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 either tall or old is both creative and not wise.
Everyone who is either not brave or not quiet is wise.
If susan is not wise or not generous then someone is both not creative and not generous.
Everyone who is calm is funny or strong and vice versa.
If mary is both not kind and humble then paul is humble.
Everyone who is both patient and brave is either brave or patient and vice versa.
If alice is either not humble or happy then someone is both not brave and not creative and vice versa.
If john is either not old or not generous then someone is both calm and not humble.
Everyone who is quiet or not creative is not old or not tall.
If paul is not curious or creative then someone is not happy and vice versa.
Everyone who is both not humble and not kind is either creative or brave.
Everyone who is not curious or happy is not patient.
If lucy is curious then susan is generous and vice versa.
If susan is both not curious and humble then alice is generous or happy and vice versa.
If someone is both patient and not patient then paul is both not calm and not generous.
Everyone who is both strong and not patient is humble or not strong.
Someone is not wise.
Someone is either not brave or kind.
Mary is not generous or tall.
Susan is either tall or strong.
Alice is either not tall or not wise.
Paul is not generous.
John is not wise or strong. | Alice is not tall. | neutral | (![X]:((tall(X)<~>old(X))=>(creative(X)&~wise(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>wise(X)))&
(((~wise(susan)|~generous(susan)))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:(calm(X)<=>(funny(X)|strong(X))))&
(((~kind(mary)&humble(mary)))=>(humble(paul)))&
(![X]:((patient(X)&brave(X))<=>(brave(X)<~>patient(X))))&
(((~humble(alice)<~>happy(alice)))<=>(?[X]:((~brave(X)&~creative(X)))))&
(((~old(john)<~>~generous(john)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((quiet(X)|~creative(X))=>(~old(X)|~tall(X))))&
(((~curious(paul)|creative(paul)))<=>(?[X]:(~happy(X))))&
(![X]:((~humble(X)&~kind(X))=>(creative(X)<~>brave(X))))&
(![X]:((~curious(X)|happy(X))=>~patient(X)))&
((curious(lucy))<=>(generous(susan)))&
(((~curious(susan)&humble(susan)))<=>((generous(alice)|happy(alice))))&
((?[X]:((patient(X)&~patient(X))))=>((~calm(paul)&~generous(paul))))&
(![X]:((strong(X)&~patient(X))=>(humble(X)|~strong(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~generous(mary)|tall(mary)))&
((tall(susan)<~>strong(susan)))&
((~tall(alice)<~>~wise(alice)))&
(~generous(paul))&
((~wise(john)|strong(john))) | ~tall(alice) | [] | null | 0 |
Everyone who is both tall and not tall is not curious or not old.
Everyone who is either funny or not happy is patient.
If someone is humble then john is either old or curious.
Everyone who is kind is not rich.
Everyone who is not old or not kind is rich or not humble and vice versa.
Everyone who is patient is both creative and patient and vice versa.
If fred is not generous then someone is not kind.
Everyone who is not brave or curious is not humble or not generous.
If someone is not funny or wise then someone is either curious or rich and vice versa.
Everyone who is either happy or old is either humble or not creative and vice versa.
Everyone who is rich or not wise is either not old or not rich and vice versa.
Everyone who is patient or funny is not brave and vice versa.
If someone is either not wise or calm then someone is strong and vice versa.
If someone is either strong or not curious then alice is either not tall or wise.
If fred is quiet then john is either not old or wise and vice versa.
Everyone who is kind is happy.
Alice is both not quiet and not funny.
Lucy is not rich or not patient.
Someone is rich or not old.
Someone is both quiet and not kind.
Someone is not funny or humble.
Someone is either not kind or happy.
Someone is either not calm or not rich.
Someone is either not happy or rich. | John is creative. | neutral | (![X]:((tall(X)&~tall(X))=>(~curious(X)|~old(X))))&
(![X]:((funny(X)<~>~happy(X))=>patient(X)))&
((?[X]:(humble(X)))=>((old(john)<~>curious(john))))&
(![X]:(kind(X)=>~rich(X)))&
(![X]:((~old(X)|~kind(X))<=>(rich(X)|~humble(X))))&
(![X]:(patient(X)<=>(creative(X)&patient(X))))&
((~generous(fred))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|curious(X))=>(~humble(X)|~generous(X))))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:((happy(X)<~>old(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((rich(X)|~wise(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((patient(X)|funny(X))<=>~brave(X)))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:(strong(X))))&
((?[X]:((strong(X)<~>~curious(X))))=>((~tall(alice)<~>wise(alice))))&
((quiet(fred))<=>((~old(john)<~>wise(john))))&
(![X]:(kind(X)=>happy(X)))&
((~quiet(alice)&~funny(alice)))&
((~rich(lucy)|~patient(lucy)))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((quiet(X)&~kind(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~happy(X)<~>rich(X)))) | creative(john) | [] | null | 0 |
Everyone who is not funny is both calm and funny and vice versa.
If someone is either not patient or quiet then susan is curious and vice versa.
If fred is strong then susan is not curious or not humble and vice versa.
Everyone who is either not happy or curious is calm and vice versa.
Everyone who is not strong or not quiet is not brave or not kind.
Everyone who is both not rich and old is either patient or happy.
Everyone who is old or kind is not curious.
Everyone who is either humble or curious is not funny and vice versa.
Everyone who is both patient and not happy is tall or not calm.
Everyone who is not funny or not calm is either kind or generous.
Everyone who is patient is both kind and tall.
If lucy is either not generous or brave then someone is both curious and not curious and vice versa.
Everyone who is not patient is wise or not calm.
If someone is both generous and not brave then john is kind and vice versa.
If someone is tall or rich then someone is both happy and humble and vice versa.
If susan is both not generous and kind then paul is kind or not rich and vice versa.
Someone is not tall.
Paul is not wise.
Someone is not patient or not kind.
Alice is not brave.
Alice is generous.
Paul is either not tall or tall. | Lucy is not kind. | neutral | (![X]:(~funny(X)<=>(calm(X)&funny(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(curious(susan)))&
((strong(fred))<=>((~curious(susan)|~humble(susan))))&
(![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:((~strong(X)|~quiet(X))=>(~brave(X)|~kind(X))))&
(![X]:((~rich(X)&old(X))=>(patient(X)<~>happy(X))))&
(![X]:((old(X)|kind(X))=>~curious(X)))&
(![X]:((humble(X)<~>curious(X))<=>~funny(X)))&
(![X]:((patient(X)&~happy(X))=>(tall(X)|~calm(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)<~>generous(X))))&
(![X]:(patient(X)=>(kind(X)&tall(X))))&
(((~generous(lucy)<~>brave(lucy)))<=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:(~patient(X)=>(wise(X)|~calm(X))))&
((?[X]:((generous(X)&~brave(X))))<=>(kind(john)))&
((?[X]:((tall(X)|rich(X))))<=>(?[X]:((happy(X)&humble(X)))))&
(((~generous(susan)&kind(susan)))<=>((kind(paul)|~rich(paul))))&
(?[X]:(~tall(X)))&
(~wise(paul))&
(?[X]:((~patient(X)|~kind(X))))&
(~brave(alice))&
(generous(alice))&
((~tall(paul)<~>tall(paul))) | ~kind(lucy) | [] | null | 0 |
Everyone who is both not funny and creative is both calm and not tall and vice versa. If susan is either not curious or not old then someone is brave and vice versa. Everyone who is humble or curious is both not calm and strong and vice versa. If someone is either patient or not funny then susan is either rich or creative and vice versa. If fred is either creative or not calm then paul is both not wise and generous and vice versa. Everyone who is either not quiet or wise is either not strong or kind. Everyone who is not funny or brave is either generous or happy. Everyone who is not happy is either not wise or not generous. If someone is not generous or patient then susan is both not creative and not rich. Everyone who is funny is not happy or rich. Everyone who is strong or humble is not humble or not rich. If john is both rich and not quiet then someone is creative or not curious. Everyone who is either not patient or calm is not generous. Everyone who is both wise and funny is both not wise and not humble and vice versa. If fred is both kind and not humble then susan is funny and vice versa. If mary is both calm and rich then someone is not calm. Someone is either not old or strong. Someone is not tall. Someone is either not wise or not rich. Alice is not happy. Alice is humble or kind. Someone is both not funny and not curious. Susan is both not rich and brave. Mary is kind. | Alice is not humble. | contradiction | (![X]:((~funny(X)&creative(X))<=>(calm(X)&~tall(X))))&
(((~curious(susan)<~>~old(susan)))<=>(?[X]:(brave(X))))&
(![X]:((humble(X)|curious(X))<=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>~funny(X))))<=>((rich(susan)<~>creative(susan))))&
(((creative(fred)<~>~calm(fred)))<=>((~wise(paul)&generous(paul))))&
(![X]:((~quiet(X)<~>wise(X))=>(~strong(X)<~>kind(X))))&
(![X]:((~funny(X)|brave(X))=>(generous(X)<~>happy(X))))&
(![X]:(~happy(X)=>(~wise(X)<~>~generous(X))))&
((?[X]:((~generous(X)|patient(X))))=>((~creative(susan)&~rich(susan))))&
(![X]:(funny(X)=>(~happy(X)|rich(X))))&
(![X]:((strong(X)|humble(X))=>(~humble(X)|~rich(X))))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(((kind(fred)&~humble(fred)))<=>(funny(susan)))&
(((calm(mary)&rich(mary)))=>(?[X]:(~calm(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~happy(alice))&
((humble(alice)|kind(alice)))&
(?[X]:((~funny(X)&~curious(X))))&
((~rich(susan)&brave(susan)))&
(kind(mary)) | ~humble(alice) | [
"p6",
"p7",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4057836389430842671520380
% SZS output start Proof for 4057836389430842671520380
7. ! [X0] : ((brave(X0) | ~funny(X0)) => (generous(X0) <~> happy(X0))) [input p6]
8. ! [X0] : (~happy(X0) => (~wise(X0) <~> ~generous(X0))) [input p7]
14. ! [X0] : ((funny(X0) & wise(X0)) <=> (~humble(X0) & ~wise(X0))) [input p13]
20. ~happy(alice) [input p19]
25. ~humble(alice) [input hypothesis]
27. ! [X0] : ((generous(X0) <~> happy(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 7]
28. ! [X0] : ((~wise(X0) <~> ~generous(X0)) | happy(X0)) [ennf transformation 8]
54. ! [X0] : (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | (~brave(X0) & funny(X0))) [nnf transformation 27]
55. ! [X0] : (((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | happy(X0)) [nnf transformation 28]
59. ! [X0] : (((funny(X0) & wise(X0)) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | (~funny(X0) | ~wise(X0)))) [nnf transformation 14]
60. ! [X0] : (((funny(X0) & wise(X0)) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~funny(X0) | ~wise(X0))) [flattening 59]
106. happy(X0) | generous(X0) | funny(X0) [cnf transformation 54]
110. ~generous(X0) | ~wise(X0) | happy(X0) [cnf transformation 55]
122. ~wise(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 60]
124. wise(X0) | humble(X0) | wise(X0) [cnf transformation 60]
135. ~happy(alice) [cnf transformation 20]
142. ~humble(alice) [cnf transformation 25]
143. ~wise(X0) | ~funny(X0) [duplicate literal removal 122]
144. wise(X0) | humble(X0) [duplicate literal removal 124]
293. 31 <=> humble(alice) [avatar definition]
294. ~humble(alice) <- (~31) [avatar component clause 293]
302. ~31 [avatar split clause 142,293]
307. ~funny(X0) | humble(X0) [resolution 144,143]
311. generous(alice) | funny(alice) [resolution 106,135]
313. 33 <=> funny(alice) [avatar definition]
315. funny(alice) <- (33) [avatar component clause 313]
317. 34 <=> generous(alice) [avatar definition]
319. generous(alice) <- (34) [avatar component clause 317]
320. 33 | 34 [avatar split clause 311,317,313]
321. humble(alice) <- (33) [resolution 315,307]
322. $false <- (~31, 33) [subsumption resolution 321,294]
323. 31 | ~33 [avatar contradiction clause 322]
348. ~wise(alice) | happy(alice) <- (34) [resolution 110,319]
350. ~wise(alice) <- (34) [subsumption resolution 348,135]
377. humble(alice) <- (34) [resolution 350,144]
378. $false <- (~31, 34) [subsumption resolution 377,294]
379. 31 | ~34 [avatar contradiction clause 378]
380. $false [avatar sat refutation 302,320,323,379]
% SZS output end Proof for 4057836389430842671520380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or patient is tall or funny and vice versa.
Everyone who is either strong or tall is both not old and not funny and vice versa.
Everyone who is not strong or not creative is funny or not kind and vice versa.
If paul is either happy or not tall then someone is humble.
Everyone who is either not old or funny is not old and vice versa.
Everyone who is not generous is not generous or not patient and vice versa.
Everyone who is not curious or not calm is old.
If mary is either not wise or strong then lucy is not wise or tall.
Everyone who is both not strong and not funny is not tall.
If john is happy or kind then someone is both not creative and not curious.
If someone is kind then susan is either not happy or not calm.
If someone is both not funny and brave then someone is both patient and quiet.
If john is either not patient or brave then someone is not happy or generous and vice versa.
If john is not wise then alice is not generous or not curious.
Everyone who is not humble is either not funny or wise and vice versa.
If fred is not brave or brave then someone is both not curious and old.
Mary is either not curious or not rich.
Someone is not curious or not funny.
Someone is not rich or humble.
Someone is not tall or rich.
Someone is both strong and not old.
Someone is patient.
Paul is tall or brave.
John is not humble or brave. | Lucy is not strong. | contradiction | (![X]:((~kind(X)|patient(X))<=>(tall(X)|funny(X))))&
(![X]:((strong(X)<~>tall(X))<=>(~old(X)&~funny(X))))&
(![X]:((~strong(X)|~creative(X))<=>(funny(X)|~kind(X))))&
(((happy(paul)<~>~tall(paul)))=>(?[X]:(humble(X))))&
(![X]:((~old(X)<~>funny(X))<=>~old(X)))&
(![X]:(~generous(X)<=>(~generous(X)|~patient(X))))&
(![X]:((~curious(X)|~calm(X))=>old(X)))&
(((~wise(mary)<~>strong(mary)))=>((~wise(lucy)|tall(lucy))))&
(![X]:((~strong(X)&~funny(X))=>~tall(X)))&
(((happy(john)|kind(john)))=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:(kind(X)))=>((~happy(susan)<~>~calm(susan))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:((patient(X)&quiet(X)))))&
(((~patient(john)<~>brave(john)))<=>(?[X]:((~happy(X)|generous(X)))))&
((~wise(john))=>((~generous(alice)|~curious(alice))))&
(![X]:(~humble(X)<=>(~funny(X)<~>wise(X))))&
(((~brave(fred)|brave(fred)))=>(?[X]:((~curious(X)&old(X)))))&
((~curious(mary)<~>~rich(mary)))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((~rich(X)|humble(X))))&
(?[X]:((~tall(X)|rich(X))))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:(patient(X)))&
((tall(paul)|brave(paul)))&
((~humble(john)|brave(john))) | ~strong(lucy) | [
"p0",
"p2",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8916170469224334956587995
% SZS output start Proof for 8916170469224334956587995
1. ! [X0] : ((patient(X0) | ~kind(X0)) <=> (funny(X0) | tall(X0))) [input p0]
3. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (~kind(X0) | funny(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> funny(X0)) <=> ~old(X0)) [input p4]
9. ! [X0] : ((~funny(X0) & ~strong(X0)) => ~tall(X0)) [input p8]
25. ~strong(lucy) [input hypothesis]
32. ! [X0] : (~tall(X0) | (funny(X0) | strong(X0))) [ennf transformation 9]
33. ! [X0] : (~tall(X0) | funny(X0) | strong(X0)) [flattening 32]
40. ! [X0] : (((patient(X0) | ~kind(X0)) | (~funny(X0) & ~tall(X0))) & ((funny(X0) | tall(X0)) | (~patient(X0) & kind(X0)))) [nnf transformation 1]
41. ! [X0] : ((patient(X0) | ~kind(X0) | (~funny(X0) & ~tall(X0))) & (funny(X0) | tall(X0) | (~patient(X0) & kind(X0)))) [flattening 40]
44. ! [X0] : (((~creative(X0) | ~strong(X0)) | (kind(X0) & ~funny(X0))) & ((~kind(X0) | funny(X0)) | (creative(X0) & strong(X0)))) [nnf transformation 3]
45. ! [X0] : ((~creative(X0) | ~strong(X0) | (kind(X0) & ~funny(X0))) & (~kind(X0) | funny(X0) | (creative(X0) & strong(X0)))) [flattening 44]
49. ! [X0] : ((((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))))) [nnf transformation 5]
77. funny(X0) | tall(X0) | kind(X0) [cnf transformation 41]
87. ~kind(X0) | funny(X0) | strong(X0) [cnf transformation 45]
94. ~old(X0) | ~old(X0) | ~funny(X0) [cnf transformation 49]
96. ~funny(X0) | old(X0) | old(X0) [cnf transformation 49]
104. ~tall(X0) | funny(X0) | strong(X0) [cnf transformation 33]
137. ~strong(lucy) [cnf transformation 25]
138. ~old(X0) | ~funny(X0) [duplicate literal removal 94]
139. ~funny(X0) | old(X0) [duplicate literal removal 96]
154. ~funny(X0) [subsumption resolution 138,139]
173. ~tall(X0) | strong(X0) [subsumption resolution 104,154]
318. tall(X1) | kind(X1) [resolution 77,154]
364. strong(X1) | kind(X1) [resolution 318,173]
401. kind(lucy) [resolution 364,137]
413. funny(lucy) | strong(lucy) [resolution 401,87]
415. strong(lucy) [subsumption resolution 413,154]
416. $false [subsumption resolution 415,137]
% SZS output end Proof for 8916170469224334956587995
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is curious then someone is not curious and vice versa. Everyone who is curious is not wise or happy. Everyone who is either not quiet or rich is both rich and happy. Everyone who is either not curious or not calm is brave and vice versa. Everyone who is not rich is either curious or happy. Everyone who is not old or kind is both patient and old. If someone is not old then someone is not tall and vice versa. If alice is either calm or generous then someone is either not quiet or not brave. Everyone who is tall is funny and vice versa. If someone is not funny or not quiet then john is not wise or happy. If someone is not generous or strong then susan is not happy or not rich and vice versa. Everyone who is either not creative or creative is not quiet or not happy and vice versa. If fred is creative or not tall then john is patient or not rich. Everyone who is either generous or quiet is patient. If john is not brave then someone is not curious. Someone is not happy. Susan is both not strong and brave. Susan is rich or curious. Fred is rich or strong. Someone is either not tall or not patient. Susan is not quiet or brave. John is funny or not kind. Someone is both not brave and calm. | Fred is tall. | entailment | ((curious(alice))<=>(?[X]:(~curious(X))))&
(![X]:(curious(X)=>(~wise(X)|happy(X))))&
(![X]:((~quiet(X)<~>rich(X))=>(rich(X)&happy(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>brave(X)))&
(![X]:(~rich(X)=>(curious(X)<~>happy(X))))&
(![X]:((~old(X)|kind(X))=>(patient(X)&old(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~tall(X))))&
(((calm(alice)<~>generous(alice)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:(tall(X)<=>funny(X)))&
((?[X]:((~funny(X)|~quiet(X))))=>((~wise(john)|happy(john))))&
((?[X]:((~generous(X)|strong(X))))<=>((~happy(susan)|~rich(susan))))&
(![X]:((~creative(X)<~>creative(X))<=>(~quiet(X)|~happy(X))))&
(((creative(fred)|~tall(fred)))=>((patient(john)|~rich(john))))&
(![X]:((generous(X)<~>quiet(X))=>patient(X)))&
((~brave(john))=>(?[X]:(~curious(X))))&
(?[X]:(~happy(X)))&
((~strong(susan)&brave(susan)))&
((rich(susan)|curious(susan)))&
((rich(fred)|strong(fred)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~quiet(susan)|brave(susan)))&
((funny(john)|~kind(john)))&
(?[X]:((~brave(X)&calm(X)))) | tall(fred) | [
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2682599802275805341697259
% SZS output start Proof for 2682599802275805341697259
6. ! [X0] : ((kind(X0) | ~old(X0)) => (old(X0) & patient(X0))) [input p5]
7. ? [X0] : ~old(X0) <=> ? [X0] : ~tall(X0) [input p6]
24. ~tall(fred) [input hypothesis]
25. ? [X0] : ~old(X0) <=> ? [X1] : ~tall(X1) [rectify 7]
26. ! [X0] : (~old(X0) => (old(X0) & patient(X0))) [pure predicate removal 6]
32. ! [X0] : ((old(X0) & patient(X0)) | old(X0)) [ennf transformation 26]
45. (? [X0] : ~old(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : old(X0)) [nnf transformation 25]
46. (? [X0] : ~old(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : old(X3)) [rectify 45]
47. ? [X0] : ~old(X0) => ~old(sK1) [choice axiom]
48. ? [X2] : ~tall(X2) => ~tall(sK2) [choice axiom]
49. (~old(sK1) | ! [X1] : tall(X1)) & (~tall(sK2) | ! [X3] : old(X3)) [skolemisation 46,48,47]
84. old(X0) | old(X0) [cnf transformation 32]
86. ~old(sK1) | tall(X1) [cnf transformation 49]
118. ~tall(fred) [cnf transformation 24]
121. old(X0) [duplicate literal removal 84]
136. tall(X1) [subsumption resolution 86,121]
222. $false [subsumption resolution 118,136]
% SZS output end Proof for 2682599802275805341697259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is curious.
Everyone who is wise is either not brave or tall and vice versa.
If someone is both not creative and strong then someone is both wise and calm.
Everyone who is both not kind and kind is funny or not patient and vice versa.
Everyone who is either not curious or quiet is both old and creative.
If fred is not patient or not quiet then lucy is either not kind or not patient and vice versa.
Everyone who is not tall or not calm is wise and vice versa.
Everyone who is not quiet or calm is either humble or happy.
If fred is both brave and not old then someone is both curious and not rich.
Everyone who is not brave is not kind or kind and vice versa.
If someone is creative then susan is old and vice versa.
Everyone who is both not happy and kind is either not tall or quiet and vice versa.
Everyone who is not curious or generous is happy.
Everyone who is not happy or generous is quiet and vice versa.
If someone is either quiet or funny then someone is humble or not funny and vice versa.
Everyone who is generous or creative is kind or quiet.
Susan is not brave.
Someone is both quiet and curious.
Someone is either brave or not old.
Someone is both not happy and not calm.
Mary is not kind.
John is not generous.
Fred is either not tall or not curious. | Susan is old. | entailment | (![X]:(rich(X)=>curious(X)))&
(![X]:(wise(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:((~creative(X)&strong(X))))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((~kind(X)&kind(X))<=>(funny(X)|~patient(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(old(X)&creative(X))))&
(((~patient(fred)|~quiet(fred)))<=>((~kind(lucy)<~>~patient(lucy))))&
(![X]:((~tall(X)|~calm(X))<=>wise(X)))&
(![X]:((~quiet(X)|calm(X))=>(humble(X)<~>happy(X))))&
(((brave(fred)&~old(fred)))=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~brave(X)<=>(~kind(X)|kind(X))))&
((?[X]:(creative(X)))<=>(old(susan)))&
(![X]:((~happy(X)&kind(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:((~curious(X)|generous(X))=>happy(X)))&
(![X]:((~happy(X)|generous(X))<=>quiet(X)))&
((?[X]:((quiet(X)<~>funny(X))))<=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:((generous(X)|creative(X))=>(kind(X)|quiet(X))))&
(~brave(susan))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:((~happy(X)&~calm(X))))&
(~kind(mary))&
(~generous(john))&
((~tall(fred)<~>~curious(fred))) | old(susan) | [
"p4",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6129198837885455335668447
% SZS output start Proof for 6129198837885455335668447
5. ! [X0] : ((~curious(X0) <~> quiet(X0)) => (creative(X0) & old(X0))) [input p4]
11. ? [X0] : creative(X0) <=> old(susan) [input p10]
13. ! [X0] : ((generous(X0) | ~curious(X0)) => happy(X0)) [input p12]
14. ! [X0] : ((generous(X0) | ~happy(X0)) <=> quiet(X0)) [input p13]
20. ? [X0] : (~calm(X0) & ~happy(X0)) [input p19]
24. ~old(susan) [input hypothesis]
30. ! [X0] : ((creative(X0) & old(X0)) | (~curious(X0) <=> quiet(X0))) [ennf transformation 5]
34. ! [X0] : (happy(X0) | (~generous(X0) & curious(X0))) [ennf transformation 13]
40. ! [X0] : ((creative(X0) & old(X0)) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) [nnf transformation 30]
50. (? [X0] : creative(X0) | ~old(susan)) & (old(susan) | ! [X0] : ~creative(X0)) [nnf transformation 11]
51. (? [X0] : creative(X0) | ~old(susan)) & (old(susan) | ! [X1] : ~creative(X1)) [rectify 50]
52. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
53. (creative(sK1) | ~old(susan)) & (old(susan) | ! [X1] : ~creative(X1)) [skolemisation 51,52]
56. ! [X0] : (((generous(X0) | ~happy(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & happy(X0)))) [nnf transformation 14]
57. ! [X0] : ((generous(X0) | ~happy(X0) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & happy(X0)))) [flattening 56]
68. ? [X0] : (~calm(X0) & ~happy(X0)) => (~calm(sK6) & ~happy(sK6)) [choice axiom]
69. ~calm(sK6) & ~happy(sK6) [skolemisation 20,68]
83. ~quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 40]
101. old(susan) | ~creative(X1) [cnf transformation 53]
109. happy(X0) | curious(X0) [cnf transformation 34]
111. happy(X0) | quiet(X0) [cnf transformation 57]
127. ~happy(sK6) [cnf transformation 69]
133. ~old(susan) [cnf transformation 24]
164. 6 <=> old(susan) [avatar definition]
173. 8 <=> ! [X1] : ~creative(X1) [avatar definition]
174. ~creative(X1) <- (8) [avatar component clause 173]
175. 8 | 6 [avatar split clause 101,164,173]
189. ~6 [avatar split clause 133,164]
191. curious(sK6) [resolution 109,127]
192. quiet(sK6) [resolution 111,127]
249. ~curious(sK6) | creative(sK6) [resolution 83,192]
254. creative(sK6) [subsumption resolution 249,191]
255. $false <- (8) [subsumption resolution 254,174]
256. ~8 [avatar contradiction clause 255]
257. $false [avatar sat refutation 175,189,256]
% SZS output end Proof for 6129198837885455335668447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or calm is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Fred is strong. | entailment | (![X]:((strong(X)|calm(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | strong(fred) | [
"p0",
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3650257398277875198430511
% SZS output start Proof for 3650257398277875198430511
1. ! [X0] : ((calm(X0) | strong(X0)) <=> (~rich(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (funny(X0) | calm(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> old(X0)) => ~humble(X0)) [input p9]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
15. ! [X0] : (old(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
23. ~strong(fred) [input hypothesis]
31. ! [X0] : (~humble(X0) | (rich(X0) <=> old(X0))) [ennf transformation 10]
35. ! [X0] : (((calm(X0) | strong(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((calm(X0) | strong(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 35]
37. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 2]
38. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 37]
56. ! [X0] : (~humble(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 31]
58. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
59. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 58]
60. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~old(X0))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~old(X0))) [flattening 60]
77. ~rich(X0) | ~strong(X0) [cnf transformation 36]
83. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 38]
110. ~humble(X0) | rich(X0) | ~old(X0) [cnf transformation 56]
116. humble(X0) | strong(X0) [cnf transformation 59]
117. funny(X0) | strong(X0) [cnf transformation 59]
122. old(X0) | strong(X0) [cnf transformation 61]
139. ~strong(fred) [cnf transformation 23]
263. ~old(X0) | ~rich(X0) | strong(X0) [resolution 83,117]
264. ~rich(X0) | strong(X0) [subsumption resolution 263,122]
265. ~rich(X0) [subsumption resolution 264,77]
275. rich(X0) | ~old(X0) | strong(X0) [resolution 110,116]
278. ~old(X0) | strong(X0) [subsumption resolution 275,265]
279. strong(X0) [subsumption resolution 278,122]
286. $false [resolution 279,139]
% SZS output end Proof for 3650257398277875198430511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is both happy and not patient.
If fred is curious or brave then someone is both quiet and rich.
Everyone who is strong or not patient is both not rich and not funny and vice versa.
If someone is either not wise or curious then someone is calm.
Everyone who is both not generous and tall is either not humble or funny.
If someone is happy or funny then mary is both strong and generous.
If someone is either brave or calm then someone is both wise and not creative and vice versa.
Everyone who is both tall and not funny is both not happy and generous and vice versa.
If someone is either quiet or creative then someone is patient or not calm and vice versa.
Everyone who is patient is both not wise and not calm and vice versa.
If someone is either not creative or not kind then someone is either happy or not kind.
Everyone who is not calm or not generous is either not generous or not tall and vice versa.
If someone is either not kind or wise then someone is both patient and brave.
Everyone who is either not wise or curious is not humble.
Everyone who is kind is quiet or kind and vice versa.
Lucy is both not humble and curious.
Someone is either patient or not quiet.
Lucy is both not happy and curious.
Someone is humble.
Someone is strong.
Paul is patient or not happy.
Alice is not patient. | Alice is kind. | neutral | ((?[X]:(patient(X)))=>(?[X]:((happy(X)&~patient(X)))))&
(((curious(fred)|brave(fred)))=>(?[X]:((quiet(X)&rich(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:(calm(X))))&
(![X]:((~generous(X)&tall(X))=>(~humble(X)<~>funny(X))))&
((?[X]:((happy(X)|funny(X))))=>((strong(mary)&generous(mary))))&
((?[X]:((brave(X)<~>calm(X))))<=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:((tall(X)&~funny(X))<=>(~happy(X)&generous(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:(patient(X)<=>(~wise(X)&~calm(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~calm(X)|~generous(X))<=>(~generous(X)<~>~tall(X))))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((patient(X)&brave(X)))))&
(![X]:((~wise(X)<~>curious(X))=>~humble(X)))&
(![X]:(kind(X)<=>(quiet(X)|kind(X))))&
((~humble(lucy)&curious(lucy)))&
(?[X]:((patient(X)<~>~quiet(X))))&
((~happy(lucy)&curious(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(strong(X)))&
((patient(paul)|~happy(paul)))&
(~patient(alice)) | kind(alice) | [] | null | 0 |
Everyone who is quiet or not strong is humble or not generous.
Everyone who is not curious is either kind or not calm and vice versa.
If someone is rich then someone is either tall or rich and vice versa.
If someone is either old or not brave then john is not strong or wise and vice versa.
Everyone who is funny or not creative is patient or not tall.
If someone is old or quiet then fred is not creative or strong and vice versa.
Everyone who is both not calm and wise is wise.
Everyone who is either not generous or calm is both calm and not funny and vice versa.
If someone is rich or not tall then someone is either not tall or not curious and vice versa.
Everyone who is not kind is not brave.
Everyone who is either not rich or not patient is either rich or brave and vice versa.
If someone is not old then someone is curious.
Everyone who is quiet is not brave and vice versa.
If lucy is both not generous and not patient then lucy is brave or not quiet.
Everyone who is both wise and humble is patient.
Everyone who is humble or calm is both not quiet and not calm.
Someone is either calm or strong.
Lucy is humble or not funny.
John is either not patient or funny.
Susan is not wise.
Someone is either kind or quiet.
Someone is either quiet or patient.
Lucy is either not strong or creative. | Lucy is not calm. | entailment | (![X]:((quiet(X)|~strong(X))=>(humble(X)|~generous(X))))&
(![X]:(~curious(X)<=>(kind(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((tall(X)<~>rich(X)))))&
((?[X]:((old(X)<~>~brave(X))))<=>((~strong(john)|wise(john))))&
(![X]:((funny(X)|~creative(X))=>(patient(X)|~tall(X))))&
((?[X]:((old(X)|quiet(X))))<=>((~creative(fred)|strong(fred))))&
(![X]:((~calm(X)&wise(X))=>wise(X)))&
(![X]:((~generous(X)<~>calm(X))<=>(calm(X)&~funny(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
(![X]:(~kind(X)=>~brave(X)))&
(![X]:((~rich(X)<~>~patient(X))<=>(rich(X)<~>brave(X))))&
((?[X]:(~old(X)))=>(?[X]:(curious(X))))&
(![X]:(quiet(X)<=>~brave(X)))&
(((~generous(lucy)&~patient(lucy)))=>((brave(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&humble(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(~quiet(X)&~calm(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((humble(lucy)|~funny(lucy)))&
((~patient(john)<~>funny(john)))&
(~wise(susan))&
(?[X]:((kind(X)<~>quiet(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
((~strong(lucy)<~>creative(lucy))) | ~calm(lucy) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8009746750030387256366918
% SZS output start Proof for 8009746750030387256366918
16. ! [X0] : ((calm(X0) | humble(X0)) => (~calm(X0) & ~quiet(X0))) [input p15]
24. calm(lucy) [input hypothesis]
40. ! [X0] : ((~calm(X0) & ~quiet(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 16]
132. ~calm(X0) | ~calm(X0) [cnf transformation 40]
145. calm(lucy) [cnf transformation 24]
146. ~calm(X0) [duplicate literal removal 132]
337. $false [subsumption resolution 145,146]
% SZS output end Proof for 8009746750030387256366918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is humble or not strong and vice versa.
Everyone who is either tall or humble is funny or tall.
If john is not wise or patient then someone is not tall.
If mary is either not patient or old then someone is either old or not quiet and vice versa.
Everyone who is strong is either humble or wise.
If paul is either not wise or wise then mary is calm and vice versa.
If someone is either wise or not quiet then lucy is either not humble or brave and vice versa.
If susan is generous then someone is both brave and rich and vice versa.
If lucy is not funny then someone is both not calm and generous and vice versa.
Everyone who is either not strong or not creative is either not humble or not tall.
Everyone who is tall is both not brave and not old and vice versa.
Everyone who is not old or not strong is either not generous or brave and vice versa.
If mary is old then someone is strong or not old.
Everyone who is both creative and curious is both calm and quiet and vice versa.
Everyone who is patient is quiet and vice versa.
Everyone who is tall or rich is either not funny or humble.
Mary is humble.
Someone is wise or happy.
Someone is not patient or calm.
Paul is both patient and not strong.
Someone is generous or not quiet.
Mary is both humble and happy.
Someone is both not brave and not curious.
Susan is not strong. | Paul is not wise. | neutral | (![X]:(calm(X)<=>(humble(X)|~strong(X))))&
(![X]:((tall(X)<~>humble(X))=>(funny(X)|tall(X))))&
(((~wise(john)|patient(john)))=>(?[X]:(~tall(X))))&
(((~patient(mary)<~>old(mary)))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:(strong(X)=>(humble(X)<~>wise(X))))&
(((~wise(paul)<~>wise(paul)))<=>(calm(mary)))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((~humble(lucy)<~>brave(lucy))))&
((generous(susan))<=>(?[X]:((brave(X)&rich(X)))))&
((~funny(lucy))<=>(?[X]:((~calm(X)&generous(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(~humble(X)<~>~tall(X))))&
(![X]:(tall(X)<=>(~brave(X)&~old(X))))&
(![X]:((~old(X)|~strong(X))<=>(~generous(X)<~>brave(X))))&
((old(mary))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((creative(X)&curious(X))<=>(calm(X)&quiet(X))))&
(![X]:(patient(X)<=>quiet(X)))&
(![X]:((tall(X)|rich(X))=>(~funny(X)<~>humble(X))))&
(humble(mary))&
(?[X]:((wise(X)|happy(X))))&
(?[X]:((~patient(X)|calm(X))))&
((patient(paul)&~strong(paul)))&
(?[X]:((generous(X)|~quiet(X))))&
((humble(mary)&happy(mary)))&
(?[X]:((~brave(X)&~curious(X))))&
(~strong(susan)) | ~wise(paul) | [] | null | 0 |
If someone is not rich then paul is either generous or calm and vice versa.
Everyone who is both old and wise is not happy or funny.
If susan is both not generous and not calm then john is not brave and vice versa.
Everyone who is not humble is either rich or not happy and vice versa.
Everyone who is either brave or not tall is both not kind and patient and vice versa.
If susan is either not generous or strong then mary is either not quiet or not kind and vice versa.
If mary is calm or not patient then someone is old or creative and vice versa.
Everyone who is not strong is both not tall and not old and vice versa.
Everyone who is both kind and funny is not strong and vice versa.
If someone is humble or patient then someone is not kind or humble.
Everyone who is both not brave and not patient is not quiet or not kind.
Everyone who is not patient is not generous or creative.
Everyone who is either tall or generous is either not strong or not rich and vice versa.
Everyone who is brave or not patient is either kind or not curious and vice versa.
Everyone who is either calm or quiet is old or not kind and vice versa.
If paul is not creative then susan is either strong or old.
Alice is either not quiet or not wise.
John is both not humble and brave.
Someone is both not kind and curious.
John is not humble or old.
John is either not old or not humble.
Someone is wise or tall.
Someone is either not tall or not quiet.
Lucy is both kind and happy. | John is brave. | entailment | ((?[X]:(~rich(X)))<=>((generous(paul)<~>calm(paul))))&
(![X]:((old(X)&wise(X))=>(~happy(X)|funny(X))))&
(((~generous(susan)&~calm(susan)))<=>(~brave(john)))&
(![X]:(~humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~kind(X)&patient(X))))&
(((~generous(susan)<~>strong(susan)))<=>((~quiet(mary)<~>~kind(mary))))&
(((calm(mary)|~patient(mary)))<=>(?[X]:((old(X)|creative(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~old(X))))&
(![X]:((kind(X)&funny(X))<=>~strong(X)))&
((?[X]:((humble(X)|patient(X))))=>(?[X]:((~kind(X)|humble(X)))))&
(![X]:((~brave(X)&~patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:(~patient(X)=>(~generous(X)|creative(X))))&
(![X]:((tall(X)<~>generous(X))<=>(~strong(X)<~>~rich(X))))&
(![X]:((brave(X)|~patient(X))<=>(kind(X)<~>~curious(X))))&
(![X]:((calm(X)<~>quiet(X))<=>(old(X)|~kind(X))))&
((~creative(paul))=>((strong(susan)<~>old(susan))))&
((~quiet(alice)<~>~wise(alice)))&
((~humble(john)&brave(john)))&
(?[X]:((~kind(X)&curious(X))))&
((~humble(john)|old(john)))&
((~old(john)<~>~humble(john)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
((kind(lucy)&happy(lucy))) | brave(john) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6041290928180096505702394
% SZS output start Proof for 6041290928180096505702394
18. brave(john) & ~humble(john) [input p17]
25. ~brave(john) [input hypothesis]
137. brave(john) [cnf transformation 18]
148. ~brave(john) [cnf transformation 25]
169. 5 <=> brave(john) [avatar definition]
271. 5 [avatar split clause 137,169]
292. ~5 [avatar split clause 148,169]
293. $false [avatar sat refutation 271,292]
% SZS output end Proof for 6041290928180096505702394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both happy and quiet is calm and vice versa.
Everyone who is kind is kind or not creative and vice versa.
Everyone who is both not funny and not tall is humble or not patient.
If lucy is not tall or not patient then someone is not happy or humble.
Everyone who is both not funny and humble is both not happy and strong.
Everyone who is not calm or not kind is humble or wise.
Everyone who is generous is kind or not strong and vice versa.
If paul is not happy then someone is funny or curious and vice versa.
Everyone who is calm or tall is either not generous or not tall.
Everyone who is not quiet or humble is not rich and vice versa.
Everyone who is not generous is either wise or creative and vice versa.
If someone is either not generous or patient then fred is not creative or generous.
If paul is both not rich and patient then someone is either generous or creative and vice versa.
Everyone who is not creative is either generous or not calm.
If someone is either funny or not happy then someone is humble.
If someone is either not rich or not old then susan is either rich or not rich and vice versa.
Someone is strong or not patient.
Paul is not humble.
Alice is either not tall or humble.
Someone is not curious or not patient.
Lucy is rich.
Paul is both curious and rich.
Lucy is old or not calm.
Someone is strong or generous. | Lucy is not tall. | entailment | (![X]:((happy(X)&quiet(X))<=>calm(X)))&
(![X]:(kind(X)<=>(kind(X)|~creative(X))))&
(![X]:((~funny(X)&~tall(X))=>(humble(X)|~patient(X))))&
(((~tall(lucy)|~patient(lucy)))=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((~funny(X)&humble(X))=>(~happy(X)&strong(X))))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)|wise(X))))&
(![X]:(generous(X)<=>(kind(X)|~strong(X))))&
((~happy(paul))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((calm(X)|tall(X))=>(~generous(X)<~>~tall(X))))&
(![X]:((~quiet(X)|humble(X))<=>~rich(X)))&
(![X]:(~generous(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>((~creative(fred)|generous(fred))))&
(((~rich(paul)&patient(paul)))<=>(?[X]:((generous(X)<~>creative(X)))))&
(![X]:(~creative(X)=>(generous(X)<~>~calm(X))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((rich(susan)<~>~rich(susan))))&
(?[X]:((strong(X)|~patient(X))))&
(~humble(paul))&
((~tall(alice)<~>humble(alice)))&
(?[X]:((~curious(X)|~patient(X))))&
(rich(lucy))&
((curious(paul)&rich(paul)))&
((old(lucy)|~calm(lucy)))&
(?[X]:((strong(X)|generous(X)))) | ~tall(lucy) | [
"p1",
"p6",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 854597196551717293860713
% SZS output start Proof for 854597196551717293860713
2. ! [X0] : (kind(X0) <=> (~creative(X0) | kind(X0))) [input p1]
7. ! [X0] : (generous(X0) <=> (~strong(X0) | kind(X0))) [input p6]
9. ! [X0] : ((tall(X0) | calm(X0)) => (~generous(X0) <~> ~tall(X0))) [input p8]
13. (patient(paul) & ~rich(paul)) <=> ? [X0] : (generous(X0) <~> creative(X0)) [input p12]
22. rich(paul) & curious(paul) [input p21]
25. tall(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) <~> ~tall(X0)) | (~tall(X0) & ~calm(X0))) [ennf transformation 9]
41. ! [X0] : ((kind(X0) | (creative(X0) & ~kind(X0))) & ((~creative(X0) | kind(X0)) | ~kind(X0))) [nnf transformation 2]
42. ! [X0] : ((kind(X0) | (creative(X0) & ~kind(X0))) & (~creative(X0) | kind(X0) | ~kind(X0))) [flattening 41]
45. ! [X0] : ((generous(X0) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | ~generous(X0))) [nnf transformation 7]
46. ! [X0] : ((generous(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | ~generous(X0))) [flattening 45]
51. ! [X0] : (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~tall(X0) & ~calm(X0))) [nnf transformation 34]
56. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X0] : ((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | (~patient(paul) | rich(paul))) [nnf transformation 13]
57. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X0] : ((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | ~patient(paul) | rich(paul)) [flattening 56]
58. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) | ~patient(paul) | rich(paul)) [rectify 57]
59. ? [X1] : ((~creative(X1) | ~generous(X1)) & (creative(X1) | generous(X1))) => ((~creative(sK2) | ~generous(sK2)) & (creative(sK2) | generous(sK2))) [choice axiom]
60. ((patient(paul) & ~rich(paul)) | ! [X0] : ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(sK2) | ~generous(sK2)) & (creative(sK2) | generous(sK2))) | ~patient(paul) | rich(paul)) [skolemisation 58,59]
82. creative(X0) | kind(X0) [cnf transformation 42]
91. ~kind(X0) | generous(X0) [cnf transformation 46]
97. ~tall(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 51]
112. ~rich(paul) | generous(X0) | ~creative(X0) [cnf transformation 60]
134. rich(paul) [cnf transformation 22]
137. tall(lucy) [cnf transformation 25]
142. ~generous(X0) | ~tall(X0) [duplicate literal removal 97]
157. 4 <=> tall(lucy) [avatar definition]
159. tall(lucy) <- (4) [avatar component clause 157]
199. 14 <=> ! [X0] : (generous(X0) | ~creative(X0)) [avatar definition]
200. ~creative(X0) | generous(X0) <- (14) [avatar component clause 199]
211. 17 <=> rich(paul) [avatar definition]
214. 14 | ~17 [avatar split clause 112,211,199]
282. 17 [avatar split clause 134,211]
292. 4 [avatar split clause 137,157]
306. generous(X0) | kind(X0) <- (14) [resolution 200,82]
308. generous(X0) <- (14) [subsumption resolution 306,91]
313. ~tall(X2) <- (14) [resolution 308,142]
344. $false <- (4, 14) [resolution 313,159]
345. ~4 | ~14 [avatar contradiction clause 344]
346. $false [avatar sat refutation 214,282,292,345]
% SZS output end Proof for 854597196551717293860713
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If susan is brave or not humble then fred is either curious or tall and vice versa. Everyone who is not kind is quiet and vice versa. If paul is happy then john is either not funny or not happy and vice versa. Everyone who is either not brave or patient is both funny and strong and vice versa. If someone is both kind and humble then someone is both calm and curious. Everyone who is not brave is creative or kind. Everyone who is both not calm and kind is creative or not generous. If paul is not patient then john is happy. Everyone who is creative or happy is not funny or not strong and vice versa. If mary is both wise and not happy then someone is happy or calm and vice versa. Everyone who is either patient or strong is tall. If someone is both funny and not curious then lucy is not patient and vice versa. Everyone who is creative or calm is tall and vice versa. If mary is not quiet then mary is either happy or curious. If someone is either old or generous then someone is either not kind or not humble and vice versa. Everyone who is both calm and not brave is not curious or rich and vice versa. Susan is humble. Someone is humble or not kind. Someone is either kind or rich. Alice is not rich. Someone is brave. Someone is both happy and funny. Lucy is both wise and brave. Paul is both calm and quiet. | Mary is happy. | contradiction | (((brave(susan)|~humble(susan)))<=>((curious(fred)<~>tall(fred))))&
(![X]:(~kind(X)<=>quiet(X)))&
((happy(paul))<=>((~funny(john)<~>~happy(john))))&
(![X]:((~brave(X)<~>patient(X))<=>(funny(X)&strong(X))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:((calm(X)&curious(X)))))&
(![X]:(~brave(X)=>(creative(X)|kind(X))))&
(![X]:((~calm(X)&kind(X))=>(creative(X)|~generous(X))))&
((~patient(paul))=>(happy(john)))&
(![X]:((creative(X)|happy(X))<=>(~funny(X)|~strong(X))))&
(((wise(mary)&~happy(mary)))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((patient(X)<~>strong(X))=>tall(X)))&
((?[X]:((funny(X)&~curious(X))))<=>(~patient(lucy)))&
(![X]:((creative(X)|calm(X))<=>tall(X)))&
((~quiet(mary))=>((happy(mary)<~>curious(mary))))&
((?[X]:((old(X)<~>generous(X))))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
(![X]:((calm(X)&~brave(X))<=>(~curious(X)|rich(X))))&
(humble(susan))&
(?[X]:((humble(X)|~kind(X))))&
(?[X]:((kind(X)<~>rich(X))))&
(~rich(alice))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)&funny(X))))&
((wise(lucy)&brave(lucy)))&
((calm(paul)&quiet(paul))) | happy(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4820547613102919351770238
% SZS output start Proof for 4820547613102919351770238
10. (~happy(mary) & wise(mary)) <=> ? [X0] : (calm(X0) | happy(X0)) [input p9]
25. happy(mary) [input hypothesis]
47. ((~happy(mary) & wise(mary)) | ! [X0] : (~calm(X0) & ~happy(X0))) & (? [X0] : (calm(X0) | happy(X0)) | (happy(mary) | ~wise(mary))) [nnf transformation 10]
48. ((~happy(mary) & wise(mary)) | ! [X0] : (~calm(X0) & ~happy(X0))) & (? [X0] : (calm(X0) | happy(X0)) | happy(mary) | ~wise(mary)) [flattening 47]
49. ((~happy(mary) & wise(mary)) | ! [X0] : (~calm(X0) & ~happy(X0))) & (? [X1] : (calm(X1) | happy(X1)) | happy(mary) | ~wise(mary)) [rectify 48]
50. ? [X1] : (calm(X1) | happy(X1)) => (calm(sK1) | happy(sK1)) [choice axiom]
51. ((~happy(mary) & wise(mary)) | ! [X0] : (~calm(X0) & ~happy(X0))) & ((calm(sK1) | happy(sK1)) | happy(mary) | ~wise(mary)) [skolemisation 49,50]
106. ~happy(mary) | ~happy(X0) [cnf transformation 51]
143. happy(mary) [cnf transformation 25]
204. 13 <=> happy(mary) [avatar definition]
205. happy(mary) <- (13) [avatar component clause 204]
209. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
210. ~happy(X0) <- (14) [avatar component clause 209]
211. 14 | ~13 [avatar split clause 106,204,209]
311. 13 [avatar split clause 143,204]
312. $false <- (13, 14) [subsumption resolution 205,210]
313. ~13 | ~14 [avatar contradiction clause 312]
316. $false [avatar sat refutation 211,311,313]
% SZS output end Proof for 4820547613102919351770238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not curious is both brave and generous and vice versa. Everyone who is not creative or wise is either tall or brave and vice versa. Everyone who is not rich or happy is either happy or calm. If fred is both not patient and happy then fred is generous and vice versa. Everyone who is not happy or calm is both funny and not brave and vice versa. If lucy is humble then john is kind. Everyone who is either not brave or not happy is patient and vice versa. If someone is both calm and strong then someone is either not generous or not curious and vice versa. Everyone who is not wise or not rich is quiet or calm. If susan is not happy or tall then someone is either calm or not calm. Everyone who is not creative or not patient is not generous and vice versa. Everyone who is both not quiet and not rich is not brave. Everyone who is either creative or not curious is not rich and vice versa. Everyone who is both humble and old is either not kind or tall. If lucy is either not funny or not old then someone is either not strong or strong. If susan is both calm and not calm then fred is both not creative and rich and vice versa. Someone is either not old or brave. Someone is creative or not tall. Paul is both not humble and brave. Mary is not strong or not curious. Paul is not brave or old. Fred is not patient or old. Someone is either funny or curious. | Lucy is not rich. | neutral | (![X]:((kind(X)|~curious(X))<=>(brave(X)&generous(X))))&
(![X]:((~creative(X)|wise(X))<=>(tall(X)<~>brave(X))))&
(![X]:((~rich(X)|happy(X))=>(happy(X)<~>calm(X))))&
(((~patient(fred)&happy(fred)))<=>(generous(fred)))&
(![X]:((~happy(X)|calm(X))<=>(funny(X)&~brave(X))))&
((humble(lucy))=>(kind(john)))&
(![X]:((~brave(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((calm(X)&strong(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((~wise(X)|~rich(X))=>(quiet(X)|calm(X))))&
(((~happy(susan)|tall(susan)))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~creative(X)|~patient(X))<=>~generous(X)))&
(![X]:((~quiet(X)&~rich(X))=>~brave(X)))&
(![X]:((creative(X)<~>~curious(X))<=>~rich(X)))&
(![X]:((humble(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~funny(lucy)<~>~old(lucy)))=>(?[X]:((~strong(X)<~>strong(X)))))&
(((calm(susan)&~calm(susan)))<=>((~creative(fred)&rich(fred))))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((creative(X)|~tall(X))))&
((~humble(paul)&brave(paul)))&
((~strong(mary)|~curious(mary)))&
((~brave(paul)|old(paul)))&
((~patient(fred)|old(fred)))&
(?[X]:((funny(X)<~>curious(X)))) | ~rich(lucy) | [] | null | 0 |
If mary is both not wise and not brave then someone is not creative and vice versa.
Everyone who is not quiet or not brave is either not old or not kind.
Everyone who is not curious or brave is both curious and not strong and vice versa.
If someone is either not creative or generous then someone is either rich or strong.
If someone is either curious or calm then someone is not tall and vice versa.
Everyone who is both generous and curious is quiet and vice versa.
If mary is either not curious or not strong then someone is not creative and vice versa.
Everyone who is humble is both calm and not humble and vice versa.
If john is not kind or not rich then lucy is either tall or not creative.
If john is calm then someone is calm or kind and vice versa.
If john is both calm and happy then susan is both not tall and rich and vice versa.
Everyone who is either creative or not patient is both brave and not wise.
Everyone who is not brave is not quiet or not tall and vice versa.
Everyone who is either not happy or old is not old or brave and vice versa.
If alice is kind then someone is not kind.
Mary is not generous.
Someone is either wise or quiet.
Someone is not curious or not generous.
Alice is wise or old.
Someone is either creative or not old.
John is not humble or rich. | Mary is quiet. | contradiction | (((~wise(mary)&~brave(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)|~brave(X))=>(~old(X)<~>~kind(X))))&
(![X]:((~curious(X)|brave(X))<=>(curious(X)&~strong(X))))&
((?[X]:((~creative(X)<~>generous(X))))=>(?[X]:((rich(X)<~>strong(X)))))&
((?[X]:((curious(X)<~>calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((generous(X)&curious(X))<=>quiet(X)))&
(((~curious(mary)<~>~strong(mary)))<=>(?[X]:(~creative(X))))&
(![X]:(humble(X)<=>(calm(X)&~humble(X))))&
(((~kind(john)|~rich(john)))=>((tall(lucy)<~>~creative(lucy))))&
((calm(john))<=>(?[X]:((calm(X)|kind(X)))))&
(((calm(john)&happy(john)))<=>((~tall(susan)&rich(susan))))&
(![X]:((creative(X)<~>~patient(X))=>(brave(X)&~wise(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|~tall(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~old(X)|brave(X))))&
((kind(alice))=>(?[X]:(~kind(X))))&
(~generous(mary))&
(?[X]:((wise(X)<~>quiet(X))))&
(?[X]:((~curious(X)|~generous(X))))&
((wise(alice)|old(alice)))&
(?[X]:((creative(X)<~>~old(X))))&
((~humble(john)|rich(john))) | quiet(mary) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 14002152813577646173482
% SZS output start Proof for 14002152813577646173482
6. ! [X0] : ((curious(X0) & generous(X0)) <=> quiet(X0)) [input p5]
16. ~generous(mary) [input p15]
22. quiet(mary) [input hypothesis]
47. ! [X0] : (((curious(X0) & generous(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((curious(X0) & generous(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | ~generous(X0))) [flattening 47]
98. ~quiet(X0) | generous(X0) [cnf transformation 48]
132. ~generous(mary) [cnf transformation 16]
140. quiet(mary) [cnf transformation 22]
311. generous(mary) [resolution 98,140]
312. $false [subsumption resolution 311,132]
% SZS output end Proof for 14002152813577646173482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and creative is not kind. If fred is funny or old then someone is both happy and kind and vice versa. Everyone who is not quiet or wise is either not curious or not tall and vice versa. Everyone who is not quiet or not patient is not patient or generous. Everyone who is happy or not patient is curious and vice versa. Everyone who is creative is both strong and generous. Everyone who is not creative or funny is kind or not funny. Everyone who is either not quiet or old is not quiet or creative and vice versa. If someone is either kind or not brave then someone is both happy and not rich and vice versa. Everyone who is either not funny or rich is either not creative or humble and vice versa. If someone is either not humble or generous then someone is both not brave and calm and vice versa. Everyone who is either not funny or funny is not creative or strong and vice versa. Everyone who is both calm and funny is both kind and not kind. Everyone who is either not old or not kind is both not patient and not wise. Everyone who is both patient and funny is not creative or not kind and vice versa. If someone is both creative and happy then someone is either not kind or old. Lucy is not funny or not tall. Susan is either not funny or not tall. Someone is either not kind or not tall. Paul is both funny and humble. Someone is not patient. Someone is either happy or not curious. Lucy is curious. | Lucy is not wise. | contradiction | (![X]:((~wise(X)&creative(X))=>~kind(X)))&
(((funny(fred)|old(fred)))<=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~patient(X)|generous(X))))&
(![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
((~funny(lucy)|~tall(lucy)))&
((~funny(susan)<~>~tall(susan)))&
(?[X]:((~kind(X)<~>~tall(X))))&
((funny(paul)&humble(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(curious(lucy)) | ~wise(lucy) | [
"p0",
"p6",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6864764545334292691523747
% SZS output start Proof for 6864764545334292691523747
1. ! [X0] : ((creative(X0) & ~wise(X0)) => ~kind(X0)) [input p0]
7. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p14]
24. ~wise(lucy) [input hypothesis]
28. ! [X0] : (~kind(X0) | (~creative(X0) | wise(X0))) [ennf transformation 1]
29. ! [X0] : (~kind(X0) | ~creative(X0) | wise(X0)) [flattening 28]
33. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 7]
34. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 33]
37. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 14]
48. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 8]
49. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 48]
63. ! [X0] : ((~wise(X0) & ~patient(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 37]
64. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 15]
65. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 64]
79. ~kind(X0) | ~creative(X0) | wise(X0) [cnf transformation 29]
99. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 34]
101. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 49]
104. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 49]
134. ~patient(X0) | ~kind(X0) | old(X0) [cnf transformation 63]
139. patient(X0) | creative(X0) [cnf transformation 65]
142. funny(X0) | kind(X0) [cnf transformation 65]
156. ~wise(lucy) [cnf transformation 24]
159. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 101]
160. ~old(X0) | quiet(X0) [duplicate literal removal 104]
161. ~funny(X0) | kind(X0) [duplicate literal removal 99]
186. ~old(X0) | creative(X0) [subsumption resolution 159,160]
250. kind(X0) [subsumption resolution 142,161]
310. ~creative(X0) | wise(X0) [resolution 79,250]
354. ~kind(X0) | old(X0) | creative(X0) [resolution 134,139]
356. old(X0) | creative(X0) [subsumption resolution 354,250]
357. creative(X0) [subsumption resolution 356,186]
396. wise(X0) [resolution 310,357]
406. $false [resolution 396,156]
% SZS output end Proof for 6864764545334292691523747
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not calm then susan is either not curious or strong. If someone is both creative and not strong then someone is both rich and quiet. Everyone who is not tall or not generous is not happy or wise. Everyone who is either not curious or not funny is not humble or funny and vice versa. Everyone who is not wise or not humble is happy. Everyone who is kind is not funny or brave. Everyone who is both not wise and brave is either not curious or not generous and vice versa. If someone is not kind or kind then someone is kind or calm. Everyone who is both not rich and not generous is not brave and vice versa. Everyone who is both not old and not quiet is not creative. If susan is not strong or not curious then paul is either not rich or not funny and vice versa. Everyone who is both quiet and brave is old or not patient. If fred is both generous and creative then fred is not generous or not curious and vice versa. Everyone who is calm is either not old or not creative and vice versa. If fred is both humble and patient then paul is either not kind or humble. If john is both calm and not wise then mary is both patient and funny and vice versa. Someone is both not rich and funny. Someone is both brave and not creative. Mary is either not wise or not tall. John is old or kind. Lucy is rich or tall. Paul is not patient. Someone is either not calm or generous. Lucy is both not creative and curious. | Lucy is generous. | entailment | ((?[X]:((calm(X)|~calm(X))))=>((~curious(susan)<~>strong(susan))))&
((?[X]:((creative(X)&~strong(X))))=>(?[X]:((rich(X)&quiet(X)))))&
(![X]:((~tall(X)|~generous(X))=>(~happy(X)|wise(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>(~humble(X)|funny(X))))&
(![X]:((~wise(X)|~humble(X))=>happy(X)))&
(![X]:(kind(X)=>(~funny(X)|brave(X))))&
(![X]:((~wise(X)&brave(X))<=>(~curious(X)<~>~generous(X))))&
((?[X]:((~kind(X)|kind(X))))=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~rich(X)&~generous(X))<=>~brave(X)))&
(![X]:((~old(X)&~quiet(X))=>~creative(X)))&
(((~strong(susan)|~curious(susan)))<=>((~rich(paul)<~>~funny(paul))))&
(![X]:((quiet(X)&brave(X))=>(old(X)|~patient(X))))&
(((generous(fred)&creative(fred)))<=>((~generous(fred)|~curious(fred))))&
(![X]:(calm(X)<=>(~old(X)<~>~creative(X))))&
(((humble(fred)&patient(fred)))=>((~kind(paul)<~>humble(paul))))&
(((calm(john)&~wise(john)))<=>((patient(mary)&funny(mary))))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((brave(X)&~creative(X))))&
((~wise(mary)<~>~tall(mary)))&
((old(john)|kind(john)))&
((rich(lucy)|tall(lucy)))&
(~patient(paul))&
(?[X]:((~calm(X)<~>generous(X))))&
((~creative(lucy)&curious(lucy))) | generous(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2275215548111480919210836
% SZS output start Proof for 2275215548111480919210836
3. ! [X0] : ((~generous(X0) | ~tall(X0)) => (wise(X0) | ~happy(X0))) [input p2]
4. ! [X0] : ((~curious(X0) <~> ~funny(X0)) <=> (funny(X0) | ~humble(X0))) [input p3]
5. ! [X0] : ((~humble(X0) | ~wise(X0)) => happy(X0)) [input p4]
7. ! [X0] : ((brave(X0) & ~wise(X0)) <=> (~curious(X0) <~> ~generous(X0))) [input p6]
24. curious(lucy) & ~creative(lucy) [input p23]
25. ~generous(lucy) [input hypothesis]
30. ! [X0] : ((wise(X0) | ~happy(X0)) | (generous(X0) & tall(X0))) [ennf transformation 3]
31. ! [X0] : (wise(X0) | ~happy(X0) | (generous(X0) & tall(X0))) [flattening 30]
32. ! [X0] : (happy(X0) | (humble(X0) & wise(X0))) [ennf transformation 5]
46. ! [X0] : ((((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | (~funny(X0) & humble(X0))) & ((funny(X0) | ~humble(X0)) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0))))) [nnf transformation 4]
47. ! [X0] : ((((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | (~funny(X0) & humble(X0))) & (funny(X0) | ~humble(X0) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0))))) [flattening 46]
48. ! [X0] : (((brave(X0) & ~wise(X0)) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | (~brave(X0) | wise(X0)))) [nnf transformation 7]
49. ! [X0] : (((brave(X0) & ~wise(X0)) | ((~curious(X0) | generous(X0)) & (~generous(X0) | curious(X0)))) & (((generous(X0) | curious(X0)) & (~generous(X0) | ~curious(X0))) | ~brave(X0) | wise(X0))) [flattening 48]
78. ~happy(X0) | wise(X0) | generous(X0) [cnf transformation 31]
80. funny(X0) | ~humble(X0) | ~curious(X0) | funny(X0) [cnf transformation 47]
82. ~funny(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 47]
86. humble(X0) | happy(X0) [cnf transformation 32]
91. ~wise(X0) | ~curious(X0) | generous(X0) [cnf transformation 49]
134. curious(lucy) [cnf transformation 24]
135. ~generous(lucy) [cnf transformation 25]
138. funny(X0) | ~humble(X0) | ~curious(X0) [duplicate literal removal 80]
139. ~funny(X0) | ~curious(X0) [duplicate literal removal 82]
171. ~humble(X0) | ~curious(X0) [subsumption resolution 138,139]
299. ~curious(X0) | happy(X0) [resolution 171,86]
300. happy(lucy) [resolution 299,134]
318. wise(lucy) | generous(lucy) [resolution 300,78]
320. wise(lucy) [subsumption resolution 318,135]
366. ~curious(lucy) | generous(lucy) [resolution 320,91]
368. generous(lucy) [subsumption resolution 366,134]
369. $false [subsumption resolution 368,135]
% SZS output end Proof for 2275215548111480919210836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not kind and quiet then someone is quiet or not tall.
Everyone who is not kind or happy is not tall or rich.
Everyone who is both not humble and not curious is not rich and vice versa.
If someone is both not funny and not rich then someone is either not generous or not old.
If someone is not generous or happy then someone is not creative and vice versa.
Everyone who is rich is both old and happy.
Everyone who is both not kind and kind is either old or tall and vice versa.
Everyone who is both not old and not generous is either generous or old.
Everyone who is either patient or old is either happy or not curious and vice versa.
Everyone who is not kind is both not strong and calm.
Everyone who is not old or generous is not wise or not old and vice versa.
Everyone who is either not happy or brave is either not calm or rich and vice versa.
Everyone who is generous or rich is either old or rich.
If someone is either funny or humble then someone is creative.
If someone is either not quiet or not kind then someone is either humble or not humble.
If someone is not curious or funny then someone is calm.
Someone is either tall or calm.
John is either kind or generous.
Lucy is not strong or not happy.
Someone is not creative or not brave.
Someone is either not creative or not curious.
Mary is not funny or strong.
Someone is either not patient or brave. | John is generous. | contradiction | (((~kind(mary)&quiet(mary)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((~kind(X)|happy(X))=>(~tall(X)|rich(X))))&
(![X]:((~humble(X)&~curious(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~rich(X))))=>(?[X]:((~generous(X)<~>~old(X)))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:(rich(X)=>(old(X)&happy(X))))&
(![X]:((~kind(X)&kind(X))<=>(old(X)<~>tall(X))))&
(![X]:((~old(X)&~generous(X))=>(generous(X)<~>old(X))))&
(![X]:((patient(X)<~>old(X))<=>(happy(X)<~>~curious(X))))&
(![X]:(~kind(X)=>(~strong(X)&calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~wise(X)|~old(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((generous(X)|rich(X))=>(old(X)<~>rich(X))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:(creative(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
((?[X]:((~curious(X)|funny(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((kind(john)<~>generous(john)))&
((~strong(lucy)|~happy(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((~creative(X)<~>~curious(X))))&
((~funny(mary)|strong(mary)))&
(?[X]:((~patient(X)<~>brave(X)))) | generous(john) | [
"p1",
"p5",
"p6",
"p7",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6154103877586057174418977
% SZS output start Proof for 6154103877586057174418977
2. ! [X0] : ((happy(X0) | ~kind(X0)) => (rich(X0) | ~tall(X0))) [input p1]
6. ! [X0] : (rich(X0) => (happy(X0) & old(X0))) [input p5]
7. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (old(X0) <~> tall(X0))) [input p6]
8. ! [X0] : ((~generous(X0) & ~old(X0)) => (generous(X0) <~> old(X0))) [input p7]
13. ! [X0] : ((rich(X0) | generous(X0)) => (old(X0) <~> rich(X0))) [input p12]
18. kind(john) <~> generous(john) [input p17]
24. generous(john) [input hypothesis]
32. ! [X0] : ((rich(X0) | ~tall(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 2]
33. ! [X0] : (rich(X0) | ~tall(X0) | (~happy(X0) & kind(X0))) [flattening 32]
35. ! [X0] : ((happy(X0) & old(X0)) | ~rich(X0)) [ennf transformation 6]
36. ! [X0] : ((generous(X0) <~> old(X0)) | (generous(X0) | old(X0))) [ennf transformation 8]
37. ! [X0] : ((generous(X0) <~> old(X0)) | generous(X0) | old(X0)) [flattening 36]
39. ! [X0] : ((old(X0) <~> rich(X0)) | (~rich(X0) & ~generous(X0))) [ennf transformation 13]
56. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~kind(X0) | kind(X0)))) [nnf transformation 7]
57. ! [X0] : (((kind(X0) & ~kind(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | ~kind(X0) | kind(X0))) [flattening 56]
58. ! [X0] : (((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | generous(X0) | old(X0)) [nnf transformation 37]
63. ! [X0] : (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | (~rich(X0) & ~generous(X0))) [nnf transformation 39]
78. (~generous(john) | ~kind(john)) & (generous(john) | kind(john)) [nnf transformation 18]
88. ~tall(X0) | rich(X0) | kind(X0) [cnf transformation 33]
98. ~rich(X0) | old(X0) [cnf transformation 35]
102. ~kind(X0) | tall(X0) | ~old(X0) [cnf transformation 57]
104. kind(X0) | tall(X0) | ~old(X0) [cnf transformation 57]
106. old(X0) | generous(X0) | generous(X0) | old(X0) [cnf transformation 58]
130. rich(X0) | old(X0) | ~generous(X0) [cnf transformation 63]
133. ~rich(X0) | ~old(X0) | ~rich(X0) [cnf transformation 63]
145. ~generous(john) | ~kind(john) [cnf transformation 78]
153. generous(john) [cnf transformation 24]
154. ~rich(X0) | ~old(X0) [duplicate literal removal 133]
155. old(X0) | generous(X0) [duplicate literal removal 106]
211. ~old(X0) | tall(X0) [subsumption resolution 102,104]
217. ~rich(X0) [subsumption resolution 154,98]
218. old(X0) | ~generous(X0) [subsumption resolution 130,217]
219. old(X0) [subsumption resolution 218,155]
255. 22 <=> kind(john) [avatar definition]
257. ~kind(john) <- (~22) [avatar component clause 255]
259. 23 <=> generous(john) [avatar definition]
262. ~22 | ~23 [avatar split clause 145,259,255]
311. 23 [avatar split clause 153,259]
320. tall(X1) [resolution 211,219]
325. rich(X0) | kind(X0) [resolution 88,320]
326. kind(X0) [subsumption resolution 325,217]
327. $false <- (~22) [resolution 326,257]
328. 22 [avatar contradiction clause 327]
329. $false [avatar sat refutation 262,311,328]
% SZS output end Proof for 6154103877586057174418977
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not creative then paul is not strong or not patient.
If someone is wise then someone is either brave or funny.
If someone is both brave and generous then someone is both not humble and strong.
If alice is both kind and not old then someone is both not humble and not creative and vice versa.
If someone is generous or wise then someone is generous.
Everyone who is either not funny or quiet is both creative and rich and vice versa.
Everyone who is tall is either quiet or brave.
Everyone who is either not brave or not funny is strong and vice versa.
Everyone who is both not tall and not funny is both not calm and tall.
Everyone who is brave or not creative is calm or not wise and vice versa.
If someone is humble or not funny then john is humble.
Everyone who is brave is both tall and strong.
If fred is both rich and not happy then mary is either funny or not creative.
If fred is creative then fred is not curious.
If lucy is not brave then fred is both patient and kind.
Everyone who is kind is not rich.
Someone is not creative.
Someone is both not brave and not humble.
Fred is humble.
Paul is either old or not wise.
Paul is not creative.
Someone is happy.
Fred is not wise.
Someone is not patient. | John is not humble. | contradiction | ((~creative(lucy))=>((~strong(paul)|~patient(paul))))&
((?[X]:(wise(X)))=>(?[X]:((brave(X)<~>funny(X)))))&
((?[X]:((brave(X)&generous(X))))=>(?[X]:((~humble(X)&strong(X)))))&
(((kind(alice)&~old(alice)))<=>(?[X]:((~humble(X)&~creative(X)))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:(generous(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(creative(X)&rich(X))))&
(![X]:(tall(X)=>(quiet(X)<~>brave(X))))&
(![X]:((~brave(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~tall(X)&~funny(X))=>(~calm(X)&tall(X))))&
(![X]:((brave(X)|~creative(X))<=>(calm(X)|~wise(X))))&
((?[X]:((humble(X)|~funny(X))))=>(humble(john)))&
(![X]:(brave(X)=>(tall(X)&strong(X))))&
(((rich(fred)&~happy(fred)))=>((funny(mary)<~>~creative(mary))))&
((creative(fred))=>(~curious(fred)))&
((~brave(lucy))=>((patient(fred)&kind(fred))))&
(![X]:(kind(X)=>~rich(X)))&
(?[X]:(~creative(X)))&
(?[X]:((~brave(X)&~humble(X))))&
(humble(fred))&
((old(paul)<~>~wise(paul)))&
(~creative(paul))&
(?[X]:(happy(X)))&
(~wise(fred))&
(?[X]:(~patient(X))) | ~humble(john) | [
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6475059984441406334436661
% SZS output start Proof for 6475059984441406334436661
11. ? [X0] : (~funny(X0) | humble(X0)) => humble(john) [input p10]
19. humble(fred) [input p18]
25. ~humble(john) [input hypothesis]
40. humble(john) | ! [X0] : (funny(X0) & ~humble(X0)) [ennf transformation 11]
101. humble(john) | ~humble(X0) [cnf transformation 40]
111. humble(fred) [cnf transformation 19]
117. ~humble(john) [cnf transformation 25]
194. 18 <=> humble(john) [avatar definition]
199. 19 <=> ! [X0] : ~humble(X0) [avatar definition]
200. ~humble(X0) <- (19) [avatar component clause 199]
201. 19 | 18 [avatar split clause 101,194,199]
226. ~18 [avatar split clause 117,194]
228. $false <- (19) [resolution 200,111]
229. ~19 [avatar contradiction clause 228]
230. $false [avatar sat refutation 201,226,229]
% SZS output end Proof for 6475059984441406334436661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is kind or old. Everyone who is either not creative or not brave is not kind or tall and vice versa. Everyone who is not creative is not funny or rich. If paul is both wise and not creative then someone is both not calm and funny. If someone is both not patient and happy then lucy is either calm or not quiet and vice versa. If someone is quiet or kind then someone is either humble or wise. If paul is wise then someone is not quiet or kind. Everyone who is either kind or not patient is both not patient and not humble and vice versa. If someone is both kind and rich then someone is not quiet or funny. If mary is either old or wise then someone is both not strong and not curious and vice versa. Everyone who is either quiet or generous is both not calm and not humble. Everyone who is not patient or not generous is either not rich or not creative. Everyone who is both strong and calm is funny or rich and vice versa. If someone is not strong then john is humble or not wise and vice versa. Everyone who is both not patient and humble is both not brave and rich. Everyone who is either not generous or old is either not creative or not generous and vice versa. Paul is curious or funny. Mary is both funny and not tall. Mary is tall or old. Someone is both not brave and not calm. John is both generous and not brave. Someone is wise or not curious. Alice is quiet or strong. Someone is humble. | Mary is not creative. | entailment | ((?[X]:(~generous(X)))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~kind(X)|tall(X))))&
(![X]:(~creative(X)=>(~funny(X)|rich(X))))&
(((wise(paul)&~creative(paul)))=>(?[X]:((~calm(X)&funny(X)))))&
((?[X]:((~patient(X)&happy(X))))<=>((calm(lucy)<~>~quiet(lucy))))&
((?[X]:((quiet(X)|kind(X))))=>(?[X]:((humble(X)<~>wise(X)))))&
((wise(paul))=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>(~patient(X)&~humble(X))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((~quiet(X)|funny(X)))))&
(((old(mary)<~>wise(mary)))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((quiet(X)<~>generous(X))=>(~calm(X)&~humble(X))))&
(![X]:((~patient(X)|~generous(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((strong(X)&calm(X))<=>(funny(X)|rich(X))))&
((?[X]:(~strong(X)))<=>((humble(john)|~wise(john))))&
(![X]:((~patient(X)&humble(X))=>(~brave(X)&rich(X))))&
(![X]:((~generous(X)<~>old(X))<=>(~creative(X)<~>~generous(X))))&
((curious(paul)|funny(paul)))&
((funny(mary)&~tall(mary)))&
((tall(mary)|old(mary)))&
(?[X]:((~brave(X)&~calm(X))))&
((generous(john)&~brave(john)))&
(?[X]:((wise(X)|~curious(X))))&
((quiet(alice)|strong(alice)))&
(?[X]:(humble(X))) | ~creative(mary) | [
"p15",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7468553127483487296261908
% SZS output start Proof for 7468553127483487296261908
16. ! [X0] : ((~generous(X0) <~> old(X0)) <=> (~creative(X0) <~> ~generous(X0))) [input p15]
18. ~tall(mary) & funny(mary) [input p17]
19. old(mary) | tall(mary) [input p18]
25. creative(mary) [input hypothesis]
76. ! [X0] : ((((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) & (((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | ((~generous(X0) | ~old(X0)) & (old(X0) | generous(X0))))) [nnf transformation 16]
136. ~generous(X0) | ~creative(X0) | ~generous(X0) | ~old(X0) [cnf transformation 76]
142. ~old(X0) | generous(X0) | ~creative(X0) | generous(X0) [cnf transformation 76]
145. ~tall(mary) [cnf transformation 18]
146. old(mary) | tall(mary) [cnf transformation 19]
154. creative(mary) [cnf transformation 25]
155. ~generous(X0) | ~creative(X0) | ~old(X0) [duplicate literal removal 136]
158. ~old(X0) | generous(X0) | ~creative(X0) [duplicate literal removal 142]
259. 23 <=> old(mary) [avatar definition]
260. old(mary) <- (23) [avatar component clause 259]
299. ~creative(X0) | ~old(X0) [subsumption resolution 155,158]
309. old(mary) [subsumption resolution 146,145]
310. 23 [avatar split clause 309,259]
331. ~old(mary) [resolution 299,154]
333. $false <- (23) [subsumption resolution 331,260]
334. ~23 [avatar contradiction clause 333]
335. $false [avatar sat refutation 310,334]
% SZS output end Proof for 7468553127483487296261908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not generous and not humble then john is not funny.
If john is not calm or humble then fred is both generous and old and vice versa.
If fred is not strong or creative then john is either not wise or creative and vice versa.
Everyone who is either calm or not old is humble or not patient.
Everyone who is either patient or creative is both not creative and not patient and vice versa.
Everyone who is either strong or curious is rich and vice versa.
Everyone who is funny or not tall is either quiet or not curious.
If mary is both old and not old then mary is either not quiet or not old.
Everyone who is either not humble or brave is either not old or not wise and vice versa.
If someone is both not generous and tall then john is either not kind or not patient and vice versa.
If alice is either not happy or patient then lucy is both kind and funny and vice versa.
Everyone who is either not calm or not quiet is either not funny or not old and vice versa.
Everyone who is either curious or not curious is either not patient or not kind.
Everyone who is either tall or not curious is either not calm or creative.
Everyone who is brave is calm and vice versa.
John is not quiet or happy.
Susan is both curious and not calm.
Someone is either rich or not rich.
Alice is either not happy or humble.
Lucy is not generous or not old.
Mary is not happy.
Someone is not funny. | John is not humble. | contradiction | (((~generous(lucy)&~humble(lucy)))=>(~funny(john)))&
(((~calm(john)|humble(john)))<=>((generous(fred)&old(fred))))&
(((~strong(fred)|creative(fred)))<=>((~wise(john)<~>creative(john))))&
(![X]:((calm(X)<~>~old(X))=>(humble(X)|~patient(X))))&
(![X]:((patient(X)<~>creative(X))<=>(~creative(X)&~patient(X))))&
(![X]:((strong(X)<~>curious(X))<=>rich(X)))&
(![X]:((funny(X)|~tall(X))=>(quiet(X)<~>~curious(X))))&
(((old(mary)&~old(mary)))=>((~quiet(mary)<~>~old(mary))))&
(![X]:((~humble(X)<~>brave(X))<=>(~old(X)<~>~wise(X))))&
((?[X]:((~generous(X)&tall(X))))<=>((~kind(john)<~>~patient(john))))&
(((~happy(alice)<~>patient(alice)))<=>((kind(lucy)&funny(lucy))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(~funny(X)<~>~old(X))))&
(![X]:((curious(X)<~>~curious(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~calm(X)<~>creative(X))))&
(![X]:(brave(X)<=>calm(X)))&
((~quiet(john)|happy(john)))&
((curious(susan)&~calm(susan)))&
(?[X]:((rich(X)<~>~rich(X))))&
((~happy(alice)<~>humble(alice)))&
((~generous(lucy)|~old(lucy)))&
(~happy(mary))&
(?[X]:(~funny(X))) | ~humble(john) | [
"p2",
"p3",
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6350224025886814536922359
% SZS output start Proof for 6350224025886814536922359
3. (creative(fred) | ~strong(fred)) <=> (~wise(john) <~> creative(john)) [input p2]
4. ! [X0] : ((calm(X0) <~> ~old(X0)) => (~patient(X0) | humble(X0))) [input p3]
5. ! [X0] : ((patient(X0) <~> creative(X0)) <=> (~patient(X0) & ~creative(X0))) [input p4]
9. ! [X0] : ((~humble(X0) <~> brave(X0)) <=> (~old(X0) <~> ~wise(X0))) [input p8]
15. ! [X0] : (brave(X0) <=> calm(X0)) [input p14]
23. ~humble(john) [input hypothesis]
26. ! [X0] : ((~patient(X0) | humble(X0)) | (calm(X0) <=> ~old(X0))) [ennf transformation 4]
27. ! [X0] : (~patient(X0) | humble(X0) | (calm(X0) <=> ~old(X0))) [flattening 26]
35. ((creative(fred) | ~strong(fred)) | ((~wise(john) | ~creative(john)) & (creative(john) | wise(john)))) & (((~creative(john) | wise(john)) & (creative(john) | ~wise(john))) | (~creative(fred) & strong(fred))) [nnf transformation 3]
36. (creative(fred) | ~strong(fred) | ((~wise(john) | ~creative(john)) & (creative(john) | wise(john)))) & (((~creative(john) | wise(john)) & (creative(john) | ~wise(john))) | (~creative(fred) & strong(fred))) [flattening 35]
37. ! [X0] : (~patient(X0) | humble(X0) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) [nnf transformation 27]
38. ! [X0] : ((((~creative(X0) | ~patient(X0)) & (creative(X0) | patient(X0))) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~creative(X0) | ~patient(X0)) & (creative(X0) | patient(X0))) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))))) [flattening 38]
43. ! [X0] : ((((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0))))) [nnf transformation 9]
53. ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 15]
69. ~creative(john) | wise(john) | ~creative(fred) [cnf transformation 36]
72. ~patient(X0) | humble(X0) | ~old(X0) | ~calm(X0) [cnf transformation 37]
73. ~patient(X0) | humble(X0) | calm(X0) | old(X0) [cnf transformation 37]
75. ~creative(X0) | patient(X0) | ~creative(X0) [cnf transformation 39]
76. ~patient(X0) | creative(X0) | ~patient(X0) [cnf transformation 39]
78. creative(X0) | patient(X0) | patient(X0) | creative(X0) [cnf transformation 39]
90. ~wise(X0) | ~old(X0) | brave(X0) | humble(X0) [cnf transformation 43]
96. ~brave(X0) | humble(X0) | ~wise(X0) | old(X0) [cnf transformation 43]
126. ~brave(X0) | calm(X0) [cnf transformation 53]
127. ~calm(X0) | brave(X0) [cnf transformation 53]
138. ~humble(john) [cnf transformation 23]
145. ~creative(X0) | patient(X0) [duplicate literal removal 75]
146. ~patient(X0) | creative(X0) [duplicate literal removal 76]
147. patient(X0) | creative(X0) [duplicate literal removal 78]
170. 6 <=> calm(john) [avatar definition]
171. calm(john) <- (6) [avatar component clause 170]
174. 7 <=> humble(john) [avatar definition]
175. ~humble(john) <- (~7) [avatar component clause 174]
183. 8 <=> creative(john) [avatar definition]
185. ~creative(john) <- (~8) [avatar component clause 183]
187. 9 <=> wise(john) [avatar definition]
188. wise(john) <- (9) [avatar component clause 187]
195. 11 <=> creative(fred) [avatar definition]
196. ~creative(fred) <- (~11) [avatar component clause 195]
200. ~11 | 9 | ~8 [avatar split clause 69,183,187,195]
204. creative(X0) [subsumption resolution 146,147]
205. patient(X0) [subsumption resolution 145,204]
270. ~7 [avatar split clause 138,174]
271. $false <- (~8) [subsumption resolution 185,204]
272. 8 [avatar contradiction clause 271]
318. ~old(X1) | humble(X1) | ~calm(X1) [resolution 72,205]
320. old(X1) | calm(X1) | humble(X1) [resolution 73,205]
331. ~old(john) | brave(john) | humble(john) <- (9) [resolution 90,188]
332. ~old(john) | brave(john) <- (~7, 9) [subsumption resolution 331,175]
334. 32 <=> brave(john) [avatar definition]
336. brave(john) <- (32) [avatar component clause 334]
338. 33 <=> old(john) [avatar definition]
339. old(john) <- (33) [avatar component clause 338]
340. ~old(john) <- (~33) [avatar component clause 338]
341. 32 | ~33 | 7 | ~9 [avatar split clause 332,187,174,338,334]
345. calm(john) | humble(john) <- (~33) [resolution 320,340]
350. calm(john) <- (~7, ~33) [subsumption resolution 345,175]
351. 6 | 7 | 33 [avatar split clause 350,338,174,170]
352. brave(john) <- (6) [resolution 171,127]
353. 32 | ~6 [avatar split clause 352,170,334]
358. calm(john) <- (32) [resolution 336,126]
372. humble(john) | ~wise(john) | old(john) <- (32) [resolution 96,336]
374. ~wise(john) | old(john) <- (~7, 32) [subsumption resolution 372,175]
375. old(john) <- (~7, 9, 32) [subsumption resolution 374,188]
378. 33 | 7 | ~9 | ~32 [avatar split clause 375,334,187,174,338]
380. humble(john) | ~calm(john) <- (33) [resolution 339,318]
381. ~calm(john) <- (~7, 33) [subsumption resolution 380,175]
384. ~6 | 7 | ~33 [avatar split clause 381,338,174,170]
385. 6 | ~32 [avatar split clause 358,334,170]
386. $false <- (~11) [subsumption resolution 196,204]
387. 11 [avatar contradiction clause 386]
388. $false [avatar sat refutation 200,270,272,341,351,353,378,384,385,387]
% SZS output end Proof for 6350224025886814536922359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or humble is either calm or not kind and vice versa.
Everyone who is both generous and humble is not rich or happy and vice versa.
Everyone who is both not tall and calm is either not generous or not quiet.
Everyone who is not funny is either not brave or not rich.
Everyone who is not generous or not humble is either not happy or rich and vice versa.
If alice is either not wise or curious then someone is both not quiet and humble.
Everyone who is either not tall or not patient is kind.
If someone is patient then paul is both tall and not rich and vice versa.
Everyone who is both creative and funny is not humble and vice versa.
If someone is either strong or rich then paul is both not humble and not calm.
If fred is both not brave and not humble then john is either not happy or strong.
Everyone who is not brave is not kind.
Everyone who is either happy or strong is not brave and vice versa.
If susan is either creative or not wise then someone is either not happy or generous and vice versa.
If someone is strong or not rich then someone is tall.
Someone is either generous or wise.
Someone is either kind or funny.
Someone is either tall or kind.
Someone is tall or kind.
Someone is wise. | Susan is calm. | contradiction | (![X]:((~tall(X)|humble(X))<=>(calm(X)<~>~kind(X))))&
(![X]:((generous(X)&humble(X))<=>(~rich(X)|happy(X))))&
(![X]:((~tall(X)&calm(X))=>(~generous(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~brave(X)<~>~rich(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~happy(X)<~>rich(X))))&
(((~wise(alice)<~>curious(alice)))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>kind(X)))&
((?[X]:(patient(X)))<=>((tall(paul)&~rich(paul))))&
(![X]:((creative(X)&funny(X))<=>~humble(X)))&
((?[X]:((strong(X)<~>rich(X))))=>((~humble(paul)&~calm(paul))))&
(((~brave(fred)&~humble(fred)))=>((~happy(john)<~>strong(john))))&
(![X]:(~brave(X)=>~kind(X)))&
(![X]:((happy(X)<~>strong(X))<=>~brave(X)))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(tall(X))))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((kind(X)<~>funny(X))))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:((tall(X)|kind(X))))&
(?[X]:(wise(X))) | calm(susan) | [
"p0",
"p1",
"p4",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3824687341039495646198497
% SZS output start Proof for 3824687341039495646198497
1. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (calm(X0) <~> ~kind(X0))) [input p0]
2. ! [X0] : ((humble(X0) & generous(X0)) <=> (happy(X0) | ~rich(X0))) [input p1]
5. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> (~happy(X0) <~> rich(X0))) [input p4]
10. ? [X0] : (strong(X0) <~> rich(X0)) => (~calm(paul) & ~humble(paul)) [input p9]
12. ! [X0] : (~brave(X0) => ~kind(X0)) [input p11]
13. ! [X0] : ((happy(X0) <~> strong(X0)) <=> ~brave(X0)) [input p12]
21. calm(susan) [input hypothesis]
28. (~calm(paul) & ~humble(paul)) | ! [X0] : (strong(X0) <=> rich(X0)) [ennf transformation 10]
31. ! [X0] : (~kind(X0) | brave(X0)) [ennf transformation 12]
33. ! [X0] : (((humble(X0) | ~tall(X0)) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (~humble(X0) & tall(X0)))) [nnf transformation 1]
34. ! [X0] : ((humble(X0) | ~tall(X0) | ((calm(X0) | kind(X0)) & (~kind(X0) | ~calm(X0)))) & (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | (~humble(X0) & tall(X0)))) [flattening 33]
35. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~humble(X0) | ~generous(X0)))) [nnf transformation 2]
36. ! [X0] : (((humble(X0) & generous(X0)) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ~humble(X0) | ~generous(X0))) [flattening 35]
39. ! [X0] : (((~humble(X0) | ~generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (humble(X0) & generous(X0)))) [nnf transformation 5]
40. ! [X0] : ((~humble(X0) | ~generous(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (humble(X0) & generous(X0)))) [flattening 39]
52. (~calm(paul) & ~humble(paul)) | ! [X0] : ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))) [nnf transformation 28]
54. ! [X0] : ((((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | brave(X0)) & (~brave(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))))) [nnf transformation 13]
78. ~calm(X0) | kind(X0) | ~humble(X0) [cnf transformation 34]
81. ~rich(X0) | happy(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 36]
82. rich(X0) | generous(X0) [cnf transformation 36]
83. ~happy(X0) | generous(X0) [cnf transformation 36]
84. rich(X0) | humble(X0) [cnf transformation 36]
85. ~happy(X0) | humble(X0) [cnf transformation 36]
92. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 40]
93. ~rich(X0) | happy(X0) | humble(X0) [cnf transformation 40]
94. ~humble(X0) | ~generous(X0) | rich(X0) | happy(X0) [cnf transformation 40]
95. ~humble(X0) | ~generous(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 40]
108. ~humble(paul) | rich(X0) | ~strong(X0) [cnf transformation 52]
114. ~kind(X0) | brave(X0) [cnf transformation 31]
115. ~brave(X0) | strong(X0) | ~happy(X0) [cnf transformation 54]
137. calm(susan) [cnf transformation 21]
138. ~generous(X0) | ~happy(X0) | ~rich(X0) [subsumption resolution 95,85]
139. ~happy(X0) | ~rich(X0) [subsumption resolution 138,83]
140. ~generous(X0) | rich(X0) | happy(X0) [subsumption resolution 94,84]
141. happy(X0) | rich(X0) [subsumption resolution 140,82]
142. happy(X0) | humble(X0) [subsumption resolution 93,141]
143. humble(X0) [subsumption resolution 142,85]
144. happy(X0) | generous(X0) [subsumption resolution 92,141]
145. generous(X0) [subsumption resolution 144,83]
188. 10 <=> ! [X0] : (rich(X0) | ~strong(X0)) [avatar definition]
189. ~strong(X0) | rich(X0) <- (10) [avatar component clause 188]
193. rich(X0) | ~strong(X0) [subsumption resolution 108,143]
194. 10 [avatar split clause 193,188]
294. 27 <=> kind(susan) [avatar definition]
296. kind(susan) <- (27) [avatar component clause 294]
299. kind(susan) | ~humble(susan) [resolution 78,137]
301. kind(susan) [subsumption resolution 299,143]
302. 27 [avatar split clause 301,294]
307. brave(susan) <- (27) [resolution 296,114]
456. strong(susan) | ~happy(susan) <- (27) [resolution 307,115]
459. 45 <=> happy(susan) [avatar definition]
460. happy(susan) <- (45) [avatar component clause 459]
461. ~happy(susan) <- (~45) [avatar component clause 459]
463. 46 <=> strong(susan) [avatar definition]
465. strong(susan) <- (46) [avatar component clause 463]
466. ~45 | 46 | ~27 [avatar split clause 456,294,463,459]
472. 48 <=> rich(susan) [avatar definition]
473. rich(susan) <- (48) [avatar component clause 472]
474. ~rich(susan) <- (~48) [avatar component clause 472]
596. rich(susan) <- (~45) [resolution 461,141]
597. $false <- (~45, ~48) [subsumption resolution 596,474]
598. 45 | 48 [avatar contradiction clause 597]
604. ~rich(susan) <- (45) [resolution 460,139]
609. rich(susan) <- (10, 46) [resolution 465,189]
612. 48 | ~10 | ~46 [avatar split clause 609,463,188,472]
613. ~48 | ~45 [avatar split clause 604,459,472]
619. happy(susan) | ~humble(susan) | ~generous(susan) <- (48) [resolution 473,81]
621. ~humble(susan) | ~generous(susan) <- (~45, 48) [subsumption resolution 619,461]
622. ~generous(susan) <- (~45, 48) [subsumption resolution 621,143]
623. $false <- (~45, 48) [subsumption resolution 622,145]
624. 45 | ~48 [avatar contradiction clause 623]
627. $false [avatar sat refutation 194,302,466,598,612,613,624]
% SZS output end Proof for 3824687341039495646198497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is kind. Everyone who is both kind and quiet is not strong. Everyone who is tall is both strong and not curious. Everyone who is either not tall or not curious is either not brave or not funny. Everyone who is either not patient or calm is brave or not rich and vice versa. If someone is both curious and not tall then someone is rich or not kind and vice versa. Everyone who is both wise and not old is either not happy or not calm and vice versa. If alice is either not rich or calm then paul is funny and vice versa. Everyone who is rich is not quiet and vice versa. If alice is either not quiet or not tall then someone is either not funny or not happy and vice versa. If someone is both not curious and old then john is not old or creative. If susan is patient or brave then mary is not kind. Everyone who is either brave or not funny is either tall or not tall and vice versa. Everyone who is either funny or strong is either not kind or not creative. Everyone who is not calm is not kind or not humble. If someone is either not brave or creative then someone is either not quiet or not creative. Someone is old. Someone is not happy. Someone is either not rich or not old. Someone is not curious. Fred is kind. Paul is either kind or brave. Someone is kind. | Alice is not strong. | entailment | (![X]:(humble(X)=>kind(X)))&
(![X]:((kind(X)&quiet(X))=>~strong(X)))&
(![X]:(tall(X)=>(strong(X)&~curious(X))))&
(![X]:((~tall(X)<~>~curious(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>calm(X))<=>(brave(X)|~rich(X))))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((wise(X)&~old(X))<=>(~happy(X)<~>~calm(X))))&
(((~rich(alice)<~>calm(alice)))<=>(funny(paul)))&
(![X]:(rich(X)<=>~quiet(X)))&
(((~quiet(alice)<~>~tall(alice)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
((?[X]:((~curious(X)&old(X))))=>((~old(john)|creative(john))))&
(((patient(susan)|brave(susan)))=>(~kind(mary)))&
(![X]:((brave(X)<~>~funny(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((funny(X)<~>strong(X))=>(~kind(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(~kind(X)|~humble(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:((~quiet(X)<~>~creative(X)))))&
(?[X]:(old(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(kind(fred))&
((kind(paul)<~>brave(paul)))&
(?[X]:(kind(X))) | ~strong(alice) | [
"p1",
"p2",
"p3",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4563995652755257902989335
% SZS output start Proof for 4563995652755257902989335
2. ! [X0] : ((quiet(X0) & kind(X0)) => ~strong(X0)) [input p1]
3. ! [X0] : (tall(X0) => (~curious(X0) & strong(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> ~curious(X0)) => (~brave(X0) <~> ~funny(X0))) [input p3]
6. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X0] : (~kind(X0) | rich(X0)) [input p5]
9. ! [X0] : (rich(X0) <=> ~quiet(X0)) [input p8]
13. ! [X0] : ((brave(X0) <~> ~funny(X0)) <=> (tall(X0) <~> ~tall(X0))) [input p12]
24. strong(alice) [input hypothesis]
25. ? [X0] : (~tall(X0) & curious(X0)) <=> ? [X1] : (~kind(X1) | rich(X1)) [rectify 6]
29. ! [X0] : (~strong(X0) | (~quiet(X0) | ~kind(X0))) [ennf transformation 2]
30. ! [X0] : (~strong(X0) | ~quiet(X0) | ~kind(X0)) [flattening 29]
31. ! [X0] : ((~curious(X0) & strong(X0)) | ~tall(X0)) [ennf transformation 3]
32. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (~tall(X0) <=> ~curious(X0))) [ennf transformation 4]
38. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 32]
41. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X1] : (~kind(X1) | rich(X1)) | ! [X0] : (tall(X0) | ~curious(X0))) [nnf transformation 25]
42. (? [X0] : (~tall(X0) & curious(X0)) | ! [X1] : (kind(X1) & ~rich(X1))) & (? [X2] : (~kind(X2) | rich(X2)) | ! [X3] : (tall(X3) | ~curious(X3))) [rectify 41]
43. ? [X0] : (~tall(X0) & curious(X0)) => (~tall(sK0) & curious(sK0)) [choice axiom]
44. ? [X2] : (~kind(X2) | rich(X2)) => (~kind(sK1) | rich(sK1)) [choice axiom]
45. ((~tall(sK0) & curious(sK0)) | ! [X1] : (kind(X1) & ~rich(X1))) & ((~kind(sK1) | rich(sK1)) | ! [X3] : (tall(X3) | ~curious(X3))) [skolemisation 42,44,43]
49. ! [X0] : ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))) [nnf transformation 9]
54. ! [X0] : ((((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0))))) [nnf transformation 13]
72. ~strong(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 30]
74. ~curious(X0) | ~tall(X0) [cnf transformation 31]
75. ~funny(X0) | ~brave(X0) | ~curious(X0) | tall(X0) [cnf transformation 38]
76. ~funny(X0) | ~brave(X0) | ~tall(X0) | curious(X0) [cnf transformation 38]
77. funny(X0) | brave(X0) | ~curious(X0) | tall(X0) [cnf transformation 38]
78. funny(X0) | brave(X0) | ~tall(X0) | curious(X0) [cnf transformation 38]
86. curious(sK0) | ~rich(X1) [cnf transformation 45]
87. curious(sK0) | kind(X1) [cnf transformation 45]
101. rich(X0) | quiet(X0) [cnf transformation 49]
117. ~funny(X0) | brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
118. ~funny(X0) | brave(X0) | tall(X0) | tall(X0) [cnf transformation 54]
119. funny(X0) | ~brave(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
120. funny(X0) | ~brave(X0) | tall(X0) | tall(X0) [cnf transformation 54]
138. strong(alice) [cnf transformation 24]
139. ~funny(X0) | brave(X0) | ~tall(X0) [duplicate literal removal 117]
140. ~funny(X0) | brave(X0) | tall(X0) [duplicate literal removal 118]
141. funny(X0) | ~brave(X0) | ~tall(X0) [duplicate literal removal 119]
142. ~brave(X0) | funny(X0) | tall(X0) [duplicate literal removal 120]
143. ~tall(X0) | brave(X0) | funny(X0) [subsumption resolution 78,74]
144. ~curious(X0) | brave(X0) | funny(X0) [subsumption resolution 77,143]
145. ~funny(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 76,74]
146. ~funny(X0) | ~brave(X0) | ~curious(X0) [subsumption resolution 75,145]
148. 1 <=> ! [X1] : kind(X1) [avatar definition]
149. kind(X1) <- (1) [avatar component clause 148]
156. 3 <=> ! [X1] : ~rich(X1) [avatar definition]
157. ~rich(X1) <- (3) [avatar component clause 156]
160. 4 <=> curious(sK0) [avatar definition]
162. curious(sK0) <- (4) [avatar component clause 160]
163. 1 | 4 [avatar split clause 87,160,148]
164. 3 | 4 [avatar split clause 86,160,156]
183. 9 <=> rich(alice) [avatar definition]
184. ~rich(alice) <- (~9) [avatar component clause 183]
185. rich(alice) <- (9) [avatar component clause 183]
198. 12 <=> quiet(alice) [avatar definition]
199. ~quiet(alice) <- (~12) [avatar component clause 198]
250. ~tall(X0) | funny(X0) [subsumption resolution 141,143]
251. ~funny(X0) | ~tall(X0) [subsumption resolution 139,145]
252. ~tall(X0) [subsumption resolution 251,250]
293. quiet(alice) <- (~9) [resolution 101,184]
295. $false <- (~9, ~12) [subsumption resolution 293,199]
296. 9 | 12 [avatar contradiction clause 295]
300. ~quiet(alice) | ~kind(alice) [resolution 72,138]
370. brave(sK0) | funny(sK0) <- (4) [resolution 144,162]
372. 42 <=> funny(sK0) [avatar definition]
374. funny(sK0) <- (42) [avatar component clause 372]
376. 43 <=> brave(sK0) [avatar definition]
378. brave(sK0) <- (43) [avatar component clause 376]
379. 42 | 43 | ~4 [avatar split clause 370,160,376,372]
380. funny(sK0) | tall(sK0) <- (43) [resolution 378,142]
381. funny(sK0) <- (43) [subsumption resolution 380,252]
382. 42 | ~43 [avatar split clause 381,376,372]
384. brave(sK0) | tall(sK0) <- (42) [resolution 374,140]
386. ~brave(sK0) | ~curious(sK0) <- (42) [resolution 146,374]
396. $false <- (3, 9) [resolution 157,185]
401. ~3 | ~9 [avatar contradiction clause 396]
402. brave(sK0) <- (42) [subsumption resolution 384,252]
403. 43 | ~42 [avatar split clause 402,372,376]
406. ~4 | ~43 | ~42 [avatar split clause 386,372,376,160]
407. ~quiet(alice) <- (1) [subsumption resolution 300,149]
408. ~12 | ~1 [avatar split clause 407,148,198]
411. $false [avatar sat refutation 163,164,296,379,382,401,403,406,408]
% SZS output end Proof for 4563995652755257902989335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy then someone is not strong or rich and vice versa. Everyone who is not patient or not brave is both not curious and not funny. If mary is both generous and not funny then john is funny or not curious and vice versa. Everyone who is strong is not patient or not funny. Everyone who is either happy or not quiet is either funny or tall. Everyone who is both curious and not happy is either happy or not patient. If alice is either not generous or patient then someone is not happy or not strong and vice versa. Everyone who is patient is not curious or wise and vice versa. Everyone who is funny is either not kind or not brave and vice versa. Everyone who is brave is both not curious and not patient and vice versa. If someone is either not generous or strong then mary is not wise and vice versa. If lucy is quiet or not brave then someone is either not strong or wise and vice versa. If alice is either humble or not tall then someone is both not generous and strong. Everyone who is not wise is either wise or not quiet and vice versa. If someone is quiet then susan is not old. If mary is not patient or not creative then lucy is either generous or not creative and vice versa. Someone is strong. Mary is not generous or not calm. Someone is funny or not quiet. Someone is tall or old. Someone is not creative or quiet. Mary is not strong. Paul is either not happy or not strong. | Lucy is not old. | neutral | ((~happy(fred))<=>(?[X]:((~strong(X)|rich(X)))))&
(![X]:((~patient(X)|~brave(X))=>(~curious(X)&~funny(X))))&
(((generous(mary)&~funny(mary)))<=>((funny(john)|~curious(john))))&
(![X]:(strong(X)=>(~patient(X)|~funny(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(funny(X)<~>tall(X))))&
(![X]:((curious(X)&~happy(X))=>(happy(X)<~>~patient(X))))&
(((~generous(alice)<~>patient(alice)))<=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:(patient(X)<=>(~curious(X)|wise(X))))&
(![X]:(funny(X)<=>(~kind(X)<~>~brave(X))))&
(![X]:(brave(X)<=>(~curious(X)&~patient(X))))&
((?[X]:((~generous(X)<~>strong(X))))<=>(~wise(mary)))&
(((quiet(lucy)|~brave(lucy)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(((humble(alice)<~>~tall(alice)))=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:(~wise(X)<=>(wise(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))=>(~old(susan)))&
(((~patient(mary)|~creative(mary)))<=>((generous(lucy)<~>~creative(lucy))))&
(?[X]:(strong(X)))&
((~generous(mary)|~calm(mary)))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((~creative(X)|quiet(X))))&
(~strong(mary))&
((~happy(paul)<~>~strong(paul))) | ~old(lucy) | [] | null | 0 |
If someone is kind then mary is both humble and quiet.
Everyone who is either generous or rich is both not happy and not creative and vice versa.
If susan is both not creative and not strong then lucy is funny or not old and vice versa.
If someone is either wise or funny then someone is either patient or not rich and vice versa.
Everyone who is both patient and not funny is strong.
Everyone who is either not tall or not happy is either not tall or not quiet.
Everyone who is brave or quiet is curious or funny.
If alice is either creative or patient then someone is kind and vice versa.
If alice is not creative or curious then alice is not patient or kind and vice versa.
If lucy is old or not curious then john is both kind and not creative and vice versa.
Everyone who is not wise is both curious and strong.
If john is not tall then lucy is both not old and old.
Everyone who is either quiet or rich is both not rich and happy.
If alice is not patient or curious then someone is both not creative and not patient and vice versa.
Everyone who is creative or not patient is either curious or generous and vice versa.
Everyone who is not funny or rich is either not patient or quiet and vice versa.
Susan is either old or wise.
Susan is humble.
Someone is old or not generous.
Alice is not tall.
Someone is either not brave or calm.
Lucy is kind or patient.
Someone is rich. | Alice is generous. | neutral | ((?[X]:(kind(X)))=>((humble(mary)&quiet(mary))))&
(![X]:((generous(X)<~>rich(X))<=>(~happy(X)&~creative(X))))&
(((~creative(susan)&~strong(susan)))<=>((funny(lucy)|~old(lucy))))&
((?[X]:((wise(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((patient(X)&~funny(X))=>strong(X)))&
(![X]:((~tall(X)<~>~happy(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((brave(X)|quiet(X))=>(curious(X)|funny(X))))&
(((creative(alice)<~>patient(alice)))<=>(?[X]:(kind(X))))&
(((~creative(alice)|curious(alice)))<=>((~patient(alice)|kind(alice))))&
(((old(lucy)|~curious(lucy)))<=>((kind(john)&~creative(john))))&
(![X]:(~wise(X)=>(curious(X)&strong(X))))&
((~tall(john))=>((~old(lucy)&old(lucy))))&
(![X]:((quiet(X)<~>rich(X))=>(~rich(X)&happy(X))))&
(((~patient(alice)|curious(alice)))<=>(?[X]:((~creative(X)&~patient(X)))))&
(![X]:((creative(X)|~patient(X))<=>(curious(X)<~>generous(X))))&
(![X]:((~funny(X)|rich(X))<=>(~patient(X)<~>quiet(X))))&
((old(susan)<~>wise(susan)))&
(humble(susan))&
(?[X]:((old(X)|~generous(X))))&
(~tall(alice))&
(?[X]:((~brave(X)<~>calm(X))))&
((kind(lucy)|patient(lucy)))&
(?[X]:(rich(X))) | generous(alice) | [] | null | 0 |
Everyone who is either not rich or creative is either happy or generous. Everyone who is not tall is not kind or rich. If mary is tall or not calm then someone is not calm or not happy and vice versa. Everyone who is not old is generous. Everyone who is rich or not patient is not tall and vice versa. If someone is both not rich and kind then fred is either rich or not generous and vice versa. Everyone who is patient or not curious is either not tall or kind. If someone is not old then john is either quiet or strong and vice versa. If someone is not humble or wise then someone is both kind and humble and vice versa. If paul is humble then susan is quiet. If someone is not calm or calm then john is old. If fred is not brave then someone is happy and vice versa. Everyone who is both kind and not creative is creative or calm. If lucy is kind then alice is both not happy and not quiet. Everyone who is not calm is not humble. Everyone who is calm is not curious or not calm and vice versa. Alice is not patient. Someone is either not creative or curious. Lucy is not tall. Paul is funny or wise. John is not wise. Susan is calm. | Mary is not brave. | neutral | (![X]:((~rich(X)<~>creative(X))=>(happy(X)<~>generous(X))))&
(![X]:(~tall(X)=>(~kind(X)|rich(X))))&
(((tall(mary)|~calm(mary)))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~old(X)=>generous(X)))&
(![X]:((rich(X)|~patient(X))<=>~tall(X)))&
((?[X]:((~rich(X)&kind(X))))<=>((rich(fred)<~>~generous(fred))))&
(![X]:((patient(X)|~curious(X))=>(~tall(X)<~>kind(X))))&
((?[X]:(~old(X)))<=>((quiet(john)<~>strong(john))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((kind(X)&humble(X)))))&
((humble(paul))=>(quiet(susan)))&
((?[X]:((~calm(X)|calm(X))))=>(old(john)))&
((~brave(fred))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)&~creative(X))=>(creative(X)|calm(X))))&
((kind(lucy))=>((~happy(alice)&~quiet(alice))))&
(![X]:(~calm(X)=>~humble(X)))&
(![X]:(calm(X)<=>(~curious(X)|~calm(X))))&
(~patient(alice))&
(?[X]:((~creative(X)<~>curious(X))))&
(~tall(lucy))&
((funny(paul)|wise(paul)))&
(~wise(john))&
(calm(susan)) | ~brave(mary) | [] | null | 0 |
Everyone who is curious or creative is either humble or happy and vice versa. If someone is either not curious or old then john is creative and vice versa. Everyone who is both not old and not brave is not tall and vice versa. Everyone who is creative or not wise is either quiet or creative. If someone is both not strong and humble then someone is both calm and not tall. If fred is either strong or not patient then someone is both calm and not rich and vice versa. Everyone who is either kind or quiet is either brave or not kind. Everyone who is not brave is not calm. If someone is both quiet and not tall then someone is not curious or curious. If fred is either not strong or quiet then someone is curious or creative. If alice is not creative or not patient then someone is happy or not patient and vice versa. If someone is not curious or old then lucy is humble. Everyone who is quiet is strong and vice versa. Everyone who is either not generous or not old is not happy. If someone is either rich or not patient then someone is creative. If someone is not happy or not humble then john is both funny and old. Paul is either tall or kind. Someone is both not humble and patient. Paul is curious. Someone is both not generous and patient. Alice is either patient or not tall. Paul is both not strong and not patient. Someone is not happy. Someone is calm. | Lucy is creative. | contradiction | (![X]:((curious(X)|creative(X))<=>(humble(X)<~>happy(X))))&
((?[X]:((~curious(X)<~>old(X))))<=>(creative(john)))&
(![X]:((~old(X)&~brave(X))<=>~tall(X)))&
(![X]:((creative(X)|~wise(X))=>(quiet(X)<~>creative(X))))&
((?[X]:((~strong(X)&humble(X))))=>(?[X]:((calm(X)&~tall(X)))))&
(((strong(fred)<~>~patient(fred)))<=>(?[X]:((calm(X)&~rich(X)))))&
(![X]:((kind(X)<~>quiet(X))=>(brave(X)<~>~kind(X))))&
(![X]:(~brave(X)=>~calm(X)))&
((?[X]:((quiet(X)&~tall(X))))=>(?[X]:((~curious(X)|curious(X)))))&
(((~strong(fred)<~>quiet(fred)))=>(?[X]:((curious(X)|creative(X)))))&
(((~creative(alice)|~patient(alice)))<=>(?[X]:((happy(X)|~patient(X)))))&
((?[X]:((~curious(X)|old(X))))=>(humble(lucy)))&
(![X]:(quiet(X)<=>strong(X)))&
(![X]:((~generous(X)<~>~old(X))=>~happy(X)))&
((?[X]:((rich(X)<~>~patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~happy(X)|~humble(X))))=>((funny(john)&old(john))))&
((tall(paul)<~>kind(paul)))&
(?[X]:((~humble(X)&patient(X))))&
(curious(paul))&
(?[X]:((~generous(X)&patient(X))))&
((patient(alice)<~>~tall(alice)))&
((~strong(paul)&~patient(paul)))&
(?[X]:(~happy(X)))&
(?[X]:(calm(X))) | creative(lucy) | [
"p2",
"p3",
"p4",
"p7",
"p11",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1421149221932804436255904
% SZS output start Proof for 1421149221932804436255904
3. ! [X0] : ((~brave(X0) & ~old(X0)) <=> ~tall(X0)) [input p2]
4. ! [X0] : ((~wise(X0) | creative(X0)) => (quiet(X0) <~> creative(X0))) [input p3]
5. ? [X0] : (humble(X0) & ~strong(X0)) => ? [X0] : (~tall(X0) & calm(X0)) [input p4]
8. ! [X0] : (~brave(X0) => ~calm(X0)) [input p7]
12. ? [X0] : (old(X0) | ~curious(X0)) => humble(lucy) [input p11]
13. ! [X0] : (quiet(X0) <=> strong(X0)) [input p12]
16. ? [X0] : (~humble(X0) | ~happy(X0)) => (old(john) & funny(john)) [input p15]
23. ? [X0] : ~happy(X0) [input p22]
25. creative(lucy) [input hypothesis]
26. ? [X0] : (humble(X0) & ~strong(X0)) => ? [X1] : (~tall(X1) & calm(X1)) [rectify 5]
29. ? [X0] : (~humble(X0) | ~happy(X0)) => old(john) [pure predicate removal 16]
30. ! [X0] : (creative(X0) => (quiet(X0) <~> creative(X0))) [pure predicate removal 4]
31. ! [X0] : ((quiet(X0) <~> creative(X0)) | ~creative(X0)) [ennf transformation 30]
32. ? [X1] : (~tall(X1) & calm(X1)) | ! [X0] : (~humble(X0) | strong(X0)) [ennf transformation 26]
34. ! [X0] : (~calm(X0) | brave(X0)) [ennf transformation 8]
37. humble(lucy) | ! [X0] : (~old(X0) & curious(X0)) [ennf transformation 12]
40. old(john) | ! [X0] : (humble(X0) & happy(X0)) [ennf transformation 29]
47. ! [X0] : (((~brave(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | old(X0)))) [nnf transformation 3]
48. ! [X0] : (((~brave(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | old(X0))) [flattening 47]
49. ! [X0] : (((~creative(X0) | ~quiet(X0)) & (creative(X0) | quiet(X0))) | ~creative(X0)) [nnf transformation 31]
50. ? [X0] : (~tall(X0) & calm(X0)) | ! [X1] : (~humble(X1) | strong(X1)) [rectify 32]
51. ? [X0] : (~tall(X0) & calm(X0)) => (~tall(sK1) & calm(sK1)) [choice axiom]
52. (~tall(sK1) & calm(sK1)) | ! [X1] : (~humble(X1) | strong(X1)) [skolemisation 50,51]
69. ! [X0] : ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0))) [nnf transformation 13]
81. ? [X0] : ~happy(X0) => ~happy(sK9) [choice axiom]
82. ~happy(sK9) [skolemisation 23,81]
97. ~brave(X0) | tall(X0) [cnf transformation 48]
99. ~creative(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 49]
100. calm(sK1) | ~humble(X1) | strong(X1) [cnf transformation 52]
101. ~tall(sK1) | ~humble(X1) | strong(X1) [cnf transformation 52]
112. ~calm(X0) | brave(X0) [cnf transformation 34]
121. humble(lucy) | ~old(X0) [cnf transformation 37]
123. ~strong(X0) | quiet(X0) [cnf transformation 69]
128. old(john) | happy(X0) [cnf transformation 40]
141. ~happy(sK9) [cnf transformation 82]
143. creative(lucy) [cnf transformation 25]
146. ~quiet(X0) | ~creative(X0) [duplicate literal removal 99]
170. 6 <=> ! [X1] : (~humble(X1) | strong(X1)) [avatar definition]
171. ~humble(X1) | strong(X1) <- (6) [avatar component clause 170]
173. 7 <=> tall(sK1) [avatar definition]
175. ~tall(sK1) <- (~7) [avatar component clause 173]
176. 6 | ~7 [avatar split clause 101,173,170]
178. 8 <=> calm(sK1) [avatar definition]
180. calm(sK1) <- (8) [avatar component clause 178]
181. 6 | 8 [avatar split clause 100,178,170]
248. 23 <=> ! [X0] : ~old(X0) [avatar definition]
249. ~old(X0) <- (23) [avatar component clause 248]
251. 24 <=> humble(lucy) [avatar definition]
253. humble(lucy) <- (24) [avatar component clause 251]
254. 23 | 24 [avatar split clause 121,251,248]
275. 30 <=> old(john) [avatar definition]
277. old(john) <- (30) [avatar component clause 275]
280. 31 <=> ! [X0] : happy(X0) [avatar definition]
281. happy(X0) <- (31) [avatar component clause 280]
282. 31 | 30 [avatar split clause 128,275,280]
311. strong(lucy) <- (6, 24) [resolution 171,253]
312. quiet(lucy) <- (6, 24) [resolution 311,123]
379. ~creative(lucy) <- (6, 24) [resolution 312,146]
381. $false <- (6, 24) [subsumption resolution 379,143]
382. ~6 | ~24 [avatar contradiction clause 381]
388. $false <- (23, 30) [resolution 249,277]
390. ~23 | ~30 [avatar contradiction clause 388]
402. brave(sK1) <- (8) [resolution 180,112]
408. $false <- (31) [resolution 281,141]
413. ~31 [avatar contradiction clause 408]
424. tall(sK1) <- (8) [resolution 402,97]
425. $false <- (~7, 8) [subsumption resolution 424,175]
426. 7 | ~8 [avatar contradiction clause 425]
427. $false [avatar sat refutation 176,181,254,282,382,390,413,426]
% SZS output end Proof for 1421149221932804436255904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not humble then someone is either not wise or kind.
Everyone who is humble or curious is either happy or not happy.
If someone is either not kind or not curious then paul is both not patient and not tall and vice versa.
If john is not quiet then alice is either old or not kind.
If susan is both wise and not patient then alice is old.
If someone is both strong and not strong then someone is kind or quiet and vice versa.
Everyone who is both not tall and not strong is not quiet or not curious and vice versa.
Everyone who is both not strong and quiet is both not strong and rich and vice versa.
Everyone who is not happy or calm is kind.
If someone is either generous or not calm then someone is either strong or not rich and vice versa.
If john is not happy or creative then paul is both rich and old and vice versa.
Everyone who is either wise or not rich is either not rich or calm.
Everyone who is either happy or not wise is not kind or not humble.
If someone is funny then mary is not wise or not quiet and vice versa.
Everyone who is either funny or creative is either creative or not brave and vice versa.
Everyone who is both not wise and not strong is generous or strong.
Fred is kind or not old.
Susan is not wise.
Someone is not calm.
Someone is not old.
Someone is not patient. | Paul is brave. | neutral | ((?[X]:((funny(X)&~humble(X))))=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((humble(X)|curious(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>((~patient(paul)&~tall(paul))))&
((~quiet(john))=>((old(alice)<~>~kind(alice))))&
(((wise(susan)&~patient(susan)))=>(old(alice)))&
((?[X]:((strong(X)&~strong(X))))<=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((~tall(X)&~strong(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|calm(X))=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(((~happy(john)|creative(john)))<=>((rich(paul)&old(paul))))&
(![X]:((wise(X)<~>~rich(X))=>(~rich(X)<~>calm(X))))&
(![X]:((happy(X)<~>~wise(X))=>(~kind(X)|~humble(X))))&
((?[X]:(funny(X)))<=>((~wise(mary)|~quiet(mary))))&
(![X]:((funny(X)<~>creative(X))<=>(creative(X)<~>~brave(X))))&
(![X]:((~wise(X)&~strong(X))=>(generous(X)|strong(X))))&
((kind(fred)|~old(fred)))&
(~wise(susan))&
(?[X]:(~calm(X)))&
(?[X]:(~old(X)))&
(?[X]:(~patient(X))) | brave(paul) | [] | null | 0 |
If alice is not tall or not quiet then mary is either not patient or not creative.
Everyone who is both not funny and not strong is not calm and vice versa.
Everyone who is either rich or not happy is not patient or not humble and vice versa.
If susan is quiet or wise then susan is either quiet or rich and vice versa.
If someone is not calm then someone is not brave.
Everyone who is both creative and not humble is not old.
If paul is both kind and not humble then someone is not patient.
If lucy is both not generous and funny then someone is either not happy or curious and vice versa.
If someone is either not calm or not patient then lucy is both strong and funny and vice versa.
If someone is not brave then lucy is either not old or not tall and vice versa.
If someone is not kind or old then someone is humble or not old and vice versa.
Everyone who is either not curious or humble is not happy or not quiet.
Everyone who is not patient is patient or not patient.
Everyone who is not happy or not rich is both not happy and not calm.
Everyone who is either generous or happy is both not wise and not humble.
Everyone who is not curious is either not quiet or not humble.
Fred is both not funny and kind.
Mary is either not humble or calm.
Someone is not funny.
Mary is either curious or kind.
Lucy is not generous or kind.
Mary is not wise or kind.
Someone is quiet or not wise. | Susan is calm. | neutral | (((~tall(alice)|~quiet(alice)))=>((~patient(mary)<~>~creative(mary))))&
(![X]:((~funny(X)&~strong(X))<=>~calm(X)))&
(![X]:((rich(X)<~>~happy(X))<=>(~patient(X)|~humble(X))))&
(((quiet(susan)|wise(susan)))<=>((quiet(susan)<~>rich(susan))))&
((?[X]:(~calm(X)))=>(?[X]:(~brave(X))))&
(![X]:((creative(X)&~humble(X))=>~old(X)))&
(((kind(paul)&~humble(paul)))=>(?[X]:(~patient(X))))&
(((~generous(lucy)&funny(lucy)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>((strong(lucy)&funny(lucy))))&
((?[X]:(~brave(X)))<=>((~old(lucy)<~>~tall(lucy))))&
((?[X]:((~kind(X)|old(X))))<=>(?[X]:((humble(X)|~old(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(~happy(X)|~quiet(X))))&
(![X]:(~patient(X)=>(patient(X)|~patient(X))))&
(![X]:((~happy(X)|~rich(X))=>(~happy(X)&~calm(X))))&
(![X]:((generous(X)<~>happy(X))=>(~wise(X)&~humble(X))))&
(![X]:(~curious(X)=>(~quiet(X)<~>~humble(X))))&
((~funny(fred)&kind(fred)))&
((~humble(mary)<~>calm(mary)))&
(?[X]:(~funny(X)))&
((curious(mary)<~>kind(mary)))&
((~generous(lucy)|kind(lucy)))&
((~wise(mary)|kind(mary)))&
(?[X]:((quiet(X)|~wise(X)))) | calm(susan) | [] | null | 0 |
Everyone who is either not old or happy is both generous and not generous and vice versa.
If someone is not calm or not curious then someone is kind.
Everyone who is both funny and not generous is either not rich or strong.
Everyone who is either wise or not wise is funny or not funny and vice versa.
If someone is not curious then mary is tall or not brave and vice versa.
If someone is both not patient and quiet then someone is either not generous or not curious and vice versa.
Everyone who is not strong is both not quiet and not tall.
Everyone who is not funny or not humble is not generous or curious and vice versa.
Everyone who is funny is both not happy and not funny.
Everyone who is either curious or calm is not rich and vice versa.
If someone is wise then someone is either not old or strong and vice versa.
Everyone who is humble or not kind is quiet and vice versa.
Everyone who is wise or not humble is wise or patient and vice versa.
If someone is both humble and kind then someone is patient or curious and vice versa.
Everyone who is both kind and not calm is both not humble and rich and vice versa.
Everyone who is not rich is both not calm and brave.
Lucy is both not tall and kind.
Someone is both not calm and not rich.
Someone is either not old or strong.
Someone is either not funny or old.
Lucy is not tall.
Someone is wise.
Someone is either patient or wise.
Alice is either not creative or patient. | Mary is funny. | contradiction | (![X]:((~old(X)<~>happy(X))<=>(generous(X)&~generous(X))))&
((?[X]:((~calm(X)|~curious(X))))=>(?[X]:(kind(X))))&
(![X]:((funny(X)&~generous(X))=>(~rich(X)<~>strong(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(funny(X)|~funny(X))))&
((?[X]:(~curious(X)))<=>((tall(mary)|~brave(mary))))&
((?[X]:((~patient(X)&quiet(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:(~strong(X)=>(~quiet(X)&~tall(X))))&
(![X]:((~funny(X)|~humble(X))<=>(~generous(X)|curious(X))))&
(![X]:(funny(X)=>(~happy(X)&~funny(X))))&
(![X]:((curious(X)<~>calm(X))<=>~rich(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~old(X)<~>strong(X)))))&
(![X]:((humble(X)|~kind(X))<=>quiet(X)))&
(![X]:((wise(X)|~humble(X))<=>(wise(X)|patient(X))))&
((?[X]:((humble(X)&kind(X))))<=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((kind(X)&~calm(X))<=>(~humble(X)&rich(X))))&
(![X]:(~rich(X)=>(~calm(X)&brave(X))))&
((~tall(lucy)&kind(lucy)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:((~funny(X)<~>old(X))))&
(~tall(lucy))&
(?[X]:(wise(X)))&
(?[X]:((patient(X)<~>wise(X))))&
((~creative(alice)<~>patient(alice))) | funny(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3833756312600184534109378
% SZS output start Proof for 3833756312600184534109378
9. ! [X0] : (funny(X0) => (~funny(X0) & ~happy(X0))) [input p8]
25. funny(mary) [input hypothesis]
34. ! [X0] : ((~funny(X0) & ~happy(X0)) | ~funny(X0)) [ennf transformation 9]
119. ~funny(X0) | ~funny(X0) [cnf transformation 34]
160. funny(mary) [cnf transformation 25]
161. ~funny(X0) [duplicate literal removal 119]
310. $false [subsumption resolution 160,161]
% SZS output end Proof for 3833756312600184534109378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not creative is not kind.
If mary is not wise or patient then mary is not tall and vice versa.
Everyone who is old is both not curious and not old.
Everyone who is not happy is kind or not wise and vice versa.
If fred is either not tall or not funny then paul is either rich or humble and vice versa.
Everyone who is either generous or not creative is either not patient or creative and vice versa.
If someone is creative or not funny then someone is both not generous and humble.
If mary is either calm or old then someone is either patient or happy and vice versa.
If someone is both calm and not humble then someone is not rich or wise and vice versa.
If someone is generous or happy then someone is either not tall or creative and vice versa.
Everyone who is either generous or not kind is either not happy or happy and vice versa.
Everyone who is not kind is not happy and vice versa.
If mary is both funny and not generous then john is curious and vice versa.
Everyone who is not generous or not calm is not rich or not curious and vice versa.
Everyone who is either not humble or not strong is not generous or not kind.
Everyone who is not humble is either not creative or not funny.
Someone is either not creative or humble.
Lucy is not curious or not rich.
Someone is creative or humble.
Lucy is brave or not tall.
Someone is either not curious or funny.
John is not creative or not happy.
Paul is brave. | Mary is strong. | neutral | (![X]:((~patient(X)&~creative(X))=>~kind(X)))&
(((~wise(mary)|patient(mary)))<=>(~tall(mary)))&
(![X]:(old(X)=>(~curious(X)&~old(X))))&
(![X]:(~happy(X)<=>(kind(X)|~wise(X))))&
(((~tall(fred)<~>~funny(fred)))<=>((rich(paul)<~>humble(paul))))&
(![X]:((generous(X)<~>~creative(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((~generous(X)&humble(X)))))&
(((calm(mary)<~>old(mary)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((generous(X)|happy(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((generous(X)<~>~kind(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(~kind(X)<=>~happy(X)))&
(((funny(mary)&~generous(mary)))<=>(curious(john)))&
(![X]:((~generous(X)|~calm(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~generous(X)|~kind(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((~curious(lucy)|~rich(lucy)))&
(?[X]:((creative(X)|humble(X))))&
((brave(lucy)|~tall(lucy)))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
(brave(paul)) | strong(mary) | [] | null | 0 |
If someone is not old or funny then paul is not humble or kind.
If lucy is either not strong or creative then alice is not kind.
Everyone who is not quiet is not generous or happy.
If someone is curious then someone is either humble or patient and vice versa.
If john is either creative or strong then someone is not wise or not strong and vice versa.
Everyone who is either calm or not curious is both strong and tall and vice versa.
If someone is both not strong and not kind then someone is not calm or not rich.
Everyone who is not quiet or not happy is either not brave or not curious.
Everyone who is not humble or kind is both tall and brave and vice versa.
Everyone who is not old or not generous is either strong or brave.
Everyone who is brave or not curious is both wise and not humble.
Everyone who is both not humble and not quiet is generous or not wise.
Everyone who is either not creative or happy is humble or not tall and vice versa.
Everyone who is creative is both brave and curious and vice versa.
Everyone who is not quiet is both not wise and quiet and vice versa.
Everyone who is not kind or not rich is either not kind or humble.
Someone is not curious.
Someone is either generous or not curious.
Someone is either generous or creative.
Someone is not calm.
John is either humble or old.
John is happy. | Lucy is not quiet. | contradiction | ((?[X]:((~old(X)|funny(X))))=>((~humble(paul)|kind(paul))))&
(((~strong(lucy)<~>creative(lucy)))=>(~kind(alice)))&
(![X]:(~quiet(X)=>(~generous(X)|happy(X))))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>patient(X)))))&
(((creative(john)<~>strong(john)))<=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((calm(X)<~>~curious(X))<=>(strong(X)&tall(X))))&
((?[X]:((~strong(X)&~kind(X))))=>(?[X]:((~calm(X)|~rich(X)))))&
(![X]:((~quiet(X)|~happy(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((~humble(X)|kind(X))<=>(tall(X)&brave(X))))&
(![X]:((~old(X)|~generous(X))=>(strong(X)<~>brave(X))))&
(![X]:((brave(X)|~curious(X))=>(wise(X)&~humble(X))))&
(![X]:((~humble(X)&~quiet(X))=>(generous(X)|~wise(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(humble(X)|~tall(X))))&
(![X]:(creative(X)<=>(brave(X)&curious(X))))&
(![X]:(~quiet(X)<=>(~wise(X)&quiet(X))))&
(![X]:((~kind(X)|~rich(X))=>(~kind(X)<~>humble(X))))&
(?[X]:(~curious(X)))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(~calm(X)))&
((humble(john)<~>old(john)))&
(happy(john)) | ~quiet(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6450196490792062014277768
% SZS output start Proof for 6450196490792062014277768
15. ! [X0] : (~quiet(X0) <=> (quiet(X0) & ~wise(X0))) [input p14]
23. ~quiet(lucy) [input hypothesis]
62. ! [X0] : ((~quiet(X0) | (~quiet(X0) | wise(X0))) & ((quiet(X0) & ~wise(X0)) | quiet(X0))) [nnf transformation 15]
63. ! [X0] : ((~quiet(X0) | ~quiet(X0) | wise(X0)) & ((quiet(X0) & ~wise(X0)) | quiet(X0))) [flattening 62]
125. quiet(X0) | quiet(X0) [cnf transformation 63]
140. ~quiet(lucy) [cnf transformation 23]
142. quiet(X0) [duplicate literal removal 125]
267. $false [subsumption resolution 140,142]
% SZS output end Proof for 6450196490792062014277768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and generous then susan is creative and vice versa. If someone is both happy and not tall then someone is creative or not creative. If susan is either wise or patient then fred is rich or quiet and vice versa. If john is both brave and not rich then someone is both not rich and not strong. Everyone who is not patient or kind is both rich and not wise and vice versa. Everyone who is both funny and not tall is not strong and vice versa. If someone is curious then someone is brave or tall and vice versa. Everyone who is generous or not quiet is either not happy or generous. If someone is either wise or not patient then john is both wise and strong. If someone is happy or wise then someone is either not brave or not rich. Everyone who is not happy is brave. If someone is not humble then someone is either creative or not quiet. If john is both not rich and not creative then john is not patient or not curious. Everyone who is both not calm and generous is either creative or not curious and vice versa. Everyone who is not kind or strong is not quiet. If someone is rich then lucy is not tall or not curious. Someone is both curious and not creative. Fred is both not creative and not rich. Lucy is either quiet or old. Someone is quiet or tall. Someone is both quiet and kind. Someone is either not curious or brave. Someone is creative. Someone is either old or not wise. | John is not kind. | entailment | ((?[X]:((kind(X)&generous(X))))<=>(creative(susan)))&
((?[X]:((happy(X)&~tall(X))))=>(?[X]:((creative(X)|~creative(X)))))&
(((wise(susan)<~>patient(susan)))<=>((rich(fred)|quiet(fred))))&
(((brave(john)&~rich(john)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~patient(X)|kind(X))<=>(rich(X)&~wise(X))))&
(![X]:((funny(X)&~tall(X))<=>~strong(X)))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)|tall(X)))))&
(![X]:((generous(X)|~quiet(X))=>(~happy(X)<~>generous(X))))&
((?[X]:((wise(X)<~>~patient(X))))=>((wise(john)&strong(john))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((~brave(X)<~>~rich(X)))))&
(![X]:(~happy(X)=>brave(X)))&
((?[X]:(~humble(X)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(((~rich(john)&~creative(john)))=>((~patient(john)|~curious(john))))&
(![X]:((~calm(X)&generous(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~kind(X)|strong(X))=>~quiet(X)))&
((?[X]:(rich(X)))=>((~tall(lucy)|~curious(lucy))))&
(?[X]:((curious(X)&~creative(X))))&
((~creative(fred)&~rich(fred)))&
((quiet(lucy)<~>old(lucy)))&
(?[X]:((quiet(X)|tall(X))))&
(?[X]:((quiet(X)&kind(X))))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:(creative(X)))&
(?[X]:((old(X)<~>~wise(X)))) | ~kind(john) | [
"p2",
"p4",
"p8",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5587699521061426364403981
% SZS output start Proof for 5587699521061426364403981
3. (wise(susan) <~> patient(susan)) <=> (quiet(fred) | rich(fred)) [input p2]
5. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (~wise(X0) & rich(X0))) [input p4]
9. ? [X0] : (wise(X0) <~> ~patient(X0)) => (strong(john) & wise(john)) [input p8]
15. ! [X0] : ((strong(X0) | ~kind(X0)) => ~quiet(X0)) [input p14]
18. ~rich(fred) & ~creative(fred) [input p17]
25. kind(john) [input hypothesis]
35. (strong(john) & wise(john)) | ! [X0] : (wise(X0) <=> ~patient(X0)) [ennf transformation 9]
40. ! [X0] : (~quiet(X0) | (~strong(X0) & kind(X0))) [ennf transformation 15]
50. (((~patient(susan) | ~wise(susan)) & (patient(susan) | wise(susan))) | (~quiet(fred) & ~rich(fred))) & ((quiet(fred) | rich(fred)) | ((wise(susan) | ~patient(susan)) & (patient(susan) | ~wise(susan)))) [nnf transformation 3]
51. (((~patient(susan) | ~wise(susan)) & (patient(susan) | wise(susan))) | (~quiet(fred) & ~rich(fred))) & (quiet(fred) | rich(fred) | ((wise(susan) | ~patient(susan)) & (patient(susan) | ~wise(susan)))) [flattening 50]
54. ! [X0] : (((kind(X0) | ~patient(X0)) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | (~kind(X0) & patient(X0)))) [nnf transformation 5]
55. ! [X0] : ((kind(X0) | ~patient(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | (~kind(X0) & patient(X0)))) [flattening 54]
64. (strong(john) & wise(john)) | ! [X0] : ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))) [nnf transformation 35]
91. quiet(fred) | rich(fred) | wise(susan) | ~patient(susan) [cnf transformation 51]
99. ~kind(X0) | rich(X0) [cnf transformation 55]
100. ~wise(X0) | patient(X0) [cnf transformation 55]
101. ~wise(X0) | ~kind(X0) [cnf transformation 55]
113. wise(john) | ~patient(X0) | ~wise(X0) [cnf transformation 64]
114. wise(john) | wise(X0) | patient(X0) [cnf transformation 64]
129. ~quiet(X0) | kind(X0) [cnf transformation 40]
135. ~rich(fred) [cnf transformation 18]
146. kind(john) [cnf transformation 25]
167. 5 <=> quiet(fred) [avatar definition]
168. quiet(fred) <- (5) [avatar component clause 167]
171. 6 <=> wise(susan) [avatar definition]
172. wise(susan) <- (6) [avatar component clause 171]
175. 7 <=> patient(susan) [avatar definition]
177. ~patient(susan) <- (~7) [avatar component clause 175]
180. 8 <=> rich(fred) [avatar definition]
182. ~rich(fred) <- (~8) [avatar component clause 180]
186. ~7 | 6 | 8 | 5 [avatar split clause 91,167,180,171,175]
232. 19 <=> ! [X0] : patient(X0) [avatar definition]
233. patient(X0) <- (19) [avatar component clause 232]
241. 21 <=> ! [X0] : ~wise(X0) [avatar definition]
242. ~wise(X0) <- (21) [avatar component clause 241]
244. wise(john) | patient(X0) [subsumption resolution 114,100]
246. 22 <=> wise(john) [avatar definition]
248. wise(john) <- (22) [avatar component clause 246]
249. 19 | 22 [avatar split clause 244,246,232]
250. wise(john) | ~wise(X0) [subsumption resolution 113,100]
251. 21 | 22 [avatar split clause 250,246,241]
289. ~8 [avatar split clause 135,180]
331. $false <- (~7, 19) [subsumption resolution 177,233]
332. 7 | ~19 [avatar contradiction clause 331]
344. kind(fred) <- (5) [resolution 129,168]
348. rich(fred) <- (5) [resolution 344,99]
349. $false <- (5, ~8) [subsumption resolution 348,182]
350. ~5 | 8 [avatar contradiction clause 349]
351. $false <- (6, 21) [subsumption resolution 172,242]
352. ~6 | ~21 [avatar contradiction clause 351]
356. ~kind(john) <- (22) [resolution 248,101]
358. $false <- (22) [subsumption resolution 356,146]
359. ~22 [avatar contradiction clause 358]
360. $false [avatar sat refutation 186,249,251,289,332,350,352,359]
% SZS output end Proof for 5587699521061426364403981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and not patient is either quiet or not curious.
Everyone who is both not rich and funny is not happy or brave and vice versa.
Everyone who is either brave or not happy is humble or generous and vice versa.
Everyone who is both old and funny is happy.
If paul is strong then someone is both not calm and not quiet and vice versa.
If fred is either kind or calm then mary is both not brave and not happy and vice versa.
Everyone who is either not old or curious is generous or not kind.
If paul is not patient then lucy is both not happy and patient.
Everyone who is either generous or not creative is creative and vice versa.
If fred is both funny and not tall then mary is wise.
If alice is both old and generous then someone is quiet.
Everyone who is both not curious and creative is brave and vice versa.
If paul is both humble and not curious then someone is tall or happy and vice versa.
Everyone who is both funny and not brave is both not creative and old and vice versa.
Everyone who is not brave or not humble is either not old or not quiet and vice versa.
If someone is not quiet then alice is calm.
Someone is not calm or not strong.
Someone is not humble.
John is calm.
Fred is either generous or not quiet. | Paul is not creative. | contradiction | (![X]:((brave(X)&~patient(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)&funny(X))<=>(~happy(X)|brave(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(humble(X)|generous(X))))&
(![X]:((old(X)&funny(X))=>happy(X)))&
((strong(paul))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(((kind(fred)<~>calm(fred)))<=>((~brave(mary)&~happy(mary))))&
(![X]:((~old(X)<~>curious(X))=>(generous(X)|~kind(X))))&
((~patient(paul))=>((~happy(lucy)&patient(lucy))))&
(![X]:((generous(X)<~>~creative(X))<=>creative(X)))&
(((funny(fred)&~tall(fred)))=>(wise(mary)))&
(((old(alice)&generous(alice)))=>(?[X]:(quiet(X))))&
(![X]:((~curious(X)&creative(X))<=>brave(X)))&
(((humble(paul)&~curious(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(![X]:((funny(X)&~brave(X))<=>(~creative(X)&old(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:(~quiet(X)))=>(calm(alice)))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(calm(john))&
((generous(fred)<~>~quiet(fred))) | ~creative(paul) | [
"p1",
"p2",
"p3",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8356864450912725547823600
% SZS output start Proof for 8356864450912725547823600
2. ! [X0] : ((funny(X0) & ~rich(X0)) <=> (brave(X0) | ~happy(X0))) [input p1]
3. ! [X0] : ((brave(X0) <~> ~happy(X0)) <=> (generous(X0) | humble(X0))) [input p2]
4. ! [X0] : ((funny(X0) & old(X0)) => happy(X0)) [input p3]
9. ! [X0] : ((generous(X0) <~> ~creative(X0)) <=> creative(X0)) [input p8]
12. ! [X0] : ((creative(X0) & ~curious(X0)) <=> brave(X0)) [input p11]
14. ! [X0] : ((~brave(X0) & funny(X0)) <=> (old(X0) & ~creative(X0))) [input p13]
21. ~creative(paul) [input hypothesis]
25. ! [X0] : (happy(X0) | (~funny(X0) | ~old(X0))) [ennf transformation 4]
26. ! [X0] : (happy(X0) | ~funny(X0) | ~old(X0)) [flattening 25]
32. ! [X0] : (((funny(X0) & ~rich(X0)) | (~brave(X0) & happy(X0))) & ((brave(X0) | ~happy(X0)) | (~funny(X0) | rich(X0)))) [nnf transformation 2]
33. ! [X0] : (((funny(X0) & ~rich(X0)) | (~brave(X0) & happy(X0))) & (brave(X0) | ~happy(X0) | ~funny(X0) | rich(X0))) [flattening 32]
34. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [nnf transformation 3]
35. ! [X0] : ((((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0))))) [flattening 34]
43. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ~creative(X0)) & (creative(X0) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [nnf transformation 9]
46. ! [X0] : (((creative(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | (~creative(X0) | curious(X0)))) [nnf transformation 12]
47. ! [X0] : (((creative(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | ~creative(X0) | curious(X0))) [flattening 46]
53. ! [X0] : (((~brave(X0) & funny(X0)) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | (brave(X0) | ~funny(X0)))) [nnf transformation 14]
54. ! [X0] : (((~brave(X0) & funny(X0)) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | brave(X0) | ~funny(X0))) [flattening 53]
65. happy(X0) | funny(X0) [cnf transformation 33]
66. ~brave(X0) | funny(X0) [cnf transformation 33]
70. ~generous(X0) | brave(X0) | ~happy(X0) [cnf transformation 35]
72. ~generous(X0) | ~brave(X0) | happy(X0) [cnf transformation 35]
73. happy(X0) | ~funny(X0) | ~old(X0) [cnf transformation 26]
86. creative(X0) | generous(X0) | creative(X0) [cnf transformation 43]
87. ~creative(X0) | generous(X0) | ~creative(X0) [cnf transformation 43]
92. ~brave(X0) | creative(X0) [cnf transformation 47]
99. ~funny(X0) | brave(X0) | old(X0) [cnf transformation 54]
114. ~creative(paul) [cnf transformation 21]
115. creative(X0) | generous(X0) [duplicate literal removal 86]
116. ~creative(X0) | generous(X0) [duplicate literal removal 87]
117. ~old(X0) | happy(X0) [subsumption resolution 73,65]
158. generous(X0) [subsumption resolution 115,116]
220. ~happy(X0) | brave(X0) [resolution 70,158]
221. ~brave(X0) | happy(X0) [resolution 72,158]
231. brave(X0) | funny(X0) [resolution 220,65]
232. funny(X0) [subsumption resolution 231,66]
234. old(X0) | brave(X0) [resolution 232,99]
240. brave(X1) | happy(X1) [resolution 234,117]
241. happy(X1) [subsumption resolution 240,221]
248. brave(X0) [resolution 241,220]
261. creative(X1) [resolution 248,92]
287. $false [resolution 261,114]
% SZS output end Proof for 8356864450912725547823600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or brave then mary is both kind and happy.
Everyone who is either not calm or strong is not calm.
If someone is wise then someone is either not curious or funny.
Everyone who is curious or generous is both not strong and humble and vice versa.
Everyone who is creative or old is happy or kind.
Everyone who is curious is both brave and not calm.
If someone is not calm then someone is either patient or tall.
Everyone who is not curious is both creative and not wise.
Everyone who is not wise is quiet or not patient.
Everyone who is both not wise and not old is strong and vice versa.
Everyone who is either not creative or not brave is either not strong or strong and vice versa.
Everyone who is patient or calm is both creative and not tall and vice versa.
Everyone who is both not wise and not kind is rich or not creative.
Everyone who is not calm or not tall is happy and vice versa.
If alice is both not kind and not tall then alice is not brave.
If paul is not happy or not tall then someone is both not quiet and rich.
Lucy is not calm or not funny.
Someone is rich.
Someone is either not quiet or not kind.
Someone is both not brave and strong.
John is kind or wise.
Alice is brave.
Someone is either not rich or quiet. | Lucy is not funny. | neutral | (((~strong(fred)<~>brave(fred)))=>((kind(mary)&happy(mary))))&
(![X]:((~calm(X)<~>strong(X))=>~calm(X)))&
((?[X]:(wise(X)))=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:((curious(X)|generous(X))<=>(~strong(X)&humble(X))))&
(![X]:((creative(X)|old(X))=>(happy(X)|kind(X))))&
(![X]:(curious(X)=>(brave(X)&~calm(X))))&
((?[X]:(~calm(X)))=>(?[X]:((patient(X)<~>tall(X)))))&
(![X]:(~curious(X)=>(creative(X)&~wise(X))))&
(![X]:(~wise(X)=>(quiet(X)|~patient(X))))&
(![X]:((~wise(X)&~old(X))<=>strong(X)))&
(![X]:((~creative(X)<~>~brave(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)&~tall(X))))&
(![X]:((~wise(X)&~kind(X))=>(rich(X)|~creative(X))))&
(![X]:((~calm(X)|~tall(X))<=>happy(X)))&
(((~kind(alice)&~tall(alice)))=>(~brave(alice)))&
(((~happy(paul)|~tall(paul)))=>(?[X]:((~quiet(X)&rich(X)))))&
((~calm(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((~brave(X)&strong(X))))&
((kind(john)|wise(john)))&
(brave(alice))&
(?[X]:((~rich(X)<~>quiet(X)))) | ~funny(lucy) | [] | null | 0 |
If paul is both not rich and not funny then someone is either not creative or quiet.
Everyone who is not brave is not strong or old and vice versa.
Everyone who is both strong and not funny is creative or curious and vice versa.
If someone is both kind and not curious then someone is both not wise and not calm and vice versa.
If paul is generous or humble then mary is either not generous or calm.
If someone is not funny or not kind then mary is not humble or not tall and vice versa.
If someone is tall then someone is either not tall or not quiet and vice versa.
Everyone who is both not curious and creative is either calm or funny.
Everyone who is both happy and not humble is both humble and not old and vice versa.
If someone is both old and rich then someone is either brave or not strong and vice versa.
Everyone who is both creative and funny is both not strong and not calm.
If someone is curious then someone is either not rich or curious and vice versa.
Everyone who is curious is not calm.
Everyone who is happy or not brave is either not strong or not kind.
Everyone who is not old or creative is humble.
If fred is not patient or happy then someone is curious.
Someone is either not rich or creative.
Someone is calm.
Someone is either not strong or not generous.
Someone is strong.
Paul is both rich and not calm.
Paul is old.
Mary is either strong or not creative.
Fred is not funny or humble. | Fred is brave. | contradiction | (((~rich(paul)&~funny(paul)))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:(~brave(X)<=>(~strong(X)|old(X))))&
(![X]:((strong(X)&~funny(X))<=>(creative(X)|curious(X))))&
((?[X]:((kind(X)&~curious(X))))<=>(?[X]:((~wise(X)&~calm(X)))))&
(((generous(paul)|humble(paul)))=>((~generous(mary)<~>calm(mary))))&
((?[X]:((~funny(X)|~kind(X))))<=>((~humble(mary)|~tall(mary))))&
((?[X]:(tall(X)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~curious(X)&creative(X))=>(calm(X)<~>funny(X))))&
(![X]:((happy(X)&~humble(X))<=>(humble(X)&~old(X))))&
((?[X]:((old(X)&rich(X))))<=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:((creative(X)&funny(X))=>(~strong(X)&~calm(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:(curious(X)=>~calm(X)))&
(![X]:((happy(X)|~brave(X))=>(~strong(X)<~>~kind(X))))&
(![X]:((~old(X)|creative(X))=>humble(X)))&
(((~patient(fred)|happy(fred)))=>(?[X]:(curious(X))))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:(calm(X)))&
(?[X]:((~strong(X)<~>~generous(X))))&
(?[X]:(strong(X)))&
((rich(paul)&~calm(paul)))&
(old(paul))&
((strong(mary)<~>~creative(mary)))&
((~funny(fred)|humble(fred))) | brave(fred) | [
"p1",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6776616205576492055146844
% SZS output start Proof for 6776616205576492055146844
2. ! [X0] : (~brave(X0) <=> (old(X0) | ~strong(X0))) [input p1]
9. ! [X0] : ((~humble(X0) & happy(X0)) <=> (~old(X0) & humble(X0))) [input p8]
15. ! [X0] : ((creative(X0) | ~old(X0)) => humble(X0)) [input p14]
25. brave(fred) [input hypothesis]
40. ! [X0] : (humble(X0) | (~creative(X0) & old(X0))) [ennf transformation 15]
45. ! [X0] : ((~brave(X0) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | brave(X0))) [nnf transformation 2]
46. ! [X0] : ((~brave(X0) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | brave(X0))) [flattening 45]
66. ! [X0] : (((~humble(X0) & happy(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (humble(X0) | ~happy(X0)))) [nnf transformation 9]
67. ! [X0] : (((~humble(X0) & happy(X0)) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | humble(X0) | ~happy(X0))) [flattening 66]
96. ~old(X0) | ~brave(X0) [cnf transformation 46]
123. ~humble(X0) | old(X0) | ~humble(X0) [cnf transformation 67]
141. humble(X0) | old(X0) [cnf transformation 40]
156. brave(fred) [cnf transformation 25]
158. ~humble(X0) | old(X0) [duplicate literal removal 123]
286. 29 <=> ! [X1] : ~brave(X1) [avatar definition]
287. ~brave(X1) <- (29) [avatar component clause 286]
335. old(X0) [subsumption resolution 141,158]
387. $false <- (29) [resolution 287,156]
388. ~29 [avatar contradiction clause 387]
392. ~brave(X0) [resolution 96,335]
393. 29 [avatar split clause 392,286]
394. $false [avatar sat refutation 388,393]
% SZS output end Proof for 6776616205576492055146844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not happy then john is both not brave and wise. Everyone who is either funny or humble is both not tall and not wise and vice versa. If someone is either calm or not quiet then john is not kind and vice versa. Everyone who is either not brave or not funny is either not kind or not humble and vice versa. If someone is not creative or not tall then lucy is not funny or not old. Everyone who is not creative is either not curious or generous and vice versa. If mary is wise or not creative then mary is either not curious or not old. If john is both humble and patient then someone is both tall and not brave and vice versa. Everyone who is not rich or tall is both not quiet and funny. Everyone who is both not creative and not quiet is either not curious or quiet and vice versa. If someone is not calm or not happy then john is not funny or not wise. Everyone who is rich is both not kind and not wise. Everyone who is both not curious and not humble is either not humble or wise and vice versa. Everyone who is strong or funny is kind and vice versa. Everyone who is not old is either not kind or quiet. If someone is not tall or not brave then someone is creative. Someone is strong. Someone is strong or not funny. Someone is not happy. Someone is either not patient or not wise. Paul is both not wise and calm. Someone is not quiet. Someone is not funny. Fred is either not brave or strong. | Alice is not happy. | contradiction | ((~happy(alice))=>((~brave(john)&wise(john))))&
(![X]:((funny(X)<~>humble(X))<=>(~tall(X)&~wise(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(~kind(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>(~kind(X)<~>~humble(X))))&
((?[X]:((~creative(X)|~tall(X))))=>((~funny(lucy)|~old(lucy))))&
(![X]:(~creative(X)<=>(~curious(X)<~>generous(X))))&
(((wise(mary)|~creative(mary)))=>((~curious(mary)<~>~old(mary))))&
(((humble(john)&patient(john)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~rich(X)|tall(X))=>(~quiet(X)&funny(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~curious(X)<~>quiet(X))))&
((?[X]:((~calm(X)|~happy(X))))=>((~funny(john)|~wise(john))))&
(![X]:(rich(X)=>(~kind(X)&~wise(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)<~>wise(X))))&
(![X]:((strong(X)|funny(X))<=>kind(X)))&
(![X]:(~old(X)=>(~kind(X)<~>quiet(X))))&
((?[X]:((~tall(X)|~brave(X))))=>(?[X]:(creative(X))))&
(?[X]:(strong(X)))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~patient(X)<~>~wise(X))))&
((~wise(paul)&calm(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:(~funny(X)))&
((~brave(fred)<~>strong(fred))) | ~happy(alice) | [
"p0",
"p8",
"p10",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 406436868144691643390061
% SZS output start Proof for 406436868144691643390061
1. ~happy(alice) => (wise(john) & ~brave(john)) [input p0]
9. ! [X0] : ((tall(X0) | ~rich(X0)) => (funny(X0) & ~quiet(X0))) [input p8]
11. ? [X0] : (~happy(X0) | ~calm(X0)) => (~wise(john) | ~funny(john)) [input p10]
12. ! [X0] : (rich(X0) => (~wise(X0) & ~kind(X0))) [input p11]
19. ? [X0] : ~happy(X0) [input p18]
25. ~happy(alice) [input hypothesis]
27. (wise(john) & ~brave(john)) | happy(alice) [ennf transformation 1]
31. ! [X0] : ((funny(X0) & ~quiet(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 9]
32. (~wise(john) | ~funny(john)) | ! [X0] : (happy(X0) & calm(X0)) [ennf transformation 11]
33. ~wise(john) | ~funny(john) | ! [X0] : (happy(X0) & calm(X0)) [flattening 32]
34. ! [X0] : ((~wise(X0) & ~kind(X0)) | ~rich(X0)) [ennf transformation 12]
65. ? [X0] : ~happy(X0) => ~happy(sK5) [choice axiom]
66. ~happy(sK5) [skolemisation 19,65]
76. wise(john) | happy(alice) [cnf transformation 27]
111. rich(X0) | funny(X0) [cnf transformation 31]
120. ~wise(john) | ~funny(john) | happy(X0) [cnf transformation 33]
122. ~rich(X0) | ~wise(X0) [cnf transformation 34]
138. ~happy(sK5) [cnf transformation 66]
147. ~happy(alice) [cnf transformation 25]
153. 1 <=> happy(alice) [avatar definition]
157. 2 <=> wise(john) [avatar definition]
159. wise(john) <- (2) [avatar component clause 157]
160. 1 | 2 [avatar split clause 76,157,153]
249. 22 <=> ! [X0] : happy(X0) [avatar definition]
250. happy(X0) <- (22) [avatar component clause 249]
252. 23 <=> funny(john) [avatar definition]
255. 22 | ~23 | ~2 [avatar split clause 120,157,252,249]
299. ~1 [avatar split clause 147,153]
305. ~wise(X0) | funny(X0) [resolution 122,111]
315. funny(john) <- (2) [resolution 305,159]
318. 23 | ~2 [avatar split clause 315,157,252]
319. $false <- (22) [resolution 250,138]
322. ~22 [avatar contradiction clause 319]
323. $false [avatar sat refutation 160,255,299,318,322]
% SZS output end Proof for 406436868144691643390061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or not generous is both patient and old and vice versa.
If someone is both rich and not patient then someone is either not kind or not funny and vice versa.
Everyone who is kind is tall and vice versa.
If someone is both not funny and not quiet then john is both wise and happy and vice versa.
If someone is either calm or creative then someone is both humble and funny.
If lucy is old then susan is not humble.
If someone is curious or not curious then john is both not quiet and not happy and vice versa.
Everyone who is both not tall and wise is not strong and vice versa.
If mary is creative then paul is not tall or generous and vice versa.
If someone is tall then susan is either tall or not funny.
Everyone who is not brave or quiet is either strong or not happy.
If someone is both not creative and rich then someone is both not wise and happy and vice versa.
Everyone who is creative or curious is both not kind and quiet.
Everyone who is patient is rich and vice versa.
If someone is not strong then someone is kind.
Everyone who is either not humble or not calm is both not rich and generous.
Someone is brave.
Someone is either not funny or funny.
Someone is tall.
Someone is curious or not old.
Someone is strong.
Fred is old.
Susan is not quiet or not humble. | John is kind. | entailment | (![X]:((generous(X)|~generous(X))<=>(patient(X)&old(X))))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:(kind(X)<=>tall(X)))&
((?[X]:((~funny(X)&~quiet(X))))<=>((wise(john)&happy(john))))&
((?[X]:((calm(X)<~>creative(X))))=>(?[X]:((humble(X)&funny(X)))))&
((old(lucy))=>(~humble(susan)))&
((?[X]:((curious(X)|~curious(X))))<=>((~quiet(john)&~happy(john))))&
(![X]:((~tall(X)&wise(X))<=>~strong(X)))&
((creative(mary))<=>((~tall(paul)|generous(paul))))&
((?[X]:(tall(X)))=>((tall(susan)<~>~funny(susan))))&
(![X]:((~brave(X)|quiet(X))=>(strong(X)<~>~happy(X))))&
((?[X]:((~creative(X)&rich(X))))<=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((creative(X)|curious(X))=>(~kind(X)&quiet(X))))&
(![X]:(patient(X)<=>rich(X)))&
((?[X]:(~strong(X)))=>(?[X]:(kind(X))))&
(![X]:((~humble(X)<~>~calm(X))=>(~rich(X)&generous(X))))&
(?[X]:(brave(X)))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:(strong(X)))&
(old(fred))&
((~quiet(susan)|~humble(susan))) | kind(john) | [
"p0",
"p1",
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3838064630674686955342197
% SZS output start Proof for 3838064630674686955342197
1. ! [X0] : ((~generous(X0) | generous(X0)) <=> (old(X0) & patient(X0))) [input p0]
2. ? [X0] : (~patient(X0) & rich(X0)) <=> ? [X0] : (~kind(X0) <~> ~funny(X0)) [input p1]
4. ? [X0] : (~quiet(X0) & ~funny(X0)) <=> (happy(john) & wise(john)) [input p3]
7. ? [X0] : (~curious(X0) | curious(X0)) <=> (~happy(john) & ~quiet(john)) [input p6]
24. ~kind(john) [input hypothesis]
25. ? [X0] : (~patient(X0) & rich(X0)) <=> ? [X1] : (~kind(X1) <~> ~funny(X1)) [rectify 2]
38. ! [X0] : (((~generous(X0) | generous(X0)) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | (generous(X0) & ~generous(X0)))) [nnf transformation 1]
39. ! [X0] : ((~generous(X0) | generous(X0) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | (generous(X0) & ~generous(X0)))) [flattening 38]
40. (? [X0] : (~patient(X0) & rich(X0)) | ! [X1] : ((~kind(X1) | funny(X1)) & (~funny(X1) | kind(X1)))) & (? [X1] : ((funny(X1) | kind(X1)) & (~funny(X1) | ~kind(X1))) | ! [X0] : (patient(X0) | ~rich(X0))) [nnf transformation 25]
41. (? [X0] : (~patient(X0) & rich(X0)) | ! [X1] : ((~kind(X1) | funny(X1)) & (~funny(X1) | kind(X1)))) & (? [X2] : ((funny(X2) | kind(X2)) & (~funny(X2) | ~kind(X2))) | ! [X3] : (patient(X3) | ~rich(X3))) [rectify 40]
42. ? [X0] : (~patient(X0) & rich(X0)) => (~patient(sK0) & rich(sK0)) [choice axiom]
43. ? [X2] : ((funny(X2) | kind(X2)) & (~funny(X2) | ~kind(X2))) => ((funny(sK1) | kind(sK1)) & (~funny(sK1) | ~kind(sK1))) [choice axiom]
44. ((~patient(sK0) & rich(sK0)) | ! [X1] : ((~kind(X1) | funny(X1)) & (~funny(X1) | kind(X1)))) & (((funny(sK1) | kind(sK1)) & (~funny(sK1) | ~kind(sK1))) | ! [X3] : (patient(X3) | ~rich(X3))) [skolemisation 41,43,42]
46. (? [X0] : (~quiet(X0) & ~funny(X0)) | (~happy(john) | ~wise(john))) & ((happy(john) & wise(john)) | ! [X0] : (quiet(X0) | funny(X0))) [nnf transformation 4]
47. (? [X0] : (~quiet(X0) & ~funny(X0)) | ~happy(john) | ~wise(john)) & ((happy(john) & wise(john)) | ! [X0] : (quiet(X0) | funny(X0))) [flattening 46]
48. (? [X0] : (~quiet(X0) & ~funny(X0)) | ~happy(john) | ~wise(john)) & ((happy(john) & wise(john)) | ! [X1] : (quiet(X1) | funny(X1))) [rectify 47]
49. ? [X0] : (~quiet(X0) & ~funny(X0)) => (~quiet(sK2) & ~funny(sK2)) [choice axiom]
50. ((~quiet(sK2) & ~funny(sK2)) | ~happy(john) | ~wise(john)) & ((happy(john) & wise(john)) | ! [X1] : (quiet(X1) | funny(X1))) [skolemisation 48,49]
55. (? [X0] : (~curious(X0) | curious(X0)) | (happy(john) | quiet(john))) & ((~happy(john) & ~quiet(john)) | ! [X0] : (curious(X0) & ~curious(X0))) [nnf transformation 7]
56. (? [X0] : (~curious(X0) | curious(X0)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X0] : (curious(X0) & ~curious(X0))) [flattening 55]
57. (? [X0] : (~curious(X0) | curious(X0)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X1] : (curious(X1) & ~curious(X1))) [rectify 56]
58. ? [X0] : (~curious(X0) | curious(X0)) => (~curious(sK4) | curious(sK4)) [choice axiom]
59. ((~curious(sK4) | curious(sK4)) | happy(john) | quiet(john)) & ((~happy(john) & ~quiet(john)) | ! [X1] : (curious(X1) & ~curious(X1))) [skolemisation 57,58]
85. patient(X0) | ~generous(X0) [cnf transformation 39]
86. patient(X0) | generous(X0) [cnf transformation 39]
94. ~patient(sK0) | ~funny(X1) | kind(X1) [cnf transformation 44]
99. happy(john) | quiet(X1) | funny(X1) [cnf transformation 50]
107. ~quiet(john) | ~curious(X1) [cnf transformation 59]
108. ~quiet(john) | curious(X1) [cnf transformation 59]
109. ~happy(john) | ~curious(X1) [cnf transformation 59]
110. ~happy(john) | curious(X1) [cnf transformation 59]
144. ~kind(john) [cnf transformation 24]
146. patient(X0) [subsumption resolution 85,86]
148. ~funny(X1) | kind(X1) [subsumption resolution 94,146]
154. 2 <=> happy(john) [avatar definition]
168. 5 <=> ! [X1] : (quiet(X1) | funny(X1)) [avatar definition]
169. quiet(X1) | funny(X1) <- (5) [avatar component clause 168]
170. 5 | 2 [avatar split clause 99,154,168]
192. 10 <=> ! [X1] : curious(X1) [avatar definition]
193. curious(X1) <- (10) [avatar component clause 192]
194. 10 | ~2 [avatar split clause 110,154,192]
196. 11 <=> ! [X1] : ~curious(X1) [avatar definition]
197. ~curious(X1) <- (11) [avatar component clause 196]
198. 11 | ~2 [avatar split clause 109,154,196]
200. 12 <=> quiet(john) [avatar definition]
202. ~quiet(john) <- (~12) [avatar component clause 200]
203. 10 | ~12 [avatar split clause 108,200,192]
204. 11 | ~12 [avatar split clause 107,200,196]
285. funny(john) <- (5, ~12) [resolution 169,202]
287. kind(john) <- (5, ~12) [resolution 285,148]
288. $false <- (5, ~12) [subsumption resolution 287,144]
289. ~5 | 12 [avatar contradiction clause 288]
290. $false <- (10, 11) [subsumption resolution 193,197]
291. ~10 | ~11 [avatar contradiction clause 290]
292. $false [avatar sat refutation 170,194,198,203,204,289,291]
% SZS output end Proof for 3838064630674686955342197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not generous is patient or curious.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Everyone who is both generous and humble is either not wise or wise and vice versa.
If someone is both not brave and generous then fred is either not wise or not quiet and vice versa.
Everyone who is not curious or strong is both patient and not curious and vice versa.
Everyone who is not curious or not calm is both not quiet and not brave and vice versa.
If alice is not tall then lucy is not rich or not tall.
If someone is brave or not humble then john is patient.
Everyone who is not kind is not tall or happy.
If someone is either brave or calm then mary is both tall and not happy.
Everyone who is both not quiet and humble is tall or not humble and vice versa.
If mary is either not patient or not funny then someone is rich and vice versa.
If susan is generous then mary is either happy or kind and vice versa.
If someone is both not funny and not creative then paul is both brave and creative.
Someone is either tall or kind.
Alice is either quiet or not quiet.
Susan is not tall.
Someone is not wise or quiet.
Susan is either curious or patient.
Someone is either not old or not calm.
John is both not wise and not funny.
Someone is funny. | Mary is not humble. | contradiction | (![X]:((quiet(X)<~>~generous(X))=>(patient(X)|curious(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((generous(X)&humble(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((~curious(X)|strong(X))<=>(patient(X)&~curious(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&~brave(X))))&
((~tall(alice))=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((brave(X)|~humble(X))))=>(patient(john)))&
(![X]:(~kind(X)=>(~tall(X)|happy(X))))&
((?[X]:((brave(X)<~>calm(X))))=>((tall(mary)&~happy(mary))))&
(![X]:((~quiet(X)&humble(X))<=>(tall(X)|~humble(X))))&
(((~patient(mary)<~>~funny(mary)))<=>(?[X]:(rich(X))))&
((generous(susan))<=>((happy(mary)<~>kind(mary))))&
((?[X]:((~funny(X)&~creative(X))))=>((brave(paul)&creative(paul))))&
(?[X]:((tall(X)<~>kind(X))))&
((quiet(alice)<~>~quiet(alice)))&
(~tall(susan))&
(?[X]:((~wise(X)|quiet(X))))&
((curious(susan)<~>patient(susan)))&
(?[X]:((~old(X)<~>~calm(X))))&
((~wise(john)&~funny(john)))&
(?[X]:(funny(X))) | ~humble(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3593232784265257553666548
% SZS output start Proof for 3593232784265257553666548
5. ! [X0] : ((humble(X0) & generous(X0)) <=> (~wise(X0) <~> wise(X0))) [input p4]
25. ~humble(mary) [input hypothesis]
42. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~humble(X0) | ~generous(X0))) [flattening 42]
85. humble(X0) | wise(X0) | wise(X0) [cnf transformation 43]
86. humble(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 43]
139. ~humble(mary) [cnf transformation 25]
144. humble(X0) | wise(X0) [duplicate literal removal 85]
145. humble(X0) | ~wise(X0) [duplicate literal removal 86]
146. humble(X0) [subsumption resolution 144,145]
282. $false [subsumption resolution 139,146]
% SZS output end Proof for 3593232784265257553666548
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either brave or not brave is not funny or not humble.
Everyone who is not old is strong and vice versa.
If paul is either not quiet or not creative then someone is funny or not tall and vice versa.
Everyone who is not creative is not curious.
If fred is humble then someone is not funny or not kind and vice versa.
If someone is not old or calm then fred is both quiet and not happy.
Everyone who is either not strong or strong is funny.
Everyone who is creative or wise is both brave and not generous and vice versa.
If mary is both curious and not quiet then someone is old or not strong.
If lucy is either not tall or tall then mary is either calm or strong and vice versa.
Everyone who is not old is kind.
If paul is both happy and not kind then someone is both creative and wise and vice versa.
Everyone who is quiet is not creative and vice versa.
Everyone who is strong is calm or not old and vice versa.
If someone is not kind then someone is patient and vice versa.
If someone is either calm or not kind then lucy is strong or not funny.
Someone is happy.
Fred is either generous or patient.
Mary is not patient.
Someone is generous or not funny.
Lucy is strong or not kind.
Someone is curious. | Lucy is kind. | entailment | (![X]:((brave(X)<~>~brave(X))=>(~funny(X)|~humble(X))))&
(![X]:(~old(X)<=>strong(X)))&
(((~quiet(paul)<~>~creative(paul)))<=>(?[X]:((funny(X)|~tall(X)))))&
(![X]:(~creative(X)=>~curious(X)))&
((humble(fred))<=>(?[X]:((~funny(X)|~kind(X)))))&
((?[X]:((~old(X)|calm(X))))=>((quiet(fred)&~happy(fred))))&
(![X]:((~strong(X)<~>strong(X))=>funny(X)))&
(![X]:((creative(X)|wise(X))<=>(brave(X)&~generous(X))))&
(((curious(mary)&~quiet(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(((~tall(lucy)<~>tall(lucy)))<=>((calm(mary)<~>strong(mary))))&
(![X]:(~old(X)=>kind(X)))&
(((happy(paul)&~kind(paul)))<=>(?[X]:((creative(X)&wise(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(![X]:(strong(X)<=>(calm(X)|~old(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(patient(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((strong(lucy)|~funny(lucy))))&
(?[X]:(happy(X)))&
((generous(fred)<~>patient(fred)))&
(~patient(mary))&
(?[X]:((generous(X)|~funny(X))))&
((strong(lucy)|~kind(lucy)))&
(?[X]:(curious(X))) | kind(lucy) | [
"p0",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3836058676412908024130798
% SZS output start Proof for 3836058676412908024130798
1. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (~humble(X0) | ~funny(X0))) [input p0]
5. humble(fred) <=> ? [X0] : (~kind(X0) | ~funny(X0)) [input p4]
7. ! [X0] : ((~strong(X0) <~> strong(X0)) => funny(X0)) [input p6]
23. ~kind(lucy) [input hypothesis]
25. ! [X0] : ((~humble(X0) | ~funny(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 1]
26. ! [X0] : (~humble(X0) | ~funny(X0) | (brave(X0) <=> ~brave(X0))) [flattening 25]
29. ! [X0] : (funny(X0) | (~strong(X0) <=> strong(X0))) [ennf transformation 7]
35. ! [X0] : (~humble(X0) | ~funny(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 26]
41. (humble(fred) | ! [X0] : (kind(X0) & funny(X0))) & (? [X0] : (~kind(X0) | ~funny(X0)) | ~humble(fred)) [nnf transformation 5]
42. (humble(fred) | ! [X0] : (kind(X0) & funny(X0))) & (? [X1] : (~kind(X1) | ~funny(X1)) | ~humble(fred)) [rectify 41]
43. ? [X1] : (~kind(X1) | ~funny(X1)) => (~kind(sK1) | ~funny(sK1)) [choice axiom]
44. (humble(fred) | ! [X0] : (kind(X0) & funny(X0))) & ((~kind(sK1) | ~funny(sK1)) | ~humble(fred)) [skolemisation 42,43]
45. ! [X0] : (funny(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 29]
72. ~humble(X0) | ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 35]
73. ~humble(X0) | ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 35]
85. humble(fred) | kind(X0) [cnf transformation 44]
90. funny(X0) | strong(X0) | strong(X0) [cnf transformation 45]
91. funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 45]
127. ~kind(lucy) [cnf transformation 23]
132. funny(X0) | strong(X0) [duplicate literal removal 90]
133. ~strong(X0) | funny(X0) [duplicate literal removal 91]
134. ~humble(X0) | ~funny(X0) | ~brave(X0) [duplicate literal removal 72]
135. ~humble(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 73]
136. ~humble(X0) | ~funny(X0) [subsumption resolution 134,135]
166. 7 <=> ! [X0] : kind(X0) [avatar definition]
167. kind(X0) <- (7) [avatar component clause 166]
169. 8 <=> humble(fred) [avatar definition]
171. humble(fred) <- (8) [avatar component clause 169]
172. 7 | 8 [avatar split clause 85,169,166]
174. 9 <=> ! [X0] : funny(X0) [avatar definition]
175. funny(X0) <- (9) [avatar component clause 174]
204. funny(X0) [subsumption resolution 132,133]
205. 9 [avatar split clause 204,174]
308. 38 <=> kind(lucy) [avatar definition]
310. ~kind(lucy) <- (~38) [avatar component clause 308]
312. ~38 [avatar split clause 127,308]
323. $false <- (7, ~38) [resolution 310,167]
324. ~7 | 38 [avatar contradiction clause 323]
358. ~funny(fred) <- (8) [resolution 136,171]
359. $false <- (8, 9) [subsumption resolution 358,175]
360. ~8 | ~9 [avatar contradiction clause 359]
361. $false [avatar sat refutation 172,205,312,324,360]
% SZS output end Proof for 3836058676412908024130798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or funny is quiet and vice versa. Everyone who is strong is either wise or quiet and vice versa. Everyone who is either rich or not humble is both not old and generous and vice versa. Everyone who is curious or creative is either not generous or funny. If mary is not generous or funny then someone is either rich or old. If paul is curious or not brave then someone is either strong or kind. If someone is either tall or patient then someone is both not happy and wise and vice versa. Everyone who is not kind is both curious and not humble and vice versa. Everyone who is curious is not creative and vice versa. Everyone who is not calm or brave is either curious or generous. Everyone who is either not brave or happy is brave. If john is not happy then someone is not brave or not tall and vice versa. If lucy is not rich or not generous then john is either not kind or not creative and vice versa. Everyone who is either not tall or funny is either quiet or happy. Everyone who is either not old or not generous is kind or not generous. Everyone who is either old or humble is either quiet or not quiet and vice versa. Someone is either strong or humble. Someone is not rich or happy. John is either not quiet or not strong. Someone is brave. Someone is either not curious or not kind. Paul is tall. Someone is either not wise or not old. Lucy is both not quiet and not old. | John is not kind. | contradiction | (![X]:((~quiet(X)<~>funny(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(wise(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>(~old(X)&generous(X))))&
(![X]:((curious(X)|creative(X))=>(~generous(X)<~>funny(X))))&
(((~generous(mary)|funny(mary)))=>(?[X]:((rich(X)<~>old(X)))))&
(((curious(paul)|~brave(paul)))=>(?[X]:((strong(X)<~>kind(X)))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:(~kind(X)<=>(curious(X)&~humble(X))))&
(![X]:(curious(X)<=>~creative(X)))&
(![X]:((~calm(X)|brave(X))=>(curious(X)<~>generous(X))))&
(![X]:((~brave(X)<~>happy(X))=>brave(X)))&
((~happy(john))<=>(?[X]:((~brave(X)|~tall(X)))))&
(((~rich(lucy)|~generous(lucy)))<=>((~kind(john)<~>~creative(john))))&
(![X]:((~tall(X)<~>funny(X))=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)<~>~generous(X))=>(kind(X)|~generous(X))))&
(![X]:((old(X)<~>humble(X))<=>(quiet(X)<~>~quiet(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:((~rich(X)|happy(X))))&
((~quiet(john)<~>~strong(john)))&
(?[X]:(brave(X)))&
(?[X]:((~curious(X)<~>~kind(X))))&
(tall(paul))&
(?[X]:((~wise(X)<~>~old(X))))&
((~quiet(lucy)&~old(lucy))) | ~kind(john) | [
"p0",
"p3",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2293598486838441959214871
% SZS output start Proof for 2293598486838441959214871
1. ! [X0] : ((~quiet(X0) <~> funny(X0)) <=> quiet(X0)) [input p0]
4. ! [X0] : ((creative(X0) | curious(X0)) => (~generous(X0) <~> funny(X0))) [input p3]
8. ! [X0] : (~kind(X0) <=> (~humble(X0) & curious(X0))) [input p7]
10. ! [X0] : ((brave(X0) | ~calm(X0)) => (curious(X0) <~> generous(X0))) [input p9]
11. ! [X0] : ((~brave(X0) <~> happy(X0)) => brave(X0)) [input p10]
12. ~happy(john) <=> ? [X0] : (~tall(X0) | ~brave(X0)) [input p11]
25. ~kind(john) [input hypothesis]
27. ! [X0] : (brave(X0) => (curious(X0) <~> generous(X0))) [pure predicate removal 10]
28. ! [X0] : ((~generous(X0) <~> funny(X0)) | (~creative(X0) & ~curious(X0))) [ennf transformation 4]
31. ! [X0] : ((curious(X0) <~> generous(X0)) | ~brave(X0)) [ennf transformation 27]
32. ! [X0] : (brave(X0) | (~brave(X0) <=> happy(X0))) [ennf transformation 11]
36. ! [X0] : ((((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0))))) [nnf transformation 1]
40. ! [X0] : (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | (~creative(X0) & ~curious(X0))) [nnf transformation 28]
52. ! [X0] : ((~kind(X0) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | kind(X0))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | kind(X0))) [flattening 52]
55. ! [X0] : (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ~brave(X0)) [nnf transformation 31]
56. ! [X0] : (brave(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) [nnf transformation 32]
57. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | happy(john)) [nnf transformation 12]
58. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & (? [X1] : (~tall(X1) | ~brave(X1)) | happy(john)) [rectify 57]
59. ? [X1] : (~tall(X1) | ~brave(X1)) => (~tall(sK4) | ~brave(sK4)) [choice axiom]
60. (~happy(john) | ! [X0] : (tall(X0) & brave(X0))) & ((~tall(sK4) | ~brave(sK4)) | happy(john)) [skolemisation 58,59]
80. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 36]
82. funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 36]
96. ~funny(X0) | generous(X0) | ~curious(X0) [cnf transformation 40]
112. kind(X0) | curious(X0) [cnf transformation 53]
118. ~generous(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 55]
119. brave(X0) | happy(X0) | brave(X0) [cnf transformation 56]
122. ~happy(john) | brave(X0) [cnf transformation 60]
157. ~kind(john) [cnf transformation 25]
163. happy(X0) | brave(X0) [duplicate literal removal 119]
164. quiet(X0) | funny(X0) [duplicate literal removal 80]
165. ~quiet(X0) | funny(X0) [duplicate literal removal 82]
166. funny(X0) [subsumption resolution 164,165]
168. ~curious(X0) | generous(X0) [subsumption resolution 96,166]
238. ~brave(X0) | ~curious(X0) [subsumption resolution 118,168]
244. 16 <=> happy(john) [avatar definition]
246. ~happy(john) <- (~16) [avatar component clause 244]
249. 17 <=> ! [X0] : brave(X0) [avatar definition]
250. brave(X0) <- (17) [avatar component clause 249]
251. 17 | ~16 [avatar split clause 122,244,249]
266. 21 <=> kind(john) [avatar definition]
268. ~kind(john) <- (~21) [avatar component clause 266]
335. ~21 [avatar split clause 157,266]
336. curious(john) <- (~21) [resolution 112,268]
343. brave(john) <- (~16) [resolution 163,246]
353. ~curious(john) <- (~16) [resolution 238,343]
356. $false <- (~16, ~21) [subsumption resolution 353,336]
357. 16 | 21 [avatar contradiction clause 356]
360. ~curious(X0) <- (17) [resolution 250,238]
366. $false <- (17, ~21) [resolution 360,336]
367. ~17 | 21 [avatar contradiction clause 366]
368. $false [avatar sat refutation 251,335,357,367]
% SZS output end Proof for 2293598486838441959214871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and tall is both quiet and not generous. Everyone who is not rich or curious is both brave and humble and vice versa. If fred is strong or not quiet then someone is both generous and happy. If someone is either not funny or tall then someone is either calm or not humble. Everyone who is patient is curious. If someone is not happy then someone is not humble or not brave. Everyone who is either old or not calm is either rich or patient and vice versa. If someone is rich then lucy is not quiet or humble and vice versa. If someone is quiet or not wise then mary is not creative and vice versa. Everyone who is either not brave or not creative is not creative or not humble and vice versa. Everyone who is not patient is either not calm or kind. If someone is either calm or tall then someone is both not calm and not generous and vice versa. If mary is happy then someone is kind or brave. If someone is tall or not kind then susan is not rich or curious and vice versa. Everyone who is either not happy or curious is both kind and not quiet and vice versa. Everyone who is either happy or humble is either not quiet or not brave and vice versa. Lucy is not tall or not brave. Fred is not happy or not quiet. Paul is both not patient and quiet. John is not creative. Lucy is quiet. Someone is both not humble and kind. Someone is funny or patient. Susan is brave. | Lucy is humble. | entailment | (![X]:((~curious(X)&tall(X))=>(quiet(X)&~generous(X))))&
(![X]:((~rich(X)|curious(X))<=>(brave(X)&humble(X))))&
(((strong(fred)|~quiet(fred)))=>(?[X]:((generous(X)&happy(X)))))&
((?[X]:((~funny(X)<~>tall(X))))=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:(patient(X)=>curious(X)))&
((?[X]:(~happy(X)))=>(?[X]:((~humble(X)|~brave(X)))))&
(![X]:((old(X)<~>~calm(X))<=>(rich(X)<~>patient(X))))&
((?[X]:(rich(X)))<=>((~quiet(lucy)|humble(lucy))))&
((?[X]:((quiet(X)|~wise(X))))<=>(~creative(mary)))&
(![X]:((~brave(X)<~>~creative(X))<=>(~creative(X)|~humble(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
((happy(mary))=>(?[X]:((kind(X)|brave(X)))))&
((?[X]:((tall(X)|~kind(X))))<=>((~rich(susan)|curious(susan))))&
(![X]:((~happy(X)<~>curious(X))<=>(kind(X)&~quiet(X))))&
(![X]:((happy(X)<~>humble(X))<=>(~quiet(X)<~>~brave(X))))&
((~tall(lucy)|~brave(lucy)))&
((~happy(fred)|~quiet(fred)))&
((~patient(paul)&quiet(paul)))&
(~creative(john))&
(quiet(lucy))&
(?[X]:((~humble(X)&kind(X))))&
(?[X]:((funny(X)|patient(X))))&
(brave(susan)) | humble(lucy) | [
"p1",
"p7",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 382105394161638711547737
% SZS output start Proof for 382105394161638711547737
2. ! [X0] : ((curious(X0) | ~rich(X0)) <=> (humble(X0) & brave(X0))) [input p1]
8. ? [X0] : rich(X0) <=> (humble(lucy) | ~quiet(lucy)) [input p7]
21. quiet(lucy) [input p20]
22. ? [X0] : (kind(X0) & ~humble(X0)) [input p21]
25. ~humble(lucy) [input hypothesis]
38. ! [X0] : (((curious(X0) | ~rich(X0)) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | (~curious(X0) & rich(X0)))) [nnf transformation 2]
39. ! [X0] : ((curious(X0) | ~rich(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | (~curious(X0) & rich(X0)))) [flattening 38]
50. (? [X0] : rich(X0) | (~humble(lucy) & quiet(lucy))) & ((humble(lucy) | ~quiet(lucy)) | ! [X0] : ~rich(X0)) [nnf transformation 8]
51. (? [X0] : rich(X0) | (~humble(lucy) & quiet(lucy))) & (humble(lucy) | ~quiet(lucy) | ! [X0] : ~rich(X0)) [flattening 50]
52. (? [X0] : rich(X0) | (~humble(lucy) & quiet(lucy))) & (humble(lucy) | ~quiet(lucy) | ! [X1] : ~rich(X1)) [rectify 51]
53. ? [X0] : rich(X0) => rich(sK3) [choice axiom]
54. (rich(sK3) | (~humble(lucy) & quiet(lucy))) & (humble(lucy) | ~quiet(lucy) | ! [X1] : ~rich(X1)) [skolemisation 52,53]
77. ? [X0] : (kind(X0) & ~humble(X0)) => (kind(sK9) & ~humble(sK9)) [choice axiom]
78. kind(sK9) & ~humble(sK9) [skolemisation 22,77]
85. humble(X0) | rich(X0) [cnf transformation 39]
104. humble(lucy) | ~quiet(lucy) | ~rich(X1) [cnf transformation 54]
148. quiet(lucy) [cnf transformation 21]
149. ~humble(sK9) [cnf transformation 78]
153. ~humble(lucy) [cnf transformation 25]
201. 11 <=> humble(lucy) [avatar definition]
210. 13 <=> quiet(lucy) [avatar definition]
215. 14 <=> ! [X1] : ~rich(X1) [avatar definition]
216. ~rich(X1) <- (14) [avatar component clause 215]
217. 14 | ~13 | 11 [avatar split clause 104,201,210,215]
328. 13 [avatar split clause 148,210]
338. ~11 [avatar split clause 153,201]
345. rich(sK9) [resolution 85,149]
352. $false <- (14) [subsumption resolution 345,216]
353. ~14 [avatar contradiction clause 352]
354. $false [avatar sat refutation 217,328,338,353]
% SZS output end Proof for 382105394161638711547737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not kind is both not happy and humble and vice versa. If someone is either quiet or not kind then someone is wise and vice versa. Everyone who is both rich and not old is both rich and strong. Everyone who is old is quiet or happy and vice versa. Everyone who is either not creative or curious is brave. Everyone who is not wise or kind is both curious and generous and vice versa. If someone is both rich and kind then someone is both tall and funny and vice versa. Everyone who is tall is either not old or rich. Everyone who is both generous and not brave is generous and vice versa. Everyone who is either not creative or happy is not generous. If someone is both tall and old then susan is not happy. Everyone who is both brave and generous is both quiet and tall and vice versa. If someone is not tall or quiet then someone is not curious and vice versa. Everyone who is not quiet is not happy. If mary is not strong then someone is either creative or not tall and vice versa. If someone is tall then someone is not curious or happy. Someone is both not rich and not strong. Someone is not old. Alice is either not kind or generous. Someone is either funny or not kind. Mary is both creative and not humble. Paul is either not kind or not happy. Paul is calm. Someone is both strong and not funny. | Paul is not funny. | entailment | (![X]:((~funny(X)<~>~kind(X))<=>(~happy(X)&humble(X))))&
((?[X]:((quiet(X)<~>~kind(X))))<=>(?[X]:(wise(X))))&
(![X]:((rich(X)&~old(X))=>(rich(X)&strong(X))))&
(![X]:(old(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>curious(X))=>brave(X)))&
(![X]:((~wise(X)|kind(X))<=>(curious(X)&generous(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(tall(X)=>(~old(X)<~>rich(X))))&
(![X]:((generous(X)&~brave(X))<=>generous(X)))&
(![X]:((~creative(X)<~>happy(X))=>~generous(X)))&
((?[X]:((tall(X)&old(X))))=>(~happy(susan)))&
(![X]:((brave(X)&generous(X))<=>(quiet(X)&tall(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~quiet(X)=>~happy(X)))&
((~strong(mary))<=>(?[X]:((creative(X)<~>~tall(X)))))&
((?[X]:(tall(X)))=>(?[X]:((~curious(X)|happy(X)))))&
(?[X]:((~rich(X)&~strong(X))))&
(?[X]:(~old(X)))&
((~kind(alice)<~>generous(alice)))&
(?[X]:((funny(X)<~>~kind(X))))&
((creative(mary)&~humble(mary)))&
((~kind(paul)<~>~happy(paul)))&
(calm(paul))&
(?[X]:((strong(X)&~funny(X)))) | ~funny(paul) | [
"p0",
"p4",
"p5",
"p8",
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8936918200141982911806142
% SZS output start Proof for 8936918200141982911806142
1. ! [X0] : ((~funny(X0) <~> ~kind(X0)) <=> (humble(X0) & ~happy(X0))) [input p0]
5. ! [X0] : ((~creative(X0) <~> curious(X0)) => brave(X0)) [input p4]
6. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (generous(X0) & curious(X0))) [input p5]
9. ! [X0] : ((~brave(X0) & generous(X0)) <=> generous(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> happy(X0)) => ~generous(X0)) [input p9]
22. ~kind(paul) <~> ~happy(paul) [input p21]
25. funny(paul) [input hypothesis]
33. ! [X0] : (brave(X0) | (~creative(X0) <=> curious(X0))) [ennf transformation 5]
35. ! [X0] : (~generous(X0) | (~creative(X0) <=> happy(X0))) [ennf transformation 10]
39. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | (~humble(X0) | happy(X0))) & ((humble(X0) & ~happy(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [nnf transformation 1]
40. ! [X0] : ((((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ~humble(X0) | happy(X0)) & ((humble(X0) & ~happy(X0)) | ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))))) [flattening 39]
48. ! [X0] : (brave(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) [nnf transformation 33]
49. ! [X0] : (((kind(X0) | ~wise(X0)) | (~generous(X0) | ~curious(X0))) & ((generous(X0) & curious(X0)) | (~kind(X0) & wise(X0)))) [nnf transformation 6]
50. ! [X0] : ((kind(X0) | ~wise(X0) | ~generous(X0) | ~curious(X0)) & ((generous(X0) & curious(X0)) | (~kind(X0) & wise(X0)))) [flattening 49]
57. ! [X0] : (((~brave(X0) & generous(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) | ~generous(X0)))) [nnf transformation 9]
58. ! [X0] : (((~brave(X0) & generous(X0)) | ~generous(X0)) & (generous(X0) | brave(X0) | ~generous(X0))) [flattening 57]
59. ! [X0] : (~generous(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) [nnf transformation 35]
82. (happy(paul) | kind(paul)) & (~happy(paul) | ~kind(paul)) [nnf transformation 22]
86. ~happy(X0) | ~funny(X0) | kind(X0) [cnf transformation 40]
101. ~curious(X0) | ~creative(X0) | brave(X0) [cnf transformation 48]
103. ~kind(X0) | curious(X0) [cnf transformation 50]
105. ~kind(X0) | generous(X0) [cnf transformation 50]
115. ~generous(X0) | ~brave(X0) [cnf transformation 58]
116. ~generous(X0) | happy(X0) | creative(X0) [cnf transformation 59]
141. ~happy(paul) | ~kind(paul) [cnf transformation 82]
142. happy(paul) | kind(paul) [cnf transformation 82]
145. funny(paul) [cnf transformation 25]
283. 33 <=> kind(paul) [avatar definition]
284. ~kind(paul) <- (~33) [avatar component clause 283]
285. kind(paul) <- (33) [avatar component clause 283]
287. 34 <=> happy(paul) [avatar definition]
288. ~happy(paul) <- (~34) [avatar component clause 287]
289. happy(paul) <- (34) [avatar component clause 287]
290. 33 | 34 [avatar split clause 142,287,283]
291. ~33 | ~34 [avatar split clause 141,287,283]
294. curious(paul) <- (33) [resolution 103,285]
296. generous(paul) <- (33) [resolution 105,285]
298. ~brave(paul) <- (33) [resolution 296,115]
304. ~creative(paul) | brave(paul) <- (33) [resolution 101,294]
306. ~creative(paul) <- (33) [subsumption resolution 304,298]
309. happy(paul) | creative(paul) <- (33) [resolution 116,296]
311. creative(paul) <- (33, ~34) [subsumption resolution 309,288]
312. $false <- (33, ~34) [subsumption resolution 311,306]
313. ~33 | 34 [avatar contradiction clause 312]
319. ~funny(paul) | kind(paul) <- (34) [resolution 289,86]
323. kind(paul) <- (34) [subsumption resolution 319,145]
324. $false <- (~33, 34) [subsumption resolution 323,284]
325. 33 | ~34 [avatar contradiction clause 324]
326. $false [avatar sat refutation 290,291,313,325]
% SZS output end Proof for 8936918200141982911806142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not happy then mary is both happy and not brave and vice versa.
If mary is either not creative or quiet then someone is not tall and vice versa.
If someone is both not rich and not kind then lucy is calm or not strong.
If someone is not happy then susan is happy and vice versa.
If john is both not quiet and rich then someone is brave and vice versa.
Everyone who is both brave and not brave is both kind and not generous and vice versa.
Everyone who is not strong or old is both not kind and not tall and vice versa.
Everyone who is both not strong and curious is kind or not generous.
Everyone who is either not wise or strong is patient.
Everyone who is not rich or not calm is both not tall and quiet.
If paul is either wise or not quiet then paul is either generous or not curious.
If alice is curious then someone is either kind or funny and vice versa.
If fred is not patient or creative then someone is both not wise and not quiet and vice versa.
Everyone who is not tall is generous or not funny and vice versa.
Everyone who is both not tall and not generous is both curious and wise and vice versa.
If someone is not curious then alice is strong or calm and vice versa.
Someone is not old.
Someone is both happy and tall.
John is either kind or not humble.
Paul is either strong or brave.
Someone is either tall or not generous.
Someone is curious or brave.
Someone is either old or brave. | Susan is not calm. | neutral | ((?[X]:((~generous(X)&~happy(X))))<=>((happy(mary)&~brave(mary))))&
(((~creative(mary)<~>quiet(mary)))<=>(?[X]:(~tall(X))))&
((?[X]:((~rich(X)&~kind(X))))=>((calm(lucy)|~strong(lucy))))&
((?[X]:(~happy(X)))<=>(happy(susan)))&
(((~quiet(john)&rich(john)))<=>(?[X]:(brave(X))))&
(![X]:((brave(X)&~brave(X))<=>(kind(X)&~generous(X))))&
(![X]:((~strong(X)|old(X))<=>(~kind(X)&~tall(X))))&
(![X]:((~strong(X)&curious(X))=>(kind(X)|~generous(X))))&
(![X]:((~wise(X)<~>strong(X))=>patient(X)))&
(![X]:((~rich(X)|~calm(X))=>(~tall(X)&quiet(X))))&
(((wise(paul)<~>~quiet(paul)))=>((generous(paul)<~>~curious(paul))))&
((curious(alice))<=>(?[X]:((kind(X)<~>funny(X)))))&
(((~patient(fred)|creative(fred)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(~tall(X)<=>(generous(X)|~funny(X))))&
(![X]:((~tall(X)&~generous(X))<=>(curious(X)&wise(X))))&
((?[X]:(~curious(X)))<=>((strong(alice)|calm(alice))))&
(?[X]:(~old(X)))&
(?[X]:((happy(X)&tall(X))))&
((kind(john)<~>~humble(john)))&
((strong(paul)<~>brave(paul)))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((old(X)<~>brave(X)))) | ~calm(susan) | [] | null | 0 |
If someone is quiet or calm then someone is either not wise or calm. Everyone who is both brave and old is calm. Everyone who is not calm is both not calm and calm. If someone is either brave or not rich then susan is both creative and calm and vice versa. Everyone who is either not brave or not kind is not curious. If mary is both not old and tall then john is not calm or curious. Everyone who is either calm or quiet is patient or calm. Everyone who is either patient or not happy is not strong or happy and vice versa. If paul is not tall then fred is not patient and vice versa. If lucy is both funny and not old then someone is not happy or brave and vice versa. Everyone who is not tall or not creative is both curious and not patient. If someone is both not tall and not patient then fred is either not wise or humble and vice versa. If someone is not patient then john is not humble and vice versa. If fred is either tall or not curious then someone is either not curious or kind and vice versa. If someone is not quiet or not strong then someone is happy or not kind. Everyone who is not wise or old is both quiet and old and vice versa. Someone is not rich. Someone is both curious and not rich. Alice is both not funny and rich. John is either not quiet or quiet. Alice is creative or wise. Alice is both not creative and curious. Susan is either not strong or not humble. Someone is tall or not creative. | John is calm. | entailment | ((?[X]:((quiet(X)|calm(X))))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((brave(X)&old(X))=>calm(X)))&
(![X]:(~calm(X)=>(~calm(X)&calm(X))))&
((?[X]:((brave(X)<~>~rich(X))))<=>((creative(susan)&calm(susan))))&
(![X]:((~brave(X)<~>~kind(X))=>~curious(X)))&
(((~old(mary)&tall(mary)))=>((~calm(john)|curious(john))))&
(![X]:((calm(X)<~>quiet(X))=>(patient(X)|calm(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(~strong(X)|happy(X))))&
((~tall(paul))<=>(~patient(fred)))&
(((funny(lucy)&~old(lucy)))<=>(?[X]:((~happy(X)|brave(X)))))&
(![X]:((~tall(X)|~creative(X))=>(curious(X)&~patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>((~wise(fred)<~>humble(fred))))&
((?[X]:(~patient(X)))<=>(~humble(john)))&
(((tall(fred)<~>~curious(fred)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~wise(X)|old(X))<=>(quiet(X)&old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)&~rich(X))))&
((~funny(alice)&rich(alice)))&
((~quiet(john)<~>quiet(john)))&
((creative(alice)|wise(alice)))&
((~creative(alice)&curious(alice)))&
((~strong(susan)<~>~humble(susan)))&
(?[X]:((tall(X)|~creative(X)))) | calm(john) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2337797428574426377341186
% SZS output start Proof for 2337797428574426377341186
3. ! [X0] : (~calm(X0) => (calm(X0) & ~calm(X0))) [input p2]
25. ~calm(john) [input hypothesis]
31. ! [X0] : ((calm(X0) & ~calm(X0)) | calm(X0)) [ennf transformation 3]
89. calm(X0) | calm(X0) [cnf transformation 31]
154. ~calm(john) [cnf transformation 25]
158. calm(X0) [duplicate literal removal 89]
370. $false [subsumption resolution 154,158]
% SZS output end Proof for 2337797428574426377341186
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or calm then alice is not generous or creative.
If susan is either kind or not creative then someone is either happy or calm and vice versa.
If someone is both not funny and funny then someone is either not brave or not kind and vice versa.
If someone is not tall or curious then lucy is old or not kind.
If susan is either tall or not kind then lucy is both creative and not patient and vice versa.
Everyone who is calm is either not calm or creative and vice versa.
Everyone who is both happy and humble is old or calm.
If fred is not old then someone is humble and vice versa.
Everyone who is both calm and not humble is creative.
Everyone who is calm is not brave.
Everyone who is both generous and kind is not generous and vice versa.
Everyone who is curious or kind is both brave and not wise.
Everyone who is both not quiet and not humble is either not creative or not brave and vice versa.
Everyone who is not quiet is either brave or generous.
Everyone who is not funny is both patient and rich and vice versa.
Everyone who is creative or not rich is either not strong or not rich.
Someone is not strong or not quiet.
Someone is either generous or not generous.
Someone is quiet or not tall.
Someone is both funny and not patient.
Lucy is not brave or not funny.
Alice is not brave or not creative.
Someone is either creative or kind.
Someone is either not funny or quiet. | Lucy is quiet. | contradiction | ((?[X]:((~old(X)|calm(X))))=>((~generous(alice)|creative(alice))))&
(((kind(susan)<~>~creative(susan)))<=>(?[X]:((happy(X)<~>calm(X)))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:((~tall(X)|curious(X))))=>((old(lucy)|~kind(lucy))))&
(((tall(susan)<~>~kind(susan)))<=>((creative(lucy)&~patient(lucy))))&
(![X]:(calm(X)<=>(~calm(X)<~>creative(X))))&
(![X]:((happy(X)&humble(X))=>(old(X)|calm(X))))&
((~old(fred))<=>(?[X]:(humble(X))))&
(![X]:((calm(X)&~humble(X))=>creative(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((generous(X)&kind(X))<=>~generous(X)))&
(![X]:((curious(X)|kind(X))=>(brave(X)&~wise(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~quiet(X)=>(brave(X)<~>generous(X))))&
(![X]:(~funny(X)<=>(patient(X)&rich(X))))&
(![X]:((creative(X)|~rich(X))=>(~strong(X)<~>~rich(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((generous(X)<~>~generous(X))))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((funny(X)&~patient(X))))&
((~brave(lucy)|~funny(lucy)))&
((~brave(alice)|~creative(alice)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:((~funny(X)<~>quiet(X)))) | quiet(lucy) | [
"p2",
"p5",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 736560565886713803640152
% SZS output start Proof for 736560565886713803640152
3. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X0] : (~brave(X0) <~> ~kind(X0)) [input p2]
6. ! [X0] : (calm(X0) <=> (~calm(X0) <~> creative(X0))) [input p5]
11. ! [X0] : ((kind(X0) & generous(X0)) <=> ~generous(X0)) [input p10]
13. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (~creative(X0) <~> ~brave(X0))) [input p12]
25. quiet(lucy) [input hypothesis]
26. ? [X0] : (funny(X0) & ~funny(X0)) <=> ? [X1] : (~brave(X1) <~> ~kind(X1)) [rectify 3]
46. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (? [X1] : ((kind(X1) | brave(X1)) & (~kind(X1) | ~brave(X1))) | ! [X0] : (~funny(X0) | funny(X0))) [nnf transformation 26]
47. (? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (? [X2] : ((kind(X2) | brave(X2)) & (~kind(X2) | ~brave(X2))) | ! [X3] : (~funny(X3) | funny(X3))) [rectify 46]
48. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK1) & ~funny(sK1)) [choice axiom]
49. ? [X2] : ((kind(X2) | brave(X2)) & (~kind(X2) | ~brave(X2))) => ((kind(sK2) | brave(sK2)) & (~kind(sK2) | ~brave(sK2))) [choice axiom]
50. ((funny(sK1) & ~funny(sK1)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (((kind(sK2) | brave(sK2)) & (~kind(sK2) | ~brave(sK2))) | ! [X3] : (~funny(X3) | funny(X3))) [skolemisation 47,49,48]
53. ! [X0] : ((calm(X0) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~calm(X0))) [nnf transformation 6]
58. ! [X0] : (((kind(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | ~generous(X0)))) [nnf transformation 11]
59. ! [X0] : (((kind(X0) & generous(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | ~generous(X0))) [flattening 58]
60. ! [X0] : (((~humble(X0) & ~quiet(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | (humble(X0) | quiet(X0)))) [nnf transformation 13]
61. ! [X0] : (((~humble(X0) & ~quiet(X0)) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | humble(X0) | quiet(X0))) [flattening 60]
94. ~funny(sK1) | ~brave(X1) | kind(X1) [cnf transformation 50]
96. funny(sK1) | ~brave(X1) | kind(X1) [cnf transformation 50]
104. creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 53]
106. calm(X0) | creative(X0) | calm(X0) [cnf transformation 53]
113. ~generous(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 59]
114. generous(X0) | generous(X0) [cnf transformation 59]
120. ~quiet(X0) | ~creative(X0) | brave(X0) [cnf transformation 61]
144. quiet(lucy) [cnf transformation 25]
146. ~generous(X0) | ~kind(X0) [duplicate literal removal 113]
147. generous(X0) [duplicate literal removal 114]
148. creative(X0) | ~calm(X0) [duplicate literal removal 104]
149. creative(X0) | calm(X0) [duplicate literal removal 106]
197. 11 <=> ! [X1] : (~brave(X1) | kind(X1)) [avatar definition]
198. ~brave(X1) | kind(X1) <- (11) [avatar component clause 197]
200. 12 <=> funny(sK1) [avatar definition]
203. 11 | 12 [avatar split clause 96,200,197]
208. 11 | ~12 [avatar split clause 94,200,197]
240. creative(X0) [subsumption resolution 148,149]
254. ~kind(X0) [subsumption resolution 146,147]
256. ~quiet(X0) | brave(X0) [subsumption resolution 120,240]
300. ~brave(X1) <- (11) [subsumption resolution 198,254]
311. brave(lucy) [resolution 256,144]
314. $false <- (11) [subsumption resolution 311,300]
315. ~11 [avatar contradiction clause 314]
318. $false [avatar sat refutation 203,208,315]
% SZS output end Proof for 736560565886713803640152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not generous is not creative or not kind and vice versa.
If paul is either not funny or not creative then someone is either generous or brave.
If fred is not funny then someone is either funny or not strong and vice versa.
If someone is both kind and rich then someone is both brave and not strong and vice versa.
If susan is not rich or not brave then someone is either humble or not happy and vice versa.
Everyone who is quiet or not curious is both not creative and happy and vice versa.
Everyone who is tall or not strong is both not tall and kind.
If someone is not brave then someone is kind and vice versa.
Everyone who is not calm or strong is both not curious and strong.
Everyone who is both not funny and kind is both not calm and not humble.
Everyone who is either not brave or kind is not strong or wise and vice versa.
If john is not curious then fred is not quiet.
If fred is strong then susan is either calm or happy.
If someone is either old or patient then someone is not creative and vice versa.
Everyone who is both not brave and rich is both not calm and creative and vice versa.
Everyone who is both kind and not strong is not kind or brave.
Lucy is not old.
Susan is both not patient and old.
Someone is both generous and not old.
Someone is either not creative or patient.
Someone is either not curious or strong.
Someone is both not curious and funny.
Someone is both wise and quiet.
Lucy is not funny or old. | John is brave. | neutral | (![X]:((tall(X)<~>~generous(X))<=>(~creative(X)|~kind(X))))&
(((~funny(paul)<~>~creative(paul)))=>(?[X]:((generous(X)<~>brave(X)))))&
((~funny(fred))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(((~rich(susan)|~brave(susan)))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~curious(X))<=>(~creative(X)&happy(X))))&
(![X]:((tall(X)|~strong(X))=>(~tall(X)&kind(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|strong(X))=>(~curious(X)&strong(X))))&
(![X]:((~funny(X)&kind(X))=>(~calm(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~strong(X)|wise(X))))&
((~curious(john))=>(~quiet(fred)))&
((strong(fred))=>((calm(susan)<~>happy(susan))))&
((?[X]:((old(X)<~>patient(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~brave(X)&rich(X))<=>(~calm(X)&creative(X))))&
(![X]:((kind(X)&~strong(X))=>(~kind(X)|brave(X))))&
(~old(lucy))&
((~patient(susan)&old(susan)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:((wise(X)&quiet(X))))&
((~funny(lucy)|old(lucy))) | brave(john) | [] | null | 0 |
Everyone who is creative is both not quiet and funny.
If someone is both generous and strong then someone is either not old or old and vice versa.
Everyone who is wise or not old is patient or not wise.
Everyone who is either happy or not generous is not brave or not curious and vice versa.
If someone is either not patient or rich then someone is either not brave or happy.
If someone is both curious and happy then someone is patient or tall and vice versa.
If fred is funny then fred is kind.
Everyone who is not calm is either brave or curious and vice versa.
If fred is both rich and not humble then someone is either not patient or curious.
Everyone who is happy is generous and vice versa.
Everyone who is creative or not patient is either old or brave.
If susan is both funny and not generous then someone is patient or not generous.
Everyone who is both happy and not quiet is both happy and not patient and vice versa.
If john is not kind or old then susan is not humble and vice versa.
Everyone who is either not happy or not quiet is brave.
Everyone who is either not curious or not creative is either not wise or not kind.
Someone is both not old and not quiet.
Mary is both wise and not quiet.
Lucy is both not creative and quiet.
Someone is either creative or not brave.
John is funny or not patient.
Someone is quiet.
Someone is both not old and calm. | Mary is not happy. | entailment | (![X]:(creative(X)=>(~quiet(X)&funny(X))))&
((?[X]:((generous(X)&strong(X))))<=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((wise(X)|~old(X))=>(patient(X)|~wise(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~brave(X)|~curious(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>(?[X]:((~brave(X)<~>happy(X)))))&
((?[X]:((curious(X)&happy(X))))<=>(?[X]:((patient(X)|tall(X)))))&
((funny(fred))=>(kind(fred)))&
(![X]:(~calm(X)<=>(brave(X)<~>curious(X))))&
(((rich(fred)&~humble(fred)))=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>(old(X)<~>brave(X))))&
(((funny(susan)&~generous(susan)))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(happy(X)&~patient(X))))&
(((~kind(john)|old(john)))<=>(~humble(susan)))&
(![X]:((~happy(X)<~>~quiet(X))=>brave(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~wise(X)<~>~kind(X))))&
(?[X]:((~old(X)&~quiet(X))))&
((wise(mary)&~quiet(mary)))&
((~creative(lucy)&quiet(lucy)))&
(?[X]:((creative(X)<~>~brave(X))))&
((funny(john)|~patient(john)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)&calm(X)))) | ~happy(mary) | [
"p2",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4455647947328149374321274
% SZS output start Proof for 4455647947328149374321274
3. ! [X0] : ((~old(X0) | wise(X0)) => (~wise(X0) | patient(X0))) [input p2]
13. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~patient(X0) & happy(X0))) [input p12]
18. ~quiet(mary) & wise(mary) [input p17]
24. happy(mary) [input hypothesis]
30. ! [X0] : ((~wise(X0) | patient(X0)) | (old(X0) & ~wise(X0))) [ennf transformation 3]
31. ! [X0] : (~wise(X0) | patient(X0) | (old(X0) & ~wise(X0))) [flattening 30]
66. ! [X0] : (((~quiet(X0) & happy(X0)) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | (quiet(X0) | ~happy(X0)))) [nnf transformation 13]
67. ! [X0] : (((~quiet(X0) & happy(X0)) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | quiet(X0) | ~happy(X0))) [flattening 66]
89. ~wise(X0) | patient(X0) | ~wise(X0) [cnf transformation 31]
119. ~happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 67]
133. wise(mary) [cnf transformation 18]
134. ~quiet(mary) [cnf transformation 18]
143. happy(mary) [cnf transformation 24]
144. ~wise(X0) | patient(X0) [duplicate literal removal 89]
299. patient(mary) [resolution 144,133]
364. quiet(mary) | ~patient(mary) [resolution 119,143]
367. ~patient(mary) [subsumption resolution 364,134]
368. $false [subsumption resolution 367,299]
% SZS output end Proof for 4455647947328149374321274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not calm is either patient or calm.
Everyone who is curious or not patient is either not generous or not calm and vice versa.
Everyone who is both curious and patient is not creative.
Everyone who is not kind is funny.
If john is either not creative or not wise then someone is either not calm or tall.
Everyone who is creative is both old and creative and vice versa.
Everyone who is either funny or not rich is either creative or not curious and vice versa.
Everyone who is generous or creative is both rich and not kind and vice versa.
Everyone who is both generous and not creative is wise or not creative and vice versa.
Everyone who is both kind and not wise is both not generous and strong.
Everyone who is not calm is not old or not humble and vice versa.
Everyone who is both funny and not strong is creative and vice versa.
Everyone who is not funny is wise.
If someone is both happy and humble then someone is both strong and funny.
Everyone who is both humble and generous is not quiet and vice versa.
If susan is either not happy or not tall then lucy is either not strong or not patient and vice versa.
Fred is not quiet or patient.
Paul is not brave or not funny.
Someone is either wise or humble.
Alice is curious.
Susan is brave or kind.
Someone is either not rich or not kind.
Paul is not quiet.
John is not old. | Alice is not old. | contradiction | (![X]:((~strong(X)&~calm(X))=>(patient(X)<~>calm(X))))&
(![X]:((curious(X)|~patient(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:((curious(X)&patient(X))=>~creative(X)))&
(![X]:(~kind(X)=>funny(X)))&
(((~creative(john)<~>~wise(john)))=>(?[X]:((~calm(X)<~>tall(X)))))&
(![X]:(creative(X)<=>(old(X)&creative(X))))&
(![X]:((funny(X)<~>~rich(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((generous(X)|creative(X))<=>(rich(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(wise(X)|~creative(X))))&
(![X]:((kind(X)&~wise(X))=>(~generous(X)&strong(X))))&
(![X]:(~calm(X)<=>(~old(X)|~humble(X))))&
(![X]:((funny(X)&~strong(X))<=>creative(X)))&
(![X]:(~funny(X)=>wise(X)))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((humble(X)&generous(X))<=>~quiet(X)))&
(((~happy(susan)<~>~tall(susan)))<=>((~strong(lucy)<~>~patient(lucy))))&
((~quiet(fred)|patient(fred)))&
((~brave(paul)|~funny(paul)))&
(?[X]:((wise(X)<~>humble(X))))&
(curious(alice))&
((brave(susan)|kind(susan)))&
(?[X]:((~rich(X)<~>~kind(X))))&
(~quiet(paul))&
(~old(john)) | ~old(alice) | [
"p1",
"p3",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 83403518869930346249648
% SZS output start Proof for 83403518869930346249648
2. ! [X0] : ((~patient(X0) | curious(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p1]
4. ! [X0] : (~kind(X0) => funny(X0)) [input p3]
6. ! [X0] : (creative(X0) <=> (creative(X0) & old(X0))) [input p5]
7. ! [X0] : ((funny(X0) <~> ~rich(X0)) <=> (creative(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((creative(X0) | generous(X0)) <=> (~kind(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & generous(X0)) <=> (~creative(X0) | wise(X0))) [input p8]
11. ! [X0] : (~calm(X0) <=> (~humble(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((~strong(X0) & funny(X0)) <=> creative(X0)) [input p11]
20. curious(alice) [input p19]
25. ~old(alice) [input hypothesis]
32. ! [X0] : (funny(X0) | kind(X0)) [ennf transformation 4]
40. ! [X0] : (((~patient(X0) | curious(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (patient(X0) & ~curious(X0)))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | curious(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (patient(X0) & ~curious(X0)))) [flattening 40]
45. ! [X0] : ((creative(X0) | (~creative(X0) | ~old(X0))) & ((creative(X0) & old(X0)) | ~creative(X0))) [nnf transformation 6]
46. ! [X0] : ((creative(X0) | ~creative(X0) | ~old(X0)) & ((creative(X0) & old(X0)) | ~creative(X0))) [flattening 45]
47. ! [X0] : ((((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | ((creative(X0) | curious(X0)) & (~curious(X0) | ~creative(X0)))) & (((curious(X0) | ~creative(X0)) & (~curious(X0) | creative(X0))) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0))))) [nnf transformation 7]
48. ! [X0] : (((creative(X0) | generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | generous(X0) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | (~creative(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (creative(X0) | ~generous(X0)))) [nnf transformation 9]
51. ! [X0] : (((~creative(X0) & generous(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | creative(X0) | ~generous(X0))) [flattening 50]
52. ! [X0] : ((~calm(X0) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | calm(X0))) [nnf transformation 11]
53. ! [X0] : ((~calm(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | calm(X0))) [flattening 52]
54. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | (strong(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0)) & (creative(X0) | strong(X0) | ~funny(X0))) [flattening 54]
70. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 41]
75. funny(X0) | kind(X0) [cnf transformation 32]
80. ~creative(X0) | old(X0) [cnf transformation 46]
83. ~rich(X0) | creative(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 47]
91. ~generous(X0) | rich(X0) [cnf transformation 49]
92. ~creative(X0) | rich(X0) [cnf transformation 49]
93. ~kind(X0) | ~generous(X0) [cnf transformation 49]
98. creative(X0) | generous(X0) [cnf transformation 51]
104. ~calm(X0) | old(X0) [cnf transformation 53]
106. ~funny(X0) | strong(X0) | creative(X0) [cnf transformation 55]
108. ~creative(X0) | ~strong(X0) [cnf transformation 55]
126. curious(alice) [cnf transformation 20]
132. ~old(alice) [cnf transformation 25]
241. generous(X0) | rich(X0) [resolution 98,92]
243. rich(X0) [subsumption resolution 241,91]
308. generous(alice) | calm(alice) [resolution 70,126]
310. 31 <=> calm(alice) [avatar definition]
312. calm(alice) <- (31) [avatar component clause 310]
314. 32 <=> generous(alice) [avatar definition]
316. generous(alice) <- (32) [avatar component clause 314]
317. 31 | 32 [avatar split clause 308,314,310]
319. old(alice) <- (31) [resolution 312,104]
320. $false <- (31) [subsumption resolution 319,132]
321. ~31 [avatar contradiction clause 320]
334. kind(X0) | creative(X0) | strong(X0) [resolution 106,75]
370. ~funny(X0) | ~curious(X0) | creative(X0) [resolution 83,243]
442. creative(X2) | strong(X2) | ~generous(X2) [resolution 334,93]
445. creative(X2) | strong(X2) [subsumption resolution 442,98]
492. old(X1) | strong(X1) [resolution 445,80]
503. ~curious(X2) | creative(X2) | kind(X2) [resolution 370,75]
521. strong(alice) [resolution 492,132]
546. creative(alice) | kind(alice) [resolution 503,126]
550. 42 <=> kind(alice) [avatar definition]
552. kind(alice) <- (42) [avatar component clause 550]
554. 43 <=> creative(alice) [avatar definition]
556. creative(alice) <- (43) [avatar component clause 554]
557. 42 | 43 [avatar split clause 546,554,550]
560. ~generous(alice) <- (42) [resolution 552,93]
562. $false <- (32, 42) [subsumption resolution 560,316]
563. ~32 | ~42 [avatar contradiction clause 562]
570. ~strong(alice) <- (43) [resolution 556,108]
575. $false <- (43) [subsumption resolution 570,521]
576. ~43 [avatar contradiction clause 575]
577. $false [avatar sat refutation 317,321,557,563,576]
% SZS output end Proof for 83403518869930346249648
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and kind is either not quiet or not calm and vice versa. Everyone who is both kind and funny is quiet and vice versa. Everyone who is rich or not happy is funny. If someone is kind then someone is humble and vice versa. If susan is tall or not curious then someone is not kind or old. Everyone who is both not wise and happy is both kind and not funny. If paul is both not calm and not quiet then someone is both old and not creative and vice versa. If alice is both not funny and not calm then someone is either not quiet or not brave. Everyone who is generous or patient is not happy and vice versa. Everyone who is tall is humble. Everyone who is either rich or not patient is either not wise or not rich. Everyone who is either kind or not wise is both not wise and happy and vice versa. Everyone who is not generous is not tall and vice versa. Everyone who is funny or not strong is strong or not happy and vice versa. Everyone who is calm is not generous and vice versa. If someone is both not tall and funny then someone is both tall and brave. Susan is either generous or wise. Susan is either not brave or not calm. Fred is both creative and not calm. Someone is both humble and not patient. Paul is either not quiet or not old. Someone is quiet. Someone is not kind. | Alice is tall. | entailment | (![X]:((quiet(X)&kind(X))<=>(~quiet(X)<~>~calm(X))))&
(![X]:((kind(X)&funny(X))<=>quiet(X)))&
(![X]:((rich(X)|~happy(X))=>funny(X)))&
((?[X]:(kind(X)))<=>(?[X]:(humble(X))))&
(((tall(susan)|~curious(susan)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~wise(X)&happy(X))=>(kind(X)&~funny(X))))&
(((~calm(paul)&~quiet(paul)))<=>(?[X]:((old(X)&~creative(X)))))&
(((~funny(alice)&~calm(alice)))=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((generous(X)|patient(X))<=>~happy(X)))&
(![X]:(tall(X)=>humble(X)))&
(![X]:((rich(X)<~>~patient(X))=>(~wise(X)<~>~rich(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~wise(X)&happy(X))))&
(![X]:(~generous(X)<=>~tall(X)))&
(![X]:((funny(X)|~strong(X))<=>(strong(X)|~happy(X))))&
(![X]:(calm(X)<=>~generous(X)))&
((?[X]:((~tall(X)&funny(X))))=>(?[X]:((tall(X)&brave(X)))))&
((generous(susan)<~>wise(susan)))&
((~brave(susan)<~>~calm(susan)))&
((creative(fred)&~calm(fred)))&
(?[X]:((humble(X)&~patient(X))))&
((~quiet(paul)<~>~old(paul)))&
(?[X]:(quiet(X)))&
(?[X]:(~kind(X))) | tall(alice) | [
"p0",
"p1",
"p2",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4548112755113168962515428
% SZS output start Proof for 4548112755113168962515428
1. ! [X0] : ((kind(X0) & quiet(X0)) <=> (~quiet(X0) <~> ~calm(X0))) [input p0]
2. ! [X0] : ((funny(X0) & kind(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : ((~happy(X0) | rich(X0)) => funny(X0)) [input p2]
13. ! [X0] : (~generous(X0) <=> ~tall(X0)) [input p12]
14. ! [X0] : ((~strong(X0) | funny(X0)) <=> (~happy(X0) | strong(X0))) [input p13]
15. ! [X0] : (calm(X0) <=> ~generous(X0)) [input p14]
24. ~tall(alice) [input hypothesis]
28. ! [X0] : (funny(X0) | (happy(X0) & ~rich(X0))) [ennf transformation 3]
37. ! [X0] : (((kind(X0) & quiet(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) & (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((kind(X0) & quiet(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0)))) & (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~kind(X0) | ~quiet(X0))) [flattening 37]
39. ! [X0] : (((funny(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~funny(X0) | ~kind(X0)))) [nnf transformation 2]
40. ! [X0] : (((funny(X0) & kind(X0)) | ~quiet(X0)) & (quiet(X0) | ~funny(X0) | ~kind(X0))) [flattening 39]
61. ! [X0] : ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))) [nnf transformation 13]
62. ! [X0] : (((~strong(X0) | funny(X0)) | (happy(X0) & ~strong(X0))) & ((~happy(X0) | strong(X0)) | (strong(X0) & ~funny(X0)))) [nnf transformation 14]
63. ! [X0] : ((~strong(X0) | funny(X0) | (happy(X0) & ~strong(X0))) & (~happy(X0) | strong(X0) | (strong(X0) & ~funny(X0)))) [flattening 62]
64. ! [X0] : ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0))) [nnf transformation 15]
77. ~calm(X0) | ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 38]
79. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 38]
81. ~calm(X0) | kind(X0) | quiet(X0) [cnf transformation 38]
83. ~funny(X0) | quiet(X0) | ~kind(X0) [cnf transformation 40]
84. ~quiet(X0) | kind(X0) [cnf transformation 40]
87. happy(X0) | funny(X0) [cnf transformation 28]
114. ~generous(X0) | tall(X0) [cnf transformation 61]
116. ~happy(X0) | strong(X0) | strong(X0) [cnf transformation 63]
117. ~strong(X0) | funny(X0) | ~strong(X0) [cnf transformation 63]
120. generous(X0) | calm(X0) [cnf transformation 64]
135. ~tall(alice) [cnf transformation 24]
136. ~happy(X0) | strong(X0) [duplicate literal removal 116]
137. ~strong(X0) | funny(X0) [duplicate literal removal 117]
142. ~calm(X0) | ~quiet(X0) | ~kind(X0) [duplicate literal removal 77]
143. ~calm(X0) | quiet(X0) [duplicate literal removal 79]
144. ~calm(X0) | ~kind(X0) [subsumption resolution 142,143]
204. 14 <=> calm(alice) [avatar definition]
206. calm(alice) <- (14) [avatar component clause 204]
272. tall(X1) | calm(X1) [resolution 120,114]
278. strong(X0) | funny(X0) [resolution 136,87]
279. funny(X0) [subsumption resolution 278,137]
313. quiet(X0) | ~kind(X0) [resolution 83,279]
320. calm(alice) [resolution 272,135]
323. 14 [avatar split clause 320,204]
324. kind(alice) | quiet(alice) <- (14) [resolution 206,81]
325. ~kind(alice) <- (14) [resolution 206,144]
327. quiet(alice) <- (14) [subsumption resolution 324,313]
341. kind(alice) <- (14) [resolution 327,84]
342. $false <- (14) [subsumption resolution 341,325]
343. ~14 [avatar contradiction clause 342]
344. $false [avatar sat refutation 323,343]
% SZS output end Proof for 4548112755113168962515428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not funny is strong. If john is both not strong and not tall then alice is not old. Everyone who is both old and generous is both not quiet and not brave and vice versa. Everyone who is not patient is both kind and not funny and vice versa. Everyone who is not brave or not strong is old. If someone is not happy then lucy is funny or not generous and vice versa. Everyone who is both quiet and not wise is not strong or quiet and vice versa. Everyone who is either old or not generous is either patient or generous and vice versa. If someone is generous or not strong then someone is not calm or tall. Everyone who is both old and generous is either not brave or patient and vice versa. If susan is either wise or not brave then susan is not calm and vice versa. Everyone who is funny or not happy is strong and vice versa. Everyone who is both not happy and calm is rich. If paul is either not generous or tall then fred is brave and vice versa. Everyone who is either not patient or creative is both not old and not generous. Alice is old or kind. Susan is either not curious or happy. Someone is either not tall or not curious. | Fred is tall. | neutral | (![X]:((~patient(X)|~funny(X))=>strong(X)))&
(((~strong(john)&~tall(john)))=>(~old(alice)))&
(![X]:((old(X)&generous(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
(![X]:((~brave(X)|~strong(X))=>old(X)))&
((?[X]:(~happy(X)))<=>((funny(lucy)|~generous(lucy))))&
(![X]:((quiet(X)&~wise(X))<=>(~strong(X)|quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:((~calm(X)|tall(X)))))&
(![X]:((old(X)&generous(X))<=>(~brave(X)<~>patient(X))))&
(((wise(susan)<~>~brave(susan)))<=>(~calm(susan)))&
(![X]:((funny(X)|~happy(X))<=>strong(X)))&
(![X]:((~happy(X)&calm(X))=>rich(X)))&
(((~generous(paul)<~>tall(paul)))<=>(brave(fred)))&
(![X]:((~patient(X)<~>creative(X))=>(~old(X)&~generous(X))))&
((old(alice)|kind(alice)))&
((~curious(susan)<~>happy(susan)))&
(?[X]:((~tall(X)<~>~curious(X)))) | tall(fred) | [] | null | 0 |
Everyone who is tall is both not humble and generous and vice versa. Everyone who is funny is curious or funny. If someone is curious then mary is tall. If john is either brave or not calm then someone is either funny or quiet and vice versa. Everyone who is both not old and tall is either not calm or calm and vice versa. If someone is not humble then someone is either not patient or not quiet and vice versa. Everyone who is both not rich and not humble is not rich. Everyone who is either happy or not calm is both curious and not creative. If someone is both not wise and not strong then paul is either not rich or tall. If someone is not old or not brave then john is calm and vice versa. Everyone who is either calm or not rich is either wise or not strong. If paul is not rich then someone is wise or not tall and vice versa. Everyone who is not creative is rich or not strong and vice versa. Everyone who is both not creative and old is not creative or happy and vice versa. Everyone who is both happy and not calm is not generous or brave. Everyone who is both not patient and calm is either curious or not old and vice versa. Mary is not kind. Someone is happy or not old. Paul is either generous or kind. Someone is either kind or creative. Someone is both generous and not patient. Someone is not rich or not tall. | Paul is tall. | entailment | (![X]:(tall(X)<=>(~humble(X)&generous(X))))&
(![X]:(funny(X)=>(curious(X)|funny(X))))&
((?[X]:(curious(X)))=>(tall(mary)))&
(((brave(john)<~>~calm(john)))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~old(X)&tall(X))<=>(~calm(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&~humble(X))=>~rich(X)))&
(![X]:((happy(X)<~>~calm(X))=>(curious(X)&~creative(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~rich(paul)<~>tall(paul))))&
((?[X]:((~old(X)|~brave(X))))<=>(calm(john)))&
(![X]:((calm(X)<~>~rich(X))=>(wise(X)<~>~strong(X))))&
((~rich(paul))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~creative(X)<=>(rich(X)|~strong(X))))&
(![X]:((~creative(X)&old(X))<=>(~creative(X)|happy(X))))&
(![X]:((happy(X)&~calm(X))=>(~generous(X)|brave(X))))&
(![X]:((~patient(X)&calm(X))<=>(curious(X)<~>~old(X))))&
(~kind(mary))&
(?[X]:((happy(X)|~old(X))))&
((generous(paul)<~>kind(paul)))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((~rich(X)|~tall(X)))) | tall(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1768543669985377999157759
% SZS output start Proof for 1768543669985377999157759
5. ! [X0] : ((tall(X0) & ~old(X0)) <=> (~calm(X0) <~> calm(X0))) [input p4]
23. ~tall(paul) [input hypothesis]
41. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~tall(X0) | old(X0)))) [nnf transformation 5]
42. ! [X0] : (((tall(X0) & ~old(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~tall(X0) | old(X0))) [flattening 41]
92. tall(X0) | calm(X0) | calm(X0) [cnf transformation 42]
93. tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 42]
139. ~tall(paul) [cnf transformation 23]
142. tall(X0) | calm(X0) [duplicate literal removal 92]
143. tall(X0) | ~calm(X0) [duplicate literal removal 93]
182. tall(X0) [subsumption resolution 142,143]
251. $false [subsumption resolution 139,182]
% SZS output end Proof for 1768543669985377999157759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not rich then mary is quiet or not old and vice versa. Everyone who is both not patient and quiet is not happy. Everyone who is old or kind is old and vice versa. If susan is either generous or not quiet then lucy is not rich. Everyone who is wise is creative or happy and vice versa. Everyone who is funny is both not creative and generous and vice versa. If paul is either tall or not creative then lucy is calm or not creative and vice versa. Everyone who is not happy or not humble is rich and vice versa. If someone is not strong or creative then mary is not rich and vice versa. If someone is both calm and not humble then fred is either not humble or funny. Everyone who is brave is either not patient or calm. Everyone who is kind or not creative is not curious or kind and vice versa. If lucy is both strong and old then someone is both quiet and strong. Everyone who is old is both not humble and not funny. If someone is not patient then fred is not happy. Everyone who is old is happy or not kind and vice versa. Someone is either not humble or not strong. Mary is not kind or wise. John is not happy. Alice is curious or not curious. Someone is either not old or kind. Someone is either not generous or quiet. | John is funny. | contradiction | ((?[X]:((~brave(X)<~>~rich(X))))<=>((quiet(mary)|~old(mary))))&
(![X]:((~patient(X)&quiet(X))=>~happy(X)))&
(![X]:((old(X)|kind(X))<=>old(X)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:((~generous(X)<~>quiet(X)))) | funny(john) | [
"p2",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 471420651445496924495212
% SZS output start Proof for 471420651445496924495212
3. ! [X0] : ((kind(X0) | old(X0)) <=> old(X0)) [input p2]
14. ! [X0] : (old(X0) => (~funny(X0) & ~humble(X0))) [input p13]
16. ! [X0] : (old(X0) <=> (~kind(X0) | happy(X0))) [input p15]
23. funny(john) [input hypothesis]
34. ! [X0] : ((~funny(X0) & ~humble(X0)) | ~old(X0)) [ennf transformation 14]
41. ! [X0] : (((kind(X0) | old(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [nnf transformation 3]
42. ! [X0] : ((kind(X0) | old(X0) | ~old(X0)) & (old(X0) | (~kind(X0) & ~old(X0)))) [flattening 41]
60. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ~old(X0))) [nnf transformation 16]
61. ! [X0] : ((old(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ~old(X0))) [flattening 60]
79. ~kind(X0) | old(X0) [cnf transformation 42]
110. ~funny(X0) | ~old(X0) [cnf transformation 34]
114. old(X0) | kind(X0) [cnf transformation 61]
124. funny(john) [cnf transformation 23]
249. old(X0) [subsumption resolution 114,79]
308. ~old(john) [resolution 110,124]
309. $false [subsumption resolution 308,249]
% SZS output end Proof for 471420651445496924495212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or curious then someone is not quiet or patient and vice versa. If someone is not brave then someone is both calm and strong and vice versa. If someone is generous or patient then someone is wise or not quiet. Everyone who is not brave is both strong and not funny and vice versa. If fred is not brave then someone is both not wise and not quiet and vice versa. If someone is both calm and not happy then mary is either not calm or not quiet and vice versa. Everyone who is not creative is not calm or not humble and vice versa. If john is either not patient or happy then lucy is both not quiet and not brave and vice versa. If someone is not brave then someone is both not tall and not generous and vice versa. If lucy is not tall then susan is patient or not curious and vice versa. Everyone who is not wise or not creative is both not brave and funny. If alice is not wise or calm then john is both not kind and old. Everyone who is not patient is both not creative and not old. Everyone who is both brave and not humble is not tall. Everyone who is happy or curious is either not calm or old. If fred is calm or not calm then alice is not tall. Mary is either tall or generous. Someone is either not rich or creative. Someone is either tall or funny. Someone is either not generous or humble. Fred is either creative or old. Someone is not tall. | Susan is wise. | entailment | ((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((~quiet(X)|patient(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)&strong(X)))))&
((?[X]:((generous(X)|patient(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:(~brave(X)<=>(strong(X)&~funny(X))))&
((~brave(fred))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((calm(X)&~happy(X))))<=>((~calm(mary)<~>~quiet(mary))))&
(![X]:(~creative(X)<=>(~calm(X)|~humble(X))))&
(((~patient(john)<~>happy(john)))<=>((~quiet(lucy)&~brave(lucy))))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)&~generous(X)))))&
((~tall(lucy))<=>((patient(susan)|~curious(susan))))&
(![X]:((~wise(X)|~creative(X))=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
(((calm(fred)|~calm(fred)))=>(~tall(alice)))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~generous(X)<~>humble(X))))&
((creative(fred)<~>old(fred)))&
(?[X]:(~tall(X))) | wise(susan) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 9149375600812037309588717
% SZS output start Proof for 9149375600812037309588717
4. ! [X0] : (~brave(X0) <=> (~funny(X0) & strong(X0))) [input p3]
11. ! [X0] : ((~creative(X0) | ~wise(X0)) => (funny(X0) & ~brave(X0))) [input p10]
23. ~wise(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) & ~brave(X0)) | (creative(X0) & wise(X0))) [ennf transformation 11]
50. ! [X0] : ((~brave(X0) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | brave(X0))) [nnf transformation 4]
51. ! [X0] : ((~brave(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | brave(X0))) [flattening 50]
95. ~funny(X0) | brave(X0) [cnf transformation 51]
121. ~brave(X0) | wise(X0) [cnf transformation 30]
123. funny(X0) | wise(X0) [cnf transformation 30]
147. ~wise(susan) [cnf transformation 23]
415. wise(X0) | brave(X0) [resolution 123,95]
416. wise(X0) [subsumption resolution 415,121]
455. $false [resolution 416,147]
% SZS output end Proof for 9149375600812037309588717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not old and patient then susan is patient or brave.
Everyone who is kind or not creative is humble and vice versa.
Everyone who is old or funny is both funny and not calm and vice versa.
Everyone who is not old or not generous is either not old or humble and vice versa.
Everyone who is brave is both not rich and not old and vice versa.
Everyone who is both calm and creative is generous or wise and vice versa.
If someone is creative or not rich then john is either calm or not kind and vice versa.
If paul is either not kind or humble then lucy is either not funny or rich and vice versa.
If paul is both not rich and not happy then someone is either quiet or brave.
Everyone who is happy is curious or brave.
If someone is strong then john is not old or happy.
Everyone who is wise is strong and vice versa.
Everyone who is funny or strong is either not wise or strong.
Everyone who is not humble is either tall or wise and vice versa.
Everyone who is not tall is not happy and vice versa.
Everyone who is not humble or not funny is both not kind and not brave and vice versa.
John is either not curious or not wise.
Someone is quiet.
John is not tall or not calm.
Lucy is either creative or not quiet.
Mary is both not wise and patient.
Someone is both not calm and not strong.
Someone is either tall or kind. | Mary is not happy. | neutral | (((~old(susan)&patient(susan)))=>((patient(susan)|brave(susan))))&
(![X]:((kind(X)|~creative(X))<=>humble(X)))&
(![X]:((old(X)|funny(X))<=>(funny(X)&~calm(X))))&
(![X]:((~old(X)|~generous(X))<=>(~old(X)<~>humble(X))))&
(![X]:(brave(X)<=>(~rich(X)&~old(X))))&
(![X]:((calm(X)&creative(X))<=>(generous(X)|wise(X))))&
((?[X]:((creative(X)|~rich(X))))<=>((calm(john)<~>~kind(john))))&
(((~kind(paul)<~>humble(paul)))<=>((~funny(lucy)<~>rich(lucy))))&
(((~rich(paul)&~happy(paul)))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(happy(X)=>(curious(X)|brave(X))))&
((?[X]:(strong(X)))=>((~old(john)|happy(john))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((funny(X)|strong(X))=>(~wise(X)<~>strong(X))))&
(![X]:(~humble(X)<=>(tall(X)<~>wise(X))))&
(![X]:(~tall(X)<=>~happy(X)))&
(![X]:((~humble(X)|~funny(X))<=>(~kind(X)&~brave(X))))&
((~curious(john)<~>~wise(john)))&
(?[X]:(quiet(X)))&
((~tall(john)|~calm(john)))&
((creative(lucy)<~>~quiet(lucy)))&
((~wise(mary)&patient(mary)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((tall(X)<~>kind(X)))) | ~happy(mary) | [] | null | 0 |
Everyone who is either not tall or funny is rich or curious and vice versa.
Everyone who is both not calm and not generous is both not kind and not tall.
If someone is not generous then someone is calm or rich and vice versa.
Everyone who is either not wise or not patient is either not wise or not calm and vice versa.
Everyone who is happy or not strong is not tall or not happy and vice versa.
Everyone who is both not old and not patient is creative or generous.
If john is not patient then someone is kind or not strong.
Everyone who is creative is not curious.
Everyone who is both not brave and not happy is not wise or wise and vice versa.
Everyone who is not happy or not old is not wise or not patient.
Everyone who is either not strong or not humble is creative and vice versa.
Everyone who is not curious is both not tall and not humble and vice versa.
Everyone who is brave or not tall is both not generous and calm and vice versa.
Everyone who is either humble or not tall is either wise or creative.
If alice is either kind or creative then susan is humble and vice versa.
Everyone who is not calm is either patient or not strong and vice versa.
Someone is either not quiet or not happy.
Someone is not calm or not happy.
Someone is happy or not wise.
Fred is generous.
Someone is patient or not humble.
John is either humble or not humble.
Someone is happy or generous.
Someone is either generous or not tall. | Susan is humble. | contradiction | (![X]:((~tall(X)<~>funny(X))<=>(rich(X)|curious(X))))&
(![X]:((~calm(X)&~generous(X))=>(~kind(X)&~tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~wise(X)<~>~calm(X))))&
(![X]:((happy(X)|~strong(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~old(X)&~patient(X))=>(creative(X)|generous(X))))&
((~patient(john))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:(creative(X)=>~curious(X)))&
(![X]:((~brave(X)&~happy(X))<=>(~wise(X)|wise(X))))&
(![X]:((~happy(X)|~old(X))=>(~wise(X)|~patient(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>creative(X)))&
(![X]:(~curious(X)<=>(~tall(X)&~humble(X))))&
(![X]:((brave(X)|~tall(X))<=>(~generous(X)&calm(X))))&
(![X]:((humble(X)<~>~tall(X))=>(wise(X)<~>creative(X))))&
(((kind(alice)<~>creative(alice)))<=>(humble(susan)))&
(![X]:(~calm(X)<=>(patient(X)<~>~strong(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:((happy(X)|~wise(X))))&
(generous(fred))&
(?[X]:((patient(X)|~humble(X))))&
((humble(john)<~>~humble(john)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((generous(X)<~>~tall(X)))) | humble(susan) | [
"p3",
"p7",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4241418183425587323585716
% SZS output start Proof for 4241418183425587323585716
4. ! [X0] : ((~wise(X0) <~> ~patient(X0)) <=> (~wise(X0) <~> ~calm(X0))) [input p3]
8. ! [X0] : (creative(X0) => ~curious(X0)) [input p7]
11. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : (~curious(X0) <=> (~humble(X0) & ~tall(X0))) [input p11]
16. ! [X0] : (~calm(X0) <=> (patient(X0) <~> ~strong(X0))) [input p15]
25. humble(susan) [input hypothesis]
32. ! [X0] : (~curious(X0) | ~creative(X0)) [ennf transformation 8]
43. ! [X0] : ((((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | ((~wise(X0) | patient(X0)) & (~patient(X0) | wise(X0))))) [nnf transformation 4]
50. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~creative(X0)) & (creative(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 11]
51. ! [X0] : ((~curious(X0) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [nnf transformation 12]
52. ! [X0] : ((~curious(X0) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | curious(X0))) [flattening 51]
57. ! [X0] : ((~calm(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) & (((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | calm(X0))) [nnf transformation 16]
85. ~calm(X0) | ~wise(X0) | ~wise(X0) | patient(X0) [cnf transformation 43]
86. calm(X0) | wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 43]
89. ~patient(X0) | ~wise(X0) | ~wise(X0) | calm(X0) [cnf transformation 43]
90. patient(X0) | wise(X0) | ~calm(X0) | wise(X0) [cnf transformation 43]
97. ~creative(X0) | ~curious(X0) [cnf transformation 32]
104. ~humble(X0) | creative(X0) | strong(X0) [cnf transformation 50]
109. ~humble(X0) | curious(X0) [cnf transformation 52]
124. ~strong(X0) | patient(X0) | calm(X0) [cnf transformation 57]
126. ~calm(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57]
139. humble(susan) [cnf transformation 25]
142. ~calm(X0) | ~wise(X0) | patient(X0) [duplicate literal removal 85]
143. calm(X0) | wise(X0) | ~patient(X0) [duplicate literal removal 86]
144. ~patient(X0) | ~wise(X0) | calm(X0) [duplicate literal removal 89]
145. patient(X0) | wise(X0) | ~calm(X0) [duplicate literal removal 90]
170. ~patient(X0) | calm(X0) [subsumption resolution 143,144]
171. ~calm(X0) | patient(X0) [subsumption resolution 142,145]
191. 10 <=> humble(susan) [avatar definition]
192. humble(susan) <- (10) [avatar component clause 191]
206. ~strong(X0) | ~patient(X0) [subsumption resolution 126,170]
207. ~strong(X0) | patient(X0) [subsumption resolution 124,171]
208. ~strong(X0) [subsumption resolution 207,206]
221. 10 [avatar split clause 139,191]
224. curious(susan) <- (10) [resolution 109,192]
269. creative(susan) | strong(susan) <- (10) [resolution 104,192]
270. creative(susan) <- (10) [subsumption resolution 269,208]
271. ~curious(susan) <- (10) [resolution 270,97]
272. $false <- (10) [subsumption resolution 271,224]
273. ~10 [avatar contradiction clause 272]
274. $false [avatar sat refutation 221,273]
% SZS output end Proof for 4241418183425587323585716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or happy is tall and vice versa.
Everyone who is both wise and tall is both funny and not wise.
If alice is both not generous and rich then fred is not strong or not kind.
Everyone who is both creative and not calm is both quiet and not brave and vice versa.
If someone is either humble or not patient then someone is quiet.
If someone is not calm or not tall then lucy is either not happy or calm and vice versa.
If alice is not patient or patient then susan is either not creative or not humble and vice versa.
Everyone who is both not curious and not kind is wise or not calm.
Everyone who is not patient is not happy and vice versa.
Everyone who is both tall and not creative is not generous or not humble and vice versa.
If susan is both happy and not strong then someone is either not old or curious and vice versa.
Everyone who is either not generous or humble is either not happy or not creative and vice versa.
If fred is both not rich and not old then lucy is either not calm or not humble and vice versa.
Everyone who is not wise is both calm and old and vice versa.
If someone is quiet or kind then someone is either not strong or not quiet.
Lucy is old or patient.
Someone is both not strong and not creative.
Someone is not calm or not quiet.
Mary is not happy.
Someone is not happy.
Susan is not curious.
Someone is kind. | Lucy is brave. | neutral | (![X]:((~happy(X)<~>happy(X))<=>tall(X)))&
(![X]:((wise(X)&tall(X))=>(funny(X)&~wise(X))))&
(((~generous(alice)&rich(alice)))=>((~strong(fred)|~kind(fred))))&
(![X]:((creative(X)&~calm(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((humble(X)<~>~patient(X))))=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>((~happy(lucy)<~>calm(lucy))))&
(((~patient(alice)|patient(alice)))<=>((~creative(susan)<~>~humble(susan))))&
(![X]:((~curious(X)&~kind(X))=>(wise(X)|~calm(X))))&
(![X]:(~patient(X)<=>~happy(X)))&
(![X]:((tall(X)&~creative(X))<=>(~generous(X)|~humble(X))))&
(((happy(susan)&~strong(susan)))<=>(?[X]:((~old(X)<~>curious(X)))))&
(![X]:((~generous(X)<~>humble(X))<=>(~happy(X)<~>~creative(X))))&
(((~rich(fred)&~old(fred)))<=>((~calm(lucy)<~>~humble(lucy))))&
(![X]:(~wise(X)<=>(calm(X)&old(X))))&
((?[X]:((quiet(X)|kind(X))))=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((old(lucy)|patient(lucy)))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~calm(X)|~quiet(X))))&
(~happy(mary))&
(?[X]:(~happy(X)))&
(~curious(susan))&
(?[X]:(kind(X))) | brave(lucy) | [] | null | 0 |
If fred is both not happy and happy then alice is kind or not generous.
If someone is either creative or funny then susan is not happy.
Everyone who is either not brave or not humble is either strong or not tall and vice versa.
Everyone who is strong or rich is not creative and vice versa.
If john is both funny and brave then fred is not brave or not rich.
If someone is both not kind and not tall then someone is not curious and vice versa.
If mary is happy or not funny then lucy is not kind and vice versa.
If someone is not quiet or rich then someone is not patient or not old.
Everyone who is brave is both not kind and old.
If someone is either not funny or not rich then someone is both kind and not kind.
If someone is both not brave and brave then lucy is quiet or brave and vice versa.
If lucy is not funny then susan is both calm and kind.
If susan is not curious then someone is both not quiet and tall and vice versa.
Everyone who is either curious or calm is either calm or not curious.
Everyone who is both kind and patient is either not calm or strong and vice versa.
Everyone who is both not brave and calm is brave and vice versa.
Someone is either not kind or patient.
Someone is either not wise or old.
Someone is either not generous or not funny.
John is creative or not kind.
Someone is either old or calm.
Someone is either strong or old.
Someone is humble. | Alice is brave. | contradiction | (((~happy(fred)&happy(fred)))=>((kind(alice)|~generous(alice))))&
((?[X]:((creative(X)<~>funny(X))))=>(~happy(susan)))&
(![X]:((~brave(X)<~>~humble(X))<=>(strong(X)<~>~tall(X))))&
(![X]:((strong(X)|rich(X))<=>~creative(X)))&
(((funny(john)&brave(john)))=>((~brave(fred)|~rich(fred))))&
((?[X]:((~kind(X)&~tall(X))))<=>(?[X]:(~curious(X))))&
(((happy(mary)|~funny(mary)))<=>(~kind(lucy)))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(brave(X)=>(~kind(X)&old(X))))&
((?[X]:((~funny(X)<~>~rich(X))))=>(?[X]:((kind(X)&~kind(X)))))&
((?[X]:((~brave(X)&brave(X))))<=>((quiet(lucy)|brave(lucy))))&
((~funny(lucy))=>((calm(susan)&kind(susan))))&
((~curious(susan))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((curious(X)<~>calm(X))=>(calm(X)<~>~curious(X))))&
(![X]:((kind(X)&patient(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((~brave(X)&calm(X))<=>brave(X)))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
((creative(john)|~kind(john)))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:(humble(X))) | brave(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9017328222440375896437598
% SZS output start Proof for 9017328222440375896437598
16. ! [X0] : ((calm(X0) & ~brave(X0)) <=> brave(X0)) [input p15]
24. brave(alice) [input hypothesis]
68. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | (~calm(X0) | brave(X0)))) [nnf transformation 16]
69. ! [X0] : (((calm(X0) & ~brave(X0)) | ~brave(X0)) & (brave(X0) | ~calm(X0) | brave(X0))) [flattening 68]
137. ~brave(X0) | ~brave(X0) [cnf transformation 69]
151. brave(alice) [cnf transformation 24]
153. ~brave(X0) [duplicate literal removal 137]
350. $false [subsumption resolution 151,153]
% SZS output end Proof for 9017328222440375896437598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and rich then someone is curious or humble. Everyone who is either creative or not tall is both not quiet and not tall. If paul is either not generous or not kind then someone is not generous and vice versa. Everyone who is both not patient and strong is not patient. If someone is either not happy or humble then fred is not kind and vice versa. If paul is not funny then lucy is brave or quiet and vice versa. Everyone who is both not funny and curious is not calm. If mary is not happy then susan is either funny or not curious and vice versa. Everyone who is humble or strong is both tall and not wise. Everyone who is kind is both not funny and not calm. Everyone who is not happy is creative and vice versa. If someone is both not quiet and not wise then someone is tall or not rich. Everyone who is brave or calm is both generous and not wise. Everyone who is either not brave or creative is either not quiet or curious and vice versa. Everyone who is rich or not funny is either happy or curious. If someone is not tall or not happy then susan is both not funny and not tall. Alice is not brave. Someone is calm. Someone is both not kind and not calm. Susan is both strong and not humble. Someone is both old and curious. Someone is tall or not old. Someone is calm or brave. Someone is strong or kind. | Lucy is not happy. | contradiction | ((?[X]:((tall(X)&rich(X))))=>(?[X]:((curious(X)|humble(X)))))&
(![X]:((creative(X)<~>~tall(X))=>(~quiet(X)&~tall(X))))&
(((~generous(paul)<~>~kind(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((~patient(X)&strong(X))=>~patient(X)))&
((?[X]:((~happy(X)<~>humble(X))))<=>(~kind(fred)))&
((~funny(paul))<=>((brave(lucy)|quiet(lucy))))&
(![X]:((~funny(X)&curious(X))=>~calm(X)))&
((~happy(mary))<=>((funny(susan)<~>~curious(susan))))&
(![X]:((humble(X)|strong(X))=>(tall(X)&~wise(X))))&
(![X]:(kind(X)=>(~funny(X)&~calm(X))))&
(![X]:(~happy(X)<=>creative(X)))&
((?[X]:((~quiet(X)&~wise(X))))=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((brave(X)|calm(X))=>(generous(X)&~wise(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((rich(X)|~funny(X))=>(happy(X)<~>curious(X))))&
((?[X]:((~tall(X)|~happy(X))))=>((~funny(susan)&~tall(susan))))&
(~brave(alice))&
(?[X]:(calm(X)))&
(?[X]:((~kind(X)&~calm(X))))&
((strong(susan)&~humble(susan)))&
(?[X]:((old(X)&curious(X))))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((strong(X)|kind(X)))) | ~happy(lucy) | [
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 218409994765594615624485
% SZS output start Proof for 218409994765594615624485
9. ! [X0] : ((strong(X0) | humble(X0)) => (~wise(X0) & tall(X0))) [input p8]
16. ? [X0] : (~happy(X0) | ~tall(X0)) => (~tall(susan) & ~funny(susan)) [input p15]
20. ~humble(susan) & strong(susan) [input p19]
25. ~happy(lucy) [input hypothesis]
31. ! [X0] : ((strong(X0) | humble(X0)) => tall(X0)) [pure predicate removal 9]
38. ! [X0] : (tall(X0) | (~strong(X0) & ~humble(X0))) [ennf transformation 31]
42. (~tall(susan) & ~funny(susan)) | ! [X0] : (happy(X0) & tall(X0)) [ennf transformation 16]
92. ~strong(X0) | tall(X0) [cnf transformation 38]
112. ~tall(susan) | happy(X0) [cnf transformation 42]
117. strong(susan) [cnf transformation 20]
124. ~happy(lucy) [cnf transformation 25]
199. 16 <=> ! [X0] : happy(X0) [avatar definition]
200. happy(X0) <- (16) [avatar component clause 199]
202. 17 <=> tall(susan) [avatar definition]
205. 16 | ~17 [avatar split clause 112,202,199]
239. tall(susan) [resolution 92,117]
243. 17 [avatar split clause 239,202]
244. $false <- (16) [resolution 200,124]
249. ~16 [avatar contradiction clause 244]
250. $false [avatar sat refutation 205,243,249]
% SZS output end Proof for 218409994765594615624485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not tall then someone is not patient. If someone is not creative then someone is either not curious or quiet. If someone is either happy or not brave then someone is both happy and creative and vice versa. Everyone who is not rich is either not rich or curious and vice versa. Everyone who is not curious is not happy and vice versa. If someone is both not rich and not brave then someone is not old and vice versa. Everyone who is both happy and patient is not strong. Everyone who is both not quiet and rich is not quiet or wise. Everyone who is creative or not rich is not strong or patient. Everyone who is either curious or old is both not curious and kind. If paul is both not strong and not kind then someone is wise or not calm and vice versa. Everyone who is not funny or not quiet is either not wise or creative. Everyone who is both curious and patient is both not strong and old. If alice is either not funny or rich then someone is either not patient or funny. Alice is not wise. Mary is both rich and not wise. Someone is either happy or calm. Susan is either not rich or patient. Mary is not creative or not patient. Alice is calm. Alice is both not curious and not creative. | Paul is curious. | contradiction | ((~tall(paul))=>(?[X]:(~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~curious(X)<~>quiet(X)))))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((happy(X)&creative(X)))))&
(![X]:(~rich(X)<=>(~rich(X)<~>curious(X))))&
(![X]:(~curious(X)<=>~happy(X)))&
((?[X]:((~rich(X)&~brave(X))))<=>(?[X]:(~old(X))))&
(![X]:((happy(X)&patient(X))=>~strong(X)))&
(![X]:((~quiet(X)&rich(X))=>(~quiet(X)|wise(X))))&
(![X]:((creative(X)|~rich(X))=>(~strong(X)|patient(X))))&
(![X]:((curious(X)<~>old(X))=>(~curious(X)&kind(X))))&
(((~strong(paul)&~kind(paul)))<=>(?[X]:((wise(X)|~calm(X)))))&
(![X]:((~funny(X)|~quiet(X))=>(~wise(X)<~>creative(X))))&
(![X]:((curious(X)&patient(X))=>(~strong(X)&old(X))))&
(((~funny(alice)<~>rich(alice)))=>(?[X]:((~patient(X)<~>funny(X)))))&
(~wise(alice))&
((rich(mary)&~wise(mary)))&
(?[X]:((happy(X)<~>calm(X))))&
((~rich(susan)<~>patient(susan)))&
((~creative(mary)|~patient(mary)))&
(calm(alice))&
((~curious(alice)&~creative(alice))) | curious(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 8074933918775382889665637
% SZS output start Proof for 8074933918775382889665637
4. ! [X0] : (~rich(X0) <=> (~rich(X0) <~> curious(X0))) [input p3]
22. curious(paul) [input hypothesis]
48. ! [X0] : ((~rich(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0)))) & (((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | rich(X0))) [nnf transformation 4]
78. ~curious(X0) | rich(X0) | rich(X0) [cnf transformation 48]
80. ~rich(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 48]
120. curious(paul) [cnf transformation 22]
122. ~curious(X0) | rich(X0) [duplicate literal removal 78]
123. ~rich(X0) | ~curious(X0) [duplicate literal removal 80]
168. ~curious(X0) [subsumption resolution 122,123]
259. $false [subsumption resolution 120,168]
% SZS output end Proof for 8074933918775382889665637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then john is not humble and vice versa.
Everyone who is humble is creative or not strong.
If mary is humble or funny then someone is either not curious or not patient.
If someone is humble or tall then someone is either funny or humble.
Everyone who is both curious and not wise is happy or humble and vice versa.
If mary is patient then someone is both calm and happy and vice versa.
If alice is both wise and not old then someone is either not calm or creative and vice versa.
If someone is either not brave or not creative then alice is curious.
Everyone who is rich or not generous is both not wise and creative.
Everyone who is not quiet or not patient is not curious and vice versa.
If someone is not quiet then someone is both not happy and old and vice versa.
If alice is patient then someone is quiet and vice versa.
Everyone who is both kind and wise is both not humble and happy and vice versa.
If alice is either not funny or quiet then someone is both not tall and curious.
If someone is both generous and humble then someone is both rich and kind and vice versa.
Everyone who is either brave or not rich is either quiet or not kind and vice versa.
Someone is tall or old.
Someone is either kind or not patient.
Mary is tall or not happy.
Alice is not patient.
Someone is generous or not strong.
Someone is either not strong or not wise.
Someone is either not funny or not brave. | Mary is not humble. | entailment | ((?[X]:(~quiet(X)))<=>(~humble(john)))&
(![X]:(humble(X)=>(creative(X)|~strong(X))))&
(((humble(mary)|funny(mary)))=>(?[X]:((~curious(X)<~>~patient(X)))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:((curious(X)&~wise(X))<=>(happy(X)|humble(X))))&
((patient(mary))<=>(?[X]:((calm(X)&happy(X)))))&
(((wise(alice)&~old(alice)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((~brave(X)<~>~creative(X))))=>(curious(alice)))&
(![X]:((rich(X)|~generous(X))=>(~wise(X)&creative(X))))&
(![X]:((~quiet(X)|~patient(X))<=>~curious(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~happy(X)&old(X)))))&
((patient(alice))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&wise(X))<=>(~humble(X)&happy(X))))&
(((~funny(alice)<~>quiet(alice)))=>(?[X]:((~tall(X)&curious(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~kind(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
((tall(mary)|~happy(mary)))&
(~patient(alice))&
(?[X]:((generous(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:((~funny(X)<~>~brave(X)))) | ~humble(mary) | [
"p4",
"p9",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 370983947756147062556547
% SZS output start Proof for 370983947756147062556547
5. ! [X0] : ((~wise(X0) & curious(X0)) <=> (humble(X0) | happy(X0))) [input p4]
10. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> ~curious(X0)) [input p9]
12. patient(alice) <=> ? [X0] : quiet(X0) [input p11]
20. ~patient(alice) [input p19]
24. humble(mary) [input hypothesis]
46. ! [X0] : (((~wise(X0) & curious(X0)) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | (wise(X0) | ~curious(X0)))) [nnf transformation 5]
47. ! [X0] : (((~wise(X0) & curious(X0)) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | wise(X0) | ~curious(X0))) [flattening 46]
58. ! [X0] : (((~patient(X0) | ~quiet(X0)) | curious(X0)) & (~curious(X0) | (patient(X0) & quiet(X0)))) [nnf transformation 10]
59. ! [X0] : ((~patient(X0) | ~quiet(X0) | curious(X0)) & (~curious(X0) | (patient(X0) & quiet(X0)))) [flattening 58]
65. (patient(alice) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~patient(alice)) [nnf transformation 12]
66. (patient(alice) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~patient(alice)) [rectify 65]
67. ? [X1] : quiet(X1) => quiet(sK7) [choice axiom]
68. (patient(alice) | ! [X0] : ~quiet(X0)) & (quiet(sK7) | ~patient(alice)) [skolemisation 66,67]
106. ~humble(X0) | curious(X0) [cnf transformation 47]
124. ~curious(X0) | quiet(X0) [cnf transformation 59]
131. patient(alice) | ~quiet(X0) [cnf transformation 68]
156. ~patient(alice) [cnf transformation 20]
162. humble(mary) [cnf transformation 24]
190. 7 <=> humble(mary) [avatar definition]
191. humble(mary) <- (7) [avatar component clause 190]
291. 29 <=> ! [X0] : ~quiet(X0) [avatar definition]
292. ~quiet(X0) <- (29) [avatar component clause 291]
294. 30 <=> patient(alice) [avatar definition]
297. 29 | 30 [avatar split clause 131,294,291]
379. ~30 [avatar split clause 156,294]
409. 7 [avatar split clause 162,190]
414. curious(mary) <- (7) [resolution 106,191]
417. quiet(mary) <- (7) [resolution 124,414]
422. $false <- (7, 29) [subsumption resolution 417,292]
423. ~7 | ~29 [avatar contradiction clause 422]
424. $false [avatar sat refutation 297,379,409,423]
% SZS output end Proof for 370983947756147062556547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or calm then mary is either old or not quiet and vice versa. Everyone who is both not brave and patient is both old and rich and vice versa. Everyone who is either not wise or not strong is both not curious and happy and vice versa. Everyone who is calm or not brave is either calm or patient. Everyone who is wise or brave is both generous and not curious. Everyone who is either not creative or calm is humble and vice versa. If mary is not generous then lucy is either brave or creative. Everyone who is old is wise or quiet and vice versa. Everyone who is either not funny or not patient is both calm and curious. If someone is both not calm and creative then paul is either not brave or not tall. If fred is either generous or not generous then mary is either kind or brave. If someone is either funny or tall then someone is both curious and not old and vice versa. Everyone who is strong or not humble is either not happy or not wise and vice versa. Everyone who is not wise is funny. Everyone who is not happy or not old is both not generous and generous and vice versa. If someone is both brave and not strong then someone is either not tall or strong. Lucy is both quiet and not kind. Lucy is either not creative or patient. Fred is both old and not brave. Alice is kind or rich. Paul is both quiet and strong. Mary is old or strong. John is funny. | Paul is not tall. | contradiction | ((?[X]:((~curious(X)|calm(X))))<=>((old(mary)<~>~quiet(mary))))&
(![X]:((~brave(X)&patient(X))<=>(old(X)&rich(X))))&
(![X]:((~wise(X)<~>~strong(X))<=>(~curious(X)&happy(X))))&
(![X]:((calm(X)|~brave(X))=>(calm(X)<~>patient(X))))&
(![X]:((wise(X)|brave(X))=>(generous(X)&~curious(X))))&
(![X]:((~creative(X)<~>calm(X))<=>humble(X)))&
((~generous(mary))=>((brave(lucy)<~>creative(lucy))))&
(![X]:(old(X)<=>(wise(X)|quiet(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(calm(X)&curious(X))))&
((?[X]:((~calm(X)&creative(X))))=>((~brave(paul)<~>~tall(paul))))&
(((generous(fred)<~>~generous(fred)))=>((kind(mary)<~>brave(mary))))&
((?[X]:((funny(X)<~>tall(X))))<=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((strong(X)|~humble(X))<=>(~happy(X)<~>~wise(X))))&
(![X]:(~wise(X)=>funny(X)))&
(![X]:((~happy(X)|~old(X))<=>(~generous(X)&generous(X))))&
((?[X]:((brave(X)&~strong(X))))=>(?[X]:((~tall(X)<~>strong(X)))))&
((quiet(lucy)&~kind(lucy)))&
((~creative(lucy)<~>patient(lucy)))&
((old(fred)&~brave(fred)))&
((kind(alice)|rich(alice)))&
((quiet(paul)&strong(paul)))&
((old(mary)|strong(mary)))&
(funny(john)) | ~tall(paul) | [
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8432715231135003282598890
% SZS output start Proof for 8432715231135003282598890
12. ? [X0] : (funny(X0) <~> tall(X0)) <=> ? [X0] : (~old(X0) & curious(X0)) [input p11]
13. ! [X0] : ((~humble(X0) | strong(X0)) <=> (~happy(X0) <~> ~wise(X0))) [input p12]
14. ! [X0] : (~wise(X0) => funny(X0)) [input p13]
15. ! [X0] : ((~old(X0) | ~happy(X0)) <=> (generous(X0) & ~generous(X0))) [input p14]
21. strong(paul) & quiet(paul) [input p20]
24. ~tall(paul) [input hypothesis]
25. ? [X0] : (funny(X0) <~> tall(X0)) <=> ? [X1] : (~old(X1) & curious(X1)) [rectify 12]
33. ! [X0] : (funny(X0) | wise(X0)) [ennf transformation 14]
51. (? [X0] : ((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | ! [X1] : (old(X1) | ~curious(X1))) & (? [X1] : (~old(X1) & curious(X1)) | ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0)))) [nnf transformation 25]
52. (? [X0] : ((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | ! [X1] : (old(X1) | ~curious(X1))) & (? [X2] : (~old(X2) & curious(X2)) | ! [X3] : ((funny(X3) | ~tall(X3)) & (tall(X3) | ~funny(X3)))) [rectify 51]
53. ? [X0] : ((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) => ((~tall(sK1) | ~funny(sK1)) & (tall(sK1) | funny(sK1))) [choice axiom]
54. ? [X2] : (~old(X2) & curious(X2)) => (~old(sK2) & curious(sK2)) [choice axiom]
55. (((~tall(sK1) | ~funny(sK1)) & (tall(sK1) | funny(sK1))) | ! [X1] : (old(X1) | ~curious(X1))) & ((~old(sK2) & curious(sK2)) | ! [X3] : ((funny(X3) | ~tall(X3)) & (tall(X3) | ~funny(X3)))) [skolemisation 52,54,53]
56. ! [X0] : (((~humble(X0) | strong(X0)) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) & (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (humble(X0) & ~strong(X0)))) [nnf transformation 13]
57. ! [X0] : ((~humble(X0) | strong(X0) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) & (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (humble(X0) & ~strong(X0)))) [flattening 56]
58. ! [X0] : (((~old(X0) | ~happy(X0)) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | (old(X0) & happy(X0)))) [nnf transformation 15]
59. ! [X0] : ((~old(X0) | ~happy(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | (old(X0) & happy(X0)))) [flattening 58]
110. ~old(sK2) | tall(X3) | ~funny(X3) [cnf transformation 55]
114. ~happy(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 57]
120. funny(X0) | wise(X0) [cnf transformation 33]
121. ~generous(X0) | happy(X0) [cnf transformation 59]
122. ~generous(X0) | old(X0) [cnf transformation 59]
123. generous(X0) | happy(X0) [cnf transformation 59]
124. generous(X0) | old(X0) [cnf transformation 59]
136. strong(paul) [cnf transformation 21]
139. ~tall(paul) [cnf transformation 24]
196. 12 <=> tall(paul) [avatar definition]
197. ~tall(paul) <- (~12) [avatar component clause 196]
234. 20 <=> old(sK2) [avatar definition]
236. ~old(sK2) <- (~20) [avatar component clause 234]
239. 21 <=> ! [X3] : (tall(X3) | ~funny(X3)) [avatar definition]
240. ~funny(X3) | tall(X3) <- (21) [avatar component clause 239]
241. 21 | ~20 [avatar split clause 110,234,239]
248. old(X0) [subsumption resolution 122,124]
249. happy(X0) [subsumption resolution 121,123]
278. ~12 [avatar split clause 139,196]
285. tall(X0) | wise(X0) <- (21) [resolution 240,120]
287. wise(paul) <- (~12, 21) [resolution 285,197]
361. ~strong(X0) | ~wise(X0) [resolution 114,249]
365. ~wise(paul) [resolution 361,136]
366. $false <- (~12, 21) [subsumption resolution 365,287]
367. 12 | ~21 [avatar contradiction clause 366]
369. $false <- (~20) [subsumption resolution 236,248]
370. 20 [avatar contradiction clause 369]
371. $false [avatar sat refutation 241,278,367,370]
% SZS output end Proof for 8432715231135003282598890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or old then someone is either not funny or brave and vice versa.
Everyone who is not curious is both quiet and curious and vice versa.
Everyone who is either not happy or funny is both not tall and old.
If paul is both not happy and happy then someone is brave and vice versa.
Everyone who is either kind or funny is calm and vice versa.
If someone is either strong or not generous then someone is both quiet and not tall.
If john is both strong and not brave then susan is not generous or creative.
Everyone who is either not kind or not creative is both not brave and not creative.
If someone is either not rich or not calm then alice is not kind or not tall.
Everyone who is not strong is not rich.
Everyone who is old is both brave and creative and vice versa.
Everyone who is strong or creative is both not wise and old.
Everyone who is either curious or not curious is either calm or not curious and vice versa.
Everyone who is either happy or wise is kind or funny and vice versa.
If someone is happy then someone is not brave or not curious.
Someone is both calm and not tall.
Someone is kind.
Someone is not generous or not old.
Someone is either rich or calm.
Alice is either not humble or not creative.
Someone is not happy.
Susan is either not tall or not curious. | Paul is not rich. | entailment | ((?[X]:((~old(X)|old(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:(~curious(X)<=>(quiet(X)&curious(X))))&
(![X]:((~happy(X)<~>funny(X))=>(~tall(X)&old(X))))&
(((~happy(paul)&happy(paul)))<=>(?[X]:(brave(X))))&
(![X]:((kind(X)<~>funny(X))<=>calm(X)))&
((?[X]:((strong(X)<~>~generous(X))))=>(?[X]:((quiet(X)&~tall(X)))))&
(((strong(john)&~brave(john)))=>((~generous(susan)|creative(susan))))&
(![X]:((~kind(X)<~>~creative(X))=>(~brave(X)&~creative(X))))&
((?[X]:((~rich(X)<~>~calm(X))))=>((~kind(alice)|~tall(alice))))&
(![X]:(~strong(X)=>~rich(X)))&
(![X]:(old(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)|creative(X))=>(~wise(X)&old(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)|funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((~brave(X)|~curious(X)))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~generous(X)|~old(X))))&
(?[X]:((rich(X)<~>calm(X))))&
((~humble(alice)<~>~creative(alice)))&
(?[X]:(~happy(X)))&
((~tall(susan)<~>~curious(susan))) | ~rich(paul) | [
"p3",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1000807346540624684521013
% SZS output start Proof for 1000807346540624684521013
4. (happy(paul) & ~happy(paul)) <=> ? [X0] : brave(X0) [input p3]
10. ! [X0] : (~strong(X0) => ~rich(X0)) [input p9]
11. ! [X0] : (old(X0) <=> (creative(X0) & brave(X0))) [input p10]
12. ! [X0] : ((creative(X0) | strong(X0)) => (old(X0) & ~wise(X0))) [input p11]
23. rich(paul) [input hypothesis]
34. ! [X0] : (~rich(X0) | strong(X0)) [ennf transformation 10]
35. ! [X0] : ((old(X0) & ~wise(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 12]
45. ((happy(paul) & ~happy(paul)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~happy(paul) | happy(paul))) [nnf transformation 4]
46. ((happy(paul) & ~happy(paul)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~happy(paul) | happy(paul)) [flattening 45]
47. ((happy(paul) & ~happy(paul)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~happy(paul) | happy(paul)) [rectify 46]
48. ? [X1] : brave(X1) => brave(sK2) [choice axiom]
49. ((happy(paul) & ~happy(paul)) | ! [X0] : ~brave(X0)) & (brave(sK2) | ~happy(paul) | happy(paul)) [skolemisation 47,48]
57. ! [X0] : ((old(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ~old(X0))) [nnf transformation 11]
58. ! [X0] : ((old(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ~old(X0))) [flattening 57]
92. ~happy(paul) | ~brave(X0) [cnf transformation 49]
93. happy(paul) | ~brave(X0) [cnf transformation 49]
109. ~rich(X0) | strong(X0) [cnf transformation 34]
110. ~old(X0) | brave(X0) [cnf transformation 58]
115. ~strong(X0) | old(X0) [cnf transformation 35]
143. rich(paul) [cnf transformation 23]
174. 5 <=> ! [X0] : ~brave(X0) [avatar definition]
175. ~brave(X0) <- (5) [avatar component clause 174]
177. 6 <=> happy(paul) [avatar definition]
180. 5 | 6 [avatar split clause 93,177,174]
181. 5 | ~6 [avatar split clause 92,177,174]
264. strong(paul) [resolution 109,143]
265. old(paul) [resolution 115,264]
267. brave(paul) [resolution 265,110]
268. $false <- (5) [subsumption resolution 267,175]
269. ~5 [avatar contradiction clause 268]
270. $false [avatar sat refutation 180,181,269]
% SZS output end Proof for 1000807346540624684521013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or creative then john is either not wise or not humble and vice versa. Everyone who is both funny and not strong is not curious or not generous. If fred is either curious or not generous then alice is both not happy and patient. If someone is either kind or not kind then someone is both not calm and not generous and vice versa. Everyone who is both funny and old is curious or strong and vice versa. If john is not old or generous then someone is brave or tall and vice versa. If someone is both not kind and patient then someone is both brave and not strong. Everyone who is either not happy or rich is either strong or funny. Everyone who is rich or happy is not brave or not creative and vice versa. If paul is not calm or not quiet then someone is both not creative and generous and vice versa. Everyone who is kind or not quiet is not strong or strong. If alice is both not strong and brave then lucy is both not wise and calm. Everyone who is curious is either not creative or tall. If lucy is not patient then someone is both not humble and patient and vice versa. Everyone who is not generous is old and vice versa. Everyone who is quiet or not kind is both old and humble and vice versa. Susan is either creative or not rich. Someone is calm. Someone is not rich. Alice is both humble and not creative. Someone is both happy and not calm. Someone is creative or generous. Someone is either humble or creative. | Paul is not calm. | neutral | ((?[X]:((funny(X)|creative(X))))<=>((~wise(john)<~>~humble(john))))&
(![X]:((funny(X)&~strong(X))=>(~curious(X)|~generous(X))))&
(((curious(fred)<~>~generous(fred)))=>((~happy(alice)&patient(alice))))&
((?[X]:((kind(X)<~>~kind(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)&old(X))<=>(curious(X)|strong(X))))&
(((~old(john)|generous(john)))<=>(?[X]:((brave(X)|tall(X)))))&
((?[X]:((~kind(X)&patient(X))))=>(?[X]:((brave(X)&~strong(X)))))&
(![X]:((~happy(X)<~>rich(X))=>(strong(X)<~>funny(X))))&
(![X]:((rich(X)|happy(X))<=>(~brave(X)|~creative(X))))&
(((~calm(paul)|~quiet(paul)))<=>(?[X]:((~creative(X)&generous(X)))))&
(![X]:((kind(X)|~quiet(X))=>(~strong(X)|strong(X))))&
(((~strong(alice)&brave(alice)))=>((~wise(lucy)&calm(lucy))))&
(![X]:(curious(X)=>(~creative(X)<~>tall(X))))&
((~patient(lucy))<=>(?[X]:((~humble(X)&patient(X)))))&
(![X]:(~generous(X)<=>old(X)))&
(![X]:((quiet(X)|~kind(X))<=>(old(X)&humble(X))))&
((creative(susan)<~>~rich(susan)))&
(?[X]:(calm(X)))&
(?[X]:(~rich(X)))&
((humble(alice)&~creative(alice)))&
(?[X]:((happy(X)&~calm(X))))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:((humble(X)<~>creative(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is kind or not humble is either tall or strong.
If someone is happy then alice is both wise and not wise.
Everyone who is both not brave and rich is both not rich and kind and vice versa.
Everyone who is either not quiet or tall is either not funny or not patient.
If john is both not old and old then someone is both old and funny.
Everyone who is not wise or tall is not wise.
If alice is both not strong and humble then someone is either not calm or not old and vice versa.
If alice is both kind and not tall then alice is brave or not happy and vice versa.
Everyone who is not brave is either humble or not funny and vice versa.
Everyone who is calm is both tall and not curious.
If fred is either not patient or humble then someone is not tall.
Everyone who is either creative or calm is not creative or happy.
Everyone who is funny is either tall or creative and vice versa.
If john is not creative then someone is happy and vice versa.
If paul is not happy or kind then someone is either tall or not brave.
John is tall or not old.
Someone is not strong.
Susan is not tall or not brave.
Someone is not rich.
Susan is old.
Someone is curious or not generous.
Someone is either humble or funny.
Mary is both not creative and curious. | Alice is humble. | entailment | (![X]:((kind(X)|~humble(X))=>(tall(X)<~>strong(X))))&
((?[X]:(happy(X)))=>((wise(alice)&~wise(alice))))&
(![X]:((~brave(X)&rich(X))<=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~funny(X)<~>~patient(X))))&
(((~old(john)&old(john)))=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~wise(X)|tall(X))=>~wise(X)))&
(((~strong(alice)&humble(alice)))<=>(?[X]:((~calm(X)<~>~old(X)))))&
(((kind(alice)&~tall(alice)))<=>((brave(alice)|~happy(alice))))&
(![X]:(~brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(calm(X)=>(tall(X)&~curious(X))))&
(((~patient(fred)<~>humble(fred)))=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>calm(X))=>(~creative(X)|happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>creative(X))))&
((~creative(john))<=>(?[X]:(happy(X))))&
(((~happy(paul)|kind(paul)))=>(?[X]:((tall(X)<~>~brave(X)))))&
((tall(john)|~old(john)))&
(?[X]:(~strong(X)))&
((~tall(susan)|~brave(susan)))&
(?[X]:(~rich(X)))&
(old(susan))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((humble(X)<~>funny(X))))&
((~creative(mary)&curious(mary))) | humble(alice) | [
"p1",
"p2",
"p7",
"p8",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8316342045131861181713696
% SZS output start Proof for 8316342045131861181713696
2. ? [X0] : happy(X0) => (~wise(alice) & wise(alice)) [input p1]
3. ! [X0] : ((rich(X0) & ~brave(X0)) <=> (kind(X0) & ~rich(X0))) [input p2]
8. (~tall(alice) & kind(alice)) <=> (~happy(alice) | brave(alice)) [input p7]
9. ! [X0] : (~brave(X0) <=> (humble(X0) <~> ~funny(X0))) [input p8]
10. ! [X0] : (calm(X0) => (~curious(X0) & tall(X0))) [input p9]
12. ! [X0] : ((creative(X0) <~> calm(X0)) => (happy(X0) | ~creative(X0))) [input p11]
13. ! [X0] : (funny(X0) <=> (tall(X0) <~> creative(X0))) [input p12]
24. ~humble(alice) [input hypothesis]
27. (~wise(alice) & wise(alice)) | ! [X0] : ~happy(X0) [ennf transformation 2]
32. ! [X0] : ((~curious(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 10]
34. ! [X0] : ((happy(X0) | ~creative(X0)) | (creative(X0) <=> calm(X0))) [ennf transformation 12]
35. ! [X0] : (happy(X0) | ~creative(X0) | (creative(X0) <=> calm(X0))) [flattening 34]
38. ! [X0] : (((rich(X0) & ~brave(X0)) | (~kind(X0) | rich(X0))) & ((kind(X0) & ~rich(X0)) | (~rich(X0) | brave(X0)))) [nnf transformation 3]
39. ! [X0] : (((rich(X0) & ~brave(X0)) | ~kind(X0) | rich(X0)) & ((kind(X0) & ~rich(X0)) | ~rich(X0) | brave(X0))) [flattening 38]
48. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & ((~happy(alice) | brave(alice)) | (tall(alice) | ~kind(alice))) [nnf transformation 8]
49. ((~tall(alice) & kind(alice)) | (happy(alice) & ~brave(alice))) & (~happy(alice) | brave(alice) | tall(alice) | ~kind(alice)) [flattening 48]
50. ! [X0] : ((~brave(X0) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | brave(X0))) [nnf transformation 9]
54. ! [X0] : (happy(X0) | ~creative(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 35]
55. ! [X0] : ((funny(X0) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | ~funny(X0))) [nnf transformation 13]
74. wise(alice) | ~happy(X0) [cnf transformation 27]
75. ~wise(alice) | ~happy(X0) [cnf transformation 27]
76. ~rich(X0) | ~rich(X0) | brave(X0) [cnf transformation 39]
79. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 39]
96. kind(alice) | happy(alice) [cnf transformation 49]
98. ~tall(alice) | happy(alice) [cnf transformation 49]
102. ~brave(X0) | humble(X0) | funny(X0) [cnf transformation 50]
103. ~calm(X0) | tall(X0) [cnf transformation 32]
107. happy(X0) | ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 54]
109. ~funny(X0) | tall(X0) | creative(X0) [cnf transformation 55]
128. ~humble(alice) [cnf transformation 24]
129. ~creative(X0) | happy(X0) | calm(X0) [duplicate literal removal 107]
130. ~rich(X0) | brave(X0) [duplicate literal removal 76]
131. ~kind(X0) | rich(X0) [duplicate literal removal 79]
133. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
134. ~happy(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(alice) [avatar definition]
139. 1 | ~2 [avatar split clause 75,136,133]
140. 1 | 2 [avatar split clause 74,136,133]
145. 4 <=> humble(alice) [avatar definition]
146. ~humble(alice) <- (~4) [avatar component clause 145]
170. 9 <=> happy(alice) [avatar definition]
171. ~happy(alice) <- (~9) [avatar component clause 170]
172. happy(alice) <- (9) [avatar component clause 170]
174. 10 <=> tall(alice) [avatar definition]
176. ~tall(alice) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 98,174,170]
179. 11 <=> brave(alice) [avatar definition]
180. brave(alice) <- (11) [avatar component clause 179]
184. 12 <=> kind(alice) [avatar definition]
186. kind(alice) <- (12) [avatar component clause 184]
187. 9 | 12 [avatar split clause 96,184,170]
262. ~4 [avatar split clause 128,145]
264. rich(alice) <- (12) [resolution 131,186]
265. brave(alice) <- (12) [resolution 264,130]
266. 11 | ~12 [avatar split clause 265,184,179]
305. humble(alice) | funny(alice) <- (11) [resolution 102,180]
307. funny(alice) <- (~4, 11) [subsumption resolution 305,146]
311. tall(alice) | creative(alice) <- (~4, 11) [resolution 109,307]
321. creative(alice) <- (~4, ~10, 11) [subsumption resolution 311,176]
369. happy(alice) | calm(alice) <- (~4, ~10, 11) [resolution 321,129]
372. calm(alice) <- (~4, ~9, ~10, 11) [subsumption resolution 369,171]
375. tall(alice) <- (~4, ~9, ~10, 11) [resolution 372,103]
376. $false <- (~4, ~9, ~10, 11) [subsumption resolution 375,176]
377. 4 | 9 | 10 | ~11 [avatar contradiction clause 376]
379. $false <- (1, 9) [subsumption resolution 172,134]
380. ~1 | ~9 [avatar contradiction clause 379]
381. $false [avatar sat refutation 139,140,177,187,262,266,377,380]
% SZS output end Proof for 8316342045131861181713696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or calm is patient and vice versa.
If lucy is kind then susan is not kind.
Everyone who is calm or not curious is either not patient or tall.
If someone is either not happy or not strong then susan is both funny and kind and vice versa.
If susan is either not funny or happy then someone is either not generous or generous.
If fred is wise then john is either happy or not happy and vice versa.
Everyone who is either wise or not brave is humble or generous.
Everyone who is strong is happy.
Everyone who is either not calm or not old is not humble and vice versa.
If john is either old or not brave then lucy is both wise and kind and vice versa.
If fred is wise or not strong then paul is strong.
If someone is creative or rich then someone is either calm or not happy and vice versa.
Everyone who is either not tall or not patient is both creative and brave.
Everyone who is not wise or kind is both funny and not strong and vice versa.
If fred is funny or curious then alice is not strong or kind and vice versa.
Paul is either calm or not generous.
Someone is not wise.
Susan is either not old or old.
Lucy is not quiet.
John is not wise.
Lucy is calm.
Someone is not strong. | Paul is wise. | entailment | (![X]:((~curious(X)|calm(X))<=>patient(X)))&
((kind(lucy))=>(~kind(susan)))&
(![X]:((calm(X)|~curious(X))=>(~patient(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>~strong(X))))<=>((funny(susan)&kind(susan))))&
(((~funny(susan)<~>happy(susan)))=>(?[X]:((~generous(X)<~>generous(X)))))&
((wise(fred))<=>((happy(john)<~>~happy(john))))&
(![X]:((wise(X)<~>~brave(X))=>(humble(X)|generous(X))))&
(![X]:(strong(X)=>happy(X)))&
(![X]:((~calm(X)<~>~old(X))<=>~humble(X)))&
(((old(john)<~>~brave(john)))<=>((wise(lucy)&kind(lucy))))&
(((wise(fred)|~strong(fred)))=>(strong(paul)))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:((~tall(X)<~>~patient(X))=>(creative(X)&brave(X))))&
(![X]:((~wise(X)|kind(X))<=>(funny(X)&~strong(X))))&
(((funny(fred)|curious(fred)))<=>((~strong(alice)|kind(alice))))&
((calm(paul)<~>~generous(paul)))&
(?[X]:(~wise(X)))&
((~old(susan)<~>old(susan)))&
(~quiet(lucy))&
(~wise(john))&
(calm(lucy))&
(?[X]:(~strong(X))) | wise(paul) | [
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 145319573084493378298583
% SZS output start Proof for 145319573084493378298583
6. wise(fred) <=> (happy(john) <~> ~happy(john)) [input p5]
11. (~strong(fred) | wise(fred)) => strong(paul) [input p10]
14. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (~strong(X0) & funny(X0))) [input p13]
23. ~wise(paul) [input hypothesis]
34. strong(paul) | (strong(fred) & ~wise(fred)) [ennf transformation 11]
47. (wise(fred) | ((happy(john) | happy(john)) & (~happy(john) | ~happy(john)))) & (((happy(john) | ~happy(john)) & (~happy(john) | happy(john))) | ~wise(fred)) [nnf transformation 6]
58. ! [X0] : (((kind(X0) | ~wise(X0)) | (strong(X0) | ~funny(X0))) & ((~strong(X0) & funny(X0)) | (~kind(X0) & wise(X0)))) [nnf transformation 14]
59. ! [X0] : ((kind(X0) | ~wise(X0) | strong(X0) | ~funny(X0)) & ((~strong(X0) & funny(X0)) | (~kind(X0) & wise(X0)))) [flattening 58]
88. wise(fred) | ~happy(john) | ~happy(john) [cnf transformation 47]
89. wise(fred) | happy(john) | happy(john) [cnf transformation 47]
101. strong(paul) | ~wise(fred) [cnf transformation 34]
115. ~strong(X0) | wise(X0) [cnf transformation 59]
130. ~wise(paul) [cnf transformation 23]
131. wise(fred) | ~happy(john) [duplicate literal removal 88]
132. wise(fred) | happy(john) [duplicate literal removal 89]
169. 8 <=> happy(john) [avatar definition]
173. 9 <=> wise(fred) [avatar definition]
176. 8 | 9 [avatar split clause 132,173,169]
177. ~8 | 9 [avatar split clause 131,173,169]
202. 14 <=> strong(paul) [avatar definition]
204. strong(paul) <- (14) [avatar component clause 202]
206. ~9 | 14 [avatar split clause 101,202,173]
278. wise(paul) <- (14) [resolution 115,204]
279. $false <- (14) [subsumption resolution 278,130]
280. ~14 [avatar contradiction clause 279]
281. $false [avatar sat refutation 176,177,206,280]
% SZS output end Proof for 145319573084493378298583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and quiet is either strong or not brave.
Everyone who is strong is happy and vice versa.
If fred is tall then someone is both not creative and strong and vice versa.
If mary is both kind and generous then someone is not patient or tall and vice versa.
If someone is not strong then someone is either generous or not quiet and vice versa.
Everyone who is not patient or not generous is old and vice versa.
If susan is both humble and not happy then lucy is both curious and not funny and vice versa.
Everyone who is not kind or not funny is either curious or generous.
If fred is both not creative and old then someone is either generous or not generous.
Everyone who is old is both not strong and not rich and vice versa.
Everyone who is either not old or not funny is both patient and not generous and vice versa.
Everyone who is either not kind or not creative is both not humble and not happy and vice versa.
Everyone who is both not quiet and not patient is not funny or wise.
If paul is not funny or patient then someone is both rich and happy and vice versa.
Everyone who is both not brave and not generous is either not patient or happy and vice versa.
If someone is either kind or funny then paul is not patient or wise and vice versa.
Someone is wise or creative.
Someone is both not brave and kind.
Fred is either not calm or old.
Someone is not brave.
John is either funny or happy.
Someone is either happy or old.
Paul is either not calm or old. | Paul is not funny. | contradiction | (![X]:((~tall(X)&quiet(X))=>(strong(X)<~>~brave(X))))&
(![X]:(strong(X)<=>happy(X)))&
((tall(fred))<=>(?[X]:((~creative(X)&strong(X)))))&
(((kind(mary)&generous(mary)))<=>(?[X]:((~patient(X)|tall(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:((~patient(X)|~generous(X))<=>old(X)))&
(((humble(susan)&~happy(susan)))<=>((curious(lucy)&~funny(lucy))))&
(![X]:((~kind(X)|~funny(X))=>(curious(X)<~>generous(X))))&
(((~creative(fred)&old(fred)))=>(?[X]:((generous(X)<~>~generous(X)))))&
(![X]:(old(X)<=>(~strong(X)&~rich(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(patient(X)&~generous(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(~humble(X)&~happy(X))))&
(![X]:((~quiet(X)&~patient(X))=>(~funny(X)|wise(X))))&
(((~funny(paul)|patient(paul)))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((~brave(X)&~generous(X))<=>(~patient(X)<~>happy(X))))&
((?[X]:((kind(X)<~>funny(X))))<=>((~patient(paul)|wise(paul))))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:((~brave(X)&kind(X))))&
((~calm(fred)<~>old(fred)))&
(?[X]:(~brave(X)))&
((funny(john)<~>happy(john)))&
(?[X]:((happy(X)<~>old(X))))&
((~calm(paul)<~>old(paul))) | ~funny(paul) | [
"p5",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7034551160049644420388208
% SZS output start Proof for 7034551160049644420388208
6. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> old(X0)) [input p5]
10. ! [X0] : (old(X0) <=> (~rich(X0) & ~strong(X0))) [input p9]
14. (patient(paul) | ~funny(paul)) <=> ? [X0] : (happy(X0) & rich(X0)) [input p13]
15. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (~patient(X0) <~> happy(X0))) [input p14]
24. ~funny(paul) [input hypothesis]
49. ! [X0] : (((~generous(X0) | ~patient(X0)) | ~old(X0)) & (old(X0) | (generous(X0) & patient(X0)))) [nnf transformation 6]
50. ! [X0] : ((~generous(X0) | ~patient(X0) | ~old(X0)) & (old(X0) | (generous(X0) & patient(X0)))) [flattening 49]
57. ! [X0] : ((old(X0) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | ~old(X0))) [nnf transformation 10]
58. ! [X0] : ((old(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | ~old(X0))) [flattening 57]
63. ((patient(paul) | ~funny(paul)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (~patient(paul) & funny(paul))) [nnf transformation 14]
64. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (~patient(paul) & funny(paul))) [flattening 63]
65. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X1] : (happy(X1) & rich(X1)) | (~patient(paul) & funny(paul))) [rectify 64]
66. ? [X1] : (happy(X1) & rich(X1)) => (happy(sK5) & rich(sK5)) [choice axiom]
67. (patient(paul) | ~funny(paul) | ! [X0] : (~happy(X0) | ~rich(X0))) & ((happy(sK5) & rich(sK5)) | (~patient(paul) & funny(paul))) [skolemisation 65,66]
68. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0)))) & (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | (generous(X0) | brave(X0)))) [nnf transformation 15]
69. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0)))) & (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | generous(X0) | brave(X0))) [flattening 68]
103. old(X0) | patient(X0) [cnf transformation 50]
104. old(X0) | generous(X0) [cnf transformation 50]
117. ~rich(X0) | ~old(X0) [cnf transformation 58]
132. rich(sK5) | funny(paul) [cnf transformation 67]
134. happy(sK5) | funny(paul) [cnf transformation 67]
142. ~patient(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 69]
161. ~funny(paul) [cnf transformation 24]
266. 23 <=> happy(sK5) [avatar definition]
268. happy(sK5) <- (23) [avatar component clause 266]
271. 24 <=> funny(paul) [avatar definition]
274. 24 | 23 [avatar split clause 134,266,271]
276. 25 <=> rich(sK5) [avatar definition]
278. rich(sK5) <- (25) [avatar component clause 276]
280. 24 | 25 [avatar split clause 132,276,271]
354. ~24 [avatar split clause 161,271]
373. ~old(sK5) <- (25) [resolution 117,278]
384. generous(sK5) <- (25) [resolution 373,104]
385. patient(sK5) <- (25) [resolution 373,103]
608. ~generous(sK5) | ~happy(sK5) <- (25) [resolution 385,142]
610. ~happy(sK5) <- (25) [subsumption resolution 608,384]
611. $false <- (23, 25) [subsumption resolution 610,268]
612. ~23 | ~25 [avatar contradiction clause 611]
615. $false [avatar sat refutation 274,280,354,612]
% SZS output end Proof for 7034551160049644420388208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not tall or not funny is both not tall and happy and vice versa. Everyone who is tall is not patient or not kind and vice versa. Everyone who is both not brave and not tall is either rich or calm and vice versa. Everyone who is either creative or kind is both quiet and rich. If lucy is old or not patient then someone is both brave and generous and vice versa. Everyone who is both not curious and not funny is not rich. Everyone who is old or not kind is both not curious and kind. If susan is either humble or not brave then paul is either not strong or not generous and vice versa. Everyone who is calm or funny is not strong. Everyone who is both old and not rich is either not brave or not quiet and vice versa. If someone is calm or not patient then fred is either not tall or not wise and vice versa. Everyone who is not creative or calm is calm or not quiet and vice versa. If someone is happy then someone is brave or wise. Everyone who is kind is either patient or not creative. Everyone who is both not curious and not quiet is both not old and funny and vice versa. Everyone who is not brave is not generous or not old and vice versa. Someone is rich or curious. Mary is not rich. Someone is both not patient and calm. Someone is curious or not humble. Someone is both quiet and not patient. Mary is either not tall or wise. | Lucy is kind. | entailment | (![X]:((~tall(X)<~>~funny(X))<=>(~tall(X)&happy(X))))&
(![X]:(tall(X)<=>(~patient(X)|~kind(X))))&
(![X]:((~brave(X)&~tall(X))<=>(rich(X)<~>calm(X))))&
(![X]:((creative(X)<~>kind(X))=>(quiet(X)&rich(X))))&
(((old(lucy)|~patient(lucy)))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&kind(X))))&
(((humble(susan)<~>~brave(susan)))<=>((~strong(paul)<~>~generous(paul))))&
(![X]:((calm(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)&~rich(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((~tall(fred)<~>~wise(fred))))&
(![X]:((~creative(X)|calm(X))<=>(calm(X)|~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(kind(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~old(X)&funny(X))))&
(![X]:(~brave(X)<=>(~generous(X)|~old(X))))&
(?[X]:((rich(X)|curious(X))))&
(~rich(mary))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~patient(X))))&
((~tall(mary)<~>wise(mary))) | kind(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8169096773855428282313099
% SZS output start Proof for 8169096773855428282313099
7. ! [X0] : ((~kind(X0) | old(X0)) => (kind(X0) & ~curious(X0))) [input p6]
23. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~curious(X0)) | (kind(X0) & ~old(X0))) [ennf transformation 7]
98. kind(X0) | kind(X0) [cnf transformation 28]
144. ~kind(lucy) [cnf transformation 23]
145. kind(X0) [duplicate literal removal 98]
268. $false [subsumption resolution 144,145]
% SZS output end Proof for 8169096773855428282313099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not curious is kind or not rich and vice versa.
Everyone who is not generous or wise is quiet and vice versa.
If someone is not old or patient then someone is both not creative and not rich.
Everyone who is both not old and not patient is wise.
Everyone who is not patient or not kind is both not happy and funny.
Everyone who is both funny and wise is both old and not creative.
If john is both not kind and not patient then john is curious.
Everyone who is tall is either curious or not wise and vice versa.
Everyone who is either calm or not patient is strong and vice versa.
Everyone who is both not generous and tall is both strong and generous.
Everyone who is either not generous or not curious is either not rich or generous.
Everyone who is happy or patient is not creative or not generous and vice versa.
Everyone who is generous or patient is both not calm and not generous.
If lucy is not happy or not strong then lucy is not funny or not strong and vice versa.
Everyone who is not calm or kind is either not generous or not patient.
If someone is creative then susan is both not generous and patient.
Someone is strong or not brave.
Susan is old or funny.
Someone is wise.
Someone is creative.
Alice is either not curious or not happy.
Someone is either happy or not happy.
Mary is not kind. | Susan is strong. | contradiction | (![X]:((~old(X)&~curious(X))<=>(kind(X)|~rich(X))))&
(![X]:((~generous(X)|wise(X))<=>quiet(X)))&
((?[X]:((~old(X)|patient(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:((~old(X)&~patient(X))=>wise(X)))&
(![X]:((~patient(X)|~kind(X))=>(~happy(X)&funny(X))))&
(![X]:((funny(X)&wise(X))=>(old(X)&~creative(X))))&
(((~kind(john)&~patient(john)))=>(curious(john)))&
(![X]:(tall(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((calm(X)<~>~patient(X))<=>strong(X)))&
(![X]:((~generous(X)&tall(X))=>(strong(X)&generous(X))))&
(![X]:((~generous(X)<~>~curious(X))=>(~rich(X)<~>generous(X))))&
(![X]:((happy(X)|patient(X))<=>(~creative(X)|~generous(X))))&
(![X]:((generous(X)|patient(X))=>(~calm(X)&~generous(X))))&
(((~happy(lucy)|~strong(lucy)))<=>((~funny(lucy)|~strong(lucy))))&
(![X]:((~calm(X)|kind(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:(creative(X)))=>((~generous(susan)&patient(susan))))&
(?[X]:((strong(X)|~brave(X))))&
((old(susan)|funny(susan)))&
(?[X]:(wise(X)))&
(?[X]:(creative(X)))&
((~curious(alice)<~>~happy(alice)))&
(?[X]:((happy(X)<~>~happy(X))))&
(~kind(mary)) | strong(susan) | [
"p8",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2551695614000334260856396
% SZS output start Proof for 2551695614000334260856396
9. ! [X0] : ((calm(X0) <~> ~patient(X0)) <=> strong(X0)) [input p8]
13. ! [X0] : ((patient(X0) | generous(X0)) => (~generous(X0) & ~calm(X0))) [input p12]
16. ? [X0] : creative(X0) => (patient(susan) & ~generous(susan)) [input p15]
20. ? [X0] : creative(X0) [input p19]
24. strong(susan) [input hypothesis]
40. ! [X0] : ((~generous(X0) & ~calm(X0)) | (~patient(X0) & ~generous(X0))) [ennf transformation 13]
42. (patient(susan) & ~generous(susan)) | ! [X0] : ~creative(X0) [ennf transformation 16]
49. ! [X0] : ((((patient(X0) | ~calm(X0)) & (~patient(X0) | calm(X0))) | ~strong(X0)) & (strong(X0) | ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))))) [nnf transformation 9]
58. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
59. creative(sK2) [skolemisation 20,58]
85. ~strong(X0) | calm(X0) | ~patient(X0) [cnf transformation 49]
98. ~calm(X0) | ~patient(X0) [cnf transformation 40]
110. patient(susan) | ~creative(X0) [cnf transformation 42]
113. creative(sK2) [cnf transformation 59]
119. strong(susan) [cnf transformation 24]
174. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
175. ~creative(X0) <- (11) [avatar component clause 174]
177. 12 <=> patient(susan) [avatar definition]
179. patient(susan) <- (12) [avatar component clause 177]
180. 11 | 12 [avatar split clause 110,177,174]
200. $false <- (11) [resolution 175,113]
201. ~11 [avatar contradiction clause 200]
276. calm(susan) | ~patient(susan) [resolution 85,119]
280. calm(susan) <- (12) [subsumption resolution 276,179]
295. ~patient(susan) <- (12) [resolution 280,98]
296. $false <- (12) [subsumption resolution 295,179]
297. ~12 [avatar contradiction clause 296]
298. $false [avatar sat refutation 180,201,297]
% SZS output end Proof for 2551695614000334260856396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both not creative and curious and vice versa.
Everyone who is kind is not kind or quiet and vice versa.
Everyone who is both not tall and humble is both generous and not curious.
Everyone who is both not humble and curious is both not brave and old.
If susan is either funny or not happy then someone is not patient.
If john is patient or generous then someone is either old or not rich and vice versa.
Everyone who is brave or strong is not curious or not old.
Everyone who is either brave or kind is not rich or humble.
If someone is either curious or rich then alice is kind or humble.
If alice is quiet or not quiet then lucy is kind.
If fred is both funny and kind then someone is not creative or tall and vice versa.
If someone is both curious and not old then someone is not kind and vice versa.
If someone is either not wise or generous then someone is either humble or not curious and vice versa.
Everyone who is strong or not calm is both not rich and not patient and vice versa.
Everyone who is either not generous or not tall is either not humble or not calm and vice versa.
If alice is both not funny and not happy then fred is both not old and old and vice versa.
Paul is either strong or humble.
Someone is either kind or strong.
Someone is not creative or rich.
Mary is not quiet or not old.
Someone is not tall or creative.
Paul is either creative or rich.
Susan is both kind and happy.
Paul is both creative and strong. | Susan is quiet. | entailment | (![X]:(rich(X)<=>(~creative(X)&curious(X))))&
(![X]:(kind(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~tall(X)&humble(X))=>(generous(X)&~curious(X))))&
(![X]:((~humble(X)&curious(X))=>(~brave(X)&old(X))))&
(((funny(susan)<~>~happy(susan)))=>(?[X]:(~patient(X))))&
(((patient(john)|generous(john)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(![X]:((brave(X)|strong(X))=>(~curious(X)|~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(~rich(X)|humble(X))))&
((?[X]:((curious(X)<~>rich(X))))=>((kind(alice)|humble(alice))))&
(((quiet(alice)|~quiet(alice)))=>(kind(lucy)))&
(((funny(fred)&kind(fred)))<=>(?[X]:((~creative(X)|tall(X)))))&
((?[X]:((curious(X)&~old(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((strong(X)|~calm(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(~humble(X)<~>~calm(X))))&
(((~funny(alice)&~happy(alice)))<=>((~old(fred)&old(fred))))&
((strong(paul)<~>humble(paul)))&
(?[X]:((kind(X)<~>strong(X))))&
(?[X]:((~creative(X)|rich(X))))&
((~quiet(mary)|~old(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((creative(paul)<~>rich(paul)))&
((kind(susan)&happy(susan)))&
((creative(paul)&strong(paul))) | quiet(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 821609771860336259652979
% SZS output start Proof for 821609771860336259652979
2. ! [X0] : (kind(X0) <=> (quiet(X0) | ~kind(X0))) [input p1]
25. ~quiet(susan) [input hypothesis]
42. ! [X0] : ((kind(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | ~kind(X0))) [nnf transformation 2]
43. ! [X0] : ((kind(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | ~kind(X0))) [flattening 42]
86. quiet(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 43]
87. kind(X0) | kind(X0) [cnf transformation 43]
155. ~quiet(susan) [cnf transformation 25]
156. quiet(X0) | ~kind(X0) [duplicate literal removal 86]
157. kind(X0) [duplicate literal removal 87]
158. quiet(X0) [subsumption resolution 156,157]
312. $false [subsumption resolution 155,158]
% SZS output end Proof for 821609771860336259652979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not old then fred is either kind or not curious and vice versa.
Everyone who is either calm or not wise is funny or not humble and vice versa.
If someone is both not quiet and strong then someone is strong.
If susan is either curious or patient then someone is humble and vice versa.
Everyone who is not rich or patient is both humble and rich and vice versa.
Everyone who is wise or not calm is both happy and calm.
If someone is not creative or not humble then someone is not kind and vice versa.
If someone is not wise then mary is not creative and vice versa.
Everyone who is tall is either not rich or not patient.
Everyone who is rich or humble is not patient and vice versa.
If fred is either funny or not old then john is either creative or patient and vice versa.
Everyone who is wise is both not patient and not kind and vice versa.
If lucy is not happy or old then someone is either creative or kind and vice versa.
If john is both patient and not strong then someone is not old or kind and vice versa.
If someone is either not old or not quiet then alice is both not humble and not generous.
Everyone who is happy or not funny is either not old or brave.
Paul is quiet.
Lucy is not curious.
Someone is not tall or tall.
John is curious.
Someone is either wise or humble. | Mary is not rich. | contradiction | ((~old(lucy))<=>((kind(fred)<~>~curious(fred))))&
(![X]:((calm(X)<~>~wise(X))<=>(funny(X)|~humble(X))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:(strong(X))))&
(((curious(susan)<~>patient(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(humble(X)&rich(X))))&
(![X]:((wise(X)|~calm(X))=>(happy(X)&calm(X))))&
((?[X]:((~creative(X)|~humble(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(~wise(X)))<=>(~creative(mary)))&
(![X]:(tall(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((rich(X)|humble(X))<=>~patient(X)))&
(((funny(fred)<~>~old(fred)))<=>((creative(john)<~>patient(john))))&
(![X]:(wise(X)<=>(~patient(X)&~kind(X))))&
(((~happy(lucy)|old(lucy)))<=>(?[X]:((creative(X)<~>kind(X)))))&
(((patient(john)&~strong(john)))<=>(?[X]:((~old(X)|kind(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~humble(alice)&~generous(alice))))&
(![X]:((happy(X)|~funny(X))=>(~old(X)<~>brave(X))))&
(quiet(paul))&
(~curious(lucy))&
(?[X]:((~tall(X)|tall(X))))&
(curious(john))&
(?[X]:((wise(X)<~>humble(X)))) | ~rich(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4254363205627503358371270
% SZS output start Proof for 4254363205627503358371270
5. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (rich(X0) & humble(X0))) [input p4]
22. ~rich(mary) [input hypothesis]
41. ! [X0] : (((patient(X0) | ~rich(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 5]
42. ! [X0] : ((patient(X0) | ~rich(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~patient(X0) & rich(X0)))) [flattening 41]
92. rich(X0) | rich(X0) [cnf transformation 42]
143. ~rich(mary) [cnf transformation 22]
145. rich(X0) [duplicate literal removal 92]
312. $false [subsumption resolution 143,145]
% SZS output end Proof for 4254363205627503358371270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is rich and vice versa. If someone is either not curious or funny then paul is not strong. If someone is not curious or humble then susan is both not brave and brave and vice versa. If someone is not rich then fred is quiet. If someone is either old or not patient then someone is not brave or not rich and vice versa. If alice is both patient and not rich then fred is either wise or not curious and vice versa. Everyone who is either wise or not quiet is kind or not tall and vice versa. If fred is not quiet or patient then someone is not wise and vice versa. If someone is either patient or strong then someone is either not rich or not calm. Everyone who is either not curious or not strong is quiet. If someone is either rich or not funny then someone is either patient or not wise. If mary is humble or old then someone is both kind and not funny and vice versa. Everyone who is funny is both not rich and tall. Everyone who is either humble or not tall is either not kind or rich. If someone is both quiet and not happy then paul is not strong and vice versa. Everyone who is not tall or patient is curious and vice versa. Someone is strong. Alice is happy. Someone is either not generous or not calm. Fred is not tall or not strong. Mary is not funny. Someone is not wise. John is both not old and funny. Lucy is not humble. | Paul is not quiet. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)<~>funny(X))))=>(~strong(paul)))&
((?[X]:((~curious(X)|humble(X))))<=>((~brave(susan)&brave(susan))))&
((?[X]:(~rich(X)))=>(quiet(fred)))&
((?[X]:((old(X)<~>~patient(X))))<=>(?[X]:((~brave(X)|~rich(X)))))&
(((patient(alice)&~rich(alice)))<=>((wise(fred)<~>~curious(fred))))&
(![X]:((wise(X)<~>~quiet(X))<=>(kind(X)|~tall(X))))&
(((~quiet(fred)|patient(fred)))<=>(?[X]:(~wise(X))))&
((?[X]:((patient(X)<~>strong(X))))=>(?[X]:((~rich(X)<~>~calm(X)))))&
(![X]:((~curious(X)<~>~strong(X))=>quiet(X)))&
((?[X]:((rich(X)<~>~funny(X))))=>(?[X]:((patient(X)<~>~wise(X)))))&
(((humble(mary)|old(mary)))<=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:(funny(X)=>(~rich(X)&tall(X))))&
(![X]:((humble(X)<~>~tall(X))=>(~kind(X)<~>rich(X))))&
((?[X]:((quiet(X)&~happy(X))))<=>(~strong(paul)))&
(![X]:((~tall(X)|patient(X))<=>curious(X)))&
(?[X]:(strong(X)))&
(happy(alice))&
(?[X]:((~generous(X)<~>~calm(X))))&
((~tall(fred)|~strong(fred)))&
(~funny(mary))&
(?[X]:(~wise(X)))&
((~old(john)&funny(john)))&
(~humble(lucy)) | ~quiet(paul) | [
"p1",
"p2",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8748931282021290353267396
% SZS output start Proof for 8748931282021290353267396
2. ? [X0] : (~curious(X0) <~> funny(X0)) => ~strong(paul) [input p1]
3. ? [X0] : (humble(X0) | ~curious(X0)) <=> (brave(susan) & ~brave(susan)) [input p2]
10. ! [X0] : ((~curious(X0) <~> ~strong(X0)) => quiet(X0)) [input p9]
23. funny(john) & ~old(john) [input p22]
25. ~quiet(paul) [input hypothesis]
30. ~strong(paul) | ! [X0] : (~curious(X0) <=> funny(X0)) [ennf transformation 2]
33. ! [X0] : (quiet(X0) | (~curious(X0) <=> ~strong(X0))) [ennf transformation 10]
42. ~strong(paul) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 30]
43. (? [X0] : (humble(X0) | ~curious(X0)) | (~brave(susan) | brave(susan))) & ((brave(susan) & ~brave(susan)) | ! [X0] : (~humble(X0) & curious(X0))) [nnf transformation 3]
44. (? [X0] : (humble(X0) | ~curious(X0)) | ~brave(susan) | brave(susan)) & ((brave(susan) & ~brave(susan)) | ! [X0] : (~humble(X0) & curious(X0))) [flattening 43]
45. (? [X0] : (humble(X0) | ~curious(X0)) | ~brave(susan) | brave(susan)) & ((brave(susan) & ~brave(susan)) | ! [X1] : (~humble(X1) & curious(X1))) [rectify 44]
46. ? [X0] : (humble(X0) | ~curious(X0)) => (humble(sK2) | ~curious(sK2)) [choice axiom]
47. ((humble(sK2) | ~curious(sK2)) | ~brave(susan) | brave(susan)) & ((brave(susan) & ~brave(susan)) | ! [X1] : (~humble(X1) & curious(X1))) [skolemisation 45,46]
66. ! [X0] : (quiet(X0) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) [nnf transformation 33]
93. ~strong(paul) | ~curious(X0) | ~funny(X0) [cnf transformation 42]
94. ~brave(susan) | curious(X1) [cnf transformation 47]
96. brave(susan) | curious(X1) [cnf transformation 47]
126. ~curious(X0) | quiet(X0) | strong(X0) [cnf transformation 66]
156. funny(john) [cnf transformation 23]
158. ~quiet(paul) [cnf transformation 25]
176. 5 <=> ! [X0] : (~curious(X0) | ~funny(X0)) [avatar definition]
177. ~curious(X0) | ~funny(X0) <- (5) [avatar component clause 176]
179. 6 <=> strong(paul) [avatar definition]
181. ~strong(paul) <- (~6) [avatar component clause 179]
182. 5 | ~6 [avatar split clause 93,179,176]
191. 9 <=> brave(susan) [avatar definition]
196. 10 <=> ! [X1] : curious(X1) [avatar definition]
197. curious(X1) <- (10) [avatar component clause 196]
198. 10 | 9 [avatar split clause 96,191,196]
200. 10 | ~9 [avatar split clause 94,191,196]
403. ~funny(X0) <- (5, 10) [subsumption resolution 177,197]
405. $false <- (5, 10) [resolution 403,156]
406. ~5 | ~10 [avatar contradiction clause 405]
414. quiet(X0) | strong(X0) <- (10) [resolution 126,197]
456. strong(paul) <- (10) [resolution 414,158]
459. $false <- (~6, 10) [subsumption resolution 456,181]
460. 6 | ~10 [avatar contradiction clause 459]
461. $false [avatar sat refutation 182,198,200,406,460]
% SZS output end Proof for 8748931282021290353267396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either strong or not funny is either creative or brave.
Everyone who is both not generous and not rich is both not calm and rich and vice versa.
Everyone who is happy is both generous and not quiet and vice versa.
Everyone who is strong is not old.
If someone is either funny or not curious then someone is not old or kind and vice versa.
If someone is both not brave and not generous then someone is either old or patient and vice versa.
Everyone who is kind or not generous is not tall or humble.
If someone is patient then fred is both not happy and not humble.
If someone is either wise or not creative then someone is wise or not happy.
Everyone who is calm or not quiet is either not curious or not tall and vice versa.
Everyone who is patient is both rich and not brave.
If susan is not generous then someone is humble or not kind and vice versa.
Everyone who is not creative or generous is patient.
If someone is not funny then someone is humble and vice versa.
If susan is either not old or brave then paul is either kind or quiet and vice versa.
Everyone who is both strong and not curious is tall.
Someone is funny.
Mary is either humble or not funny.
Fred is either not calm or strong.
Someone is either not happy or generous.
John is not old.
John is either not humble or not rich.
Someone is either rich or not quiet.
Someone is either funny or not tall. | John is not rich. | contradiction | (![X]:((strong(X)<~>~funny(X))=>(creative(X)<~>brave(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~calm(X)&rich(X))))&
(![X]:(happy(X)<=>(generous(X)&~quiet(X))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((funny(X)<~>~curious(X))))<=>(?[X]:((~old(X)|kind(X)))))&
((?[X]:((~brave(X)&~generous(X))))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:((kind(X)|~generous(X))=>(~tall(X)|humble(X))))&
((?[X]:(patient(X)))=>((~happy(fred)&~humble(fred))))&
((?[X]:((wise(X)<~>~creative(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((calm(X)|~quiet(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:(patient(X)=>(rich(X)&~brave(X))))&
((~generous(susan))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~creative(X)|generous(X))=>patient(X)))&
((?[X]:(~funny(X)))<=>(?[X]:(humble(X))))&
(((~old(susan)<~>brave(susan)))<=>((kind(paul)<~>quiet(paul))))&
(![X]:((strong(X)&~curious(X))=>tall(X)))&
(?[X]:(funny(X)))&
((humble(mary)<~>~funny(mary)))&
((~calm(fred)<~>strong(fred)))&
(?[X]:((~happy(X)<~>generous(X))))&
(~old(john))&
((~humble(john)<~>~rich(john)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:((funny(X)<~>~tall(X)))) | ~rich(john) | [
"p1",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7744047256512400297231386
% SZS output start Proof for 7744047256512400297231386
2. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (rich(X0) & ~calm(X0))) [input p1]
11. ! [X0] : (patient(X0) => (~brave(X0) & rich(X0))) [input p10]
13. ! [X0] : ((generous(X0) | ~creative(X0)) => patient(X0)) [input p12]
25. ~rich(john) [input hypothesis]
36. ! [X0] : ((~brave(X0) & rich(X0)) | ~patient(X0)) [ennf transformation 11]
37. ! [X0] : (patient(X0) | (~generous(X0) & creative(X0))) [ennf transformation 13]
41. ! [X0] : (((~rich(X0) & ~generous(X0)) | (~rich(X0) | calm(X0))) & ((rich(X0) & ~calm(X0)) | (rich(X0) | generous(X0)))) [nnf transformation 2]
42. ! [X0] : (((~rich(X0) & ~generous(X0)) | ~rich(X0) | calm(X0)) & ((rich(X0) & ~calm(X0)) | rich(X0) | generous(X0))) [flattening 41]
90. rich(X0) | rich(X0) | generous(X0) [cnf transformation 42]
121. ~patient(X0) | rich(X0) [cnf transformation 36]
127. ~generous(X0) | patient(X0) [cnf transformation 37]
153. ~rich(john) [cnf transformation 25]
154. rich(X0) | generous(X0) [duplicate literal removal 90]
342. 42 <=> rich(john) [avatar definition]
343. ~rich(john) <- (~42) [avatar component clause 342]
367. ~42 [avatar split clause 153,342]
375. generous(john) <- (~42) [resolution 154,343]
377. patient(john) <- (~42) [resolution 375,127]
403. rich(john) <- (~42) [resolution 377,121]
404. $false <- (~42) [subsumption resolution 403,343]
405. 42 [avatar contradiction clause 404]
406. $false [avatar sat refutation 367,405]
% SZS output end Proof for 7744047256512400297231386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is either not old or not humble and vice versa.
Everyone who is both not old and not funny is both not kind and curious.
If lucy is happy or patient then someone is both not generous and not patient and vice versa.
Everyone who is not happy or tall is both not happy and brave.
If someone is not humble or tall then someone is not wise or creative and vice versa.
Everyone who is both brave and old is not generous or not creative and vice versa.
Everyone who is both wise and not happy is brave and vice versa.
If lucy is wise or funny then alice is wise.
If paul is humble then paul is not tall or not kind.
Everyone who is both not brave and funny is both not curious and not calm and vice versa.
Everyone who is either not curious or not happy is either generous or wise.
Everyone who is tall is humble and vice versa.
Everyone who is both kind and wise is both quiet and brave and vice versa.
Everyone who is either not quiet or not generous is not old or not funny and vice versa.
Everyone who is not generous or generous is either old or humble.
Everyone who is either not old or patient is both wise and not wise and vice versa.
Lucy is not happy.
Paul is not happy.
Mary is both funny and not brave.
Someone is not wise or funny.
Someone is not curious or happy.
Mary is either not patient or not funny.
Someone is not old or generous. | Alice is tall. | contradiction | (![X]:(~humble(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~old(X)&~funny(X))=>(~kind(X)&curious(X))))&
(((happy(lucy)|patient(lucy)))<=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~happy(X)|tall(X))=>(~happy(X)&brave(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(![X]:((brave(X)&old(X))<=>(~generous(X)|~creative(X))))&
(![X]:((wise(X)&~happy(X))<=>brave(X)))&
(((wise(lucy)|funny(lucy)))=>(wise(alice)))&
((humble(paul))=>((~tall(paul)|~kind(paul))))&
(![X]:((~brave(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(generous(X)<~>wise(X))))&
(![X]:(tall(X)<=>humble(X)))&
(![X]:((kind(X)&wise(X))<=>(quiet(X)&brave(X))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~old(X)|~funny(X))))&
(![X]:((~generous(X)|generous(X))=>(old(X)<~>humble(X))))&
(![X]:((~old(X)<~>patient(X))<=>(wise(X)&~wise(X))))&
(~happy(lucy))&
(~happy(paul))&
((funny(mary)&~brave(mary)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~curious(X)|happy(X))))&
((~patient(mary)<~>~funny(mary)))&
(?[X]:((~old(X)|generous(X)))) | tall(alice) | [
"p0",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6815353111960822694555334
% SZS output start Proof for 6815353111960822694555334
1. ! [X0] : (~humble(X0) <=> (~old(X0) <~> ~humble(X0))) [input p0]
12. ! [X0] : (tall(X0) <=> humble(X0)) [input p11]
15. ! [X0] : ((generous(X0) | ~generous(X0)) => (old(X0) <~> humble(X0))) [input p14]
24. tall(alice) [input hypothesis]
33. ! [X0] : ((old(X0) <~> humble(X0)) | (~generous(X0) & generous(X0))) [ennf transformation 15]
34. ! [X0] : ((~humble(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0)))) & (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | humble(X0))) [nnf transformation 1]
52. ! [X0] : ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))) [nnf transformation 12]
57. ! [X0] : (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (~generous(X0) & generous(X0))) [nnf transformation 33]
68. humble(X0) | old(X0) | humble(X0) [cnf transformation 34]
69. ~humble(X0) | ~humble(X0) | old(X0) [cnf transformation 34]
105. ~tall(X0) | humble(X0) [cnf transformation 52]
119. ~humble(X0) | ~old(X0) | generous(X0) [cnf transformation 57]
120. ~humble(X0) | ~old(X0) | ~generous(X0) [cnf transformation 57]
136. tall(alice) [cnf transformation 24]
137. humble(X0) | old(X0) [duplicate literal removal 68]
138. ~humble(X0) | old(X0) [duplicate literal removal 69]
139. old(X0) [subsumption resolution 137,138]
226. ~humble(X0) | ~generous(X0) [subsumption resolution 120,139]
227. ~humble(X0) | generous(X0) [subsumption resolution 119,139]
228. ~humble(X0) [subsumption resolution 227,226]
268. humble(alice) [resolution 105,136]
269. $false [subsumption resolution 268,228]
% SZS output end Proof for 6815353111960822694555334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not calm then someone is rich or not brave.
Everyone who is curious or patient is both humble and not humble.
Everyone who is both funny and not wise is creative or patient and vice versa.
Everyone who is not tall is funny or humble and vice versa.
Everyone who is happy or generous is both strong and generous.
If lucy is creative or strong then alice is not funny or curious and vice versa.
If someone is not rich or not quiet then someone is either not strong or happy and vice versa.
If someone is brave or not funny then lucy is both brave and wise.
If someone is either brave or old then someone is either not strong or humble.
If fred is either kind or funny then someone is either tall or happy and vice versa.
Everyone who is calm is both not generous and wise.
If john is either not old or not rich then paul is curious or not funny.
If someone is not brave then mary is not rich or not wise and vice versa.
If someone is rich or not rich then john is either brave or not curious.
If john is both calm and not quiet then someone is generous.
If john is either wise or generous then someone is both generous and brave and vice versa.
Someone is either not quiet or creative.
John is both not old and not humble.
Someone is not curious.
Alice is both happy and not quiet.
Susan is either old or brave.
Someone is both brave and old. | Lucy is strong. | neutral | ((?[X]:((~old(X)|~calm(X))))=>(?[X]:((rich(X)|~brave(X)))))&
(![X]:((curious(X)|patient(X))=>(humble(X)&~humble(X))))&
(![X]:((funny(X)&~wise(X))<=>(creative(X)|patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|humble(X))))&
(![X]:((happy(X)|generous(X))=>(strong(X)&generous(X))))&
(((creative(lucy)|strong(lucy)))<=>((~funny(alice)|curious(alice))))&
((?[X]:((~rich(X)|~quiet(X))))<=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((brave(X)|~funny(X))))=>((brave(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>old(X))))=>(?[X]:((~strong(X)<~>humble(X)))))&
(((kind(fred)<~>funny(fred)))<=>(?[X]:((tall(X)<~>happy(X)))))&
(![X]:(calm(X)=>(~generous(X)&wise(X))))&
(((~old(john)<~>~rich(john)))=>((curious(paul)|~funny(paul))))&
((?[X]:(~brave(X)))<=>((~rich(mary)|~wise(mary))))&
((?[X]:((rich(X)|~rich(X))))=>((brave(john)<~>~curious(john))))&
(((calm(john)&~quiet(john)))=>(?[X]:(generous(X))))&
(((wise(john)<~>generous(john)))<=>(?[X]:((generous(X)&brave(X)))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((~old(john)&~humble(john)))&
(?[X]:(~curious(X)))&
((happy(alice)&~quiet(alice)))&
((old(susan)<~>brave(susan)))&
(?[X]:((brave(X)&old(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is both not funny and not curious is not generous. Everyone who is not creative is curious. If someone is not tall then alice is both wise and generous and vice versa. If lucy is not patient or calm then someone is both strong and not calm and vice versa. Everyone who is either curious or not creative is quiet or creative and vice versa. If john is either not calm or brave then someone is both brave and not quiet. If someone is either curious or tall then susan is both not calm and not brave. Everyone who is both rich and creative is both not patient and not quiet. Everyone who is not strong is both not funny and happy and vice versa. If mary is not quiet or not strong then someone is both humble and not quiet. If someone is generous then alice is wise or creative and vice versa. Everyone who is both not generous and not strong is not quiet or calm and vice versa. Everyone who is either not funny or not rich is either not wise or not rich and vice versa. Everyone who is both not brave and generous is either funny or not strong and vice versa. Everyone who is happy is either creative or not tall and vice versa. Everyone who is either calm or patient is not rich or not strong. Paul is brave. Someone is both not generous and not funny. Paul is both brave and not kind. Someone is creative or not patient. Someone is either rich or not old. Someone is quiet or not humble. Susan is either wise or creative. | Paul is happy. | contradiction | (![X]:((~funny(X)&~curious(X))=>~generous(X)))&
(![X]:(~creative(X)=>curious(X)))&
((?[X]:(~tall(X)))<=>((wise(alice)&generous(alice))))&
(((~patient(lucy)|calm(lucy)))<=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((curious(X)<~>~creative(X))<=>(quiet(X)|creative(X))))&
(((~calm(john)<~>brave(john)))=>(?[X]:((brave(X)&~quiet(X)))))&
((?[X]:((curious(X)<~>tall(X))))=>((~calm(susan)&~brave(susan))))&
(![X]:((rich(X)&creative(X))=>(~patient(X)&~quiet(X))))&
(![X]:(~strong(X)<=>(~funny(X)&happy(X))))&
(((~quiet(mary)|~strong(mary)))=>(?[X]:((humble(X)&~quiet(X)))))&
((?[X]:(generous(X)))<=>((wise(alice)|creative(alice))))&
(![X]:((~generous(X)&~strong(X))<=>(~quiet(X)|calm(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~wise(X)<~>~rich(X))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)<~>~strong(X))))&
(![X]:(happy(X)<=>(creative(X)<~>~tall(X))))&
(![X]:((calm(X)<~>patient(X))=>(~rich(X)|~strong(X))))&
(brave(paul))&
(?[X]:((~generous(X)&~funny(X))))&
((brave(paul)&~kind(paul)))&
(?[X]:((creative(X)|~patient(X))))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((quiet(X)|~humble(X))))&
((wise(susan)<~>creative(susan))) | happy(paul) | [
"p8",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6411946497424029458521346
% SZS output start Proof for 6411946497424029458521346
9. ! [X0] : (~strong(X0) <=> (happy(X0) & ~funny(X0))) [input p8]
14. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (funny(X0) <~> ~strong(X0))) [input p13]
17. brave(paul) [input p16]
24. happy(paul) [input hypothesis]
52. ! [X0] : ((~strong(X0) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | strong(X0))) [nnf transformation 9]
53. ! [X0] : ((~strong(X0) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | strong(X0))) [flattening 52]
64. ! [X0] : (((generous(X0) & ~brave(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | (~generous(X0) | brave(X0)))) [nnf transformation 14]
65. ! [X0] : (((generous(X0) & ~brave(X0)) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | ~generous(X0) | brave(X0))) [flattening 64]
104. ~funny(X0) | strong(X0) [cnf transformation 53]
106. ~happy(X0) | ~strong(X0) | funny(X0) [cnf transformation 53]
129. ~brave(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 65]
130. ~brave(X0) | funny(X0) | strong(X0) [cnf transformation 65]
139. brave(paul) [cnf transformation 17]
149. happy(paul) [cnf transformation 24]
271. ~brave(X0) | strong(X0) [subsumption resolution 130,104]
272. ~brave(X0) | ~funny(X0) [subsumption resolution 129,271]
336. strong(paul) [resolution 271,139]
340. ~funny(paul) [resolution 272,139]
345. ~strong(paul) | funny(paul) [resolution 106,149]
347. funny(paul) [subsumption resolution 345,336]
348. $false [subsumption resolution 347,340]
% SZS output end Proof for 6411946497424029458521346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not generous is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Everyone who is either not calm or kind is not happy and vice versa.
If someone is both not brave and wise then alice is curious or generous and vice versa.
If someone is either not wise or humble then mary is both not patient and generous and vice versa.
Everyone who is happy is not wise and vice versa.
Everyone who is either not rich or not funny is generous or not patient.
Everyone who is old is both calm and generous.
Everyone who is creative is both not patient and not brave.
If someone is not curious or not wise then someone is either not quiet or patient and vice versa.
Everyone who is not quiet is either not brave or not funny.
If someone is both generous and not wise then susan is either not rich or not curious.
Everyone who is happy is either generous or not humble and vice versa.
If paul is funny then mary is humble or not kind and vice versa.
Paul is not quiet or not wise.
Someone is not tall.
Someone is brave or not curious.
Lucy is brave or patient.
Someone is both not tall and not calm.
Fred is either not tall or calm.
Someone is both quiet and strong. | Lucy is not old. | entailment | (![X]:((~strong(X)&~generous(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>kind(X))<=>~happy(X)))&
((?[X]:((~brave(X)&wise(X))))<=>((curious(alice)|generous(alice))))&
((?[X]:((~wise(X)<~>humble(X))))<=>((~patient(mary)&generous(mary))))&
(![X]:(happy(X)<=>~wise(X)))&
(![X]:((~rich(X)<~>~funny(X))=>(generous(X)|~patient(X))))&
(![X]:(old(X)=>(calm(X)&generous(X))))&
(![X]:(creative(X)=>(~patient(X)&~brave(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:(~quiet(X)=>(~brave(X)<~>~funny(X))))&
((?[X]:((generous(X)&~wise(X))))=>((~rich(susan)<~>~curious(susan))))&
(![X]:(happy(X)<=>(generous(X)<~>~humble(X))))&
((funny(paul))<=>((humble(mary)|~kind(mary))))&
((~quiet(paul)|~wise(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((brave(X)|~curious(X))))&
((brave(lucy)|patient(lucy)))&
(?[X]:((~tall(X)&~calm(X))))&
((~tall(fred)<~>calm(fred)))&
(?[X]:((quiet(X)&strong(X)))) | ~old(lucy) | [
"p0",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6043770488796780788575961
% SZS output start Proof for 6043770488796780788575961
1. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (~kind(X0) | ~happy(X0))) [input p0]
5. ! [X0] : ((~calm(X0) <~> kind(X0)) <=> ~happy(X0)) [input p4]
10. ! [X0] : (old(X0) => (generous(X0) & calm(X0))) [input p9]
24. old(lucy) [input hypothesis]
31. ! [X0] : ((generous(X0) & calm(X0)) | ~old(X0)) [ennf transformation 10]
34. ! [X0] : (((~generous(X0) & ~strong(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (generous(X0) | strong(X0)))) [nnf transformation 1]
35. ! [X0] : (((~generous(X0) & ~strong(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | generous(X0) | strong(X0))) [flattening 34]
43. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | happy(X0)) & (~happy(X0) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [nnf transformation 5]
78. ~generous(X0) | happy(X0) [cnf transformation 35]
79. ~generous(X0) | kind(X0) [cnf transformation 35]
97. ~calm(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 43]
115. ~old(X0) | calm(X0) [cnf transformation 31]
116. ~old(X0) | generous(X0) [cnf transformation 31]
144. old(lucy) [cnf transformation 24]
342. calm(lucy) [resolution 115,144]
343. generous(lucy) [resolution 116,144]
349. kind(lucy) [resolution 343,79]
350. happy(lucy) [resolution 343,78]
388. ~happy(lucy) | ~kind(lucy) [resolution 97,342]
398. ~kind(lucy) [subsumption resolution 388,350]
399. $false [subsumption resolution 398,349]
% SZS output end Proof for 6043770488796780788575961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is old. Everyone who is wise or not wise is both funny and not old. If someone is both not creative and not humble then mary is not happy or not old. If someone is happy or not wise then lucy is not generous. If alice is both not creative and not calm then mary is strong. Everyone who is old or not humble is wise or humble and vice versa. Everyone who is either strong or not happy is either quiet or not old and vice versa. If someone is old or not funny then someone is kind and vice versa. Everyone who is rich or not kind is rich or not humble and vice versa. If someone is either not old or tall then someone is both generous and not humble. Everyone who is either happy or wise is either patient or not funny. Everyone who is either brave or funny is not happy or brave and vice versa. If someone is kind or not tall then someone is both humble and creative. Everyone who is either generous or not happy is either not calm or rich and vice versa. Everyone who is not tall is either not old or not kind. Everyone who is both not creative and curious is both not brave and not calm and vice versa. Someone is both not old and quiet. Mary is generous or not strong. John is rich. Susan is not kind or old. | Lucy is humble. | contradiction | (![X]:(~creative(X)=>old(X)))&
(![X]:((wise(X)|~wise(X))=>(funny(X)&~old(X))))&
((?[X]:((~creative(X)&~humble(X))))=>((~happy(mary)|~old(mary))))&
((?[X]:((happy(X)|~wise(X))))=>(~generous(lucy)))&
(((~creative(alice)&~calm(alice)))=>(strong(mary)))&
(![X]:((old(X)|~humble(X))<=>(wise(X)|humble(X))))&
(![X]:((strong(X)<~>~happy(X))<=>(quiet(X)<~>~old(X))))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(kind(X))))&
(![X]:((rich(X)|~kind(X))<=>(rich(X)|~humble(X))))&
((?[X]:((~old(X)<~>tall(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((happy(X)<~>wise(X))=>(patient(X)<~>~funny(X))))&
(![X]:((brave(X)<~>funny(X))<=>(~happy(X)|brave(X))))&
((?[X]:((kind(X)|~tall(X))))=>(?[X]:((humble(X)&creative(X)))))&
(![X]:((generous(X)<~>~happy(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~kind(X))))&
(![X]:((~creative(X)&curious(X))<=>(~brave(X)&~calm(X))))&
(?[X]:((~old(X)&quiet(X))))&
((generous(mary)|~strong(mary)))&
(rich(john))&
((~kind(susan)|old(susan))) | humble(lucy) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 90705435490146286256697
% SZS output start Proof for 90705435490146286256697
2. ! [X0] : ((~wise(X0) | wise(X0)) => (~old(X0) & funny(X0))) [input p1]
6. ! [X0] : ((~humble(X0) | old(X0)) <=> (humble(X0) | wise(X0))) [input p5]
21. humble(lucy) [input hypothesis]
26. ! [X0] : ((~old(X0) & funny(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 2]
36. ! [X0] : (((~humble(X0) | old(X0)) | (~humble(X0) & ~wise(X0))) & ((humble(X0) | wise(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 6]
37. ! [X0] : ((~humble(X0) | old(X0) | (~humble(X0) & ~wise(X0))) & (humble(X0) | wise(X0) | (humble(X0) & ~old(X0)))) [flattening 36]
65. ~old(X0) | ~wise(X0) [cnf transformation 26]
66. ~old(X0) | wise(X0) [cnf transformation 26]
74. ~humble(X0) | old(X0) | ~humble(X0) [cnf transformation 37]
127. humble(lucy) [cnf transformation 21]
131. ~humble(X0) | old(X0) [duplicate literal removal 74]
132. ~old(X0) [subsumption resolution 65,66]
159. ~humble(X0) [subsumption resolution 131,132]
200. $false [subsumption resolution 127,159]
% SZS output end Proof for 90705435490146286256697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If john is not happy or not patient then someone is kind.
If someone is both funny and not funny then someone is patient and vice versa.
Everyone who is generous or quiet is tall or not happy.
Everyone who is not calm is either rich or not quiet and vice versa.
Everyone who is creative is either rich or creative and vice versa.
If someone is both not generous and not kind then someone is either not funny or not generous.
If mary is old then someone is strong or humble.
Everyone who is either not old or quiet is not creative.
Everyone who is either not strong or old is not wise or calm.
Everyone who is old or not strong is not happy or not funny and vice versa.
If someone is both strong and not brave then lucy is both old and not curious.
If someone is patient then someone is generous.
Everyone who is not strong is not tall and vice versa.
If alice is both not calm and funny then someone is brave or humble.
Everyone who is not generous is not calm or calm.
If fred is both not kind and not calm then alice is strong or not creative.
Someone is not happy or not wise.
John is generous.
Someone is quiet.
Mary is both strong and not funny.
Someone is both not creative and not happy.
Someone is either wise or not rich.
Mary is not creative or not quiet.
Someone is both not wise and not rich. | Fred is not kind. | neutral | (((~happy(john)|~patient(john)))=>(?[X]:(kind(X))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|quiet(X))=>(tall(X)|~happy(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
((?[X]:((~generous(X)&~kind(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((old(mary))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~old(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~strong(X)<~>old(X))=>(~wise(X)|calm(X))))&
(![X]:((old(X)|~strong(X))<=>(~happy(X)|~funny(X))))&
((?[X]:((strong(X)&~brave(X))))=>((old(lucy)&~curious(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
(![X]:(~strong(X)<=>~tall(X)))&
(((~calm(alice)&funny(alice)))=>(?[X]:((brave(X)|humble(X)))))&
(![X]:(~generous(X)=>(~calm(X)|calm(X))))&
(((~kind(fred)&~calm(fred)))=>((strong(alice)|~creative(alice))))&
(?[X]:((~happy(X)|~wise(X))))&
(generous(john))&
(?[X]:(quiet(X)))&
((strong(mary)&~funny(mary)))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((wise(X)<~>~rich(X))))&
((~creative(mary)|~quiet(mary)))&
(?[X]:((~wise(X)&~rich(X)))) | ~kind(fred) | [] | null | 0 |
Everyone who is not strong or not creative is either tall or not quiet and vice versa.
Everyone who is either happy or not tall is both creative and old.
Everyone who is both not wise and creative is not wise.
Everyone who is either old or patient is both not strong and creative.
Everyone who is both not quiet and not tall is creative or not humble.
If someone is either brave or not quiet then someone is old or tall and vice versa.
Everyone who is not humble is not rich or not quiet.
Everyone who is funny is not brave and vice versa.
Everyone who is not wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is 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.
John is not old or not tall.
Someone is patient.
Alice is funny or curious.
Someone is either calm or rich.
John is not wise or not generous.
Someone is either not old or wise.
Someone is calm or brave.
Susan is curious. | John is not generous. | contradiction | (![X]:((~strong(X)|~creative(X))<=>(tall(X)<~>~quiet(X))))&
(![X]:((happy(X)<~>~tall(X))=>(creative(X)&old(X))))&
(![X]:((~wise(X)&creative(X))=>~wise(X)))&
(![X]:((old(X)<~>patient(X))=>(~strong(X)&creative(X))))&
(![X]:((~quiet(X)&~tall(X))=>(creative(X)|~humble(X))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(?[X]:((old(X)|tall(X)))))&
(![X]:(~humble(X)=>(~rich(X)|~quiet(X))))&
(![X]:(funny(X)<=>~brave(X)))&
(![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![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))))&
((~old(john)|~tall(john)))&
(?[X]:(patient(X)))&
((funny(alice)|curious(alice)))&
(?[X]:((calm(X)<~>rich(X))))&
((~wise(john)|~generous(john)))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((calm(X)|brave(X))))&
(curious(susan)) | ~generous(john) | [
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8545305280731240511594097
% SZS output start Proof for 8545305280731240511594097
10. ! [X0] : ((curious(X0) | ~humble(X0)) => generous(X0)) [input p9]
13. (~humble(john) | ~curious(john)) => ? [X0] : (~quiet(X0) & calm(X0)) [input p12]
14. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p13]
25. ~generous(john) [input hypothesis]
36. ! [X0] : (generous(X0) | (~curious(X0) & humble(X0))) [ennf transformation 10]
37. ? [X0] : (~quiet(X0) & calm(X0)) | (humble(john) & curious(john)) [ennf transformation 13]
53. ? [X0] : (~quiet(X0) & calm(X0)) => (~quiet(sK2) & calm(sK2)) [choice axiom]
54. (~quiet(sK2) & calm(sK2)) | (humble(john) & curious(john)) [skolemisation 37,53]
55. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 14]
56. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 55]
98. ~curious(X0) | generous(X0) [cnf transformation 36]
104. calm(sK2) | curious(john) [cnf transformation 54]
109. ~funny(X0) | ~funny(X0) [cnf transformation 56]
110. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 56]
127. ~generous(john) [cnf transformation 25]
128. ~funny(X0) [duplicate literal removal 109]
129. ~calm(X0) | funny(X0) [duplicate literal removal 110]
175. 11 <=> curious(john) [avatar definition]
177. curious(john) <- (11) [avatar component clause 175]
180. 12 <=> calm(sK2) [avatar definition]
182. calm(sK2) <- (12) [avatar component clause 180]
184. 11 | 12 [avatar split clause 104,180,175]
220. 20 <=> generous(john) [avatar definition]
222. ~generous(john) <- (~20) [avatar component clause 220]
243. ~20 [avatar split clause 127,220]
253. generous(john) <- (11) [resolution 98,177]
255. $false <- (11, ~20) [subsumption resolution 253,222]
256. ~11 | 20 [avatar contradiction clause 255]
267. funny(sK2) <- (12) [resolution 129,182]
272. $false <- (12) [subsumption resolution 267,128]
273. ~12 [avatar contradiction clause 272]
274. $false [avatar sat refutation 184,243,256,273]
% SZS output end Proof for 8545305280731240511594097
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both calm and not quiet then someone is either not quiet or not brave and vice versa.
Everyone who is both curious and old is either not tall or not quiet and vice versa.
Everyone who is either not funny or quiet is quiet or not funny.
Everyone who is not funny is not happy and vice versa.
Everyone who is not curious is happy or not quiet.
Everyone who is not humble or not brave is wise.
If someone is not wise then someone is either happy or strong and vice versa.
Everyone who is either not patient or humble is rich or curious and vice versa.
Everyone who is both generous and not humble is not calm.
If someone is kind then someone is quiet and vice versa.
If someone is not brave or not old then someone is curious.
Everyone who is kind is not kind.
If someone is either not curious or quiet then someone is tall or brave and vice versa.
Everyone who is both not quiet and kind is humble or not curious and vice versa.
If mary is either creative or tall then alice is not creative or rich and vice versa.
If someone is not quiet or quiet then lucy is either not humble or creative.
Someone is both happy and curious.
Someone is patient or creative.
Susan is either not strong or not wise.
Someone is patient or not brave.
Someone is not patient or not rich. | Alice is not old. | entailment | ((?[X]:((calm(X)&~quiet(X))))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
(![X]:((curious(X)&old(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((~funny(X)<~>quiet(X))=>(quiet(X)|~funny(X))))&
(![X]:(~funny(X)<=>~happy(X)))&
(![X]:(~curious(X)=>(happy(X)|~quiet(X))))&
(![X]:((~humble(X)|~brave(X))=>wise(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((happy(X)<~>strong(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(rich(X)|curious(X))))&
(![X]:((generous(X)&~humble(X))=>~calm(X)))&
((?[X]:(kind(X)))<=>(?[X]:(quiet(X))))&
((?[X]:((~brave(X)|~old(X))))=>(?[X]:(curious(X))))&
(![X]:(kind(X)=>~kind(X)))&
((?[X]:((~curious(X)<~>quiet(X))))<=>(?[X]:((tall(X)|brave(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(humble(X)|~curious(X))))&
(((creative(mary)<~>tall(mary)))<=>((~creative(alice)|rich(alice))))&
((?[X]:((~quiet(X)|quiet(X))))=>((~humble(lucy)<~>creative(lucy))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((patient(X)|creative(X))))&
((~strong(susan)<~>~wise(susan)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((~patient(X)|~rich(X)))) | ~old(alice) | [
"p1",
"p9",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5853635736133083043531518
% SZS output start Proof for 5853635736133083043531518
2. ! [X0] : ((old(X0) & curious(X0)) <=> (~tall(X0) <~> ~quiet(X0))) [input p1]
10. ? [X0] : kind(X0) <=> ? [X0] : quiet(X0) [input p9]
12. ! [X0] : (kind(X0) => ~kind(X0)) [input p11]
13. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X0] : (brave(X0) | tall(X0)) [input p12]
14. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (~curious(X0) | humble(X0))) [input p13]
22. old(alice) [input hypothesis]
25. ? [X0] : kind(X0) <=> ? [X1] : quiet(X1) [rectify 10]
27. ? [X0] : (~curious(X0) <~> quiet(X0)) <=> ? [X1] : (brave(X1) | tall(X1)) [rectify 13]
35. ! [X0] : (~kind(X0) | ~kind(X0)) [ennf transformation 12]
42. ! [X0] : (((old(X0) & curious(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~old(X0) | ~curious(X0)))) [nnf transformation 2]
43. ! [X0] : (((old(X0) & curious(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~old(X0) | ~curious(X0))) [flattening 42]
53. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : ~kind(X0)) [nnf transformation 25]
54. (? [X0] : kind(X0) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : ~kind(X3)) [rectify 53]
55. ? [X0] : kind(X0) => kind(sK4) [choice axiom]
56. ? [X2] : quiet(X2) => quiet(sK5) [choice axiom]
57. (kind(sK4) | ! [X1] : ~quiet(X1)) & (quiet(sK5) | ! [X3] : ~kind(X3)) [skolemisation 54,56,55]
61. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X1] : (brave(X1) | tall(X1)) | ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) [nnf transformation 27]
62. (? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ! [X1] : (~brave(X1) & ~tall(X1))) & (? [X2] : (brave(X2) | tall(X2)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [rectify 61]
63. ? [X0] : ((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) => ((~quiet(sK7) | curious(sK7)) & (quiet(sK7) | ~curious(sK7))) [choice axiom]
64. ? [X2] : (brave(X2) | tall(X2)) => (brave(sK8) | tall(sK8)) [choice axiom]
65. (((~quiet(sK7) | curious(sK7)) & (quiet(sK7) | ~curious(sK7))) | ! [X1] : (~brave(X1) & ~tall(X1))) & ((brave(sK8) | tall(sK8)) | ! [X3] : ((~curious(X3) | ~quiet(X3)) & (quiet(X3) | curious(X3)))) [skolemisation 62,64,63]
66. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | (~kind(X0) | quiet(X0)))) [nnf transformation 14]
67. ! [X0] : (((kind(X0) & ~quiet(X0)) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ~kind(X0) | quiet(X0))) [flattening 66]
87. ~old(X0) | tall(X0) | quiet(X0) | ~curious(X0) [cnf transformation 43]
110. kind(sK4) | ~quiet(X1) [cnf transformation 57]
113. ~kind(X0) | ~kind(X0) [cnf transformation 35]
116. quiet(sK7) | ~curious(sK7) | ~tall(X1) [cnf transformation 65]
124. kind(X0) | curious(X0) [cnf transformation 67]
142. old(alice) [cnf transformation 22]
143. ~kind(X0) [duplicate literal removal 113]
203. 14 <=> ! [X1] : ~quiet(X1) [avatar definition]
204. ~quiet(X1) <- (14) [avatar component clause 203]
206. 15 <=> kind(sK4) [avatar definition]
208. kind(sK4) <- (15) [avatar component clause 206]
209. 14 | 15 [avatar split clause 110,206,203]
211. 16 <=> ! [X3] : ~kind(X3) [avatar definition]
212. ~kind(X3) <- (16) [avatar component clause 211]
230. 16 [avatar split clause 143,211]
235. 22 <=> curious(sK7) [avatar definition]
236. ~curious(sK7) <- (~22) [avatar component clause 235]
239. 23 <=> quiet(sK7) [avatar definition]
240. quiet(sK7) <- (23) [avatar component clause 239]
244. 24 <=> ! [X1] : ~tall(X1) [avatar definition]
245. ~tall(X1) <- (24) [avatar component clause 244]
248. 24 | ~22 | 23 [avatar split clause 116,239,235,244]
346. $false <- (15, 16) [subsumption resolution 208,212]
347. ~15 | ~16 [avatar contradiction clause 346]
360. curious(X0) <- (16) [resolution 124,212]
361. $false <- (16, ~22) [resolution 360,236]
362. ~16 | 22 [avatar contradiction clause 361]
363. $false <- (14, 23) [subsumption resolution 240,204]
364. ~14 | ~23 [avatar contradiction clause 363]
391. tall(alice) | quiet(alice) | ~curious(alice) [resolution 87,142]
392. quiet(alice) | ~curious(alice) <- (24) [subsumption resolution 391,245]
393. ~curious(alice) <- (14, 24) [subsumption resolution 392,204]
394. $false <- (14, 16, 24) [subsumption resolution 393,360]
395. ~14 | ~16 | ~24 [avatar contradiction clause 394]
396. $false [avatar sat refutation 209,230,248,347,362,364,395]
% SZS output end Proof for 5853635736133083043531518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not generous is happy or not brave.
Everyone who is strong is not generous or rich.
If paul is not patient or kind then lucy is either brave or quiet.
Everyone who is not patient or not quiet is not calm.
If alice is both not calm and not curious then mary is not kind and vice versa.
Everyone who is old or not humble is both patient and not brave and vice versa.
If someone is either not kind or not funny then someone is tall or wise and vice versa.
If someone is either not funny or not patient then someone is both calm and not funny and vice versa.
Everyone who is brave is not humble.
If paul is both brave and strong then john is wise or calm and vice versa.
If susan is both not calm and funny then someone is both generous and not creative.
If alice is either calm or not curious then susan is curious and vice versa.
Everyone who is either not brave or quiet is both tall and creative and vice versa.
If someone is calm then someone is both brave and not happy.
Everyone who is not generous or not rich is both patient and not wise.
Everyone who is kind or not brave is generous and vice versa.
Mary is both not happy and patient.
Paul is humble or not humble.
Fred is either not old or creative.
Someone is creative.
John is not tall or happy.
John is not strong. | Fred is not generous. | contradiction | (![X]:((~quiet(X)&~generous(X))=>(happy(X)|~brave(X))))&
(![X]:(strong(X)=>(~generous(X)|rich(X))))&
(((~patient(paul)|kind(paul)))=>((brave(lucy)<~>quiet(lucy))))&
(![X]:((~patient(X)|~quiet(X))=>~calm(X)))&
(((~calm(alice)&~curious(alice)))<=>(~kind(mary)))&
(![X]:((old(X)|~humble(X))<=>(patient(X)&~brave(X))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>(?[X]:((tall(X)|wise(X)))))&
((?[X]:((~funny(X)<~>~patient(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:(brave(X)=>~humble(X)))&
(((brave(paul)&strong(paul)))<=>((wise(john)|calm(john))))&
(((~calm(susan)&funny(susan)))=>(?[X]:((generous(X)&~creative(X)))))&
(((calm(alice)<~>~curious(alice)))<=>(curious(susan)))&
(![X]:((~brave(X)<~>quiet(X))<=>(tall(X)&creative(X))))&
((?[X]:(calm(X)))=>(?[X]:((brave(X)&~happy(X)))))&
(![X]:((~generous(X)|~rich(X))=>(patient(X)&~wise(X))))&
(![X]:((kind(X)|~brave(X))<=>generous(X)))&
((~happy(mary)&patient(mary)))&
((humble(paul)|~humble(paul)))&
((~old(fred)<~>creative(fred)))&
(?[X]:(creative(X)))&
((~tall(john)|happy(john)))&
(~strong(john)) | ~generous(fred) | [
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1816000175115475292293286
% SZS output start Proof for 1816000175115475292293286
6. ! [X0] : ((~humble(X0) | old(X0)) <=> (~brave(X0) & patient(X0))) [input p5]
9. ! [X0] : (brave(X0) => ~humble(X0)) [input p8]
16. ! [X0] : ((~brave(X0) | kind(X0)) <=> generous(X0)) [input p15]
23. ~generous(fred) [input hypothesis]
33. ! [X0] : (~humble(X0) | ~brave(X0)) [ennf transformation 9]
41. ! [X0] : (((~humble(X0) | old(X0)) | (brave(X0) | ~patient(X0))) & ((~brave(X0) & patient(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 6]
42. ! [X0] : ((~humble(X0) | old(X0) | brave(X0) | ~patient(X0)) & ((~brave(X0) & patient(X0)) | (humble(X0) & ~old(X0)))) [flattening 41]
63. ! [X0] : (((~brave(X0) | kind(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) & ~kind(X0)))) [nnf transformation 16]
64. ! [X0] : ((~brave(X0) | kind(X0) | ~generous(X0)) & (generous(X0) | (brave(X0) & ~kind(X0)))) [flattening 63]
81. ~brave(X0) | humble(X0) [cnf transformation 42]
95. ~humble(X0) | ~brave(X0) [cnf transformation 33]
118. generous(X0) | brave(X0) [cnf transformation 64]
128. ~generous(fred) [cnf transformation 23]
229. ~brave(X0) [subsumption resolution 95,81]
287. generous(X0) [subsumption resolution 118,229]
307. $false [subsumption resolution 128,287]
% SZS output end Proof for 1816000175115475292293286
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and happy is kind and vice versa.
If lucy is quiet or calm then john is creative or not generous.
If alice is both strong and kind then mary is not calm or generous.
If mary is either creative or not patient then someone is either strong or quiet.
Everyone who is strong or wise is either quiet or happy and vice versa.
If someone is not old or not brave then someone is either not kind or not happy.
Everyone who is old or not kind is not generous.
If john is both not old and creative then someone is either kind or generous and vice versa.
Everyone who is not creative or wise is either old or not kind and vice versa.
Everyone who is both not brave and not creative is either quiet or wise.
Everyone who is either not humble or not happy is either not kind or creative and vice versa.
If someone is not generous or humble then someone is not generous and vice versa.
If someone is strong then someone is not wise or humble and vice versa.
If someone is both not calm and not humble then someone is calm or wise and vice versa.
If alice is either patient or funny then susan is patient and vice versa.
Everyone who is both not old and happy is both not wise and quiet.
Someone is calm or brave.
Someone is curious.
Someone is not rich or not brave.
Paul is brave.
Mary is curious.
Someone is both calm and funny. | Mary is not patient. | entailment | (![X]:((~kind(X)&happy(X))<=>kind(X)))&
(((quiet(lucy)|calm(lucy)))=>((creative(john)|~generous(john))))&
(((strong(alice)&kind(alice)))=>((~calm(mary)|generous(mary))))&
(((creative(mary)<~>~patient(mary)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((strong(X)|wise(X))<=>(quiet(X)<~>happy(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:((old(X)|~kind(X))=>~generous(X)))&
(((~old(john)&creative(john)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((~creative(X)|wise(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~brave(X)&~creative(X))=>(quiet(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~kind(X)<~>creative(X))))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((calm(X)|wise(X)))))&
(((patient(alice)<~>funny(alice)))<=>(patient(susan)))&
(![X]:((~old(X)&happy(X))=>(~wise(X)&quiet(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(brave(paul))&
(curious(mary))&
(?[X]:((calm(X)&funny(X)))) | ~patient(mary) | [
"p0",
"p3",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1385811840802229749136050
% SZS output start Proof for 1385811840802229749136050
1. ! [X0] : ((happy(X0) & ~kind(X0)) <=> kind(X0)) [input p0]
4. (creative(mary) <~> ~patient(mary)) => ? [X0] : (strong(X0) <~> quiet(X0)) [input p3]
5. ! [X0] : ((wise(X0) | strong(X0)) <=> (quiet(X0) <~> happy(X0))) [input p4]
6. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X0] : (~kind(X0) <~> ~happy(X0)) [input p5]
9. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (old(X0) <~> ~kind(X0))) [input p8]
23. patient(mary) [input hypothesis]
24. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [rectify 6]
31. ? [X0] : ~old(X0) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [pure predicate removal 24]
39. ? [X0] : (strong(X0) <~> quiet(X0)) | (creative(mary) <=> ~patient(mary)) [ennf transformation 4]
40. ? [X1] : (~kind(X1) <~> ~happy(X1)) | ! [X0] : old(X0) [ennf transformation 31]
44. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) | kind(X0)))) [nnf transformation 1]
45. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | ~happy(X0) | kind(X0))) [flattening 44]
46. ? [X0] : ((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | ((creative(mary) | patient(mary)) & (~patient(mary) | ~creative(mary))) [nnf transformation 39]
47. ? [X0] : ((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) => ((~quiet(sK0) | ~strong(sK0)) & (quiet(sK0) | strong(sK0))) [choice axiom]
48. ((~quiet(sK0) | ~strong(sK0)) & (quiet(sK0) | strong(sK0))) | ((creative(mary) | patient(mary)) & (~patient(mary) | ~creative(mary))) [skolemisation 46,47]
49. ! [X0] : (((wise(X0) | strong(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (~wise(X0) & ~strong(X0)))) [nnf transformation 5]
50. ! [X0] : ((wise(X0) | strong(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (~wise(X0) & ~strong(X0)))) [flattening 49]
51. ? [X1] : ((happy(X1) | kind(X1)) & (~happy(X1) | ~kind(X1))) | ! [X0] : old(X0) [nnf transformation 40]
52. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ! [X1] : old(X1) [rectify 51]
53. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) => ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) [choice axiom]
54. ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) | ! [X1] : old(X1) [skolemisation 52,53]
60. ! [X0] : (((wise(X0) | ~creative(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 9]
61. ! [X0] : ((wise(X0) | ~creative(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [flattening 60]
81. kind(X0) | ~happy(X0) | kind(X0) [cnf transformation 45]
82. ~kind(X0) | ~kind(X0) [cnf transformation 45]
87. quiet(sK0) | strong(sK0) | ~patient(mary) | ~creative(mary) [cnf transformation 48]
89. ~quiet(sK0) | ~strong(sK0) | ~patient(mary) | ~creative(mary) [cnf transformation 48]
91. happy(X0) | quiet(X0) | ~strong(X0) [cnf transformation 50]
95. wise(X0) | strong(X0) | happy(X0) | ~quiet(X0) [cnf transformation 50]
98. happy(sK1) | kind(sK1) | old(X1) [cnf transformation 54]
109. kind(X0) | ~old(X0) | creative(X0) [cnf transformation 61]
110. kind(X0) | ~old(X0) | ~wise(X0) [cnf transformation 61]
140. patient(mary) [cnf transformation 23]
141. kind(X0) | ~happy(X0) [duplicate literal removal 81]
142. ~kind(X0) [duplicate literal removal 82]
143. ~happy(X0) [subsumption resolution 141,142]
163. 5 <=> patient(mary) [avatar definition]
167. 6 <=> creative(mary) [avatar definition]
168. ~creative(mary) <- (~6) [avatar component clause 167]
171. 7 <=> strong(sK0) [avatar definition]
172. strong(sK0) <- (7) [avatar component clause 171]
173. ~strong(sK0) <- (~7) [avatar component clause 171]
175. 8 <=> quiet(sK0) [avatar definition]
176. quiet(sK0) <- (8) [avatar component clause 175]
177. ~quiet(sK0) <- (~8) [avatar component clause 175]
179. ~6 | ~5 | ~7 | ~8 [avatar split clause 89,175,171,163,167]
181. ~6 | ~5 | 7 | 8 [avatar split clause 87,175,171,163,167]
182. ~quiet(X0) | strong(X0) | wise(X0) [subsumption resolution 95,143]
184. ~strong(X0) | quiet(X0) [subsumption resolution 91,143]
185. kind(sK1) | old(X1) [subsumption resolution 98,143]
186. old(X1) [subsumption resolution 185,142]
188. ~old(X0) | ~wise(X0) [subsumption resolution 110,142]
189. ~wise(X0) [subsumption resolution 188,186]
190. ~old(X0) | creative(X0) [subsumption resolution 109,142]
191. creative(X0) [subsumption resolution 190,186]
230. 5 [avatar split clause 140,163]
233. $false <- (~6) [subsumption resolution 168,191]
234. 6 [avatar contradiction clause 233]
241. quiet(sK0) <- (7) [resolution 184,172]
243. $false <- (7, ~8) [subsumption resolution 241,177]
244. ~7 | 8 [avatar contradiction clause 243]
245. strong(sK0) | wise(sK0) <- (8) [resolution 182,176]
246. wise(sK0) <- (~7, 8) [subsumption resolution 245,173]
247. $false <- (~7, 8) [subsumption resolution 246,189]
248. 7 | ~8 [avatar contradiction clause 247]
249. $false [avatar sat refutation 179,181,230,234,244,248]
% SZS output end Proof for 1385811840802229749136050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or not strong then someone is tall or strong.
If someone is either strong or rich then alice is both not creative and not funny.
Everyone who is old is rich.
Everyone who is brave is both not funny and not wise and vice versa.
If someone is both not humble and kind then john is not patient.
Everyone who is not patient or not funny is either not humble or not strong and vice versa.
Everyone who is either happy or patient is both humble and funny and vice versa.
Everyone who is both happy and old is either calm or not humble.
Everyone who is rich is not funny and vice versa.
Everyone who is both not rich and funny is not funny or tall and vice versa.
Everyone who is both creative and not creative is patient.
If alice is either not tall or old then fred is not generous.
If someone is strong or not generous then lucy is not generous or curious and vice versa.
If lucy is either not tall or not generous then paul is both curious and not funny and vice versa.
Everyone who is calm is happy or rich and vice versa.
Someone is either not rich or not kind.
Someone is calm.
Someone is brave or not wise.
Lucy is either rich or not quiet.
Alice is humble.
Someone is both not wise and not curious. | Fred is not happy. | contradiction | ((?[X]:((~tall(X)|~strong(X))))=>(?[X]:((tall(X)|strong(X)))))&
((?[X]:((strong(X)<~>rich(X))))=>((~creative(alice)&~funny(alice))))&
(![X]:(old(X)=>rich(X)))&
(![X]:(brave(X)<=>(~funny(X)&~wise(X))))&
((?[X]:((~humble(X)&kind(X))))=>(~patient(john)))&
(![X]:((~patient(X)|~funny(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:((happy(X)<~>patient(X))<=>(humble(X)&funny(X))))&
(![X]:((happy(X)&old(X))=>(calm(X)<~>~humble(X))))&
(![X]:(rich(X)<=>~funny(X)))&
(![X]:((~rich(X)&funny(X))<=>(~funny(X)|tall(X))))&
(![X]:((creative(X)&~creative(X))=>patient(X)))&
(((~tall(alice)<~>old(alice)))=>(~generous(fred)))&
((?[X]:((strong(X)|~generous(X))))<=>((~generous(lucy)|curious(lucy))))&
(((~tall(lucy)<~>~generous(lucy)))<=>((curious(paul)&~funny(paul))))&
(![X]:(calm(X)<=>(happy(X)|rich(X))))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:(calm(X)))&
(?[X]:((brave(X)|~wise(X))))&
((rich(lucy)<~>~quiet(lucy)))&
(humble(alice))&
(?[X]:((~wise(X)&~curious(X)))) | ~happy(fred) | [
"p1",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 91843134711608365678608
% SZS output start Proof for 91843134711608365678608
2. ? [X0] : (strong(X0) <~> rich(X0)) => (~funny(alice) & ~creative(alice)) [input p1]
6. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~humble(X0) <~> ~strong(X0))) [input p5]
7. ! [X0] : ((happy(X0) <~> patient(X0)) <=> (funny(X0) & humble(X0))) [input p6]
9. ! [X0] : (rich(X0) <=> ~funny(X0)) [input p8]
10. ! [X0] : ((funny(X0) & ~rich(X0)) <=> (tall(X0) | ~funny(X0))) [input p9]
22. ~happy(fred) [input hypothesis]
30. (~funny(alice) & ~creative(alice)) | ! [X0] : (strong(X0) <=> rich(X0)) [ennf transformation 2]
41. (~funny(alice) & ~creative(alice)) | ! [X0] : ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))) [nnf transformation 30]
42. ! [X0] : (((~funny(X0) | ~patient(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (funny(X0) & patient(X0)))) [nnf transformation 6]
43. ! [X0] : ((~funny(X0) | ~patient(X0) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0)))) & (((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (funny(X0) & patient(X0)))) [flattening 42]
44. ! [X0] : ((((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | (~funny(X0) | ~humble(X0))) & ((funny(X0) & humble(X0)) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ~funny(X0) | ~humble(X0)) & ((funny(X0) & humble(X0)) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))))) [flattening 44]
47. ! [X0] : ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))) [nnf transformation 9]
48. ! [X0] : (((funny(X0) & ~rich(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~funny(X0) | rich(X0)))) [nnf transformation 10]
49. ! [X0] : (((funny(X0) & ~rich(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~funny(X0) | rich(X0))) [flattening 48]
72. ~funny(alice) | rich(X0) | ~strong(X0) [cnf transformation 41]
78. patient(X0) | humble(X0) | strong(X0) [cnf transformation 43]
81. ~patient(X0) | ~funny(X0) | ~humble(X0) | strong(X0) [cnf transformation 43]
83. ~patient(X0) | happy(X0) | humble(X0) [cnf transformation 45]
86. ~humble(X0) | happy(X0) | ~funny(X0) | patient(X0) [cnf transformation 45]
90. ~funny(X0) | ~rich(X0) [cnf transformation 47]
95. funny(X0) | funny(X0) [cnf transformation 49]
120. ~happy(fred) [cnf transformation 22]
122. funny(X0) [duplicate literal removal 95]
143. 6 <=> funny(alice) [avatar definition]
145. ~funny(alice) <- (~6) [avatar component clause 143]
148. 7 <=> ! [X0] : (rich(X0) | ~strong(X0)) [avatar definition]
149. ~strong(X0) | rich(X0) <- (7) [avatar component clause 148]
150. 7 | ~6 [avatar split clause 72,143,148]
240. $false <- (~6) [subsumption resolution 145,122]
241. 6 [avatar contradiction clause 240]
242. ~rich(X0) [resolution 90,122]
297. happy(X0) | humble(X0) | humble(X0) | strong(X0) [resolution 83,78]
299. happy(X0) | humble(X0) | strong(X0) [duplicate literal removal 297]
393. humble(fred) | strong(fred) [resolution 299,120]
401. 38 <=> strong(fred) [avatar definition]
403. strong(fred) <- (38) [avatar component clause 401]
405. 39 <=> humble(fred) [avatar definition]
407. humble(fred) <- (39) [avatar component clause 405]
408. 38 | 39 [avatar split clause 393,405,401]
433. happy(fred) | ~funny(fred) | patient(fred) <- (39) [resolution 407,86]
436. ~funny(fred) | patient(fred) <- (39) [subsumption resolution 433,120]
437. patient(fred) <- (39) [subsumption resolution 436,122]
444. ~funny(fred) | ~humble(fred) | strong(fred) <- (39) [resolution 437,81]
448. ~humble(fred) | strong(fred) <- (39) [subsumption resolution 444,122]
449. strong(fred) <- (39) [subsumption resolution 448,407]
450. 38 | ~39 [avatar split clause 449,405,401]
451. rich(fred) <- (7, 38) [resolution 403,149]
452. $false <- (7, 38) [subsumption resolution 451,242]
453. ~7 | ~38 [avatar contradiction clause 452]
454. $false [avatar sat refutation 150,241,408,450,453]
% SZS output end Proof for 91843134711608365678608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old then susan is either patient or curious. Everyone who is not calm is both quiet and not generous. If someone is not funny or not patient then lucy is both not rich and brave. If mary is both happy and humble then lucy is both not generous and creative. If mary is not curious then someone is either old or brave. If someone is both old and rich then alice is not brave or quiet. Everyone who is not creative is not quiet and vice versa. Everyone who is both not patient and generous is either not happy or not curious. Everyone who is either not tall or curious is either patient or kind and vice versa. If susan is creative then someone is both humble and tall. If someone is not quiet or not patient then someone is both not rich and generous. If paul is either humble or not curious then paul is not calm. Everyone who is curious or brave is both not brave and calm and vice versa. Everyone who is creative or not brave is not kind and vice versa. If someone is not quiet then someone is either not funny or humble. Everyone who is generous or old is not brave or not strong and vice versa. Someone is either humble or not kind. John is either not patient or not old. Someone is not curious. Someone is either patient or not rich. Fred is funny or not patient. Susan is either rich or not kind. | Mary is not patient. | contradiction | ((old(lucy))=>((patient(susan)<~>curious(susan))))&
(![X]:(~calm(X)=>(quiet(X)&~generous(X))))&
((?[X]:((~funny(X)|~patient(X))))=>((~rich(lucy)&brave(lucy))))&
(((happy(mary)&humble(mary)))=>((~generous(lucy)&creative(lucy))))&
((~curious(mary))=>(?[X]:((old(X)<~>brave(X)))))&
((?[X]:((old(X)&rich(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)&generous(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(patient(X)<~>kind(X))))&
((creative(susan))=>(?[X]:((humble(X)&tall(X)))))&
((?[X]:((~quiet(X)|~patient(X))))=>(?[X]:((~rich(X)&generous(X)))))&
(((humble(paul)<~>~curious(paul)))=>(~calm(paul)))&
(![X]:((curious(X)|brave(X))<=>(~brave(X)&calm(X))))&
(![X]:((creative(X)|~brave(X))<=>~kind(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:((generous(X)|old(X))<=>(~brave(X)|~strong(X))))&
(?[X]:((humble(X)<~>~kind(X))))&
((~patient(john)<~>~old(john)))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)<~>~rich(X))))&
((funny(fred)|~patient(fred)))&
((rich(susan)<~>~kind(susan))) | ~patient(mary) | [
"p2",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7611736171597288959293682
% SZS output start Proof for 7611736171597288959293682
3. ? [X0] : (~patient(X0) | ~funny(X0)) => (brave(lucy) & ~rich(lucy)) [input p2]
13. ! [X0] : ((brave(X0) | curious(X0)) <=> (calm(X0) & ~brave(X0))) [input p12]
23. ~patient(mary) [input hypothesis]
28. (brave(lucy) & ~rich(lucy)) | ! [X0] : (patient(X0) & funny(X0)) [ennf transformation 3]
53. ! [X0] : (((brave(X0) | curious(X0)) | (~calm(X0) | brave(X0))) & ((calm(X0) & ~brave(X0)) | (~brave(X0) & ~curious(X0)))) [nnf transformation 13]
54. ! [X0] : ((brave(X0) | curious(X0) | ~calm(X0) | brave(X0)) & ((calm(X0) & ~brave(X0)) | (~brave(X0) & ~curious(X0)))) [flattening 53]
80. brave(lucy) | patient(X0) [cnf transformation 28]
107. ~brave(X0) | ~brave(X0) [cnf transformation 54]
130. ~patient(mary) [cnf transformation 23]
131. ~brave(X0) [duplicate literal removal 107]
148. 4 <=> ! [X0] : patient(X0) [avatar definition]
149. patient(X0) <- (4) [avatar component clause 148]
151. 5 <=> brave(lucy) [avatar definition]
153. brave(lucy) <- (5) [avatar component clause 151]
154. 4 | 5 [avatar split clause 80,151,148]
295. $false <- (5) [subsumption resolution 153,131]
296. ~5 [avatar contradiction clause 295]
297. $false <- (4) [resolution 149,130]
298. ~4 [avatar contradiction clause 297]
299. $false [avatar sat refutation 154,296,298]
% SZS output end Proof for 7611736171597288959293682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either strong or not tall is both happy and funny and vice versa. If someone is brave or humble then someone is not happy and vice versa. If susan is both strong and not generous then someone is either not creative or happy. Everyone who is either not kind or not tall is calm or not generous and vice versa. If someone is either not old or not calm then alice is both not calm and not humble and vice versa. Everyone who is not happy is either happy or not patient and vice versa. Everyone who is both not strong and not old is either not generous or not curious and vice versa. If someone is tall or not old then paul is either not patient or not curious. If someone is not humble or not tall then lucy is both old and creative. Everyone who is generous is either generous or not humble and vice versa. Everyone who is both funny and quiet is both generous and strong and vice versa. If lucy is either not happy or old then mary is either not patient or wise. If someone is not patient then someone is either calm or not humble and vice versa. If lucy is either curious or not brave then john is either not strong or quiet. Everyone who is not kind or old is either not calm or humble and vice versa. Everyone who is not patient or not rich is either not happy or not creative and vice versa. Lucy is kind. Lucy is either not calm or happy. John is not curious or creative. Someone is either generous or funny. Fred is calm or happy. Paul is wise or curious. Someone is not kind or curious. | Susan is old. | neutral | (![X]:((strong(X)<~>~tall(X))<=>(happy(X)&funny(X))))&
((?[X]:((brave(X)|humble(X))))<=>(?[X]:(~happy(X))))&
(((strong(susan)&~generous(susan)))=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:((~kind(X)<~>~tall(X))<=>(calm(X)|~generous(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>((~calm(alice)&~humble(alice))))&
(![X]:(~happy(X)<=>(happy(X)<~>~patient(X))))&
(![X]:((~strong(X)&~old(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:((tall(X)|~old(X))))=>((~patient(paul)<~>~curious(paul))))&
((?[X]:((~humble(X)|~tall(X))))=>((old(lucy)&creative(lucy))))&
(![X]:(generous(X)<=>(generous(X)<~>~humble(X))))&
(![X]:((funny(X)&quiet(X))<=>(generous(X)&strong(X))))&
(((~happy(lucy)<~>old(lucy)))=>((~patient(mary)<~>wise(mary))))&
((?[X]:(~patient(X)))<=>(?[X]:((calm(X)<~>~humble(X)))))&
(((curious(lucy)<~>~brave(lucy)))=>((~strong(john)<~>quiet(john))))&
(![X]:((~kind(X)|old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~patient(X)|~rich(X))<=>(~happy(X)<~>~creative(X))))&
(kind(lucy))&
((~calm(lucy)<~>happy(lucy)))&
((~curious(john)|creative(john)))&
(?[X]:((generous(X)<~>funny(X))))&
((calm(fred)|happy(fred)))&
((wise(paul)|curious(paul)))&
(?[X]:((~kind(X)|curious(X)))) | old(susan) | [] | null | 0 |
Everyone who is brave is humble or patient and vice versa.
Everyone who is not old is brave or not generous and vice versa.
If lucy is both rich and kind then someone is both not brave and generous.
Everyone who is either curious or not quiet is strong or not quiet and vice versa.
Everyone who is both creative and strong is humble.
Everyone who is creative or not kind is both not quiet and generous and vice versa.
Everyone who is both not old and strong is not strong or not happy and vice versa.
If someone is either creative or humble then paul is both not tall and not quiet and vice versa.
If paul is not quiet then someone is not creative and vice versa.
Everyone who is both not curious and not happy is not happy or tall.
Everyone who is calm is not patient and vice versa.
Everyone who is both wise and not humble is both humble and generous.
If someone is not curious or kind then someone is either not happy or not strong and vice versa.
Everyone who is both not humble and humble is quiet.
If someone is not calm then fred is generous and vice versa.
If susan is both funny and not creative then lucy is not brave and vice versa.
Lucy is either not wise or creative.
Someone is not brave.
Someone is not brave or brave.
Someone is not funny or not tall.
Someone is both quiet and patient.
Someone is not humble or not kind.
Paul is not kind or not generous.
Paul is not calm or quiet. | Fred is humble. | neutral | (![X]:(brave(X)<=>(humble(X)|patient(X))))&
(![X]:(~old(X)<=>(brave(X)|~generous(X))))&
(((rich(lucy)&kind(lucy)))=>(?[X]:((~brave(X)&generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((creative(X)&strong(X))=>humble(X)))&
(![X]:((creative(X)|~kind(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~old(X)&strong(X))<=>(~strong(X)|~happy(X))))&
((?[X]:((creative(X)<~>humble(X))))<=>((~tall(paul)&~quiet(paul))))&
((~quiet(paul))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)&~happy(X))=>(~happy(X)|tall(X))))&
(![X]:(calm(X)<=>~patient(X)))&
(![X]:((wise(X)&~humble(X))=>(humble(X)&generous(X))))&
((?[X]:((~curious(X)|kind(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~humble(X)&humble(X))=>quiet(X)))&
((?[X]:(~calm(X)))<=>(generous(fred)))&
(((funny(susan)&~creative(susan)))<=>(~brave(lucy)))&
((~wise(lucy)<~>creative(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|brave(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:((~humble(X)|~kind(X))))&
((~kind(paul)|~generous(paul)))&
((~calm(paul)|quiet(paul))) | humble(fred) | [] | null | 0 |
If alice is either not generous or not creative then fred is either humble or not tall. Everyone who is not tall is both generous and patient. If someone is not brave or not strong then someone is not tall or quiet. If someone is both kind and funny then lucy is not generous and vice versa. Everyone who is rich or calm is either funny or generous and vice versa. Everyone who is either creative or not funny is not rich or creative and vice versa. Everyone who is funny is either not generous or not rich and vice versa. Everyone who is brave is not curious and vice versa. Everyone who is calm is both patient and not funny and vice versa. If someone is either brave or not quiet then someone is both not tall and not happy and vice versa. Everyone who is quiet is both not wise and happy. Everyone who is both humble and not calm is tall. If someone is not patient or calm then susan is happy or not wise. Everyone who is humble or not patient is happy and vice versa. If john is not old or happy then mary is both not curious and humble. If john is calm then someone is not rich or curious and vice versa. Paul is either kind or funny. Someone is either not generous or calm. Someone is not old. Someone is not curious or not generous. Lucy is both funny and not curious. Lucy is either funny or calm. Someone is both patient and brave. | Fred is quiet. | contradiction | (((~generous(alice)<~>~creative(alice)))=>((humble(fred)<~>~tall(fred))))&
(![X]:(~tall(X)=>(generous(X)&patient(X))))&
((?[X]:((~brave(X)|~strong(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:((kind(X)&funny(X))))<=>(~generous(lucy)))&
(![X]:((rich(X)|calm(X))<=>(funny(X)<~>generous(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~rich(X)|creative(X))))&
(![X]:(funny(X)<=>(~generous(X)<~>~rich(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:(calm(X)<=>(patient(X)&~funny(X))))&
((?[X]:((brave(X)<~>~quiet(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:(quiet(X)=>(~wise(X)&happy(X))))&
(![X]:((humble(X)&~calm(X))=>tall(X)))&
((?[X]:((~patient(X)|calm(X))))=>((happy(susan)|~wise(susan))))&
(![X]:((humble(X)|~patient(X))<=>happy(X)))&
(((~old(john)|happy(john)))=>((~curious(mary)&humble(mary))))&
((calm(john))<=>(?[X]:((~rich(X)|curious(X)))))&
((kind(paul)<~>funny(paul)))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:(~old(X)))&
(?[X]:((~curious(X)|~generous(X))))&
((funny(lucy)&~curious(lucy)))&
((funny(lucy)<~>calm(lucy)))&
(?[X]:((patient(X)&brave(X)))) | quiet(fred) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3783780815494071949455578
% SZS output start Proof for 3783780815494071949455578
2. ! [X0] : (~tall(X0) => (patient(X0) & generous(X0))) [input p1]
5. ! [X0] : ((calm(X0) | rich(X0)) <=> (funny(X0) <~> generous(X0))) [input p4]
6. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (creative(X0) | ~rich(X0))) [input p5]
7. ! [X0] : (funny(X0) <=> (~generous(X0) <~> ~rich(X0))) [input p6]
8. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p7]
9. ! [X0] : (calm(X0) <=> (~funny(X0) & patient(X0))) [input p8]
10. ? [X0] : (brave(X0) <~> ~quiet(X0)) <=> ? [X0] : (~happy(X0) & ~tall(X0)) [input p9]
16. calm(john) <=> ? [X0] : (curious(X0) | ~rich(X0)) [input p15]
24. quiet(fred) [input hypothesis]
26. ? [X0] : (brave(X0) <~> ~quiet(X0)) <=> ? [X1] : (~happy(X1) & ~tall(X1)) [rectify 10]
31. ! [X0] : ((patient(X0) & generous(X0)) | tall(X0)) [ennf transformation 2]
45. ! [X0] : (((calm(X0) | rich(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~calm(X0) & ~rich(X0)))) [nnf transformation 5]
46. ! [X0] : ((calm(X0) | rich(X0) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (~calm(X0) & ~rich(X0)))) [flattening 45]
47. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & ((creative(X0) | ~rich(X0)) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 6]
48. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | (~creative(X0) & rich(X0))) & (creative(X0) | ~rich(X0) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [flattening 47]
49. ! [X0] : ((funny(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) & (((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | ~funny(X0))) [nnf transformation 7]
50. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 8]
51. ! [X0] : ((calm(X0) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [nnf transformation 9]
52. ! [X0] : ((calm(X0) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | ~calm(X0))) [flattening 51]
53. (? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ! [X1] : (happy(X1) | tall(X1))) & (? [X1] : (~happy(X1) & ~tall(X1)) | ! [X0] : ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) [nnf transformation 26]
54. (? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | ! [X1] : (happy(X1) | tall(X1))) & (? [X2] : (~happy(X2) & ~tall(X2)) | ! [X3] : ((brave(X3) | quiet(X3)) & (~quiet(X3) | ~brave(X3)))) [rectify 53]
55. ? [X0] : ((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) => ((quiet(sK2) | ~brave(sK2)) & (~quiet(sK2) | brave(sK2))) [choice axiom]
56. ? [X2] : (~happy(X2) & ~tall(X2)) => (~happy(sK3) & ~tall(sK3)) [choice axiom]
57. (((quiet(sK2) | ~brave(sK2)) & (~quiet(sK2) | brave(sK2))) | ! [X1] : (happy(X1) | tall(X1))) & ((~happy(sK3) & ~tall(sK3)) | ! [X3] : ((brave(X3) | quiet(X3)) & (~quiet(X3) | ~brave(X3)))) [skolemisation 54,56,55]
60. (calm(john) | ! [X0] : (~curious(X0) & rich(X0))) & (? [X0] : (curious(X0) | ~rich(X0)) | ~calm(john)) [nnf transformation 16]
61. (calm(john) | ! [X0] : (~curious(X0) & rich(X0))) & (? [X1] : (curious(X1) | ~rich(X1)) | ~calm(john)) [rectify 60]
62. ? [X1] : (curious(X1) | ~rich(X1)) => (curious(sK4) | ~rich(sK4)) [choice axiom]
63. (calm(john) | ! [X0] : (~curious(X0) & rich(X0))) & ((curious(sK4) | ~rich(sK4)) | ~calm(john)) [skolemisation 61,62]
79. tall(X0) | generous(X0) [cnf transformation 31]
85. ~rich(X0) | funny(X0) | generous(X0) [cnf transformation 46]
86. ~calm(X0) | funny(X0) | generous(X0) [cnf transformation 46]
87. ~rich(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 46]
92. creative(X0) | ~rich(X0) | creative(X0) | funny(X0) [cnf transformation 48]
96. funny(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
100. funny(X0) | ~generous(X0) | rich(X0) [cnf transformation 49]
102. curious(X0) | brave(X0) [cnf transformation 50]
104. ~calm(X0) | ~funny(X0) [cnf transformation 52]
106. ~tall(sK3) | ~quiet(X3) | ~brave(X3) [cnf transformation 57]
122. calm(john) | rich(X0) [cnf transformation 63]
123. calm(john) | ~curious(X0) [cnf transformation 63]
136. quiet(fred) [cnf transformation 24]
137. creative(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 92]
138. ~creative(X0) | funny(X0) [duplicate literal removal 96]
160. 5 <=> ! [X1] : brave(X1) [avatar definition]
161. brave(X1) <- (5) [avatar component clause 160]
189. ~rich(X0) | funny(X0) [subsumption resolution 137,138]
190. ~generous(X0) | funny(X0) [subsumption resolution 100,189]
213. 17 <=> ! [X3] : (~quiet(X3) | ~brave(X3)) [avatar definition]
214. ~quiet(X3) | ~brave(X3) <- (17) [avatar component clause 213]
217. 18 <=> tall(sK3) [avatar definition]
219. ~tall(sK3) <- (~18) [avatar component clause 217]
221. 17 | ~18 [avatar split clause 106,217,213]
243. 23 <=> ! [X0] : ~curious(X0) [avatar definition]
244. ~curious(X0) <- (23) [avatar component clause 243]
246. 24 <=> calm(john) [avatar definition]
248. calm(john) <- (24) [avatar component clause 246]
249. 23 | 24 [avatar split clause 123,246,243]
251. 25 <=> ! [X0] : rich(X0) [avatar definition]
252. rich(X0) <- (25) [avatar component clause 251]
253. 25 | 24 [avatar split clause 122,246,251]
293. generous(sK3) <- (~18) [resolution 79,219]
298. ~funny(john) <- (24) [resolution 104,248]
305. funny(john) | generous(john) <- (24) [resolution 86,248]
306. generous(john) <- (24) [subsumption resolution 305,298]
307. funny(john) <- (24) [resolution 306,190]
308. $false <- (24) [subsumption resolution 307,298]
309. ~24 [avatar contradiction clause 308]
310. brave(X0) <- (23) [resolution 244,102]
311. 5 | ~23 [avatar split clause 310,243,160]
315. funny(X0) | generous(X0) <- (25) [resolution 252,85]
318. funny(X0) <- (25) [subsumption resolution 315,190]
324. ~funny(X0) | ~generous(X0) <- (25) [resolution 87,252]
325. ~generous(X0) <- (25) [subsumption resolution 324,318]
333. $false <- (~18, 25) [resolution 325,293]
334. 18 | ~25 [avatar contradiction clause 333]
336. ~quiet(X3) <- (5, 17) [subsumption resolution 214,161]
337. $false <- (5, 17) [resolution 336,136]
340. ~5 | ~17 [avatar contradiction clause 337]
341. $false [avatar sat refutation 221,249,253,309,311,334,340]
% SZS output end Proof for 3783780815494071949455578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or calm then alice is not humble or creative and vice versa.
If someone is both not patient and creative then someone is wise and vice versa.
If lucy is both patient and not generous then someone is not curious or calm and vice versa.
Everyone who is not generous is either not kind or not quiet.
If someone is either not strong or rich then lucy is not happy or not kind.
Everyone who is both rich and not kind is brave or curious.
If someone is wise then alice is both not old and happy.
If alice is either patient or not tall then alice is not kind and vice versa.
If fred is funny then mary is both strong and not rich and vice versa.
Everyone who is both curious and not tall is both tall and not brave and vice versa.
If alice is not creative then mary is both rich and generous and vice versa.
If paul is not funny then someone is not quiet.
If someone is both not brave and wise then paul is both not calm and not tall.
Everyone who is not kind or not quiet is both not calm and old and vice versa.
Everyone who is either not strong or rich is happy or not creative and vice versa.
Everyone who is not humble is either strong or happy and vice versa.
Paul is either not happy or old.
Someone is funny.
Paul is either not curious or not creative.
Fred is either quiet or not generous.
Someone is either not strong or not curious.
Alice is wise.
Someone is either tall or not rich.
Someone is not happy. | Fred is funny. | neutral | ((?[X]:((old(X)<~>calm(X))))<=>((~humble(alice)|creative(alice))))&
((?[X]:((~patient(X)&creative(X))))<=>(?[X]:(wise(X))))&
(((patient(lucy)&~generous(lucy)))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:(~generous(X)=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~strong(X)<~>rich(X))))=>((~happy(lucy)|~kind(lucy))))&
(![X]:((rich(X)&~kind(X))=>(brave(X)|curious(X))))&
((?[X]:(wise(X)))=>((~old(alice)&happy(alice))))&
(((patient(alice)<~>~tall(alice)))<=>(~kind(alice)))&
((funny(fred))<=>((strong(mary)&~rich(mary))))&
(![X]:((curious(X)&~tall(X))<=>(tall(X)&~brave(X))))&
((~creative(alice))<=>((rich(mary)&generous(mary))))&
((~funny(paul))=>(?[X]:(~quiet(X))))&
((?[X]:((~brave(X)&wise(X))))=>((~calm(paul)&~tall(paul))))&
(![X]:((~kind(X)|~quiet(X))<=>(~calm(X)&old(X))))&
(![X]:((~strong(X)<~>rich(X))<=>(happy(X)|~creative(X))))&
(![X]:(~humble(X)<=>(strong(X)<~>happy(X))))&
((~happy(paul)<~>old(paul)))&
(?[X]:(funny(X)))&
((~curious(paul)<~>~creative(paul)))&
((quiet(fred)<~>~generous(fred)))&
(?[X]:((~strong(X)<~>~curious(X))))&
(wise(alice))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:(~happy(X))) | funny(fred) | [] | null | 0 |
Everyone who is not creative is not curious and vice versa. Everyone who is both old and tall is both not strong and kind and vice versa. Everyone who is not funny is happy. Everyone who is either not brave or patient is not happy. Everyone who is both creative and not curious is either wise or quiet. If mary is generous or not quiet then alice is both humble and not strong. If paul is funny then lucy is curious or happy and vice versa. If alice is not wise then someone is either wise or rich. Everyone who is either patient or funny is rich and vice versa. If someone is either not creative or not humble then someone is calm. If someone is brave or not old then susan is both not happy and old. If john is not humble or quiet then someone is either rich or not strong. Everyone who is either tall or not kind is quiet or not patient. Everyone who is funny is both not calm and not creative. Everyone who is both not humble and rich is generous and vice versa. If someone is either not wise or funny then someone is both quiet and not quiet. Susan is not calm or kind. Susan is either quiet or patient. Lucy is either creative or tall. Lucy is either happy or not humble. Someone is both not calm and not humble. Someone is either not old or happy. Alice is funny. | Alice is creative. | contradiction | (![X]:(~creative(X)<=>~curious(X)))&
(![X]:((old(X)&tall(X))<=>(~strong(X)&kind(X))))&
(![X]:(~funny(X)=>happy(X)))&
(![X]:((~brave(X)<~>patient(X))=>~happy(X)))&
(![X]:((creative(X)&~curious(X))=>(wise(X)<~>quiet(X))))&
(((generous(mary)|~quiet(mary)))=>((humble(alice)&~strong(alice))))&
((funny(paul))<=>((curious(lucy)|happy(lucy))))&
((~wise(alice))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((patient(X)<~>funny(X))<=>rich(X)))&
((?[X]:((~creative(X)<~>~humble(X))))=>(?[X]:(calm(X))))&
((?[X]:((brave(X)|~old(X))))=>((~happy(susan)&old(susan))))&
(((~humble(john)|quiet(john)))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((tall(X)<~>~kind(X))=>(quiet(X)|~patient(X))))&
(![X]:(funny(X)=>(~calm(X)&~creative(X))))&
(![X]:((~humble(X)&rich(X))<=>generous(X)))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((quiet(X)&~quiet(X)))))&
((~calm(susan)|kind(susan)))&
((quiet(susan)<~>patient(susan)))&
((creative(lucy)<~>tall(lucy)))&
((happy(lucy)<~>~humble(lucy)))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(funny(alice)) | creative(alice) | [
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9146000738324305042384956
% SZS output start Proof for 9146000738324305042384956
14. ! [X0] : (funny(X0) => (~creative(X0) & ~calm(X0))) [input p13]
23. funny(alice) [input p22]
24. creative(alice) [input hypothesis]
39. ! [X0] : ((~creative(X0) & ~calm(X0)) | ~funny(X0)) [ennf transformation 14]
111. ~funny(X0) | ~creative(X0) [cnf transformation 39]
128. funny(alice) [cnf transformation 23]
129. creative(alice) [cnf transformation 24]
299. ~creative(alice) [resolution 111,128]
303. $false [subsumption resolution 299,129]
% SZS output end Proof for 9146000738324305042384956
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is patient.
If someone is not patient then fred is both not old and not tall and vice versa.
Everyone who is either old or generous is both creative and brave.
Everyone who is both quiet and curious is not patient or not brave.
Everyone who is not quiet or not creative is either curious or not rich.
If susan is both not humble and not old then mary is not happy and vice versa.
Everyone who is both not funny and not old is humble and vice versa.
If mary is either not strong or happy then someone is both not quiet and not humble and vice versa.
Everyone who is both happy and not patient is not generous or not patient and vice versa.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is both curious and patient is not happy or funny and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
If mary is both not curious and creative then lucy is either not generous or not kind.
If someone is not funny or not creative then someone is either tall or old.
Someone is not generous or not calm.
Paul is old or funny.
Someone is either wise or not strong.
Fred is both happy and kind.
Someone is not brave or wise.
Fred is either not wise or curious. | Mary is brave. | contradiction | (![X]:((~old(X)|generous(X))=>patient(X)))&
((?[X]:(~patient(X)))<=>((~old(fred)&~tall(fred))))&
(![X]:((old(X)<~>generous(X))=>(creative(X)&brave(X))))&
(![X]:((quiet(X)&curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(curious(X)<~>~rich(X))))&
(((~humble(susan)&~old(susan)))<=>(~happy(mary)))&
(![X]:((~funny(X)&~old(X))<=>humble(X)))&
(((~strong(mary)<~>happy(mary)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((curious(X)&patient(X))<=>(~happy(X)|funny(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~curious(mary)&creative(mary)))=>((~generous(lucy)<~>~kind(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(?[X]:((~generous(X)|~calm(X))))&
((old(paul)|funny(paul)))&
(?[X]:((wise(X)<~>~strong(X))))&
((happy(fred)&kind(fred)))&
(?[X]:((~brave(X)|wise(X))))&
((~wise(fred)<~>curious(fred))) | brave(mary) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2146825844554336522833130
% SZS output start Proof for 2146825844554336522833130
1. ! [X0] : ((generous(X0) | ~old(X0)) => patient(X0)) [input p0]
2. ? [X0] : ~patient(X0) <=> (~tall(fred) & ~old(fred)) [input p1]
3. ! [X0] : ((old(X0) <~> generous(X0)) => (brave(X0) & creative(X0))) [input p2]
4. ! [X0] : ((curious(X0) & quiet(X0)) => (~brave(X0) | ~patient(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (curious(X0) <~> ~rich(X0))) [input p4]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> humble(X0)) [input p6]
8. (~strong(mary) <~> happy(mary)) <=> ? [X0] : (~humble(X0) & ~quiet(X0)) [input p7]
9. ! [X0] : ((~patient(X0) & happy(X0)) <=> (~patient(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (strong(X0) | ~happy(X0))) [input p9]
13. ! [X0] : ((~generous(X0) | happy(X0)) <=> ~creative(X0)) [input p12]
14. creative(mary) <=> ? [X0] : (rich(X0) <~> ~humble(X0)) [input p13]
23. brave(mary) [input hypothesis]
26. ! [X0] : (patient(X0) | (~generous(X0) & old(X0))) [ennf transformation 1]
27. ! [X0] : ((brave(X0) & creative(X0)) | (old(X0) <=> generous(X0))) [ennf transformation 3]
28. ! [X0] : ((~brave(X0) | ~patient(X0)) | (~curious(X0) | ~quiet(X0))) [ennf transformation 4]
29. ! [X0] : (~brave(X0) | ~patient(X0) | ~curious(X0) | ~quiet(X0)) [flattening 28]
30. ! [X0] : ((curious(X0) <~> ~rich(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 5]
34. (? [X0] : ~patient(X0) | (tall(fred) | old(fred))) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [nnf transformation 2]
35. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [rectify 35]
37. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
38. (~patient(sK0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [skolemisation 36,37]
39. ! [X0] : ((brave(X0) & creative(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 27]
40. ! [X0] : (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (creative(X0) & quiet(X0))) [nnf transformation 30]
43. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | (old(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | old(X0) | funny(X0))) [flattening 43]
45. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & (? [X0] : (~humble(X0) & ~quiet(X0)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [nnf transformation 8]
46. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & (? [X1] : (~humble(X1) & ~quiet(X1)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [rectify 45]
47. ? [X1] : (~humble(X1) & ~quiet(X1)) => (~humble(sK1) & ~quiet(sK1)) [choice axiom]
48. (((~happy(mary) | strong(mary)) & (happy(mary) | ~strong(mary))) | ! [X0] : (humble(X0) | quiet(X0))) & ((~humble(sK1) & ~quiet(sK1)) | ((~strong(mary) | ~happy(mary)) & (happy(mary) | strong(mary)))) [skolemisation 46,47]
49. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & ((~patient(X0) | ~generous(X0)) | (patient(X0) | ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & (~patient(X0) | ~generous(X0) | patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 10]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | patient(X0) | creative(X0))) [flattening 51]
56. ! [X0] : (((~generous(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : ((~generous(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [flattening 56]
58. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X0] : ((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~creative(mary)) [nnf transformation 14]
59. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) | ~creative(mary)) [rectify 58]
60. ? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) => ((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) [choice axiom]
61. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) | ~creative(mary)) [skolemisation 59,60]
73. patient(X0) | old(X0) [cnf transformation 26]
74. ~generous(X0) | patient(X0) [cnf transformation 26]
75. ~old(fred) | patient(X1) [cnf transformation 38]
76. ~tall(fred) | patient(X1) [cnf transformation 38]
77. ~patient(sK0) | tall(fred) | old(fred) [cnf transformation 38]
78. ~old(X0) | generous(X0) | creative(X0) [cnf transformation 39]
79. ~generous(X0) | old(X0) | creative(X0) [cnf transformation 39]
82. ~curious(X0) | ~patient(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 29]
84. ~rich(X0) | curious(X0) | creative(X0) [cnf transformation 40]
92. ~humble(X0) | ~old(X0) [cnf transformation 44]
98. ~happy(mary) | strong(mary) | humble(X0) | quiet(X0) [cnf transformation 48]
101. happy(X0) | patient(X0) [cnf transformation 50]
102. ~patient(X0) | generous(X0) [cnf transformation 50]
107. ~patient(X0) | happy(X0) [cnf transformation 52]
108. ~strong(X0) | ~patient(X0) [cnf transformation 52]
122. ~creative(X0) | ~happy(X0) [cnf transformation 57]
128. creative(mary) | rich(X0) | humble(X0) [cnf transformation 61]
143. brave(mary) [cnf transformation 23]
145. 1 <=> old(fred) [avatar definition]
149. 2 <=> tall(fred) [avatar definition]
153. 3 <=> patient(sK0) [avatar definition]
155. ~patient(sK0) <- (~3) [avatar component clause 153]
156. 1 | 2 | ~3 [avatar split clause 77,153,149,145]
158. 4 <=> ! [X1] : patient(X1) [avatar definition]
159. patient(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 [avatar split clause 76,149,158]
161. 4 | ~1 [avatar split clause 75,145,158]
163. 5 <=> happy(mary) [avatar definition]
164. ~happy(mary) <- (~5) [avatar component clause 163]
178. 8 <=> ! [X0] : (humble(X0) | quiet(X0)) [avatar definition]
179. humble(X0) | quiet(X0) <- (8) [avatar component clause 178]
181. 9 <=> strong(mary) [avatar definition]
183. strong(mary) <- (9) [avatar component clause 181]
184. 8 | 9 | ~5 [avatar split clause 98,163,181,178]
198. happy(X0) [subsumption resolution 107,101]
205. ~creative(X0) [subsumption resolution 122,198]
206. humble(X0) | rich(X0) [subsumption resolution 128,205]
263. $false <- (~5) [subsumption resolution 164,198]
264. 5 [avatar contradiction clause 263]
265. old(sK0) <- (~3) [resolution 73,155]
272. ~patient(mary) <- (9) [resolution 183,108]
275. ~old(X0) | rich(X0) [resolution 206,92]
280. generous(sK0) | creative(sK0) <- (~3) [resolution 78,265]
282. generous(sK0) <- (~3) [subsumption resolution 280,205]
293. patient(sK0) <- (~3) [resolution 282,74]
294. $false <- (~3) [subsumption resolution 293,155]
295. 3 [avatar contradiction clause 294]
296. $false <- (4, 9) [resolution 159,272]
297. generous(X0) <- (4) [resolution 159,102]
298. ~4 | ~9 [avatar contradiction clause 296]
302. ~old(X1) | quiet(X1) <- (8) [resolution 179,92]
304. old(X1) | creative(X1) <- (4) [resolution 297,79]
306. old(X1) <- (4) [subsumption resolution 304,205]
376. rich(X0) <- (4) [resolution 275,306]
389. quiet(X0) <- (4, 8) [resolution 302,306]
397. curious(X4) | creative(X4) <- (4) [resolution 376,84]
401. curious(X4) <- (4) [subsumption resolution 397,205]
416. ~patient(X0) | ~brave(X0) | ~quiet(X0) <- (4) [resolution 401,82]
421. ~brave(X0) | ~quiet(X0) <- (4) [subsumption resolution 416,159]
422. ~brave(X0) <- (4, 8) [subsumption resolution 421,389]
431. $false <- (4, 8) [resolution 422,143]
433. ~4 | ~8 [avatar contradiction clause 431]
434. $false [avatar sat refutation 156,160,161,184,264,295,298,433]
% SZS output end Proof for 2146825844554336522833130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not generous then lucy is old or calm and vice versa.
If someone is old or quiet then lucy is either patient or not creative.
Everyone who is old or patient is old and vice versa.
Everyone who is not curious or wise is happy and vice versa.
Everyone who is not brave or rich is both kind and brave.
Everyone who is either funny or creative is both calm and not kind.
Everyone who is not patient or not kind is both not old and quiet and vice versa.
Everyone who is both not rich and not wise is kind and vice versa.
If someone is either generous or brave then someone is either kind or tall and vice versa.
If someone is not quiet or not brave then someone is generous and vice versa.
If someone is creative then someone is either quiet or strong.
Everyone who is either not quiet or brave is both not old and not quiet.
If someone is not kind then susan is not patient.
Everyone who is either tall or not kind is not patient and vice versa.
If fred is curious then fred is calm.
Everyone who is either not curious or old is not old or kind and vice versa.
Paul is strong.
Someone is not old or patient.
Someone is either not curious or not calm.
Susan is either wise or brave.
Lucy is either not humble or not brave.
Mary is both old and not tall. | Lucy is generous. | contradiction | ((~generous(lucy))<=>((old(lucy)|calm(lucy))))&
((?[X]:((old(X)|quiet(X))))=>((patient(lucy)<~>~creative(lucy))))&
(![X]:((old(X)|patient(X))<=>old(X)))&
(![X]:((~curious(X)|wise(X))<=>happy(X)))&
(![X]:((~brave(X)|rich(X))=>(kind(X)&brave(X))))&
(![X]:((funny(X)<~>creative(X))=>(calm(X)&~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~old(X)&quiet(X))))&
(![X]:((~rich(X)&~wise(X))<=>kind(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:(generous(X))))&
((?[X]:(creative(X)))=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((~quiet(X)<~>brave(X))=>(~old(X)&~quiet(X))))&
((?[X]:(~kind(X)))=>(~patient(susan)))&
(![X]:((tall(X)<~>~kind(X))<=>~patient(X)))&
((curious(fred))=>(calm(fred)))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)|kind(X))))&
(strong(paul))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~curious(X)<~>~calm(X))))&
((wise(susan)<~>brave(susan)))&
((~humble(lucy)<~>~brave(lucy)))&
((old(mary)&~tall(mary))) | generous(lucy) | [
"p0",
"p2",
"p4",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7365529266887759166376032
% SZS output start Proof for 7365529266887759166376032
1. ~generous(lucy) <=> (calm(lucy) | old(lucy)) [input p0]
3. ! [X0] : ((patient(X0) | old(X0)) <=> old(X0)) [input p2]
5. ! [X0] : ((rich(X0) | ~brave(X0)) => (brave(X0) & kind(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (quiet(X0) & ~old(X0))) [input p6]
12. ! [X0] : ((~quiet(X0) <~> brave(X0)) => (~quiet(X0) & ~old(X0))) [input p11]
23. generous(lucy) [input hypothesis]
28. ! [X0] : ((brave(X0) & kind(X0)) | (~rich(X0) & brave(X0))) [ennf transformation 5]
31. ! [X0] : ((~quiet(X0) & ~old(X0)) | (~quiet(X0) <=> brave(X0))) [ennf transformation 12]
34. (~generous(lucy) | (~calm(lucy) & ~old(lucy))) & ((calm(lucy) | old(lucy)) | generous(lucy)) [nnf transformation 1]
35. (~generous(lucy) | (~calm(lucy) & ~old(lucy))) & (calm(lucy) | old(lucy) | generous(lucy)) [flattening 34]
37. ! [X0] : (((patient(X0) | old(X0)) | ~old(X0)) & (old(X0) | (~patient(X0) & ~old(X0)))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | old(X0) | ~old(X0)) & (old(X0) | (~patient(X0) & ~old(X0)))) [flattening 37]
40. ! [X0] : (((~kind(X0) | ~patient(X0)) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 7]
41. ! [X0] : ((~kind(X0) | ~patient(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | (kind(X0) & patient(X0)))) [flattening 40]
58. ! [X0] : ((~quiet(X0) & ~old(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) [nnf transformation 31]
70. ~generous(lucy) | ~old(lucy) [cnf transformation 35]
77. ~patient(X0) | old(X0) [cnf transformation 38]
81. brave(X0) | brave(X0) [cnf transformation 28]
89. patient(X0) | quiet(X0) [cnf transformation 41]
111. ~quiet(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 58]
134. generous(lucy) [cnf transformation 23]
137. ~quiet(X0) | ~brave(X0) [duplicate literal removal 111]
138. brave(X0) [duplicate literal removal 81]
144. 2 <=> generous(lucy) [avatar definition]
149. 3 <=> old(lucy) [avatar definition]
151. ~old(lucy) <- (~3) [avatar component clause 149]
152. ~3 | ~2 [avatar split clause 70,144,149]
155. 4 <=> ! [X0] : ~quiet(X0) [avatar definition]
156. ~quiet(X0) <- (4) [avatar component clause 155]
233. ~quiet(X0) [subsumption resolution 137,138]
234. 4 [avatar split clause 233,155]
266. 2 [avatar split clause 134,144]
278. quiet(X0) | old(X0) [resolution 89,77]
283. old(X0) <- (4) [subsumption resolution 278,156]
296. $false <- (~3, 4) [resolution 283,151]
299. 3 | ~4 [avatar contradiction clause 296]
300. $false [avatar sat refutation 152,234,266,299]
% SZS output end Proof for 7365529266887759166376032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not curious or not humble and vice versa. If susan is both humble and quiet then mary is creative or kind and vice versa. Everyone who is either brave or not brave is both not strong and generous. Everyone who is both not old and not curious is not happy or curious and vice versa. Everyone who is either happy or generous is either funny or not patient. If someone is either not kind or brave then susan is either humble or creative. Everyone who is both funny and not creative is either rich or not patient and vice versa. Everyone who is both generous and not patient is both not kind and humble. If someone is either strong or tall then alice is humble. Everyone who is both not calm and not curious is old or rich and vice versa. If someone is funny or not brave then someone is not curious or not kind and vice versa. If someone is not wise or not old then lucy is curious or not calm and vice versa. Everyone who is not calm is old. If alice is both not humble and funny then someone is not curious and vice versa. If susan is not strong then someone is not happy or curious and vice versa. Everyone who is wise is not patient. Someone is brave. Someone is either happy or funny. Someone is not quiet or strong. Lucy is not calm or brave. Mary is old. Lucy is either not rich or quiet. John is both funny and not kind. | Mary is tall. | contradiction | (![X]:((~calm(X)<~>kind(X))<=>(~curious(X)<~>~humble(X))))&
(((humble(susan)&quiet(susan)))<=>((creative(mary)|kind(mary))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:(wise(X)=>~patient(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy)))&
((funny(john)&~kind(john))) | tall(mary) | [
"p2",
"p3",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5944290137891688859568892
% SZS output start Proof for 5944290137891688859568892
3. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (generous(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p3]
9. ? [X0] : (strong(X0) <~> tall(X0)) => humble(alice) [input p8]
14. (funny(alice) & ~humble(alice)) <=> ? [X0] : ~curious(X0) [input p13]
24. tall(mary) [input hypothesis]
26. ! [X0] : ((generous(X0) & ~strong(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 3]
31. humble(alice) | ! [X0] : (strong(X0) <=> tall(X0)) [ennf transformation 9]
37. ! [X0] : ((generous(X0) & ~strong(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 26]
38. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 4]
39. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 38]
44. humble(alice) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0))) [nnf transformation 31]
57. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(alice) | humble(alice))) [nnf transformation 14]
58. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | ~funny(alice) | humble(alice)) [flattening 57]
59. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | ~funny(alice) | humble(alice)) [rectify 58]
60. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
61. ((funny(alice) & ~humble(alice)) | ! [X0] : curious(X0)) & (~curious(sK3) | ~funny(alice) | humble(alice)) [skolemisation 59,60]
87. ~strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 37]
88. ~strong(X0) | brave(X0) | brave(X0) [cnf transformation 37]
95. ~curious(X0) | ~curious(X0) [cnf transformation 39]
113. humble(alice) | strong(X0) | ~tall(X0) [cnf transformation 44]
129. ~humble(alice) | curious(X0) [cnf transformation 61]
145. tall(mary) [cnf transformation 24]
147. ~curious(X0) [duplicate literal removal 95]
148. ~strong(X0) | ~brave(X0) [duplicate literal removal 87]
149. ~strong(X0) | brave(X0) [duplicate literal removal 88]
174. ~strong(X0) [subsumption resolution 148,149]
194. humble(alice) | ~tall(X0) [subsumption resolution 113,174]
196. 8 <=> ! [X0] : ~tall(X0) [avatar definition]
197. ~tall(X0) <- (8) [avatar component clause 196]
199. 9 <=> humble(alice) [avatar definition]
202. 8 | 9 [avatar split clause 194,199,196]
242. ~humble(alice) [subsumption resolution 129,147]
243. ~9 [avatar split clause 242,199]
272. $false <- (8) [resolution 197,145]
273. ~8 [avatar contradiction clause 272]
274. $false [avatar sat refutation 202,243,273]
% SZS output end Proof for 5944290137891688859568892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is rich.
If john is funny or not strong then someone is not old or patient.
If paul is not wise then alice is both not curious and not calm and vice versa.
Everyone who is not humble is both not calm and brave.
If paul is either patient or not humble then fred is wise or strong.
Everyone who is funny or not wise is rich and vice versa.
Everyone who is either kind or not kind is either not rich or not tall.
Everyone who is tall is both not patient and not wise and vice versa.
Everyone who is either brave or humble is strong or generous.
If paul is not happy then john is both brave and quiet and vice versa.
Everyone who is both not patient and not quiet is both humble and not brave.
Everyone who is not patient or not funny is either not wise or not patient and vice versa.
Everyone who is either not kind or tall is not generous.
Everyone who is not quiet is either rich or not old and vice versa.
Everyone who is both funny and calm is not wise or humble and vice versa.
Mary is not happy or patient.
Susan is both not generous and brave.
Alice is kind.
Fred is both patient and kind.
Fred is either humble or creative.
John is either calm or not tall.
Fred is either strong or not patient. | John is funny. | entailment | (![X]:(~tall(X)=>rich(X)))&
(((funny(john)|~strong(john)))=>(?[X]:((~old(X)|patient(X)))))&
((~wise(paul))<=>((~curious(alice)&~calm(alice))))&
(![X]:(~humble(X)=>(~calm(X)&brave(X))))&
(((patient(paul)<~>~humble(paul)))=>((wise(fred)|strong(fred))))&
(![X]:((funny(X)|~wise(X))<=>rich(X)))&
(![X]:((kind(X)<~>~kind(X))=>(~rich(X)<~>~tall(X))))&
(![X]:(tall(X)<=>(~patient(X)&~wise(X))))&
(![X]:((brave(X)<~>humble(X))=>(strong(X)|generous(X))))&
((~happy(paul))<=>((brave(john)&quiet(john))))&
(![X]:((~patient(X)&~quiet(X))=>(humble(X)&~brave(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>tall(X))=>~generous(X)))&
(![X]:(~quiet(X)<=>(rich(X)<~>~old(X))))&
(![X]:((funny(X)&calm(X))<=>(~wise(X)|humble(X))))&
((~happy(mary)|patient(mary)))&
((~generous(susan)&brave(susan)))&
(kind(alice))&
((patient(fred)&kind(fred)))&
((humble(fred)<~>creative(fred)))&
((calm(john)<~>~tall(john)))&
((strong(fred)<~>~patient(fred))) | funny(john) | [
"p0",
"p5",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3132504637234414543465991
% SZS output start Proof for 3132504637234414543465991
1. ! [X0] : (~tall(X0) => rich(X0)) [input p0]
6. ! [X0] : ((~wise(X0) | funny(X0)) <=> rich(X0)) [input p5]
8. ! [X0] : (tall(X0) <=> (~wise(X0) & ~patient(X0))) [input p7]
15. ! [X0] : ((calm(X0) & funny(X0)) <=> (humble(X0) | ~wise(X0))) [input p14]
23. ~funny(john) [input hypothesis]
24. ! [X0] : (rich(X0) | tall(X0)) [ennf transformation 1]
40. ! [X0] : (((~wise(X0) | funny(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 6]
41. ! [X0] : ((~wise(X0) | funny(X0) | ~rich(X0)) & (rich(X0) | (wise(X0) & ~funny(X0)))) [flattening 40]
43. ! [X0] : ((tall(X0) | (wise(X0) | patient(X0))) & ((~wise(X0) & ~patient(X0)) | ~tall(X0))) [nnf transformation 8]
44. ! [X0] : ((tall(X0) | wise(X0) | patient(X0)) & ((~wise(X0) & ~patient(X0)) | ~tall(X0))) [flattening 43]
52. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 15]
53. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ~calm(X0) | ~funny(X0))) [flattening 52]
57. rich(X0) | tall(X0) [cnf transformation 24]
68. wise(X0) | rich(X0) [cnf transformation 41]
69. ~wise(X0) | funny(X0) | ~rich(X0) [cnf transformation 41]
75. ~wise(X0) | ~tall(X0) [cnf transformation 44]
97. wise(X0) | funny(X0) [cnf transformation 53]
113. ~funny(john) [cnf transformation 23]
134. 4 <=> funny(john) [avatar definition]
136. ~funny(john) <- (~4) [avatar component clause 134]
220. ~4 [avatar split clause 113,134]
223. ~tall(X0) | rich(X0) [resolution 75,68]
224. rich(X0) [subsumption resolution 223,57]
245. funny(X1) | ~rich(X1) | funny(X1) [resolution 69,97]
250. funny(X1) | ~rich(X1) [duplicate literal removal 245]
252. funny(X1) [subsumption resolution 250,224]
253. $false <- (~4) [resolution 252,136]
255. 4 [avatar contradiction clause 253]
256. $false [avatar sat refutation 220,255]
% SZS output end Proof for 3132504637234414543465991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is either creative or quiet and vice versa. If mary is both not funny and not kind then someone is patient or old. Everyone who is not brave is both calm and creative. Everyone who is either happy or not brave is both quiet and not generous and vice versa. Everyone who is both not strong and humble is both not patient and not generous. Everyone who is either not strong or not quiet is either curious or not funny and vice versa. If someone is not generous then someone is both not funny and not calm and vice versa. If lucy is both not humble and not wise then someone is curious and vice versa. Everyone who is tall is either funny or not creative. Everyone who is funny is both not happy and not calm. Everyone who is either not rich or tall is both not calm and not wise and vice versa. Everyone who is both not wise and curious is either funny or calm and vice versa. Everyone who is wise is not kind. If susan is not old or not strong then fred is both not patient and not quiet and vice versa. If lucy is not brave then mary is calm or not generous and vice versa. Everyone who is both rich and calm is either strong or generous. Someone is humble. Fred is either not patient or not humble. Alice is both not rich and not humble. Someone is both not old and not calm. Someone is either humble or not funny. Mary is quiet. Someone is wise. Susan is kind. | Mary is quiet. | entailment | (![X]:(~humble(X)<=>(creative(X)<~>quiet(X))))&
(((~funny(mary)&~kind(mary)))=>(?[X]:((patient(X)|old(X)))))&
(![X]:(~brave(X)=>(calm(X)&creative(X))))&
(![X]:((happy(X)<~>~brave(X))<=>(quiet(X)&~generous(X))))&
(![X]:((~strong(X)&humble(X))=>(~patient(X)&~generous(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(curious(X)<~>~funny(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~funny(X)&~calm(X)))))&
(((~humble(lucy)&~wise(lucy)))<=>(?[X]:(curious(X))))&
(![X]:(tall(X)=>(funny(X)<~>~creative(X))))&
(![X]:(funny(X)=>(~happy(X)&~calm(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(~calm(X)&~wise(X))))&
(![X]:((~wise(X)&curious(X))<=>(funny(X)<~>calm(X))))&
(![X]:(wise(X)=>~kind(X)))&
(((~old(susan)|~strong(susan)))<=>((~patient(fred)&~quiet(fred))))&
((~brave(lucy))<=>((calm(mary)|~generous(mary))))&
(![X]:((rich(X)&calm(X))=>(strong(X)<~>generous(X))))&
(?[X]:(humble(X)))&
((~patient(fred)<~>~humble(fred)))&
((~rich(alice)&~humble(alice)))&
(?[X]:((~old(X)&~calm(X))))&
(?[X]:((humble(X)<~>~funny(X))))&
(quiet(mary))&
(?[X]:(wise(X)))&
(kind(susan)) | quiet(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1070495591779491787487512
% SZS output start Proof for 1070495591779491787487512
22. quiet(mary) [input p21]
25. ~quiet(mary) [input hypothesis]
138. quiet(mary) [cnf transformation 22]
141. ~quiet(mary) [cnf transformation 25]
254. $false [subsumption resolution 141,138]
% SZS output end Proof for 1070495591779491787487512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is not generous or curious and vice versa.
Everyone who is both quiet and creative is rich.
If lucy is both creative and not curious then paul is both happy and not old and vice versa.
If someone is both curious and not creative then someone is both happy and brave and vice versa.
If lucy is either old or kind then someone is brave.
Everyone who is not rich or curious is both funny and not quiet and vice versa.
If someone is either not strong or generous then susan is tall and vice versa.
Everyone who is curious or not calm is patient or not patient and vice versa.
Everyone who is both not strong and patient is either humble or not rich and vice versa.
Everyone who is either not old or not funny is generous.
Everyone who is either not curious or happy is both not calm and not strong.
Everyone who is generous or brave is both not old and happy.
If paul is both creative and not brave then paul is tall and vice versa.
If alice is patient or humble then someone is both generous and not quiet and vice versa.
Everyone who is either brave or not patient is either tall or not old and vice versa.
If someone is not humble or patient then paul is quiet or not rich.
Someone is not strong or patient.
Someone is humble or not old.
Susan is either not calm or rich.
Paul is either not quiet or wise.
Someone is humble or old.
Paul is either not patient or patient.
Someone is not brave. | Paul is not calm. | neutral | ((?[X]:(~rich(X)))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((quiet(X)&creative(X))=>rich(X)))&
(((creative(lucy)&~curious(lucy)))<=>((happy(paul)&~old(paul))))&
((?[X]:((curious(X)&~creative(X))))<=>(?[X]:((happy(X)&brave(X)))))&
(((old(lucy)<~>kind(lucy)))=>(?[X]:(brave(X))))&
(![X]:((~rich(X)|curious(X))<=>(funny(X)&~quiet(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(tall(susan)))&
(![X]:((curious(X)|~calm(X))<=>(patient(X)|~patient(X))))&
(![X]:((~strong(X)&patient(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~funny(X))=>generous(X)))&
(![X]:((~curious(X)<~>happy(X))=>(~calm(X)&~strong(X))))&
(![X]:((generous(X)|brave(X))=>(~old(X)&happy(X))))&
(((creative(paul)&~brave(paul)))<=>(tall(paul)))&
(((patient(alice)|humble(alice)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((brave(X)<~>~patient(X))<=>(tall(X)<~>~old(X))))&
((?[X]:((~humble(X)|patient(X))))=>((quiet(paul)|~rich(paul))))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:((humble(X)|~old(X))))&
((~calm(susan)<~>rich(susan)))&
((~quiet(paul)<~>wise(paul)))&
(?[X]:((humble(X)|old(X))))&
((~patient(paul)<~>patient(paul)))&
(?[X]:(~brave(X))) | ~calm(paul) | [] | null | 0 |
Everyone who is old is both not quiet and creative.
If someone is both not tall and calm then someone is wise and vice versa.
If susan is not quiet or strong then someone is not generous or not wise.
Everyone who is both not calm and not curious is not calm or not strong and vice versa.
Everyone who is both wise and not funny is either not funny or patient and vice versa.
Everyone who is either brave or not old is both not rich and not wise.
If susan is not old then someone is not kind and vice versa.
Everyone who is both not generous and not tall is strong.
Everyone who is quiet is either not humble or not quiet.
If someone is either strong or not curious then paul is either not kind or wise.
Everyone who is both not curious and not patient is patient and vice versa.
Everyone who is either not creative or not kind is not happy and vice versa.
Everyone who is either curious or not brave is either happy or rich.
If fred is funny then mary is either curious or calm and vice versa.
If someone is brave or not brave then susan is either curious or not wise and vice versa.
Everyone who is creative is not tall and vice versa.
Alice is either not kind or not generous.
Alice is tall.
Mary is both not brave and calm.
Someone is not kind.
Someone is strong.
Someone is not rich.
Someone is both not tall and wise.
Someone is quiet or creative. | Susan is not wise. | contradiction | (![X]:(old(X)=>(~quiet(X)&creative(X))))&
((?[X]:((~tall(X)&calm(X))))<=>(?[X]:(wise(X))))&
(((~quiet(susan)|strong(susan)))=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~calm(X)&~curious(X))<=>(~calm(X)|~strong(X))))&
(![X]:((wise(X)&~funny(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)<~>~old(X))=>(~rich(X)&~wise(X))))&
((~old(susan))<=>(?[X]:(~kind(X))))&
(![X]:((~generous(X)&~tall(X))=>strong(X)))&
(![X]:(quiet(X)=>(~humble(X)<~>~quiet(X))))&
((?[X]:((strong(X)<~>~curious(X))))=>((~kind(paul)<~>wise(paul))))&
(![X]:((~curious(X)&~patient(X))<=>patient(X)))&
(![X]:((~creative(X)<~>~kind(X))<=>~happy(X)))&
(![X]:((curious(X)<~>~brave(X))=>(happy(X)<~>rich(X))))&
((funny(fred))<=>((curious(mary)<~>calm(mary))))&
((?[X]:((brave(X)|~brave(X))))<=>((curious(susan)<~>~wise(susan))))&
(![X]:(creative(X)<=>~tall(X)))&
((~kind(alice)<~>~generous(alice)))&
(tall(alice))&
((~brave(mary)&calm(mary)))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
(?[X]:(~rich(X)))&
(?[X]:((~tall(X)&wise(X))))&
(?[X]:((quiet(X)|creative(X)))) | ~wise(susan) | [
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2370973376369791077352430
% SZS output start Proof for 2370973376369791077352430
11. ! [X0] : ((~patient(X0) & ~curious(X0)) <=> patient(X0)) [input p10]
15. ? [X0] : (~brave(X0) | brave(X0)) <=> (curious(susan) <~> ~wise(susan)) [input p14]
25. ~wise(susan) [input hypothesis]
53. ! [X0] : (((~patient(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) | curious(X0)))) [nnf transformation 11]
54. ! [X0] : (((~patient(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | patient(X0) | curious(X0))) [flattening 53]
58. (? [X0] : (~brave(X0) | brave(X0)) | ((curious(susan) | wise(susan)) & (~wise(susan) | ~curious(susan)))) & (((wise(susan) | ~curious(susan)) & (~wise(susan) | curious(susan))) | ! [X0] : (brave(X0) & ~brave(X0))) [nnf transformation 15]
59. (? [X0] : (~brave(X0) | brave(X0)) | ((curious(susan) | wise(susan)) & (~wise(susan) | ~curious(susan)))) & (((wise(susan) | ~curious(susan)) & (~wise(susan) | curious(susan))) | ! [X1] : (brave(X1) & ~brave(X1))) [rectify 58]
60. ? [X0] : (~brave(X0) | brave(X0)) => (~brave(sK4) | brave(sK4)) [choice axiom]
61. ((~brave(sK4) | brave(sK4)) | ((curious(susan) | wise(susan)) & (~wise(susan) | ~curious(susan)))) & (((wise(susan) | ~curious(susan)) & (~wise(susan) | curious(susan))) | ! [X1] : (brave(X1) & ~brave(X1))) [skolemisation 59,60]
105. patient(X0) | patient(X0) | curious(X0) [cnf transformation 54]
107. ~patient(X0) | ~patient(X0) [cnf transformation 54]
122. wise(susan) | ~curious(susan) | ~brave(X1) [cnf transformation 61]
123. wise(susan) | ~curious(susan) | brave(X1) [cnf transformation 61]
139. ~wise(susan) [cnf transformation 25]
140. patient(X0) | curious(X0) [duplicate literal removal 105]
141. ~patient(X0) [duplicate literal removal 107]
220. curious(X0) [subsumption resolution 140,141]
233. wise(susan) | brave(X1) [subsumption resolution 123,220]
235. 19 <=> ! [X1] : brave(X1) [avatar definition]
236. brave(X1) <- (19) [avatar component clause 235]
238. 20 <=> wise(susan) [avatar definition]
241. 19 | 20 [avatar split clause 233,238,235]
242. wise(susan) | ~brave(X1) [subsumption resolution 122,220]
244. 21 <=> ! [X1] : ~brave(X1) [avatar definition]
245. ~brave(X1) <- (21) [avatar component clause 244]
246. 21 | 20 [avatar split clause 242,238,244]
267. ~20 [avatar split clause 139,238]
268. $false <- (19, 21) [subsumption resolution 236,245]
269. ~19 | ~21 [avatar contradiction clause 268]
270. $false [avatar sat refutation 241,246,267,269]
% SZS output end Proof for 2370973376369791077352430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either creative or humble is tall and vice versa.
If someone is either tall or old then someone is both not creative and not kind.
If someone is not quiet then mary is not generous or not tall.
Everyone who is either generous or happy is both old and not creative.
If someone is not kind then paul is either quiet or curious.
Everyone who is not strong or calm is both humble and not wise and vice versa.
If alice is not rich or strong then someone is not happy or patient and vice versa.
Everyone who is both not generous and old is either generous or strong and vice versa.
Everyone who is not wise is both kind and not kind.
Everyone who is happy or not curious is humble.
Everyone who is either not happy or brave is both not strong and not rich.
Everyone who is not calm or not quiet is either funny or wise.
Everyone who is not strong is either rich or strong and vice versa.
Everyone who is either rich or strong is either creative or not brave and vice versa.
If alice is either wise or tall then paul is not curious.
If someone is both not creative and not wise then susan is patient.
Someone is not patient.
Susan is curious or not old.
Alice is patient.
John is either not patient or not kind.
Paul is both tall and not quiet.
Alice is either not kind or humble.
John is happy or humble. | Susan is not funny. | entailment | (![X]:((creative(X)<~>humble(X))<=>tall(X)))&
((?[X]:((tall(X)<~>old(X))))=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:(~quiet(X)))=>((~generous(mary)|~tall(mary))))&
(![X]:((generous(X)<~>happy(X))=>(old(X)&~creative(X))))&
((?[X]:(~kind(X)))=>((quiet(paul)<~>curious(paul))))&
(![X]:((~strong(X)|calm(X))<=>(humble(X)&~wise(X))))&
(((~rich(alice)|strong(alice)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>strong(X))))&
(![X]:(~wise(X)=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|~curious(X))=>humble(X)))&
(![X]:((~happy(X)<~>brave(X))=>(~strong(X)&~rich(X))))&
(![X]:((~calm(X)|~quiet(X))=>(funny(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>strong(X))))&
(![X]:((rich(X)<~>strong(X))<=>(creative(X)<~>~brave(X))))&
(((wise(alice)<~>tall(alice)))=>(~curious(paul)))&
((?[X]:((~creative(X)&~wise(X))))=>(patient(susan)))&
(?[X]:(~patient(X)))&
((curious(susan)|~old(susan)))&
(patient(alice))&
((~patient(john)<~>~kind(john)))&
((tall(paul)&~quiet(paul)))&
((~kind(alice)<~>humble(alice)))&
((happy(john)|humble(john))) | ~funny(susan) | [
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8879724300535827940599175
% SZS output start Proof for 8879724300535827940599175
6. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~wise(X0) & humble(X0))) [input p5]
9. ! [X0] : (~wise(X0) => (~kind(X0) & kind(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | ~calm(X0)) => (funny(X0) <~> wise(X0))) [input p11]
24. funny(susan) [input hypothesis]
31. ! [X0] : ((~kind(X0) & kind(X0)) | wise(X0)) [ennf transformation 9]
34. ! [X0] : ((funny(X0) <~> wise(X0)) | (quiet(X0) & calm(X0))) [ennf transformation 12]
44. ! [X0] : (((calm(X0) | ~strong(X0)) | (wise(X0) | ~humble(X0))) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 6]
45. ! [X0] : ((calm(X0) | ~strong(X0) | wise(X0) | ~humble(X0)) & ((~wise(X0) & humble(X0)) | (~calm(X0) & strong(X0)))) [flattening 44]
54. ! [X0] : (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | (quiet(X0) & calm(X0))) [nnf transformation 34]
80. ~wise(X0) | ~calm(X0) [cnf transformation 45]
92. kind(X0) | wise(X0) [cnf transformation 31]
93. ~kind(X0) | wise(X0) [cnf transformation 31]
102. ~wise(X0) | ~funny(X0) | calm(X0) [cnf transformation 54]
129. funny(susan) [cnf transformation 24]
204. wise(X0) [subsumption resolution 92,93]
206. ~funny(X0) | calm(X0) [subsumption resolution 102,204]
254. ~calm(X0) [resolution 80,204]
259. calm(susan) [resolution 206,129]
260. $false [subsumption resolution 259,254]
% SZS output end Proof for 8879724300535827940599175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both curious and wise then lucy is not curious and vice versa. Everyone who is quiet or not funny is patient or not humble and vice versa. Everyone who is both happy and calm is wise or not brave and vice versa. If lucy is both happy and not old then someone is both not wise and not strong. If someone is both funny and not rich then lucy is not tall. Everyone who is either rich or not funny is patient and vice versa. Everyone who is both not funny and rich is not wise or strong and vice versa. If susan is either curious or tall then someone is both not strong and calm. If someone is both not curious and funny then susan is both happy and not kind and vice versa. Everyone who is rich or not strong is generous and vice versa. Everyone who is not quiet or humble is brave or not calm. Everyone who is not tall is either not calm or humble and vice versa. Everyone who is either calm or humble is both creative and generous and vice versa. Everyone who is both not funny and not brave is not funny or strong and vice versa. If someone is not wise then someone is either funny or not tall. Everyone who is either not patient or not tall is both tall and not brave and vice versa. Mary is not brave. Alice is not wise or not rich. John is either wise or quiet. Someone is quiet or not wise. Someone is either calm or curious. Someone is either not old or not patient. Mary is patient or curious. Someone is either old or not old. | Alice is not tall. | contradiction | (((curious(lucy)&wise(lucy)))<=>(~curious(lucy)))&
(![X]:((quiet(X)|~funny(X))<=>(patient(X)|~humble(X))))&
(![X]:((happy(X)&calm(X))<=>(wise(X)|~brave(X))))&
(((happy(lucy)&~old(lucy)))=>(?[X]:((~wise(X)&~strong(X)))))&
((?[X]:((funny(X)&~rich(X))))=>(~tall(lucy)))&
(![X]:((rich(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~funny(X)&rich(X))<=>(~wise(X)|strong(X))))&
(((curious(susan)<~>tall(susan)))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((~curious(X)&funny(X))))<=>((happy(susan)&~kind(susan))))&
(![X]:((rich(X)|~strong(X))<=>generous(X)))&
(![X]:((~quiet(X)|humble(X))=>(brave(X)|~calm(X))))&
(![X]:(~tall(X)<=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>humble(X))<=>(creative(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~funny(X)|strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(tall(X)&~brave(X))))&
(~brave(mary))&
((~wise(alice)|~rich(alice)))&
((wise(john)<~>quiet(john)))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
((patient(mary)|curious(mary)))&
(?[X]:((old(X)<~>~old(X)))) | ~tall(alice) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p10",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8137614100202709552109122
% SZS output start Proof for 8137614100202709552109122
1. (wise(lucy) & curious(lucy)) <=> ~curious(lucy) [input p0]
2. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (~humble(X0) | patient(X0))) [input p1]
3. ! [X0] : ((calm(X0) & happy(X0)) <=> (~brave(X0) | wise(X0))) [input p2]
5. ? [X0] : (~rich(X0) & funny(X0)) => ~tall(lucy) [input p4]
7. ! [X0] : ((rich(X0) & ~funny(X0)) <=> (strong(X0) | ~wise(X0))) [input p6]
11. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : (~tall(X0) <=> (~calm(X0) <~> humble(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
16. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> (~brave(X0) & tall(X0))) [input p15]
18. ~rich(alice) | ~wise(alice) [input p17]
25. ~tall(alice) [input hypothesis]
29. ~tall(lucy) | ! [X0] : (rich(X0) | ~funny(X0)) [ennf transformation 5]
31. ! [X0] : ((~calm(X0) | brave(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 11]
32. ! [X0] : (~calm(X0) | brave(X0) | (~humble(X0) & quiet(X0))) [flattening 31]
34. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | (~wise(lucy) | ~curious(lucy))) [nnf transformation 1]
35. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | ~wise(lucy) | ~curious(lucy)) [flattening 34]
36. ! [X0] : (((~funny(X0) | quiet(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~funny(X0) | quiet(X0) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | (funny(X0) & ~quiet(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | ~calm(X0) | ~happy(X0))) [flattening 38]
43. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | (~rich(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ~rich(X0) | funny(X0))) [flattening 43]
55. ! [X0] : ((~tall(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(X0))) [nnf transformation 12]
58. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 14]
59. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | brave(X0) | funny(X0))) [flattening 58]
64. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 16]
65. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [flattening 64]
78. ~curious(lucy) | ~wise(lucy) | ~curious(lucy) [cnf transformation 35]
79. curious(lucy) | curious(lucy) [cnf transformation 35]
82. ~humble(X0) | patient(X0) | funny(X0) [cnf transformation 37]
89. brave(X0) | calm(X0) [cnf transformation 39]
92. ~tall(lucy) | rich(X0) | ~funny(X0) [cnf transformation 29]
98. ~funny(X0) | wise(X0) [cnf transformation 44]
114. ~calm(X0) | brave(X0) | ~humble(X0) [cnf transformation 32]
115. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 55]
128. ~brave(X0) | funny(X0) [cnf transformation 59]
133. tall(X0) | ~patient(X0) | tall(X0) [cnf transformation 65]
136. ~tall(X0) | ~patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 65]
139. ~rich(alice) | ~wise(alice) [cnf transformation 18]
150. ~tall(alice) [cnf transformation 25]
151. ~patient(X0) | tall(X0) [duplicate literal removal 133]
152. ~tall(X0) | ~patient(X0) | brave(X0) [duplicate literal removal 136]
153. ~curious(lucy) | ~wise(lucy) [duplicate literal removal 78]
154. curious(lucy) [duplicate literal removal 79]
156. 1 <=> curious(lucy) [avatar definition]
160. 2 <=> wise(lucy) [avatar definition]
161. ~wise(lucy) <- (~2) [avatar component clause 160]
164. 1 [avatar split clause 154,156]
165. ~2 | ~1 [avatar split clause 153,156,160]
185. 7 <=> ! [X0] : (rich(X0) | ~funny(X0)) [avatar definition]
186. ~funny(X0) | rich(X0) <- (7) [avatar component clause 185]
188. 8 <=> tall(lucy) [avatar definition]
190. ~tall(lucy) <- (~8) [avatar component clause 188]
191. 7 | ~8 [avatar split clause 92,188,185]
235. ~humble(X0) | brave(X0) [subsumption resolution 114,89]
251. 21 <=> wise(alice) [avatar definition]
255. 22 <=> rich(alice) [avatar definition]
257. ~rich(alice) <- (~22) [avatar component clause 255]
258. ~21 | ~22 [avatar split clause 139,255,251]
319. calm(X0) | funny(X0) [resolution 128,89]
342. 35 <=> funny(alice) [avatar definition]
344. funny(alice) <- (35) [avatar component clause 342]
354. 37 <=> humble(alice) [avatar definition]
356. humble(alice) <- (37) [avatar component clause 354]
380. 41 <=> humble(lucy) [avatar definition]
382. humble(lucy) <- (41) [avatar component clause 380]
390. tall(X0) | humble(X0) | funny(X0) [resolution 115,319]
414. patient(alice) | funny(alice) <- (37) [resolution 356,82]
563. humble(X0) | funny(X0) | ~patient(X0) | brave(X0) [resolution 390,152]
567. humble(lucy) | funny(lucy) <- (~8) [resolution 390,190]
569. humble(alice) | funny(alice) [resolution 390,150]
572. funny(X0) | ~patient(X0) | brave(X0) [subsumption resolution 563,235]
573. funny(X0) | ~patient(X0) [subsumption resolution 572,128]
575. 55 <=> funny(lucy) [avatar definition]
576. ~funny(lucy) <- (~55) [avatar component clause 575]
577. funny(lucy) <- (55) [avatar component clause 575]
578. 55 | 41 | 8 [avatar split clause 567,188,380,575]
594. wise(lucy) <- (55) [resolution 577,98]
595. $false <- (~2, 55) [subsumption resolution 594,161]
596. 2 | ~55 [avatar contradiction clause 595]
606. 59 <=> patient(lucy) [avatar definition]
607. patient(lucy) <- (59) [avatar component clause 606]
608. ~patient(lucy) <- (~59) [avatar component clause 606]
622. rich(alice) <- (7, 35) [resolution 186,344]
624. $false <- (7, ~22, 35) [subsumption resolution 622,257]
625. ~7 | 22 | ~35 [avatar contradiction clause 624]
633. funny(alice) <- (37) [subsumption resolution 414,573]
634. 35 | ~37 [avatar split clause 633,354,342]
650. 35 | 37 [avatar split clause 569,354,342]
659. wise(alice) <- (35) [resolution 344,98]
662. 21 | ~35 [avatar split clause 659,342,251]
693. tall(lucy) <- (59) [resolution 607,151]
696. $false <- (~8, 59) [subsumption resolution 693,190]
697. 8 | ~59 [avatar contradiction clause 696]
726. patient(lucy) | funny(lucy) <- (41) [resolution 382,82]
729. funny(lucy) <- (41, ~59) [subsumption resolution 726,608]
730. $false <- (41, ~55, ~59) [subsumption resolution 729,576]
731. ~41 | 55 | 59 [avatar contradiction clause 730]
737. $false [avatar sat refutation 164,165,191,258,578,596,625,634,650,662,697,731]
% SZS output end Proof for 8137614100202709552109122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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