~wise(mary)))<=>((~tall(susan)&~creative(susan))))&
((?[X]:((~tall(X)&~old(X))))<=>(~wise(mary)))&
(![X]:((happy(X)&generous(X))<=>(~patient(X)|~humble(X))))&
(![X]:(~strong(X)=>(humble(X)<~>patient(X))))&
((?[X]:((creative(X)<~>patient(X))))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((~old(X)&brave(X))))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>kind(X)))&
((?[X]:((~tall(X)<~>~funny(X))))=>((quiet(fred)|calm(fred))))&
(?[X]:((funny(X)&curious(X))))&
((~calm(susan)<~>~wise(susan)))&
((~old(susan)&~creative(susan)))&
(?[X]:((funny(X)<~>generous(X))))&
((generous(john)<~>rich(john)))&
((~creative(john)|patient(john)))&
((rich(john)&~curious(john))) | rich(paul) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4014916049061662995945903
% SZS output start Proof for 4014916049061662995945903
5. ! [X0] : ((~strong(X0) | ~rich(X0)) => (~humble(X0) & ~generous(X0))) [input p4]
11. ! [X0] : ((generous(X0) & happy(X0)) <=> (~humble(X0) | ~patient(X0))) [input p10]
24. ~rich(paul) [input hypothesis]
28. ! [X0] : ((~humble(X0) & ~generous(X0)) | (strong(X0) & rich(X0))) [ennf transformation 5]
58. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | (~generous(X0) | ~happy(X0)))) [nnf transformation 11]
59. ! [X0] : (((generous(X0) & happy(X0)) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | ~generous(X0) | ~happy(X0))) [flattening 58]
93. ~generous(X0) | rich(X0) [cnf transformation 28]
95. ~humble(X0) | rich(X0) [cnf transformation 28]
117. generous(X0) | humble(X0) [cnf transformation 59]
149. ~rich(paul) [cnf transformation 24]
340. humble(X1) | rich(X1) [resolution 117,93]
346. rich(X1) [subsumption resolution 340,95]
363. $false [resolution 346,149]
% SZS output end Proof for 4014916049061662995945903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or strong is not generous.
Everyone who is not strong is calm or not calm and vice versa.
If fred is funny then someone is either rich or brave.
If someone is strong then fred is happy or calm and vice versa.
If someone is not quiet then someone is not humble.
Everyone who is either not tall or creative is both not tall and curious.
If susan is rich or not tall then someone is both not kind and kind.
If susan is not kind then susan is either not old or kind and vice versa.
Everyone who is either brave or not tall is both not happy and humble.
Everyone who is not wise is both quiet and humble and vice versa.
Everyone who is rich is rich or not rich.
Everyone who is both not happy and not curious is both not brave and kind and vice versa.
If someone is not patient or brave then someone is happy.
Everyone who is both not calm and happy is brave or calm and vice versa.
Everyone who is calm is either not patient or brave.
If mary is both curious and creative then alice is either brave or quiet.
Paul is either not curious or old.
Mary is not generous.
Someone is either not humble or not brave.
Someone is either not quiet or strong.
Fred is either not kind or not generous.
Someone is either not humble or curious. | Susan is creative. | contradiction | (![X]:((~rich(X)<~>strong(X))=>~generous(X)))&
(![X]:(~strong(X)<=>(calm(X)|~calm(X))))&
((funny(fred))=>(?[X]:((rich(X)<~>brave(X)))))&
((?[X]:(strong(X)))<=>((happy(fred)|calm(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)<~>creative(X))=>(~tall(X)&curious(X))))&
(((rich(susan)|~tall(susan)))=>(?[X]:((~kind(X)&kind(X)))))&
((~kind(susan))<=>((~old(susan)<~>kind(susan))))&
(![X]:((brave(X)<~>~tall(X))=>(~happy(X)&humble(X))))&
(![X]:(~wise(X)<=>(quiet(X)&humble(X))))&
(![X]:(rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~brave(X)&kind(X))))&
((?[X]:((~patient(X)|brave(X))))=>(?[X]:(happy(X))))&
(![X]:((~calm(X)&happy(X))<=>(brave(X)|calm(X))))&
(![X]:(calm(X)=>(~patient(X)<~>brave(X))))&
(((curious(mary)&creative(mary)))=>((brave(alice)<~>quiet(alice))))&
((~curious(paul)<~>old(paul)))&
(~generous(mary))&
(?[X]:((~humble(X)<~>~brave(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
((~kind(fred)<~>~generous(fred)))&
(?[X]:((~humble(X)<~>curious(X)))) | creative(susan) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7973067484859070142926019
% SZS output start Proof for 7973067484859070142926019
6. ! [X0] : ((~tall(X0) <~> creative(X0)) => (curious(X0) & ~tall(X0))) [input p5]
7. (~tall(susan) | rich(susan)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p6]
23. creative(susan) [input hypothesis]
29. ! [X0] : ((curious(X0) & ~tall(X0)) | (~tall(X0) <=> creative(X0))) [ennf transformation 6]
30. ? [X0] : (kind(X0) & ~kind(X0)) | (tall(susan) & ~rich(susan)) [ennf transformation 7]
49. ! [X0] : ((curious(X0) & ~tall(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) [nnf transformation 29]
50. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK2) & ~kind(sK2)) [choice axiom]
51. (kind(sK2) & ~kind(sK2)) | (tall(susan) & ~rich(susan)) [skolemisation 30,50]
84. ~tall(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 49]
88. ~kind(sK2) | tall(susan) [cnf transformation 51]
90. kind(sK2) | tall(susan) [cnf transformation 51]
126. creative(susan) [cnf transformation 23]
132. ~creative(X0) | ~tall(X0) [duplicate literal removal 84]
145. 3 <=> tall(susan) [avatar definition]
147. tall(susan) <- (3) [avatar component clause 145]
149. 4 <=> kind(sK2) [avatar definition]
152. 3 | 4 [avatar split clause 90,149,145]
158. 3 | ~4 [avatar split clause 88,149,145]
242. ~tall(susan) [resolution 132,126]
243. $false <- (3) [subsumption resolution 242,147]
244. ~3 [avatar contradiction clause 243]
245. $false [avatar sat refutation 152,158,244]
% SZS output end Proof for 7973067484859070142926019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is curious or calm and vice versa. If someone is not funny then paul is curious or tall. Everyone who is curious is either tall or not funny. If someone is patient or not old then someone is quiet and vice versa. Everyone who is either kind or generous is old or quiet and vice versa. If someone is both calm and creative then someone is either not creative or old. Everyone who is not happy is not strong and vice versa. Everyone who is rich is not curious or not patient and vice versa. If someone is both not brave and quiet then someone is both not kind and quiet and vice versa. If fred is either not curious or happy then john is both rich and not calm. Everyone who is old is both creative and not happy and vice versa. Everyone who is old or not strong is curious. If alice is either not quiet or not generous then someone is both not curious and not rich and vice versa. If someone is not patient then someone is both not funny and curious and vice versa. If someone is not rich or curious then someone is both brave and not brave. Susan is kind. Alice is either funny or calm. Someone is either creative or not wise. Someone is either old or generous. John is either old or tall. Someone is not kind. John is generous. Someone is not creative or happy. | Susan is patient. | entailment | (![X]:(~quiet(X)<=>(curious(X)|calm(X))))&
((?[X]:(~funny(X)))=>((curious(paul)|tall(paul))))&
(![X]:(curious(X)=>(tall(X)<~>~funny(X))))&
((?[X]:((patient(X)|~old(X))))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)<~>generous(X))<=>(old(X)|quiet(X))))&
((?[X]:((calm(X)&creative(X))))=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(rich(X)<=>(~curious(X)|~patient(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((~kind(X)&quiet(X)))))&
(((~curious(fred)<~>happy(fred)))=>((rich(john)&~calm(john))))&
(![X]:(old(X)<=>(creative(X)&~happy(X))))&
(![X]:((old(X)|~strong(X))=>curious(X)))&
(((~quiet(alice)<~>~generous(alice)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((~funny(X)&curious(X)))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((brave(X)&~brave(X)))))&
(kind(susan))&
((funny(alice)<~>calm(alice)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((old(X)<~>generous(X))))&
((old(john)<~>tall(john)))&
(?[X]:(~kind(X)))&
(generous(john))&
(?[X]:((~creative(X)|happy(X)))) | patient(susan) | [
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 306647368050552532571446
% SZS output start Proof for 306647368050552532571446
14. ? [X0] : ~patient(X0) <=> ? [X0] : (curious(X0) & ~funny(X0)) [input p13]
15. ? [X0] : (curious(X0) | ~rich(X0)) => ? [X0] : (~brave(X0) & brave(X0)) [input p14]
24. ~patient(susan) [input hypothesis]
28. ? [X0] : ~patient(X0) <=> ? [X1] : (curious(X1) & ~funny(X1)) [rectify 14]
29. ? [X0] : (curious(X0) | ~rich(X0)) => ? [X1] : (~brave(X1) & brave(X1)) [rectify 15]
36. ? [X1] : (~brave(X1) & brave(X1)) | ! [X0] : (~curious(X0) & rich(X0)) [ennf transformation 29]
66. (? [X0] : ~patient(X0) | ! [X1] : (~curious(X1) | funny(X1))) & (? [X1] : (curious(X1) & ~funny(X1)) | ! [X0] : patient(X0)) [nnf transformation 28]
67. (? [X0] : ~patient(X0) | ! [X1] : (~curious(X1) | funny(X1))) & (? [X2] : (curious(X2) & ~funny(X2)) | ! [X3] : patient(X3)) [rectify 66]
68. ? [X0] : ~patient(X0) => ~patient(sK6) [choice axiom]
69. ? [X2] : (curious(X2) & ~funny(X2)) => (curious(sK7) & ~funny(sK7)) [choice axiom]
70. (~patient(sK6) | ! [X1] : (~curious(X1) | funny(X1))) & ((curious(sK7) & ~funny(sK7)) | ! [X3] : patient(X3)) [skolemisation 67,69,68]
71. ? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : (~curious(X1) & rich(X1)) [rectify 36]
72. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK8) & brave(sK8)) [choice axiom]
73. (~brave(sK8) & brave(sK8)) | ! [X1] : (~curious(X1) & rich(X1)) [skolemisation 71,72]
128. curious(sK7) | patient(X3) [cnf transformation 70]
131. brave(sK8) | ~curious(X1) [cnf transformation 73]
133. ~brave(sK8) | ~curious(X1) [cnf transformation 73]
146. ~patient(susan) [cnf transformation 24]
271. 29 <=> ! [X3] : patient(X3) [avatar definition]
272. patient(X3) <- (29) [avatar component clause 271]
274. 30 <=> curious(sK7) [avatar definition]
276. curious(sK7) <- (30) [avatar component clause 274]
277. 29 | 30 [avatar split clause 128,274,271]
284. 32 <=> ! [X1] : ~curious(X1) [avatar definition]
285. ~curious(X1) <- (32) [avatar component clause 284]
287. 33 <=> brave(sK8) [avatar definition]
290. 32 | ~33 [avatar split clause 133,287,284]
295. 32 | 33 [avatar split clause 131,287,284]
356. $false <- (29) [resolution 272,146]
357. ~29 [avatar contradiction clause 356]
360. $false <- (30, 32) [subsumption resolution 276,285]
361. ~30 | ~32 [avatar contradiction clause 360]
362. $false [avatar sat refutation 277,290,295,357,361]
% SZS output end Proof for 306647368050552532571446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not funny is either quiet or patient and vice versa.
Everyone who is not calm or not quiet is both not wise and not patient and vice versa.
Everyone who is not curious is either wise or generous and vice versa.
Everyone who is not happy or not kind is not calm.
Everyone who is old or not generous is not strong or not brave and vice versa.
Everyone who is either tall or not curious is old or tall and vice versa.
Everyone who is kind or not happy is both not wise and funny.
If someone is not quiet then mary is creative or not calm and vice versa.
Everyone who is both calm and tall is brave.
If lucy is generous then someone is curious.
Everyone who is patient or creative is generous or not kind.
Everyone who is wise or not generous is calm.
If lucy is kind or humble then someone is both kind and patient and vice versa.
If someone is either not strong or funny then someone is either creative or patient and vice versa.
Someone is not kind.
Someone is either curious or patient.
Someone is not patient.
Someone is both not happy and funny.
Mary is not patient or not calm.
Someone is either not humble or not wise.
Someone is both humble and quiet. | Lucy is not calm. | neutral | (![X]:((strong(X)<~>~funny(X))<=>(quiet(X)<~>patient(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(~wise(X)&~patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>generous(X))))&
(![X]:((~happy(X)|~kind(X))=>~calm(X)))&
(![X]:((old(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(old(X)|tall(X))))&
(![X]:((kind(X)|~happy(X))=>(~wise(X)&funny(X))))&
((?[X]:(~quiet(X)))<=>((creative(mary)|~calm(mary))))&
(![X]:((calm(X)&tall(X))=>brave(X)))&
((generous(lucy))=>(?[X]:(curious(X))))&
(![X]:((patient(X)|creative(X))=>(generous(X)|~kind(X))))&
(![X]:((wise(X)|~generous(X))=>calm(X)))&
(((kind(lucy)|humble(lucy)))<=>(?[X]:((kind(X)&patient(X)))))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((creative(X)<~>patient(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~happy(X)&funny(X))))&
((~patient(mary)|~calm(mary)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((humble(X)&quiet(X)))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not creative or not old is both not creative and curious and vice versa.
Everyone who is quiet is either curious or not kind.
If susan is both not creative and not humble then paul is funny or not generous.
Everyone who is calm or happy is either old or creative and vice versa.
Everyone who is either creative or strong is either brave or funny and vice versa.
Everyone who is not old is both patient and quiet and vice versa.
Everyone who is either quiet or curious is both rich and happy and vice versa.
Everyone who is both strong and funny is quiet or not brave.
If paul is not funny or generous then someone is both wise and not happy.
Everyone who is both not rich and strong is either not rich or calm and vice versa.
If someone is not rich then someone is not calm or kind.
Everyone who is either quiet or creative is both not funny and generous and vice versa.
If someone is both not kind and not calm then someone is not rich and vice versa.
Everyone who is either not wise or not creative is not calm and vice versa.
If someone is not rich or not happy then paul is both strong and rich and vice versa.
Everyone who is happy or not creative is both not wise and creative.
Susan is both not tall and not generous.
Someone is not happy.
Lucy is not patient.
Someone is not old or not curious.
Someone is brave or not brave.
Someone is not generous or humble. | Paul is not patient. | entailment | (![X]:((~creative(X)|~old(X))<=>(~creative(X)&curious(X))))&
(![X]:(quiet(X)=>(curious(X)<~>~kind(X))))&
(((~creative(susan)&~humble(susan)))=>((funny(paul)|~generous(paul))))&
(![X]:((calm(X)|happy(X))<=>(old(X)<~>creative(X))))&
(![X]:((creative(X)<~>strong(X))<=>(brave(X)<~>funny(X))))&
(![X]:(~old(X)<=>(patient(X)&quiet(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(rich(X)&happy(X))))&
(![X]:((strong(X)&funny(X))=>(quiet(X)|~brave(X))))&
(((~funny(paul)|generous(paul)))=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~rich(X)&strong(X))<=>(~rich(X)<~>calm(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((quiet(X)<~>creative(X))<=>(~funny(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)<~>~creative(X))<=>~calm(X)))&
((?[X]:((~rich(X)|~happy(X))))<=>((strong(paul)&rich(paul))))&
(![X]:((happy(X)|~creative(X))=>(~wise(X)&creative(X))))&
((~tall(susan)&~generous(susan)))&
(?[X]:(~happy(X)))&
(~patient(lucy))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~generous(X)|humble(X)))) | ~patient(paul) | [
"p0",
"p3",
"p5",
"p8",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1224003796572354613677189
% SZS output start Proof for 1224003796572354613677189
1. ! [X0] : ((~old(X0) | ~creative(X0)) <=> (curious(X0) & ~creative(X0))) [input p0]
4. ! [X0] : ((happy(X0) | calm(X0)) <=> (old(X0) <~> creative(X0))) [input p3]
6. ! [X0] : (~old(X0) <=> (quiet(X0) & patient(X0))) [input p5]
9. (generous(paul) | ~funny(paul)) => ? [X0] : (~happy(X0) & wise(X0)) [input p8]
12. ! [X0] : ((quiet(X0) <~> creative(X0)) <=> (generous(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((~wise(X0) <~> ~creative(X0)) <=> ~calm(X0)) [input p13]
16. ! [X0] : ((~creative(X0) | happy(X0)) => (creative(X0) & ~wise(X0))) [input p15]
23. patient(paul) [input hypothesis]
32. ? [X0] : (~happy(X0) & wise(X0)) | (~generous(paul) & funny(paul)) [ennf transformation 9]
34. ! [X0] : ((creative(X0) & ~wise(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 16]
35. ! [X0] : (((~old(X0) | ~creative(X0)) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | (old(X0) & creative(X0)))) [nnf transformation 1]
36. ! [X0] : ((~old(X0) | ~creative(X0) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | (old(X0) & creative(X0)))) [flattening 35]
38. ! [X0] : (((happy(X0) | calm(X0)) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) & (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | (~happy(X0) & ~calm(X0)))) [nnf transformation 4]
39. ! [X0] : ((happy(X0) | calm(X0) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) & (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | (~happy(X0) & ~calm(X0)))) [flattening 38]
41. ! [X0] : ((~old(X0) | (~quiet(X0) | ~patient(X0))) & ((quiet(X0) & patient(X0)) | old(X0))) [nnf transformation 6]
42. ! [X0] : ((~old(X0) | ~quiet(X0) | ~patient(X0)) & ((quiet(X0) & patient(X0)) | old(X0))) [flattening 41]
45. ? [X0] : (~happy(X0) & wise(X0)) => (~happy(sK0) & wise(sK0)) [choice axiom]
46. (~happy(sK0) & wise(sK0)) | (~generous(paul) & funny(paul)) [skolemisation 32,45]
52. ! [X0] : ((((~creative(X0) | ~quiet(X0)) & (creative(X0) | quiet(X0))) | (~generous(X0) | funny(X0))) & ((generous(X0) & ~funny(X0)) | ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))))) [nnf transformation 12]
53. ! [X0] : ((((~creative(X0) | ~quiet(X0)) & (creative(X0) | quiet(X0))) | ~generous(X0) | funny(X0)) & ((generous(X0) & ~funny(X0)) | ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))))) [flattening 52]
59. ! [X0] : ((((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | calm(X0)) & (~calm(X0) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0))))) [nnf transformation 14]
72. ~creative(X0) | old(X0) [cnf transformation 36]
80. ~creative(X0) | ~old(X0) | ~calm(X0) [cnf transformation 39]
94. ~patient(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 42]
102. wise(sK0) | funny(paul) [cnf transformation 46]
114. ~funny(X0) | quiet(X0) | ~creative(X0) [cnf transformation 53]
124. ~creative(X0) | ~wise(X0) | calm(X0) [cnf transformation 59]
134. creative(X0) | creative(X0) [cnf transformation 34]
140. patient(paul) [cnf transformation 23]
141. creative(X0) [duplicate literal removal 134]
145. ~calm(X0) | ~creative(X0) [subsumption resolution 80,72]
158. 3 <=> funny(paul) [avatar definition]
160. funny(paul) <- (3) [avatar component clause 158]
163. 4 <=> wise(sK0) [avatar definition]
165. wise(sK0) <- (4) [avatar component clause 163]
167. 3 | 4 [avatar split clause 102,163,158]
199. ~wise(X0) | ~creative(X0) [subsumption resolution 124,145]
234. old(X0) [resolution 72,141]
241. ~quiet(paul) | ~old(paul) [resolution 94,140]
243. ~quiet(paul) [subsumption resolution 241,234]
295. quiet(paul) | ~creative(paul) <- (3) [resolution 114,160]
296. ~creative(paul) <- (3) [subsumption resolution 295,243]
297. $false <- (3) [subsumption resolution 296,141]
298. ~3 [avatar contradiction clause 297]
300. ~creative(sK0) <- (4) [resolution 165,199]
302. $false <- (4) [subsumption resolution 300,141]
303. ~4 [avatar contradiction clause 302]
304. $false [avatar sat refutation 167,298,303]
% SZS output end Proof for 1224003796572354613677189
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
If someone is brave then someone is not funny or patient.
If lucy is not creative or humble then lucy is not quiet.
If alice is not generous then alice is either happy or not creative and vice versa.
Lucy is either not strong or curious.
John is both old and generous.
Susan is not brave or not generous.
Someone is either not patient or patient.
Susan is quiet or generous.
Someone is not strong or not generous.
Susan is quiet or happy. | John is tall. | entailment | (![X]:((~calm(X)&~happy(X))<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
((?[X]:(brave(X)))=>(?[X]:((~funny(X)|patient(X)))))&
(((~creative(lucy)|humble(lucy)))=>(~quiet(lucy)))&
((~generous(alice))<=>((happy(alice)<~>~creative(alice))))&
((~strong(lucy)<~>curious(lucy)))&
((old(john)&generous(john)))&
((~brave(susan)|~generous(susan)))&
(?[X]:((~patient(X)<~>patient(X))))&
((quiet(susan)|generous(susan)))&
(?[X]:((~strong(X)|~generous(X))))&
((quiet(susan)|happy(susan))) | tall(john) | [
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1490760358791548486859378
% SZS output start Proof for 1490760358791548486859378
3. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p2]
5. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p5]
24. ~tall(john) [input hypothesis]
32. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 5]
33. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 6]
34. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 33]
43. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 3]
44. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 43]
47. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 32]
88. ~funny(X0) | ~funny(X0) [cnf transformation 44]
89. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 44]
92. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 47]
97. funny(X0) | patient(X0) | tall(X0) [cnf transformation 34]
141. ~tall(john) [cnf transformation 24]
145. ~funny(X0) [duplicate literal removal 88]
146. ~calm(X0) | funny(X0) [duplicate literal removal 89]
180. tall(X0) | patient(X0) [subsumption resolution 97,145]
326. patient(john) [resolution 180,141]
330. tall(john) | calm(john) [resolution 92,326]
332. calm(john) [subsumption resolution 330,141]
334. funny(john) [resolution 332,146]
335. $false [subsumption resolution 334,145]
% SZS output end Proof for 1490760358791548486859378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and tall then someone is funny or creative and vice versa.
If someone is creative then someone is either happy or kind and vice versa.
If susan is either strong or not humble then mary is not funny or not generous.
Everyone who is both generous and not funny is both creative and not happy.
Everyone who is funny or rich is either not old or generous.
Everyone who is happy or not brave is not happy or not kind.
Everyone who is either humble or brave is either calm or not wise and vice versa.
If mary is not funny then someone is not rich or not strong and vice versa.
Everyone who is quiet or generous is both not wise and generous.
Everyone who is funny or not quiet is either wise or not old and vice versa.
If someone is generous or not tall then lucy is not quiet.
Everyone who is not brave is both not funny and not generous and vice versa.
Everyone who is creative is both not curious and curious and vice versa.
If someone is tall then fred is both old and not happy.
If someone is generous or funny then someone is either funny or not funny and vice versa.
If someone is either rich or curious then someone is not curious and vice versa.
Someone is either not curious or not humble.
Someone is not wise.
Susan is both not curious and not brave.
Someone is not strong.
Fred is not patient.
Someone is funny or curious.
Someone is not quiet or old. | Fred is wise. | entailment | ((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((funny(X)|creative(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((happy(X)<~>kind(X)))))&
(((strong(susan)<~>~humble(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((generous(X)&~funny(X))=>(creative(X)&~happy(X))))&
(![X]:((funny(X)|rich(X))=>(~old(X)<~>generous(X))))&
(![X]:((happy(X)|~brave(X))=>(~happy(X)|~kind(X))))&
(![X]:((humble(X)<~>brave(X))<=>(calm(X)<~>~wise(X))))&
((~funny(mary))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((quiet(X)|generous(X))=>(~wise(X)&generous(X))))&
(![X]:((funny(X)|~quiet(X))<=>(wise(X)<~>~old(X))))&
((?[X]:((generous(X)|~tall(X))))=>(~quiet(lucy)))&
(![X]:(~brave(X)<=>(~funny(X)&~generous(X))))&
(![X]:(creative(X)<=>(~curious(X)&curious(X))))&
((?[X]:(tall(X)))=>((old(fred)&~happy(fred))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~funny(X)))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:(~curious(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~wise(X)))&
((~curious(susan)&~brave(susan)))&
(?[X]:(~strong(X)))&
(~patient(fred))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((~quiet(X)|old(X)))) | wise(fred) | [
"p0",
"p3",
"p8",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1238303230761611160479410
% SZS output start Proof for 1238303230761611160479410
1. ? [X0] : (tall(X0) & ~rich(X0)) <=> ? [X0] : (creative(X0) | funny(X0)) [input p0]
4. ! [X0] : ((~funny(X0) & generous(X0)) => (~happy(X0) & creative(X0))) [input p3]
9. ! [X0] : ((generous(X0) | quiet(X0)) => (generous(X0) & ~wise(X0))) [input p8]
10. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (wise(X0) <~> ~old(X0))) [input p9]
13. ! [X0] : (creative(X0) <=> (curious(X0) & ~curious(X0))) [input p12]
14. ? [X0] : tall(X0) => (~happy(fred) & old(fred)) [input p13]
15. ? [X0] : (funny(X0) | generous(X0)) <=> ? [X0] : (funny(X0) <~> ~funny(X0)) [input p14]
24. ~wise(fred) [input hypothesis]
25. ? [X0] : (tall(X0) & ~rich(X0)) <=> ? [X1] : (creative(X1) | funny(X1)) [rectify 1]
27. ? [X0] : (funny(X0) | generous(X0)) <=> ? [X1] : (funny(X1) <~> ~funny(X1)) [rectify 15]
32. ! [X0] : ((~happy(X0) & creative(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & creative(X0)) | funny(X0) | ~generous(X0)) [flattening 32]
37. ! [X0] : ((generous(X0) & ~wise(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 9]
39. (~happy(fred) & old(fred)) | ! [X0] : ~tall(X0) [ennf transformation 14]
40. (? [X0] : (tall(X0) & ~rich(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X1] : (creative(X1) | funny(X1)) | ! [X0] : (~tall(X0) | rich(X0))) [nnf transformation 25]
41. (? [X0] : (tall(X0) & ~rich(X0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & (? [X2] : (creative(X2) | funny(X2)) | ! [X3] : (~tall(X3) | rich(X3))) [rectify 40]
42. ? [X0] : (tall(X0) & ~rich(X0)) => (tall(sK0) & ~rich(sK0)) [choice axiom]
43. ? [X2] : (creative(X2) | funny(X2)) => (creative(sK1) | funny(sK1)) [choice axiom]
44. ((tall(sK0) & ~rich(sK0)) | ! [X1] : (~creative(X1) & ~funny(X1))) & ((creative(sK1) | funny(sK1)) | ! [X3] : (~tall(X3) | rich(X3))) [skolemisation 41,43,42]
57. ! [X0] : (((~quiet(X0) | funny(X0)) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [nnf transformation 10]
58. ! [X0] : ((~quiet(X0) | funny(X0) | ((wise(X0) | old(X0)) & (~old(X0) | ~wise(X0)))) & (((old(X0) | ~wise(X0)) & (~old(X0) | wise(X0))) | (quiet(X0) & ~funny(X0)))) [flattening 57]
61. ! [X0] : ((creative(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [nnf transformation 13]
62. ! [X0] : ((creative(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~creative(X0))) [flattening 61]
63. (? [X0] : (funny(X0) | generous(X0)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (? [X1] : ((funny(X1) | ~funny(X1)) & (~funny(X1) | funny(X1))) | ! [X0] : (~funny(X0) & ~generous(X0))) [nnf transformation 27]
64. (? [X0] : (funny(X0) | generous(X0)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (? [X2] : ((funny(X2) | ~funny(X2)) & (~funny(X2) | funny(X2))) | ! [X3] : (~funny(X3) & ~generous(X3))) [rectify 63]
65. ? [X0] : (funny(X0) | generous(X0)) => (funny(sK5) | generous(sK5)) [choice axiom]
66. ? [X2] : ((funny(X2) | ~funny(X2)) & (~funny(X2) | funny(X2))) => ((funny(sK6) | ~funny(sK6)) & (~funny(sK6) | funny(sK6))) [choice axiom]
67. ((funny(sK5) | generous(sK5)) | ! [X1] : ((funny(X1) | funny(X1)) & (~funny(X1) | ~funny(X1)))) & (((funny(sK6) | ~funny(sK6)) & (~funny(sK6) | funny(sK6))) | ! [X3] : (~funny(X3) & ~generous(X3))) [skolemisation 64,66,65]
87. tall(sK0) | ~funny(X1) [cnf transformation 44]
95. ~generous(X0) | funny(X0) | creative(X0) [cnf transformation 33]
116. ~quiet(X0) | generous(X0) [cnf transformation 37]
118. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 58]
119. ~old(X0) | wise(X0) | quiet(X0) [cnf transformation 58]
129. ~curious(X0) | ~creative(X0) [cnf transformation 62]
130. ~creative(X0) | curious(X0) [cnf transformation 62]
132. old(fred) | ~tall(X0) [cnf transformation 39]
139. funny(sK5) | generous(sK5) | funny(X1) | funny(X1) [cnf transformation 67]
152. ~wise(fred) [cnf transformation 24]
154. funny(sK5) | generous(sK5) | funny(X1) [duplicate literal removal 139]
157. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
158. ~creative(X1) <- (1) [avatar component clause 157]
160. 2 <=> tall(sK0) [avatar definition]
162. tall(sK0) <- (2) [avatar component clause 160]
165. 3 <=> ! [X1] : ~funny(X1) [avatar definition]
166. ~funny(X1) <- (3) [avatar component clause 165]
167. 3 | 2 [avatar split clause 87,160,165]
257. ~creative(X0) [subsumption resolution 129,130]
258. 1 [avatar split clause 257,157]
260. 24 <=> ! [X0] : ~tall(X0) [avatar definition]
261. ~tall(X0) <- (24) [avatar component clause 260]
268. 26 <=> old(fred) [avatar definition]
270. old(fred) <- (26) [avatar component clause 268]
271. 24 | 26 [avatar split clause 132,268,260]
273. 27 <=> ! [X1] : funny(X1) [avatar definition]
274. funny(X1) <- (27) [avatar component clause 273]
276. 28 <=> generous(sK5) [avatar definition]
278. generous(sK5) <- (28) [avatar component clause 276]
280. 29 <=> funny(sK5) [avatar definition]
282. funny(sK5) <- (29) [avatar component clause 280]
283. 27 | 28 | 29 [avatar split clause 154,280,276,273]
340. $false <- (3, 27) [subsumption resolution 166,274]
341. ~3 | ~27 [avatar contradiction clause 340]
351. funny(sK5) | creative(sK5) <- (28) [resolution 95,278]
352. creative(sK5) <- (3, 28) [subsumption resolution 351,166]
353. $false <- (1, 3, 28) [subsumption resolution 352,158]
354. ~1 | ~3 | ~28 [avatar contradiction clause 353]
355. $false <- (3, 29) [subsumption resolution 282,166]
356. ~3 | ~29 [avatar contradiction clause 355]
357. $false <- (2, 24) [subsumption resolution 162,261]
358. ~2 | ~24 [avatar contradiction clause 357]
368. 42 <=> funny(fred) [avatar definition]
372. 43 <=> generous(fred) [avatar definition]
374. generous(fred) <- (43) [avatar component clause 372]
382. wise(fred) | ~funny(fred) <- (26) [resolution 118,270]
383. wise(fred) | quiet(fred) <- (26) [resolution 119,270]
384. quiet(fred) <- (26) [subsumption resolution 383,152]
385. generous(fred) <- (26) [resolution 384,116]
387. 43 | ~26 [avatar split clause 385,268,372]
393. funny(fred) | creative(fred) <- (43) [resolution 374,95]
398. funny(fred) <- (1, 43) [subsumption resolution 393,158]
399. 42 | ~1 | ~43 [avatar split clause 398,372,157,368]
400. ~funny(fred) <- (26) [subsumption resolution 382,152]
401. ~42 | ~26 [avatar split clause 400,268,368]
402. $false [avatar sat refutation 167,258,271,283,341,354,356,358,387,399,401]
% SZS output end Proof for 1238303230761611160479410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not tall or old then someone is either calm or funny and vice versa.
Everyone who is not brave or quiet is both not brave and not funny.
If someone is rich or strong then lucy is not funny and vice versa.
Everyone who is not quiet is both not strong and creative and vice versa.
If lucy is both not curious and not creative then someone is both not creative and rich.
Everyone who is not kind or generous is quiet or not rich and vice versa.
If someone is both generous and not curious then someone is either not kind or not quiet and vice versa.
Everyone who is both not old and funny is patient or tall and vice versa.
Everyone who is both generous and not patient is creative and vice versa.
Everyone who is either not strong or not humble is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Everyone who is not curious or calm is old.
If someone is strong or wise then mary is both funny and generous and vice versa.
Everyone who is not quiet is either old or curious and vice versa.
Everyone who is not creative or not curious is both not wise and not strong.
Everyone who is not creative or happy is either not old or happy and vice versa.
Lucy is both rich and old.
Alice is not patient or not happy.
Paul is either calm or not kind.
Someone is not curious or not kind.
Lucy is humble.
Someone is funny or quiet. | Lucy is funny. | contradiction | ((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~brave(X)|quiet(X))=>(~brave(X)&~funny(X))))&
((?[X]:((rich(X)|strong(X))))<=>(~funny(lucy)))&
(![X]:(~quiet(X)<=>(~strong(X)&creative(X))))&
(((~curious(lucy)&~creative(lucy)))=>(?[X]:((~creative(X)&rich(X)))))&
(![X]:((~kind(X)|generous(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((~old(X)&funny(X))<=>(patient(X)|tall(X))))&
(![X]:((generous(X)&~patient(X))<=>creative(X)))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((?[X]:((strong(X)|wise(X))))<=>((funny(mary)&generous(mary))))&
(![X]:(~quiet(X)<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)|~curious(X))=>(~wise(X)&~strong(X))))&
(![X]:((~creative(X)|happy(X))<=>(~old(X)<~>happy(X))))&
((rich(lucy)&old(lucy)))&
((~patient(alice)|~happy(alice)))&
((calm(paul)<~>~kind(paul)))&
(?[X]:((~curious(X)|~kind(X))))&
(humble(lucy))&
(?[X]:((funny(X)|quiet(X)))) | funny(lucy) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7471062490159093006574743
% SZS output start Proof for 7471062490159093006574743
3. ? [X0] : (strong(X0) | rich(X0)) <=> ~funny(lucy) [input p2]
17. old(lucy) & rich(lucy) [input p16]
23. funny(lucy) [input hypothesis]
37. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X0] : (~strong(X0) & ~rich(X0))) [nnf transformation 3]
38. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [rectify 37]
39. ? [X0] : (strong(X0) | rich(X0)) => (strong(sK2) | rich(sK2)) [choice axiom]
40. ((strong(sK2) | rich(sK2)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [skolemisation 38,39]
87. ~funny(lucy) | ~rich(X1) [cnf transformation 40]
140. rich(lucy) [cnf transformation 17]
148. funny(lucy) [cnf transformation 23]
188. 9 <=> funny(lucy) [avatar definition]
205. 13 <=> ! [X1] : ~rich(X1) [avatar definition]
206. ~rich(X1) <- (13) [avatar component clause 205]
207. 13 | ~9 [avatar split clause 87,188,205]
344. 9 [avatar split clause 148,188]
345. $false <- (13) [resolution 206,140]
346. ~13 [avatar contradiction clause 345]
347. $false [avatar sat refutation 207,344,346]
% SZS output end Proof for 7471062490159093006574743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not quiet is both not strong and kind.
Everyone who is either tall or not patient is not creative.
If paul is not creative then alice is not wise or wise and vice versa.
If someone is either not kind or curious then lucy is quiet and vice versa.
Everyone who is creative or not calm is either tall or not funny and vice versa.
Everyone who is either not patient or happy is either not curious or not tall and vice versa.
If someone is not kind then someone is rich or humble and vice versa.
If someone is both not kind and not quiet then someone is both not funny and old.
If someone is both not creative and wise then lucy is rich.
If susan is wise or rich then someone is rich or not brave and vice versa.
Everyone who is either not curious or not brave is both not humble and calm and vice versa.
If someone is tall or wise then someone is not generous or not rich.
Everyone who is old is not happy or happy and vice versa.
If alice is not old or not kind then someone is both not wise and happy and vice versa.
Everyone who is brave or old is wise and vice versa.
Someone is either happy or calm.
Someone is not kind or tall.
Someone is both creative and not strong.
Someone is humble or not kind.
Mary is either happy or generous.
Mary is either rich or happy.
Paul is curious or generous.
Alice is not creative. | Alice is old. | entailment | (![X]:((tall(X)<~>~quiet(X))=>(~strong(X)&kind(X))))&
(![X]:((tall(X)<~>~patient(X))=>~creative(X)))&
((~creative(paul))<=>((~wise(alice)|wise(alice))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(quiet(lucy)))&
(![X]:((creative(X)|~calm(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((rich(X)|humble(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~creative(X)&wise(X))))=>(rich(lucy)))&
(((wise(susan)|rich(susan)))<=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((~curious(X)<~>~brave(X))<=>(~humble(X)&calm(X))))&
((?[X]:((tall(X)|wise(X))))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:(old(X)<=>(~happy(X)|happy(X))))&
(((~old(alice)|~kind(alice)))<=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((brave(X)|old(X))<=>wise(X)))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:((creative(X)&~strong(X))))&
(?[X]:((humble(X)|~kind(X))))&
((happy(mary)<~>generous(mary)))&
((rich(mary)<~>happy(mary)))&
((curious(paul)|generous(paul)))&
(~creative(alice)) | old(alice) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 94456473527795691432701
% SZS output start Proof for 94456473527795691432701
13. ! [X0] : (old(X0) <=> (happy(X0) | ~happy(X0))) [input p12]
24. ~old(alice) [input hypothesis]
64. ! [X0] : ((old(X0) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | ~old(X0))) [nnf transformation 13]
65. ! [X0] : ((old(X0) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ~old(X0))) [flattening 64]
128. old(X0) | happy(X0) [cnf transformation 65]
129. old(X0) | ~happy(X0) [cnf transformation 65]
149. ~old(alice) [cnf transformation 24]
266. old(X0) [subsumption resolution 128,129]
340. $false [subsumption resolution 149,266]
% SZS output end Proof for 94456473527795691432701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or tall then lucy is either wise or brave and vice versa. If someone is not brave then paul is either generous or not patient. Everyone who is both not tall and funny is both not creative and tall and vice versa. If fred is patient then paul is both generous and not calm and vice versa. If someone is calm or not strong then john is either not generous or not brave and vice versa. Everyone who is either strong or generous is both funny and not curious. Everyone who is both generous and humble is not curious or tall and vice versa. Everyone who is both strong and not happy is not quiet or humble. If someone is not kind or creative then john is wise and vice versa. If someone is humble or kind then lucy is both not humble and not wise. Everyone who is calm or humble is either not strong or generous. Everyone who is not quiet is both not happy and not wise and vice versa. Everyone who is tall is both not humble and not patient. Everyone who is either strong or calm is not kind or patient. If someone is both old and calm then someone is not funny. Everyone who is generous is either generous or old and vice versa. Mary is both rich and not curious. Someone is not strong. Someone is both not happy and patient. John is not kind. Paul is old or not humble. Paul is not kind or not tall. Alice is strong. Mary is both calm and wise. | John is old. | contradiction | ((?[X]:((~kind(X)<~>tall(X))))<=>((wise(lucy)<~>brave(lucy))))&
((?[X]:(~brave(X)))=>((generous(paul)<~>~patient(paul))))&
(![X]:((~tall(X)&funny(X))<=>(~creative(X)&tall(X))))&
((patient(fred))<=>((generous(paul)&~calm(paul))))&
((?[X]:((calm(X)|~strong(X))))<=>((~generous(john)<~>~brave(john))))&
(![X]:((strong(X)<~>generous(X))=>(funny(X)&~curious(X))))&
(![X]:((generous(X)&humble(X))<=>(~curious(X)|tall(X))))&
(![X]:((strong(X)&~happy(X))=>(~quiet(X)|humble(X))))&
((?[X]:((~kind(X)|creative(X))))<=>(wise(john)))&
((?[X]:((humble(X)|kind(X))))=>((~humble(lucy)&~wise(lucy))))&
(![X]:((calm(X)|humble(X))=>(~strong(X)<~>generous(X))))&
(![X]:(~quiet(X)<=>(~happy(X)&~wise(X))))&
(![X]:(tall(X)=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(~kind(X)|patient(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:(~funny(X))))&
(![X]:(generous(X)<=>(generous(X)<~>old(X))))&
((rich(mary)&~curious(mary)))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)&patient(X))))&
(~kind(john))&
((old(paul)|~humble(paul)))&
((~kind(paul)|~tall(paul)))&
(strong(alice))&
((calm(mary)&wise(mary))) | old(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1874364408510952046959139
% SZS output start Proof for 1874364408510952046959139
16. ! [X0] : (generous(X0) <=> (generous(X0) <~> old(X0))) [input p15]
25. old(john) [input hypothesis]
65. ! [X0] : ((generous(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0)))) & (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | ~generous(X0))) [nnf transformation 16]
122. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 65]
124. generous(X0) | generous(X0) | ~old(X0) [cnf transformation 65]
135. old(john) [cnf transformation 25]
136. ~old(X0) | ~generous(X0) [duplicate literal removal 122]
137. generous(X0) | ~old(X0) [duplicate literal removal 124]
266. ~old(X0) [subsumption resolution 136,137]
268. $false [subsumption resolution 135,266]
% SZS output end Proof for 1874364408510952046959139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both happy and not rich then someone is either creative or patient. Everyone who is both old and creative is calm or not strong and vice versa. Everyone who is both not creative and patient is not old. Everyone who is strong is both calm and generous. If susan is not quiet then lucy is quiet. Everyone who is both old and funny is either rich or not brave. If paul is generous then mary is kind. Everyone who is either quiet or not happy is either not happy or brave. Everyone who is not kind is both quiet and not brave and vice versa. Everyone who is both strong and happy is rich or creative. If someone is both not old and not humble then lucy is creative. If someone is either not rich or not kind then someone is happy and vice versa. If someone is not tall or not generous then paul is not brave. Everyone who is either not patient or not humble is not brave. If someone is both not patient and not brave then paul is kind or rich and vice versa. Everyone who is not strong is both not tall and tall and vice versa. Fred is humble. Paul is either not happy or patient. Lucy is funny. Someone is calm or not tall. Someone is both not curious and creative. | Lucy is not strong. | contradiction | (((happy(alice)&~rich(alice)))=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((old(X)&creative(X))<=>(calm(X)|~strong(X))))&
(![X]:((~creative(X)&patient(X))=>~old(X)))&
(![X]:(strong(X)=>(calm(X)&generous(X))))&
((~quiet(susan))=>(quiet(lucy)))&
(![X]:((old(X)&funny(X))=>(rich(X)<~>~brave(X))))&
((generous(paul))=>(kind(mary)))&
(![X]:((quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(![X]:(~kind(X)<=>(quiet(X)&~brave(X))))&
(![X]:((strong(X)&happy(X))=>(rich(X)|creative(X))))&
((?[X]:((~old(X)&~humble(X))))=>(creative(lucy)))&
((?[X]:((~rich(X)<~>~kind(X))))<=>(?[X]:(happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(~brave(paul)))&
(![X]:((~patient(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((kind(paul)|rich(paul))))&
(![X]:(~strong(X)<=>(~tall(X)&tall(X))))&
(humble(fred))&
((~happy(paul)<~>patient(paul)))&
(funny(lucy))&
(?[X]:((calm(X)|~tall(X))))&
(?[X]:((~curious(X)&creative(X)))) | ~strong(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3964369853254079793880945
% SZS output start Proof for 3964369853254079793880945
16. ! [X0] : (~strong(X0) <=> (tall(X0) & ~tall(X0))) [input p15]
22. ~strong(lucy) [input hypothesis]
60. ! [X0] : ((~strong(X0) | (~tall(X0) | tall(X0))) & ((tall(X0) & ~tall(X0)) | strong(X0))) [nnf transformation 16]
61. ! [X0] : ((~strong(X0) | ~tall(X0) | tall(X0)) & ((tall(X0) & ~tall(X0)) | strong(X0))) [flattening 60]
103. ~tall(X0) | strong(X0) [cnf transformation 61]
104. tall(X0) | strong(X0) [cnf transformation 61]
112. ~strong(lucy) [cnf transformation 22]
221. strong(X0) [subsumption resolution 103,104]
241. $false [subsumption resolution 112,221]
% SZS output end Proof for 3964369853254079793880945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not generous is not generous and vice versa.
Everyone who is either curious or not old is not rich or not generous and vice versa.
Everyone who is either quiet or generous is both tall and old and vice versa.
If someone is not kind or not generous then fred is either kind or brave.
If susan is not funny then mary is both old and not tall and vice versa.
Everyone who is both not generous and not tall is not kind or quiet and vice versa.
If mary is not patient then someone is either brave or strong and vice versa.
If paul is strong or brave then mary is both not creative and humble and vice versa.
If someone is not brave or curious then alice is both not creative and rich and vice versa.
If susan is either not happy or not calm then someone is both not funny and creative.
Everyone who is not kind or happy is kind or not happy.
If paul is kind or not patient then paul is brave or not wise and vice versa.
Everyone who is both humble and not humble is both funny and not humble and vice versa.
If someone is not patient or not quiet then someone is funny or wise.
Everyone who is not strong is humble or not patient.
Everyone who is not strong is not wise.
Someone is patient.
Someone is not calm.
Fred is both generous and not humble.
Someone is both brave and rich.
Someone is both not generous and kind.
Someone is either not quiet or strong.
Someone is not funny or quiet. | Fred is not quiet. | entailment | (![X]:((~wise(X)&~generous(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~old(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(tall(X)&old(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((kind(fred)<~>brave(fred))))&
((~funny(susan))<=>((old(mary)&~tall(mary))))&
(![X]:((~generous(X)&~tall(X))<=>(~kind(X)|quiet(X))))&
((~patient(mary))<=>(?[X]:((brave(X)<~>strong(X)))))&
(((strong(paul)|brave(paul)))<=>((~creative(mary)&humble(mary))))&
((?[X]:((~brave(X)|curious(X))))<=>((~creative(alice)&rich(alice))))&
(((~happy(susan)<~>~calm(susan)))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~kind(X)|happy(X))=>(kind(X)|~happy(X))))&
(((kind(paul)|~patient(paul)))<=>((brave(paul)|~wise(paul))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~strong(X)=>(humble(X)|~patient(X))))&
(![X]:(~strong(X)=>~wise(X)))&
(?[X]:(patient(X)))&
(?[X]:(~calm(X)))&
((generous(fred)&~humble(fred)))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((~funny(X)|quiet(X)))) | ~quiet(fred) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1656544530455855701741503
% SZS output start Proof for 1656544530455855701741503
6. ! [X0] : ((~tall(X0) & ~generous(X0)) <=> (quiet(X0) | ~kind(X0))) [input p5]
19. ~humble(fred) & generous(fred) [input p18]
24. quiet(fred) [input hypothesis]
43. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | (tall(X0) | generous(X0)))) [nnf transformation 6]
44. ! [X0] : (((~tall(X0) & ~generous(X0)) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | tall(X0) | generous(X0))) [flattening 43]
103. ~quiet(X0) | ~generous(X0) [cnf transformation 44]
140. generous(fred) [cnf transformation 19]
149. quiet(fred) [cnf transformation 24]
330. ~generous(fred) [resolution 103,149]
331. $false [subsumption resolution 330,140]
% SZS output end Proof for 1656544530455855701741503
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and strong then someone is both creative and tall.
If fred is not strong or not calm then paul is either not humble or strong and vice versa.
Everyone who is either not generous or old is both happy and not funny and vice versa.
Everyone who is not curious is both not generous and not quiet and vice versa.
If someone is both funny and wise then someone is either wise or rich.
Everyone who is both not rich and patient is either not kind or strong.
If someone is both not kind and not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is not strong is patient or not tall.
Someone is rich or not happy.
Someone is either happy or not tall.
Susan is calm or kind.
Someone is generous or brave.
Susan is either not rich or not kind. | Paul is not brave. | neutral | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:((creative(X)&tall(X)))))&
(((~strong(fred)|~calm(fred)))<=>((~humble(paul)<~>strong(paul))))&
(![X]:((~generous(X)<~>old(X))<=>(happy(X)&~funny(X))))&
(![X]:(~curious(X)<=>(~generous(X)&~quiet(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~rich(X)&patient(X))=>(~kind(X)<~>strong(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((generous(X)|brave(X))))&
((~rich(susan)<~>~kind(susan))) | ~brave(paul) | [] | null | 0 |
Everyone who is both funny and curious is either creative or not kind.
Everyone who is either not tall or not brave is rich or quiet.
Everyone who is rich is either not funny or tall.
Everyone who is curious or old is rich or not old and vice versa.
Everyone who is brave is generous or not old and vice versa.
If paul is not funny then someone is both wise and not generous.
If someone is either curious or tall then someone is not curious.
If paul is either not curious or patient then lucy is either not old or old.
Everyone who is not patient or curious is not creative.
Everyone who is wise or not creative is both patient and not rich.
If someone is both not strong and not patient then susan is either tall or not patient.
Everyone who is not tall or not humble is both not wise and not patient.
If someone is either creative or not generous then someone is not old.
If someone is not tall then lucy is not rich.
If mary is wise or not funny then john is either quiet or creative.
If someone is not generous or generous then someone is calm and vice versa.
John is either not tall or humble.
Someone is either not old or tall.
Someone is not rich or not brave.
Someone is either old or generous.
Someone is patient or generous.
Someone is not calm or strong.
Fred is both not strong and humble. | Lucy is tall. | entailment | (![X]:((funny(X)&curious(X))=>(creative(X)<~>~kind(X))))&
(![X]:((~tall(X)<~>~brave(X))=>(rich(X)|quiet(X))))&
(![X]:(rich(X)=>(~funny(X)<~>tall(X))))&
(![X]:((curious(X)|old(X))<=>(rich(X)|~old(X))))&
(![X]:(brave(X)<=>(generous(X)|~old(X))))&
((~funny(paul))=>(?[X]:((wise(X)&~generous(X)))))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:(~curious(X))))&
(((~curious(paul)<~>patient(paul)))=>((~old(lucy)<~>old(lucy))))&
(![X]:((~patient(X)|curious(X))=>~creative(X)))&
(![X]:((wise(X)|~creative(X))=>(patient(X)&~rich(X))))&
((?[X]:((~strong(X)&~patient(X))))=>((tall(susan)<~>~patient(susan))))&
(![X]:((~tall(X)|~humble(X))=>(~wise(X)&~patient(X))))&
((?[X]:((creative(X)<~>~generous(X))))=>(?[X]:(~old(X))))&
((?[X]:(~tall(X)))=>(~rich(lucy)))&
(((wise(mary)|~funny(mary)))=>((quiet(john)<~>creative(john))))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:(calm(X))))&
((~tall(john)<~>humble(john)))&
(?[X]:((~old(X)<~>tall(X))))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:((old(X)<~>generous(X))))&
(?[X]:((patient(X)|generous(X))))&
(?[X]:((~calm(X)|strong(X))))&
((~strong(fred)&humble(fred))) | tall(lucy) | [
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3095967850087459908772779
% SZS output start Proof for 3095967850087459908772779
9. ! [X0] : ((curious(X0) | ~patient(X0)) => ~creative(X0)) [input p8]
10. ! [X0] : ((~creative(X0) | wise(X0)) => (~rich(X0) & patient(X0))) [input p9]
12. ! [X0] : ((~humble(X0) | ~tall(X0)) => (~patient(X0) & ~wise(X0))) [input p11]
24. ~tall(lucy) [input hypothesis]
36. ! [X0] : (~creative(X0) | (~curious(X0) & patient(X0))) [ennf transformation 9]
37. ! [X0] : ((~rich(X0) & patient(X0)) | (creative(X0) & ~wise(X0))) [ennf transformation 10]
39. ! [X0] : ((~patient(X0) & ~wise(X0)) | (humble(X0) & tall(X0))) [ennf transformation 12]
102. ~creative(X0) | patient(X0) [cnf transformation 36]
105. patient(X0) | creative(X0) [cnf transformation 37]
112. ~patient(X0) | tall(X0) [cnf transformation 39]
135. ~tall(lucy) [cnf transformation 24]
164. patient(X0) [subsumption resolution 105,102]
166. tall(X0) [subsumption resolution 112,164]
240. $false [subsumption resolution 135,166]
% SZS output end Proof for 3095967850087459908772779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or old then someone is both funny and curious.
If someone is either not happy or not curious then susan is not curious or not strong.
Everyone who is patient or not brave is generous.
Everyone who is both not generous and kind is not funny.
If someone is both not funny and funny then someone is not generous.
If john is both happy and not rich then lucy is old or wise and vice versa.
Everyone who is either generous or patient is not old.
Everyone who is patient is either brave or wise and vice versa.
Everyone who is both calm and funny is both old and tall.
If susan is humble then susan is either quiet or not humble.
If someone is either not old or strong then someone is not wise or not quiet and vice versa.
If someone is either funny or curious then alice is both not generous and generous.
Everyone who is generous is either not creative or not tall and vice versa.
Everyone who is not tall or kind is not brave or old.
Everyone who is both happy and brave is both patient and not patient and vice versa.
Everyone who is not curious is both not kind and funny and vice versa.
Someone is brave.
Someone is either not humble or not creative.
Susan is either not curious or patient.
Someone is curious.
Someone is not curious or strong.
John is either quiet or not wise.
Someone is both patient and wise. | Alice is generous. | entailment | ((?[X]:((patient(X)|old(X))))=>(?[X]:((funny(X)&curious(X)))))&
((?[X]:((~happy(X)<~>~curious(X))))=>((~curious(susan)|~strong(susan))))&
(![X]:((patient(X)|~brave(X))=>generous(X)))&
(![X]:((~generous(X)&kind(X))=>~funny(X)))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:(~generous(X))))&
(((happy(john)&~rich(john)))<=>((old(lucy)|wise(lucy))))&
(![X]:((generous(X)<~>patient(X))=>~old(X)))&
(![X]:(patient(X)<=>(brave(X)<~>wise(X))))&
(![X]:((calm(X)&funny(X))=>(old(X)&tall(X))))&
((humble(susan))=>((quiet(susan)<~>~humble(susan))))&
((?[X]:((~old(X)<~>strong(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
((?[X]:((funny(X)<~>curious(X))))=>((~generous(alice)&generous(alice))))&
(![X]:(generous(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~tall(X)|kind(X))=>(~brave(X)|old(X))))&
(![X]:((happy(X)&brave(X))<=>(patient(X)&~patient(X))))&
(![X]:(~curious(X)<=>(~kind(X)&funny(X))))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)<~>~creative(X))))&
((~curious(susan)<~>patient(susan)))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)|strong(X))))&
((quiet(john)<~>~wise(john)))&
(?[X]:((patient(X)&wise(X)))) | generous(alice) | [
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8234145710333276406568338
% SZS output start Proof for 8234145710333276406568338
4. ! [X0] : ((kind(X0) & ~generous(X0)) => ~funny(X0)) [input p3]
12. ? [X0] : (funny(X0) <~> curious(X0)) => (generous(alice) & ~generous(alice)) [input p11]
16. ! [X0] : (~curious(X0) <=> (funny(X0) & ~kind(X0))) [input p15]
24. ~generous(alice) [input hypothesis]
33. ! [X0] : (~funny(X0) | (~kind(X0) | generous(X0))) [ennf transformation 4]
34. ! [X0] : (~funny(X0) | ~kind(X0) | generous(X0)) [flattening 33]
38. (generous(alice) & ~generous(alice)) | ! [X0] : (funny(X0) <=> curious(X0)) [ennf transformation 12]
58. (generous(alice) & ~generous(alice)) | ! [X0] : ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))) [nnf transformation 38]
62. ! [X0] : ((~curious(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | curious(X0))) [nnf transformation 16]
63. ! [X0] : ((~curious(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | curious(X0))) [flattening 62]
85. ~kind(X0) | ~funny(X0) | generous(X0) [cnf transformation 34]
108. generous(alice) | curious(X0) | ~funny(X0) [cnf transformation 58]
109. generous(alice) | funny(X0) | ~curious(X0) [cnf transformation 58]
121. curious(X0) | funny(X0) [cnf transformation 63]
122. ~curious(X0) | ~funny(X0) | kind(X0) [cnf transformation 63]
134. ~generous(alice) [cnf transformation 24]
235. 23 <=> ! [X0] : (funny(X0) | ~curious(X0)) [avatar definition]
236. funny(X0) | ~curious(X0) <- (23) [avatar component clause 235]
238. 24 <=> generous(alice) [avatar definition]
239. ~generous(alice) <- (~24) [avatar component clause 238]
241. 23 | 24 [avatar split clause 109,238,235]
243. 25 <=> ! [X0] : (curious(X0) | ~funny(X0)) [avatar definition]
244. curious(X0) | ~funny(X0) <- (25) [avatar component clause 243]
245. 25 | 24 [avatar split clause 108,238,243]
284. ~24 [avatar split clause 134,238]
285. curious(X0) <- (25) [subsumption resolution 244,121]
286. funny(X0) <- (23, 25) [subsumption resolution 236,285]
394. ~funny(X1) | kind(X1) <- (25) [resolution 122,285]
396. kind(X1) <- (23, 25) [subsumption resolution 394,286]
411. ~funny(X1) | generous(X1) <- (23, 25) [resolution 396,85]
413. generous(X1) <- (23, 25) [subsumption resolution 411,286]
449. $false <- (23, ~24, 25) [resolution 413,239]
452. ~23 | 24 | ~25 [avatar contradiction clause 449]
453. $false [avatar sat refutation 241,245,284,452]
% SZS output end Proof for 8234145710333276406568338
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is happy.
If susan is either not humble or quiet then paul is either not rich or not patient.
If lucy is old or strong then alice is either generous or kind and vice versa.
If someone is curious then alice is funny and vice versa.
If someone is not kind then someone is both funny and not humble.
If paul is not creative then someone is both quiet and not strong.
Everyone who is not creative or calm is either tall or not rich.
If paul is not wise or tall then someone is happy and vice versa.
If lucy is either strong or not curious then john is either not tall or quiet and vice versa.
If someone is brave or generous then someone is both calm and kind.
If someone is not tall then someone is both not happy and not wise and vice versa.
Everyone who is both old and curious is creative and vice versa.
If mary is either not strong or kind then someone is either not wise or brave.
If someone is not old or not strong then someone is not generous or wise and vice versa.
If someone is not rich or quiet then someone is either humble or tall.
If someone is both quiet and curious then susan is not happy and vice versa.
Someone is brave.
Fred is both rich and not creative.
Alice is both not happy and humble.
Paul is both generous and not humble.
Someone is calm or rich.
Susan is either curious or kind.
Someone is either not wise or patient.
Susan is either not wise or wise. | Alice is not happy. | entailment | ((?[X]:(funny(X)))=>(?[X]:(happy(X))))&
(((~humble(susan)<~>quiet(susan)))=>((~rich(paul)<~>~patient(paul))))&
(((old(lucy)|strong(lucy)))<=>((generous(alice)<~>kind(alice))))&
((?[X]:(curious(X)))<=>(funny(alice)))&
((?[X]:(~kind(X)))=>(?[X]:((funny(X)&~humble(X)))))&
((~creative(paul))=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((~creative(X)|calm(X))=>(tall(X)<~>~rich(X))))&
(((~wise(paul)|tall(paul)))<=>(?[X]:(happy(X))))&
(((strong(lucy)<~>~curious(lucy)))<=>((~tall(john)<~>quiet(john))))&
((?[X]:((brave(X)|generous(X))))=>(?[X]:((calm(X)&kind(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~happy(X)&~wise(X)))))&
(![X]:((old(X)&curious(X))<=>creative(X)))&
(((~strong(mary)<~>kind(mary)))=>(?[X]:((~wise(X)<~>brave(X)))))&
((?[X]:((~old(X)|~strong(X))))<=>(?[X]:((~generous(X)|wise(X)))))&
((?[X]:((~rich(X)|quiet(X))))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((quiet(X)&curious(X))))<=>(~happy(susan)))&
(?[X]:(brave(X)))&
((rich(fred)&~creative(fred)))&
((~happy(alice)&humble(alice)))&
((generous(paul)&~humble(paul)))&
(?[X]:((calm(X)|rich(X))))&
((curious(susan)<~>kind(susan)))&
(?[X]:((~wise(X)<~>patient(X))))&
((~wise(susan)<~>wise(susan))) | ~happy(alice) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7683741850167379230495175
% SZS output start Proof for 7683741850167379230495175
19. humble(alice) & ~happy(alice) [input p18]
25. happy(alice) [input hypothesis]
157. ~happy(alice) [cnf transformation 19]
168. happy(alice) [cnf transformation 25]
453. $false [subsumption resolution 168,157]
% SZS output end Proof for 7683741850167379230495175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not generous is both not old and not happy.
Everyone who is not patient or quiet is not wise or generous and vice versa.
If susan is both not calm and creative then alice is not old or not kind and vice versa.
If lucy is creative or not wise then someone is either not strong or happy.
Everyone who is either not creative or not wise is both not funny and not creative.
If lucy is either generous or rich then someone is either not calm or not creative.
Everyone who is both not strong and not rich is either not curious or humble and vice versa.
If someone is not rich then lucy is calm or rich.
Everyone who is either not brave or wise is both not calm and not brave.
If someone is either not curious or strong then someone is not patient and vice versa.
Everyone who is generous or not curious is both rich and not calm.
If lucy is not calm then susan is either funny or not brave and vice versa.
If someone is creative then fred is either not brave or kind and vice versa.
If fred is both humble and patient then someone is both humble and patient and vice versa.
Everyone who is either patient or not humble is rich.
Everyone who is not creative is calm or funny and vice versa.
Alice is either strong or tall.
Someone is calm or not quiet.
Lucy is not tall or patient.
Susan is either funny or not creative.
Susan is kind.
Someone is brave.
Paul is both not patient and wise. | Alice is not kind. | contradiction | (![X]:((strong(X)|~generous(X))=>(~old(X)&~happy(X))))&
(![X]:((~patient(X)|quiet(X))<=>(~wise(X)|generous(X))))&
(((~calm(susan)&creative(susan)))<=>((~old(alice)|~kind(alice))))&
(((creative(lucy)|~wise(lucy)))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((~creative(X)<~>~wise(X))=>(~funny(X)&~creative(X))))&
(((generous(lucy)<~>rich(lucy)))=>(?[X]:((~calm(X)<~>~creative(X)))))&
(![X]:((~strong(X)&~rich(X))<=>(~curious(X)<~>humble(X))))&
((?[X]:(~rich(X)))=>((calm(lucy)|rich(lucy))))&
(![X]:((~brave(X)<~>wise(X))=>(~calm(X)&~brave(X))))&
((?[X]:((~curious(X)<~>strong(X))))<=>(?[X]:(~patient(X))))&
(![X]:((generous(X)|~curious(X))=>(rich(X)&~calm(X))))&
((~calm(lucy))<=>((funny(susan)<~>~brave(susan))))&
((?[X]:(creative(X)))<=>((~brave(fred)<~>kind(fred))))&
(((humble(fred)&patient(fred)))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:((patient(X)<~>~humble(X))=>rich(X)))&
(![X]:(~creative(X)<=>(calm(X)|funny(X))))&
((strong(alice)<~>tall(alice)))&
(?[X]:((calm(X)|~quiet(X))))&
((~tall(lucy)|patient(lucy)))&
((funny(susan)<~>~creative(susan)))&
(kind(susan))&
(?[X]:(brave(X)))&
((~patient(paul)&wise(paul))) | ~kind(alice) | [
"p2",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3861578180687633564895628
% SZS output start Proof for 3861578180687633564895628
3. (creative(susan) & ~calm(susan)) <=> (~kind(alice) | ~old(alice)) [input p2]
16. ! [X0] : (~creative(X0) <=> (funny(X0) | calm(X0))) [input p15]
20. funny(susan) <~> ~creative(susan) [input p19]
24. ~kind(alice) [input hypothesis]
37. ((creative(susan) & ~calm(susan)) | (kind(alice) & old(alice))) & ((~kind(alice) | ~old(alice)) | (~creative(susan) | calm(susan))) [nnf transformation 3]
38. ((creative(susan) & ~calm(susan)) | (kind(alice) & old(alice))) & (~kind(alice) | ~old(alice) | ~creative(susan) | calm(susan)) [flattening 37]
65. ! [X0] : ((~creative(X0) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | creative(X0))) [nnf transformation 16]
66. ! [X0] : ((~creative(X0) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | creative(X0))) [flattening 65]
70. (creative(susan) | ~funny(susan)) & (~creative(susan) | funny(susan)) [nnf transformation 20]
85. creative(susan) | kind(alice) [cnf transformation 38]
133. ~creative(X0) | ~funny(X0) [cnf transformation 66]
138. ~creative(susan) | funny(susan) [cnf transformation 70]
144. ~kind(alice) [cnf transformation 24]
148. 1 <=> kind(alice) [avatar definition]
152. 2 <=> creative(susan) [avatar definition]
155. 1 | 2 [avatar split clause 85,152,148]
329. ~creative(susan) [subsumption resolution 138,133]
330. ~2 [avatar split clause 329,152]
331. ~1 [avatar split clause 144,148]
332. $false [avatar sat refutation 155,330,331]
% SZS output end Proof for 3861578180687633564895628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not calm then someone is both brave and calm and vice versa.
Everyone who is either not strong or not tall is not rich or generous and vice versa.
Everyone who is both not creative and wise is patient or creative and vice versa.
Everyone who is rich or funny is both rich and not curious and vice versa.
If someone is both not curious and humble then someone is either not kind or not tall.
If lucy is both not curious and patient then alice is curious or not wise.
Everyone who is not generous is not funny or not curious and vice versa.
If someone is not calm then someone is both not generous and funny.
Everyone who is either not creative or not rich is either rich or not happy.
Everyone who is not strong or patient is funny and vice versa.
If fred is creative then mary is creative or quiet.
If mary is either wise or not tall then someone is not creative or strong and vice versa.
Everyone who is either not quiet or not happy is patient.
Everyone who is either rich or curious is both brave and not kind.
Everyone who is both not old and not patient is either happy or not kind.
Everyone who is not rich or not curious is not generous or brave and vice versa.
Susan is patient or rich.
Susan is tall or wise.
Someone is not creative.
Someone is tall.
Someone is not generous or funny.
Someone is not patient.
Someone is not old or patient. | Mary is wise. | neutral | ((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((brave(X)&calm(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~rich(X)|generous(X))))&
(![X]:((~creative(X)&wise(X))<=>(patient(X)|creative(X))))&
(![X]:((rich(X)|funny(X))<=>(rich(X)&~curious(X))))&
((?[X]:((~curious(X)&humble(X))))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(((~curious(lucy)&patient(lucy)))=>((curious(alice)|~wise(alice))))&
(![X]:(~generous(X)<=>(~funny(X)|~curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~generous(X)&funny(X)))))&
(![X]:((~creative(X)<~>~rich(X))=>(rich(X)<~>~happy(X))))&
(![X]:((~strong(X)|patient(X))<=>funny(X)))&
((creative(fred))=>((creative(mary)|quiet(mary))))&
(((wise(mary)<~>~tall(mary)))<=>(?[X]:((~creative(X)|strong(X)))))&
(![X]:((~quiet(X)<~>~happy(X))=>patient(X)))&
(![X]:((rich(X)<~>curious(X))=>(brave(X)&~kind(X))))&
(![X]:((~old(X)&~patient(X))=>(happy(X)<~>~kind(X))))&
(![X]:((~rich(X)|~curious(X))<=>(~generous(X)|brave(X))))&
((patient(susan)|rich(susan)))&
((tall(susan)|wise(susan)))&
(?[X]:(~creative(X)))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~old(X)|patient(X)))) | wise(mary) | [] | null | 0 |
Everyone who is funny or not creative is not generous or rich and vice versa. Everyone who is both curious and not kind is funny or generous and vice versa. Everyone who is not calm is either funny or quiet. Everyone who is either old or not tall is funny or old and vice versa. If lucy is both not humble and not creative then mary is not rich or patient. If paul is both not creative and funny then someone is humble or calm. Everyone who is not calm is rich and vice versa. Everyone who is either quiet or not generous is both not curious and not wise. If fred is both quiet and happy then john is either generous or not wise. Everyone who is tall is not kind or patient. Everyone who is not tall or calm is calm. Everyone who is not kind is both not calm and calm and vice versa. If paul is not calm then someone is either creative or not calm. Everyone who is either quiet or not rich is both rich and generous and vice versa. Everyone who is generous or not rich is either tall or not patient and vice versa. If someone is humble or tall then someone is not humble or not strong. Someone is either not happy or not humble. Someone is patient or not humble. Someone is humble. Fred is curious or not creative. Alice is either not brave or not wise. Lucy is both not wise and curious. Lucy is either funny or calm. | Mary is not quiet. | contradiction | (![X]:((funny(X)|~creative(X))<=>(~generous(X)|rich(X))))&
(![X]:((curious(X)&~kind(X))<=>(funny(X)|generous(X))))&
(![X]:(~calm(X)=>(funny(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|old(X))))&
(((~humble(lucy)&~creative(lucy)))=>((~rich(mary)|patient(mary))))&
(((~creative(paul)&funny(paul)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:(~calm(X)<=>rich(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~curious(X)&~wise(X))))&
(((quiet(fred)&happy(fred)))=>((generous(john)<~>~wise(john))))&
(![X]:(tall(X)=>(~kind(X)|patient(X))))&
(![X]:((~tall(X)|calm(X))=>calm(X)))&
(![X]:(~kind(X)<=>(~calm(X)&calm(X))))&
((~calm(paul))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:(humble(X)))&
((curious(fred)|~creative(fred)))&
((~brave(alice)<~>~wise(alice)))&
((~wise(lucy)&curious(lucy)))&
((funny(lucy)<~>calm(lucy))) | ~quiet(mary) | [
"p1",
"p2",
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9118471520045399704451020
% SZS output start Proof for 9118471520045399704451020
2. ! [X0] : ((~kind(X0) & curious(X0)) <=> (generous(X0) | funny(X0))) [input p1]
3. ! [X0] : (~calm(X0) => (funny(X0) <~> quiet(X0))) [input p2]
7. ! [X0] : (~calm(X0) <=> rich(X0)) [input p6]
8. ! [X0] : ((quiet(X0) <~> ~generous(X0)) => (~wise(X0) & ~curious(X0))) [input p7]
12. ! [X0] : (~kind(X0) <=> (calm(X0) & ~calm(X0))) [input p11]
14. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (generous(X0) & rich(X0))) [input p13]
24. ~quiet(mary) [input hypothesis]
27. ! [X0] : ((funny(X0) <~> quiet(X0)) | calm(X0)) [ennf transformation 3]
32. ! [X0] : ((~wise(X0) & ~curious(X0)) | (quiet(X0) <=> ~generous(X0))) [ennf transformation 8]
41. ! [X0] : (((~kind(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | (kind(X0) | ~curious(X0)))) [nnf transformation 2]
42. ! [X0] : (((~kind(X0) & curious(X0)) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | kind(X0) | ~curious(X0))) [flattening 41]
43. ! [X0] : (((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | calm(X0)) [nnf transformation 27]
48. ! [X0] : ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))) [nnf transformation 7]
49. ! [X0] : ((~wise(X0) & ~curious(X0)) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) [nnf transformation 32]
51. ! [X0] : ((~kind(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | kind(X0))) [nnf transformation 12]
52. ! [X0] : ((~kind(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | kind(X0))) [flattening 51]
56. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 14]
57. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [flattening 56]
75. ~generous(X0) | curious(X0) [cnf transformation 42]
76. ~kind(X0) | ~funny(X0) [cnf transformation 42]
78. quiet(X0) | funny(X0) | calm(X0) [cnf transformation 43]
89. ~calm(X0) | ~rich(X0) [cnf transformation 48]
90. ~curious(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 49]
99. ~calm(X0) | kind(X0) [cnf transformation 52]
100. calm(X0) | kind(X0) [cnf transformation 52]
105. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 57]
106. generous(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 57]
127. ~quiet(mary) [cnf transformation 24]
128. quiet(X0) | rich(X0) [duplicate literal removal 105]
142. 3 <=> rich(mary) [avatar definition]
143. rich(mary) <- (3) [avatar component clause 142]
167. ~quiet(X0) | ~generous(X0) [subsumption resolution 90,75]
186. kind(X0) [subsumption resolution 99,100]
202. ~quiet(X0) | ~rich(X0) [subsumption resolution 106,167]
254. ~funny(X0) [resolution 76,186]
263. rich(mary) [resolution 128,127]
266. 3 [avatar split clause 263,142]
279. funny(X0) | calm(X0) | ~rich(X0) [resolution 78,202]
282. calm(X0) | ~rich(X0) [subsumption resolution 279,254]
283. ~rich(X0) [subsumption resolution 282,89]
291. $false <- (3) [resolution 283,143]
292. ~3 [avatar contradiction clause 291]
294. $false [avatar sat refutation 266,292]
% SZS output end Proof for 9118471520045399704451020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or calm is either not calm or not humble.
Everyone who is either not quiet or funny is both not curious and curious.
Everyone who is not patient or not generous is quiet or kind.
If someone is not funny then fred is generous or not brave and vice versa.
Everyone who is either not tall or kind is not calm and vice versa.
Everyone who is either strong or not creative is not strong.
Everyone who is funny or tall is not funny and vice versa.
Everyone who is generous is calm.
Everyone who is either not happy or tall is both not calm and not curious.
Everyone who is funny or not funny is creative and vice versa.
If someone is patient then someone is both not tall and not kind.
If fred is both strong and funny then lucy is not happy and vice versa.
Everyone who is not happy is calm or not kind.
Everyone who is not tall is either kind or not old and vice versa.
If someone is both funny and not funny then someone is quiet or not brave.
Everyone who is both tall and quiet is either not generous or not happy and vice versa.
John is either funny or kind.
Someone is either not kind or curious.
Someone is both tall and wise.
Someone is not old or not kind.
Mary is either not wise or humble. | Lucy is not old. | entailment | (![X]:((brave(X)<~>calm(X))=>(~calm(X)<~>~humble(X))))&
(![X]:((~quiet(X)<~>funny(X))=>(~curious(X)&curious(X))))&
(![X]:((~patient(X)|~generous(X))=>(quiet(X)|kind(X))))&
((?[X]:(~funny(X)))<=>((generous(fred)|~brave(fred))))&
(![X]:((~tall(X)<~>kind(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~creative(X))=>~strong(X)))&
(![X]:((funny(X)|tall(X))<=>~funny(X)))&
(![X]:(generous(X)=>calm(X)))&
(![X]:((~happy(X)<~>tall(X))=>(~calm(X)&~curious(X))))&
(![X]:((funny(X)|~funny(X))<=>creative(X)))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)&~kind(X)))))&
(((strong(fred)&funny(fred)))<=>(~happy(lucy)))&
(![X]:(~happy(X)=>(calm(X)|~kind(X))))&
(![X]:(~tall(X)<=>(kind(X)<~>~old(X))))&
((?[X]:((funny(X)&~funny(X))))=>(?[X]:((quiet(X)|~brave(X)))))&
(![X]:((tall(X)&quiet(X))<=>(~generous(X)<~>~happy(X))))&
((funny(john)<~>kind(john)))&
(?[X]:((~kind(X)<~>curious(X))))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((~old(X)|~kind(X))))&
((~wise(mary)<~>humble(mary))) | ~old(lucy) | [
"p4",
"p6",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2213289172386169416833498
% SZS output start Proof for 2213289172386169416833498
5. ! [X0] : ((~tall(X0) <~> kind(X0)) <=> ~calm(X0)) [input p4]
7. ! [X0] : ((tall(X0) | funny(X0)) <=> ~funny(X0)) [input p6]
9. ! [X0] : ((~happy(X0) <~> tall(X0)) => (~curious(X0) & ~calm(X0))) [input p8]
12. (funny(fred) & strong(fred)) <=> ~happy(lucy) [input p11]
14. ! [X0] : (~tall(X0) <=> (kind(X0) <~> ~old(X0))) [input p13]
22. old(lucy) [input hypothesis]
31. ! [X0] : ((~curious(X0) & ~calm(X0)) | (~happy(X0) <=> tall(X0))) [ennf transformation 9]
43. ! [X0] : ((((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | calm(X0)) & (~calm(X0) | ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))))) [nnf transformation 5]
45. ! [X0] : (((tall(X0) | funny(X0)) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((tall(X0) | funny(X0) | funny(X0)) & (~funny(X0) | (~tall(X0) & ~funny(X0)))) [flattening 45]
47. ! [X0] : ((~curious(X0) & ~calm(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) [nnf transformation 31]
53. ((funny(fred) & strong(fred)) | happy(lucy)) & (~happy(lucy) | (~funny(fred) | ~strong(fred))) [nnf transformation 12]
54. ((funny(fred) & strong(fred)) | happy(lucy)) & (~happy(lucy) | ~funny(fred) | ~strong(fred)) [flattening 53]
55. ! [X0] : ((~tall(X0) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | tall(X0))) [nnf transformation 14]
85. ~tall(X0) | kind(X0) | calm(X0) [cnf transformation 43]
89. ~funny(X0) | ~funny(X0) [cnf transformation 46]
91. tall(X0) | funny(X0) | funny(X0) [cnf transformation 46]
94. ~happy(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 47]
104. funny(fred) | happy(lucy) [cnf transformation 54]
108. ~old(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 55]
126. old(lucy) [cnf transformation 22]
127. ~funny(X0) [duplicate literal removal 89]
128. tall(X0) | funny(X0) [duplicate literal removal 91]
166. happy(lucy) [subsumption resolution 104,127]
228. kind(X0) | calm(X0) | funny(X0) [resolution 85,128]
232. kind(X0) | calm(X0) [subsumption resolution 228,127]
253. ~calm(lucy) | ~tall(lucy) [resolution 94,166]
255. 19 <=> tall(lucy) [avatar definition]
256. tall(lucy) <- (19) [avatar component clause 255]
257. ~tall(lucy) <- (~19) [avatar component clause 255]
259. 20 <=> calm(lucy) [avatar definition]
261. ~calm(lucy) <- (~20) [avatar component clause 259]
262. ~19 | ~20 [avatar split clause 253,259,255]
267. funny(lucy) <- (~19) [resolution 257,128]
268. $false <- (~19) [subsumption resolution 267,127]
269. 19 [avatar contradiction clause 268]
289. ~tall(lucy) | ~kind(lucy) [resolution 108,126]
290. ~kind(lucy) <- (19) [subsumption resolution 289,256]
322. calm(lucy) <- (19) [resolution 232,290]
328. $false <- (19, ~20) [subsumption resolution 322,261]
329. ~19 | 20 [avatar contradiction clause 328]
330. $false [avatar sat refutation 262,269,329]
% SZS output end Proof for 2213289172386169416833498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not generous is not generous or rich.
If someone is not curious or not kind then alice is curious.
If mary is both quiet and wise then someone is either patient or not curious and vice versa.
If someone is patient or old then someone is both not rich and brave.
Everyone who is not patient is either calm or rich.
If john is either not funny or funny then someone is generous.
Everyone who is creative is generous or not curious.
Everyone who is calm is both not brave and not rich.
Everyone who is not funny is both quiet and not calm and vice versa.
If someone is curious then someone is either humble or not wise and vice versa.
If lucy is both patient and not generous then someone is not old.
Everyone who is creative is curious or not rich and vice versa.
Everyone who is both not humble and not patient is creative.
If someone is either tall or not curious then fred is not generous.
Everyone who is either not quiet or not generous is both creative and kind.
Everyone who is both kind and not calm is either rich or not brave and vice versa.
Fred is kind or generous.
Fred is happy or rich.
Susan is both not kind and rich.
Paul is not patient.
Paul is either patient or not funny.
Someone is funny.
John is either not curious or patient.
John is both rich and not wise. | Paul is not funny. | entailment | (![X]:((~rich(X)&~generous(X))=>(~generous(X)|rich(X))))&
((?[X]:((~curious(X)|~kind(X))))=>(curious(alice)))&
(((quiet(mary)&wise(mary)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
((?[X]:((patient(X)|old(X))))=>(?[X]:((~rich(X)&brave(X)))))&
(![X]:(~patient(X)=>(calm(X)<~>rich(X))))&
(((~funny(john)<~>funny(john)))=>(?[X]:(generous(X))))&
(![X]:(creative(X)=>(generous(X)|~curious(X))))&
(![X]:(calm(X)=>(~brave(X)&~rich(X))))&
(![X]:(~funny(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>~wise(X)))))&
(((patient(lucy)&~generous(lucy)))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(curious(X)|~rich(X))))&
(![X]:((~humble(X)&~patient(X))=>creative(X)))&
((?[X]:((tall(X)<~>~curious(X))))=>(~generous(fred)))&
(![X]:((~quiet(X)<~>~generous(X))=>(creative(X)&kind(X))))&
(![X]:((kind(X)&~calm(X))<=>(rich(X)<~>~brave(X))))&
((kind(fred)|generous(fred)))&
((happy(fred)|rich(fred)))&
((~kind(susan)&rich(susan)))&
(~patient(paul))&
((patient(paul)<~>~funny(paul)))&
(?[X]:(funny(X)))&
((~curious(john)<~>patient(john)))&
((rich(john)&~wise(john))) | ~funny(paul) | [
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8210581605143088543428073
% SZS output start Proof for 8210581605143088543428073
20. ~patient(paul) [input p19]
21. patient(paul) <~> ~funny(paul) [input p20]
25. funny(paul) [input hypothesis]
69. (funny(paul) | ~patient(paul)) & (~funny(paul) | patient(paul)) [nnf transformation 21]
117. ~patient(paul) [cnf transformation 20]
118. ~funny(paul) | patient(paul) [cnf transformation 69]
125. funny(paul) [cnf transformation 25]
238. ~funny(paul) [subsumption resolution 118,117]
249. $false [subsumption resolution 125,238]
% SZS output end Proof for 8210581605143088543428073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not happy is both not old and not happy and vice versa.
Everyone who is both generous and creative is either not curious or curious.
Everyone who is humble or wise is either not strong or creative and vice versa.
Everyone who is either not brave or quiet is not kind.
If someone is not funny then alice is kind.
Everyone who is both humble and happy is either brave or not creative.
Everyone who is not quiet or patient is brave and vice versa.
If someone is either not calm or wise then john is not generous or rich and vice versa.
Everyone who is not funny or generous is not funny or kind and vice versa.
Everyone who is not curious is happy or not humble.
If someone is both not funny and not creative then john is both not generous and not old.
Everyone who is either strong or not happy is calm and vice versa.
If someone is both curious and not kind then fred is creative.
Everyone who is calm is kind and vice versa.
Everyone who is not quiet is both calm and not calm.
Everyone who is not patient is creative or brave and vice versa.
Lucy is not curious.
Susan is quiet or not rich.
Susan is not curious or not calm.
Someone is wise.
John is either happy or not creative.
John is either wise or generous. | Fred is quiet. | entailment | (![X]:((tall(X)&~happy(X))<=>(~old(X)&~happy(X))))&
(![X]:((generous(X)&creative(X))=>(~curious(X)<~>curious(X))))&
(![X]:((humble(X)|wise(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((~brave(X)<~>quiet(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(kind(alice)))&
(![X]:((humble(X)&happy(X))=>(brave(X)<~>~creative(X))))&
(![X]:((~quiet(X)|patient(X))<=>brave(X)))&
((?[X]:((~calm(X)<~>wise(X))))<=>((~generous(john)|rich(john))))&
(![X]:((~funny(X)|generous(X))<=>(~funny(X)|kind(X))))&
(![X]:(~curious(X)=>(happy(X)|~humble(X))))&
((?[X]:((~funny(X)&~creative(X))))=>((~generous(john)&~old(john))))&
(![X]:((strong(X)<~>~happy(X))<=>calm(X)))&
((?[X]:((curious(X)&~kind(X))))=>(creative(fred)))&
(![X]:(calm(X)<=>kind(X)))&
(![X]:(~quiet(X)=>(calm(X)&~calm(X))))&
(![X]:(~patient(X)<=>(creative(X)|brave(X))))&
(~curious(lucy))&
((quiet(susan)|~rich(susan)))&
((~curious(susan)|~calm(susan)))&
(?[X]:(wise(X)))&
((happy(john)<~>~creative(john)))&
((wise(john)<~>generous(john))) | quiet(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6564728311098297218534584
% SZS output start Proof for 6564728311098297218534584
15. ! [X0] : (~quiet(X0) => (~calm(X0) & calm(X0))) [input p14]
23. ~quiet(fred) [input hypothesis]
34. ! [X0] : ((~calm(X0) & calm(X0)) | quiet(X0)) [ennf transformation 15]
99. calm(X0) | quiet(X0) [cnf transformation 34]
100. ~calm(X0) | quiet(X0) [cnf transformation 34]
112. ~quiet(fred) [cnf transformation 23]
166. quiet(X0) [subsumption resolution 99,100]
194. $false [subsumption resolution 112,166]
% SZS output end Proof for 6564728311098297218534584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not creative or not calm then someone is both not kind and humble and vice versa.
Everyone who is not curious is either not old or calm and vice versa.
Everyone who is tall or not old is not old and vice versa.
If alice is rich or not generous then john is both humble and wise and vice versa.
Everyone who is either funny or patient is not strong or calm and vice versa.
Everyone who is not old is both quiet and not tall.
Everyone who is not wise or kind is either not tall or not kind and vice versa.
If susan is funny or brave then paul is tall.
If alice is both curious and not quiet then someone is quiet and vice versa.
Everyone who is either generous or not curious is either humble or creative.
Everyone who is creative is both not wise and generous and vice versa.
Everyone who is calm or not wise is not brave or quiet.
If someone is both not funny and creative then fred is patient or not calm and vice versa.
Everyone who is humble or not kind is not brave.
Everyone who is both not tall and funny is either tall or strong and vice versa.
Everyone who is both happy and creative is both not kind and tall.
Fred is not creative or not wise.
Paul is both not rich and not strong.
Paul is either not quiet or humble.
Someone is not generous or not kind.
Susan is old.
Mary is generous.
Alice is either tall or rich. | Mary is funny. | neutral | (((~creative(john)<~>~calm(john)))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:(~curious(X)<=>(~old(X)<~>calm(X))))&
(![X]:((tall(X)|~old(X))<=>~old(X)))&
(((rich(alice)|~generous(alice)))<=>((humble(john)&wise(john))))&
(![X]:((funny(X)<~>patient(X))<=>(~strong(X)|calm(X))))&
(![X]:(~old(X)=>(quiet(X)&~tall(X))))&
(![X]:((~wise(X)|kind(X))<=>(~tall(X)<~>~kind(X))))&
(((funny(susan)|brave(susan)))=>(tall(paul)))&
(((curious(alice)&~quiet(alice)))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)<~>~curious(X))=>(humble(X)<~>creative(X))))&
(![X]:(creative(X)<=>(~wise(X)&generous(X))))&
(![X]:((calm(X)|~wise(X))=>(~brave(X)|quiet(X))))&
((?[X]:((~funny(X)&creative(X))))<=>((patient(fred)|~calm(fred))))&
(![X]:((humble(X)|~kind(X))=>~brave(X)))&
(![X]:((~tall(X)&funny(X))<=>(tall(X)<~>strong(X))))&
(![X]:((happy(X)&creative(X))=>(~kind(X)&tall(X))))&
((~creative(fred)|~wise(fred)))&
((~rich(paul)&~strong(paul)))&
((~quiet(paul)<~>humble(paul)))&
(?[X]:((~generous(X)|~kind(X))))&
(old(susan))&
(generous(mary))&
((tall(alice)<~>rich(alice))) | funny(mary) | [] | null | 0 |
If someone is either not calm or rich then lucy is not quiet or not creative.
If someone is humble then someone is not quiet or not calm.
Everyone who is either not rich or quiet is not generous.
Everyone who is funny is not humble or wise and vice versa.
If john is happy or calm then someone is either not tall or funny.
If john is either generous or not kind then mary is rich or generous and vice versa.
If someone is not curious or not kind then john is both kind and not creative.
If someone is not calm or humble then someone is either old or kind.
Everyone who is either old or not rich is brave.
If susan is either old or curious then paul is both quiet and not creative.
Everyone who is not wise or not quiet is both tall and not patient and vice versa.
Everyone who is kind is humble.
Everyone who is quiet is creative.
If paul is either funny or patient then someone is either not creative or patient and vice versa.
Everyone who is both not wise and patient is both not funny and not brave and vice versa.
Fred is both funny and quiet.
Fred is not humble.
Susan is either generous or not curious.
Someone is both happy and kind.
John is either not brave or not strong.
Someone is happy. | Susan is not brave. | neutral | ((?[X]:((~calm(X)<~>rich(X))))=>((~quiet(lucy)|~creative(lucy))))&
((?[X]:(humble(X)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((~rich(X)<~>quiet(X))=>~generous(X)))&
(![X]:(funny(X)<=>(~humble(X)|wise(X))))&
(((happy(john)|calm(john)))=>(?[X]:((~tall(X)<~>funny(X)))))&
(((generous(john)<~>~kind(john)))<=>((rich(mary)|generous(mary))))&
((?[X]:((~curious(X)|~kind(X))))=>((kind(john)&~creative(john))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((old(X)<~>kind(X)))))&
(![X]:((old(X)<~>~rich(X))=>brave(X)))&
(((old(susan)<~>curious(susan)))=>((quiet(paul)&~creative(paul))))&
(![X]:((~wise(X)|~quiet(X))<=>(tall(X)&~patient(X))))&
(![X]:(kind(X)=>humble(X)))&
(![X]:(quiet(X)=>creative(X)))&
(((funny(paul)<~>patient(paul)))<=>(?[X]:((~creative(X)<~>patient(X)))))&
(![X]:((~wise(X)&patient(X))<=>(~funny(X)&~brave(X))))&
((funny(fred)&quiet(fred)))&
(~humble(fred))&
((generous(susan)<~>~curious(susan)))&
(?[X]:((happy(X)&kind(X))))&
((~brave(john)<~>~strong(john)))&
(?[X]:(happy(X))) | ~brave(susan) | [] | null | 0 |
Everyone who is both wise and not funny is both generous and happy.
Everyone who is either funny or not patient is not rich or not kind.
Everyone who is either quiet or happy is quiet or not strong.
If someone is strong or curious then mary is both not brave and not rich.
Everyone who is both wise and quiet is not patient or not calm.
Everyone who is rich is not patient and vice versa.
If mary is brave then fred is not wise or not old.
Everyone who is not happy is both not brave and old.
Everyone who is either not humble or not happy is strong or tall and vice versa.
If someone is not calm or humble then someone is kind or not funny.
Everyone who is both not curious and not brave is both brave and quiet.
Everyone who is either brave or not brave is both kind and not rich.
If john is not brave or not funny then someone is either strong or patient.
Everyone who is not rich or quiet is either not tall or rich.
Everyone who is creative or not rich is either not funny or humble.
If someone is not happy then susan is not curious or funny and vice versa.
Paul is either not patient or wise.
Someone is curious or patient.
Paul is either tall or not generous.
Someone is not happy or humble.
Susan is both creative and wise.
Someone is not curious.
John is curious or not old. | Paul is humble. | entailment | (![X]:((wise(X)&~funny(X))=>(generous(X)&happy(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~rich(X)|~kind(X))))&
(![X]:((quiet(X)<~>happy(X))=>(quiet(X)|~strong(X))))&
((?[X]:((strong(X)|curious(X))))=>((~brave(mary)&~rich(mary))))&
(![X]:((wise(X)&quiet(X))=>(~patient(X)|~calm(X))))&
(![X]:(rich(X)<=>~patient(X)))&
((brave(mary))=>((~wise(fred)|~old(fred))))&
(![X]:(~happy(X)=>(~brave(X)&old(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(strong(X)|tall(X))))&
((?[X]:((~calm(X)|humble(X))))=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((~curious(X)&~brave(X))=>(brave(X)&quiet(X))))&
(![X]:((brave(X)<~>~brave(X))=>(kind(X)&~rich(X))))&
(((~brave(john)|~funny(john)))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~rich(X)|quiet(X))=>(~tall(X)<~>rich(X))))&
(![X]:((creative(X)|~rich(X))=>(~funny(X)<~>humble(X))))&
((?[X]:(~happy(X)))<=>((~curious(susan)|funny(susan))))&
((~patient(paul)<~>wise(paul)))&
(?[X]:((curious(X)|patient(X))))&
((tall(paul)<~>~generous(paul)))&
(?[X]:((~happy(X)|humble(X))))&
((creative(susan)&wise(susan)))&
(?[X]:(~curious(X)))&
((curious(john)|~old(john))) | humble(paul) | [
"p0",
"p5",
"p11",
"p13",
"p14",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1441714620886050244793896
% SZS output start Proof for 1441714620886050244793896
1. ! [X0] : ((~funny(X0) & wise(X0)) => (happy(X0) & generous(X0))) [input p0]
6. ! [X0] : (rich(X0) <=> ~patient(X0)) [input p5]
12. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (~rich(X0) & kind(X0))) [input p11]
14. ! [X0] : ((quiet(X0) | ~rich(X0)) => (~tall(X0) <~> rich(X0))) [input p13]
15. ! [X0] : ((~rich(X0) | creative(X0)) => (~funny(X0) <~> humble(X0))) [input p14]
17. ~patient(paul) <~> wise(paul) [input p16]
19. tall(paul) <~> ~generous(paul) [input p18]
24. ~humble(paul) [input hypothesis]
26. ! [X0] : ((happy(X0) & generous(X0)) | (funny(X0) | ~wise(X0))) [ennf transformation 1]
27. ! [X0] : ((happy(X0) & generous(X0)) | funny(X0) | ~wise(X0)) [flattening 26]
41. ! [X0] : ((~rich(X0) & kind(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 12]
43. ! [X0] : ((~tall(X0) <~> rich(X0)) | (~quiet(X0) & rich(X0))) [ennf transformation 14]
44. ! [X0] : ((~funny(X0) <~> humble(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 15]
47. ! [X0] : ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))) [nnf transformation 6]
53. ! [X0] : ((~rich(X0) & kind(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 41]
57. ! [X0] : (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~quiet(X0) & rich(X0))) [nnf transformation 43]
58. ! [X0] : (((~humble(X0) | funny(X0)) & (humble(X0) | ~funny(X0))) | (rich(X0) & ~creative(X0))) [nnf transformation 44]
64. (~wise(paul) | patient(paul)) & (wise(paul) | ~patient(paul)) [nnf transformation 17]
67. (generous(paul) | ~tall(paul)) & (~generous(paul) | tall(paul)) [nnf transformation 19]
72. ~wise(X0) | funny(X0) | generous(X0) [cnf transformation 27]
84. rich(X0) | patient(X0) [cnf transformation 47]
100. ~rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 53]
101. ~rich(X0) | brave(X0) | brave(X0) [cnf transformation 53]
106. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 57]
111. humble(X0) | ~funny(X0) | rich(X0) [cnf transformation 58]
117. wise(paul) | ~patient(paul) [cnf transformation 64]
120. ~generous(paul) | tall(paul) [cnf transformation 67]
127. ~humble(paul) [cnf transformation 24]
128. rich(X0) | ~tall(X0) [duplicate literal removal 106]
131. ~rich(X0) | ~brave(X0) [duplicate literal removal 100]
132. ~rich(X0) | brave(X0) [duplicate literal removal 101]
178. ~rich(X0) [subsumption resolution 131,132]
201. ~tall(X0) [subsumption resolution 128,178]
203. ~funny(X0) | humble(X0) [subsumption resolution 111,178]
223. 19 <=> patient(paul) [avatar definition]
224. ~patient(paul) <- (~19) [avatar component clause 223]
227. 20 <=> wise(paul) [avatar definition]
228. wise(paul) <- (20) [avatar component clause 227]
231. ~19 | 20 [avatar split clause 117,227,223]
241. ~generous(paul) [subsumption resolution 120,201]
261. patient(X1) [resolution 84,178]
263. $false <- (~19) [resolution 261,224]
264. 19 [avatar contradiction clause 263]
275. funny(paul) | generous(paul) <- (20) [resolution 72,228]
281. funny(paul) <- (20) [subsumption resolution 275,241]
285. humble(paul) <- (20) [resolution 281,203]
286. $false <- (20) [subsumption resolution 285,127]
287. ~20 [avatar contradiction clause 286]
288. $false [avatar sat refutation 231,264,287]
% SZS output end Proof for 1441714620886050244793896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either funny or not quiet is not curious and vice versa. If lucy is not tall or not quiet then alice is either old or not happy and vice versa. Everyone who is wise is strong. Everyone who is funny is either not old or old and vice versa. Everyone who is kind or generous is either creative or not rich. If lucy is curious then someone is either not brave or not happy and vice versa. If someone is both calm and not quiet then someone is not tall and vice versa. If someone is either kind or not funny then someone is not kind or not happy and vice versa. Everyone who is not creative is both old and curious. Everyone who is both patient and brave is not happy or not quiet. Everyone who is either not quiet or not kind is not strong or happy and vice versa. Everyone who is brave is both not old and wise. Everyone who is both not generous and creative is either happy or creative. If susan is not funny then someone is not quiet or wise. Everyone who is generous or funny is both old and not curious and vice versa. Everyone who is either not old or not tall is not quiet. Someone is generous. Someone is either generous or not happy. Fred is not kind. Susan is both funny and not rich. Someone is both humble and not happy. Someone is creative or not funny. Someone is both not rich and calm. Someone is either not old or tall. | Alice is not tall. | contradiction | (![X]:((funny(X)<~>~quiet(X))<=>~curious(X)))&
(((~tall(lucy)|~quiet(lucy)))<=>((old(alice)<~>~happy(alice))))&
(![X]:(wise(X)=>strong(X)))&
(![X]:(funny(X)<=>(~old(X)<~>old(X))))&
(![X]:((kind(X)|generous(X))=>(creative(X)<~>~rich(X))))&
((curious(lucy))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((~kind(X)|~happy(X)))))&
(![X]:(~creative(X)=>(old(X)&curious(X))))&
(![X]:((patient(X)&brave(X))=>(~happy(X)|~quiet(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(~strong(X)|happy(X))))&
(![X]:(brave(X)=>(~old(X)&wise(X))))&
(![X]:((~generous(X)&creative(X))=>(happy(X)<~>creative(X))))&
((~funny(susan))=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((generous(X)|funny(X))<=>(old(X)&~curious(X))))&
(![X]:((~old(X)<~>~tall(X))=>~quiet(X)))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)<~>~happy(X))))&
(~kind(fred))&
((funny(susan)&~rich(susan)))&
(?[X]:((humble(X)&~happy(X))))&
(?[X]:((creative(X)|~funny(X))))&
(?[X]:((~rich(X)&calm(X))))&
(?[X]:((~old(X)<~>tall(X)))) | ~tall(alice) | [
"p0",
"p3",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8086322814818255888102881
% SZS output start Proof for 8086322814818255888102881
1. ! [X0] : ((funny(X0) <~> ~quiet(X0)) <=> ~curious(X0)) [input p0]
4. ! [X0] : (funny(X0) <=> (~old(X0) <~> old(X0))) [input p3]
15. ! [X0] : ((funny(X0) | generous(X0)) <=> (~curious(X0) & old(X0))) [input p14]
16. ! [X0] : ((~old(X0) <~> ~tall(X0)) => ~quiet(X0)) [input p15]
25. ~tall(alice) [input hypothesis]
37. ! [X0] : (~quiet(X0) | (~old(X0) <=> ~tall(X0))) [ennf transformation 16]
38. ! [X0] : ((((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | curious(X0)) & (~curious(X0) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0))))) [nnf transformation 1]
41. ! [X0] : ((funny(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~funny(X0))) [nnf transformation 4]
62. ! [X0] : (((funny(X0) | generous(X0)) | (curious(X0) | ~old(X0))) & ((~curious(X0) & old(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 15]
63. ! [X0] : ((funny(X0) | generous(X0) | curious(X0) | ~old(X0)) & ((~curious(X0) & old(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 62]
64. ! [X0] : (~quiet(X0) | ((~old(X0) | tall(X0)) & (~tall(X0) | old(X0)))) [nnf transformation 37]
82. ~funny(X0) | quiet(X0) | curious(X0) [cnf transformation 38]
92. funny(X0) | old(X0) | old(X0) [cnf transformation 41]
93. funny(X0) | ~old(X0) | ~old(X0) [cnf transformation 41]
125. old(X0) | ~funny(X0) [cnf transformation 63]
127. ~curious(X0) | ~funny(X0) [cnf transformation 63]
130. ~quiet(X0) | ~old(X0) | tall(X0) [cnf transformation 64]
143. ~tall(alice) [cnf transformation 25]
145. funny(X0) | old(X0) [duplicate literal removal 92]
146. ~old(X0) | funny(X0) [duplicate literal removal 93]
169. funny(X0) [subsumption resolution 145,146]
193. 10 <=> ! [X1] : tall(X1) [avatar definition]
194. tall(X1) <- (10) [avatar component clause 193]
240. ~curious(X0) [subsumption resolution 127,169]
241. old(X0) [subsumption resolution 125,169]
242. ~quiet(X0) | tall(X0) [subsumption resolution 130,241]
277. quiet(X0) | curious(X0) [resolution 82,169]
278. quiet(X0) [subsumption resolution 277,240]
281. tall(X1) [resolution 278,242]
283. 10 [avatar split clause 281,193]
284. $false <- (10) [resolution 194,143]
287. ~10 [avatar contradiction clause 284]
288. $false [avatar sat refutation 283,287]
% SZS output end Proof for 8086322814818255888102881
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is both funny and not generous and vice versa. If someone is both not tall and generous then alice is not kind. If someone is creative then someone is both not patient and funny and vice versa. If someone is not curious or not kind then someone is both not strong and kind. If someone is both patient and creative then someone is both curious and not happy. Everyone who is funny or not generous is not calm or happy and vice versa. If someone is both not patient and generous then fred is not curious or humble. Everyone who is both rich and not quiet is not strong or humble. Everyone who is not tall is not brave and vice versa. Everyone who is both not brave and calm is either not calm or humble. Everyone who is both not kind and happy is both kind and quiet. If someone is wise or old then mary is both not funny and funny and vice versa. If someone is both not curious and generous then someone is not creative and vice versa. Everyone who is both old and happy is both funny and not wise. Everyone who is not funny or curious is both rich and not rich. If someone is either not kind or not happy then someone is not curious. Fred is rich or not calm. Someone is not creative. Someone is both not calm and generous. Alice is not happy or kind. Lucy is curious or not strong. Someone is not rich. Someone is kind. | Lucy is not strong. | entailment | (![X]:((brave(X)<~>~strong(X))<=>(funny(X)&~generous(X))))&
((?[X]:((~tall(X)&generous(X))))=>(~kind(alice)))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((~curious(X)|~kind(X))))=>(?[X]:((~strong(X)&kind(X)))))&
((?[X]:((patient(X)&creative(X))))=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((funny(X)|~generous(X))<=>(~calm(X)|happy(X))))&
((?[X]:((~patient(X)&generous(X))))=>((~curious(fred)|humble(fred))))&
(![X]:((rich(X)&~quiet(X))=>(~strong(X)|humble(X))))&
(![X]:(~tall(X)<=>~brave(X)))&
(![X]:((~brave(X)&calm(X))=>(~calm(X)<~>humble(X))))&
(![X]:((~kind(X)&happy(X))=>(kind(X)&quiet(X))))&
((?[X]:((wise(X)|old(X))))<=>((~funny(mary)&funny(mary))))&
((?[X]:((~curious(X)&generous(X))))<=>(?[X]:(~creative(X))))&
(![X]:((old(X)&happy(X))=>(funny(X)&~wise(X))))&
(![X]:((~funny(X)|curious(X))=>(rich(X)&~rich(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:(~curious(X))))&
((rich(fred)|~calm(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~calm(X)&generous(X))))&
((~happy(alice)|kind(alice)))&
((curious(lucy)|~strong(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:(kind(X))) | ~strong(lucy) | [
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5985891572806211170576680
% SZS output start Proof for 5985891572806211170576680
15. ! [X0] : ((curious(X0) | ~funny(X0)) => (~rich(X0) & rich(X0))) [input p14]
21. ~strong(lucy) | curious(lucy) [input p20]
24. strong(lucy) [input hypothesis]
45. ! [X0] : ((~rich(X0) & rich(X0)) | (~curious(X0) & funny(X0))) [ennf transformation 15]
121. rich(X0) | ~curious(X0) [cnf transformation 45]
123. ~rich(X0) | ~curious(X0) [cnf transformation 45]
131. ~strong(lucy) | curious(lucy) [cnf transformation 21]
134. strong(lucy) [cnf transformation 24]
244. ~curious(X0) [subsumption resolution 121,123]
255. ~strong(lucy) [subsumption resolution 131,244]
256. $false [subsumption resolution 134,255]
% SZS output end Proof for 5985891572806211170576680
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then paul is both not rich and not strong.
Everyone who is either not calm or not curious is both funny and not old and vice versa.
Everyone who is both not humble and not strong is either not rich or not strong and vice versa.
If someone is both happy and not curious then alice is both generous and not old and vice versa.
Everyone who is not wise is either not happy or wise.
Everyone who is not rich or not humble is both not kind and rich.
Everyone who is happy or not brave is either quiet or old and vice versa.
Everyone who is wise or not curious is not strong and vice versa.
Everyone who is not patient is patient.
If susan is brave then someone is tall.
Everyone who is not old or happy is both old and not wise and vice versa.
If someone is either funny or kind then someone is strong.
Everyone who is both not strong and not wise is either not generous or old.
If someone is not brave then john is not calm or funny.
If someone is either not kind or generous then lucy is both not brave and not creative.
Lucy is not humble.
Someone is either not rich or quiet.
Someone is both not creative and not calm. | Paul is happy. | contradiction | ((?[X]:(~brave(X)))=>((~rich(paul)&~strong(paul))))&
(![X]:((~calm(X)<~>~curious(X))<=>(funny(X)&~old(X))))&
(![X]:((~humble(X)&~strong(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((happy(X)&~curious(X))))<=>((generous(alice)&~old(alice))))&
(![X]:(~wise(X)=>(~happy(X)<~>wise(X))))&
(![X]:((~rich(X)|~humble(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)|~brave(X))<=>(quiet(X)<~>old(X))))&
(![X]:((wise(X)|~curious(X))<=>~strong(X)))&
(![X]:(~patient(X)=>patient(X)))&
((brave(susan))=>(?[X]:(tall(X))))&
(![X]:((~old(X)|happy(X))<=>(old(X)&~wise(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~wise(X))=>(~generous(X)<~>old(X))))&
((?[X]:(~brave(X)))=>((~calm(john)|funny(john))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~brave(lucy)&~creative(lucy))))&
(~humble(lucy))&
(?[X]:((~rich(X)<~>quiet(X))))&
(?[X]:((~creative(X)&~calm(X)))) | happy(paul) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 532235246535424721016866
% SZS output start Proof for 532235246535424721016866
5. ! [X0] : (~wise(X0) => (~happy(X0) <~> wise(X0))) [input p4]
11. ! [X0] : ((happy(X0) | ~old(X0)) <=> (~wise(X0) & old(X0))) [input p10]
19. happy(paul) [input hypothesis]
26. ! [X0] : ((~happy(X0) <~> wise(X0)) | wise(X0)) [ennf transformation 5]
43. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | wise(X0)) [nnf transformation 26]
48. ! [X0] : (((happy(X0) | ~old(X0)) | (wise(X0) | ~old(X0))) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 11]
49. ! [X0] : ((happy(X0) | ~old(X0) | wise(X0) | ~old(X0)) & ((~wise(X0) & old(X0)) | (~happy(X0) & old(X0)))) [flattening 48]
79. wise(X0) | ~happy(X0) | wise(X0) [cnf transformation 43]
97. ~wise(X0) | ~happy(X0) [cnf transformation 49]
110. happy(paul) [cnf transformation 19]
114. wise(X0) | ~happy(X0) [duplicate literal removal 79]
155. ~happy(X0) [subsumption resolution 97,114]
190. $false [subsumption resolution 110,155]
% SZS output end Proof for 532235246535424721016866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is either quiet or not kind.
Everyone who is kind or not kind is both calm and not patient and vice versa.
If john is both not patient and not creative then fred is wise.
Everyone who is not humble is not creative or curious.
If john is not happy then someone is either not wise or not old and vice versa.
Everyone who is either rich or happy is both happy and funny.
Everyone who is creative or happy is either not brave or not creative.
Everyone who is both curious and not wise is either not wise or not brave and vice versa.
If someone is either not curious or not rich then someone is strong or not old.
If susan is not patient or funny then fred is either wise or not happy and vice versa.
Everyone who is either humble or happy is funny or generous and vice versa.
If someone is either not brave or not creative then lucy is wise or not old.
Everyone who is rich or not patient is both not humble and not curious and vice versa.
Everyone who is both not funny and not creative is both not wise and creative and vice versa.
Everyone who is either wise or tall is both calm and quiet.
Someone is not generous or not funny.
Someone is humble or not kind.
Mary is not quiet or brave.
Someone is not curious or not creative.
Fred is either strong or not old.
Someone is not creative. | Fred is not funny. | contradiction | (![X]:(quiet(X)=>(quiet(X)<~>~kind(X))))&
(![X]:((kind(X)|~kind(X))<=>(calm(X)&~patient(X))))&
(((~patient(john)&~creative(john)))=>(wise(fred)))&
(![X]:(~humble(X)=>(~creative(X)|curious(X))))&
((~happy(john))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((rich(X)<~>happy(X))=>(happy(X)&funny(X))))&
(![X]:((creative(X)|happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((curious(X)&~wise(X))<=>(~wise(X)<~>~brave(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(?[X]:((strong(X)|~old(X)))))&
(((~patient(susan)|funny(susan)))<=>((wise(fred)<~>~happy(fred))))&
(![X]:((humble(X)<~>happy(X))<=>(funny(X)|generous(X))))&
((?[X]:((~brave(X)<~>~creative(X))))=>((wise(lucy)|~old(lucy))))&
(![X]:((rich(X)|~patient(X))<=>(~humble(X)&~curious(X))))&
(![X]:((~funny(X)&~creative(X))<=>(~wise(X)&creative(X))))&
(![X]:((wise(X)<~>tall(X))=>(calm(X)&quiet(X))))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((humble(X)|~kind(X))))&
((~quiet(mary)|brave(mary)))&
(?[X]:((~curious(X)|~creative(X))))&
((strong(fred)<~>~old(fred)))&
(?[X]:(~creative(X))) | ~funny(fred) | [
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7268125871977347938610565
% SZS output start Proof for 7268125871977347938610565
7. ! [X0] : ((happy(X0) | creative(X0)) => (~brave(X0) <~> ~creative(X0))) [input p6]
8. ! [X0] : ((~wise(X0) & curious(X0)) <=> (~wise(X0) <~> ~brave(X0))) [input p7]
14. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> (creative(X0) & ~wise(X0))) [input p13]
22. ~funny(fred) [input hypothesis]
30. ! [X0] : ((~brave(X0) <~> ~creative(X0)) | (~happy(X0) & ~creative(X0))) [ennf transformation 7]
43. ! [X0] : (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~happy(X0) & ~creative(X0))) [nnf transformation 30]
44. ! [X0] : (((~wise(X0) & curious(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (wise(X0) | ~curious(X0)))) [nnf transformation 8]
45. ! [X0] : (((~wise(X0) & curious(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | wise(X0) | ~curious(X0))) [flattening 44]
57. ! [X0] : (((~creative(X0) & ~funny(X0)) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | (creative(X0) | funny(X0)))) [nnf transformation 14]
58. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | creative(X0) | funny(X0))) [flattening 57]
86. ~creative(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 43]
95. ~wise(X0) | ~wise(X0) | brave(X0) [cnf transformation 45]
118. creative(X0) | creative(X0) | funny(X0) [cnf transformation 58]
120. ~creative(X0) | ~creative(X0) | wise(X0) [cnf transformation 58]
132. ~funny(fred) [cnf transformation 22]
133. funny(X0) | creative(X0) [duplicate literal removal 118]
134. ~creative(X0) | wise(X0) [duplicate literal removal 120]
136. ~wise(X0) | brave(X0) [duplicate literal removal 95]
137. ~brave(X0) | ~creative(X0) [duplicate literal removal 86]
148. 2 <=> wise(fred) [avatar definition]
150. wise(fred) <- (2) [avatar component clause 148]
254. creative(fred) [resolution 133,132]
255. wise(fred) [resolution 254,134]
256. brave(fred) <- (2) [resolution 136,150]
257. ~creative(fred) <- (2) [resolution 137,256]
258. $false <- (2) [subsumption resolution 257,254]
259. ~2 [avatar contradiction clause 258]
260. 2 [avatar split clause 255,148]
261. $false [avatar sat refutation 259,260]
% SZS output end Proof for 7268125871977347938610565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either not old or not calm. If john is quiet or not tall then someone is not curious or tall. Everyone who is either not creative or patient is not rich. If paul is not tall or not strong then alice is both not patient and happy and vice versa. If someone is calm then alice is both happy and not calm and vice versa. If alice is not calm or not patient then lucy is not old or not brave and vice versa. Everyone who is both not calm and patient is either tall or not creative. If someone is both not tall and not funny then someone is not strong or not funny and vice versa. Everyone who is brave is happy. Everyone who is calm or strong is both brave and creative and vice versa. Everyone who is both tall and curious is either strong or not strong and vice versa. Everyone who is strong is either tall or not brave and vice versa. Everyone who is not tall is not patient or not humble. Everyone who is not patient is not old or not generous. If susan is both calm and not humble then fred is either not strong or not calm and vice versa. If mary is either wise or not creative then someone is kind and vice versa. Fred is kind or not strong. Someone is either not calm or not happy. John is not old or not creative. Someone is either not funny or funny. Someone is creative. | Mary is not rich. | neutral | (![X]:(~curious(X)=>(~old(X)<~>~calm(X))))&
(((quiet(john)|~tall(john)))=>(?[X]:((~curious(X)|tall(X)))))&
(![X]:((~creative(X)<~>patient(X))=>~rich(X)))&
(((~tall(paul)|~strong(paul)))<=>((~patient(alice)&happy(alice))))&
((?[X]:(calm(X)))<=>((happy(alice)&~calm(alice))))&
(((~calm(alice)|~patient(alice)))<=>((~old(lucy)|~brave(lucy))))&
(![X]:((~calm(X)&patient(X))=>(tall(X)<~>~creative(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:((calm(X)|strong(X))<=>(brave(X)&creative(X))))&
(![X]:((tall(X)&curious(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(strong(X)<=>(tall(X)<~>~brave(X))))&
(![X]:(~tall(X)=>(~patient(X)|~humble(X))))&
(![X]:(~patient(X)=>(~old(X)|~generous(X))))&
(((calm(susan)&~humble(susan)))<=>((~strong(fred)<~>~calm(fred))))&
(((wise(mary)<~>~creative(mary)))<=>(?[X]:(kind(X))))&
((kind(fred)|~strong(fred)))&
(?[X]:((~calm(X)<~>~happy(X))))&
((~old(john)|~creative(john)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:(creative(X))) | ~rich(mary) | [] | null | 0 |
If mary is creative or not tall then john is either wise or strong and vice versa.
If lucy is both kind and not creative then alice is strong or not calm and vice versa.
Everyone who is not calm or calm is either not quiet or not strong.
Everyone who is not patient or funny is calm or old.
If john is not creative then susan is funny.
Everyone who is not calm or not brave is not patient or not kind and vice versa.
Everyone who is not tall is either not old or not rich.
If susan is either not calm or not quiet then someone is strong and vice versa.
If fred is either old or not old then paul is brave.
Everyone who is either funny or brave is both not patient and not brave and vice versa.
If paul is both not generous and rich then someone is either creative or not wise.
Everyone who is generous or old is both creative and not strong.
If mary is both not tall and rich then fred is both not happy and happy.
If john is tall then alice is not kind.
If someone is both not tall and kind then susan is either humble or not happy and vice versa.
Everyone who is strong or curious is not kind or not tall.
Paul is either wise or not curious.
Someone is humble or not creative.
Someone is strong or not humble.
John is both strong and not patient.
Someone is both creative and rich.
Someone is happy.
Someone is not brave or generous. | John is funny. | entailment | (((creative(mary)|~tall(mary)))<=>((wise(john)<~>strong(john))))&
(((kind(lucy)&~creative(lucy)))<=>((strong(alice)|~calm(alice))))&
(![X]:((~calm(X)|calm(X))=>(~quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)|funny(X))=>(calm(X)|old(X))))&
((~creative(john))=>(funny(susan)))&
(![X]:((~calm(X)|~brave(X))<=>(~patient(X)|~kind(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~rich(X))))&
(((~calm(susan)<~>~quiet(susan)))<=>(?[X]:(strong(X))))&
(((old(fred)<~>~old(fred)))=>(brave(paul)))&
(![X]:((funny(X)<~>brave(X))<=>(~patient(X)&~brave(X))))&
(((~generous(paul)&rich(paul)))=>(?[X]:((creative(X)<~>~wise(X)))))&
(![X]:((generous(X)|old(X))=>(creative(X)&~strong(X))))&
(((~tall(mary)&rich(mary)))=>((~happy(fred)&happy(fred))))&
((tall(john))=>(~kind(alice)))&
((?[X]:((~tall(X)&kind(X))))<=>((humble(susan)<~>~happy(susan))))&
(![X]:((strong(X)|curious(X))=>(~kind(X)|~tall(X))))&
((wise(paul)<~>~curious(paul)))&
(?[X]:((humble(X)|~creative(X))))&
(?[X]:((strong(X)|~humble(X))))&
((strong(john)&~patient(john)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)|generous(X)))) | funny(john) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2304025276163816646666261
% SZS output start Proof for 2304025276163816646666261
10. ! [X0] : ((funny(X0) <~> brave(X0)) <=> (~brave(X0) & ~patient(X0))) [input p9]
20. ~patient(john) & strong(john) [input p19]
24. ~funny(john) [input hypothesis]
52. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | (brave(X0) | patient(X0))) & ((~brave(X0) & ~patient(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~brave(X0) | ~funny(X0)) & (brave(X0) | funny(X0))) | brave(X0) | patient(X0)) & ((~brave(X0) & ~patient(X0)) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0))))) [flattening 52]
105. ~brave(X0) | funny(X0) | ~brave(X0) [cnf transformation 53]
106. brave(X0) | funny(X0) | brave(X0) | patient(X0) [cnf transformation 53]
130. ~patient(john) [cnf transformation 20]
135. ~funny(john) [cnf transformation 24]
136. ~brave(X0) | funny(X0) [duplicate literal removal 105]
137. brave(X0) | funny(X0) | patient(X0) [duplicate literal removal 106]
386. funny(X2) | patient(X2) | funny(X2) [resolution 137,136]
387. funny(X2) | patient(X2) [duplicate literal removal 386]
412. patient(john) [resolution 387,135]
415. $false [subsumption resolution 412,130]
% SZS output end Proof for 2304025276163816646666261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits