premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is strong is humble or not strong and vice versa. If someone is either happy or not rich then paul is not tall or not curious and vice versa. Everyone who is not humble or not brave is either not rich or not strong. Everyone who is not tall is either creative or wise. Everyone who is either generous or wise is both not old and wise and vice versa. Everyone who is not wise is brave or not patient and vice versa. If mary is both funny and not creative then someone is not quiet. If someone is either not curious or brave then alice is both not patient and generous and vice versa. If someone is happy then lucy is not rich. Everyone who is both not strong and curious is both old and curious. If someone is either wise or creative then alice is funny or not wise and vice versa. If someone is both funny and not wise then paul is not funny or calm. If someone is humble then someone is not calm and vice versa. Everyone who is both creative and not strong is both not strong and old. Everyone who is either not curious or brave is quiet and vice versa. If lucy is not happy or wise then someone is old. Someone is either happy or funny. Someone is quiet or not rich. Alice is not generous. John is not rich or not tall. Susan is strong. Someone is happy. Someone is either curious or not funny. Someone is calm. | Paul is strong. | entailment | (![X]:(strong(X)<=>(humble(X)|~strong(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>((~tall(paul)|~curious(paul))))&
(![X]:((~humble(X)|~brave(X))=>(~rich(X)<~>~strong(X))))&
(![X]:(~tall(X)=>(creative(X)<~>wise(X))))&
(![X]:((generous(X)<~>wise(X))<=>(~old(X)&wise(X))))&
(![X]:(~wise(X)<=>(brave(X)|~patient(X))))&
(((funny(mary)&~creative(mary)))=>(?[X]:(~quiet(X))))&
((?[X]:((~curious(X)<~>brave(X))))<=>((~patient(alice)&generous(alice))))&
((?[X]:(happy(X)))=>(~rich(lucy)))&
(![X]:((~strong(X)&curious(X))=>(old(X)&curious(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>((funny(alice)|~wise(alice))))&
((?[X]:((funny(X)&~wise(X))))=>((~funny(paul)|calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&~strong(X))=>(~strong(X)&old(X))))&
(![X]:((~curious(X)<~>brave(X))<=>quiet(X)))&
(((~happy(lucy)|wise(lucy)))=>(?[X]:(old(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((quiet(X)|~rich(X))))&
(~generous(alice))&
((~rich(john)|~tall(john)))&
(strong(susan))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:(calm(X))) | strong(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8653583134230246399687011
% SZS output start Proof for 8653583134230246399687011
1. ! [X0] : (strong(X0) <=> (~strong(X0) | humble(X0))) [input p0]
25. ~strong(paul) [input hypothesis]
39. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | ~strong(X0))) [nnf transformation 1]
40. ! [X0] : ((strong(X0) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | ~strong(X0))) [flattening 39]
86. strong(X0) | strong(X0) [cnf transformation 40]
145. ~strong(paul) [cnf transformation 25]
149. strong(X0) [duplicate literal removal 86]
323. $false [subsumption resolution 145,149]
% SZS output end Proof for 8653583134230246399687011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or brave then someone is not strong or not funny.
If mary is both brave and patient then alice is both not generous and not quiet.
Everyone who is either generous or not curious is both not humble and creative and vice versa.
If susan is both not humble and calm then susan is funny or calm and vice versa.
Everyone who is not patient is not happy and vice versa.
If fred is not quiet then someone is both not humble and not happy and vice versa.
If someone is not patient or not quiet then mary is both not rich and curious and vice versa.
If someone is either not calm or brave then alice is not wise or not kind.
If someone is either not patient or not quiet then someone is both strong and old.
Everyone who is either not wise or rich is both happy and funny and vice versa.
Everyone who is kind is calm and vice versa.
If someone is either kind or generous then fred is not patient or creative and vice versa.
If alice is kind or not quiet then mary is either not creative or not quiet and vice versa.
Everyone who is either calm or funny is both strong and tall.
If susan is both not tall and generous then someone is either rich or not tall.
Everyone who is old is not rich.
Someone is either not wise or tall.
Fred is both rich and patient.
Fred is not calm.
Lucy is old.
Someone is not humble or happy.
Someone is both humble and not quiet.
Someone is funny.
Someone is both funny and strong. | Fred is kind. | contradiction | ((?[X]:((kind(X)|brave(X))))=>(?[X]:((~strong(X)|~funny(X)))))&
(((brave(mary)&patient(mary)))=>((~generous(alice)&~quiet(alice))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)&creative(X))))&
(((~humble(susan)&calm(susan)))<=>((funny(susan)|calm(susan))))&
(![X]:(~patient(X)<=>~happy(X)))&
((~quiet(fred))<=>(?[X]:((~humble(X)&~happy(X)))))&
((?[X]:((~patient(X)|~quiet(X))))<=>((~rich(mary)&curious(mary))))&
((?[X]:((~calm(X)<~>brave(X))))=>((~wise(alice)|~kind(alice))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:((strong(X)&old(X)))))&
(![X]:((~wise(X)<~>rich(X))<=>(happy(X)&funny(X))))&
(![X]:(kind(X)<=>calm(X)))&
((?[X]:((kind(X)<~>generous(X))))<=>((~patient(fred)|creative(fred))))&
(((kind(alice)|~quiet(alice)))<=>((~creative(mary)<~>~quiet(mary))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&tall(X))))&
(((~tall(susan)&generous(susan)))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(old(X)=>~rich(X)))&
(?[X]:((~wise(X)<~>tall(X))))&
((rich(fred)&patient(fred)))&
(~calm(fred))&
(old(lucy))&
(?[X]:((~humble(X)|happy(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)&strong(X)))) | kind(fred) | [
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6825195349233613254404525
% SZS output start Proof for 6825195349233613254404525
11. ! [X0] : (kind(X0) <=> calm(X0)) [input p10]
19. ~calm(fred) [input p18]
25. kind(fred) [input hypothesis]
62. ! [X0] : ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))) [nnf transformation 11]
122. ~kind(X0) | calm(X0) [cnf transformation 62]
147. ~calm(fred) [cnf transformation 19]
155. kind(fred) [cnf transformation 25]
365. calm(fred) [resolution 122,155]
367. $false [subsumption resolution 365,147]
% SZS output end Proof for 6825195349233613254404525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then alice is not tall or not generous and vice versa.
Everyone who is tall or not old is not creative and vice versa.
If fred is both not quiet and tall then john is wise or not old and vice versa.
Everyone who is both tall and not funny is not old or happy.
Everyone who is either not kind or kind is both strong and kind.
If someone is both creative and not wise then someone is humble.
Everyone who is either not quiet or not humble is not generous.
If someone is not strong or generous then someone is either brave or not wise and vice versa.
If john is either not patient or brave then someone is both not wise and creative.
If john is kind or not wise then someone is not old or funny.
If someone is both happy and not patient then someone is both not quiet and not creative.
If someone is funny then someone is curious or happy.
Everyone who is not funny is both creative and not funny.
Everyone who is not funny or not quiet is either curious or humble.
Everyone who is either tall or not strong is both curious and not quiet.
Everyone who is quiet is quiet or not quiet.
Susan is kind or not humble.
Alice is either not quiet or funny.
Someone is not brave.
Mary is tall or humble.
Someone is old or humble.
Someone is old. | John is patient. | neutral | ((old(alice))<=>((~tall(alice)|~generous(alice))))&
(![X]:((tall(X)|~old(X))<=>~creative(X)))&
(((~quiet(fred)&tall(fred)))<=>((wise(john)|~old(john))))&
(![X]:((tall(X)&~funny(X))=>(~old(X)|happy(X))))&
(![X]:((~kind(X)<~>kind(X))=>(strong(X)&kind(X))))&
((?[X]:((creative(X)&~wise(X))))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>~generous(X)))&
((?[X]:((~strong(X)|generous(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((~patient(john)<~>brave(john)))=>(?[X]:((~wise(X)&creative(X)))))&
(((kind(john)|~wise(john)))=>(?[X]:((~old(X)|funny(X)))))&
((?[X]:((happy(X)&~patient(X))))=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:(funny(X)))=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~funny(X)=>(creative(X)&~funny(X))))&
(![X]:((~funny(X)|~quiet(X))=>(curious(X)<~>humble(X))))&
(![X]:((tall(X)<~>~strong(X))=>(curious(X)&~quiet(X))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((kind(susan)|~humble(susan)))&
((~quiet(alice)<~>funny(alice)))&
(?[X]:(~brave(X)))&
((tall(mary)|humble(mary)))&
(?[X]:((old(X)|humble(X))))&
(?[X]:(old(X))) | patient(john) | [] | null | 0 |
Everyone who is rich or brave is creative. Everyone who is not calm or not creative is either strong or not tall. If someone is either kind or humble then paul is funny or not curious. Everyone who is humble is not old or strong and vice versa. Everyone who is both not calm and not creative is not quiet and vice versa. Everyone who is both creative and not generous is either not kind or not wise and vice versa. If someone is either rich or not quiet then alice is either tall or not quiet and vice versa. Everyone who is either not rich or calm is not creative or not generous. If john is either happy or not calm then someone is not curious or not wise. Everyone who is strong is both funny and creative and vice versa. Everyone who is both happy and quiet is funny or not humble and vice versa. If someone is both old and not tall then someone is generous and vice versa. If paul is both patient and not humble then alice is both strong and not tall. If someone is not strong or brave then lucy is not generous and vice versa. If lucy is either generous or not humble then someone is kind or creative and vice versa. Everyone who is both kind and not generous is either generous or not generous and vice versa. Someone is rich or not calm. Alice is not creative or not wise. Someone is not patient or creative. Someone is either not calm or not kind. Someone is humble or not quiet. Mary is not funny or curious. | Mary is not creative. | neutral | (![X]:((rich(X)|brave(X))=>creative(X)))&
(![X]:((~calm(X)|~creative(X))=>(strong(X)<~>~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))=>((funny(paul)|~curious(paul))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
(![X]:((~calm(X)&~creative(X))<=>~quiet(X)))&
(![X]:((creative(X)&~generous(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>((tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)<~>calm(X))=>(~creative(X)|~generous(X))))&
(((happy(john)<~>~calm(john)))=>(?[X]:((~curious(X)|~wise(X)))))&
(![X]:(strong(X)<=>(funny(X)&creative(X))))&
(![X]:((happy(X)&quiet(X))<=>(funny(X)|~humble(X))))&
((?[X]:((old(X)&~tall(X))))<=>(?[X]:(generous(X))))&
(((patient(paul)&~humble(paul)))=>((strong(alice)&~tall(alice))))&
((?[X]:((~strong(X)|brave(X))))<=>(~generous(lucy)))&
(((generous(lucy)<~>~humble(lucy)))<=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(?[X]:((rich(X)|~calm(X))))&
((~creative(alice)|~wise(alice)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|curious(mary))) | ~creative(mary) | [] | null | 0 |
If lucy is not old or not brave then mary is either wise or kind and vice versa. If someone is both creative and not rich then alice is either not rich or not old. Everyone who is either not quiet or rich is not curious and vice versa. Everyone who is not old is quiet. If someone is both not wise and calm then someone is either curious or humble and vice versa. If someone is not old then someone is strong or not calm. If someone is tall or not curious then someone is tall or not kind. If paul is not rich then someone is not patient or rich and vice versa. Everyone who is rich is brave. If someone is either tall or not generous then susan is both not rich and not funny and vice versa. Everyone who is tall or kind is both rich and not calm and vice versa. Everyone who is humble or patient is funny and vice versa. Everyone who is not generous or not happy is not rich or not funny. If alice is quiet or tall then mary is either not generous or calm. If someone is either not old or happy then someone is either not kind or not brave and vice versa. If someone is either creative or rich then susan is either kind or tall and vice versa. Susan is both generous and brave. Someone is either not wise or kind. Someone is old or not generous. Someone is not curious. Someone is both not calm and generous. Susan is patient. Alice is not generous. Lucy is tall. | Alice is patient. | contradiction | (((~old(lucy)|~brave(lucy)))<=>((wise(mary)<~>kind(mary))))&
((?[X]:((creative(X)&~rich(X))))=>((~rich(alice)<~>~old(alice))))&
(![X]:((~quiet(X)<~>rich(X))<=>~curious(X)))&
(![X]:(~old(X)=>quiet(X)))&
((?[X]:((~wise(X)&calm(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
((?[X]:(~old(X)))=>(?[X]:((strong(X)|~calm(X)))))&
((?[X]:((tall(X)|~curious(X))))=>(?[X]:((tall(X)|~kind(X)))))&
((~rich(paul))<=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:(rich(X)=>brave(X)))&
((?[X]:((tall(X)<~>~generous(X))))<=>((~rich(susan)&~funny(susan))))&
(![X]:((tall(X)|kind(X))<=>(rich(X)&~calm(X))))&
(![X]:((humble(X)|patient(X))<=>funny(X)))&
(![X]:((~generous(X)|~happy(X))=>(~rich(X)|~funny(X))))&
(((quiet(alice)|tall(alice)))=>((~generous(mary)<~>calm(mary))))&
((?[X]:((~old(X)<~>happy(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
((?[X]:((creative(X)<~>rich(X))))<=>((kind(susan)<~>tall(susan))))&
((generous(susan)&brave(susan)))&
(?[X]:((~wise(X)<~>kind(X))))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~calm(X)&generous(X))))&
(patient(susan))&
(~generous(alice))&
(tall(lucy)) | patient(alice) | [
"p9",
"p10",
"p11",
"p12",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8803205845117321782400028
% SZS output start Proof for 8803205845117321782400028
10. ? [X0] : (tall(X0) <~> ~generous(X0)) <=> (~funny(susan) & ~rich(susan)) [input p9]
11. ! [X0] : ((kind(X0) | tall(X0)) <=> (~calm(X0) & rich(X0))) [input p10]
12. ! [X0] : ((patient(X0) | humble(X0)) <=> funny(X0)) [input p11]
13. ! [X0] : ((~happy(X0) | ~generous(X0)) => (~funny(X0) | ~rich(X0))) [input p12]
22. patient(susan) [input p21]
23. ~generous(alice) [input p22]
25. patient(alice) [input hypothesis]
35. ! [X0] : ((~funny(X0) | ~rich(X0)) | (happy(X0) & generous(X0))) [ennf transformation 13]
36. ! [X0] : (~funny(X0) | ~rich(X0) | (happy(X0) & generous(X0))) [flattening 35]
54. (? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (funny(susan) | rich(susan))) & ((~funny(susan) & ~rich(susan)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [nnf transformation 10]
55. (? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | funny(susan) | rich(susan)) & ((~funny(susan) & ~rich(susan)) | ! [X0] : ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) [flattening 54]
56. (? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | funny(susan) | rich(susan)) & ((~funny(susan) & ~rich(susan)) | ! [X1] : ((tall(X1) | generous(X1)) & (~generous(X1) | ~tall(X1)))) [rectify 55]
57. ? [X0] : ((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) => ((generous(sK4) | ~tall(sK4)) & (~generous(sK4) | tall(sK4))) [choice axiom]
58. (((generous(sK4) | ~tall(sK4)) & (~generous(sK4) | tall(sK4))) | funny(susan) | rich(susan)) & ((~funny(susan) & ~rich(susan)) | ! [X1] : ((tall(X1) | generous(X1)) & (~generous(X1) | ~tall(X1)))) [skolemisation 56,57]
59. ! [X0] : (((kind(X0) | tall(X0)) | (calm(X0) | ~rich(X0))) & ((~calm(X0) & rich(X0)) | (~kind(X0) & ~tall(X0)))) [nnf transformation 11]
60. ! [X0] : ((kind(X0) | tall(X0) | calm(X0) | ~rich(X0)) & ((~calm(X0) & rich(X0)) | (~kind(X0) & ~tall(X0)))) [flattening 59]
61. ! [X0] : (((patient(X0) | humble(X0)) | ~funny(X0)) & (funny(X0) | (~patient(X0) & ~humble(X0)))) [nnf transformation 12]
62. ! [X0] : ((patient(X0) | humble(X0) | ~funny(X0)) & (funny(X0) | (~patient(X0) & ~humble(X0)))) [flattening 61]
110. ~funny(susan) | tall(X1) | generous(X1) [cnf transformation 58]
113. ~tall(X0) | rich(X0) [cnf transformation 60]
119. ~patient(X0) | funny(X0) [cnf transformation 62]
121. ~funny(X0) | ~rich(X0) | generous(X0) [cnf transformation 36]
151. patient(susan) [cnf transformation 22]
152. ~generous(alice) [cnf transformation 23]
154. patient(alice) [cnf transformation 25]
181. 6 <=> rich(alice) [avatar definition]
183. rich(alice) <- (6) [avatar component clause 181]
263. 25 <=> funny(susan) [avatar definition]
277. 28 <=> ! [X1] : (tall(X1) | generous(X1)) [avatar definition]
278. generous(X1) | tall(X1) <- (28) [avatar component clause 277]
279. 28 | ~25 [avatar split clause 110,263,277]
287. 30 <=> tall(alice) [avatar definition]
288. tall(alice) <- (30) [avatar component clause 287]
405. funny(susan) [resolution 119,151]
406. funny(alice) [resolution 119,154]
409. 25 [avatar split clause 405,263]
410. tall(alice) <- (28) [resolution 278,152]
417. 30 | ~28 [avatar split clause 410,277,287]
419. rich(alice) <- (30) [resolution 288,113]
422. 6 | ~30 [avatar split clause 419,287,181]
472. ~rich(alice) | generous(alice) [resolution 121,406]
473. generous(alice) <- (6) [subsumption resolution 472,183]
474. $false <- (6) [subsumption resolution 473,152]
475. ~6 [avatar contradiction clause 474]
476. $false [avatar sat refutation 279,409,417,422,475]
% SZS output end Proof for 8803205845117321782400028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not strong or funny then paul is humble.
If john is not patient or not humble then susan is not tall or not generous and vice versa.
Everyone who is not quiet or generous is both curious and not humble.
If someone is happy or not strong then john is not rich or rich.
If someone is quiet or not brave then someone is rich or not calm.
If alice is both not funny and strong then mary is curious.
Everyone who is not happy or not creative is generous.
If susan is not strong or tall then someone is either quiet or not strong and vice versa.
If someone is both not patient and humble then someone is not kind or not wise and vice versa.
Everyone who is quiet or not wise is not strong and vice versa.
Everyone who is calm is patient.
Everyone who is calm or old is both not old and not rich.
If someone is brave or not strong then paul is wise.
Everyone who is not quiet is either not old or quiet and vice versa.
Everyone who is both old and happy is both strong and not calm and vice versa.
Someone is both not patient and not generous.
Someone is both not kind and not tall.
Someone is both humble and not old.
Someone is not tall or not rich.
Fred is not tall or generous.
Someone is both happy and not strong.
Lucy is not humble or not patient. | Alice is old. | contradiction | ((?[X]:((~strong(X)<~>funny(X))))=>(humble(paul)))&
(((~patient(john)|~humble(john)))<=>((~tall(susan)|~generous(susan))))&
(![X]:((~quiet(X)|generous(X))=>(curious(X)&~humble(X))))&
((?[X]:((happy(X)|~strong(X))))=>((~rich(john)|rich(john))))&
((?[X]:((quiet(X)|~brave(X))))=>(?[X]:((rich(X)|~calm(X)))))&
(((~funny(alice)&strong(alice)))=>(curious(mary)))&
(![X]:((~happy(X)|~creative(X))=>generous(X)))&
(((~strong(susan)|tall(susan)))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~strong(X)))&
(![X]:(calm(X)=>patient(X)))&
(![X]:((calm(X)|old(X))=>(~old(X)&~rich(X))))&
((?[X]:((brave(X)|~strong(X))))=>(wise(paul)))&
(![X]:(~quiet(X)<=>(~old(X)<~>quiet(X))))&
(![X]:((old(X)&happy(X))<=>(strong(X)&~calm(X))))&
(?[X]:((~patient(X)&~generous(X))))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((~tall(X)|~rich(X))))&
((~tall(fred)|generous(fred)))&
(?[X]:((happy(X)&~strong(X))))&
((~humble(lucy)|~patient(lucy))) | old(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5629416074966712354709997
% SZS output start Proof for 5629416074966712354709997
12. ! [X0] : ((old(X0) | calm(X0)) => (~rich(X0) & ~old(X0))) [input p11]
23. old(alice) [input hypothesis]
36. ! [X0] : ((~rich(X0) & ~old(X0)) | (~old(X0) & ~calm(X0))) [ennf transformation 12]
98. ~old(X0) | ~old(X0) [cnf transformation 36]
122. old(alice) [cnf transformation 23]
125. ~old(X0) [duplicate literal removal 98]
269. $false [subsumption resolution 122,125]
% SZS output end Proof for 5629416074966712354709997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or happy is both patient and brave and vice versa.
Everyone who is wise or strong is not rich and vice versa.
If fred is not brave or not patient then lucy is both not tall and quiet.
If fred is not strong then lucy is both not humble and brave.
Everyone who is either not creative or creative is patient and vice versa.
Everyone who is not happy is both not generous and not calm and vice versa.
Everyone who is either kind or wise is either wise or not wise and vice versa.
If lucy is kind then john is not patient and vice versa.
If someone is brave then mary is curious and vice versa.
If someone is either not wise or not creative then someone is calm or wise and vice versa.
If paul is not strong then alice is either not old or patient.
If someone is tall then mary is quiet.
If someone is both not generous and not happy then alice is kind or patient and vice versa.
Everyone who is happy or strong is happy and vice versa.
Everyone who is creative or quiet is either not kind or not creative.
Everyone who is either quiet or not calm is rich or not quiet and vice versa.
Mary is old or quiet.
Susan is curious.
Someone is both brave and patient.
Someone is either calm or not creative.
John is funny or not happy.
Paul is both happy and patient. | John is not curious. | neutral | (![X]:((~kind(X)|happy(X))<=>(patient(X)&brave(X))))&
(![X]:((wise(X)|strong(X))<=>~rich(X)))&
(((~brave(fred)|~patient(fred)))=>((~tall(lucy)&quiet(lucy))))&
((~strong(fred))=>((~humble(lucy)&brave(lucy))))&
(![X]:((~creative(X)<~>creative(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(~generous(X)&~calm(X))))&
(![X]:((kind(X)<~>wise(X))<=>(wise(X)<~>~wise(X))))&
((kind(lucy))<=>(~patient(john)))&
((?[X]:(brave(X)))<=>(curious(mary)))&
((?[X]:((~wise(X)<~>~creative(X))))<=>(?[X]:((calm(X)|wise(X)))))&
((~strong(paul))=>((~old(alice)<~>patient(alice))))&
((?[X]:(tall(X)))=>(quiet(mary)))&
((?[X]:((~generous(X)&~happy(X))))<=>((kind(alice)|patient(alice))))&
(![X]:((happy(X)|strong(X))<=>happy(X)))&
(![X]:((creative(X)|quiet(X))=>(~kind(X)<~>~creative(X))))&
(![X]:((quiet(X)<~>~calm(X))<=>(rich(X)|~quiet(X))))&
((old(mary)|quiet(mary)))&
(curious(susan))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((calm(X)<~>~creative(X))))&
((funny(john)|~happy(john)))&
((happy(paul)&patient(paul))) | ~curious(john) | [] | null | 0 |
If someone is not generous then someone is either happy or not curious. If lucy is both not curious and not generous then fred is brave and vice versa. Everyone who is both old and not generous is not tall or not curious and vice versa. Everyone who is either patient or tall is not creative and vice versa. Everyone who is both not strong and not calm is either not patient or not curious. If someone is either not humble or creative then lucy is either generous or wise. Everyone who is happy is both quiet and not tall and vice versa. Everyone who is either wise or humble is either creative or humble and vice versa. Everyone who is old is both not wise and generous. Everyone who is not strong or happy is either tall or not strong. Everyone who is both old and not wise is kind and vice versa. Everyone who is kind is both not wise and wise. Everyone who is old or not funny is not funny. Everyone who is patient or quiet is either rich or not calm and vice versa. Everyone who is calm or humble is either happy or not wise. Susan is tall or rich. Alice is not rich or not generous. Paul is humble. Fred is both not quiet and not rich. | Alice is not humble. | neutral | ((?[X]:(~generous(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((~curious(lucy)&~generous(lucy)))<=>(brave(fred)))&
(![X]:((old(X)&~generous(X))<=>(~tall(X)|~curious(X))))&
(![X]:((patient(X)<~>tall(X))<=>~creative(X)))&
(![X]:((~strong(X)&~calm(X))=>(~patient(X)<~>~curious(X))))&
((?[X]:((~humble(X)<~>creative(X))))=>((generous(lucy)<~>wise(lucy))))&
(![X]:(happy(X)<=>(quiet(X)&~tall(X))))&
(![X]:((wise(X)<~>humble(X))<=>(creative(X)<~>humble(X))))&
(![X]:(old(X)=>(~wise(X)&generous(X))))&
(![X]:((~strong(X)|happy(X))=>(tall(X)<~>~strong(X))))&
(![X]:((old(X)&~wise(X))<=>kind(X)))&
(![X]:(kind(X)=>(~wise(X)&wise(X))))&
(![X]:((old(X)|~funny(X))=>~funny(X)))&
(![X]:((patient(X)|quiet(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((calm(X)|humble(X))=>(happy(X)<~>~wise(X))))&
((tall(susan)|rich(susan)))&
((~rich(alice)|~generous(alice)))&
(humble(paul))&
((~quiet(fred)&~rich(fred))) | ~humble(alice) | [] | null | 0 |
If someone is quiet then paul is generous or tall.
If fred is strong or old then someone is not funny and vice versa.
Everyone who is not kind or not strong is both not creative and not humble.
If someone is either not calm or wise then mary is both curious and not curious.
Everyone who is both not curious and not funny is both not funny and not wise.
Everyone who is generous or curious is not generous or not funny and vice versa.
If someone is both strong and old then someone is not funny and vice versa.
If someone is not tall or humble then someone is quiet.
Everyone who is not strong is rich.
Everyone who is both not creative and strong is tall or calm.
Everyone who is not old is either kind or old and vice versa.
If susan is old then mary is both not humble and generous and vice versa.
Everyone who is not wise is calm.
If someone is both not wise and wise then someone is rich and vice versa.
If susan is both not funny and calm then someone is both quiet and funny and vice versa.
If fred is not funny or kind then someone is either not strong or brave.
Paul is either generous or humble.
Someone is both not brave and generous.
Someone is not patient or not curious.
Fred is generous or not funny.
Mary is funny or not rich.
John is patient.
Fred is not patient. | Fred is old. | neutral | ((?[X]:(quiet(X)))=>((generous(paul)|tall(paul))))&
(((strong(fred)|old(fred)))<=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)|~strong(X))=>(~creative(X)&~humble(X))))&
((?[X]:((~calm(X)<~>wise(X))))=>((curious(mary)&~curious(mary))))&
(![X]:((~curious(X)&~funny(X))=>(~funny(X)&~wise(X))))&
(![X]:((generous(X)|curious(X))<=>(~generous(X)|~funny(X))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~tall(X)|humble(X))))=>(?[X]:(quiet(X))))&
(![X]:(~strong(X)=>rich(X)))&
(![X]:((~creative(X)&strong(X))=>(tall(X)|calm(X))))&
(![X]:(~old(X)<=>(kind(X)<~>old(X))))&
((old(susan))<=>((~humble(mary)&generous(mary))))&
(![X]:(~wise(X)=>calm(X)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:(rich(X))))&
(((~funny(susan)&calm(susan)))<=>(?[X]:((quiet(X)&funny(X)))))&
(((~funny(fred)|kind(fred)))=>(?[X]:((~strong(X)<~>brave(X)))))&
((generous(paul)<~>humble(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:((~patient(X)|~curious(X))))&
((generous(fred)|~funny(fred)))&
((funny(mary)|~rich(mary)))&
(patient(john))&
(~patient(fred)) | old(fred) | [] | null | 0 |
Everyone who is either humble or kind is both not strong and strong and vice versa. Everyone who is not generous or not quiet is either strong or kind and vice versa. Everyone who is not wise or not creative is both not funny and strong and vice versa. If mary is kind or not patient then alice is either tall or curious and vice versa. Everyone who is not creative is both brave and kind and vice versa. Everyone who is not funny or not patient is not rich and vice versa. Everyone who is not patient or not curious is not happy and vice versa. If john is happy or not creative then someone is wise. Everyone who is not tall or rich is not rich and vice versa. Everyone who is either not happy or not old is calm and vice versa. If mary is both brave and old then someone is either not strong or brave and vice versa. Everyone who is funny is not creative or kind and vice versa. If someone is both creative and calm then someone is either quiet or not calm and vice versa. Everyone who is either not humble or not brave is not strong and vice versa. If john is funny or humble then mary is either quiet or old and vice versa. Everyone who is calm or not brave is either not tall or not happy and vice versa. Someone is not wise. Someone is brave. Someone is both not kind and not rich. Someone is creative or not humble. Someone is patient. | Alice is generous. | entailment | (![X]:((humble(X)<~>kind(X))<=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(strong(X)<~>kind(X))))&
(![X]:((~wise(X)|~creative(X))<=>(~funny(X)&strong(X))))&
(((kind(mary)|~patient(mary)))<=>((tall(alice)<~>curious(alice))))&
(![X]:(~creative(X)<=>(brave(X)&kind(X))))&
(![X]:((~funny(X)|~patient(X))<=>~rich(X)))&
(![X]:((~patient(X)|~curious(X))<=>~happy(X)))&
(((happy(john)|~creative(john)))=>(?[X]:(wise(X))))&
(![X]:((~tall(X)|rich(X))<=>~rich(X)))&
(![X]:((~happy(X)<~>~old(X))<=>calm(X)))&
(((brave(mary)&old(mary)))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:(funny(X)<=>(~creative(X)|kind(X))))&
((?[X]:((creative(X)&calm(X))))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>~brave(X))<=>~strong(X)))&
(((funny(john)|humble(john)))<=>((quiet(mary)<~>old(mary))))&
(![X]:((calm(X)|~brave(X))<=>(~tall(X)<~>~happy(X))))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((creative(X)|~humble(X))))&
(?[X]:(patient(X))) | generous(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4696725175445021573677411
% SZS output start Proof for 4696725175445021573677411
1. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (strong(X0) & ~strong(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (strong(X0) <~> kind(X0))) [input p1]
3. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (strong(X0) & ~funny(X0))) [input p2]
4. (~patient(mary) | kind(mary)) <=> (tall(alice) <~> curious(alice)) [input p3]
5. ! [X0] : (~creative(X0) <=> (kind(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~patient(X0) | ~funny(X0)) <=> ~rich(X0)) [input p5]
7. ! [X0] : ((~curious(X0) | ~patient(X0)) <=> ~happy(X0)) [input p6]
9. ! [X0] : ((rich(X0) | ~tall(X0)) <=> ~rich(X0)) [input p8]
10. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> calm(X0)) [input p9]
11. (old(mary) & brave(mary)) <=> ? [X0] : (~strong(X0) <~> brave(X0)) [input p10]
12. ! [X0] : (funny(X0) <=> (kind(X0) | ~creative(X0))) [input p11]
14. ! [X0] : ((~humble(X0) <~> ~brave(X0)) <=> ~strong(X0)) [input p13]
15. (humble(john) | funny(john)) <=> (quiet(mary) <~> old(mary)) [input p14]
16. ! [X0] : ((~brave(X0) | calm(X0)) <=> (~tall(X0) <~> ~happy(X0))) [input p15]
22. ~generous(alice) [input hypothesis]
25. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 1]
26. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [flattening 25]
27. ! [X0] : (((~quiet(X0) | ~generous(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (quiet(X0) & generous(X0)))) [nnf transformation 2]
28. ! [X0] : ((~quiet(X0) | ~generous(X0) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0)))) & (((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (quiet(X0) & generous(X0)))) [flattening 27]
29. ! [X0] : (((~creative(X0) | ~wise(X0)) | (~strong(X0) | funny(X0))) & ((strong(X0) & ~funny(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 3]
30. ! [X0] : ((~creative(X0) | ~wise(X0) | ~strong(X0) | funny(X0)) & ((strong(X0) & ~funny(X0)) | (creative(X0) & wise(X0)))) [flattening 29]
31. ((~patient(mary) | kind(mary)) | ((tall(alice) | ~curious(alice)) & (curious(alice) | ~tall(alice)))) & (((~curious(alice) | ~tall(alice)) & (curious(alice) | tall(alice))) | (patient(mary) & ~kind(mary))) [nnf transformation 4]
32. (~patient(mary) | kind(mary) | ((tall(alice) | ~curious(alice)) & (curious(alice) | ~tall(alice)))) & (((~curious(alice) | ~tall(alice)) & (curious(alice) | tall(alice))) | (patient(mary) & ~kind(mary))) [flattening 31]
33. ! [X0] : ((~creative(X0) | (~kind(X0) | ~brave(X0))) & ((kind(X0) & brave(X0)) | creative(X0))) [nnf transformation 5]
34. ! [X0] : ((~creative(X0) | ~kind(X0) | ~brave(X0)) & ((kind(X0) & brave(X0)) | creative(X0))) [flattening 33]
35. ! [X0] : (((~patient(X0) | ~funny(X0)) | rich(X0)) & (~rich(X0) | (patient(X0) & funny(X0)))) [nnf transformation 6]
36. ! [X0] : ((~patient(X0) | ~funny(X0) | rich(X0)) & (~rich(X0) | (patient(X0) & funny(X0)))) [flattening 35]
37. ! [X0] : (((~curious(X0) | ~patient(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & patient(X0)))) [nnf transformation 7]
38. ! [X0] : ((~curious(X0) | ~patient(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & patient(X0)))) [flattening 37]
41. ! [X0] : (((rich(X0) | ~tall(X0)) | rich(X0)) & (~rich(X0) | (~rich(X0) & tall(X0)))) [nnf transformation 9]
42. ! [X0] : ((rich(X0) | ~tall(X0) | rich(X0)) & (~rich(X0) | (~rich(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 10]
44. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X0] : ((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~old(mary) | ~brave(mary))) [nnf transformation 11]
45. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X0] : ((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | ~old(mary) | ~brave(mary)) [flattening 44]
46. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (? [X1] : ((~brave(X1) | strong(X1)) & (brave(X1) | ~strong(X1))) | ~old(mary) | ~brave(mary)) [rectify 45]
47. ? [X1] : ((~brave(X1) | strong(X1)) & (brave(X1) | ~strong(X1))) => ((~brave(sK1) | strong(sK1)) & (brave(sK1) | ~strong(sK1))) [choice axiom]
48. ((old(mary) & brave(mary)) | ! [X0] : ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (((~brave(sK1) | strong(sK1)) & (brave(sK1) | ~strong(sK1))) | ~old(mary) | ~brave(mary)) [skolemisation 46,47]
49. ! [X0] : ((funny(X0) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | ~funny(X0))) [nnf transformation 12]
50. ! [X0] : ((funny(X0) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | ~funny(X0))) [flattening 49]
56. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | strong(X0)) & (~strong(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [nnf transformation 14]
57. ((humble(john) | funny(john)) | ((quiet(mary) | ~old(mary)) & (old(mary) | ~quiet(mary)))) & (((~old(mary) | ~quiet(mary)) & (old(mary) | quiet(mary))) | (~humble(john) & ~funny(john))) [nnf transformation 15]
58. (humble(john) | funny(john) | ((quiet(mary) | ~old(mary)) & (old(mary) | ~quiet(mary)))) & (((~old(mary) | ~quiet(mary)) & (old(mary) | quiet(mary))) | (~humble(john) & ~funny(john))) [flattening 57]
59. ! [X0] : (((~brave(X0) | calm(X0)) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (brave(X0) & ~calm(X0)))) [nnf transformation 16]
60. ! [X0] : ((~brave(X0) | calm(X0) | ((~tall(X0) | happy(X0)) & (~happy(X0) | tall(X0)))) & (((happy(X0) | tall(X0)) & (~happy(X0) | ~tall(X0))) | (brave(X0) & ~calm(X0)))) [flattening 59]
71. ~strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 26]
73. ~humble(X0) | kind(X0) | strong(X0) [cnf transformation 26]
77. generous(X0) | strong(X0) | kind(X0) [cnf transformation 28]
78. quiet(X0) | strong(X0) | kind(X0) [cnf transformation 28]
79. ~strong(X0) | ~kind(X0) | generous(X0) [cnf transformation 28]
84. ~funny(X0) | creative(X0) [cnf transformation 30]
93. ~patient(mary) | kind(mary) | tall(alice) | ~curious(alice) [cnf transformation 32]
96. ~brave(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 34]
99. ~patient(X0) | ~funny(X0) | rich(X0) [cnf transformation 36]
100. ~happy(X0) | patient(X0) [cnf transformation 38]
101. ~happy(X0) | curious(X0) [cnf transformation 38]
106. ~rich(X0) | ~rich(X0) [cnf transformation 42]
107. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 42]
108. ~old(X0) | calm(X0) | happy(X0) [cnf transformation 43]
110. ~calm(X0) | ~happy(X0) | ~old(X0) [cnf transformation 43]
114. brave(mary) | brave(X0) | strong(X0) [cnf transformation 48]
115. brave(mary) | ~strong(X0) | ~brave(X0) [cnf transformation 48]
116. old(mary) | brave(X0) | strong(X0) [cnf transformation 48]
117. old(mary) | ~strong(X0) | ~brave(X0) [cnf transformation 48]
118. kind(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 50]
119. funny(X0) | creative(X0) [cnf transformation 50]
120. ~kind(X0) | funny(X0) [cnf transformation 50]
127. ~brave(X0) | ~strong(X0) | humble(X0) [cnf transformation 56]
129. ~brave(X0) | ~humble(X0) | strong(X0) [cnf transformation 56]
135. humble(john) | funny(john) | old(mary) | ~quiet(mary) [cnf transformation 58]
139. ~calm(X0) | tall(X0) | happy(X0) [cnf transformation 60]
140. happy(X0) | tall(X0) | brave(X0) [cnf transformation 60]
141. ~happy(X0) | calm(X0) | ~brave(X0) | tall(X0) [cnf transformation 60]
149. ~generous(alice) [cnf transformation 22]
150. ~rich(X0) [duplicate literal removal 106]
151. ~tall(X0) | rich(X0) [duplicate literal removal 107]
153. ~humble(X0) | kind(X0) [subsumption resolution 71,73]
155. 1 <=> curious(alice) [avatar definition]
159. 2 <=> tall(alice) [avatar definition]
160. ~tall(alice) <- (~2) [avatar component clause 159]
161. tall(alice) <- (2) [avatar component clause 159]
163. 3 <=> kind(mary) [avatar definition]
164. ~kind(mary) <- (~3) [avatar component clause 163]
165. kind(mary) <- (3) [avatar component clause 163]
167. 4 <=> patient(mary) [avatar definition]
168. patient(mary) <- (4) [avatar component clause 167]
170. ~1 | 2 | 3 | ~4 [avatar split clause 93,167,163,159,155]
186. 7 <=> happy(john) [avatar definition]
187. happy(john) <- (7) [avatar component clause 186]
188. ~happy(john) <- (~7) [avatar component clause 186]
191. 8 <=> ! [X0] : (~strong(X0) | ~brave(X0)) [avatar definition]
192. ~brave(X0) | ~strong(X0) <- (8) [avatar component clause 191]
194. 9 <=> old(mary) [avatar definition]
196. old(mary) <- (9) [avatar component clause 194]
197. 8 | 9 [avatar split clause 117,194,191]
199. 10 <=> ! [X0] : (brave(X0) | strong(X0)) [avatar definition]
200. brave(X0) | strong(X0) <- (10) [avatar component clause 199]
201. 10 | 9 [avatar split clause 116,194,199]
203. 11 <=> brave(mary) [avatar definition]
204. ~brave(mary) <- (~11) [avatar component clause 203]
205. brave(mary) <- (11) [avatar component clause 203]
206. 8 | 11 [avatar split clause 115,203,191]
207. 10 | 11 [avatar split clause 114,203,199]
218. creative(X0) [subsumption resolution 119,84]
219. ~funny(X0) | kind(X0) [subsumption resolution 118,218]
248. 20 <=> quiet(mary) [avatar definition]
249. ~quiet(mary) <- (~20) [avatar component clause 248]
252. 21 <=> funny(john) [avatar definition]
254. funny(john) <- (21) [avatar component clause 252]
256. 22 <=> humble(john) [avatar definition]
258. humble(john) <- (22) [avatar component clause 256]
260. ~20 | 9 | 21 | 22 [avatar split clause 135,256,252,194,248]
266. rich(alice) <- (2) [resolution 151,161]
267. $false <- (2) [subsumption resolution 266,150]
268. ~2 [avatar contradiction clause 267]
272. strong(alice) | kind(alice) [resolution 77,149]
274. 23 <=> kind(alice) [avatar definition]
276. kind(alice) <- (23) [avatar component clause 274]
278. 24 <=> strong(alice) [avatar definition]
280. strong(alice) <- (24) [avatar component clause 278]
281. 23 | 24 [avatar split clause 272,278,274]
283. strong(mary) | kind(mary) <- (~20) [resolution 78,249]
293. strong(mary) <- (~3, ~20) [subsumption resolution 283,164]
329. ~kind(X0) | ~creative(X0) | strong(X0) <- (10) [resolution 96,200]
332. ~kind(X0) | strong(X0) <- (10) [subsumption resolution 329,218]
384. 36 <=> humble(mary) [avatar definition]
419. tall(john) | brave(john) <- (~7) [resolution 140,188]
422. brave(X2) | tall(X2) | curious(X2) [resolution 140,101]
423. brave(X3) | tall(X3) | patient(X3) [resolution 140,100]
426. 38 <=> brave(john) [avatar definition]
428. brave(john) <- (38) [avatar component clause 426]
430. 39 <=> tall(john) [avatar definition]
432. tall(john) <- (39) [avatar component clause 430]
433. 38 | 39 | 7 [avatar split clause 419,186,430,426]
459. ~kind(john) | ~creative(john) <- (38) [resolution 428,96]
462. ~kind(john) <- (38) [subsumption resolution 459,218]
488. strong(alice) <- (10, 23) [resolution 332,276]
489. 24 | ~10 | ~23 [avatar split clause 488,274,199,278]
492. ~kind(alice) | generous(alice) <- (24) [resolution 280,79]
495. generous(alice) <- (23, 24) [subsumption resolution 492,276]
496. $false <- (23, 24) [subsumption resolution 495,149]
497. ~23 | ~24 [avatar contradiction clause 496]
513. calm(mary) | happy(mary) <- (9) [resolution 196,108]
515. 47 <=> happy(mary) [avatar definition]
516. ~happy(mary) <- (~47) [avatar component clause 515]
517. happy(mary) <- (47) [avatar component clause 515]
519. 48 <=> calm(mary) [avatar definition]
521. calm(mary) <- (48) [avatar component clause 519]
522. 47 | 48 | ~9 [avatar split clause 513,194,519,515]
524. ~humble(mary) | strong(mary) <- (11) [resolution 205,129]
525. ~strong(mary) | humble(mary) <- (11) [resolution 205,127]
527. humble(mary) <- (~3, 11, ~20) [subsumption resolution 525,293]
530. 36 | 3 | ~11 | 20 [avatar split clause 527,248,203,163,384]
544. kind(john) <- (21) [resolution 254,219]
547. $false <- (21, 38) [subsumption resolution 544,462]
548. ~21 | ~38 [avatar contradiction clause 547]
550. kind(john) <- (22) [resolution 258,153]
554. rich(john) <- (39) [resolution 432,151]
555. $false <- (39) [subsumption resolution 554,150]
556. ~39 [avatar contradiction clause 555]
561. patient(john) <- (7) [resolution 187,100]
577. 51 <=> tall(mary) [avatar definition]
578. ~tall(mary) <- (~51) [avatar component clause 577]
579. tall(mary) <- (51) [avatar component clause 577]
584. ~happy(mary) | ~old(mary) <- (48) [resolution 521,110]
587. ~old(mary) <- (47, 48) [subsumption resolution 584,517]
588. $false <- (9, 47, 48) [subsumption resolution 587,196]
589. ~9 | ~47 | ~48 [avatar contradiction clause 588]
599. funny(john) <- (22) [resolution 550,120]
600. 21 | ~22 [avatar split clause 599,256,252]
605. ~funny(john) | rich(john) <- (7) [resolution 561,99]
610. ~funny(john) <- (7) [subsumption resolution 605,150]
611. ~21 | ~7 [avatar split clause 610,186,252]
626. 52 <=> strong(mary) [avatar definition]
627. strong(mary) <- (52) [avatar component clause 626]
635. 52 | ~36 | ~11 [avatar split clause 524,203,384,626]
705. rich(mary) <- (51) [resolution 579,151]
706. $false <- (51) [subsumption resolution 705,150]
707. ~51 [avatar contradiction clause 706]
710. tall(mary) | happy(mary) <- (48) [resolution 521,139]
714. happy(mary) <- (48, ~51) [subsumption resolution 710,578]
715. $false <- (~47, 48, ~51) [subsumption resolution 714,516]
716. 47 | ~48 | 51 [avatar contradiction clause 715]
719. tall(mary) | patient(mary) <- (~11) [resolution 204,423]
728. ~strong(X0) | tall(X0) | patient(X0) <- (8) [resolution 192,423]
729. ~strong(X1) | tall(X1) | curious(X1) <- (8) [resolution 192,422]
740. strong(X4) | ~kind(X4) | ~creative(X4) <- (10) [resolution 200,96]
745. ~kind(X4) | strong(X4) <- (10) [subsumption resolution 740,218]
765. calm(mary) | ~brave(mary) | tall(mary) <- (47) [resolution 517,141]
769. patient(mary) <- (47) [resolution 517,100]
778. tall(mary) | patient(mary) <- (8, 52) [resolution 728,627]
793. tall(alice) | curious(alice) <- (8, 24) [resolution 729,280]
796. curious(alice) <- (~2, 8, 24) [subsumption resolution 793,160]
799. 1 | 2 | ~8 | ~24 [avatar split clause 796,278,191,159,155]
800. patient(mary) <- (8, ~51, 52) [subsumption resolution 778,578]
801. 4 | ~8 | 51 | ~52 [avatar split clause 800,626,577,191,167]
802. 4 | ~47 [avatar split clause 769,515,167]
803. patient(mary) <- (~11, ~51) [subsumption resolution 719,578]
804. 4 | 11 | 51 [avatar split clause 803,577,203,167]
813. strong(mary) <- (3, 10) [resolution 165,745]
816. funny(mary) <- (3) [resolution 165,120]
822. 52 | ~3 | ~10 [avatar split clause 813,199,163,626]
826. calm(mary) | ~brave(mary) <- (47, ~51) [subsumption resolution 765,578]
827. ~11 | 48 | ~47 | 51 [avatar split clause 826,577,515,519,203]
828. ~funny(mary) | rich(mary) <- (4) [resolution 168,99]
829. rich(mary) <- (3, 4) [subsumption resolution 828,816]
830. $false <- (3, 4) [subsumption resolution 829,150]
831. ~3 | ~4 [avatar contradiction clause 830]
832. $false [avatar sat refutation 170,197,201,206,207,260,268,281,433,489,497,522,530,548,556,589,600,611,635,707,716,799,801,802,804,822,827,831]
% SZS output end Proof for 4696725175445021573677411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or happy is tall or creative.
If someone is both not patient and kind then alice is both happy and not funny.
Everyone who is not curious is both old and calm and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is wise is either patient or rich.
If someone is funny then lucy is not tall or curious.
Everyone who is either old or happy is not funny or generous and vice versa.
If someone is not kind then lucy is both not strong and not brave.
Everyone who is both calm and curious is both not curious and brave and vice versa.
If someone is both funny and not old then mary is both not funny and not kind.
Everyone who is brave or not tall is either old or brave and vice versa.
If someone is both not creative and not funny then someone is either not strong or not funny.
If alice is either not old or not brave then someone is both tall and old and vice versa.
Everyone who is strong or not funny is not wise or generous.
If alice is both wise and patient then susan is both not creative and not tall.
If alice is both humble and not tall then susan is either not generous or not calm and vice versa.
Susan is not funny or happy.
Someone is funny.
Someone is not quiet or wise.
Someone is not creative or not old.
Someone is not humble.
Someone is both not tall and brave.
Someone is not curious or not generous.
Someone is not funny. | Alice is funny. | neutral | (![X]:((rich(X)|happy(X))=>(tall(X)|creative(X))))&
((?[X]:((~patient(X)&kind(X))))=>((happy(alice)&~funny(alice))))&
(![X]:(~curious(X)<=>(old(X)&calm(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:(wise(X)=>(patient(X)<~>rich(X))))&
((?[X]:(funny(X)))=>((~tall(lucy)|curious(lucy))))&
(![X]:((old(X)<~>happy(X))<=>(~funny(X)|generous(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)&~brave(lucy))))&
(![X]:((calm(X)&curious(X))<=>(~curious(X)&brave(X))))&
((?[X]:((funny(X)&~old(X))))=>((~funny(mary)&~kind(mary))))&
(![X]:((brave(X)|~tall(X))<=>(old(X)<~>brave(X))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~old(alice)<~>~brave(alice)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((strong(X)|~funny(X))=>(~wise(X)|generous(X))))&
(((wise(alice)&patient(alice)))=>((~creative(susan)&~tall(susan))))&
(((humble(alice)&~tall(alice)))<=>((~generous(susan)<~>~calm(susan))))&
((~funny(susan)|happy(susan)))&
(?[X]:(funny(X)))&
(?[X]:((~quiet(X)|wise(X))))&
(?[X]:((~creative(X)|~old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)&brave(X))))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:(~funny(X))) | funny(alice) | [] | null | 0 |
If someone is either tall or not brave then someone is both creative and not humble and vice versa.
Everyone who is both quiet and wise is both not calm and not quiet.
Everyone who is either rich or old is not tall or old.
Everyone who is not happy is strong and vice versa.
Everyone who is not brave or not calm is both not kind and not patient and vice versa.
Everyone who is strong or happy is not strong and vice versa.
If paul is old or kind then someone is funny or kind.
Everyone who is not patient is either quiet or curious and vice versa.
Everyone who is brave is not kind or strong and vice versa.
If alice is not generous or not tall then paul is not kind or not brave.
Everyone who is both old and not wise is not patient or kind.
If lucy is not calm then someone is both not tall and not quiet and vice versa.
Everyone who is not old is both curious and tall.
If someone is both not happy and generous then lucy is not rich and vice versa.
If someone is not funny then alice is both not tall and strong and vice versa.
If someone is generous then susan is both not funny and calm and vice versa.
Someone is wise.
Someone is either not happy or quiet.
Someone is either not brave or curious.
Susan is either curious or not brave.
Mary is happy or not tall.
Lucy is either calm or tall. | Susan is rich. | neutral | ((?[X]:((tall(X)<~>~brave(X))))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((quiet(X)&wise(X))=>(~calm(X)&~quiet(X))))&
(![X]:((rich(X)<~>old(X))=>(~tall(X)|old(X))))&
(![X]:(~happy(X)<=>strong(X)))&
(![X]:((~brave(X)|~calm(X))<=>(~kind(X)&~patient(X))))&
(![X]:((strong(X)|happy(X))<=>~strong(X)))&
(((old(paul)|kind(paul)))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:(~patient(X)<=>(quiet(X)<~>curious(X))))&
(![X]:(brave(X)<=>(~kind(X)|strong(X))))&
(((~generous(alice)|~tall(alice)))=>((~kind(paul)|~brave(paul))))&
(![X]:((old(X)&~wise(X))=>(~patient(X)|kind(X))))&
((~calm(lucy))<=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:(~old(X)=>(curious(X)&tall(X))))&
((?[X]:((~happy(X)&generous(X))))<=>(~rich(lucy)))&
((?[X]:(~funny(X)))<=>((~tall(alice)&strong(alice))))&
((?[X]:(generous(X)))<=>((~funny(susan)&calm(susan))))&
(?[X]:(wise(X)))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
((curious(susan)<~>~brave(susan)))&
((happy(mary)|~tall(mary)))&
((calm(lucy)<~>tall(lucy))) | rich(susan) | [] | null | 0 |
Everyone who is both happy and creative is both brave and not funny. If someone is either not funny or not kind then john is not curious and vice versa. Everyone who is either not humble or rich is either not quiet or not generous and vice versa. If john is either patient or generous then someone is both not humble and brave. Everyone who is both generous and not rich is not happy or old and vice versa. Everyone who is both calm and creative is quiet. If susan is not generous or tall then someone is kind and vice versa. If someone is not humble then someone is both not strong and not wise and vice versa. If paul is brave then someone is both wise and funny. Everyone who is happy is either old or rich. Everyone who is either tall or not curious is either not creative or brave. Everyone who is not kind is either not patient or curious and vice versa. If someone is either tall or patient then someone is either not calm or not kind. Everyone who is wise is funny. If someone is both humble and curious then alice is either happy or not happy. If fred is not generous then someone is not humble or not strong and vice versa. Fred is not curious. Susan is tall. Someone is not rich. Fred is creative or not brave. Fred is either not curious or not wise. Lucy is both not humble and not funny. Someone is not funny. Someone is strong. | Fred is funny. | entailment | (![X]:((happy(X)&creative(X))=>(brave(X)&~funny(X))))&
((?[X]:((~funny(X)<~>~kind(X))))<=>(~curious(john)))&
(![X]:((~humble(X)<~>rich(X))<=>(~quiet(X)<~>~generous(X))))&
(((patient(john)<~>generous(john)))=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~happy(X)|old(X))))&
(![X]:((calm(X)&creative(X))=>quiet(X)))&
(((~generous(susan)|tall(susan)))<=>(?[X]:(kind(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~strong(X)&~wise(X)))))&
((brave(paul))=>(?[X]:((wise(X)&funny(X)))))&
(![X]:(happy(X)=>(old(X)<~>rich(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~creative(X)<~>brave(X))))&
(![X]:(~kind(X)<=>(~patient(X)<~>curious(X))))&
((?[X]:((tall(X)<~>patient(X))))=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:(wise(X)=>funny(X)))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)<~>~happy(alice))))&
((~generous(fred))<=>(?[X]:((~humble(X)|~strong(X)))))&
(~curious(fred))&
(tall(susan))&
(?[X]:(~rich(X)))&
((creative(fred)|~brave(fred)))&
((~curious(fred)<~>~wise(fred)))&
((~humble(lucy)&~funny(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:(strong(X))) | funny(fred) | [
"p13",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1393626061803055938208810
% SZS output start Proof for 1393626061803055938208810
14. ! [X0] : (wise(X0) => funny(X0)) [input p13]
17. ~curious(fred) [input p16]
21. ~curious(fred) <~> ~wise(fred) [input p20]
25. ~funny(fred) [input hypothesis]
37. ! [X0] : (funny(X0) | ~wise(X0)) [ennf transformation 14]
75. (wise(fred) | curious(fred)) & (~wise(fred) | ~curious(fred)) [nnf transformation 21]
126. ~wise(X0) | funny(X0) [cnf transformation 37]
132. ~curious(fred) [cnf transformation 17]
137. wise(fred) | curious(fred) [cnf transformation 75]
142. ~funny(fred) [cnf transformation 25]
284. wise(fred) [subsumption resolution 137,132]
287. funny(fred) [resolution 126,284]
288. $false [subsumption resolution 287,142]
% SZS output end Proof for 1393626061803055938208810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both rich and creative. Everyone who is rich is both not strong and humble. If someone is brave or kind then someone is both old and not brave. If john is brave then someone is both generous and not generous and vice versa. Everyone who is both old and not happy is kind or tall. Everyone who is patient is both not wise and generous. If susan is not tall then someone is either not quiet or not wise and vice versa. Everyone who is either not funny or creative is not wise and vice versa. If alice is either not tall or brave then someone is both patient and not old. If someone is either not creative or not quiet then someone is either not wise or quiet. If fred is old or not generous then someone is both not tall and generous. If susan is both not quiet and not strong then fred is either not kind or strong. Everyone who is rich is either not tall or old and vice versa. Everyone who is not funny or strong is not creative or not wise. If susan is both kind and not kind then someone is not humble or not wise and vice versa. If paul is either happy or curious then someone is either humble or not humble. Someone is either not patient or not funny. John is not creative or not calm. John is curious or not creative. Lucy is either not strong or not brave. Paul is not quiet or not curious. Lucy is either not generous or happy. Fred is both tall and generous. Someone is not tall or creative. | Lucy is creative. | contradiction | (![X]:(creative(X)=>(rich(X)&creative(X))))&
(![X]:(rich(X)=>(~strong(X)&humble(X))))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((old(X)&~brave(X)))))&
((brave(john))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((old(X)&~happy(X))=>(kind(X)|tall(X))))&
(![X]:(patient(X)=>(~wise(X)&generous(X))))&
((~tall(susan))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((~funny(X)<~>creative(X))<=>~wise(X)))&
(((~tall(alice)<~>brave(alice)))=>(?[X]:((patient(X)&~old(X)))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(((old(fred)|~generous(fred)))=>(?[X]:((~tall(X)&generous(X)))))&
(((~quiet(susan)&~strong(susan)))=>((~kind(fred)<~>strong(fred))))&
(![X]:(rich(X)<=>(~tall(X)<~>old(X))))&
(![X]:((~funny(X)|strong(X))=>(~creative(X)|~wise(X))))&
(((kind(susan)&~kind(susan)))<=>(?[X]:((~humble(X)|~wise(X)))))&
(((happy(paul)<~>curious(paul)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(?[X]:((~patient(X)<~>~funny(X))))&
((~creative(john)|~calm(john)))&
((curious(john)|~creative(john)))&
((~strong(lucy)<~>~brave(lucy)))&
((~quiet(paul)|~curious(paul)))&
((~generous(lucy)<~>happy(lucy)))&
((tall(fred)&generous(fred)))&
(?[X]:((~tall(X)|creative(X)))) | creative(lucy) | [
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 698817925371301234998077
% SZS output start Proof for 698817925371301234998077
8. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> ~wise(X0)) [input p7]
14. ! [X0] : ((strong(X0) | ~funny(X0)) => (~wise(X0) | ~creative(X0))) [input p13]
15. (~kind(susan) & kind(susan)) <=> ? [X0] : (~wise(X0) | ~humble(X0)) [input p14]
25. creative(lucy) [input hypothesis]
40. ! [X0] : ((~wise(X0) | ~creative(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 14]
41. ! [X0] : (~wise(X0) | ~creative(X0) | (~strong(X0) & funny(X0))) [flattening 40]
54. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | wise(X0)) & (~wise(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 8]
66. ((~kind(susan) & kind(susan)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X0] : (~wise(X0) | ~humble(X0)) | (kind(susan) | ~kind(susan))) [nnf transformation 15]
67. ((~kind(susan) & kind(susan)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X0] : (~wise(X0) | ~humble(X0)) | kind(susan) | ~kind(susan)) [flattening 66]
68. ((~kind(susan) & kind(susan)) | ! [X0] : (wise(X0) & humble(X0))) & (? [X1] : (~wise(X1) | ~humble(X1)) | kind(susan) | ~kind(susan)) [rectify 67]
69. ? [X1] : (~wise(X1) | ~humble(X1)) => (~wise(sK6) | ~humble(sK6)) [choice axiom]
70. ((~kind(susan) & kind(susan)) | ! [X0] : (wise(X0) & humble(X0))) & ((~wise(sK6) | ~humble(sK6)) | kind(susan) | ~kind(susan)) [skolemisation 68,69]
99. ~wise(X0) | creative(X0) | funny(X0) [cnf transformation 54]
100. ~funny(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 54]
121. ~wise(X0) | ~creative(X0) | funny(X0) [cnf transformation 41]
125. kind(susan) | wise(X0) [cnf transformation 70]
127. ~kind(susan) | wise(X0) [cnf transformation 70]
143. creative(lucy) [cnf transformation 25]
270. ~wise(X0) | funny(X0) [subsumption resolution 121,99]
272. 28 <=> ! [X0] : wise(X0) [avatar definition]
273. wise(X0) <- (28) [avatar component clause 272]
275. 29 <=> kind(susan) [avatar definition]
278. 28 | ~29 [avatar split clause 127,275,272]
283. 28 | 29 [avatar split clause 125,275,272]
355. funny(X0) <- (28) [resolution 270,273]
358. ~wise(X0) | ~creative(X0) <- (28) [resolution 100,355]
360. ~creative(X0) <- (28) [subsumption resolution 358,273]
364. $false <- (28) [resolution 360,143]
365. ~28 [avatar contradiction clause 364]
366. $false [avatar sat refutation 278,283,365]
% SZS output end Proof for 698817925371301234998077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both humble and quiet.
If fred is happy or not creative then fred is both not rich and not happy and vice versa.
If someone is quiet or calm then someone is both wise and not patient and vice versa.
If susan is both happy and old then paul is both strong and kind and vice versa.
If fred is not curious or humble then alice is rich or brave.
If mary is not kind or not funny then mary is both not happy and curious and vice versa.
Everyone who is both not quiet and patient is rich and vice versa.
If someone is kind then alice is both not happy and humble.
Everyone who is either patient or not strong is either not generous or curious and vice versa.
If lucy is either tall or not rich then alice is both not humble and not tall and vice versa.
If mary is either strong or kind then fred is patient and vice versa.
If alice is not curious then someone is not rich and vice versa.
Everyone who is both not wise and not happy is either not patient or not quiet.
If lucy is not brave or not humble then someone is not generous or not calm.
If alice is old then someone is not funny and vice versa.
If paul is either not tall or quiet then someone is not wise or strong and vice versa.
Someone is creative or not patient.
Someone is either not strong or not generous.
Someone is either brave or happy.
Someone is not curious.
Mary is quiet.
Someone is both old and not strong.
Someone is both not calm and tall.
Someone is either calm or kind. | Mary is not quiet. | contradiction | (![X]:(kind(X)=>(humble(X)&quiet(X))))&
(((happy(fred)|~creative(fred)))<=>((~rich(fred)&~happy(fred))))&
((?[X]:((quiet(X)|calm(X))))<=>(?[X]:((wise(X)&~patient(X)))))&
(((happy(susan)&old(susan)))<=>((strong(paul)&kind(paul))))&
(((~curious(fred)|humble(fred)))=>((rich(alice)|brave(alice))))&
(((~kind(mary)|~funny(mary)))<=>((~happy(mary)&curious(mary))))&
(![X]:((~quiet(X)&patient(X))<=>rich(X)))&
((?[X]:(kind(X)))=>((~happy(alice)&humble(alice))))&
(![X]:((patient(X)<~>~strong(X))<=>(~generous(X)<~>curious(X))))&
(((tall(lucy)<~>~rich(lucy)))<=>((~humble(alice)&~tall(alice))))&
(((strong(mary)<~>kind(mary)))<=>(patient(fred)))&
((~curious(alice))<=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~happy(X))=>(~patient(X)<~>~quiet(X))))&
(((~brave(lucy)|~humble(lucy)))=>(?[X]:((~generous(X)|~calm(X)))))&
((old(alice))<=>(?[X]:(~funny(X))))&
(((~tall(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)|strong(X)))))&
(?[X]:((creative(X)|~patient(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
(?[X]:((brave(X)<~>happy(X))))&
(?[X]:(~curious(X)))&
(quiet(mary))&
(?[X]:((old(X)&~strong(X))))&
(?[X]:((~calm(X)&tall(X))))&
(?[X]:((calm(X)<~>kind(X)))) | ~quiet(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1281115393069946681769433
% SZS output start Proof for 1281115393069946681769433
21. quiet(mary) [input p20]
25. ~quiet(mary) [input hypothesis]
149. quiet(mary) [cnf transformation 21]
156. ~quiet(mary) [cnf transformation 25]
419. $false [subsumption resolution 156,149]
% SZS output end Proof for 1281115393069946681769433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not funny then paul is calm or not old. Everyone who is curious or patient is old or curious and vice versa. Everyone who is either not creative or funny is generous and vice versa. Everyone who is humble is both calm and not humble. If someone is not generous or patient then susan is not tall and vice versa. If someone is both tall and kind then someone is either curious or not curious and vice versa. If someone is both strong and not creative then someone is not happy or not funny. Everyone who is either not rich or not patient is wise or not strong and vice versa. Everyone who is both calm and not humble is quiet or not old and vice versa. Everyone who is both not old and curious is rich. Everyone who is tall is generous or strong. Everyone who is either not brave or not humble is happy or not wise. Everyone who is funny is either old or not kind. Everyone who is both not patient and not rich is not quiet and vice versa. Lucy is either not kind or patient. Someone is either creative or not strong. Paul is not creative. Someone is both not humble and not creative. Someone is either strong or creative. Someone is either not tall or kind. Someone is not strong. | Susan is not patient. | neutral | ((~funny(john))=>((calm(paul)|~old(paul))))&
(![X]:((curious(X)|patient(X))<=>(old(X)|curious(X))))&
(![X]:((~creative(X)<~>funny(X))<=>generous(X)))&
(![X]:(humble(X)=>(calm(X)&~humble(X))))&
((?[X]:((~generous(X)|patient(X))))<=>(~tall(susan)))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))<=>(wise(X)|~strong(X))))&
(![X]:((calm(X)&~humble(X))<=>(quiet(X)|~old(X))))&
(![X]:((~old(X)&curious(X))=>rich(X)))&
(![X]:(tall(X)=>(generous(X)|strong(X))))&
(![X]:((~brave(X)<~>~humble(X))=>(happy(X)|~wise(X))))&
(![X]:(funny(X)=>(old(X)<~>~kind(X))))&
(![X]:((~patient(X)&~rich(X))<=>~quiet(X)))&
((~kind(lucy)<~>patient(lucy)))&
(?[X]:((creative(X)<~>~strong(X))))&
(~creative(paul))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:((strong(X)<~>creative(X))))&
(?[X]:((~tall(X)<~>kind(X))))&
(?[X]:(~strong(X))) | ~patient(susan) | [] | null | 0 |
Everyone who is both funny and not rich is either not patient or old and vice versa. If lucy is either rich or not generous then alice is both calm and curious. Everyone who is both creative and happy is both brave and not happy and vice versa. Everyone who is not tall or rich is not strong and vice versa. If john is both not tall and not calm then paul is both not kind and not strong. If someone is not creative then fred is not funny and vice versa. Everyone who is both not calm and not happy is either not wise or not tall. Everyone who is wise or not funny is both not rich and not funny and vice versa. Everyone who is both not curious and not kind is not humble and vice versa. Everyone who is patient or calm is not humble or rich and vice versa. If fred is either funny or strong then someone is both humble and not generous. Everyone who is tall is both wise and quiet and vice versa. If mary is old then someone is not old or not wise and vice versa. If someone is either not kind or calm then susan is either not strong or generous and vice versa. Everyone who is patient or not quiet is both not curious and not rich and vice versa. Everyone who is not wise or not generous is not tall. Someone is both not wise and calm. Someone is strong or rich. Someone is either brave or not kind. Mary is both not creative and quiet. Someone is not strong or not humble. Mary is rich. Fred is either not generous or not kind. | Mary is happy. | neutral | (![X]:((funny(X)&~rich(X))<=>(~patient(X)<~>old(X))))&
(((rich(lucy)<~>~generous(lucy)))=>((calm(alice)&curious(alice))))&
(![X]:((creative(X)&happy(X))<=>(brave(X)&~happy(X))))&
(![X]:((~tall(X)|rich(X))<=>~strong(X)))&
(((~tall(john)&~calm(john)))=>((~kind(paul)&~strong(paul))))&
((?[X]:(~creative(X)))<=>(~funny(fred)))&
(![X]:((~calm(X)&~happy(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((wise(X)|~funny(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~curious(X)&~kind(X))<=>~humble(X)))&
(![X]:((patient(X)|calm(X))<=>(~humble(X)|rich(X))))&
(((funny(fred)<~>strong(fred)))=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:(tall(X)<=>(wise(X)&quiet(X))))&
((old(mary))<=>(?[X]:((~old(X)|~wise(X)))))&
((?[X]:((~kind(X)<~>calm(X))))<=>((~strong(susan)<~>generous(susan))))&
(![X]:((patient(X)|~quiet(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~wise(X)|~generous(X))=>~tall(X)))&
(?[X]:((~wise(X)&calm(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((~creative(mary)&quiet(mary)))&
(?[X]:((~strong(X)|~humble(X))))&
(rich(mary))&
((~generous(fred)<~>~kind(fred))) | happy(mary) | [] | null | 0 |
If paul is either not old or not wise then paul is either not patient or not wise. If someone is both not strong and brave then john is both patient and not creative and vice versa. If someone is either not tall or not old then someone is happy. Everyone who is either kind or wise is either not kind or not brave and vice versa. If someone is both humble and old then john is not tall or not wise and vice versa. If alice is not kind then someone is quiet or wise and vice versa. Everyone who is humble or tall is not strong and vice versa. If lucy is curious or not brave then alice is patient or not curious. If john is both happy and funny then alice is either not tall or not brave. Everyone who is not funny or quiet is either kind or brave and vice versa. Everyone who is both not kind and patient is both not funny and humble. Everyone who is calm or old is either kind or not brave. If john is either generous or rich then someone is either not funny or not curious and vice versa. Everyone who is not brave or strong is both not rich and curious. Everyone who is not wise or creative is both not rich and not happy. Everyone who is not brave is happy or not strong and vice versa. Fred is either not brave or not old. John is both not rich and kind. Someone is not happy or curious. Lucy is either curious or strong. Lucy is both not kind and not wise. Someone is either happy or generous. | Paul is tall. | contradiction | (((~old(paul)<~>~wise(paul)))=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~strong(X)&brave(X))))<=>((patient(john)&~creative(john))))&
((?[X]:((~tall(X)<~>~old(X))))=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>wise(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:((humble(X)&old(X))))<=>((~tall(john)|~wise(john))))&
((~kind(alice))<=>(?[X]:((quiet(X)|wise(X)))))&
(![X]:((humble(X)|tall(X))<=>~strong(X)))&
(((curious(lucy)|~brave(lucy)))=>((patient(alice)|~curious(alice))))&
(((happy(john)&funny(john)))=>((~tall(alice)<~>~brave(alice))))&
(![X]:((~funny(X)|quiet(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~kind(X)&patient(X))=>(~funny(X)&humble(X))))&
(![X]:((calm(X)|old(X))=>(kind(X)<~>~brave(X))))&
(((generous(john)<~>rich(john)))<=>(?[X]:((~funny(X)<~>~curious(X)))))&
(![X]:((~brave(X)|strong(X))=>(~rich(X)&curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~rich(X)&~happy(X))))&
(![X]:(~brave(X)<=>(happy(X)|~strong(X))))&
((~brave(fred)<~>~old(fred)))&
((~rich(john)&kind(john)))&
(?[X]:((~happy(X)|curious(X))))&
((curious(lucy)<~>strong(lucy)))&
((~kind(lucy)&~wise(lucy)))&
(?[X]:((happy(X)<~>generous(X)))) | tall(paul) | [
"p0",
"p2",
"p3",
"p6",
"p9",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2699378771993452884159927
% SZS output start Proof for 2699378771993452884159927
1. (~old(paul) <~> ~wise(paul)) => (~patient(paul) <~> ~wise(paul)) [input p0]
3. ? [X0] : (~tall(X0) <~> ~old(X0)) => ? [X0] : happy(X0) [input p2]
4. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (~kind(X0) <~> ~brave(X0))) [input p3]
7. ! [X0] : ((tall(X0) | humble(X0)) <=> ~strong(X0)) [input p6]
10. ! [X0] : ((quiet(X0) | ~funny(X0)) <=> (kind(X0) <~> brave(X0))) [input p9]
11. ! [X0] : ((patient(X0) & ~kind(X0)) => (humble(X0) & ~funny(X0))) [input p10]
12. ! [X0] : ((old(X0) | calm(X0)) => (kind(X0) <~> ~brave(X0))) [input p11]
15. ! [X0] : ((creative(X0) | ~wise(X0)) => (~happy(X0) & ~rich(X0))) [input p14]
16. ! [X0] : (~brave(X0) <=> (~strong(X0) | happy(X0))) [input p15]
23. tall(paul) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> ~old(X0)) => ? [X1] : happy(X1) [rectify 3]
25. ! [X0] : (old(X0) => (kind(X0) <~> ~brave(X0))) [pure predicate removal 12]
26. (~patient(paul) <~> ~wise(paul)) | (~old(paul) <=> ~wise(paul)) [ennf transformation 1]
27. ? [X1] : happy(X1) | ! [X0] : (~tall(X0) <=> ~old(X0)) [ennf transformation 24]
32. ! [X0] : ((humble(X0) & ~funny(X0)) | (~patient(X0) | kind(X0))) [ennf transformation 11]
33. ! [X0] : ((humble(X0) & ~funny(X0)) | ~patient(X0) | kind(X0)) [flattening 32]
34. ! [X0] : ((kind(X0) <~> ~brave(X0)) | ~old(X0)) [ennf transformation 25]
36. ! [X0] : ((~happy(X0) & ~rich(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 15]
37. ((wise(paul) | patient(paul)) & (~wise(paul) | ~patient(paul))) | ((~old(paul) | wise(paul)) & (~wise(paul) | old(paul))) [nnf transformation 26]
43. ? [X1] : happy(X1) | ! [X0] : ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))) [nnf transformation 27]
44. ? [X0] : happy(X0) | ! [X1] : ((~tall(X1) | old(X1)) & (~old(X1) | tall(X1))) [rectify 43]
45. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
46. happy(sK1) | ! [X1] : ((~tall(X1) | old(X1)) & (~old(X1) | tall(X1))) [skolemisation 44,45]
47. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 4]
57. ! [X0] : (((tall(X0) | humble(X0)) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~humble(X0)))) [nnf transformation 7]
58. ! [X0] : ((tall(X0) | humble(X0) | strong(X0)) & (~strong(X0) | (~tall(X0) & ~humble(X0)))) [flattening 57]
60. ! [X0] : (((quiet(X0) | ~funny(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (~quiet(X0) & funny(X0)))) [nnf transformation 10]
61. ! [X0] : ((quiet(X0) | ~funny(X0) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | (~quiet(X0) & funny(X0)))) [flattening 60]
62. ! [X0] : (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~old(X0)) [nnf transformation 34]
67. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | brave(X0))) [nnf transformation 16]
68. ! [X0] : ((~brave(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | brave(X0))) [flattening 67]
79. wise(paul) | patient(paul) | ~old(paul) | wise(paul) [cnf transformation 37]
85. happy(sK1) | ~tall(X1) | old(X1) [cnf transformation 46]
89. brave(X0) | kind(X0) | kind(X0) | ~wise(X0) [cnf transformation 47]
93. ~wise(X0) | ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 47]
103. ~tall(X0) | ~strong(X0) [cnf transformation 58]
109. funny(X0) | kind(X0) | brave(X0) [cnf transformation 61]
115. ~funny(X0) | ~patient(X0) | kind(X0) [cnf transformation 33]
118. ~kind(X0) | brave(X0) | ~old(X0) [cnf transformation 62]
133. ~happy(X0) | wise(X0) [cnf transformation 36]
136. ~happy(X0) | ~brave(X0) [cnf transformation 68]
137. ~brave(X0) | strong(X0) [cnf transformation 68]
149. tall(paul) [cnf transformation 23]
151. brave(X0) | kind(X0) | ~wise(X0) [duplicate literal removal 89]
153. ~kind(X0) | ~wise(X0) | brave(X0) [duplicate literal removal 93]
155. wise(paul) | patient(paul) | ~old(paul) [duplicate literal removal 79]
157. 1 <=> old(paul) [avatar definition]
158. old(paul) <- (1) [avatar component clause 157]
159. ~old(paul) <- (~1) [avatar component clause 157]
161. 2 <=> patient(paul) [avatar definition]
163. patient(paul) <- (2) [avatar component clause 161]
165. 3 <=> wise(paul) [avatar definition]
167. wise(paul) <- (3) [avatar component clause 165]
168. ~1 | 2 | 3 [avatar split clause 155,165,161,157]
189. 8 <=> ! [X1] : (~brave(X1) | strong(X1)) [avatar definition]
190. ~brave(X1) | strong(X1) <- (8) [avatar component clause 189]
194. 9 <=> ! [X1] : (~tall(X1) | old(X1)) [avatar definition]
195. ~tall(X1) | old(X1) <- (9) [avatar component clause 194]
197. 10 <=> happy(sK1) [avatar definition]
199. happy(sK1) <- (10) [avatar component clause 197]
200. 9 | 10 [avatar split clause 85,197,194]
205. ~wise(X0) | brave(X0) [subsumption resolution 151,153]
318. 8 [avatar split clause 137,189]
353. ~strong(paul) [resolution 103,149]
363. old(paul) <- (9) [resolution 195,149]
364. $false <- (~1, 9) [subsumption resolution 363,159]
365. 1 | ~9 [avatar contradiction clause 364]
368. ~brave(sK1) <- (10) [resolution 199,136]
370. wise(sK1) <- (10) [resolution 199,133]
374. brave(sK1) <- (10) [resolution 370,205]
375. $false <- (10) [subsumption resolution 374,368]
376. ~10 [avatar contradiction clause 375]
378. brave(paul) <- (3) [resolution 167,205]
384. strong(paul) <- (3, 8) [resolution 378,190]
385. $false <- (3, 8) [subsumption resolution 384,353]
386. ~3 | ~8 [avatar contradiction clause 385]
415. ~patient(X0) | kind(X0) | kind(X0) | brave(X0) [resolution 115,109]
416. ~patient(X0) | kind(X0) | brave(X0) [duplicate literal removal 415]
435. 44 <=> kind(paul) [avatar definition]
437. kind(paul) <- (44) [avatar component clause 435]
492. brave(paul) | ~old(paul) <- (44) [resolution 437,118]
494. brave(paul) <- (1, 44) [subsumption resolution 492,158]
540. kind(paul) | brave(paul) <- (2) [resolution 416,163]
585. strong(paul) <- (1, 8, 44) [resolution 494,190]
588. $false <- (1, 8, 44) [subsumption resolution 585,353]
589. ~1 | ~8 | ~44 [avatar contradiction clause 588]
591. 55 <=> brave(paul) [avatar definition]
593. brave(paul) <- (55) [avatar component clause 591]
594. 55 | 44 | ~2 [avatar split clause 540,161,435,591]
617. strong(paul) <- (8, 55) [resolution 593,190]
626. $false <- (8, 55) [subsumption resolution 617,353]
627. ~8 | ~55 [avatar contradiction clause 626]
628. $false [avatar sat refutation 168,200,318,365,376,386,589,594,627]
% SZS output end Proof for 2699378771993452884159927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not funny is both not tall and happy and vice versa. Everyone who is tall is not patient or not kind and vice versa. Everyone who is both not brave and not tall is either rich or calm and vice versa. Everyone who is either creative or kind is both quiet and rich. If lucy is old or not patient then someone is both brave and generous and vice versa. Everyone who is both not curious and not funny is not rich. Everyone who is old or not kind is both not curious and kind. If susan is either humble or not brave then paul is either not strong or not generous and vice versa. Everyone who is calm or funny is not strong. Everyone who is both old and not rich is either not brave or not quiet and vice versa. If someone is calm or not patient then fred is either not tall or not wise and vice versa. Everyone who is not creative or calm is calm or not quiet and vice versa. If someone is happy then someone is brave or wise. Everyone who is kind is either patient or not creative. Everyone who is both not curious and not quiet is both not old and funny and vice versa. Everyone who is not brave is not generous or not old and vice versa. Someone is rich or curious. Mary is not rich. Someone is both not patient and calm. Someone is curious or not humble. Someone is both quiet and not patient. Mary is either not tall or wise. | Lucy is not quiet. | contradiction | (![X]:((~tall(X)<~>~funny(X))<=>(~tall(X)&happy(X))))&
(![X]:(tall(X)<=>(~patient(X)|~kind(X))))&
(![X]:((~brave(X)&~tall(X))<=>(rich(X)<~>calm(X))))&
(![X]:((creative(X)<~>kind(X))=>(quiet(X)&rich(X))))&
(((old(lucy)|~patient(lucy)))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:((old(X)|~kind(X))=>(~curious(X)&kind(X))))&
(((humble(susan)<~>~brave(susan)))<=>((~strong(paul)<~>~generous(paul))))&
(![X]:((calm(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)&~rich(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((calm(X)|~patient(X))))<=>((~tall(fred)<~>~wise(fred))))&
(![X]:((~creative(X)|calm(X))<=>(calm(X)|~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(kind(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~old(X)&funny(X))))&
(![X]:(~brave(X)<=>(~generous(X)|~old(X))))&
(?[X]:((rich(X)|curious(X))))&
(~rich(mary))&
(?[X]:((~patient(X)&calm(X))))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~patient(X))))&
((~tall(mary)<~>wise(mary))) | ~quiet(lucy) | [
"p3",
"p4",
"p6",
"p9",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 60785607387969641498924
% SZS output start Proof for 60785607387969641498924
4. ! [X0] : ((creative(X0) <~> kind(X0)) => (rich(X0) & quiet(X0))) [input p3]
5. (~patient(lucy) | old(lucy)) <=> ? [X0] : (generous(X0) & brave(X0)) [input p4]
7. ! [X0] : ((~kind(X0) | old(X0)) => (kind(X0) & ~curious(X0))) [input p6]
10. ! [X0] : ((~rich(X0) & old(X0)) <=> (~brave(X0) <~> ~quiet(X0))) [input p9]
14. ! [X0] : (kind(X0) => (patient(X0) <~> ~creative(X0))) [input p13]
15. ! [X0] : ((~quiet(X0) & ~curious(X0)) <=> (funny(X0) & ~old(X0))) [input p14]
16. ! [X0] : (~brave(X0) <=> (~old(X0) | ~generous(X0))) [input p15]
19. ? [X0] : (calm(X0) & ~patient(X0)) [input p18]
23. ~quiet(lucy) [input hypothesis]
25. ! [X0] : ((rich(X0) & quiet(X0)) | (creative(X0) <=> kind(X0))) [ennf transformation 4]
28. ! [X0] : ((kind(X0) & ~curious(X0)) | (kind(X0) & ~old(X0))) [ennf transformation 7]
31. ! [X0] : ((patient(X0) <~> ~creative(X0)) | ~kind(X0)) [ennf transformation 14]
38. ! [X0] : ((rich(X0) & quiet(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0)))) [nnf transformation 25]
39. ((~patient(lucy) | old(lucy)) | ! [X0] : (~generous(X0) | ~brave(X0))) & (? [X0] : (generous(X0) & brave(X0)) | (patient(lucy) & ~old(lucy))) [nnf transformation 5]
40. (~patient(lucy) | old(lucy) | ! [X0] : (~generous(X0) | ~brave(X0))) & (? [X0] : (generous(X0) & brave(X0)) | (patient(lucy) & ~old(lucy))) [flattening 39]
41. (~patient(lucy) | old(lucy) | ! [X0] : (~generous(X0) | ~brave(X0))) & (? [X1] : (generous(X1) & brave(X1)) | (patient(lucy) & ~old(lucy))) [rectify 40]
42. ? [X1] : (generous(X1) & brave(X1)) => (generous(sK0) & brave(sK0)) [choice axiom]
43. (~patient(lucy) | old(lucy) | ! [X0] : (~generous(X0) | ~brave(X0))) & ((generous(sK0) & brave(sK0)) | (patient(lucy) & ~old(lucy))) [skolemisation 41,42]
45. ! [X0] : (((~rich(X0) & old(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0)))) & (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (rich(X0) | ~old(X0)))) [nnf transformation 10]
46. ! [X0] : (((~rich(X0) & old(X0)) | ((~brave(X0) | quiet(X0)) & (~quiet(X0) | brave(X0)))) & (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | rich(X0) | ~old(X0))) [flattening 45]
56. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ~kind(X0)) [nnf transformation 31]
57. ! [X0] : (((~quiet(X0) & ~curious(X0)) | (~funny(X0) | old(X0))) & ((funny(X0) & ~old(X0)) | (quiet(X0) | curious(X0)))) [nnf transformation 15]
58. ! [X0] : (((~quiet(X0) & ~curious(X0)) | ~funny(X0) | old(X0)) & ((funny(X0) & ~old(X0)) | quiet(X0) | curious(X0))) [flattening 57]
59. ! [X0] : ((~brave(X0) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | brave(X0))) [nnf transformation 16]
60. ! [X0] : ((~brave(X0) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | brave(X0))) [flattening 59]
63. ? [X0] : (calm(X0) & ~patient(X0)) => (calm(sK4) & ~patient(sK4)) [choice axiom]
64. calm(sK4) & ~patient(sK4) [skolemisation 19,63]
86. ~kind(X0) | creative(X0) | quiet(X0) [cnf transformation 38]
88. ~kind(X0) | creative(X0) | rich(X0) [cnf transformation 38]
93. ~patient(lucy) | old(lucy) | ~generous(X0) | ~brave(X0) [cnf transformation 43]
95. ~curious(X0) | ~old(X0) [cnf transformation 28]
98. kind(X0) | kind(X0) [cnf transformation 28]
113. ~quiet(X0) | ~rich(X0) | brave(X0) [cnf transformation 46]
126. ~creative(X0) | patient(X0) | ~kind(X0) [cnf transformation 56]
128. ~old(X0) | quiet(X0) | curious(X0) [cnf transformation 58]
133. ~brave(X0) | generous(X0) [cnf transformation 60]
137. ~patient(sK4) [cnf transformation 64]
144. ~quiet(lucy) [cnf transformation 23]
145. kind(X0) [duplicate literal removal 98]
149. 1 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
150. ~generous(X0) | ~brave(X0) <- (1) [avatar component clause 149]
152. 2 <=> old(lucy) [avatar definition]
154. old(lucy) <- (2) [avatar component clause 152]
156. 3 <=> patient(lucy) [avatar definition]
159. 1 | 2 | ~3 [avatar split clause 93,156,152,149]
215. 14 <=> ! [X1] : patient(X1) [avatar definition]
216. patient(X1) <- (14) [avatar component clause 215]
237. ~creative(X0) | patient(X0) [subsumption resolution 126,145]
239. ~old(X0) | quiet(X0) [subsumption resolution 128,95]
325. quiet(X1) | creative(X1) [resolution 86,145]
327. creative(lucy) [resolution 325,144]
329. creative(X1) | rich(X1) [resolution 88,145]
332. patient(lucy) [resolution 327,237]
335. 3 [avatar split clause 332,156]
336. ~brave(X0) <- (1) [subsumption resolution 150,133]
370. ~rich(X0) | brave(X0) | creative(X0) [resolution 113,325]
372. ~rich(X0) | creative(X0) <- (1) [subsumption resolution 370,336]
373. creative(X0) <- (1) [subsumption resolution 372,329]
387. patient(X3) <- (1) [resolution 373,237]
388. 14 | ~1 [avatar split clause 387,149,215]
392. $false <- (14) [resolution 216,137]
395. ~14 [avatar contradiction clause 392]
408. quiet(lucy) <- (2) [resolution 154,239]
409. $false <- (2) [subsumption resolution 408,144]
410. ~2 [avatar contradiction clause 409]
411. $false [avatar sat refutation 159,335,388,395,410]
% SZS output end Proof for 60785607387969641498924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then someone is either not funny or not quiet and vice versa.
Everyone who is not quiet or not rich is either wise or not happy.
If paul is both tall and not old then someone is brave or creative.
Everyone who is both not strong and not creative is not strong or not tall and vice versa.
Everyone who is calm is not creative or old.
If someone is either not quiet or calm then fred is old or not brave.
Everyone who is either not tall or humble is either not funny or kind.
Everyone who is either not brave or not generous is either quiet or not funny.
If mary is either not kind or tall then john is both not generous and not brave and vice versa.
If paul is not strong or not brave then someone is not calm.
If mary is both funny and patient then someone is either not happy or wise.
Everyone who is either old or rich is either not brave or rich and vice versa.
If someone is either tall or not curious then someone is strong and vice versa.
If mary is not funny then someone is not quiet or creative and vice versa.
If lucy is either not kind or not strong then alice is not creative or rich.
Everyone who is brave is either patient or not generous.
Susan is not strong or humble.
Fred is not creative or brave.
John is creative.
Someone is either creative or not quiet.
Susan is tall.
Someone is either kind or not quiet.
Someone is not brave or not curious. | Mary is not rich. | neutral | ((?[X]:(curious(X)))<=>(?[X]:((~funny(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)|~rich(X))=>(wise(X)<~>~happy(X))))&
(((tall(paul)&~old(paul)))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(~strong(X)|~tall(X))))&
(![X]:(calm(X)=>(~creative(X)|old(X))))&
((?[X]:((~quiet(X)<~>calm(X))))=>((old(fred)|~brave(fred))))&
(![X]:((~tall(X)<~>humble(X))=>(~funny(X)<~>kind(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(quiet(X)<~>~funny(X))))&
(((~kind(mary)<~>tall(mary)))<=>((~generous(john)&~brave(john))))&
(((~strong(paul)|~brave(paul)))=>(?[X]:(~calm(X))))&
(((funny(mary)&patient(mary)))=>(?[X]:((~happy(X)<~>wise(X)))))&
(![X]:((old(X)<~>rich(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((tall(X)<~>~curious(X))))<=>(?[X]:(strong(X))))&
((~funny(mary))<=>(?[X]:((~quiet(X)|creative(X)))))&
(((~kind(lucy)<~>~strong(lucy)))=>((~creative(alice)|rich(alice))))&
(![X]:(brave(X)=>(patient(X)<~>~generous(X))))&
((~strong(susan)|humble(susan)))&
((~creative(fred)|brave(fred)))&
(creative(john))&
(?[X]:((creative(X)<~>~quiet(X))))&
(tall(susan))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:((~brave(X)|~curious(X)))) | ~rich(mary) | [] | null | 0 |
Everyone who is either not creative or not old is both not calm and not strong.
If someone is both not humble and creative then someone is both not happy and wise and vice versa.
Everyone who is both not strong and humble is both old and not humble and vice versa.
Everyone who is not kind or not creative is not creative or wise.
Everyone who is both not patient and not wise is not creative and vice versa.
Everyone who is both not tall and not happy is strong.
If alice is both not curious and creative then someone is both generous and not funny and vice versa.
Everyone who is not strong or not creative is both funny and not kind.
If susan is not kind or not rich then someone is both old and not old.
Everyone who is either not patient or creative is both not wise and not creative.
If alice is not brave then fred is either not humble or strong and vice versa.
Everyone who is either old or happy is either not calm or calm.
Everyone who is not happy or creative is either calm or not old.
Everyone who is not brave or creative is both old and happy.
If paul is either not calm or not curious then mary is not brave.
If paul is either not happy or not generous then john is calm.
Someone is kind.
Paul is both curious and not quiet.
John is either not calm or not old.
Someone is both tall and not creative.
Someone is not patient.
Alice is both strong and generous. | Susan is not humble. | contradiction | (![X]:((~creative(X)<~>~old(X))=>(~calm(X)&~strong(X))))&
((?[X]:((~humble(X)&creative(X))))<=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:((~strong(X)&humble(X))<=>(old(X)&~humble(X))))&
(![X]:((~kind(X)|~creative(X))=>(~creative(X)|wise(X))))&
(![X]:((~patient(X)&~wise(X))<=>~creative(X)))&
(![X]:((~tall(X)&~happy(X))=>strong(X)))&
(((~curious(alice)&creative(alice)))<=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:((~strong(X)|~creative(X))=>(funny(X)&~kind(X))))&
(((~kind(susan)|~rich(susan)))=>(?[X]:((old(X)&~old(X)))))&
(![X]:((~patient(X)<~>creative(X))=>(~wise(X)&~creative(X))))&
((~brave(alice))<=>((~humble(fred)<~>strong(fred))))&
(![X]:((old(X)<~>happy(X))=>(~calm(X)<~>calm(X))))&
(![X]:((~happy(X)|creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((~brave(X)|creative(X))=>(old(X)&happy(X))))&
(((~calm(paul)<~>~curious(paul)))=>(~brave(mary)))&
(((~happy(paul)<~>~generous(paul)))=>(calm(john)))&
(?[X]:(kind(X)))&
((curious(paul)&~quiet(paul)))&
((~calm(john)<~>~old(john)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:(~patient(X)))&
((strong(alice)&generous(alice))) | ~humble(susan) | [
"p1",
"p2",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5768317838559446556172104
% SZS output start Proof for 5768317838559446556172104
2. ? [X0] : (creative(X0) & ~humble(X0)) <=> ? [X0] : (wise(X0) & ~happy(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~strong(X0)) <=> (~humble(X0) & old(X0))) [input p2]
8. ! [X0] : ((~creative(X0) | ~strong(X0)) => (~kind(X0) & funny(X0))) [input p7]
9. (~rich(susan) | ~kind(susan)) => ? [X0] : (~old(X0) & old(X0)) [input p8]
14. ! [X0] : ((creative(X0) | ~brave(X0)) => (happy(X0) & old(X0))) [input p13]
23. ~humble(susan) [input hypothesis]
24. ? [X0] : (creative(X0) & ~humble(X0)) <=> ? [X1] : (wise(X1) & ~happy(X1)) [rectify 2]
26. ~kind(susan) => ? [X0] : (~old(X0) & old(X0)) [pure predicate removal 9]
32. ! [X0] : ((~kind(X0) & funny(X0)) | (creative(X0) & strong(X0))) [ennf transformation 8]
33. ? [X0] : (~old(X0) & old(X0)) | kind(susan) [ennf transformation 26]
37. ! [X0] : ((happy(X0) & old(X0)) | (~creative(X0) & brave(X0))) [ennf transformation 14]
41. (? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : (~wise(X1) | happy(X1))) & (? [X1] : (wise(X1) & ~happy(X1)) | ! [X0] : (~creative(X0) | humble(X0))) [nnf transformation 24]
42. (? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : (~wise(X1) | happy(X1))) & (? [X2] : (wise(X2) & ~happy(X2)) | ! [X3] : (~creative(X3) | humble(X3))) [rectify 41]
43. ? [X0] : (creative(X0) & ~humble(X0)) => (creative(sK0) & ~humble(sK0)) [choice axiom]
44. ? [X2] : (wise(X2) & ~happy(X2)) => (wise(sK1) & ~happy(sK1)) [choice axiom]
45. ((creative(sK0) & ~humble(sK0)) | ! [X1] : (~wise(X1) | happy(X1))) & ((wise(sK1) & ~happy(sK1)) | ! [X3] : (~creative(X3) | humble(X3))) [skolemisation 42,44,43]
46. ! [X0] : (((humble(X0) & ~strong(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (~humble(X0) | strong(X0)))) [nnf transformation 3]
47. ! [X0] : (((humble(X0) & ~strong(X0)) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | ~humble(X0) | strong(X0))) [flattening 46]
55. ? [X0] : (~old(X0) & old(X0)) => (~old(sK3) & old(sK3)) [choice axiom]
56. (~old(sK3) & old(sK3)) | kind(susan) [skolemisation 33,55]
74. ~happy(sK1) | ~creative(X3) | humble(X3) [cnf transformation 45]
75. wise(sK1) | ~creative(X3) | humble(X3) [cnf transformation 45]
76. ~humble(sK0) | ~wise(X1) | happy(X1) [cnf transformation 45]
77. creative(sK0) | ~wise(X1) | happy(X1) [cnf transformation 45]
81. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 47]
94. ~kind(X0) | creative(X0) [cnf transformation 32]
95. old(sK3) | kind(susan) [cnf transformation 56]
96. ~old(sK3) | kind(susan) [cnf transformation 56]
114. ~creative(X0) | old(X0) [cnf transformation 37]
129. ~humble(susan) [cnf transformation 23]
132. ~old(X0) | humble(X0) [duplicate literal removal 81]
134. 1 <=> ! [X1] : (~wise(X1) | happy(X1)) [avatar definition]
135. ~wise(X1) | happy(X1) <- (1) [avatar component clause 134]
137. 2 <=> creative(sK0) [avatar definition]
139. creative(sK0) <- (2) [avatar component clause 137]
140. 1 | 2 [avatar split clause 77,137,134]
142. 3 <=> humble(sK0) [avatar definition]
144. ~humble(sK0) <- (~3) [avatar component clause 142]
145. 1 | ~3 [avatar split clause 76,142,134]
147. 4 <=> ! [X3] : (~creative(X3) | humble(X3)) [avatar definition]
148. ~creative(X3) | humble(X3) <- (4) [avatar component clause 147]
150. 5 <=> wise(sK1) [avatar definition]
152. wise(sK1) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 75,150,147]
155. 6 <=> happy(sK1) [avatar definition]
157. ~happy(sK1) <- (~6) [avatar component clause 155]
158. 4 | ~6 [avatar split clause 74,155,147]
183. 12 <=> kind(susan) [avatar definition]
185. kind(susan) <- (12) [avatar component clause 183]
187. 13 <=> old(sK3) [avatar definition]
190. 12 | ~13 [avatar split clause 96,187,183]
191. 12 | 13 [avatar split clause 95,187,183]
248. creative(susan) <- (12) [resolution 94,185]
251. old(sK0) <- (2) [resolution 114,139]
261. humble(sK0) <- (2) [resolution 251,132]
262. $false <- (2, ~3) [subsumption resolution 261,144]
263. ~2 | 3 [avatar contradiction clause 262]
264. humble(susan) <- (4, 12) [resolution 148,248]
266. $false <- (4, 12) [subsumption resolution 264,129]
267. ~4 | ~12 [avatar contradiction clause 266]
268. happy(sK1) <- (1, 5) [resolution 152,135]
270. $false <- (1, 5, ~6) [subsumption resolution 268,157]
271. ~1 | ~5 | 6 [avatar contradiction clause 270]
272. $false [avatar sat refutation 140,145,153,158,190,191,263,267,271]
% SZS output end Proof for 5768317838559446556172104
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or funny is not old and vice versa. If someone is not humble or not generous then someone is both not humble and kind and vice versa. Everyone who is not quiet is both happy and humble. If someone is both not brave and not quiet then john is both not strong and kind and vice versa. If mary is not creative or not quiet then someone is both not wise and curious and vice versa. If lucy is either not generous or not calm then paul is patient. Everyone who is both not curious and not old is both creative and strong and vice versa. Everyone who is both humble and happy is either creative or old. Everyone who is either not creative or tall is not calm or not kind. Everyone who is not curious or quiet is not brave or not generous. If john is old then john is either not funny or not curious and vice versa. Everyone who is strong or rich is both funny and old and vice versa. If fred is both not calm and not curious then mary is not curious or tall and vice versa. Everyone who is either creative or not humble is both not curious and creative and vice versa. Everyone who is both creative and brave is brave or not old and vice versa. If fred is both patient and not generous then someone is either not kind or not generous and vice versa. Someone is not kind. Paul is happy. Mary is humble or not kind. Someone is wise or kind. Mary is wise or happy. Susan is either brave or calm. Someone is both not kind and funny. | Paul is curious. | entailment | (![X]:((old(X)|funny(X))<=>~old(X)))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:((~humble(X)&kind(X)))))&
(![X]:(~quiet(X)=>(happy(X)&humble(X))))&
((?[X]:((~brave(X)&~quiet(X))))<=>((~strong(john)&kind(john))))&
(((~creative(mary)|~quiet(mary)))<=>(?[X]:((~wise(X)&curious(X)))))&
(((~generous(lucy)<~>~calm(lucy)))=>(patient(paul)))&
(![X]:((~curious(X)&~old(X))<=>(creative(X)&strong(X))))&
(![X]:((humble(X)&happy(X))=>(creative(X)<~>old(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~calm(X)|~kind(X))))&
(![X]:((~curious(X)|quiet(X))=>(~brave(X)|~generous(X))))&
((old(john))<=>((~funny(john)<~>~curious(john))))&
(![X]:((strong(X)|rich(X))<=>(funny(X)&old(X))))&
(((~calm(fred)&~curious(fred)))<=>((~curious(mary)|tall(mary))))&
(![X]:((creative(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:((creative(X)&brave(X))<=>(brave(X)|~old(X))))&
(((patient(fred)&~generous(fred)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(?[X]:(~kind(X)))&
(happy(paul))&
((humble(mary)|~kind(mary)))&
(?[X]:((wise(X)|kind(X))))&
((wise(mary)|happy(mary)))&
((brave(susan)<~>calm(susan)))&
(?[X]:((~kind(X)&funny(X)))) | curious(paul) | [
"p0",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 504494994806351375799404
% SZS output start Proof for 504494994806351375799404
1. ! [X0] : ((funny(X0) | old(X0)) <=> ~old(X0)) [input p0]
7. ! [X0] : ((~old(X0) & ~curious(X0)) <=> (strong(X0) & creative(X0))) [input p6]
12. ! [X0] : ((rich(X0) | strong(X0)) <=> (old(X0) & funny(X0))) [input p11]
24. ~curious(paul) [input hypothesis]
34. ! [X0] : (((funny(X0) | old(X0)) | old(X0)) & (~old(X0) | (~funny(X0) & ~old(X0)))) [nnf transformation 1]
35. ! [X0] : ((funny(X0) | old(X0) | old(X0)) & (~old(X0) | (~funny(X0) & ~old(X0)))) [flattening 34]
52. ! [X0] : (((~old(X0) & ~curious(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (old(X0) | curious(X0)))) [nnf transformation 7]
53. ! [X0] : (((~old(X0) & ~curious(X0)) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | old(X0) | curious(X0))) [flattening 52]
57. ! [X0] : (((rich(X0) | strong(X0)) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 12]
58. ! [X0] : ((rich(X0) | strong(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | (~rich(X0) & ~strong(X0)))) [flattening 57]
77. ~old(X0) | ~old(X0) [cnf transformation 35]
99. strong(X0) | old(X0) | curious(X0) [cnf transformation 53]
114. old(X0) | ~strong(X0) [cnf transformation 58]
148. ~curious(paul) [cnf transformation 24]
151. ~old(X0) [duplicate literal removal 77]
244. curious(X0) | strong(X0) [subsumption resolution 99,151]
258. ~strong(X0) [subsumption resolution 114,151]
351. strong(paul) [resolution 244,148]
356. $false [subsumption resolution 351,258]
% SZS output end Proof for 504494994806351375799404
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is not rich.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Someone is funny.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is rich.
Someone is not humble or not strong. | Fred is calm. | entailment | (![X]:((strong(X)|~wise(X))=>~rich(X)))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(funny(X)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)|~strong(X)))) | calm(fred) | [
"p0",
"p1",
"p4",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7985576739479275622385591
% SZS output start Proof for 7985576739479275622385591
1. ! [X0] : ((~wise(X0) | strong(X0)) => ~rich(X0)) [input p0]
2. ! [X0] : (old(X0) <=> ~rich(X0)) [input p1]
5. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) | generous(X0))) [input p4]
10. ! [X0] : (funny(X0) <=> (~calm(X0) <~> ~old(X0))) [input p9]
14. ! [X0] : ((~rich(X0) <~> wise(X0)) => calm(X0)) [input p13]
16. ! [X0] : ((wise(X0) & kind(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p15]
23. ~calm(fred) [input hypothesis]
25. ! [X0] : (~wise(X0) => ~rich(X0)) [pure predicate removal 1]
27. ! [X0] : (~rich(X0) | wise(X0)) [ennf transformation 25]
34. ! [X0] : (calm(X0) | (~rich(X0) <=> wise(X0))) [ennf transformation 14]
36. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 5]
40. ! [X0] : ((rich(X0) | ~old(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | (~rich(X0) & old(X0)))) [flattening 39]
48. ! [X0] : ((funny(X0) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~funny(X0))) [nnf transformation 10]
55. ! [X0] : (calm(X0) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0)))) [nnf transformation 34]
57. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (~wise(X0) | ~kind(X0)))) [nnf transformation 16]
58. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | ~wise(X0) | ~kind(X0))) [flattening 57]
70. ~rich(X0) | wise(X0) [cnf transformation 27]
71. ~old(X0) | ~rich(X0) [cnf transformation 36]
72. old(X0) | rich(X0) [cnf transformation 36]
79. rich(X0) | ~old(X0) | ~generous(X0) [cnf transformation 40]
80. rich(X0) | ~old(X0) | kind(X0) [cnf transformation 40]
94. ~funny(X0) | calm(X0) | old(X0) [cnf transformation 48]
95. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 48]
108. calm(X0) | wise(X0) | rich(X0) [cnf transformation 55]
109. calm(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 55]
114. ~funny(X0) | generous(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 58]
117. funny(X0) | generous(X0) | kind(X0) [cnf transformation 58]
128. ~calm(fred) [cnf transformation 23]
131. ~old(X0) | kind(X0) [subsumption resolution 80,71]
132. ~generous(X0) | ~old(X0) [subsumption resolution 79,71]
205. ~rich(X0) | calm(X0) [subsumption resolution 109,70]
206. calm(X0) | wise(X0) [subsumption resolution 108,205]
238. 22 <=> calm(fred) [avatar definition]
239. ~calm(fred) <- (~22) [avatar component clause 238]
249. ~22 [avatar split clause 128,238]
259. wise(fred) <- (~22) [resolution 206,239]
390. funny(X0) | calm(X0) | rich(X0) [resolution 95,72]
391. calm(X0) | funny(X0) [subsumption resolution 390,205]
425. generous(X1) | kind(X1) | calm(X1) | old(X1) [resolution 117,94]
437. calm(X1) | kind(X1) | generous(X1) [subsumption resolution 425,131]
522. funny(fred) <- (~22) [resolution 391,239]
559. kind(fred) | generous(fred) <- (~22) [resolution 437,239]
563. 56 <=> generous(fred) [avatar definition]
565. generous(fred) <- (56) [avatar component clause 563]
567. 57 <=> kind(fred) [avatar definition]
569. kind(fred) <- (57) [avatar component clause 567]
570. 56 | 57 | 22 [avatar split clause 559,238,567,563]
709. generous(fred) | ~wise(fred) | ~kind(fred) <- (~22) [resolution 522,114]
712. calm(fred) | old(fred) <- (~22) [resolution 522,94]
715. old(fred) <- (~22) [subsumption resolution 712,239]
716. ~old(fred) <- (56) [resolution 565,132]
717. $false <- (~22, 56) [subsumption resolution 716,715]
718. 22 | ~56 [avatar contradiction clause 717]
719. generous(fred) | ~kind(fred) <- (~22) [subsumption resolution 709,259]
720. generous(fred) <- (~22, 57) [subsumption resolution 719,569]
721. 56 | 22 | ~57 [avatar split clause 720,567,238,563]
722. $false [avatar sat refutation 249,570,718,721]
% SZS output end Proof for 7985576739479275622385591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or wise is both not patient and generous and vice versa.
Everyone who is either not curious or old is either rich or not kind and vice versa.
If paul is not strong then someone is either creative or not creative and vice versa.
Everyone who is kind or curious is both tall and creative and vice versa.
Everyone who is happy or not quiet is brave.
Everyone who is creative is not rich or not quiet and vice versa.
If lucy is not calm then someone is either not wise or wise.
If lucy is both not happy and not humble then lucy is not quiet and vice versa.
If someone is not generous or not strong then fred is both kind and old and vice versa.
If someone is patient or not creative then someone is either humble or not patient and vice versa.
If someone is not old then alice is both not humble and humble and vice versa.
If someone is brave or quiet then someone is not curious and vice versa.
If someone is not humble then someone is either old or funny.
Everyone who is both not tall and happy is both funny and not tall and vice versa.
If someone is either wise or not curious then someone is both not calm and curious and vice versa.
If john is both quiet and not calm then alice is both not quiet and rich.
Someone is not tall.
Susan is not rich or not brave.
Susan is either curious or not rich.
Someone is either not funny or curious.
Mary is both not quiet and calm.
Someone is either not rich or not happy.
Someone is either humble or not quiet. | Paul is not happy. | neutral | (![X]:((rich(X)|wise(X))<=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)<~>old(X))<=>(rich(X)<~>~kind(X))))&
((~strong(paul))<=>(?[X]:((creative(X)<~>~creative(X)))))&
(![X]:((kind(X)|curious(X))<=>(tall(X)&creative(X))))&
(![X]:((happy(X)|~quiet(X))=>brave(X)))&
(![X]:(creative(X)<=>(~rich(X)|~quiet(X))))&
((~calm(lucy))=>(?[X]:((~wise(X)<~>wise(X)))))&
(((~happy(lucy)&~humble(lucy)))<=>(~quiet(lucy)))&
((?[X]:((~generous(X)|~strong(X))))<=>((kind(fred)&old(fred))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((humble(X)<~>~patient(X)))))&
((?[X]:(~old(X)))<=>((~humble(alice)&humble(alice))))&
((?[X]:((brave(X)|quiet(X))))<=>(?[X]:(~curious(X))))&
((?[X]:(~humble(X)))=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~tall(X)&happy(X))<=>(funny(X)&~tall(X))))&
((?[X]:((wise(X)<~>~curious(X))))<=>(?[X]:((~calm(X)&curious(X)))))&
(((quiet(john)&~calm(john)))=>((~quiet(alice)&rich(alice))))&
(?[X]:(~tall(X)))&
((~rich(susan)|~brave(susan)))&
((curious(susan)<~>~rich(susan)))&
(?[X]:((~funny(X)<~>curious(X))))&
((~quiet(mary)&calm(mary)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((humble(X)<~>~quiet(X)))) | ~happy(paul) | [] | null | 0 |
Everyone who is either not rich or creative is either happy or generous. Everyone who is not tall is not kind or rich. If mary is tall or not calm then someone is not calm or not happy and vice versa. Everyone who is not old is generous. Everyone who is rich or not patient is not tall and vice versa. If someone is both not rich and kind then fred is either rich or not generous and vice versa. Everyone who is patient or not curious is either not tall or kind. If someone is not old then john is either quiet or strong and vice versa. If someone is not humble or wise then someone is both kind and humble and vice versa. If paul is humble then susan is quiet. If someone is not calm or calm then john is old. If fred is not brave then someone is happy and vice versa. Everyone who is both kind and not creative is creative or calm. If lucy is kind then alice is both not happy and not quiet. Everyone who is not calm is not humble. Everyone who is calm is not curious or not calm and vice versa. Alice is not patient. Someone is either not creative or curious. Lucy is not tall. Paul is funny or wise. John is not wise. Susan is calm. | Lucy is kind. | contradiction | (![X]:((~rich(X)<~>creative(X))=>(happy(X)<~>generous(X))))&
(![X]:(~tall(X)=>(~kind(X)|rich(X))))&
(((tall(mary)|~calm(mary)))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~old(X)=>generous(X)))&
(![X]:((rich(X)|~patient(X))<=>~tall(X)))&
((?[X]:((~rich(X)&kind(X))))<=>((rich(fred)<~>~generous(fred))))&
(![X]:((patient(X)|~curious(X))=>(~tall(X)<~>kind(X))))&
((?[X]:(~old(X)))<=>((quiet(john)<~>strong(john))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:((kind(X)&humble(X)))))&
((humble(paul))=>(quiet(susan)))&
((?[X]:((~calm(X)|calm(X))))=>(old(john)))&
((~brave(fred))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)&~creative(X))=>(creative(X)|calm(X))))&
((kind(lucy))=>((~happy(alice)&~quiet(alice))))&
(![X]:(~calm(X)=>~humble(X)))&
(![X]:(calm(X)<=>(~curious(X)|~calm(X))))&
(~patient(alice))&
(?[X]:((~creative(X)<~>curious(X))))&
(~tall(lucy))&
((funny(paul)|wise(paul)))&
(~wise(john))&
(calm(susan)) | kind(lucy) | [
"p6",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 924885443092486550275961
% SZS output start Proof for 924885443092486550275961
7. ! [X0] : ((~curious(X0) | patient(X0)) => (~tall(X0) <~> kind(X0))) [input p6]
16. ! [X0] : (calm(X0) <=> (~calm(X0) | ~curious(X0))) [input p15]
19. ~tall(lucy) [input p18]
23. kind(lucy) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> kind(X0)) | (curious(X0) & ~patient(X0))) [ennf transformation 7]
49. ! [X0] : (((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | (curious(X0) & ~patient(X0))) [nnf transformation 30]
63. ! [X0] : ((calm(X0) | (calm(X0) & curious(X0))) & ((~calm(X0) | ~curious(X0)) | ~calm(X0))) [nnf transformation 16]
64. ! [X0] : ((calm(X0) | (calm(X0) & curious(X0))) & (~calm(X0) | ~curious(X0) | ~calm(X0))) [flattening 63]
90. ~kind(X0) | tall(X0) | curious(X0) [cnf transformation 49]
109. ~calm(X0) | ~curious(X0) | ~calm(X0) [cnf transformation 64]
111. calm(X0) | calm(X0) [cnf transformation 64]
115. ~tall(lucy) [cnf transformation 19]
118. kind(lucy) [cnf transformation 23]
119. ~curious(X0) | ~calm(X0) [duplicate literal removal 109]
120. calm(X0) [duplicate literal removal 111]
135. 4 <=> ! [X0] : calm(X0) [avatar definition]
136. calm(X0) <- (4) [avatar component clause 135]
255. 30 <=> kind(lucy) [avatar definition]
256. kind(lucy) <- (30) [avatar component clause 255]
268. 4 [avatar split clause 120,135]
279. 30 [avatar split clause 118,255]
343. tall(lucy) | curious(lucy) <- (30) [resolution 90,256]
346. curious(lucy) <- (30) [subsumption resolution 343,115]
351. ~calm(lucy) <- (30) [resolution 346,119]
352. $false <- (4, 30) [subsumption resolution 351,136]
353. ~4 | ~30 [avatar contradiction clause 352]
354. $false [avatar sat refutation 268,279,353]
% SZS output end Proof for 924885443092486550275961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or quiet is not brave. Everyone who is either brave or not creative is happy. If someone is both not old and not quiet then someone is calm or not funny. If someone is calm or not calm then alice is not happy and vice versa. Everyone who is not funny is both not happy and not brave and vice versa. Everyone who is creative is not generous and vice versa. If someone is both not tall and humble then john is both quiet and not quiet. Everyone who is not calm is both calm and funny and vice versa. If john is both not rich and happy then someone is not funny or not happy. If someone is either not wise or not patient then lucy is generous and vice versa. If mary is both calm and not brave then someone is kind or not funny and vice versa. Everyone who is either tall or not old is both not happy and not quiet. If someone is not generous then mary is quiet or not rich. If alice is generous or calm then someone is tall. Everyone who is funny or not rich is either creative or not patient. Someone is quiet. Paul is either not rich or wise. Someone is either not funny or rich. Someone is calm. Susan is both wise and old. Mary is wise or funny. Someone is either not strong or happy. Paul is curious. | Susan is wise. | entailment | (![X]:((~happy(X)<~>quiet(X))=>~brave(X)))&
(![X]:((brave(X)<~>~creative(X))=>happy(X)))&
((?[X]:((~old(X)&~quiet(X))))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((calm(X)|~calm(X))))<=>(~happy(alice)))&
(![X]:(~funny(X)<=>(~happy(X)&~brave(X))))&
(![X]:(creative(X)<=>~generous(X)))&
((?[X]:((~tall(X)&humble(X))))=>((quiet(john)&~quiet(john))))&
(![X]:(~calm(X)<=>(calm(X)&funny(X))))&
(((~rich(john)&happy(john)))=>(?[X]:((~funny(X)|~happy(X)))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(generous(lucy)))&
(((calm(mary)&~brave(mary)))<=>(?[X]:((kind(X)|~funny(X)))))&
(![X]:((tall(X)<~>~old(X))=>(~happy(X)&~quiet(X))))&
((?[X]:(~generous(X)))=>((quiet(mary)|~rich(mary))))&
(((generous(alice)|calm(alice)))=>(?[X]:(tall(X))))&
(![X]:((funny(X)|~rich(X))=>(creative(X)<~>~patient(X))))&
(?[X]:(quiet(X)))&
((~rich(paul)<~>wise(paul)))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:(calm(X)))&
((wise(susan)&old(susan)))&
((wise(mary)|funny(mary)))&
(?[X]:((~strong(X)<~>happy(X))))&
(curious(paul)) | wise(susan) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 339245301739110412999862
% SZS output start Proof for 339245301739110412999862
20. old(susan) & wise(susan) [input p19]
24. ~wise(susan) [input hypothesis]
121. wise(susan) [cnf transformation 20]
126. ~wise(susan) [cnf transformation 24]
282. $false [subsumption resolution 126,121]
% SZS output end Proof for 339245301739110412999862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and happy then someone is not quiet or not humble and vice versa.
If paul is not wise or not creative then someone is both strong and not brave and vice versa.
Everyone who is either not brave or brave is either creative or happy and vice versa.
Everyone who is either generous or funny is either wise or curious.
Everyone who is not old or tall is either not creative or humble.
Everyone who is either not patient or kind is either not rich or not funny and vice versa.
Everyone who is not patient is not old.
If paul is creative or happy then susan is not funny and vice versa.
Everyone who is both wise and old is either humble or creative.
If someone is brave or not humble then someone is not rich or not strong and vice versa.
Everyone who is both old and not tall is either not generous or humble.
If someone is both old and not creative then fred is patient or calm.
Everyone who is both creative and not happy is either not brave or quiet and vice versa.
If someone is calm or rich then someone is either not funny or not brave.
Everyone who is either rich or generous is either not creative or not kind.
Everyone who is humble or not happy is both generous and not humble and vice versa.
Mary is funny or rich.
John is funny or happy.
Alice is both funny and quiet.
John is either not funny or not humble.
Someone is both quiet and not patient.
Paul is either not curious or not strong.
Someone is either not wise or not curious. | Susan is not wise. | neutral | ((?[X]:((~brave(X)&happy(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(paul)|~creative(paul)))<=>(?[X]:((strong(X)&~brave(X)))))&
(![X]:((~brave(X)<~>brave(X))<=>(creative(X)<~>happy(X))))&
(![X]:((generous(X)<~>funny(X))=>(wise(X)<~>curious(X))))&
(![X]:((~old(X)|tall(X))=>(~creative(X)<~>humble(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:(~patient(X)=>~old(X)))&
(((creative(paul)|happy(paul)))<=>(~funny(susan)))&
(![X]:((wise(X)&old(X))=>(humble(X)<~>creative(X))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:((~rich(X)|~strong(X)))))&
(![X]:((old(X)&~tall(X))=>(~generous(X)<~>humble(X))))&
((?[X]:((old(X)&~creative(X))))=>((patient(fred)|calm(fred))))&
(![X]:((creative(X)&~happy(X))<=>(~brave(X)<~>quiet(X))))&
((?[X]:((calm(X)|rich(X))))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((rich(X)<~>generous(X))=>(~creative(X)<~>~kind(X))))&
(![X]:((humble(X)|~happy(X))<=>(generous(X)&~humble(X))))&
((funny(mary)|rich(mary)))&
((funny(john)|happy(john)))&
((funny(alice)&quiet(alice)))&
((~funny(john)<~>~humble(john)))&
(?[X]:((quiet(X)&~patient(X))))&
((~curious(paul)<~>~strong(paul)))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~wise(susan) | [] | null | 0 |
Everyone who is old is both not kind and not old and vice versa.
If someone is not generous then someone is not quiet.
If someone is not patient then alice is both wise and not generous and vice versa.
Everyone who is not brave is either not rich or not curious.
Everyone who is both not tall and quiet is not funny or wise and vice versa.
If someone is either happy or patient then someone is old.
If someone is either humble or strong then lucy is both happy and strong.
Everyone who is either happy or tall is either humble or old.
If lucy is both calm and not funny then someone is either not tall or not quiet and vice versa.
Everyone who is either not rich or curious is either not rich or not humble.
If someone is both not creative and wise then alice is either not tall or calm and vice versa.
If someone is both patient and strong then someone is creative.
If someone is either not old or not brave then alice is not wise or not quiet and vice versa.
If someone is not wise then someone is either funny or not creative.
If lucy is creative or not quiet then lucy is not humble or calm.
If someone is curious or not old then paul is either calm or not rich.
Someone is both happy and not curious.
Someone is either rich or patient.
Paul is both strong and rich.
Someone is both tall and not wise.
Someone is not funny or strong.
Someone is not funny or humble.
Someone is not strong.
Someone is calm or not patient. | Lucy is kind. | entailment | (![X]:(old(X)<=>(~kind(X)&~old(X))))&
((?[X]:(~generous(X)))=>(?[X]:(~quiet(X))))&
((?[X]:(~patient(X)))<=>((wise(alice)&~generous(alice))))&
(![X]:(~brave(X)=>(~rich(X)<~>~curious(X))))&
(![X]:((~tall(X)&quiet(X))<=>(~funny(X)|wise(X))))&
((?[X]:((happy(X)<~>patient(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)<~>strong(X))))=>((happy(lucy)&strong(lucy))))&
(![X]:((happy(X)<~>tall(X))=>(humble(X)<~>old(X))))&
(((calm(lucy)&~funny(lucy)))<=>(?[X]:((~tall(X)<~>~quiet(X)))))&
(![X]:((~rich(X)<~>curious(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:((~creative(X)&wise(X))))<=>((~tall(alice)<~>calm(alice))))&
((?[X]:((patient(X)&strong(X))))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(alice)|~quiet(alice))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~creative(X)))))&
(((creative(lucy)|~quiet(lucy)))=>((~humble(lucy)|calm(lucy))))&
((?[X]:((curious(X)|~old(X))))=>((calm(paul)<~>~rich(paul))))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:((rich(X)<~>patient(X))))&
((strong(paul)&rich(paul)))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)|~patient(X)))) | kind(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5011810188078993378532855
% SZS output start Proof for 5011810188078993378532855
1. ! [X0] : (old(X0) <=> (~old(X0) & ~kind(X0))) [input p0]
25. ~kind(lucy) [input hypothesis]
41. ! [X0] : ((old(X0) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | ~old(X0))) [nnf transformation 1]
42. ! [X0] : ((old(X0) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | ~old(X0))) [flattening 41]
99. ~old(X0) | ~old(X0) [cnf transformation 42]
100. old(X0) | old(X0) | kind(X0) [cnf transformation 42]
165. ~kind(lucy) [cnf transformation 25]
168. ~old(X0) [duplicate literal removal 99]
169. kind(X0) | old(X0) [duplicate literal removal 100]
390. old(lucy) [resolution 169,165]
391. $false [subsumption resolution 390,168]
% SZS output end Proof for 5011810188078993378532855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not creative and calm then alice is not wise.
If mary is not tall or not wise then someone is tall and vice versa.
If paul is calm or not brave then someone is either creative or not quiet.
Everyone who is not patient or not rich is both patient and kind.
Everyone who is curious is not happy or patient.
If someone is both rich and not brave then someone is not strong or calm and vice versa.
Everyone who is both not generous and not kind is either not old or wise.
If someone is funny or brave then alice is either old or strong and vice versa.
Everyone who is happy or humble is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Everyone who is not calm or quiet is both not funny and happy.
Everyone who is generous or not kind is either not wise or not patient.
Everyone who is wise or humble is generous and vice versa.
Someone is not tall.
Fred is generous.
Lucy is not humble.
Susan is funny or not quiet.
John is tall.
Someone is either not quiet or not rich.
Someone is either not funny or curious. | Lucy is not wise. | entailment | (((~creative(alice)&calm(alice)))=>(~wise(alice)))&
(((~tall(mary)|~wise(mary)))<=>(?[X]:(tall(X))))&
(((calm(paul)|~brave(paul)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((~patient(X)|~rich(X))=>(patient(X)&kind(X))))&
(![X]:(curious(X)=>(~happy(X)|patient(X))))&
((?[X]:((rich(X)&~brave(X))))<=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~generous(X)&~kind(X))=>(~old(X)<~>wise(X))))&
((?[X]:((funny(X)|brave(X))))<=>((old(alice)<~>strong(alice))))&
(![X]:((happy(X)|humble(X))=>(~happy(X)<~>rich(X))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
(![X]:((~calm(X)|quiet(X))=>(~funny(X)&happy(X))))&
(![X]:((generous(X)|~kind(X))=>(~wise(X)<~>~patient(X))))&
(![X]:((wise(X)|humble(X))<=>generous(X)))&
(?[X]:(~tall(X)))&
(generous(fred))&
(~humble(lucy))&
((funny(susan)|~quiet(susan)))&
(tall(john))&
(?[X]:((~quiet(X)<~>~rich(X))))&
(?[X]:((~funny(X)<~>curious(X)))) | ~wise(lucy) | [
"p3",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 478808113257150922828123
% SZS output start Proof for 478808113257150922828123
4. ! [X0] : ((~rich(X0) | ~patient(X0)) => (kind(X0) & patient(X0))) [input p3]
15. ! [X0] : ((~kind(X0) | generous(X0)) => (~wise(X0) <~> ~patient(X0))) [input p14]
16. ! [X0] : ((humble(X0) | wise(X0)) <=> generous(X0)) [input p15]
24. wise(lucy) [input hypothesis]
29. ! [X0] : ((kind(X0) & patient(X0)) | (rich(X0) & patient(X0))) [ennf transformation 4]
38. ! [X0] : ((~wise(X0) <~> ~patient(X0)) | (kind(X0) & ~generous(X0))) [ennf transformation 15]
61. ! [X0] : (((patient(X0) | wise(X0)) & (~patient(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0))) [nnf transformation 38]
62. ! [X0] : (((humble(X0) | wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [nnf transformation 16]
63. ! [X0] : ((humble(X0) | wise(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & ~wise(X0)))) [flattening 62]
80. patient(X0) | patient(X0) [cnf transformation 29]
118. ~patient(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 61]
122. generous(X0) | ~wise(X0) [cnf transformation 63]
134. wise(lucy) [cnf transformation 24]
136. patient(X0) [duplicate literal removal 80]
259. ~wise(X0) | ~generous(X0) [subsumption resolution 118,136]
261. ~wise(X0) [subsumption resolution 122,259]
283. $false [subsumption resolution 134,261]
% SZS output end Proof for 478808113257150922828123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and kind is not creative or strong and vice versa. If john is either not curious or not creative then someone is both not creative and curious. Everyone who is not funny is funny. If fred is not happy then someone is not quiet or calm. If alice is both quiet and not strong then paul is calm or not patient and vice versa. If mary is both generous and patient then fred is not happy and vice versa. If someone is either not tall or old then someone is calm and vice versa. If susan is not funny then mary is either not patient or humble. If john is either strong or kind then someone is both not calm and creative. If someone is rich or generous then someone is not tall. Everyone who is not curious is not kind. Everyone who is both brave and not calm is not strong and vice versa. Everyone who is quiet or wise is both not creative and not patient and vice versa. If fred is both tall and wise then lucy is both not quiet and not kind and vice versa. Everyone who is both brave and not brave is not patient or calm and vice versa. Alice is both not tall and patient. Susan is either old or not brave. Susan is both funny and strong. Mary is either creative or brave. Someone is both kind and creative. | Lucy is not generous. | neutral | (![X]:((funny(X)&kind(X))<=>(~creative(X)|strong(X))))&
(((~curious(john)<~>~creative(john)))=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:(~funny(X)=>funny(X)))&
((~happy(fred))=>(?[X]:((~quiet(X)|calm(X)))))&
(((quiet(alice)&~strong(alice)))<=>((calm(paul)|~patient(paul))))&
(((generous(mary)&patient(mary)))<=>(~happy(fred)))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:(calm(X))))&
((~funny(susan))=>((~patient(mary)<~>humble(mary))))&
(((strong(john)<~>kind(john)))=>(?[X]:((~calm(X)&creative(X)))))&
((?[X]:((rich(X)|generous(X))))=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)=>~kind(X)))&
(![X]:((brave(X)&~calm(X))<=>~strong(X)))&
(![X]:((quiet(X)|wise(X))<=>(~creative(X)&~patient(X))))&
(((tall(fred)&wise(fred)))<=>((~quiet(lucy)&~kind(lucy))))&
(![X]:((brave(X)&~brave(X))<=>(~patient(X)|calm(X))))&
((~tall(alice)&patient(alice)))&
((old(susan)<~>~brave(susan)))&
((funny(susan)&strong(susan)))&
((creative(mary)<~>brave(mary)))&
(?[X]:((kind(X)&creative(X)))) | ~generous(lucy) | [] | null | 0 |
If susan is creative then someone is both quiet and not wise.
Everyone who is generous is either not creative or calm and vice versa.
Everyone who is tall or not calm is either not quiet or not old and vice versa.
If someone is not creative then someone is creative or not humble and vice versa.
Everyone who is not creative is calm and vice versa.
If mary is both generous and not strong then someone is not wise or not brave and vice versa.
If someone is not generous then someone is old and vice versa.
If lucy is not patient then someone is humble and vice versa.
Everyone who is quiet or generous is both not brave and old.
If someone is calm or not quiet then someone is either not wise or not funny and vice versa.
If someone is tall then mary is not strong and vice versa.
Everyone who is both rich and funny is old or not kind.
Everyone who is either funny or curious is either rich or not kind.
If paul is both not old and not rich then someone is wise or not generous and vice versa.
Everyone who is both not brave and patient is either not creative or not kind and vice versa.
If fred is both not happy and not strong then susan is both not rich and tall.
Lucy is either not humble or not brave.
Someone is either kind or tall.
John is not generous.
Alice is either not wise or old.
Someone is not tall or not generous.
John is either patient or not old.
Someone is humble or creative.
Someone is not old or kind. | Susan is quiet. | contradiction | ((creative(susan))=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:(generous(X)<=>(~creative(X)<~>calm(X))))&
(![X]:((tall(X)|~calm(X))<=>(~quiet(X)<~>~old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:(~creative(X)<=>calm(X)))&
(((generous(mary)&~strong(mary)))<=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:(old(X))))&
((~patient(lucy))<=>(?[X]:(humble(X))))&
(![X]:((quiet(X)|generous(X))=>(~brave(X)&old(X))))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:((~wise(X)<~>~funny(X)))))&
((?[X]:(tall(X)))<=>(~strong(mary)))&
(![X]:((rich(X)&funny(X))=>(old(X)|~kind(X))))&
(![X]:((funny(X)<~>curious(X))=>(rich(X)<~>~kind(X))))&
(((~old(paul)&~rich(paul)))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:((~brave(X)&patient(X))<=>(~creative(X)<~>~kind(X))))&
(((~happy(fred)&~strong(fred)))=>((~rich(susan)&tall(susan))))&
((~humble(lucy)<~>~brave(lucy)))&
(?[X]:((kind(X)<~>tall(X))))&
(~generous(john))&
((~wise(alice)<~>old(alice)))&
(?[X]:((~tall(X)|~generous(X))))&
((patient(john)<~>~old(john)))&
(?[X]:((humble(X)|creative(X))))&
(?[X]:((~old(X)|kind(X)))) | quiet(susan) | [
"p1",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5476608622310810766266121
% SZS output start Proof for 5476608622310810766266121
2. ! [X0] : (generous(X0) <=> (~creative(X0) <~> calm(X0))) [input p1]
5. ! [X0] : (~creative(X0) <=> calm(X0)) [input p4]
6. (~strong(mary) & generous(mary)) <=> ? [X0] : (~brave(X0) | ~wise(X0)) [input p5]
9. ! [X0] : ((generous(X0) | quiet(X0)) => (old(X0) & ~brave(X0))) [input p8]
25. quiet(susan) [input hypothesis]
31. ! [X0] : ((old(X0) & ~brave(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 9]
37. ! [X0] : ((generous(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) & (((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~generous(X0))) [nnf transformation 2]
45. ! [X0] : ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))) [nnf transformation 5]
46. ((~strong(mary) & generous(mary)) | ! [X0] : (brave(X0) & wise(X0))) & (? [X0] : (~brave(X0) | ~wise(X0)) | (strong(mary) | ~generous(mary))) [nnf transformation 6]
47. ((~strong(mary) & generous(mary)) | ! [X0] : (brave(X0) & wise(X0))) & (? [X0] : (~brave(X0) | ~wise(X0)) | strong(mary) | ~generous(mary)) [flattening 46]
48. ((~strong(mary) & generous(mary)) | ! [X0] : (brave(X0) & wise(X0))) & (? [X1] : (~brave(X1) | ~wise(X1)) | strong(mary) | ~generous(mary)) [rectify 47]
49. ? [X1] : (~brave(X1) | ~wise(X1)) => (~brave(sK3) | ~wise(sK3)) [choice axiom]
50. ((~strong(mary) & generous(mary)) | ! [X0] : (brave(X0) & wise(X0))) & ((~brave(sK3) | ~wise(sK3)) | strong(mary) | ~generous(mary)) [skolemisation 48,49]
91. ~generous(X0) | ~creative(X0) | calm(X0) [cnf transformation 37]
92. ~calm(X0) | creative(X0) | ~generous(X0) [cnf transformation 37]
104. calm(X0) | creative(X0) [cnf transformation 45]
105. ~calm(X0) | ~creative(X0) [cnf transformation 45]
108. generous(mary) | brave(X0) [cnf transformation 50]
115. ~brave(X0) | ~quiet(X0) [cnf transformation 31]
155. quiet(susan) [cnf transformation 25]
195. 10 <=> ! [X0] : brave(X0) [avatar definition]
196. brave(X0) <- (10) [avatar component clause 195]
207. 13 <=> generous(mary) [avatar definition]
209. generous(mary) <- (13) [avatar component clause 207]
210. 10 | 13 [avatar split clause 108,207,195]
399. ~creative(mary) | calm(mary) <- (13) [resolution 91,209]
400. calm(mary) <- (13) [subsumption resolution 399,104]
401. creative(X0) | ~generous(X0) | creative(X0) [resolution 92,104]
402. ~generous(X0) | creative(X0) [duplicate literal removal 401]
404. ~creative(mary) <- (13) [resolution 400,105]
412. creative(mary) <- (13) [resolution 402,209]
413. $false <- (13) [subsumption resolution 412,404]
414. ~13 [avatar contradiction clause 413]
416. ~quiet(X1) <- (10) [resolution 196,115]
424. $false <- (10) [resolution 416,155]
425. ~10 [avatar contradiction clause 424]
426. $false [avatar sat refutation 210,414,425]
% SZS output end Proof for 5476608622310810766266121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy is curious or humble.
If someone is both not kind and creative then someone is either curious or not generous.
Everyone who is funny is either humble or not calm and vice versa.
If someone is not wise or not generous then mary is strong and vice versa.
If fred is either old or funny then paul is not strong.
Everyone who is both not strong and rich is both strong and old.
Everyone who is either not curious or funny is either not calm or not kind and vice versa.
Everyone who is either not creative or not brave is curious.
Everyone who is both creative and wise is both not generous and happy.
If fred is both not calm and not old then someone is both patient and generous.
Everyone who is both not happy and not brave is either humble or not humble and vice versa.
Everyone who is tall is either not generous or generous and vice versa.
If someone is not creative or funny then someone is either funny or not strong and vice versa.
If paul is wise or generous then fred is old or generous.
If someone is not strong then someone is not brave or not humble and vice versa.
Everyone who is happy is not old.
Lucy is not tall or humble.
Someone is either calm or happy.
Fred is either curious or not patient.
Someone is both not rich and not quiet.
Someone is not creative.
Lucy is both not strong and generous.
Someone is not creative or kind. | Fred is curious. | neutral | (![X]:(~happy(X)=>(curious(X)|humble(X))))&
((?[X]:((~kind(X)&creative(X))))=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(funny(X)<=>(humble(X)<~>~calm(X))))&
((?[X]:((~wise(X)|~generous(X))))<=>(strong(mary)))&
(((old(fred)<~>funny(fred)))=>(~strong(paul)))&
(![X]:((~strong(X)&rich(X))=>(strong(X)&old(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~calm(X)<~>~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))=>curious(X)))&
(![X]:((creative(X)&wise(X))=>(~generous(X)&happy(X))))&
(((~calm(fred)&~old(fred)))=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((~happy(X)&~brave(X))<=>(humble(X)<~>~humble(X))))&
(![X]:(tall(X)<=>(~generous(X)<~>generous(X))))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(((wise(paul)|generous(paul)))=>((old(fred)|generous(fred))))&
((?[X]:(~strong(X)))<=>(?[X]:((~brave(X)|~humble(X)))))&
(![X]:(happy(X)=>~old(X)))&
((~tall(lucy)|humble(lucy)))&
(?[X]:((calm(X)<~>happy(X))))&
((curious(fred)<~>~patient(fred)))&
(?[X]:((~rich(X)&~quiet(X))))&
(?[X]:(~creative(X)))&
((~strong(lucy)&generous(lucy)))&
(?[X]:((~creative(X)|kind(X)))) | curious(fred) | [] | null | 0 |
Everyone who is not old or not wise is not kind or quiet and vice versa.
If fred is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Everyone who is both calm and happy is either kind or humble and vice versa.
Everyone who is either not creative or not strong is patient and vice versa.
If alice is both not calm and not kind then someone is quiet and vice versa.
If lucy is both generous and happy then mary is curious.
Everyone who is both not quiet and not rich is strong or wise and vice versa.
If paul is either not patient or not creative then someone is kind or curious.
Everyone who is quiet is not creative.
If someone is either happy or curious then someone is either not old or quiet and vice versa.
Everyone who is either curious or funny is not humble or not calm and vice versa.
Susan is either not old or not humble.
Someone is not calm or not strong.
Someone is not wise or brave.
Someone is humble.
Someone is brave or not wise.
Someone is not curious or not creative. | Fred is patient. | neutral | (![X]:((~old(X)|~wise(X))<=>(~kind(X)|quiet(X))))&
(((~brave(fred)&~old(fred)))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((calm(X)&happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>patient(X)))&
(((~calm(alice)&~kind(alice)))<=>(?[X]:(quiet(X))))&
(((generous(lucy)&happy(lucy)))=>(curious(mary)))&
(![X]:((~quiet(X)&~rich(X))<=>(strong(X)|wise(X))))&
(((~patient(paul)<~>~creative(paul)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(quiet(X)=>~creative(X)))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((~old(X)<~>quiet(X)))))&
(![X]:((curious(X)<~>funny(X))<=>(~humble(X)|~calm(X))))&
((~old(susan)<~>~humble(susan)))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:((~wise(X)|brave(X))))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:((~curious(X)|~creative(X)))) | patient(fred) | [] | null | 0 |
Everyone who is either tall or happy is both not rich and wise.
If someone is both patient and not creative then john is either not curious or happy and vice versa.
If alice is wise or patient then mary is both tall and old and vice versa.
If someone is humble or not humble then someone is humble and vice versa.
Everyone who is both tall and not old is both happy and strong.
If fred is creative then someone is tall or not patient and vice versa.
Everyone who is both generous and not humble is happy or creative and vice versa.
If someone is not calm then someone is either patient or not creative.
Everyone who is either kind or funny is calm and vice versa.
Everyone who is not humble is either not tall or quiet and vice versa.
If john is not rich or kind then someone is both brave and not creative.
Everyone who is either generous or quiet is strong or brave and vice versa.
If someone is not humble then mary is both not strong and funny.
Everyone who is both quiet and not happy is rich or quiet.
If mary is both calm and not curious then fred is both rich and wise.
If someone is generous then someone is either not wise or not brave.
Someone is either wise or tall.
John is both not funny and not brave.
John is humble.
Someone is not generous.
Someone is not tall or quiet.
Paul is either not rich or not creative.
Someone is not strong or not quiet.
Mary is not brave or curious. | Fred is humble. | contradiction | (![X]:((tall(X)<~>happy(X))=>(~rich(X)&wise(X))))&
((?[X]:((patient(X)&~creative(X))))<=>((~curious(john)<~>happy(john))))&
(((wise(alice)|patient(alice)))<=>((tall(mary)&old(mary))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&~old(X))=>(happy(X)&strong(X))))&
((creative(fred))<=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:((generous(X)&~humble(X))<=>(happy(X)|creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((kind(X)<~>funny(X))<=>calm(X)))&
(![X]:(~humble(X)<=>(~tall(X)<~>quiet(X))))&
(((~rich(john)|kind(john)))=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((generous(X)<~>quiet(X))<=>(strong(X)|brave(X))))&
((?[X]:(~humble(X)))=>((~strong(mary)&funny(mary))))&
(![X]:((quiet(X)&~happy(X))=>(rich(X)|quiet(X))))&
(((calm(mary)&~curious(mary)))=>((rich(fred)&wise(fred))))&
((?[X]:(generous(X)))=>(?[X]:((~wise(X)<~>~brave(X)))))&
(?[X]:((wise(X)<~>tall(X))))&
((~funny(john)&~brave(john)))&
(humble(john))&
(?[X]:(~generous(X)))&
(?[X]:((~tall(X)|quiet(X))))&
((~rich(paul)<~>~creative(paul)))&
(?[X]:((~strong(X)|~quiet(X))))&
((~brave(mary)|curious(mary))) | humble(fred) | [
"p2",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7304211642553643867536929
% SZS output start Proof for 7304211642553643867536929
3. (patient(alice) | wise(alice)) <=> (old(mary) & tall(mary)) [input p2]
6. creative(fred) <=> ? [X0] : (~patient(X0) | tall(X0)) [input p5]
7. ! [X0] : ((~humble(X0) & generous(X0)) <=> (creative(X0) | happy(X0))) [input p6]
25. humble(fred) [input hypothesis]
45. ((patient(alice) | wise(alice)) | (~old(mary) | ~tall(mary))) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [nnf transformation 3]
46. (patient(alice) | wise(alice) | ~old(mary) | ~tall(mary)) & ((old(mary) & tall(mary)) | (~patient(alice) & ~wise(alice))) [flattening 45]
52. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X0] : (~patient(X0) | tall(X0)) | ~creative(fred)) [nnf transformation 6]
53. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & (? [X1] : (~patient(X1) | tall(X1)) | ~creative(fred)) [rectify 52]
54. ? [X1] : (~patient(X1) | tall(X1)) => (~patient(sK3) | tall(sK3)) [choice axiom]
55. (creative(fred) | ! [X0] : (patient(X0) & ~tall(X0))) & ((~patient(sK3) | tall(sK3)) | ~creative(fred)) [skolemisation 53,54]
56. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (humble(X0) | ~generous(X0)))) [nnf transformation 7]
57. ! [X0] : (((~humble(X0) & generous(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | humble(X0) | ~generous(X0))) [flattening 56]
93. tall(mary) | ~patient(alice) [cnf transformation 46]
103. creative(fred) | ~tall(X0) [cnf transformation 55]
104. creative(fred) | patient(X0) [cnf transformation 55]
109. ~humble(X0) | ~creative(X0) [cnf transformation 57]
148. humble(fred) [cnf transformation 25]
175. 6 <=> tall(mary) [avatar definition]
176. tall(mary) <- (6) [avatar component clause 175]
187. 9 <=> patient(alice) [avatar definition]
188. ~patient(alice) <- (~9) [avatar component clause 187]
193. ~9 | 6 [avatar split clause 93,175,187]
208. 13 <=> ! [X0] : patient(X0) [avatar definition]
209. patient(X0) <- (13) [avatar component clause 208]
211. 14 <=> creative(fred) [avatar definition]
213. creative(fred) <- (14) [avatar component clause 211]
214. 13 | 14 [avatar split clause 104,211,208]
216. 15 <=> ! [X0] : ~tall(X0) [avatar definition]
217. ~tall(X0) <- (15) [avatar component clause 216]
218. 15 | 14 [avatar split clause 103,211,216]
348. $false <- (~9, 13) [resolution 209,188]
353. 9 | ~13 [avatar contradiction clause 348]
354. $false <- (6, 15) [subsumption resolution 176,217]
355. ~6 | ~15 [avatar contradiction clause 354]
366. ~creative(fred) [resolution 109,148]
388. $false <- (14) [subsumption resolution 366,213]
389. ~14 [avatar contradiction clause 388]
390. $false [avatar sat refutation 193,214,218,353,355,389]
% SZS output end Proof for 7304211642553643867536929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or wise then alice is calm. Everyone who is either not kind or not happy is either not quiet or old and vice versa. If someone is not old then susan is not funny. If mary is patient then someone is not calm and vice versa. 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. 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. | Susan is not kind. | entailment | ((?[X]:((old(X)|wise(X))))=>(calm(alice)))&
(![X]:((~kind(X)<~>~happy(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[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))))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | ~kind(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1754437276293098380526816
% SZS output start Proof for 1754437276293098380526816
1. ? [X0] : (wise(X0) | old(X0)) => calm(alice) [input p0]
2. ! [X0] : ((~kind(X0) <~> ~happy(X0)) <=> (~quiet(X0) <~> old(X0))) [input p1]
3. ? [X0] : ~old(X0) => ~funny(susan) [input p2]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (rich(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) <~> calm(X0)) <=> (~brave(X0) & kind(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p10]
14. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~tall(X0) <~> brave(X0))) [input p13]
22. kind(susan) [input hypothesis]
23. ? [X0] : old(X0) => calm(alice) [pure predicate removal 1]
25. calm(alice) | ! [X0] : ~old(X0) [ennf transformation 23]
26. ~funny(susan) | ! [X0] : old(X0) [ennf transformation 3]
29. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 10]
30. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 29]
34. ! [X0] : ((((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0))))) [nnf transformation 2]
43. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [flattening 43]
45. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [flattening 45]
49. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 49]
55. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 14]
66. calm(alice) | ~old(X0) [cnf transformation 25]
72. ~quiet(X0) | ~kind(X0) | ~happy(X0) | ~old(X0) [cnf transformation 34]
75. ~funny(susan) | old(X0) [cnf transformation 26]
85. ~funny(X0) | happy(X0) [cnf transformation 44]
90. ~quiet(X0) | kind(X0) | ~calm(X0) [cnf transformation 46]
93. ~quiet(X0) | calm(X0) | brave(X0) | ~kind(X0) [cnf transformation 46]
102. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 30]
105. ~calm(X0) | funny(X0) [cnf transformation 50]
106. ~calm(X0) | quiet(X0) [cnf transformation 50]
119. ~brave(X0) | tall(X0) | tall(X0) | ~quiet(X0) [cnf transformation 55]
124. ~tall(X0) | ~quiet(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 55]
135. kind(susan) [cnf transformation 22]
137. ~brave(X0) | tall(X0) | ~quiet(X0) [duplicate literal removal 119]
139. ~tall(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 124]
140. quiet(X0) | calm(X0) [duplicate literal removal 102]
142. 1 <=> ! [X0] : ~old(X0) [avatar definition]
143. ~old(X0) <- (1) [avatar component clause 142]
145. 2 <=> calm(alice) [avatar definition]
147. calm(alice) <- (2) [avatar component clause 145]
148. 1 | 2 [avatar split clause 66,145,142]
150. 3 <=> ! [X0] : old(X0) [avatar definition]
151. old(X0) <- (3) [avatar component clause 150]
153. 4 <=> funny(susan) [avatar definition]
156. 3 | ~4 [avatar split clause 75,153,150]
195. quiet(X0) [subsumption resolution 106,140]
225. ~tall(X0) | ~brave(X0) [subsumption resolution 139,195]
226. ~brave(X0) | tall(X0) [subsumption resolution 137,195]
227. ~brave(X0) [subsumption resolution 226,225]
283. funny(alice) <- (2) [resolution 105,147]
284. happy(alice) <- (2) [resolution 283,85]
288. ~calm(X2) | kind(X2) [resolution 90,195]
290. kind(alice) <- (2) [resolution 288,147]
405. ~happy(X2) | ~kind(X2) | ~old(X2) [resolution 72,195]
458. calm(X2) | brave(X2) | ~kind(X2) | calm(X2) [resolution 93,140]
460. calm(X2) | brave(X2) | ~kind(X2) [duplicate literal removal 458]
462. ~kind(X2) | calm(X2) [subsumption resolution 460,227]
472. calm(susan) [resolution 462,135]
493. funny(susan) [resolution 472,105]
496. 4 [avatar split clause 493,153]
527. ~kind(alice) | ~old(alice) <- (2) [resolution 405,284]
532. ~old(alice) <- (2) [subsumption resolution 527,290]
533. $false <- (2, 3) [subsumption resolution 532,151]
534. ~2 | ~3 [avatar contradiction clause 533]
552. $false <- (1, 3) [subsumption resolution 143,151]
553. ~1 | ~3 [avatar contradiction clause 552]
554. $false [avatar sat refutation 148,156,496,534,553]
% SZS output end Proof for 1754437276293098380526816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not happy is not funny.
Everyone who is either brave or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Someone is both patient and not quiet.
John is not rich or not creative.
Paul is either not brave or happy.
Susan is either happy or not generous.
Someone is both tall and kind.
Susan is not creative. | Paul is not rich. | entailment | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((brave(X)<~>~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((patient(X)&~quiet(X))))&
((~rich(john)|~creative(john)))&
((~brave(paul)<~>happy(paul)))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((tall(X)&kind(X))))&
(~creative(susan)) | ~rich(paul) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9084096333689090352363762
% SZS output start Proof for 9084096333689090352363762
6. ! [X0] : (~happy(X0) <=> (~rich(X0) <~> brave(X0))) [input p5]
19. ~brave(paul) <~> happy(paul) [input p18]
23. rich(paul) [input hypothesis]
49. ! [X0] : ((~happy(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | happy(X0))) [nnf transformation 6]
68. (~happy(paul) | brave(paul)) & (happy(paul) | ~brave(paul)) [nnf transformation 19]
84. ~rich(X0) | brave(X0) | happy(X0) [cnf transformation 49]
87. ~rich(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 49]
121. happy(paul) | ~brave(paul) [cnf transformation 68]
122. ~happy(paul) | brave(paul) [cnf transformation 68]
128. rich(paul) [cnf transformation 23]
155. 7 <=> brave(paul) [avatar definition]
157. brave(paul) <- (7) [avatar component clause 155]
254. 29 <=> happy(paul) [avatar definition]
255. happy(paul) <- (29) [avatar component clause 254]
257. 7 | ~29 [avatar split clause 122,254,155]
258. ~7 | 29 [avatar split clause 121,254,155]
271. brave(paul) | happy(paul) [resolution 84,128]
275. 29 | 7 [avatar split clause 271,155,254]
278. ~happy(paul) | ~brave(paul) [resolution 87,128]
279. ~brave(paul) <- (29) [subsumption resolution 278,255]
280. $false <- (7, 29) [subsumption resolution 279,157]
281. ~7 | ~29 [avatar contradiction clause 280]
282. $false [avatar sat refutation 257,258,275,281]
% SZS output end Proof for 9084096333689090352363762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or funny then someone is not old and vice versa.
If someone is rich then someone is funny or not rich.
Everyone who is rich or calm is either patient or not kind.
Everyone who is not kind is wise.
Everyone who is not generous is both not rich and humble.
If someone is not rich or generous then someone is both patient and not creative.
Everyone who is not calm is both not calm and patient and vice versa.
Everyone who is humble or generous is not generous and vice versa.
If someone is curious then someone is brave or not old and vice versa.
Everyone who is quiet is either kind or creative and vice versa.
Everyone who is either not old or not kind is either not strong or not rich.
Everyone who is either not patient or not rich is both funny and not quiet and vice versa.
If paul is humble or not old then someone is not patient.
Everyone who is both rich and not funny is both not curious and not tall.
If fred is both kind and not patient then someone is not wise and vice versa.
If someone is not curious or not humble then someone is either calm or strong and vice versa.
John is brave or not quiet.
Paul is either not tall or old.
Someone is not wise or not rich.
Mary is not creative or brave.
Someone is not creative or not patient.
Someone is either funny or humble.
Someone is both not tall and humble. | Mary is brave. | neutral | ((?[X]:((wise(X)|funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:(rich(X)))=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((rich(X)|calm(X))=>(patient(X)<~>~kind(X))))&
(![X]:(~kind(X)=>wise(X)))&
(![X]:(~generous(X)=>(~rich(X)&humble(X))))&
((?[X]:((~rich(X)|generous(X))))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:(~calm(X)<=>(~calm(X)&patient(X))))&
(![X]:((humble(X)|generous(X))<=>~generous(X)))&
((?[X]:(curious(X)))<=>(?[X]:((brave(X)|~old(X)))))&
(![X]:(quiet(X)<=>(kind(X)<~>creative(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~strong(X)<~>~rich(X))))&
(![X]:((~patient(X)<~>~rich(X))<=>(funny(X)&~quiet(X))))&
(((humble(paul)|~old(paul)))=>(?[X]:(~patient(X))))&
(![X]:((rich(X)&~funny(X))=>(~curious(X)&~tall(X))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(~wise(X))))&
((?[X]:((~curious(X)|~humble(X))))<=>(?[X]:((calm(X)<~>strong(X)))))&
((brave(john)|~quiet(john)))&
((~tall(paul)<~>old(paul)))&
(?[X]:((~wise(X)|~rich(X))))&
((~creative(mary)|brave(mary)))&
(?[X]:((~creative(X)|~patient(X))))&
(?[X]:((funny(X)<~>humble(X))))&
(?[X]:((~tall(X)&humble(X)))) | brave(mary) | [] | null | 0 |
Everyone who is not creative is both brave and not kind and vice versa.
Everyone who is both not rich and not brave is not old or old and vice versa.
Everyone who is either not calm or humble is not old or funny.
If john is old then alice is either rich or not brave.
If alice is either old or not kind then alice is not happy or happy.
If fred is either rich or old then john is both not humble and funny.
If susan is both not patient and not wise then alice is both not humble and curious.
If someone is not patient then someone is brave or not generous and vice versa.
If paul is tall or not humble then someone is not rich or not quiet and vice versa.
Everyone who is happy or not kind is both tall and not strong.
Everyone who is either not generous or not funny is humble or not calm.
If mary is either brave or not strong then lucy is happy and vice versa.
If someone is generous or humble then paul is not old and vice versa.
If paul is old then someone is both rich and not creative.
If fred is kind or not old then fred is both not brave and creative.
Everyone who is both not brave and not humble is brave.
Lucy is either not quiet or creative.
Someone is either not strong or rich.
Someone is either not quiet or creative.
Fred is either brave or quiet.
Someone is both old and not funny. | Susan is strong. | neutral | (![X]:(~creative(X)<=>(brave(X)&~kind(X))))&
(![X]:((~rich(X)&~brave(X))<=>(~old(X)|old(X))))&
(![X]:((~calm(X)<~>humble(X))=>(~old(X)|funny(X))))&
((old(john))=>((rich(alice)<~>~brave(alice))))&
(((old(alice)<~>~kind(alice)))=>((~happy(alice)|happy(alice))))&
(((rich(fred)<~>old(fred)))=>((~humble(john)&funny(john))))&
(((~patient(susan)&~wise(susan)))=>((~humble(alice)&curious(alice))))&
((?[X]:(~patient(X)))<=>(?[X]:((brave(X)|~generous(X)))))&
(((tall(paul)|~humble(paul)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)|~kind(X))=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>~funny(X))=>(humble(X)|~calm(X))))&
(((brave(mary)<~>~strong(mary)))<=>(happy(lucy)))&
((?[X]:((generous(X)|humble(X))))<=>(~old(paul)))&
((old(paul))=>(?[X]:((rich(X)&~creative(X)))))&
(((kind(fred)|~old(fred)))=>((~brave(fred)&creative(fred))))&
(![X]:((~brave(X)&~humble(X))=>brave(X)))&
((~quiet(lucy)<~>creative(lucy)))&
(?[X]:((~strong(X)<~>rich(X))))&
(?[X]:((~quiet(X)<~>creative(X))))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((old(X)&~funny(X)))) | strong(susan) | [] | null | 0 |
If someone is both tall and brave then susan is not wise. If lucy is quiet or not creative then someone is happy or not patient and vice versa. Everyone who is either rich or curious is old. If someone is both calm and rich then someone is not brave. If fred is either not old or humble then someone is not strong. Everyone who is funny is both calm and not rich. If paul is rich or happy then lucy is not curious or tall. Everyone who is wise is strong and vice versa. Everyone who is either creative or rich is either not kind or quiet. Everyone who is brave or humble is not generous and vice versa. If susan is either old or funny then someone is kind. If fred is old then someone is either generous or humble and vice versa. If mary is not creative then mary is either calm or brave and vice versa. Everyone who is old is funny and vice versa. If someone is not old then fred is either not humble or not tall and vice versa. Everyone who is either strong or not wise is brave and vice versa. Lucy is rich. Someone is happy or not rich. Mary is both not calm and not wise. Fred is either not kind or not strong. Alice is wise. Someone is not patient. Someone is both old and brave. Someone is either not tall or rich. | Mary is not old. | entailment | ((?[X]:((tall(X)&brave(X))))=>(~wise(susan)))&
(((quiet(lucy)|~creative(lucy)))<=>(?[X]:((happy(X)|~patient(X)))))&
(![X]:((rich(X)<~>curious(X))=>old(X)))&
((?[X]:((calm(X)&rich(X))))=>(?[X]:(~brave(X))))&
(((~old(fred)<~>humble(fred)))=>(?[X]:(~strong(X))))&
(![X]:(funny(X)=>(calm(X)&~rich(X))))&
(((rich(paul)|happy(paul)))=>((~curious(lucy)|tall(lucy))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((creative(X)<~>rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)|humble(X))<=>~generous(X)))&
(((old(susan)<~>funny(susan)))=>(?[X]:(kind(X))))&
((old(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((~creative(mary))<=>((calm(mary)<~>brave(mary))))&
(![X]:(old(X)<=>funny(X)))&
((?[X]:(~old(X)))<=>((~humble(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>~wise(X))<=>brave(X)))&
(rich(lucy))&
(?[X]:((happy(X)|~rich(X))))&
((~calm(mary)&~wise(mary)))&
((~kind(fred)<~>~strong(fred)))&
(wise(alice))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)&brave(X))))&
(?[X]:((~tall(X)<~>rich(X)))) | ~old(mary) | [
"p5",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 760317248880884334587121
% SZS output start Proof for 760317248880884334587121
6. ! [X0] : (funny(X0) => (~rich(X0) & calm(X0))) [input p5]
14. ! [X0] : (old(X0) <=> funny(X0)) [input p13]
19. ~wise(mary) & ~calm(mary) [input p18]
25. old(mary) [input hypothesis]
31. ! [X0] : ((~rich(X0) & calm(X0)) | ~funny(X0)) [ennf transformation 6]
60. ! [X0] : ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))) [nnf transformation 14]
86. ~funny(X0) | calm(X0) [cnf transformation 31]
109. ~old(X0) | funny(X0) [cnf transformation 60]
121. ~calm(mary) [cnf transformation 19]
131. old(mary) [cnf transformation 25]
244. 26 <=> calm(mary) [avatar definition]
245. ~calm(mary) <- (~26) [avatar component clause 244]
282. ~26 [avatar split clause 121,244]
315. funny(mary) [resolution 109,131]
322. calm(mary) [resolution 315,86]
323. $false <- (~26) [subsumption resolution 322,245]
324. 26 [avatar contradiction clause 323]
325. $false [avatar sat refutation 282,324]
% SZS output end Proof for 760317248880884334587121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not wise is patient and vice versa.
Everyone who is both patient and not calm is either rich or not curious and vice versa.
If susan is both not strong and not tall then someone is either not rich or not strong.
If someone is both not tall and not brave then someone is funny or kind and vice versa.
If someone is not quiet then someone is both humble and funny.
If someone is generous then lucy is not generous or not curious and vice versa.
If mary is curious or not rich then someone is either not funny or old.
Everyone who is both not humble and not tall is either calm or generous.
Everyone who is both not tall and not patient is either not funny or happy and vice versa.
If paul is not calm or calm then john is not rich and vice versa.
Everyone who is both calm and strong is either quiet or not generous and vice versa.
Everyone who is not generous or funny is strong or brave and vice versa.
If alice is old then fred is kind or not happy and vice versa.
If lucy is both not curious and calm then paul is either not patient or not generous.
If someone is either calm or quiet then paul is both not tall and not curious.
Everyone who is tall is both not kind and kind and vice versa.
Someone is happy or generous.
Someone is not patient or tall.
John is either not creative or quiet.
Someone is not kind.
Someone is not old or tall.
Someone is humble or not patient.
Someone is either not creative or not brave.
Someone is both calm and not wise. | John is not tall. | entailment | (![X]:((quiet(X)<~>~wise(X))<=>patient(X)))&
(![X]:((patient(X)&~calm(X))<=>(rich(X)<~>~curious(X))))&
(((~strong(susan)&~tall(susan)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
((?[X]:((~tall(X)&~brave(X))))<=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((humble(X)&funny(X)))))&
((?[X]:(generous(X)))<=>((~generous(lucy)|~curious(lucy))))&
(((curious(mary)|~rich(mary)))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((~humble(X)&~tall(X))=>(calm(X)<~>generous(X))))&
(![X]:((~tall(X)&~patient(X))<=>(~funny(X)<~>happy(X))))&
(((~calm(paul)|calm(paul)))<=>(~rich(john)))&
(![X]:((calm(X)&strong(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~generous(X)|funny(X))<=>(strong(X)|brave(X))))&
((old(alice))<=>((kind(fred)|~happy(fred))))&
(((~curious(lucy)&calm(lucy)))=>((~patient(paul)<~>~generous(paul))))&
((?[X]:((calm(X)<~>quiet(X))))=>((~tall(paul)&~curious(paul))))&
(![X]:(tall(X)<=>(~kind(X)&kind(X))))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:((~patient(X)|tall(X))))&
((~creative(john)<~>quiet(john)))&
(?[X]:(~kind(X)))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~creative(X)<~>~brave(X))))&
(?[X]:((calm(X)&~wise(X)))) | ~tall(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8832516362392800659619726
% SZS output start Proof for 8832516362392800659619726
16. ! [X0] : (tall(X0) <=> (kind(X0) & ~kind(X0))) [input p15]
25. tall(john) [input hypothesis]
72. ! [X0] : ((tall(X0) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | ~tall(X0))) [nnf transformation 16]
73. ! [X0] : ((tall(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | ~tall(X0))) [flattening 72]
141. ~kind(X0) | ~tall(X0) [cnf transformation 73]
142. kind(X0) | ~tall(X0) [cnf transformation 73]
154. tall(john) [cnf transformation 25]
306. ~tall(X0) [subsumption resolution 141,142]
338. $false [subsumption resolution 154,306]
% SZS output end Proof for 8832516362392800659619726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall or not curious then john is not brave or not tall.
If someone is either happy or not calm then someone is either not rich or not strong and vice versa.
If john is not wise then paul is not quiet.
If someone is not strong or not calm then someone is happy.
Everyone who is either not creative or kind is both not happy and brave.
Everyone who is tall is not quiet or strong.
Everyone who is kind is not curious.
If someone is strong or not happy then fred is both not funny and brave and vice versa.
Everyone who is quiet or rich is either not calm or not quiet.
If fred is funny then someone is old or not humble and vice versa.
Everyone who is not tall is creative.
If john is wise then lucy is not calm and vice versa.
If lucy is not happy or not patient then someone is not funny or kind.
Everyone who is not humble or kind is either generous or not funny.
Everyone who is not patient is both creative and not wise.
If mary is both generous and wise then someone is strong.
Someone is not curious.
Alice is not calm or wise.
Mary is both not happy and not old.
Paul is both strong and creative.
Fred is not creative or humble.
Someone is not curious or not happy.
Lucy is wise or brave.
Someone is kind or not generous. | Paul is not creative. | contradiction | (((tall(alice)|~curious(alice)))=>((~brave(john)|~tall(john))))&
((?[X]:((happy(X)<~>~calm(X))))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
((~wise(john))=>(~quiet(paul)))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(happy(X))))&
(![X]:((~creative(X)<~>kind(X))=>(~happy(X)&brave(X))))&
(![X]:(tall(X)=>(~quiet(X)|strong(X))))&
(![X]:(kind(X)=>~curious(X)))&
((?[X]:((strong(X)|~happy(X))))<=>((~funny(fred)&brave(fred))))&
(![X]:((quiet(X)|rich(X))=>(~calm(X)<~>~quiet(X))))&
((funny(fred))<=>(?[X]:((old(X)|~humble(X)))))&
(![X]:(~tall(X)=>creative(X)))&
((wise(john))<=>(~calm(lucy)))&
(((~happy(lucy)|~patient(lucy)))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:((~humble(X)|kind(X))=>(generous(X)<~>~funny(X))))&
(![X]:(~patient(X)=>(creative(X)&~wise(X))))&
(((generous(mary)&wise(mary)))=>(?[X]:(strong(X))))&
(?[X]:(~curious(X)))&
((~calm(alice)|wise(alice)))&
((~happy(mary)&~old(mary)))&
((strong(paul)&creative(paul)))&
((~creative(fred)|humble(fred)))&
(?[X]:((~curious(X)|~happy(X))))&
((wise(lucy)|brave(lucy)))&
(?[X]:((kind(X)|~generous(X)))) | ~creative(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2887052108493392529747872
% SZS output start Proof for 2887052108493392529747872
20. creative(paul) & strong(paul) [input p19]
25. ~creative(paul) [input hypothesis]
120. creative(paul) [cnf transformation 20]
125. ~creative(paul) [cnf transformation 25]
323. $false [subsumption resolution 125,120]
% SZS output end Proof for 2887052108493392529747872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not old or not creative then someone is patient.
If someone is happy then paul is not calm and vice versa.
Everyone who is rich is either tall or humble.
If alice is both not generous and generous then alice is not brave and vice versa.
Everyone who is not strong or rich is both not creative and not funny.
If someone is brave then mary is not old or kind.
Everyone who is either not strong or not wise is quiet and vice versa.
Everyone who is both quiet and not kind is wise.
If susan is both not old and curious then fred is either generous or not strong.
Everyone who is not strong or not tall is both not brave and not curious and vice versa.
If alice is either not kind or kind then paul is not happy or brave and vice versa.
Everyone who is either wise or calm is brave.
If someone is not quiet or not rich then someone is both not tall and generous.
If someone is either not rich or not strong then someone is kind or old.
Everyone who is both generous and happy is either not brave or tall and vice versa.
Everyone who is rich is not rich.
Someone is not generous.
Someone is tall or not kind.
Someone is either funny or not kind.
John is both kind and not curious.
Someone is not wise or tall.
Someone is patient or humble.
Someone is either brave or funny.
Mary is not funny or not curious. | Paul is brave. | neutral | (((~old(mary)|~creative(mary)))=>(?[X]:(patient(X))))&
((?[X]:(happy(X)))<=>(~calm(paul)))&
(![X]:(rich(X)=>(tall(X)<~>humble(X))))&
(((~generous(alice)&generous(alice)))<=>(~brave(alice)))&
(![X]:((~strong(X)|rich(X))=>(~creative(X)&~funny(X))))&
((?[X]:(brave(X)))=>((~old(mary)|kind(mary))))&
(![X]:((~strong(X)<~>~wise(X))<=>quiet(X)))&
(![X]:((quiet(X)&~kind(X))=>wise(X)))&
(((~old(susan)&curious(susan)))=>((generous(fred)<~>~strong(fred))))&
(![X]:((~strong(X)|~tall(X))<=>(~brave(X)&~curious(X))))&
(((~kind(alice)<~>kind(alice)))<=>((~happy(paul)|brave(paul))))&
(![X]:((wise(X)<~>calm(X))=>brave(X)))&
((?[X]:((~quiet(X)|~rich(X))))=>(?[X]:((~tall(X)&generous(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((generous(X)&happy(X))<=>(~brave(X)<~>tall(X))))&
(![X]:(rich(X)=>~rich(X)))&
(?[X]:(~generous(X)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((funny(X)<~>~kind(X))))&
((kind(john)&~curious(john)))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((patient(X)|humble(X))))&
(?[X]:((brave(X)<~>funny(X))))&
((~funny(mary)|~curious(mary))) | brave(paul) | [] | null | 0 |
Everyone who is both quiet and patient is kind. Everyone who is humble is either not old or not kind. If someone is both not curious and strong then fred is tall or not humble and vice versa. Everyone who is either brave or not wise is either not funny or wise and vice versa. If someone is not calm or not generous then mary is funny and vice versa. If someone is wise then alice is either generous or not old and vice versa. If paul is not wise then someone is not creative and vice versa. Everyone who is both not curious and not generous is both not kind and happy and vice versa. If mary is generous then susan is not old or not kind and vice versa. Everyone who is both old and not wise is both not humble and not rich. Everyone who is both happy and not curious is not happy or calm and vice versa. Everyone who is not happy is patient and vice versa. Everyone who is strong is either not brave or not curious. If someone is either quiet or humble then lucy is happy and vice versa. If lucy is both not generous and not old then someone is both not creative and old and vice versa. Everyone who is not wise or not happy is rich or humble. Alice is not kind. Someone is not humble or kind. Someone is curious. Mary is both not creative and not kind. Paul is not funny. Fred is both not wise and creative. Alice is not quiet or not patient. | Fred is rich. | neutral | (![X]:((quiet(X)&patient(X))=>kind(X)))&
(![X]:(humble(X)=>(~old(X)<~>~kind(X))))&
((?[X]:((~curious(X)&strong(X))))<=>((tall(fred)|~humble(fred))))&
(![X]:((brave(X)<~>~wise(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((~calm(X)|~generous(X))))<=>(funny(mary)))&
((?[X]:(wise(X)))<=>((generous(alice)<~>~old(alice))))&
((~wise(paul))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~kind(X)&happy(X))))&
((generous(mary))<=>((~old(susan)|~kind(susan))))&
(![X]:((old(X)&~wise(X))=>(~humble(X)&~rich(X))))&
(![X]:((happy(X)&~curious(X))<=>(~happy(X)|calm(X))))&
(![X]:(~happy(X)<=>patient(X)))&
(![X]:(strong(X)=>(~brave(X)<~>~curious(X))))&
((?[X]:((quiet(X)<~>humble(X))))<=>(happy(lucy)))&
(((~generous(lucy)&~old(lucy)))<=>(?[X]:((~creative(X)&old(X)))))&
(![X]:((~wise(X)|~happy(X))=>(rich(X)|humble(X))))&
(~kind(alice))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(curious(X)))&
((~creative(mary)&~kind(mary)))&
(~funny(paul))&
((~wise(fred)&creative(fred)))&
((~quiet(alice)|~patient(alice))) | rich(fred) | [] | null | 0 |
Everyone who is either not curious or funny is both old and patient.
Everyone who is both not old and not strong is both calm and tall.
Everyone who is either not wise or happy is either quiet or not curious.
Everyone who is both tall and calm is not calm and vice versa.
If someone is either funny or tall then alice is either happy or kind.
Everyone who is not tall is either wise or not rich.
Everyone who is not generous is not strong or not humble.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Someone is both not curious and not tall.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Someone is not tall.
Mary is rich. | Paul is kind. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&patient(X))))&
(![X]:((~old(X)&~strong(X))=>(calm(X)&tall(X))))&
(![X]:((~wise(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((tall(X)&calm(X))<=>~calm(X)))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>kind(alice))))&
(![X]:(~tall(X)=>(wise(X)<~>~rich(X))))&
(![X]:(~generous(X)=>(~strong(X)|~humble(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((~curious(X)&~tall(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:(~tall(X)))&
(rich(mary)) | kind(paul) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7731119867844553634679643
% SZS output start Proof for 7731119867844553634679643
4. ! [X0] : ((calm(X0) & tall(X0)) <=> ~calm(X0)) [input p3]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
24. ~kind(paul) [input hypothesis]
38. ! [X0] : (((calm(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | (~calm(X0) | ~tall(X0)))) [nnf transformation 4]
39. ! [X0] : (((calm(X0) & tall(X0)) | calm(X0)) & (~calm(X0) | ~calm(X0) | ~tall(X0))) [flattening 38]
42. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
43. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 42]
81. calm(X0) | calm(X0) [cnf transformation 39]
91. kind(X0) | ~calm(X0) [cnf transformation 43]
125. ~kind(paul) [cnf transformation 24]
127. calm(X0) [duplicate literal removal 81]
146. kind(X0) [subsumption resolution 91,127]
230. $false [subsumption resolution 125,146]
% SZS output end Proof for 7731119867844553634679643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and calm is both quiet and kind.
Everyone who is either not curious or kind is either kind or tall and vice versa.
Everyone who is either not strong or not wise is rich or wise.
Everyone who is patient or rich is either brave or not funny and vice versa.
If susan is rich then someone is either not quiet or not funny and vice versa.
If someone is either humble or not funny then susan is both not patient and not funny and vice versa.
Everyone who is both not brave and not funny is either strong or not kind and vice versa.
If someone is either humble or not patient then someone is strong or not generous and vice versa.
If paul is patient then mary is not generous.
Everyone who is both not curious and not tall is either generous or not wise.
Everyone who is not calm is both strong and wise and vice versa.
Everyone who is both patient and not patient is not curious and vice versa.
Everyone who is both not tall and brave is not calm and vice versa.
Everyone who is both rich and patient is not patient.
Everyone who is kind is either not generous or kind.
Everyone who is humble is quiet and vice versa.
Someone is either patient or generous.
Someone is both not wise and not kind.
Mary is not brave.
Someone is either creative or happy.
Paul is not creative.
Lucy is either not humble or happy.
Mary is creative.
Someone is happy. | Mary is not rich. | neutral | (![X]:((happy(X)&calm(X))=>(quiet(X)&kind(X))))&
(![X]:((~curious(X)<~>kind(X))<=>(kind(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(rich(X)|wise(X))))&
(![X]:((patient(X)|rich(X))<=>(brave(X)<~>~funny(X))))&
((rich(susan))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
((?[X]:((humble(X)<~>~funny(X))))<=>((~patient(susan)&~funny(susan))))&
(![X]:((~brave(X)&~funny(X))<=>(strong(X)<~>~kind(X))))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((strong(X)|~generous(X)))))&
((patient(paul))=>(~generous(mary)))&
(![X]:((~curious(X)&~tall(X))=>(generous(X)<~>~wise(X))))&
(![X]:(~calm(X)<=>(strong(X)&wise(X))))&
(![X]:((patient(X)&~patient(X))<=>~curious(X)))&
(![X]:((~tall(X)&brave(X))<=>~calm(X)))&
(![X]:((rich(X)&patient(X))=>~patient(X)))&
(![X]:(kind(X)=>(~generous(X)<~>kind(X))))&
(![X]:(humble(X)<=>quiet(X)))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(~brave(mary))&
(?[X]:((creative(X)<~>happy(X))))&
(~creative(paul))&
((~humble(lucy)<~>happy(lucy)))&
(creative(mary))&
(?[X]:(happy(X))) | ~rich(mary) | [] | null | 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. | Mary 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(mary) | [] | null | 0 |
If someone is both not strong and not funny then lucy is not wise.
If someone is both happy and calm then someone is both not generous and not old and vice versa.
Everyone who is both not tall and not kind is both quiet and generous.
If paul is both not generous and not creative then someone is both strong and brave.
Everyone who is both creative and kind is generous.
Everyone who is not creative or wise is either not calm or rich and vice versa.
Everyone who is not curious or tall is both not happy and old and vice versa.
If mary is both calm and not tall then someone is not tall.
Everyone who is either generous or not old is either kind or not curious.
Everyone who is not tall or not humble is both patient and strong.
If fred is either tall or patient then someone is not happy.
Everyone who is both calm and not kind is not patient or not tall and vice versa.
Everyone who is happy or not funny is not kind or not generous.
Everyone who is creative is either not strong or quiet and vice versa.
If paul is old or tall then someone is either not kind or happy and vice versa.
If someone is either not wise or wise then susan is generous.
Someone is either not generous or kind.
Lucy is wise or curious.
Lucy is funny.
Fred is not rich or patient.
Mary is either strong or tall.
Alice is humble or not calm.
Someone is quiet.
Mary is either brave or not humble. | Lucy is wise. | neutral | ((?[X]:((~strong(X)&~funny(X))))=>(~wise(lucy)))&
((?[X]:((happy(X)&calm(X))))<=>(?[X]:((~generous(X)&~old(X)))))&
(![X]:((~tall(X)&~kind(X))=>(quiet(X)&generous(X))))&
(((~generous(paul)&~creative(paul)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:((creative(X)&kind(X))=>generous(X)))&
(![X]:((~creative(X)|wise(X))<=>(~calm(X)<~>rich(X))))&
(![X]:((~curious(X)|tall(X))<=>(~happy(X)&old(X))))&
(((calm(mary)&~tall(mary)))=>(?[X]:(~tall(X))))&
(![X]:((generous(X)<~>~old(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~tall(X)|~humble(X))=>(patient(X)&strong(X))))&
(((tall(fred)<~>patient(fred)))=>(?[X]:(~happy(X))))&
(![X]:((calm(X)&~kind(X))<=>(~patient(X)|~tall(X))))&
(![X]:((happy(X)|~funny(X))=>(~kind(X)|~generous(X))))&
(![X]:(creative(X)<=>(~strong(X)<~>quiet(X))))&
(((old(paul)|tall(paul)))<=>(?[X]:((~kind(X)<~>happy(X)))))&
((?[X]:((~wise(X)<~>wise(X))))=>(generous(susan)))&
(?[X]:((~generous(X)<~>kind(X))))&
((wise(lucy)|curious(lucy)))&
(funny(lucy))&
((~rich(fred)|patient(fred)))&
((strong(mary)<~>tall(mary)))&
((humble(alice)|~calm(alice)))&
(?[X]:(quiet(X)))&
((brave(mary)<~>~humble(mary))) | wise(lucy) | [] | null | 0 |
Everyone who is not tall or kind is both not rich and humble and vice versa.
Everyone who is not strong or brave is not patient.
Everyone who is both rich and patient is funny or not old and vice versa.
Everyone who is both not old and old is both patient and not generous.
If alice is rich then paul is not brave and vice versa.
Everyone who is not rich is either funny or not creative and vice versa.
If fred is not generous or generous then alice is both not happy and not kind.
Everyone who is rich is either brave or tall.
If someone is either not generous or kind then someone is either not kind or not curious and vice versa.
If someone is not creative then paul is either not calm or funny and vice versa.
Everyone who is either not strong or not wise is both humble and wise and vice versa.
Everyone who is not strong is tall and vice versa.
If mary is rich or old then alice is either not funny or not generous.
If someone is both not old and quiet then someone is either not humble or not generous.
Everyone who is both happy and not brave is not old and vice versa.
Everyone who is both generous and kind is either not wise or not old.
Someone is not calm or kind.
Alice is either not wise or calm.
Someone is not quiet or not wise.
Fred is not quiet or humble.
Lucy is either quiet or not creative.
Lucy is both not funny and curious.
Paul is either tall or not kind.
Someone is tall. | Alice is not funny. | entailment | (![X]:((~tall(X)|kind(X))<=>(~rich(X)&humble(X))))&
(![X]:((~strong(X)|brave(X))=>~patient(X)))&
(![X]:((rich(X)&patient(X))<=>(funny(X)|~old(X))))&
(![X]:((~old(X)&old(X))=>(patient(X)&~generous(X))))&
((rich(alice))<=>(~brave(paul)))&
(![X]:(~rich(X)<=>(funny(X)<~>~creative(X))))&
(((~generous(fred)|generous(fred)))=>((~happy(alice)&~kind(alice))))&
(![X]:(rich(X)=>(brave(X)<~>tall(X))))&
((?[X]:((~generous(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
((?[X]:(~creative(X)))<=>((~calm(paul)<~>funny(paul))))&
(![X]:((~strong(X)<~>~wise(X))<=>(humble(X)&wise(X))))&
(![X]:(~strong(X)<=>tall(X)))&
(((rich(mary)|old(mary)))=>((~funny(alice)<~>~generous(alice))))&
((?[X]:((~old(X)&quiet(X))))=>(?[X]:((~humble(X)<~>~generous(X)))))&
(![X]:((happy(X)&~brave(X))<=>~old(X)))&
(![X]:((generous(X)&kind(X))=>(~wise(X)<~>~old(X))))&
(?[X]:((~calm(X)|kind(X))))&
((~wise(alice)<~>calm(alice)))&
(?[X]:((~quiet(X)|~wise(X))))&
((~quiet(fred)|humble(fred)))&
((quiet(lucy)<~>~creative(lucy)))&
((~funny(lucy)&curious(lucy)))&
((tall(paul)<~>~kind(paul)))&
(?[X]:(tall(X))) | ~funny(alice) | [
"p0",
"p1",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2802485620165467553187552
% SZS output start Proof for 2802485620165467553187552
1. ! [X0] : ((kind(X0) | ~tall(X0)) <=> (humble(X0) & ~rich(X0))) [input p0]
2. ! [X0] : ((brave(X0) | ~strong(X0)) => ~patient(X0)) [input p1]
3. ! [X0] : ((patient(X0) & rich(X0)) <=> (~old(X0) | funny(X0))) [input p2]
12. ! [X0] : (~strong(X0) <=> tall(X0)) [input p11]
25. funny(alice) [input hypothesis]
28. ! [X0] : (~patient(X0) | (~brave(X0) & strong(X0))) [ennf transformation 2]
37. ! [X0] : (((kind(X0) | ~tall(X0)) | (~humble(X0) | rich(X0))) & ((humble(X0) & ~rich(X0)) | (~kind(X0) & tall(X0)))) [nnf transformation 1]
38. ! [X0] : ((kind(X0) | ~tall(X0) | ~humble(X0) | rich(X0)) & ((humble(X0) & ~rich(X0)) | (~kind(X0) & tall(X0)))) [flattening 37]
39. ! [X0] : (((patient(X0) & rich(X0)) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | (~patient(X0) | ~rich(X0)))) [nnf transformation 3]
40. ! [X0] : (((patient(X0) & rich(X0)) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | ~patient(X0) | ~rich(X0))) [flattening 39]
55. ! [X0] : ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))) [nnf transformation 12]
73. ~rich(X0) | tall(X0) [cnf transformation 38]
78. ~patient(X0) | strong(X0) [cnf transformation 28]
81. ~funny(X0) | rich(X0) [cnf transformation 40]
83. ~funny(X0) | patient(X0) [cnf transformation 40]
118. ~strong(X0) | ~tall(X0) [cnf transformation 55]
142. funny(alice) [cnf transformation 25]
150. 2 <=> rich(alice) [avatar definition]
152. rich(alice) <- (2) [avatar component clause 150]
234. 19 <=> funny(alice) [avatar definition]
236. funny(alice) <- (19) [avatar component clause 234]
319. 19 [avatar split clause 142,234]
320. tall(alice) <- (2) [resolution 73,152]
323. rich(alice) <- (19) [resolution 81,236]
324. patient(alice) <- (19) [resolution 83,236]
326. strong(alice) <- (19) [resolution 324,78]
328. ~tall(alice) <- (19) [resolution 118,326]
329. $false <- (2, 19) [subsumption resolution 328,320]
330. ~2 | ~19 [avatar contradiction clause 329]
331. 2 | ~19 [avatar split clause 323,234,150]
332. $false [avatar sat refutation 319,330,331]
% SZS output end Proof for 2802485620165467553187552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not patient then john is rich or humble. If someone is not creative then paul is funny and vice versa. Everyone who is both not curious and curious is brave or humble and vice versa. Everyone who is either creative or funny is not kind. Everyone who is either generous or brave is not patient or quiet. If someone is quiet then someone is not quiet and vice versa. Everyone who is not happy or not patient is both strong and funny and vice versa. If lucy is either wise or not creative then john is both old and not old and vice versa. If someone is either calm or not tall then someone is either not funny or wise and vice versa. If alice is not wise then someone is both not strong and not old and vice versa. If paul is both not funny and calm then john is curious. If mary is either not patient or funny then lucy is either not quiet or funny and vice versa. If someone is not wise or wise then someone is not happy and vice versa. Everyone who is either kind or tall is rich or calm and vice versa. If someone is either not quiet or kind then someone is not humble or creative and vice versa. Paul is both generous and not happy. Someone is either generous or not kind. Someone is not wise or brave. Fred is either not funny or kind. Fred is both not patient and not generous. Mary is both calm and creative. Paul is both not humble and not patient. | John is calm. | neutral | ((~patient(paul))=>((rich(john)|humble(john))))&
((?[X]:(~creative(X)))<=>(funny(paul)))&
(![X]:((~curious(X)&curious(X))<=>(brave(X)|humble(X))))&
(![X]:((creative(X)<~>funny(X))=>~kind(X)))&
(![X]:((generous(X)<~>brave(X))=>(~patient(X)|quiet(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)|~patient(X))<=>(strong(X)&funny(X))))&
(((wise(lucy)<~>~creative(lucy)))<=>((old(john)&~old(john))))&
((?[X]:((calm(X)<~>~tall(X))))<=>(?[X]:((~funny(X)<~>wise(X)))))&
((~wise(alice))<=>(?[X]:((~strong(X)&~old(X)))))&
(((~funny(paul)&calm(paul)))=>(curious(john)))&
(((~patient(mary)<~>funny(mary)))<=>((~quiet(lucy)<~>funny(lucy))))&
((?[X]:((~wise(X)|wise(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)<~>tall(X))<=>(rich(X)|calm(X))))&
((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((~humble(X)|creative(X)))))&
((generous(paul)&~happy(paul)))&
(?[X]:((generous(X)<~>~kind(X))))&
(?[X]:((~wise(X)|brave(X))))&
((~funny(fred)<~>kind(fred)))&
((~patient(fred)&~generous(fred)))&
((calm(mary)&creative(mary)))&
((~humble(paul)&~patient(paul))) | calm(john) | [] | null | 0 |
Everyone who is either not kind or not humble is both not patient and funny.
Everyone who is either not generous or funny is either not brave or not quiet.
Everyone who is not quiet is not brave or not rich and vice versa.
If someone is not quiet then paul is brave and vice versa.
Everyone who is humble or not brave is not funny or not happy.
If someone is either not humble or not kind then alice is both humble and not quiet and vice versa.
Everyone who is not happy is either not humble or not calm.
Everyone who is both patient and not kind is not wise or not calm and vice versa.
Everyone who is both not generous and creative is both old and not patient.
If someone is either happy or creative then someone is either not calm or funny and vice versa.
Everyone who is both brave and tall is not generous or funny.
Everyone who is not patient or generous is either not calm or not old and vice versa.
Everyone who is not strong or humble is not funny or not tall and vice versa.
Everyone who is not kind is old or quiet.
If mary is either not calm or humble then someone is not rich or not humble and vice versa.
If john is happy or humble then alice is quiet or not funny.
Someone is kind or generous.
Someone is not old or not happy.
Someone is either not creative or not quiet.
John is both not wise and not calm.
Someone is happy.
Alice is both tall and not creative.
Someone is both not creative and curious.
John is both not calm and not brave. | John is tall. | neutral | (![X]:((~kind(X)<~>~humble(X))=>(~patient(X)&funny(X))))&
(![X]:((~generous(X)<~>funny(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
((?[X]:(~quiet(X)))<=>(brave(paul)))&
(![X]:((humble(X)|~brave(X))=>(~funny(X)|~happy(X))))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((humble(alice)&~quiet(alice))))&
(![X]:(~happy(X)=>(~humble(X)<~>~calm(X))))&
(![X]:((patient(X)&~kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~generous(X)&creative(X))=>(old(X)&~patient(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:((~calm(X)<~>funny(X)))))&
(![X]:((brave(X)&tall(X))=>(~generous(X)|funny(X))))&
(![X]:((~patient(X)|generous(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((~strong(X)|humble(X))<=>(~funny(X)|~tall(X))))&
(![X]:(~kind(X)=>(old(X)|quiet(X))))&
(((~calm(mary)<~>humble(mary)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((happy(john)|humble(john)))=>((quiet(alice)|~funny(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((~old(X)|~happy(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
((~wise(john)&~calm(john)))&
(?[X]:(happy(X)))&
((tall(alice)&~creative(alice)))&
(?[X]:((~creative(X)&curious(X))))&
((~calm(john)&~brave(john))) | tall(john) | [] | null | 0 |
Everyone who is happy or not generous is both not funny and wise.
If someone is tall then mary is both curious and not old and vice versa.
If someone is old then susan is tall and vice versa.
If lucy is both not happy and not generous then lucy is either humble or not kind and vice versa.
Everyone who is not rich or not creative is either curious or quiet and vice versa.
If fred is both not tall and not strong then fred is either funny or not funny and vice versa.
Everyone who is either not generous or not brave is calm or not creative and vice versa.
If someone is not strong then lucy is not patient and vice versa.
Everyone who is wise or not curious is not brave or wise and vice versa.
Everyone who is both not funny and not kind is both not creative and curious and vice versa.
Everyone who is rich is creative.
If someone is either wise or calm then lucy is not strong or not quiet and vice versa.
Everyone who is both tall and humble is wise or not creative and vice versa.
If someone is not calm or curious then alice is rich or not kind and vice versa.
If someone is not tall then john is both not humble and not happy.
If john is not curious or not calm then someone is both not wise and not old.
Someone is both not quiet and humble.
Someone is curious.
John is tall.
Lucy is not happy or not curious.
Someone is old.
Someone is happy. | Lucy is not humble. | neutral | (![X]:((happy(X)|~generous(X))=>(~funny(X)&wise(X))))&
((?[X]:(tall(X)))<=>((curious(mary)&~old(mary))))&
((?[X]:(old(X)))<=>(tall(susan)))&
(((~happy(lucy)&~generous(lucy)))<=>((humble(lucy)<~>~kind(lucy))))&
(![X]:((~rich(X)|~creative(X))<=>(curious(X)<~>quiet(X))))&
(((~tall(fred)&~strong(fred)))<=>((funny(fred)<~>~funny(fred))))&
(![X]:((~generous(X)<~>~brave(X))<=>(calm(X)|~creative(X))))&
((?[X]:(~strong(X)))<=>(~patient(lucy)))&
(![X]:((wise(X)|~curious(X))<=>(~brave(X)|wise(X))))&
(![X]:((~funny(X)&~kind(X))<=>(~creative(X)&curious(X))))&
(![X]:(rich(X)=>creative(X)))&
((?[X]:((wise(X)<~>calm(X))))<=>((~strong(lucy)|~quiet(lucy))))&
(![X]:((tall(X)&humble(X))<=>(wise(X)|~creative(X))))&
((?[X]:((~calm(X)|curious(X))))<=>((rich(alice)|~kind(alice))))&
((?[X]:(~tall(X)))=>((~humble(john)&~happy(john))))&
(((~curious(john)|~calm(john)))=>(?[X]:((~wise(X)&~old(X)))))&
(?[X]:((~quiet(X)&humble(X))))&
(?[X]:(curious(X)))&
(tall(john))&
((~happy(lucy)|~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:(happy(X))) | ~humble(lucy) | [] | null | 0 |
Everyone who is both not generous and not curious is brave. If someone is both rich and happy then fred is both not quiet and calm and vice versa. Everyone who is both not humble and creative is funny. If lucy is strong or not kind then paul is strong or curious and vice versa. Everyone who is tall or not strong is both curious and not kind. Everyone who is either not strong or not humble is not funny. If mary is not rich or tall then someone is funny or happy. If someone is both strong and not old then alice is humble or not funny. Everyone who is brave or not patient is either kind or not quiet and vice versa. If paul is both calm and not old then paul is both curious and not rich. If alice is both not brave and not tall then someone is not patient. Everyone who is tall or not quiet is kind. Everyone who is both rich and not creative is calm or not calm and vice versa. If someone is either funny or not kind then someone is both not curious and happy and vice versa. Everyone who is both not funny and not kind is not brave or not quiet and vice versa. If someone is not happy or patient then someone is both not curious and patient. Fred is either strong or not old. Paul is humble. Fred is either not curious or humble. Someone is either generous or not quiet. John is not calm or funny. Someone is either not curious or not quiet. | Paul is brave. | entailment | (![X]:((~generous(X)&~curious(X))=>brave(X)))&
((?[X]:((rich(X)&happy(X))))<=>((~quiet(fred)&calm(fred))))&
(![X]:((~humble(X)&creative(X))=>funny(X)))&
(((strong(lucy)|~kind(lucy)))<=>((strong(paul)|curious(paul))))&
(![X]:((tall(X)|~strong(X))=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
(((~rich(mary)|tall(mary)))=>(?[X]:((funny(X)|happy(X)))))&
((?[X]:((strong(X)&~old(X))))=>((humble(alice)|~funny(alice))))&
(![X]:((brave(X)|~patient(X))<=>(kind(X)<~>~quiet(X))))&
(((calm(paul)&~old(paul)))=>((curious(paul)&~rich(paul))))&
(((~brave(alice)&~tall(alice)))=>(?[X]:(~patient(X))))&
(![X]:((tall(X)|~quiet(X))=>kind(X)))&
(![X]:((rich(X)&~creative(X))<=>(calm(X)|~calm(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~brave(X)|~quiet(X))))&
((?[X]:((~happy(X)|patient(X))))=>(?[X]:((~curious(X)&patient(X)))))&
((strong(fred)<~>~old(fred)))&
(humble(paul))&
((~curious(fred)<~>humble(fred)))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~calm(john)|funny(john)))&
(?[X]:((~curious(X)<~>~quiet(X)))) | brave(paul) | [
"p1",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1291892509528828045422886
% SZS output start Proof for 1291892509528828045422886
2. ? [X0] : (happy(X0) & rich(X0)) <=> (calm(fred) & ~quiet(fred)) [input p1]
12. ! [X0] : ((~quiet(X0) | tall(X0)) => kind(X0)) [input p11]
13. ! [X0] : ((~creative(X0) & rich(X0)) <=> (~calm(X0) | calm(X0))) [input p12]
14. ? [X0] : (funny(X0) <~> ~kind(X0)) <=> ? [X0] : (happy(X0) & ~curious(X0)) [input p13]
15. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (~quiet(X0) | ~brave(X0))) [input p14]
23. ~brave(paul) [input hypothesis]
24. ? [X0] : (funny(X0) <~> ~kind(X0)) <=> ? [X1] : (happy(X1) & ~curious(X1)) [rectify 14]
39. ! [X0] : (kind(X0) | (quiet(X0) & ~tall(X0))) [ennf transformation 12]
41. (? [X0] : (happy(X0) & rich(X0)) | (~calm(fred) | quiet(fred))) & ((calm(fred) & ~quiet(fred)) | ! [X0] : (~happy(X0) | ~rich(X0))) [nnf transformation 2]
42. (? [X0] : (happy(X0) & rich(X0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X0] : (~happy(X0) | ~rich(X0))) [flattening 41]
43. (? [X0] : (happy(X0) & rich(X0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X1] : (~happy(X1) | ~rich(X1))) [rectify 42]
44. ? [X0] : (happy(X0) & rich(X0)) => (happy(sK0) & rich(sK0)) [choice axiom]
45. ((happy(sK0) & rich(sK0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X1] : (~happy(X1) | ~rich(X1))) [skolemisation 43,44]
55. ! [X0] : (((~creative(X0) & rich(X0)) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | (creative(X0) | ~rich(X0)))) [nnf transformation 13]
56. ! [X0] : (((~creative(X0) & rich(X0)) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | creative(X0) | ~rich(X0))) [flattening 55]
57. (? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X1] : (happy(X1) & ~curious(X1)) | ! [X0] : ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) [nnf transformation 24]
58. (? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X2] : (happy(X2) & ~curious(X2)) | ! [X3] : ((funny(X3) | kind(X3)) & (~kind(X3) | ~funny(X3)))) [rectify 57]
59. ? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) => ((kind(sK3) | ~funny(sK3)) & (~kind(sK3) | funny(sK3))) [choice axiom]
60. ? [X2] : (happy(X2) & ~curious(X2)) => (happy(sK4) & ~curious(sK4)) [choice axiom]
61. (((kind(sK3) | ~funny(sK3)) & (~kind(sK3) | funny(sK3))) | ! [X1] : (~happy(X1) | curious(X1))) & ((happy(sK4) & ~curious(sK4)) | ! [X3] : ((funny(X3) | kind(X3)) & (~kind(X3) | ~funny(X3)))) [skolemisation 58,60,59]
62. ! [X0] : (((~kind(X0) & ~funny(X0)) | (quiet(X0) & brave(X0))) & ((~quiet(X0) | ~brave(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 15]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | (quiet(X0) & brave(X0))) & (~quiet(X0) | ~brave(X0) | kind(X0) | funny(X0))) [flattening 62]
76. ~quiet(fred) | ~happy(X1) | ~rich(X1) [cnf transformation 45]
104. kind(X0) | quiet(X0) [cnf transformation 39]
106. rich(X0) | ~calm(X0) [cnf transformation 56]
107. calm(X0) | rich(X0) [cnf transformation 56]
113. happy(sK4) | funny(X3) | kind(X3) [cnf transformation 61]
117. ~funny(X0) | brave(X0) [cnf transformation 63]
119. ~kind(X0) | brave(X0) [cnf transformation 63]
120. ~kind(X0) | quiet(X0) [cnf transformation 63]
135. ~brave(paul) [cnf transformation 23]
137. 1 <=> quiet(fred) [avatar definition]
138. ~quiet(fred) <- (~1) [avatar component clause 137]
155. 5 <=> ! [X1] : (~happy(X1) | ~rich(X1)) [avatar definition]
156. ~happy(X1) | ~rich(X1) <- (5) [avatar component clause 155]
158. 5 | ~1 [avatar split clause 76,137,155]
238. rich(X0) [subsumption resolution 106,107]
253. 26 <=> ! [X3] : (funny(X3) | kind(X3)) [avatar definition]
254. kind(X3) | funny(X3) <- (26) [avatar component clause 253]
256. 27 <=> happy(sK4) [avatar definition]
258. happy(sK4) <- (27) [avatar component clause 256]
259. 26 | 27 [avatar split clause 113,256,253]
270. quiet(X0) [subsumption resolution 120,104]
322. $false <- (~1) [subsumption resolution 138,270]
323. 1 [avatar contradiction clause 322]
324. ~happy(X1) <- (5) [subsumption resolution 156,238]
326. $false <- (5, 27) [resolution 324,258]
327. ~5 | ~27 [avatar contradiction clause 326]
341. funny(X0) | brave(X0) <- (26) [resolution 254,119]
345. brave(X0) <- (26) [subsumption resolution 341,117]
351. $false <- (26) [resolution 345,135]
352. ~26 [avatar contradiction clause 351]
353. $false [avatar sat refutation 158,259,323,327,352]
% SZS output end Proof for 1291892509528828045422886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not kind and not happy then someone is wise. Everyone who is either not tall or not patient is either not curious or not old. If alice is either funny or brave then someone is not creative or generous and vice versa. If susan is calm or not patient then paul is both not curious and calm. Everyone who is either not wise or calm is not calm and vice versa. If alice is either not wise or calm then susan is curious or not old. Everyone who is either funny or brave is not generous or not humble and vice versa. Everyone who is either kind or strong is calm and vice versa. Everyone who is old is either rich or calm and vice versa. Everyone who is both not strong and not tall is both quiet and not tall and vice versa. If someone is both not funny and curious then someone is both quiet and not humble and vice versa. If fred is either strong or not creative then someone is patient or creative. If susan is both not brave and wise then someone is calm. Everyone who is both wise and generous is both not quiet and curious and vice versa. If fred is not quiet or not kind then someone is both happy and creative and vice versa. If susan is both strong and not patient then someone is either curious or quiet. Mary is calm or funny. Someone is not creative or humble. Someone is either not strong or generous. Someone is not brave. Lucy is not wise or patient. Mary is either not strong or curious. | Lucy is tall. | neutral | (((~kind(mary)&~happy(mary)))=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(~curious(X)<~>~old(X))))&
(((funny(alice)<~>brave(alice)))<=>(?[X]:((~creative(X)|generous(X)))))&
(((calm(susan)|~patient(susan)))=>((~curious(paul)&calm(paul))))&
(![X]:((~wise(X)<~>calm(X))<=>~calm(X)))&
(((~wise(alice)<~>calm(alice)))=>((curious(susan)|~old(susan))))&
(![X]:((funny(X)<~>brave(X))<=>(~generous(X)|~humble(X))))&
(![X]:((kind(X)<~>strong(X))<=>calm(X)))&
(![X]:(old(X)<=>(rich(X)<~>calm(X))))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)&~tall(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((quiet(X)&~humble(X)))))&
(((strong(fred)<~>~creative(fred)))=>(?[X]:((patient(X)|creative(X)))))&
(((~brave(susan)&wise(susan)))=>(?[X]:(calm(X))))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)&curious(X))))&
(((~quiet(fred)|~kind(fred)))<=>(?[X]:((happy(X)&creative(X)))))&
(((strong(susan)&~patient(susan)))=>(?[X]:((curious(X)<~>quiet(X)))))&
((calm(mary)|funny(mary)))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((~strong(X)<~>generous(X))))&
(?[X]:(~brave(X)))&
((~wise(lucy)|patient(lucy)))&
((~strong(mary)<~>curious(mary))) | tall(lucy) | [] | null | 0 |
Everyone who is both patient and not funny is not rich or rich and vice versa.
Everyone who is not creative or not quiet is either not calm or funny and vice versa.
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
Mary is generous.
Someone is kind or strong.
Lucy is not tall or not rich.
Mary is tall.
Fred is generous.
Alice is calm or strong. | Paul is kind. | contradiction | (![X]:((patient(X)&~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(~calm(X)<~>funny(X))))&
(![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
(generous(mary))&
(?[X]:((kind(X)|strong(X))))&
((~tall(lucy)|~rich(lucy)))&
(tall(mary))&
(generous(fred))&
((calm(alice)|strong(alice))) | kind(paul) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5463904374634304073245207
% SZS output start Proof for 5463904374634304073245207
1. ! [X0] : ((~funny(X0) & patient(X0)) <=> (rich(X0) | ~rich(X0))) [input p0]
4. ! [X0] : ((curious(X0) | ~curious(X0)) <=> generous(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p6]
9. ! [X0] : ((~old(X0) | happy(X0)) <=> (~kind(X0) | funny(X0))) [input p8]
21. kind(paul) [input hypothesis]
24. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 6]
29. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | (funny(X0) | ~patient(X0)))) [nnf transformation 1]
30. ! [X0] : (((~funny(X0) & patient(X0)) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | funny(X0) | ~patient(X0))) [flattening 29]
33. ! [X0] : (((curious(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 4]
34. ! [X0] : ((curious(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [flattening 33]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 7]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | funny(X0) | patient(X0))) [flattening 36]
42. ! [X0] : (((~old(X0) | happy(X0)) | (kind(X0) & ~funny(X0))) & ((~kind(X0) | funny(X0)) | (old(X0) & ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : ((~old(X0) | happy(X0) | (kind(X0) & ~funny(X0))) & (~kind(X0) | funny(X0) | (old(X0) & ~happy(X0)))) [flattening 42]
59. patient(X0) | rich(X0) [cnf transformation 30]
60. ~rich(X0) | patient(X0) [cnf transformation 30]
61. ~funny(X0) | rich(X0) [cnf transformation 30]
62. ~rich(X0) | ~funny(X0) [cnf transformation 30]
71. generous(X0) | curious(X0) [cnf transformation 34]
72. ~curious(X0) | generous(X0) [cnf transformation 34]
78. ~curious(X0) | happy(X0) [cnf transformation 24]
82. ~patient(X0) | ~generous(X0) | curious(X0) [cnf transformation 37]
88. ~kind(X0) | funny(X0) | ~happy(X0) [cnf transformation 43]
113. kind(paul) [cnf transformation 21]
114. ~funny(X0) [subsumption resolution 61,62]
115. patient(X0) [subsumption resolution 59,60]
119. generous(X0) [subsumption resolution 71,72]
120. ~generous(X0) | curious(X0) [subsumption resolution 82,115]
121. curious(X0) [subsumption resolution 120,119]
145. ~happy(X0) | ~kind(X0) [subsumption resolution 88,114]
196. happy(X0) [resolution 78,121]
203. ~kind(X0) [resolution 145,196]
206. $false [resolution 203,113]
% SZS output end Proof for 5463904374634304073245207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is wise or kind. If someone is kind then paul is kind or not brave. If paul is not brave then lucy is not rich or kind. If susan is either not strong or patient then someone is funny and vice versa. If someone is both not tall and creative then someone is not generous or quiet and vice versa. If someone is not tall then someone is not wise or not generous and vice versa. If john is both brave and not kind then mary is either tall or not generous and vice versa. If lucy is either not wise or not quiet then alice is not happy and vice versa. Everyone who is creative or not tall is both not strong and not funny. Everyone who is either wise or not wise is quiet. If someone is kind then john is not humble. If someone is both funny and strong then someone is either not generous or kind. If someone is brave then fred is strong or generous. Everyone who is rich or not wise is not curious or not quiet and vice versa. Everyone who is not strong or tall is either tall or generous. Everyone who is both calm and not creative is either humble or generous and vice versa. Paul is either happy or not funny. Mary is strong or not funny. Someone is either happy or tall. Alice is happy or not humble. Someone is both humble and not brave. Mary is brave or not wise. Someone is both not funny and not generous. Someone is either not funny or not rich. | Paul is not brave. | neutral | (![X]:(~patient(X)=>(wise(X)|kind(X))))&
((?[X]:(kind(X)))=>((kind(paul)|~brave(paul))))&
((~brave(paul))=>((~rich(lucy)|kind(lucy))))&
(((~strong(susan)<~>patient(susan)))<=>(?[X]:(funny(X))))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((~wise(X)|~generous(X)))))&
(((brave(john)&~kind(john)))<=>((tall(mary)<~>~generous(mary))))&
(((~wise(lucy)<~>~quiet(lucy)))<=>(~happy(alice)))&
(![X]:((creative(X)|~tall(X))=>(~strong(X)&~funny(X))))&
(![X]:((wise(X)<~>~wise(X))=>quiet(X)))&
((?[X]:(kind(X)))=>(~humble(john)))&
((?[X]:((funny(X)&strong(X))))=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:(brave(X)))=>((strong(fred)|generous(fred))))&
(![X]:((rich(X)|~wise(X))<=>(~curious(X)|~quiet(X))))&
(![X]:((~strong(X)|tall(X))=>(tall(X)<~>generous(X))))&
(![X]:((calm(X)&~creative(X))<=>(humble(X)<~>generous(X))))&
((happy(paul)<~>~funny(paul)))&
((strong(mary)|~funny(mary)))&
(?[X]:((happy(X)<~>tall(X))))&
((happy(alice)|~humble(alice)))&
(?[X]:((humble(X)&~brave(X))))&
((brave(mary)|~wise(mary)))&
(?[X]:((~funny(X)&~generous(X))))&
(?[X]:((~funny(X)<~>~rich(X)))) | ~brave(paul) | [] | null | 0 |
Everyone who is both not calm and kind is generous and vice versa.
If someone is both not quiet and not kind then susan is both creative and not patient and vice versa.
If susan is both not curious and not old then alice is both not tall and strong and vice versa.
Everyone who is tall or not generous is not curious or old.
Everyone who is both tall and not tall is quiet or not quiet.
If paul is both not old and not tall then alice is either not humble or calm.
If alice is either not generous or wise then lucy is not creative or not kind and vice versa.
If someone is either calm or quiet then someone is both not brave and calm.
Everyone who is not calm is either brave or not rich.
Everyone who is both not humble and quiet is both not brave and not creative and vice versa.
If someone is both kind and not humble then susan is generous.
Everyone who is either not old or tall is both brave and not kind and vice versa.
Everyone who is either funny or not old is old.
If fred is wise then someone is either generous or not strong and vice versa.
Everyone who is both not quiet and strong is both not humble and curious and vice versa.
If someone is not calm or not strong then someone is both tall and not generous and vice versa.
Someone is not calm or happy.
Susan is both creative and old.
Someone is both not tall and not brave.
Mary is both quiet and not funny.
Susan is both rich and humble.
Someone is not old or wise.
Fred is either not happy or wise.
Someone is not rich. | Susan is old. | entailment | (![X]:((~calm(X)&kind(X))<=>generous(X)))&
((?[X]:((~quiet(X)&~kind(X))))<=>((creative(susan)&~patient(susan))))&
(((~curious(susan)&~old(susan)))<=>((~tall(alice)&strong(alice))))&
(![X]:((tall(X)|~generous(X))=>(~curious(X)|old(X))))&
(![X]:((tall(X)&~tall(X))=>(quiet(X)|~quiet(X))))&
(((~old(paul)&~tall(paul)))=>((~humble(alice)<~>calm(alice))))&
(((~generous(alice)<~>wise(alice)))<=>((~creative(lucy)|~kind(lucy))))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:(~calm(X)=>(brave(X)<~>~rich(X))))&
(![X]:((~humble(X)&quiet(X))<=>(~brave(X)&~creative(X))))&
((?[X]:((kind(X)&~humble(X))))=>(generous(susan)))&
(![X]:((~old(X)<~>tall(X))<=>(brave(X)&~kind(X))))&
(![X]:((funny(X)<~>~old(X))=>old(X)))&
((wise(fred))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~calm(X)|~strong(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
(?[X]:((~calm(X)|happy(X))))&
((creative(susan)&old(susan)))&
(?[X]:((~tall(X)&~brave(X))))&
((quiet(mary)&~funny(mary)))&
((rich(susan)&humble(susan)))&
(?[X]:((~old(X)|wise(X))))&
((~happy(fred)<~>wise(fred)))&
(?[X]:(~rich(X))) | old(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7415857901492070114241382
% SZS output start Proof for 7415857901492070114241382
18. old(susan) & creative(susan) [input p17]
25. ~old(susan) [input hypothesis]
136. old(susan) [cnf transformation 18]
147. ~old(susan) [cnf transformation 25]
181. 8 <=> old(susan) [avatar definition]
319. 8 [avatar split clause 136,181]
336. ~8 [avatar split clause 147,181]
337. $false [avatar sat refutation 319,336]
% SZS output end Proof for 7415857901492070114241382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or funny is both old and not creative.
Everyone who is old or not curious is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Mary is rich. | Fred is not humble. | entailment | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|~curious(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(rich(mary)) | ~humble(fred) | [
"p0",
"p1",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 729055089410851002989468
% SZS output start Proof for 729055089410851002989468
1. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~creative(X0) & old(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | old(X0)) => (~strong(X0) & ~old(X0))) [input p1]
6. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p5]
8. ! [X0] : ((calm(X0) | ~curious(X0)) <=> (kind(X0) & ~humble(X0))) [input p7]
20. humble(fred) [input hypothesis]
22. ! [X0] : ((~creative(X0) & old(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 1]
23. ! [X0] : ((~strong(X0) & ~old(X0)) | (curious(X0) & ~old(X0))) [ennf transformation 2]
25. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 6]
30. ! [X0] : ((~creative(X0) & old(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 22]
38. ! [X0] : (((calm(X0) | ~curious(X0)) | (~kind(X0) | humble(X0))) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [nnf transformation 8]
39. ! [X0] : ((calm(X0) | ~curious(X0) | ~kind(X0) | humble(X0)) & ((kind(X0) & ~humble(X0)) | (~calm(X0) & curious(X0)))) [flattening 38]
57. ~funny(X0) | ~curious(X0) | old(X0) [cnf transformation 30]
60. ~old(X0) | ~old(X0) [cnf transformation 23]
76. ~curious(X0) | funny(X0) [cnf transformation 25]
80. ~humble(X0) | curious(X0) [cnf transformation 39]
111. humble(fred) [cnf transformation 20]
112. ~old(X0) [duplicate literal removal 60]
195. 17 <=> humble(fred) [avatar definition]
196. humble(fred) <- (17) [avatar component clause 195]
220. 17 [avatar split clause 111,195]
221. curious(fred) <- (17) [resolution 80,196]
223. funny(fred) <- (17) [resolution 221,76]
230. ~curious(fred) | old(fred) <- (17) [resolution 57,223]
232. old(fred) <- (17) [subsumption resolution 230,221]
233. $false <- (17) [subsumption resolution 232,112]
234. ~17 [avatar contradiction clause 233]
236. $false [avatar sat refutation 220,234]
% SZS output end Proof for 729055089410851002989468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or rich is either calm or happy and vice versa.
Everyone who is both creative and humble is both not wise and not creative.
If someone is both wise and patient then someone is either generous or tall.
If fred is both kind and not quiet then someone is not curious or generous and vice versa.
If someone is both humble and not brave then someone is either not kind or not calm and vice versa.
Everyone who is both wise and calm is not curious or funny and vice versa.
Everyone who is either curious or not generous is both not quiet and happy.
Everyone who is funny or not wise is tall or not curious and vice versa.
Everyone who is both not creative and not brave is brave and vice versa.
If fred is calm then someone is both wise and not patient and vice versa.
If someone is not quiet then alice is either rich or not kind.
If someone is either not rich or kind then someone is old or not rich.
If fred is humble or calm then john is both generous and tall.
If someone is not happy or not wise then john is both not patient and funny.
Everyone who is either humble or strong is both not old and not brave.
If mary is both not curious and wise then someone is both patient and not quiet.
Mary is either generous or not old.
Someone is either not happy or kind.
Mary is not quiet.
Fred is not calm.
Susan is both not kind and happy.
Someone is not wise or tall.
Susan is brave or strong.
Fred is either brave or not calm. | Alice is not happy. | contradiction | (![X]:((~strong(X)<~>rich(X))<=>(calm(X)<~>happy(X))))&
(![X]:((creative(X)&humble(X))=>(~wise(X)&~creative(X))))&
((?[X]:((wise(X)&patient(X))))=>(?[X]:((generous(X)<~>tall(X)))))&
(((kind(fred)&~quiet(fred)))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((humble(X)&~brave(X))))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((wise(X)&calm(X))<=>(~curious(X)|funny(X))))&
(![X]:((curious(X)<~>~generous(X))=>(~quiet(X)&happy(X))))&
(![X]:((funny(X)|~wise(X))<=>(tall(X)|~curious(X))))&
(![X]:((~creative(X)&~brave(X))<=>brave(X)))&
((calm(fred))<=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:(~quiet(X)))=>((rich(alice)<~>~kind(alice))))&
((?[X]:((~rich(X)<~>kind(X))))=>(?[X]:((old(X)|~rich(X)))))&
(((humble(fred)|calm(fred)))=>((generous(john)&tall(john))))&
((?[X]:((~happy(X)|~wise(X))))=>((~patient(john)&funny(john))))&
(![X]:((humble(X)<~>strong(X))=>(~old(X)&~brave(X))))&
(((~curious(mary)&wise(mary)))=>(?[X]:((patient(X)&~quiet(X)))))&
((generous(mary)<~>~old(mary)))&
(?[X]:((~happy(X)<~>kind(X))))&
(~quiet(mary))&
(~calm(fred))&
((~kind(susan)&happy(susan)))&
(?[X]:((~wise(X)|tall(X))))&
((brave(susan)|strong(susan)))&
((brave(fred)<~>~calm(fred))) | ~happy(alice) | [
"p5",
"p8",
"p9",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 970289639858058989319536
% SZS output start Proof for 970289639858058989319536
6. ! [X0] : ((calm(X0) & wise(X0)) <=> (funny(X0) | ~curious(X0))) [input p5]
9. ! [X0] : ((~brave(X0) & ~creative(X0)) <=> brave(X0)) [input p8]
10. calm(fred) <=> ? [X0] : (~patient(X0) & wise(X0)) [input p9]
14. ? [X0] : (~wise(X0) | ~happy(X0)) => (funny(john) & ~patient(john)) [input p13]
24. brave(fred) <~> ~calm(fred) [input p23]
25. ~happy(alice) [input hypothesis]
36. (funny(john) & ~patient(john)) | ! [X0] : (wise(X0) & happy(X0)) [ennf transformation 14]
55. ! [X0] : (((calm(X0) & wise(X0)) | (~funny(X0) & curious(X0))) & ((funny(X0) | ~curious(X0)) | (~calm(X0) | ~wise(X0)))) [nnf transformation 6]
56. ! [X0] : (((calm(X0) & wise(X0)) | (~funny(X0) & curious(X0))) & (funny(X0) | ~curious(X0) | ~calm(X0) | ~wise(X0))) [flattening 55]
60. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | creative(X0)))) [nnf transformation 9]
61. ! [X0] : (((~brave(X0) & ~creative(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | creative(X0))) [flattening 60]
62. (calm(fred) | ! [X0] : (patient(X0) | ~wise(X0))) & (? [X0] : (~patient(X0) & wise(X0)) | ~calm(fred)) [nnf transformation 10]
63. (calm(fred) | ! [X0] : (patient(X0) | ~wise(X0))) & (? [X1] : (~patient(X1) & wise(X1)) | ~calm(fred)) [rectify 62]
64. ? [X1] : (~patient(X1) & wise(X1)) => (~patient(sK4) & wise(sK4)) [choice axiom]
65. (calm(fred) | ! [X0] : (patient(X0) | ~wise(X0))) & ((~patient(sK4) & wise(sK4)) | ~calm(fred)) [skolemisation 63,64]
80. (calm(fred) | ~brave(fred)) & (~calm(fred) | brave(fred)) [nnf transformation 24]
106. ~funny(X0) | wise(X0) [cnf transformation 56]
119. ~brave(X0) | ~brave(X0) [cnf transformation 61]
122. calm(fred) | patient(X0) | ~wise(X0) [cnf transformation 65]
131. ~patient(john) | happy(X0) [cnf transformation 36]
133. funny(john) | happy(X0) [cnf transformation 36]
151. ~calm(fred) | brave(fred) [cnf transformation 80]
153. ~happy(alice) [cnf transformation 25]
155. ~brave(X0) [duplicate literal removal 119]
232. 17 <=> ! [X0] : (patient(X0) | ~wise(X0)) [avatar definition]
233. ~wise(X0) | patient(X0) <- (17) [avatar component clause 232]
235. 18 <=> calm(fred) [avatar definition]
238. 17 | 18 [avatar split clause 122,235,232]
298. 32 <=> funny(john) [avatar definition]
300. funny(john) <- (32) [avatar component clause 298]
303. 33 <=> ! [X0] : happy(X0) [avatar definition]
304. happy(X0) <- (33) [avatar component clause 303]
305. 33 | 32 [avatar split clause 133,298,303]
307. 34 <=> patient(john) [avatar definition]
309. ~patient(john) <- (~34) [avatar component clause 307]
311. 33 | ~34 [avatar split clause 131,307,303]
351. ~calm(fred) [subsumption resolution 151,155]
352. ~18 [avatar split clause 351,235]
358. wise(john) <- (32) [resolution 106,300]
378. patient(john) <- (17, 32) [resolution 233,358]
379. $false <- (17, 32, ~34) [subsumption resolution 378,309]
380. ~17 | ~32 | 34 [avatar contradiction clause 379]
383. $false <- (33) [resolution 304,153]
386. ~33 [avatar contradiction clause 383]
387. $false [avatar sat refutation 238,305,311,352,380,386]
% SZS output end Proof for 970289639858058989319536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and patient then someone is either kind or not creative.
Everyone who is not tall or not strong is both generous and patient and vice versa.
Everyone who is both not kind and quiet is not patient and vice versa.
Everyone who is not creative or not strong is tall and vice versa.
Everyone who is either old or curious is not quiet.
Everyone who is both quiet and not rich is either patient or rich.
If john is not funny or not happy then someone is both not creative and not humble and vice versa.
Everyone who is curious or not rich is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
Everyone who is either brave or wise is both not humble and not funny and vice versa.
Fred is either brave or not curious.
Someone is creative.
Someone is not funny.
Someone is humble or calm.
Someone is funny.
Someone is both happy and curious.
Someone is either not generous or not strong. | Lucy is not brave. | neutral | ((?[X]:((~quiet(X)&patient(X))))=>(?[X]:((kind(X)<~>~creative(X)))))&
(![X]:((~tall(X)|~strong(X))<=>(generous(X)&patient(X))))&
(![X]:((~kind(X)&quiet(X))<=>~patient(X)))&
(![X]:((~creative(X)|~strong(X))<=>tall(X)))&
(![X]:((old(X)<~>curious(X))=>~quiet(X)))&
(![X]:((quiet(X)&~rich(X))=>(patient(X)<~>rich(X))))&
(((~funny(john)|~happy(john)))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((brave(fred)<~>~curious(fred)))&
(?[X]:(creative(X)))&
(?[X]:(~funny(X)))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((~generous(X)<~>~strong(X)))) | ~brave(lucy) | [] | null | 0 |
If paul is either happy or not calm then someone is both happy and not tall. Everyone who is either not tall or not funny is not happy or not humble. If paul is not quiet then someone is humble or brave. Everyone who is funny is both happy and patient and vice versa. Everyone who is either wise or not creative is not curious. If alice is not strong or not rich then fred is not happy or patient. Everyone who is kind is not creative or not brave and vice versa. Everyone who is old is not kind or not humble and vice versa. If mary is either not strong or not quiet then someone is not strong or funny. Everyone who is either not rich or patient is funny or strong. Everyone who is not strong or strong is not old and vice versa. Everyone who is brave is either not old or rich and vice versa. If lucy is either funny or strong then someone is both rich and creative. Everyone who is not quiet is both patient and not brave and vice versa. Everyone who is either not kind or creative is both funny and not curious and vice versa. Everyone who is both not funny and tall is not humble or creative and vice versa. Someone is not strong. John is rich. Someone is not happy or generous. Someone is generous. Susan is kind. Someone is either not tall or creative. Someone is either quiet or not patient. | Paul is not calm. | neutral | (((happy(paul)<~>~calm(paul)))=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~funny(X))=>(~happy(X)|~humble(X))))&
((~quiet(paul))=>(?[X]:((humble(X)|brave(X)))))&
(![X]:(funny(X)<=>(happy(X)&patient(X))))&
(![X]:((wise(X)<~>~creative(X))=>~curious(X)))&
(((~strong(alice)|~rich(alice)))=>((~happy(fred)|patient(fred))))&
(![X]:(kind(X)<=>(~creative(X)|~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(![X]:(brave(X)<=>(~old(X)<~>rich(X))))&
(((funny(lucy)<~>strong(lucy)))=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~quiet(X)<=>(patient(X)&~brave(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(funny(X)&~curious(X))))&
(![X]:((~funny(X)&tall(X))<=>(~humble(X)|creative(X))))&
(?[X]:(~strong(X)))&
(rich(john))&
(?[X]:((~happy(X)|generous(X))))&
(?[X]:(generous(X)))&
(kind(susan))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | ~calm(paul) | [] | null | 0 |
Everyone who is tall is quiet or not tall and vice versa.
If someone is either not creative or not tall then someone is patient.
Everyone who is not creative or quiet is either humble or not brave and vice versa.
Everyone who is both not strong and not quiet is both humble and happy and vice versa.
If alice is either calm or happy then mary is curious.
If mary is patient then mary is kind and vice versa.
If lucy is not curious or brave then paul is not brave and vice versa.
If alice is old or not curious then mary is both not brave and calm and vice versa.
If someone is not kind or strong then lucy is patient or not kind and vice versa.
Everyone who is patient is generous and vice versa.
If alice is either not generous or patient then fred is strong or not creative.
Everyone who is not humble or not happy is both not patient and not calm.
Everyone who is not kind or not generous is happy and vice versa.
If someone is quiet then susan is either old or strong.
If someone is wise then someone is not creative.
Everyone who is both not old and wise is old or wise.
Someone is not old or not patient.
Someone is strong or humble.
John is happy. | John is not patient. | entailment | (![X]:(tall(X)<=>(quiet(X)|~tall(X))))&
((?[X]:((~creative(X)<~>~tall(X))))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)|quiet(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(((calm(alice)<~>happy(alice)))=>(curious(mary)))&
((patient(mary))<=>(kind(mary)))&
(((~curious(lucy)|brave(lucy)))<=>(~brave(paul)))&
(((old(alice)|~curious(alice)))<=>((~brave(mary)&calm(mary))))&
((?[X]:((~kind(X)|strong(X))))<=>((patient(lucy)|~kind(lucy))))&
(![X]:(patient(X)<=>generous(X)))&
(((~generous(alice)<~>patient(alice)))=>((strong(fred)|~creative(fred))))&
(![X]:((~humble(X)|~happy(X))=>(~patient(X)&~calm(X))))&
(![X]:((~kind(X)|~generous(X))<=>happy(X)))&
((?[X]:(quiet(X)))=>((old(susan)<~>strong(susan))))&
((?[X]:(wise(X)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)&wise(X))=>(old(X)|wise(X))))&
(?[X]:((~old(X)|~patient(X))))&
(?[X]:((strong(X)|humble(X))))&
(happy(john)) | ~patient(john) | [
"p0",
"p3",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8034543197282836047675635
% SZS output start Proof for 8034543197282836047675635
1. ! [X0] : (tall(X0) <=> (~tall(X0) | quiet(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> (happy(X0) & humble(X0))) [input p3]
12. ! [X0] : ((~happy(X0) | ~humble(X0)) => (~calm(X0) & ~patient(X0))) [input p11]
19. happy(john) [input p18]
20. patient(john) [input hypothesis]
27. ! [X0] : ((~calm(X0) & ~patient(X0)) | (happy(X0) & humble(X0))) [ennf transformation 12]
32. ! [X0] : ((tall(X0) | (tall(X0) & ~quiet(X0))) & ((~tall(X0) | quiet(X0)) | ~tall(X0))) [nnf transformation 1]
33. ! [X0] : ((tall(X0) | (tall(X0) & ~quiet(X0))) & (~tall(X0) | quiet(X0) | ~tall(X0))) [flattening 32]
40. ! [X0] : (((~quiet(X0) & ~strong(X0)) | (~happy(X0) | ~humble(X0))) & ((happy(X0) & humble(X0)) | (quiet(X0) | strong(X0)))) [nnf transformation 4]
41. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~happy(X0) | ~humble(X0)) & ((happy(X0) & humble(X0)) | quiet(X0) | strong(X0))) [flattening 40]
65. ~tall(X0) | quiet(X0) | ~tall(X0) [cnf transformation 33]
67. tall(X0) | tall(X0) [cnf transformation 33]
79. ~quiet(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 41]
100. ~patient(X0) | humble(X0) [cnf transformation 27]
113. happy(john) [cnf transformation 19]
114. patient(john) [cnf transformation 20]
116. ~tall(X0) | quiet(X0) [duplicate literal removal 65]
117. tall(X0) [duplicate literal removal 67]
118. quiet(X0) [subsumption resolution 116,117]
130. ~happy(X0) | ~humble(X0) [subsumption resolution 79,118]
278. humble(john) [resolution 100,114]
295. ~humble(john) [resolution 130,113]
298. $false [subsumption resolution 295,278]
% SZS output end Proof for 8034543197282836047675635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not tall is not wise or not generous and vice versa. If mary is both not patient and brave then fred is either not tall or tall. If someone is either not old or not happy then someone is both calm and old. Everyone who is old is strong. Everyone who is tall is both funny and not tall. If someone is rich then someone is old or calm and vice versa. If someone is both not patient and not happy then susan is not creative and vice versa. If paul is not strong then someone is not tall or quiet and vice versa. If john is quiet or calm then someone is either not funny or wise. If someone is either wise or generous then mary is both not brave and not calm. If someone is not brave or not happy then someone is old or generous and vice versa. If lucy is not old then susan is not wise and vice versa. If someone is not curious then someone is both strong and generous and vice versa. If someone is not strong then paul is either creative or generous and vice versa. If someone is funny or not curious then alice is not generous. Someone is calm. Someone is either creative or patient. Someone is curious or not generous. Fred is not rich. Someone is either old or not kind. Paul is not strong or not quiet. Fred is kind or not generous. | Alice is wise. | contradiction | (![X]:((~generous(X)<~>~tall(X))<=>(~wise(X)|~generous(X))))&
(((~patient(mary)&brave(mary)))=>((~tall(fred)<~>tall(fred))))&
((?[X]:((~old(X)<~>~happy(X))))=>(?[X]:((calm(X)&old(X)))))&
(![X]:(old(X)=>strong(X)))&
(![X]:(tall(X)=>(funny(X)&~tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:((old(X)|calm(X)))))&
((?[X]:((~patient(X)&~happy(X))))<=>(~creative(susan)))&
((~strong(paul))<=>(?[X]:((~tall(X)|quiet(X)))))&
(((quiet(john)|calm(john)))=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:((wise(X)<~>generous(X))))=>((~brave(mary)&~calm(mary))))&
((?[X]:((~brave(X)|~happy(X))))<=>(?[X]:((old(X)|generous(X)))))&
((~old(lucy))<=>(~wise(susan)))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)&generous(X)))))&
((?[X]:(~strong(X)))<=>((creative(paul)<~>generous(paul))))&
((?[X]:((funny(X)|~curious(X))))=>(~generous(alice)))&
(?[X]:(calm(X)))&
(?[X]:((creative(X)<~>patient(X))))&
(?[X]:((curious(X)|~generous(X))))&
(~rich(fred))&
(?[X]:((old(X)<~>~kind(X))))&
((~strong(paul)|~quiet(paul)))&
((kind(fred)|~generous(fred))) | wise(alice) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4999993563476407979824592
% SZS output start Proof for 4999993563476407979824592
1. ! [X0] : ((~generous(X0) <~> ~tall(X0)) <=> (~generous(X0) | ~wise(X0))) [input p0]
5. ! [X0] : (tall(X0) => (~tall(X0) & funny(X0))) [input p4]
23. wise(alice) [input hypothesis]
32. ! [X0] : ((~tall(X0) & funny(X0)) | ~tall(X0)) [ennf transformation 5]
36. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (generous(X0) & wise(X0))) & ((~generous(X0) | ~wise(X0)) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [nnf transformation 1]
37. ! [X0] : ((((tall(X0) | generous(X0)) & (~tall(X0) | ~generous(X0))) | (generous(X0) & wise(X0))) & (~generous(X0) | ~wise(X0) | ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))))) [flattening 36]
86. ~generous(X0) | ~wise(X0) | ~generous(X0) | tall(X0) [cnf transformation 37]
90. tall(X0) | generous(X0) | generous(X0) [cnf transformation 37]
99. ~tall(X0) | ~tall(X0) [cnf transformation 32]
141. wise(alice) [cnf transformation 23]
142. ~tall(X0) [duplicate literal removal 99]
143. ~generous(X0) | ~wise(X0) | tall(X0) [duplicate literal removal 86]
144. tall(X0) | generous(X0) [duplicate literal removal 90]
145. ~wise(X0) | tall(X0) [subsumption resolution 143,144]
399. tall(alice) [resolution 145,141]
400. $false [subsumption resolution 399,142]
% SZS output end Proof for 4999993563476407979824592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either patient or kind.
Everyone who is not calm or not funny is either not humble or brave.
Everyone who is not calm is not brave or patient.
Everyone who is quiet or wise is patient or not strong.
Everyone who is either not humble or quiet is not strong.
Everyone who is both humble and not calm is not old and vice versa.
Everyone who is not wise is either wise or curious and vice versa.
Everyone who is both not calm and strong is not kind.
If someone is not old then mary is either not creative or not tall.
Everyone who is not strong is old or tall and vice versa.
If someone is rich or kind then someone is curious and vice versa.
Everyone who is wise is not strong and vice versa.
If paul is old or not humble then someone is not happy.
Everyone who is strong or kind is not curious and vice versa.
If alice is tall then john is both wise and not tall.
Everyone who is both not wise and brave is not calm.
Alice is either not happy or tall.
Someone is not creative.
Lucy is not generous.
Someone is rich or patient.
John is tall.
Someone is not generous.
Someone is either curious or not old.
Lucy is both tall and not rich. | Alice is old. | entailment | (![X]:(~tall(X)=>(patient(X)<~>kind(X))))&
(![X]:((~calm(X)|~funny(X))=>(~humble(X)<~>brave(X))))&
(![X]:(~calm(X)=>(~brave(X)|patient(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~strong(X))))&
(![X]:((~humble(X)<~>quiet(X))=>~strong(X)))&
(![X]:((humble(X)&~calm(X))<=>~old(X)))&
(![X]:(~wise(X)<=>(wise(X)<~>curious(X))))&
(![X]:((~calm(X)&strong(X))=>~kind(X)))&
((?[X]:(~old(X)))=>((~creative(mary)<~>~tall(mary))))&
(![X]:(~strong(X)<=>(old(X)|tall(X))))&
((?[X]:((rich(X)|kind(X))))<=>(?[X]:(curious(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(((old(paul)|~humble(paul)))=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|kind(X))<=>~curious(X)))&
((tall(alice))=>((wise(john)&~tall(john))))&
(![X]:((~wise(X)&brave(X))=>~calm(X)))&
((~happy(alice)<~>tall(alice)))&
(?[X]:(~creative(X)))&
(~generous(lucy))&
(?[X]:((rich(X)|patient(X))))&
(tall(john))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>~old(X))))&
((tall(lucy)&~rich(lucy))) | old(alice) | [
"p6",
"p9",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8895912324475858370315221
% SZS output start Proof for 8895912324475858370315221
7. ! [X0] : (~wise(X0) <=> (wise(X0) <~> curious(X0))) [input p6]
10. ! [X0] : (~strong(X0) <=> (tall(X0) | old(X0))) [input p9]
14. ! [X0] : ((kind(X0) | strong(X0)) <=> ~curious(X0)) [input p13]
15. tall(alice) => (~tall(john) & wise(john)) [input p14]
21. tall(john) [input p20]
25. ~old(alice) [input hypothesis]
41. (~tall(john) & wise(john)) | ~tall(alice) [ennf transformation 15]
49. ! [X0] : ((~wise(X0) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | wise(X0))) [nnf transformation 7]
51. ! [X0] : ((~strong(X0) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | strong(X0))) [nnf transformation 10]
52. ! [X0] : ((~strong(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | strong(X0))) [flattening 51]
61. ! [X0] : (((kind(X0) | strong(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) & ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : ((kind(X0) | strong(X0) | curious(X0)) & (~curious(X0) | (~kind(X0) & ~strong(X0)))) [flattening 61]
83. curious(X0) | wise(X0) | wise(X0) [cnf transformation 49]
85. ~wise(X0) | curious(X0) | ~wise(X0) [cnf transformation 49]
90. old(X0) | tall(X0) | strong(X0) [cnf transformation 52]
100. ~curious(X0) | ~strong(X0) [cnf transformation 62]
104. ~tall(john) | ~tall(alice) [cnf transformation 41]
110. tall(john) [cnf transformation 21]
115. ~old(alice) [cnf transformation 25]
116. curious(X0) | wise(X0) [duplicate literal removal 83]
117. ~wise(X0) | curious(X0) [duplicate literal removal 85]
118. curious(X0) [subsumption resolution 116,117]
157. ~strong(X0) [subsumption resolution 100,118]
159. 9 <=> tall(alice) [avatar definition]
161. ~tall(alice) <- (~9) [avatar component clause 159]
163. 10 <=> tall(john) [avatar definition]
166. ~9 | ~10 [avatar split clause 104,163,159]
187. 10 [avatar split clause 110,163]
233. tall(alice) | strong(alice) [resolution 90,115]
236. strong(alice) <- (~9) [subsumption resolution 233,161]
237. $false <- (~9) [subsumption resolution 236,157]
238. 9 [avatar contradiction clause 237]
240. $false [avatar sat refutation 166,187,238]
% SZS output end Proof for 8895912324475858370315221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both generous and not rich then someone is either not calm or brave and vice versa.
If paul is both patient and not creative then john is both not quiet and not humble and vice versa.
Everyone who is either not old or old is creative or not creative and vice versa.
Everyone who is not generous is both funny and not funny.
If someone is not calm or not rich then someone is both not calm and patient.
If lucy is tall then fred is not wise or rich.
Everyone who is both tall and not rich is both tall and generous and vice versa.
If someone is both not funny and funny then someone is both kind and calm and vice versa.
If susan is not rich then alice is not funny or not generous.
If john is either strong or not generous then susan is both kind and not old and vice versa.
Everyone who is not kind is not funny or curious.
If someone is both not wise and wise then lucy is both not curious and not happy.
If someone is either tall or kind then alice is not rich.
If paul is either quiet or not happy then someone is brave.
If someone is generous or strong then someone is not old and vice versa.
If mary is quiet or patient then someone is both not tall and strong and vice versa.
Someone is kind.
Mary is either rich or not patient.
Susan is not tall or patient.
Mary is both calm and not tall.
Susan is both generous and patient.
Mary is not old or humble.
Someone is either not brave or not kind.
Mary is both not brave and not funny. | Paul is not generous. | contradiction | (((generous(paul)&~rich(paul)))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(((patient(paul)&~creative(paul)))<=>((~quiet(john)&~humble(john))))&
(![X]:((~old(X)<~>old(X))<=>(creative(X)|~creative(X))))&
(![X]:(~generous(X)=>(funny(X)&~funny(X))))&
((?[X]:((~calm(X)|~rich(X))))=>(?[X]:((~calm(X)&patient(X)))))&
((tall(lucy))=>((~wise(fred)|rich(fred))))&
(![X]:((tall(X)&~rich(X))<=>(tall(X)&generous(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:((kind(X)&calm(X)))))&
((~rich(susan))=>((~funny(alice)|~generous(alice))))&
(((strong(john)<~>~generous(john)))<=>((kind(susan)&~old(susan))))&
(![X]:(~kind(X)=>(~funny(X)|curious(X))))&
((?[X]:((~wise(X)&wise(X))))=>((~curious(lucy)&~happy(lucy))))&
((?[X]:((tall(X)<~>kind(X))))=>(~rich(alice)))&
(((quiet(paul)<~>~happy(paul)))=>(?[X]:(brave(X))))&
((?[X]:((generous(X)|strong(X))))<=>(?[X]:(~old(X))))&
(((quiet(mary)|patient(mary)))<=>(?[X]:((~tall(X)&strong(X)))))&
(?[X]:(kind(X)))&
((rich(mary)<~>~patient(mary)))&
((~tall(susan)|patient(susan)))&
((calm(mary)&~tall(mary)))&
((generous(susan)&patient(susan)))&
((~old(mary)|humble(mary)))&
(?[X]:((~brave(X)<~>~kind(X))))&
((~brave(mary)&~funny(mary))) | ~generous(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3067229530521672135361101
% SZS output start Proof for 3067229530521672135361101
4. ! [X0] : (~generous(X0) => (~funny(X0) & funny(X0))) [input p3]
25. ~generous(paul) [input hypothesis]
29. ! [X0] : ((~funny(X0) & funny(X0)) | generous(X0)) [ennf transformation 4]
97. funny(X0) | generous(X0) [cnf transformation 29]
98. ~funny(X0) | generous(X0) [cnf transformation 29]
147. ~generous(paul) [cnf transformation 25]
198. generous(X0) [subsumption resolution 97,98]
363. $false [subsumption resolution 147,198]
% SZS output end Proof for 3067229530521672135361101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or curious then someone is not humble and vice versa. Everyone who is not tall is both not funny and not humble and vice versa. Everyone who is both curious and not funny is not quiet or happy. Everyone who is brave or not generous is either tall or rich and vice versa. Everyone who is not patient or not old is not wise or not old. Everyone who is kind is not strong or wise and vice versa. Everyone who is both old and not humble is both old and patient and vice versa. If someone is not rich or not brave then someone is both creative and rich and vice versa. Everyone who is either not tall or not quiet is old and vice versa. Everyone who is humble or not kind is either tall or happy. Everyone who is either not kind or strong is not generous and vice versa. If susan is brave or not strong then mary is not patient or not brave. Everyone who is either tall or quiet is either not wise or strong and vice versa. If someone is either humble or brave then someone is both quiet and tall and vice versa. If someone is not quiet or wise then someone is not funny or creative and vice versa. If someone is happy then someone is not quiet and vice versa. Someone is old. Someone is not strong. Alice is either kind or tall. Someone is either curious or not happy. Someone is either quiet or curious. Lucy is either not kind or not calm. Alice is curious or not humble. Someone is both humble and not strong. | Susan is strong. | neutral | ((?[X]:((kind(X)|curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)<=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&~funny(X))=>(~quiet(X)|happy(X))))&
(![X]:((brave(X)|~generous(X))<=>(tall(X)<~>rich(X))))&
(![X]:((~patient(X)|~old(X))=>(~wise(X)|~old(X))))&
(![X]:(kind(X)<=>(~strong(X)|wise(X))))&
(![X]:((old(X)&~humble(X))<=>(old(X)&patient(X))))&
((?[X]:((~rich(X)|~brave(X))))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>old(X)))&
(![X]:((humble(X)|~kind(X))=>(tall(X)<~>happy(X))))&
(![X]:((~kind(X)<~>strong(X))<=>~generous(X)))&
(((brave(susan)|~strong(susan)))=>((~patient(mary)|~brave(mary))))&
(![X]:((tall(X)<~>quiet(X))<=>(~wise(X)<~>strong(X))))&
((?[X]:((humble(X)<~>brave(X))))<=>(?[X]:((quiet(X)&tall(X)))))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:((~funny(X)|creative(X)))))&
((?[X]:(happy(X)))<=>(?[X]:(~quiet(X))))&
(?[X]:(old(X)))&
(?[X]:(~strong(X)))&
((kind(alice)<~>tall(alice)))&
(?[X]:((curious(X)<~>~happy(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
((~kind(lucy)<~>~calm(lucy)))&
((curious(alice)|~humble(alice)))&
(?[X]:((humble(X)&~strong(X)))) | strong(susan) | [] | null | 0 |
If someone is not strong or funny then paul is both patient and old.
If someone is both humble and wise then paul is not old.
If paul is not tall then someone is either not kind or not creative.
If someone is kind or not brave then someone is quiet or not calm and vice versa.
Everyone who is creative is not patient or not happy and vice versa.
Everyone who is both quiet and calm is both wise and kind and vice versa.
Everyone who is both not strong and creative is not brave or not strong and vice versa.
If someone is either not rich or not humble then john is not quiet.
If mary is not happy or creative then alice is either generous or kind and vice versa.
If susan is not patient or generous then mary is both not curious and not humble and vice versa.
If fred is curious or not generous then susan is patient or not humble and vice versa.
If john is not patient or happy then someone is both not rich and not brave.
If lucy is humble or brave then fred is strong.
If someone is not old or quiet then paul is not calm.
If alice is either generous or creative then susan is brave or not happy and vice versa.
Alice is happy.
Alice is not calm or not kind.
Someone is either not generous or strong.
Fred is both not brave and calm.
Susan is both rich and generous.
Someone is either funny or not generous.
Someone is both curious and not creative. | John is not generous. | neutral | ((?[X]:((~strong(X)|funny(X))))=>((patient(paul)&old(paul))))&
((?[X]:((humble(X)&wise(X))))=>(~old(paul)))&
((~tall(paul))=>(?[X]:((~kind(X)<~>~creative(X)))))&
((?[X]:((kind(X)|~brave(X))))<=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:(creative(X)<=>(~patient(X)|~happy(X))))&
(![X]:((quiet(X)&calm(X))<=>(wise(X)&kind(X))))&
(![X]:((~strong(X)&creative(X))<=>(~brave(X)|~strong(X))))&
((?[X]:((~rich(X)<~>~humble(X))))=>(~quiet(john)))&
(((~happy(mary)|creative(mary)))<=>((generous(alice)<~>kind(alice))))&
(((~patient(susan)|generous(susan)))<=>((~curious(mary)&~humble(mary))))&
(((curious(fred)|~generous(fred)))<=>((patient(susan)|~humble(susan))))&
(((~patient(john)|happy(john)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((humble(lucy)|brave(lucy)))=>(strong(fred)))&
((?[X]:((~old(X)|quiet(X))))=>(~calm(paul)))&
(((generous(alice)<~>creative(alice)))<=>((brave(susan)|~happy(susan))))&
(happy(alice))&
((~calm(alice)|~kind(alice)))&
(?[X]:((~generous(X)<~>strong(X))))&
((~brave(fred)&calm(fred)))&
((rich(susan)&generous(susan)))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:((curious(X)&~creative(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both not brave and not humble is both not wise and calm and vice versa. Everyone who is kind or not strong is not tall and vice versa. Everyone who is both rich and not old is not happy or not tall. If fred is both strong and old then mary is not brave or brave and vice versa. Everyone who is old or patient is not strong or not quiet and vice versa. Everyone who is both funny and not quiet is not humble and vice versa. If someone is kind or not patient then someone is funny. If mary is either not tall or patient then someone is not strong or generous and vice versa. Everyone who is patient or not happy is not tall. Everyone who is either not old or happy is either not calm or old. If someone is both not generous and curious then fred is not old or tall. Everyone who is not humble or not curious is strong or humble and vice versa. If john is wise then someone is tall or not brave and vice versa. Someone is not wise or not generous. Someone is creative or not old. Someone is either tall or not tall. Alice is not generous. Susan is either not happy or funny. Alice is either calm or creative. | Susan is not happy. | neutral | (![X]:((~brave(X)&~humble(X))<=>(~wise(X)&calm(X))))&
(![X]:((kind(X)|~strong(X))<=>~tall(X)))&
(![X]:((rich(X)&~old(X))=>(~happy(X)|~tall(X))))&
(((strong(fred)&old(fred)))<=>((~brave(mary)|brave(mary))))&
(![X]:((old(X)|patient(X))<=>(~strong(X)|~quiet(X))))&
(![X]:((funny(X)&~quiet(X))<=>~humble(X)))&
((?[X]:((kind(X)|~patient(X))))=>(?[X]:(funny(X))))&
(((~tall(mary)<~>patient(mary)))<=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:((patient(X)|~happy(X))=>~tall(X)))&
(![X]:((~old(X)<~>happy(X))=>(~calm(X)<~>old(X))))&
((?[X]:((~generous(X)&curious(X))))=>((~old(fred)|tall(fred))))&
(![X]:((~humble(X)|~curious(X))<=>(strong(X)|humble(X))))&
((wise(john))<=>(?[X]:((tall(X)|~brave(X)))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
(~generous(alice))&
((~happy(susan)<~>funny(susan)))&
((calm(alice)<~>creative(alice))) | ~happy(susan) | [] | null | 0 |
If susan is not calm then someone is not happy. Everyone who is both not patient and not happy is either not quiet or not tall and vice versa. If someone is either not brave or not calm then fred is both kind and humble. If john is patient or not funny then lucy is both not wise and not happy and vice versa. Everyone who is both quiet and not funny is tall and vice versa. Everyone who is not tall is not old or not kind and vice versa. Everyone who is quiet is both brave and funny and vice versa. If someone is both calm and creative then mary is both not tall and not humble and vice versa. If alice is either rich or not old then someone is not rich and vice versa. Everyone who is not kind or not brave is old and vice versa. Everyone who is both strong and not rich is either rich or not generous and vice versa. If susan is generous or not old then alice is humble and vice versa. Everyone who is either strong or calm is both not patient and calm and vice versa. Everyone who is kind or quiet is either not brave or rich and vice versa. Everyone who is old or rich is either quiet or rich and vice versa. Everyone who is not happy is patient. Someone is either rich or not wise. Someone is both funny and not creative. Someone is not wise. Mary is not funny. Alice is calm or not rich. Fred is both curious and not patient. | Alice is not strong. | neutral | ((~calm(susan))=>(?[X]:(~happy(X))))&
(![X]:((~patient(X)&~happy(X))<=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~brave(X)<~>~calm(X))))=>((kind(fred)&humble(fred))))&
(((patient(john)|~funny(john)))<=>((~wise(lucy)&~happy(lucy))))&
(![X]:((quiet(X)&~funny(X))<=>tall(X)))&
(![X]:(~tall(X)<=>(~old(X)|~kind(X))))&
(![X]:(quiet(X)<=>(brave(X)&funny(X))))&
((?[X]:((calm(X)&creative(X))))<=>((~tall(mary)&~humble(mary))))&
(((rich(alice)<~>~old(alice)))<=>(?[X]:(~rich(X))))&
(![X]:((~kind(X)|~brave(X))<=>old(X)))&
(![X]:((strong(X)&~rich(X))<=>(rich(X)<~>~generous(X))))&
(((generous(susan)|~old(susan)))<=>(humble(alice)))&
(![X]:((strong(X)<~>calm(X))<=>(~patient(X)&calm(X))))&
(![X]:((kind(X)|quiet(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((old(X)|rich(X))<=>(quiet(X)<~>rich(X))))&
(![X]:(~happy(X)=>patient(X)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:(~wise(X)))&
(~funny(mary))&
((calm(alice)|~rich(alice)))&
((curious(fred)&~patient(fred))) | ~strong(alice) | [] | null | 0 |
Everyone who is calm is both not rich and happy.
If someone is not patient then fred is not humble.
Everyone who is either calm or not strong is not patient.
Everyone who is not wise or tall is both happy and tall and vice versa.
Everyone who is not strong or not calm is not creative or not funny and vice versa.
If fred is funny or not humble then alice is not funny or patient and vice versa.
If someone is rich then paul is both strong and not quiet and vice versa.
If john is not happy or creative then fred is generous and vice versa.
Everyone who is both not curious and funny is both not generous and not patient and vice versa.
Everyone who is both strong and not curious is not humble.
Everyone who is creative or tall is both brave and tall.
Everyone who is not strong is either quiet or patient and vice versa.
Everyone who is not creative is creative or humble.
Everyone who is either generous or funny is either calm or not brave.
Everyone who is both not tall and kind is both strong and not quiet.
If john is calm then lucy is either not curious or not generous.
Someone is both not rich and not humble.
Alice is either wise or not rich.
Susan is not quiet.
Paul is either patient or happy.
Mary is both not patient and rich.
John is calm or quiet. | Fred is tall. | entailment | (![X]:(calm(X)=>(~rich(X)&happy(X))))&
((?[X]:(~patient(X)))=>(~humble(fred)))&
(![X]:((calm(X)<~>~strong(X))=>~patient(X)))&
(![X]:((~wise(X)|tall(X))<=>(happy(X)&tall(X))))&
(![X]:((~strong(X)|~calm(X))<=>(~creative(X)|~funny(X))))&
(((funny(fred)|~humble(fred)))<=>((~funny(alice)|patient(alice))))&
((?[X]:(rich(X)))<=>((strong(paul)&~quiet(paul))))&
(((~happy(john)|creative(john)))<=>(generous(fred)))&
(![X]:((~curious(X)&funny(X))<=>(~generous(X)&~patient(X))))&
(![X]:((strong(X)&~curious(X))=>~humble(X)))&
(![X]:((creative(X)|tall(X))=>(brave(X)&tall(X))))&
(![X]:(~strong(X)<=>(quiet(X)<~>patient(X))))&
(![X]:(~creative(X)=>(creative(X)|humble(X))))&
(![X]:((generous(X)<~>funny(X))=>(calm(X)<~>~brave(X))))&
(![X]:((~tall(X)&kind(X))=>(strong(X)&~quiet(X))))&
((calm(john))=>((~curious(lucy)<~>~generous(lucy))))&
(?[X]:((~rich(X)&~humble(X))))&
((wise(alice)<~>~rich(alice)))&
(~quiet(susan))&
((patient(paul)<~>happy(paul)))&
((~patient(mary)&rich(mary)))&
((calm(john)|quiet(john))) | tall(fred) | [
"p1",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6603829936570072779865454
% SZS output start Proof for 6603829936570072779865454
2. ? [X0] : ~patient(X0) => ~humble(fred) [input p1]
11. ! [X0] : ((tall(X0) | creative(X0)) => (tall(X0) & brave(X0))) [input p10]
13. ! [X0] : (~creative(X0) => (humble(X0) | creative(X0))) [input p12]
21. rich(mary) & ~patient(mary) [input p20]
23. ~tall(fred) [input hypothesis]
26. ~humble(fred) | ! [X0] : patient(X0) [ennf transformation 2]
30. ! [X0] : ((tall(X0) & brave(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 11]
31. ! [X0] : ((humble(X0) | creative(X0)) | creative(X0)) [ennf transformation 13]
32. ! [X0] : (humble(X0) | creative(X0) | creative(X0)) [flattening 31]
60. ~humble(fred) | patient(X0) [cnf transformation 26]
89. ~creative(X0) | tall(X0) [cnf transformation 30]
95. humble(X0) | creative(X0) | creative(X0) [cnf transformation 32]
109. ~patient(mary) [cnf transformation 21]
112. ~tall(fred) [cnf transformation 23]
113. creative(X0) | humble(X0) [duplicate literal removal 95]
115. 1 <=> ! [X0] : patient(X0) [avatar definition]
116. patient(X0) <- (1) [avatar component clause 115]
118. 2 <=> humble(fred) [avatar definition]
121. 1 | ~2 [avatar split clause 60,118,115]
221. tall(X0) | humble(X0) [resolution 113,89]
226. humble(fred) [resolution 221,112]
231. 2 [avatar split clause 226,118]
232. $false <- (1) [resolution 116,109]
234. ~1 [avatar contradiction clause 232]
235. $false [avatar sat refutation 121,231,234]
% SZS output end Proof for 6603829936570072779865454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not old then someone is not old or tall. Everyone who is either rich or curious is strong or generous. Everyone who is quiet is either not wise or not creative. Everyone who is both generous and old is humble or wise. If someone is both not wise and not brave then someone is either not humble or not quiet. Everyone who is happy or not happy is both not humble and kind. Everyone who is both not funny and quiet is curious or strong and vice versa. If someone is either generous or not quiet then paul is both not generous and not quiet and vice versa. If fred is rich then someone is both not rich and not patient and vice versa. If someone is both humble and not creative then someone is not old or not humble. Everyone who is either not humble or not kind is both not wise and not patient and vice versa. Everyone who is not kind or curious is either humble or not brave and vice versa. If someone is both strong and tall then paul is funny and vice versa. If paul is both generous and quiet then someone is wise and vice versa. If someone is not calm or quiet then someone is not tall or generous and vice versa. Everyone who is both patient and not funny is both not patient and not happy and vice versa. Someone is not tall. Someone is both creative and quiet. Paul is either kind or curious. Someone is quiet. Paul is not curious. Someone is either not calm or humble. Alice is either not rich or wise. | Alice is not kind. | contradiction | ((?[X]:((~creative(X)&~old(X))))=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((rich(X)<~>curious(X))=>(strong(X)|generous(X))))&
(![X]:(quiet(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((generous(X)&old(X))=>(humble(X)|wise(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((happy(X)|~happy(X))=>(~humble(X)&kind(X))))&
(![X]:((~funny(X)&quiet(X))<=>(curious(X)|strong(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>((~generous(paul)&~quiet(paul))))&
((rich(fred))<=>(?[X]:((~rich(X)&~patient(X)))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~kind(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
((?[X]:((strong(X)&tall(X))))<=>(funny(paul)))&
(((generous(paul)&quiet(paul)))<=>(?[X]:(wise(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~patient(X)&~happy(X))))&
(?[X]:(~tall(X)))&
(?[X]:((creative(X)&quiet(X))))&
((kind(paul)<~>curious(paul)))&
(?[X]:(quiet(X)))&
(~curious(paul))&
(?[X]:((~calm(X)<~>humble(X))))&
((~rich(alice)<~>wise(alice))) | ~kind(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6252324629324767636228833
% SZS output start Proof for 6252324629324767636228833
6. ! [X0] : ((~happy(X0) | happy(X0)) => (kind(X0) & ~humble(X0))) [input p5]
24. ~kind(alice) [input hypothesis]
36. ! [X0] : ((kind(X0) & ~humble(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 6]
102. kind(X0) | ~happy(X0) [cnf transformation 36]
103. kind(X0) | happy(X0) [cnf transformation 36]
156. ~kind(alice) [cnf transformation 24]
184. kind(X0) [subsumption resolution 102,103]
296. $false [subsumption resolution 156,184]
% SZS output end Proof for 6252324629324767636228833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not old is rich and vice versa.
If paul is both not generous and wise then susan is either not curious or not kind.
If paul is patient then someone is both tall and not kind.
Everyone who is both happy and not wise is wise.
Everyone who is both not calm and generous is not calm.
If someone is not strong or not wise then john is not old.
Everyone who is both not funny and patient is not rich and vice versa.
If someone is both happy and not generous then lucy is both strong and not kind and vice versa.
If fred is not wise then fred is funny and vice versa.
If someone is not quiet or not calm then mary is both not patient and not funny and vice versa.
Everyone who is both creative and not calm is either patient or not kind.
Everyone who is old or rich is not rich.
If mary is not humble or not brave then someone is not patient or not creative.
If paul is quiet then someone is not happy or not wise and vice versa.
If mary is wise or not brave then lucy is either not creative or humble.
If john is either not humble or not rich then someone is old or happy.
Someone is kind.
Someone is not tall or not quiet.
Paul is not wise.
Someone is not curious or wise.
Someone is humble.
Someone is both kind and not old. | Paul is not rich. | entailment | (![X]:((kind(X)<~>~old(X))<=>rich(X)))&
(((~generous(paul)&wise(paul)))=>((~curious(susan)<~>~kind(susan))))&
((patient(paul))=>(?[X]:((tall(X)&~kind(X)))))&
(![X]:((happy(X)&~wise(X))=>wise(X)))&
(![X]:((~calm(X)&generous(X))=>~calm(X)))&
((?[X]:((~strong(X)|~wise(X))))=>(~old(john)))&
(![X]:((~funny(X)&patient(X))<=>~rich(X)))&
((?[X]:((happy(X)&~generous(X))))<=>((strong(lucy)&~kind(lucy))))&
((~wise(fred))<=>(funny(fred)))&
((?[X]:((~quiet(X)|~calm(X))))<=>((~patient(mary)&~funny(mary))))&
(![X]:((creative(X)&~calm(X))=>(patient(X)<~>~kind(X))))&
(![X]:((old(X)|rich(X))=>~rich(X)))&
(((~humble(mary)|~brave(mary)))=>(?[X]:((~patient(X)|~creative(X)))))&
((quiet(paul))<=>(?[X]:((~happy(X)|~wise(X)))))&
(((wise(mary)|~brave(mary)))=>((~creative(lucy)<~>humble(lucy))))&
(((~humble(john)<~>~rich(john)))=>(?[X]:((old(X)|happy(X)))))&
(?[X]:(kind(X)))&
(?[X]:((~tall(X)|~quiet(X))))&
(~wise(paul))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:(humble(X)))&
(?[X]:((kind(X)&~old(X)))) | ~rich(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3065340009039249263728742
% SZS output start Proof for 3065340009039249263728742
12. ! [X0] : ((rich(X0) | old(X0)) => ~rich(X0)) [input p11]
23. rich(paul) [input hypothesis]
36. ! [X0] : (~rich(X0) | (~rich(X0) & ~old(X0))) [ennf transformation 12]
107. ~rich(X0) | ~rich(X0) [cnf transformation 36]
123. rich(paul) [cnf transformation 23]
124. ~rich(X0) [duplicate literal removal 107]
305. $false [subsumption resolution 123,124]
% SZS output end Proof for 3065340009039249263728742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is both old and not happy is generous or not rich and vice versa.
Everyone who is either not tall or not wise is either patient or tall and vice versa.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Someone is calm.
John is both calm and brave.
Alice is funny.
Mary is either not brave or tall.
Someone is both not kind and humble.
Someone is not tall or not wise.
Paul is not kind or curious.
John is quiet or not strong. | Fred is not happy. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&~happy(X))<=>(generous(X)|~rich(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(?[X]:(calm(X)))&
((calm(john)&brave(john)))&
(funny(alice))&
((~brave(mary)<~>tall(mary)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~tall(X)|~wise(X))))&
((~kind(paul)|curious(paul)))&
((quiet(john)|~strong(john))) | ~happy(fred) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6111552482766725947374552
% SZS output start Proof for 6111552482766725947374552
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~happy(X0) & old(X0)) <=> (~rich(X0) | generous(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) <~> tall(X0))) [input p3]
5. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p4]
6. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p5]
10. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p9]
23. ~happy(fred) [input hypothesis]
27. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
28. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 5]
37. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 27]
38. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 3]
39. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | happy(X0) | ~old(X0))) [flattening 38]
40. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 4]
41. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 6]
45. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 10]
46. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 45]
47. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 46]
48. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
49. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 47,48]
75. ~creative(X0) | happy(X0) | ~old(X0) [cnf transformation 37]
79. rich(X0) | old(X0) [cnf transformation 39]
82. tall(X0) | patient(X0) | ~wise(X0) | tall(X0) [cnf transformation 40]
87. ~wise(X0) | ~tall(X0) | patient(X0) | ~tall(X0) [cnf transformation 40]
90. ~rich(X0) | happy(X0) [cnf transformation 28]
92. ~patient(X0) | happy(X0) | creative(X0) [cnf transformation 41]
102. creative(fred) | wise(X1) [cnf transformation 49]
131. ~happy(fred) [cnf transformation 23]
132. tall(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 82]
134. ~wise(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 87]
137. ~wise(X0) | patient(X0) [subsumption resolution 132,134]
139. 1 <=> creative(fred) [avatar definition]
140. creative(fred) <- (1) [avatar component clause 139]
152. 4 <=> ! [X1] : wise(X1) [avatar definition]
153. wise(X1) <- (4) [avatar component clause 152]
155. 4 | 1 [avatar split clause 102,139,152]
264. happy(X0) | old(X0) [resolution 90,79]
291. happy(fred) | ~old(fred) <- (1) [resolution 75,140]
292. ~old(fred) <- (1) [subsumption resolution 291,131]
318. old(fred) [resolution 264,131]
324. $false <- (1) [subsumption resolution 318,292]
325. ~1 [avatar contradiction clause 324]
326. patient(X0) <- (4) [resolution 153,137]
337. creative(X1) | happy(X1) <- (4) [resolution 326,92]
424. happy(X2) | happy(X2) | ~old(X2) <- (4) [resolution 337,75]
429. happy(X2) | ~old(X2) <- (4) [duplicate literal removal 424]
431. happy(X2) <- (4) [subsumption resolution 429,264]
437. $false <- (4) [resolution 431,131]
443. ~4 [avatar contradiction clause 437]
444. $false [avatar sat refutation 155,325,443]
% SZS output end Proof for 6111552482766725947374552
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or tall then paul is either strong or not generous and vice versa.
Everyone who is curious or patient is both not kind and not happy.
If mary is not wise then someone is both quiet and not patient and vice versa.
Everyone who is not generous is not patient and vice versa.
Everyone who is tall or not curious is both strong and not strong.
Everyone who is old is both not kind and not calm and vice versa.
Everyone who is patient is old or not quiet.
If someone is both tall and brave then someone is both not wise and funny and vice versa.
Everyone who is either not strong or not brave is both not happy and not creative and vice versa.
Everyone who is generous or funny is brave.
Everyone who is not creative is not quiet or wise.
If alice is not generous then paul is brave or not strong and vice versa.
Everyone who is either not brave or not rich is not old or patient.
Everyone who is strong or tall is not patient and vice versa.
If someone is tall then john is creative or not calm and vice versa.
Everyone who is creative or calm is not tall or quiet.
Fred is either not funny or not quiet.
Someone is not funny or strong.
Someone is both not patient and old.
Someone is not funny or not happy.
Alice is both not tall and patient.
John is not old. | John is strong. | neutral | ((?[X]:((kind(X)|tall(X))))<=>((strong(paul)<~>~generous(paul))))&
(![X]:((curious(X)|patient(X))=>(~kind(X)&~happy(X))))&
((~wise(mary))<=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((tall(X)|~curious(X))=>(strong(X)&~strong(X))))&
(![X]:(old(X)<=>(~kind(X)&~calm(X))))&
(![X]:(patient(X)=>(old(X)|~quiet(X))))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~strong(X)<~>~brave(X))<=>(~happy(X)&~creative(X))))&
(![X]:((generous(X)|funny(X))=>brave(X)))&
(![X]:(~creative(X)=>(~quiet(X)|wise(X))))&
((~generous(alice))<=>((brave(paul)|~strong(paul))))&
(![X]:((~brave(X)<~>~rich(X))=>(~old(X)|patient(X))))&
(![X]:((strong(X)|tall(X))<=>~patient(X)))&
((?[X]:(tall(X)))<=>((creative(john)|~calm(john))))&
(![X]:((creative(X)|calm(X))=>(~tall(X)|quiet(X))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((~patient(X)&old(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((~tall(alice)&patient(alice)))&
(~old(john)) | strong(john) | [] | null | 0 |
If fred is not wise or quiet then mary is both not patient and not happy and vice versa.
If susan is both wise and not curious then mary is not strong or patient.
Everyone who is not calm or old is brave.
Everyone who is either old or not rich is rich and vice versa.
Everyone who is both not quiet and not patient is both quiet and not kind.
Everyone who is both not kind and not generous is not brave.
If lucy is happy then someone is creative.
Everyone who is either curious or not humble is creative.
Everyone who is creative or brave is both not happy and generous.
If mary is brave or not rich then fred is calm or not generous and vice versa.
Everyone who is both strong and creative is either funny or not happy.
If mary is both patient and calm then susan is calm or strong and vice versa.
Everyone who is happy or not quiet is either humble or strong and vice versa.
Everyone who is not quiet is brave.
If mary is not old then someone is either not quiet or strong and vice versa.
If someone is not patient then someone is either not tall or humble.
Someone is not generous or not creative.
Lucy is either rich or not quiet.
Someone is either tall or brave.
Paul is not wise.
Someone is not creative or humble.
Someone is both brave and not happy.
Lucy is humble or not patient. | Fred is not generous. | contradiction | (((~wise(fred)|quiet(fred)))<=>((~patient(mary)&~happy(mary))))&
(((wise(susan)&~curious(susan)))=>((~strong(mary)|patient(mary))))&
(![X]:((~calm(X)|old(X))=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>rich(X)))&
(![X]:((~quiet(X)&~patient(X))=>(quiet(X)&~kind(X))))&
(![X]:((~kind(X)&~generous(X))=>~brave(X)))&
((happy(lucy))=>(?[X]:(creative(X))))&
(![X]:((curious(X)<~>~humble(X))=>creative(X)))&
(![X]:((creative(X)|brave(X))=>(~happy(X)&generous(X))))&
(((brave(mary)|~rich(mary)))<=>((calm(fred)|~generous(fred))))&
(![X]:((strong(X)&creative(X))=>(funny(X)<~>~happy(X))))&
(((patient(mary)&calm(mary)))<=>((calm(susan)|strong(susan))))&
(![X]:((happy(X)|~quiet(X))<=>(humble(X)<~>strong(X))))&
(![X]:(~quiet(X)=>brave(X)))&
((~old(mary))<=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~tall(X)<~>humble(X)))))&
(?[X]:((~generous(X)|~creative(X))))&
((rich(lucy)<~>~quiet(lucy)))&
(?[X]:((tall(X)<~>brave(X))))&
(~wise(paul))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((brave(X)&~happy(X))))&
((humble(lucy)|~patient(lucy))) | ~generous(fred) | [
"p2",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8629241635606661338979963
% SZS output start Proof for 8629241635606661338979963
3. ! [X0] : ((old(X0) | ~calm(X0)) => brave(X0)) [input p2]
4. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> rich(X0)) [input p3]
9. ! [X0] : ((brave(X0) | creative(X0)) => (generous(X0) & ~happy(X0))) [input p8]
24. ~generous(fred) [input hypothesis]
28. ! [X0] : (brave(X0) | (~old(X0) & calm(X0))) [ennf transformation 3]
35. ! [X0] : ((generous(X0) & ~happy(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 9]
42. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~rich(X0)) & (rich(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 4]
78. ~old(X0) | brave(X0) [cnf transformation 28]
80. rich(X0) | old(X0) | rich(X0) [cnf transformation 42]
81. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 42]
92. ~brave(X0) | generous(X0) [cnf transformation 35]
127. ~generous(fred) [cnf transformation 24]
129. rich(X0) | old(X0) [duplicate literal removal 80]
130. ~rich(X0) | old(X0) [duplicate literal removal 81]
165. old(X0) [subsumption resolution 129,130]
176. 10 <=> generous(fred) [avatar definition]
177. ~generous(fred) <- (~10) [avatar component clause 176]
267. ~10 [avatar split clause 127,176]
269. brave(X0) [resolution 78,165]
276. generous(X0) [resolution 92,269]
280. $false <- (~10) [resolution 276,177]
281. 10 [avatar contradiction clause 280]
282. $false [avatar sat refutation 267,281]
% SZS output end Proof for 8629241635606661338979963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either brave or strong then fred is kind or not tall and vice versa. If john is generous then someone is both not patient and not rich and vice versa. If someone is not creative then someone is both not tall and humble and vice versa. If someone is not funny then someone is generous. Everyone who is either not quiet or not curious is not generous and vice versa. If someone is not patient then someone is either not old or not patient. If mary is both old and quiet then lucy is either not creative or not quiet and vice versa. Everyone who is either not strong or not brave is either tall or not calm and vice versa. If mary is creative then someone is both patient and funny. Everyone who is rich or not happy is not funny and vice versa. Everyone who is both not strong and not happy is not wise and vice versa. If someone is not quiet or brave then someone is not curious. If someone is either humble or old then mary is old. Everyone who is both strong and rich is curious or funny. If someone is patient then susan is not calm. If mary is not happy then someone is not strong and vice versa. Someone is both rich and happy. John is tall or brave. Someone is funny. Someone is either humble or not brave. John is not brave or old. Susan is either curious or kind. Lucy is patient. | John is generous. | neutral | (((brave(mary)<~>strong(mary)))<=>((kind(fred)|~tall(fred))))&
((generous(john))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~tall(X)&humble(X)))))&
((?[X]:(~funny(X)))=>(?[X]:(generous(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~old(X)<~>~patient(X)))))&
(((old(mary)&quiet(mary)))<=>((~creative(lucy)<~>~quiet(lucy))))&
(![X]:((~strong(X)<~>~brave(X))<=>(tall(X)<~>~calm(X))))&
((creative(mary))=>(?[X]:((patient(X)&funny(X)))))&
(![X]:((rich(X)|~happy(X))<=>~funny(X)))&
(![X]:((~strong(X)&~happy(X))<=>~wise(X)))&
((?[X]:((~quiet(X)|brave(X))))=>(?[X]:(~curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>(old(mary)))&
(![X]:((strong(X)&rich(X))=>(curious(X)|funny(X))))&
((?[X]:(patient(X)))=>(~calm(susan)))&
((~happy(mary))<=>(?[X]:(~strong(X))))&
(?[X]:((rich(X)&happy(X))))&
((tall(john)|brave(john)))&
(?[X]:(funny(X)))&
(?[X]:((humble(X)<~>~brave(X))))&
((~brave(john)|old(john)))&
((curious(susan)<~>kind(susan)))&
(patient(lucy)) | generous(john) | [] | null | 0 |
Everyone who is both wise and not brave is either not strong or wise.
Everyone who is either not funny or generous is not happy or creative and vice versa.
Everyone who is not generous or not wise is both brave and not curious and vice versa.
Everyone who is both curious and kind is quiet or not patient and vice versa.
If alice is not curious or not kind then someone is both creative and humble.
Everyone who is either patient or happy is both not happy and not curious.
Everyone who is not generous is both not kind and generous and vice versa.
Everyone who is creative is either not old or curious and vice versa.
If someone is either not happy or rich then someone is calm.
Everyone who is not kind is not curious and vice versa.
Everyone who is either not patient or not brave is happy or not kind.
If lucy is either not happy or not brave then alice is not quiet or funny.
If john is both calm and happy then someone is both curious and not rich.
If someone is not strong then someone is both not rich and happy and vice versa.
Everyone who is not tall or humble is kind.
If susan is both not quiet and rich then someone is both not strong and not old and vice versa.
Someone is curious or patient.
Someone is both rich and strong.
Someone is either not calm or not tall.
Someone is old.
Someone is both creative and not rich.
Mary is either not generous or not happy. | Mary is happy. | contradiction | (![X]:((wise(X)&~brave(X))=>(~strong(X)<~>wise(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(~happy(X)|creative(X))))&
(![X]:((~generous(X)|~wise(X))<=>(brave(X)&~curious(X))))&
(![X]:((curious(X)&kind(X))<=>(quiet(X)|~patient(X))))&
(((~curious(alice)|~kind(alice)))=>(?[X]:((creative(X)&humble(X)))))&
(![X]:((patient(X)<~>happy(X))=>(~happy(X)&~curious(X))))&
(![X]:(~generous(X)<=>(~kind(X)&generous(X))))&
(![X]:(creative(X)<=>(~old(X)<~>curious(X))))&
((?[X]:((~happy(X)<~>rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~kind(X)<=>~curious(X)))&
(![X]:((~patient(X)<~>~brave(X))=>(happy(X)|~kind(X))))&
(((~happy(lucy)<~>~brave(lucy)))=>((~quiet(alice)|funny(alice))))&
(((calm(john)&happy(john)))=>(?[X]:((curious(X)&~rich(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~rich(X)&happy(X)))))&
(![X]:((~tall(X)|humble(X))=>kind(X)))&
(((~quiet(susan)&rich(susan)))<=>(?[X]:((~strong(X)&~old(X)))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((rich(X)&strong(X))))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:(old(X)))&
(?[X]:((creative(X)&~rich(X))))&
((~generous(mary)<~>~happy(mary))) | happy(mary) | [
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7721601233035247365938418
% SZS output start Proof for 7721601233035247365938418
7. ! [X0] : (~generous(X0) <=> (generous(X0) & ~kind(X0))) [input p6]
22. ~generous(mary) <~> ~happy(mary) [input p21]
23. happy(mary) [input hypothesis]
48. ! [X0] : ((~generous(X0) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | generous(X0))) [nnf transformation 7]
49. ! [X0] : ((~generous(X0) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | generous(X0))) [flattening 48]
81. (happy(mary) | generous(mary)) & (~happy(mary) | ~generous(mary)) [nnf transformation 22]
109. generous(X0) | generous(X0) [cnf transformation 49]
142. ~happy(mary) | ~generous(mary) [cnf transformation 81]
144. happy(mary) [cnf transformation 23]
145. generous(X0) [duplicate literal removal 109]
274. ~happy(mary) [subsumption resolution 142,145]
275. $false [subsumption resolution 144,274]
% SZS output end Proof for 7721601233035247365938418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is either not curious or calm then alice is both not calm and wise and vice versa.
Everyone who is generous is both not old and tall and vice versa.
Everyone who is creative is either humble or not strong and vice versa.
Everyone who is either tall or not strong is not creative and vice versa.
Everyone who is either happy or not tall is both creative and strong and vice versa.
Everyone who is strong is not generous or rich.
If someone is not generous or not wise then alice is not curious.
If mary is both patient and creative then someone is either not patient or not strong.
If someone is either creative or generous then someone is not quiet or wise.
If fred is not funny or not creative then someone is either not patient or generous and vice versa.
Everyone who is either patient or happy is not quiet and vice versa.
If someone is not happy or not tall then someone is either not happy or not strong and vice versa.
Everyone who is both rich and not strong is either creative or not tall and vice versa.
Everyone who is funny is rich and vice versa.
If paul is both not rich and not happy then someone is not tall and vice versa.
If someone is either not funny or brave then someone is either curious or not wise and vice versa.
Someone is not funny.
Someone is either not creative or brave.
Someone is either not quiet or not generous.
Susan is either strong or patient.
Someone is creative.
John is happy.
Someone is both funny and wise.
Someone is patient. | John is creative. | contradiction | ((?[X]:((~curious(X)<~>calm(X))))<=>((~calm(alice)&wise(alice))))&
(![X]:(generous(X)<=>(~old(X)&tall(X))))&
(![X]:(creative(X)<=>(humble(X)<~>~strong(X))))&
(![X]:((tall(X)<~>~strong(X))<=>~creative(X)))&
(![X]:((happy(X)<~>~tall(X))<=>(creative(X)&strong(X))))&
(![X]:(strong(X)=>(~generous(X)|rich(X))))&
((?[X]:((~generous(X)|~wise(X))))=>(~curious(alice)))&
(((patient(mary)&creative(mary)))=>(?[X]:((~patient(X)<~>~strong(X)))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:((~quiet(X)|wise(X)))))&
(((~funny(fred)|~creative(fred)))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:((patient(X)<~>happy(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|~tall(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((rich(X)&~strong(X))<=>(creative(X)<~>~tall(X))))&
(![X]:(funny(X)<=>rich(X)))&
(((~rich(paul)&~happy(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(?[X]:(~funny(X)))&
(?[X]:((~creative(X)<~>brave(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((strong(susan)<~>patient(susan)))&
(?[X]:(creative(X)))&
(happy(john))&
(?[X]:((funny(X)&wise(X))))&
(?[X]:(patient(X))) | creative(john) | [
"p3",
"p4",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 888596692618690351442003
% SZS output start Proof for 888596692618690351442003
4. ! [X0] : ((tall(X0) <~> ~strong(X0)) <=> ~creative(X0)) [input p3]
5. ! [X0] : ((happy(X0) <~> ~tall(X0)) <=> (strong(X0) & creative(X0))) [input p4]
22. happy(john) [input p21]
25. creative(john) [input hypothesis]
43. ! [X0] : ((((strong(X0) | ~tall(X0)) & (~strong(X0) | tall(X0))) | creative(X0)) & (~creative(X0) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0))))) [nnf transformation 4]
44. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [nnf transformation 5]
45. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [flattening 44]
105. ~strong(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 43]
106. ~creative(X0) | tall(X0) | strong(X0) [cnf transformation 43]
111. ~happy(X0) | ~tall(X0) | strong(X0) [cnf transformation 45]
114. tall(X0) | ~happy(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 45]
165. happy(john) [cnf transformation 22]
169. creative(john) [cnf transformation 25]
198. ~happy(X0) | tall(X0) | ~creative(X0) [subsumption resolution 114,106]
436. 55 <=> strong(john) [avatar definition]
438. strong(john) <- (55) [avatar component clause 436]
440. 56 <=> tall(john) [avatar definition]
441. ~tall(john) <- (~56) [avatar component clause 440]
459. ~creative(john) | ~tall(john) <- (55) [resolution 438,105]
462. ~tall(john) <- (55) [subsumption resolution 459,169]
463. ~56 | ~55 [avatar split clause 462,436,440]
492. ~tall(john) | strong(john) [resolution 111,165]
505. 55 | ~56 [avatar split clause 492,440,436]
656. tall(john) | ~creative(john) [resolution 198,165]
661. ~creative(john) <- (~56) [subsumption resolution 656,441]
662. $false <- (~56) [subsumption resolution 661,169]
663. 56 [avatar contradiction clause 662]
664. $false [avatar sat refutation 463,505,663]
% SZS output end Proof for 888596692618690351442003
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not rich is not old and vice versa.
If someone is kind then someone is both not happy and tall.
If someone is not strong or not rich then someone is either not kind or not funny and vice versa.
If someone is not brave then mary is rich and vice versa.
Everyone who is both not wise and not strong is not brave or curious.
If susan is not old then alice is not strong and vice versa.
If mary is happy then someone is both creative and not wise.
Everyone who is both not wise and not funny is either not creative or not rich.
Everyone who is either not humble or not happy is both not tall and happy and vice versa.
If someone is both not patient and not creative then susan is humble or generous and vice versa.
Everyone who is not rich or wise is both not calm and not rich.
Everyone who is either not tall or happy is happy and vice versa.
If susan is either not curious or not rich then paul is both not quiet and humble and vice versa.
If lucy is either humble or not humble then susan is not strong.
If someone is both creative and not tall then someone is humble and vice versa.
If someone is tall or generous then someone is either patient or not curious and vice versa.
Someone is either tall or not tall.
Someone is either not brave or not humble.
Paul is wise.
Someone is tall or not humble.
Someone is both wise and not funny.
Paul is either quiet or not patient. | Susan is not strong. | entailment | (![X]:((strong(X)<~>~rich(X))<=>~old(X)))&
((?[X]:(kind(X)))=>(?[X]:((~happy(X)&tall(X)))))&
((?[X]:((~strong(X)|~rich(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:(~brave(X)))<=>(rich(mary)))&
(![X]:((~wise(X)&~strong(X))=>(~brave(X)|curious(X))))&
((~old(susan))<=>(~strong(alice)))&
((happy(mary))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:((~wise(X)&~funny(X))=>(~creative(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~tall(X)&happy(X))))&
((?[X]:((~patient(X)&~creative(X))))<=>((humble(susan)|generous(susan))))&
(![X]:((~rich(X)|wise(X))=>(~calm(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))<=>happy(X)))&
(((~curious(susan)<~>~rich(susan)))<=>((~quiet(paul)&humble(paul))))&
(((humble(lucy)<~>~humble(lucy)))=>(~strong(susan)))&
((?[X]:((creative(X)&~tall(X))))<=>(?[X]:(humble(X))))&
((?[X]:((tall(X)|generous(X))))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(?[X]:((tall(X)<~>~tall(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(wise(paul))&
(?[X]:((tall(X)|~humble(X))))&
(?[X]:((wise(X)&~funny(X))))&
((quiet(paul)<~>~patient(paul))) | ~strong(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1754630419862795334326389
% SZS output start Proof for 1754630419862795334326389
14. (humble(lucy) <~> ~humble(lucy)) => ~strong(susan) [input p13]
23. strong(susan) [input hypothesis]
36. ~strong(susan) | (humble(lucy) <=> ~humble(lucy)) [ennf transformation 14]
64. ~strong(susan) | ((humble(lucy) | humble(lucy)) & (~humble(lucy) | ~humble(lucy))) [nnf transformation 36]
130. ~strong(susan) | ~humble(lucy) | ~humble(lucy) [cnf transformation 64]
131. ~strong(susan) | humble(lucy) | humble(lucy) [cnf transformation 64]
151. strong(susan) [cnf transformation 23]
152. ~strong(susan) | ~humble(lucy) [duplicate literal removal 130]
153. ~strong(susan) | humble(lucy) [duplicate literal removal 131]
290. 29 <=> humble(lucy) [avatar definition]
294. 30 <=> strong(susan) [avatar definition]
297. 29 | ~30 [avatar split clause 153,294,290]
298. ~29 | ~30 [avatar split clause 152,294,290]
324. 30 [avatar split clause 151,294]
325. $false [avatar sat refutation 297,298,324]
% SZS output end Proof for 1754630419862795334326389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not old or not kind then paul is both not strong and not creative and vice versa. If mary is not curious then susan is not strong. Everyone who is either creative or kind is either tall or happy. Everyone who is either kind or calm is rich and vice versa. Everyone who is kind is patient or not creative and vice versa. Everyone who is brave is either not old or not tall. If alice is kind then fred is both funny and not funny. If someone is not creative then someone is either generous or not kind. Everyone who is not calm or creative is wise or not generous. If someone is either not kind or generous then someone is creative. Everyone who is not funny is funny or generous. If alice is patient then someone is creative. Everyone who is both not calm and not quiet is quiet or not happy and vice versa. Everyone who is not quiet or humble is not happy. Everyone who is old is strong. If lucy is either not happy or funny then john is either brave or not patient. Someone is not generous. Someone is either not rich or strong. Mary is not kind or happy. Paul is funny. Someone is curious. | Mary is calm. | contradiction | (((~old(susan)|~kind(susan)))<=>((~strong(paul)&~creative(paul))))&
((~curious(mary))=>(~strong(susan)))&
(![X]:((creative(X)<~>kind(X))=>(tall(X)<~>happy(X))))&
(![X]:((kind(X)<~>calm(X))<=>rich(X)))&
(![X]:(kind(X)<=>(patient(X)|~creative(X))))&
(![X]:(brave(X)=>(~old(X)<~>~tall(X))))&
((kind(alice))=>((funny(fred)&~funny(fred))))&
((?[X]:(~creative(X)))=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:((~calm(X)|creative(X))=>(wise(X)|~generous(X))))&
((?[X]:((~kind(X)<~>generous(X))))=>(?[X]:(creative(X))))&
(![X]:(~funny(X)=>(funny(X)|generous(X))))&
((patient(alice))=>(?[X]:(creative(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(quiet(X)|~happy(X))))&
(![X]:((~quiet(X)|humble(X))=>~happy(X)))&
(![X]:(old(X)=>strong(X)))&
(((~happy(lucy)<~>funny(lucy)))=>((brave(john)<~>~patient(john))))&
(?[X]:(~generous(X)))&
(?[X]:((~rich(X)<~>strong(X))))&
((~kind(mary)|happy(mary)))&
(funny(paul))&
(?[X]:(curious(X))) | calm(mary) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7086096143240792414766569
% SZS output start Proof for 7086096143240792414766569
13. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> (~happy(X0) | quiet(X0))) [input p12]
14. ! [X0] : ((humble(X0) | ~quiet(X0)) => ~happy(X0)) [input p13]
22. calm(mary) [input hypothesis]
25. ! [X0] : (~quiet(X0) => ~happy(X0)) [pure predicate removal 14]
37. ! [X0] : (~happy(X0) | quiet(X0)) [ennf transformation 25]
57. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (happy(X0) & ~quiet(X0))) & ((~happy(X0) | quiet(X0)) | (quiet(X0) | calm(X0)))) [nnf transformation 13]
58. ! [X0] : (((~quiet(X0) & ~calm(X0)) | (happy(X0) & ~quiet(X0))) & (~happy(X0) | quiet(X0) | quiet(X0) | calm(X0))) [flattening 57]
93. ~calm(X0) | happy(X0) [cnf transformation 58]
94. ~quiet(X0) | ~quiet(X0) [cnf transformation 58]
96. ~happy(X0) | quiet(X0) [cnf transformation 37]
107. calm(mary) [cnf transformation 22]
109. ~quiet(X0) [duplicate literal removal 94]
177. ~happy(X0) [subsumption resolution 96,109]
206. happy(mary) [resolution 93,107]
207. $false [subsumption resolution 206,177]
% SZS output end Proof for 7086096143240792414766569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or happy is brave or generous. Everyone who is brave is kind and vice versa. If someone is either happy or not brave then susan is wise or not creative. If someone is either not funny or strong then someone is both tall and creative and vice versa. If someone is both not happy and wise then someone is both not curious and not creative. If someone is both strong and quiet then someone is not generous or not happy and vice versa. Everyone who is not humble is either not funny or not quiet. If someone is not patient or not generous then someone is either not generous or wise and vice versa. Everyone who is either not happy or creative is either not old or not generous. Everyone who is either not strong or not funny is either patient or generous and vice versa. Everyone who is both not curious and happy is funny or not creative. If someone is brave then someone is either patient or creative and vice versa. Everyone who is either not wise or quiet is not funny and vice versa. Everyone who is not calm or not quiet is creative or funny. Everyone who is generous is both not wise and calm. Everyone who is quiet is not strong. Susan is not old. Susan is not strong or not old. Lucy is tall. Someone is either not wise or kind. Someone is not old or tall. Paul is old or not rich. | Lucy is not funny. | entailment | (![X]:((funny(X)|happy(X))=>(brave(X)|generous(X))))&
(![X]:(brave(X)<=>kind(X)))&
((?[X]:((happy(X)<~>~brave(X))))=>((wise(susan)|~creative(susan))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:((~curious(X)&~creative(X)))))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(~humble(X)=>(~funny(X)<~>~quiet(X))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~old(X)<~>~generous(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~curious(X)&happy(X))=>(funny(X)|~creative(X))))&
((?[X]:(brave(X)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~funny(X)))&
(![X]:((~calm(X)|~quiet(X))=>(creative(X)|funny(X))))&
(![X]:(generous(X)=>(~wise(X)&calm(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(~old(susan))&
((~strong(susan)|~old(susan)))&
(tall(lucy))&
(?[X]:((~wise(X)<~>kind(X))))&
(?[X]:((~old(X)|tall(X))))&
((old(paul)|~rich(paul))) | ~funny(lucy) | [
"p5",
"p7",
"p9",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2465787583694675649618809
% SZS output start Proof for 2465787583694675649618809
6. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p5]
8. ? [X0] : (~generous(X0) | ~patient(X0)) <=> ? [X0] : (~generous(X0) <~> wise(X0)) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~funny(X0)) <=> (patient(X0) <~> generous(X0))) [input p9]
13. ! [X0] : ((~wise(X0) <~> quiet(X0)) <=> ~funny(X0)) [input p12]
15. ! [X0] : (generous(X0) => (calm(X0) & ~wise(X0))) [input p14]
16. ! [X0] : (quiet(X0) => ~strong(X0)) [input p15]
23. funny(lucy) [input hypothesis]
26. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | ~generous(X1)) [rectify 6]
27. ? [X0] : (~generous(X0) | ~patient(X0)) <=> ? [X1] : (~generous(X1) <~> wise(X1)) [rectify 8]
31. ! [X0] : (generous(X0) => ~wise(X0)) [pure predicate removal 15]
43. ! [X0] : (~wise(X0) | ~generous(X0)) [ennf transformation 31]
44. ! [X0] : (~strong(X0) | ~quiet(X0)) [ennf transformation 16]
55. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ! [X0] : (~quiet(X0) | ~strong(X0))) [nnf transformation 26]
56. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X2] : (~happy(X2) | ~generous(X2)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [rectify 55]
57. ? [X0] : (quiet(X0) & strong(X0)) => (quiet(sK3) & strong(sK3)) [choice axiom]
58. ? [X2] : (~happy(X2) | ~generous(X2)) => (~happy(sK4) | ~generous(sK4)) [choice axiom]
59. ((quiet(sK3) & strong(sK3)) | ! [X1] : (happy(X1) & generous(X1))) & ((~happy(sK4) | ~generous(sK4)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [skolemisation 56,58,57]
60. (? [X0] : (~generous(X0) | ~patient(X0)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (? [X1] : ((~wise(X1) | generous(X1)) & (wise(X1) | ~generous(X1))) | ! [X0] : (generous(X0) & patient(X0))) [nnf transformation 27]
61. (? [X0] : (~generous(X0) | ~patient(X0)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (? [X2] : ((~wise(X2) | generous(X2)) & (wise(X2) | ~generous(X2))) | ! [X3] : (generous(X3) & patient(X3))) [rectify 60]
62. ? [X0] : (~generous(X0) | ~patient(X0)) => (~generous(sK5) | ~patient(sK5)) [choice axiom]
63. ? [X2] : ((~wise(X2) | generous(X2)) & (wise(X2) | ~generous(X2))) => ((~wise(sK6) | generous(sK6)) & (wise(sK6) | ~generous(sK6))) [choice axiom]
64. ((~generous(sK5) | ~patient(sK5)) | ! [X1] : ((~generous(X1) | ~wise(X1)) & (wise(X1) | generous(X1)))) & (((~wise(sK6) | generous(sK6)) & (wise(sK6) | ~generous(sK6))) | ! [X3] : (generous(X3) & patient(X3))) [skolemisation 61,63,62]
66. ! [X0] : ((((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))))) [nnf transformation 10]
72. ! [X0] : ((((~quiet(X0) | wise(X0)) & (quiet(X0) | ~wise(X0))) | funny(X0)) & (~funny(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0))))) [nnf transformation 13]
93. strong(sK3) | generous(X1) [cnf transformation 59]
95. quiet(sK3) | generous(X1) [cnf transformation 59]
97. wise(sK6) | ~generous(sK6) | patient(X3) [cnf transformation 64]
109. ~patient(X0) | ~generous(X0) | ~funny(X0) | strong(X0) [cnf transformation 66]
120. ~funny(X0) | quiet(X0) | wise(X0) [cnf transformation 72]
125. ~wise(X0) | ~generous(X0) [cnf transformation 43]
126. ~strong(X0) | ~quiet(X0) [cnf transformation 44]
133. funny(lucy) [cnf transformation 23]
198. 16 <=> quiet(sK3) [avatar definition]
200. quiet(sK3) <- (16) [avatar component clause 198]
203. 17 <=> ! [X1] : generous(X1) [avatar definition]
204. generous(X1) <- (17) [avatar component clause 203]
205. 17 | 16 [avatar split clause 95,198,203]
207. 18 <=> strong(sK3) [avatar definition]
211. 17 | 18 [avatar split clause 93,207,203]
213. 19 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
214. ~quiet(X3) | ~strong(X3) <- (19) [avatar component clause 213]
225. 22 <=> ! [X1] : (~generous(X1) | ~wise(X1)) [avatar definition]
226. ~wise(X1) | ~generous(X1) <- (22) [avatar component clause 225]
241. 26 <=> generous(sK6) [avatar definition]
242. ~generous(sK6) <- (~26) [avatar component clause 241]
245. 27 <=> wise(sK6) [avatar definition]
246. wise(sK6) <- (27) [avatar component clause 245]
250. 28 <=> ! [X3] : patient(X3) [avatar definition]
251. patient(X3) <- (28) [avatar component clause 250]
254. 28 | ~26 | 27 [avatar split clause 97,245,241,250]
280. 22 [avatar split clause 125,225]
281. 19 [avatar split clause 126,213]
313. ~strong(sK3) <- (16, 19) [resolution 214,200]
316. ~18 | ~16 | ~19 [avatar split clause 313,213,198,207]
317. $false <- (17, ~26) [resolution 204,242]
318. ~17 | 26 [avatar contradiction clause 317]
320. ~generous(sK6) <- (22, 27) [resolution 226,246]
321. $false <- (17, 22, 27) [subsumption resolution 320,204]
322. ~17 | ~22 | ~27 [avatar contradiction clause 321]
339. quiet(lucy) | wise(lucy) [resolution 120,133]
343. 39 <=> wise(lucy) [avatar definition]
345. wise(lucy) <- (39) [avatar component clause 343]
347. 40 <=> quiet(lucy) [avatar definition]
349. quiet(lucy) <- (40) [avatar component clause 347]
350. 39 | 40 [avatar split clause 339,347,343]
360. ~generous(lucy) <- (22, 39) [resolution 345,226]
361. $false <- (17, 22, 39) [subsumption resolution 360,204]
362. ~17 | ~22 | ~39 [avatar contradiction clause 361]
366. ~strong(lucy) <- (19, 40) [resolution 349,214]
407. ~generous(X0) | ~funny(X0) | strong(X0) <- (28) [resolution 109,251]
408. ~funny(X0) | strong(X0) <- (17, 28) [subsumption resolution 407,204]
409. strong(lucy) <- (17, 28) [resolution 408,133]
411. $false <- (17, 19, 28, 40) [subsumption resolution 409,366]
412. ~17 | ~19 | ~28 | ~40 [avatar contradiction clause 411]
415. $false [avatar sat refutation 205,211,254,280,281,316,318,322,350,362,412]
% SZS output end Proof for 2465787583694675649618809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or brave is not funny.
Everyone who is either not old or not patient is both rich and not patient.
If someone is either not creative or not tall then alice is not old or rich.
Everyone who is both not curious and not quiet is not happy or not calm.
Everyone who is both kind and humble is curious or not creative.
If susan is not rich or not strong then alice is both not brave and strong and vice versa.
If paul is either not strong or calm then someone is either not generous or funny and vice versa.
Everyone who is calm or not patient is not funny or happy and vice versa.
Everyone who is creative or not happy is both not quiet and not wise and vice versa.
If mary is not patient or not old then fred is happy or humble and vice versa.
Everyone who is both not kind and not humble is not tall or not humble.
Everyone who is both not brave and not generous is either generous or not brave and vice versa.
If someone is not generous then someone is not curious and vice versa.
If someone is both not curious and generous then someone is wise or brave and vice versa.
If someone is generous or not creative then someone is both wise and generous and vice versa.
Everyone who is brave or not kind is both happy and kind and vice versa.
Alice is generous or not quiet.
Someone is either wise or calm.
Lucy is not humble or not quiet.
Someone is not tall.
Paul is either not funny or not happy.
Someone is either not brave or not calm.
Someone is patient or not old.
Someone is both humble and curious. | Mary is not wise. | entailment | (![X]:((~old(X)<~>brave(X))=>~funny(X)))&
(![X]:((~old(X)<~>~patient(X))=>(rich(X)&~patient(X))))&
((?[X]:((~creative(X)<~>~tall(X))))=>((~old(alice)|rich(alice))))&
(![X]:((~curious(X)&~quiet(X))=>(~happy(X)|~calm(X))))&
(![X]:((kind(X)&humble(X))=>(curious(X)|~creative(X))))&
(((~rich(susan)|~strong(susan)))<=>((~brave(alice)&strong(alice))))&
(((~strong(paul)<~>calm(paul)))<=>(?[X]:((~generous(X)<~>funny(X)))))&
(![X]:((calm(X)|~patient(X))<=>(~funny(X)|happy(X))))&
(![X]:((creative(X)|~happy(X))<=>(~quiet(X)&~wise(X))))&
(((~patient(mary)|~old(mary)))<=>((happy(fred)|humble(fred))))&
(![X]:((~kind(X)&~humble(X))=>(~tall(X)|~humble(X))))&
(![X]:((~brave(X)&~generous(X))<=>(generous(X)<~>~brave(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&generous(X))))<=>(?[X]:((wise(X)|brave(X)))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((brave(X)|~kind(X))<=>(happy(X)&kind(X))))&
((generous(alice)|~quiet(alice)))&
(?[X]:((wise(X)<~>calm(X))))&
((~humble(lucy)|~quiet(lucy)))&
(?[X]:(~tall(X)))&
((~funny(paul)<~>~happy(paul)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((patient(X)|~old(X))))&
(?[X]:((humble(X)&curious(X)))) | ~wise(mary) | [
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8516876901634303300268279
% SZS output start Proof for 8516876901634303300268279
9. ! [X0] : ((~happy(X0) | creative(X0)) <=> (~wise(X0) & ~quiet(X0))) [input p8]
12. ! [X0] : ((~generous(X0) & ~brave(X0)) <=> (generous(X0) <~> ~brave(X0))) [input p11]
15. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X0] : (generous(X0) & wise(X0)) [input p14]
16. ! [X0] : ((~kind(X0) | brave(X0)) <=> (kind(X0) & happy(X0))) [input p15]
25. wise(mary) [input hypothesis]
28. ? [X0] : (~creative(X0) | generous(X0)) <=> ? [X1] : (generous(X1) & wise(X1)) [rectify 15]
50. ! [X0] : (((~happy(X0) | creative(X0)) | (wise(X0) | quiet(X0))) & ((~wise(X0) & ~quiet(X0)) | (happy(X0) & ~creative(X0)))) [nnf transformation 9]
51. ! [X0] : ((~happy(X0) | creative(X0) | wise(X0) | quiet(X0)) & ((~wise(X0) & ~quiet(X0)) | (happy(X0) & ~creative(X0)))) [flattening 50]
54. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0)))) & (((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | (generous(X0) | brave(X0)))) [nnf transformation 12]
55. ! [X0] : (((~generous(X0) & ~brave(X0)) | ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0)))) & (((brave(X0) | ~generous(X0)) & (~brave(X0) | generous(X0))) | generous(X0) | brave(X0))) [flattening 54]
66. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (~generous(X1) | ~wise(X1))) & (? [X1] : (generous(X1) & wise(X1)) | ! [X0] : (creative(X0) & ~generous(X0))) [nnf transformation 28]
67. (? [X0] : (~creative(X0) | generous(X0)) | ! [X1] : (~generous(X1) | ~wise(X1))) & (? [X2] : (generous(X2) & wise(X2)) | ! [X3] : (creative(X3) & ~generous(X3))) [rectify 66]
68. ? [X0] : (~creative(X0) | generous(X0)) => (~creative(sK5) | generous(sK5)) [choice axiom]
69. ? [X2] : (generous(X2) & wise(X2)) => (generous(sK6) & wise(sK6)) [choice axiom]
70. ((~creative(sK5) | generous(sK5)) | ! [X1] : (~generous(X1) | ~wise(X1))) & ((generous(sK6) & wise(sK6)) | ! [X3] : (creative(X3) & ~generous(X3))) [skolemisation 67,69,68]
71. ! [X0] : (((~kind(X0) | brave(X0)) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | (kind(X0) & ~brave(X0)))) [nnf transformation 16]
72. ! [X0] : ((~kind(X0) | brave(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | (kind(X0) & ~brave(X0)))) [flattening 71]
115. ~wise(X0) | ~creative(X0) [cnf transformation 51]
116. ~wise(X0) | happy(X0) [cnf transformation 51]
127. ~generous(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 55]
137. wise(sK6) | creative(X3) [cnf transformation 70]
139. generous(sK6) | creative(X3) [cnf transformation 70]
144. kind(X0) | kind(X0) [cnf transformation 72]
145. ~kind(X0) | brave(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 72]
158. wise(mary) [cnf transformation 25]
159. kind(X0) [duplicate literal removal 144]
160. ~kind(X0) | brave(X0) | ~happy(X0) [duplicate literal removal 145]
164. ~generous(X0) | ~brave(X0) [duplicate literal removal 127]
314. 33 <=> ! [X3] : creative(X3) [avatar definition]
315. creative(X3) <- (33) [avatar component clause 314]
317. 34 <=> generous(sK6) [avatar definition]
319. generous(sK6) <- (34) [avatar component clause 317]
320. 33 | 34 [avatar split clause 139,317,314]
326. 36 <=> wise(sK6) [avatar definition]
328. wise(sK6) <- (36) [avatar component clause 326]
329. 33 | 36 [avatar split clause 137,326,314]
396. ~creative(mary) [resolution 115,158]
399. $false <- (33) [subsumption resolution 396,315]
400. ~33 [avatar contradiction clause 399]
406. happy(sK6) <- (36) [resolution 116,328]
410. ~brave(sK6) <- (34) [resolution 164,319]
461. ~happy(X0) | brave(X0) [resolution 160,159]
533. brave(sK6) <- (36) [resolution 461,406]
536. $false <- (34, 36) [subsumption resolution 533,410]
537. ~34 | ~36 [avatar contradiction clause 536]
538. $false [avatar sat refutation 320,329,400,537]
% SZS output end Proof for 8516876901634303300268279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not curious.
If mary is wise or quiet then someone is both not generous and not patient and vice versa.
If lucy is either wise or not old then someone is not funny and vice versa.
Everyone who is either quiet or calm is patient or not happy and vice versa.
If someone is either curious or not strong then someone is not funny or not curious and vice versa.
Everyone who is not strong or not tall is both not patient and not old and vice versa.
If someone is both curious and funny then paul is not kind.
If fred is both not creative and old then mary is both humble and not kind.
If susan is either humble or not happy then alice is both not tall and not happy.
Everyone who is both not old and not happy is not humble or tall and vice versa.
If alice is strong then alice is humble and vice versa.
Everyone who is both wise and creative is patient and vice versa.
If someone is kind or not tall then fred is both not patient and quiet.
Everyone who is both creative and strong is either not calm or not strong and vice versa.
If susan is either brave or calm then someone is not humble.
Everyone who is not tall or strong is both quiet and not strong and vice versa.
Alice is either not curious or not kind.
Someone is not kind.
Susan is old or not old.
John is either not strong or not generous.
Fred is brave or not quiet.
Someone is not funny.
Someone is either calm or not creative. | Susan is humble. | contradiction | (![X]:(generous(X)=>~curious(X)))&
(((wise(mary)|quiet(mary)))<=>(?[X]:((~generous(X)&~patient(X)))))&
(((wise(lucy)<~>~old(lucy)))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(patient(X)|~happy(X))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(~patient(X)&~old(X))))&
((?[X]:((curious(X)&funny(X))))=>(~kind(paul)))&
(((~creative(fred)&old(fred)))=>((humble(mary)&~kind(mary))))&
(((humble(susan)<~>~happy(susan)))=>((~tall(alice)&~happy(alice))))&
(![X]:((~old(X)&~happy(X))<=>(~humble(X)|tall(X))))&
((strong(alice))<=>(humble(alice)))&
(![X]:((wise(X)&creative(X))<=>patient(X)))&
((?[X]:((kind(X)|~tall(X))))=>((~patient(fred)&quiet(fred))))&
(![X]:((creative(X)&strong(X))<=>(~calm(X)<~>~strong(X))))&
(((brave(susan)<~>calm(susan)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)|strong(X))<=>(quiet(X)&~strong(X))))&
((~curious(alice)<~>~kind(alice)))&
(?[X]:(~kind(X)))&
((old(susan)|~old(susan)))&
((~strong(john)<~>~generous(john)))&
((brave(fred)|~quiet(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((calm(X)<~>~creative(X)))) | humble(susan) | [
"p3",
"p5",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7223744205499797009169333
% SZS output start Proof for 7223744205499797009169333
4. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (~happy(X0) | patient(X0))) [input p3]
6. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (~old(X0) & ~patient(X0))) [input p5]
10. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (tall(X0) | ~humble(X0))) [input p9]
14. ! [X0] : ((strong(X0) & creative(X0)) <=> (~calm(X0) <~> ~strong(X0))) [input p13]
16. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (~strong(X0) & quiet(X0))) [input p15]
24. humble(susan) [input hypothesis]
42. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 42]
49. ! [X0] : (((~tall(X0) | ~strong(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | ~strong(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [flattening 49]
52. ! [X0] : (((~happy(X0) & ~old(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (happy(X0) | old(X0)))) [nnf transformation 10]
53. ! [X0] : (((~happy(X0) & ~old(X0)) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | happy(X0) | old(X0))) [flattening 52]
57. ! [X0] : (((strong(X0) & creative(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (~strong(X0) | ~creative(X0)))) [nnf transformation 14]
58. ! [X0] : (((strong(X0) & creative(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ~strong(X0) | ~creative(X0))) [flattening 57]
62. ! [X0] : (((strong(X0) | ~tall(X0)) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 16]
63. ! [X0] : ((strong(X0) | ~tall(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | (~strong(X0) & tall(X0)))) [flattening 62]
83. ~happy(X0) | patient(X0) | calm(X0) | ~quiet(X0) [cnf transformation 43]
86. happy(X0) | quiet(X0) | calm(X0) [cnf transformation 43]
95. ~patient(X0) | strong(X0) [cnf transformation 50]
98. ~old(X0) | tall(X0) [cnf transformation 50]
107. tall(X0) | ~humble(X0) | happy(X0) | old(X0) [cnf transformation 53]
109. ~old(X0) | ~tall(X0) [cnf transformation 53]
111. ~tall(X0) | ~happy(X0) [cnf transformation 53]
126. strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 58]
129. tall(X0) | quiet(X0) [cnf transformation 63]
132. ~strong(X0) | ~strong(X0) [cnf transformation 63]
133. strong(X0) | ~tall(X0) | strong(X0) | ~quiet(X0) [cnf transformation 63]
144. humble(susan) [cnf transformation 24]
145. ~strong(X0) [duplicate literal removal 132]
146. ~tall(X0) | strong(X0) | ~quiet(X0) [duplicate literal removal 133]
148. ~calm(X0) | strong(X0) [duplicate literal removal 126]
250. 23 <=> happy(susan) [avatar definition]
251. ~happy(susan) <- (~23) [avatar component clause 250]
252. happy(susan) <- (23) [avatar component clause 250]
254. 24 <=> humble(susan) [avatar definition]
256. humble(susan) <- (24) [avatar component clause 254]
269. ~old(X0) [subsumption resolution 109,98]
270. ~humble(X0) | tall(X0) | happy(X0) [subsumption resolution 107,269]
301. 33 <=> calm(susan) [avatar definition]
302. calm(susan) <- (33) [avatar component clause 301]
303. ~calm(susan) <- (~33) [avatar component clause 301]
332. 24 [avatar split clause 144,254]
335. ~happy(X0) | quiet(X0) [resolution 129,111]
336. quiet(susan) | calm(susan) <- (~23) [resolution 86,251]
340. 39 <=> quiet(susan) [avatar definition]
342. quiet(susan) <- (39) [avatar component clause 340]
343. 33 | 39 | 23 [avatar split clause 336,250,340,301]
348. strong(susan) <- (33) [resolution 302,148]
349. $false <- (33) [subsumption resolution 348,145]
350. ~33 [avatar contradiction clause 349]
392. tall(susan) | happy(susan) <- (24) [resolution 270,256]
393. tall(susan) <- (~23, 24) [subsumption resolution 392,251]
394. strong(susan) | ~quiet(susan) <- (~23, 24) [resolution 393,146]
396. ~quiet(susan) <- (~23, 24) [subsumption resolution 394,145]
397. $false <- (~23, 24, 39) [subsumption resolution 396,342]
398. 23 | ~24 | ~39 [avatar contradiction clause 397]
406. quiet(susan) <- (23) [resolution 335,252]
409. patient(susan) | calm(susan) | ~quiet(susan) <- (23) [resolution 83,252]
411. patient(susan) | ~quiet(susan) <- (23, ~33) [subsumption resolution 409,303]
412. patient(susan) <- (23, ~33, 39) [subsumption resolution 411,342]
417. strong(susan) <- (23, ~33, 39) [resolution 412,95]
419. $false <- (23, ~33, 39) [subsumption resolution 417,145]
420. ~23 | 33 | ~39 [avatar contradiction clause 419]
426. 39 | ~23 [avatar split clause 406,250,340]
427. $false [avatar sat refutation 332,343,350,398,420,426]
% SZS output end Proof for 7223744205499797009169333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and happy is not wise.
Everyone who is either creative or patient is not quiet and vice versa.
Everyone who is old is both rich and not wise.
If someone is not generous or happy then someone is both old and not tall and vice versa.
If alice is both not curious and creative then someone is both not curious and rich.
Everyone who is both not old and not kind is either not happy or not kind and vice versa.
Everyone who is both creative and not calm is either not strong or quiet and vice versa.
Everyone who is both generous and kind is not curious and vice versa.
Everyone who is not humble is both not wise and funny and vice versa.
Everyone who is not generous is both calm and not humble.
If someone is both curious and not old then alice is both funny and calm and vice versa.
Everyone who is both patient and not creative is not patient or rich and vice versa.
Everyone who is happy is not humble or patient.
Everyone who is curious or not happy is not funny and vice versa.
If someone is either quiet or brave then paul is both humble and tall.
Everyone who is either creative or not brave is both strong and curious and vice versa.
Paul is either tall or quiet.
Paul is kind or humble.
Paul is either not funny or not happy.
Alice is tall.
Mary is either tall or strong.
Mary is both curious and brave.
Someone is strong or tall.
Someone is wise or creative. | Alice is not old. | neutral | (![X]:((~humble(X)&happy(X))=>~wise(X)))&
(![X]:((creative(X)<~>patient(X))<=>~quiet(X)))&
(![X]:(old(X)=>(rich(X)&~wise(X))))&
((?[X]:((~generous(X)|happy(X))))<=>(?[X]:((old(X)&~tall(X)))))&
(((~curious(alice)&creative(alice)))=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((creative(X)&~calm(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&kind(X))<=>~curious(X)))&
(![X]:(~humble(X)<=>(~wise(X)&funny(X))))&
(![X]:(~generous(X)=>(calm(X)&~humble(X))))&
((?[X]:((curious(X)&~old(X))))<=>((funny(alice)&calm(alice))))&
(![X]:((patient(X)&~creative(X))<=>(~patient(X)|rich(X))))&
(![X]:(happy(X)=>(~humble(X)|patient(X))))&
(![X]:((curious(X)|~happy(X))<=>~funny(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>((humble(paul)&tall(paul))))&
(![X]:((creative(X)<~>~brave(X))<=>(strong(X)&curious(X))))&
((tall(paul)<~>quiet(paul)))&
((kind(paul)|humble(paul)))&
((~funny(paul)<~>~happy(paul)))&
(tall(alice))&
((tall(mary)<~>strong(mary)))&
((curious(mary)&brave(mary)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((wise(X)|creative(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is not tall or calm is both strong and funny and vice versa.
If someone is either not generous or not kind then alice is both not old and not generous and vice versa.
Everyone who is both not tall and old is both wise and not quiet.
Everyone who is happy or humble is both not tall and patient.
If someone is both wise and tall then someone is either quiet or not tall.
Everyone who is happy is generous and vice versa.
If fred is both old and quiet then someone is both not funny and not quiet and vice versa.
If alice is either not happy or not patient then susan is either creative or happy and vice versa.
Everyone who is either happy or strong is not patient.
If someone is both not kind and tall then alice is both not tall and not strong and vice versa.
If mary is either not curious or not funny then someone is wise.
If someone is patient or curious then someone is brave.
Everyone who is either generous or not patient is calm or humble.
Everyone who is curious is not creative and vice versa.
Everyone who is either not generous or rich is kind.
Someone is either rich or funny.
Lucy is both calm and old.
Paul is quiet.
Fred is both not quiet and not curious.
Someone is patient. | Mary is calm. | neutral | (![X]:((~tall(X)|calm(X))<=>(strong(X)&funny(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((~old(alice)&~generous(alice))))&
(![X]:((~tall(X)&old(X))=>(wise(X)&~quiet(X))))&
(![X]:((happy(X)|humble(X))=>(~tall(X)&patient(X))))&
((?[X]:((wise(X)&tall(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(((old(fred)&quiet(fred)))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~happy(alice)<~>~patient(alice)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((happy(X)<~>strong(X))=>~patient(X)))&
((?[X]:((~kind(X)&tall(X))))<=>((~tall(alice)&~strong(alice))))&
(((~curious(mary)<~>~funny(mary)))=>(?[X]:(wise(X))))&
((?[X]:((patient(X)|curious(X))))=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~patient(X))=>(calm(X)|humble(X))))&
(![X]:(curious(X)<=>~creative(X)))&
(![X]:((~generous(X)<~>rich(X))=>kind(X)))&
(?[X]:((rich(X)<~>funny(X))))&
((calm(lucy)&old(lucy)))&
(quiet(paul))&
((~quiet(fred)&~curious(fred)))&
(?[X]:(patient(X))) | calm(mary) | [] | null | 0 |
Everyone who is patient is not funny and vice versa.
If someone is calm or brave then someone is not curious or not calm and vice versa.
Everyone who is not quiet is either not wise or not patient and vice versa.
Everyone who is happy or curious is either curious or not wise and vice versa.
Everyone who is either not calm or strong is tall or curious and vice versa.
If paul is either not old or not humble then someone is both not happy and not generous and vice versa.
Everyone who is rich is happy or not rich and vice versa.
If someone is brave or kind then mary is both funny and not patient and vice versa.
If lucy is not brave or not kind then someone is both creative and rich.
Everyone who is generous or kind is either not rich or not strong and vice versa.
If someone is either humble or not quiet then someone is patient or old.
If someone is both not tall and not strong then someone is not tall.
Everyone who is rich or funny is not happy or calm and vice versa.
Everyone who is either not strong or curious is either not quiet or not curious.
Everyone who is kind or not kind is kind.
Everyone who is humble is calm or kind and vice versa.
Someone is creative.
Fred is either not strong or creative.
Fred is brave.
Someone is not generous or not brave.
Someone is not humble or happy. | Lucy is not tall. | entailment | (![X]:(patient(X)<=>~funny(X)))&
((?[X]:((calm(X)|brave(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>~patient(X))))&
(![X]:((happy(X)|curious(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(tall(X)|curious(X))))&
(((~old(paul)<~>~humble(paul)))<=>(?[X]:((~happy(X)&~generous(X)))))&
(![X]:(rich(X)<=>(happy(X)|~rich(X))))&
((?[X]:((brave(X)|kind(X))))<=>((funny(mary)&~patient(mary))))&
(((~brave(lucy)|~kind(lucy)))=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((generous(X)|kind(X))<=>(~rich(X)<~>~strong(X))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((patient(X)|old(X)))))&
((?[X]:((~tall(X)&~strong(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)|funny(X))<=>(~happy(X)|calm(X))))&
(![X]:((~strong(X)<~>curious(X))=>(~quiet(X)<~>~curious(X))))&
(![X]:((kind(X)|~kind(X))=>kind(X)))&
(![X]:(humble(X)<=>(calm(X)|kind(X))))&
(?[X]:(creative(X)))&
((~strong(fred)<~>creative(fred)))&
(brave(fred))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((~humble(X)|happy(X)))) | ~tall(lucy) | [
"p4",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7133894573938449707885709
% SZS output start Proof for 7133894573938449707885709
5. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (curious(X0) | tall(X0))) [input p4]
7. ! [X0] : (rich(X0) <=> (~rich(X0) | happy(X0))) [input p6]
10. ! [X0] : ((kind(X0) | generous(X0)) <=> (~rich(X0) <~> ~strong(X0))) [input p9]
13. ! [X0] : ((funny(X0) | rich(X0)) <=> (calm(X0) | ~happy(X0))) [input p12]
15. ! [X0] : ((~kind(X0) | kind(X0)) => kind(X0)) [input p14]
22. tall(lucy) [input hypothesis]
30. ! [X0] : (kind(X0) | (kind(X0) & ~kind(X0))) [ennf transformation 15]
40. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 5]
41. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 40]
46. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | ~rich(X0))) [nnf transformation 7]
47. ! [X0] : ((rich(X0) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | ~rich(X0))) [flattening 46]
55. ! [X0] : (((kind(X0) | generous(X0)) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : ((kind(X0) | generous(X0) | ((~rich(X0) | strong(X0)) & (~strong(X0) | rich(X0)))) & (((strong(X0) | rich(X0)) & (~strong(X0) | ~rich(X0))) | (~kind(X0) & ~generous(X0)))) [flattening 55]
64. ! [X0] : (((funny(X0) | rich(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (~funny(X0) & ~rich(X0)))) [nnf transformation 13]
65. ! [X0] : ((funny(X0) | rich(X0) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | (~funny(X0) & ~rich(X0)))) [flattening 64]
94. ~tall(X0) | ~calm(X0) | strong(X0) [cnf transformation 41]
104. ~rich(X0) | happy(X0) | ~rich(X0) [cnf transformation 47]
106. rich(X0) | rich(X0) [cnf transformation 47]
117. ~strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 56]
125. calm(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 65]
134. kind(X0) | kind(X0) [cnf transformation 30]
144. tall(lucy) [cnf transformation 22]
145. kind(X0) [duplicate literal removal 134]
148. ~rich(X0) | happy(X0) [duplicate literal removal 104]
149. rich(X0) [duplicate literal removal 106]
153. 1 <=> ! [X1] : calm(X1) [avatar definition]
154. calm(X1) <- (1) [avatar component clause 153]
209. happy(X0) [subsumption resolution 148,149]
250. ~kind(X0) | ~strong(X0) [subsumption resolution 117,149]
277. calm(X0) | ~rich(X0) [subsumption resolution 125,209]
278. calm(X0) [subsumption resolution 277,149]
279. 1 [avatar split clause 278,153]
306. ~strong(X0) [resolution 250,145]
314. ~calm(lucy) | strong(lucy) [resolution 94,144]
315. strong(lucy) <- (1) [subsumption resolution 314,154]
316. $false <- (1) [subsumption resolution 315,306]
317. ~1 [avatar contradiction clause 316]
318. $false [avatar sat refutation 279,317]
% SZS output end Proof for 7133894573938449707885709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not curious is curious.
If someone is either rich or funny then someone is both humble and creative and vice versa.
If john is both not generous and generous then someone is either humble or tall.
Everyone who is not kind or creative is not calm or old and vice versa.
If alice is funny or kind then alice is not quiet or quiet and vice versa.
Everyone who is both quiet and rich is both curious and kind.
Everyone who is not tall or creative is creative and vice versa.
If paul is either happy or not wise then someone is humble and vice versa.
If lucy is either not funny or not strong then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
Fred is either curious or not calm.
Someone is calm or tall.
Fred is either quiet or not patient.
Someone is either not brave or not calm.
Someone is brave or creative. | Lucy is not old. | entailment | (![X]:((~happy(X)<~>~curious(X))=>curious(X)))&
((?[X]:((rich(X)<~>funny(X))))<=>(?[X]:((humble(X)&creative(X)))))&
(((~generous(john)&generous(john)))=>(?[X]:((humble(X)<~>tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)|old(X))))&
(((funny(alice)|kind(alice)))<=>((~quiet(alice)|quiet(alice))))&
(![X]:((quiet(X)&rich(X))=>(curious(X)&kind(X))))&
(![X]:((~tall(X)|creative(X))<=>creative(X)))&
(((happy(paul)<~>~wise(paul)))<=>(?[X]:(humble(X))))&
(((~funny(lucy)<~>~strong(lucy)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
((curious(fred)<~>~calm(fred)))&
(?[X]:((calm(X)|tall(X))))&
((quiet(fred)<~>~patient(fred)))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((brave(X)|creative(X)))) | ~old(lucy) | [
"p0",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1826966638444484287390148
% SZS output start Proof for 1826966638444484287390148
1. ! [X0] : ((~happy(X0) <~> ~curious(X0)) => curious(X0)) [input p0]
8. (happy(paul) <~> ~wise(paul)) <=> ? [X0] : humble(X0) [input p7]
10. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p9]
12. ! [X0] : ((~funny(X0) & wise(X0)) <=> (~happy(X0) | rich(X0))) [input p11]
13. ? [X0] : (~brave(X0) | old(X0)) <=> (~quiet(susan) & humble(susan)) [input p12]
21. old(lucy) [input hypothesis]
24. ! [X0] : (curious(X0) | (~happy(X0) <=> ~curious(X0))) [ennf transformation 1]
29. ! [X0] : (curious(X0) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0)))) [nnf transformation 24]
44. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [nnf transformation 8]
45. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [rectify 44]
46. ? [X1] : humble(X1) => humble(sK3) [choice axiom]
47. (((wise(paul) | ~happy(paul)) & (~wise(paul) | happy(paul))) | ! [X0] : ~humble(X0)) & (humble(sK3) | ((happy(paul) | wise(paul)) & (~wise(paul) | ~happy(paul)))) [skolemisation 45,46]
52. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 10]
53. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 52]
59. ! [X0] : (((~funny(X0) & wise(X0)) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | (funny(X0) | ~wise(X0)))) [nnf transformation 12]
60. ! [X0] : (((~funny(X0) & wise(X0)) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | funny(X0) | ~wise(X0))) [flattening 59]
61. (? [X0] : (~brave(X0) | old(X0)) | (quiet(susan) | ~humble(susan))) & ((~quiet(susan) & humble(susan)) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 13]
62. (? [X0] : (~brave(X0) | old(X0)) | quiet(susan) | ~humble(susan)) & ((~quiet(susan) & humble(susan)) | ! [X0] : (brave(X0) & ~old(X0))) [flattening 61]
63. (? [X0] : (~brave(X0) | old(X0)) | quiet(susan) | ~humble(susan)) & ((~quiet(susan) & humble(susan)) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 62]
64. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK7) | old(sK7)) [choice axiom]
65. ((~brave(sK7) | old(sK7)) | quiet(susan) | ~humble(susan)) & ((~quiet(susan) & humble(susan)) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 63,64]
82. curious(X0) | ~happy(X0) | curious(X0) [cnf transformation 29]
106. ~wise(paul) | happy(paul) | ~humble(X0) [cnf transformation 47]
117. ~curious(X0) | ~curious(X0) [cnf transformation 53]
124. wise(X0) | happy(X0) [cnf transformation 60]
127. humble(susan) | ~old(X1) [cnf transformation 65]
152. old(lucy) [cnf transformation 21]
157. ~curious(X0) [duplicate literal removal 117]
159. ~happy(X0) | curious(X0) [duplicate literal removal 82]
206. 11 <=> ! [X0] : ~humble(X0) [avatar definition]
207. ~humble(X0) <- (11) [avatar component clause 206]
209. 12 <=> happy(paul) [avatar definition]
210. happy(paul) <- (12) [avatar component clause 209]
211. ~happy(paul) <- (~12) [avatar component clause 209]
213. 13 <=> wise(paul) [avatar definition]
214. ~wise(paul) <- (~13) [avatar component clause 213]
217. 11 | 12 | ~13 [avatar split clause 106,213,209,206]
279. 27 <=> humble(susan) [avatar definition]
280. humble(susan) <- (27) [avatar component clause 279]
300. 32 <=> ! [X1] : ~old(X1) [avatar definition]
301. ~old(X1) <- (32) [avatar component clause 300]
304. 32 | 27 [avatar split clause 127,279,300]
381. $false <- (11, 27) [resolution 280,207]
382. ~11 | ~27 [avatar contradiction clause 381]
385. $false <- (32) [resolution 301,152]
386. ~32 [avatar contradiction clause 385]
389. happy(paul) <- (~13) [resolution 124,214]
390. $false <- (~12, ~13) [subsumption resolution 389,211]
391. 12 | 13 [avatar contradiction clause 390]
397. curious(paul) <- (12) [resolution 159,210]
399. $false <- (12) [subsumption resolution 397,157]
400. ~12 [avatar contradiction clause 399]
403. $false [avatar sat refutation 217,304,382,386,391,400]
% SZS output end Proof for 1826966638444484287390148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not patient and wise then susan is both not kind and not humble and vice versa.
Everyone who is either quiet or tall is both curious and not rich.
If someone is not kind or brave then paul is either strong or brave and vice versa.
If paul is not curious then paul is not old.
Everyone who is either quiet or not humble is both tall and strong and vice versa.
Everyone who is either old or calm is both old and kind.
Everyone who is old or not quiet is either not strong or tall.
Everyone who is not creative or generous is either brave or happy and vice versa.
Everyone who is both not calm and wise is quiet or not quiet.
Everyone who is not happy or strong is both not funny and not kind.
Everyone who is either old or not strong is not calm.
Everyone who is curious is both patient and not curious and vice versa.
If mary is both not creative and tall then someone is both happy and quiet.
If lucy is both not old and strong then someone is both not old and patient.
Everyone who is not strong is not curious.
Everyone who is funny or quiet is humble or wise and vice versa.
Someone is creative or tall.
Paul is wise or quiet.
Mary is not wise.
Someone is both not curious and not patient.
Mary is either kind or not funny.
Lucy is brave.
Paul is wise. | Susan is not old. | entailment | ((?[X]:((~patient(X)&wise(X))))<=>((~kind(susan)&~humble(susan))))&
(![X]:((quiet(X)<~>tall(X))=>(curious(X)&~rich(X))))&
((?[X]:((~kind(X)|brave(X))))<=>((strong(paul)<~>brave(paul))))&
((~curious(paul))=>(~old(paul)))&
(![X]:((quiet(X)<~>~humble(X))<=>(tall(X)&strong(X))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(![X]:((old(X)|~quiet(X))=>(~strong(X)<~>tall(X))))&
(![X]:((~creative(X)|generous(X))<=>(brave(X)<~>happy(X))))&
(![X]:((~calm(X)&wise(X))=>(quiet(X)|~quiet(X))))&
(![X]:((~happy(X)|strong(X))=>(~funny(X)&~kind(X))))&
(![X]:((old(X)<~>~strong(X))=>~calm(X)))&
(![X]:(curious(X)<=>(patient(X)&~curious(X))))&
(((~creative(mary)&tall(mary)))=>(?[X]:((happy(X)&quiet(X)))))&
(((~old(lucy)&strong(lucy)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:(~strong(X)=>~curious(X)))&
(![X]:((funny(X)|quiet(X))<=>(humble(X)|wise(X))))&
(?[X]:((creative(X)|tall(X))))&
((wise(paul)|quiet(paul)))&
(~wise(mary))&
(?[X]:((~curious(X)&~patient(X))))&
((kind(mary)<~>~funny(mary)))&
(brave(lucy))&
(wise(paul)) | ~old(susan) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 688204979602808246484203
% SZS output start Proof for 688204979602808246484203
1. ? [X0] : (wise(X0) & ~patient(X0)) <=> (~humble(susan) & ~kind(susan)) [input p0]
2. ! [X0] : ((quiet(X0) <~> tall(X0)) => (~rich(X0) & curious(X0))) [input p1]
5. ! [X0] : ((quiet(X0) <~> ~humble(X0)) <=> (strong(X0) & tall(X0))) [input p4]
6. ! [X0] : ((old(X0) <~> calm(X0)) => (kind(X0) & old(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | old(X0)) => (~strong(X0) <~> tall(X0))) [input p6]
11. ! [X0] : ((old(X0) <~> ~strong(X0)) => ~calm(X0)) [input p10]
12. ! [X0] : (curious(X0) <=> (~curious(X0) & patient(X0))) [input p11]
23. wise(paul) [input p22]
24. old(susan) [input hypothesis]
25. ! [X0] : ((quiet(X0) <~> tall(X0)) => curious(X0)) [pure predicate removal 2]
26. ! [X0] : (curious(X0) | (quiet(X0) <=> tall(X0))) [ennf transformation 25]
28. ! [X0] : ((kind(X0) & old(X0)) | (old(X0) <=> calm(X0))) [ennf transformation 6]
29. ! [X0] : ((~strong(X0) <~> tall(X0)) | (quiet(X0) & ~old(X0))) [ennf transformation 7]
33. ! [X0] : (~calm(X0) | (old(X0) <=> ~strong(X0))) [ennf transformation 11]
39. (? [X0] : (wise(X0) & ~patient(X0)) | (humble(susan) | kind(susan))) & ((~humble(susan) & ~kind(susan)) | ! [X0] : (~wise(X0) | patient(X0))) [nnf transformation 1]
40. (? [X0] : (wise(X0) & ~patient(X0)) | humble(susan) | kind(susan)) & ((~humble(susan) & ~kind(susan)) | ! [X0] : (~wise(X0) | patient(X0))) [flattening 39]
41. (? [X0] : (wise(X0) & ~patient(X0)) | humble(susan) | kind(susan)) & ((~humble(susan) & ~kind(susan)) | ! [X1] : (~wise(X1) | patient(X1))) [rectify 40]
42. ? [X0] : (wise(X0) & ~patient(X0)) => (wise(sK0) & ~patient(sK0)) [choice axiom]
43. ((wise(sK0) & ~patient(sK0)) | humble(susan) | kind(susan)) & ((~humble(susan) & ~kind(susan)) | ! [X1] : (~wise(X1) | patient(X1))) [skolemisation 41,42]
44. ! [X0] : (curious(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) [nnf transformation 26]
49. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | (~strong(X0) | ~tall(X0))) & ((strong(X0) & tall(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [nnf transformation 5]
50. ! [X0] : ((((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | ~strong(X0) | ~tall(X0)) & ((strong(X0) & tall(X0)) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0))))) [flattening 49]
51. ! [X0] : ((kind(X0) & old(X0)) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) [nnf transformation 28]
52. ! [X0] : (((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | (quiet(X0) & ~old(X0))) [nnf transformation 29]
55. ! [X0] : (~calm(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) [nnf transformation 33]
56. ! [X0] : ((curious(X0) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | ~curious(X0))) [nnf transformation 12]
57. ! [X0] : ((curious(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | ~curious(X0))) [flattening 56]
69. ~kind(susan) | ~wise(X1) | patient(X1) [cnf transformation 43]
70. ~humble(susan) | ~wise(X1) | patient(X1) [cnf transformation 43]
73. ~quiet(X0) | tall(X0) | curious(X0) [cnf transformation 44]
74. ~tall(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
83. tall(X0) | quiet(X0) | humble(X0) [cnf transformation 50]
89. old(X0) | old(X0) | ~calm(X0) [cnf transformation 51]
90. ~old(X0) | calm(X0) | kind(X0) [cnf transformation 51]
94. ~old(X0) | strong(X0) | ~tall(X0) [cnf transformation 52]
107. ~calm(X0) | ~strong(X0) | ~old(X0) [cnf transformation 55]
110. ~curious(X0) | ~curious(X0) [cnf transformation 57]
111. curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 57]
129. wise(paul) [cnf transformation 23]
130. old(susan) [cnf transformation 24]
131. ~curious(X0) [duplicate literal removal 110]
132. ~patient(X0) | curious(X0) [duplicate literal removal 111]
133. ~calm(X0) | old(X0) [duplicate literal removal 89]
135. 1 <=> kind(susan) [avatar definition]
136. ~kind(susan) <- (~1) [avatar component clause 135]
139. 2 <=> humble(susan) [avatar definition]
140. ~humble(susan) <- (~2) [avatar component clause 139]
153. 5 <=> ! [X1] : (~wise(X1) | patient(X1)) [avatar definition]
154. ~wise(X1) | patient(X1) <- (5) [avatar component clause 153]
155. 5 | ~2 [avatar split clause 70,139,153]
156. 5 | ~1 [avatar split clause 69,135,153]
194. ~calm(X0) | ~strong(X0) [subsumption resolution 107,133]
241. 24 <=> wise(paul) [avatar definition]
243. wise(paul) <- (24) [avatar component clause 241]
259. 24 [avatar split clause 129,241]
261. quiet(X0) | humble(X0) | quiet(X0) | curious(X0) [resolution 83,74]
262. quiet(X0) | humble(X0) | curious(X0) [duplicate literal removal 261]
272. quiet(X0) | humble(X0) [subsumption resolution 262,131]
282. humble(X2) | tall(X2) | curious(X2) [resolution 272,73]
283. tall(X2) | humble(X2) [subsumption resolution 282,131]
284. calm(susan) | kind(susan) [resolution 90,130]
285. calm(susan) <- (~1) [subsumption resolution 284,136]
286. ~strong(susan) <- (~1) [resolution 285,194]
295. strong(susan) | ~tall(susan) [resolution 94,130]
296. ~tall(susan) <- (~1) [subsumption resolution 295,286]
300. humble(susan) <- (~1) [resolution 296,283]
302. $false <- (~1, ~2) [subsumption resolution 300,140]
303. 1 | 2 [avatar contradiction clause 302]
327. patient(paul) <- (5, 24) [resolution 154,243]
334. curious(paul) <- (5, 24) [resolution 327,132]
335. $false <- (5, 24) [subsumption resolution 334,131]
336. ~5 | ~24 [avatar contradiction clause 335]
337. $false [avatar sat refutation 155,156,259,303,336]
% SZS output end Proof for 688204979602808246484203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious then alice is curious and vice versa.
Everyone who is either not old or not strong is old or quiet and vice versa.
If alice is both not generous and brave then mary is both creative and not calm and vice versa.
Everyone who is not tall is either not brave or not strong and vice versa.
If someone is wise or generous then someone is either creative or not funny and vice versa.
Everyone who is both tall and kind is either not old or old and vice versa.
Everyone who is funny is either not strong or kind.
If someone is calm or curious then someone is both not brave and not happy and vice versa.
Everyone who is both humble and tall is not curious.
Everyone who is rich or not strong is not wise and vice versa.
Everyone who is patient is funny or not rich.
If susan is both generous and not quiet then someone is kind.
Everyone who is rich or not curious is happy or not funny and vice versa.
Everyone who is both not humble and quiet is not brave and vice versa.
If paul is either strong or not funny then someone is not patient.
If someone is both tall and not kind then susan is not generous and vice versa.
Mary is kind or not calm.
Someone is not creative or brave.
Someone is either not old or happy.
Someone is generous.
Fred is rich.
Someone is not creative or not strong.
Paul is not curious or creative. | Paul is not brave. | neutral | ((?[X]:((curious(X)<~>~curious(X))))<=>(curious(alice)))&
(![X]:((~old(X)<~>~strong(X))<=>(old(X)|quiet(X))))&
(((~generous(alice)&brave(alice)))<=>((creative(mary)&~calm(mary))))&
(![X]:(~tall(X)<=>(~brave(X)<~>~strong(X))))&
((?[X]:((wise(X)|generous(X))))<=>(?[X]:((creative(X)<~>~funny(X)))))&
(![X]:((tall(X)&kind(X))<=>(~old(X)<~>old(X))))&
(![X]:(funny(X)=>(~strong(X)<~>kind(X))))&
((?[X]:((calm(X)|curious(X))))<=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((humble(X)&tall(X))=>~curious(X)))&
(![X]:((rich(X)|~strong(X))<=>~wise(X)))&
(![X]:(patient(X)=>(funny(X)|~rich(X))))&
(((generous(susan)&~quiet(susan)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)|~curious(X))<=>(happy(X)|~funny(X))))&
(![X]:((~humble(X)&quiet(X))<=>~brave(X)))&
(((strong(paul)<~>~funny(paul)))=>(?[X]:(~patient(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(~generous(susan)))&
((kind(mary)|~calm(mary)))&
(?[X]:((~creative(X)|brave(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:(generous(X)))&
(rich(fred))&
(?[X]:((~creative(X)|~strong(X))))&
((~curious(paul)|creative(paul))) | ~brave(paul) | [] | null | 0 |
If someone is not rich then someone is either not humble or wise. Everyone who is not generous or not brave is not strong. Everyone who is brave is creative or not tall and vice versa. If someone is happy then susan is both calm and rich and vice versa. If someone is both not happy and generous then someone is either kind or not curious and vice versa. Everyone who is happy or generous is not strong or kind. Everyone who is either creative or not rich is either not humble or not wise. If lucy is both not wise and curious then someone is both not calm and kind. If someone is either not calm or rich then alice is wise or not generous and vice versa. If someone is not rich or curious then alice is either brave or funny and vice versa. Everyone who is not humble is both humble and not patient and vice versa. If lucy is either not rich or not generous then fred is either not kind or patient. If lucy is either not rich or generous then lucy is not generous or brave. Everyone who is not curious is either old or not tall. If someone is not humble then susan is creative. Everyone who is either generous or humble is creative or not patient. Alice is not old. Someone is not patient or not quiet. Someone is creative or tall. John is quiet. Fred is both quiet and not creative. Someone is both tall and happy. Someone is not wise or kind. | Susan is not calm. | contradiction | ((?[X]:(~rich(X)))=>(?[X]:((~humble(X)<~>wise(X)))))&
(![X]:((~generous(X)|~brave(X))=>~strong(X)))&
(![X]:(brave(X)<=>(creative(X)|~tall(X))))&
((?[X]:(happy(X)))<=>((calm(susan)&rich(susan))))&
((?[X]:((~happy(X)&generous(X))))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((happy(X)|generous(X))=>(~strong(X)|kind(X))))&
(![X]:((creative(X)<~>~rich(X))=>(~humble(X)<~>~wise(X))))&
(((~wise(lucy)&curious(lucy)))=>(?[X]:((~calm(X)&kind(X)))))&
((?[X]:((~calm(X)<~>rich(X))))<=>((wise(alice)|~generous(alice))))&
((?[X]:((~rich(X)|curious(X))))<=>((brave(alice)<~>funny(alice))))&
(![X]:(~humble(X)<=>(humble(X)&~patient(X))))&
(((~rich(lucy)<~>~generous(lucy)))=>((~kind(fred)<~>patient(fred))))&
(((~rich(lucy)<~>generous(lucy)))=>((~generous(lucy)|brave(lucy))))&
(![X]:(~curious(X)=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))=>(creative(susan)))&
(![X]:((generous(X)<~>humble(X))=>(creative(X)|~patient(X))))&
(~old(alice))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((creative(X)|tall(X))))&
(quiet(john))&
((quiet(fred)&~creative(fred)))&
(?[X]:((tall(X)&happy(X))))&
(?[X]:((~wise(X)|kind(X)))) | ~calm(susan) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8862581761191990965610019
% SZS output start Proof for 8862581761191990965610019
4. ? [X0] : happy(X0) <=> (rich(susan) & calm(susan)) [input p3]
22. ? [X0] : (happy(X0) & tall(X0)) [input p21]
24. ~calm(susan) [input hypothesis]
46. (? [X0] : happy(X0) | (~rich(susan) | ~calm(susan))) & ((rich(susan) & calm(susan)) | ! [X0] : ~happy(X0)) [nnf transformation 4]
47. (? [X0] : happy(X0) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X0] : ~happy(X0)) [flattening 46]
48. (? [X0] : happy(X0) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X1] : ~happy(X1)) [rectify 47]
49. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
50. (happy(sK1) | ~rich(susan) | ~calm(susan)) & ((rich(susan) & calm(susan)) | ! [X1] : ~happy(X1)) [skolemisation 48,49]
78. ? [X0] : (happy(X0) & tall(X0)) => (happy(sK9) & tall(sK9)) [choice axiom]
79. happy(sK9) & tall(sK9) [skolemisation 22,78]
87. calm(susan) | ~happy(X1) [cnf transformation 50]
135. happy(sK9) [cnf transformation 79]
137. ~calm(susan) [cnf transformation 24]
155. 4 <=> calm(susan) [avatar definition]
168. 7 <=> ! [X1] : ~happy(X1) [avatar definition]
169. ~happy(X1) <- (7) [avatar component clause 168]
171. 7 | 4 [avatar split clause 87,155,168]
327. ~4 [avatar split clause 137,155]
330. $false <- (7) [resolution 169,135]
331. ~7 [avatar contradiction clause 330]
332. $false [avatar sat refutation 171,327,331]
% SZS output end Proof for 8862581761191990965610019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or creative is both not funny and not creative and vice versa. If susan is brave then lucy is calm or not rich and vice versa. Everyone who is funny is both not curious and curious and vice versa. If someone is not strong then someone is humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. Everyone who is creative is calm or not funny. Everyone who is wise is not strong or not rich and vice versa. If someone is patient or not funny then fred is both not generous and patient. Everyone who is both not patient and not tall is calm and vice versa. If someone is both not patient and rich then someone is not curious. If someone is old or generous then someone is not rich or not quiet and vice versa. If mary is not kind then alice is happy or calm. Everyone who is not kind is not happy. Someone is not tall or old. Someone is either not strong or not generous. Someone is both brave and not wise. John is creative. Alice is brave or not strong. | Paul is tall. | contradiction | (![X]:((~wise(X)<~>creative(X))<=>(~funny(X)&~creative(X))))&
((brave(susan))<=>((calm(lucy)|~rich(lucy))))&
(![X]:(funny(X)<=>(~curious(X)&curious(X))))&
((?[X]:(~strong(X)))=>(?[X]:(humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
(![X]:((~patient(X)&~tall(X))<=>calm(X)))&
((?[X]:((~patient(X)&rich(X))))=>(?[X]:(~curious(X))))&
((?[X]:((old(X)|generous(X))))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((~kind(mary))=>((happy(alice)|calm(alice))))&
(![X]:(~kind(X)=>~happy(X)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((~strong(X)<~>~generous(X))))&
(?[X]:((brave(X)&~wise(X))))&
(creative(john))&
((brave(alice)|~strong(alice))) | tall(paul) | [
"p0",
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 822915928516402296858861
% SZS output start Proof for 822915928516402296858861
1. ! [X0] : ((~wise(X0) <~> creative(X0)) <=> (~creative(X0) & ~funny(X0))) [input p0]
3. ! [X0] : (funny(X0) <=> (curious(X0) & ~curious(X0))) [input p2]
8. ! [X0] : ((~kind(X0) | tall(X0)) => (wise(X0) & happy(X0))) [input p7]
22. tall(paul) [input hypothesis]
26. ! [X0] : (tall(X0) => (wise(X0) & happy(X0))) [pure predicate removal 8]
31. ! [X0] : ((wise(X0) & happy(X0)) | ~tall(X0)) [ennf transformation 26]
36. ! [X0] : ((((~creative(X0) | wise(X0)) & (creative(X0) | ~wise(X0))) | (creative(X0) | funny(X0))) & ((~creative(X0) & ~funny(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~creative(X0) | wise(X0)) & (creative(X0) | ~wise(X0))) | creative(X0) | funny(X0)) & ((~creative(X0) & ~funny(X0)) | ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))))) [flattening 36]
40. ! [X0] : ((funny(X0) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | ~funny(X0))) [nnf transformation 3]
41. ! [X0] : ((funny(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | ~funny(X0))) [flattening 40]
71. ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 37]
72. creative(X0) | ~wise(X0) | creative(X0) | funny(X0) [cnf transformation 37]
77. ~curious(X0) | ~funny(X0) [cnf transformation 41]
78. ~funny(X0) | curious(X0) [cnf transformation 41]
94. ~tall(X0) | wise(X0) [cnf transformation 31]
118. tall(paul) [cnf transformation 22]
120. ~creative(X0) | ~wise(X0) [duplicate literal removal 71]
121. ~wise(X0) | creative(X0) | funny(X0) [duplicate literal removal 72]
137. ~funny(X0) [subsumption resolution 77,78]
261. wise(paul) [resolution 94,118]
280. creative(paul) | funny(paul) [resolution 121,261]
283. creative(paul) [subsumption resolution 280,137]
286. ~wise(paul) [resolution 283,120]
287. $false [subsumption resolution 286,261]
% SZS output end Proof for 822915928516402296858861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not patient or wise then someone is either curious or not kind. If someone is both creative and not funny then mary is not old and vice versa. Everyone who is not old is kind. Everyone who is not quiet is both wise and not happy and vice versa. Everyone who is not calm or not old is both quiet and not curious and vice versa. If someone is both humble and calm then mary is kind or not patient and vice versa. Everyone who is wise or strong is both not strong and humble. Everyone who is both not humble and not calm is patient or rich and vice versa. Everyone who is both not humble and generous is not patient and vice versa. If someone is not creative then susan is both not brave and happy and vice versa. Everyone who is both creative and not quiet is either not old or not tall and vice versa. Everyone who is either not creative or not wise is either patient or tall and vice versa. If alice is both funny and not kind then alice is not quiet or not strong and vice versa. If someone is both not tall and tall then someone is calm. Everyone who is not brave is both creative and not tall and vice versa. John is not humble. John is not kind or not tall. Someone is either funny or not patient. Someone is strong or not rich. Someone is curious or not funny. Someone is not creative or not humble. Mary is either not wise or not funny. | Mary is humble. | contradiction | (((~patient(john)<~>wise(john)))=>(?[X]:((curious(X)<~>~kind(X)))))&
((?[X]:((creative(X)&~funny(X))))<=>(~old(mary)))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~quiet(X)<=>(wise(X)&~happy(X))))&
(![X]:((~calm(X)|~old(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((humble(X)&calm(X))))<=>((kind(mary)|~patient(mary))))&
(![X]:((wise(X)|strong(X))=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)|rich(X))))&
(![X]:((~humble(X)&generous(X))<=>~patient(X)))&
((?[X]:(~creative(X)))<=>((~brave(susan)&happy(susan))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(((funny(alice)&~kind(alice)))<=>((~quiet(alice)|~strong(alice))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:(~brave(X)<=>(creative(X)&~tall(X))))&
(~humble(john))&
((~kind(john)|~tall(john)))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~creative(X)|~humble(X))))&
((~wise(mary)<~>~funny(mary))) | humble(mary) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8890505069660570465880656
% SZS output start Proof for 8890505069660570465880656
8. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> (rich(X0) | patient(X0))) [input p7]
9. ! [X0] : ((generous(X0) & ~humble(X0)) <=> ~patient(X0)) [input p8]
23. humble(mary) [input hypothesis]
45. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (calm(X0) | humble(X0)))) [nnf transformation 8]
46. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | calm(X0) | humble(X0))) [flattening 45]
47. ! [X0] : (((generous(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | (~generous(X0) | humble(X0)))) [nnf transformation 9]
48. ! [X0] : (((generous(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | ~generous(X0) | humble(X0))) [flattening 47]
100. ~humble(X0) | ~patient(X0) [cnf transformation 46]
105. ~humble(X0) | patient(X0) [cnf transformation 48]
142. humble(mary) [cnf transformation 23]
206. ~humble(X0) [subsumption resolution 105,100]
269. $false [subsumption resolution 142,206]
% SZS output end Proof for 8890505069660570465880656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not rich is both not brave and not generous and vice versa. Everyone who is both wise and patient is strong. If alice is curious or humble then john is tall and vice versa. If someone is either patient or rich then john is calm and vice versa. Everyone who is either not wise or not rich is not creative and vice versa. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. If someone is not creative or quiet then someone is both wise and not wise. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Mary is humble. | contradiction | (![X]:((humble(X)|~rich(X))<=>(~brave(X)&~generous(X))))&
(![X]:((wise(X)&patient(X))=>strong(X)))&
(((curious(alice)|humble(alice)))<=>(tall(john)))&
((?[X]:((patient(X)<~>rich(X))))<=>(calm(john)))&
(![X]:((~wise(X)<~>~rich(X))<=>~creative(X)))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | humble(mary) | [
"p0",
"p5",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3992885098738200455138597
% SZS output start Proof for 3992885098738200455138597
1. ! [X0] : ((~rich(X0) | humble(X0)) <=> (~generous(X0) & ~brave(X0))) [input p0]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
7. ! [X0] : (~kind(X0) <=> wise(X0)) [input p6]
11. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p10]
15. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p14]
23. humble(mary) [input hypothesis]
24. ? [X0] : (~brave(X0) & ~quiet(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 11]
25. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 15]
28. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
35. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 25]
36. ! [X0] : (((~rich(X0) | humble(X0)) | (generous(X0) | brave(X0))) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((~rich(X0) | humble(X0) | generous(X0) | brave(X0)) & ((~generous(X0) & ~brave(X0)) | (rich(X0) & ~humble(X0)))) [flattening 36]
45. ! [X0] : ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))) [nnf transformation 7]
50. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (brave(X0) | quiet(X0))) [nnf transformation 24]
51. (? [X0] : (~brave(X0) & ~quiet(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (brave(X3) | quiet(X3))) [rectify 50]
52. ? [X0] : (~brave(X0) & ~quiet(X0)) => (~brave(sK1) & ~quiet(sK1)) [choice axiom]
53. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK2) & ~wise(sK2)) [choice axiom]
54. ((~brave(sK1) & ~quiet(sK1)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK2) & ~wise(sK2)) | ! [X3] : (brave(X3) | quiet(X3))) [skolemisation 51,53,52]
59. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 35]
60. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK4) & wise(sK4)) [choice axiom]
61. (~wise(sK4) & wise(sK4)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 59,60]
70. ~brave(X0) | ~humble(X0) [cnf transformation 37]
90. ~kind(X0) | ~creative(X0) [cnf transformation 28]
91. kind(X0) | wise(X0) [cnf transformation 45]
103. ~wise(sK2) | brave(X3) | quiet(X3) [cnf transformation 54]
115. wise(sK4) | creative(X1) [cnf transformation 61]
116. wise(sK4) | ~quiet(X1) [cnf transformation 61]
117. ~wise(sK4) | creative(X1) [cnf transformation 61]
118. ~wise(sK4) | ~quiet(X1) [cnf transformation 61]
129. humble(mary) [cnf transformation 23]
197. 15 <=> ! [X3] : (brave(X3) | quiet(X3)) [avatar definition]
198. brave(X3) | quiet(X3) <- (15) [avatar component clause 197]
205. 17 <=> wise(sK2) [avatar definition]
207. ~wise(sK2) <- (~17) [avatar component clause 205]
208. 15 | ~17 [avatar split clause 103,205,197]
232. 23 <=> ! [X1] : ~quiet(X1) [avatar definition]
233. ~quiet(X1) <- (23) [avatar component clause 232]
235. 24 <=> wise(sK4) [avatar definition]
238. 23 | ~24 [avatar split clause 118,235,232]
240. 25 <=> ! [X1] : creative(X1) [avatar definition]
241. creative(X1) <- (25) [avatar component clause 240]
242. 25 | ~24 [avatar split clause 117,235,240]
243. 23 | 24 [avatar split clause 116,235,232]
244. 25 | 24 [avatar split clause 115,235,240]
292. wise(X0) | ~creative(X0) [resolution 91,90]
295. wise(X0) <- (25) [subsumption resolution 292,241]
297. $false <- (~17, 25) [resolution 295,207]
298. 17 | ~25 [avatar contradiction clause 297]
299. brave(X3) <- (15, 23) [subsumption resolution 198,233]
302. ~humble(X1) <- (15, 23) [resolution 299,70]
308. $false <- (15, 23) [resolution 302,129]
309. ~15 | ~23 [avatar contradiction clause 308]
310. $false [avatar sat refutation 208,238,242,243,244,298,309]
% SZS output end Proof for 3992885098738200455138597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is old then someone is either not happy or not rich and vice versa. Everyone who is either quiet or wise is tall. Everyone who is not brave or happy is both wise and not rich and vice versa. Everyone who is either strong or not curious is both not quiet and not tall. Everyone who is either not kind or strong is either humble or not generous. Everyone who is not funny is either not quiet or funny and vice versa. If mary is either strong or generous then susan is brave or not curious. If someone is not funny then someone is either not brave or brave. Everyone who is both not generous and not quiet is wise or generous and vice versa. If alice is humble or tall then john is either not rich or rich. Everyone who is either not kind or not wise is both not kind and kind and vice versa. Everyone who is both not wise and calm is either not curious or not strong. Everyone who is both wise and not curious is both not curious and tall. Everyone who is both kind and not wise is either patient or creative. If someone is not creative then someone is creative or wise and vice versa. Everyone who is either not happy or not wise is both humble and rich. Paul is brave. Someone is funny or not quiet. Someone is not wise or not rich. Mary is not rich or not kind. Someone is old or creative. | Mary is not old. | contradiction | ((old(mary))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((quiet(X)<~>wise(X))=>tall(X)))&
(![X]:((~brave(X)|happy(X))<=>(wise(X)&~rich(X))))&
(![X]:((strong(X)<~>~curious(X))=>(~quiet(X)&~tall(X))))&
(![X]:((~kind(X)<~>strong(X))=>(humble(X)<~>~generous(X))))&
(![X]:(~funny(X)<=>(~quiet(X)<~>funny(X))))&
(((strong(mary)<~>generous(mary)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:((~generous(X)&~quiet(X))<=>(wise(X)|generous(X))))&
(((humble(alice)|tall(alice)))=>((~rich(john)<~>rich(john))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~kind(X)&kind(X))))&
(![X]:((~wise(X)&calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((wise(X)&~curious(X))=>(~curious(X)&tall(X))))&
(![X]:((kind(X)&~wise(X))=>(patient(X)<~>creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((creative(X)|wise(X)))))&
(![X]:((~happy(X)<~>~wise(X))=>(humble(X)&rich(X))))&
(brave(paul))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~wise(X)|~rich(X))))&
((~rich(mary)|~kind(mary)))&
(?[X]:((old(X)|creative(X)))) | ~old(mary) | [
"p0",
"p2",
"p5",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4638386490040903498839871
% SZS output start Proof for 4638386490040903498839871
1. old(mary) <=> ? [X0] : (~happy(X0) <~> ~rich(X0)) [input p0]
3. ! [X0] : ((happy(X0) | ~brave(X0)) <=> (~rich(X0) & wise(X0))) [input p2]
6. ! [X0] : (~funny(X0) <=> (~quiet(X0) <~> funny(X0))) [input p5]
9. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (generous(X0) | wise(X0))) [input p8]
16. ! [X0] : ((~happy(X0) <~> ~wise(X0)) => (rich(X0) & humble(X0))) [input p15]
22. ~old(mary) [input hypothesis]
37. ! [X0] : ((rich(X0) & humble(X0)) | (~happy(X0) <=> ~wise(X0))) [ennf transformation 16]
38. (old(mary) | ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (? [X0] : ((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ~old(mary)) [nnf transformation 1]
39. (old(mary) | ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (? [X1] : ((rich(X1) | happy(X1)) & (~rich(X1) | ~happy(X1))) | ~old(mary)) [rectify 38]
40. ? [X1] : ((rich(X1) | happy(X1)) & (~rich(X1) | ~happy(X1))) => ((rich(sK0) | happy(sK0)) & (~rich(sK0) | ~happy(sK0))) [choice axiom]
41. (old(mary) | ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(sK0) | happy(sK0)) & (~rich(sK0) | ~happy(sK0))) | ~old(mary)) [skolemisation 39,40]
43. ! [X0] : (((happy(X0) | ~brave(X0)) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | (~happy(X0) & brave(X0)))) [nnf transformation 3]
44. ! [X0] : ((happy(X0) | ~brave(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | (~happy(X0) & brave(X0)))) [flattening 43]
47. ! [X0] : ((~funny(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | funny(X0))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~generous(X0) & ~wise(X0))) & ((generous(X0) | wise(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 9]
54. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~generous(X0) & ~wise(X0))) & (generous(X0) | wise(X0) | quiet(X0) | generous(X0))) [flattening 53]
64. ! [X0] : ((rich(X0) & humble(X0)) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) [nnf transformation 37]
73. old(mary) | ~rich(X0) | happy(X0) [cnf transformation 41]
74. old(mary) | ~happy(X0) | rich(X0) [cnf transformation 41]
80. ~rich(X0) | ~happy(X0) [cnf transformation 44]
90. funny(X0) | ~quiet(X0) | funny(X0) [cnf transformation 47]
93. ~funny(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 47]
98. generous(X0) | wise(X0) | quiet(X0) | generous(X0) [cnf transformation 54]
100. ~generous(X0) | ~generous(X0) [cnf transformation 54]
122. rich(X0) | ~wise(X0) | happy(X0) [cnf transformation 64]
129. ~old(mary) [cnf transformation 22]
134. generous(X0) | wise(X0) | quiet(X0) [duplicate literal removal 98]
135. ~generous(X0) [duplicate literal removal 100]
136. funny(X0) | ~quiet(X0) [duplicate literal removal 90]
137. ~funny(X0) | ~quiet(X0) [duplicate literal removal 93]
139. 1 <=> ! [X0] : (~happy(X0) | rich(X0)) [avatar definition]
140. ~happy(X0) | rich(X0) <- (1) [avatar component clause 139]
142. 2 <=> old(mary) [avatar definition]
145. 1 | 2 [avatar split clause 74,142,139]
147. 3 <=> ! [X0] : (~rich(X0) | happy(X0)) [avatar definition]
148. ~rich(X0) | happy(X0) <- (3) [avatar component clause 147]
149. 3 | 2 [avatar split clause 73,142,147]
160. ~quiet(X0) [subsumption resolution 136,137]
179. wise(X0) | quiet(X0) [subsumption resolution 134,135]
180. wise(X0) [subsumption resolution 179,160]
184. rich(X0) | happy(X0) [subsumption resolution 122,180]
197. ~2 [avatar split clause 129,142]
198. ~rich(X0) <- (3) [subsumption resolution 148,80]
199. ~happy(X0) <- (1, 3) [subsumption resolution 140,198]
205. happy(X2) <- (3) [resolution 184,198]
211. $false <- (1, 3) [subsumption resolution 205,199]
212. ~1 | ~3 [avatar contradiction clause 211]
213. $false [avatar sat refutation 145,149,197,212]
% SZS output end Proof for 4638386490040903498839871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either humble or not quiet. If fred is both generous and not wise then fred is wise or not old and vice versa. Everyone who is both not kind and quiet is not creative. If someone is not tall or calm then someone is not quiet and vice versa. Everyone who is both not happy and calm is either patient or generous and vice versa. Everyone who is curious or not creative is not kind or kind and vice versa. Everyone who is either not funny or not wise is either funny or not wise. If alice is not happy or kind then someone is both quiet and not funny. If fred is either not tall or not funny then someone is calm and vice versa. Everyone who is not patient is brave. Everyone who is wise or quiet is not rich or strong. If paul is brave then someone is happy and vice versa. Everyone who is calm is both kind and patient. Everyone who is old or kind is either wise or funny and vice versa. If john is either rich or not generous then someone is funny and vice versa. If fred is either brave or not old then someone is either curious or creative and vice versa. Someone is both quiet and not happy. Susan is not humble. Someone is not humble. Susan is either quiet or curious. Paul is not calm or not quiet. Lucy is strong or generous. Someone is patient. | Fred is not funny. | entailment | (![X]:(~patient(X)=>(humble(X)<~>~quiet(X))))&
(((generous(fred)&~wise(fred)))<=>((wise(fred)|~old(fred))))&
(![X]:((~kind(X)&quiet(X))=>~creative(X)))&
((?[X]:((~tall(X)|calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&calm(X))<=>(patient(X)<~>generous(X))))&
(![X]:((curious(X)|~creative(X))<=>(~kind(X)|kind(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(funny(X)<~>~wise(X))))&
(((~happy(alice)|kind(alice)))=>(?[X]:((quiet(X)&~funny(X)))))&
(((~tall(fred)<~>~funny(fred)))<=>(?[X]:(calm(X))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|kind(X))<=>(wise(X)<~>funny(X))))&
(((rich(john)<~>~generous(john)))<=>(?[X]:(funny(X))))&
(((brave(fred)<~>~old(fred)))<=>(?[X]:((curious(X)<~>creative(X)))))&
(?[X]:((quiet(X)&~happy(X))))&
(~humble(susan))&
(?[X]:(~humble(X)))&
((quiet(susan)<~>curious(susan)))&
((~calm(paul)|~quiet(paul)))&
((strong(lucy)|generous(lucy)))&
(?[X]:(patient(X))) | ~funny(fred) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 303785101363472963209868
% SZS output start Proof for 303785101363472963209868
2. (~wise(fred) & generous(fred)) <=> (~old(fred) | wise(fred)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~wise(X0)) => (funny(X0) <~> ~wise(X0))) [input p6]
24. funny(fred) [input hypothesis]
31. ! [X0] : ((funny(X0) <~> ~wise(X0)) | (~funny(X0) <=> ~wise(X0))) [ennf transformation 7]
36. ((~wise(fred) & generous(fred)) | (old(fred) & ~wise(fred))) & ((~old(fred) | wise(fred)) | (wise(fred) | ~generous(fred))) [nnf transformation 2]
37. ((~wise(fred) & generous(fred)) | (old(fred) & ~wise(fred))) & (~old(fred) | wise(fred) | wise(fred) | ~generous(fred)) [flattening 36]
47. ! [X0] : (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) [nnf transformation 31]
80. ~wise(fred) | ~wise(fred) [cnf transformation 37]
99. wise(X0) | ~funny(X0) | ~funny(X0) | wise(X0) [cnf transformation 47]
139. funny(fred) [cnf transformation 24]
141. ~funny(X0) | wise(X0) [duplicate literal removal 99]
143. ~wise(fred) [duplicate literal removal 80]
149. 2 <=> wise(fred) [avatar definition]
151. ~wise(fred) <- (~2) [avatar component clause 149]
153. ~2 [avatar split clause 143,149]
211. 15 <=> funny(fred) [avatar definition]
213. funny(fred) <- (15) [avatar component clause 211]
303. 15 [avatar split clause 139,211]
308. wise(fred) <- (15) [resolution 141,213]
310. $false <- (~2, 15) [subsumption resolution 308,151]
311. 2 | ~15 [avatar contradiction clause 310]
312. $false [avatar sat refutation 153,303,311]
% SZS output end Proof for 303785101363472963209868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or creative then paul is not patient or curious. If someone is either not brave or tall then alice is happy. Everyone who is not wise is both patient and not tall. If paul is funny or creative then someone is patient and vice versa. Everyone who is either not tall or brave is happy and vice versa. Everyone who is not wise is either funny or not rich and vice versa. If someone is either not wise or not humble then alice is either strong or not old and vice versa. Everyone who is not brave is either not patient or not tall and vice versa. If someone is not kind then lucy is either quiet or rich. If john is both curious and not wise then paul is either creative or not tall and vice versa. Everyone who is not rich or not generous is both brave and quiet. Everyone who is not quiet is curious or not kind. Everyone who is quiet or humble is patient or generous and vice versa. Everyone who is either wise or not quiet is not wise or not old and vice versa. If someone is calm or not old then alice is strong or curious and vice versa. Everyone who is both wise and not happy is not happy and vice versa. Someone is not tall or not calm. Someone is not generous or not funny. Lucy is either not calm or generous. Lucy is not kind. Mary is not funny or funny. Someone is patient. Someone is either not quiet or happy. Lucy is both not calm and brave. | Lucy is kind. | contradiction | (((~happy(fred)|creative(fred)))=>((~patient(paul)|curious(paul))))&
((?[X]:((~brave(X)<~>tall(X))))=>(happy(alice)))&
(![X]:(~wise(X)=>(patient(X)&~tall(X))))&
(((funny(paul)|creative(paul)))<=>(?[X]:(patient(X))))&
(![X]:((~tall(X)<~>brave(X))<=>happy(X)))&
(![X]:(~wise(X)<=>(funny(X)<~>~rich(X))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>((strong(alice)<~>~old(alice))))&
(![X]:(~brave(X)<=>(~patient(X)<~>~tall(X))))&
((?[X]:(~kind(X)))=>((quiet(lucy)<~>rich(lucy))))&
(((curious(john)&~wise(john)))<=>((creative(paul)<~>~tall(paul))))&
(![X]:((~rich(X)|~generous(X))=>(brave(X)&quiet(X))))&
(![X]:(~quiet(X)=>(curious(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))<=>(patient(X)|generous(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~wise(X)|~old(X))))&
((?[X]:((calm(X)|~old(X))))<=>((strong(alice)|curious(alice))))&
(![X]:((wise(X)&~happy(X))<=>~happy(X)))&
(?[X]:((~tall(X)|~calm(X))))&
(?[X]:((~generous(X)|~funny(X))))&
((~calm(lucy)<~>generous(lucy)))&
(~kind(lucy))&
((~funny(mary)|funny(mary)))&
(?[X]:(patient(X)))&
(?[X]:((~quiet(X)<~>happy(X))))&
((~calm(lucy)&brave(lucy))) | kind(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7394611974810831307419618
% SZS output start Proof for 7394611974810831307419618
20. ~kind(lucy) [input p19]
25. kind(lucy) [input hypothesis]
134. ~kind(lucy) [cnf transformation 20]
141. kind(lucy) [cnf transformation 25]
317. $false [subsumption resolution 141,134]
% SZS output end Proof for 7394611974810831307419618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or quiet is not curious. Everyone who is both old and not rich is creative and vice versa. Everyone who is not rich is not patient and vice versa. Everyone who is not creative is both quiet and generous and vice versa. If someone is not brave or not generous then someone is either rich or not rich. If john is either not happy or tall then mary is both funny and tall. Everyone who is either patient or not creative is happy or not strong. Everyone who is generous is both kind and curious and vice versa. Everyone who is either strong or generous is not funny or rich and vice versa. Everyone who is not creative is both not brave and strong. If someone is funny then someone is not curious or not brave. Everyone who is not patient or not old is not strong or not curious and vice versa. If someone is happy or rich then john is either not rich or not humble. Everyone who is both calm and not tall is humble or tall. Everyone who is either not old or curious is not rich or humble and vice versa. If someone is not brave or generous then mary is both not kind and happy. Fred is humble or not curious. Alice is not generous. Someone is quiet or tall. Mary is not strong. Paul is both not rich and humble. Someone is happy or funny. Fred is either not calm or calm. | Fred is not rich. | entailment | (![X]:((~funny(X)<~>quiet(X))=>~curious(X)))&
(![X]:((old(X)&~rich(X))<=>creative(X)))&
(![X]:(~rich(X)<=>~patient(X)))&
(![X]:(~creative(X)<=>(quiet(X)&generous(X))))&
((?[X]:((~brave(X)|~generous(X))))=>(?[X]:((rich(X)<~>~rich(X)))))&
(((~happy(john)<~>tall(john)))=>((funny(mary)&tall(mary))))&
(![X]:((patient(X)<~>~creative(X))=>(happy(X)|~strong(X))))&
(![X]:(generous(X)<=>(kind(X)&curious(X))))&
(![X]:((strong(X)<~>generous(X))<=>(~funny(X)|rich(X))))&
(![X]:(~creative(X)=>(~brave(X)&strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~curious(X)|~brave(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~strong(X)|~curious(X))))&
((?[X]:((happy(X)|rich(X))))=>((~rich(john)<~>~humble(john))))&
(![X]:((calm(X)&~tall(X))=>(humble(X)|tall(X))))&
(![X]:((~old(X)<~>curious(X))<=>(~rich(X)|humble(X))))&
((?[X]:((~brave(X)|generous(X))))=>((~kind(mary)&happy(mary))))&
((humble(fred)|~curious(fred)))&
(~generous(alice))&
(?[X]:((quiet(X)|tall(X))))&
(~strong(mary))&
((~rich(paul)&humble(paul)))&
(?[X]:((happy(X)|funny(X))))&
((~calm(fred)<~>calm(fred))) | ~rich(fred) | [
"p1",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1261819635843099545159087
% SZS output start Proof for 1261819635843099545159087
2. ! [X0] : ((~rich(X0) & old(X0)) <=> creative(X0)) [input p1]
4. ! [X0] : (~creative(X0) <=> (generous(X0) & quiet(X0))) [input p3]
9. ! [X0] : ((strong(X0) <~> generous(X0)) <=> (rich(X0) | ~funny(X0))) [input p8]
10. ! [X0] : (~creative(X0) => (strong(X0) & ~brave(X0))) [input p9]
24. rich(fred) [input hypothesis]
32. ! [X0] : ((strong(X0) & ~brave(X0)) | creative(X0)) [ennf transformation 10]
39. ! [X0] : (((~rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) | ~old(X0)))) [nnf transformation 2]
40. ! [X0] : (((~rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | rich(X0) | ~old(X0))) [flattening 39]
42. ! [X0] : ((~creative(X0) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | creative(X0))) [nnf transformation 4]
43. ! [X0] : ((~creative(X0) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | creative(X0))) [flattening 42]
52. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [flattening 52]
71. ~creative(X0) | ~rich(X0) [cnf transformation 40]
75. generous(X0) | creative(X0) [cnf transformation 43]
95. ~strong(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 53]
97. strong(X0) | creative(X0) [cnf transformation 32]
127. rich(fred) [cnf transformation 24]
162. 8 <=> ! [X0] : ~rich(X0) [avatar definition]
163. ~rich(X0) <- (8) [avatar component clause 162]
284. ~generous(X1) | ~rich(X1) | creative(X1) [resolution 95,97]
285. ~rich(X1) | creative(X1) [subsumption resolution 284,75]
286. ~rich(X1) [subsumption resolution 285,71]
287. 8 [avatar split clause 286,162]
288. $false <- (8) [resolution 163,127]
289. ~8 [avatar contradiction clause 288]
290. $false [avatar sat refutation 287,289]
% SZS output end Proof for 1261819635843099545159087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not rich is not curious or not rich and vice versa. If alice is humble then john is both rich and not creative. If someone is quiet then john is either creative or kind. If someone is curious then someone is humble or funny. Everyone who is creative or curious is rich or not calm and vice versa. If alice is not generous then someone is both not tall and humble. Everyone who is either not happy or kind is happy or wise. Everyone who is creative is both not kind and kind. If john is brave or funny then susan is strong or not strong and vice versa. If alice is either old or patient then someone is strong. Everyone who is either not quiet or calm is both not quiet and not funny. Everyone who is either not wise or humble is funny and vice versa. Everyone who is either not curious or not strong is either not wise or not brave and vice versa. Everyone who is tall is happy. Everyone who is both not kind and not quiet is either rich or tall. Everyone who is not wise is not generous. Someone is both not brave and not generous. Lucy is kind. Mary is tall. Susan is not curious. Fred is rich or creative. John is not patient or not funny. | Lucy is not tall. | neutral | (![X]:((~old(X)<~>~rich(X))<=>(~curious(X)|~rich(X))))&
((humble(alice))=>((rich(john)&~creative(john))))&
((?[X]:(quiet(X)))=>((creative(john)<~>kind(john))))&
((?[X]:(curious(X)))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((creative(X)|curious(X))<=>(rich(X)|~calm(X))))&
((~generous(alice))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:((~happy(X)<~>kind(X))=>(happy(X)|wise(X))))&
(![X]:(creative(X)=>(~kind(X)&kind(X))))&
(((brave(john)|funny(john)))<=>((strong(susan)|~strong(susan))))&
(((old(alice)<~>patient(alice)))=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~quiet(X)&~funny(X))))&
(![X]:((~wise(X)<~>humble(X))<=>funny(X)))&
(![X]:((~curious(X)<~>~strong(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(tall(X)=>happy(X)))&
(![X]:((~kind(X)&~quiet(X))=>(rich(X)<~>tall(X))))&
(![X]:(~wise(X)=>~generous(X)))&
(?[X]:((~brave(X)&~generous(X))))&
(kind(lucy))&
(tall(mary))&
(~curious(susan))&
((rich(fred)|creative(fred)))&
((~patient(john)|~funny(john))) | ~tall(lucy) | [] | null | 0 |
Everyone who is not rich is either calm or not generous.
Everyone who is either calm or quiet is creative and vice versa.
Everyone who is either rich or not happy is not creative.
If mary is both not happy and not old then someone is humble or tall and vice versa.
Everyone who is either not curious or old is not patient and vice versa.
If john is not brave or not wise then someone is generous and vice versa.
If someone is not wise then john is either not kind or calm.
If someone is strong or tall then someone is either not curious or not quiet and vice versa.
Everyone who is not humble or rich is both funny and not generous.
If someone is either wise or strong then john is funny or not rich.
Everyone who is both not funny and generous is either not quiet or happy and vice versa.
If susan is both creative and not tall then someone is not rich or not kind.
If fred is brave then someone is both not strong and strong.
Everyone who is curious is happy.
If alice is either not rich or creative then fred is brave and vice versa.
If susan is patient or not strong then john is either rich or not funny and vice versa.
Someone is both not strong and not calm.
Someone is either not tall or old.
John is not brave.
Alice is curious or creative.
Someone is kind.
Someone is not happy or strong. | John is happy. | neutral | (![X]:(~rich(X)=>(calm(X)<~>~generous(X))))&
(![X]:((calm(X)<~>quiet(X))<=>creative(X)))&
(![X]:((rich(X)<~>~happy(X))=>~creative(X)))&
(((~happy(mary)&~old(mary)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~curious(X)<~>old(X))<=>~patient(X)))&
(((~brave(john)|~wise(john)))<=>(?[X]:(generous(X))))&
((?[X]:(~wise(X)))=>((~kind(john)<~>calm(john))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((~humble(X)|rich(X))=>(funny(X)&~generous(X))))&
((?[X]:((wise(X)<~>strong(X))))=>((funny(john)|~rich(john))))&
(![X]:((~funny(X)&generous(X))<=>(~quiet(X)<~>happy(X))))&
(((creative(susan)&~tall(susan)))=>(?[X]:((~rich(X)|~kind(X)))))&
((brave(fred))=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:(curious(X)=>happy(X)))&
(((~rich(alice)<~>creative(alice)))<=>(brave(fred)))&
(((patient(susan)|~strong(susan)))<=>((rich(john)<~>~funny(john))))&
(?[X]:((~strong(X)&~calm(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~brave(john))&
((curious(alice)|creative(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|strong(X)))) | happy(john) | [] | null | 0 |
If paul is calm then someone is strong.
If someone is either tall or not brave then someone is both quiet and curious.
If someone is either strong or not calm then someone is not funny or not strong.
If paul is not funny then paul is either quiet or humble and vice versa.
Everyone who is curious is both patient and wise and vice versa.
Everyone who is both rich and curious is both not quiet and not happy and vice versa.
Everyone who is either patient or generous is not tall and vice versa.
If fred is both creative and patient then paul is not curious or not kind.
Everyone who is not happy is not creative or not patient.
Everyone who is funny or brave is both patient and not wise and vice versa.
Everyone who is not tall is either quiet or humble and vice versa.
Everyone who is happy or patient is not tall.
If someone is not old then john is either brave or not old.
If paul is either not creative or not funny then someone is both calm and not curious and vice versa.
Everyone who is not kind is either not patient or not humble.
Everyone who is either not wise or generous is funny or old.
Someone is not creative or calm.
Someone is both strong and generous.
Someone is either funny or creative.
Someone is not tall.
Lucy is both not happy and humble.
Susan is either not funny or wise.
Someone is not rich or strong.
Susan is both not happy and quiet. | Paul is not tall. | entailment | ((calm(paul))=>(?[X]:(strong(X))))&
((?[X]:((tall(X)<~>~brave(X))))=>(?[X]:((quiet(X)&curious(X)))))&
((?[X]:((strong(X)<~>~calm(X))))=>(?[X]:((~funny(X)|~strong(X)))))&
((~funny(paul))<=>((quiet(paul)<~>humble(paul))))&
(![X]:(curious(X)<=>(patient(X)&wise(X))))&
(![X]:((rich(X)&curious(X))<=>(~quiet(X)&~happy(X))))&
(![X]:((patient(X)<~>generous(X))<=>~tall(X)))&
(((creative(fred)&patient(fred)))=>((~curious(paul)|~kind(paul))))&
(![X]:(~happy(X)=>(~creative(X)|~patient(X))))&
(![X]:((funny(X)|brave(X))<=>(patient(X)&~wise(X))))&
(![X]:(~tall(X)<=>(quiet(X)<~>humble(X))))&
(![X]:((happy(X)|patient(X))=>~tall(X)))&
((?[X]:(~old(X)))=>((brave(john)<~>~old(john))))&
(((~creative(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>~humble(X))))&
(![X]:((~wise(X)<~>generous(X))=>(funny(X)|old(X))))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:((strong(X)&generous(X))))&
(?[X]:((funny(X)<~>creative(X))))&
(?[X]:(~tall(X)))&
((~happy(lucy)&humble(lucy)))&
((~funny(susan)<~>wise(susan)))&
(?[X]:((~rich(X)|strong(X))))&
((~happy(susan)&quiet(susan))) | ~tall(paul) | [
"p3",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5856328922449902085334370
% SZS output start Proof for 5856328922449902085334370
4. ~funny(paul) <=> (quiet(paul) <~> humble(paul)) [input p3]
10. ! [X0] : ((brave(X0) | funny(X0)) <=> (~wise(X0) & patient(X0))) [input p9]
11. ! [X0] : (~tall(X0) <=> (quiet(X0) <~> humble(X0))) [input p10]
12. ! [X0] : ((patient(X0) | happy(X0)) => ~tall(X0)) [input p11]
25. tall(paul) [input hypothesis]
35. ! [X0] : (~tall(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 12]
50. (~funny(paul) | ((quiet(paul) | ~humble(paul)) & (humble(paul) | ~quiet(paul)))) & (((~humble(paul) | ~quiet(paul)) & (humble(paul) | quiet(paul))) | funny(paul)) [nnf transformation 4]
56. ! [X0] : (((brave(X0) | funny(X0)) | (wise(X0) | ~patient(X0))) & ((~wise(X0) & patient(X0)) | (~brave(X0) & ~funny(X0)))) [nnf transformation 10]
57. ! [X0] : ((brave(X0) | funny(X0) | wise(X0) | ~patient(X0)) & ((~wise(X0) & patient(X0)) | (~brave(X0) & ~funny(X0)))) [flattening 56]
58. ! [X0] : ((~tall(X0) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | tall(X0))) [nnf transformation 11]
85. humble(paul) | quiet(paul) | funny(paul) [cnf transformation 50]
86. ~humble(paul) | ~quiet(paul) | funny(paul) [cnf transformation 50]
102. ~funny(X0) | patient(X0) [cnf transformation 57]
109. ~quiet(X0) | humble(X0) | ~tall(X0) [cnf transformation 58]
110. ~humble(X0) | quiet(X0) | ~tall(X0) [cnf transformation 58]
112. ~patient(X0) | ~tall(X0) [cnf transformation 35]
138. tall(paul) [cnf transformation 25]
183. 11 <=> humble(paul) [avatar definition]
184. humble(paul) <- (11) [avatar component clause 183]
185. ~humble(paul) <- (~11) [avatar component clause 183]
187. 12 <=> quiet(paul) [avatar definition]
188. ~quiet(paul) <- (~12) [avatar component clause 187]
189. quiet(paul) <- (12) [avatar component clause 187]
191. 13 <=> funny(paul) [avatar definition]
192. funny(paul) <- (13) [avatar component clause 191]
196. 13 | ~12 | ~11 [avatar split clause 86,183,187,191]
197. 13 | 12 | 11 [avatar split clause 85,183,187,191]
354. quiet(paul) | ~tall(paul) <- (11) [resolution 110,184]
357. ~tall(paul) <- (11, ~12) [subsumption resolution 354,188]
358. $false <- (11, ~12) [subsumption resolution 357,138]
359. ~11 | 12 [avatar contradiction clause 358]
361. humble(paul) | ~tall(paul) <- (12) [resolution 189,109]
362. ~tall(paul) <- (~11, 12) [subsumption resolution 361,185]
363. $false <- (~11, 12) [subsumption resolution 362,138]
364. 11 | ~12 [avatar contradiction clause 363]
365. patient(paul) <- (13) [resolution 192,102]
390. ~tall(paul) <- (13) [resolution 365,112]
392. $false <- (13) [subsumption resolution 390,138]
393. ~13 [avatar contradiction clause 392]
394. $false [avatar sat refutation 196,197,359,364,393]
% SZS output end Proof for 5856328922449902085334370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not creative is patient.
If susan is either patient or not tall then someone is curious and vice versa.
Everyone who is either tall or patient is either not brave or old and vice versa.
If someone is calm or patient then alice is both curious and rich.
If someone is both not calm and not generous then alice is both not happy and creative and vice versa.
If susan is either not tall or tall then lucy is not happy or kind and vice versa.
Everyone who is not happy is not calm and vice versa.
Everyone who is either not patient or brave is calm or happy.
Everyone who is both not strong and curious is not brave and vice versa.
Everyone who is quiet or old is rich or old and vice versa.
Everyone who is both not wise and not humble is either not tall or not calm.
If lucy is not brave or creative then someone is both rich and not calm.
Everyone who is not funny or brave is both funny and not quiet.
Everyone who is both happy and not happy is curious.
Everyone who is not funny or humble is either wise or not humble and vice versa.
If someone is brave then lucy is both curious and old.
Fred is quiet.
Alice is creative or patient.
Lucy is creative.
Someone is curious.
Someone is both rich and tall.
Someone is funny or happy.
Someone is not wise or old.
Lucy is both patient and strong. | Lucy is not kind. | contradiction | (![X]:((quiet(X)&~creative(X))=>patient(X)))&
(((patient(susan)<~>~tall(susan)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~brave(X)<~>old(X))))&
((?[X]:((calm(X)|patient(X))))=>((curious(alice)&rich(alice))))&
((?[X]:((~calm(X)&~generous(X))))<=>((~happy(alice)&creative(alice))))&
(((~tall(susan)<~>tall(susan)))<=>((~happy(lucy)|kind(lucy))))&
(![X]:(~happy(X)<=>~calm(X)))&
(![X]:((~patient(X)<~>brave(X))=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&curious(X))<=>~brave(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)|old(X))))&
(![X]:((~wise(X)&~humble(X))=>(~tall(X)<~>~calm(X))))&
(((~brave(lucy)|creative(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~funny(X)|brave(X))=>(funny(X)&~quiet(X))))&
(![X]:((happy(X)&~happy(X))=>curious(X)))&
(![X]:((~funny(X)|humble(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:(brave(X)))=>((curious(lucy)&old(lucy))))&
(quiet(fred))&
((creative(alice)|patient(alice)))&
(creative(lucy))&
(?[X]:(curious(X)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:((~wise(X)|old(X))))&
((patient(lucy)&strong(lucy))) | ~kind(lucy) | [
"p5",
"p6",
"p7",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 237209015879711247817439
% SZS output start Proof for 237209015879711247817439
6. (~tall(susan) <~> tall(susan)) <=> (kind(lucy) | ~happy(lucy)) [input p5]
7. ! [X0] : (~happy(X0) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((~patient(X0) <~> brave(X0)) => (happy(X0) | calm(X0))) [input p7]
9. ! [X0] : ((curious(X0) & ~strong(X0)) <=> ~brave(X0)) [input p8]
24. strong(lucy) & patient(lucy) [input p23]
25. ~kind(lucy) [input hypothesis]
29. ! [X0] : ((happy(X0) | calm(X0)) | (~patient(X0) <=> brave(X0))) [ennf transformation 8]
30. ! [X0] : (happy(X0) | calm(X0) | (~patient(X0) <=> brave(X0))) [flattening 29]
48. (((~tall(susan) | tall(susan)) & (tall(susan) | ~tall(susan))) | (~kind(lucy) & happy(lucy))) & ((kind(lucy) | ~happy(lucy)) | ((~tall(susan) | ~tall(susan)) & (tall(susan) | tall(susan)))) [nnf transformation 6]
49. (((~tall(susan) | tall(susan)) & (tall(susan) | ~tall(susan))) | (~kind(lucy) & happy(lucy))) & (kind(lucy) | ~happy(lucy) | ((~tall(susan) | ~tall(susan)) & (tall(susan) | tall(susan)))) [flattening 48]
50. ! [X0] : ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))) [nnf transformation 7]
51. ! [X0] : (happy(X0) | calm(X0) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) [nnf transformation 30]
52. ! [X0] : (((curious(X0) & ~strong(X0)) | brave(X0)) & (~brave(X0) | (~curious(X0) | strong(X0)))) [nnf transformation 9]
53. ! [X0] : (((curious(X0) & ~strong(X0)) | brave(X0)) & (~brave(X0) | ~curious(X0) | strong(X0))) [flattening 52]
90. kind(lucy) | ~happy(lucy) | tall(susan) | tall(susan) [cnf transformation 49]
91. kind(lucy) | ~happy(lucy) | ~tall(susan) | ~tall(susan) [cnf transformation 49]
96. ~calm(X0) | happy(X0) [cnf transformation 50]
99. happy(X0) | calm(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 51]
101. ~strong(X0) | brave(X0) [cnf transformation 53]
134. patient(lucy) [cnf transformation 24]
135. strong(lucy) [cnf transformation 24]
136. ~kind(lucy) [cnf transformation 25]
140. kind(lucy) | ~happy(lucy) | tall(susan) [duplicate literal removal 90]
141. kind(lucy) | ~happy(lucy) | ~tall(susan) [duplicate literal removal 91]
150. 3 <=> tall(susan) [avatar definition]
203. 14 <=> happy(lucy) [avatar definition]
205. ~happy(lucy) <- (~14) [avatar component clause 203]
207. 15 <=> kind(lucy) [avatar definition]
210. ~3 | ~14 | 15 [avatar split clause 141,207,203,150]
211. 3 | ~14 | 15 [avatar split clause 140,207,203,150]
212. ~brave(X0) | ~patient(X0) | happy(X0) [subsumption resolution 99,96]
224. 18 <=> brave(lucy) [avatar definition]
226. brave(lucy) <- (18) [avatar component clause 224]
256. ~15 [avatar split clause 136,207]
259. brave(lucy) [resolution 101,135]
262. 18 [avatar split clause 259,224]
321. ~patient(lucy) | happy(lucy) <- (18) [resolution 212,226]
323. happy(lucy) <- (18) [subsumption resolution 321,134]
324. $false <- (~14, 18) [subsumption resolution 323,205]
325. 14 | ~18 [avatar contradiction clause 324]
326. $false [avatar sat refutation 210,211,256,262,325]
% SZS output end Proof for 237209015879711247817439
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Subsets and Splits