premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If lucy is both strong and funny then someone is not patient and vice versa.
If mary is curious then someone is not curious.
Everyone who is generous or humble is not rich or old and vice versa.
If mary is either not funny or funny then someone is not brave and vice versa.
Everyone who is curious is either not patient or not rich.
Everyone who is old is tall or brave and vice versa.
If mary is funny or not rich then alice is not kind or not wise.
If someone is both not quiet and curious then someone is patient and vice versa.
Everyone who is both humble and brave is humble or not creative and vice versa.
Everyone who is not tall is either not old or not wise.
Everyone who is both not happy and funny is not creative or not quiet.
Everyone who is both not rich and tall is not happy and vice versa.
If mary is both calm and patient then lucy is not humble or funny and vice versa.
If someone is not generous then someone is not quiet or not kind and vice versa.
If susan is not wise or brave then susan is both tall and not generous.
If someone is strong then someone is tall or not old and vice versa.
Lucy is both not humble and creative.
Fred is both tall and quiet.
Mary is either creative or strong.
Lucy is either not happy or not curious.
Paul is not kind or curious.
Someone is either humble or not old.
Someone is funny or calm.
Fred is not wise or not funny. | Paul is generous. | neutral | (((strong(lucy)&funny(lucy)))<=>(?[X]:(~patient(X))))&
((curious(mary))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)|humble(X))<=>(~rich(X)|old(X))))&
(((~funny(mary)<~>funny(mary)))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>(~patient(X)<~>~rich(X))))&
(![X]:(old(X)<=>(tall(X)|brave(X))))&
(((funny(mary)|~rich(mary)))=>((~kind(alice)|~wise(alice))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&brave(X))<=>(humble(X)|~creative(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~wise(X))))&
(![X]:((~happy(X)&funny(X))=>(~creative(X)|~quiet(X))))&
(![X]:((~rich(X)&tall(X))<=>~happy(X)))&
(((calm(mary)&patient(mary)))<=>((~humble(lucy)|funny(lucy))))&
((?[X]:(~generous(X)))<=>(?[X]:((~quiet(X)|~kind(X)))))&
(((~wise(susan)|brave(susan)))=>((tall(susan)&~generous(susan))))&
((?[X]:(strong(X)))<=>(?[X]:((tall(X)|~old(X)))))&
((~humble(lucy)&creative(lucy)))&
((tall(fred)&quiet(fred)))&
((creative(mary)<~>strong(mary)))&
((~happy(lucy)<~>~curious(lucy)))&
((~kind(paul)|curious(paul)))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((funny(X)|calm(X))))&
((~wise(fred)|~funny(fred))) | generous(paul) | [] | null | 0 |
Everyone who is generous is both not creative and quiet and vice versa.
If someone is kind then someone is not funny and vice versa.
If someone is either not generous or wise then mary is brave.
If alice is patient then someone is strong or not tall.
Everyone who is either not wise or not funny is either tall or not funny and vice versa.
Everyone who is happy or tall is tall.
If someone is either curious or calm then someone is either wise or funny.
Everyone who is patient or not curious is funny or happy and vice versa.
Everyone who is not tall or creative is not funny.
If someone is either not happy or generous then someone is both curious and not tall.
Everyone who is not curious is both not calm and not kind.
Everyone who is both humble and not humble is either not funny or not kind and vice versa.
Everyone who is not happy is either not curious or not humble and vice versa.
Everyone who is not brave is both tall and generous and vice versa.
Everyone who is not brave is old or funny and vice versa.
If someone is not happy then lucy is curious and vice versa.
Someone is generous.
Mary is either not old or not wise.
Mary is both tall and rich.
Susan is old or funny.
Someone is strong.
Someone is not old or not happy.
Paul is either not brave or wise. | Lucy is not kind. | neutral | (![X]:(generous(X)<=>(~creative(X)&quiet(X))))&
((?[X]:(kind(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~generous(X)<~>wise(X))))=>(brave(mary)))&
((patient(alice))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((~wise(X)<~>~funny(X))<=>(tall(X)<~>~funny(X))))&
(![X]:((happy(X)|tall(X))=>tall(X)))&
((?[X]:((curious(X)<~>calm(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:((patient(X)|~curious(X))<=>(funny(X)|happy(X))))&
(![X]:((~tall(X)|creative(X))=>~funny(X)))&
((?[X]:((~happy(X)<~>generous(X))))=>(?[X]:((curious(X)&~tall(X)))))&
(![X]:(~curious(X)=>(~calm(X)&~kind(X))))&
(![X]:((humble(X)&~humble(X))<=>(~funny(X)<~>~kind(X))))&
(![X]:(~happy(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:(~brave(X)<=>(tall(X)&generous(X))))&
(![X]:(~brave(X)<=>(old(X)|funny(X))))&
((?[X]:(~happy(X)))<=>(curious(lucy)))&
(?[X]:(generous(X)))&
((~old(mary)<~>~wise(mary)))&
((tall(mary)&rich(mary)))&
((old(susan)|funny(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)|~happy(X))))&
((~brave(paul)<~>wise(paul))) | ~kind(lucy) | [] | null | 0 |
Everyone who is both quiet and not funny is happy and vice versa. If someone is calm then john is not tall or not patient. Everyone who is humble is curious or not wise. Everyone who is either not strong or kind is not humble or not creative. If someone is not rich or generous then fred is either not humble or not strong and vice versa. Everyone who is calm or not patient is not quiet. If mary is kind then someone is creative and vice versa. If paul is tall then susan is either calm or quiet and vice versa. Everyone who is humble is not strong and vice versa. If john is not kind then susan is either not wise or not calm. If someone is either old or quiet then someone is old or generous and vice versa. Everyone who is either rich or not creative is either not rich or humble. Everyone who is either not quiet or curious is either creative or not old and vice versa. Everyone who is not kind is not generous or generous and vice versa. If alice is not kind then susan is funny. Everyone who is either not curious or rich is both not tall and rich and vice versa. John is either creative or curious. Someone is both not humble and curious. Someone is not quiet or tall. Lucy is not happy or humble. Someone is tall. Someone is both old and strong. | Alice is not calm. | neutral | (![X]:((quiet(X)&~funny(X))<=>happy(X)))&
((?[X]:(calm(X)))=>((~tall(john)|~patient(john))))&
(![X]:(humble(X)=>(curious(X)|~wise(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~humble(X)|~creative(X))))&
((?[X]:((~rich(X)|generous(X))))<=>((~humble(fred)<~>~strong(fred))))&
(![X]:((calm(X)|~patient(X))=>~quiet(X)))&
((kind(mary))<=>(?[X]:(creative(X))))&
((tall(paul))<=>((calm(susan)<~>quiet(susan))))&
(![X]:(humble(X)<=>~strong(X)))&
((~kind(john))=>((~wise(susan)<~>~calm(susan))))&
((?[X]:((old(X)<~>quiet(X))))<=>(?[X]:((old(X)|generous(X)))))&
(![X]:((rich(X)<~>~creative(X))=>(~rich(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(creative(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(~generous(X)|generous(X))))&
((~kind(alice))=>(funny(susan)))&
(![X]:((~curious(X)<~>rich(X))<=>(~tall(X)&rich(X))))&
((creative(john)<~>curious(john)))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~quiet(X)|tall(X))))&
((~happy(lucy)|humble(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((old(X)&strong(X)))) | ~calm(alice) | [] | null | 0 |
Everyone who is either not creative or not funny is either not brave or not calm.
Everyone who is rich or not rich is either creative or happy and vice versa.
If fred is either not quiet or generous then lucy is humble.
If mary is not generous or curious then someone is both not creative and tall and vice versa.
Everyone who is either curious or wise is either not old or brave and vice versa.
Everyone who is happy is both not curious and not tall.
If lucy is either old or not funny then paul is both happy and curious and vice versa.
If paul is either patient or not wise then lucy is not calm.
If someone is kind or not brave then someone is both rich and not generous.
Everyone who is not strong or wise is either quiet or curious and vice versa.
If john is both rich and not brave then mary is not quiet or strong.
Everyone who is wise is either quiet or not curious and vice versa.
If someone is either not rich or calm then someone is not strong and vice versa.
If susan is not brave or not curious then alice is not wise and vice versa.
Everyone who is not brave is not kind or not patient.
If someone is creative then susan is either not kind or quiet.
Alice is either brave or calm.
Someone is not rich.
Susan is not tall.
Susan is either happy or brave.
Mary is quiet.
Susan is either not strong or not calm.
Someone is rich.
Fred is either funny or calm. | John is strong. | contradiction | (![X]:((~creative(X)<~>~funny(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(creative(X)<~>happy(X))))&
(((~quiet(fred)<~>generous(fred)))=>(humble(lucy)))&
(((~generous(mary)|curious(mary)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:((curious(X)<~>wise(X))<=>(~old(X)<~>brave(X))))&
(![X]:(happy(X)=>(~curious(X)&~tall(X))))&
(((old(lucy)<~>~funny(lucy)))<=>((happy(paul)&curious(paul))))&
(((patient(paul)<~>~wise(paul)))=>(~calm(lucy)))&
((?[X]:((kind(X)|~brave(X))))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:((~strong(X)|wise(X))<=>(quiet(X)<~>curious(X))))&
(((rich(john)&~brave(john)))=>((~quiet(mary)|strong(mary))))&
(![X]:(wise(X)<=>(quiet(X)<~>~curious(X))))&
((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(~strong(X))))&
(((~brave(susan)|~curious(susan)))<=>(~wise(alice)))&
(![X]:(~brave(X)=>(~kind(X)|~patient(X))))&
((?[X]:(creative(X)))=>((~kind(susan)<~>quiet(susan))))&
((brave(alice)<~>calm(alice)))&
(?[X]:(~rich(X)))&
(~tall(susan))&
((happy(susan)<~>brave(susan)))&
(quiet(mary))&
((~strong(susan)<~>~calm(susan)))&
(?[X]:(rich(X)))&
((funny(fred)<~>calm(fred))) | strong(john) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 647962824379872047796979
% SZS output start Proof for 647962824379872047796979
10. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (quiet(X0) <~> curious(X0))) [input p9]
12. ! [X0] : (wise(X0) <=> (quiet(X0) <~> ~curious(X0))) [input p11]
25. strong(john) [input hypothesis]
53. ! [X0] : (((wise(X0) | ~strong(X0)) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [nnf transformation 10]
54. ! [X0] : ((wise(X0) | ~strong(X0) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) & (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | (~wise(X0) & strong(X0)))) [flattening 53]
55. ! [X0] : ((wise(X0) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0)))) & (((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ~wise(X0))) [nnf transformation 12]
110. ~wise(X0) | quiet(X0) | curious(X0) [cnf transformation 54]
112. ~wise(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 54]
113. ~strong(X0) | wise(X0) | curious(X0) | ~quiet(X0) [cnf transformation 54]
114. ~strong(X0) | wise(X0) | quiet(X0) | ~curious(X0) [cnf transformation 54]
116. ~curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 55]
117. curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 55]
118. wise(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 55]
119. wise(X0) | quiet(X0) | curious(X0) [cnf transformation 55]
142. strong(john) [cnf transformation 25]
238. curious(X0) | quiet(X0) [subsumption resolution 119,110]
239. ~curious(X0) | ~quiet(X0) [subsumption resolution 118,112]
240. ~wise(X0) | curious(X0) [subsumption resolution 117,110]
241. ~wise(X0) | quiet(X0) [subsumption resolution 116,110]
394. wise(john) | curious(john) | ~quiet(john) [resolution 113,142]
398. wise(john) | ~quiet(john) [subsumption resolution 394,239]
400. 40 <=> quiet(john) [avatar definition]
401. quiet(john) <- (40) [avatar component clause 400]
402. ~quiet(john) <- (~40) [avatar component clause 400]
404. 41 <=> wise(john) [avatar definition]
406. wise(john) <- (41) [avatar component clause 404]
407. ~40 | 41 [avatar split clause 398,404,400]
411. wise(john) | quiet(john) | ~curious(john) [resolution 114,142]
415. wise(john) | ~curious(john) <- (~40) [subsumption resolution 411,402]
417. 42 <=> curious(john) [avatar definition]
418. curious(john) <- (42) [avatar component clause 417]
419. ~curious(john) <- (~42) [avatar component clause 417]
420. ~42 | 41 | 40 [avatar split clause 415,400,404,417]
515. quiet(john) <- (~42) [resolution 419,238]
518. 40 | 42 [avatar split clause 515,417,400]
523. quiet(john) <- (41) [resolution 406,241]
524. curious(john) <- (41) [resolution 406,240]
533. 42 | ~41 [avatar split clause 524,404,417]
536. 40 | ~41 [avatar split clause 523,404,400]
539. ~quiet(john) <- (42) [resolution 418,239]
541. $false <- (40, 42) [subsumption resolution 539,401]
542. ~40 | ~42 [avatar contradiction clause 541]
543. $false [avatar sat refutation 407,420,518,533,536,542]
% SZS output end Proof for 647962824379872047796979
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or humble then someone is kind.
Everyone who is either calm or not curious is not tall.
Everyone who is either humble or not happy is either quiet or not tall and vice versa.
If fred is not humble or humble then lucy is not curious or curious and vice versa.
If susan is tall or not creative then mary is either not wise or rich.
Everyone who is not creative or quiet is either not happy or not brave.
Everyone who is either not tall or not humble is creative or not humble and vice versa.
If someone is creative or not creative then alice is both not creative and not wise and vice versa.
If susan is curious then paul is strong or not creative and vice versa.
Everyone who is strong or not quiet is funny or wise.
Everyone who is both curious and not kind is patient and vice versa.
Everyone who is both not generous and not brave is not kind.
Everyone who is both rich and not patient is both brave and happy and vice versa.
Everyone who is either not strong or not patient is not quiet and vice versa.
Everyone who is not brave is funny or not funny and vice versa.
If fred is either not curious or quiet then someone is either not old or humble and vice versa.
Susan is both rich and not old.
Paul is both not kind and not creative.
Someone is either not calm or wise.
John is not rich or not curious.
John is not patient.
Someone is old or not generous.
Someone is curious or not happy.
Paul is either rich or not humble. | Mary is not curious. | neutral | ((?[X]:((wise(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((calm(X)<~>~curious(X))=>~tall(X)))&
(![X]:((humble(X)<~>~happy(X))<=>(quiet(X)<~>~tall(X))))&
(((~humble(fred)|humble(fred)))<=>((~curious(lucy)|curious(lucy))))&
(((tall(susan)|~creative(susan)))=>((~wise(mary)<~>rich(mary))))&
(![X]:((~creative(X)|quiet(X))=>(~happy(X)<~>~brave(X))))&
(![X]:((~tall(X)<~>~humble(X))<=>(creative(X)|~humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(alice)&~wise(alice))))&
((curious(susan))<=>((strong(paul)|~creative(paul))))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)|wise(X))))&
(![X]:((curious(X)&~kind(X))<=>patient(X)))&
(![X]:((~generous(X)&~brave(X))=>~kind(X)))&
(![X]:((rich(X)&~patient(X))<=>(brave(X)&happy(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>~quiet(X)))&
(![X]:(~brave(X)<=>(funny(X)|~funny(X))))&
(((~curious(fred)<~>quiet(fred)))<=>(?[X]:((~old(X)<~>humble(X)))))&
((rich(susan)&~old(susan)))&
((~kind(paul)&~creative(paul)))&
(?[X]:((~calm(X)<~>wise(X))))&
((~rich(john)|~curious(john)))&
(~patient(john))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((curious(X)|~happy(X))))&
((rich(paul)<~>~humble(paul))) | ~curious(mary) | [] | null | 0 |
If alice is not rich or tall then someone is not brave and vice versa. Everyone who is either not old or not rich is both brave and not rich and vice versa. Everyone who is both curious and not kind is both not calm and not happy and vice versa. Everyone who is rich or curious is not tall or wise and vice versa. If someone is happy or tall then alice is rich and vice versa. If someone is both calm and old then someone is patient. If mary is wise or happy then susan is funny and vice versa. If someone is funny then john is either not humble or old and vice versa. If lucy is either not humble or humble then alice is happy. Everyone who is not patient or not kind is both not tall and not curious and vice versa. If susan is not tall then alice is not humble or patient. Everyone who is either not rich or not creative is not quiet or quiet and vice versa. If lucy is generous then someone is brave or not brave and vice versa. Everyone who is curious or not tall is patient. Everyone who is both not humble and generous is both calm and not patient and vice versa. Everyone who is either not calm or brave is kind and vice versa. Mary is tall. Someone is either calm or not creative. Alice is humble or not kind. Someone is either curious or old. Lucy is not wise. Mary is either not generous or not kind. Mary is not old. | Mary is funny. | neutral | (((~rich(alice)|tall(alice)))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(brave(X)&~rich(X))))&
(![X]:((curious(X)&~kind(X))<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)|curious(X))<=>(~tall(X)|wise(X))))&
((?[X]:((happy(X)|tall(X))))<=>(rich(alice)))&
((?[X]:((calm(X)&old(X))))=>(?[X]:(patient(X))))&
(((wise(mary)|happy(mary)))<=>(funny(susan)))&
((?[X]:(funny(X)))<=>((~humble(john)<~>old(john))))&
(((~humble(lucy)<~>humble(lucy)))=>(happy(alice)))&
(![X]:((~patient(X)|~kind(X))<=>(~tall(X)&~curious(X))))&
((~tall(susan))=>((~humble(alice)|patient(alice))))&
(![X]:((~rich(X)<~>~creative(X))<=>(~quiet(X)|quiet(X))))&
((generous(lucy))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((curious(X)|~tall(X))=>patient(X)))&
(![X]:((~humble(X)&generous(X))<=>(calm(X)&~patient(X))))&
(![X]:((~calm(X)<~>brave(X))<=>kind(X)))&
(tall(mary))&
(?[X]:((calm(X)<~>~creative(X))))&
((humble(alice)|~kind(alice)))&
(?[X]:((curious(X)<~>old(X))))&
(~wise(lucy))&
((~generous(mary)<~>~kind(mary)))&
(~old(mary)) | funny(mary) | [] | null | 0 |
If susan is curious then john is not brave and vice versa.
Everyone who is not patient is humble.
If someone is calm or not brave then lucy is not patient or curious and vice versa.
Everyone who is not funny or kind is not calm or not brave and vice versa.
If someone is quiet then john is both not curious and not happy and vice versa.
If someone is not creative or not strong then someone is either not strong or happy.
If someone is either wise or not generous then lucy is wise and vice versa.
If someone is not curious or happy then paul is either not quiet or quiet and vice versa.
If someone is either patient or rich then someone is both not brave and not calm.
Everyone who is both not happy and quiet is both not wise and generous and vice versa.
If someone is not calm or quiet then someone is patient or not funny and vice versa.
Everyone who is both humble and not kind is humble.
Everyone who is not curious or happy is generous.
Everyone who is tall or humble is not brave or not calm.
If someone is strong or not brave then susan is creative or old.
Everyone who is generous or strong is not quiet.
Someone is patient.
Alice is not quiet or not generous.
Someone is both not patient and not calm.
Someone is curious.
Someone is either not rich or not generous.
John is either patient or not strong.
Susan is curious or quiet. | John is quiet. | contradiction | ((curious(susan))<=>(~brave(john)))&
(![X]:(~patient(X)=>humble(X)))&
((?[X]:((calm(X)|~brave(X))))<=>((~patient(lucy)|curious(lucy))))&
(![X]:((~funny(X)|kind(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(quiet(X)))<=>((~curious(john)&~happy(john))))&
((?[X]:((~creative(X)|~strong(X))))=>(?[X]:((~strong(X)<~>happy(X)))))&
((?[X]:((wise(X)<~>~generous(X))))<=>(wise(lucy)))&
((?[X]:((~curious(X)|happy(X))))<=>((~quiet(paul)<~>quiet(paul))))&
((?[X]:((patient(X)<~>rich(X))))=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(~wise(X)&generous(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((humble(X)&~kind(X))=>humble(X)))&
(![X]:((~curious(X)|happy(X))=>generous(X)))&
(![X]:((tall(X)|humble(X))=>(~brave(X)|~calm(X))))&
((?[X]:((strong(X)|~brave(X))))=>((creative(susan)|old(susan))))&
(![X]:((generous(X)|strong(X))=>~quiet(X)))&
(?[X]:(patient(X)))&
((~quiet(alice)|~generous(alice)))&
(?[X]:((~patient(X)&~calm(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)<~>~generous(X))))&
((patient(john)<~>~strong(john)))&
((curious(susan)|quiet(susan))) | quiet(john) | [
"p4",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1491860784295387546495700
% SZS output start Proof for 1491860784295387546495700
5. ? [X0] : quiet(X0) <=> (~happy(john) & ~curious(john)) [input p4]
13. ! [X0] : ((happy(X0) | ~curious(X0)) => generous(X0)) [input p12]
16. ! [X0] : ((strong(X0) | generous(X0)) => ~quiet(X0)) [input p15]
24. quiet(john) [input hypothesis]
36. ! [X0] : (generous(X0) | (~happy(X0) & curious(X0))) [ennf transformation 13]
39. ! [X0] : (~quiet(X0) | (~strong(X0) & ~generous(X0))) [ennf transformation 16]
48. (? [X0] : quiet(X0) | (happy(john) | curious(john))) & ((~happy(john) & ~curious(john)) | ! [X0] : ~quiet(X0)) [nnf transformation 5]
49. (? [X0] : quiet(X0) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X0] : ~quiet(X0)) [flattening 48]
50. (? [X0] : quiet(X0) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X1] : ~quiet(X1)) [rectify 49]
51. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
52. (quiet(sK1) | happy(john) | curious(john)) & ((~happy(john) & ~curious(john)) | ! [X1] : ~quiet(X1)) [skolemisation 50,51]
97. ~curious(john) | ~quiet(X1) [cnf transformation 52]
125. generous(X0) | curious(X0) [cnf transformation 36]
128. ~generous(X0) | ~quiet(X0) [cnf transformation 39]
140. quiet(john) [cnf transformation 24]
180. 9 <=> curious(john) [avatar definition]
193. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
194. ~quiet(X1) <- (12) [avatar component clause 193]
196. 12 | ~9 [avatar split clause 97,180,193]
320. ~quiet(X0) | curious(X0) [resolution 128,125]
321. curious(john) [resolution 320,140]
325. 9 [avatar split clause 321,180]
326. $false <- (12) [resolution 194,140]
329. ~12 [avatar contradiction clause 326]
330. $false [avatar sat refutation 196,325,329]
% SZS output end Proof for 1491860784295387546495700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either creative or not humble is either strong or not tall.
Everyone who is not quiet is either old or kind and vice versa.
If someone is both rich and not old then alice is strong or tall and vice versa.
If mary is not brave then someone is happy or not tall and vice versa.
If someone is happy then someone is both not strong and wise and vice versa.
Everyone who is not wise or humble is both quiet and humble and vice versa.
Everyone who is humble or generous is either not strong or generous and vice versa.
If someone is either patient or funny then someone is either patient or quiet and vice versa.
If mary is both not old and not patient then fred is not old.
Everyone who is either not calm or curious is either funny or not rich.
Everyone who is happy or not quiet is both calm and not quiet.
If someone is either quiet or not kind then someone is rich or old and vice versa.
If someone is creative or not happy then someone is not wise or not tall.
If alice is curious or not humble then susan is both not curious and not strong and vice versa.
Everyone who is both tall and curious is tall and vice versa.
If mary is both calm and not humble then someone is not patient or not wise.
John is not happy.
Someone is both wise and not strong.
Susan is wise.
Someone is not strong or not kind.
John is either not quiet or strong.
Lucy is happy.
John is rich.
Fred is both happy and funny. | Lucy is not wise. | contradiction | (![X]:((creative(X)<~>~humble(X))=>(strong(X)<~>~tall(X))))&
(![X]:(~quiet(X)<=>(old(X)<~>kind(X))))&
((?[X]:((rich(X)&~old(X))))<=>((strong(alice)|tall(alice))))&
((~brave(mary))<=>(?[X]:((happy(X)|~tall(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((~wise(X)|humble(X))<=>(quiet(X)&humble(X))))&
(![X]:((humble(X)|generous(X))<=>(~strong(X)<~>generous(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>quiet(X)))))&
(((~old(mary)&~patient(mary)))=>(~old(fred)))&
(![X]:((~calm(X)<~>curious(X))=>(funny(X)<~>~rich(X))))&
(![X]:((happy(X)|~quiet(X))=>(calm(X)&~quiet(X))))&
((?[X]:((quiet(X)<~>~kind(X))))<=>(?[X]:((rich(X)|old(X)))))&
((?[X]:((creative(X)|~happy(X))))=>(?[X]:((~wise(X)|~tall(X)))))&
(((curious(alice)|~humble(alice)))<=>((~curious(susan)&~strong(susan))))&
(![X]:((tall(X)&curious(X))<=>tall(X)))&
(((calm(mary)&~humble(mary)))=>(?[X]:((~patient(X)|~wise(X)))))&
(~happy(john))&
(?[X]:((wise(X)&~strong(X))))&
(wise(susan))&
(?[X]:((~strong(X)|~kind(X))))&
((~quiet(john)<~>strong(john)))&
(happy(lucy))&
(rich(john))&
((happy(fred)&funny(fred))) | ~wise(lucy) | [
"p5",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 53222110550577672384607
% SZS output start Proof for 53222110550577672384607
6. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (humble(X0) & quiet(X0))) [input p5]
11. ! [X0] : ((~quiet(X0) | happy(X0)) => (~quiet(X0) & calm(X0))) [input p10]
22. happy(lucy) [input p21]
25. ~wise(lucy) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & calm(X0)) | (quiet(X0) & ~happy(X0))) [ennf transformation 11]
54. ! [X0] : (((humble(X0) | ~wise(X0)) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 6]
55. ! [X0] : ((humble(X0) | ~wise(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | (~humble(X0) & wise(X0)))) [flattening 54]
102. wise(X0) | quiet(X0) [cnf transformation 55]
128. ~happy(X0) | ~quiet(X0) [cnf transformation 34]
154. happy(lucy) [cnf transformation 22]
158. ~wise(lucy) [cnf transformation 25]
384. quiet(lucy) [resolution 102,158]
393. ~quiet(lucy) [resolution 128,154]
395. $false [subsumption resolution 393,384]
% SZS output end Proof for 53222110550577672384607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or not generous then fred is both not brave and not generous and vice versa. If someone is either strong or not patient then fred is either funny or not patient. Everyone who is either not happy or curious is either rich or not calm and vice versa. Everyone who is not wise or not curious is curious or calm and vice versa. Everyone who is kind or old is calm or not old. If someone is creative then someone is both patient and not patient. Everyone who is curious is both not strong and rich. If someone is wise then susan is both wise and not kind and vice versa. If someone is funny then someone is not funny or not calm and vice versa. Everyone who is either not kind or brave is both generous and not funny. Everyone who is either not patient or old is either generous or not tall and vice versa. Everyone who is humble or creative is not strong. If someone is not patient then mary is either not humble or wise. If someone is not happy then mary is both not calm and creative and vice versa. Everyone who is strong is both brave and calm and vice versa. Alice is not curious. Mary is both not patient and not tall. Someone is either not brave or funny. Someone is either humble or not humble. Alice is funny or not wise. | Alice is not happy. | contradiction | ((?[X]:((~wise(X)<~>~generous(X))))<=>((~brave(fred)&~generous(fred))))&
((?[X]:((strong(X)<~>~patient(X))))=>((funny(fred)<~>~patient(fred))))&
(![X]:((~happy(X)<~>curious(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((~wise(X)|~curious(X))<=>(curious(X)|calm(X))))&
(![X]:((kind(X)|old(X))=>(calm(X)|~old(X))))&
((?[X]:(creative(X)))=>(?[X]:((patient(X)&~patient(X)))))&
(![X]:(curious(X)=>(~strong(X)&rich(X))))&
((?[X]:(wise(X)))<=>((wise(susan)&~kind(susan))))&
((?[X]:(funny(X)))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~kind(X)<~>brave(X))=>(generous(X)&~funny(X))))&
(![X]:((~patient(X)<~>old(X))<=>(generous(X)<~>~tall(X))))&
(![X]:((humble(X)|creative(X))=>~strong(X)))&
((?[X]:(~patient(X)))=>((~humble(mary)<~>wise(mary))))&
((?[X]:(~happy(X)))<=>((~calm(mary)&creative(mary))))&
(![X]:(strong(X)<=>(brave(X)&calm(X))))&
(~curious(alice))&
((~patient(mary)&~tall(mary)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
((funny(alice)|~wise(alice))) | ~happy(alice) | [
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 861174066862858576047044
% SZS output start Proof for 861174066862858576047044
6. ? [X0] : creative(X0) => ? [X0] : (~patient(X0) & patient(X0)) [input p5]
14. ? [X0] : ~happy(X0) <=> (creative(mary) & ~calm(mary)) [input p13]
21. ~happy(alice) [input hypothesis]
22. ? [X0] : creative(X0) => ? [X1] : (~patient(X1) & patient(X1)) [rectify 6]
27. ? [X1] : (~patient(X1) & patient(X1)) | ! [X0] : ~creative(X0) [ennf transformation 22]
41. ? [X0] : (~patient(X0) & patient(X0)) | ! [X1] : ~creative(X1) [rectify 27]
42. ? [X0] : (~patient(X0) & patient(X0)) => (~patient(sK1) & patient(sK1)) [choice axiom]
43. (~patient(sK1) & patient(sK1)) | ! [X1] : ~creative(X1) [skolemisation 41,42]
57. (? [X0] : ~happy(X0) | (~creative(mary) | calm(mary))) & ((creative(mary) & ~calm(mary)) | ! [X0] : happy(X0)) [nnf transformation 14]
58. (? [X0] : ~happy(X0) | ~creative(mary) | calm(mary)) & ((creative(mary) & ~calm(mary)) | ! [X0] : happy(X0)) [flattening 57]
59. (? [X0] : ~happy(X0) | ~creative(mary) | calm(mary)) & ((creative(mary) & ~calm(mary)) | ! [X1] : happy(X1)) [rectify 58]
60. ? [X0] : ~happy(X0) => ~happy(sK5) [choice axiom]
61. (~happy(sK5) | ~creative(mary) | calm(mary)) & ((creative(mary) & ~calm(mary)) | ! [X1] : happy(X1)) [skolemisation 59,60]
94. patient(sK1) | ~creative(X1) [cnf transformation 43]
95. ~patient(sK1) | ~creative(X1) [cnf transformation 43]
121. creative(mary) | happy(X1) [cnf transformation 61]
134. ~happy(alice) [cnf transformation 21]
185. 11 <=> ! [X1] : ~creative(X1) [avatar definition]
186. ~creative(X1) <- (11) [avatar component clause 185]
188. 12 <=> patient(sK1) [avatar definition]
191. 11 | ~12 [avatar split clause 95,188,185]
192. 11 | 12 [avatar split clause 94,188,185]
253. 27 <=> creative(mary) [avatar definition]
254. creative(mary) <- (27) [avatar component clause 253]
262. 29 <=> ! [X1] : happy(X1) [avatar definition]
263. happy(X1) <- (29) [avatar component clause 262]
264. 29 | 27 [avatar split clause 121,253,262]
285. $false <- (11, 27) [resolution 254,186]
286. ~11 | ~27 [avatar contradiction clause 285]
287. $false <- (29) [resolution 263,134]
290. ~29 [avatar contradiction clause 287]
291. $false [avatar sat refutation 191,192,264,286,290]
% SZS output end Proof for 861174066862858576047044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both patient and not funny then someone is brave and vice versa. Everyone who is both wise and old is both not humble and not wise. If someone is calm or rich then someone is not wise or not quiet and vice versa. Everyone who is not tall is not funny and vice versa. If someone is either curious or not happy then someone is either rich or not brave and vice versa. If fred is either not funny or not generous then someone is both not humble and not strong and vice versa. If john is either not funny or not brave then alice is not old and vice versa. Everyone who is humble is either not kind or brave. If someone is not rich then mary is both wise and patient. If someone is both patient and brave then alice is not funny or calm. If someone is curious or not calm then someone is both curious and calm and vice versa. Everyone who is both rich and not curious is not wise. Everyone who is both not strong and curious is either creative or not old and vice versa. If lucy is not old then lucy is not calm. Everyone who is both not rich and kind is both wise and brave. Everyone who is both not generous and strong is both strong and wise. Susan is not old. Someone is both kind and brave. John is either humble or not kind. Someone is not old. Alice is not old. Someone is rich. Susan is both not creative and generous. Someone is both old and humble. | Alice is old. | contradiction | (((patient(alice)&~funny(alice)))<=>(?[X]:(brave(X))))&
(![X]:((wise(X)&old(X))=>(~humble(X)&~wise(X))))&
((?[X]:((calm(X)|rich(X))))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:(~tall(X)<=>~funny(X)))&
((?[X]:((curious(X)<~>~happy(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(((~funny(fred)<~>~generous(fred)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(((~funny(john)<~>~brave(john)))<=>(~old(alice)))&
(![X]:(humble(X)=>(~kind(X)<~>brave(X))))&
((?[X]:(~rich(X)))=>((wise(mary)&patient(mary))))&
((?[X]:((patient(X)&brave(X))))=>((~funny(alice)|calm(alice))))&
((?[X]:((curious(X)|~calm(X))))<=>(?[X]:((curious(X)&calm(X)))))&
(![X]:((rich(X)&~curious(X))=>~wise(X)))&
(![X]:((~strong(X)&curious(X))<=>(creative(X)<~>~old(X))))&
((~old(lucy))=>(~calm(lucy)))&
(![X]:((~rich(X)&kind(X))=>(wise(X)&brave(X))))&
(![X]:((~generous(X)&strong(X))=>(strong(X)&wise(X))))&
(~old(susan))&
(?[X]:((kind(X)&brave(X))))&
((humble(john)<~>~kind(john)))&
(?[X]:(~old(X)))&
(~old(alice))&
(?[X]:(rich(X)))&
((~creative(susan)&generous(susan)))&
(?[X]:((old(X)&humble(X)))) | old(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 628125855030454836445819
% SZS output start Proof for 628125855030454836445819
21. ~old(alice) [input p20]
25. old(alice) [input hypothesis]
134. ~old(alice) [cnf transformation 21]
140. old(alice) [cnf transformation 25]
254. 26 <=> old(alice) [avatar definition]
339. ~26 [avatar split clause 134,254]
340. 26 [avatar split clause 140,254]
341. $false [avatar sat refutation 339,340]
% SZS output end Proof for 628125855030454836445819
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and wise is quiet or happy and vice versa.
If someone is kind then someone is not brave.
If john is not happy or tall then someone is not calm or not kind and vice versa.
If someone is either generous or not rich then lucy is both not creative and not patient and vice versa.
Everyone who is both strong and funny is either not funny or not strong and vice versa.
Everyone who is not humble is not happy.
If susan is both brave and rich then someone is happy and vice versa.
Everyone who is not patient is not strong.
If alice is both old and kind then someone is wise or not quiet.
Everyone who is old or not brave is happy.
Everyone who is both funny and not humble is not strong or not brave.
If someone is both brave and not brave then someone is either not wise or old and vice versa.
Everyone who is wise is both calm and brave and vice versa.
Everyone who is funny or brave is not happy and vice versa.
Everyone who is either not curious or not creative is either not calm or old.
Everyone who is either not creative or not generous is calm or not kind.
Fred is calm or quiet.
Someone is either wise or happy.
John is not kind.
Someone is either not wise or not patient.
Someone is calm or not curious. | Fred is wise. | entailment | (![X]:((~patient(X)&wise(X))<=>(quiet(X)|happy(X))))&
((?[X]:(kind(X)))=>(?[X]:(~brave(X))))&
(((~happy(john)|tall(john)))<=>(?[X]:((~calm(X)|~kind(X)))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~creative(lucy)&~patient(lucy))))&
(![X]:((strong(X)&funny(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:(~humble(X)=>~happy(X)))&
(((brave(susan)&rich(susan)))<=>(?[X]:(happy(X))))&
(![X]:(~patient(X)=>~strong(X)))&
(((old(alice)&kind(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((old(X)|~brave(X))=>happy(X)))&
(![X]:((funny(X)&~humble(X))=>(~strong(X)|~brave(X))))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(wise(X)<=>(calm(X)&brave(X))))&
(![X]:((funny(X)|brave(X))<=>~happy(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~calm(X)<~>old(X))))&
(![X]:((~creative(X)<~>~generous(X))=>(calm(X)|~kind(X))))&
((calm(fred)|quiet(fred)))&
(?[X]:((wise(X)<~>happy(X))))&
(~kind(john))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((calm(X)|~curious(X)))) | wise(fred) | [
"p0",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1394997789547560300358343
% SZS output start Proof for 1394997789547560300358343
1. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (happy(X0) | quiet(X0))) [input p0]
10. ! [X0] : ((~brave(X0) | old(X0)) => happy(X0)) [input p9]
12. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X0] : (~wise(X0) <~> old(X0)) [input p11]
22. ~wise(fred) [input hypothesis]
24. ? [X0] : (~brave(X0) & brave(X0)) <=> ? [X1] : (~wise(X1) <~> old(X1)) [rectify 12]
31. ! [X0] : (happy(X0) | (brave(X0) & ~old(X0))) [ennf transformation 10]
35. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~wise(X0) | patient(X0))) [flattening 35]
59. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (? [X1] : ((~old(X1) | wise(X1)) & (old(X1) | ~wise(X1))) | ! [X0] : (brave(X0) | ~brave(X0))) [nnf transformation 24]
60. (? [X0] : (~brave(X0) & brave(X0)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (? [X2] : ((~old(X2) | wise(X2)) & (old(X2) | ~wise(X2))) | ! [X3] : (brave(X3) | ~brave(X3))) [rectify 59]
61. ? [X0] : (~brave(X0) & brave(X0)) => (~brave(sK5) & brave(sK5)) [choice axiom]
62. ? [X2] : ((~old(X2) | wise(X2)) & (old(X2) | ~wise(X2))) => ((~old(sK6) | wise(sK6)) & (old(sK6) | ~wise(sK6))) [choice axiom]
63. ((~brave(sK5) & brave(sK5)) | ! [X1] : ((~wise(X1) | ~old(X1)) & (old(X1) | wise(X1)))) & (((~old(sK6) | wise(sK6)) & (old(sK6) | ~wise(sK6))) | ! [X3] : (brave(X3) | ~brave(X3))) [skolemisation 60,62,61]
82. ~happy(X0) | wise(X0) [cnf transformation 36]
105. ~old(X0) | happy(X0) [cnf transformation 31]
109. brave(sK5) | old(X1) | wise(X1) [cnf transformation 63]
111. ~brave(sK5) | old(X1) | wise(X1) [cnf transformation 63]
132. ~wise(fred) [cnf transformation 22]
221. 20 <=> brave(sK5) [avatar definition]
226. 21 <=> ! [X1] : (old(X1) | wise(X1)) [avatar definition]
227. old(X1) | wise(X1) <- (21) [avatar component clause 226]
228. 21 | ~20 [avatar split clause 111,221,226]
230. 21 | 20 [avatar split clause 109,221,226]
273. wise(X1) | happy(X1) <- (21) [resolution 227,105]
284. wise(X1) <- (21) [subsumption resolution 273,82]
303. $false <- (21) [resolution 284,132]
307. ~21 [avatar contradiction clause 303]
309. $false [avatar sat refutation 228,230,307]
% SZS output end Proof for 1394997789547560300358343
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then alice is both not funny and wise and vice versa. If lucy is not curious then someone is both funny and not kind. Everyone who is not kind or calm is old or wise and vice versa. If john is not strong or not rich then alice is either calm or not happy. Everyone who is not humble is both generous and creative. If someone is not quiet or rich then someone is creative. If paul is not old then someone is either not quiet or curious. If someone is either humble or not tall then lucy is either not quiet or not creative. Everyone who is not patient is not quiet. Everyone who is both not kind and wise is calm or generous and vice versa. If someone is generous or creative then someone is both not funny and funny. Everyone who is not calm is not humble and vice versa. If someone is either not strong or generous then someone is old or calm and vice versa. Everyone who is both not generous and not patient is both not strong and strong and vice versa. Everyone who is both not generous and not strong is not kind. Paul is humble or not curious. Fred is both wise and not generous. Someone is brave. Paul is either old or not calm. Someone is not strong or not humble. | John is not kind. | entailment | ((?[X]:(brave(X)))<=>((~funny(alice)&wise(alice))))&
((~curious(lucy))=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((~kind(X)|calm(X))<=>(old(X)|wise(X))))&
(((~strong(john)|~rich(john)))=>((calm(alice)<~>~happy(alice))))&
(![X]:(~humble(X)=>(generous(X)&creative(X))))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:(creative(X))))&
((~old(paul))=>(?[X]:((~quiet(X)<~>curious(X)))))&
((?[X]:((humble(X)<~>~tall(X))))=>((~quiet(lucy)<~>~creative(lucy))))&
(![X]:(~patient(X)=>~quiet(X)))&
(![X]:((~kind(X)&wise(X))<=>(calm(X)|generous(X))))&
((?[X]:((generous(X)|creative(X))))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((~generous(X)&~patient(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~strong(X))=>~kind(X)))&
((humble(paul)|~curious(paul)))&
((wise(fred)&~generous(fred)))&
(?[X]:(brave(X)))&
((old(paul)<~>~calm(paul)))&
(?[X]:((~strong(X)|~humble(X)))) | ~kind(john) | [
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6137289846209954610761123
% SZS output start Proof for 6137289846209954610761123
5. ! [X0] : (~humble(X0) => (creative(X0) & generous(X0))) [input p4]
10. ! [X0] : ((wise(X0) & ~kind(X0)) <=> (generous(X0) | calm(X0))) [input p9]
11. ? [X0] : (creative(X0) | generous(X0)) => ? [X0] : (funny(X0) & ~funny(X0)) [input p10]
12. ! [X0] : (~calm(X0) <=> ~humble(X0)) [input p11]
21. kind(john) [input hypothesis]
23. ? [X0] : (creative(X0) | generous(X0)) => ? [X1] : (funny(X1) & ~funny(X1)) [rectify 11]
27. ! [X0] : ((creative(X0) & generous(X0)) | humble(X0)) [ennf transformation 5]
32. ? [X1] : (funny(X1) & ~funny(X1)) | ! [X0] : (~creative(X0) & ~generous(X0)) [ennf transformation 23]
52. ! [X0] : (((wise(X0) & ~kind(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~wise(X0) | kind(X0)))) [nnf transformation 10]
53. ! [X0] : (((wise(X0) & ~kind(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | ~wise(X0) | kind(X0))) [flattening 52]
54. ? [X0] : (funny(X0) & ~funny(X0)) | ! [X1] : (~creative(X1) & ~generous(X1)) [rectify 32]
55. ? [X0] : (funny(X0) & ~funny(X0)) => (funny(sK4) & ~funny(sK4)) [choice axiom]
56. (funny(sK4) & ~funny(sK4)) | ! [X1] : (~creative(X1) & ~generous(X1)) [skolemisation 54,55]
57. ! [X0] : ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))) [nnf transformation 12]
83. generous(X0) | humble(X0) [cnf transformation 27]
95. ~calm(X0) | ~kind(X0) [cnf transformation 53]
99. ~funny(sK4) | ~generous(X1) [cnf transformation 56]
101. funny(sK4) | ~generous(X1) [cnf transformation 56]
103. ~humble(X0) | calm(X0) [cnf transformation 57]
123. kind(john) [cnf transformation 21]
225. 23 <=> funny(sK4) [avatar definition]
230. 24 <=> ! [X1] : ~generous(X1) [avatar definition]
231. ~generous(X1) <- (24) [avatar component clause 230]
232. 24 | 23 [avatar split clause 101,225,230]
234. 24 | ~23 [avatar split clause 99,225,230]
302. humble(X0) <- (24) [resolution 83,231]
312. calm(X0) <- (24) [resolution 103,302]
320. ~kind(X2) <- (24) [resolution 312,95]
330. $false <- (24) [resolution 320,123]
331. ~24 [avatar contradiction clause 330]
332. $false [avatar sat refutation 232,234,331]
% SZS output end Proof for 6137289846209954610761123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not generous or calm then someone is either patient or generous and vice versa.
Everyone who is not generous or not curious is not strong.
If someone is both happy and not wise then paul is curious and vice versa.
Everyone who is not humble is not happy.
If lucy is curious then alice is both not creative and not patient and vice versa.
Everyone who is both creative and not calm is both not creative and wise.
Everyone who is either strong or not strong is both humble and funny.
Everyone who is either not quiet or wise is either not brave or not patient.
If alice is humble or not calm then lucy is wise.
Everyone who is either tall or not kind is not generous.
If john is not creative then alice is either not strong or creative.
Everyone who is not funny or calm is both old and not creative and vice versa.
Everyone who is both brave and not strong is either not tall or not wise.
If susan is not curious then john is both rich and quiet and vice versa.
Everyone who is not wise is not tall or not funny.
If someone is both not rich and humble then john is both not rich and kind.
Someone is not calm.
Paul is both curious and happy.
Paul is calm.
Fred is rich or kind.
Mary is either tall or not curious.
Alice is not rich.
Someone is both not tall and humble. | Lucy is not creative. | entailment | ((?[X]:((~generous(X)<~>calm(X))))<=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~generous(X)|~curious(X))=>~strong(X)))&
((?[X]:((happy(X)&~wise(X))))<=>(curious(paul)))&
(![X]:(~humble(X)=>~happy(X)))&
((curious(lucy))<=>((~creative(alice)&~patient(alice))))&
(![X]:((creative(X)&~calm(X))=>(~creative(X)&wise(X))))&
(![X]:((strong(X)<~>~strong(X))=>(humble(X)&funny(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(~brave(X)<~>~patient(X))))&
(((humble(alice)|~calm(alice)))=>(wise(lucy)))&
(![X]:((tall(X)<~>~kind(X))=>~generous(X)))&
((~creative(john))=>((~strong(alice)<~>creative(alice))))&
(![X]:((~funny(X)|calm(X))<=>(old(X)&~creative(X))))&
(![X]:((brave(X)&~strong(X))=>(~tall(X)<~>~wise(X))))&
((~curious(susan))<=>((rich(john)&quiet(john))))&
(![X]:(~wise(X)=>(~tall(X)|~funny(X))))&
((?[X]:((~rich(X)&humble(X))))=>((~rich(john)&kind(john))))&
(?[X]:(~calm(X)))&
((curious(paul)&happy(paul)))&
(calm(paul))&
((rich(fred)|kind(fred)))&
((tall(mary)<~>~curious(mary)))&
(~rich(alice))&
(?[X]:((~tall(X)&humble(X)))) | ~creative(lucy) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5530765532161697560512433
% SZS output start Proof for 5530765532161697560512433
6. ! [X0] : ((~calm(X0) & creative(X0)) => (wise(X0) & ~creative(X0))) [input p5]
12. ! [X0] : ((calm(X0) | ~funny(X0)) <=> (~creative(X0) & old(X0))) [input p11]
24. creative(lucy) [input hypothesis]
28. ! [X0] : ((wise(X0) & ~creative(X0)) | (calm(X0) | ~creative(X0))) [ennf transformation 6]
29. ! [X0] : ((wise(X0) & ~creative(X0)) | calm(X0) | ~creative(X0)) [flattening 28]
55. ! [X0] : (((calm(X0) | ~funny(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (~calm(X0) & funny(X0)))) [nnf transformation 12]
56. ! [X0] : ((calm(X0) | ~funny(X0) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | (~calm(X0) & funny(X0)))) [flattening 55]
82. ~creative(X0) | calm(X0) | ~creative(X0) [cnf transformation 29]
101. ~creative(X0) | ~calm(X0) [cnf transformation 56]
121. creative(lucy) [cnf transformation 24]
126. ~creative(X0) | calm(X0) [duplicate literal removal 82]
221. ~creative(X0) [subsumption resolution 101,126]
269. $false [subsumption resolution 121,221]
% SZS output end Proof for 5530765532161697560512433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not generous is either not kind or not quiet.
Everyone who is not humble is not funny.
Everyone who is quiet or funny is not brave.
If someone is quiet or not calm then someone is either not old or not tall.
Everyone who is not patient or wise is curious or not quiet.
If someone is generous then mary is both old and not humble and vice versa.
If lucy is both not quiet and old then alice is both rich and not calm and vice versa.
Everyone who is not curious is not happy or not quiet and vice versa.
If lucy is not tall then someone is not strong and vice versa.
If lucy is old then someone is both calm and happy and vice versa.
Everyone who is old is both not quiet and humble and vice versa.
If someone is either calm or rich then alice is either not old or not wise and vice versa.
If lucy is either brave or funny then someone is both not generous and not humble and vice versa.
If someone is both strong and tall then someone is not quiet and vice versa.
Everyone who is either happy or kind is both old and kind.
If someone is generous or not kind then someone is either patient or brave.
Someone is both not funny and not strong.
Someone is either funny or not tall.
Someone is not wise.
Someone is not curious.
Someone is not quiet or humble.
Someone is calm or not funny.
Someone is not kind or not rich.
Someone is both patient and not strong. | Lucy is brave. | neutral | (![X]:((~kind(X)&~generous(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:(~humble(X)=>~funny(X)))&
(![X]:((quiet(X)|funny(X))=>~brave(X)))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((~old(X)<~>~tall(X)))))&
(![X]:((~patient(X)|wise(X))=>(curious(X)|~quiet(X))))&
((?[X]:(generous(X)))<=>((old(mary)&~humble(mary))))&
(((~quiet(lucy)&old(lucy)))<=>((rich(alice)&~calm(alice))))&
(![X]:(~curious(X)<=>(~happy(X)|~quiet(X))))&
((~tall(lucy))<=>(?[X]:(~strong(X))))&
((old(lucy))<=>(?[X]:((calm(X)&happy(X)))))&
(![X]:(old(X)<=>(~quiet(X)&humble(X))))&
((?[X]:((calm(X)<~>rich(X))))<=>((~old(alice)<~>~wise(alice))))&
(((brave(lucy)<~>funny(lucy)))<=>(?[X]:((~generous(X)&~humble(X)))))&
((?[X]:((strong(X)&tall(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((happy(X)<~>kind(X))=>(old(X)&kind(X))))&
((?[X]:((generous(X)|~kind(X))))=>(?[X]:((patient(X)<~>brave(X)))))&
(?[X]:((~funny(X)&~strong(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)|humble(X))))&
(?[X]:((calm(X)|~funny(X))))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((patient(X)&~strong(X)))) | brave(lucy) | [] | null | 0 |
If someone is both not calm and happy then paul is either not funny or calm. Everyone who is both patient and not kind is either kind or funny and vice versa. Everyone who is not brave or not tall is either strong or humble. If mary is not old then someone is either funny or kind. Everyone who is not humble is both not old and not humble. Everyone who is quiet or generous is kind or not calm. If someone is both rich and not funny then fred is either not humble or not generous. Everyone who is not rich or humble is not kind. If someone is brave then paul is not happy and vice versa. Everyone who is both not patient and patient is both curious and quiet and vice versa. If john is not kind then john is either not generous or not quiet and vice versa. If susan is curious then susan is either not rich or calm and vice versa. Everyone who is not rich is either funny or not creative. If alice is both not humble and not quiet then alice is either curious or humble and vice versa. Everyone who is either not quiet or not brave is either humble or not wise and vice versa. Everyone who is funny is both rich and not curious and vice versa. Someone is old or not happy. Alice is either kind or not humble. Alice is either not happy or wise. John is both wise and not calm. Someone is either patient or not kind. Someone is either not calm or old. Paul is both not funny and not creative. Someone is either not creative or generous. | Alice is old. | contradiction | ((?[X]:((~calm(X)&happy(X))))=>((~funny(paul)<~>calm(paul))))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)<~>funny(X))))&
(![X]:((~brave(X)|~tall(X))=>(strong(X)<~>humble(X))))&
((~old(mary))=>(?[X]:((funny(X)<~>kind(X)))))&
(![X]:(~humble(X)=>(~old(X)&~humble(X))))&
(![X]:((quiet(X)|generous(X))=>(kind(X)|~calm(X))))&
((?[X]:((rich(X)&~funny(X))))=>((~humble(fred)<~>~generous(fred))))&
(![X]:((~rich(X)|humble(X))=>~kind(X)))&
((?[X]:(brave(X)))<=>(~happy(paul)))&
(![X]:((~patient(X)&patient(X))<=>(curious(X)&quiet(X))))&
((~kind(john))<=>((~generous(john)<~>~quiet(john))))&
((curious(susan))<=>((~rich(susan)<~>calm(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>~creative(X))))&
(((~humble(alice)&~quiet(alice)))<=>((curious(alice)<~>humble(alice))))&
(![X]:((~quiet(X)<~>~brave(X))<=>(humble(X)<~>~wise(X))))&
(![X]:(funny(X)<=>(rich(X)&~curious(X))))&
(?[X]:((old(X)|~happy(X))))&
((kind(alice)<~>~humble(alice)))&
((~happy(alice)<~>wise(alice)))&
((wise(john)&~calm(john)))&
(?[X]:((patient(X)<~>~kind(X))))&
(?[X]:((~calm(X)<~>old(X))))&
((~funny(paul)&~creative(paul)))&
(?[X]:((~creative(X)<~>generous(X)))) | old(alice) | [
"p4",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8525670853705246328197762
% SZS output start Proof for 8525670853705246328197762
5. ! [X0] : (~humble(X0) => (~humble(X0) & ~old(X0))) [input p4]
8. ! [X0] : ((humble(X0) | ~rich(X0)) => ~kind(X0)) [input p7]
18. kind(alice) <~> ~humble(alice) [input p17]
25. old(alice) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~old(X0)) | humble(X0)) [ennf transformation 5]
34. ! [X0] : (~kind(X0) | (~humble(X0) & rich(X0))) [ennf transformation 8]
60. (humble(alice) | ~kind(alice)) & (~humble(alice) | kind(alice)) [nnf transformation 18]
83. ~old(X0) | humble(X0) [cnf transformation 30]
90. ~kind(X0) | ~humble(X0) [cnf transformation 34]
125. ~humble(alice) | kind(alice) [cnf transformation 60]
126. humble(alice) | ~kind(alice) [cnf transformation 60]
139. old(alice) [cnf transformation 25]
235. 19 <=> humble(alice) [avatar definition]
237. ~humble(alice) <- (~19) [avatar component clause 235]
258. ~kind(alice) [subsumption resolution 126,90]
259. ~humble(alice) [subsumption resolution 125,258]
260. ~19 [avatar split clause 259,235]
302. humble(alice) [resolution 83,139]
304. $false <- (~19) [subsumption resolution 302,237]
305. 19 [avatar contradiction clause 304]
306. $false [avatar sat refutation 260,305]
% SZS output end Proof for 8525670853705246328197762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both rich and humble then fred is not happy or old.
Everyone who is not funny is either not happy or old.
Everyone who is both brave and kind is either wise or not generous and vice versa.
Everyone who is not wise is kind and vice versa.
Everyone who is either calm or happy is both not creative and not tall.
Everyone who is both not kind and not quiet is calm.
If john is not calm then alice is either not rich or not quiet.
If someone is creative then susan is not patient or not happy.
Everyone who is both patient and kind is wise or strong.
If someone is generous or not brave then fred is tall or rich and vice versa.
If fred is either humble or calm then someone is funny.
Everyone who is either not brave or not creative is not happy or not creative.
If someone is patient then fred is both humble and not kind.
If someone is either not rich or wise then someone is not funny.
If someone is either not brave or rich then mary is both not patient and not kind.
Everyone who is not curious or curious is either not strong or generous and vice versa.
Fred is either quiet or curious.
Someone is both calm and not tall.
Mary is quiet.
Someone is generous or curious.
Susan is funny.
Alice is both not kind and patient.
Paul is not curious.
Fred is not strong. | Alice is strong. | contradiction | (((rich(john)&humble(john)))=>((~happy(fred)|old(fred))))&
(![X]:(~funny(X)=>(~happy(X)<~>old(X))))&
(![X]:((brave(X)&kind(X))<=>(wise(X)<~>~generous(X))))&
(![X]:(~wise(X)<=>kind(X)))&
(![X]:((calm(X)<~>happy(X))=>(~creative(X)&~tall(X))))&
(![X]:((~kind(X)&~quiet(X))=>calm(X)))&
((~calm(john))=>((~rich(alice)<~>~quiet(alice))))&
((?[X]:(creative(X)))=>((~patient(susan)|~happy(susan))))&
(![X]:((patient(X)&kind(X))=>(wise(X)|strong(X))))&
((?[X]:((generous(X)|~brave(X))))<=>((tall(fred)|rich(fred))))&
(((humble(fred)<~>calm(fred)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~happy(X)|~creative(X))))&
((?[X]:(patient(X)))=>((humble(fred)&~kind(fred))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>rich(X))))=>((~patient(mary)&~kind(mary))))&
(![X]:((~curious(X)|curious(X))<=>(~strong(X)<~>generous(X))))&
((quiet(fred)<~>curious(fred)))&
(?[X]:((calm(X)&~tall(X))))&
(quiet(mary))&
(?[X]:((generous(X)|curious(X))))&
(funny(susan))&
((~kind(alice)&patient(alice)))&
(~curious(paul))&
(~strong(fred)) | strong(alice) | [
"p2",
"p3",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5959411975830871791320143
% SZS output start Proof for 5959411975830871791320143
3. ! [X0] : ((kind(X0) & brave(X0)) <=> (wise(X0) <~> ~generous(X0))) [input p2]
4. ! [X0] : (~wise(X0) <=> kind(X0)) [input p3]
16. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~strong(X0) <~> generous(X0))) [input p15]
22. patient(alice) & ~kind(alice) [input p21]
25. strong(alice) [input hypothesis]
45. ! [X0] : (((kind(X0) & brave(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0)))) & (((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | (~kind(X0) | ~brave(X0)))) [nnf transformation 3]
46. ! [X0] : (((kind(X0) & brave(X0)) | ((wise(X0) | generous(X0)) & (~generous(X0) | ~wise(X0)))) & (((generous(X0) | ~wise(X0)) & (~generous(X0) | wise(X0))) | ~kind(X0) | ~brave(X0))) [flattening 45]
47. ! [X0] : ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))) [nnf transformation 4]
64. ! [X0] : (((curious(X0) | ~curious(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | (~curious(X0) & curious(X0)))) [nnf transformation 16]
65. ! [X0] : ((curious(X0) | ~curious(X0) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | (~curious(X0) & curious(X0)))) [flattening 64]
78. ~generous(X0) | kind(X0) | ~wise(X0) [cnf transformation 46]
80. wise(X0) | kind(X0) [cnf transformation 47]
107. generous(X0) | ~strong(X0) | curious(X0) [cnf transformation 65]
108. generous(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 65]
120. ~kind(alice) [cnf transformation 22]
124. strong(alice) [cnf transformation 25]
250. ~strong(X0) | generous(X0) [subsumption resolution 107,108]
272. generous(alice) [resolution 250,124]
287. 35 <=> wise(alice) [avatar definition]
288. wise(alice) <- (35) [avatar component clause 287]
289. ~wise(alice) <- (~35) [avatar component clause 287]
299. kind(alice) <- (~35) [resolution 289,80]
300. $false <- (~35) [subsumption resolution 299,120]
301. 35 [avatar contradiction clause 300]
303. kind(alice) | ~wise(alice) [resolution 78,272]
305. ~wise(alice) [subsumption resolution 303,120]
306. $false <- (35) [subsumption resolution 305,288]
307. ~35 [avatar contradiction clause 306]
308. $false [avatar sat refutation 301,307]
% SZS output end Proof for 5959411975830871791320143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then someone is tall. Everyone who is both kind and not generous is either not brave or not generous and vice versa. Everyone who is generous is not brave and vice versa. If lucy is generous then john is creative. If fred is generous then someone is both creative and not strong. Everyone who is both not happy and tall is both brave and strong. If someone is not humble or not old then john is either not quiet or not old and vice versa. Everyone who is not kind is not strong or patient and vice versa. If paul is kind or not curious then someone is either curious or not rich. Everyone who is both calm and not funny is either creative or not wise. If someone is either not brave or not patient then someone is calm or happy. Everyone who is either not wise or not patient is humble or patient. Everyone who is patient or not strong is not curious and vice versa. If someone is either calm or not happy then someone is not tall. If someone is either calm or kind then lucy is both humble and not rich. John is happy or kind. Someone is not calm. Alice is strong or tall. Alice is old or not old. Paul is creative or not humble. Susan is not generous or curious. | Lucy is not quiet. | neutral | ((?[X]:(~happy(X)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~generous(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:(generous(X)<=>~brave(X)))&
((generous(lucy))=>(creative(john)))&
((generous(fred))=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((~happy(X)&tall(X))=>(brave(X)&strong(X))))&
((?[X]:((~humble(X)|~old(X))))<=>((~quiet(john)<~>~old(john))))&
(![X]:(~kind(X)<=>(~strong(X)|patient(X))))&
(((kind(paul)|~curious(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((calm(X)&~funny(X))=>(creative(X)<~>~wise(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~wise(X)<~>~patient(X))=>(humble(X)|patient(X))))&
(![X]:((patient(X)|~strong(X))<=>~curious(X)))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:(~tall(X))))&
((?[X]:((calm(X)<~>kind(X))))=>((humble(lucy)&~rich(lucy))))&
((happy(john)|kind(john)))&
(?[X]:(~calm(X)))&
((strong(alice)|tall(alice)))&
((old(alice)|~old(alice)))&
((creative(paul)|~humble(paul)))&
((~generous(susan)|curious(susan))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is generous or rich is both not wise and not calm.
If someone is not happy or not generous then paul is either happy or not generous and vice versa.
Everyone who is both tall and generous is not happy or not kind and vice versa.
Everyone who is both not funny and brave is creative and vice versa.
If someone is not generous or strong then someone is both quiet and not humble and vice versa.
If lucy is not happy or humble then someone is generous or not strong.
If someone is not brave or not creative then paul is not wise or tall.
Everyone who is both not curious and old is creative or not curious and vice versa.
Everyone who is either not happy or not strong is either wise or not brave.
Everyone who is either not creative or creative is rich or not strong and vice versa.
If someone is both not happy and not tall then someone is both not curious and wise.
Everyone who is funny is not wise and vice versa.
If someone is both not tall and quiet then someone is strong and vice versa.
If someone is not brave or not funny then fred is not tall and vice versa.
Everyone who is not quiet or not tall is either quiet or not strong and vice versa.
If john is either not tall or patient then paul is either not humble or curious and vice versa.
Someone is happy or not quiet.
Mary is rich.
Someone is both curious and not wise.
John is both tall and quiet.
Fred is either not rich or not tall.
Someone is both tall and rich.
Paul is both not rich and not quiet.
Someone is not humble. | Fred is kind. | entailment | (![X]:((generous(X)|rich(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~happy(X)|~generous(X))))<=>((happy(paul)<~>~generous(paul))))&
(![X]:((tall(X)&generous(X))<=>(~happy(X)|~kind(X))))&
(![X]:((~funny(X)&brave(X))<=>creative(X)))&
((?[X]:((~generous(X)|strong(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((~happy(lucy)|humble(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((?[X]:((~brave(X)|~creative(X))))=>((~wise(paul)|tall(paul))))&
(![X]:((~curious(X)&old(X))<=>(creative(X)|~curious(X))))&
(![X]:((~happy(X)<~>~strong(X))=>(wise(X)<~>~brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(rich(X)|~strong(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(funny(X)<=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(~tall(fred)))&
(![X]:((~quiet(X)|~tall(X))<=>(quiet(X)<~>~strong(X))))&
(((~tall(john)<~>patient(john)))<=>((~humble(paul)<~>curious(paul))))&
(?[X]:((happy(X)|~quiet(X))))&
(rich(mary))&
(?[X]:((curious(X)&~wise(X))))&
((tall(john)&quiet(john)))&
((~rich(fred)<~>~tall(fred)))&
(?[X]:((tall(X)&rich(X))))&
((~rich(paul)&~quiet(paul)))&
(?[X]:(~humble(X))) | kind(fred) | [
"p1",
"p2",
"p8",
"p9",
"p11",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4820016775909345940599895
% SZS output start Proof for 4820016775909345940599895
2. ? [X0] : (~generous(X0) | ~happy(X0)) <=> (happy(paul) <~> ~generous(paul)) [input p1]
3. ! [X0] : ((generous(X0) & tall(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
9. ! [X0] : ((~happy(X0) <~> ~strong(X0)) => (wise(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~strong(X0) | rich(X0))) [input p9]
12. ! [X0] : (funny(X0) <=> ~wise(X0)) [input p11]
14. ? [X0] : (~funny(X0) | ~brave(X0)) <=> ~tall(fred) [input p13]
23. ~quiet(paul) & ~rich(paul) [input p22]
25. ~kind(fred) [input hypothesis]
34. ! [X0] : ((wise(X0) <~> ~brave(X0)) | (~happy(X0) <=> ~strong(X0))) [ennf transformation 9]
36. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X0] : (generous(X0) & happy(X0))) [nnf transformation 2]
37. (? [X0] : (~generous(X0) | ~happy(X0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [rectify 36]
38. ? [X0] : (~generous(X0) | ~happy(X0)) => (~generous(sK0) | ~happy(sK0)) [choice axiom]
39. ((~generous(sK0) | ~happy(sK0)) | ((happy(paul) | generous(paul)) & (~generous(paul) | ~happy(paul)))) & (((generous(paul) | ~happy(paul)) & (~generous(paul) | happy(paul))) | ! [X1] : (generous(X1) & happy(X1))) [skolemisation 37,38]
40. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((generous(X0) & tall(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~generous(X0) | ~tall(X0))) [flattening 40]
53. ! [X0] : (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) [nnf transformation 34]
54. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 10]
55. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 54]
59. ! [X0] : ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))) [nnf transformation 12]
65. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X0] : (funny(X0) & brave(X0))) [nnf transformation 14]
66. (? [X0] : (~funny(X0) | ~brave(X0)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [rectify 65]
67. ? [X0] : (~funny(X0) | ~brave(X0)) => (~funny(sK7) | ~brave(sK7)) [choice axiom]
68. ((~funny(sK7) | ~brave(sK7)) | tall(fred)) & (~tall(fred) | ! [X1] : (funny(X1) & brave(X1))) [skolemisation 66,67]
83. ~generous(paul) | happy(paul) | happy(X1) [cnf transformation 39]
91. kind(X0) | tall(X0) [cnf transformation 41]
92. happy(X0) | generous(X0) [cnf transformation 41]
112. ~brave(X0) | wise(X0) | ~happy(X0) | strong(X0) [cnf transformation 53]
115. ~strong(X0) | rich(X0) | creative(X0) | creative(X0) [cnf transformation 55]
116. ~strong(X0) | rich(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 55]
123. ~funny(X0) | ~wise(X0) [cnf transformation 59]
128. ~tall(fred) | brave(X1) [cnf transformation 68]
129. ~tall(fred) | funny(X1) [cnf transformation 68]
155. ~rich(paul) [cnf transformation 23]
158. ~kind(fred) [cnf transformation 25]
161. ~strong(X0) | rich(X0) | creative(X0) [duplicate literal removal 115]
162. ~strong(X0) | rich(X0) | ~creative(X0) [duplicate literal removal 116]
164. 1 <=> generous(paul) [avatar definition]
165. ~generous(paul) <- (~1) [avatar component clause 164]
168. 2 <=> happy(paul) [avatar definition]
169. ~happy(paul) <- (~2) [avatar component clause 168]
170. happy(paul) <- (2) [avatar component clause 168]
186. 6 <=> ! [X1] : happy(X1) [avatar definition]
187. happy(X1) <- (6) [avatar component clause 186]
190. 6 | 2 | ~1 [avatar split clause 83,164,168,186]
240. 18 <=> wise(paul) [avatar definition]
241. wise(paul) <- (18) [avatar component clause 240]
242. ~wise(paul) <- (~18) [avatar component clause 240]
249. 20 <=> ! [X0] : brave(X0) [avatar definition]
250. brave(X0) <- (20) [avatar component clause 249]
252. ~strong(X0) | rich(X0) [subsumption resolution 161,162]
272. 25 <=> tall(fred) [avatar definition]
285. 28 <=> ! [X1] : funny(X1) [avatar definition]
286. funny(X1) <- (28) [avatar component clause 285]
287. 28 | ~25 [avatar split clause 129,272,285]
288. 20 | ~25 [avatar split clause 128,272,249]
333. tall(fred) [resolution 91,158]
334. generous(paul) <- (~2) [resolution 92,169]
335. $false <- (~1, ~2) [subsumption resolution 334,165]
336. 1 | 2 [avatar contradiction clause 335]
351. ~happy(X0) | wise(X0) | strong(X0) <- (20) [resolution 112,250]
358. 25 [avatar split clause 333,272]
417. ~wise(X0) <- (28) [resolution 286,123]
469. wise(paul) | strong(paul) <- (2, 20) [resolution 351,170]
474. strong(paul) <- (2, ~18, 20) [subsumption resolution 469,242]
480. rich(paul) <- (2, ~18, 20) [resolution 474,252]
485. $false <- (2, ~18, 20) [subsumption resolution 480,155]
486. ~2 | 18 | ~20 [avatar contradiction clause 485]
488. $false <- (18, 28) [subsumption resolution 241,417]
489. ~18 | ~28 [avatar contradiction clause 488]
490. $false <- (~2, 6) [subsumption resolution 169,187]
491. 2 | ~6 [avatar contradiction clause 490]
492. $false [avatar sat refutation 190,287,288,336,358,486,489,491]
% SZS output end Proof for 4820016775909345940599895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not humble and not brave then mary is both not tall and curious.
Everyone who is both not rich and not creative is either not humble or humble and vice versa.
If someone is curious then someone is either not quiet or not generous.
If someone is either not rich or patient then paul is either funny or not curious and vice versa.
If paul is either quiet or not wise then someone is both generous and brave and vice versa.
If fred is rich or humble then susan is both funny and not brave and vice versa.
Everyone who is either not strong or brave is humble.
Everyone who is curious or not calm is either not happy or humble.
If someone is not generous then someone is both not rich and creative.
If lucy is both not humble and not creative then paul is rich or not brave.
Everyone who is humble is curious or not rich.
If someone is strong or rich then fred is both patient and creative and vice versa.
If someone is old or humble then susan is not rich or funny.
Everyone who is not old or old is both not tall and patient and vice versa.
Everyone who is both humble and kind is either not creative or humble.
If john is strong then susan is strong or old and vice versa.
Lucy is either not patient or not humble.
Someone is both patient and old.
John is not wise.
Someone is either generous or wise.
Someone is not strong.
Someone is both happy and not old. | Paul is quiet. | neutral | (((~humble(mary)&~brave(mary)))=>((~tall(mary)&curious(mary))))&
(![X]:((~rich(X)&~creative(X))<=>(~humble(X)<~>humble(X))))&
((?[X]:(curious(X)))=>(?[X]:((~quiet(X)<~>~generous(X)))))&
((?[X]:((~rich(X)<~>patient(X))))<=>((funny(paul)<~>~curious(paul))))&
(((quiet(paul)<~>~wise(paul)))<=>(?[X]:((generous(X)&brave(X)))))&
(((rich(fred)|humble(fred)))<=>((funny(susan)&~brave(susan))))&
(![X]:((~strong(X)<~>brave(X))=>humble(X)))&
(![X]:((curious(X)|~calm(X))=>(~happy(X)<~>humble(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~rich(X)&creative(X)))))&
(((~humble(lucy)&~creative(lucy)))=>((rich(paul)|~brave(paul))))&
(![X]:(humble(X)=>(curious(X)|~rich(X))))&
((?[X]:((strong(X)|rich(X))))<=>((patient(fred)&creative(fred))))&
((?[X]:((old(X)|humble(X))))=>((~rich(susan)|funny(susan))))&
(![X]:((~old(X)|old(X))<=>(~tall(X)&patient(X))))&
(![X]:((humble(X)&kind(X))=>(~creative(X)<~>humble(X))))&
((strong(john))<=>((strong(susan)|old(susan))))&
((~patient(lucy)<~>~humble(lucy)))&
(?[X]:((patient(X)&old(X))))&
(~wise(john))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((happy(X)&~old(X)))) | quiet(paul) | [] | null | 0 |
If someone is not happy or not wise then paul is either patient or generous and vice versa. If mary is old then lucy is not happy or brave. Everyone who is tall or not old is not generous. Everyone who is both not curious and not wise is quiet or generous and vice versa. If fred is both patient and curious then someone is not funny. Everyone who is either brave or not kind is both not tall and generous. Everyone who is quiet or not generous is both rich and not kind. Everyone who is not funny is wise. If john is not brave or not generous then susan is both not creative and not funny and vice versa. Everyone who is both tall and not happy is rich and vice versa. If someone is not funny then fred is both not wise and not old. Everyone who is both curious and happy is both not tall and calm. If someone is not old then someone is either calm or happy and vice versa. If mary is not brave or not patient then alice is both tall and kind. Everyone who is not tall or happy is either tall or not wise. Everyone who is funny is both not calm and generous and vice versa. Lucy is either humble or rich. Someone is both not happy and not humble. Someone is generous. Someone is either wise or not creative. Someone is not brave or not rich. Someone is not tall or not happy. | John is brave. | entailment | ((?[X]:((~happy(X)|~wise(X))))<=>((patient(paul)<~>generous(paul))))&
((old(mary))=>((~happy(lucy)|brave(lucy))))&
(![X]:((tall(X)|~old(X))=>~generous(X)))&
(![X]:((~curious(X)&~wise(X))<=>(quiet(X)|generous(X))))&
(((patient(fred)&curious(fred)))=>(?[X]:(~funny(X))))&
(![X]:((brave(X)<~>~kind(X))=>(~tall(X)&generous(X))))&
(![X]:((quiet(X)|~generous(X))=>(rich(X)&~kind(X))))&
(![X]:(~funny(X)=>wise(X)))&
(((~brave(john)|~generous(john)))<=>((~creative(susan)&~funny(susan))))&
(![X]:((tall(X)&~happy(X))<=>rich(X)))&
((?[X]:(~funny(X)))=>((~wise(fred)&~old(fred))))&
(![X]:((curious(X)&happy(X))=>(~tall(X)&calm(X))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(((~brave(mary)|~patient(mary)))=>((tall(alice)&kind(alice))))&
(![X]:((~tall(X)|happy(X))=>(tall(X)<~>~wise(X))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
((humble(lucy)<~>rich(lucy)))&
(?[X]:((~happy(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~tall(X)|~happy(X)))) | brave(john) | [
"p2",
"p7",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 413795926806203613692146
% SZS output start Proof for 413795926806203613692146
3. ! [X0] : ((~old(X0) | tall(X0)) => ~generous(X0)) [input p2]
8. ! [X0] : (~funny(X0) => wise(X0)) [input p7]
9. (~generous(john) | ~brave(john)) <=> (~funny(susan) & ~creative(susan)) [input p8]
11. ? [X0] : ~funny(X0) => (~old(fred) & ~wise(fred)) [input p10]
16. ! [X0] : (funny(X0) <=> (generous(X0) & ~calm(X0))) [input p15]
23. ~brave(john) [input hypothesis]
27. ! [X0] : (~generous(X0) | (old(X0) & ~tall(X0))) [ennf transformation 3]
32. ! [X0] : (wise(X0) | funny(X0)) [ennf transformation 8]
33. (~old(fred) & ~wise(fred)) | ! [X0] : funny(X0) [ennf transformation 11]
47. ((~generous(john) | ~brave(john)) | (funny(susan) | creative(susan))) & ((~funny(susan) & ~creative(susan)) | (generous(john) & brave(john))) [nnf transformation 9]
48. (~generous(john) | ~brave(john) | funny(susan) | creative(susan)) & ((~funny(susan) & ~creative(susan)) | (generous(john) & brave(john))) [flattening 47]
57. ! [X0] : ((funny(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [nnf transformation 16]
58. ! [X0] : ((funny(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~funny(X0))) [flattening 57]
79. ~generous(X0) | old(X0) [cnf transformation 27]
94. funny(X0) | wise(X0) [cnf transformation 32]
97. ~funny(susan) | brave(john) [cnf transformation 48]
103. ~wise(fred) | funny(X0) [cnf transformation 33]
104. ~old(fred) | funny(X0) [cnf transformation 33]
120. ~funny(X0) | generous(X0) [cnf transformation 58]
131. ~brave(john) [cnf transformation 23]
192. 14 <=> funny(susan) [avatar definition]
193. ~funny(susan) <- (~14) [avatar component clause 192]
196. 15 <=> brave(john) [avatar definition]
205. 15 | ~14 [avatar split clause 97,192,196]
209. 17 <=> ! [X0] : funny(X0) [avatar definition]
210. funny(X0) <- (17) [avatar component clause 209]
212. 18 <=> old(fred) [avatar definition]
214. ~old(fred) <- (~18) [avatar component clause 212]
215. 17 | ~18 [avatar split clause 104,212,209]
217. 19 <=> wise(fred) [avatar definition]
219. ~wise(fred) <- (~19) [avatar component clause 217]
220. 17 | ~19 [avatar split clause 103,217,209]
304. ~15 [avatar split clause 131,196]
311. $false <- (~14, 17) [resolution 210,193]
312. 14 | ~17 [avatar contradiction clause 311]
326. generous(X0) | wise(X0) [resolution 120,94]
454. old(X2) | wise(X2) [resolution 326,79]
544. wise(fred) <- (~18) [resolution 454,214]
546. $false <- (~18, ~19) [subsumption resolution 544,219]
547. 18 | 19 [avatar contradiction clause 546]
548. $false [avatar sat refutation 205,215,220,304,312,547]
% SZS output end Proof for 413795926806203613692146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or creative is both not happy and old. If someone is not creative or not brave then susan is not generous. If someone is either not rich or creative then john is not funny. Everyone who is calm is funny and vice versa. If someone is both rich and not patient then someone is not happy or quiet and vice versa. Everyone who is both not curious and curious is either kind or not kind. Everyone who is not strong or wise is both funny and not funny and vice versa. If lucy is either generous or not rich then fred is either strong or not calm and vice versa. If someone is either not wise or old then john is both kind and not strong. Everyone who is either not old or not patient is either quiet or wise. Everyone who is kind or not funny is both not kind and not happy and vice versa. Everyone who is both brave and curious is kind. Everyone who is strong or creative is curious. Everyone who is curious is both not calm and not tall. John is not happy or not quiet. Someone is either curious or tall. Someone is both not funny and not kind. Mary is rich. Susan is either happy or not generous. Someone is not kind or not rich. Paul is both not funny and old. Someone is either not calm or wise. | John is not kind. | entailment | (![X]:((old(X)|creative(X))=>(~happy(X)&old(X))))&
((?[X]:((~creative(X)|~brave(X))))=>(~generous(susan)))&
((?[X]:((~rich(X)<~>creative(X))))=>(~funny(john)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((~curious(X)&curious(X))=>(kind(X)<~>~kind(X))))&
(![X]:((~strong(X)|wise(X))<=>(funny(X)&~funny(X))))&
(((generous(lucy)<~>~rich(lucy)))<=>((strong(fred)<~>~calm(fred))))&
((?[X]:((~wise(X)<~>old(X))))=>((kind(john)&~strong(john))))&
(![X]:((~old(X)<~>~patient(X))=>(quiet(X)<~>wise(X))))&
(![X]:((kind(X)|~funny(X))<=>(~kind(X)&~happy(X))))&
(![X]:((brave(X)&curious(X))=>kind(X)))&
(![X]:((strong(X)|creative(X))=>curious(X)))&
(![X]:(curious(X)=>(~calm(X)&~tall(X))))&
((~happy(john)|~quiet(john)))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~funny(X)&~kind(X))))&
(rich(mary))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((~kind(X)|~rich(X))))&
((~funny(paul)&old(paul)))&
(?[X]:((~calm(X)<~>wise(X)))) | ~kind(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 759332760986080317760266
% SZS output start Proof for 759332760986080317760266
11. ! [X0] : ((~funny(X0) | kind(X0)) <=> (~happy(X0) & ~kind(X0))) [input p10]
23. kind(john) [input hypothesis]
49. ! [X0] : (((~funny(X0) | kind(X0)) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | (funny(X0) & ~kind(X0)))) [nnf transformation 11]
50. ! [X0] : ((~funny(X0) | kind(X0) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | (funny(X0) & ~kind(X0)))) [flattening 49]
100. ~kind(X0) | ~kind(X0) [cnf transformation 50]
123. kind(john) [cnf transformation 23]
124. ~kind(X0) [duplicate literal removal 100]
225. $false [subsumption resolution 123,124]
% SZS output end Proof for 759332760986080317760266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not tall is both generous and brave and vice versa.
If mary is both not wise and old then fred is not happy and vice versa.
If someone is not kind then alice is both not quiet and not calm.
Everyone who is both not quiet and not strong is not patient or kind.
If lucy is not wise then someone is patient and vice versa.
Everyone who is both not patient and not happy is both funny and creative and vice versa.
Everyone who is not kind or calm is tall.
Everyone who is humble is not creative and vice versa.
Everyone who is not wise or not strong is either not creative or not strong.
If someone is both generous and not rich then someone is not humble or strong and vice versa.
If alice is both quiet and generous then alice is both not quiet and calm.
If alice is not patient then someone is not wise and vice versa.
Everyone who is not strong is both generous and not rich.
If mary is both curious and old then susan is either not wise or old and vice versa.
If someone is brave or old then alice is either patient or not kind and vice versa.
Everyone who is creative or not old is both not brave and not rich and vice versa.
Fred is not rich or tall.
Someone is either creative or not happy.
Someone is not quiet.
Paul is calm or not brave.
Someone is creative.
Someone is not strong or not tall.
Lucy is humble or quiet.
Mary is both patient and not quiet. | Alice is patient. | contradiction | (![X]:((~funny(X)|~tall(X))<=>(generous(X)&brave(X))))&
(((~wise(mary)&old(mary)))<=>(~happy(fred)))&
((?[X]:(~kind(X)))=>((~quiet(alice)&~calm(alice))))&
(![X]:((~quiet(X)&~strong(X))=>(~patient(X)|kind(X))))&
((~wise(lucy))<=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&~happy(X))<=>(funny(X)&creative(X))))&
(![X]:((~kind(X)|calm(X))=>tall(X)))&
(![X]:(humble(X)<=>~creative(X)))&
(![X]:((~wise(X)|~strong(X))=>(~creative(X)<~>~strong(X))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
(((quiet(alice)&generous(alice)))=>((~quiet(alice)&calm(alice))))&
((~patient(alice))<=>(?[X]:(~wise(X))))&
(![X]:(~strong(X)=>(generous(X)&~rich(X))))&
(((curious(mary)&old(mary)))<=>((~wise(susan)<~>old(susan))))&
((?[X]:((brave(X)|old(X))))<=>((patient(alice)<~>~kind(alice))))&
(![X]:((creative(X)|~old(X))<=>(~brave(X)&~rich(X))))&
((~rich(fred)|tall(fred)))&
(?[X]:((creative(X)<~>~happy(X))))&
(?[X]:(~quiet(X)))&
((calm(paul)|~brave(paul)))&
(?[X]:(creative(X)))&
(?[X]:((~strong(X)|~tall(X))))&
((humble(lucy)|quiet(lucy)))&
((patient(mary)&~quiet(mary))) | patient(alice) | [
"p4",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 9179012104781389244791585
% SZS output start Proof for 9179012104781389244791585
5. ~wise(lucy) <=> ? [X0] : patient(X0) [input p4]
12. ~patient(alice) <=> ? [X0] : ~wise(X0) [input p11]
24. ~quiet(mary) & patient(mary) [input p23]
25. patient(alice) [input hypothesis]
39. (~wise(lucy) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | wise(lucy)) [nnf transformation 5]
40. (~wise(lucy) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | wise(lucy)) [rectify 39]
41. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
42. (~wise(lucy) | ! [X0] : ~patient(X0)) & (patient(sK0) | wise(lucy)) [skolemisation 40,41]
52. (~patient(alice) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | patient(alice)) [nnf transformation 12]
53. (~patient(alice) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | patient(alice)) [rectify 52]
54. ? [X1] : ~wise(X1) => ~wise(sK3) [choice axiom]
55. (~patient(alice) | ! [X0] : wise(X0)) & (~wise(sK3) | patient(alice)) [skolemisation 53,54]
85. ~wise(lucy) | ~patient(X0) [cnf transformation 42]
106. ~patient(alice) | wise(X0) [cnf transformation 55]
134. patient(mary) [cnf transformation 24]
136. patient(alice) [cnf transformation 25]
168. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
169. ~patient(X0) <- (7) [avatar component clause 168]
171. 8 <=> wise(lucy) [avatar definition]
173. ~wise(lucy) <- (~8) [avatar component clause 171]
174. 7 | ~8 [avatar split clause 85,171,168]
217. 18 <=> ! [X0] : wise(X0) [avatar definition]
218. wise(X0) <- (18) [avatar component clause 217]
220. 19 <=> patient(alice) [avatar definition]
223. 18 | ~19 [avatar split clause 106,220,217]
317. 19 [avatar split clause 136,220]
320. $false <- (7) [resolution 169,134]
321. ~7 [avatar contradiction clause 320]
322. $false <- (~8, 18) [subsumption resolution 173,218]
323. 8 | ~18 [avatar contradiction clause 322]
324. $false [avatar sat refutation 174,223,317,321,323]
% SZS output end Proof for 9179012104781389244791585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not humble then someone is not brave or curious and vice versa.
If someone is creative then susan is either strong or calm and vice versa.
If someone is both not calm and rich then someone is not strong.
If alice is either rich or not humble then susan is not strong or not generous and vice versa.
If mary is both generous and kind then mary is happy or not calm.
If fred is creative then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Paul is both humble and not curious.
Fred is either not rich or humble.
Someone is both wise and not rich.
Fred is either patient or quiet. | John is not strong. | neutral | (((patient(lucy)|~humble(lucy)))<=>(?[X]:((~brave(X)|curious(X)))))&
((?[X]:(creative(X)))<=>((strong(susan)<~>calm(susan))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:(~strong(X))))&
(((rich(alice)<~>~humble(alice)))<=>((~strong(susan)|~generous(susan))))&
(((generous(mary)&kind(mary)))=>((happy(mary)|~calm(mary))))&
((creative(fred))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
((humble(paul)&~curious(paul)))&
((~rich(fred)<~>humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
((patient(fred)<~>quiet(fred))) | ~strong(john) | [] | null | 0 |
Everyone who is not strong or brave is quiet and vice versa.
If alice is either not strong or happy then someone is not kind.
Everyone who is either not tall or not brave is both not wise and not calm.
Everyone who is strong is not quiet or wise.
Everyone who is both not wise and not creative is both not patient and old.
If someone is patient then john is both calm and not kind.
Everyone who is creative is either funny or generous.
If someone is either old or not patient then lucy is not rich.
If mary is either not strong or quiet then john is kind.
If someone is creative then someone is both funny and rich.
Everyone who is not patient is quiet.
Everyone who is brave or not curious is both creative and not tall.
Everyone who is either not quiet or kind is either not humble or not creative and vice versa.
Everyone who is both not calm and brave is either quiet or wise and vice versa.
Everyone who is brave or not creative is strong and vice versa.
Everyone who is calm or happy is creative or curious.
Someone is funny or kind.
Someone is not patient.
Lucy is either strong or not brave.
Someone is kind or creative.
Someone is not patient or not humble. | Mary is not creative. | contradiction | (![X]:((~strong(X)|brave(X))<=>quiet(X)))&
(((~strong(alice)<~>happy(alice)))=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)<~>~brave(X))=>(~wise(X)&~calm(X))))&
(![X]:(strong(X)=>(~quiet(X)|wise(X))))&
(![X]:((~wise(X)&~creative(X))=>(~patient(X)&old(X))))&
((?[X]:(patient(X)))=>((calm(john)&~kind(john))))&
(![X]:(creative(X)=>(funny(X)<~>generous(X))))&
((?[X]:((old(X)<~>~patient(X))))=>(~rich(lucy)))&
(((~strong(mary)<~>quiet(mary)))=>(kind(john)))&
((?[X]:(creative(X)))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
(![X]:((brave(X)|~curious(X))=>(creative(X)&~tall(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~humble(X)<~>~creative(X))))&
(![X]:((~calm(X)&brave(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((brave(X)|~creative(X))<=>strong(X)))&
(![X]:((calm(X)|happy(X))=>(creative(X)|curious(X))))&
(?[X]:((funny(X)|kind(X))))&
(?[X]:(~patient(X)))&
((strong(lucy)<~>~brave(lucy)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~patient(X)|~humble(X)))) | ~creative(mary) | [
"p0",
"p4",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8913104441295432424288882
% SZS output start Proof for 8913104441295432424288882
1. ! [X0] : ((brave(X0) | ~strong(X0)) <=> quiet(X0)) [input p0]
5. ! [X0] : ((~creative(X0) & ~wise(X0)) => (old(X0) & ~patient(X0))) [input p4]
11. ! [X0] : (~patient(X0) => quiet(X0)) [input p10]
12. ! [X0] : ((~curious(X0) | brave(X0)) => (~tall(X0) & creative(X0))) [input p11]
14. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (quiet(X0) <~> wise(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | brave(X0)) <=> strong(X0)) [input p14]
22. ~creative(mary) [input hypothesis]
25. ! [X0] : (brave(X0) => (~tall(X0) & creative(X0))) [pure predicate removal 12]
30. ! [X0] : ((old(X0) & ~patient(X0)) | (creative(X0) | wise(X0))) [ennf transformation 5]
31. ! [X0] : ((old(X0) & ~patient(X0)) | creative(X0) | wise(X0)) [flattening 30]
37. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 11]
38. ! [X0] : ((~tall(X0) & creative(X0)) | ~brave(X0)) [ennf transformation 25]
39. ! [X0] : (((brave(X0) | ~strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 1]
40. ! [X0] : ((brave(X0) | ~strong(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & strong(X0)))) [flattening 39]
52. ! [X0] : (((brave(X0) & ~calm(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~brave(X0) | calm(X0)))) [nnf transformation 14]
53. ! [X0] : (((brave(X0) & ~calm(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~brave(X0) | calm(X0))) [flattening 52]
54. ! [X0] : (((~creative(X0) | brave(X0)) | ~strong(X0)) & (strong(X0) | (creative(X0) & ~brave(X0)))) [nnf transformation 15]
55. ! [X0] : ((~creative(X0) | brave(X0) | ~strong(X0)) & (strong(X0) | (creative(X0) & ~brave(X0)))) [flattening 54]
66. ~brave(X0) | quiet(X0) [cnf transformation 40]
67. ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 40]
75. ~patient(X0) | creative(X0) | wise(X0) [cnf transformation 31]
87. patient(X0) | quiet(X0) [cnf transformation 37]
88. ~brave(X0) | creative(X0) [cnf transformation 38]
103. brave(X0) | quiet(X0) | ~wise(X0) [cnf transformation 53]
105. creative(X0) | strong(X0) [cnf transformation 55]
113. ~creative(mary) [cnf transformation 22]
154. 10 <=> quiet(mary) [avatar definition]
155. quiet(mary) <- (10) [avatar component clause 154]
158. 11 <=> strong(mary) [avatar definition]
159. strong(mary) <- (11) [avatar component clause 158]
160. ~strong(mary) <- (~11) [avatar component clause 158]
175. ~wise(X0) | quiet(X0) [subsumption resolution 103,66]
215. strong(mary) [resolution 105,113]
217. $false <- (~11) [subsumption resolution 215,160]
218. 11 [avatar contradiction clause 217]
242. creative(X0) | wise(X0) | quiet(X0) [resolution 75,87]
243. creative(X0) | quiet(X0) [subsumption resolution 242,175]
244. quiet(mary) [resolution 243,113]
247. 10 [avatar split clause 244,154]
250. ~strong(mary) | brave(mary) <- (10) [resolution 155,67]
252. brave(mary) <- (10, 11) [subsumption resolution 250,159]
262. creative(mary) <- (10, 11) [resolution 252,88]
264. $false <- (10, 11) [subsumption resolution 262,113]
265. ~10 | ~11 [avatar contradiction clause 264]
266. $false [avatar sat refutation 218,247,265]
% SZS output end Proof for 8913104441295432424288882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then john is not creative or patient.
Everyone who is patient is calm and vice versa.
If john is patient or humble then john is not patient.
If paul is either humble or not patient then someone is not calm.
If john is either not happy or rich then someone is old or not strong and vice versa.
Everyone who is not quiet or not happy is both not funny and rich and vice versa.
Everyone who is either not quiet or calm is both kind and not brave and vice versa.
Everyone who is either old or not strong is both patient and not happy and vice versa.
Everyone who is both not curious and rich is not strong.
Everyone who is both not calm and not quiet is both calm and not creative.
Everyone who is both not calm and curious is not funny or not quiet and vice versa.
If someone is not creative or strong then fred is quiet or humble.
If mary is either humble or happy then someone is not happy or humble and vice versa.
Everyone who is either quiet or tall is either not tall or brave and vice versa.
Everyone who is quiet or not rich is both quiet and not wise.
Someone is kind or funny.
Someone is rich or not kind.
Susan is not happy.
Someone is either strong or not tall.
Someone is either generous or not quiet.
Susan is not rich or old.
Mary is not kind or not tall. | John is happy. | entailment | ((?[X]:(~humble(X)))=>((~creative(john)|patient(john))))&
(![X]:(patient(X)<=>calm(X)))&
(((patient(john)|humble(john)))=>(~patient(john)))&
(((humble(paul)<~>~patient(paul)))=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)|~kind(X))))&
(~happy(susan))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | happy(john) | [
"p4",
"p5",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3657533957663582085866141
% SZS output start Proof for 3657533957663582085866141
5. (~happy(john) <~> rich(john)) <=> ? [X0] : (~strong(X0) | old(X0)) [input p4]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (rich(X0) & ~funny(X0))) [input p5]
18. ~happy(susan) [input p17]
21. old(susan) | ~rich(susan) [input p20]
23. ~happy(john) [input hypothesis]
40. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & (? [X0] : (~strong(X0) | old(X0)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [nnf transformation 5]
41. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & (? [X1] : (~strong(X1) | old(X1)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [rectify 40]
42. ? [X1] : (~strong(X1) | old(X1)) => (~strong(sK1) | old(sK1)) [choice axiom]
43. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & ((~strong(sK1) | old(sK1)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [skolemisation 41,42]
44. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
45. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [flattening 44]
78. ~rich(john) | happy(john) | ~old(X0) [cnf transformation 43]
83. rich(X0) | happy(X0) [cnf transformation 45]
125. ~happy(susan) [cnf transformation 18]
130. old(susan) | ~rich(susan) [cnf transformation 21]
132. ~happy(john) [cnf transformation 23]
175. 9 <=> happy(john) [avatar definition]
176. ~happy(john) <- (~9) [avatar component clause 175]
179. 10 <=> rich(john) [avatar definition]
181. ~rich(john) <- (~10) [avatar component clause 179]
184. 11 <=> ! [X0] : ~old(X0) [avatar definition]
185. ~old(X0) <- (11) [avatar component clause 184]
186. 11 | 9 | ~10 [avatar split clause 78,179,175,184]
262. 26 <=> rich(susan) [avatar definition]
264. ~rich(susan) <- (~26) [avatar component clause 262]
266. 27 <=> old(susan) [avatar definition]
268. old(susan) <- (27) [avatar component clause 266]
269. ~26 | 27 [avatar split clause 130,266,262]
279. ~9 [avatar split clause 132,175]
280. happy(john) <- (~10) [resolution 83,181]
281. happy(susan) <- (~26) [resolution 83,264]
282. $false <- (~9, ~10) [subsumption resolution 280,176]
283. 9 | 10 [avatar contradiction clause 282]
284. $false <- (~26) [subsumption resolution 281,125]
285. 26 [avatar contradiction clause 284]
290. $false <- (11, 27) [resolution 268,185]
291. ~11 | ~27 [avatar contradiction clause 290]
292. $false [avatar sat refutation 186,269,279,283,285,291]
% SZS output end Proof for 3657533957663582085866141
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is happy then someone is either not creative or tall.
Everyone who is not happy is rich and vice versa.
If someone is either not creative or curious then someone is not generous or curious and vice versa.
If someone is strong or not rich then fred is either not wise or not happy and vice versa.
If lucy is rich then paul is either not calm or curious.
If fred is both calm and not creative then alice is either generous or not patient and vice versa.
Everyone who is both not rich and not patient is not brave or not curious and vice versa.
If john is either patient or tall then mary is happy or rich.
If lucy is both humble and not wise then paul is not kind or not wise.
Everyone who is funny or creative is both creative and not humble and vice versa.
If someone is either not tall or not rich then someone is either tall or patient.
If someone is generous then john is either not funny or rich.
If john is both kind and not creative then fred is both not generous and creative.
Everyone who is strong is both not patient and wise and vice versa.
Everyone who is not patient or not kind is both humble and not creative.
Everyone who is quiet or creative is not brave or happy and vice versa.
Paul is creative.
Someone is either generous or not tall.
Someone is both wise and not curious.
Fred is not strong or curious.
Mary is not brave.
Alice is not brave.
Someone is not creative. | Paul is strong. | contradiction | ((happy(fred))=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:(~happy(X)<=>rich(X)))&
((?[X]:((~creative(X)<~>curious(X))))<=>(?[X]:((~generous(X)|curious(X)))))&
((?[X]:((strong(X)|~rich(X))))<=>((~wise(fred)<~>~happy(fred))))&
((rich(lucy))=>((~calm(paul)<~>curious(paul))))&
(((calm(fred)&~creative(fred)))<=>((generous(alice)<~>~patient(alice))))&
(![X]:((~rich(X)&~patient(X))<=>(~brave(X)|~curious(X))))&
(((patient(john)<~>tall(john)))=>((happy(mary)|rich(mary))))&
(((humble(lucy)&~wise(lucy)))=>((~kind(paul)|~wise(paul))))&
(![X]:((funny(X)|creative(X))<=>(creative(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
((?[X]:(generous(X)))=>((~funny(john)<~>rich(john))))&
(((kind(john)&~creative(john)))=>((~generous(fred)&creative(fred))))&
(![X]:(strong(X)<=>(~patient(X)&wise(X))))&
(![X]:((~patient(X)|~kind(X))=>(humble(X)&~creative(X))))&
(![X]:((quiet(X)|creative(X))<=>(~brave(X)|happy(X))))&
(creative(paul))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((wise(X)&~curious(X))))&
((~strong(fred)|curious(fred)))&
(~brave(mary))&
(~brave(alice))&
(?[X]:(~creative(X))) | strong(paul) | [
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3146579772140946745652884
% SZS output start Proof for 3146579772140946745652884
14. ! [X0] : (strong(X0) <=> (wise(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~kind(X0) | ~patient(X0)) => (~creative(X0) & humble(X0))) [input p14]
17. creative(paul) [input p16]
24. strong(paul) [input hypothesis]
37. ! [X0] : ((~creative(X0) & humble(X0)) | (kind(X0) & patient(X0))) [ennf transformation 15]
64. ! [X0] : ((strong(X0) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | ~strong(X0))) [nnf transformation 14]
65. ! [X0] : ((strong(X0) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ~strong(X0))) [flattening 64]
120. ~patient(X0) | ~strong(X0) [cnf transformation 65]
125. ~creative(X0) | patient(X0) [cnf transformation 37]
131. creative(paul) [cnf transformation 17]
140. strong(paul) [cnf transformation 24]
349. patient(paul) [resolution 125,131]
350. ~strong(paul) [resolution 349,120]
353. $false [subsumption resolution 350,140]
% SZS output end Proof for 3146579772140946745652884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and calm is not funny or not humble and vice versa.
Everyone who is generous or not patient is either quiet or not funny and vice versa.
If someone is either not quiet or not funny then alice is either not generous or not creative.
If someone is wise or not calm then someone is generous.
Everyone who is both not patient and humble is either funny or not kind and vice versa.
If someone is tall or not quiet then someone is both old and not curious.
Everyone who is both not calm and not quiet is either not happy or not strong and vice versa.
If paul is patient then alice is not patient.
If john is both strong and not patient then someone is curious or brave and vice versa.
Everyone who is not strong or creative is both not curious and rich and vice versa.
If mary is either funny or not curious then someone is happy or not creative and vice versa.
Everyone who is both kind and not funny is not kind.
Everyone who is not curious or not calm is humble.
If someone is either generous or brave then alice is both not generous and brave and vice versa.
Everyone who is not funny or happy is both not creative and brave and vice versa.
Someone is not creative.
Someone is both wise and strong.
Alice is either not tall or patient.
Someone is either strong or funny.
Someone is either brave or not generous.
Alice is both not curious and generous.
Alice is either not humble or not wise. | John is not generous. | contradiction | (![X]:((~calm(X)&calm(X))<=>(~funny(X)|~humble(X))))&
(![X]:((generous(X)|~patient(X))<=>(quiet(X)<~>~funny(X))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>((~generous(alice)<~>~creative(alice))))&
((?[X]:((wise(X)|~calm(X))))=>(?[X]:(generous(X))))&
(![X]:((~patient(X)&humble(X))<=>(funny(X)<~>~kind(X))))&
((?[X]:((tall(X)|~quiet(X))))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(~happy(X)<~>~strong(X))))&
((patient(paul))=>(~patient(alice)))&
(((strong(john)&~patient(john)))<=>(?[X]:((curious(X)|brave(X)))))&
(![X]:((~strong(X)|creative(X))<=>(~curious(X)&rich(X))))&
(((funny(mary)<~>~curious(mary)))<=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((kind(X)&~funny(X))=>~kind(X)))&
(![X]:((~curious(X)|~calm(X))=>humble(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>((~generous(alice)&brave(alice))))&
(![X]:((~funny(X)|happy(X))<=>(~creative(X)&brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((wise(X)&strong(X))))&
((~tall(alice)<~>patient(alice)))&
(?[X]:((strong(X)<~>funny(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
((~curious(alice)&generous(alice)))&
((~humble(alice)<~>~wise(alice))) | ~generous(john) | [
"p0",
"p1",
"p6",
"p8",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2712742163666320022154697
% SZS output start Proof for 2712742163666320022154697
1. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~humble(X0) | ~funny(X0))) [input p0]
2. ! [X0] : ((~patient(X0) | generous(X0)) <=> (quiet(X0) <~> ~funny(X0))) [input p1]
7. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> (~happy(X0) <~> ~strong(X0))) [input p6]
9. (~patient(john) & strong(john)) <=> ? [X0] : (brave(X0) | curious(X0)) [input p8]
14. ? [X0] : (generous(X0) <~> brave(X0)) <=> (brave(alice) & ~generous(alice)) [input p13]
15. ! [X0] : ((happy(X0) | ~funny(X0)) <=> (brave(X0) & ~creative(X0))) [input p14]
21. generous(alice) & ~curious(alice) [input p20]
23. ~generous(john) [input hypothesis]
34. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & ((~humble(X0) | ~funny(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 1]
35. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & (~humble(X0) | ~funny(X0) | ~calm(X0) | calm(X0))) [flattening 34]
36. ! [X0] : (((~patient(X0) | generous(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (patient(X0) & ~generous(X0)))) [nnf transformation 2]
37. ! [X0] : ((~patient(X0) | generous(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (patient(X0) & ~generous(X0)))) [flattening 36]
47. ! [X0] : (((~quiet(X0) & ~calm(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | (quiet(X0) | calm(X0)))) [nnf transformation 7]
48. ! [X0] : (((~quiet(X0) & ~calm(X0)) | ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0)))) & (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | quiet(X0) | calm(X0))) [flattening 47]
49. ((~patient(john) & strong(john)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X0] : (brave(X0) | curious(X0)) | (patient(john) | ~strong(john))) [nnf transformation 9]
50. ((~patient(john) & strong(john)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X0] : (brave(X0) | curious(X0)) | patient(john) | ~strong(john)) [flattening 49]
51. ((~patient(john) & strong(john)) | ! [X0] : (~brave(X0) & ~curious(X0))) & (? [X1] : (brave(X1) | curious(X1)) | patient(john) | ~strong(john)) [rectify 50]
52. ? [X1] : (brave(X1) | curious(X1)) => (brave(sK2) | curious(sK2)) [choice axiom]
53. ((~patient(john) & strong(john)) | ! [X0] : (~brave(X0) & ~curious(X0))) & ((brave(sK2) | curious(sK2)) | patient(john) | ~strong(john)) [skolemisation 51,52]
60. (? [X0] : ((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | (~brave(alice) | generous(alice))) & ((brave(alice) & ~generous(alice)) | ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0)))) [nnf transformation 14]
61. (? [X0] : ((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | ~brave(alice) | generous(alice)) & ((brave(alice) & ~generous(alice)) | ! [X0] : ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0)))) [flattening 60]
62. (? [X0] : ((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | ~brave(alice) | generous(alice)) & ((brave(alice) & ~generous(alice)) | ! [X1] : ((generous(X1) | ~brave(X1)) & (brave(X1) | ~generous(X1)))) [rectify 61]
63. ? [X0] : ((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) => ((~brave(sK4) | ~generous(sK4)) & (brave(sK4) | generous(sK4))) [choice axiom]
64. (((~brave(sK4) | ~generous(sK4)) & (brave(sK4) | generous(sK4))) | ~brave(alice) | generous(alice)) & ((brave(alice) & ~generous(alice)) | ! [X1] : ((generous(X1) | ~brave(X1)) & (brave(X1) | ~generous(X1)))) [skolemisation 62,63]
65. ! [X0] : (((happy(X0) | ~funny(X0)) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | (~happy(X0) & funny(X0)))) [nnf transformation 15]
66. ! [X0] : ((happy(X0) | ~funny(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | (~happy(X0) & funny(X0)))) [flattening 65]
80. ~calm(X0) | funny(X0) [cnf transformation 35]
82. funny(X0) | calm(X0) [cnf transformation 35]
85. ~funny(X0) | quiet(X0) | patient(X0) [cnf transformation 37]
108. ~strong(X0) | ~quiet(X0) | happy(X0) [cnf transformation 48]
113. strong(john) | ~brave(X0) [cnf transformation 53]
115. ~patient(john) | ~brave(X0) [cnf transformation 53]
130. ~generous(alice) | brave(X1) | ~generous(X1) [cnf transformation 64]
131. ~generous(alice) | generous(X1) | ~brave(X1) [cnf transformation 64]
139. ~happy(X0) | brave(X0) [cnf transformation 66]
151. generous(alice) [cnf transformation 21]
154. ~generous(john) [cnf transformation 23]
157. funny(X0) [subsumption resolution 80,82]
159. quiet(X0) | patient(X0) [subsumption resolution 85,157]
166. 2 <=> generous(alice) [avatar definition]
168. generous(alice) <- (2) [avatar component clause 166]
210. 11 <=> ! [X0] : ~brave(X0) [avatar definition]
211. ~brave(X0) <- (11) [avatar component clause 210]
213. 12 <=> patient(john) [avatar definition]
215. ~patient(john) <- (~12) [avatar component clause 213]
216. 11 | ~12 [avatar split clause 115,213,210]
222. 14 <=> strong(john) [avatar definition]
224. strong(john) <- (14) [avatar component clause 222]
225. 11 | 14 [avatar split clause 113,222,210]
275. 25 <=> ! [X1] : (generous(X1) | ~brave(X1)) [avatar definition]
276. ~brave(X1) | generous(X1) <- (25) [avatar component clause 275]
279. 26 <=> ! [X1] : (brave(X1) | ~generous(X1)) [avatar definition]
280. ~generous(X1) | brave(X1) <- (26) [avatar component clause 279]
282. 25 | ~2 [avatar split clause 131,166,275]
283. 26 | ~2 [avatar split clause 130,166,279]
302. 2 [avatar split clause 151,166]
313. brave(alice) <- (2, 26) [resolution 280,168]
315. $false <- (2, 11, 26) [subsumption resolution 313,211]
316. ~2 | ~11 | ~26 [avatar contradiction clause 315]
327. 30 <=> happy(john) [avatar definition]
329. happy(john) <- (30) [avatar component clause 327]
362. ~quiet(john) | happy(john) <- (14) [resolution 108,224]
367. 38 <=> quiet(john) [avatar definition]
369. ~quiet(john) <- (~38) [avatar component clause 367]
370. 30 | ~38 | ~14 [avatar split clause 362,222,367,327]
386. patient(john) <- (~38) [resolution 369,159]
387. $false <- (~12, ~38) [subsumption resolution 386,215]
388. 12 | 38 [avatar contradiction clause 387]
391. brave(john) <- (30) [resolution 329,139]
452. generous(john) <- (25, 30) [resolution 391,276]
453. $false <- (25, 30) [subsumption resolution 452,154]
454. ~25 | ~30 [avatar contradiction clause 453]
455. $false [avatar sat refutation 216,225,282,283,302,316,370,388,454]
% SZS output end Proof for 2712742163666320022154697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both quiet and kind is either not tall or brave and vice versa. If lucy is both not wise and not kind then someone is both creative and not strong. Everyone who is both not happy and not strong is not funny or not brave and vice versa. Everyone who is both humble and not patient is not kind and vice versa. If someone is wise or not humble then someone is quiet. If john is either brave or not rich then lucy is funny or happy. If john is both humble and not curious then someone is calm or not tall. If someone is patient or not quiet then someone is funny or not patient. If someone is both curious and not humble then someone is both calm and not old. Everyone who is funny or not humble is both not creative and strong. Everyone who is either not funny or patient is patient or quiet and vice versa. If someone is both not strong and not old then someone is brave or funny. Everyone who is either not strong or funny is both kind and brave. Everyone who is both quiet and not rich is both happy and tall. If someone is either not tall or not generous then someone is old and vice versa. If someone is not funny then fred is not kind or creative and vice versa. Someone is both old and not creative. Someone is both not wise and happy. Someone is either humble or not rich. Someone is either not brave or old. Fred is not humble or old. Someone is either not brave or happy. Someone is kind or brave. | Fred is not creative. | entailment | (![X]:((quiet(X)&kind(X))<=>(~tall(X)<~>brave(X))))&
(((~wise(lucy)&~kind(lucy)))=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((~happy(X)&~strong(X))<=>(~funny(X)|~brave(X))))&
(![X]:((humble(X)&~patient(X))<=>~kind(X)))&
((?[X]:((wise(X)|~humble(X))))=>(?[X]:(quiet(X))))&
(((brave(john)<~>~rich(john)))=>((funny(lucy)|happy(lucy))))&
(((humble(john)&~curious(john)))=>(?[X]:((calm(X)|~tall(X)))))&
((?[X]:((patient(X)|~quiet(X))))=>(?[X]:((funny(X)|~patient(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((funny(X)|~humble(X))=>(~creative(X)&strong(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(patient(X)|quiet(X))))&
((?[X]:((~strong(X)&~old(X))))=>(?[X]:((brave(X)|funny(X)))))&
(![X]:((~strong(X)<~>funny(X))=>(kind(X)&brave(X))))&
(![X]:((quiet(X)&~rich(X))=>(happy(X)&tall(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:(old(X))))&
((?[X]:(~funny(X)))<=>((~kind(fred)|creative(fred))))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:((~wise(X)&happy(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((~brave(X)<~>old(X))))&
((~humble(fred)|old(fred)))&
(?[X]:((~brave(X)<~>happy(X))))&
(?[X]:((kind(X)|brave(X)))) | ~creative(fred) | [
"p2",
"p3",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3586660946537670656306790
% SZS output start Proof for 3586660946537670656306790
3. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (~brave(X0) | ~funny(X0))) [input p2]
4. ! [X0] : ((~patient(X0) & humble(X0)) <=> ~kind(X0)) [input p3]
10. ! [X0] : ((~humble(X0) | funny(X0)) => (strong(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((~funny(X0) <~> patient(X0)) <=> (quiet(X0) | patient(X0))) [input p10]
13. ! [X0] : ((~strong(X0) <~> funny(X0)) => (brave(X0) & kind(X0))) [input p12]
24. creative(fred) [input hypothesis]
39. ! [X0] : ((strong(X0) & ~creative(X0)) | (humble(X0) & ~funny(X0))) [ennf transformation 10]
41. ! [X0] : ((brave(X0) & kind(X0)) | (~strong(X0) <=> funny(X0))) [ennf transformation 13]
48. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | (strong(X0) | happy(X0)))) [nnf transformation 3]
49. ! [X0] : (((~strong(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | strong(X0) | happy(X0))) [flattening 48]
50. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | (patient(X0) | ~humble(X0)))) [nnf transformation 4]
51. ! [X0] : (((~patient(X0) & humble(X0)) | kind(X0)) & (~kind(X0) | patient(X0) | ~humble(X0))) [flattening 50]
59. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [nnf transformation 11]
60. ! [X0] : ((((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0))))) [flattening 59]
64. ! [X0] : ((brave(X0) & kind(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0)))) [nnf transformation 41]
101. ~strong(X0) | funny(X0) [cnf transformation 49]
103. ~humble(X0) | patient(X0) | ~kind(X0) [cnf transformation 51]
112. ~funny(X0) | ~creative(X0) [cnf transformation 39]
113. ~creative(X0) | humble(X0) [cnf transformation 39]
114. ~funny(X0) | strong(X0) [cnf transformation 39]
120. ~patient(X0) | funny(X0) | ~patient(X0) [cnf transformation 60]
123. kind(X0) | funny(X0) | strong(X0) [cnf transformation 64]
124. kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 64]
148. creative(fred) [cnf transformation 24]
150. ~patient(X0) | funny(X0) [duplicate literal removal 120]
227. ~funny(X0) | kind(X0) [subsumption resolution 124,114]
228. kind(X0) | funny(X0) [subsumption resolution 123,101]
229. kind(X0) [subsumption resolution 228,227]
256. 24 <=> creative(fred) [avatar definition]
257. creative(fred) <- (24) [avatar component clause 256]
290. 31 <=> humble(fred) [avatar definition]
291. humble(fred) <- (31) [avatar component clause 290]
307. 24 [avatar split clause 148,256]
316. humble(fred) <- (24) [resolution 113,257]
319. 31 | ~24 [avatar split clause 316,256,290]
375. patient(fred) | ~kind(fred) <- (31) [resolution 103,291]
377. patient(fred) <- (31) [subsumption resolution 375,229]
378. funny(fred) <- (31) [resolution 377,150]
415. ~creative(fred) <- (31) [resolution 378,112]
416. $false <- (24, 31) [subsumption resolution 415,257]
417. ~24 | ~31 [avatar contradiction clause 416]
418. $false [avatar sat refutation 307,319,417]
% SZS output end Proof for 3586660946537670656306790
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or generous then someone is not wise or not humble and vice versa.
If someone is both brave and not quiet then paul is happy or wise and vice versa.
Everyone who is both not funny and happy is not funny and vice versa.
Everyone who is old or kind is brave or funny.
If mary is either not happy or not funny then fred is not funny or old.
If someone is either curious or not happy then john is wise or not happy and vice versa.
Everyone who is not humble or not strong is generous or not tall and vice versa.
Everyone who is either not strong or not old is either tall or happy.
Everyone who is both brave and not kind is either not brave or generous and vice versa.
Everyone who is either tall or patient is both not old and not funny and vice versa.
Everyone who is either creative or not wise is patient.
If someone is not happy then someone is both not tall and not wise and vice versa.
If mary is not funny then mary is either not kind or strong and vice versa.
If mary is either not kind or patient then someone is either not quiet or not wise and vice versa.
Everyone who is not brave is curious or not tall and vice versa.
Everyone who is calm or old is both humble and not rich and vice versa.
Mary is either not generous or quiet.
Lucy is curious or not kind.
Someone is both kind and not rich.
Someone is both not brave and not quiet.
Alice is not patient or creative.
Alice is not brave or curious.
Someone is both wise and old.
Fred is not funny. | Lucy is not old. | neutral | ((?[X]:((~wise(X)|generous(X))))<=>(?[X]:((~wise(X)|~humble(X)))))&
((?[X]:((brave(X)&~quiet(X))))<=>((happy(paul)|wise(paul))))&
(![X]:((~funny(X)&happy(X))<=>~funny(X)))&
(![X]:((old(X)|kind(X))=>(brave(X)|funny(X))))&
(((~happy(mary)<~>~funny(mary)))=>((~funny(fred)|old(fred))))&
((?[X]:((curious(X)<~>~happy(X))))<=>((wise(john)|~happy(john))))&
(![X]:((~humble(X)|~strong(X))<=>(generous(X)|~tall(X))))&
(![X]:((~strong(X)<~>~old(X))=>(tall(X)<~>happy(X))))&
(![X]:((brave(X)&~kind(X))<=>(~brave(X)<~>generous(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~old(X)&~funny(X))))&
(![X]:((creative(X)<~>~wise(X))=>patient(X)))&
((?[X]:(~happy(X)))<=>(?[X]:((~tall(X)&~wise(X)))))&
((~funny(mary))<=>((~kind(mary)<~>strong(mary))))&
(((~kind(mary)<~>patient(mary)))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:(~brave(X)<=>(curious(X)|~tall(X))))&
(![X]:((calm(X)|old(X))<=>(humble(X)&~rich(X))))&
((~generous(mary)<~>quiet(mary)))&
((curious(lucy)|~kind(lucy)))&
(?[X]:((kind(X)&~rich(X))))&
(?[X]:((~brave(X)&~quiet(X))))&
((~patient(alice)|creative(alice)))&
((~brave(alice)|curious(alice)))&
(?[X]:((wise(X)&old(X))))&
(~funny(fred)) | ~old(lucy) | [] | null | 0 |
Everyone who is both not quiet and not strong is not wise and vice versa. Everyone who is either not rich or not quiet is both brave and curious. Everyone who is creative or patient is either not quiet or not brave and vice versa. Everyone who is not generous is not kind or not creative and vice versa. Everyone who is either not patient or not creative is creative and vice versa. Everyone who is both curious and not quiet is wise and vice versa. Everyone who is not rich or creative is both old and rich and vice versa. Everyone who is either patient or strong is not humble and vice versa. Everyone who is not calm is either not kind or not rich and vice versa. If someone is not tall then susan is old or not happy. Everyone who is rich is old. Everyone who is both not brave and patient is not quiet or not patient. Everyone who is either not strong or rich is brave or calm. Everyone who is calm or not brave is not brave or funny and vice versa. If someone is both not tall and not creative then someone is either wise or funny and vice versa. If someone is both creative and not generous then john is both not creative and not tall and vice versa. Someone is either not creative or generous. Someone is both not patient and happy. Lucy is not patient. Someone is both rich and happy. John is not quiet or not brave. Someone is strong. | Susan is quiet. | contradiction | (![X]:((~quiet(X)&~strong(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~quiet(X))=>(brave(X)&curious(X))))&
(![X]:((creative(X)|patient(X))<=>(~quiet(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~creative(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>creative(X)))&
(![X]:((curious(X)&~quiet(X))<=>wise(X)))&
(![X]:((~rich(X)|creative(X))<=>(old(X)&rich(X))))&
(![X]:((patient(X)<~>strong(X))<=>~humble(X)))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
((?[X]:(~tall(X)))=>((old(susan)|~happy(susan))))&
(![X]:(rich(X)=>old(X)))&
(![X]:((~brave(X)&patient(X))=>(~quiet(X)|~patient(X))))&
(![X]:((~strong(X)<~>rich(X))=>(brave(X)|calm(X))))&
(![X]:((calm(X)|~brave(X))<=>(~brave(X)|funny(X))))&
((?[X]:((~tall(X)&~creative(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((creative(X)&~generous(X))))<=>((~creative(john)&~tall(john))))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:((~patient(X)&happy(X))))&
(~patient(lucy))&
(?[X]:((rich(X)&happy(X))))&
((~quiet(john)|~brave(john)))&
(?[X]:(strong(X))) | quiet(susan) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7716412403197455558160301
% SZS output start Proof for 7716412403197455558160301
1. ! [X0] : ((~strong(X0) & ~quiet(X0)) <=> ~wise(X0)) [input p0]
6. ! [X0] : ((~quiet(X0) & curious(X0)) <=> wise(X0)) [input p5]
23. quiet(susan) [input hypothesis]
33. ! [X0] : (((~strong(X0) & ~quiet(X0)) | wise(X0)) & (~wise(X0) | (strong(X0) | quiet(X0)))) [nnf transformation 1]
34. ! [X0] : (((~strong(X0) & ~quiet(X0)) | wise(X0)) & (~wise(X0) | strong(X0) | quiet(X0))) [flattening 33]
41. ! [X0] : (((~quiet(X0) & curious(X0)) | ~wise(X0)) & (wise(X0) | (quiet(X0) | ~curious(X0)))) [nnf transformation 6]
42. ! [X0] : (((~quiet(X0) & curious(X0)) | ~wise(X0)) & (wise(X0) | quiet(X0) | ~curious(X0))) [flattening 41]
69. ~quiet(X0) | wise(X0) [cnf transformation 34]
90. ~quiet(X0) | ~wise(X0) [cnf transformation 42]
128. quiet(susan) [cnf transformation 23]
135. ~quiet(X0) [subsumption resolution 90,69]
216. $false [subsumption resolution 128,135]
% SZS output end Proof for 7716412403197455558160301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not wise is not tall or not strong and vice versa.
If paul is not wise or tall then fred is not strong.
Everyone who is rich or not strong is not brave or not kind and vice versa.
Everyone who is not kind or patient is both not brave and not tall.
Everyone who is creative is rich and vice versa.
If alice is rich then mary is both patient and not happy and vice versa.
Everyone who is not kind is funny or creative.
If susan is not happy then someone is both not happy and not kind.
Everyone who is not generous or not calm is either funny or patient and vice versa.
Everyone who is both quiet and not tall is both generous and not wise and vice versa.
Everyone who is not curious or not generous is generous.
Everyone who is either creative or not happy is old or happy.
Everyone who is both not curious and not funny is not patient or happy and vice versa.
Everyone who is either not old or not funny is both kind and not strong and vice versa.
Everyone who is quiet is generous and vice versa.
If fred is either creative or not wise then someone is both brave and not patient.
Susan is not humble.
Someone is humble or brave.
Someone is wise.
Someone is either not rich or rich.
Paul is both strong and not kind.
Someone is not brave or calm. | Paul is generous. | entailment | (![X]:((~patient(X)&~wise(X))<=>(~tall(X)|~strong(X))))&
(((~wise(paul)|tall(paul)))=>(~strong(fred)))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | generous(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1272404427803069556873733
% SZS output start Proof for 1272404427803069556873733
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p10]
23. ~generous(paul) [input hypothesis]
29. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
98. generous(X0) | generous(X0) [cnf transformation 29]
126. ~generous(paul) [cnf transformation 23]
128. generous(X0) [duplicate literal removal 98]
210. $false [subsumption resolution 126,128]
% SZS output end Proof for 1272404427803069556873733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is happy then someone is brave.
Everyone who is humble is wise or not happy and vice versa.
Everyone who is rich or curious is both generous and not creative and vice versa.
Everyone who is either not wise or not humble is either curious or not funny and vice versa.
Everyone who is both rich and creative is either quiet or not happy.
Everyone who is both not rich and calm is both not kind and not humble and vice versa.
If paul is not curious then someone is either rich or not tall.
Everyone who is either not happy or not kind is not quiet.
If someone is not creative or not wise then fred is both wise and not rich and vice versa.
If someone is not generous then someone is funny and vice versa.
Everyone who is funny is either quiet or funny.
If john is not humble then john is curious or not curious and vice versa.
Everyone who is either old or strong is both not curious and not patient and vice versa.
Everyone who is either quiet or not wise is not rich and vice versa.
If mary is not tall or not funny then someone is quiet or tall and vice versa.
Someone is not happy.
Mary is rich or happy.
Fred is not old.
Someone is both happy and rich.
Someone is both not happy and old.
Paul is either rich or not patient. | Paul is not happy. | neutral | ((happy(mary))=>(?[X]:(brave(X))))&
(![X]:(humble(X)<=>(wise(X)|~happy(X))))&
(![X]:((rich(X)|curious(X))<=>(generous(X)&~creative(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((rich(X)&creative(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((~rich(X)&calm(X))<=>(~kind(X)&~humble(X))))&
((~curious(paul))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>~kind(X))=>~quiet(X)))&
((?[X]:((~creative(X)|~wise(X))))<=>((wise(fred)&~rich(fred))))&
((?[X]:(~generous(X)))<=>(?[X]:(funny(X))))&
(![X]:(funny(X)=>(quiet(X)<~>funny(X))))&
((~humble(john))<=>((curious(john)|~curious(john))))&
(![X]:((old(X)<~>strong(X))<=>(~curious(X)&~patient(X))))&
(![X]:((quiet(X)<~>~wise(X))<=>~rich(X)))&
(((~tall(mary)|~funny(mary)))<=>(?[X]:((quiet(X)|tall(X)))))&
(?[X]:(~happy(X)))&
((rich(mary)|happy(mary)))&
(~old(fred))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:((~happy(X)&old(X))))&
((rich(paul)<~>~patient(paul))) | ~happy(paul) | [] | null | 0 |
Everyone who is not strong is both humble and not calm. Everyone who is not happy is creative or not wise and vice versa. If someone is not brave then lucy is not kind. Everyone who is either wise or curious is both not wise and not patient. If mary is either kind or not old then someone is calm or strong and vice versa. Everyone who is either brave or rich is both not old and funny. If lucy is both not generous and not old then someone is not tall. If paul is not creative then someone is tall or not funny and vice versa. Everyone who is humble or calm is either rich or happy and vice versa. If mary is wise or not quiet then lucy is both not quiet and rich and vice versa. Everyone who is humble or not kind is not rich. Everyone who is not humble is either quiet or not kind and vice versa. Everyone who is both not humble and not brave is not old and vice versa. If john is both calm and kind then someone is old and vice versa. Everyone who is both humble and patient is both not generous and quiet and vice versa. If someone is not brave then someone is both brave and not wise. Someone is both rich and not humble. Lucy is either not creative or not funny. Lucy is strong. Someone is not curious or patient. Lucy is brave. Someone is not curious or tall. | Lucy is generous. | entailment | (![X]:(~strong(X)=>(humble(X)&~calm(X))))&
(![X]:(~happy(X)<=>(creative(X)|~wise(X))))&
((?[X]:(~brave(X)))=>(~kind(lucy)))&
(![X]:((wise(X)<~>curious(X))=>(~wise(X)&~patient(X))))&
(((kind(mary)<~>~old(mary)))<=>(?[X]:((calm(X)|strong(X)))))&
(![X]:((brave(X)<~>rich(X))=>(~old(X)&funny(X))))&
(((~generous(lucy)&~old(lucy)))=>(?[X]:(~tall(X))))&
((~creative(paul))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((humble(X)|calm(X))<=>(rich(X)<~>happy(X))))&
(((wise(mary)|~quiet(mary)))<=>((~quiet(lucy)&rich(lucy))))&
(![X]:((humble(X)|~kind(X))=>~rich(X)))&
(![X]:(~humble(X)<=>(quiet(X)<~>~kind(X))))&
(![X]:((~humble(X)&~brave(X))<=>~old(X)))&
(((calm(john)&kind(john)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)&patient(X))<=>(~generous(X)&quiet(X))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)&~wise(X)))))&
(?[X]:((rich(X)&~humble(X))))&
((~creative(lucy)<~>~funny(lucy)))&
(strong(lucy))&
(?[X]:((~curious(X)|patient(X))))&
(brave(lucy))&
(?[X]:((~curious(X)|tall(X)))) | generous(lucy) | [
"p5",
"p10",
"p11",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3515468447898751264925417
% SZS output start Proof for 3515468447898751264925417
6. ! [X0] : ((brave(X0) <~> rich(X0)) => (funny(X0) & ~old(X0))) [input p5]
11. ! [X0] : ((~kind(X0) | humble(X0)) => ~rich(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (quiet(X0) <~> ~kind(X0))) [input p11]
13. ! [X0] : ((~brave(X0) & ~humble(X0)) <=> ~old(X0)) [input p12]
15. ! [X0] : ((patient(X0) & humble(X0)) <=> (quiet(X0) & ~generous(X0))) [input p14]
21. brave(lucy) [input p20]
23. ~generous(lucy) [input hypothesis]
28. ! [X0] : ((funny(X0) & ~old(X0)) | (brave(X0) <=> rich(X0))) [ennf transformation 6]
31. ! [X0] : (~rich(X0) | (kind(X0) & ~humble(X0))) [ennf transformation 11]
40. ! [X0] : ((funny(X0) & ~old(X0)) | ((brave(X0) | ~rich(X0)) & (rich(X0) | ~brave(X0)))) [nnf transformation 28]
51. ! [X0] : ((~humble(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | humble(X0))) [nnf transformation 12]
52. ! [X0] : (((~brave(X0) & ~humble(X0)) | old(X0)) & (~old(X0) | (brave(X0) | humble(X0)))) [nnf transformation 13]
53. ! [X0] : (((~brave(X0) & ~humble(X0)) | old(X0)) & (~old(X0) | brave(X0) | humble(X0))) [flattening 52]
59. ! [X0] : (((patient(X0) & humble(X0)) | (~quiet(X0) | generous(X0))) & ((quiet(X0) & ~generous(X0)) | (~patient(X0) | ~humble(X0)))) [nnf transformation 15]
60. ! [X0] : (((patient(X0) & humble(X0)) | ~quiet(X0) | generous(X0)) & ((quiet(X0) & ~generous(X0)) | ~patient(X0) | ~humble(X0))) [flattening 59]
87. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 40]
106. ~rich(X0) | ~humble(X0) [cnf transformation 31]
107. ~rich(X0) | kind(X0) [cnf transformation 31]
108. ~kind(X0) | quiet(X0) | humble(X0) [cnf transformation 51]
114. ~brave(X0) | old(X0) [cnf transformation 53]
120. ~quiet(X0) | humble(X0) | generous(X0) [cnf transformation 60]
130. brave(lucy) [cnf transformation 21]
132. ~generous(lucy) [cnf transformation 23]
138. 2 <=> kind(lucy) [avatar definition]
139. kind(lucy) <- (2) [avatar component clause 138]
169. 8 <=> generous(lucy) [avatar definition]
170. ~generous(lucy) <- (~8) [avatar component clause 169]
173. 9 <=> old(lucy) [avatar definition]
175. old(lucy) <- (9) [avatar component clause 173]
203. 16 <=> quiet(lucy) [avatar definition]
205. quiet(lucy) <- (16) [avatar component clause 203]
207. 17 <=> rich(lucy) [avatar definition]
208. rich(lucy) <- (17) [avatar component clause 207]
279. ~8 [avatar split clause 132,169]
287. kind(lucy) <- (17) [resolution 107,208]
290. 2 | ~17 [avatar split clause 287,207,138]
294. old(lucy) [resolution 114,130]
307. 9 [avatar split clause 294,173]
311. rich(lucy) | ~brave(lucy) <- (9) [resolution 87,175]
327. rich(lucy) <- (9) [subsumption resolution 311,130]
328. 17 | ~9 [avatar split clause 327,173,207]
333. ~humble(lucy) <- (17) [resolution 208,106]
406. quiet(lucy) | humble(lucy) <- (2) [resolution 108,139]
447. humble(lucy) | generous(lucy) <- (16) [resolution 120,205]
450. generous(lucy) <- (16, 17) [subsumption resolution 447,333]
451. $false <- (~8, 16, 17) [subsumption resolution 450,170]
452. 8 | ~16 | ~17 [avatar contradiction clause 451]
454. quiet(lucy) <- (2, 17) [subsumption resolution 406,333]
455. 16 | ~2 | ~17 [avatar split clause 454,207,138,203]
456. $false [avatar sat refutation 279,290,307,328,452,455]
% SZS output end Proof for 3515468447898751264925417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not old or strong then mary is both not tall and not kind. Everyone who is either not calm or calm is calm. If fred is wise then john is not creative or humble. If someone is both not kind and curious then fred is not rich or not humble and vice versa. If john is not rich then someone is not curious. Everyone who is not strong or calm is either not happy or not rich and vice versa. Everyone who is rich is not kind and vice versa. Everyone who is either not old or patient is not happy or not funny. Everyone who is both kind and generous is both not calm and creative. Everyone who is either creative or not curious is both not happy and not humble. Everyone who is either not calm or wise is rich and vice versa. Everyone who is either funny or kind is not tall or tall. Everyone who is either not curious or not generous is not old and vice versa. If fred is both creative and curious then susan is not funny and vice versa. Everyone who is curious or patient is either happy or old and vice versa. If someone is either not curious or tall then someone is either not curious or wise. Paul is both strong and funny. Fred is either old or funny. Paul is patient or not calm. Susan is happy or quiet. John is curious or calm. Fred is not strong. Mary is not happy or tall. | Susan is not calm. | contradiction | (((~old(mary)<~>strong(mary)))=>((~tall(mary)&~kind(mary))))&
(![X]:((~calm(X)<~>calm(X))=>calm(X)))&
((wise(fred))=>((~creative(john)|humble(john))))&
((?[X]:((~kind(X)&curious(X))))<=>((~rich(fred)|~humble(fred))))&
((~rich(john))=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)|calm(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(rich(X)<=>~kind(X)))&
(![X]:((~old(X)<~>patient(X))=>(~happy(X)|~funny(X))))&
(![X]:((kind(X)&generous(X))=>(~calm(X)&creative(X))))&
(![X]:((creative(X)<~>~curious(X))=>(~happy(X)&~humble(X))))&
(![X]:((~calm(X)<~>wise(X))<=>rich(X)))&
(![X]:((funny(X)<~>kind(X))=>(~tall(X)|tall(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>~old(X)))&
(((creative(fred)&curious(fred)))<=>(~funny(susan)))&
(![X]:((curious(X)|patient(X))<=>(happy(X)<~>old(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:((~curious(X)<~>wise(X)))))&
((strong(paul)&funny(paul)))&
((old(fred)<~>funny(fred)))&
((patient(paul)|~calm(paul)))&
((happy(susan)|quiet(susan)))&
((curious(john)|calm(john)))&
(~strong(fred))&
((~happy(mary)|tall(mary))) | ~calm(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6109171270712842301427859
% SZS output start Proof for 6109171270712842301427859
2. ! [X0] : ((~calm(X0) <~> calm(X0)) => calm(X0)) [input p1]
24. ~calm(susan) [input hypothesis]
28. ! [X0] : (calm(X0) | (~calm(X0) <=> calm(X0))) [ennf transformation 2]
41. ! [X0] : (calm(X0) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) [nnf transformation 28]
70. calm(X0) | calm(X0) | calm(X0) [cnf transformation 41]
126. ~calm(susan) [cnf transformation 24]
127. calm(X0) [duplicate literal removal 70]
249. $false [subsumption resolution 126,127]
% SZS output end Proof for 6109171270712842301427859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not strong then mary is funny. Everyone who is both quiet and happy is creative or not curious and vice versa. Everyone who is not happy or not humble is both creative and not curious. Everyone who is either funny or rich is either creative or kind and vice versa. If someone is either not brave or not wise then someone is either not strong or not calm. If susan is both not calm and kind then someone is either calm or not wise and vice versa. Everyone who is either not brave or not old is kind or not quiet. If susan is both curious and calm then someone is calm. Everyone who is either funny or rich is both not strong and quiet and vice versa. If someone is not curious or not kind then susan is not curious or rich and vice versa. If someone is creative or not funny then susan is either not patient or patient. Everyone who is both not calm and strong is either curious or not wise and vice versa. If john is rich then someone is both tall and not tall. If fred is not humble then someone is not creative or not funny. If someone is either not strong or happy then susan is both tall and calm. If someone is either not brave or not humble then lucy is not humble. John is either not humble or not brave. Paul is not humble or not tall. Someone is both generous and not quiet. John is kind. Someone is either not strong or not quiet. Someone is not generous or not brave. Alice is calm or not kind. Someone is either not creative or patient. | Mary is funny. | entailment | ((?[X]:((quiet(X)&~strong(X))))=>(funny(mary)))&
(![X]:((quiet(X)&happy(X))<=>(creative(X)|~curious(X))))&
(![X]:((~happy(X)|~humble(X))=>(creative(X)&~curious(X))))&
(![X]:((funny(X)<~>rich(X))<=>(creative(X)<~>kind(X))))&
((?[X]:((~brave(X)<~>~wise(X))))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(((~calm(susan)&kind(susan)))<=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:((~brave(X)<~>~old(X))=>(kind(X)|~quiet(X))))&
(((curious(susan)&calm(susan)))=>(?[X]:(calm(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~curious(X)|~kind(X))))<=>((~curious(susan)|rich(susan))))&
((?[X]:((creative(X)|~funny(X))))=>((~patient(susan)<~>patient(susan))))&
(![X]:((~calm(X)&strong(X))<=>(curious(X)<~>~wise(X))))&
((rich(john))=>(?[X]:((tall(X)&~tall(X)))))&
((~humble(fred))=>(?[X]:((~creative(X)|~funny(X)))))&
((?[X]:((~strong(X)<~>happy(X))))=>((tall(susan)&calm(susan))))&
((?[X]:((~brave(X)<~>~humble(X))))=>(~humble(lucy)))&
((~humble(john)<~>~brave(john)))&
((~humble(paul)|~tall(paul)))&
(?[X]:((generous(X)&~quiet(X))))&
(kind(john))&
(?[X]:((~strong(X)<~>~quiet(X))))&
(?[X]:((~generous(X)|~brave(X))))&
((calm(alice)|~kind(alice)))&
(?[X]:((~creative(X)<~>patient(X)))) | funny(mary) | [
"p0",
"p1",
"p2",
"p5",
"p11",
"p14",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3707586803036515099677577
% SZS output start Proof for 3707586803036515099677577
1. ? [X0] : (~strong(X0) & quiet(X0)) => funny(mary) [input p0]
2. ! [X0] : ((happy(X0) & quiet(X0)) <=> (~curious(X0) | creative(X0))) [input p1]
3. ! [X0] : ((~humble(X0) | ~happy(X0)) => (~curious(X0) & creative(X0))) [input p2]
6. (kind(susan) & ~calm(susan)) <=> ? [X0] : (calm(X0) <~> ~wise(X0)) [input p5]
12. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p11]
15. ? [X0] : (~strong(X0) <~> happy(X0)) => (calm(susan) & tall(susan)) [input p14]
16. ? [X0] : (~brave(X0) <~> ~humble(X0)) => ~humble(lucy) [input p15]
17. ~humble(john) <~> ~brave(john) [input p16]
21. ? [X0] : (~strong(X0) <~> ~quiet(X0)) [input p20]
25. ~funny(mary) [input hypothesis]
27. funny(mary) | ! [X0] : (strong(X0) | ~quiet(X0)) [ennf transformation 1]
28. ! [X0] : ((~curious(X0) & creative(X0)) | (humble(X0) & happy(X0))) [ennf transformation 3]
37. (calm(susan) & tall(susan)) | ! [X0] : (~strong(X0) <=> happy(X0)) [ennf transformation 15]
38. ~humble(lucy) | ! [X0] : (~brave(X0) <=> ~humble(X0)) [ennf transformation 16]
39. ! [X0] : (((happy(X0) & quiet(X0)) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 2]
40. ! [X0] : (((happy(X0) & quiet(X0)) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~happy(X0) | ~quiet(X0))) [flattening 39]
46. ((kind(susan) & ~calm(susan)) | ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (? [X0] : ((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (~kind(susan) | calm(susan))) [nnf transformation 6]
47. ((kind(susan) & ~calm(susan)) | ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (? [X0] : ((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | ~kind(susan) | calm(susan)) [flattening 46]
48. ((kind(susan) & ~calm(susan)) | ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (? [X1] : ((wise(X1) | ~calm(X1)) & (~wise(X1) | calm(X1))) | ~kind(susan) | calm(susan)) [rectify 47]
49. ? [X1] : ((wise(X1) | ~calm(X1)) & (~wise(X1) | calm(X1))) => ((wise(sK1) | ~calm(sK1)) & (~wise(sK1) | calm(sK1))) [choice axiom]
50. ((kind(susan) & ~calm(susan)) | ! [X0] : ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0)))) & (((wise(sK1) | ~calm(sK1)) & (~wise(sK1) | calm(sK1))) | ~kind(susan) | calm(susan)) [skolemisation 48,49]
62. ! [X0] : (((strong(X0) & ~calm(X0)) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | (~strong(X0) | calm(X0)))) [nnf transformation 12]
63. ! [X0] : (((strong(X0) & ~calm(X0)) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ~strong(X0) | calm(X0))) [flattening 62]
68. (calm(susan) & tall(susan)) | ! [X0] : ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))) [nnf transformation 37]
69. ~humble(lucy) | ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 38]
70. (brave(john) | humble(john)) & (~brave(john) | ~humble(john)) [nnf transformation 17]
73. ? [X0] : ((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) [nnf transformation 21]
74. ? [X0] : ((quiet(X0) | strong(X0)) & (~quiet(X0) | ~strong(X0))) => ((quiet(sK7) | strong(sK7)) & (~quiet(sK7) | ~strong(sK7))) [choice axiom]
75. (quiet(sK7) | strong(sK7)) & (~quiet(sK7) | ~strong(sK7)) [skolemisation 73,74]
81. funny(mary) | strong(X0) | ~quiet(X0) [cnf transformation 27]
83. ~creative(X0) | quiet(X0) [cnf transformation 40]
86. curious(X0) | happy(X0) [cnf transformation 40]
88. humble(X0) | creative(X0) [cnf transformation 28]
89. ~curious(X0) | happy(X0) [cnf transformation 28]
90. ~curious(X0) | humble(X0) [cnf transformation 28]
105. ~calm(susan) | ~wise(X0) | ~calm(X0) [cnf transformation 50]
106. ~calm(susan) | calm(X0) | wise(X0) [cnf transformation 50]
126. ~wise(X0) | curious(X0) | ~strong(X0) | calm(X0) [cnf transformation 63]
129. ~calm(X0) | curious(X0) | wise(X0) [cnf transformation 63]
138. calm(susan) | ~strong(X0) | ~happy(X0) [cnf transformation 68]
139. ~humble(lucy) | ~humble(X0) | brave(X0) [cnf transformation 69]
140. ~humble(lucy) | ~brave(X0) | humble(X0) [cnf transformation 69]
141. ~brave(john) | ~humble(john) [cnf transformation 70]
142. brave(john) | humble(john) [cnf transformation 70]
148. quiet(sK7) | strong(sK7) [cnf transformation 75]
153. ~funny(mary) [cnf transformation 25]
155. 1 <=> ! [X0] : (strong(X0) | ~quiet(X0)) [avatar definition]
156. ~quiet(X0) | strong(X0) <- (1) [avatar component clause 155]
158. 2 <=> funny(mary) [avatar definition]
161. 1 | 2 [avatar split clause 81,158,155]
162. happy(X0) [subsumption resolution 89,86]
182. 7 <=> ! [X0] : (calm(X0) | wise(X0)) [avatar definition]
183. calm(X0) | wise(X0) <- (7) [avatar component clause 182]
190. 9 <=> ! [X0] : (~wise(X0) | ~calm(X0)) [avatar definition]
191. ~calm(X0) | ~wise(X0) <- (9) [avatar component clause 190]
194. 10 <=> calm(susan) [avatar definition]
197. 7 | ~10 [avatar split clause 106,194,182]
198. 9 | ~10 [avatar split clause 105,194,190]
263. calm(susan) | ~strong(X0) [subsumption resolution 138,162]
265. 25 <=> ! [X0] : ~strong(X0) [avatar definition]
266. ~strong(X0) <- (25) [avatar component clause 265]
267. 25 | 10 [avatar split clause 263,194,265]
275. 27 <=> ! [X0] : (~brave(X0) | humble(X0)) [avatar definition]
276. ~brave(X0) | humble(X0) <- (27) [avatar component clause 275]
278. 28 <=> humble(lucy) [avatar definition]
280. ~humble(lucy) <- (~28) [avatar component clause 278]
281. 27 | ~28 [avatar split clause 140,278,275]
283. 29 <=> ! [X0] : (~humble(X0) | brave(X0)) [avatar definition]
284. ~humble(X0) | brave(X0) <- (29) [avatar component clause 283]
285. 29 | ~28 [avatar split clause 139,278,283]
287. 30 <=> humble(john) [avatar definition]
288. ~humble(john) <- (~30) [avatar component clause 287]
289. humble(john) <- (30) [avatar component clause 287]
291. 31 <=> brave(john) [avatar definition]
292. ~brave(john) <- (~31) [avatar component clause 291]
293. brave(john) <- (31) [avatar component clause 291]
294. 30 | 31 [avatar split clause 142,291,287]
295. ~30 | ~31 [avatar split clause 141,291,287]
306. 34 <=> strong(sK7) [avatar definition]
308. strong(sK7) <- (34) [avatar component clause 306]
310. 35 <=> quiet(sK7) [avatar definition]
312. quiet(sK7) <- (35) [avatar component clause 310]
313. 34 | 35 [avatar split clause 148,310,306]
343. ~2 [avatar split clause 153,158]
435. $false <- (25, 34) [resolution 266,308]
436. ~25 | ~34 [avatar contradiction clause 435]
441. strong(sK7) <- (1, 35) [resolution 312,156]
442. $false <- (1, 25, 35) [subsumption resolution 441,266]
443. ~1 | ~25 | ~35 [avatar contradiction clause 442]
470. wise(X0) | curious(X0) | wise(X0) <- (7) [resolution 183,129]
475. wise(X0) | curious(X0) <- (7) [duplicate literal removal 470]
580. brave(john) <- (29, 30) [resolution 284,289]
583. $false <- (29, 30, ~31) [subsumption resolution 580,292]
584. ~29 | ~30 | 31 [avatar contradiction clause 583]
587. humble(john) <- (27, 31) [resolution 293,276]
588. $false <- (27, ~30, 31) [subsumption resolution 587,288]
589. ~27 | 30 | ~31 [avatar contradiction clause 588]
590. creative(lucy) <- (~28) [resolution 280,88]
633. quiet(lucy) <- (~28) [resolution 590,83]
650. curious(X0) | curious(X0) | ~strong(X0) | calm(X0) <- (7) [resolution 475,126]
655. ~strong(X0) | curious(X0) | calm(X0) <- (7) [duplicate literal removal 650]
667. 69 <=> strong(lucy) [avatar definition]
668. strong(lucy) <- (69) [avatar component clause 667]
740. strong(lucy) <- (1, ~28) [resolution 633,156]
747. 69 | ~1 | 28 [avatar split clause 740,278,155,667]
808. curious(lucy) | calm(lucy) <- (7, 69) [resolution 668,655]
810. 87 <=> calm(lucy) [avatar definition]
812. calm(lucy) <- (87) [avatar component clause 810]
814. 88 <=> curious(lucy) [avatar definition]
816. curious(lucy) <- (88) [avatar component clause 814]
817. 87 | 88 | ~7 | ~69 [avatar split clause 808,667,182,814,810]
850. ~wise(lucy) <- (9, 87) [resolution 812,191]
852. 93 <=> wise(lucy) [avatar definition]
854. ~wise(lucy) <- (~93) [avatar component clause 852]
856. ~93 | ~9 | ~87 [avatar split clause 850,810,190,852]
925. curious(lucy) <- (7, ~93) [resolution 854,475]
927. 88 | ~7 | 93 [avatar split clause 925,852,182,814]
930. humble(lucy) <- (88) [resolution 816,90]
931. $false <- (~28, 88) [subsumption resolution 930,280]
932. 28 | ~88 [avatar contradiction clause 931]
933. $false [avatar sat refutation 161,197,198,267,281,285,294,295,313,343,436,443,584,589,747,817,856,927,932]
% SZS output end Proof for 3707586803036515099677577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If fred is brave then someone is both tall and not brave and vice versa. Everyone who is patient or calm is creative or kind and vice versa. If someone is not old or strong then someone is rich or quiet. If someone is both not strong and not brave then john is happy. If someone is not generous then lucy is either not generous or patient and vice versa. Everyone who is either not tall or not generous is both humble and not humble. If someone is not wise then someone is not old and vice versa. Everyone who is not creative is both quiet and strong and vice versa. If someone is not patient or not humble then lucy is not brave. Everyone who is not strong or rich is both not rich and curious. If someone is wise then mary is both brave and not happy and vice versa. Everyone who is both quiet and generous is not wise or calm and vice versa. Everyone who is not calm is both curious and happy and vice versa. Everyone who is quiet or not tall is not generous or not strong and vice versa. If someone is humble or not curious then someone is either not kind or not calm and vice versa. If mary is both not wise and strong then lucy is both creative and kind and vice versa. Someone is patient or happy. Someone is either tall or not old. Someone is not happy. Someone is both humble and calm. Someone is both tall and happy. Someone is generous or not kind. Susan is either not old or patient. Someone is either generous or old. | Lucy is not kind. | entailment | ((brave(fred))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((patient(X)|calm(X))<=>(creative(X)|kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
((?[X]:((~strong(X)&~brave(X))))=>(happy(john)))&
((?[X]:(~generous(X)))<=>((~generous(lucy)<~>patient(lucy))))&
(![X]:((~tall(X)<~>~generous(X))=>(humble(X)&~humble(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(~old(X))))&
(![X]:(~creative(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>(~brave(lucy)))&
(![X]:((~strong(X)|rich(X))=>(~rich(X)&curious(X))))&
((?[X]:(wise(X)))<=>((brave(mary)&~happy(mary))))&
(![X]:((quiet(X)&generous(X))<=>(~wise(X)|calm(X))))&
(![X]:(~calm(X)<=>(curious(X)&happy(X))))&
(![X]:((quiet(X)|~tall(X))<=>(~generous(X)|~strong(X))))&
((?[X]:((humble(X)|~curious(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((~wise(mary)&strong(mary)))<=>((creative(lucy)&kind(lucy))))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((tall(X)<~>~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)&calm(X))))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((generous(X)|~kind(X))))&
((~old(susan)<~>patient(susan)))&
(?[X]:((generous(X)<~>old(X)))) | ~kind(lucy) | [
"p1",
"p4",
"p7",
"p10",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6880222751943882622960255
% SZS output start Proof for 6880222751943882622960255
2. ! [X0] : ((calm(X0) | patient(X0)) <=> (kind(X0) | creative(X0))) [input p1]
5. ? [X0] : ~generous(X0) <=> (~generous(lucy) <~> patient(lucy)) [input p4]
8. ! [X0] : (~creative(X0) <=> (strong(X0) & quiet(X0))) [input p7]
11. ? [X0] : wise(X0) <=> (~happy(mary) & brave(mary)) [input p10]
12. ! [X0] : ((generous(X0) & quiet(X0)) <=> (calm(X0) | ~wise(X0))) [input p11]
13. ! [X0] : (~calm(X0) <=> (happy(X0) & curious(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | quiet(X0)) <=> (~strong(X0) | ~generous(X0))) [input p13]
16. (strong(mary) & ~wise(mary)) <=> (kind(lucy) & creative(lucy)) [input p15]
25. kind(lucy) [input hypothesis]
38. ! [X0] : (((calm(X0) | patient(X0)) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((calm(X0) | patient(X0) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | (~calm(X0) & ~patient(X0)))) [flattening 38]
43. (? [X0] : ~generous(X0) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X0] : generous(X0)) [nnf transformation 5]
44. (? [X0] : ~generous(X0) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X1] : generous(X1)) [rectify 43]
45. ? [X0] : ~generous(X0) => ~generous(sK2) [choice axiom]
46. (~generous(sK2) | ((~generous(lucy) | ~patient(lucy)) & (patient(lucy) | generous(lucy)))) & (((~patient(lucy) | generous(lucy)) & (patient(lucy) | ~generous(lucy))) | ! [X1] : generous(X1)) [skolemisation 44,45]
53. ! [X0] : ((~creative(X0) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | creative(X0))) [nnf transformation 8]
54. ! [X0] : ((~creative(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | creative(X0))) [flattening 53]
55. (? [X0] : wise(X0) | (happy(mary) | ~brave(mary))) & ((~happy(mary) & brave(mary)) | ! [X0] : ~wise(X0)) [nnf transformation 11]
56. (? [X0] : wise(X0) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X0] : ~wise(X0)) [flattening 55]
57. (? [X0] : wise(X0) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X1] : ~wise(X1)) [rectify 56]
58. ? [X0] : wise(X0) => wise(sK5) [choice axiom]
59. (wise(sK5) | happy(mary) | ~brave(mary)) & ((~happy(mary) & brave(mary)) | ! [X1] : ~wise(X1)) [skolemisation 57,58]
60. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~generous(X0) | ~quiet(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & quiet(X0)) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | ~generous(X0) | ~quiet(X0))) [flattening 60]
62. ! [X0] : ((~calm(X0) | (~happy(X0) | ~curious(X0))) & ((happy(X0) & curious(X0)) | calm(X0))) [nnf transformation 13]
63. ! [X0] : ((~calm(X0) | ~happy(X0) | ~curious(X0)) & ((happy(X0) & curious(X0)) | calm(X0))) [flattening 62]
64. ! [X0] : (((~tall(X0) | quiet(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (tall(X0) & ~quiet(X0)))) [nnf transformation 14]
65. ! [X0] : ((~tall(X0) | quiet(X0) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | (tall(X0) & ~quiet(X0)))) [flattening 64]
71. ((strong(mary) & ~wise(mary)) | (~kind(lucy) | ~creative(lucy))) & ((kind(lucy) & creative(lucy)) | (~strong(mary) | wise(mary))) [nnf transformation 16]
72. ((strong(mary) & ~wise(mary)) | ~kind(lucy) | ~creative(lucy)) & ((kind(lucy) & creative(lucy)) | ~strong(mary) | wise(mary)) [flattening 71]
96. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 39]
101. ~patient(lucy) | generous(lucy) | generous(X1) [cnf transformation 46]
110. quiet(X0) | creative(X0) [cnf transformation 54]
111. strong(X0) | creative(X0) [cnf transformation 54]
120. ~happy(mary) | ~wise(X1) [cnf transformation 59]
123. wise(X0) | quiet(X0) [cnf transformation 61]
124. ~calm(X0) | quiet(X0) [cnf transformation 61]
125. wise(X0) | generous(X0) [cnf transformation 61]
126. ~calm(X0) | generous(X0) [cnf transformation 61]
128. happy(X0) | calm(X0) [cnf transformation 63]
130. ~generous(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 65]
142. ~wise(mary) | ~kind(lucy) | ~creative(lucy) [cnf transformation 72]
143. strong(mary) | ~kind(lucy) | ~creative(lucy) [cnf transformation 72]
157. kind(lucy) [cnf transformation 25]
202. 11 <=> patient(lucy) [avatar definition]
204. ~patient(lucy) <- (~11) [avatar component clause 202]
206. 12 <=> generous(lucy) [avatar definition]
207. generous(lucy) <- (12) [avatar component clause 206]
208. ~generous(lucy) <- (~12) [avatar component clause 206]
216. 14 <=> ! [X1] : generous(X1) [avatar definition]
217. generous(X1) <- (14) [avatar component clause 216]
218. 14 | 12 | ~11 [avatar split clause 101,202,206,216]
252. 22 <=> happy(mary) [avatar definition]
253. ~happy(mary) <- (~22) [avatar component clause 252]
261. 24 <=> ! [X1] : ~wise(X1) [avatar definition]
262. ~wise(X1) <- (24) [avatar component clause 261]
263. 24 | ~22 [avatar split clause 120,252,261]
300. 33 <=> creative(lucy) [avatar definition]
302. ~creative(lucy) <- (~33) [avatar component clause 300]
304. 34 <=> kind(lucy) [avatar definition]
305. kind(lucy) <- (34) [avatar component clause 304]
308. 35 <=> strong(mary) [avatar definition]
310. strong(mary) <- (35) [avatar component clause 308]
311. ~33 | ~34 | 35 [avatar split clause 143,308,304,300]
313. 36 <=> wise(mary) [avatar definition]
315. ~wise(mary) <- (~36) [avatar component clause 313]
316. ~33 | ~34 | ~36 [avatar split clause 142,313,304,300]
367. 34 [avatar split clause 157,304]
380. calm(mary) <- (~22) [resolution 128,253]
384. generous(mary) <- (~22) [resolution 380,126]
385. quiet(mary) <- (~22) [resolution 380,124]
438. patient(lucy) | calm(lucy) <- (34) [resolution 96,305]
441. calm(lucy) <- (~11, 34) [subsumption resolution 438,204]
446. generous(lucy) <- (~11, 34) [resolution 441,126]
448. $false <- (~11, ~12, 34) [subsumption resolution 446,208]
449. 11 | 12 | ~34 [avatar contradiction clause 448]
499. ~strong(lucy) | ~quiet(lucy) <- (12) [resolution 130,207]
507. 63 <=> quiet(lucy) [avatar definition]
509. ~quiet(lucy) <- (~63) [avatar component clause 507]
511. 64 <=> strong(lucy) [avatar definition]
513. ~strong(lucy) <- (~64) [avatar component clause 511]
514. ~63 | ~64 | ~12 [avatar split clause 499,206,511,507]
576. creative(lucy) <- (~64) [resolution 513,111]
581. 33 | 64 [avatar split clause 576,511,300]
593. quiet(mary) <- (~36) [resolution 315,123]
638. ~strong(mary) | ~quiet(mary) <- (~22) [resolution 384,130]
640. ~quiet(mary) <- (~22, 35) [subsumption resolution 638,310]
641. $false <- (~22, 35) [subsumption resolution 640,385]
642. 22 | ~35 [avatar contradiction clause 641]
645. generous(X0) <- (24) [resolution 262,125]
648. 14 | ~24 [avatar split clause 645,261,216]
652. creative(lucy) <- (~63) [resolution 509,110]
653. $false <- (~33, ~63) [subsumption resolution 652,302]
654. 33 | 63 [avatar contradiction clause 653]
655. ~quiet(X0) | ~strong(X0) <- (14) [resolution 217,130]
688. ~strong(X1) | creative(X1) <- (14) [resolution 655,110]
690. ~strong(mary) <- (14, ~36) [resolution 655,593]
696. creative(X1) <- (14) [subsumption resolution 688,111]
697. $false <- (14, 35, ~36) [subsumption resolution 690,310]
698. ~14 | ~35 | 36 [avatar contradiction clause 697]
703. $false <- (14, ~33) [subsumption resolution 302,696]
704. ~14 | 33 [avatar contradiction clause 703]
707. $false [avatar sat refutation 218,263,311,316,367,449,514,581,642,648,654,698,704]
% SZS output end Proof for 6880222751943882622960255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is both curious and generous. If alice is wise or not creative then someone is either kind or wise. If someone is not strong or humble then someone is either calm or quiet and vice versa. Everyone who is either not kind or not strong is both happy and not curious. If someone is rich or not old then someone is strong and vice versa. If lucy is either creative or quiet then someone is strong and vice versa. If susan is either humble or not calm then someone is kind or not kind. Everyone who is patient or wise is both not kind and not wise and vice versa. Everyone who is not brave or happy is both rich and not funny. Everyone who is both funny and not rich is either tall or calm. If alice is either not generous or not brave then someone is not kind or not humble and vice versa. Everyone who is wise or not strong is either wise or not calm. Everyone who is either tall or generous is quiet or calm and vice versa. Everyone who is strong or not kind is curious. If mary is kind then alice is not patient or not funny and vice versa. Everyone who is either curious or not tall is both quiet and not rich and vice versa. Susan is either calm or not old. Someone is not happy. Someone is tall. Someone is either old or not generous. Paul is not tall or calm. Fred is either creative or not strong. | Susan is not rich. | neutral | (![X]:(generous(X)=>(curious(X)&generous(X))))&
(((wise(alice)|~creative(alice)))=>(?[X]:((kind(X)<~>wise(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((~kind(X)<~>~strong(X))=>(happy(X)&~curious(X))))&
((?[X]:((rich(X)|~old(X))))<=>(?[X]:(strong(X))))&
(((creative(lucy)<~>quiet(lucy)))<=>(?[X]:(strong(X))))&
(((humble(susan)<~>~calm(susan)))=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((patient(X)|wise(X))<=>(~kind(X)&~wise(X))))&
(![X]:((~brave(X)|happy(X))=>(rich(X)&~funny(X))))&
(![X]:((funny(X)&~rich(X))=>(tall(X)<~>calm(X))))&
(((~generous(alice)<~>~brave(alice)))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((wise(X)|~strong(X))=>(wise(X)<~>~calm(X))))&
(![X]:((tall(X)<~>generous(X))<=>(quiet(X)|calm(X))))&
(![X]:((strong(X)|~kind(X))=>curious(X)))&
((kind(mary))<=>((~patient(alice)|~funny(alice))))&
(![X]:((curious(X)<~>~tall(X))<=>(quiet(X)&~rich(X))))&
((calm(susan)<~>~old(susan)))&
(?[X]:(~happy(X)))&
(?[X]:(tall(X)))&
(?[X]:((old(X)<~>~generous(X))))&
((~tall(paul)|calm(paul)))&
((creative(fred)<~>~strong(fred))) | ~rich(susan) | [] | null | 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 not old. | 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)) | ~old(susan) | [
"p0",
"p5",
"p7",
"p9",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8444944703879566419752705
% SZS output start Proof for 8444944703879566419752705
1. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (~rich(X0) | kind(X0))) [input p0]
6. ! [X0] : ((wise(X0) & funny(X0)) => (~creative(X0) & old(X0))) [input p5]
8. ! [X0] : (tall(X0) <=> (curious(X0) <~> ~wise(X0))) [input p7]
10. ! [X0] : ((tall(X0) & ~generous(X0)) => (generous(X0) & strong(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> ~curious(X0)) => (~rich(X0) <~> generous(X0))) [input p10]
13. ! [X0] : ((patient(X0) | generous(X0)) => (~generous(X0) & ~calm(X0))) [input p12]
18. funny(susan) | old(susan) [input p17]
24. ~old(susan) [input hypothesis]
26. ! [X0] : ((curious(X0) <~> ~wise(X0)) => tall(X0)) [unused predicate definition removal 8]
32. ! [X0] : ((~creative(X0) & old(X0)) | (~wise(X0) | ~funny(X0))) [ennf transformation 6]
33. ! [X0] : ((~creative(X0) & old(X0)) | ~wise(X0) | ~funny(X0)) [flattening 32]
36. ! [X0] : (tall(X0) | (curious(X0) <=> ~wise(X0))) [ennf transformation 26]
37. ! [X0] : ((generous(X0) & strong(X0)) | (~tall(X0) | generous(X0))) [ennf transformation 10]
38. ! [X0] : ((generous(X0) & strong(X0)) | ~tall(X0) | generous(X0)) [flattening 37]
39. ! [X0] : ((~rich(X0) <~> generous(X0)) | (~generous(X0) <=> ~curious(X0))) [ennf transformation 11]
40. ! [X0] : ((~generous(X0) & ~calm(X0)) | (~patient(X0) & ~generous(X0))) [ennf transformation 13]
43. ! [X0] : (((~curious(X0) & ~old(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (curious(X0) | old(X0)))) [nnf transformation 1]
44. ! [X0] : (((~curious(X0) & ~old(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | curious(X0) | old(X0))) [flattening 43]
48. ! [X0] : (tall(X0) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) [nnf transformation 36]
50. ! [X0] : (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) [nnf transformation 39]
68. ~curious(X0) | rich(X0) [cnf transformation 44]
78. ~funny(X0) | ~wise(X0) | old(X0) [cnf transformation 33]
82. tall(X0) | curious(X0) | wise(X0) [cnf transformation 48]
88. generous(X0) | ~tall(X0) | generous(X0) [cnf transformation 38]
89. generous(X0) | ~rich(X0) | ~curious(X0) | generous(X0) [cnf transformation 50]
99. ~generous(X0) | ~generous(X0) [cnf transformation 40]
111. funny(susan) | old(susan) [cnf transformation 18]
119. ~old(susan) [cnf transformation 24]
120. ~generous(X0) [duplicate literal removal 99]
121. generous(X0) | ~rich(X0) | ~curious(X0) [duplicate literal removal 89]
123. ~tall(X0) | generous(X0) [duplicate literal removal 88]
156. ~curious(X0) | generous(X0) [subsumption resolution 121,68]
182. 13 <=> old(susan) [avatar definition]
183. ~old(susan) <- (~13) [avatar component clause 182]
186. 14 <=> funny(susan) [avatar definition]
188. funny(susan) <- (14) [avatar component clause 186]
189. 13 | 14 [avatar split clause 111,186,182]
200. ~13 [avatar split clause 119,182]
220. ~wise(susan) | old(susan) <- (14) [resolution 78,188]
223. ~wise(susan) <- (~13, 14) [subsumption resolution 220,183]
240. curious(X0) | wise(X0) | generous(X0) [resolution 82,123]
241. wise(X0) | curious(X0) [subsumption resolution 240,120]
282. curious(susan) <- (~13, 14) [resolution 241,223]
287. generous(susan) <- (~13, 14) [resolution 282,156]
289. $false <- (~13, 14) [subsumption resolution 287,120]
290. 13 | ~14 [avatar contradiction clause 289]
291. $false [avatar sat refutation 189,200,290]
% SZS output end Proof for 8444944703879566419752705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either happy or not curious is not tall or curious and vice versa.
Everyone who is not wise is either not kind or humble and vice versa.
If lucy is curious or not kind then lucy is both not funny and generous and vice versa.
Everyone who is both not quiet and generous is both not tall and not happy.
Everyone who is both humble and not generous is not funny or rich and vice versa.
If susan is both quiet and strong then fred is both tall and not funny and vice versa.
If someone is both not rich and patient then someone is both patient and curious.
If mary is not curious then someone is either quiet or not funny.
Everyone who is either humble or not funny is either strong or kind.
If someone is happy then someone is both not funny and not strong and vice versa.
If someone is either not happy or wise then someone is either not brave or strong.
Everyone who is not kind is both not creative and not generous and vice versa.
Everyone who is kind is not brave and vice versa.
If susan is happy or not tall then someone is not kind or not humble and vice versa.
Everyone who is both not generous and not creative is calm or patient and vice versa.
If susan is strong then alice is not calm or not quiet and vice versa.
Susan is happy.
John is funny.
Someone is not old.
Fred is both curious and wise.
Someone is not creative.
Lucy is either not wise or not brave.
Mary is happy or not quiet. | Lucy is patient. | contradiction | (![X]:((happy(X)<~>~curious(X))<=>(~tall(X)|curious(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>humble(X))))&
(((curious(lucy)|~kind(lucy)))<=>((~funny(lucy)&generous(lucy))))&
(![X]:((~quiet(X)&generous(X))=>(~tall(X)&~happy(X))))&
(![X]:((humble(X)&~generous(X))<=>(~funny(X)|rich(X))))&
(((quiet(susan)&strong(susan)))<=>((tall(fred)&~funny(fred))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:((patient(X)&curious(X)))))&
((~curious(mary))=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(strong(X)<~>kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~creative(X)&~generous(X))))&
(![X]:(kind(X)<=>~brave(X)))&
(((happy(susan)|~tall(susan)))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((~generous(X)&~creative(X))<=>(calm(X)|patient(X))))&
((strong(susan))<=>((~calm(alice)|~quiet(alice))))&
(happy(susan))&
(funny(john))&
(?[X]:(~old(X)))&
((curious(fred)&wise(fred)))&
(?[X]:(~creative(X)))&
((~wise(lucy)<~>~brave(lucy)))&
((happy(mary)|~quiet(mary))) | patient(lucy) | [
"p2",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6516577421045008488717101
% SZS output start Proof for 6516577421045008488717101
3. (~kind(lucy) | curious(lucy)) <=> (generous(lucy) & ~funny(lucy)) [input p2]
12. ! [X0] : (~kind(X0) <=> (~generous(X0) & ~creative(X0))) [input p11]
15. ! [X0] : ((~creative(X0) & ~generous(X0)) <=> (patient(X0) | calm(X0))) [input p14]
24. patient(lucy) [input hypothesis]
38. ((~kind(lucy) | curious(lucy)) | (~generous(lucy) | funny(lucy))) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [nnf transformation 3]
39. (~kind(lucy) | curious(lucy) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [flattening 38]
60. ! [X0] : ((~kind(X0) | (generous(X0) | creative(X0))) & ((~generous(X0) & ~creative(X0)) | kind(X0))) [nnf transformation 12]
61. ! [X0] : ((~kind(X0) | generous(X0) | creative(X0)) & ((~generous(X0) & ~creative(X0)) | kind(X0))) [flattening 60]
68. ! [X0] : (((~creative(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (creative(X0) | generous(X0)))) [nnf transformation 15]
69. ! [X0] : (((~creative(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | creative(X0) | generous(X0))) [flattening 68]
88. generous(lucy) | kind(lucy) [cnf transformation 39]
118. ~kind(X0) | generous(X0) | creative(X0) [cnf transformation 61]
127. ~patient(X0) | ~generous(X0) [cnf transformation 69]
129. ~creative(X0) | ~patient(X0) [cnf transformation 69]
141. patient(lucy) [cnf transformation 24]
150. 2 <=> generous(lucy) [avatar definition]
152. ~generous(lucy) <- (~2) [avatar component clause 150]
158. 4 <=> kind(lucy) [avatar definition]
159. kind(lucy) <- (4) [avatar component clause 158]
162. 4 | 2 [avatar split clause 88,150,158]
310. ~generous(lucy) [resolution 127,141]
413. generous(lucy) | creative(lucy) <- (4) [resolution 118,159]
415. creative(lucy) <- (~2, 4) [subsumption resolution 413,152]
482. ~patient(lucy) <- (~2, 4) [resolution 415,129]
484. $false <- (~2, 4) [subsumption resolution 482,141]
485. 2 | ~4 [avatar contradiction clause 484]
491. ~2 [avatar split clause 310,150]
492. $false [avatar sat refutation 162,485,491]
% SZS output end Proof for 6516577421045008488717101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and quiet then someone is either not creative or not strong. Everyone who is curious is not kind. If someone is strong then john is either wise or not patient and vice versa. If fred is both not curious and rich then mary is either not patient or quiet. Everyone who is not quiet is either not humble or not strong and vice versa. Everyone who is both creative and rich is either not patient or creative and vice versa. Everyone who is both generous and patient is either not happy or not creative and vice versa. Everyone who is funny is strong or old. Everyone who is both not humble and funny is not humble or patient and vice versa. Everyone who is not strong or not curious is either generous or wise. If someone is both humble and kind then alice is both not patient and old and vice versa. Everyone who is either not creative or humble is both generous and old and vice versa. If susan is not quiet or generous then mary is either strong or brave. Everyone who is both tall and brave is funny and vice versa. Everyone who is funny or wise is quiet and vice versa. If alice is not curious or kind then susan is both not wise and quiet and vice versa. Lucy is quiet or happy. Someone is not curious. Someone is humble. John is quiet or rich. Someone is not rich or rich. Someone is patient or kind. Paul is both not kind and not rich. | Susan is not rich. | neutral | (((~rich(lucy)&quiet(lucy)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(![X]:(curious(X)=>~kind(X)))&
((?[X]:(strong(X)))<=>((wise(john)<~>~patient(john))))&
(((~curious(fred)&rich(fred)))=>((~patient(mary)<~>quiet(mary))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)&rich(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((generous(X)&patient(X))<=>(~happy(X)<~>~creative(X))))&
(![X]:(funny(X)=>(strong(X)|old(X))))&
(![X]:((~humble(X)&funny(X))<=>(~humble(X)|patient(X))))&
(![X]:((~strong(X)|~curious(X))=>(generous(X)<~>wise(X))))&
((?[X]:((humble(X)&kind(X))))<=>((~patient(alice)&old(alice))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)&old(X))))&
(((~quiet(susan)|generous(susan)))=>((strong(mary)<~>brave(mary))))&
(![X]:((tall(X)&brave(X))<=>funny(X)))&
(![X]:((funny(X)|wise(X))<=>quiet(X)))&
(((~curious(alice)|kind(alice)))<=>((~wise(susan)&quiet(susan))))&
((quiet(lucy)|happy(lucy)))&
(?[X]:(~curious(X)))&
(?[X]:(humble(X)))&
((quiet(john)|rich(john)))&
(?[X]:((~rich(X)|rich(X))))&
(?[X]:((patient(X)|kind(X))))&
((~kind(paul)&~rich(paul))) | ~rich(susan) | [] | null | 0 |
If someone is curious or strong then someone is not generous and vice versa. If fred is tall then someone is both funny and quiet. Everyone who is not funny or not patient is both not wise and humble. Everyone who is either not calm or generous is both not humble and wise. If susan is kind then someone is not tall or not humble and vice versa. If mary is both tall and curious then someone is both curious and not old and vice versa. Everyone who is both not strong and creative is either calm or happy. Everyone who is calm is either not generous or tall and vice versa. If mary is not rich then susan is either not old or not tall. If lucy is not creative then someone is either not curious or kind. Everyone who is either brave or strong is either not strong or funny and vice versa. If fred is not patient or old then lucy is both not old and curious and vice versa. Everyone who is either not tall or old is funny. Everyone who is patient is either not wise or not creative and vice versa. Everyone who is not tall is kind or not brave. Someone is either not curious or funny. John is either wise or not curious. Lucy is rich or not funny. Someone is not kind. Someone is both not wise and not rich. John is either not brave or not generous. Someone is not brave. Someone is either rich or curious. | Susan is not kind. | contradiction | ((?[X]:((curious(X)|strong(X))))<=>(?[X]:(~generous(X))))&
((tall(fred))=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:((~funny(X)|~patient(X))=>(~wise(X)&humble(X))))&
(![X]:((~calm(X)<~>generous(X))=>(~humble(X)&wise(X))))&
((kind(susan))<=>(?[X]:((~tall(X)|~humble(X)))))&
(((tall(mary)&curious(mary)))<=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((~strong(X)&creative(X))=>(calm(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~generous(X)<~>tall(X))))&
((~rich(mary))=>((~old(susan)<~>~tall(susan))))&
((~creative(lucy))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((brave(X)<~>strong(X))<=>(~strong(X)<~>funny(X))))&
(((~patient(fred)|old(fred)))<=>((~old(lucy)&curious(lucy))))&
(![X]:((~tall(X)<~>old(X))=>funny(X)))&
(![X]:(patient(X)<=>(~wise(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(kind(X)|~brave(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((wise(john)<~>~curious(john)))&
((rich(lucy)|~funny(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~rich(X))))&
((~brave(john)<~>~generous(john)))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>curious(X)))) | ~kind(susan) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7321555962386047524590344
% SZS output start Proof for 7321555962386047524590344
4. ! [X0] : ((~calm(X0) <~> generous(X0)) => (wise(X0) & ~humble(X0))) [input p3]
5. kind(susan) <=> ? [X0] : (~humble(X0) | ~tall(X0)) [input p4]
8. ! [X0] : (calm(X0) <=> (~generous(X0) <~> tall(X0))) [input p7]
24. ~kind(susan) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~humble(X0)) | (~calm(X0) <=> generous(X0))) [ennf transformation 4]
44. ! [X0] : ((wise(X0) & ~humble(X0)) | ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0)))) [nnf transformation 29]
45. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & (? [X0] : (~humble(X0) | ~tall(X0)) | ~kind(susan)) [nnf transformation 5]
46. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & (? [X1] : (~humble(X1) | ~tall(X1)) | ~kind(susan)) [rectify 45]
47. ? [X1] : (~humble(X1) | ~tall(X1)) => (~humble(sK3) | ~tall(sK3)) [choice axiom]
48. (kind(susan) | ! [X0] : (humble(X0) & tall(X0))) & ((~humble(sK3) | ~tall(sK3)) | ~kind(susan)) [skolemisation 46,47]
55. ! [X0] : ((calm(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | ~calm(X0))) [nnf transformation 8]
87. ~humble(X0) | generous(X0) | calm(X0) [cnf transformation 44]
88. ~calm(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 44]
92. kind(susan) | tall(X0) [cnf transformation 48]
93. kind(susan) | humble(X0) [cnf transformation 48]
101. ~calm(X0) | generous(X0) | ~tall(X0) [cnf transformation 55]
103. ~tall(X0) | ~generous(X0) | calm(X0) [cnf transformation 55]
141. ~kind(susan) [cnf transformation 24]
147. 1 <=> ! [X1] : generous(X1) [avatar definition]
148. generous(X1) <- (1) [avatar component clause 147]
180. 9 <=> ! [X0] : humble(X0) [avatar definition]
181. humble(X0) <- (9) [avatar component clause 180]
183. 10 <=> kind(susan) [avatar definition]
186. 9 | 10 [avatar split clause 93,183,180]
188. 11 <=> ! [X0] : tall(X0) [avatar definition]
189. tall(X0) <- (11) [avatar component clause 188]
190. 11 | 10 [avatar split clause 92,183,188]
325. ~10 [avatar split clause 141,183]
337. calm(X2) | generous(X2) <- (9) [resolution 87,181]
346. generous(X1) | ~tall(X1) | generous(X1) <- (9) [resolution 101,337]
347. generous(X1) | ~tall(X1) <- (9) [duplicate literal removal 346]
350. generous(X1) <- (9, 11) [subsumption resolution 347,189]
351. 1 | ~9 | ~11 [avatar split clause 350,188,180,147]
371. ~generous(X0) | calm(X0) <- (11) [resolution 103,189]
372. calm(X0) <- (1, 11) [subsumption resolution 371,148]
376. ~humble(X3) | ~generous(X3) <- (1, 11) [resolution 372,88]
378. ~generous(X3) <- (1, 9, 11) [subsumption resolution 376,181]
379. $false <- (1, 9, 11) [subsumption resolution 378,148]
380. ~1 | ~9 | ~11 [avatar contradiction clause 379]
381. $false [avatar sat refutation 186,190,325,351,380]
% SZS output end Proof for 7321555962386047524590344
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not old is not old or humble.
Everyone who is both patient and rich is tall and vice versa.
Everyone who is either patient or not rich is both brave and calm.
If mary is funny or happy then someone is not generous.
Everyone who is creative or not strong is not old and vice versa.
If someone is not creative or kind then paul is either not funny or generous and vice versa.
If susan is either not patient or not quiet then someone is both patient and quiet.
Everyone who is either not creative or not brave is both patient and not generous.
If john is either patient or kind then someone is either tall or not quiet.
If someone is generous then someone is both kind and not funny.
Everyone who is generous or not brave is either not creative or old.
Everyone who is either not quiet or humble is creative.
Everyone who is rich is both not old and not wise.
Everyone who is both brave and not wise is not quiet or rich and vice versa.
Everyone who is both funny and patient is both not kind and creative and vice versa.
If lucy is either kind or not happy then someone is either old or not brave.
Paul is either happy or not humble.
Someone is either not wise or happy.
Someone is both not creative and tall.
Someone is not tall or not generous.
Paul is both not rich and not generous.
Alice is either not happy or calm.
John is either generous or brave.
Someone is either kind or patient. | Paul is generous. | contradiction | (![X]:((~humble(X)<~>~old(X))=>(~old(X)|humble(X))))&
(![X]:((patient(X)&rich(X))<=>tall(X)))&
(![X]:((patient(X)<~>~rich(X))=>(brave(X)&calm(X))))&
(((funny(mary)|happy(mary)))=>(?[X]:(~generous(X))))&
(![X]:((creative(X)|~strong(X))<=>~old(X)))&
((?[X]:((~creative(X)|kind(X))))<=>((~funny(paul)<~>generous(paul))))&
(((~patient(susan)<~>~quiet(susan)))=>(?[X]:((patient(X)&quiet(X)))))&
(![X]:((~creative(X)<~>~brave(X))=>(patient(X)&~generous(X))))&
(((patient(john)<~>kind(john)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((generous(X)|~brave(X))=>(~creative(X)<~>old(X))))&
(![X]:((~quiet(X)<~>humble(X))=>creative(X)))&
(![X]:(rich(X)=>(~old(X)&~wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(~quiet(X)|rich(X))))&
(![X]:((funny(X)&patient(X))<=>(~kind(X)&creative(X))))&
(((kind(lucy)<~>~happy(lucy)))=>(?[X]:((old(X)<~>~brave(X)))))&
((happy(paul)<~>~humble(paul)))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((~tall(X)|~generous(X))))&
((~rich(paul)&~generous(paul)))&
((~happy(alice)<~>calm(alice)))&
((generous(john)<~>brave(john)))&
(?[X]:((kind(X)<~>patient(X)))) | generous(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6277279546927867190593174
% SZS output start Proof for 6277279546927867190593174
21. ~generous(paul) & ~rich(paul) [input p20]
25. generous(paul) [input hypothesis]
146. ~generous(paul) [cnf transformation 21]
153. generous(paul) [cnf transformation 25]
170. 4 <=> generous(paul) [avatar definition]
301. ~4 [avatar split clause 146,170]
332. 4 [avatar split clause 153,170]
333. $false [avatar sat refutation 301,332]
% SZS output end Proof for 6277279546927867190593174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not old then someone is not quiet and vice versa.
If susan is calm then someone is not patient and vice versa.
If paul is either not brave or not humble then john is both not generous and not happy.
Everyone who is both not rich and humble is both not creative and not wise and vice versa.
If someone is not rich or rich then someone is not strong.
If someone is both not wise and tall then someone is both not funny and happy and vice versa.
Everyone who is both not brave and not rich is patient.
Everyone who is not brave is patient or not strong and vice versa.
Everyone who is either not brave or curious is not strong.
If paul is either rich or not quiet then someone is both not strong and calm and vice versa.
Everyone who is either happy or not creative is either not brave or not curious and vice versa.
Everyone who is patient is either funny or not wise and vice versa.
Everyone who is either not old or not calm is either kind or rich.
Everyone who is either rich or not happy is both not funny and not humble.
If someone is both not humble and not funny then someone is either not creative or not humble.
Everyone who is curious or wise is both calm and strong.
Alice is either not old or happy.
Susan is patient.
Susan is both not funny and curious.
Mary is happy or not quiet.
Mary is both not funny and not calm.
Paul is both rich and not humble.
Someone is not happy or not calm.
Someone is either not brave or wise. | Susan is not patient. | contradiction | ((~old(paul))<=>(?[X]:(~quiet(X))))&
((calm(susan))<=>(?[X]:(~patient(X))))&
(((~brave(paul)<~>~humble(paul)))=>((~generous(john)&~happy(john))))&
(![X]:((~rich(X)&humble(X))<=>(~creative(X)&~wise(X))))&
((?[X]:((~rich(X)|rich(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:((~funny(X)&happy(X)))))&
(![X]:((~brave(X)&~rich(X))=>patient(X)))&
(![X]:(~brave(X)<=>(patient(X)|~strong(X))))&
(![X]:((~brave(X)<~>curious(X))=>~strong(X)))&
(((rich(paul)<~>~quiet(paul)))<=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(patient(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~old(X)<~>~calm(X))=>(kind(X)<~>rich(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~funny(X)&~humble(X))))&
((?[X]:((~humble(X)&~funny(X))))=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)&strong(X))))&
((~old(alice)<~>happy(alice)))&
(patient(susan))&
((~funny(susan)&curious(susan)))&
((happy(mary)|~quiet(mary)))&
((~funny(mary)&~calm(mary)))&
((rich(paul)&~humble(paul)))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((~brave(X)<~>wise(X)))) | ~patient(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3010171405857993306751633
% SZS output start Proof for 3010171405857993306751633
18. patient(susan) [input p17]
25. ~patient(susan) [input hypothesis]
135. patient(susan) [cnf transformation 18]
146. ~patient(susan) [cnf transformation 25]
308. $false [subsumption resolution 146,135]
% SZS output end Proof for 3010171405857993306751633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not funny then someone is kind or not tall.
Everyone who is either funny or rich is not quiet or not rich and vice versa.
If fred is either not quiet or not kind then someone is both not brave and brave and vice versa.
If susan is either not wise or not tall then mary is curious and vice versa.
Everyone who is calm or rich is not brave or not happy and vice versa.
Everyone who is both not old and not strong is happy or not tall and vice versa.
Everyone who is creative or not tall is either not kind or brave.
Everyone who is quiet or kind is not tall and vice versa.
If someone is happy or humble then someone is either not humble or not calm and vice versa.
Everyone who is not creative is strong or not generous and vice versa.
If john is curious then someone is both not curious and happy and vice versa.
Everyone who is not happy or not tall is both quiet and wise.
Everyone who is quiet is not patient or not old.
If someone is humble then lucy is funny or not quiet and vice versa.
Everyone who is not kind is either strong or creative.
If lucy is either curious or tall then someone is not happy and vice versa.
Someone is either not creative or not calm.
Fred is both calm and not creative.
Someone is either not brave or not tall.
Lucy is either not kind or humble.
Alice is either not kind or patient.
Mary is kind or wise. | Mary is not strong. | entailment | ((?[X]:((old(X)&~funny(X))))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:((funny(X)<~>rich(X))<=>(~quiet(X)|~rich(X))))&
(((~quiet(fred)<~>~kind(fred)))<=>(?[X]:((~brave(X)&brave(X)))))&
(((~wise(susan)<~>~tall(susan)))<=>(curious(mary)))&
(![X]:((calm(X)|rich(X))<=>(~brave(X)|~happy(X))))&
(![X]:((~old(X)&~strong(X))<=>(happy(X)|~tall(X))))&
(![X]:((creative(X)|~tall(X))=>(~kind(X)<~>brave(X))))&
(![X]:((quiet(X)|kind(X))<=>~tall(X)))&
((?[X]:((happy(X)|humble(X))))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(![X]:(~creative(X)<=>(strong(X)|~generous(X))))&
((curious(john))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:((~happy(X)|~tall(X))=>(quiet(X)&wise(X))))&
(![X]:(quiet(X)=>(~patient(X)|~old(X))))&
((?[X]:(humble(X)))<=>((funny(lucy)|~quiet(lucy))))&
(![X]:(~kind(X)=>(strong(X)<~>creative(X))))&
(((curious(lucy)<~>tall(lucy)))<=>(?[X]:(~happy(X))))&
(?[X]:((~creative(X)<~>~calm(X))))&
((calm(fred)&~creative(fred)))&
(?[X]:((~brave(X)<~>~tall(X))))&
((~kind(lucy)<~>humble(lucy)))&
((~kind(alice)<~>patient(alice)))&
((kind(mary)|wise(mary))) | ~strong(mary) | [
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3045347019236317407334691
% SZS output start Proof for 3045347019236317407334691
6. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (~tall(X0) | happy(X0))) [input p5]
8. ! [X0] : ((kind(X0) | quiet(X0)) <=> ~tall(X0)) [input p7]
12. ! [X0] : ((~tall(X0) | ~happy(X0)) => (wise(X0) & quiet(X0))) [input p11]
23. strong(mary) [input hypothesis]
28. ! [X0] : ((wise(X0) & quiet(X0)) | (tall(X0) & happy(X0))) [ennf transformation 12]
44. ! [X0] : (((~strong(X0) & ~old(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (strong(X0) | old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~strong(X0) & ~old(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | strong(X0) | old(X0))) [flattening 44]
47. ! [X0] : (((kind(X0) | quiet(X0)) | tall(X0)) & (~tall(X0) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 8]
48. ! [X0] : ((kind(X0) | quiet(X0) | tall(X0)) & (~tall(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 47]
102. ~strong(X0) | ~happy(X0) [cnf transformation 45]
103. ~strong(X0) | tall(X0) [cnf transformation 45]
108. ~quiet(X0) | ~tall(X0) [cnf transformation 48]
123. happy(X0) | quiet(X0) [cnf transformation 28]
148. strong(mary) [cnf transformation 23]
336. ~happy(mary) [resolution 102,148]
337. tall(mary) [resolution 103,148]
347. quiet(mary) [resolution 123,336]
355. ~tall(mary) [resolution 347,108]
356. $false [subsumption resolution 355,337]
% SZS output end Proof for 3045347019236317407334691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or not quiet then susan is both not funny and not generous. Everyone who is not creative is not calm or not rich and vice versa. Everyone who is either brave or creative is both old and quiet and vice versa. Everyone who is both not wise and not patient is old and vice versa. If someone is either not kind or not funny then paul is not tall or not curious. Everyone who is both patient and quiet is either kind or wise and vice versa. If someone is either wise or happy then alice is not tall. If paul is not creative then mary is wise and vice versa. Everyone who is not curious or not tall is both strong and not curious. If alice is not brave or not strong then john is not kind and vice versa. If alice is tall then lucy is either not brave or patient. If someone is humble or kind then someone is both not patient and wise and vice versa. Everyone who is funny or not brave is old or not creative and vice versa. Everyone who is either not generous or not tall is both brave and not brave. Everyone who is either brave or not kind is strong and vice versa. Everyone who is not patient or happy is quiet or creative and vice versa. Someone is either tall or not generous. Alice is both not creative and not kind. Someone is both humble and not kind. Someone is not funny or creative. Alice is both happy and not calm. Someone is not happy. Alice is brave or quiet. Mary is either generous or not curious. | Alice is old. | contradiction | ((?[X]:((wise(X)|~quiet(X))))=>((~funny(susan)&~generous(susan))))&
(![X]:(~creative(X)<=>(~calm(X)|~rich(X))))&
(![X]:((brave(X)<~>creative(X))<=>(old(X)&quiet(X))))&
(![X]:((~wise(X)&~patient(X))<=>old(X)))&
((?[X]:((~kind(X)<~>~funny(X))))=>((~tall(paul)|~curious(paul))))&
(![X]:((patient(X)&quiet(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((wise(X)<~>happy(X))))=>(~tall(alice)))&
((~creative(paul))<=>(wise(mary)))&
(![X]:((~curious(X)|~tall(X))=>(strong(X)&~curious(X))))&
(((~brave(alice)|~strong(alice)))<=>(~kind(john)))&
((tall(alice))=>((~brave(lucy)<~>patient(lucy))))&
((?[X]:((humble(X)|kind(X))))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((funny(X)|~brave(X))<=>(old(X)|~creative(X))))&
(![X]:((~generous(X)<~>~tall(X))=>(brave(X)&~brave(X))))&
(![X]:((brave(X)<~>~kind(X))<=>strong(X)))&
(![X]:((~patient(X)|happy(X))<=>(quiet(X)|creative(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
((~creative(alice)&~kind(alice)))&
(?[X]:((humble(X)&~kind(X))))&
(?[X]:((~funny(X)|creative(X))))&
((happy(alice)&~calm(alice)))&
(?[X]:(~happy(X)))&
((brave(alice)|quiet(alice)))&
((generous(mary)<~>~curious(mary))) | old(alice) | [
"p2",
"p3",
"p6",
"p8",
"p14",
"p17",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5687168252449172621160359
% SZS output start Proof for 5687168252449172621160359
3. ! [X0] : ((brave(X0) <~> creative(X0)) <=> (quiet(X0) & old(X0))) [input p2]
4. ! [X0] : ((~patient(X0) & ~wise(X0)) <=> old(X0)) [input p3]
7. ? [X0] : (wise(X0) <~> happy(X0)) => ~tall(alice) [input p6]
9. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~curious(X0) & strong(X0))) [input p8]
15. ! [X0] : ((brave(X0) <~> ~kind(X0)) <=> strong(X0)) [input p14]
18. ~kind(alice) & ~creative(alice) [input p17]
21. ~calm(alice) & happy(alice) [input p20]
23. quiet(alice) | brave(alice) [input p22]
25. old(alice) [input hypothesis]
30. ~tall(alice) | ! [X0] : (wise(X0) <=> happy(X0)) [ennf transformation 7]
31. ! [X0] : ((~curious(X0) & strong(X0)) | (tall(X0) & curious(X0))) [ennf transformation 9]
36. ! [X0] : ((((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0))))) [flattening 36]
38. ! [X0] : (((~patient(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | (patient(X0) | wise(X0)))) [nnf transformation 4]
39. ! [X0] : (((~patient(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | patient(X0) | wise(X0))) [flattening 38]
43. ~tall(alice) | ! [X0] : ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))) [nnf transformation 30]
56. ! [X0] : ((((kind(X0) | ~brave(X0)) & (~kind(X0) | brave(X0))) | ~strong(X0)) & (strong(X0) | ((brave(X0) | kind(X0)) & (~kind(X0) | ~brave(X0))))) [nnf transformation 15]
80. ~old(X0) | brave(X0) | ~quiet(X0) | creative(X0) [cnf transformation 37]
83. ~old(X0) | ~wise(X0) [cnf transformation 39]
94. ~tall(alice) | wise(X0) | ~happy(X0) [cnf transformation 43]
98. strong(X0) | tall(X0) [cnf transformation 31]
122. ~strong(X0) | ~brave(X0) | kind(X0) [cnf transformation 56]
129. ~creative(alice) [cnf transformation 18]
130. ~kind(alice) [cnf transformation 18]
134. happy(alice) [cnf transformation 21]
137. quiet(alice) | brave(alice) [cnf transformation 23]
140. old(alice) [cnf transformation 25]
176. 9 <=> ! [X0] : (wise(X0) | ~happy(X0)) [avatar definition]
177. ~happy(X0) | wise(X0) <- (9) [avatar component clause 176]
179. 10 <=> tall(alice) [avatar definition]
182. 9 | ~10 [avatar split clause 94,179,176]
202. 15 <=> brave(alice) [avatar definition]
204. ~brave(alice) <- (~15) [avatar component clause 202]
206. 16 <=> strong(alice) [avatar definition]
207. strong(alice) <- (16) [avatar component clause 206]
208. ~strong(alice) <- (~16) [avatar component clause 206]
264. 28 <=> quiet(alice) [avatar definition]
266. quiet(alice) <- (28) [avatar component clause 264]
267. 15 | 28 [avatar split clause 137,264,202]
278. ~wise(alice) [resolution 83,140]
280. tall(alice) <- (~16) [resolution 98,208]
283. 10 | 16 [avatar split clause 280,206,179]
285. wise(alice) <- (9) [resolution 177,134]
286. $false <- (9) [subsumption resolution 285,278]
287. ~9 [avatar contradiction clause 286]
418. ~brave(alice) | kind(alice) <- (16) [resolution 122,207]
424. ~brave(alice) <- (16) [subsumption resolution 418,130]
425. ~15 | ~16 [avatar split clause 424,206,202]
522. brave(alice) | ~quiet(alice) | creative(alice) [resolution 80,140]
523. ~quiet(alice) | creative(alice) <- (~15) [subsumption resolution 522,204]
524. creative(alice) <- (~15, 28) [subsumption resolution 523,266]
525. $false <- (~15, 28) [subsumption resolution 524,129]
526. 15 | ~28 [avatar contradiction clause 525]
527. $false [avatar sat refutation 182,267,283,287,425,526]
% SZS output end Proof for 5687168252449172621160359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not calm is both not kind and not wise and vice versa.
If john is both not quiet and tall then fred is kind and vice versa.
Everyone who is either not strong or calm is both generous and not curious and vice versa.
Everyone who is quiet is both not old and not wise and vice versa.
Everyone who is not tall or not old is either not wise or happy.
Everyone who is both humble and not calm is not generous or curious.
Everyone who is both happy and strong is both brave and not strong and vice versa.
Everyone who is funny or generous is both wise and not curious.
If someone is either generous or not happy then someone is humble or not kind.
If john is both not patient and not humble then alice is not happy or not calm and vice versa.
Everyone who is not creative is not tall or not kind and vice versa.
Everyone who is not creative is both not wise and patient.
Everyone who is not curious is both calm and not curious.
If someone is either not old or rich then someone is tall.
Everyone who is not tall is funny or not wise.
If someone is quiet or not kind then john is rich and vice versa.
Mary is not wise or generous.
Someone is either quiet or not humble.
Someone is curious.
Alice is humble or not happy.
John is not tall or generous.
Someone is rich.
John is both not wise and not calm. | Mary is not generous. | neutral | (![X]:((~humble(X)&~calm(X))<=>(~kind(X)&~wise(X))))&
(((~quiet(john)&tall(john)))<=>(kind(fred)))&
(![X]:((~strong(X)<~>calm(X))<=>(generous(X)&~curious(X))))&
(![X]:(quiet(X)<=>(~old(X)&~wise(X))))&
(![X]:((~tall(X)|~old(X))=>(~wise(X)<~>happy(X))))&
(![X]:((humble(X)&~calm(X))=>(~generous(X)|curious(X))))&
(![X]:((happy(X)&strong(X))<=>(brave(X)&~strong(X))))&
(![X]:((funny(X)|generous(X))=>(wise(X)&~curious(X))))&
((?[X]:((generous(X)<~>~happy(X))))=>(?[X]:((humble(X)|~kind(X)))))&
(((~patient(john)&~humble(john)))<=>((~happy(alice)|~calm(alice))))&
(![X]:(~creative(X)<=>(~tall(X)|~kind(X))))&
(![X]:(~creative(X)=>(~wise(X)&patient(X))))&
(![X]:(~curious(X)=>(calm(X)&~curious(X))))&
((?[X]:((~old(X)<~>rich(X))))=>(?[X]:(tall(X))))&
(![X]:(~tall(X)=>(funny(X)|~wise(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>(rich(john)))&
((~wise(mary)|generous(mary)))&
(?[X]:((quiet(X)<~>~humble(X))))&
(?[X]:(curious(X)))&
((humble(alice)|~happy(alice)))&
((~tall(john)|generous(john)))&
(?[X]:(rich(X)))&
((~wise(john)&~calm(john))) | ~generous(mary) | [] | null | 0 |
Everyone who is either kind or curious is not curious or not humble. Everyone who is not old is either not old or kind and vice versa. If someone is not humble then fred is calm or happy and vice versa. Everyone who is both not funny and happy is not funny and vice versa. If lucy is both wise and humble then someone is both quiet and rich. If john is either wise or not brave then alice is either not generous or old and vice versa. Everyone who is both rich and not happy is either not patient or not brave. Everyone who is both not generous and funny is either generous or kind. Everyone who is both not funny and brave is brave. Everyone who is calm is patient and vice versa. If alice is both humble and not wise then fred is old. If fred is not old then someone is both old and not calm and vice versa. Everyone who is not kind or kind is patient. Everyone who is not wise or not strong is either not generous or humble. If someone is curious then someone is both creative and patient and vice versa. Everyone who is either not patient or old is either creative or patient and vice versa. Mary is either not brave or not strong. Someone is both not kind and brave. Someone is either not funny or kind. Alice is both patient and humble. Susan is not brave. Paul is either not humble or happy. Mary is both not old and quiet. | Fred is not calm. | contradiction | (![X]:((kind(X)<~>curious(X))=>(~curious(X)|~humble(X))))&
(![X]:(~old(X)<=>(~old(X)<~>kind(X))))&
((?[X]:(~humble(X)))<=>((calm(fred)|happy(fred))))&
(![X]:((~funny(X)&happy(X))<=>~funny(X)))&
(((wise(lucy)&humble(lucy)))=>(?[X]:((quiet(X)&rich(X)))))&
(((wise(john)<~>~brave(john)))<=>((~generous(alice)<~>old(alice))))&
(![X]:((rich(X)&~happy(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~generous(X)&funny(X))=>(generous(X)<~>kind(X))))&
(![X]:((~funny(X)&brave(X))=>brave(X)))&
(![X]:(calm(X)<=>patient(X)))&
(((humble(alice)&~wise(alice)))=>(old(fred)))&
((~old(fred))<=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((~kind(X)|kind(X))=>patient(X)))&
(![X]:((~wise(X)|~strong(X))=>(~generous(X)<~>humble(X))))&
((?[X]:(curious(X)))<=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~patient(X)<~>old(X))<=>(creative(X)<~>patient(X))))&
((~brave(mary)<~>~strong(mary)))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~funny(X)<~>kind(X))))&
((patient(alice)&humble(alice)))&
(~brave(susan))&
((~humble(paul)<~>happy(paul)))&
((~old(mary)&quiet(mary))) | ~calm(fred) | [
"p1",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 987226494197368163813709
% SZS output start Proof for 987226494197368163813709
2. ! [X0] : (~old(X0) <=> (~old(X0) <~> kind(X0))) [input p1]
10. ! [X0] : (calm(X0) <=> patient(X0)) [input p9]
13. ! [X0] : ((kind(X0) | ~kind(X0)) => patient(X0)) [input p12]
24. ~calm(fred) [input hypothesis]
40. ! [X0] : (patient(X0) | (~kind(X0) & kind(X0))) [ennf transformation 13]
43. ! [X0] : ((~old(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | old(X0))) [nnf transformation 2]
56. ! [X0] : ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))) [nnf transformation 10]
78. ~kind(X0) | old(X0) | old(X0) [cnf transformation 43]
80. ~old(X0) | ~old(X0) | ~kind(X0) [cnf transformation 43]
102. ~patient(X0) | calm(X0) [cnf transformation 56]
107. patient(X0) | kind(X0) [cnf transformation 40]
136. ~calm(fred) [cnf transformation 24]
142. ~kind(X0) | old(X0) [duplicate literal removal 78]
143. ~old(X0) | ~kind(X0) [duplicate literal removal 80]
145. ~kind(X0) [subsumption resolution 142,143]
156. 3 <=> calm(fred) [avatar definition]
158. ~calm(fred) <- (~3) [avatar component clause 156]
229. patient(X0) [subsumption resolution 107,145]
271. ~3 [avatar split clause 136,156]
275. calm(X0) [resolution 102,229]
276. $false <- (~3) [resolution 275,158]
278. 3 [avatar contradiction clause 276]
279. $false [avatar sat refutation 271,278]
% SZS output end Proof for 987226494197368163813709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is either brave or old and vice versa.
If someone is not creative then fred is both not rich and not curious.
If fred is both quiet and not humble then someone is either not generous or patient and vice versa.
If susan is both not happy and old then alice is patient and vice versa.
Everyone who is not rich or humble is either not humble or not quiet.
Everyone who is both generous and not strong is not old and vice versa.
Everyone who is not old is rich or strong and vice versa.
Everyone who is either not kind or not tall is strong or not happy.
Everyone who is either brave or not wise is not curious or brave and vice versa.
Everyone who is either strong or not creative is either not funny or rich and vice versa.
If someone is either not tall or calm then lucy is patient and vice versa.
Everyone who is generous is either not quiet or not creative and vice versa.
If someone is either tall or calm then someone is both tall and not strong and vice versa.
Everyone who is both not wise and not calm is funny or curious and vice versa.
Everyone who is not patient is either not rich or not funny and vice versa.
If susan is old or creative then someone is patient or wise.
Susan is both not generous and not strong.
Someone is creative or funny.
Lucy is rich.
Someone is not rich.
Mary is either calm or happy.
Someone is both not calm and patient.
Paul is both not happy and patient. | Alice is not creative. | neutral | (![X]:((calm(X)|~old(X))<=>(brave(X)<~>old(X))))&
((?[X]:(~creative(X)))=>((~rich(fred)&~curious(fred))))&
(((quiet(fred)&~humble(fred)))<=>(?[X]:((~generous(X)<~>patient(X)))))&
(((~happy(susan)&old(susan)))<=>(patient(alice)))&
(![X]:((~rich(X)|humble(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((generous(X)&~strong(X))<=>~old(X)))&
(![X]:(~old(X)<=>(rich(X)|strong(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(strong(X)|~happy(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(~curious(X)|brave(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((~tall(X)<~>calm(X))))<=>(patient(lucy)))&
(![X]:(generous(X)<=>(~quiet(X)<~>~creative(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
(![X]:((~wise(X)&~calm(X))<=>(funny(X)|curious(X))))&
(![X]:(~patient(X)<=>(~rich(X)<~>~funny(X))))&
(((old(susan)|creative(susan)))=>(?[X]:((patient(X)|wise(X)))))&
((~generous(susan)&~strong(susan)))&
(?[X]:((creative(X)|funny(X))))&
(rich(lucy))&
(?[X]:(~rich(X)))&
((calm(mary)<~>happy(mary)))&
(?[X]:((~calm(X)&patient(X))))&
((~happy(paul)&patient(paul))) | ~creative(alice) | [] | null | 0 |
Everyone who is both kind and not strong is either not humble or not wise.
If someone is not strong or strong then john is wise and vice versa.
If paul is both generous and kind then someone is not wise and vice versa.
If fred is either creative or generous then someone is curious or not generous and vice versa.
Everyone who is either funny or not humble is either not calm or not patient.
If fred is both not patient and not quiet then someone is both not curious and curious and vice versa.
Everyone who is not strong or strong is both quiet and generous.
If someone is either not quiet or not tall then fred is funny or not patient.
If someone is both rich and calm then someone is both wise and not calm and vice versa.
If someone is both calm and not curious then fred is both not happy and not quiet.
Everyone who is either not humble or not tall is wise or not quiet and vice versa.
If someone is not wise then lucy is both strong and wise and vice versa.
Everyone who is both not curious and not generous is calm.
Everyone who is not quiet is both not humble and creative.
If lucy is both quiet and not funny then someone is either brave or not brave.
Everyone who is both not humble and happy is both not old and not rich.
Susan is wise or humble.
Someone is either calm or generous.
Someone is not generous or generous.
Mary is both funny and not wise.
John is both patient and not tall.
Paul is either not curious or tall.
Someone is not old or not humble. | Fred is not creative. | entailment | (![X]:((kind(X)&~strong(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(wise(john)))&
(((generous(paul)&kind(paul)))<=>(?[X]:(~wise(X))))&
(((creative(fred)<~>generous(fred)))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((funny(X)<~>~humble(X))=>(~calm(X)<~>~patient(X))))&
(((~patient(fred)&~quiet(fred)))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((~strong(X)|strong(X))=>(quiet(X)&generous(X))))&
((?[X]:((~quiet(X)<~>~tall(X))))=>((funny(fred)|~patient(fred))))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((wise(X)&~calm(X)))))&
((?[X]:((calm(X)&~curious(X))))=>((~happy(fred)&~quiet(fred))))&
(![X]:((~humble(X)<~>~tall(X))<=>(wise(X)|~quiet(X))))&
((?[X]:(~wise(X)))<=>((strong(lucy)&wise(lucy))))&
(![X]:((~curious(X)&~generous(X))=>calm(X)))&
(![X]:(~quiet(X)=>(~humble(X)&creative(X))))&
(((quiet(lucy)&~funny(lucy)))=>(?[X]:((brave(X)<~>~brave(X)))))&
(![X]:((~humble(X)&happy(X))=>(~old(X)&~rich(X))))&
((wise(susan)|humble(susan)))&
(?[X]:((calm(X)<~>generous(X))))&
(?[X]:((~generous(X)|generous(X))))&
((funny(mary)&~wise(mary)))&
((patient(john)&~tall(john)))&
((~curious(paul)<~>tall(paul)))&
(?[X]:((~old(X)|~humble(X)))) | ~creative(fred) | [
"p1",
"p3",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3555973810223200833163106
% SZS output start Proof for 3555973810223200833163106
2. ? [X0] : (strong(X0) | ~strong(X0)) <=> wise(john) [input p1]
4. (creative(fred) <~> generous(fred)) <=> ? [X0] : (~generous(X0) | curious(X0)) [input p3]
7. ! [X0] : ((strong(X0) | ~strong(X0)) => (generous(X0) & quiet(X0))) [input p6]
9. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X0] : (~calm(X0) & wise(X0)) [input p8]
10. ? [X0] : (~curious(X0) & calm(X0)) => (~quiet(fred) & ~happy(fred)) [input p9]
24. creative(fred) [input hypothesis]
25. ? [X0] : (calm(X0) & rich(X0)) <=> ? [X1] : (~calm(X1) & wise(X1)) [rectify 9]
28. ? [X0] : (~curious(X0) & calm(X0)) => ~quiet(fred) [pure predicate removal 10]
33. ! [X0] : ((generous(X0) & quiet(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 7]
36. ~quiet(fred) | ! [X0] : (curious(X0) | ~calm(X0)) [ennf transformation 28]
43. (? [X0] : (strong(X0) | ~strong(X0)) | ~wise(john)) & (wise(john) | ! [X0] : (~strong(X0) & strong(X0))) [nnf transformation 2]
44. (? [X0] : (strong(X0) | ~strong(X0)) | ~wise(john)) & (wise(john) | ! [X1] : (~strong(X1) & strong(X1))) [rectify 43]
45. ? [X0] : (strong(X0) | ~strong(X0)) => (strong(sK0) | ~strong(sK0)) [choice axiom]
46. ((strong(sK0) | ~strong(sK0)) | ~wise(john)) & (wise(john) | ! [X1] : (~strong(X1) & strong(X1))) [skolemisation 44,45]
52. (((~generous(fred) | ~creative(fred)) & (generous(fred) | creative(fred))) | ! [X0] : (generous(X0) & ~curious(X0))) & (? [X0] : (~generous(X0) | curious(X0)) | ((creative(fred) | ~generous(fred)) & (generous(fred) | ~creative(fred)))) [nnf transformation 4]
53. (((~generous(fred) | ~creative(fred)) & (generous(fred) | creative(fred))) | ! [X0] : (generous(X0) & ~curious(X0))) & (? [X1] : (~generous(X1) | curious(X1)) | ((creative(fred) | ~generous(fred)) & (generous(fred) | ~creative(fred)))) [rectify 52]
54. ? [X1] : (~generous(X1) | curious(X1)) => (~generous(sK2) | curious(sK2)) [choice axiom]
55. (((~generous(fred) | ~creative(fred)) & (generous(fred) | creative(fred))) | ! [X0] : (generous(X0) & ~curious(X0))) & ((~generous(sK2) | curious(sK2)) | ((creative(fred) | ~generous(fred)) & (generous(fred) | ~creative(fred)))) [skolemisation 53,54]
63. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : (calm(X1) | ~wise(X1))) & (? [X1] : (~calm(X1) & wise(X1)) | ! [X0] : (~calm(X0) | ~rich(X0))) [nnf transformation 25]
64. (? [X0] : (calm(X0) & rich(X0)) | ! [X1] : (calm(X1) | ~wise(X1))) & (? [X2] : (~calm(X2) & wise(X2)) | ! [X3] : (~calm(X3) | ~rich(X3))) [rectify 63]
65. ? [X0] : (calm(X0) & rich(X0)) => (calm(sK4) & rich(sK4)) [choice axiom]
66. ? [X2] : (~calm(X2) & wise(X2)) => (~calm(sK5) & wise(sK5)) [choice axiom]
67. ((calm(sK4) & rich(sK4)) | ! [X1] : (calm(X1) | ~wise(X1))) & ((~calm(sK5) & wise(sK5)) | ! [X3] : (~calm(X3) | ~rich(X3))) [skolemisation 64,66,65]
86. wise(john) | strong(X1) [cnf transformation 46]
87. wise(john) | ~strong(X1) [cnf transformation 46]
96. ~generous(fred) | ~creative(fred) | ~curious(X0) [cnf transformation 55]
106. quiet(X0) | strong(X0) [cnf transformation 33]
107. ~strong(X0) | quiet(X0) [cnf transformation 33]
108. generous(X0) | strong(X0) [cnf transformation 33]
109. ~strong(X0) | generous(X0) [cnf transformation 33]
115. calm(sK4) | calm(X1) | ~wise(X1) [cnf transformation 67]
116. ~quiet(fred) | curious(X0) | ~calm(X0) [cnf transformation 36]
141. creative(fred) [cnf transformation 24]
143. 1 <=> ! [X1] : ~strong(X1) [avatar definition]
144. ~strong(X1) <- (1) [avatar component clause 143]
146. 2 <=> wise(john) [avatar definition]
148. wise(john) <- (2) [avatar component clause 146]
149. 1 | 2 [avatar split clause 87,146,143]
151. 3 <=> ! [X1] : strong(X1) [avatar definition]
152. strong(X1) <- (3) [avatar component clause 151]
153. 3 | 2 [avatar split clause 86,146,151]
173. 8 <=> ! [X0] : generous(X0) [avatar definition]
174. generous(X0) <- (8) [avatar component clause 173]
176. 9 <=> creative(fred) [avatar definition]
180. 10 <=> generous(fred) [avatar definition]
182. ~generous(fred) <- (~10) [avatar component clause 180]
185. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
186. ~curious(X0) <- (11) [avatar component clause 185]
187. 11 | ~9 | ~10 [avatar split clause 96,180,176,185]
214. generous(X0) [subsumption resolution 108,109]
215. 8 [avatar split clause 214,173]
216. quiet(X0) [subsumption resolution 106,107]
227. 19 <=> ! [X1] : (calm(X1) | ~wise(X1)) [avatar definition]
228. ~wise(X1) | calm(X1) <- (19) [avatar component clause 227]
230. 20 <=> calm(sK4) [avatar definition]
232. calm(sK4) <- (20) [avatar component clause 230]
233. 19 | 20 [avatar split clause 115,230,227]
252. ~calm(X0) | curious(X0) [subsumption resolution 116,216]
300. 9 [avatar split clause 141,176]
303. $false <- (8, ~10) [resolution 182,174]
304. ~8 | 10 [avatar contradiction clause 303]
311. calm(john) <- (2, 19) [resolution 228,148]
314. curious(john) <- (2, 19) [resolution 252,311]
315. $false <- (2, 11, 19) [subsumption resolution 314,186]
316. ~2 | ~11 | ~19 [avatar contradiction clause 315]
317. curious(sK4) <- (20) [resolution 232,252]
318. $false <- (11, 20) [subsumption resolution 317,186]
319. ~11 | ~20 [avatar contradiction clause 318]
320. $false <- (1, 3) [subsumption resolution 144,152]
321. ~1 | ~3 [avatar contradiction clause 320]
322. $false [avatar sat refutation 149,153,187,215,233,300,304,316,319,321]
% SZS output end Proof for 3555973810223200833163106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is tall then john is either not humble or not wise.
Everyone who is either not creative or quiet is not rich or not generous.
If someone is happy then alice is happy or not curious.
Everyone who is not tall or happy is creative and vice versa.
Everyone who is funny is not curious.
If someone is either happy or not generous then someone is brave or calm and vice versa.
Everyone who is either not creative or strong is curious and vice versa.
If someone is generous or not tall then alice is not creative.
If someone is both not happy and not tall then someone is patient and vice versa.
If lucy is funny or generous then someone is not creative.
If someone is not rich then someone is both not tall and tall.
Everyone who is either not creative or not happy is not happy or strong and vice versa.
If someone is both not creative and not funny then someone is either not wise or creative and vice versa.
If john is not strong then someone is rich or patient and vice versa.
If someone is not tall or not quiet then someone is not rich.
Someone is either humble or not quiet.
Someone is not wise.
Alice is both tall and creative.
Someone is either brave or funny.
Someone is both creative and tall.
Someone is not kind.
Someone is either wise or rich. | Susan is brave. | contradiction | ((tall(susan))=>((~humble(john)<~>~wise(john))))&
(![X]:((~creative(X)<~>quiet(X))=>(~rich(X)|~generous(X))))&
((?[X]:(happy(X)))=>((happy(alice)|~curious(alice))))&
(![X]:((~tall(X)|happy(X))<=>creative(X)))&
(![X]:(funny(X)=>~curious(X)))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~creative(X)<~>strong(X))<=>curious(X)))&
((?[X]:((generous(X)|~tall(X))))=>(~creative(alice)))&
((?[X]:((~happy(X)&~tall(X))))<=>(?[X]:(patient(X))))&
(((funny(lucy)|generous(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~tall(X)&tall(X)))))&
(![X]:((~creative(X)<~>~happy(X))<=>(~happy(X)|strong(X))))&
((?[X]:((~creative(X)&~funny(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
((~strong(john))<=>(?[X]:((rich(X)|patient(X)))))&
((?[X]:((~tall(X)|~quiet(X))))=>(?[X]:(~rich(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:(~wise(X)))&
((tall(alice)&creative(alice)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)<~>rich(X)))) | brave(susan) | [
"p3",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8915029218532939345887486
% SZS output start Proof for 8915029218532939345887486
4. ! [X0] : ((happy(X0) | ~tall(X0)) <=> creative(X0)) [input p3]
6. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X0] : (calm(X0) | brave(X0)) [input p5]
8. ? [X0] : (~tall(X0) | generous(X0)) => ~creative(alice) [input p7]
12. ! [X0] : ((~creative(X0) <~> ~happy(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
23. brave(susan) [input hypothesis]
24. ? [X0] : (happy(X0) <~> ~generous(X0)) <=> ? [X1] : (calm(X1) | brave(X1)) [rectify 6]
38. ~creative(alice) | ! [X0] : (tall(X0) & ~generous(X0)) [ennf transformation 8]
44. ! [X0] : (((happy(X0) | ~tall(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 4]
45. ! [X0] : ((happy(X0) | ~tall(X0) | ~creative(X0)) & (creative(X0) | (~happy(X0) & tall(X0)))) [flattening 44]
46. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & (? [X1] : (calm(X1) | brave(X1)) | ! [X0] : ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) [nnf transformation 24]
47. (? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & (? [X2] : (calm(X2) | brave(X2)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [rectify 46]
48. ? [X0] : ((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) => ((generous(sK0) | ~happy(sK0)) & (~generous(sK0) | happy(sK0))) [choice axiom]
49. ? [X2] : (calm(X2) | brave(X2)) => (calm(sK1) | brave(sK1)) [choice axiom]
50. (((generous(sK0) | ~happy(sK0)) & (~generous(sK0) | happy(sK0))) | ! [X1] : (~calm(X1) & ~brave(X1))) & ((calm(sK1) | brave(sK1)) | ! [X3] : ((happy(X3) | generous(X3)) & (~generous(X3) | ~happy(X3)))) [skolemisation 47,49,48]
62. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [nnf transformation 12]
63. ! [X0] : ((((happy(X0) | creative(X0)) & (~happy(X0) | ~creative(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~creative(X0) | happy(X0)) & (~happy(X0) | creative(X0))))) [flattening 62]
95. ~happy(X0) | creative(X0) [cnf transformation 45]
96. ~creative(X0) | ~tall(X0) | happy(X0) [cnf transformation 45]
102. generous(sK0) | ~happy(sK0) | ~brave(X1) [cnf transformation 50]
106. ~creative(alice) | ~generous(X0) [cnf transformation 38]
107. ~creative(alice) | tall(X0) [cnf transformation 38]
119. happy(X0) | creative(X0) | happy(X0) [cnf transformation 63]
143. brave(susan) [cnf transformation 23]
145. happy(X0) | creative(X0) [duplicate literal removal 119]
176. 8 <=> happy(sK0) [avatar definition]
178. ~happy(sK0) <- (~8) [avatar component clause 176]
180. 9 <=> generous(sK0) [avatar definition]
182. generous(sK0) <- (9) [avatar component clause 180]
185. 10 <=> ! [X1] : ~brave(X1) [avatar definition]
186. ~brave(X1) <- (10) [avatar component clause 185]
187. 10 | ~8 | 9 [avatar split clause 102,180,176,185]
207. 15 <=> ! [X0] : tall(X0) [avatar definition]
208. tall(X0) <- (15) [avatar component clause 207]
210. 16 <=> creative(alice) [avatar definition]
212. ~creative(alice) <- (~16) [avatar component clause 210]
213. 15 | ~16 [avatar split clause 107,210,207]
215. 17 <=> ! [X0] : ~generous(X0) [avatar definition]
216. ~generous(X0) <- (17) [avatar component clause 215]
217. 17 | ~16 [avatar split clause 106,210,215]
263. creative(X0) [subsumption resolution 145,95]
338. $false <- (~16) [subsumption resolution 212,263]
339. 16 [avatar contradiction clause 338]
351. ~tall(X1) | happy(X1) [resolution 96,263]
352. happy(X1) <- (15) [subsumption resolution 351,208]
353. $false <- (~8, 15) [resolution 352,178]
355. 8 | ~15 [avatar contradiction clause 353]
356. $false <- (9, 17) [subsumption resolution 182,216]
357. ~9 | ~17 [avatar contradiction clause 356]
358. $false <- (10) [resolution 186,143]
363. ~10 [avatar contradiction clause 358]
364. $false [avatar sat refutation 187,213,217,339,355,357,363]
% SZS output end Proof for 8915029218532939345887486
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not patient then mary is both tall and kind and vice versa. Everyone who is not funny is not generous or not brave and vice versa. Everyone who is happy is both not creative and rich. Everyone who is not wise or quiet is either not strong or humble and vice versa. If someone is not humble then alice is not calm or not tall and vice versa. Everyone who is either not humble or not calm is not kind or rich and vice versa. Everyone who is either tall or creative is not strong or old and vice versa. If paul is either not patient or not wise then mary is either not humble or not calm. Everyone who is not tall or creative is creative or not creative. Everyone who is both not curious and creative is tall and vice versa. If someone is either not quiet or strong then paul is generous or not generous and vice versa. Everyone who is not kind or funny is funny or rich. If someone is both rich and funny then someone is wise or not calm and vice versa. If mary is happy or curious then someone is rich or not kind and vice versa. If someone is happy or not patient then lucy is both calm and not rich and vice versa. If someone is not patient then alice is both calm and not brave and vice versa. Someone is not quiet or rich. Someone is creative or curious. Lucy is not creative. Someone is either not strong or quiet. Someone is not patient. Someone is not old or old. | Paul is not wise. | entailment | ((?[X]:((happy(X)|~patient(X))))<=>((tall(mary)&kind(mary))))&
(![X]:(~funny(X)<=>(~generous(X)|~brave(X))))&
(![X]:(happy(X)=>(~creative(X)&rich(X))))&
(![X]:((~wise(X)|quiet(X))<=>(~strong(X)<~>humble(X))))&
((?[X]:(~humble(X)))<=>((~calm(alice)|~tall(alice))))&
(![X]:((~humble(X)<~>~calm(X))<=>(~kind(X)|rich(X))))&
(![X]:((tall(X)<~>creative(X))<=>(~strong(X)|old(X))))&
(((~patient(paul)<~>~wise(paul)))=>((~humble(mary)<~>~calm(mary))))&
(![X]:((~tall(X)|creative(X))=>(creative(X)|~creative(X))))&
(![X]:((~curious(X)&creative(X))<=>tall(X)))&
((?[X]:((~quiet(X)<~>strong(X))))<=>((generous(paul)|~generous(paul))))&
(![X]:((~kind(X)|funny(X))=>(funny(X)|rich(X))))&
((?[X]:((rich(X)&funny(X))))<=>(?[X]:((wise(X)|~calm(X)))))&
(((happy(mary)|curious(mary)))<=>(?[X]:((rich(X)|~kind(X)))))&
((?[X]:((happy(X)|~patient(X))))<=>((calm(lucy)&~rich(lucy))))&
((?[X]:(~patient(X)))<=>((calm(alice)&~brave(alice))))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((creative(X)|curious(X))))&
(~creative(lucy))&
(?[X]:((~strong(X)<~>quiet(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~old(X)|old(X)))) | ~wise(paul) | [
"p0",
"p2",
"p9",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7071976633352315779444195
% SZS output start Proof for 7071976633352315779444195
1. ? [X0] : (~patient(X0) | happy(X0)) <=> (kind(mary) & tall(mary)) [input p0]
3. ! [X0] : (happy(X0) => (rich(X0) & ~creative(X0))) [input p2]
10. ! [X0] : ((creative(X0) & ~curious(X0)) <=> tall(X0)) [input p9]
13. ? [X0] : (funny(X0) & rich(X0)) <=> ? [X0] : (~calm(X0) | wise(X0)) [input p12]
14. (curious(mary) | happy(mary)) <=> ? [X0] : (~kind(X0) | rich(X0)) [input p13]
21. ? [X0] : ~patient(X0) [input p20]
23. wise(paul) [input hypothesis]
24. ? [X0] : (funny(X0) & rich(X0)) <=> ? [X1] : (~calm(X1) | wise(X1)) [rectify 13]
25. ! [X0] : ((rich(X0) & ~creative(X0)) | ~happy(X0)) [ennf transformation 3]
31. (? [X0] : (~patient(X0) | happy(X0)) | (~kind(mary) | ~tall(mary))) & ((kind(mary) & tall(mary)) | ! [X0] : (patient(X0) & ~happy(X0))) [nnf transformation 1]
32. (? [X0] : (~patient(X0) | happy(X0)) | ~kind(mary) | ~tall(mary)) & ((kind(mary) & tall(mary)) | ! [X0] : (patient(X0) & ~happy(X0))) [flattening 31]
33. (? [X0] : (~patient(X0) | happy(X0)) | ~kind(mary) | ~tall(mary)) & ((kind(mary) & tall(mary)) | ! [X1] : (patient(X1) & ~happy(X1))) [rectify 32]
34. ? [X0] : (~patient(X0) | happy(X0)) => (~patient(sK0) | happy(sK0)) [choice axiom]
35. ((~patient(sK0) | happy(sK0)) | ~kind(mary) | ~tall(mary)) & ((kind(mary) & tall(mary)) | ! [X1] : (patient(X1) & ~happy(X1))) [skolemisation 33,34]
50. ! [X0] : (((creative(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) | curious(X0)))) [nnf transformation 10]
51. ! [X0] : (((creative(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | ~creative(X0) | curious(X0))) [flattening 50]
57. (? [X0] : (funny(X0) & rich(X0)) | ! [X1] : (calm(X1) & ~wise(X1))) & (? [X1] : (~calm(X1) | wise(X1)) | ! [X0] : (~funny(X0) | ~rich(X0))) [nnf transformation 24]
58. (? [X0] : (funny(X0) & rich(X0)) | ! [X1] : (calm(X1) & ~wise(X1))) & (? [X2] : (~calm(X2) | wise(X2)) | ! [X3] : (~funny(X3) | ~rich(X3))) [rectify 57]
59. ? [X0] : (funny(X0) & rich(X0)) => (funny(sK3) & rich(sK3)) [choice axiom]
60. ? [X2] : (~calm(X2) | wise(X2)) => (~calm(sK4) | wise(sK4)) [choice axiom]
61. ((funny(sK3) & rich(sK3)) | ! [X1] : (calm(X1) & ~wise(X1))) & ((~calm(sK4) | wise(sK4)) | ! [X3] : (~funny(X3) | ~rich(X3))) [skolemisation 58,60,59]
62. ((curious(mary) | happy(mary)) | ! [X0] : (kind(X0) & ~rich(X0))) & (? [X0] : (~kind(X0) | rich(X0)) | (~curious(mary) & ~happy(mary))) [nnf transformation 14]
63. (curious(mary) | happy(mary) | ! [X0] : (kind(X0) & ~rich(X0))) & (? [X0] : (~kind(X0) | rich(X0)) | (~curious(mary) & ~happy(mary))) [flattening 62]
64. (curious(mary) | happy(mary) | ! [X0] : (kind(X0) & ~rich(X0))) & (? [X1] : (~kind(X1) | rich(X1)) | (~curious(mary) & ~happy(mary))) [rectify 63]
65. ? [X1] : (~kind(X1) | rich(X1)) => (~kind(sK5) | rich(sK5)) [choice axiom]
66. (curious(mary) | happy(mary) | ! [X0] : (kind(X0) & ~rich(X0))) & ((~kind(sK5) | rich(sK5)) | (~curious(mary) & ~happy(mary))) [skolemisation 64,65]
84. ? [X0] : ~patient(X0) => ~patient(sK11) [choice axiom]
85. ~patient(sK11) [skolemisation 21,84]
89. tall(mary) | patient(X1) [cnf transformation 35]
96. ~creative(X0) | ~happy(X0) [cnf transformation 25]
126. ~curious(X0) | ~tall(X0) [cnf transformation 51]
127. ~tall(X0) | creative(X0) [cnf transformation 51]
137. rich(sK3) | ~wise(X1) [cnf transformation 61]
143. curious(mary) | happy(mary) | ~rich(X0) [cnf transformation 66]
158. ~patient(sK11) [cnf transformation 85]
160. wise(paul) [cnf transformation 23]
163. 1 <=> tall(mary) [avatar definition]
164. tall(mary) <- (1) [avatar component clause 163]
180. 5 <=> ! [X1] : patient(X1) [avatar definition]
181. patient(X1) <- (5) [avatar component clause 180]
187. 5 | 1 [avatar split clause 89,163,180]
208. 11 <=> wise(paul) [avatar definition]
210. wise(paul) <- (11) [avatar component clause 208]
252. 20 <=> ! [X1] : ~wise(X1) [avatar definition]
253. ~wise(X1) <- (20) [avatar component clause 252]
256. 21 <=> rich(sK3) [avatar definition]
258. rich(sK3) <- (21) [avatar component clause 256]
260. 20 | 21 [avatar split clause 137,256,252]
277. 26 <=> happy(mary) [avatar definition]
281. 27 <=> curious(mary) [avatar definition]
283. curious(mary) <- (27) [avatar component clause 281]
286. 28 <=> ! [X0] : ~rich(X0) [avatar definition]
287. ~rich(X0) <- (28) [avatar component clause 286]
288. 28 | 26 | 27 [avatar split clause 143,281,277,286]
359. 11 [avatar split clause 160,208]
360. $false <- (11, 20) [subsumption resolution 210,253]
361. ~11 | ~20 [avatar contradiction clause 360]
366. $false <- (5) [resolution 181,158]
367. ~5 [avatar contradiction clause 366]
373. ~tall(mary) <- (27) [resolution 126,283]
374. $false <- (1, 27) [subsumption resolution 373,164]
375. ~1 | ~27 [avatar contradiction clause 374]
377. creative(mary) <- (1) [resolution 127,164]
379. ~happy(mary) <- (1) [resolution 377,96]
382. ~26 | ~1 [avatar split clause 379,163,277]
385. $false <- (21, 28) [resolution 287,258]
386. ~21 | ~28 [avatar contradiction clause 385]
387. $false [avatar sat refutation 187,260,288,359,361,367,375,382,386]
% SZS output end Proof for 7071976633352315779444195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is calm or old.
Everyone who is tall or not brave is both not quiet and not happy and vice versa.
Everyone who is either not curious or not wise is wise and vice versa.
Everyone who is either humble or calm is both patient and not creative.
If susan is not generous or funny then someone is not curious and vice versa.
Everyone who is patient or not happy is either quiet or not kind and vice versa.
If someone is either quiet or not strong then someone is both not generous and kind.
If paul is not strong or not calm then fred is kind and vice versa.
Everyone who is not generous is humble and vice versa.
If alice is quiet then someone is both not wise and brave and vice versa.
Everyone who is either brave or calm is not tall or not happy and vice versa.
Everyone who is not happy or kind is not calm or humble and vice versa.
If someone is rich or old then susan is patient.
If someone is humble then someone is both kind and calm.
If someone is both not creative and not generous then susan is both not patient and brave and vice versa.
If mary is both quiet and calm then someone is rich or happy and vice versa.
Someone is not creative.
Someone is patient.
Someone is not old or brave.
Alice is not old or not tall. | Susan is funny. | entailment | (![X]:(~brave(X)=>(calm(X)|old(X))))&
(![X]:((tall(X)|~brave(X))<=>(~quiet(X)&~happy(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>wise(X)))&
(![X]:((humble(X)<~>calm(X))=>(patient(X)&~creative(X))))&
(((~generous(susan)|funny(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((patient(X)|~happy(X))<=>(quiet(X)<~>~kind(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((~generous(X)&kind(X)))))&
(((~strong(paul)|~calm(paul)))<=>(kind(fred)))&
(![X]:(~generous(X)<=>humble(X)))&
((quiet(alice))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(~tall(X)|~happy(X))))&
(![X]:((~happy(X)|kind(X))<=>(~calm(X)|humble(X))))&
((?[X]:((rich(X)|old(X))))=>(patient(susan)))&
((?[X]:(humble(X)))=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~creative(X)&~generous(X))))<=>((~patient(susan)&brave(susan))))&
(((quiet(mary)&calm(mary)))<=>(?[X]:((rich(X)|happy(X)))))&
(?[X]:(~creative(X)))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)|brave(X))))&
((~old(alice)|~tall(alice))) | funny(susan) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7577987677339278927583684
% SZS output start Proof for 7577987677339278927583684
2. ! [X0] : ((~brave(X0) | tall(X0)) <=> (~happy(X0) & ~quiet(X0))) [input p1]
3. ! [X0] : ((~curious(X0) <~> ~wise(X0)) <=> wise(X0)) [input p2]
5. (funny(susan) | ~generous(susan)) <=> ? [X0] : ~curious(X0) [input p4]
6. ! [X0] : ((~happy(X0) | patient(X0)) <=> (quiet(X0) <~> ~kind(X0))) [input p5]
9. ! [X0] : (~generous(X0) <=> humble(X0)) [input p8]
11. ! [X0] : ((brave(X0) <~> calm(X0)) <=> (~happy(X0) | ~tall(X0))) [input p10]
14. ? [X0] : humble(X0) => ? [X0] : (calm(X0) & kind(X0)) [input p13]
16. (calm(mary) & quiet(mary)) <=> ? [X0] : (happy(X0) | rich(X0)) [input p15]
21. ~funny(susan) [input hypothesis]
23. ? [X0] : humble(X0) => ? [X1] : (calm(X1) & kind(X1)) [rectify 14]
29. ? [X1] : (calm(X1) & kind(X1)) | ! [X0] : ~humble(X0) [ennf transformation 23]
30. ! [X0] : (((~brave(X0) | tall(X0)) | (happy(X0) | quiet(X0))) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [nnf transformation 2]
31. ! [X0] : ((~brave(X0) | tall(X0) | happy(X0) | quiet(X0)) & ((~happy(X0) & ~quiet(X0)) | (brave(X0) & ~tall(X0)))) [flattening 30]
32. ! [X0] : ((((wise(X0) | curious(X0)) & (~wise(X0) | ~curious(X0))) | ~wise(X0)) & (wise(X0) | ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0))))) [nnf transformation 3]
34. ((funny(susan) | ~generous(susan)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(susan) & generous(susan))) [nnf transformation 5]
35. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (~funny(susan) & generous(susan))) [flattening 34]
36. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | (~funny(susan) & generous(susan))) [rectify 35]
37. ? [X1] : ~curious(X1) => ~curious(sK0) [choice axiom]
38. (funny(susan) | ~generous(susan) | ! [X0] : curious(X0)) & (~curious(sK0) | (~funny(susan) & generous(susan))) [skolemisation 36,37]
39. ! [X0] : (((~happy(X0) | patient(X0)) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [nnf transformation 6]
40. ! [X0] : ((~happy(X0) | patient(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0)))) & (((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | (happy(X0) & ~patient(X0)))) [flattening 39]
47. ! [X0] : ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))) [nnf transformation 9]
52. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [nnf transformation 11]
53. ! [X0] : ((((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))))) [flattening 52]
56. ? [X0] : (calm(X0) & kind(X0)) | ! [X1] : ~humble(X1) [rectify 29]
57. ? [X0] : (calm(X0) & kind(X0)) => (calm(sK3) & kind(sK3)) [choice axiom]
58. (calm(sK3) & kind(sK3)) | ! [X1] : ~humble(X1) [skolemisation 56,57]
64. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | (~calm(mary) | ~quiet(mary))) [nnf transformation 16]
65. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X0] : (happy(X0) | rich(X0)) | ~calm(mary) | ~quiet(mary)) [flattening 64]
66. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & (? [X1] : (happy(X1) | rich(X1)) | ~calm(mary) | ~quiet(mary)) [rectify 65]
67. ? [X1] : (happy(X1) | rich(X1)) => (happy(sK5) | rich(sK5)) [choice axiom]
68. ((calm(mary) & quiet(mary)) | ! [X0] : (~happy(X0) & ~rich(X0))) & ((happy(sK5) | rich(sK5)) | ~calm(mary) | ~quiet(mary)) [skolemisation 66,67]
76. ~quiet(X0) | ~tall(X0) [cnf transformation 31]
77. ~quiet(X0) | brave(X0) [cnf transformation 31]
82. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 32]
83. ~wise(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 32]
91. funny(susan) | ~generous(susan) | curious(X0) [cnf transformation 38]
93. ~kind(X0) | quiet(X0) | happy(X0) [cnf transformation 40]
105. generous(X0) | humble(X0) [cnf transformation 47]
114. ~calm(X0) | ~brave(X0) | tall(X0) [cnf transformation 53]
122. kind(sK3) | ~humble(X1) [cnf transformation 58]
123. calm(sK3) | ~humble(X1) [cnf transformation 58]
130. quiet(mary) | ~happy(X0) [cnf transformation 68]
132. calm(mary) | ~happy(X0) [cnf transformation 68]
137. ~funny(susan) [cnf transformation 21]
138. wise(X0) | ~curious(X0) [duplicate literal removal 82]
139. ~wise(X0) | ~curious(X0) [duplicate literal removal 83]
140. ~curious(X0) [subsumption resolution 138,139]
141. funny(susan) | ~generous(susan) [subsumption resolution 91,140]
143. 1 <=> generous(susan) [avatar definition]
145. ~generous(susan) <- (~1) [avatar component clause 143]
147. 2 <=> funny(susan) [avatar definition]
150. ~1 | 2 [avatar split clause 141,147,143]
216. 17 <=> ! [X1] : ~humble(X1) [avatar definition]
217. ~humble(X1) <- (17) [avatar component clause 216]
219. 18 <=> calm(sK3) [avatar definition]
221. calm(sK3) <- (18) [avatar component clause 219]
222. 17 | 18 [avatar split clause 123,219,216]
224. 19 <=> kind(sK3) [avatar definition]
226. kind(sK3) <- (19) [avatar component clause 224]
227. 17 | 19 [avatar split clause 122,224,216]
248. 24 <=> ! [X0] : ~happy(X0) [avatar definition]
249. ~happy(X0) <- (24) [avatar component clause 248]
251. 25 <=> calm(mary) [avatar definition]
253. calm(mary) <- (25) [avatar component clause 251]
254. 24 | 25 [avatar split clause 132,251,248]
257. 26 <=> quiet(mary) [avatar definition]
259. quiet(mary) <- (26) [avatar component clause 257]
260. 24 | 26 [avatar split clause 130,257,248]
289. ~2 [avatar split clause 137,147]
290. humble(susan) <- (~1) [resolution 105,145]
293. $false <- (~1, 17) [subsumption resolution 290,217]
294. 1 | ~17 [avatar contradiction clause 293]
370. quiet(sK3) | happy(sK3) <- (19) [resolution 93,226]
391. ~brave(sK3) | tall(sK3) <- (18) [resolution 114,221]
397. 43 <=> tall(sK3) [avatar definition]
401. 44 <=> brave(sK3) [avatar definition]
403. ~brave(sK3) <- (~44) [avatar component clause 401]
404. 43 | ~44 | ~18 [avatar split clause 391,219,401,397]
405. quiet(sK3) <- (19, 24) [subsumption resolution 370,249]
425. brave(sK3) <- (19, 24) [resolution 405,77]
426. ~tall(sK3) <- (19, 24) [resolution 405,76]
427. $false <- (19, 24, ~44) [subsumption resolution 425,403]
428. ~19 | ~24 | 44 [avatar contradiction clause 427]
429. ~43 | ~19 | ~24 [avatar split clause 426,248,224,397]
444. ~brave(mary) | tall(mary) <- (25) [resolution 253,114]
456. 51 <=> brave(mary) [avatar definition]
458. ~brave(mary) <- (~51) [avatar component clause 456]
461. 52 <=> tall(mary) [avatar definition]
464. 52 | ~51 | ~25 [avatar split clause 444,251,456,461]
471. brave(mary) <- (26) [resolution 259,77]
472. ~tall(mary) <- (26) [resolution 259,76]
478. $false <- (26, ~51) [subsumption resolution 471,458]
479. ~26 | 51 [avatar contradiction clause 478]
480. ~52 | ~26 [avatar split clause 472,257,461]
481. $false [avatar sat refutation 150,222,227,254,260,289,294,404,428,429,464,479,480]
% SZS output end Proof for 7577987677339278927583684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not humble or rich then susan is either not kind or not curious and vice versa.
If paul is not happy then alice is either not calm or old.
Everyone who is not patient or tall is either funny or not strong.
If john is either not rich or curious then someone is both tall and not old and vice versa.
Everyone who is not tall or not funny is either not strong or generous.
Everyone who is both not creative and not rich is either tall or happy.
Everyone who is not rich is not kind.
If someone is both not creative and not generous then someone is not curious.
If someone is either not kind or not old then someone is kind and vice versa.
Everyone who is not rich or not funny is either quiet or generous.
Everyone who is brave is both rich and not rich.
Everyone who is either not generous or curious is both old and tall.
If someone is either not patient or tall then someone is both strong and kind.
If someone is patient or quiet then someone is both funny and not curious.
Everyone who is either not happy or creative is not kind and vice versa.
If paul is not calm then susan is either not humble or humble.
Alice is not tall or not calm.
Mary is creative.
Someone is not rich.
Lucy is quiet or not calm.
Someone is both funny and not quiet.
Mary is both not calm and not wise.
Someone is both generous and rich.
Someone is rich. | Alice is not brave. | entailment | (((~humble(mary)|rich(mary)))<=>((~kind(susan)<~>~curious(susan))))&
((~happy(paul))=>((~calm(alice)<~>old(alice))))&
(![X]:((~patient(X)|tall(X))=>(funny(X)<~>~strong(X))))&
(((~rich(john)<~>curious(john)))<=>(?[X]:((tall(X)&~old(X)))))&
(![X]:((~tall(X)|~funny(X))=>(~strong(X)<~>generous(X))))&
(![X]:((~creative(X)&~rich(X))=>(tall(X)<~>happy(X))))&
(![X]:(~rich(X)=>~kind(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(?[X]:(kind(X))))&
(![X]:((~rich(X)|~funny(X))=>(quiet(X)<~>generous(X))))&
(![X]:(brave(X)=>(rich(X)&~rich(X))))&
(![X]:((~generous(X)<~>curious(X))=>(old(X)&tall(X))))&
((?[X]:((~patient(X)<~>tall(X))))=>(?[X]:((strong(X)&kind(X)))))&
((?[X]:((patient(X)|quiet(X))))=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))<=>~kind(X)))&
((~calm(paul))=>((~humble(susan)<~>humble(susan))))&
((~tall(alice)|~calm(alice)))&
(creative(mary))&
(?[X]:(~rich(X)))&
((quiet(lucy)|~calm(lucy)))&
(?[X]:((funny(X)&~quiet(X))))&
((~calm(mary)&~wise(mary)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:(rich(X))) | ~brave(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 474499372505310745636051
% SZS output start Proof for 474499372505310745636051
11. ! [X0] : (brave(X0) => (~rich(X0) & rich(X0))) [input p10]
25. brave(alice) [input hypothesis]
39. ! [X0] : ((~rich(X0) & rich(X0)) | ~brave(X0)) [ennf transformation 11]
115. rich(X0) | ~brave(X0) [cnf transformation 39]
116. ~rich(X0) | ~brave(X0) [cnf transformation 39]
145. brave(alice) [cnf transformation 25]
240. ~brave(X0) [subsumption resolution 115,116]
291. $false [subsumption resolution 145,240]
% SZS output end Proof for 474499372505310745636051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both tall and funny then someone is either not creative or not rich and vice versa.
If someone is not creative then someone is both tall and brave and vice versa.
If lucy is either not happy or not curious then someone is either old or not happy and vice versa.
If paul is curious or not happy then someone is not humble and vice versa.
Everyone who is not humble or not kind is tall.
Everyone who is both curious and quiet is both creative and wise.
Everyone who is not generous or tall is either patient or tall and vice versa.
If john is either old or tall then john is either not old or funny and vice versa.
Everyone who is both not old and quiet is quiet or not humble and vice versa.
Everyone who is not funny is not generous and vice versa.
Everyone who is either kind or not generous is not kind or not happy.
Everyone who is not quiet is both generous and funny.
Everyone who is not happy or not wise is not brave or patient and vice versa.
Everyone who is either not humble or creative is not curious.
If mary is not funny then lucy is either not curious or creative and vice versa.
If mary is either not tall or generous then someone is either kind or not tall.
Alice is both wise and not creative.
Someone is not kind or old.
Someone is strong or patient.
Mary is both patient and creative.
Someone is creative or not happy.
Paul is not funny.
Susan is both not rich and old.
Mary is not generous. | Alice is not creative. | entailment | (((tall(mary)&funny(mary)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((tall(X)&brave(X)))))&
(((~happy(lucy)<~>~curious(lucy)))<=>(?[X]:((old(X)<~>~happy(X)))))&
(((curious(paul)|~happy(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|~kind(X))=>tall(X)))&
(![X]:((curious(X)&quiet(X))=>(creative(X)&wise(X))))&
(![X]:((~generous(X)|tall(X))<=>(patient(X)<~>tall(X))))&
(((old(john)<~>tall(john)))<=>((~old(john)<~>funny(john))))&
(![X]:((~old(X)&quiet(X))<=>(quiet(X)|~humble(X))))&
(![X]:(~funny(X)<=>~generous(X)))&
(![X]:((kind(X)<~>~generous(X))=>(~kind(X)|~happy(X))))&
(![X]:(~quiet(X)=>(generous(X)&funny(X))))&
(![X]:((~happy(X)|~wise(X))<=>(~brave(X)|patient(X))))&
(![X]:((~humble(X)<~>creative(X))=>~curious(X)))&
((~funny(mary))<=>((~curious(lucy)<~>creative(lucy))))&
(((~tall(mary)<~>generous(mary)))=>(?[X]:((kind(X)<~>~tall(X)))))&
((wise(alice)&~creative(alice)))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:((strong(X)|patient(X))))&
((patient(mary)&creative(mary)))&
(?[X]:((creative(X)|~happy(X))))&
(~funny(paul))&
((~rich(susan)&old(susan)))&
(~generous(mary)) | ~creative(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7353209258365356522569262
% SZS output start Proof for 7353209258365356522569262
17. ~creative(alice) & wise(alice) [input p16]
25. creative(alice) [input hypothesis]
137. ~creative(alice) [cnf transformation 17]
146. creative(alice) [cnf transformation 25]
314. $false [subsumption resolution 146,137]
% SZS output end Proof for 7353209258365356522569262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not strong then lucy is not old and vice versa.
Everyone who is both not patient and not humble is patient and vice versa.
Everyone who is generous is either not patient or humble.
Everyone who is both not happy and not old is tall and vice versa.
Everyone who is either creative or rich is generous or not rich and vice versa.
If someone is not humble or not wise then someone is quiet.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Mary is curious or not funny.
Someone is not quiet.
John is both not calm and not brave.
Mary is both not patient and kind.
Someone is not happy or not generous. | John is not happy. | neutral | ((?[X]:((~curious(X)|~strong(X))))<=>(~old(lucy)))&
(![X]:((~patient(X)&~humble(X))<=>patient(X)))&
(![X]:(generous(X)=>(~patient(X)<~>humble(X))))&
(![X]:((~happy(X)&~old(X))<=>tall(X)))&
(![X]:((creative(X)<~>rich(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))=>(?[X]:(quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
((curious(mary)|~funny(mary)))&
(?[X]:(~quiet(X)))&
((~calm(john)&~brave(john)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is either not calm or not brave is curious and vice versa. If someone is both not tall and not quiet then someone is both not tall and creative. Everyone who is either not kind or not rich is either strong or happy and vice versa. If someone is not quiet or brave then someone is curious and vice versa. Everyone who is both brave and not funny is not happy or not wise. If lucy is both funny and wise then paul is rich. Everyone who is calm or rich is not old and vice versa. If fred is either not calm or kind then alice is both not wise and patient. Everyone who is both not calm and not wise is not calm and vice versa. If paul is either not brave or not calm then someone is not wise or happy. Everyone who is either tall or not old is rich or curious. If susan is either brave or quiet then someone is not patient and vice versa. If alice is not tall then alice is not generous or kind. Everyone who is either calm or patient is both not patient and patient and vice versa. If someone is not quiet or not calm then someone is not calm and vice versa. Everyone who is both not wise and curious is not old or patient. Someone is both patient and happy. Someone is not calm. Lucy is not rich. Paul is old. Lucy is both generous and strong. Someone is both funny and not generous. Paul is not tall or kind. Someone is either calm or tall. | Paul is not brave. | entailment | (![X]:((~calm(X)<~>~brave(X))<=>curious(X)))&
((?[X]:((~tall(X)&~quiet(X))))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)&~funny(X))=>(~happy(X)|~wise(X))))&
(((funny(lucy)&wise(lucy)))=>(rich(paul)))&
(![X]:((calm(X)|rich(X))<=>~old(X)))&
(((~calm(fred)<~>kind(fred)))=>((~wise(alice)&patient(alice))))&
(![X]:((~calm(X)&~wise(X))<=>~calm(X)))&
(((~brave(paul)<~>~calm(paul)))=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((tall(X)<~>~old(X))=>(rich(X)|curious(X))))&
(((brave(susan)<~>quiet(susan)))<=>(?[X]:(~patient(X))))&
((~tall(alice))=>((~generous(alice)|kind(alice))))&
(![X]:((calm(X)<~>patient(X))<=>(~patient(X)&patient(X))))&
((?[X]:((~quiet(X)|~calm(X))))<=>(?[X]:(~calm(X))))&
(![X]:((~wise(X)&curious(X))=>(~old(X)|patient(X))))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:(~calm(X)))&
(~rich(lucy))&
(old(paul))&
((generous(lucy)&strong(lucy)))&
(?[X]:((funny(X)&~generous(X))))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>tall(X)))) | ~brave(paul) | [
"p0",
"p6",
"p8",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 506091122318912788686310
% SZS output start Proof for 506091122318912788686310
1. ! [X0] : ((~calm(X0) <~> ~brave(X0)) <=> curious(X0)) [input p0]
7. ! [X0] : ((rich(X0) | calm(X0)) <=> ~old(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> ~calm(X0)) [input p8]
14. ! [X0] : ((calm(X0) <~> patient(X0)) <=> (patient(X0) & ~patient(X0))) [input p13]
16. ! [X0] : ((curious(X0) & ~wise(X0)) => (patient(X0) | ~old(X0))) [input p15]
20. old(paul) [input p19]
25. brave(paul) [input hypothesis]
41. ! [X0] : ((patient(X0) | ~old(X0)) | (~curious(X0) | wise(X0))) [ennf transformation 16]
42. ! [X0] : (patient(X0) | ~old(X0) | ~curious(X0) | wise(X0)) [flattening 41]
43. ! [X0] : ((((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | ~curious(X0)) & (curious(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0))))) [nnf transformation 1]
53. ! [X0] : (((rich(X0) | calm(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & ~calm(X0)))) [nnf transformation 7]
54. ! [X0] : ((rich(X0) | calm(X0) | old(X0)) & (~old(X0) | (~rich(X0) & ~calm(X0)))) [flattening 53]
56. ! [X0] : (((~wise(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) | calm(X0)))) [nnf transformation 9]
57. ! [X0] : (((~wise(X0) & ~calm(X0)) | calm(X0)) & (~calm(X0) | wise(X0) | calm(X0))) [flattening 56]
66. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [nnf transformation 14]
67. ! [X0] : ((((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0))))) [flattening 66]
82. ~brave(X0) | curious(X0) | calm(X0) [cnf transformation 43]
100. ~old(X0) | ~calm(X0) [cnf transformation 54]
109. ~wise(X0) | calm(X0) [cnf transformation 57]
120. ~patient(X0) | calm(X0) | ~patient(X0) [cnf transformation 67]
128. ~old(X0) | patient(X0) | ~curious(X0) | wise(X0) [cnf transformation 42]
133. old(paul) [cnf transformation 20]
141. brave(paul) [cnf transformation 25]
142. ~patient(X0) | calm(X0) [duplicate literal removal 120]
212. 16 <=> calm(paul) [avatar definition]
213. ~calm(paul) <- (~16) [avatar component clause 212]
216. 17 <=> brave(paul) [avatar definition]
217. brave(paul) <- (17) [avatar component clause 216]
299. 17 [avatar split clause 141,216]
302. ~calm(paul) [resolution 100,133]
303. ~16 [avatar split clause 302,212]
310. curious(paul) | calm(paul) <- (17) [resolution 82,217]
312. curious(paul) <- (~16, 17) [subsumption resolution 310,213]
471. patient(paul) | ~curious(paul) | wise(paul) [resolution 128,133]
474. patient(paul) | wise(paul) <- (~16, 17) [subsumption resolution 471,312]
476. 57 <=> wise(paul) [avatar definition]
478. wise(paul) <- (57) [avatar component clause 476]
480. 58 <=> patient(paul) [avatar definition]
482. patient(paul) <- (58) [avatar component clause 480]
483. 57 | 58 | 16 | ~17 [avatar split clause 474,216,212,480,476]
486. calm(paul) <- (57) [resolution 478,109]
497. $false <- (~16, 57) [subsumption resolution 486,213]
498. 16 | ~57 [avatar contradiction clause 497]
499. calm(paul) <- (58) [resolution 482,142]
500. $false <- (~16, 58) [subsumption resolution 499,213]
501. 16 | ~58 [avatar contradiction clause 500]
502. $false [avatar sat refutation 299,303,483,498,501]
% SZS output end Proof for 506091122318912788686310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not funny and vice versa. If someone is either tall or happy then someone is happy or not humble. Everyone who is either not wise or old is either not old or old. If someone is both tall and brave then someone is not rich. If someone is both not calm and brave then john is curious. If fred is either tall or calm then someone is both not old and not creative. If someone is not old then someone is both rich and not generous. If mary is not creative or not wise then someone is either brave or tall. If someone is both not kind and not strong then susan is both calm and wise and vice versa. If alice is happy or not quiet then someone is not brave. Everyone who is quiet is not kind. If someone is either not calm or creative then paul is both not patient and not wise and vice versa. Everyone who is not happy or creative is not rich or not creative and vice versa. If susan is patient or strong then susan is both kind and curious and vice versa. Everyone who is both wise and not old is both not happy and not calm and vice versa. Everyone who is old or creative is not curious. Susan is strong or rich. Someone is not wise or calm. Someone is either not calm or humble. Mary is not creative or old. Someone is not funny or quiet. Fred is both happy and kind. Someone is either rich or not strong. Someone is either calm or rich. | Fred is not quiet. | entailment | (![X]:(happy(X)<=>~funny(X)))&
((?[X]:((tall(X)<~>happy(X))))=>(?[X]:((happy(X)|~humble(X)))))&
(![X]:((~wise(X)<~>old(X))=>(~old(X)<~>old(X))))&
((?[X]:((tall(X)&brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~calm(X)&brave(X))))=>(curious(john)))&
(((tall(fred)<~>calm(fred)))=>(?[X]:((~old(X)&~creative(X)))))&
((?[X]:(~old(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(((~creative(mary)|~wise(mary)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:((~kind(X)&~strong(X))))<=>((calm(susan)&wise(susan))))&
(((happy(alice)|~quiet(alice)))=>(?[X]:(~brave(X))))&
(![X]:(quiet(X)=>~kind(X)))&
((?[X]:((~calm(X)<~>creative(X))))<=>((~patient(paul)&~wise(paul))))&
(![X]:((~happy(X)|creative(X))<=>(~rich(X)|~creative(X))))&
(((patient(susan)|strong(susan)))<=>((kind(susan)&curious(susan))))&
(![X]:((wise(X)&~old(X))<=>(~happy(X)&~calm(X))))&
(![X]:((old(X)|creative(X))=>~curious(X)))&
((strong(susan)|rich(susan)))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((~calm(X)<~>humble(X))))&
((~creative(mary)|old(mary)))&
(?[X]:((~funny(X)|quiet(X))))&
((happy(fred)&kind(fred)))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:((calm(X)<~>rich(X)))) | ~quiet(fred) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4251705268846707147428450
% SZS output start Proof for 4251705268846707147428450
11. ! [X0] : (quiet(X0) => ~kind(X0)) [input p10]
22. kind(fred) & happy(fred) [input p21]
25. quiet(fred) [input hypothesis]
38. ! [X0] : (~kind(X0) | ~quiet(X0)) [ennf transformation 11]
114. ~quiet(X0) | ~kind(X0) [cnf transformation 38]
143. kind(fred) [cnf transformation 22]
148. quiet(fred) [cnf transformation 25]
381. ~kind(fred) [resolution 114,148]
382. $false [subsumption resolution 381,143]
% SZS output end Proof for 4251705268846707147428450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and patient is either curious or not rich.
Everyone who is not curious is not patient or not humble and vice versa.
If lucy is either rich or brave then someone is both funny and not old.
If alice is either funny or not tall then fred is either brave or not tall and vice versa.
If someone is not rich then paul is both not quiet and creative and vice versa.
If someone is not happy or not generous then someone is old or not tall.
If someone is strong or funny then john is both not old and not tall.
Everyone who is either quiet or happy is patient and vice versa.
Everyone who is patient or not old is either not funny or not strong.
Everyone who is quiet or wise is happy and vice versa.
Everyone who is both not curious and happy is not rich.
If someone is either calm or curious then someone is either funny or not curious and vice versa.
Everyone who is calm or not brave is both not humble and not quiet and vice versa.
Everyone who is both tall and kind is kind and vice versa.
Everyone who is both brave and calm is not humble or not wise.
Everyone who is either not patient or quiet is both kind and quiet and vice versa.
Mary is both not patient and not creative.
Someone is creative.
Someone is curious.
Someone is both calm and not humble.
Mary is happy or calm.
Someone is not rich or not calm.
Someone is not happy or not patient.
Someone is not funny or happy. | Paul is not creative. | contradiction | (![X]:((kind(X)&patient(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~curious(X)<=>(~patient(X)|~humble(X))))&
(((rich(lucy)<~>brave(lucy)))=>(?[X]:((funny(X)&~old(X)))))&
(((funny(alice)<~>~tall(alice)))<=>((brave(fred)<~>~tall(fred))))&
((?[X]:(~rich(X)))<=>((~quiet(paul)&creative(paul))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((old(X)|~tall(X)))))&
((?[X]:((strong(X)|funny(X))))=>((~old(john)&~tall(john))))&
(![X]:((quiet(X)<~>happy(X))<=>patient(X)))&
(![X]:((patient(X)|~old(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((quiet(X)|wise(X))<=>happy(X)))&
(![X]:((~curious(X)&happy(X))=>~rich(X)))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((calm(X)|~brave(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((tall(X)&kind(X))<=>kind(X)))&
(![X]:((brave(X)&calm(X))=>(~humble(X)|~wise(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(kind(X)&quiet(X))))&
((~patient(mary)&~creative(mary)))&
(?[X]:(creative(X)))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~humble(X))))&
((happy(mary)|calm(mary)))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((~happy(X)|~patient(X))))&
(?[X]:((~funny(X)|happy(X)))) | ~creative(paul) | [
"p1",
"p4",
"p10",
"p12",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6328674052570677236232797
% SZS output start Proof for 6328674052570677236232797
2. ! [X0] : (~curious(X0) <=> (~humble(X0) | ~patient(X0))) [input p1]
5. ? [X0] : ~rich(X0) <=> (creative(paul) & ~quiet(paul)) [input p4]
11. ! [X0] : ((happy(X0) & ~curious(X0)) => ~rich(X0)) [input p10]
13. ! [X0] : ((~brave(X0) | calm(X0)) <=> (~quiet(X0) & ~humble(X0))) [input p12]
16. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (quiet(X0) & kind(X0))) [input p15]
17. ~creative(mary) & ~patient(mary) [input p16]
21. calm(mary) | happy(mary) [input p20]
25. ~creative(paul) [input hypothesis]
35. ! [X0] : (~rich(X0) | (~happy(X0) | curious(X0))) [ennf transformation 11]
36. ! [X0] : (~rich(X0) | ~happy(X0) | curious(X0)) [flattening 35]
40. ! [X0] : ((~curious(X0) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | curious(X0))) [nnf transformation 2]
41. ! [X0] : ((~curious(X0) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | curious(X0))) [flattening 40]
46. (? [X0] : ~rich(X0) | (~creative(paul) | quiet(paul))) & ((creative(paul) & ~quiet(paul)) | ! [X0] : rich(X0)) [nnf transformation 5]
47. (? [X0] : ~rich(X0) | ~creative(paul) | quiet(paul)) & ((creative(paul) & ~quiet(paul)) | ! [X0] : rich(X0)) [flattening 46]
48. (? [X0] : ~rich(X0) | ~creative(paul) | quiet(paul)) & ((creative(paul) & ~quiet(paul)) | ! [X1] : rich(X1)) [rectify 47]
49. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
50. (~rich(sK1) | ~creative(paul) | quiet(paul)) & ((creative(paul) & ~quiet(paul)) | ! [X1] : rich(X1)) [skolemisation 48,49]
63. ! [X0] : (((~brave(X0) | calm(X0)) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | (brave(X0) & ~calm(X0)))) [nnf transformation 13]
64. ! [X0] : ((~brave(X0) | calm(X0) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | (brave(X0) & ~calm(X0)))) [flattening 63]
67. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~quiet(X0) | ~kind(X0))) & ((quiet(X0) & kind(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 16]
68. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~quiet(X0) | ~kind(X0)) & ((quiet(X0) & kind(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 67]
84. ~curious(X0) | patient(X0) [cnf transformation 41]
99. creative(paul) | rich(X1) [cnf transformation 50]
117. ~happy(X0) | ~rich(X0) | curious(X0) [cnf transformation 36]
128. ~calm(X0) | ~quiet(X0) [cnf transformation 64]
137. quiet(X0) | quiet(X0) | patient(X0) [cnf transformation 68]
141. ~patient(mary) [cnf transformation 17]
147. calm(mary) | happy(mary) [cnf transformation 21]
151. ~creative(paul) [cnf transformation 25]
152. quiet(X0) | patient(X0) [duplicate literal removal 137]
203. 10 <=> creative(paul) [avatar definition]
212. 12 <=> ! [X1] : rich(X1) [avatar definition]
213. rich(X1) <- (12) [avatar component clause 212]
214. 12 | 10 [avatar split clause 99,203,212]
283. 28 <=> happy(mary) [avatar definition]
285. happy(mary) <- (28) [avatar component clause 283]
287. 29 <=> calm(mary) [avatar definition]
289. calm(mary) <- (29) [avatar component clause 287]
290. 28 | 29 [avatar split clause 147,287,283]
318. ~10 [avatar split clause 151,203]
421. 47 <=> quiet(mary) [avatar definition]
422. ~quiet(mary) <- (~47) [avatar component clause 421]
426. ~quiet(mary) <- (29) [resolution 289,128]
428. ~47 | ~29 [avatar split clause 426,287,421]
433. patient(mary) <- (~47) [resolution 422,152]
434. $false <- (~47) [subsumption resolution 433,141]
435. 47 [avatar contradiction clause 434]
456. ~rich(mary) | curious(mary) <- (28) [resolution 117,285]
458. curious(mary) <- (12, 28) [subsumption resolution 456,213]
509. patient(mary) <- (12, 28) [resolution 458,84]
510. $false <- (12, 28) [subsumption resolution 509,141]
511. ~12 | ~28 [avatar contradiction clause 510]
512. $false [avatar sat refutation 214,290,318,428,435,511]
% SZS output end Proof for 6328674052570677236232797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either funny or wise then someone is both humble and strong and vice versa. Everyone who is both kind and rich is both not rich and not old and vice versa. Everyone who is quiet or not tall is both old and not quiet. Everyone who is not kind or not generous is quiet. If susan is both generous and calm then john is happy. Everyone who is both brave and old is kind and vice versa. Everyone who is calm or wise is not happy. Everyone who is either generous or not curious is both kind and not humble and vice versa. If someone is either funny or not brave then someone is curious and vice versa. Everyone who is both not creative and not patient is either curious or not curious and vice versa. Everyone who is not wise or brave is kind and vice versa. Everyone who is not patient is either calm or not quiet. If someone is either tall or curious then john is both rich and patient and vice versa. If someone is either not old or curious then someone is both funny and happy. Everyone who is strong is tall. Paul is calm or kind. Someone is not kind or curious. Mary is rich or generous. John is not tall. Mary is not rich. Lucy is strong or not humble. Someone is tall or not humble. | Paul is calm. | contradiction | (((funny(mary)<~>wise(mary)))<=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((kind(X)&rich(X))<=>(~rich(X)&~old(X))))&
(![X]:((quiet(X)|~tall(X))=>(old(X)&~quiet(X))))&
(![X]:((~kind(X)|~generous(X))=>quiet(X)))&
(((generous(susan)&calm(susan)))=>(happy(john)))&
(![X]:((brave(X)&old(X))<=>kind(X)))&
(![X]:((calm(X)|wise(X))=>~happy(X)))&
(![X]:((generous(X)<~>~curious(X))<=>(kind(X)&~humble(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)&~patient(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~wise(X)|brave(X))<=>kind(X)))&
(![X]:(~patient(X)=>(calm(X)<~>~quiet(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>((rich(john)&patient(john))))&
((?[X]:((~old(X)<~>curious(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(strong(X)=>tall(X)))&
((calm(paul)|kind(paul)))&
(?[X]:((~kind(X)|curious(X))))&
((rich(mary)|generous(mary)))&
(~tall(john))&
(~rich(mary))&
((strong(lucy)|~humble(lucy)))&
(?[X]:((tall(X)|~humble(X)))) | calm(paul) | [
"p2",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2016697646509184517967752
% SZS output start Proof for 2016697646509184517967752
3. ! [X0] : ((~tall(X0) | quiet(X0)) => (~quiet(X0) & old(X0))) [input p2]
10. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p9]
12. ! [X0] : (~patient(X0) => (calm(X0) <~> ~quiet(X0))) [input p11]
23. calm(paul) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & old(X0)) | (tall(X0) & ~quiet(X0))) [ennf transformation 3]
31. ! [X0] : ((calm(X0) <~> ~quiet(X0)) | patient(X0)) [ennf transformation 12]
49. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (patient(X0) | creative(X0)))) [nnf transformation 10]
50. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | patient(X0) | creative(X0))) [flattening 49]
53. ! [X0] : (((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | patient(X0)) [nnf transformation 31]
79. ~quiet(X0) | ~quiet(X0) [cnf transformation 26]
103. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 50]
104. ~patient(X0) | curious(X0) | curious(X0) [cnf transformation 50]
109. quiet(X0) | ~calm(X0) | patient(X0) [cnf transformation 53]
128. calm(paul) [cnf transformation 23]
131. ~patient(X0) | ~curious(X0) [duplicate literal removal 103]
132. ~patient(X0) | curious(X0) [duplicate literal removal 104]
133. ~quiet(X0) [duplicate literal removal 79]
196. ~patient(X0) [subsumption resolution 131,132]
198. ~calm(X0) | patient(X0) [subsumption resolution 109,133]
199. ~calm(X0) [subsumption resolution 198,196]
233. $false [subsumption resolution 128,199]
% SZS output end Proof for 2016697646509184517967752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is funny then lucy is both brave and curious.
If john is not happy then lucy is either brave or wise.
Everyone who is both not strong and not old is either not calm or not creative and vice versa.
Everyone who is either not brave or patient is both not happy and old and vice versa.
If someone is creative or not rich then someone is tall or brave.
If susan is not rich or not happy then someone is tall and vice versa.
Everyone who is calm is not generous and vice versa.
Everyone who is not brave is strong and vice versa.
If someone is generous then someone is kind or not funny.
If someone is not humble then someone is old and vice versa.
Everyone who is either humble or rich is not quiet.
Everyone who is calm is both humble and not quiet and vice versa.
If someone is not old or not curious then someone is both generous and not patient.
Everyone who is both not strong and not old is curious or not strong and vice versa.
If fred is humble or not wise then someone is either not kind or old and vice versa.
Everyone who is rich is both not creative and old.
Someone is either not strong or not calm.
Someone is kind.
Someone is rich or not humble.
Someone is either not patient or tall.
Fred is patient or brave.
Fred is both wise and strong.
John is either not wise or not creative.
Someone is either humble or brave. | Fred is not brave. | entailment | ((funny(susan))=>((brave(lucy)&curious(lucy))))&
((~happy(john))=>((brave(lucy)<~>wise(lucy))))&
(![X]:((~strong(X)&~old(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(~happy(X)&old(X))))&
((?[X]:((creative(X)|~rich(X))))=>(?[X]:((tall(X)|brave(X)))))&
(((~rich(susan)|~happy(susan)))<=>(?[X]:(tall(X))))&
(![X]:(calm(X)<=>~generous(X)))&
(![X]:(~brave(X)<=>strong(X)))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)|~funny(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(old(X))))&
(![X]:((humble(X)<~>rich(X))=>~quiet(X)))&
(![X]:(calm(X)<=>(humble(X)&~quiet(X))))&
((?[X]:((~old(X)|~curious(X))))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~strong(X)&~old(X))<=>(curious(X)|~strong(X))))&
(((humble(fred)|~wise(fred)))<=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:(rich(X)=>(~creative(X)&old(X))))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
((patient(fred)|brave(fred)))&
((wise(fred)&strong(fred)))&
((~wise(john)<~>~creative(john)))&
(?[X]:((humble(X)<~>brave(X)))) | ~brave(fred) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6415938460618895618432704
% SZS output start Proof for 6415938460618895618432704
8. ! [X0] : (~brave(X0) <=> strong(X0)) [input p7]
22. strong(fred) & wise(fred) [input p21]
25. brave(fred) [input hypothesis]
51. ! [X0] : ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0))) [nnf transformation 8]
106. ~strong(X0) | ~brave(X0) [cnf transformation 51]
139. strong(fred) [cnf transformation 22]
144. brave(fred) [cnf transformation 25]
289. 33 <=> brave(fred) [avatar definition]
291. brave(fred) <- (33) [avatar component clause 289]
314. 33 [avatar split clause 144,289]
325. ~brave(fred) [resolution 106,139]
328. $false <- (33) [subsumption resolution 325,291]
329. ~33 [avatar contradiction clause 328]
330. $false [avatar sat refutation 314,329]
% SZS output end Proof for 6415938460618895618432704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is either happy or not wise and vice versa.
Everyone who is not curious or not creative is both not brave and curious.
Everyone who is humble is rich or not humble.
If mary is not brave then mary is old or not happy and vice versa.
If fred is either generous or not creative then mary is either not curious or tall and vice versa.
If alice is not quiet or not humble then john is either not old or brave and vice versa.
If alice is strong or not calm then someone is either not creative or creative.
If alice is not strong then susan is not old and vice versa.
If someone is wise or generous then someone is not patient and vice versa.
If someone is either rich or not strong then john is not kind or not calm and vice versa.
If someone is both not old and happy then alice is either humble or quiet and vice versa.
If someone is either not creative or not strong then someone is not quiet or creative.
If someone is not strong or not calm then someone is both not old and rich and vice versa.
If fred is not humble or quiet then mary is either not calm or strong.
Everyone who is either not humble or wise is generous or quiet.
If someone is both creative and humble then lucy is not funny.
Alice is both wise and not quiet.
Someone is not tall.
Someone is happy.
Mary is either not generous or not quiet.
Fred is not calm.
Someone is not generous or not patient.
Susan is either not quiet or humble. | Susan is not old. | neutral | (![X]:((~wise(X)|quiet(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~curious(X)|~creative(X))=>(~brave(X)&curious(X))))&
(![X]:(humble(X)=>(rich(X)|~humble(X))))&
((~brave(mary))<=>((old(mary)|~happy(mary))))&
(((generous(fred)<~>~creative(fred)))<=>((~curious(mary)<~>tall(mary))))&
(((~quiet(alice)|~humble(alice)))<=>((~old(john)<~>brave(john))))&
(((strong(alice)|~calm(alice)))=>(?[X]:((~creative(X)<~>creative(X)))))&
((~strong(alice))<=>(~old(susan)))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>((~kind(john)|~calm(john))))&
((?[X]:((~old(X)&happy(X))))<=>((humble(alice)<~>quiet(alice))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~quiet(X)|creative(X)))))&
((?[X]:((~strong(X)|~calm(X))))<=>(?[X]:((~old(X)&rich(X)))))&
(((~humble(fred)|quiet(fred)))=>((~calm(mary)<~>strong(mary))))&
(![X]:((~humble(X)<~>wise(X))=>(generous(X)|quiet(X))))&
((?[X]:((creative(X)&humble(X))))=>(~funny(lucy)))&
((wise(alice)&~quiet(alice)))&
(?[X]:(~tall(X)))&
(?[X]:(happy(X)))&
((~generous(mary)<~>~quiet(mary)))&
(~calm(fred))&
(?[X]:((~generous(X)|~patient(X))))&
((~quiet(susan)<~>humble(susan))) | ~old(susan) | [] | null | 0 |
Everyone who is tall or not strong is not brave. Everyone who is both old and tall is both not calm and not strong. Everyone who is both not patient and creative is either not happy or kind and vice versa. Everyone who is both not tall and not strong is both creative and quiet and vice versa. Everyone who is rich or not brave is both not generous and tall and vice versa. If alice is not creative or not brave then someone is creative or generous and vice versa. Everyone who is both not rich and not humble is not brave or kind and vice versa. Everyone who is both not patient and happy is not patient and vice versa. Everyone who is humble or not patient is both creative and not wise. Everyone who is either creative or old is old. If mary is curious or not old then someone is either brave or not kind. Everyone who is not happy or brave is not calm. Everyone who is either not happy or generous is either old or curious and vice versa. If someone is not calm or wise then alice is either generous or strong and vice versa. Everyone who is either funny or not quiet is both wise and not kind and vice versa. Everyone who is either not patient or not quiet is both not brave and kind and vice versa. Fred is either brave or not patient. Paul is quiet. Fred is generous or not old. Paul is generous. Someone is both not tall and happy. Paul is both not creative and generous. Someone is tall. | Fred is happy. | contradiction | (![X]:((tall(X)|~strong(X))=>~brave(X)))&
(![X]:((old(X)&tall(X))=>(~calm(X)&~strong(X))))&
(![X]:((~patient(X)&creative(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)&~strong(X))<=>(creative(X)&quiet(X))))&
(![X]:((rich(X)|~brave(X))<=>(~generous(X)&tall(X))))&
(((~creative(alice)|~brave(alice)))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~brave(X)|kind(X))))&
(![X]:((~patient(X)&happy(X))<=>~patient(X)))&
(![X]:((humble(X)|~patient(X))=>(creative(X)&~wise(X))))&
(![X]:((creative(X)<~>old(X))=>old(X)))&
(((curious(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~happy(X)|brave(X))=>~calm(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)<~>curious(X))))&
((?[X]:((~calm(X)|wise(X))))<=>((generous(alice)<~>strong(alice))))&
(![X]:((funny(X)<~>~quiet(X))<=>(wise(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~brave(X)&kind(X))))&
((brave(fred)<~>~patient(fred)))&
(quiet(paul))&
((generous(fred)|~old(fred)))&
(generous(paul))&
(?[X]:((~tall(X)&happy(X))))&
((~creative(paul)&generous(paul)))&
(?[X]:(tall(X))) | happy(fred) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p9",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 820700468765051725992612
% SZS output start Proof for 820700468765051725992612
1. ! [X0] : ((~strong(X0) | tall(X0)) => ~brave(X0)) [input p0]
3. ! [X0] : ((creative(X0) & ~patient(X0)) <=> (~happy(X0) <~> kind(X0))) [input p2]
4. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (quiet(X0) & creative(X0))) [input p3]
5. ! [X0] : ((~brave(X0) | rich(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
7. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (kind(X0) | ~brave(X0))) [input p6]
9. ! [X0] : ((~patient(X0) | humble(X0)) => (~wise(X0) & creative(X0))) [input p8]
10. ! [X0] : ((creative(X0) <~> old(X0)) => old(X0)) [input p9]
16. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p15]
17. brave(fred) <~> ~patient(fred) [input p16]
19. ~old(fred) | generous(fred) [input p18]
24. happy(fred) [input hypothesis]
25. ! [X0] : (~brave(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 1]
28. ! [X0] : ((~wise(X0) & creative(X0)) | (patient(X0) & ~humble(X0))) [ennf transformation 9]
29. ! [X0] : (old(X0) | (creative(X0) <=> old(X0))) [ennf transformation 10]
32. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (~creative(X0) | patient(X0)))) [nnf transformation 3]
33. ! [X0] : (((creative(X0) & ~patient(X0)) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ~creative(X0) | patient(X0))) [flattening 32]
34. ! [X0] : (((~strong(X0) & ~tall(X0)) | (~quiet(X0) | ~creative(X0))) & ((quiet(X0) & creative(X0)) | (strong(X0) | tall(X0)))) [nnf transformation 4]
35. ! [X0] : (((~strong(X0) & ~tall(X0)) | ~quiet(X0) | ~creative(X0)) & ((quiet(X0) & creative(X0)) | strong(X0) | tall(X0))) [flattening 34]
36. ! [X0] : (((~brave(X0) | rich(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 5]
37. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (brave(X0) & ~rich(X0)))) [flattening 36]
43. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | (humble(X0) | rich(X0)))) [nnf transformation 7]
44. ! [X0] : (((~humble(X0) & ~rich(X0)) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | humble(X0) | rich(X0))) [flattening 43]
47. ! [X0] : (old(X0) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0)))) [nnf transformation 29]
58. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [nnf transformation 16]
59. ! [X0] : ((((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0))))) [flattening 58]
60. (patient(fred) | ~brave(fred)) & (~patient(fred) | brave(fred)) [nnf transformation 17]
65. ~brave(X0) | ~tall(X0) [cnf transformation 25]
66. ~brave(X0) | strong(X0) [cnf transformation 25]
72. ~kind(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 33]
78. ~quiet(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 35]
80. ~generous(X0) | brave(X0) [cnf transformation 37]
81. ~rich(X0) | tall(X0) [cnf transformation 37]
88. ~brave(X0) | kind(X0) | humble(X0) | rich(X0) [cnf transformation 44]
96. ~humble(X0) | creative(X0) [cnf transformation 28]
97. creative(X0) | patient(X0) [cnf transformation 28]
100. old(X0) | old(X0) | ~creative(X0) [cnf transformation 47]
129. ~patient(X0) | ~brave(X0) | quiet(X0) [cnf transformation 59]
134. ~patient(fred) | brave(fred) [cnf transformation 60]
135. patient(fred) | ~brave(fred) [cnf transformation 60]
137. ~old(fred) | generous(fred) [cnf transformation 19]
144. happy(fred) [cnf transformation 24]
145. ~creative(X0) | old(X0) [duplicate literal removal 100]
221. 17 <=> brave(fred) [avatar definition]
222. brave(fred) <- (17) [avatar component clause 221]
223. ~brave(fred) <- (~17) [avatar component clause 221]
225. 18 <=> patient(fred) [avatar definition]
226. ~patient(fred) <- (~18) [avatar component clause 225]
227. patient(fred) <- (18) [avatar component clause 225]
228. ~17 | 18 [avatar split clause 135,225,221]
229. 17 | ~18 [avatar split clause 134,225,221]
231. 19 <=> generous(fred) [avatar definition]
233. generous(fred) <- (19) [avatar component clause 231]
235. 20 <=> old(fred) [avatar definition]
237. ~old(fred) <- (~20) [avatar component clause 235]
238. 19 | ~20 [avatar split clause 137,235,231]
250. patient(X0) | old(X0) [resolution 145,97]
295. old(fred) <- (~18) [resolution 250,226]
297. $false <- (~18, ~20) [subsumption resolution 295,237]
298. 18 | 20 [avatar contradiction clause 297]
299. strong(fred) <- (17) [resolution 222,66]
300. ~tall(fred) <- (17) [resolution 222,65]
313. ~brave(fred) | quiet(fred) <- (18) [resolution 129,227]
314. quiet(fred) <- (17, 18) [subsumption resolution 313,222]
316. ~strong(fred) | ~creative(fred) <- (17, 18) [resolution 314,78]
318. ~creative(fred) <- (17, 18) [subsumption resolution 316,299]
354. kind(fred) | humble(fred) | rich(fred) <- (17) [resolution 88,222]
357. 27 <=> rich(fred) [avatar definition]
359. rich(fred) <- (27) [avatar component clause 357]
361. 28 <=> humble(fred) [avatar definition]
363. humble(fred) <- (28) [avatar component clause 361]
365. 29 <=> kind(fred) [avatar definition]
367. kind(fred) <- (29) [avatar component clause 365]
368. 27 | 28 | 29 | ~17 [avatar split clause 354,221,365,361,357]
372. ~happy(fred) | ~patient(fred) <- (29) [resolution 367,72]
376. ~patient(fred) <- (29) [subsumption resolution 372,144]
377. $false <- (18, 29) [subsumption resolution 376,227]
378. ~18 | ~29 [avatar contradiction clause 377]
381. tall(fred) <- (27) [resolution 359,81]
382. $false <- (17, 27) [subsumption resolution 381,300]
383. ~17 | ~27 [avatar contradiction clause 382]
387. creative(fred) <- (28) [resolution 363,96]
390. $false <- (17, 18, 28) [subsumption resolution 387,318]
391. ~17 | ~18 | ~28 [avatar contradiction clause 390]
395. brave(fred) <- (19) [resolution 233,80]
397. $false <- (~17, 19) [subsumption resolution 395,223]
398. 17 | ~19 [avatar contradiction clause 397]
399. $false [avatar sat refutation 228,229,238,298,368,378,383,391,398]
% SZS output end Proof for 820700468765051725992612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then someone is not curious and vice versa.
If someone is either not patient or not brave then someone is either not funny or old and vice versa.
Everyone who is both not calm and humble is calm or not brave and vice versa.
If someone is either old or tall then someone is both not creative and brave.
Everyone who is wise or tall is both not generous and not humble.
If lucy is not generous then someone is both humble and rich and vice versa.
Everyone who is not humble is not strong.
Everyone who is not humble or not tall is not brave or not happy.
If someone is strong or not funny then someone is patient.
Everyone who is both old and generous is both generous and kind and vice versa.
Everyone who is either patient or not rich is not generous.
Everyone who is strong or generous is not curious and vice versa.
Everyone who is both strong and not wise is either not brave or not curious.
Everyone who is either creative or humble is curious and vice versa.
If john is old or kind then someone is calm and vice versa.
Everyone who is both not happy and not strong is not rich.
Someone is not generous or calm.
Susan is not creative or not wise.
Alice is either brave or not wise.
Susan is either brave or not funny.
Fred is happy.
Someone is either not generous or old.
Susan is either not curious or kind. | Fred is not tall. | entailment | ((?[X]:(curious(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~patient(X)<~>~brave(X))))<=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)|~brave(X))))&
((?[X]:((old(X)<~>tall(X))))=>(?[X]:((~creative(X)&brave(X)))))&
(![X]:((wise(X)|tall(X))=>(~generous(X)&~humble(X))))&
((~generous(lucy))<=>(?[X]:((humble(X)&rich(X)))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((~humble(X)|~tall(X))=>(~brave(X)|~happy(X))))&
((?[X]:((strong(X)|~funny(X))))=>(?[X]:(patient(X))))&
(![X]:((old(X)&generous(X))<=>(generous(X)&kind(X))))&
(![X]:((patient(X)<~>~rich(X))=>~generous(X)))&
(![X]:((strong(X)|generous(X))<=>~curious(X)))&
(![X]:((strong(X)&~wise(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((creative(X)<~>humble(X))<=>curious(X)))&
(((old(john)|kind(john)))<=>(?[X]:(calm(X))))&
(![X]:((~happy(X)&~strong(X))=>~rich(X)))&
(?[X]:((~generous(X)|calm(X))))&
((~creative(susan)|~wise(susan)))&
((brave(alice)<~>~wise(alice)))&
((brave(susan)<~>~funny(susan)))&
(happy(fred))&
(?[X]:((~generous(X)<~>old(X))))&
((~curious(susan)<~>kind(susan))) | ~tall(fred) | [
"p2",
"p4",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8953678892392822789312452
% SZS output start Proof for 8953678892392822789312452
3. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (~brave(X0) | calm(X0))) [input p2]
5. ! [X0] : ((tall(X0) | wise(X0)) => (~humble(X0) & ~generous(X0))) [input p4]
8. ! [X0] : ((~tall(X0) | ~humble(X0)) => (~happy(X0) | ~brave(X0))) [input p7]
21. happy(fred) [input p20]
24. tall(fred) [input hypothesis]
30. ! [X0] : ((~humble(X0) & ~generous(X0)) | (~tall(X0) & ~wise(X0))) [ennf transformation 5]
32. ! [X0] : ((~happy(X0) | ~brave(X0)) | (tall(X0) & humble(X0))) [ennf transformation 8]
33. ! [X0] : (~happy(X0) | ~brave(X0) | (tall(X0) & humble(X0))) [flattening 32]
50. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | (~humble(X0) | calm(X0)))) [nnf transformation 3]
51. ! [X0] : (((humble(X0) & ~calm(X0)) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ~humble(X0) | calm(X0))) [flattening 50]
97. humble(X0) | brave(X0) [cnf transformation 51]
105. ~tall(X0) | ~humble(X0) [cnf transformation 30]
110. ~happy(X0) | ~brave(X0) | humble(X0) [cnf transformation 33]
139. happy(fred) [cnf transformation 21]
144. tall(fred) [cnf transformation 24]
236. ~happy(X0) | humble(X0) [subsumption resolution 110,97]
304. ~humble(fred) [resolution 105,144]
308. humble(fred) [resolution 236,139]
309. $false [subsumption resolution 308,304]
% SZS output end Proof for 8953678892392822789312452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous is both curious and not funny and vice versa.
Everyone who is both wise and not tall is either not happy or curious.
Everyone who is either not kind or not generous is funny.
If someone is either rich or not creative then someone is either not kind or not funny.
Everyone who is not happy or not old is brave or wise and vice versa.
If someone is both kind and happy then someone is old.
Everyone who is kind is both not wise and calm.
If someone is patient or not curious then susan is not brave or tall and vice versa.
If someone is funny or brave then someone is not generous or happy and vice versa.
If someone is either not quiet or not wise then someone is both quiet and not strong and vice versa.
Everyone who is both not calm and brave is both generous and not wise and vice versa.
Everyone who is either not old or not funny is both not strong and not curious and vice versa.
If susan is either wise or not kind then someone is both not curious and funny and vice versa.
If john is not creative or curious then lucy is not quiet.
If someone is kind then someone is strong and vice versa.
Everyone who is not quiet is both not rich and not quiet.
Someone is either curious or wise.
Someone is either not tall or old.
Someone is either not curious or not quiet.
Someone is calm.
Someone is tall or not quiet.
Lucy is either happy or not patient.
Fred is both tall and creative.
Someone is not brave. | John is curious. | neutral | (![X]:(~generous(X)<=>(curious(X)&~funny(X))))&
(![X]:((wise(X)&~tall(X))=>(~happy(X)<~>curious(X))))&
(![X]:((~kind(X)<~>~generous(X))=>funny(X)))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
(![X]:((~happy(X)|~old(X))<=>(brave(X)|wise(X))))&
((?[X]:((kind(X)&happy(X))))=>(?[X]:(old(X))))&
(![X]:(kind(X)=>(~wise(X)&calm(X))))&
((?[X]:((patient(X)|~curious(X))))<=>((~brave(susan)|tall(susan))))&
((?[X]:((funny(X)|brave(X))))<=>(?[X]:((~generous(X)|happy(X)))))&
((?[X]:((~quiet(X)<~>~wise(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(![X]:((~calm(X)&brave(X))<=>(generous(X)&~wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~strong(X)&~curious(X))))&
(((wise(susan)<~>~kind(susan)))<=>(?[X]:((~curious(X)&funny(X)))))&
(((~creative(john)|curious(john)))=>(~quiet(lucy)))&
((?[X]:(kind(X)))<=>(?[X]:(strong(X))))&
(![X]:(~quiet(X)=>(~rich(X)&~quiet(X))))&
(?[X]:((curious(X)<~>wise(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:(calm(X)))&
(?[X]:((tall(X)|~quiet(X))))&
((happy(lucy)<~>~patient(lucy)))&
((tall(fred)&creative(fred)))&
(?[X]:(~brave(X))) | curious(john) | [] | null | 0 |
Everyone who is both not old and not tall is either old or patient.
Everyone who is either happy or not rich is quiet.
If someone is both tall and curious then someone is funny and vice versa.
Everyone who is either not happy or not strong is both not brave and patient and vice versa.
If someone is not strong or not funny then fred is either funny or happy.
Everyone who is both not brave and not funny is either calm or funny.
If someone is either generous or not happy then someone is not kind or not happy.
Everyone who is both not strong and not patient is either humble or not creative.
Everyone who is both not calm and not brave is both not curious and not wise and vice versa.
Everyone who is either brave or not quiet is either not wise or not rich.
Everyone who is funny is not generous.
Everyone who is not generous or not old is not curious.
Everyone who is both not kind and not brave is either rich or brave and vice versa.
Everyone who is old or not wise is calm or not patient.
Everyone who is both not strong and curious is not curious or curious.
If lucy is not strong or not happy then paul is generous and vice versa.
Someone is calm.
Someone is both funny and calm.
Lucy is not quiet or calm.
Someone is not kind.
Susan is not kind.
Paul is not wise or rich.
Susan is not funny or not humble. | Lucy is not patient. | neutral | (![X]:((~old(X)&~tall(X))=>(old(X)<~>patient(X))))&
(![X]:((happy(X)<~>~rich(X))=>quiet(X)))&
((?[X]:((tall(X)&curious(X))))<=>(?[X]:(funny(X))))&
(![X]:((~happy(X)<~>~strong(X))<=>(~brave(X)&patient(X))))&
((?[X]:((~strong(X)|~funny(X))))=>((funny(fred)<~>happy(fred))))&
(![X]:((~brave(X)&~funny(X))=>(calm(X)<~>funny(X))))&
((?[X]:((generous(X)<~>~happy(X))))=>(?[X]:((~kind(X)|~happy(X)))))&
(![X]:((~strong(X)&~patient(X))=>(humble(X)<~>~creative(X))))&
(![X]:((~calm(X)&~brave(X))<=>(~curious(X)&~wise(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(~wise(X)<~>~rich(X))))&
(![X]:(funny(X)=>~generous(X)))&
(![X]:((~generous(X)|~old(X))=>~curious(X)))&
(![X]:((~kind(X)&~brave(X))<=>(rich(X)<~>brave(X))))&
(![X]:((old(X)|~wise(X))=>(calm(X)|~patient(X))))&
(![X]:((~strong(X)&curious(X))=>(~curious(X)|curious(X))))&
(((~strong(lucy)|~happy(lucy)))<=>(generous(paul)))&
(?[X]:(calm(X)))&
(?[X]:((funny(X)&calm(X))))&
((~quiet(lucy)|calm(lucy)))&
(?[X]:(~kind(X)))&
(~kind(susan))&
((~wise(paul)|rich(paul)))&
((~funny(susan)|~humble(susan))) | ~patient(lucy) | [] | null | 0 |
If mary is both not kind and not brave then someone is both rich and not funny and vice versa.
Everyone who is kind or not tall is not creative or brave and vice versa.
If alice is creative then mary is rich.
If alice is either patient or kind then someone is both kind and quiet.
Everyone who is both strong and creative is curious and vice versa.
If someone is not humble then someone is both humble and generous.
If john is quiet then someone is both not humble and happy and vice versa.
Everyone who is not creative or not patient is either not quiet or not funny.
If susan is not funny or humble then john is both strong and not quiet.
Everyone who is not calm is tall.
Everyone who is quiet or curious is both not kind and not humble.
Everyone who is not tall is both not creative and not brave and vice versa.
Everyone who is both happy and patient is both old and brave.
Everyone who is both not patient and brave is not rich or not brave and vice versa.
Everyone who is not brave or not wise is both not happy and strong.
Everyone who is creative is both not generous and not curious and vice versa.
John is tall.
Someone is wise.
Alice is both not generous and not humble.
Someone is both funny and not wise.
Someone is not calm.
Lucy is generous.
Someone is both not humble and not creative. | John is not quiet. | entailment | (((~kind(mary)&~brave(mary)))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((kind(X)|~tall(X))<=>(~creative(X)|brave(X))))&
((creative(alice))=>(rich(mary)))&
(((patient(alice)<~>kind(alice)))=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:((strong(X)&creative(X))<=>curious(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)&generous(X)))))&
((quiet(john))<=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:((~creative(X)|~patient(X))=>(~quiet(X)<~>~funny(X))))&
(((~funny(susan)|humble(susan)))=>((strong(john)&~quiet(john))))&
(![X]:(~calm(X)=>tall(X)))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))&
(![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))&
(![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~generous(X)&~curious(X))))&
(tall(john))&
(?[X]:(wise(X)))&
((~generous(alice)&~humble(alice)))&
(?[X]:((funny(X)&~wise(X))))&
(?[X]:(~calm(X)))&
(generous(lucy))&
(?[X]:((~humble(X)&~creative(X)))) | ~quiet(john) | [
"p1",
"p10",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 872682350489984952908316
% SZS output start Proof for 872682350489984952908316
2. ! [X0] : ((~tall(X0) | kind(X0)) <=> (brave(X0) | ~creative(X0))) [input p1]
11. ! [X0] : ((curious(X0) | quiet(X0)) => (~humble(X0) & ~kind(X0))) [input p10]
14. ! [X0] : ((brave(X0) & ~patient(X0)) <=> (~brave(X0) | ~rich(X0))) [input p13]
17. tall(john) [input p16]
24. quiet(john) [input hypothesis]
33. ! [X0] : ((~humble(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 11]
42. ! [X0] : (((~tall(X0) | kind(X0)) | (~brave(X0) & creative(X0))) & ((brave(X0) | ~creative(X0)) | (tall(X0) & ~kind(X0)))) [nnf transformation 2]
43. ! [X0] : ((~tall(X0) | kind(X0) | (~brave(X0) & creative(X0))) & (brave(X0) | ~creative(X0) | (tall(X0) & ~kind(X0)))) [flattening 42]
59. ! [X0] : (((brave(X0) & ~patient(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~brave(X0) | patient(X0)))) [nnf transformation 14]
60. ! [X0] : (((brave(X0) & ~patient(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~brave(X0) | patient(X0))) [flattening 59]
78. ~tall(X0) | kind(X0) | ~brave(X0) [cnf transformation 43]
101. ~quiet(X0) | ~kind(X0) [cnf transformation 33]
113. brave(X0) | brave(X0) [cnf transformation 60]
121. tall(john) [cnf transformation 17]
131. quiet(john) [cnf transformation 24]
133. brave(X0) [duplicate literal removal 113]
203. 16 <=> quiet(john) [avatar definition]
205. quiet(john) <- (16) [avatar component clause 203]
236. 16 [avatar split clause 131,203]
244. ~kind(john) <- (16) [resolution 101,205]
282. kind(john) | ~brave(john) [resolution 78,121]
285. ~brave(john) <- (16) [subsumption resolution 282,244]
286. $false <- (16) [subsumption resolution 285,133]
287. ~16 [avatar contradiction clause 286]
291. $false [avatar sat refutation 236,287]
% SZS output end Proof for 872682350489984952908316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either patient or quiet then someone is both patient and calm and vice versa. Everyone who is both wise and old is both calm and not curious. Everyone who is strong is not calm. Everyone who is tall or generous is either rich or not strong. Everyone who is both generous and not generous is both patient and not old. Everyone who is strong or humble is calm or creative. If someone is both not kind and curious then someone is rich and vice versa. Everyone who is not funny or not kind is both kind and quiet. Everyone who is either not creative or rich is patient or quiet. If fred is either generous or not old then someone is brave. Everyone who is both not rich and not patient is either not wise or funny and vice versa. Everyone who is both not brave and not curious is old or not creative. Everyone who is not rich or generous is not rich. Everyone who is either not wise or rich is not rich and vice versa. Everyone who is both old and humble is not humble or quiet. Everyone who is either not happy or calm is both happy and curious. Susan is either rich or not humble. Paul is rich or not humble. Someone is funny. Susan is not strong. John is both calm and not humble. Someone is either not calm or curious. John is quiet or rich. Alice is not kind or tall. | Susan is rich. | contradiction | (((patient(alice)<~>quiet(alice)))<=>(?[X]:((patient(X)&calm(X)))))&
(![X]:((wise(X)&old(X))=>(calm(X)&~curious(X))))&
(![X]:(strong(X)=>~calm(X)))&
(![X]:((tall(X)|generous(X))=>(rich(X)<~>~strong(X))))&
(![X]:((generous(X)&~generous(X))=>(patient(X)&~old(X))))&
(![X]:((strong(X)|humble(X))=>(calm(X)|creative(X))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:(rich(X))))&
(![X]:((~funny(X)|~kind(X))=>(kind(X)&quiet(X))))&
(![X]:((~creative(X)<~>rich(X))=>(patient(X)|quiet(X))))&
(((generous(fred)<~>~old(fred)))=>(?[X]:(brave(X))))&
(![X]:((~rich(X)&~patient(X))<=>(~wise(X)<~>funny(X))))&
(![X]:((~brave(X)&~curious(X))=>(old(X)|~creative(X))))&
(![X]:((~rich(X)|generous(X))=>~rich(X)))&
(![X]:((~wise(X)<~>rich(X))<=>~rich(X)))&
(![X]:((old(X)&humble(X))=>(~humble(X)|quiet(X))))&
(![X]:((~happy(X)<~>calm(X))=>(happy(X)&curious(X))))&
((rich(susan)<~>~humble(susan)))&
((rich(paul)|~humble(paul)))&
(?[X]:(funny(X)))&
(~strong(susan))&
((calm(john)&~humble(john)))&
(?[X]:((~calm(X)<~>curious(X))))&
((quiet(john)|rich(john)))&
((~kind(alice)|tall(alice))) | rich(susan) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 343890065787865677453709
% SZS output start Proof for 343890065787865677453709
7. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : rich(X0) [input p6]
8. ! [X0] : ((~kind(X0) | ~funny(X0)) => (quiet(X0) & kind(X0))) [input p7]
25. rich(susan) [input hypothesis]
26. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : rich(X1) [rectify 7]
38. ! [X0] : ((quiet(X0) & kind(X0)) | (kind(X0) & funny(X0))) [ennf transformation 8]
48. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 26]
49. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 48]
50. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK1) & ~kind(sK1)) [choice axiom]
51. ? [X2] : rich(X2) => rich(sK2) [choice axiom]
52. ((curious(sK1) & ~kind(sK1)) | ! [X1] : ~rich(X1)) & (rich(sK2) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 49,51,50]
79. ~kind(sK1) | ~rich(X1) [cnf transformation 52]
82. kind(X0) | kind(X0) [cnf transformation 38]
114. rich(susan) [cnf transformation 25]
118. kind(X0) [duplicate literal removal 82]
146. 6 <=> ! [X1] : ~rich(X1) [avatar definition]
147. ~rich(X1) <- (6) [avatar component clause 146]
154. 8 <=> kind(sK1) [avatar definition]
156. ~kind(sK1) <- (~8) [avatar component clause 154]
157. 6 | ~8 [avatar split clause 79,154,146]
168. 11 <=> rich(susan) [avatar definition]
169. rich(susan) <- (11) [avatar component clause 168]
206. 11 [avatar split clause 114,168]
207. $false <- (6, 11) [resolution 169,147]
208. ~6 | ~11 [avatar contradiction clause 207]
209. $false <- (~8) [subsumption resolution 156,118]
210. 8 [avatar contradiction clause 209]
211. $false [avatar sat refutation 157,206,208,210]
% SZS output end Proof for 343890065787865677453709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or not rich then john is both tall and not calm and vice versa. Everyone who is either not strong or wise is not kind. If mary is tall or calm then someone is not creative or wise and vice versa. If fred is not creative or not happy then susan is tall or not kind and vice versa. If someone is not brave or tall then someone is either creative or strong. Everyone who is not calm or not rich is either curious or calm and vice versa. If lucy is either not happy or not tall then susan is not rich or not kind. If someone is funny or not patient then someone is both not kind and creative. If fred is either curious or not generous then paul is tall and vice versa. Everyone who is either not patient or curious is either not strong or not calm and vice versa. If someone is not creative then someone is either not rich or not patient and vice versa. If someone is brave or not humble then alice is not kind. If someone is not strong then someone is both brave and rich. If someone is not tall or rich then someone is either not rich or curious and vice versa. Everyone who is both calm and not curious is not funny. Someone is both strong and not kind. John is both not wise and kind. Paul is either brave or not happy. Mary is both quiet and patient. Fred is not humble. Paul is both rich and quiet. Alice is both tall and rich. Someone is tall or not humble. | John is not patient. | contradiction | ((?[X]:((curious(X)<~>~rich(X))))<=>((tall(john)&~calm(john))))&
(![X]:((~strong(X)<~>wise(X))=>~kind(X)))&
(((tall(mary)|calm(mary)))<=>(?[X]:((~creative(X)|wise(X)))))&
(((~creative(fred)|~happy(fred)))<=>((tall(susan)|~kind(susan))))&
((?[X]:((~brave(X)|tall(X))))=>(?[X]:((creative(X)<~>strong(X)))))&
(![X]:((~calm(X)|~rich(X))<=>(curious(X)<~>calm(X))))&
(((~happy(lucy)<~>~tall(lucy)))=>((~rich(susan)|~kind(susan))))&
((?[X]:((funny(X)|~patient(X))))=>(?[X]:((~kind(X)&creative(X)))))&
(((curious(fred)<~>~generous(fred)))<=>(tall(paul)))&
(![X]:((~patient(X)<~>curious(X))<=>(~strong(X)<~>~calm(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
((?[X]:((brave(X)|~humble(X))))=>(~kind(alice)))&
((?[X]:(~strong(X)))=>(?[X]:((brave(X)&rich(X)))))&
((?[X]:((~tall(X)|rich(X))))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((calm(X)&~curious(X))=>~funny(X)))&
(?[X]:((strong(X)&~kind(X))))&
((~wise(john)&kind(john)))&
((brave(paul)<~>~happy(paul)))&
((quiet(mary)&patient(mary)))&
(~humble(fred))&
((rich(paul)&quiet(paul)))&
((tall(alice)&rich(alice)))&
(?[X]:((tall(X)|~humble(X)))) | ~patient(john) | [
"p0",
"p1",
"p5",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8451962629294627364935900
% SZS output start Proof for 8451962629294627364935900
1. ? [X0] : (curious(X0) <~> ~rich(X0)) <=> (~calm(john) & tall(john)) [input p0]
2. ! [X0] : ((~strong(X0) <~> wise(X0)) => ~kind(X0)) [input p1]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (curious(X0) <~> calm(X0))) [input p5]
10. ! [X0] : ((~patient(X0) <~> curious(X0)) <=> (~strong(X0) <~> ~calm(X0))) [input p9]
17. kind(john) & ~wise(john) [input p16]
24. ~patient(john) [input hypothesis]
34. ! [X0] : (~kind(X0) | (~strong(X0) <=> wise(X0))) [ennf transformation 2]
41. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | (calm(john) | ~tall(john))) & ((~calm(john) & tall(john)) | ! [X0] : ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [nnf transformation 1]
42. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X0] : ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) [flattening 41]
43. (? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X1] : ((curious(X1) | rich(X1)) & (~rich(X1) | ~curious(X1)))) [rectify 42]
44. ? [X0] : ((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) => ((rich(sK0) | ~curious(sK0)) & (~rich(sK0) | curious(sK0))) [choice axiom]
45. (((rich(sK0) | ~curious(sK0)) & (~rich(sK0) | curious(sK0))) | calm(john) | ~tall(john)) & ((~calm(john) & tall(john)) | ! [X1] : ((curious(X1) | rich(X1)) & (~rich(X1) | ~curious(X1)))) [skolemisation 43,44]
46. ! [X0] : (~kind(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) [nnf transformation 34]
58. ! [X0] : (((~rich(X0) | ~calm(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (rich(X0) & calm(X0)))) [nnf transformation 6]
59. ! [X0] : ((~rich(X0) | ~calm(X0) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) & (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (rich(X0) & calm(X0)))) [flattening 58]
65. ! [X0] : ((((~curious(X0) | patient(X0)) & (curious(X0) | ~patient(X0))) | ((~strong(X0) | calm(X0)) & (~calm(X0) | strong(X0)))) & (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | ((~patient(X0) | ~curious(X0)) & (curious(X0) | patient(X0))))) [nnf transformation 10]
86. ~calm(john) | ~rich(X1) | ~curious(X1) [cnf transformation 45]
90. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 46]
104. calm(X0) | curious(X0) | calm(X0) [cnf transformation 59]
107. ~calm(X0) | ~curious(X0) | rich(X0) [cnf transformation 59]
109. ~rich(X0) | ~calm(X0) | curious(X0) | ~calm(X0) [cnf transformation 59]
118. ~calm(X0) | ~strong(X0) | curious(X0) | patient(X0) [cnf transformation 65]
125. ~curious(X0) | patient(X0) | ~strong(X0) | calm(X0) [cnf transformation 65]
142. ~wise(john) [cnf transformation 17]
143. kind(john) [cnf transformation 17]
152. ~patient(john) [cnf transformation 24]
153. calm(X0) | curious(X0) [duplicate literal removal 104]
154. ~calm(X0) | ~rich(X0) | curious(X0) [duplicate literal removal 109]
160. 2 <=> calm(john) [avatar definition]
162. calm(john) <- (2) [avatar component clause 160]
178. 6 <=> ! [X1] : (~rich(X1) | ~curious(X1)) [avatar definition]
179. ~rich(X1) | ~curious(X1) <- (6) [avatar component clause 178]
180. 6 | ~2 [avatar split clause 86,160,178]
290. ~strong(X0) | patient(X0) | calm(X0) [subsumption resolution 125,153]
293. ~strong(X0) | curious(X0) | patient(X0) [subsumption resolution 118,290]
352. 43 <=> ! [X3] : ~rich(X3) [avatar definition]
353. ~rich(X3) <- (43) [avatar component clause 352]
409. wise(john) | strong(john) [resolution 90,143]
419. ~rich(X1) | curious(X1) | curious(X1) [resolution 154,153]
420. ~rich(X1) | curious(X1) [duplicate literal removal 419]
423. ~rich(X1) <- (6) [subsumption resolution 420,179]
424. 43 | ~6 [avatar split clause 423,178,352]
482. strong(john) [subsumption resolution 409,142]
502. curious(john) | patient(john) [resolution 482,293]
503. patient(john) | calm(john) [resolution 482,290]
504. calm(john) [subsumption resolution 503,152]
507. 2 [avatar split clause 504,160]
508. curious(john) [subsumption resolution 502,152]
512. ~curious(john) | rich(john) <- (2) [resolution 162,107]
513. rich(john) <- (2) [subsumption resolution 512,508]
514. $false <- (2, 43) [subsumption resolution 513,353]
515. ~2 | ~43 [avatar contradiction clause 514]
516. $false [avatar sat refutation 180,424,507,515]
% SZS output end Proof for 8451962629294627364935900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not tall then susan is not quiet.
Everyone who is both not strong and not old is both not tall and not happy.
Everyone who is either patient or not calm is not patient and vice versa.
Everyone who is both generous and funny is curious and vice versa.
If paul is either humble or not humble then fred is creative and vice versa.
Everyone who is patient is either generous or curious.
If someone is funny or old then someone is both patient and quiet and vice versa.
If someone is either not rich or not wise then susan is not humble or not generous.
Everyone who is creative or not tall is old or curious and vice versa.
If someone is either funny or not brave then mary is either funny or not brave.
If someone is patient then someone is happy and vice versa.
If someone is both strong and old then susan is calm and vice versa.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Susan is curious.
John is both tall and not strong.
Someone is either not calm or not quiet.
Paul is either not patient or not creative.
Fred is either not wise or creative.
Someone is not old.
Fred is both generous and strong.
Someone is wise. | Paul is calm. | contradiction | ((?[X]:((~brave(X)<~>~tall(X))))=>(~quiet(susan)))&
(![X]:((~strong(X)&~old(X))=>(~tall(X)&~happy(X))))&
(![X]:((patient(X)<~>~calm(X))<=>~patient(X)))&
(![X]:((generous(X)&funny(X))<=>curious(X)))&
(((humble(paul)<~>~humble(paul)))<=>(creative(fred)))&
(![X]:(patient(X)=>(generous(X)<~>curious(X))))&
((?[X]:((funny(X)|old(X))))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))=>((~humble(susan)|~generous(susan))))&
(![X]:((creative(X)|~tall(X))<=>(old(X)|curious(X))))&
((?[X]:((funny(X)<~>~brave(X))))=>((funny(mary)<~>~brave(mary))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(curious(susan))&
((tall(john)&~strong(john)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((~patient(paul)<~>~creative(paul)))&
((~wise(fred)<~>creative(fred)))&
(?[X]:(~old(X)))&
((generous(fred)&strong(fred)))&
(?[X]:(wise(X))) | calm(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7442209563786568777162824
% SZS output start Proof for 7442209563786568777162824
3. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> ~patient(X0)) [input p2]
25. calm(paul) [input hypothesis]
41. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | patient(X0)) & (~patient(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 3]
79. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 41]
81. ~calm(X0) | patient(X0) | patient(X0) [cnf transformation 41]
140. calm(paul) [cnf transformation 25]
147. ~patient(X0) | ~calm(X0) [duplicate literal removal 79]
148. ~calm(X0) | patient(X0) [duplicate literal removal 81]
161. ~calm(X0) [subsumption resolution 147,148]
309. $false [subsumption resolution 140,161]
% SZS output end Proof for 7442209563786568777162824
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not curious is not patient or quiet and vice versa. If fred is quiet then someone is either not patient or generous and vice versa. Everyone who is not calm or calm is curious or not generous. Everyone who is both kind and not rich is both rich and calm. Everyone who is either tall or not funny is brave or quiet and vice versa. Everyone who is both not old and not curious is both wise and patient and vice versa. If someone is either funny or not kind then mary is happy or not old and vice versa. If someone is tall then mary is not funny and vice versa. Everyone who is both generous and brave is either happy or not old and vice versa. If someone is patient or kind then alice is not creative. If someone is either not funny or not happy then alice is brave. Everyone who is both not patient and curious is curious or quiet. If susan is either funny or tall then alice is both patient and not rich and vice versa. Everyone who is not humble is not humble or not tall. If lucy is either funny or not kind then someone is humble or not tall and vice versa. Everyone who is either not happy or not generous is both patient and strong and vice versa. Someone is strong. Alice is tall. Someone is rich. Someone is not kind or patient. Someone is not funny or brave. Someone is not calm. Someone is either not wise or quiet. | Alice is not calm. | neutral | (![X]:((generous(X)&~curious(X))<=>(~patient(X)|quiet(X))))&
((quiet(fred))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:((~calm(X)|calm(X))=>(curious(X)|~generous(X))))&
(![X]:((kind(X)&~rich(X))=>(rich(X)&calm(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)|quiet(X))))&
(![X]:((~old(X)&~curious(X))<=>(wise(X)&patient(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>((happy(mary)|~old(mary))))&
((?[X]:(tall(X)))<=>(~funny(mary)))&
(![X]:((generous(X)&brave(X))<=>(happy(X)<~>~old(X))))&
((?[X]:((patient(X)|kind(X))))=>(~creative(alice)))&
((?[X]:((~funny(X)<~>~happy(X))))=>(brave(alice)))&
(![X]:((~patient(X)&curious(X))=>(curious(X)|quiet(X))))&
(((funny(susan)<~>tall(susan)))<=>((patient(alice)&~rich(alice))))&
(![X]:(~humble(X)=>(~humble(X)|~tall(X))))&
(((funny(lucy)<~>~kind(lucy)))<=>(?[X]:((humble(X)|~tall(X)))))&
(![X]:((~happy(X)<~>~generous(X))<=>(patient(X)&strong(X))))&
(?[X]:(strong(X)))&
(tall(alice))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|patient(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~wise(X)<~>quiet(X)))) | ~calm(alice) | [] | null | 0 |
If john is rich or quiet then someone is quiet or tall and vice versa. Everyone who is both curious and brave is not wise. If someone is both not brave and not old then john is both happy and not happy. Everyone who is not wise is both not tall and not funny and vice versa. Everyone who is not humble is either calm or happy. Everyone who is not funny or kind is both tall and not kind and vice versa. Everyone who is not humble is curious and vice versa. Everyone who is both not kind and not generous is both kind and not calm and vice versa. Everyone who is not strong or not rich is either generous or brave and vice versa. Everyone who is generous is either not humble or generous. Everyone who is both not old and not generous is not old or tall. If someone is either not old or happy then fred is not patient and vice versa. If john is not patient then someone is not quiet or patient and vice versa. If someone is both not tall and not humble then someone is either funny or not quiet and vice versa. If fred is either calm or not wise then someone is both not old and tall. If someone is not wise then susan is both strong and old and vice versa. John is either not calm or curious. Someone is not quiet. Someone is not rich or tall. Paul is either strong or generous. Alice is both brave and not old. Paul is either not patient or not strong. | Paul is curious. | contradiction | (((rich(john)|quiet(john)))<=>(?[X]:((quiet(X)|tall(X)))))&
(![X]:((curious(X)&brave(X))=>~wise(X)))&
((?[X]:((~brave(X)&~old(X))))=>((happy(john)&~happy(john))))&
(![X]:(~wise(X)<=>(~tall(X)&~funny(X))))&
(![X]:(~humble(X)=>(calm(X)<~>happy(X))))&
(![X]:((~funny(X)|kind(X))<=>(tall(X)&~kind(X))))&
(![X]:(~humble(X)<=>curious(X)))&
(![X]:((~kind(X)&~generous(X))<=>(kind(X)&~calm(X))))&
(![X]:((~strong(X)|~rich(X))<=>(generous(X)<~>brave(X))))&
(![X]:(generous(X)=>(~humble(X)<~>generous(X))))&
(![X]:((~old(X)&~generous(X))=>(~old(X)|tall(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>(~patient(fred)))&
((~patient(john))<=>(?[X]:((~quiet(X)|patient(X)))))&
((?[X]:((~tall(X)&~humble(X))))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(((calm(fred)<~>~wise(fred)))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(~wise(X)))<=>((strong(susan)&old(susan))))&
((~calm(john)<~>curious(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|tall(X))))&
((strong(paul)<~>generous(paul)))&
((brave(alice)&~old(alice)))&
((~patient(paul)<~>~strong(paul))) | curious(paul) | [
"p5",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8522924760687038652720300
% SZS output start Proof for 8522924760687038652720300
6. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (~kind(X0) & tall(X0))) [input p5]
7. ! [X0] : (~humble(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (~calm(X0) & kind(X0))) [input p7]
10. ! [X0] : (generous(X0) => (~humble(X0) <~> generous(X0))) [input p9]
23. curious(paul) [input hypothesis]
29. ! [X0] : ((~humble(X0) <~> generous(X0)) | ~generous(X0)) [ennf transformation 10]
41. ! [X0] : (((kind(X0) | ~funny(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (~kind(X0) & funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((kind(X0) | ~funny(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | (~kind(X0) & funny(X0)))) [flattening 41]
43. ! [X0] : ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))) [nnf transformation 7]
44. ! [X0] : (((~generous(X0) & ~kind(X0)) | (calm(X0) | ~kind(X0))) & ((~calm(X0) & kind(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 8]
45. ! [X0] : (((~generous(X0) & ~kind(X0)) | calm(X0) | ~kind(X0)) & ((~calm(X0) & kind(X0)) | generous(X0) | kind(X0))) [flattening 44]
48. ! [X0] : (((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | ~generous(X0)) [nnf transformation 29]
92. ~kind(X0) | ~kind(X0) [cnf transformation 42]
95. ~humble(X0) | ~curious(X0) [cnf transformation 43]
96. kind(X0) | generous(X0) | kind(X0) [cnf transformation 45]
107. ~generous(X0) | humble(X0) | ~generous(X0) [cnf transformation 48]
139. curious(paul) [cnf transformation 23]
140. ~generous(X0) | humble(X0) [duplicate literal removal 107]
141. kind(X0) | generous(X0) [duplicate literal removal 96]
143. ~kind(X0) [duplicate literal removal 92]
181. generous(X0) [subsumption resolution 141,143]
185. humble(X0) [subsumption resolution 140,181]
296. ~curious(X1) [resolution 95,185]
299. $false [resolution 296,139]
% SZS output end Proof for 8522924760687038652720300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not tall then lucy is both not strong and not generous.
Everyone who is both not calm and not rich is either not calm or not rich.
Everyone who is calm is either not tall or kind.
Everyone who is both kind and not old is both creative and not old.
If susan is both strong and wise then someone is either tall or not tall.
Everyone who is both curious and creative is both wise and not kind.
If mary is quiet then someone is quiet or not generous and vice versa.
If someone is both not calm and not old then mary is not strong.
Everyone who is either tall or old is curious and vice versa.
Everyone who is humble is both not patient and patient and vice versa.
If paul is either not quiet or not humble then susan is patient or not quiet.
Everyone who is not tall or not wise is curious.
Everyone who is either strong or not brave is either not calm or not tall and vice versa.
Everyone who is creative or not humble is either not creative or creative.
If someone is kind then susan is creative.
If someone is either patient or not wise then alice is both not happy and not patient and vice versa.
Someone is generous.
Alice is both not kind and patient.
Someone is not brave.
Someone is both funny and not curious.
Paul is both not strong and not brave.
Paul is both wise and not rich.
Mary is both not tall and not happy.
Someone is not patient or not creative. | Susan is not humble. | entailment | (((~calm(lucy)<~>~tall(lucy)))=>((~strong(lucy)&~generous(lucy))))&
(![X]:((~calm(X)&~rich(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(calm(X)=>(~tall(X)<~>kind(X))))&
(![X]:((kind(X)&~old(X))=>(creative(X)&~old(X))))&
(((strong(susan)&wise(susan)))=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((curious(X)&creative(X))=>(wise(X)&~kind(X))))&
((quiet(mary))<=>(?[X]:((quiet(X)|~generous(X)))))&
((?[X]:((~calm(X)&~old(X))))=>(~strong(mary)))&
(![X]:((tall(X)<~>old(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~patient(X)&patient(X))))&
(((~quiet(paul)<~>~humble(paul)))=>((patient(susan)|~quiet(susan))))&
(![X]:((~tall(X)|~wise(X))=>curious(X)))&
(![X]:((strong(X)<~>~brave(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((creative(X)|~humble(X))=>(~creative(X)<~>creative(X))))&
((?[X]:(kind(X)))=>(creative(susan)))&
((?[X]:((patient(X)<~>~wise(X))))<=>((~happy(alice)&~patient(alice))))&
(?[X]:(generous(X)))&
((~kind(alice)&patient(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((funny(X)&~curious(X))))&
((~strong(paul)&~brave(paul)))&
((wise(paul)&~rich(paul)))&
((~tall(mary)&~happy(mary)))&
(?[X]:((~patient(X)|~creative(X)))) | ~humble(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4357317937711919726462539
% SZS output start Proof for 4357317937711919726462539
10. ! [X0] : (humble(X0) <=> (patient(X0) & ~patient(X0))) [input p9]
25. humble(susan) [input hypothesis]
54. ! [X0] : ((humble(X0) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ~humble(X0))) [nnf transformation 10]
55. ! [X0] : ((humble(X0) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ~humble(X0))) [flattening 54]
94. ~patient(X0) | ~humble(X0) [cnf transformation 55]
95. patient(X0) | ~humble(X0) [cnf transformation 55]
132. humble(susan) [cnf transformation 25]
185. ~humble(X0) [subsumption resolution 94,95]
246. $false [subsumption resolution 132,185]
% SZS output end Proof for 4357317937711919726462539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and creative is kind or creative and vice versa. If someone is not creative then someone is both not humble and not creative. If someone is either old or not patient then someone is funny and vice versa. If fred is both not rich and curious then paul is both happy and not tall and vice versa. If lucy is either not curious or brave then john is either not generous or not funny and vice versa. Everyone who is either not patient or generous is old or brave. If someone is wise then someone is both not happy and brave and vice versa. Everyone who is old is either not tall or generous. If fred is not tall then mary is creative or not quiet and vice versa. Everyone who is not brave is either not generous or strong. Everyone who is either not patient or not wise is both not calm and not funny and vice versa. If someone is not tall or generous then someone is either not happy or curious and vice versa. Everyone who is tall or rich is not kind or not funny and vice versa. Everyone who is either not curious or not rich is both not creative and rich. Everyone who is not creative or not strong is both brave and not patient and vice versa. If someone is not curious then mary is not brave and vice versa. Someone is rich or not calm. Someone is both not calm and not rich. Alice is funny. Someone is both not kind and not strong. Lucy is either not wise or not kind. John is not creative or strong. Susan is not patient or funny. | Alice is strong. | neutral | (![X]:((~patient(X)&creative(X))<=>(kind(X)|creative(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~humble(X)&~creative(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>(?[X]:(funny(X))))&
(((~rich(fred)&curious(fred)))<=>((happy(paul)&~tall(paul))))&
(((~curious(lucy)<~>brave(lucy)))<=>((~generous(john)<~>~funny(john))))&
(![X]:((~patient(X)<~>generous(X))=>(old(X)|brave(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)&brave(X)))))&
(![X]:(old(X)=>(~tall(X)<~>generous(X))))&
((~tall(fred))<=>((creative(mary)|~quiet(mary))))&
(![X]:(~brave(X)=>(~generous(X)<~>strong(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>(~calm(X)&~funny(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(![X]:((tall(X)|rich(X))<=>(~kind(X)|~funny(X))))&
(![X]:((~curious(X)<~>~rich(X))=>(~creative(X)&rich(X))))&
(![X]:((~creative(X)|~strong(X))<=>(brave(X)&~patient(X))))&
((?[X]:(~curious(X)))<=>(~brave(mary)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((~calm(X)&~rich(X))))&
(funny(alice))&
(?[X]:((~kind(X)&~strong(X))))&
((~wise(lucy)<~>~kind(lucy)))&
((~creative(john)|strong(john)))&
((~patient(susan)|funny(susan))) | strong(alice) | [] | null | 0 |
Everyone who is curious or kind is both curious and not brave.
Everyone who is either patient or generous is either quiet or not quiet and vice versa.
Everyone who is both brave and funny is either not funny or kind.
If someone is rich or calm then someone is both humble and happy and vice versa.
If someone is either not strong or brave then alice is both not happy and not curious and vice versa.
If susan is both not brave and not happy then john is either not happy or generous.
Everyone who is either strong or generous is either not kind or quiet.
Everyone who is either not funny or calm is either strong or not calm.
Everyone who is not wise is wise or not curious and vice versa.
Everyone who is wise is both happy and not creative.
If paul is not strong or brave then someone is humble or tall.
If susan is patient or strong then someone is not strong and vice versa.
Everyone who is either not old or not funny is either not humble or funny.
Everyone who is either not generous or brave is patient and vice versa.
Everyone who is calm is not curious or patient.
Everyone who is both happy and not old is not creative.
Someone is both calm and patient.
Someone is either tall or not calm.
Alice is happy or calm.
John is either calm or not wise.
Someone is both not calm and not rich. | Alice is not kind. | entailment | (![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((patient(X)<~>generous(X))<=>(quiet(X)<~>~quiet(X))))&
(![X]:((brave(X)&funny(X))=>(~funny(X)<~>kind(X))))&
((?[X]:((rich(X)|calm(X))))<=>(?[X]:((humble(X)&happy(X)))))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~happy(alice)&~curious(alice))))&
(((~brave(susan)&~happy(susan)))=>((~happy(john)<~>generous(john))))&
(![X]:((strong(X)<~>generous(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((~funny(X)<~>calm(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~wise(X)<=>(wise(X)|~curious(X))))&
(![X]:(wise(X)=>(happy(X)&~creative(X))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((humble(X)|tall(X)))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~generous(X)<~>brave(X))<=>patient(X)))&
(![X]:(calm(X)=>(~curious(X)|patient(X))))&
(![X]:((happy(X)&~old(X))=>~creative(X)))&
(?[X]:((calm(X)&patient(X))))&
(?[X]:((tall(X)<~>~calm(X))))&
((happy(alice)|calm(alice)))&
((calm(john)<~>~wise(john)))&
(?[X]:((~calm(X)&~rich(X)))) | ~kind(alice) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7475772071021442466690894
% SZS output start Proof for 7475772071021442466690894
1. ! [X0] : ((kind(X0) | curious(X0)) => (~brave(X0) & curious(X0))) [input p0]
9. ! [X0] : (~wise(X0) <=> (~curious(X0) | wise(X0))) [input p8]
22. kind(alice) [input hypothesis]
26. ! [X0] : ((~brave(X0) & curious(X0)) | (~kind(X0) & ~curious(X0))) [ennf transformation 1]
53. ! [X0] : ((~wise(X0) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | wise(X0))) [nnf transformation 9]
54. ! [X0] : ((~wise(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | wise(X0))) [flattening 53]
73. ~kind(X0) | curious(X0) [cnf transformation 26]
107. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 54]
108. ~wise(X0) | ~wise(X0) [cnf transformation 54]
134. kind(alice) [cnf transformation 22]
137. ~curious(X0) | wise(X0) [duplicate literal removal 107]
138. ~wise(X0) [duplicate literal removal 108]
225. ~curious(X0) [subsumption resolution 137,138]
287. curious(alice) [resolution 73,134]
288. $false [subsumption resolution 287,225]
% SZS output end Proof for 7475772071021442466690894
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not funny then lucy is quiet or creative and vice versa.
Everyone who is either kind or strong is not tall.
If someone is not patient or not generous then fred is kind.
Everyone who is humble is calm or not kind and vice versa.
If susan is not creative then alice is not funny or not kind and vice versa.
Everyone who is both generous and not calm is not patient or not happy.
Everyone who is either not old or not calm is either funny or calm.
If alice is either not happy or patient then lucy is not happy or not quiet.
Everyone who is both wise and not wise is generous and vice versa.
If someone is both not tall and not wise then mary is curious and vice versa.
If someone is curious then john is not happy or brave and vice versa.
Everyone who is both not calm and curious is either not wise or not funny and vice versa.
Everyone who is not brave is quiet or not calm.
Everyone who is funny or humble is not old.
Everyone who is either wise or creative is not strong.
If susan is either not calm or not happy then someone is funny or not calm and vice versa.
Someone is patient or not funny.
Someone is both not rich and not curious.
Alice is both not wise and creative.
Someone is not quiet or rich.
Susan is both calm and not rich.
John is either calm or not tall.
Susan is not creative or not humble. | Susan is funny. | contradiction | ((?[X]:((tall(X)|~funny(X))))<=>((quiet(lucy)|creative(lucy))))&
(![X]:((kind(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~patient(X)|~generous(X))))=>(kind(fred)))&
(![X]:(humble(X)<=>(calm(X)|~kind(X))))&
((~creative(susan))<=>((~funny(alice)|~kind(alice))))&
(![X]:((generous(X)&~calm(X))=>(~patient(X)|~happy(X))))&
(![X]:((~old(X)<~>~calm(X))=>(funny(X)<~>calm(X))))&
(((~happy(alice)<~>patient(alice)))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((wise(X)&~wise(X))<=>generous(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>(curious(mary)))&
((?[X]:(curious(X)))<=>((~happy(john)|brave(john))))&
(![X]:((~calm(X)&curious(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:(~brave(X)=>(quiet(X)|~calm(X))))&
(![X]:((funny(X)|humble(X))=>~old(X)))&
(![X]:((wise(X)<~>creative(X))=>~strong(X)))&
(((~calm(susan)<~>~happy(susan)))<=>(?[X]:((funny(X)|~calm(X)))))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((~rich(X)&~curious(X))))&
((~wise(alice)&creative(alice)))&
(?[X]:((~quiet(X)|rich(X))))&
((calm(susan)&~rich(susan)))&
((calm(john)<~>~tall(john)))&
((~creative(susan)|~humble(susan))) | funny(susan) | [
"p6",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 39990855224980897923504
% SZS output start Proof for 39990855224980897923504
7. ! [X0] : ((~old(X0) <~> ~calm(X0)) => (funny(X0) <~> calm(X0))) [input p6]
14. ! [X0] : ((humble(X0) | funny(X0)) => ~old(X0)) [input p13]
21. ~rich(susan) & calm(susan) [input p20]
24. funny(susan) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> calm(X0)) | (~old(X0) <=> ~calm(X0))) [ennf transformation 7]
36. ! [X0] : (~old(X0) | (~humble(X0) & ~funny(X0))) [ennf transformation 14]
46. ! [X0] : (((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) [nnf transformation 31]
89. ~calm(X0) | ~funny(X0) | ~calm(X0) | old(X0) [cnf transformation 46]
109. ~old(X0) | ~funny(X0) [cnf transformation 36]
125. calm(susan) [cnf transformation 21]
130. funny(susan) [cnf transformation 24]
132. ~calm(X0) | ~funny(X0) | old(X0) [duplicate literal removal 89]
241. 25 <=> calm(susan) [avatar definition]
243. calm(susan) <- (25) [avatar component clause 241]
283. 25 [avatar split clause 125,241]
329. ~funny(susan) | old(susan) <- (25) [resolution 132,243]
330. old(susan) <- (25) [subsumption resolution 329,130]
333. ~funny(susan) <- (25) [resolution 330,109]
336. $false <- (25) [subsumption resolution 333,130]
337. ~25 [avatar contradiction clause 336]
338. $false [avatar sat refutation 283,337]
% SZS output end Proof for 39990855224980897923504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or happy then alice is kind or not creative and vice versa. Everyone who is both not happy and not strong is both old and curious. If someone is curious then susan is not curious. If lucy is old then someone is either curious or not quiet. If paul is either tall or patient then someone is both funny and wise. Everyone who is both happy and not calm is patient and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. If someone is not curious or not generous then fred is both creative and old and vice versa. Someone is either funny or not calm. Lucy is not wise or calm. Susan is rich. Susan is not calm. Someone is both humble and rich. Someone is generous or wise. Paul is not strong or not generous. Alice is not generous. | Lucy is old. | contradiction | ((?[X]:((wise(X)<~>happy(X))))<=>((kind(alice)|~creative(alice))))&
(![X]:((~happy(X)&~strong(X))=>(old(X)&curious(X))))&
((?[X]:(curious(X)))=>(~curious(susan)))&
((old(lucy))=>(?[X]:((curious(X)<~>~quiet(X)))))&
(((tall(paul)<~>patient(paul)))=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((happy(X)&~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((creative(fred)&old(fred))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X))))&
((~strong(paul)|~generous(paul)))&
(~generous(alice)) | old(lucy) | [
"p7",
"p11",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3204385210370657108188055
% SZS output start Proof for 3204385210370657108188055
8. ! [X0] : ((old(X0) | generous(X0)) => (tall(X0) & ~curious(X0))) [input p7]
12. (~tall(lucy) & strong(lucy)) <=> old(fred) [input p11]
16. ? [X0] : (~generous(X0) | ~curious(X0)) <=> (old(fred) & creative(fred)) [input p15]
24. ~generous(alice) [input p23]
25. old(lucy) [input hypothesis]
35. ! [X0] : ((tall(X0) & ~curious(X0)) | (~old(X0) & ~generous(X0))) [ennf transformation 8]
58. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | (tall(lucy) | ~strong(lucy))) [nnf transformation 12]
59. ((~tall(lucy) & strong(lucy)) | ~old(fred)) & (old(fred) | tall(lucy) | ~strong(lucy)) [flattening 58]
66. (? [X0] : (~generous(X0) | ~curious(X0)) | (~old(fred) | ~creative(fred))) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [nnf transformation 16]
67. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X0] : (generous(X0) & curious(X0))) [flattening 66]
68. (? [X0] : (~generous(X0) | ~curious(X0)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [rectify 67]
69. ? [X0] : (~generous(X0) | ~curious(X0)) => (~generous(sK4) | ~curious(sK4)) [choice axiom]
70. ((~generous(sK4) | ~curious(sK4)) | ~old(fred) | ~creative(fred)) & ((old(fred) & creative(fred)) | ! [X1] : (generous(X1) & curious(X1))) [skolemisation 68,69]
101. ~old(X0) | tall(X0) [cnf transformation 35]
117. ~tall(lucy) | ~old(fred) [cnf transformation 59]
132. old(fred) | generous(X1) [cnf transformation 70]
141. ~generous(alice) [cnf transformation 24]
142. old(lucy) [cnf transformation 25]
180. 9 <=> old(lucy) [avatar definition]
181. old(lucy) <- (9) [avatar component clause 180]
252. 24 <=> old(fred) [avatar definition]
256. 25 <=> tall(lucy) [avatar definition]
258. ~tall(lucy) <- (~25) [avatar component clause 256]
259. ~24 | ~25 [avatar split clause 117,256,252]
267. 27 <=> ! [X1] : generous(X1) [avatar definition]
268. generous(X1) <- (27) [avatar component clause 267]
269. 27 | 24 [avatar split clause 132,252,267]
310. 9 [avatar split clause 142,180]
323. $false <- (27) [resolution 268,141]
324. ~27 [avatar contradiction clause 323]
329. tall(lucy) <- (9) [resolution 101,181]
331. $false <- (9, ~25) [subsumption resolution 329,258]
332. ~9 | 25 [avatar contradiction clause 331]
333. $false [avatar sat refutation 259,269,310,324,332]
% SZS output end Proof for 3204385210370657108188055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and not calm then someone is either funny or strong and vice versa.
Everyone who is both not kind and funny is both not rich and funny.
If someone is funny then susan is either generous or old.
If john is not calm or not creative then someone is either quiet or patient and vice versa.
Everyone who is both not rich and brave is calm or not funny and vice versa.
Everyone who is either not old or not brave is both not curious and quiet.
Everyone who is generous is both humble and not funny and vice versa.
Everyone who is either not strong or calm is old or not generous and vice versa.
Everyone who is strong is brave and vice versa.
If mary is not generous then someone is either not funny or not happy and vice versa.
Everyone who is both wise and not old is either not generous or brave.
Everyone who is both not quiet and wise is not patient or not quiet.
Everyone who is either wise or not brave is either not generous or strong and vice versa.
Everyone who is either not wise or not strong is both old and generous.
If someone is generous then john is both not calm and not funny and vice versa.
If someone is creative or curious then someone is either brave or not brave and vice versa.
Someone is generous or old.
Fred is wise or not wise.
John is not old or tall.
Someone is not funny.
Paul is creative.
Paul is both not calm and happy.
Mary is not creative.
Someone is old or not brave. | Susan is calm. | contradiction | ((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((funny(X)<~>strong(X)))))&
(![X]:((~kind(X)&funny(X))=>(~rich(X)&funny(X))))&
((?[X]:(funny(X)))=>((generous(susan)<~>old(susan))))&
(((~calm(john)|~creative(john)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:((~rich(X)&brave(X))<=>(calm(X)|~funny(X))))&
(![X]:((~old(X)<~>~brave(X))=>(~curious(X)&quiet(X))))&
(![X]:(generous(X)<=>(humble(X)&~funny(X))))&
(![X]:((~strong(X)<~>calm(X))<=>(old(X)|~generous(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~generous(mary))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((wise(X)&~old(X))=>(~generous(X)<~>brave(X))))&
(![X]:((~quiet(X)&wise(X))=>(~patient(X)|~quiet(X))))&
(![X]:((wise(X)<~>~brave(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(old(X)&generous(X))))&
((?[X]:(generous(X)))<=>((~calm(john)&~funny(john))))&
((?[X]:((creative(X)|curious(X))))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(?[X]:((generous(X)|old(X))))&
((wise(fred)|~wise(fred)))&
((~old(john)|tall(john)))&
(?[X]:(~funny(X)))&
(creative(paul))&
((~calm(paul)&happy(paul)))&
(~creative(mary))&
(?[X]:((old(X)|~brave(X)))) | calm(susan) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1542893505782091414295135
% SZS output start Proof for 1542893505782091414295135
3. ? [X0] : funny(X0) => (generous(susan) <~> old(susan)) [input p2]
5. ! [X0] : ((brave(X0) & ~rich(X0)) <=> (~funny(X0) | calm(X0))) [input p4]
8. ! [X0] : ((~strong(X0) <~> calm(X0)) <=> (~generous(X0) | old(X0))) [input p7]
9. ! [X0] : (strong(X0) <=> brave(X0)) [input p8]
10. ~generous(mary) <=> ? [X0] : (~funny(X0) <~> ~happy(X0)) [input p9]
13. ! [X0] : ((wise(X0) <~> ~brave(X0)) <=> (~generous(X0) <~> strong(X0))) [input p12]
14. ! [X0] : ((~wise(X0) <~> ~strong(X0)) => (generous(X0) & old(X0))) [input p13]
22. happy(paul) & ~calm(paul) [input p21]
25. calm(susan) [input hypothesis]
30. (generous(susan) <~> old(susan)) | ! [X0] : ~funny(X0) [ennf transformation 3]
36. ! [X0] : ((generous(X0) & old(X0)) | (~wise(X0) <=> ~strong(X0))) [ennf transformation 14]
42. ((~old(susan) | ~generous(susan)) & (old(susan) | generous(susan))) | ! [X0] : ~funny(X0) [nnf transformation 30]
48. ! [X0] : (((brave(X0) & ~rich(X0)) | (funny(X0) & ~calm(X0))) & ((~funny(X0) | calm(X0)) | (~brave(X0) | rich(X0)))) [nnf transformation 5]
49. ! [X0] : (((brave(X0) & ~rich(X0)) | (funny(X0) & ~calm(X0))) & (~funny(X0) | calm(X0) | ~brave(X0) | rich(X0))) [flattening 48]
53. ! [X0] : ((((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0))))) [flattening 53]
55. ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))) [nnf transformation 9]
56. (~generous(mary) | ! [X0] : ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) & (? [X0] : ((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | generous(mary)) [nnf transformation 10]
57. (~generous(mary) | ! [X0] : ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) & (? [X1] : ((happy(X1) | funny(X1)) & (~happy(X1) | ~funny(X1))) | generous(mary)) [rectify 56]
58. ? [X1] : ((happy(X1) | funny(X1)) & (~happy(X1) | ~funny(X1))) => ((happy(sK3) | funny(sK3)) & (~happy(sK3) | ~funny(sK3))) [choice axiom]
59. (~generous(mary) | ! [X0] : ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0)))) & (((happy(sK3) | funny(sK3)) & (~happy(sK3) | ~funny(sK3))) | generous(mary)) [skolemisation 57,58]
61. ! [X0] : ((((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | ((~generous(X0) | ~strong(X0)) & (strong(X0) | generous(X0)))) & (((~strong(X0) | generous(X0)) & (strong(X0) | ~generous(X0))) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0))))) [nnf transformation 13]
62. ! [X0] : ((generous(X0) & old(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) [nnf transformation 36]
86. ~old(susan) | ~generous(susan) | ~funny(X0) [cnf transformation 42]
96. ~calm(X0) | brave(X0) [cnf transformation 49]
97. brave(X0) | funny(X0) [cnf transformation 49]
106. ~generous(X0) | old(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 54]
108. ~strong(X0) | calm(X0) | generous(X0) [cnf transformation 54]
110. ~calm(X0) | strong(X0) | generous(X0) [cnf transformation 54]
111. ~strong(X0) | brave(X0) [cnf transformation 55]
112. ~brave(X0) | strong(X0) [cnf transformation 55]
115. ~generous(mary) | ~happy(X0) | funny(X0) [cnf transformation 59]
122. ~strong(X0) | generous(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 61]
125. ~brave(X0) | wise(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 61]
126. brave(X0) | ~wise(X0) | strong(X0) | generous(X0) [cnf transformation 61]
130. generous(X0) | ~strong(X0) | wise(X0) [cnf transformation 62]
146. happy(paul) [cnf transformation 22]
149. calm(susan) [cnf transformation 25]
184. 8 <=> ! [X0] : ~funny(X0) [avatar definition]
185. ~funny(X0) <- (8) [avatar component clause 184]
187. 9 <=> generous(susan) [avatar definition]
188. generous(susan) <- (9) [avatar component clause 187]
191. 10 <=> old(susan) [avatar definition]
194. 8 | ~9 | ~10 [avatar split clause 86,191,187,184]
228. 18 <=> generous(mary) [avatar definition]
230. ~generous(mary) <- (~18) [avatar component clause 228]
233. 19 <=> ! [X0] : (~happy(X0) | funny(X0)) [avatar definition]
234. ~happy(X0) | funny(X0) <- (19) [avatar component clause 233]
235. 19 | ~18 [avatar split clause 115,228,233]
246. ~wise(X0) | strong(X0) | generous(X0) [subsumption resolution 126,112]
247. ~generous(X0) | wise(X0) | ~strong(X0) [subsumption resolution 125,111]
248. ~wise(X0) | ~brave(X0) | generous(X0) [subsumption resolution 122,246]
250. ~strong(X0) | wise(X0) [subsumption resolution 130,247]
299. brave(susan) [resolution 96,149]
311. strong(X0) | funny(X0) [resolution 112,97]
312. strong(susan) [resolution 112,299]
341. wise(susan) [resolution 312,250]
352. generous(X0) | calm(X0) | funny(X0) [resolution 108,311]
425. funny(paul) <- (19) [resolution 234,146]
441. old(susan) | ~strong(susan) | ~calm(susan) <- (9) [resolution 106,188]
452. 37 <=> calm(mary) [avatar definition]
453. calm(mary) <- (37) [avatar component clause 452]
482. old(susan) | ~calm(susan) <- (9) [subsumption resolution 441,312]
483. old(susan) <- (9) [subsumption resolution 482,149]
484. 10 | ~9 [avatar split clause 483,187,191]
491. $false <- (8, 19) [resolution 425,185]
493. ~8 | ~19 [avatar contradiction clause 491]
513. ~brave(susan) | generous(susan) [resolution 341,248]
534. generous(susan) [subsumption resolution 513,299]
558. 46 <=> strong(mary) [avatar definition]
560. strong(mary) <- (46) [avatar component clause 558]
569. 48 <=> brave(mary) [avatar definition]
571. brave(mary) <- (48) [avatar component clause 569]
573. 49 <=> wise(mary) [avatar definition]
575. wise(mary) <- (49) [avatar component clause 573]
609. 9 [avatar split clause 534,187]
743. calm(mary) | funny(mary) <- (~18) [resolution 352,230]
749. calm(mary) <- (8, ~18) [subsumption resolution 743,185]
750. 37 | ~8 | 18 [avatar split clause 749,228,184,452]
751. strong(mary) | generous(mary) <- (37) [resolution 453,110]
752. brave(mary) <- (37) [resolution 453,96]
753. strong(mary) <- (~18, 37) [subsumption resolution 751,230]
754. 46 | 18 | ~37 [avatar split clause 753,452,228,558]
755. 48 | ~37 [avatar split clause 752,452,569]
757. wise(mary) <- (46) [resolution 560,250]
759. 49 | ~46 [avatar split clause 757,558,573]
770. ~brave(mary) | generous(mary) <- (49) [resolution 575,248]
776. generous(mary) <- (48, 49) [subsumption resolution 770,571]
777. $false <- (~18, 48, 49) [subsumption resolution 776,230]
778. 18 | ~48 | ~49 [avatar contradiction clause 777]
779. $false [avatar sat refutation 194,235,484,493,609,750,754,755,759,778]
% SZS output end Proof for 1542893505782091414295135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is quiet.
Everyone who is either curious or strong is not wise or not funny and vice versa.
If mary is either not funny or not calm then someone is not rich and vice versa.
If fred is either old or wise then paul is not calm and vice versa.
Everyone who is either not brave or tall is both wise and happy and vice versa.
Everyone who is either tall or not generous is not generous or not patient and vice versa.
Everyone who is strong is either not brave or humble.
If someone is generous then someone is creative or kind and vice versa.
Everyone who is not funny is creative or not creative and vice versa.
Everyone who is either not generous or kind is not generous or not kind and vice versa.
Everyone who is not wise or not generous is both not humble and not kind and vice versa.
If paul is both not curious and not funny then someone is strong.
Everyone who is creative or not wise is both not happy and tall and vice versa.
Everyone who is calm is not old or not wise and vice versa.
John is patient.
Mary is both not kind and not funny.
John is either creative or patient.
Someone is both old and not generous.
Someone is wise or not generous.
John is either curious or quiet. | Mary is not creative. | entailment | (![X]:(~curious(X)=>quiet(X)))&
(![X]:((curious(X)<~>strong(X))<=>(~wise(X)|~funny(X))))&
(((~funny(mary)<~>~calm(mary)))<=>(?[X]:(~rich(X))))&
(((old(fred)<~>wise(fred)))<=>(~calm(paul)))&
(![X]:((~brave(X)<~>tall(X))<=>(wise(X)&happy(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)|~patient(X))))&
(![X]:(strong(X)=>(~brave(X)<~>humble(X))))&
((?[X]:(generous(X)))<=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(~funny(X)<=>(creative(X)|~creative(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~wise(X)|~generous(X))<=>(~humble(X)&~kind(X))))&
(((~curious(paul)&~funny(paul)))=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~wise(X))<=>(~happy(X)&tall(X))))&
(![X]:(calm(X)<=>(~old(X)|~wise(X))))&
(patient(john))&
((~kind(mary)&~funny(mary)))&
((creative(john)<~>patient(john)))&
(?[X]:((old(X)&~generous(X))))&
(?[X]:((wise(X)|~generous(X))))&
((curious(john)<~>quiet(john))) | ~creative(mary) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 460984359496034236265392
% SZS output start Proof for 460984359496034236265392
8. ? [X0] : generous(X0) <=> ? [X0] : (kind(X0) | creative(X0)) [input p7]
10. ! [X0] : ((~generous(X0) <~> kind(X0)) <=> (~kind(X0) | ~generous(X0))) [input p9]
21. creative(mary) [input hypothesis]
22. ? [X0] : generous(X0) <=> ? [X1] : (kind(X1) | creative(X1)) [rectify 8]
39. (? [X0] : generous(X0) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X1] : (kind(X1) | creative(X1)) | ! [X0] : ~generous(X0)) [nnf transformation 22]
40. (? [X0] : generous(X0) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X2] : (kind(X2) | creative(X2)) | ! [X3] : ~generous(X3)) [rectify 39]
41. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
42. ? [X2] : (kind(X2) | creative(X2)) => (kind(sK2) | creative(sK2)) [choice axiom]
43. (generous(sK1) | ! [X1] : (~kind(X1) & ~creative(X1))) & ((kind(sK2) | creative(sK2)) | ! [X3] : ~generous(X3)) [skolemisation 40,42,41]
46. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [nnf transformation 10]
47. ! [X0] : ((((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))))) [flattening 46]
92. generous(sK1) | ~creative(X1) [cnf transformation 43]
98. ~kind(X0) | ~generous(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 47]
100. kind(X0) | ~generous(X0) | kind(X0) [cnf transformation 47]
101. ~kind(X0) | generous(X0) | generous(X0) [cnf transformation 47]
127. creative(mary) [cnf transformation 21]
128. ~kind(X0) | ~generous(X0) [duplicate literal removal 98]
129. ~generous(X0) | kind(X0) [duplicate literal removal 100]
130. ~kind(X0) | generous(X0) [duplicate literal removal 101]
170. 8 <=> ! [X1] : ~kind(X1) [avatar definition]
171. ~kind(X1) <- (8) [avatar component clause 170]
173. 9 <=> generous(sK1) [avatar definition]
175. generous(sK1) <- (9) [avatar component clause 173]
178. 10 <=> ! [X1] : ~creative(X1) [avatar definition]
179. ~creative(X1) <- (10) [avatar component clause 178]
180. 10 | 9 [avatar split clause 92,173,178]
194. ~kind(X0) [subsumption resolution 128,130]
195. 8 [avatar split clause 194,170]
229. $false <- (10) [resolution 179,127]
230. ~10 [avatar contradiction clause 229]
238. kind(sK1) <- (9) [resolution 129,175]
239. $false <- (8, 9) [subsumption resolution 238,171]
240. ~8 | ~9 [avatar contradiction clause 239]
241. $false [avatar sat refutation 180,195,230,240]
% SZS output end Proof for 460984359496034236265392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is curious then john is not strong or not curious and vice versa. If lucy is not strong then someone is not brave or not wise and vice versa. Everyone who is not generous is not happy or not calm. If someone is not tall then someone is not kind and vice versa. If alice is both not generous and not brave then mary is strong. If someone is calm or not wise then someone is both not wise and not quiet. If fred is wise then lucy is either not kind or generous. Everyone who is either brave or not strong is not rich or curious and vice versa. If john is happy then susan is generous. If someone is either patient or kind then someone is kind or not kind and vice versa. Everyone who is both not rich and rich is old or tall. Everyone who is not funny is both curious and not patient and vice versa. Everyone who is not humble or patient is wise and vice versa. Everyone who is not kind is both wise and patient and vice versa. Everyone who is not funny is either not brave or brave and vice versa. If someone is both kind and wise then fred is both not humble and not wise. Lucy is both not rich and generous. Someone is happy or old. Someone is happy. Someone is not strong or not generous. Fred is not old. John is both humble and creative. Someone is kind. Paul is either funny or rich. | Paul is not humble. | contradiction | ((curious(john))<=>((~strong(john)|~curious(john))))&
((~strong(lucy))<=>(?[X]:((~brave(X)|~wise(X)))))&
(![X]:(~generous(X)=>(~happy(X)|~calm(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(~kind(X))))&
(((~generous(alice)&~brave(alice)))=>(strong(mary)))&
((?[X]:((calm(X)|~wise(X))))=>(?[X]:((~wise(X)&~quiet(X)))))&
((wise(fred))=>((~kind(lucy)<~>generous(lucy))))&
(![X]:((brave(X)<~>~strong(X))<=>(~rich(X)|curious(X))))&
((happy(john))=>(generous(susan)))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((~rich(lucy)&generous(lucy)))&
(?[X]:((happy(X)|old(X))))&
(?[X]:(happy(X)))&
(?[X]:((~strong(X)|~generous(X))))&
(~old(fred))&
((humble(john)&creative(john)))&
(?[X]:(kind(X)))&
((funny(paul)<~>rich(paul))) | ~humble(paul) | [
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5937850403336927609137859
% SZS output start Proof for 5937850403336927609137859
12. ! [X0] : (~funny(X0) <=> (~patient(X0) & curious(X0))) [input p11]
13. ! [X0] : ((patient(X0) | ~humble(X0)) <=> wise(X0)) [input p12]
14. ! [X0] : (~kind(X0) <=> (patient(X0) & wise(X0))) [input p13]
15. ! [X0] : (~funny(X0) <=> (~brave(X0) <~> brave(X0))) [input p14]
16. ? [X0] : (wise(X0) & kind(X0)) => (~wise(fred) & ~humble(fred)) [input p15]
25. ~humble(paul) [input hypothesis]
40. (~wise(fred) & ~humble(fred)) | ! [X0] : (~wise(X0) | ~kind(X0)) [ennf transformation 16]
63. ! [X0] : ((~funny(X0) | (patient(X0) | ~curious(X0))) & ((~patient(X0) & curious(X0)) | funny(X0))) [nnf transformation 12]
64. ! [X0] : ((~funny(X0) | patient(X0) | ~curious(X0)) & ((~patient(X0) & curious(X0)) | funny(X0))) [flattening 63]
65. ! [X0] : (((patient(X0) | ~humble(X0)) | ~wise(X0)) & (wise(X0) | (~patient(X0) & humble(X0)))) [nnf transformation 13]
66. ! [X0] : ((patient(X0) | ~humble(X0) | ~wise(X0)) & (wise(X0) | (~patient(X0) & humble(X0)))) [flattening 65]
67. ! [X0] : ((~kind(X0) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | kind(X0))) [nnf transformation 14]
68. ! [X0] : ((~kind(X0) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | kind(X0))) [flattening 67]
69. ! [X0] : ((~funny(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | funny(X0))) [nnf transformation 15]
106. ~patient(X0) | funny(X0) [cnf transformation 64]
108. humble(X0) | wise(X0) [cnf transformation 66]
112. patient(X0) | kind(X0) [cnf transformation 68]
116. ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 69]
117. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 69]
118. ~humble(fred) | ~wise(X0) | ~kind(X0) [cnf transformation 40]
119. ~wise(fred) | ~wise(X0) | ~kind(X0) [cnf transformation 40]
130. ~humble(paul) [cnf transformation 25]
131. ~funny(X0) | brave(X0) [duplicate literal removal 116]
132. ~funny(X0) | ~brave(X0) [duplicate literal removal 117]
158. 6 <=> ! [X1] : kind(X1) [avatar definition]
159. kind(X1) <- (6) [avatar component clause 158]
192. 14 <=> wise(fred) [avatar definition]
230. ~funny(X0) [subsumption resolution 131,132]
232. 22 <=> ! [X0] : (~wise(X0) | ~kind(X0)) [avatar definition]
233. ~kind(X0) | ~wise(X0) <- (22) [avatar component clause 232]
234. 22 | ~14 [avatar split clause 119,192,232]
236. 23 <=> humble(fred) [avatar definition]
238. ~humble(fred) <- (~23) [avatar component clause 236]
239. 22 | ~23 [avatar split clause 118,236,232]
264. wise(paul) [resolution 108,130]
265. wise(fred) <- (~23) [resolution 108,238]
268. 14 | 23 [avatar split clause 265,236,192]
271. kind(X1) | funny(X1) [resolution 112,106]
273. kind(X1) [subsumption resolution 271,230]
274. 6 [avatar split clause 273,158]
281. ~wise(X0) <- (6, 22) [resolution 233,159]
287. $false <- (6, 22) [resolution 281,264]
288. ~6 | ~22 [avatar contradiction clause 287]
290. $false [avatar sat refutation 234,239,268,274,288]
% SZS output end Proof for 5937850403336927609137859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either generous or wise then susan is not curious or not happy.
Everyone who is quiet or curious is not old or old and vice versa.
Everyone who is kind or funny is either not curious or rich and vice versa.
If lucy is either patient or generous then someone is either not strong or patient.
If lucy is either not generous or creative then paul is not funny or brave.
If fred is kind then fred is either not curious or creative.
Everyone who is not old or kind is tall and vice versa.
Everyone who is either not funny or not curious is not calm or not strong and vice versa.
If someone is not rich then someone is strong or not old and vice versa.
Everyone who is old or not humble is curious or not funny.
If someone is both not wise and funny then someone is either strong or not generous and vice versa.
Everyone who is either calm or brave is strong or funny.
If someone is both generous and quiet then someone is not creative or not humble and vice versa.
If someone is both not brave and humble then someone is calm and vice versa.
If john is quiet then susan is not generous or not quiet and vice versa.
Everyone who is either not strong or funny is both not calm and strong and vice versa.
Fred is not strong or not creative.
Lucy is either not patient or not old.
Someone is old.
Fred is curious or old.
Alice is brave.
Someone is both calm and not wise.
John is both not kind and not humble. | Susan is wise. | neutral | (((generous(john)<~>wise(john)))=>((~curious(susan)|~happy(susan))))&
(![X]:((quiet(X)|curious(X))<=>(~old(X)|old(X))))&
(![X]:((kind(X)|funny(X))<=>(~curious(X)<~>rich(X))))&
(((patient(lucy)<~>generous(lucy)))=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~generous(lucy)<~>creative(lucy)))=>((~funny(paul)|brave(paul))))&
((kind(fred))=>((~curious(fred)<~>creative(fred))))&
(![X]:((~old(X)|kind(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~curious(X))<=>(~calm(X)|~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)|~humble(X))=>(curious(X)|~funny(X))))&
((?[X]:((~wise(X)&funny(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>brave(X))=>(strong(X)|funny(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:(calm(X))))&
((quiet(john))<=>((~generous(susan)|~quiet(susan))))&
(![X]:((~strong(X)<~>funny(X))<=>(~calm(X)&strong(X))))&
((~strong(fred)|~creative(fred)))&
((~patient(lucy)<~>~old(lucy)))&
(?[X]:(old(X)))&
((curious(fred)|old(fred)))&
(brave(alice))&
(?[X]:((calm(X)&~wise(X))))&
((~kind(john)&~humble(john))) | wise(susan) | [] | null | 0 |
Everyone who is quiet or strong is either humble or happy.
Everyone who is both funny and humble is rich.
Everyone who is both happy and not wise is rich and vice versa.
If someone is quiet or not curious then fred is both not rich and old and vice versa.
If someone is either old or not humble then john is both not quiet and not brave.
Everyone who is tall is kind or not curious and vice versa.
Everyone who is either wise or tall is both creative and strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
If lucy is both rich and not strong then paul is not curious or curious.
Everyone who is both rich and brave is not strong.
Someone is creative.
Someone is either not kind or not quiet.
Fred is either not strong or not calm.
Someone is either not old or not quiet.
Someone is wise.
Susan is not patient.
Alice is either happy or not old. | Lucy is funny. | entailment | (![X]:((quiet(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:((funny(X)&humble(X))=>rich(X)))&
(![X]:((happy(X)&~wise(X))<=>rich(X)))&
((?[X]:((quiet(X)|~curious(X))))<=>((~rich(fred)&old(fred))))&
((?[X]:((old(X)<~>~humble(X))))=>((~quiet(john)&~brave(john))))&
(![X]:(tall(X)<=>(kind(X)|~curious(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&strong(X))))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(((rich(lucy)&~strong(lucy)))=>((~curious(paul)|curious(paul))))&
(![X]:((rich(X)&brave(X))=>~strong(X)))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
((~strong(fred)<~>~calm(fred)))&
(?[X]:((~old(X)<~>~quiet(X))))&
(?[X]:(wise(X)))&
(~patient(susan))&
((happy(alice)<~>~old(alice))) | funny(lucy) | [
"p2",
"p5",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 933783406896291429545646
% SZS output start Proof for 933783406896291429545646
3. ! [X0] : ((~wise(X0) & happy(X0)) <=> rich(X0)) [input p2]
6. ! [X0] : (tall(X0) <=> (~curious(X0) | kind(X0))) [input p5]
9. ! [X0] : ((~generous(X0) | strong(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p8]
11. ! [X0] : ((~funny(X0) & brave(X0)) <=> (~happy(X0) & rich(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | ~strong(X0)) => (creative(X0) & curious(X0))) [input p11]
14. ? [X0] : (~brave(X0) | ~strong(X0)) <=> (~wise(fred) & ~curious(fred)) [input p13]
24. ~funny(lucy) [input hypothesis]
29. ! [X0] : ((~calm(X0) | ~strong(X0)) => curious(X0)) [pure predicate removal 12]
38. ! [X0] : (curious(X0) | (calm(X0) & strong(X0))) [ennf transformation 29]
44. ! [X0] : (((~wise(X0) & happy(X0)) | ~rich(X0)) & (rich(X0) | (wise(X0) | ~happy(X0)))) [nnf transformation 3]
45. ! [X0] : (((~wise(X0) & happy(X0)) | ~rich(X0)) & (rich(X0) | wise(X0) | ~happy(X0))) [flattening 44]
52. ! [X0] : ((tall(X0) | (curious(X0) & ~kind(X0))) & ((~curious(X0) | kind(X0)) | ~tall(X0))) [nnf transformation 6]
53. ! [X0] : ((tall(X0) | (curious(X0) & ~kind(X0))) & (~curious(X0) | kind(X0) | ~tall(X0))) [flattening 52]
55. ! [X0] : (((~generous(X0) | strong(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 9]
56. ! [X0] : ((~generous(X0) | strong(X0) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (generous(X0) & ~strong(X0)))) [flattening 55]
58. ! [X0] : (((~funny(X0) & brave(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 11]
59. ! [X0] : (((~funny(X0) & brave(X0)) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | funny(X0) | ~brave(X0))) [flattening 58]
62. (? [X0] : (~brave(X0) | ~strong(X0)) | (wise(fred) | curious(fred))) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [nnf transformation 14]
63. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X0] : (brave(X0) & strong(X0))) [flattening 62]
64. (? [X0] : (~brave(X0) | ~strong(X0)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [rectify 63]
65. ? [X0] : (~brave(X0) | ~strong(X0)) => (~brave(sK1) | ~strong(sK1)) [choice axiom]
66. ((~brave(sK1) | ~strong(sK1)) | wise(fred) | curious(fred)) & ((~wise(fred) & ~curious(fred)) | ! [X1] : (brave(X1) & strong(X1))) [skolemisation 64,65]
83. ~rich(X0) | happy(X0) [cnf transformation 45]
96. tall(X0) | curious(X0) [cnf transformation 53]
102. curious(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 56]
108. ~brave(X0) | funny(X0) | rich(X0) [cnf transformation 59]
109. ~brave(X0) | funny(X0) | ~happy(X0) [cnf transformation 59]
112. curious(X0) | strong(X0) [cnf transformation 38]
118. ~curious(fred) | brave(X1) [cnf transformation 66]
133. ~funny(lucy) [cnf transformation 24]
152. 5 <=> ! [X1] : curious(X1) [avatar definition]
153. curious(X1) <- (5) [avatar component clause 152]
180. ~strong(X0) | curious(X0) [subsumption resolution 102,96]
183. curious(X0) [subsumption resolution 112,180]
184. 5 [avatar split clause 183,152]
201. 14 <=> curious(fred) [avatar definition]
202. ~curious(fred) <- (~14) [avatar component clause 201]
218. 18 <=> ! [X1] : brave(X1) [avatar definition]
219. brave(X1) <- (18) [avatar component clause 218]
225. 18 | ~14 [avatar split clause 118,201,218]
269. $false <- (5, ~14) [resolution 202,153]
270. ~5 | 14 [avatar contradiction clause 269]
315. rich(X0) | funny(X0) <- (18) [resolution 108,219]
316. funny(X0) | ~happy(X0) <- (18) [resolution 109,219]
318. funny(X0) | happy(X0) <- (18) [resolution 315,83]
320. funny(X0) <- (18) [subsumption resolution 318,316]
337. $false <- (18) [resolution 320,133]
341. ~18 [avatar contradiction clause 337]
343. $false [avatar sat refutation 184,225,270,341]
% SZS output end Proof for 933783406896291429545646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is generous or not patient then someone is not strong or happy and vice versa. If john is both happy and not funny then someone is both quiet and not funny and vice versa. Everyone who is not funny or not kind is kind or not tall and vice versa. If alice is not humble then paul is either old or not strong and vice versa. If john is not calm then susan is humble or curious. Everyone who is not quiet is tall. If paul is either not strong or quiet then someone is both not wise and not tall and vice versa. If someone is not rich then susan is both curious and strong. If alice is both not rich and not wise then lucy is creative and vice versa. If paul is not wise then susan is not patient or brave. Everyone who is generous or not humble is funny or not patient. Everyone who is not tall is not funny and vice versa. If fred is quiet or not strong then someone is strong or not funny and vice versa. Everyone who is not old or tall is not funny or generous. If someone is generous then someone is either not wise or calm. Everyone who is not calm is not rich. Lucy is not calm. Paul is not generous or not curious. Someone is creative. Mary is either not patient or not tall. Someone is patient. John is not kind or not rich. John is not humble or not generous. | Susan is not curious. | contradiction | (((generous(alice)|~patient(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
(((happy(john)&~funny(john)))<=>(?[X]:((quiet(X)&~funny(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(kind(X)|~tall(X))))&
((~humble(alice))<=>((old(paul)<~>~strong(paul))))&
((~calm(john))=>((humble(susan)|curious(susan))))&
(![X]:(~quiet(X)=>tall(X)))&
(((~strong(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))=>((curious(susan)&strong(susan))))&
(((~rich(alice)&~wise(alice)))<=>(creative(lucy)))&
((~wise(paul))=>((~patient(susan)|brave(susan))))&
(![X]:((generous(X)|~humble(X))=>(funny(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((quiet(fred)|~strong(fred)))<=>(?[X]:((strong(X)|~funny(X)))))&
(![X]:((~old(X)|tall(X))=>(~funny(X)|generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(~calm(X)=>~rich(X)))&
(~calm(lucy))&
((~generous(paul)|~curious(paul)))&
(?[X]:(creative(X)))&
((~patient(mary)<~>~tall(mary)))&
(?[X]:(patient(X)))&
((~kind(john)|~rich(john)))&
((~humble(john)|~generous(john))) | ~curious(susan) | [
"p7",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3198263402505054338560879
% SZS output start Proof for 3198263402505054338560879
8. ? [X0] : ~rich(X0) => (strong(susan) & curious(susan)) [input p7]
16. ! [X0] : (~calm(X0) => ~rich(X0)) [input p15]
17. ~calm(lucy) [input p16]
24. ~curious(susan) [input hypothesis]
30. (strong(susan) & curious(susan)) | ! [X0] : rich(X0) [ennf transformation 8]
36. ! [X0] : (~rich(X0) | calm(X0)) [ennf transformation 16]
95. curious(susan) | rich(X0) [cnf transformation 30]
112. ~rich(X0) | calm(X0) [cnf transformation 36]
113. ~calm(lucy) [cnf transformation 17]
121. ~curious(susan) [cnf transformation 24]
198. 17 <=> curious(susan) [avatar definition]
224. 22 <=> ! [X0] : rich(X0) [avatar definition]
225. rich(X0) <- (22) [avatar component clause 224]
231. 22 | 17 [avatar split clause 95,198,224]
324. ~17 [avatar split clause 121,198]
332. calm(X0) <- (22) [resolution 112,225]
333. $false <- (22) [resolution 332,113]
336. ~22 [avatar contradiction clause 333]
337. $false [avatar sat refutation 231,324,336]
% SZS output end Proof for 3198263402505054338560879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not tall is not patient and vice versa.
Everyone who is both generous and not wise is tall or curious.
Everyone who is brave is either happy or not curious.
If someone is both tall and patient then someone is not wise and vice versa.
Everyone who is not tall is happy and vice versa.
If john is either not patient or strong then someone is both brave and funny and vice versa.
Everyone who is both not kind and kind is both not tall and brave and vice versa.
If john is either not creative or tall then alice is both happy and not quiet and vice versa.
Everyone who is either not patient or not humble is not patient and vice versa.
If mary is both not calm and not rich then lucy is not wise or not quiet and vice versa.
Everyone who is either old or creative is either not patient or quiet.
If someone is not creative or rich then alice is generous.
If paul is not generous then someone is not humble and vice versa.
Everyone who is not old is either not kind or not generous and vice versa.
If someone is either generous or not quiet then lucy is not calm and vice versa.
If john is calm then someone is not tall and vice versa.
Fred is not funny.
Susan is strong or rich.
Fred is both quiet and patient.
Someone is patient or not funny.
Someone is not patient.
Someone is both calm and not generous.
Alice is not funny.
Someone is generous. | Paul is not humble. | contradiction | (![X]:((~kind(X)<~>~tall(X))<=>~patient(X)))&
(![X]:((generous(X)&~wise(X))=>(tall(X)|curious(X))))&
(![X]:(brave(X)=>(happy(X)<~>~curious(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:(~wise(X))))&
(![X]:(~tall(X)<=>happy(X)))&
(((~patient(john)<~>strong(john)))<=>(?[X]:((brave(X)&funny(X)))))&
(![X]:((~kind(X)&kind(X))<=>(~tall(X)&brave(X))))&
(((~creative(john)<~>tall(john)))<=>((happy(alice)&~quiet(alice))))&
(![X]:((~patient(X)<~>~humble(X))<=>~patient(X)))&
(((~calm(mary)&~rich(mary)))<=>((~wise(lucy)|~quiet(lucy))))&
(![X]:((old(X)<~>creative(X))=>(~patient(X)<~>quiet(X))))&
((?[X]:((~creative(X)|rich(X))))=>(generous(alice)))&
((~generous(paul))<=>(?[X]:(~humble(X))))&
(![X]:(~old(X)<=>(~kind(X)<~>~generous(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(~calm(lucy)))&
((calm(john))<=>(?[X]:(~tall(X))))&
(~funny(fred))&
((strong(susan)|rich(susan)))&
((quiet(fred)&patient(fred)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:(~patient(X)))&
(?[X]:((calm(X)&~generous(X))))&
(~funny(alice))&
(?[X]:(generous(X))) | ~humble(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 513387260811919775691561
% SZS output start Proof for 513387260811919775691561
9. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> ~patient(X0)) [input p8]
25. ~humble(paul) [input hypothesis]
48. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | patient(X0)) & (~patient(X0) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 9]
102. ~patient(X0) | ~patient(X0) | humble(X0) [cnf transformation 48]
104. humble(X0) | patient(X0) | patient(X0) [cnf transformation 48]
138. ~humble(paul) [cnf transformation 25]
139. ~patient(X0) | humble(X0) [duplicate literal removal 102]
140. humble(X0) | patient(X0) [duplicate literal removal 104]
210. humble(X0) [subsumption resolution 139,140]
298. $false [subsumption resolution 138,210]
% SZS output end Proof for 513387260811919775691561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not wise is brave and vice versa.
Everyone who is rich is quiet or kind.
If someone is either not funny or not strong then fred is not old and vice versa.
Everyone who is both generous and quiet is either humble or not humble.
If someone is both not tall and happy then lucy is not patient or quiet.
Everyone who is both not patient and not rich is strong.
Everyone who is both rich and strong is both not funny and wise and vice versa.
Everyone who is both not creative and humble is either not calm or funny.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Everyone who is not quiet is not kind.
Everyone who is not quiet or patient is either not calm or brave and vice versa.
If someone is rich then someone is either creative or generous and vice versa.
If lucy is not curious then someone is both wise and not strong and vice versa.
If someone is curious or not creative then someone is not wise or not funny and vice versa.
If someone is quiet or funny then someone is not quiet or tall and vice versa.
Lucy is either not quiet or not tall.
Fred is rich.
Alice is either not funny or wise.
Someone is both creative and rich.
Someone is either not brave or wise.
Someone is patient.
Alice is not wise.
Someone is both not brave and not old. | Alice is not old. | entailment | (![X]:((strong(X)|~wise(X))<=>brave(X)))&
(![X]:(rich(X)=>(quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(~old(fred)))&
(![X]:((generous(X)&quiet(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~tall(X)&happy(X))))=>((~patient(lucy)|quiet(lucy))))&
(![X]:((~patient(X)&~rich(X))=>strong(X)))&
(![X]:((rich(X)&strong(X))<=>(~funny(X)&wise(X))))&
(![X]:((~creative(X)&humble(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((~quiet(X)|patient(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~curious(lucy))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((curious(X)|~creative(X))))<=>(?[X]:((~wise(X)|~funny(X)))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(fred))&
((~funny(alice)<~>wise(alice)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(patient(X)))&
(~wise(alice))&
(?[X]:((~brave(X)&~old(X)))) | ~old(alice) | [
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1636843973647049951277820
% SZS output start Proof for 1636843973647049951277820
9. ! [X0] : ((~old(X0) | ~kind(X0)) => (~happy(X0) & ~old(X0))) [input p8]
10. ! [X0] : ((generous(X0) | old(X0)) <=> (~quiet(X0) & calm(X0))) [input p9]
11. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p10]
25. old(alice) [input hypothesis]
29. ! [X0] : ((~old(X0) | ~kind(X0)) => ~old(X0)) [pure predicate removal 9]
39. ! [X0] : (~old(X0) | (old(X0) & kind(X0))) [ennf transformation 29]
40. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 11]
51. ! [X0] : (((generous(X0) | old(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [nnf transformation 10]
52. ! [X0] : ((generous(X0) | old(X0) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [flattening 51]
102. ~old(X0) | kind(X0) [cnf transformation 39]
106. ~old(X0) | ~quiet(X0) [cnf transformation 52]
109. ~kind(X0) | quiet(X0) [cnf transformation 40]
144. old(alice) [cnf transformation 25]
304. kind(alice) [resolution 102,144]
306. ~quiet(alice) [resolution 106,144]
307. quiet(alice) [resolution 109,304]
308. $false [subsumption resolution 307,306]
% SZS output end Proof for 1636843973647049951277820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not curious then someone is either wise or not tall and vice versa.
Everyone who is both not generous and not wise is curious.
Everyone who is either wise or not funny is either not brave or not strong and vice versa.
Everyone who is either not strong or not quiet is rich or not creative and vice versa.
Everyone who is either wise or tall is both not brave and not calm and vice versa.
Everyone who is both generous and strong is both not brave and calm and vice versa.
Everyone who is not calm or tall is both old and not curious.
If fred is either not funny or old then someone is either patient or not tall.
If paul is both happy and not calm then someone is kind or rich.
If john is either funny or generous then alice is humble or not tall and vice versa.
Everyone who is not kind is both not humble and not old.
If someone is both not humble and tall then alice is humble or not creative and vice versa.
If paul is both not patient and kind then lucy is both not strong and calm and vice versa.
Everyone who is not kind or not curious is either not happy or not curious.
Everyone who is either not quiet or not patient is happy or not strong.
Everyone who is both humble and not kind is funny and vice versa.
John is both not calm and wise.
Someone is not generous or not tall.
Someone is funny or not humble.
Someone is old or wise.
Fred is generous or not creative.
Someone is both not patient and not curious.
Mary is both not calm and not wise. | Mary is not rich. | neutral | ((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((~generous(X)&~wise(X))=>curious(X)))&
(![X]:((wise(X)<~>~funny(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(rich(X)|~creative(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)&~calm(X))))&
(![X]:((generous(X)&strong(X))<=>(~brave(X)&calm(X))))&
(![X]:((~calm(X)|tall(X))=>(old(X)&~curious(X))))&
(((~funny(fred)<~>old(fred)))=>(?[X]:((patient(X)<~>~tall(X)))))&
(((happy(paul)&~calm(paul)))=>(?[X]:((kind(X)|rich(X)))))&
(((funny(john)<~>generous(john)))<=>((humble(alice)|~tall(alice))))&
(![X]:(~kind(X)=>(~humble(X)&~old(X))))&
((?[X]:((~humble(X)&tall(X))))<=>((humble(alice)|~creative(alice))))&
(((~patient(paul)&kind(paul)))<=>((~strong(lucy)&calm(lucy))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(happy(X)|~strong(X))))&
(![X]:((humble(X)&~kind(X))<=>funny(X)))&
((~calm(john)&wise(john)))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((old(X)|wise(X))))&
((generous(fred)|~creative(fred)))&
(?[X]:((~patient(X)&~curious(X))))&
((~calm(mary)&~wise(mary))) | ~rich(mary) | [] | null | 0 |
If someone is not tall then susan is both not kind and rich and vice versa. If someone is both not creative and wise then someone is not rich or not humble. Everyone who is either not tall or humble is both rich and calm and vice versa. If paul is not brave then john is humble or old and vice versa. Everyone who is either creative or brave is both brave and not creative and vice versa. If alice is curious then susan is not patient. Everyone who is not funny or not wise is both not creative and curious and vice versa. Everyone who is not old is either strong or not funny. Everyone who is not wise or not creative is calm and vice versa. If someone is either rich or funny then someone is either not calm or not strong. Everyone who is not creative is not quiet and vice versa. Everyone who is funny or curious is rich or not rich. Everyone who is either patient or not kind is rich and vice versa. Everyone who is happy is both not funny and creative. If someone is not patient or curious then someone is either kind or not patient and vice versa. If paul is both brave and not quiet then someone is not quiet and vice versa. Someone is either curious or old. Lucy is both not tall and not generous. Someone is creative or happy. Paul is either creative or happy. Paul is happy or creative. Mary is quiet or not kind. | Alice is curious. | neutral | ((?[X]:(~tall(X)))<=>((~kind(susan)&rich(susan))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:((~tall(X)<~>humble(X))<=>(rich(X)&calm(X))))&
((~brave(paul))<=>((humble(john)|old(john))))&
(![X]:((creative(X)<~>brave(X))<=>(brave(X)&~creative(X))))&
((curious(alice))=>(~patient(susan)))&
(![X]:((~funny(X)|~wise(X))<=>(~creative(X)&curious(X))))&
(![X]:(~old(X)=>(strong(X)<~>~funny(X))))&
(![X]:((~wise(X)|~creative(X))<=>calm(X)))&
((?[X]:((rich(X)<~>funny(X))))=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((funny(X)|curious(X))=>(rich(X)|~rich(X))))&
(![X]:((patient(X)<~>~kind(X))<=>rich(X)))&
(![X]:(happy(X)=>(~funny(X)&creative(X))))&
((?[X]:((~patient(X)|curious(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(((brave(paul)&~quiet(paul)))<=>(?[X]:(~quiet(X))))&
(?[X]:((curious(X)<~>old(X))))&
((~tall(lucy)&~generous(lucy)))&
(?[X]:((creative(X)|happy(X))))&
((creative(paul)<~>happy(paul)))&
((happy(paul)|creative(paul)))&
((quiet(mary)|~kind(mary))) | curious(alice) | [] | null | 0 |
Everyone who is both curious and not curious is both not rich and brave. If john is not old then someone is both rich and not funny and vice versa. If susan is either not wise or funny then someone is either not strong or generous and vice versa. Everyone who is not kind is either not strong or not calm and vice versa. Everyone who is not calm is humble. Everyone who is both not patient and patient is not tall and vice versa. Everyone who is patient or happy is happy and vice versa. If paul is strong or quiet then someone is brave. Everyone who is both creative and not strong is both kind and creative. Everyone who is both generous and not strong is both not rich and kind. Everyone who is curious is not creative. Everyone who is not brave is both strong and not kind and vice versa. If mary is not old then someone is both calm and not funny and vice versa. Everyone who is either strong or curious is both not old and not tall and vice versa. Everyone who is either not humble or patient is either calm or not quiet and vice versa. Everyone who is either not brave or not humble is creative. Alice is not rich or not kind. Someone is both humble and not rich. Someone is both curious and brave. Someone is not patient. Someone is tall or not patient. Paul is either happy or rich. Mary is calm. | John is not old. | neutral | (![X]:((curious(X)&~curious(X))=>(~rich(X)&brave(X))))&
((~old(john))<=>(?[X]:((rich(X)&~funny(X)))))&
(((~wise(susan)<~>funny(susan)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(~kind(X)<=>(~strong(X)<~>~calm(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((~patient(X)&patient(X))<=>~tall(X)))&
(![X]:((patient(X)|happy(X))<=>happy(X)))&
(((strong(paul)|quiet(paul)))=>(?[X]:(brave(X))))&
(![X]:((creative(X)&~strong(X))=>(kind(X)&creative(X))))&
(![X]:((generous(X)&~strong(X))=>(~rich(X)&kind(X))))&
(![X]:(curious(X)=>~creative(X)))&
(![X]:(~brave(X)<=>(strong(X)&~kind(X))))&
((~old(mary))<=>(?[X]:((calm(X)&~funny(X)))))&
(![X]:((strong(X)<~>curious(X))<=>(~old(X)&~tall(X))))&
(![X]:((~humble(X)<~>patient(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~humble(X))=>creative(X)))&
((~rich(alice)|~kind(alice)))&
(?[X]:((humble(X)&~rich(X))))&
(?[X]:((curious(X)&brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:((tall(X)|~patient(X))))&
((happy(paul)<~>rich(paul)))&
(calm(mary)) | ~old(john) | [] | null | 0 |
Everyone who is both humble and not tall is either not tall or not curious.
If mary is either not old or happy then paul is both happy and creative.
Everyone who is both not creative and not kind is not old and vice versa.
If paul is either not calm or not tall then someone is either not strong or not brave and vice versa.
Everyone who is not old is not happy and vice versa.
Everyone who is either not generous or not humble is either not old or quiet and vice versa.
Everyone who is creative or happy is not humble and vice versa.
Everyone who is either not kind or curious is either creative or humble.
If someone is generous or brave then mary is not curious and vice versa.
Everyone who is brave is either humble or not rich and vice versa.
If someone is both not rich and not humble then someone is generous and vice versa.
If someone is both not wise and not creative then someone is either brave or creative.
If alice is either brave or not generous then someone is brave and vice versa.
Everyone who is either old or humble is generous.
Everyone who is wise is both rich and not calm and vice versa.
Everyone who is strong is brave and vice versa.
Susan is not kind or humble.
Mary is both not creative and not brave.
Someone is happy or not calm.
Someone is either happy or strong.
Alice is either not curious or not kind. | Mary is not curious. | entailment | (![X]:((humble(X)&~tall(X))=>(~tall(X)<~>~curious(X))))&
(((~old(mary)<~>happy(mary)))=>((happy(paul)&creative(paul))))&
(![X]:((~creative(X)&~kind(X))<=>~old(X)))&
(((~calm(paul)<~>~tall(paul)))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:((~generous(X)<~>~humble(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((creative(X)|happy(X))<=>~humble(X)))&
(![X]:((~kind(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>(~curious(mary)))&
(![X]:(brave(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:((~rich(X)&~humble(X))))<=>(?[X]:(generous(X))))&
((?[X]:((~wise(X)&~creative(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(((brave(alice)<~>~generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>humble(X))=>generous(X)))&
(![X]:(wise(X)<=>(rich(X)&~calm(X))))&
(![X]:(strong(X)<=>brave(X)))&
((~kind(susan)|humble(susan)))&
((~creative(mary)&~brave(mary)))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((happy(X)<~>strong(X))))&
((~curious(alice)<~>~kind(alice))) | ~curious(mary) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 510080027429997858996933
% SZS output start Proof for 510080027429997858996933
9. ? [X0] : (brave(X0) | generous(X0)) <=> ~curious(mary) [input p8]
13. (brave(alice) <~> ~generous(alice)) <=> ? [X0] : brave(X0) [input p12]
22. curious(mary) [input hypothesis]
46. (? [X0] : (brave(X0) | generous(X0)) | curious(mary)) & (~curious(mary) | ! [X0] : (~brave(X0) & ~generous(X0))) [nnf transformation 9]
47. (? [X0] : (brave(X0) | generous(X0)) | curious(mary)) & (~curious(mary) | ! [X1] : (~brave(X1) & ~generous(X1))) [rectify 46]
48. ? [X0] : (brave(X0) | generous(X0)) => (brave(sK1) | generous(sK1)) [choice axiom]
49. ((brave(sK1) | generous(sK1)) | curious(mary)) & (~curious(mary) | ! [X1] : (~brave(X1) & ~generous(X1))) [skolemisation 47,48]
60. (((generous(alice) | ~brave(alice)) & (~generous(alice) | brave(alice))) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ((brave(alice) | generous(alice)) & (~generous(alice) | ~brave(alice)))) [nnf transformation 13]
61. (((generous(alice) | ~brave(alice)) & (~generous(alice) | brave(alice))) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ((brave(alice) | generous(alice)) & (~generous(alice) | ~brave(alice)))) [rectify 60]
62. ? [X1] : brave(X1) => brave(sK5) [choice axiom]
63. (((generous(alice) | ~brave(alice)) & (~generous(alice) | brave(alice))) | ! [X0] : ~brave(X0)) & (brave(sK5) | ((brave(alice) | generous(alice)) & (~generous(alice) | ~brave(alice)))) [skolemisation 61,62]
106. ~curious(mary) | ~generous(X1) [cnf transformation 49]
107. ~curious(mary) | ~brave(X1) [cnf transformation 49]
119. brave(sK5) | brave(alice) | generous(alice) [cnf transformation 63]
136. curious(mary) [cnf transformation 22]
189. 11 <=> curious(mary) [avatar definition]
202. 14 <=> ! [X1] : ~brave(X1) [avatar definition]
203. ~brave(X1) <- (14) [avatar component clause 202]
204. 14 | ~11 [avatar split clause 107,189,202]
206. 15 <=> ! [X1] : ~generous(X1) [avatar definition]
207. ~generous(X1) <- (15) [avatar component clause 206]
208. 15 | ~11 [avatar split clause 106,189,206]
241. 23 <=> brave(alice) [avatar definition]
242. brave(alice) <- (23) [avatar component clause 241]
245. 24 <=> generous(alice) [avatar definition]
247. generous(alice) <- (24) [avatar component clause 245]
251. 25 <=> brave(sK5) [avatar definition]
253. brave(sK5) <- (25) [avatar component clause 251]
254. 24 | 23 | 25 [avatar split clause 119,251,241,245]
296. 11 [avatar split clause 136,189]
298. $false <- (14, 23) [resolution 242,203]
299. ~14 | ~23 [avatar contradiction clause 298]
300. $false <- (15, 24) [subsumption resolution 247,207]
301. ~15 | ~24 [avatar contradiction clause 300]
302. $false <- (14, 25) [subsumption resolution 253,203]
303. ~14 | ~25 [avatar contradiction clause 302]
304. $false [avatar sat refutation 204,208,254,296,299,301,303]
% SZS output end Proof for 510080027429997858996933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and brave is not happy or not kind and vice versa.
If someone is both not curious and patient then susan is quiet and vice versa.
Everyone who is kind or humble is both strong and not quiet.
Everyone who is either not happy or not calm is either not brave or tall.
If someone is brave then fred is strong or rich.
Everyone who is creative is both not creative and not brave and vice versa.
Everyone who is either not funny or happy is calm or brave and vice versa.
If lucy is not strong then someone is either not humble or not creative.
If someone is either not patient or not happy then someone is either patient or humble and vice versa.
Everyone who is either not quiet or generous is either happy or funny.
Everyone who is old is patient or not wise.
Everyone who is funny or brave is not wise and vice versa.
If lucy is either patient or not calm then mary is not generous or strong.
If someone is both happy and strong then john is strong and vice versa.
If someone is either creative or not strong then mary is both happy and not creative.
If fred is not generous then someone is not curious or old and vice versa.
Fred is either old or quiet.
Someone is both not happy and curious.
John is either not quiet or rich.
Alice is either not rich or patient.
Alice is brave.
Alice is both kind and not humble. | Alice is curious. | neutral | (![X]:((strong(X)&brave(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~curious(X)&patient(X))))<=>(quiet(susan)))&
(![X]:((kind(X)|humble(X))=>(strong(X)&~quiet(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(~brave(X)<~>tall(X))))&
((?[X]:(brave(X)))=>((strong(fred)|rich(fred))))&
(![X]:(creative(X)<=>(~creative(X)&~brave(X))))&
(![X]:((~funny(X)<~>happy(X))<=>(calm(X)|brave(X))))&
((~strong(lucy))=>(?[X]:((~humble(X)<~>~creative(X)))))&
((?[X]:((~patient(X)<~>~happy(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~quiet(X)<~>generous(X))=>(happy(X)<~>funny(X))))&
(![X]:(old(X)=>(patient(X)|~wise(X))))&
(![X]:((funny(X)|brave(X))<=>~wise(X)))&
(((patient(lucy)<~>~calm(lucy)))=>((~generous(mary)|strong(mary))))&
((?[X]:((happy(X)&strong(X))))<=>(strong(john)))&
((?[X]:((creative(X)<~>~strong(X))))=>((happy(mary)&~creative(mary))))&
((~generous(fred))<=>(?[X]:((~curious(X)|old(X)))))&
((old(fred)<~>quiet(fred)))&
(?[X]:((~happy(X)&curious(X))))&
((~quiet(john)<~>rich(john)))&
((~rich(alice)<~>patient(alice)))&
(brave(alice))&
((kind(alice)&~humble(alice))) | curious(alice) | [] | null | 0 |
If john is both not kind and not rich then mary is either creative or kind and vice versa.
If someone is either not curious or patient then someone is not old and vice versa.
If mary is both humble and calm then someone is not kind.
Everyone who is not curious is not kind and vice versa.
Everyone who is not patient or not curious is both curious and funny.
Everyone who is curious or old is both kind and not funny and vice versa.
If john is not brave then someone is tall or brave.
If paul is patient or not tall then fred is not quiet.
If someone is either tall or wise then someone is not strong and vice versa.
If paul is strong or not old then someone is either not creative or not brave.
Everyone who is both old and happy is both not wise and curious and vice versa.
Everyone who is both not curious and humble is either tall or humble.
Everyone who is humble or not brave is both patient and quiet.
Everyone who is either curious or tall is not patient.
Everyone who is either not old or not generous is either not old or not humble.
Mary is not generous or not kind.
John is creative.
Susan is both generous and curious.
Paul is either not old or kind.
Someone is both not wise and not brave.
Fred is both generous and patient.
Susan is old or not generous. | Fred is old. | entailment | (((~kind(john)&~rich(john)))<=>((creative(mary)<~>kind(mary))))&
((?[X]:((~curious(X)<~>patient(X))))<=>(?[X]:(~old(X))))&
(((humble(mary)&calm(mary)))=>(?[X]:(~kind(X))))&
(![X]:(~curious(X)<=>~kind(X)))&
(![X]:((~patient(X)|~curious(X))=>(curious(X)&funny(X))))&
(![X]:((curious(X)|old(X))<=>(kind(X)&~funny(X))))&
((~brave(john))=>(?[X]:((tall(X)|brave(X)))))&
(((patient(paul)|~tall(paul)))=>(~quiet(fred)))&
((?[X]:((tall(X)<~>wise(X))))<=>(?[X]:(~strong(X))))&
(((strong(paul)|~old(paul)))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((old(X)&happy(X))<=>(~wise(X)&curious(X))))&
(![X]:((~curious(X)&humble(X))=>(tall(X)<~>humble(X))))&
(![X]:((humble(X)|~brave(X))=>(patient(X)&quiet(X))))&
(![X]:((curious(X)<~>tall(X))=>~patient(X)))&
(![X]:((~old(X)<~>~generous(X))=>(~old(X)<~>~humble(X))))&
((~generous(mary)|~kind(mary)))&
(creative(john))&
((generous(susan)&curious(susan)))&
((~old(paul)<~>kind(paul)))&
(?[X]:((~wise(X)&~brave(X))))&
((generous(fred)&patient(fred)))&
((old(susan)|~generous(susan))) | old(fred) | [
"p4",
"p5",
"p7",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8681243952161938993115615
% SZS output start Proof for 8681243952161938993115615
5. ! [X0] : ((~curious(X0) | ~patient(X0)) => (funny(X0) & curious(X0))) [input p4]
6. ! [X0] : ((old(X0) | curious(X0)) <=> (~funny(X0) & kind(X0))) [input p5]
8. (~tall(paul) | patient(paul)) => ~quiet(fred) [input p7]
13. ! [X0] : ((~brave(X0) | humble(X0)) => (quiet(X0) & patient(X0))) [input p12]
15. ! [X0] : ((~old(X0) <~> ~generous(X0)) => (~old(X0) <~> ~humble(X0))) [input p14]
21. patient(fred) & generous(fred) [input p20]
23. ~old(fred) [input hypothesis]
27. ! [X0] : ((funny(X0) & curious(X0)) | (curious(X0) & patient(X0))) [ennf transformation 5]
29. ~quiet(fred) | (tall(paul) & ~patient(paul)) [ennf transformation 8]
33. ! [X0] : ((quiet(X0) & patient(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 13]
35. ! [X0] : ((~old(X0) <~> ~humble(X0)) | (~old(X0) <=> ~generous(X0))) [ennf transformation 15]
44. ! [X0] : (((old(X0) | curious(X0)) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | (~old(X0) & ~curious(X0)))) [nnf transformation 6]
45. ! [X0] : ((old(X0) | curious(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | (~old(X0) & ~curious(X0)))) [flattening 44]
60. ! [X0] : (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0)))) [nnf transformation 35]
77. curious(X0) | curious(X0) [cnf transformation 27]
78. funny(X0) | patient(X0) [cnf transformation 27]
82. ~funny(X0) | ~curious(X0) [cnf transformation 45]
86. ~quiet(fred) | ~patient(paul) [cnf transformation 29]
104. ~humble(X0) | quiet(X0) [cnf transformation 33]
110. humble(X0) | old(X0) | ~generous(X0) | old(X0) [cnf transformation 60]
120. generous(fred) [cnf transformation 21]
123. ~old(fred) [cnf transformation 23]
125. ~generous(X0) | old(X0) | humble(X0) [duplicate literal removal 110]
127. curious(X0) [duplicate literal removal 77]
175. ~funny(X0) [subsumption resolution 82,127]
194. 15 <=> quiet(fred) [avatar definition]
199. 16 <=> patient(paul) [avatar definition]
201. ~patient(paul) <- (~16) [avatar component clause 199]
202. ~16 | ~15 [avatar split clause 86,194,199]
269. patient(X0) [resolution 78,175]
291. old(fred) | humble(fred) [resolution 125,120]
292. humble(fred) [subsumption resolution 291,123]
294. quiet(fred) [resolution 292,104]
298. 15 [avatar split clause 294,194]
299. $false <- (~16) [subsumption resolution 201,269]
300. 16 [avatar contradiction clause 299]
301. $false [avatar sat refutation 202,298,300]
% SZS output end Proof for 8681243952161938993115615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or rich is both rich and not strong and vice versa. If alice is funny then paul is not old or strong. Everyone who is happy is not patient and vice versa. Everyone who is not quiet or rich is curious. Everyone who is either curious or not patient is funny. Everyone who is brave or humble is both humble and not humble and vice versa. Everyone who is either not strong or not quiet is not calm. Everyone who is generous is both humble and generous and vice versa. Everyone who is either rich or not strong is either not quiet or not tall and vice versa. Everyone who is either funny or happy is both wise and quiet. If someone is generous or rich then someone is not curious or not humble. Everyone who is brave is either not generous or tall. If someone is not curious or wise then someone is either not old or happy. Everyone who is not generous or not happy is not calm and vice versa. Everyone who is either wise or not calm is not humble or not curious. Everyone who is not calm is either not brave or creative. Fred is patient. Paul is not tall or not rich. Susan is both kind and not creative. Someone is curious. Susan is not quiet or not creative. Someone is strong or generous. | Alice is humble. | contradiction | (![X]:((tall(X)<~>rich(X))<=>(rich(X)&~strong(X))))&
((funny(alice))=>((~old(paul)|strong(paul))))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((~quiet(X)|rich(X))=>curious(X)))&
(![X]:((curious(X)<~>~patient(X))=>funny(X)))&
(![X]:((brave(X)|humble(X))<=>(humble(X)&~humble(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>~calm(X)))&
(![X]:(generous(X)<=>(humble(X)&generous(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)<~>happy(X))=>(wise(X)&quiet(X))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:(brave(X)=>(~generous(X)<~>tall(X))))&
((?[X]:((~curious(X)|wise(X))))=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~generous(X)|~happy(X))<=>~calm(X)))&
(![X]:((wise(X)<~>~calm(X))=>(~humble(X)|~curious(X))))&
(![X]:(~calm(X)=>(~brave(X)<~>creative(X))))&
(patient(fred))&
((~tall(paul)|~rich(paul)))&
((kind(susan)&~creative(susan)))&
(?[X]:(curious(X)))&
((~quiet(susan)|~creative(susan)))&
(?[X]:((strong(X)|generous(X)))) | humble(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6995225165572926024527415
% SZS output start Proof for 6995225165572926024527415
6. ! [X0] : ((humble(X0) | brave(X0)) <=> (~humble(X0) & humble(X0))) [input p5]
23. humble(alice) [input hypothesis]
43. ! [X0] : (((humble(X0) | brave(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (~humble(X0) & ~brave(X0)))) [nnf transformation 6]
44. ! [X0] : ((humble(X0) | brave(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (~humble(X0) & ~brave(X0)))) [flattening 43]
82. ~humble(X0) | ~humble(X0) [cnf transformation 44]
122. humble(alice) [cnf transformation 23]
123. ~humble(X0) [duplicate literal removal 82]
170. $false [subsumption resolution 122,123]
% SZS output end Proof for 6995225165572926024527415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not creative is brave.
If lucy is not old then someone is creative or not kind.
If someone is both not wise and rich then someone is not old and vice versa.
If alice is not quiet or not generous then someone is not kind or patient and vice versa.
Everyone who is both humble and not brave is both quiet and not patient.
Everyone who is both not patient and brave is rich and vice versa.
Everyone who is not creative or not happy is old or not brave and vice versa.
If paul is not curious or calm then fred is both tall and not calm.
Everyone who is not brave is not creative or old and vice versa.
Everyone who is both not kind and not humble is either kind or rich and vice versa.
Everyone who is either humble or old is not brave.
If someone is creative or not curious then mary is both not generous and not tall and vice versa.
If mary is not curious or tall then mary is wise or calm and vice versa.
Everyone who is old or funny is both not wise and strong and vice versa.
Everyone who is not patient or strong is either not rich or not calm.
Everyone who is humble is not creative or strong.
Someone is either brave or not quiet.
Someone is either generous or not strong.
John is both not strong and not funny.
Fred is both old and not rich.
Someone is both wise and not patient. | Lucy is not calm. | neutral | (![X]:((~funny(X)|~creative(X))=>brave(X)))&
((~old(lucy))=>(?[X]:((creative(X)|~kind(X)))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(~old(X))))&
(((~quiet(alice)|~generous(alice)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((humble(X)&~brave(X))=>(quiet(X)&~patient(X))))&
(![X]:((~patient(X)&brave(X))<=>rich(X)))&
(![X]:((~creative(X)|~happy(X))<=>(old(X)|~brave(X))))&
(((~curious(paul)|calm(paul)))=>((tall(fred)&~calm(fred))))&
(![X]:(~brave(X)<=>(~creative(X)|old(X))))&
(![X]:((~kind(X)&~humble(X))<=>(kind(X)<~>rich(X))))&
(![X]:((humble(X)<~>old(X))=>~brave(X)))&
((?[X]:((creative(X)|~curious(X))))<=>((~generous(mary)&~tall(mary))))&
(((~curious(mary)|tall(mary)))<=>((wise(mary)|calm(mary))))&
(![X]:((old(X)|funny(X))<=>(~wise(X)&strong(X))))&
(![X]:((~patient(X)|strong(X))=>(~rich(X)<~>~calm(X))))&
(![X]:(humble(X)=>(~creative(X)|strong(X))))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
((~strong(john)&~funny(john)))&
((old(fred)&~rich(fred)))&
(?[X]:((wise(X)&~patient(X)))) | ~calm(lucy) | [] | null | 0 |
If someone is humble then alice is not curious or humble and vice versa.
If someone is either not tall or calm then paul is both funny and rich and vice versa.
If alice is kind then lucy is happy and vice versa.
If paul is not creative then fred is either quiet or not happy and vice versa.
Everyone who is both happy and funny is both happy and strong and vice versa.
If mary is old then someone is curious or patient.
Everyone who is strong is both tall and humble and vice versa.
If john is creative then susan is not creative.
Everyone who is both wise and happy is not old.
Everyone who is either happy or quiet is not brave.
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
John is both tall and not strong.
Someone is either not patient or not happy.
Fred is both not wise and strong.
Fred is humble.
Mary is both not patient and not kind.
Someone is either creative or old.
Susan is curious.
Someone is either calm or tall. | Alice is not strong. | neutral | ((?[X]:(humble(X)))<=>((~curious(alice)|humble(alice))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((funny(paul)&rich(paul))))&
((kind(alice))<=>(happy(lucy)))&
((~creative(paul))<=>((quiet(fred)<~>~happy(fred))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
((old(mary))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(strong(X)<=>(tall(X)&humble(X))))&
((creative(john))=>(~creative(susan)))&
(![X]:((wise(X)&happy(X))=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))=>~brave(X)))&
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((~wise(fred)&strong(fred)))&
(humble(fred))&
((~patient(mary)&~kind(mary)))&
(?[X]:((creative(X)<~>old(X))))&
(curious(susan))&
(?[X]:((calm(X)<~>tall(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is either not curious or wise is both funny and not humble and vice versa. Everyone who is tall or brave is not kind. If someone is either generous or kind then alice is either strong or not strong. Everyone who is calm is funny. Everyone who is funny or not wise is either wise or quiet. Everyone who is either brave or old is humble or not tall and vice versa. Everyone who is either tall or not funny is either brave or not generous. If someone is calm or not quiet then fred is calm. Everyone who is either not wise or not rich is funny. Everyone who is both strong and not generous is not tall. Everyone who is funny or not humble is not calm or generous and vice versa. If someone is generous then john is tall and vice versa. If alice is both not humble and not tall then fred is not rich or not humble. Everyone who is brave or not brave is not funny or not wise. Everyone who is wise is not humble. Everyone who is both strong and not generous is not humble or wise and vice versa. Someone is not brave or patient. Susan is not generous. Fred is both not rich and not generous. Someone is both not wise and kind. John is both not old and tall. Someone is not tall or creative. Susan is not brave. Fred is both funny and not creative. | Alice is tall. | neutral | (![X]:((~curious(X)<~>wise(X))<=>(funny(X)&~humble(X))))&
(![X]:((tall(X)|brave(X))=>~kind(X)))&
((?[X]:((generous(X)<~>kind(X))))=>((strong(alice)<~>~strong(alice))))&
(![X]:(calm(X)=>funny(X)))&
(![X]:((funny(X)|~wise(X))=>(wise(X)<~>quiet(X))))&
(![X]:((brave(X)<~>old(X))<=>(humble(X)|~tall(X))))&
(![X]:((tall(X)<~>~funny(X))=>(brave(X)<~>~generous(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(calm(fred)))&
(![X]:((~wise(X)<~>~rich(X))=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|~wise(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((strong(X)&~generous(X))<=>(~humble(X)|wise(X))))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:((~wise(X)&kind(X))))&
((~old(john)&tall(john)))&
(?[X]:((~tall(X)|creative(X))))&
(~brave(susan))&
((funny(fred)&~creative(fred))) | tall(alice) | [] | null | 0 |
If someone is calm or curious then someone is either not creative or quiet and vice versa.
Everyone who is not curious is wise.
If paul is both kind and generous then someone is both wise and rich and vice versa.
Everyone who is both curious and strong is not strong or quiet and vice versa.
Everyone who is either not happy or creative is old or generous.
Everyone who is quiet or rich is either patient or not kind.
Everyone who is either generous or not rich is not calm or not brave.
If someone is either creative or calm then someone is either wise or calm and vice versa.
Everyone who is both tall and funny is either not happy or not humble and vice versa.
Everyone who is either happy or humble is either quiet or not curious and vice versa.
Everyone who is not rich or not calm is old or not old.
If someone is either generous or rich then paul is both generous and not curious.
Everyone who is not quiet is either not curious or not creative.
Everyone who is both curious and not humble is not brave or old and vice versa.
Everyone who is kind is both not patient and not creative.
Everyone who is calm is both not humble and not rich.
Paul is either not patient or not generous.
Someone is strong.
Someone is calm or not brave.
Someone is either not patient or not quiet.
Someone is either not curious or funny. | Paul is generous. | neutral | ((?[X]:((calm(X)|curious(X))))<=>(?[X]:((~creative(X)<~>quiet(X)))))&
(![X]:(~curious(X)=>wise(X)))&
(((kind(paul)&generous(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((curious(X)&strong(X))<=>(~strong(X)|quiet(X))))&
(![X]:((~happy(X)<~>creative(X))=>(old(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(patient(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~rich(X))=>(~calm(X)|~brave(X))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((tall(X)&funny(X))<=>(~happy(X)<~>~humble(X))))&
(![X]:((happy(X)<~>humble(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((~rich(X)|~calm(X))=>(old(X)|~old(X))))&
((?[X]:((generous(X)<~>rich(X))))=>((generous(paul)&~curious(paul))))&
(![X]:(~quiet(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((curious(X)&~humble(X))<=>(~brave(X)|old(X))))&
(![X]:(kind(X)=>(~patient(X)&~creative(X))))&
(![X]:(calm(X)=>(~humble(X)&~rich(X))))&
((~patient(paul)<~>~generous(paul)))&
(?[X]:(strong(X)))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((~curious(X)<~>funny(X)))) | generous(paul) | [] | null | 0 |
If fred is patient then fred is either not brave or quiet and vice versa.
If susan is not generous then someone is rich and vice versa.
Everyone who is either not tall or rich is both happy and tall.
Everyone who is either wise or tall is not brave.
If susan is either kind or not humble then someone is happy or patient and vice versa.
Everyone who is not creative or rich is either quiet or not curious and vice versa.
Everyone who is both brave and old is tall and vice versa.
Everyone who is either not humble or tall is not wise and vice versa.
Everyone who is generous or brave is either not happy or kind.
Everyone who is either old or patient is either not happy or wise.
If susan is not old then someone is patient.
Everyone who is both not rich and patient is not strong.
Everyone who is not curious or not calm is not quiet.
Everyone who is not wise is strong or not old and vice versa.
If someone is both not old and generous then someone is both happy and funny and vice versa.
Everyone who is either not rich or not wise is either not creative or curious.
Someone is not funny.
Mary is happy or strong.
Lucy is both not creative and not wise.
Someone is calm or not humble.
Mary is funny or not brave.
Someone is both not happy and tall.
John is either strong or generous. | Lucy is quiet. | contradiction | ((patient(fred))<=>((~brave(fred)<~>quiet(fred))))&
((~generous(susan))<=>(?[X]:(rich(X))))&
(![X]:((~tall(X)<~>rich(X))=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>tall(X))=>~brave(X)))&
(((kind(susan)<~>~humble(susan)))<=>(?[X]:((happy(X)|patient(X)))))&
(![X]:((~creative(X)|rich(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((brave(X)&old(X))<=>tall(X)))&
(![X]:((~humble(X)<~>tall(X))<=>~wise(X)))&
(![X]:((generous(X)|brave(X))=>(~happy(X)<~>kind(X))))&
(![X]:((old(X)<~>patient(X))=>(~happy(X)<~>wise(X))))&
((~old(susan))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&patient(X))=>~strong(X)))&
(![X]:((~curious(X)|~calm(X))=>~quiet(X)))&
(![X]:(~wise(X)<=>(strong(X)|~old(X))))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~rich(X)<~>~wise(X))=>(~creative(X)<~>curious(X))))&
(?[X]:(~funny(X)))&
((happy(mary)|strong(mary)))&
((~creative(lucy)&~wise(lucy)))&
(?[X]:((calm(X)|~humble(X))))&
((funny(mary)|~brave(mary)))&
(?[X]:((~happy(X)&tall(X))))&
((strong(john)<~>generous(john))) | quiet(lucy) | [
"p2",
"p3",
"p6",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 21291046424918351159137
% SZS output start Proof for 21291046424918351159137
3. ! [X0] : ((~tall(X0) <~> rich(X0)) => (tall(X0) & happy(X0))) [input p2]
4. ! [X0] : ((wise(X0) <~> tall(X0)) => ~brave(X0)) [input p3]
7. ! [X0] : ((old(X0) & brave(X0)) <=> tall(X0)) [input p6]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) => ~quiet(X0)) [input p12]
16. ! [X0] : ((~rich(X0) <~> ~wise(X0)) => (~creative(X0) <~> curious(X0))) [input p15]
19. ~wise(lucy) & ~creative(lucy) [input p18]
24. quiet(lucy) [input hypothesis]
26. ! [X0] : (~curious(X0) => ~quiet(X0)) [pure predicate removal 13]
28. ! [X0] : ((tall(X0) & happy(X0)) | (~tall(X0) <=> rich(X0))) [ennf transformation 3]
29. ! [X0] : (~brave(X0) | (wise(X0) <=> tall(X0))) [ennf transformation 4]
35. ! [X0] : (~quiet(X0) | curious(X0)) [ennf transformation 26]
36. ! [X0] : ((~creative(X0) <~> curious(X0)) | (~rich(X0) <=> ~wise(X0))) [ennf transformation 16]
42. ! [X0] : ((tall(X0) & happy(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) [nnf transformation 28]
43. ! [X0] : (~brave(X0) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) [nnf transformation 29]
50. ! [X0] : (((old(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | (~old(X0) | ~brave(X0)))) [nnf transformation 7]
51. ! [X0] : (((old(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | ~old(X0) | ~brave(X0))) [flattening 50]
64. ! [X0] : (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) [nnf transformation 36]
78. tall(X0) | rich(X0) | tall(X0) [cnf transformation 42]
81. ~tall(X0) | wise(X0) | ~brave(X0) [cnf transformation 43]
95. ~tall(X0) | brave(X0) [cnf transformation 51]
111. ~quiet(X0) | curious(X0) [cnf transformation 35]
122. ~curious(X0) | creative(X0) | ~rich(X0) | wise(X0) [cnf transformation 64]
125. ~creative(lucy) [cnf transformation 19]
126. ~wise(lucy) [cnf transformation 19]
132. quiet(lucy) [cnf transformation 24]
133. tall(X0) | rich(X0) [duplicate literal removal 78]
260. curious(lucy) [resolution 111,132]
265. rich(X1) | brave(X1) [resolution 133,95]
277. wise(X0) | ~brave(X0) | rich(X0) [resolution 81,133]
279. wise(X0) | rich(X0) [subsumption resolution 277,265]
292. rich(lucy) [resolution 279,126]
372. creative(lucy) | ~rich(lucy) | wise(lucy) [resolution 122,260]
373. ~rich(lucy) | wise(lucy) [subsumption resolution 372,125]
374. wise(lucy) [subsumption resolution 373,292]
375. $false [subsumption resolution 374,126]
% SZS output end Proof for 21291046424918351159137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is happy or brave and vice versa.
If susan is either creative or tall then fred is not strong.
If fred is quiet or not rich then susan is not happy or not old.
Everyone who is rich or not wise is not brave.
Everyone who is not strong or not generous is strong.
If fred is either not old or kind then someone is strong and vice versa.
Everyone who is not brave is both happy and not wise and vice versa.
Everyone who is both not wise and rich is either generous or brave and vice versa.
If susan is either strong or happy then paul is either patient or not tall and vice versa.
Everyone who is brave is either tall or not brave and vice versa.
Everyone who is either not humble or not old is both tall and old and vice versa.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
If alice is not tall or not wise then someone is both not creative and tall.
Someone is both not calm and quiet.
John is either not patient or wise.
Someone is patient.
Alice is calm or not creative.
Someone is not kind. | Susan is brave. | neutral | (![X]:(funny(X)<=>(happy(X)|brave(X))))&
(((creative(susan)<~>tall(susan)))=>(~strong(fred)))&
(((quiet(fred)|~rich(fred)))=>((~happy(susan)|~old(susan))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(![X]:((~strong(X)|~generous(X))=>strong(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(strong(X))))&
(![X]:(~brave(X)<=>(happy(X)&~wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(((~tall(alice)|~wise(alice)))=>(?[X]:((~creative(X)&tall(X)))))&
(?[X]:((~calm(X)&quiet(X))))&
((~patient(john)<~>wise(john)))&
(?[X]:(patient(X)))&
((calm(alice)|~creative(alice)))&
(?[X]:(~kind(X))) | brave(susan) | [] | null | 0 |
Everyone who is not strong or creative is humble or happy and vice versa.
If someone is both not wise and curious then susan is both kind and not strong and vice versa.
If someone is not quiet or brave then alice is either brave or quiet and vice versa.
Everyone who is generous or brave is kind and vice versa.
If someone is both not kind and calm then mary is both not calm and not happy and vice versa.
If alice is calm or quiet then someone is both not curious and not kind.
If mary is both generous and rich then someone is both not strong and patient and vice versa.
Everyone who is both not brave and happy is wise and vice versa.
If someone is not creative or not patient then someone is quiet or patient and vice versa.
If mary is not rich then paul is generous.
Everyone who is patient is not tall.
Everyone who is not generous or humble is not calm.
Everyone who is brave is both not funny and tall and vice versa.
If fred is rich or wise then someone is generous or curious and vice versa.
Everyone who is strong is old and vice versa.
If someone is brave or not quiet then susan is either creative or funny and vice versa.
Paul is either old or not quiet.
Susan is not quiet or happy.
Someone is both strong and funny.
Lucy is kind or creative.
Susan is old or brave.
Someone is not strong.
Someone is either not old or calm.
Someone is either curious or patient. | Lucy is humble. | neutral | (![X]:((~strong(X)|creative(X))<=>(humble(X)|happy(X))))&
((?[X]:((~wise(X)&curious(X))))<=>((kind(susan)&~strong(susan))))&
((?[X]:((~quiet(X)|brave(X))))<=>((brave(alice)<~>quiet(alice))))&
(![X]:((generous(X)|brave(X))<=>kind(X)))&
((?[X]:((~kind(X)&calm(X))))<=>((~calm(mary)&~happy(mary))))&
(((calm(alice)|quiet(alice)))=>(?[X]:((~curious(X)&~kind(X)))))&
(((generous(mary)&rich(mary)))<=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~brave(X)&happy(X))<=>wise(X)))&
((?[X]:((~creative(X)|~patient(X))))<=>(?[X]:((quiet(X)|patient(X)))))&
((~rich(mary))=>(generous(paul)))&
(![X]:(patient(X)=>~tall(X)))&
(![X]:((~generous(X)|humble(X))=>~calm(X)))&
(![X]:(brave(X)<=>(~funny(X)&tall(X))))&
(((rich(fred)|wise(fred)))<=>(?[X]:((generous(X)|curious(X)))))&
(![X]:(strong(X)<=>old(X)))&
((?[X]:((brave(X)|~quiet(X))))<=>((creative(susan)<~>funny(susan))))&
((old(paul)<~>~quiet(paul)))&
((~quiet(susan)|happy(susan)))&
(?[X]:((strong(X)&funny(X))))&
((kind(lucy)|creative(lucy)))&
((old(susan)|brave(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((~old(X)<~>calm(X))))&
(?[X]:((curious(X)<~>patient(X)))) | humble(lucy) | [] | null | 0 |
If john is happy or curious then someone is either not tall or curious and vice versa.
Everyone who is both not tall and brave is either not strong or generous and vice versa.
Everyone who is both creative and funny is both not curious and generous and vice versa.
If john is either strong or not happy then susan is either calm or strong.
Everyone who is both not curious and wise is both not tall and calm.
Everyone who is wise or patient is both patient and funny.
Everyone who is rich is not happy.
Everyone who is humble is not generous and vice versa.
Everyone who is either calm or old is not creative and vice versa.
Everyone who is either not brave or not rich is either not funny or creative and vice versa.
Everyone who is both patient and old is both kind and not curious and vice versa.
Everyone who is both not old and not humble is both not brave and creative and vice versa.
Everyone who is both not creative and generous is not brave or not humble and vice versa.
Everyone who is brave is either patient or not calm and vice versa.
Everyone who is not rich is patient or curious.
If john is not patient or humble then fred is either not funny or old and vice versa.
Someone is not curious.
Susan is either not generous or not brave.
Someone is both not generous and not kind.
Someone is either strong or not tall.
Paul is both not strong and not kind.
Paul is tall.
Someone is both strong and humble.
Someone is not rich. | Fred is not brave. | contradiction | (((happy(john)|curious(john)))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~tall(X)&brave(X))<=>(~strong(X)<~>generous(X))))&
(![X]:((creative(X)&funny(X))<=>(~curious(X)&generous(X))))&
(((strong(john)<~>~happy(john)))=>((calm(susan)<~>strong(susan))))&
(![X]:((~curious(X)&wise(X))=>(~tall(X)&calm(X))))&
(![X]:((wise(X)|patient(X))=>(patient(X)&funny(X))))&
(![X]:(rich(X)=>~happy(X)))&
(![X]:(humble(X)<=>~generous(X)))&
(![X]:((calm(X)<~>old(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>~rich(X))<=>(~funny(X)<~>creative(X))))&
(![X]:((patient(X)&old(X))<=>(kind(X)&~curious(X))))&
(![X]:((~old(X)&~humble(X))<=>(~brave(X)&creative(X))))&
(![X]:((~creative(X)&generous(X))<=>(~brave(X)|~humble(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(patient(X)|curious(X))))&
(((~patient(john)|humble(john)))<=>((~funny(fred)<~>old(fred))))&
(?[X]:(~curious(X)))&
((~generous(susan)<~>~brave(susan)))&
(?[X]:((~generous(X)&~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
((~strong(paul)&~kind(paul)))&
(tall(paul))&
(?[X]:((strong(X)&humble(X))))&
(?[X]:(~rich(X))) | ~brave(fred) | [
"p1",
"p2",
"p7",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 207933508391379338183842
% SZS output start Proof for 207933508391379338183842
2. ! [X0] : ((brave(X0) & ~tall(X0)) <=> (~strong(X0) <~> generous(X0))) [input p1]
3. ! [X0] : ((funny(X0) & creative(X0)) <=> (generous(X0) & ~curious(X0))) [input p2]
8. ! [X0] : (humble(X0) <=> ~generous(X0)) [input p7]
9. ! [X0] : ((calm(X0) <~> old(X0)) <=> ~creative(X0)) [input p8]
11. ! [X0] : ((old(X0) & patient(X0)) <=> (~curious(X0) & kind(X0))) [input p10]
12. ! [X0] : ((~humble(X0) & ~old(X0)) <=> (creative(X0) & ~brave(X0))) [input p11]
13. ! [X0] : ((generous(X0) & ~creative(X0)) <=> (~humble(X0) | ~brave(X0))) [input p12]
14. ! [X0] : (brave(X0) <=> (patient(X0) <~> ~calm(X0))) [input p13]
25. ~brave(fred) [input hypothesis]
38. ! [X0] : (((brave(X0) & ~tall(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | (~brave(X0) | tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((brave(X0) & ~tall(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) & (((~generous(X0) | strong(X0)) & (generous(X0) | ~strong(X0))) | ~brave(X0) | tall(X0))) [flattening 38]
40. ! [X0] : (((funny(X0) & creative(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (~funny(X0) | ~creative(X0)))) [nnf transformation 3]
41. ! [X0] : (((funny(X0) & creative(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | ~funny(X0) | ~creative(X0))) [flattening 40]
43. ! [X0] : ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0))) [nnf transformation 8]
44. ! [X0] : ((((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | creative(X0)) & (~creative(X0) | ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))))) [nnf transformation 9]
46. ! [X0] : (((old(X0) & patient(X0)) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | (~old(X0) | ~patient(X0)))) [nnf transformation 11]
47. ! [X0] : (((old(X0) & patient(X0)) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | ~old(X0) | ~patient(X0))) [flattening 46]
48. ! [X0] : (((~humble(X0) & ~old(X0)) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | (humble(X0) | old(X0)))) [nnf transformation 12]
49. ! [X0] : (((~humble(X0) & ~old(X0)) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | humble(X0) | old(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) & ~creative(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (~generous(X0) | creative(X0)))) [nnf transformation 13]
51. ! [X0] : (((generous(X0) & ~creative(X0)) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~generous(X0) | creative(X0))) [flattening 50]
52. ! [X0] : ((brave(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) & (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | ~brave(X0))) [nnf transformation 14]
77. generous(X0) | brave(X0) | strong(X0) [cnf transformation 39]
78. ~generous(X0) | ~strong(X0) | brave(X0) [cnf transformation 39]
81. ~generous(X0) | creative(X0) | curious(X0) [cnf transformation 41]
90. ~humble(X0) | ~generous(X0) [cnf transformation 43]
95. ~old(X0) | ~calm(X0) | creative(X0) [cnf transformation 44]
105. ~old(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 47]
109. old(X0) | humble(X0) | creative(X0) [cnf transformation 49]
113. ~creative(X0) | brave(X0) [cnf transformation 51]
114. ~creative(X0) | humble(X0) [cnf transformation 51]
115. generous(X0) | brave(X0) [cnf transformation 51]
120. patient(X0) | brave(X0) | calm(X0) [cnf transformation 52]
141. ~brave(fred) [cnf transformation 25]
187. 10 <=> old(fred) [avatar definition]
188. old(fred) <- (10) [avatar component clause 187]
189. ~old(fred) <- (~10) [avatar component clause 187]
239. ~strong(X1) | brave(X1) | brave(X1) [resolution 78,115]
241. ~strong(X1) | brave(X1) [duplicate literal removal 239]
244. creative(X0) | curious(X0) | brave(X0) | strong(X0) [resolution 81,77]
247. creative(X0) | curious(X0) | brave(X0) [subsumption resolution 244,241]
248. brave(X0) | curious(X0) [subsumption resolution 247,113]
261. curious(fred) [resolution 248,141]
267. 20 <=> creative(fred) [avatar definition]
269. creative(fred) <- (20) [avatar component clause 267]
271. 21 <=> calm(fred) [avatar definition]
280. ~calm(fred) | creative(fred) <- (10) [resolution 95,188]
287. 22 <=> patient(fred) [avatar definition]
289. ~patient(fred) <- (~22) [avatar component clause 287]
296. ~curious(fred) | ~patient(fred) <- (10) [resolution 105,188]
352. brave(fred) | calm(fred) <- (~22) [resolution 120,289]
365. calm(fred) <- (~22) [subsumption resolution 352,141]
368. 20 | ~21 | ~10 [avatar split clause 280,187,271,267]
372. 32 <=> generous(fred) [avatar definition]
373. ~generous(fred) <- (~32) [avatar component clause 372]
376. 21 | 22 [avatar split clause 365,287,271]
377. ~patient(fred) <- (10) [subsumption resolution 296,261]
378. ~22 | ~10 [avatar split clause 377,187,287]
379. humble(fred) | creative(fred) <- (~10) [resolution 189,109]
382. brave(fred) <- (20) [resolution 269,113]
383. $false <- (20) [subsumption resolution 382,141]
384. ~20 [avatar contradiction clause 383]
386. humble(fred) <- (~10) [subsumption resolution 379,114]
441. ~generous(fred) <- (~10) [resolution 386,90]
442. ~32 | 10 [avatar split clause 441,187,372]
444. brave(fred) <- (~32) [resolution 373,115]
446. $false <- (~32) [subsumption resolution 444,141]
447. 32 [avatar contradiction clause 446]
448. $false [avatar sat refutation 368,376,378,384,442,447]
% SZS output end Proof for 207933508391379338183842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble and rich is either old or humble.
Everyone who is both not strong and not curious is either not funny or old and vice versa.
Everyone who is either funny or creative is tall.
If john is both not happy and brave then john is not rich or not patient and vice versa.
Everyone who is both not generous and not strong is curious.
If mary is not wise then someone is either not happy or happy and vice versa.
If lucy is not curious then someone is both not calm and not generous and vice versa.
If lucy is either generous or calm then someone is both wise and strong.
Everyone who is kind or wise is not creative.
If lucy is either humble or quiet then someone is not funny or not kind and vice versa.
Everyone who is both funny and happy is either tall or patient and vice versa.
Everyone who is not funny is either not curious or humble.
If someone is not creative then someone is wise or not happy and vice versa.
If susan is both quiet and not funny then someone is either not tall or not calm and vice versa.
Everyone who is happy or funny is not funny.
Everyone who is both not curious and patient is either not generous or not tall and vice versa.
Someone is rich.
Paul is patient.
Someone is generous or not wise.
Someone is patient or generous.
Someone is both not happy and not kind.
Someone is not kind or not curious.
Alice is not rich. | Paul is not old. | contradiction | (![X]:((~humble(X)&rich(X))=>(old(X)<~>humble(X))))&
(![X]:((~strong(X)&~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((funny(X)<~>creative(X))=>tall(X)))&
(((~happy(john)&brave(john)))<=>((~rich(john)|~patient(john))))&
(![X]:((~generous(X)&~strong(X))=>curious(X)))&
((~wise(mary))<=>(?[X]:((~happy(X)<~>happy(X)))))&
((~curious(lucy))<=>(?[X]:((~calm(X)&~generous(X)))))&
(((generous(lucy)<~>calm(lucy)))=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((kind(X)|wise(X))=>~creative(X)))&
(((humble(lucy)<~>quiet(lucy)))<=>(?[X]:((~funny(X)|~kind(X)))))&
(![X]:((funny(X)&happy(X))<=>(tall(X)<~>patient(X))))&
(![X]:(~funny(X)=>(~curious(X)<~>humble(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((wise(X)|~happy(X)))))&
(((quiet(susan)&~funny(susan)))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((happy(X)|funny(X))=>~funny(X)))&
(![X]:((~curious(X)&patient(X))<=>(~generous(X)<~>~tall(X))))&
(?[X]:(rich(X)))&
(patient(paul))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((patient(X)|generous(X))))&
(?[X]:((~happy(X)&~kind(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(~rich(alice)) | ~old(paul) | [
"p1",
"p4",
"p10",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 475431434732849772764369
% SZS output start Proof for 475431434732849772764369
2. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> (~funny(X0) <~> old(X0))) [input p1]
5. ! [X0] : ((~strong(X0) & ~generous(X0)) => curious(X0)) [input p4]
11. ! [X0] : ((happy(X0) & funny(X0)) <=> (tall(X0) <~> patient(X0))) [input p10]
15. ! [X0] : ((funny(X0) | happy(X0)) => ~funny(X0)) [input p14]
16. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (~generous(X0) <~> ~tall(X0))) [input p15]
18. patient(paul) [input p17]
24. ~old(paul) [input hypothesis]
29. ! [X0] : (curious(X0) | (strong(X0) | generous(X0))) [ennf transformation 5]
30. ! [X0] : (curious(X0) | strong(X0) | generous(X0)) [flattening 29]
34. ! [X0] : (~funny(X0) | (~funny(X0) & ~happy(X0))) [ennf transformation 15]
36. ! [X0] : (((~curious(X0) & ~strong(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (curious(X0) | strong(X0)))) [nnf transformation 2]
37. ! [X0] : (((~curious(X0) & ~strong(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | curious(X0) | strong(X0))) [flattening 36]
56. ! [X0] : (((happy(X0) & funny(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~happy(X0) | ~funny(X0)))) [nnf transformation 11]
57. ! [X0] : (((happy(X0) & funny(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~happy(X0) | ~funny(X0))) [flattening 56]
69. ! [X0] : (((patient(X0) & ~curious(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (~patient(X0) | curious(X0)))) [nnf transformation 16]
70. ! [X0] : (((patient(X0) & ~curious(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0)))) & (((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | ~patient(X0) | curious(X0))) [flattening 69]
85. ~strong(X0) | old(X0) | funny(X0) [cnf transformation 37]
87. ~curious(X0) | old(X0) | funny(X0) [cnf transformation 37]
96. generous(X0) | strong(X0) | curious(X0) [cnf transformation 30]
119. ~patient(X0) | tall(X0) | funny(X0) [cnf transformation 57]
134. ~funny(X0) | ~funny(X0) [cnf transformation 34]
135. ~generous(X0) | ~tall(X0) | ~patient(X0) | curious(X0) [cnf transformation 70]
142. patient(paul) [cnf transformation 18]
149. ~old(paul) [cnf transformation 24]
150. ~funny(X0) [duplicate literal removal 134]
357. tall(paul) | funny(paul) [resolution 119,142]
360. tall(paul) [subsumption resolution 357,150]
384. 43 <=> curious(paul) [avatar definition]
385. curious(paul) <- (43) [avatar component clause 384]
386. ~curious(paul) <- (~43) [avatar component clause 384]
445. ~tall(X1) | ~patient(X1) | curious(X1) | strong(X1) | curious(X1) [resolution 135,96]
448. ~patient(X1) | ~tall(X1) | curious(X1) | strong(X1) [duplicate literal removal 445]
577. ~tall(paul) | curious(paul) | strong(paul) [resolution 448,142]
582. curious(paul) | strong(paul) [subsumption resolution 577,360]
583. strong(paul) <- (~43) [subsumption resolution 582,386]
587. old(paul) | funny(paul) <- (~43) [resolution 583,85]
588. funny(paul) <- (~43) [subsumption resolution 587,149]
589. $false <- (~43) [subsumption resolution 588,150]
590. 43 [avatar contradiction clause 589]
600. old(paul) | funny(paul) <- (43) [resolution 385,87]
602. funny(paul) <- (43) [subsumption resolution 600,149]
603. $false <- (43) [subsumption resolution 602,150]
604. ~43 [avatar contradiction clause 603]
605. $false [avatar sat refutation 590,604]
% SZS output end Proof for 475431434732849772764369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits